University of Surreyepubs.surrey.ac.uk/844581/1/10149064.pdf · ABSTRACT The flow field in two-phase boiling and gas-liquid Stirred Tank Reactors, STR, was examined in relation to

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PERFORMANCE PARAMETERS FOR BOILING AND GASSED STIRRED

TANK REACTORS I n (

by Athanasios N. Katsanevakis

A thesis submitted for the degree of Doctor of Philosophy

Department o f Chemical and Process Engineering University o f Surrey,Guildford, GU2 5XH,

Surrey United Kingdom

A p ril 1994

orrj GeoScbpa

orovg yovsig poo

K ai o' bnoiov rov Styopa

ABSTRACT

The flow field in two-phase boiling and gas-liquid Stirred Tank Reactors, ST R ,

was examined in relation to cavity formation and the associated Relative Power

Demand, RPD.

The cavitation process has been classified in various stages for both radial and

axial impellers operating in boiling water.

Experiments done in a boiling reactor o f 0.45 m diameter agitated by radial and

axial impellers showed that the Relative Power Demand, RPD, can be correlated

w ell with the help o f a new formulation o f Cavitation number named the

Cavagitation number.

Differences in R PD between gas-sparged and boiling reactors detected during the

experiments imply that there are differences in the mechanism o f cavity formation

in the two systems. These differences are explained b y a consistent physical

model. The model was shown to be adequate for most o f the features o f both

boiling and sparged reactors reported in the literature.

The flow field in a two-phase boiling reactor has been investigated for the first

time in the open literature using Laser Doppler Velocimetry, L D V , in conditions

where the R PD was as low as 0.55. Measurements gave important data o f the w ay

the flow field is changed by the presence o f the second phase which forms stable

cavities behind impeller blades. The results also quantified the associated flow

field changes in the impeller discharge stream and in the bulk o f the reactor.

The two-phase flow field was quantitatively described with the help o f a simple

model derived on the basis o f energy balances calculated around the impeller. The

model estimates liquid flow rates and mean liquid velocities in the two-phase

system using data o f the corresponding single-phase system coupled with

information about the RPD . Knowledge o f the void fraction seems to improve the

model predictions which were shown to be in fairly good agreement with the data

o f mean flow rates that exist in the literature. L D V measurements done in a

boiling stirred tank o f 0.45 m diameter showed that flow rates can be predicted

within an accuracy o f around 10% and mean liquid velocities with an accuracy

better than 25% , even without taking into account void fraction. M odel predictions

can be used as input values for numerical codes available for the calculation o f

I V

flows in two-phase stirred tank reactors. Application o f the model is independent

o f geometry and scale.

(c) Ath, N. K»tsan«vakis

V

I would like to take this opportunity to express my heartfelt thanks to:

Professor John M. Smith for his sustained supervision encouragement and advice throughout the course of this research work,

Science and Engineering Research Council for financial support through the CAR 103 project,

Imperial Chemical Industries and especially Dr John Middleton for the loan of the laser equipment used in this work,

Dr Fanny Plaka for her help when starting the work with the Laser Doppler Anemometer,

The staff of the Department of Chemical and Process Engineering at University of Surrey and especially Dr Ughur Tuziin for some useful discussions and Peter Pennington, Dave Amall, Ken George, Austin Harrup, John Webb and the staff of the departmental workshop for their help while setting up the experimental equipment used in this work.

I would like also to thank Joseph and Nicolas Katsanevakis, my brother and father, who patiently substituting me in professional responsibilities during my absence from Greece.

Finally I would like to thank my wife. I am deeply grateful for her patience and love I received from her during this work. It is to her that I dedicate it in gratitude and affection.

ACKNOWLEDGEMENTS

A. N. K.

CONTENTS

page

CHAPTER 2 - BACKGROUND

Aerated Stirred Tank Reactors2.1. Introduction 42.2. Cavity formation regimes

2.2.1. Cavitation of Radial impellers 52.2.2. Cavitation of axial impellers 8

2.3. Power consumption and Flooding2.3.1. Power consumption and Flooding of radial

impellers 92.3.2. Power consumption and Flooding of axial

impellers 132.4. Two-phase flow maps 132.5. Conclusions 15 Boiling Stirred Tank Reactors2.6. Introduction 152.7. Previous research concerning boiling STR

2.7.1. Cavitation regimes 152.7.2. Relative Power Demand 17

2.8. Conclusions 17

CHAPTER 1 - INTRODUCTION 1

CHAPTER 3 - CAVITY VISUALISATION IN BOILING STIRRED TANK REACTORS

19

20 20

3.1. Introduction3.2. The experimental arrangement

3.2.1. Small scale experimental rig3.2.2. Main experimental rig

3.3. Visualisation studies3.3.1. The experimental procedure 233.3.2. Results and discussion 24

3.4. Conclusions 32

CHAPTER 4-POWER DEMAND IN BOILING MECHANICALLY AGITATED REACTORS

4.1. Introduction . 334.2. Background 344.3. Experimental rig and experimental procedure 354.4. Theoretical background 394.5.Results and discussion

4.5.1. Presentation of the data 434.5.2. Initial cavitation stages 464.5.3. Influence of vapour generation rate 464.5.4. Influence of the location where vapour is generated 484.5.5. Influence of geometric parameters

4.5.5.1. Radial impellers4.5.5.1.1. Height and clearance 494.5.5.1.2. T/D ratio 51

4.5.5.2. Axial impellers 514.6. Equation fit 53

4.6.1. Radial impellers 544.6.2. Axial impellers 574.6.3. Overview of the results 59

4.7. Relation to data with gassed impellers 624.8. Conclusions 64

CHAPTER 5 - A UNIFIED APPROACH TO CAVITATION PHENOMENA IN TWO-PHASE AGITATION

5.1. Introduction5.2. A descriptive physical model of the mechanism of cavity evolution

65

66

viii

5.3. Quantitative aspects of the mode! of cavity evolution 6 8

5.4. Validation of the model using literature data 705.5. Conclusions 75

CHAPTER 6 - THE FLOW FIELD IN A TWO-PHASE STR. A predictive model.

6.1. Introduction 766.2. Derivation of the model 776.3. Limitations of the model 836.4. Mean velocities 856.5. Extension of the model 8 6

6 .6 . Applications-comparison of the model equations 876.7. Validation of the model 896 .8 . Conclusions 91

CHAPTER 7 - THE FLOW FIELD IN A TWO-PHASE STR. Velocity and turbulence measurements.

7.1. Introductiion 937.2.Experimental arrangement and equipment 957.3. Measurements 987.4. The impeller discharge flow

7.4.1. Rushton impellers 1007.4.1.1. Mean velocities 1037.4.1.2. Root Mean Squares of velocity fluctuations 114

7.4.2. Hollow blade impeller with the faces convex 1247.4.2.1. Mean velocities 1247.4.2.2. Root mean squares of velocity fluctuations 124

7.5. Flow in the bulk 1297.5.1. Rushton impeller 129

7.5.1.1. Mean velocities 1297.5.1.2. Root mean squares of velocity fluctuations 129

7.5.2. Axial downwards pumping impeller 1327.5.2.1. Mean velocities 132

7.5.2.2. Root mean squares of velocities7.6. Conclusions

132135

CHAPTER 8 - THE FLOW FIELD IN A TWO-PHASE STR. Validation of the model.

8.1. Introduction 1368.2. Flow rates 1378.3. Mean velocities . 1398.4. Accuracy of the model predictions 1468.5. Conclusions 149

CHAPTER 9 - CONCLUSIONS AND RECOMMENDATIONS.

9.1. Conclusions 1519.2. Recommendations for future work 154

REFERENCES 156

Appendix 1Analysis of energy balance equation for turbulent systems - The stress tensor in newtonian fluids. 163

Appendix 2Data and calculations for Relative Power Demand in Boiling Stirred Tank Reactors.2.1. Notation 1692.2. Temperature correlation of cavagitation number 1702.3. Relative Power Demand Data for the Radial and Axial Impellers 172

Appendix 3Data of Velocity measurements.3.1. Calculation of radial velocity components 2223.2. Errors associated with the calculation procedure 223

X

3.3. The Laser Doppler equipment used 2243.4. Data of velocity measurements 226

N O T A T I O N

Symbols

D impeller diameter, [m]E energy [J]g gravity acceleration, [m/s2]h height, [m]1 length, [m]lo reference length, [m]N revolutions per second, [ s 1]P Power, [W].P pressure, [N/m2]pa atmospheric pressure [Pa]Pg gassed power, [W]Pi pressure at impeller level, [Pa]po local pressurepst static pressurePu ungassed powerpv vapour pressurepvs vapour pressure at the surface

Q Volume flow, [m3 /s]Qg volume flow of the gasR radial distance from tank axisS submergence [m]s surface, [m2] or submergence [m]T tank diameter, [m]t time, [s]ti temperature at impeller stream, [°C]u internal energy per unit mass, [J/kg]V velocity, [m/s]V velocity tensorV volume, [m3]Vtip tip velocity

X l l

Ws shaft work per unit time, [W]

Subscripts< > quantity included is integral based average quantity1 conditions at inlet2 conditions at outletlph Single-phase

2 ph Two-phasea atmosphere

g gas or gassedi impellerL liquidn vertical component0 local or characteristic quantitiess surface or shaftSt staticu ungassed or uncavitatedv vapourw wetted

bold letters indicate tensors

Abbreviations and Dimensionless Groups.

CAgN cavagitation number defined in eq. (4.3) as (2*S*g)/ V tip 2

clrc clearance [m]CN cavitation number, (p-pv)/ 0.5pLVtip 2

Cp pressure coefficient, Ap/ 0.5pLVt ip 2 where Ap = impeller generateddowpressure

f.p.s. frames per secondf.s.d. Full scale deflectionF/A frequency - analogueFI flow number, Q/N*D3

Fr Froude number for mixing, N2 D/ghght height [m]LDV / LDA Laser Doppler Velocimetry / Anemometry

LDV or LDA Laser Doppler Velocimetry/AnemometryNp Power number, P/(pL N 3 D5)PBT Pitched Blade Turbinepine ang. plane angle [°]Re impeller Reynolds number, (pLN D2)/ pRMFL Relative Mean Flow Rate, (Flow-rate),ph/(flow-rate)lphRMS Root Mean SquareRMV Relative mean velocity, V,ph/VlphRPC Relative pumping capacity, (Pump.capacity)2ph/(pump.capacity)RPD Relative Power demand, Np2ph/NplphS-P Single-phaseSERC Science and Engineering Research Council.T-P Two-phasev.r or V.R. vapour rate [dm3 /min].

Greek letters

a void or gas fraction %

P parameters defined in chapter 6

A difference between inlet and outlete total energy per unit mass, [J/kg] / factor in par. 6.3 / % error in

chap. 8 .0 angle [°]K coefficient in eq. (6.15)X second viscosity coefficient in Appendix 1A coefficient in eq. (6.15)

M first viscosity coefficient / dynamic viscosity, [N.s/m2]

P density

Pl liquid densityT stress tensor; [N/m2]

1

C h a p t e r 1

IN T R O D U C T IO N

Mechanically Agitated Stirred Tanks are frequently used in the Chemical andProcess Industry for mixing, solid suspension, gas-liquid contacting, chemical*reactions, multiphase reactions, fermentation processes, biochemical processes, etc.

Stirred tanks are very often used for multiphase reactions where gas is dispersed into liquid. Sometimes suspension of solids is also involved. Design, hydrodynamics and performance of these reactors is the subject of several review articles and textbooks, e.g.[19, 23, 65, 72]. The importance of impeller two-phase hydrodynamics on the gas dispersion mechanism and on the total performance of a two-phase reactor has been highlighted. Stable cavities formed behind impeller blades during two-phase agitation have been found to determine the operating regimes of the reactor. Correlations for power draw, flooding regimes, gas fraction, mass transfer rates, solids’ suspension, etc. during two-phase agitation have been established and have been successfully used in industry.

Unfortunately there is still a lack of both experimental information and theoretical knowledge about the changes of the main parameters of the flow field when switching between single and two-phase operation in a stirred tank; this is a major

\CHAPTER 1. INTRODUCTION. 2

drawback in limiting the application of computational methods to the calculation of mass transfer or chemical reaction rates in two-phase Stirred Tank Reactors -STRs-. Most of the available computational methods presuppose a known flow field to solve their models for mass transfer or chemical reaction rates [5, 35, 36].

Mechanically agitated vessels in which the second phase consists of vapour or a mixture of vapour and gas belong to the wider group of two-phase stirred tanks. There are many processes taking place in agitated vessels where considerable vapour evolution occurs. Examples include:

(a) organic syntheses carried out under reflux,(b) exothermic reactions in which solvent boil-off controls the temperature.(c) liquid phase reactions generating a volatile product,(d) some forced circulation evaporative crystallisers,(e) incorporation or dispersion of solids into volatile liquids with high speed impellers.

Literature concerning boiling agitated vessels is limited. It has been reported that the hydrodynamic regimes of boiling and gas sparged systems are generally similar, with the development of cavities of various types behind the impeller blades, [10, 59, 61]. There is no information about the power draw of an impeller in a boiling liquid nor for the relations between boiling and gas sparged systems. Process engineers concerned with the operation of boiling systems have tended to assume either that the effect of vapour loading on the impeller will correspond roughly to that with sparged gas at a similar volumetric rate or that the impeller is flooded and probably not very effective in its mixing action.

The present thesis concerns both boiling and two-phase gas sparged Stirred Tank Reactors,-STRs-. Boiling mechanically agitated vessels have been investigated in terms of operating regimes defined by the various cavitation stages and power draw. A simple model is then formulated for the prediction of the liquid phase flow field in two-phase agitated vessels. Experimental measurements are used to give new data about the turbulent velocity field in a two-phase stirred tank and to validate the model.

\CHAPTER 1. INTRODUCTION. 3

Chapter 2 presents background information from the literature for gas-liquid and boiling Stirred Tank Reactors, -STRs-.

In chapter 3 the operating regimes in a boiling reactor and their relationship to gassed reactors have been investigated.

Power Demand is a major design parameter for an STR. Variation of Power demand in a boiling STR and its relation to performance in gassed reactors are described in chapter 4.

A unified approach to cavitation phenomena in both boiling and gas-sparged vessels together with an attempt to validate it using data from the literature are given in chapter 5.

A simple model for the prediction of the liquid phase flow field in a two-phase gas-liquid STR has been derived in chapter 6 . The model is based on energy balances and uses data from the single-phase flow field and Relative Power Demand, -RPD-.

In chapter 7 data of liquid two-phase mean and Root Mean Squares of velocity fluctuations in a boiling STR when the Relative Power Demand levels were as low as 0.55 are presented for the first time in open literature.

In chapter 8 data presented in chapter 7 are used to validate the model derived in chapter 6 .

Conclusions and recommendations for further work are presented in chapter 9.

4

C h a p t e r 2

B A C K G R O U N D

Aerated Stirred Tank Reactors -STR-.

2.1 Introduction

Stirred Tank Reactors are commonly used for gas dispersion into liquids. A schematic view of a typical gas-liquid STR is shown in fig. 2.1. Gas issupplied from a sparger underneath the impeller. As it passes through the impeller, it is broken into small bubbles increasing the contact area and so enhancing mass transfer and chemical reaction rates. The bubbles coalescebecoming larger, finally escaping towards the free surface.

During the operation of impellers in gas-liquid systems, ventilated cavitiestend to form behind the impeller blades as a result of the local hydrodynamic conditions [8 , 44, 77, 78]. The various cavity formation stages define different flow patterns for the operation of a STR. This happens because cavities drastically affect the impeller region flow field which in

\CHAPTER 2. BACKGROUND. 5

turn controls the bulk flow and all the velocity-dependent processes [6 , 81,

The different cavity formation regimes have been related to the changes of power consumption, mass transfer, etc. detected in STR operation under gas loading [81, 84],

2.2 Cavity formation regimes

2.2.1 Cavitation of radial impellers

Cavity formation is the most remarkable phenomenon taking place in gas- liquid operation of an STR because it controls, via the change of the impeller region flow field, all the velocity dependent processes in the impeller region and in the bulk. Cavity formation is a result of the nature of single-phase flow around the impeller blades, [44, 77, 78].

Depending on the geometry of the blades, trailing roll vortices develop behind the impeller blades, [6 6 , 77], fig. 2.2.This is a result of separation vortices and the radial motion of the liquid which sweeps away all the separation vortices producing a trailing roll vortex, fig. 2.3.For a standard Rushton turbine these vortices develop first at a value of impeller Reynolds number of about 200, [78]. The location of the vortex

84].

Fig. 2.1 Gas-liquid STR

1 CHAPTER 2. BACKGROUND. 6

d i r e c t i o n o f r o t a t i o n

Fig. 2.2. Trailing vortices behind a Fig. 2.3. Generation of a trailing vortex.Rushton impeller blade, from [78].

axis depends on the Reynolds number and D/T ratio reaching its final trajectory at about Re=104, [78, 91]. If an impeller operates in a gas-liquid system gas is drawn towards the low pressure core of the vortex, forming cavities. This phenomenon is described e.g. by Van’t Riet and Smith, 1973, [77] or Nienow and Wisdom, 1974, [44]. These cavities are ventilated cavities with a continuous supply and removal of gas in contrast to vapour cavitation which occurs when the local pressure falls below the saturation pressure of the liquid at the ambient temperature, [4, 92].

Research workers in the field distinguish among four types of cavities and consequently cavitation regimes namely vortex, clinging, large and ragged, fig. 2.4, [11,14,43,79,81].The different cavitation stages can be followed if we assume an experiment where impeller speed is kept constant and gas supply increases starting from zero.Vortex cavitation is the first stage which develops at small gas rates. Gas occupies the core of the trailing vortices and vortex motion dominates the flow around the impeller blades. The vortex cavity configuration is symmetrical with the pairs of cavities behind successive blades of approximately the same size.

With increasing gas rate vortex cavities change gradually to clinging cavities. During clinging cavitation there is still a weak trailing vortex motion of the liquid around the impeller blades, [44, 62]. Developed clinging cavities are in touch with the impeller blades. The outflow from the cavities still has a strong radial direction [11,44,62]. Again clinging cavities form a stable symmetrical configuration.


On increasing the gas flow-rate the next stage in cavity formation is large cavities. Now the rear of the blade is covered by a single big bubble with clear smooth surfaces. Vortex motion is not evident [62, 81]. Outflow from the rear of the blades is more tangential than radial and has been exploited in an experimental technique for determining the transition between clinging and

v o r t e x c a v i t y----------------------- L c lin g in g c a v i t y

large cavities using the difference in the intensity of the radial outflow associated with these cavity types, [81]. The large cavity configuration is usually not symmetrical. There are alternate bigger and smaller large cavities at the rear of successive blades. At high impeller speeds and high gas rates there is a moment where the three large cavities grow further until they envelop the three successive blades; a configuration called bridging cavities, fig.2.4.d, [11].The final stage of ragged cavities, fig. 2.4.e, is reached when the impeller is flooded by an excess of gas. Ragged cavities are all of the same size with unsettled surfaces and undefined shape as a result of vibrations, [81].

iCHAPTER 2. BACKGROUND. 8

The same cavity formation regimes can be detected if instead of varying the gas flow rate at constant speed we change the impeller speed at constant gas flow rate [44].

Warmoeskerken and Smith, 1981, [85], investigated quantitatively the effect of various parameters on the onset of the 3-3 configuration which was found to be a very characteristic and stable configuration for cavity type evolution in aerated tanks. This configuration consists of three large cavities alternating with three clinging cavities behind successive blades, fig. 2.5, or six large cavities of two different sizes.

Fig. 2.5. The 3-3 configuration, from [82].

3 c l in g in g a n d 3 la r g e c a v i t i e s

The reason for this asymmetry is unclear but it is believed to be a result of uneven gas distribution from the sparger, [81]. Parameters affecting cavity formation were investigated in terms of their influence on the onset of the 3-3 configuration, [81]. It was found that conditions leading to cavity formation are a weak function of bottom shape, impeller height and coalescence properties. The transition at which large cavities just form can be summarised in eq. (2 .1 ), [81],: C]

FI g> 3.8 10 - 3 (Re2 /Fr) 0,067V'(T/D) (2.1)

2.2.2 Cavitation of axial impellers

There are few publications in the open literature concerning cavity development with axial flow impellers, [6 , 65, 81]. The single-phase impeller region flow field was investigated by Tatterson et al., 1980, [6 6 ], who used stereoscopic visualisation techniques. They observed a downward flow over the blades in small scale equipment combined with a trailing vortex system in larger scale experiments.

\CHAPTER 2. BACKGROUND. j V 9

When axial impellers operate in gas-liquid systems cavities can be detected which can be classified similarly to those found with Rushton turbines, [81].

At constant stirrer speed and low gas rates the trailing vortex is filled with gas bubbles -vortex cavity- fig. 2.6.a. Increasing gas flow results in the development of clinging cavities fig. 2 .6 .b, giving their place to large cavities fig. 2 .6 .c, at even higher gas rates.

With a down-pumping axial flow impeller there is a natural conflict between the downward liquid velocity and gas bubbles trying to rise from the sparger towards the impeller. At low impeller speeds or high gas rates gas reaches the impeller directly while at lower gas rates or high impeller speeds there is an indirect loading of the impeller through recirculation loops.

Fig. 2.6. Cavity types of gassed PBT, from [81].

2.3 Power consumption and Flooding

2.3.1 Power consumption and Flooding of radial impellers

Power consumption is an important parameter of stirred tank operation. This is because power demand determines the operating costs of the process and is for that reason frequently used in comparing the efficiency of equipment and operating methods. Power demand often provides a basis for predicting the mixing times or


the gas fraction and mass transfer coefficient of the dispersion, particularly for scale-up procedures, [60, 65]. Besides this local energy dissipation, which is a result of the power demanded by a mixing system, affects micromixing and mass transfer and influences bubble and droplet dissipation, e.g.[27].

It is well known, from the early work of Rushton et al., [54], that during agitation of newtonian liquids in fully baffled vessels, Power number, Np = P/(pN3 D5), is essentially constant for operation in the turbulent region and is characteristic for every impeller -tank configuration.

Power number usually changes in two-phase operation. It is well known that in similar conditions e.g. with equal impeller speeds, the gassed power consumption is usually lower than that in the ungassed system. This difference cannot be eliminated simply by substituting the density of the liquid with the density of the mixture resulting from the presence of gas bubbles. Gas bubbles form stable cavities in the low pressure regions behind the impeller blades, [44, 77]. Cavities behind a body will lower the form drag, [7, 28]. The streamlining effect created by the cavities results in a drag coefficient change which is reflected in the Power number change, [67]. Biesecker, 1972, [8 ], and later Van't Riet, 1975, [78], have shown that this gives a plausible explanation for the observed power reduction of gassed impellers.

Relative Power Demand -RPD-, Pg/Pu, Gas flow number, Fl=Qg/ND3, and Froude number, Fr=N2 D/g, have been used to correlate the power input change for the various cavity states in gas-sparged two-phase agitated vessels. Froude number correlates the inertia to the gravity, or buoyancy, forces experienced by a bubble. Flow number correlates the intensity of ventilation of the impeller region to the volume which is swept by the impeller in a unit of time. Finally the gassed to ungassed power ratio -RPD- correlates the change of the impeller power number as a result of operating in a two- phase -gas-liquid- system.

Two ways of obtaining RPD data as a function of flow number have commonly been used either keeping the impeller speed constant and varying the gas rate or vice-versa, [11, 45], Atypical result for a Rushton impeller is presented in fig. 2.7. The dotted line shows the point where the


achievement of the 3-3 structure occurs at the inflection point of the curve, [82]. Fig. 2.8 shows Pg/Pu for different impeller speeds.

Fig. 2.7. Gassed RPD of a Rushton impeller, from [82].

The authors were unable to suggest a factor to bring the curves completely together. Taking into account a relative recirculation factor the curves could be united as far as the inflection point where the 3-3 structure develops but not the rest of them, fig. 2.9, [82].

K30.10-*5 120

Fig. 2.8. Gassed RPD of a Rushton impeller, from [82].

•A, . *\7 V A*

T * O A A m D • 0.176 m

O N • 2 A N . 6 S '1

X N O * - 1 0 z 4A 1

. N,A S '1 V N « O *• N .Sr '

Fi • aei ■ i* v

i I i I i1001O-3 120O 20 AO 60 SO

Fig. 2.9. RPD data taking into account a recirculation factor, from [82].

Fig. 2.10. Curve fitting for RPD data, | from [581. \

GiS Flow Number Q/ND3 N rcv/aec x Flooding v Q Utru/aec


RPD was approximated by straight lines using short-cut methods, [84]. More accurate curve fitting developed for RPD results has given a family of lines suitable for predicting Relative Power Demand of gassed Rushton impellers, fig. 2.10, [58].

If the gas flow rate which can be handled by the impeller is exceeded then flooding occurs. This is associated with a small jump of RPD, fig. 2.7. When flooded the impeller cannot pump the gas effectively. The gas escapes towards the free surface, [45]. Flooding is an undesirable phenomenon because it usually means poor gas dispersion as the vessel works rather like a bubble column. Generally there is not good agreement between researchers about the equation describing the onset of flooding, [83, 8 8 ]. The reason is that not all the workers in the field have used the same definition of flooding and there is probably a significant discrepancy arising from the different geometries used. Some authors defined as flooding the point where gas is not circulated throughout the vessel [45]. In the present thesis we shall adopt the definition of Warmoeskerken and Smith, 1985, [83]. According to this definition, flooding occurs when the impeller cannot pump the gas radially and the gas escapes vertically towards the free surface. Flooding was regarded as a result of the balance between the power input from the gas and the power input through the agitator. Starting from theoretical aspects these authors found the onset of flooding for a vessel with aT/D = 2.5 to be given by the equation

Fl=1.2*Fr.

which is a special case of the correlation proposed by Nienow et al., 1985, [43],

FI = 30 (D/T)3 5 Fr

The influence of sparger height and geometry has also been studied, [45, 83]. Despite small differences and occasional hysteresis phenomena the above equation was found to describe the onset of flooding sufficiently accurately, [43].


As in the case of radial impellers, power number variations of axial impellers operating in two-phase gas-sparged reactors have been related to the formation of cavities behind the impeller blades. Correlation of RPD with flow number alone seems to be insufficient as is clear from fig. 2 .1 1 , [81].In contrast to the corresponding curves for Rushton turbines, power curves for downwards pumping pitched blade impellers at different impeller speeds intersect. This phenomenon was related to the interdependence of three effects: the formation of large cavities, gas recirculation to the stirrer and the transition between the direct and indirect loading regimes, [81].

2 .3 .2 P o w e r c o n s u m p t io n a n d f lo o d in g o f a x ia l im p e l le r s

Fig. 2.11. RPD of a gassed PBT at different impeller speeds, from [81].

Downwards pumping pitched blade impellers give different power curves from upwards pumping ones. This reflects the different way gas introduced by the sparger interferes with the flow generated by the impeller, [14],

2.4 Two-phase flow maps

With the help of Pg/Pu relations two-phase flow maps describing the operation of impellers into air-water systems have been constructed [84], A typical example using dimensionless variables is shown in fig. 2 .1 2 . Warmoeskerkem and Smith, 1986, [84], have shown the dependence of gas fraction and mass transfer coefficient on the different flow regimes


produced by the various cavitation stages in a gas-liquid stirred tank. Their data have then been incorporated into two-phase flow maps which describe the different operation regimes with the corresponding gas fraction and kl*a values, [84].

Fig. 2.12. Two-phase flow map for the operation of a gassed Rushton impeller, from [84].

Unfortunately the flow maps presented deal only with a T/D ratio of 2.5 and air-water systems though the published equations include the T/D ratio so appropriate flow maps can easily be constructed. Further work is needed to extend application of flow maps to other impeller geometries and working fluids.

The importance and influence of the different flow conditions produced by the various cavitation stages on the processes taking place in an STR is now largely highlighted. Cavity formation seems to change flow field which in turn influences downstream conditions resulting in changes of local dissipation rates, local size of bubbles or drops, mass transfer and chemical reaction rates.A quantitative description of the way the flow field changes according to the different cavitation regimes would be of great importance. This could lead via the use of various existing physical models, e.g. [35, 6 ], to a more accurate quantitative local and global description of the various processes taking place in an STR. Influences of parameters like working fluids or geometry would then be easily explored.


2.5 Conclusions

The importance and the influence of the different flow conditions produced by the various cavitation stages on the processes taking place in a two- phase gas-liquid mechanically agitated vessel is now largely highlighted. The changes in the flow field resulting from cavity formation are reflected in both the power draw of the impeller and variation in the processes that take place in the tank.A general quantitative description of the flow field variations according to the different cavitation regimes would be of great value.

Boiling Stirred T a n k Reactors - S T R - .

2.6 Introduction

Despite the extensive information in the literature about gas-liquid Stirred Tank .Reactors, there is very little relevant to boiling ones despite their frequent use in the Chemical and Process industries. Processes such as polymerisation, hydrogenation and nitration, take place in boiling reactors. Many industrial stirred tank reactors also exploit solvent boil-off as a means of removing excess heat.

2.7 Previous research concerning boiling STR

2.7.1 Cavitation regimes.

Despite the thorough investigation of ventilated cavity regimes in gas-liquid systems little attention has been paid to cavitation in boiling stirred tanks. Breber, 1986, [10], was the first known to the present author to investigate boiling STR. He used a two-blade 0.065m diameter radial impeller in a


0.26m diameter glass vessel to investigate the Relative Power Demand while the impeller operates in boiling liquid. As far as the cavitation regime is concerned he distinguished between two stages: the initial cavitation regime and the supercavitation regime where a big stable cavity is formed behind each blade.

More detailed investigation of cavitation regimes in boiling STR is that of Smith and Verbeek, 1988, [61]. They performed their experiments in a glass beaker of 0.162 m diameter using Rushton type impellers of T/D ratios 2.5 and 3.0. The beaker was heated up to the boiling point with the help of a glycerol solution bath in a larger container outside the beaker. With the help of the bath the temperature in the bulk of the beaker was kept constant within few hundredths of a degree for significant time intervals. Smith & Verbeek found similar cavitation stages as had been observed in aerated tanks namely vortex, clinging and large cavities. They also found that under certain conditions a variety of cavity structures could form behind the impeller blades. These asymmetric structures included clinging, vortex and no cavity or a cavity only behind the upper part of the blade, etc. The asymmetric structures were observed only in gentle agitation conditions, just below the boiling point. They tried unsuccessfully to correlate the onset of the different cavitation regimes namely vortex, clinging, large, and bridging cavities for different D/T ratios with the help of a cavitation number.

Smith & Smit, 1989, [59], extended the previous work doing experiments in two vessel sizes of 0.162 and 0.203 m diameter with Rushton impellers of 5.4, 6.9, 8.4 cm diameter. They detected the different cavitation regimes formed in the large beaker using both 5.4 and 8.4 cm impellers and they found that the onset of the different cavitation regimes is correlated well using the fractional underpressure piv/pist at the impeller level and the group (ND)2. The piv/pist is the ratio between the saturated vapour pressure of the water at the temperature at the impeller level and the ambient pressure at the impeller level, atmospheric plus hydrostatic. (ND) 2 correlates the pressure field generated by the impeller since the latter is proportional to the square of the tip velocity. The data correlate well for different impeller sizes with some scatter during the initial cavitation stages. An extensive series of comparable measurements made in the 16.2 and 20.3 cm diameter vessels with the 5.4 cm diameter impeller showed that container size has no influence on the transitions. Despite the fact that the shape of the detected cavities appears similar to the cavities produced in a gassed


system no clear distinction was made between the different physics of a gassed ventilated and a vapour cavity, [4, 92], Cavity formation is still treated phenomenologically. The physical changes which occur during the various cavitation stages need to be highlighted together with their influences on important mixing parameters like power demand or flow field changes in the tank.

2.7.2 Relative Power Demand.

The only work known to the present author that deals with power draw in boiling systems is that of Breber, 1986, [10]. The experimental equipment consisted of a 0.26 m diameter glass vessel with a 0.065 m diameter two-blade radial impeller. The vessel was heated up to the boiling point with the help of electric resistance tape which was wound outside the glass wall of the vessel. RPD was correlated with impeller Reynolds number. Data were interpreted using a linear relationship with two slopes: a steep linear decrease during the first cavitation stages and further linear decrease of smaller slope after supercavitation started.Unfortunately factors like impeller size, impeller clearance and liquid depth were not taken into account. According to the more recent investigation by Smith and Smit, 1989, [59], these factors might be of great importance because they control the fractional underpressure and the pressure distribution around the impeller blades. Consequently they control the onset of the various cavitation regimes which in turn affect drastically power number drop.

2.8 Conclusions.

The existing knowledge concerning boiling Mechanically Agitated Reactors is limited to the investigation of different cavitation regimes produced by radial impellers operating in boiling liquids. There is no reliable or generally applicable relation established between the different cavitation stages detected and any variation of power draw or flow field in the tank. Moreover our


knowledge about cavity formation in boiling STRs lacks a sound physical background. Cavity shape is similar to that produced in aerated vessels but themechanism of vapour cavity formation is different, [4, 92]; this may lead todifferent results in terms of power draw or flooding.

A detailed study of cavity formation and its influence on important mixingparameters such as Relative Power Demand or mean flow field and turbulencecharacteristics in boiling STR would be very important not only in promoting knowledge in the field of two-phase mixing but in the wider field of two-phase gas-liquid fluid dynamics as well. This is the subject of the following chapters.

C h a p t e r 3

C avity v isu a lisa tio n in b o ilin g Stirred T ank R eactors

3.1 Introduction

It has already been mentioned in chapter 2 that the impeller region flow field is of great importance in STR operation. It controls via the bulk flow field all the velocity dependent parameters such as mixing, gas fraction, mass transfer, chemical reaction rate. Therefore much research has been devoted towards the investigation of the flow field in the impeller region. In gas-liquid systems the most remarkable characteristic of the impeller region flow field is the formation of stable cavities at the rear of the impeller blades. These cavities are considered to have a strong influence on the flow field around the blades and consequently in the bulk. This is the reason why a study of the two-phase fluid dynamics in an STR usually starts with the investigation of cavity development behind the impeller blades. Investigation of the physics of cavity formation can lead to a physically meaningful, generally applicable interpretation for the mechanism. Visual observation of the impeller region is usually a first necessary step. In this way many impeller-region flow field characteristics can be resolved and useful results can be obtained.

\CHAPTER 3. CAVITY VISUALISATION. 2 0

3.2 The experimental arrangement

Cavity visualisation experiments have been performed in two experimental rigs of different sizes. The smaller consisted of a glass beaker of 0.125 m diameter and the larger of a glass & stainless steel reactor of 0.45 m inner diameter.

3.2.1 Small scale experimental rig.

In the first visualisation experiments a microwave oven was used to heat up the contents of a small beaker of 0.125 m diameter representing the vessel. The beaker was equipped with 4 perspex baffles of a tenth of vessel diameter wide. The aim of this experiment was to use the microwave oven so that a relatively uniform temperature of the batch could be achieved. This could simulate an exothermic reaction in the vessel. The microwave experiment provided useful visualisation data as will be explained later. The geometry of the system can be seen schematically in fig. 3.1. The speed of the shaft was controllable. All the components inside the oven i.e. stirrer, baffles, shaft were made of plastic material, -perspex or tufhol- and glass.

Fig. 3.1. Dimensions of the small experimental rig, in [mm].

3.2.2 Main experimental rig.

The main experimental rig which has been built is shown in picture 3.1. A standard glass pipe section 450 mm I/D, 500 mm long, equipped with a stainless steel cover and dished base has been used as the mixing vessel. This medium sized scale equipment has been chosen so that a geometric analogy with tanks used in real processes can be achieved.

1 CHAPTER 3. CAVITY VISUALISATION. 21

A specially constructed frame supports the tank and permits rotational positioning of the vessel around its axis, pic. 3.1. A moveable baffle system has been constructed. The size and the speed of the agitator assembly necessitated the use of a loosely fitting PTFE sleeve at the bottom of the vessel as a steady bearing. A mechanical cartridge seal can be fitted to the shaft entry hole on the top plate so that in principle the vessel can be operated at reduced pressure. A glass window in the bottom cover permits observation of the impeller region from below. The impeller position can be adjusted so that clearance from the lowest point of the dished base could be 1/3T or greater. The main dimensions of the vessel are shown in fig. 3.2.

All d im en sio n s in m m

Fig. 3 .2 . Main experim ental rig.

\CHAPTER 3. CAVITY VISUALISATION. 2 2

Picture 3 .1 . View of th e main experim ental rig.

\CHAPTER 3. CAVITY VISUALISATION. 23

Three cartridge electric heaters each of 1.25 kW full power mounted through the vessel base are used to heat up the bulk of the vessel. An appropriate reflux system has been constructed consisted of a condensing heat exchanger and a dividing head. The vapour rate is measured by means of measuring the condensate rate by weighting. Special care has been paid to prevent condensation before vapour reaches the dividing head: a strip resistance was used to keep the surface temperature of the vapour pipe above the dew point of the vapour.

Stable temperature conditions of ±0.07 °K can be achieved with the help of a platinum resistance thermometer of ±0.025 °K accuracy used with an accurate thyristor controller. The thermal input and consequently the vapour rate produced can be set in the range of 0 - 1 0 0 % of the full power of the heaters.

The drive motor is a specially wound AC motor driven by a variable frequency generator. This allows continuous variation of the impeller speed at suitable torque in the range up to 10 Hz. The agitator shaft carries a VIBROMETER torque torsion transmitter to indicate torque, speed and power input at the impeller shaft with accuracy ± 0 .1 % off.s.d.

3.3 Visualisation studies.

3.3.1 The experimental procedure.

With the help of an EKTAPRO high speed video system on loan from SERC visualisation studies have been performed at a speed of 1000 f.p.s. Cavity formation has been observed in two directions in the main experimental rig, viewing from the bottom and the side but only from the side in the small rig in the microwave oven. For the experiments in the microwave oven a Rushton turbine of 6 6 mm diameter was used. During the more extensive experiments in the 0.45 m vessel Rushton turbines of 240 and 180 mm diameter as well as axial 45° inclined blades upward pumping impeller of 225 mm diameter have been used. All the investigations were performed at atmospheric pressure. The working fluid was filtered tap water. Two thermal input rates of 100% and 75% of the nominal 3.75

\CHAPTER 3. CAVITY VISUALISATION 24

kW input were used. Cavity evolution has been recorded on video tapes for later study.

33.2 Results and discussion.

Cavity structures detected in the small scale experiment were in agreement with previous investigations in the literature, Smith and Verbeek, [61]. During gentle agitation conditions randomly travelling bubbles of similar size to the hydrodynamic structures generated by the impeller blades were captured behind the blades, resulting in a large variety of symmetric and asymmetric structures, [61]. In the 0.45 m diameter vessel, where bubble size was much smaller than the size of the impeller blades, only symmetric cavitation structures have been detected. With the help of the video recordings the following stages of cavity formation have been determined as impeller speed is increased from rest in boiling liquid.

Initiation fig. 3.3.a.

Many tiny bubbles roll in the vortices behind the impeller blades but no stable, void of liquid, structure exists at the rear of the blades. At every point relative to the rotating impeller both liquid and gas velocity components exist. The tiny bubbles at the rear of impeller blades do not coalesce. They keep their individuality drawn there by the lower pressure which occurs in the vortex core, [77]. This stage is more evident when many tiny bubbles exist in the system and the liquid is sufficiently subcooled so that no real vaporous cavitation occurs, [4]. The tiny bubbles can originate from dissolved gas in the system or from subcooled boiling.

Vortex cavities fig. 3.3.b, picture 3.2 & 3.3.

The core of the trailing vortices start to be void of liquid. This kind of vaporous cavitation was detected firstly in the upper vortex of the blade, followed after significant increase of the speed, in the lower vortex. This demonstrates the

1 CHAPTER 3. CAVITY VISUALISATION 25

sensitivity of vaporous cavitation to the local static pressure head. It could also help in determining the relationship between the pressure evolution in the vortex core and the impeller speed. Vortex cavitation starts at about 3/4 of the blade length inwards from the impeller tip. This is in agreement with the location of the lowest pressure point as reported in the existing literature, [78]. No part of the elongated bubble which occupies the core of the trailing vortex touches the blade, fig. 3.3.b. There is uninterrupted vortex circulation of liquid around the vapour filled vortex core, fig. 3.3.b. As impeller speed is increased the vortex cavities become longer and thicker. This indicates that increasing speed results in the expansion of the low pressure regions because all the other parameters like temperature and consequently vapour pressure are kept constant. Finally the inner part of the cavity touches the blade. Separation starts at that point - the inner blade tip-, fig. 3.3.C. Increasing the impeller speed separation extends towards the outer blade tip, fig. 3.3.d. Circulation is still present and sheets of liquid which are separated from the horizontal blade edge circulate around the thick vortex cavity and are swept out by the radial outflow component. Little by little with increasing impeller speed vortex cavity becomes thicker and vortex pitch longer. This longer trailing vortex pitch seems to be the precursor of an early three dimensional jet re- entrainement.

Clinging cavities, fig. 3.3.e, pic. 3.2 & 3.3.

The final stage of vortex cavity evolution, separation along the whole length of the horizontal blade edge, could be assumed to be the first stage of clinging cavitation. Now separation over the inner horizontal blade edge forms a clear glassy cavity surface which is distorted downwards by the strong vortex turbulent outflow of the liquid motion. With increasing impeller speed separation at the outer vertical edge of the blade becomes stronger. Finally the vortex circulation of the liquid around the cavity is not strong enough, or vortex circulation pitch becomes so elongated, that separation all over the outer blade tip cannot be prevented. This is the point at which large cavitation starts. It is not clear which is the primary reason for separation on the outer blade tip. A combination of weaker vortex motion together with long vortex pitch may be a reasonable explanation.

Figu

re

3.3.

Cavit

y sh

apes

of

Rush

ton

impe

ller.

Picture 3.2. Cavity types of Rushton 240 mm impeller: a vortex, b clinging, c large.

iCHAPTER 3. CA VITY VISUALISATION.

;'vs v̂ '̂ivJivfti■Mffl

(m mm v, w mv/st'v//,//. s & ,t// tV' «'v ,///k, iVtA ///V/MVA/v -

,, /a-. /,/. ^ /At, /.,y//,•,/'"?// //////////■/. ,///s/////J///f//s//r///f//S///S,/Sft////A /̂//

Picture 3.2. Cavity types of Rushton 240 mm impeller: a vortex, b clinging, c large.

\CHAPTER 3. CA VITY VISUALISA TION.

' .Ill IIIIIJdld .

a clinging, b clinging to large, c large, d large cavities of tw o different sizes.


0>O1 c iS+-Q§ WiN■DOiw w

a clinging, b clinging to large, c large, d large cavities of tw o different sizes.

Picture 3 .4 . Cavity types of PBT: a small, b, c & d developed cavitation

X

1 CHAPTER 3. CA VITY VISUALISATION.

< ffeE y.y:: ■

//ytfyj/yw’ ;; Srj-j

I *

• • : ■ ■ : '■■■•■■' . ■■'■.■:■:: ;;;.;

Picture 3 .4 . Cavity types of PBT: a small, b, c & d developed cavitation


Large cavities, fig. 3.3. f , pic. 3.2 & 3.3.

When large cavities are present at the rear of the blades, separation occurs around the whole periphery of the blade resulting in cavities with surfaces which seem smooth and glassy and are distorted downstream by the turbulent liquid flow. With increasing impeller speed large cavities grow further. Beyond a certain point three cavities continue to grow while the other three start to reduce their size giving rise to a 3-3 large cavity structure, pic. 3.3. The three cavities grow further until at

^ sUouW very high speeds they'envelop the following blade forming bridging cavities. The reason of this asymmetry is not clear. In gassed stirred tanks a similar asymmetry was explained in terms of uneven gas distribution from the sparger, [81, 85]. In our experiment where there is no sparger, this asymmetry still exists but only later when large cavities have already been formed. The reason for the detected asymmetry may be the dynamic interaction of cavity growth and the impeller region flow field generated by the blades. The impeller still pumps liquid. The flow around the cavity in a radial direction relative to the impeller blades seems now weaker. This may be a result of a gradual change in direction with increasing impeller speed. Three dimensional jet re-entrainement is evident at the rear of the cavity; it is swept out by the liquid outflow in a wake consisting of a vapour-liquid mixture in a very turbulent field. During our experiments there was no impeller flooding detected as in gas liquid systems, [45, 8 8 ]. This may be expected according to the approach developed by Warmoeskerken and Smith, 1985, [83]; in the absence of sparger it seems that there is no significant gas energy input into the impeller region so the only factor affecting the flow field and the pumping of the liquid is the impeller. Decreasing the speed the same stages of cavity formation were found without detectable differences. At lower vapour generation rates, 75% of the full power, there were also no obvious differences in cavity form or size.

Axial impellers, fig. 3.5, pic. 3.4.

During operation of the axial impeller cavitation starts in the trailing vortex at the outer blade tip, fig. 3.5.a. Vortex motion is evident but appears weaker than with Rushton impellers. Separation at the outer horizontal blade edge is present even at low impeller speeds, fig. 3.5.a, pic. 3.4. With increasing speed separation extends inwards. The whole vapour sheet bubble is forced to fold because of the vortices


formed at the impeller edges, fig. 3.5.b, pic. 3.4. This folding vortex motion is present even during the very developed cavitation stages where a big vapour sheet cavity covers nearly the whole blade, pic. 3.4. The tail of the cavity breaks out by this vortex-folding motion, pic. 3.4, fig. 3.5.

Fig. 3.5. Cavity shapes of the Pitched Blade Turbine.

The distinction between vortex, clinging and large cavities is weak since large cavities, in the sense of separation occurring at the blade edges, exist almost from the beginning and the tail of the cavities is still in vortex motion during even very developed cavitation stages. This is quite different from the large change that occurs between vortex and clinging cavities in radial impellers.

D


3.4 Conclusions.

Cavity visualisation experiments have been performed in a 0.45 m boiling vessel agitated with Rushton turbines and a pitched, 45°, 6 blade impeller. Cavitation in boiling agitated vessels depends only on the impeller speed and not on the vapour generation rate, at least during the present experiments where, as it is the usual operating mode in practice, vapour generated by the heaters was not sent directly in the impeller region. The cavitation stages detected, namely initiation, vortex, clinging, large and bridging, are simply standard cavity configurations defining a continuous evolution of the cavity form. Despite the similar cavity shapes to those of gassed cavities in gas-sparged vessels, there is a different physical process behind vaporous cavitation. In gassed systems cavities are a result of the combined effects of the flow field generated by the impeller and the gas sparged to the impeller region whereas in the boiling systems investigated, cavitation seems to depend solely on the flow and pressure field generated by the impeller in a liquid of a given temperature. No clinging - large 3-3 structure has been detected during Rushton impeller operation. In fact a 3-3 structure which consisted of large cavities of two different sizes has been detected only after the formation of six large cavities of the same size. Even during very developed cavitation the impeller continues to pump liquid.

With axial impellers there is no clear distinction between the different cavitation stages since separation and vortex motion are present during the whole cavity evolution process.

It would be desirable to relate quantitatively the cavity evolution process with changes which might occur in important mixing parameters such as power input, flow field or turbulence characteristics. This is the subject of the following chapters.

33

C h a p t e r 4

P o w er D em a n d in B o ilin g M ech a n ica lly A g ita ted R eactors.

4.1 Introduction.

Power input is one of the most important parameters in mixing vessels. It determines operational costs and is used as a basis in many scaling-up procedures, [60, 93], in determining mixing times, [23], etc.

Power input is usually expressed in terms of the dimensionless Power number, P/(pN3 D5). In single phase fully baffled systems working with newtonian liquids Power number is fairly constant in the turbulent region, characteristic for every impeller-tank configuration, [54], and is determined experimentally.When an impeller operates in a two-phase system the Power number changes from its single-phase value, [65]. The same is true for boiling systems, [10, 58]. Usually this Power number variation is measured via RPD-Relative Power Demand- which is the ratio of the two-phase Power number to the single-phase Power number of an impeller-tank configuration at the same impeller speed.

\CHAPIER 4. POWER DEMAND. 34

Although RPD in gassed systems has been sufficiently investigated this is not the case for boiling systems. In this chapter general correlations will be derived for the estimation of RPD in boiling Stirred Tank Reactors. Visualisation of cavity formation reported in the previous chapter will be used to give a physical explanation of the phenomena controlling Power number changes. Finally RPD in boiling and aerated systems will be compared.

4.2 Background.

Changes of impeller Power number during operation in gassed two-phase STRs have been widely investigated. It is well known that under similar conditions i.e. equal impeller speeds, the gassed power consumption is usually lower than that in an ungassed system. Early attempts to explain this reduction in Power number were in terms of the lower density of the mixture of liquid and gas bubbles the impeller experiences, [13], but it has been shown that this factor cannot fully explain the phenomenon. Power number reduction must be explained by a change in the drag coefficient of the impeller blades because of the formation of large cavities at the rear of the blades when operating in gassed systems, [8, 44, 77]. It is known that cavities behind bodies will reduce the form drag coefficient, Batchelor, 1967, [7] or Logvinovich, 1969, [28]. It is also expected that the drag of impeller blades will also be reduced when cavities are formed behind them. Drag reduction is then experienced by power number reduction in the shaft of the impeller, [67]. Biesecker, 1972, [8], Van’t Riet and Smith, 1973, [77], Nienow and Wisdom, 1974, [44], have shown that cavity formation is a plausible explanation of Power number reduction of impellers operating in two-phase systems.

Although the reason for Power number changes and the overall evolution of the phenomenon is known, e.g. [81, 65, 39], the physical mechanism and the factors affecting the formation and evolution of the big stable cavities behind impeller blades need more investigation, Manning and Jameson, 1991, [37].

The available knowledge concerning Power number changes in boiling systems is much poorer, with the only work known to the present author being that of Breber, 1986, [10], who investigated RPD of a two-blade radial impeller operating in boiling liquid in a 0.26 m diameter glass vessel -see also paragraph 2.7.2-.

\CHAPTER 4. POWER DEMAND. 35

Correlation derived by Breber is specific to the geometry checked and seems to be unsatisfactory because important cavitation parameters like static head above impeller level, were not checked or taken into account.Finally there is still a need for physical reasoning of the cavity formation mechanism in boiling STR highlighting the differences between boiling-vaporous and ventilated-gassed cavitation.

4.3 Experimental rig and experimental procedure.

The experimental rig has been described in chapter 3, fig. 3.2, picture 3.1. Only details o f the power and vapour rate measurement methods and the impellers used will be described here.

Torque on the impeller shaft was measured with the help o f a Vibrometer TE 106/M4 torque transducer with a combined error o f ±0.1% f.s.d. ranging from 1 to 20 Nm. Speed was measured by a PDC 753 M9 F/A -Frequency/Analogue- converter with quartz stabilised time base with ± 1 RPM. The instrument can be connected with an oscilloscope so that the time evolution o f torque, speed or power can be detected. The only power loss on the shaft except that o f the impeller during the present experiments was a loosely fitting PTFE sleeve at the bottom of the vessel. This steady bearing was necessary in the present equipment to prevent vibration because o f impeller and shaft imbalance during high speed operation. The small torque due to the bottom bearing could not be measured directly since it was well below the accurate range o f the meter; a small correction, determined from comparative experiments with and without the steady bearing in place, was applied to all the present results. Comparative experiments were done before and after each set of measurements to ensure the highest possible accuracy.

Vapour rate in the vessel was measured by measuring the reflux from the dividing head which was fitted below the condenser. The condenser was calculated and checked to be of much higher capacity than that necessary to condense the vapour produced at the highest vapour rates in the vessel. The system was thoroughly checked for vapour leakages. The reflux rate was measured with the help of a balance with 0.01 gr resolution. Thermal power input in the tank by the three 1.25 kW immersion heaters could be controlled via an accurate thyristor controller


from 0 to 100% of the full power. It was also possible to run the experiment with only two or one instead o f three heaters on.The liquid bulk temperature was measured using a platinum resistance electronic thermometer o f ±0.025 °K accuracy. The measuring bulb of the thermometer was placed at the impeller level. The atmospheric pressure could be measured with a conventional mercury barometer.

Single-phase Power numbers were determined at temperatures well below those leading to the initiation of cavitation. Because o f the sensitivity o f impeller power number to bottom clearance and also the presence of internal obstructions, in the present case heating elements and the use of the associated vapour deflector caps, separate determinations o f the uncavitated Power number Npu were carried out over a range o f speeds for each configuration. These single-phase power number measurements were restricted by the need to avoid surface air entrainement. It is known that when there is significant gas flow through the impeller zone of an agitated vessel the influence o f surface entrainement is relatively unimportant, Nienow et al ,1979, [42.J, so there should be no effect from drawndown during two-phase measurements at the higher speeds used in some of the boiling experiments.The mean value o f the single-phase Power number measurements before surface aeration starts was used for the calculation of the RPD ratio in the two-phase experiments. An example o f the single-phase Power numbers is shown in fig. 4.1. The measurements used for the calculation o f the single-phase Power number in the turbulent region are those up to 175RPM where the Power number starts to fall because of surface aeration.

76.5

6£ 5.5 I 5 | 4.5© 45£ 3.5

32.5

250 75 100 125 150 175 200 225 250

RPM

Fig.4.1 Uncavitated power number Pu

Rushton impeller D = 240mm, T = 450mm' " I t

♦ h = 580mm, c = 337mm

❖¥ A A A A A f

♦ + ♦' * r i


Adjusting impeller speed to produce a given torque was found to be the best experimental procedure for the present equipment. The experiments were performed with both increasing and decreasing the impeller speed.

Three types of impellers were used, picture 4.1 :a. Conventional Rushton turbines o f three different diameters.b. Three six blade 45 degrees pitched blade impellers.c. A hollow blade disc turbine which could be driven with the faces o f the six blades either concave or convex.Fig. 4.2 details the principal dimensions of the impellers.

R u sh ton im p e lle r s , 6 b la d es

38 r=̂ -

!i

D0 .25 D------- g*

0.2D

Rushton(diam.) h

240180126

121020

C o n ca v e-C o n v ex , 6 b la d es

38 fct

<3- D0 25 D

---------- EH

0.2D

R = 0 .1 ID

PBT, 6 b la d es

i- PBT (diam.) h

225200165

0.2D0.22D0.22D

Fig. 4.2. Dimensions of the impellers in [mm].


Picture 4 .1 . Impellers used in th e experim ents

I CHAPTER 4. POWER DEMAND. 39

4.4 Theoretical Background.

Cavitation in two-phase Mechanically Agitated Stirred Tank Reactors is o f interest because it influences power demand and all the related processes. Cavitation starts when the local pressure of the liquid falls below the vapour pressure o f the liquid. Then the liquid "boils” locally resulting in the formation of bubbles and regions of vapour. Using dimensional analysis it can be shown, [55], that if vapour pressure is an important factor then a suitable similarity parameter is the Euler number or Cavitation number

(P - pv)CN = ------------ (4.1)

1/2 p V2

where pv is the vapour pressure at the local temperature, p and V are a characteristic pressure and velocity respectively. Usually quantities pv, p and V are defined using reference quantities of the system because the real ones are hard if not impossible to determine. Turbulence, which plays an important role in the onset of cavitation, [3, 4], makes accurate description o f the above parameters even more difficult. However the use o f a cavitation number in the form defined by eq. (4.1) has proved to be useful in correlating cavitation phenomena in engineering practice, [3, 4, 28, 92].

I f local pressure falls to the boiling pressure at the local liquid temperature then, as a result of boiling, vapour cavitation occurs. In the same way a gas cavity can develop when gas can accumulate at points o f low pressure. Although in both cases cavitation number is used in literature for determining the probability of such cavitation to occur, there are some parameters such as mass or heat transfer resulting in condensation or evaporation which may have very little effect on gaseous cavitation but are o f great importance in vaporous cavitation, [3, 4, 92].

In the literature o f gas-sparged stirred tank reactors Relative Power Demand -RPD- which is a result of cavitation, is often shown as a function o f Gas Flow number,

Fl= Qg/(ND3)

Fig. 4.3 illustrates the idealised form of the RPD vs FI number for a gassed Rushton turbine if the effects of surface aeration are neglected. The curves are


smoothed from data obtained with a 0.176 m impeller in a 0.44m diameter tank. The figure demonstrates that Gas Flow number is not of itself sufficient to fully characterise the evolution of the cavities and consequently the power demand changes.

i !i.ij- ' v

0 0.02 0.04 0.06 0.00 0.1 0.12 0.14 0.16 0.10 0.2Gas Flo* Number Q/ND3

N r e v / s e c x F lo o d in g V Q l l t r c / s e c

Fig. 4 .3 . RPD of Rushton impeller. T/D = 2.5. From [581.

A similar approach might be considered in a boiling system i.e. to use some function of the total vapour generation rate Qv instead of the sparged gas rate Qg. This is likely to be unsatisfactory for both geometric and physical reasons. The location of vapour generation in a boiling system is usually unknown so that comparison with conditions where gas is supplied directly by a sparger into an impeller is difficult. Factors such as static head above the impeller level cannot be incorporated easily in this approach despite the fact that they are very important for an impeller operating in boiling liquid, Smith and Verbeek, 1988, [61].

Cavitation number as it is described in eq. (4.1) is a ratio of quantities with energy dimensions. The denominator is a measure of the kinetic energy available in the liquid while numerator is a measure of the energy needed to reach boiling conditions. If the denominator is high and/or numerator is low then the probability of cavitation occurring is high. On die other hand if denominator is small and/or numerator is high then the cavitation probability is low.

In the impeller region of a boiling reactor, the flow field is highly turbulent very complicated and usually unknown. Moreover turbulent pressure fluctuations play an important role in the initiation and further development of cavitation


phenomena, [4]. It is therefore not very helpful trying to describe cavitation number using mean values o f the liquid velocities and pressures in the impeller region.

This problem can be overcome by using easily measurable quantities as reference as is the usual case in engineering practice, [4, 55].A suitable reference measure of the liquid velocity in the impeller region is the impeller tip velocity Vtip.Velocity, pressure and temperature fields in a boiling reactor are usually unknown. A reference measure of the pressure p at impeller level may be the pressure pi at impeller level if the liquid were still. Similarly a suitable reference measure of the vapour pressure at impeller level may be the vapour pressure at boiling temperature if reactor is boiling, or at the nominal temperature if it is below boiling point, at the free surface o f the reactor, pvs.The Cavitation number then can be written as:

(Pi - Pvs)CN = ---------------- (4.2)

1/2 Pl Vtip2

If the reactor is a free boiling reactor eq.(4.2) can be rewritten as :

S pL g 2 S gCN » ------------ =------------- = CAgN (4.3)

1/2 pL Vtip2 Vtip2

because in a free boiling reactor vapour pressure at the free surface approximates atmospheric pressure so that (pi - pvs ) equals approximately liquid head aboveimpeller level (S pL g) where S is the submergence.This final form of cavitation number can be named as Agitation Cavitation number or C avagitation number, CAgN, and may be suitable to describe the behaviour of boiling or near boiling Stirred Tank Reactors. For near boiling systems submergence must be corrected for nominal temperature differences. I f reactor operates under over or underpressure then submergence must be corrected for the associated pressure differences.The Agitation Cavitation, Cavagitation, number defined by eq. (4.3) can also be written as

1 S 2CAgN = — ( ---------- ) (4.4)

Fr D 7I2


It is important to note that the Cavagitation number specified by equations (4.3) and (4.4), does not correspond rigorously to the traditional formulation of cavitation number used to describe ventilated cavities since the pressure within the vapour cavity may not be equal to the vapour pressure pvs and is strongly affected by both the local fluid mechanics and thermal factors. The hydrodynamic influences include the difference between the liquid density and that of the two- phase mixture above the level o f the impeller, the radial pressure gradients generated by the forced vortex rotation within the immediate confines o f the impeller and the pressure effects in the spinning trailing vortices that develop from impeller tips at low local vapour fractions.It is important to notice that this form of Cavagitation number is independent o f the complicated pressure or temperature field generated in the reactor. Only a nominal reactor temperature is needed to define whether reactor is boiling or not and it is presupposed that temperature in the impeller region is correlated well with the nominal temperature of the reactor. This oversimplification may cause several problems since a temperature difference o f a few hundredths of a degree result in significant vapour pressure differences. Small temperature differences of this scale may be caused by improper mixing, by drawndown of air, by different heat losses through the vessel wall or from superheated surfaces in the reactor.Differences in temperature may be also an effect o f size and shape; a boiling laboratory scale reactor of say 30 It capacity is expected to show smaller bulk temperatures than a 6 m3 industrial scale vessel simply because heat losses from the small vessel will have a much larger effect in bulk temperature than in the large vessel where large heat capacity will suppress any significant temperature deviations, at least near the impeller. Although in each case the nominal reactor temperature may be boiling temperature at the corresponding atmospheric pressure these small temperature differences can create locally significant vapour pressure deviations.

Another form of Cavagitation number may be obtained by using the vapour pressure at the temperature measured at the impeller discharge stream as reference quantity for the vapour pressure. In this case p can again be represented by the pressure pi at impeller level i f the liquid were still,

pi = pa + pst (4.5)

I CHAPTER 4. POWER DEMAND. 43

where pa is the atmospheric pressure and pst is the static pressure head at impeller level if the liquid were still and

pv = pvi (4.6)

where pvi is the vapour pressure at the temperature ti in the impeller discharge stream.Using eqs (4.5) and (4.6) equation (4.1) is written

pa + pst - pvi pst pa - pviC N = ------------------------ =------------------- + -------------- (4.7)

112 pL Vtip2 1H pL Vtip2 1 /2 p l Vtip2

In eq. (4.7) the first term in the right hand-side is just the Cavagitation number as defined in eq. (4.3) and second term again has the form of a Cavitation number playing the role of a temperature correction term. This last term might be very useful in comparative procedures i.e. it is the term which defines how 'similar' in terms of cavitation parameters two experiments are. If this last term has the same value then corresponding experiments can be safely correlated with the use of Cavagitation number even if they are not equivalent in terms of e.g. heat insulation or heat generation rates.Unfortunately in order to determine this temperature correction term accurate temperature measurements or predictions are needed. Predictions o f temperature in the impeller discharge stream in a stirred vessel with accuracy o f few hundredths o f a degree are difficult if not impossible. On the other hand temperature measurements are not normally possible. However when this term can be estimated a safe correlation with the use o f Cavagitation number may be done.

4.5 Results and discussion.

4.5.1 Presentation of the data

Using the reciprocal of Cavagitation number as defined by eq. (4.3) or (4.7), Relative Power Demand, -RPD-, can be shown to fall in a similar way to that associated with the conventional plots for gas-liquid systems, fig. 4.3.


Fig. 4.4 plots the RPD against the reciprocal o f the Cavagitation number as defined by eq. (4.3) i.e. essentially with increasing cavity size for the Rushton 180mm diameter impeller.

1.2

0.8

8= 06 DC

0 . 4

0.2

01 2 3 4 5 6 7

1/CAgN

It is important to note that during the experiment from which data for fig. 4.4 come, the temperature at impeller level was not steady but was falling by as much as 0.25 °K with increased impeller speed, possibly because o f enhanced heat losses due to vigorous liquid circulation in the vessel and/or air draw-down through the free surface of the reactor. This small temperature change corresponds to approximately 840 Pa or nearly 9 cm of boiling water head. Taking into account that submergence during this experiment was 22.5 cm then submergence variation due to temperature variation during the experim ent was about 40% that o f the real liquid depth at impeller level. In another similar experiment with the 180mm Rushton impeller but with liquid height 58 cm and impeller clearance 15 cm, fig. 4.5, temperature variation during the experiment was 0.15 °K corresponding to 500 Pa or approximately 5.5 cm of boiling water head which is only about 12% of the real submergence of 43cm.Comparison o f the previous two experiments shows that an increase o f liquid volume from about 70 It to about 90 It and submergence from 22.5 cm to 43 cm enhances confidence in the simple Cavagitation number defined by eq. (4.3) by about 3.5 times. It is then expected that at industrial scale where vessel volumes and consequently vessel heat capacities are much greater than the volume of the midsized experimental vessel used in this study and where submergence is

Fig .4 .4 R P D fo r R ush ton Im peller, 0 = 1 80mmh = 4 5 0 m m , c = 2 2 5 m m , T = 4 5 0 m m , A t = 0 . 2 4 4 o C

: tem p.correlation :

no: tem p.corre latlon...... ......................

A

.............. 4 * .....

A„ A A a ........

A

A' ^ \ ^ A............................................................/A A ....................^ A A A A


expected to be much higher than in the case o f laboratory scale equipment, application o f Cavagitation number in the simple form defined by eq. (4.3) may be done with confidence keeping all the advantages o f simplicity; it may be possible to use the nominal reactor temperature and avoiding the need for difficult if not impossible accurate temperature measurements in the impeller discharge stream.

1.2

1

0.8

0 . 4

0.2

02 3 5 6 7

1/CAgN

It is also evident that in order to correlate results from data series obtained from measurements in this medium scale laboratory equipment and to use them for investigation of parameters like the D/T ratio, it is necessary to correct submergence for temperature deviations arising during each experimental run. This is the method applied to all the data presented here; Cavagitation number in the simple form defined by eq. (4.3) is used after the submergence has been corrected for temperature deviations from the initial temperature at impeller level. In this way data readily useful for industrial scale applications, where use of Cavagitation number in the form defined by eq. (4.3) seems to be the only feasible approach, have been obtained. For comparison the Cavagitation number without temperature correction can also be calculated from the data in Appendix 2. In the same Appendix data for the calculation o f the correction factor in eq. (4.7) can also be found. The initial and final temperature at impeller level are also given for each run. During the initial experimental runs the temperature at impeller level was read with each set o f measurements together with torque, speed, and vapour rate. After it was found that temperature changes can be approximated nearly linearly with

Fig.4.5 R P D fo r R ush ton Impeller, D=180m mh = 5 8 0 m r n , c = 1 5 5 m m , T = 4 5 0 m m , A t = 0 . 1 4 o C

..........A ...............

a a

▲

n o tern p .^ r e la t io n 1

AIfc

A a

▲ Aa * A A

t 1 1 1 1---- 1---- 1---- •---- r


impeller speed without significant errors for the present experiments, see Appendix 2, only initial final and a few intermediate temperature measurements were made. The temperature measurements used for this approximation can also be found in the corresponding data sets measurements in Appendix 2.

4.5.2 Initial cavitation stages.

It is not clear whether the small increase of the power draw in the early cavitation stages, fig. 4.5, is a result o f error because o f the way RPD was calculated using the mean value of a series of measurements over a wide range of speeds until surface aeration starts, fig. 4.1, for the single-phase Power number calculation, or is the boiling equivalent of the phenomenon reported previously in the literature by e.g. Van't Riet et al, 1976, [74], where a small amount o f gas tends to increase the power number o f an impeller by as much as 10% or so above its ungassed value. As this small RPD increase takes place at low impeller speeds o f little practical importance, no further attention has been paid to it.

4.5.3 Influence of vapour generation rate.

Fig. 4.6 and fig. 4.7 show the Relative Power Demand o f the 240mm and 180mm Rushton impellers respectively under different vapour generation rates. The independence of RPD from vapour generation rate is characteristic. Despite the variation of vapour generation rate over a wide range no important influences on the RPD curves are detectable. With axial impellers results again showed no influence of the vapour generation rate on RPD, fig. 4.8.

\CHAPTER 4. POWER DEMAND.

Fig .4 .6 R P D fo r v a rio u s v a p o u r ratesh = 5 8 0 m m , c = 3 3 7 m m , T = 4 5 0 m m , R u s h t o n 2 4 0 m m i m p e l l e r

1/CAgN

F ig ,4.7 R P D fo r v a rio u s v a p o u r ratesh = 4 5 0 m m , c = 1 5 0 m m , T = 4 5 Q m m , R u s h t o n 1 8 0 m m i m p e l l e r

1/CAgN

Fig .4 .8 R P D for vario u s va p ou r ratesh = 4 5 0 m m , c = 1 5 0 m m , T = 4 5 0 m m

P B T 2 2 5 m m i m p e l l e r u p w a r d s p u m p i n g

1/CAgN


It can be seen from fig. 4.9 that in the experimental equipment used vapour loads impeller in a direct /indirect way through recirculation loops as a result o f the relative position of the heaters. This vapour loading configuration is the more usual in boiling reactors. Specially constructed vapour deflector caps have been used to investigate the influence o f the location of vapour generation on RPD. Vapour may be prevented from reaching the impeller region using vapour deflectors o f semicircular cross section which guided the vapour generated on the heaters to the free surface of the reactor, fig. 4.10. Only minor differences have been detected with these different impeller vapour loading modes, fig. 4.11. The same is true for other impeller tank configurations.

4.5.4 Influence of the location where vapour is generated.

Flg.4.11 R P D fo r v a rio u s va p ou r loading w aysh = 4 5 0 m m tc = 2 2 5 m m , T = 4 5 0 m m . R u s h t o n 1 8 0 m m i m p e l l e r

V a p o u r t o t h j ^ f r e e s u r f a c e J

• : n o v a p o u y i e f l e c t o n B . ; :

' \

*’ 1

-

£ 3

& A , _: C A - g j .

■a e > \

1 i j i i 1 i ■ , ■ , „r _ |

1 2 3 4 5 6 71/CAgN


4.5.5 Influence of geometric parameters.

4 .5 .5 .1 R a d ia l im p e lle rs

4.5.5.1.1 Height and clearance.

A wide range of clearances and heights has been checked. As is shown in fig. 4.12 and fig. 4.13 the submergence based Agitation Cavitation number performs quite well. There is a significant discrepancy only when the impeller approaches close to the free surface o f the bulk, especially with the concave and convex impellers, fig. 4.13a. The reason for this discrepancy is not clear. Significantly increased impeller region velocities, as impeller approaches the free surface, and consequently reduced cavity sizes, [3], might be a possible explanation. Although the curves o f fig. 4.13a can be brought together by taking into account an impeller diameter to submergence based coefficient for data which are closer than one and half impeller diameters to the free surface, fig. 4.13b, no further attention has been paid to this : for most o f the mixing processes in practice, submergence depths are larger than the impeller diameter for performance reasons, e.g. [45]. For the range o f practical interest height and clearance seem to have little effect on Relative Power Demand which correlates well with submergence based Cavagitation number.

Fig .4 .12 R P D fo r the R ush ton 240mm Im pellerT - 4 5 0 m m , V a p o u r r a t e = 1 0 4 d m 3 / m i n

1/CAgN

I CHAPTER 4. POWER DEMAND.Fig.4.13 RPD for the Rushton 180mm impellerT=450mm, Vapour rate=104dm3/min

1/CAgN

F ig ,4 .13a R P D fo r th e ho llow b laded ImpellerD = 1 8 0 r n m , T = 4 5 0 m m , V a p o u r r a t e = 1 0 4 d m 3 / m i n

1.2

1 -

0.8 J

§ 0.6 E

0 , 4 -

° i » A

If *a *a

..... »

■concave,h:= 4^ m m ,ce*i5onim

concave,h=45gm tTi,c= 225m m

■concave,h:=5a^m m ,CRi50m ni

convex,h=45Qjrnm ,C3lS0rnm :

eo n vex ;h = M 5 ^ m ic= 2 25 m m :

convex,h ±&80nim iea1&Qmm :

3 41/CAgN

1.2Fig .4 .13b R P D fo r the hollow b laded im peller

D = 1 8 0 m m , T = 4 5 0 m m , V a p o u r r a t e = 1 0 4 d m 3 / m l n

1 -

0.8

a 0.6 a

0 . 4 -

0.2 -

<%....\ i v *

*■ t

\'< ib..........

A

■ concave,h:=45£m m ,c=:i sqm m

con ca ve , h:=45griim,ci=;225mrn

concave,h:= 58gm m ,c= :l50m m

• conyex;h4=4S^nm(C=1B0rnm:

: convex,hi=45^ rim )C-225m m :

i con vex,h 4=S0bmiPiQ=1 so m m :

1 1 1------3 4

[1/CAgN]*{(h-c)/(1.5*D)} A 0.S


4.5.5.1.2 T/D ratio.

Fig. 4.14 shows RPD against (CAgN)-1 for Rushton 240, 180 and 129 mm diameter impellers. It can be seen that influence of T/D ratio is significant with the 129mm impeller forming a clearly different data curve.

Fig .4 .14 R P D fo r R ushton im pellersT = 4 5 0 m m , h = 4 5 0 m m , c = 1 5 Q m m , V a p o u r r a t e = 1 0 4 d m 3 / m l n

1/CAgN

4 .5 .5 .2 A x ia l im p e lle rs

Height and clearance have little effect on the RPD of radial impellers , providing that the submergence is larger than one and half impeller diameters. This is not the case for axial ones; for axial downwards pumping impellers clearance seems to be the important factor for RPD data fitting, fig. 4.15. I f an axial impeller pumps upwards then submergence may be more important than clearance, fig. 4.16. On the other hand in the case of axial impellers the D/T ratio seems to be unimportant factor for Relative Power Demand correlation, fig. 4.17.

RPD

RP

D


Fig.4.15 RPD for the 200mm PBT pump.downwardsT=450mm, Vapour rai9=104dm3/mln

4 5 Q m m ^ c k t s p m r n Jh : = 5 8 0 m m ^ = : i 5 0 m m j

h ; = S B Q m r t i j C = 2 2 5 m m |[ i j L“S ® g , I

* ^ -^ ^ .

* ^ D A *

................<<3

<U□<3

-x

* A : j

1 2 3 4 5 6 71/CAgN

Fig .4 .16 R P D fo r th e 200mm P B T pum p.upw ardeT = 4 5 0 m m , V a p o u r r a t e = 1 0 4 d m 3 / m l n

1/CAgN

Fig .4 .17 R P D fo r P B T pum ping dow nw ardsT = 4 5 0 m m , V a p o u r r a t e = 1 0 4 d m 3 / m l n

. . . . . . . . . . . . . . . . . . . . i . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

: D = ; 2 o d m m , h : = 4 j o m i T i , c i = ; i 5 o m m j

• D j 206m m , h : a 5g 0m m , c = : i S 0m r n

: D = l 6 S m m , h = 3 8 0 n i m , c = i 5 0 m m j

1 = 1 0 A! i ° A A

A j 1

1 2 3 4 5 6 71/CAgN


The reason for these different geometric factors influencing RPD with radial and axial impellers might be the different pressure losses associated with obstacles in impeller discharge flow. An obstacle may increase pressure and reduce velocity inside the impeller region resulting in lower cavitation probability, eq. (4.1), with consequently reduced cavity sizes and higher RPD. This tendency is clear in fig. 4.14 where the tank wall which forms an obstacle is much closer to the 240mm impeller. Similarly in fig. 4.15 the tank bottom which forms the principal obstacle for the downward pumping axial impeller is closer to the data with the smaller clearance which in turn are those with the higher RPD. Upwards pumping axial impellers show a weaker but generally similar behaviour with height as the most important parameter, fig. 4.16. With radial Rushton impellers D/T ratio seems to be the most important parameter for RPD correlation while clearance and height have a small but distinguishable effect on RPD of axial impellers pumping downwards and upwards respectively.

4.6 Equation fit.

The data of fig. 4.13 can be approximated sufficiently well within regions of interest by a power law relationship of the form RPD=A*CAgNB. In fig. 4.18 the solid line represents the relation

RPD =0.695*CAgN 0 45

Plg.4.18 P ow er law approxim ation o f the R P D dataD = 1 8 0 m m , T = 4 5 0 m m , V a p o u r r a t e = 1 0 4 d m 3 / m i n

1/CAgN


I f log(RPD) is plotted against log(CAgN) in the y axis and in the x axis respectively, fig. 4.19, data points fall approximately on a straight line that can be approximated by a power law fit where the exponent B is the inclination.It is convenient to define a critical value for the Cavagitation number as that below which power draw is less than in the corresponding single-phase system. For the data of fig. 4.19 the critical CAgN is about 1.4.

4.6.1 Radial impellers

Figures 4.19, 4.20, and 4.21 show the data for the three different Rushton impellers used in the present experiments. Details and relative errors o f the curve fitting in the following figures 4.19 to 4.27 can be found in paragraph 4.6.3.

The D/T ratio has some effect on the exponent B while the constant A, and consequently interception o f RPD lines at CAgN=T, remain approximately the same for all impeller-tank configurations used during the present experiments. The effect of D/T ratio on exponent B is shown in fig. 4.21a.

Figure 4.22 shows the results for the disc turbine with concave blades and fig. 4.23 presents the corresponding data for this same turbine driven with the faces convex. The different tendency of the various impeller types to develop large cavities is reflected in the different RPD at given Cavagitation number values and in the different critical CAgN.

log

[RP

D]


Fig.4.19, RPD for the Rushton 180mm impellerT=450mm, Vapour rate=104dm3/mln

log [C A g N ]

F ig .4.20. R P D fo r the R ushton 240m m Im pellerT = 4 5 0 m m , V a p o u r r a t e = 1 0 4 d m 3 / m l n

log [C A g N ]

Flg .4 .21. R P D fo r the R ushton 129mm Im pellerT = 4 5 0 m m , V a p o u r r a t e = 1 0 4 d m 3 / m l n

log [CAgN]

log

[RP

D]

\CHAPTER 4. POWER DEMAND. 56Flg .4 .21a. D ep en d en ce o f B on D/T ratio

R u s h t o n i m p e l l e r s , T = 4 5 0 m mB

D/T ratio

Fig.4.22. R P D fo r co n ca v e radial im pellerD = 1 8 0 m m , T = 4 5 0 m m , V a p o u r r e

lo g [C A g N ]

Fig.4 .23. R P D fo r con ve x radial im pellerD = 1 8 0 m m , T = 4 5 0 m m , V a p o u r r a t e = 1 0 4 d m 3 / m i n

!og[CAgN]


4.6.2 Axial impellers.

The results for the 200mm and the 165mm diameter 6 pitched blade impellers operating in downward pumping mode are shown in fig. 4.24. Scatter is generally higher than with radial impellers. Unsteady variation o f the power draw during two-phase operation may be one reason.Different clearances produce a small change of exponent B. As it was difficult to resolve it safely and for simplicity reasons this small effect of clearance on exponent B has been neglected.

Fig.4.24. R P D fo r th e dow nw ards pum ping P B TT = 4 5 0 m m , V a p o u r r a t e = 1 0 4 d m 3 / m i n , d i m . i n m m

Log[CAgN]

Figure 4.25 presents the data for the 200 and 165 mm PBT pumping upwards. RPD is higher than the corresponding RPD of downward pumping operation. This can be explained by the upward action of buoyancy forces acting on the cavities behind impeller blades. In downward mode operation the forces resulting from liquid pumping act downwards while buoyancy forces act upwards. As a combined result o f these forces the cavity remains within the impeller blades preventing vigorous pumping. During upwards operation both groups o f forces act upwards so a smaller part o f the cavities remains within the impeller blades with smaller effect on the liquid pumping capacity o f the impeller, leading to a higher corresponding RPD. Again possible small effects of height on the exponent B, fig. 4.16, have been neglected.

CHAPTER 4. POWER DEMAND. 58

0.1

-0.1 -

oaK -o2 -

- 0 . 4

- 0 , 5

Fig.4 .25. R P D fo r the upw ards pum ping P B TT = 4 5 0 m m , V a p o u r r a t e = 1 0 4 d m 3 / m i n , d i m . l n m m

! M : I/i Qtc \

|a j r

: j f | |

- 0 . 8 - 0 . 6 - 0 . 4 - 0 . 2 0 . 2 0 , 4 0 . 6 0 . 8

P=2(K)jH=^50jC=150;

O = 2 00,h= 580.C = 1S 0:

p =200jh =580jc =225 ■

0 = 165,11 =/|50jC = 150

D=l65jhx̂ 80jC=1S0; p =165jh =^80|c-2 2 5 ■

ilne:Rpp'= .i ; i s * C A g N ^ b

1.2lo g [C A g N ]

Data for the axial 225mm diameter impeller are shown in figs 4.26 and 4.27. Scatter is not small but the increased slope of the data is evident compared with the data o f the 200 and 165mm impellers. It is important to note that the 225mm diameter impeller is not geometrically similar to the 200 or 165mm diameter impellers, fig. 4.2. The smaller solidity ratio o f this impeller, [6], may be the reason for the significantly increased slope of the data in figs 4.26 and 4.27. However it should be noted that the constant A o f the power law fit is approximately the same for all the axial impellers operating in the same mode, downwards or upwards pumping.

Fig.4 .26. R P D o f the 225mm upw ards pum ping P B TT = 4 5 0 m m , V a p o u r r a t e = 1 0 4 d m 3 / m t n , d i m . i n m m

log[CAgN]

1 CHAPTER 4. POWER DEMAND. 59

F ig .4.27. R P D o f the 225mm dow nw ards pum ping P B TT = 4 5 0 m m , V a p o u r r a t e = 1 0 4 d m 3 / m i n , d i m . i n m m

lo g [C A g N ]

4.6.3 Overview of the results.

Figures 4.19 to 4.27 imply that cavitation of the impellers used seems to be a three stage process. This can be easily seen in fig. 4.19. During the initial cavitation stages where vortex cavities are formed, fig. 3.3.b, the cavitation process is slower in terms of RPD drop, this being represented by the smaller slope o f the RPD data, line A-B, fig. 4.28.

Fig.4 .28. T h e three stag e cavitation p ro cess.R u s h t o n 1 8 0 m m i m p e l l e r , T = 4 5 0 m m , V . r . = l 0 4 d m 3 / m i n


This may be a result o f the persistence o f the vortex outflow caused by the trailing vortices formed behind impeller blades. This first stage is also evident with convex radial impeller and with axial impellers. It is scarcely present during concave impeller operation, fig. 4.22, probably because of the weaker nature o f the separation vortices formed during the operation of this impeller. The second stage is represented by line B-C in fig. 4.28. During this stage clinging and large cavities, fig. 3.3.c-e, develop behind Rushton impeller blades. The steeper inclination o f the RPD data suggest that the cavitation process is now faster. Finally the third stage of the cavitation process is formed by the rest of the data, line C-D, fig. 4.28. These data belong to the region where cavities formed behind Rushton impeller blades start changing sizes with 3 o f them becoming smaller and three larger i.e. they are large cavities of two different sizes, pic. 3.3.d. The smaller slope o f line C-D shows that RPD drop during this stage is smaller. This third stage was achieved only with the 180, 129mm Rushton impeller and with the convex radial impeller. RPM limitations prevented operation of the Rushton 240mm and the concave impellers at sufficiently high speed to achieve this third stage of the cavitation process. Because o f the different nature of the flow around axial impeller blades it is not evident whether axial impellers will show a similar behaviour when operating at very high speeds.However, despite the above analysis, approximation of RPD data with a single line seems to the best approach for engineering purposes; impellers are not usually operated in the initial cavitation region where speeds are relatively low which would result in improper mixing, and errors arising from the simple one line approximation are relatively small. The parameters for the lines of the figs 4.19 to 4.27 corresponding to the power law fit together with the relative errors, represented in a way by the correlation coefficient1, associated with the power law approximation of the RPD data are given in Table 4.1. Lines in figs 4.19 to 4.27 were fitted by linear regression calculated on all the data with RPD less than 0.95 for radial impellers and 0.9 for axial impellers so that they do not take into account the initial reduced slope region.For the present experimental results constant A is characteristic o f every impeller type and is independent from impeller-tank geometry. Exponent B for Radial impellers depends on D/T ratio and for axial impellers depends slightly on clearance or height when the impeller pumps downwards or upwards respectively.

Correlation coefficient is defined here as: V (St - Sr)/St where St = £ (yi - y)2 and Sr = £ Ei2. The si is the error or residual i.e. the difference between the true value yi and the calculated one from the equation fitted and "y is the mean value of all the data yi. Sums are taken over all the data i=l to n used for the regression, Chapra, S., Canale, R., Numerical Methods for Engineers, McGraw Hill Int. Editions, 1989.


R u s h t o n [ j ) = 2 4 0 m m

R u s h t o n 1 ^ = 1 8 0 m m

R u s h t o n 1 ^ = 1 2 9 m m

P B T , D = 2 0 0 j n m , d o w n . p .

j P B T , D = 2 0 0 i j j i m , u p w a r d s

) C o n c a v e , j j ) = 1 8 0 m m

i C o n v e x j g ^ l 8 0 m moaa: -0.2

1 - 0 . 8 - 0 . 6 - 0 . 4 0 0 , 2 0 . 4 0 . 6 0 . 8 1 1 . 2log (C A g N )

F ig .4 .2 9 .C om p arison o f va rio u s im pellersT = 4 5 0 m m , h = 4 5 0 m m , c = 1 5 0 m m , V a p o u r r a t e = 1 0 4 d m 3 / m l n

Table 4.1. Parameters for power law fit. Relative Power DemandRPD = A * CAgN B.

Impeller Const. A Expnt B cor.coef.

Crit.CAgN

Rushton, 0.24m diameter 0.682 0.4 0.96 2.6



Concave, 0.18m diameter 0.97 0.4 0.98 1.08

Convex, 0.18m diameter 0.58 0.4 0.98 3.9

PBT, dn, 0.225m diameter, S.R.=1.07 1.05 0.57 0.91 0.91



PBT, up, 0.225m diameter, S.R.=1.07 1.14 0.59 0.92 0.8



S.R.= Solidity Ratio = total surface o f blades/ (7r*D2/4)


Critical Cavagitation numbers are also given in the table indicating the tendency of a particular impeller to cavitate. The well known ability o f concave impellers to maintain higher power levels when dispersing gas in gas-liquid systems, [79], is also reflected in the boiling analogue, table 4.1 and fig. 4.29 where RPD data from different impellers are shown in the same plot. The power law relationship predicts reduced power levels whenever Cavagitation number is less than the critical CAgN given in Table 4.1. Curves are reasonably linear until the point where they peak before settling back to unity in the incipient cavitation regime.

4.7 Relation to data with gassed impellers.

Cavity visualisation reported in chapter 3 has shown that the shape of vapour cavities produced in boiling systems is similar to those in gassed systems. It has been shown in this chapter that prevention o f vapour recirculation and vapour generation rate have practically no influence on the RPD of impellers operating in boiling systems, figs 4.11 and 4.6-8 respectively. Prevention o f gas recirculation in aerated systems results in higher RPD, [75], fig. 4.30, which means that behaviour of impellers in terms o f RPD is quite different in boiling and in aerated systems.

Fig. 4.30. Effect of gas recirculation on RPD, from [751.


Another approach may suggest that since there is little to prevent cavity growth in a boiling system it might be expected that the cavities formed are of approximately the same size as those formed in gassed systems just before flooding. This might expected to result in similar ratios for RPD. Figure 4.31 shows that this is not the case. In our experiments boiling RPD is significantly higher than the corresponding gassed preflooding one.

A g ita t io n F ro u d e N u m b e r

Fig. 4 .3 1 . Relative pow er dem and in boiling and g a ssed sy stem s. From [58].

In fig. 4.31 preflooding RPD limit -solid line-is represented by the equation

RPD = 0.24 Fr -°-3 (4.8)

which gives to a high degree o f accuracy the Pg/Pu ratio for a Rushton impeller of D/T = 0.4 just before flooding for Froude numbers above about 0.02, [58]. Clearance, D/T ratio and submergence are the same in both gassed and boiling systems. Total vapour evolution in the tank is 104 dm3/min. A vapour flow number resulting from this total vapour evolution is within the range o f flooding gas flow numbers for the lower speed data although such a vapour flow number might not be comparable with a traditional gas flow number used in aerated tanks, because in our experiments vapour was not generated directly underneath the impeller.

CHAPTER 4. POWER DEMAND. 64

These differences in Power number suggest that there may be more general differences in the process of cavity formation between boiling and gassed systems. If this is indeed so it might have implications for much other work using air-water to simulate vapour-liquid flows. The differences emphasise the importance of establishing the mechanism of cavity formation in two-phase stirred tanks. A unified approach applicable to both gassed and boiling systems might explain those differences. This is the subject of the next chapter.

4.8 Conclusions.

Relative Power Demand in Boiling Mechanically Agitated Stirred Tanks is a function of the Agitation Cavitation , Cavagitation, Number,

CAgN = 2*S*g/ Vtip2

A good approximation of the data obtained for both radial and axial impellers is given by

RPD = A( CAgN)B

where A is a constant characteristic for every impeller type and B an exponent which depends on the impeller-tank geometry.Detected differences of Relative Power Demand in boiling and aerated systems imply that there are differences in the cavitation mechanisms of boiling and gas- liquid stirred tanks.

65

C h a p t e r 5

A U N I F I E D A P P R O A C H

T O C A V I T A T I O N P H E N O M E N A

I N T W O - P H A S E A G I T A T I O N

5.1 Introduction

In the previous chapter the Cavitation-Agitation (Cavagitation) number was shown to be the single and necessary parameter to correlate Relative Power Demand in boiling stirred tanks. Despite the broad and successful use of cavitation number in many engineering disciplines it has not previously been used for correlating RPD in gassed STRs. In aerated tank practice it is usual to correlate RPD with the Gas Flow number, Flg=Qg/N*D3, either keeping impeller speed or gas flow rate constant. Results have shown that RPD is not solely dependent on Gas Flow number, [82], fig. 4.3. Recent publications, e.g. Manning and Jameson, 1991, [37], have shown that better understanding of the physical processes of cavity formation behind impeller blades operating in stirred tank reactors may lead to a unified theory for cavity formation in two-phase agitation with useful practical applications.

1 CHAPTER 5. A UNIFIED APPROACH. 66

In this chapter a new approach to the phenomena which can describe cavity development in either aerated or boiling cavitation is presented and is validated qualitatively and quantitatively using experimental data existing in the literature.

5.2 A descriptive physical model o f the mechanism o f cavity evolution.

An impeller working in a single-phase fluid generates mean pressure fields, extending from the blades to the whole o f the tank, [78], Like the mean velocity field this pressure distribution depends on the stirrer Reynolds number, [47, 78], or if liquid properties are not taken into account, on impeller speed. When gas is present in the flow it accumulates in the lower pressure regions at the rear of impeller blades, forming cavities, [77].

I f the impeller speed is steady, so also is the mean pressure field. I f gas is now introduced to load the impeller, at low gas rates small (vortex) cavities are formed in the lower pressure regions along the core o f trailing vortices behind impeller blades, [11, 44, 81]. Usually the sparger is smaller than the diameter of the impeller and most of the gas supplied passes through the ventilated cavities behind the blades before being released from the downstream end. With an increasing gas flow rate the volume rate o f the gas passing through the cavities also increases. With the higher gas rate the pressure within the cavity is also raised, e.g. [56], so the cavity expands towards regions o f higher pressure. This cavity expansion can be easily followed by considering the ventilated cavitation number

CN = (pst-pc)/(0.5*p* V2) (5.1)

A pressure increase inside the cavity corresponds to a smaller cavitation number and consequently a larger cavity. Cavity expansion is a dynamic phenomenon and continues until an equilibrium is reached between the newly formed pressure field in the liquid and the pressure o f the already expanded cavity under the new gas flow-rate. The cavity is now at higher pressure and bigger, again following a mean equal pressure surface. The gas still passes through the cavity and is ventilated from the rear. Keeping impeller speed constant and increasing gas flow rate further, the internal pressure increases and the cavity expands. There are also

CHAPTER 5. A UNIFIED APPROACH. 67

likely to be pressure field changes in the liquid around the cavity to match the newly formed conditions.

At sufficiently high gas flow rates the corresponding internal cavity pressure has been increased so much that the cavity will try to expand to an isobar which does not form a closed surface with the impeller blades, fig. 5.1. As a result the cavity "breaks" and other routes, generally upwards, are now available for the ventilation o f the gas. This is the "flooding" point. The flow field has now been changed drastically and is controlled by both the action o f the impeller and the gas coming out from the sparger.

Fig. 5.1. Mean single-phase isobar field behind a blade of an impeller

To return to the preflooding situation following flooding, the gas rate must be reduced considerably to return to the previous conditions and to stop the gas following the new routes formed after flooding. This is the reason o f the hysterisis at the flooding point which has been reported, [45], and occasionally in the RPD curve when decreasing gas flow rate during RPD experiments, [81]. The reason for ragged cavity formation, [43, chapter 2], may also be explained now. Vibrations may be the result o f the unsteady movement of the cavity wall between the critical isobar and the position it tries to occupy after-flooding.

\CHAPTER 5. A UNIFIED APPROACH. 6 8

5.3 Quantitative aspects o f the model o f cavity evolution. -D e riv a tio n o f a s u ita b le c a v ita tio n p a ra m e te r-

Van't Riet & Smith, [15], reported that for a Rushton impeller operating in a stirred tank the generated downpressure Ap is a function of Reynolds number,

Ap =fi(Re) (5.2)

Downpressure Ap is the difference between the static pressure under operating conditions and the static pressure at rest at the same point and essentially gives the impeller generated static pressure field, pigst in the tank during single phase operation. From eq. (5.2)

pigst = f2(Re) (5.3)

or if liquid properties are not taken into account

pigst = f3(Vtip). (5.4)

The functions f may be characteristic for each impeller type and may depend on other parameters such as the geometry of the impeller-tank system.

The pressure inside the cavity during two-phase operation can be assumed to depend among other things on the gas flow rate Qg and impeller Re number, or impeller speed, as

pc = d>( Qg, Re ) = <&(Flg*N*D3, Re) (5.5)

The dependence of pc on gas flow rate and impeller Reynolds number may also be characteristic for each impeller type but may also depend on other parameters such as sparger type or the geometry of the impeller-tank system. The function also has to be determined experimentally.

Cavitation number is usually defined as

pst- pcCN = ------------

0.5*p*V2(5.6)

CHAPTER S. A UNIFIED APPROACH 69

where pc is the gas or vapour pressure, p is the liquid density and pst and V a characteristic pressure and velocity respectively.

In engineering practice, as has already been shown in chapter 4, it is usual to use easily measurable reference quantities in eq. (5.6).In a two-phase vessel several assumptions can be made for the most appropriate reference quantities to be used in defining a cavitation number based on eq. (5.6). Impeller tip speed Vtip and liquid density Pl may provide a suitable basis for the kinetic energy term. Pressure inside the cavity, which may assumed to be steady within a cavity, can also be used for the gas pressure. Liquid pressure in a two- phase vessel is very difficult to measure. It is also difficult to decide on the best location for liquid pressure measurement. The situation becomes more complicated if we assume that possible points o f interest for pressure measurements may be inside a cavity during two-phase operation.Therefore it might be helpful if liquid pressure pst can be considered as if in single- phase operation though keeping all other parameters the same. I f this is the case then using eqs. (5.3) and (5.5), eq. (5.6) can be written for an impeller operating in a two-phase stirred tank as

f(Re) - 0 (Q g,Re)CN = ---------------------------------- (5.7)

0.5 *Pl* Vtip2

Eq. (5.7) gives a form o f cavitation number which may be suitable for use in two- phase mechanically agitated systems. It is important to note that in eq. (5.7) the numerator represents a measure o f the amount of energy needed at a location o f a single-phase system to reach cavitation conditions when switching to two-phase operation.

In boiling reactors, without sparged gas, the function 3>(Qg, Re) is essentially constant and equals approximately the vapour pressure at the local temperature. Eq. (5.7) can then be written

f(Re) - pcCN = -------------------- (5.8)

0.5 *pL* Vtip2

Eq. (5.8) denotes that cavitation number in boiling stirred tanks depends on impeller speed or more generally on the impeller region flow field and on the

\CHAPTER 5. A UNIFIED APPROACH. 70

vapour pressure at the local conditions in the reactor. Experiments have verified this, [58, chap.4].With increasing impeller speed f(Re) becomes smaller, [78], giving a smaller cavitation number and consequently bigger cavities and lower RPD. Recent experimental research has proved that this is really the case, [58].

In aerated vessels both functions in the numerator on the right hand side o f eq. (5.7) may not be constant. Keeping stirrer speed constant and increasing gas flow rate the first part o f the numerator will be constant while the second part is expected to increase because cavity pressure is increased with increased gas flow rate through it, e.g. [56]. This results in smaller Cavitation numbers and reduced RPD which has been found in practice, [11, 65, 82].

Eq. (5.7) predicts that if gas flow rate is kept constant and impeller speed is changed then, depending on the functions f and and on the numerator o f the right hand-side o f eq. (5.7), cavitation number may increase or decrease or both. This prediction will be checked in the next paragraph using data from the literature.

5.4 Validation o f the model using literature data.

For Rushton impellers some pressure data measured behind impeller blades can be found in open literature, e.g. VanTt Riet and Smith, 1975, [78], fig. 5.2.

Fig. 5.2. Pressure coefficient versus impeller Reynolds number for Rushton impeller. From [78].


A logarithmic regression o f their measurements gives for Re numbers higher than about103

Cp = -2.1 + 0.4*(ln Re) (5.9)

where

Cp—(pst-undisturbed - pst-operated )/(0.5 *pL*Vtip2) (5.10)

Numerator (pst-undisturbed - pst-operated ) is the downpressure Ap generated by the impeller given as a positive value. From eq. (5.9) and (5.10)

pst-oper. — pst-und. - 0.5*PL*Vtip2{ -2.1+0.4(lnRe)} (5.11)

Manning and Jameson, 1991, [37], have measured pressure evolution inside a cavity at the centre o f the rear o f a blade of a two-blade Rushton impeller. Although they interpreted their results in a very different way their measurements will be used to validate the previously derived model.Figs 5.3 and 5.4 are adapted from Van’t Riet and Smith, 1976, [78], and show how the pressure coefficient changes outside the vortex core. Despite having no details about the exact position o f the pressure measurements it can be concluded that at the centre at the rear o f the blade, pressure coefficient is about eight times smaller than at the point where data for eq. (5.11) were measured.

Cp - 0 5 step 0-5 till 4 0 isobars in a vertical flat plane at the position indicated by A Isobars withaccuracy ±0-4; — , isobars with accuracy ±0-8: D = 48cnv

N„, = 3 x I03.

Fig. 5.3. Vertical isobar field, from [78].

The Cp = 0-5 step 0 5 till 5-5 isobars in the “horizontal" plane through the vortex axis. —, Isobars with accuracy -0-4;

. isobars with accuracy ±0-8; D - 48 cm: NR. = 3 x 105.

Fig. 5.4. Horizontal isobar field, from [78].


So the impeller generated liquid underpressure pig at the centre at the rear o f the blade during single-phase operation may be approximated by:

pst-und.-pst-oper. = pig = 0.0625*PL*Vtip2(-2.1+0.4(lnRe)) (5.12)

In eq. (5.12) pig is given as a positive value.Figure 5.5 shows the results o f Manning and Jameson concerning cavity length and cavity internal pressure pc with another curve plotted representing the corresponding single-phase static underpressure pig derived by eq. (5.12). Both pressures ,pc and pig, are measured with reference to the total pressure-static head- at impeller level.

Fig .5 .5 . P re ssu re in teractions & cavity s ize8

7

6

5

- I 4

3

2

1

05 0 , 0 0 0 1 0 0 , 0 0 0 1 5 0 , 0 0 0 2 0 0 , 0 0 0 2 5 0 , 0 0 0

R e

- 5 0 0

-1000

-1500

- 2 5 0 0

.•Jrtnn

L = c a v i t y l e n g t h / b l a d e h e i g h t , R e = R e y n o l d s n u m b e r P c = c a v i t y p r e s s u r e , P i g = l m p e l . g e n e r a t e d p r e s .Q g = 1 9 . 5 l t / m i n / b l a d , D = 1 8 5 , T = 5 8 0 , h = 5 8 0 , c = 1 8 5 [ m m ]

The difference between the two pressure curves o f fig. 5.5 represents the numerator o f eq. (5.7). The pig-pc and Cavitation number calculated from these data are shown in fig. 5.6. A negative cavitation number means that the point in question will be located in a cavity. Comparing figures 5.5 and 5.6 it can be seen that this is the case.

Using 19.5 lit/min per blade as gas flow rate, being the air flow used in the experiment by Manning and Jameson, the gas flow number can be calculated. Fig. 5.7 shows Gas Flow number versus cavitation number calculated using this

\CHAFTER 5. A UNIFIED APPROACH. 73

approach. Taking into account that the small cavitation numbers correspond to large cavities and low RPD values, fig. 5.7 can be easily related to the well known curves for RPD where gas flow-rate is kept constant and impeller speed changes, fig. 5.8.

F ig .5 .6 .P reesu re d ifferen ces & Cavitation num ber

P I ^ P c

C a v l t a t l o j j i n u m b e r

4 0 0 —

3 0 0 -

200 - 100 -

0 ---'S'&..100 -£-200 - a

- 3 0 0 -

- 4 0 0 - —

- 5 0 0 -

- 6 0 0 -

- 7 0 0 - - - - - - -5 0 0 0 0 100000 1 5 0 0 0 0

Re200000 -0.2

2 5 0 0 0 0

P r e s s u r e d l f f e r e n c e = P l g - P c [ P a ] R u s h t o n t y p e i m p e l l e r

F lg .5 .7 .G a s F low num b er v s C avita tion num ber

(G as FI num b er p er blade) * 1 0 A «3I------------------------------------- —I S t e a d y g a s f l o w r a t e 1 9 . 5 t t / m i n * b l a d e


Comparing figures 5.7 and 5.8 it is evident that the cavitation number in fig. 5.7 demonstrates all the tendencies of the RPD in fig. 5.8. Taking into account that the smaller the cavitation number the smaller the RPD and vice-versa fig. 5.7 shows that cavitation number in the form derived above may be a single sufficient parameter to describe Relative Power Demand changes in two-phase gas-sparged vessels.

Fig. 5.8. RPD of gassed Rushton impeller at constant gas flow-rate. From [451.

Figures 5.5, 5.6 and 5.7 have several other important features. Despite the data coming from very different experiments, the region with the greatest negative value o f cavitation number is very close to the region where the detected cavity size is the largest. This gives support to the approach that cavity growth and consequently RPD are basically dependent on the relation between the pressure field generated by the stirrer during single-phase operation and the pressure inside the ventilated cavity. It is also worth mentioning that the cavity nearly vanishes approximately at the point where pressure difference and consequently cavitation number comes close to zero at the right hand-side o f the plot o f fig. 5.5 and 5.6. In the first stages o f cavitation in fig. 5.5 there is a significant difference between the point where cavity becomes o f detectable length and where pressure difference and consequently cavitation number becomes less than zero. The explanation is that this first region is the region o f flooding, [45], where the previously derived model is not of value as there are more routes for the ventilation o f the gas from the sparger besides the one passing through impeller blade cavities.


Despite the encouraging results emerging from the above analysis there are several important differences between the two experiments where the data come from. Van't Riet’s single-phase measurements were with a standard Rushton turbine with six blades while during Manning and Jameson's measurements of the cavity pressure the impeller was a Rushton type disc turbine but with only two blades. However it might be assumed that at the point where measurements were performed - the centre o f the rear o f the blade- the influence o f the different number o f blades on the pressures used in the present approach might be minor. Another inaccuracy arises from the fact that liquid pressures at the point in question had to be estimated from pressure contours. This extrapolation definitely introduces some uncertainty. However basic features o f fig. 5.7 remain even if pig is somewhat inaccurate. It is relevant that the shape o f the curve in fig. 5.7 is a result o f the way pig and pc depend on stirrer speed and is not sensitive to the absolute values of pig and pc.

5.5 Conclusions.

A model based on the interactions of pressures inside and outside cavities has been formulated to explain cavitation phenomena in two-phase stirred tanks. The model predicts that a cavitation number modified in terms o f pressure differences between the single-phase liquid pressure generated by the stirrer and the pressure inside the cavity formed behind stirrer blades in two-phase operation might be capable o f correlating as a single variable RPD results in two-phase agitation. Functions o f liquid pressure and the pressure inside the cavity, which may be characteristic for every impeller type and may also depend on other system characteristics like D/T ratio or sparger type, must be determined experimentally. Validation of the model using existing experimental results from literature is encouraging in the sense that cavitation number in the modified form shows a dependence on Gas Flow number which is similar to the Relative Power Demand o f gas-sparged vessels.

76

C h a p t e r 6

T H E F L O W F I E L D

I N A T W O - P H A S E S T R .

A p r e d i c t i v e m o d e l .

6.1 Introduction.

It has been shown in chapter 2 that one o f the most important mixing parameters in stirred tanks is velocity field. Almost all the processes taking place in a STR such as mass transfer or chemical reaction are driven by the velocity field generated by the action o f the impeller. A t the present state of development, numerical codes used to estimate performance in stirred tanks have to calculate or have to be fed with a known velocity field.There are several methods available for calculating velocity field in single-phase stirred tanks. Most of these methods need experimental data as boundary conditions, [20, 22, 24, 38, 49, 50]. On the other hand little information is available about two-phase gas-liquid stirred tanks. Most attempts to correlate the

\CHAPTER 6. A PREDICTIVE MODEL. 11

liquid velocity field in two-phase operation with that developed in a single-phase generally lack either a theoretical basis or experimental validation, e.g. [6]. Visualisation o f the impeller region reported in chapter 3 showed that velocity field, especially near the boundaries of the impeller swept volume, is highly turbulent, with the second phase forming cavities behind impeller blades. Cavities develop in size and shape depending on various parameters such as impeller speed and gas flow rate in gassed systems or impeller speed and submergence in boiling ones. Video recordings show that cavity development results in flow field changes near the impeller region. Cavities change instantly and irregularly in shape and size according to the local conditions. The free surfaces of the boundaries o f the cavities are unstable. Cavity tails are broken producing irregular bubbles o f a wide range o f sizes. The whole picture is one o f chaotic motion which seems hard if not impossible to analyse, especially near impeller boundaries, using the common CFD discretised approach.The unstable and irregular characteristics o f the flow field forced the use o f an integral energy approach to get some indication of the general characteristics of the flow field in two-phase gas-liquid stirred tanks.A straight-forward energy balance applied to the boundaries o f a control volume which contains the impeller provides the basis for the derivation o f relationships between single and two-phase liquid mean velocity fields. The results can be used to predict conditions at any point in the vessel using arguments based on differences between overlapping control volumes providing that the flow fields are comparable.The model is validated from data existing in the literature and, in a following chapter, with new two-phase velocity measurements obtained by Laser-Doppler methods.

6.2 Derivation o f the model.

Let S be a surface which bounds a control volume v which includes the impeller o f a stirred tank. An integral energy balance over this control volume gives:

dE /d t+ j p V n d S + J [T.Vn]dS + Ws = j p e V n d S + j ([dpE]/dt)dv (6.1)


where e= U + 1/2 V2 4-gh is the total energy per unit mass of fluid.

In eq. (6.1) surface integrals represent the energy which crosses the boundaries of the control volume and has to be considered all over the surface S of the control volume. The volume integral represents energy accumulation in the control volume. The convention about the sign o f the energy fluxes is that energy which enters or is given to or is generated in and work done on the control volume is positive. In eq. (6.1) the first term represents the energy rate which is supplied to the system as heat, the second and third terms represent the work done, positive or negative, on the control volume boundaries by pressures and stresses respectively, the fourth term is the energy which is given to the system by the impeller - shaft work-, the fifth term is the net transfer o f energy through the control volume boundaries because o f flow and the last term represents the rate o f accumulation of energy in the control volume V. Other energy sources, e.g. electrical, have been excluded. In eq. (6.1) the convention used is that pressure is not included in the normal stress terms o f the stress tensor, - see Appendix 1-.

For steady state with no heat exchange eq. (6.1) reduces to

J p Vn dS + J [T.Vn ]dS + Ws = f p E Vl, dS (6.2)s s s

Eq. (6.2) may be assumed to be valid for both laminar and turbulent systems. For an exact analysis in turbulent systems all the fluctuating components, e.g. pressure p or velocity Vn, have to be replaced by their instantaneous values consisting of mean and fluctuating parts, [68, p.271], e.g. p = p+p\ Unfortunately this would result in products of such instantaneous quantities as p'Vn or t ' W which are generally not zero. An exact analysis taking into account the instantaneous quantities is usually impracticable, [68], and in practice the error is small, [Appendix 1, 68]. Henceforth the instantaneous values will not be used. The notation without the overbar will signify for the rest of this chapter the time- averaged values. This simplification is fully discussed in Appendix I.

The total surface o f the control volume is generally S = Sw + Sj + S2 where the first term is surface which is in contact with wetted solid boundaries, e.g. baffles, and the last two terms represent surfaces where the velocity vector points inwards

CHAPTER 6. A PREDICTIVE MODEL. 79

and outwards relative to the control volume respectively. The integrals over Sw vanish because the no-slip condition means that Vn is zero. Eq. (6.2) is then rewritten:

- Ws = J p Vn dS + I [T.Vn ]dS - { p E Vn dS (6.3)S]+S2 Sj+S, Sj+S,

If we restrict consideration to low viscosity systems then [x.Vn ] approaches zero. This assumption is discussed in detail in Appendix 1. Eq. (6.3) then becomes:

- Ws = J p Vn dS - { p E Vn dS (6.4)Sj+S-. Sj+S?

Assuming that fluid density is constant over inlet and outlet surfaces, the integrals in eq.(6.4) can be evaluated as:

Ws=p2[<(E2-p2/p2)V2> S 2] - Pit<(Ei-pi/pi')V1> S[] (6.5)

where velocity vectors Vn have been replaced with the corresponding values of the vertical to the control volume surface velocities Vj and V2, areas S! and S2 represent the inflow and outflow surfaces of the control volume and quantities in o represent integral based average quantities over these surfaces defined as:

< 0» = ( J s O ds) /( J Sds) = ( j s0> ds)/ S Assuming that pj ~ p2 and applying the mass conservation law between the

inlet and outlet of the control volume,<V2> S 2 = <V j> S j = Q (6.6)

where Q is the total volumetric flow rate through inlet and outlet controlvolume surfaces. Using eq. (6.6), eq. (6.5) is rewritten:

Ws/Q = p{<(E2-p2/p2)V2> /< V 2> - <(El-Pl/Pl)V!> /<Vi>}

= p {(y2< v 22>/ p /3) + / p ,^ + g<h2>/p2 - <p2>/p p2 -( 1/2<V12>/ p,<3> + <Uj>/ + gch^/pfc* - /p p ^ 1)}

wherepp* = <v><v>2/<y3>j p(2) = <V>2/<V2>, pw = <V><V>n-1/<Vn> p(L»= <V>/<UV>, pan = <h><V>/<hV>, P = <V>/<pV>

Assuming that ps inlet « Ps outlet

Ws/Q p = y2A<V2 >/ p(3)+ A/ P(U,+ gA<h>/ pa'»- A/p p̂ > (6.7)

i CHAPTER 6; A PREDICTIVE MODEL. 80

It is perhaps worth noting that the left hand-side o f this equation is an expression proportional to the liquid head [Ws/Q p g] generated by the impeller. If we assume that h does not change very much between the inlet and outlet of the control volume, eq.(6.7) becomes:

Ws = Q p{ 1/2 A<V2 > / ^ 3) + A/ - A/p fl} (6.8)

At this point let us examine the significance of these A and Aterms.

Although the argument is general, it may be easier to follow if the immediate swept volume of the impeller is considered as the control volume. A represents the integrated mean pressure difference between those parts of the surface of the control volume where inflow and outflow are occurring. The volumetric throughput o f an impeller is determined in the same way as the operating point o f a pump: i.e. it is determined by the balance between thepressure developed by the impeller and the external resistance in the fluid circuit. When we consider a control volume that includes the impeller, the local pressure in the fluid is increased from <pj> to <p2> as a result o f the impeller action and then falls back to <p]> because of pressure losses along the mean flow path. As the flow-rate of the fluid circulating in the tank is increased, so will the pressure difference A. In incompressible turbulent flow of a newtonian fluid the relation between pressure difference and velocity is essentially, [55], :

A oc p < V2> (6.9)

Since for any arbitrary cross section S of the flow S<V> = Q, then the pressuredifference is proportional to the product of density with the square of the volumetric flow rate, i.e.

A = xp Q2 (6.10)

where in the fully turbulent region k depends on the tank and impeller geometries.

The A term represents the change of internal energy a unit mass o f fluid experiences as it moves through the control volume. For a system where there is no heat exchange through the boundaries A represents the amount of energy per unit mass of fluid dissipated into heat due to friction losses i.e.


A = Efriction / Qp = Efriction / <V>Sp (6.11)

In an incompressible inewtonian flowiEfriction = p Vo3 lo2 /(R e), [9, p .215] (6.12)

where Vo and lo is a reference velocity and length respectively. Selecting a reference velocity to be <V> and reference length V S, eqs (6.11) and (6.12) imply that in the fully turbulent region, where friction losses are independent of Re number, then /(R e ) is constant, and

Since for any arbitrary cross section S o f the flow S<V>=Q, then A is proportional to the square o f the volumetric flow rate, i.e.

where X in the fully turbulent region depends on geometrical factors.

The same result comes out more simply by assuming that the amount o f the energy converted into friction losses is proportional to A because A is the driving force needed in a circuit to maintain flow, which in turn creates frictional losses. This argument is easy to follow if we consider the flow in a horizontal pipe of constant cross section. I f there is no heat transfer through the pipe wall then friction losses between two locations are proportional to the pressure drop between these two points. To show this we can write the Bernoulli equation for a unit mass o f fluid, for this situation,

A oc <V>2 (6.13)

A = X Q2 (6.14)

V ^ /2 + p j/p = V22/2 + p2/p -t- f

where f is the friction losses per unit mass o f fluid. As V!=V2 then

(pi - P2 v p = A p /p = f

Therefore for a unit mass basis:


A oc A/p or using eq. (6.10)

A = X Q 2which is again eq. (6.14).where X depends on impeller and tank geometries.Using eqs (6.6), (6.10) and (6.14) eq.(6.8) becomes

Ws = Q3p { X /p ^ - icflfeH- (l/2po'»)( 1/S22 - 1 /S /)} (6.15a)where P(V> = p<2' p(3).It is possible to derive an equation similar to eq. (6.15a) in a simpler way starting with an extended Bernoulli equation written for the inlet and outlet points of a mean streamline crossing a control volume that includes the impeller of a tank.

A V ^ + Ap /p +g Ah + AU = W(s)This equation gives the energy increase W(s) a unit mass of fluid experiences while passing through the control volume. For the total volumetric flow generated by the action of the impeller this equation gives

Qp (A V ^ + A p /p + g Ah +A U ) = Ws Assuming that Ah * 0 and following the previously mentioned reasoning for Ap and AU terms,

Ws = Q3p { A + *+ l/2 ( 1/S22 - 1 /S /)} (6.15b)which is similar to eq. (6.15a).This approach presupposes motion o f the fluid along streamlines and lacks direct insight o f the assumptions made to arrive at eq. (6.7).Equations (6.15) have been developed for a single-phase system. In a two-phase system with gas phase dispersed into liquid the most simplified approach is to assume, on the basis of the very small density of the gas compared with the density of the liquid, that the presence of a small fraction of gas, say less than 5%, may not significantly affect the energy balance of eq. (6.15) and may be neglected outside the impeller swept volume. In othgrwords it may be assumed that the flow of the liquid dominates the flow field and the energy transfer in the vessel, with gas playing a relatively insignificant rolejoutside the impeller swept volume. We write therefore:

W s 2pb 3 Q l 3 * p L* { A / p w - K /p » H - ( l / 2 r ’) ( 1 / S 22 - l / S i 2 ) } 2pb.L ( 6 . 1 6 )

If we were to assume that the parameters X, k, (3, S j and S2 do not change very much because of the presence of the second phase, which may be reasonable in the light of the previously made assumption that liquid flow is dominant, then from eqs (6.15) and (6.16) we would have:

\CHAPTER 6. A PREDICTIVE MODEL, 83

Wslph/W s2ph= [ Qlph / Q2Ph I3 (6.17)

Equation (6.17) implies that the relative change in pumping capacity of an impeller operating in a two-phase system is proportional to the cube root o f the ratio between the power inputs in the single-phase and the two-phase systems.

6.3 Limitations o f the model.

If the single-phase flow field in a mixing vessel is known, eq. (6.17) can be used to estimate the mean liquid pumping capacities in two-phase operation on the basis of relative power demand. However the assumptions made in arriving at eqs (6.15) and (6.17) impose important limitations.

a. It is assumed in deriving eq. (6.4) that the viscosity o f the fluid in the vessel is low enough to be ignored - Appendix 1-. Eqs 6j6l 10) and (6.14) have also been derived on the assumption o f a fully turbulent/newtonian incompressible fluid. These assumptions limit applications of eq. (6.15) and consequently eq. (6.17) to systems o f low viscosity incompressible newtonian fluids working in the fully turbulent region where power number is not a function of Re number.

b. Equation (6.15) has been derived on the basis that fluid density is the same as it passes through the inlet and outlet control volume surfaces. In two-phase conditions this seems to be a reasonable assumption if applied only to the liquid phase.

c. The requirement o f small height differences between inlet and outlet o f the control volume can be met by appropriately defining the control volumes. The important factor is the potential energy a unit mass o f fluid gains while moving through the control volume compared with the sum of kinetic, internal and pressure energy gain. This factor can be expressed as

e = | gA<h>/ { 1/2A<V2> + A- (A/p)} |

I CHAPTER 6. A PREDICTIVE MODEL. 84

If e is small then neglect of height differences can be done safely. If the control volume is defined symmetrically around radial pumping impellers, gA<h> approaches zero as a result o f the general flow field induced by a radial impeller, fig. 6.1. With axial impellers depending on the choice of the control volume gA<h> may approach zero if the control volume extends towards the tank wall, fig.6.2, a, or may form a significant part of internal energy content if the control volume is chosen to be like in fig. 6.2, b.

d. Another important assumption made in arriving in eq. (6.16) is that gas based terms have little effect on the energy balance equation and only liquid need to be considered in writing energy balances outside the impeller swept volume. This gross assumption directly places a limit of low gas rates on the application of the model. With increasing gas rate, void fraction, energy carried by the gas, slip velocity, interfacial energy transfer e.t.c. may become important, drastically affecting energy balances.

e. Parameters $ which are equal to unity if velocity profile is flat, were assumed to be approximately the same between inlet and outlet control volume surfaces. Although in many engineering applications of integral energy approach such an assumption is satisfactory, [68], this may not be the case for stirred tank reactors. However this assumption can be met by appropriately defining the control volume so that velocity profiles over inlet and outlet control volume surfaces are of the same degree o f "flatness".

Fig. 6.1. Flow field induced by a radial impeller.

Fig. 6.2. Flow field inducedby an axial impeller.


f. Finally to arrive at eq. (6.17) it is necessary to assume that X, k , p, Si and S2 do not change very much while switching from single to two-phase operation in the tank. It is important to note that X and k depend on geometrical factors which remain the same in both single and two-phase operation since eq. (6.16) is considered for the same system as eq. (6.15) except for the presence of a small gas fraction. Therefore it is expected that X and k remain approximately the same in both single and two-phase operation.Sj and S2 are the inlet and outlet surfaces of the control volume where the velocity vector points inwards and outwards. Eq. (6.17) applies only if the areas of inlet and outlet surfaces remain approximately the same in both single and two-phase operation. It is very difficult to estimate a priori the extent of inlet and outlet surface changes as they are an effect o f the variations occurring in the general flow pattern. It seems reasonable to assume that if control volume boundaries are not very far from the impeller region where liquid velocities are dominated by the impeller action and the impeller is operating well away from the flooding, only small changes of inlet and outlet control volume surfaces are likely to occur when switching from single to two-phase operation. In some cases it might be expected that areas of in and out-flows -Si and S2 - could be modified quite drastically by the presence of the second phase. For example, if the surface o f the chosen control volume is very close to the impeller, the presence of large gas cavities will change the areas through which there is significant liquid outflow. Difficulties could also be expected in regions where buoyancy forces are significant or where secondary flows develop. Either or both of these conditions probably apply in the upper regions of tall vessels.The same reasoning is applicable to parameters $ which depend on how equally "flat" the liquid velocity profiles are when switching between single and two-phase operation. Despite it is difficult to estimate this apriori it may be reasonable to assume that at regions where Sj and S2 remain unchanged, parameters (3 between single and two-phase operation are expected to be reasonably equal.

6.4 Mean velocities.

Despite all the admitted limitations in the simple analysis, it does have the virtue of providing a straightforward and immediate approximation for the velocity field developed by a gassed impeller because it is also valid for more remote control volumes in that these can always be expressed as differences between control


volumes containing the impeller. Assume that A and B are two such control volumes with flow-rates Qa and Qb through them. The flow-rate through the volume A-B is Qa - n*Qb where n is a number which depends on the relative position and size of the volumes A and B.From eq. (6.17) we have that

(Qa2phV(Qaipb) = {(Ws2ph)/(Wslpb)} i« = (Qb2pb)/(Qblpb) (6.18)

from which replacement o f Qa, b and Qb, h gives for the volume A-B:

Q̂ ph - n*Qb,,:phQalph - n*Qblph

Ws,:ph

Wslph i

2ph

1/3(6.19)

The number n is the same in both single and two-phase operation because it has been assumed that the areas of in and outfloware unchanged. ^ p&r&we-lers Since eq. (6.19) will also apply to any small control volume which is the difference between two larger ones containing the impeller, this implies that eq. (6.17) must also apply to the mean velocities at any arbitrary points in the single and two-phase systems:

[V2ph / V, J = (Ws2ph / Wslph )l/3 (6.20)

6.5 Extension o f the model

If the gas fraction is relatively large then the assumption that the influences of the gas-phase on the energy balance can be neglected may not be valid. In this case it may be possible to assume that the two phases form a homogeneous mixture with little variation of void fraction from point to point which can be considered as a new fluid. The two-phase system can then be treated according to the homogeneous theory, [21, 70]. All the assumptions made to arrive to eq. (6.15) must be applicable to the homogeneous two-phase mixture. If this is the case then energy balance can be written for this situation as:

Ws2pb = Q,pb3 p2pb { A /r> - K/V*H- (l/2p«v>)( 1/S22 - 1/S,2)}2pb (6.21)

If a is the mean void fraction at the inlet and outlet of the control volume then

iCHAPTER 6. A PREDICTIVE MODEL. 87

and eq. (6.21) can be rewritten

Ws2pb = [QL2ph / (1-a)]3 p2ph { X /$<*- pH- ( l / 2 r ) ( 1/S22 - 1/S!2)}2ph (6.21a)

If we assume that A, k , (3, Sj, and S2 do not change very much eq. (6.21a) combined with eq.(6.15) gives

(WsJph / Wslph) = [QUph/Q lph ]3* (1 -a)'3 * [ p!ph/p „J

or rearranging terms

[QiVQi ̂1 = 1 wv >1/3 (>-“)[ M M 1'3 <6-22)

Taking into account that p2ph= a*pg + (l-a)*p lph and assuming that a*pg approaches zero then eq. (6.22) can be re-written

[QiVQiph 1 = (Ws2ph / Wslph )l/3 (l-a)2/3 (6.23)

Equation (6.23) estimates the relative change in liquid pumping capacity of an impeller which operates in a two-phase mixture of known mean void fraction on the basis o f Relative Power Demand.

Using the same arguments as those used to derive eq. (6.20) mean liquid velocities in two-phase vessels can be estimated in the regions where previously made assumptions are valid, by

[VlW I = (Ws2ph / Wslph )»« (1-a) 2/3 (6.24)

Qoph - Q lop h/(l-a) (6.22)

6.6 Applications - comparison o f the model equations.

If eq. (6.17) is applied to a typical situation of a two-phase stirred tank reactor with a Relative Power Demand, -RPD-, of 0.7, it predicts that the liquid pumping capacity of the impeller will be reduced by 11.5% i.e. Relative Pumping Capacity,

\CHAPTER 6. A PREDICTIVE MODEL. 8 8

-RPC-, will be about 0.88 and Relative Mean Velocities, -RMV-, throughout the tank will be affected according to eq. (6.20) to the same extent.

Such conditions could apply typically when air is supplied with a sparger underneath a Rushton impeller operating at 4 rps in water in a 0.45 m diameter tank with T/D=2.5. The mean gas fraction in the tank o f this situation is about 4%, [81].In this situation the mean density o f the two-phase mixture is about 958 kg/m3 at 20 °C compared with a water density o f about 998 kg/m3.Eq. (6.23) then predicts that RPC will be about 0.86 which is only 2.2% lower than prediction of eq. (6.17) done without knowing void fraction and working liquids.In another typical situation with 8.7% mean gas fraction achieved by a Rushton impeller o f 0.48 m diameter operating at 2.5 rps which disperses air into water in a tank o f 1.2 m diameter with RPD of about 0.35, [81], eq. (6.23) predicts that RPC will be about 0.66 while eq. (6.17) predicts that RPC will be about 0.7 giving about 6% higher prediction.

Fig .6 .3 . M odel pred ictions M ean flow rates and m ean ve locities

Fig. 6.3 shows predictions o f model eqs (6.17) and (6.23) for Relative Pumping Capacity, and consequently according to eqs (6.20) and (6.24) for Relative Mean Liquid Velocities, as function o f RPD and mean void fraction in the vessel. Fig.6.3 shows that the effect o f void fraction is greater when operating at higher RPD. On the other hand higher RPD usually means a lower gas fraction if the other parameters are the same. This means that at high RPD it is rather difficult to

\CHAPTER 6: A PREDICTIVE MODEL. 89

achieve mean gas fractions higher than 5%, except in the confines o f the impeller, so that application of eqs (6.17) and (6.20) instead o f (6.23) and (6.24) will give predictions with relative error generally smaller than 4-5% without any information concerning void fraction in the vessel. Velocities predicted from eqs (6.20) or (6.24) may be used as input values for numerical simulations o f two-phase stirred tank flows, e.g. [6, 34, 35, 36].

6.7 Validation o f the model.

The only work known to the present author concerning impeller pumping capacities in two-phase stirred tanks is that o f Lu and Ju, 1987 & 1989, [29, 30, 31]. Lu and Ju measured velocities with a hot film anemometer in an aerated stirred tank of 0.288 m inner diameter agitated by Rushton impellers of 7.2, 9.6 and 14.4cm diameter. They calculated the impeller radial liquid pumping capacities and derived a correlation for impeller liquid pumping capacity applicable to systems geometrically similar to the experimental one.

They found that their data were well correlated by the equation

Ql = 1.25*10-3 (Pg/V)0-412(D /T)131 [2-(Q/D3)]°-28 (6.25)

where Ql, [m3s 1], is the liquid impeller pumping capacity during two-phase operation, Pg impeller power demand during aeration, V, [m3], liquid volume in the vessel, and Q air flow rate in m3/s. I f eq. (6.25) is considered in a system where Q=0 and in the same system loaded with Q tn3/s o f air then dividing the two resulting equations we get:

Q V Q Liph = (Pg/?)0'412 [2-(Fl*N)]°-28/ 1.214 (6.26)

For aerated Rushton impellers several data can be found in literature concerning RPD and mean gas fraction o f the tank. Table 6.1 presents some data for Rushton impellers operating in vessels with T/D=2.5. Impeller speed, FI number and RPD have been taken from Warmoeskerken's thesis, [81]. Mean gas fraction at the

I CHAPTER 6. A PREDICTIVE MODEL. 90

Table 6.1. Comparison of model predictions with correlation of Lu & Ju, 1S ci00FI, RPD &Ct% data from t81] cor.of Lu&Ju

Tim] N [rps] FI RPD RPDfl 6 % Cav.str. eq.6.17 eq.6.23 eq.6.26 %differ0.440 3.000 0.020 0.860 0.415 1.800 clinging 0.951 0.940 0.932 0.8320.440 3.000 0.030 0.670 0.415 2.000 3-3 0.875 0.863 0.837 3.1420.440 3.000 0.050 0.530 0.415 2.350 Large 0.809 0.797 0.753 5.7540.440 3.000 0.070 0.480 0.415 2.600 Large 0.783 0.769 0.716 7.3880.440 4.000 0.030 0.620 0.349 3.000 3-3 0.853 0.836 0.807 3 .5250.440 4.000 0.070 0.425 0.349 4.000 Large 0.752 0.732 0.674 8 .5880.440 5.000 0.020 0.780 0.305 3.600 clinging 0.921 0.898 0.890 0.9520.440 5.000 0.030 0.560 0.305 4.000 3-3 0.824 0.802 0.770 4 .1 0 70.440 5.000 0.040 0.460 0.305 4.150 Large 0.772 0.750 0.705 6 .4360.440 5.000 0.050 0.430 0.305 4.600 Large 0.755 0.731 0.680 7.5130.440 5.000 0.070 0.365 0.305 5.400 Large 0.715 0.689 0.626 10.1010.440 6.000 0.027 0.550 0.274 4.750 3-3 0.819 0.793 0.763 3.9010.440 6.000 0.040 0.440 0.274 5.000 Large 0.761 0.735 0.688 6.8480.440 6.000 0.050 0.395 0.274 5.500 Large 0.734 0.707 0.652 8.4300.440 6.000 0.070 0.345 0.274 6.700 Large 0.701 0.670 0.604 10.915

1.200 1.500 0.030 0.785 0.465 2.800 clinging 0.922 0.905 0.899 0.6501.200 1.500 0.038 0.670 0.465 3.050 3-3 0.875 0.857 0.841 1.9131.200 1.500 0.050 0.595 0.465 3.400 large 0.841 0.822 0.799 2 .8901.200 1.500 0.060 0.565 0.465 3.800 large 0.827 0.806 0.780 3.2511.200 1.500 0.070 0.540 0.465 4.250 large 0.814 0.791 0.764 3.5241.200 2.000 0.025 0.765 0.391 r 4.000 clinging 0.915 0.890 0.889 0.0951.200 2.000 0.035 0.635 0.391 4.500 3-3 0.860 0.834 0.821 1.5121.200 2.000 0.050 0.505 0.391 5.250 large 0.796 0.768 0.744 3 .2691.200 2.000 0.060 0.475 0.391 5.750 large 0.780 0.750 0.723 3 .7101.200 2.000 0.070 0.460 0.391 6.100 large 0.772 0.740 0.712 4 .0261.200 2.500 0.020 0.780 0.342 5.000 clinging 0.921 0.890 0.896 -0.7531.200 2.500 0.033 0.550 0.342 5.900 3-3 0.819 0.787 0.773 1.8461.200 2.500 0.040 0.475 0.342 6.150 large 0.780 0.748 0.725 3 .1101.200 2.500 0.050 0.450 0.342 6.750 large 0.766 0.731 0.707 3.4911.200 2.500 0.060 0.425 0.342 7.200 large 0.752 0.715 0.688 4.0141.200 2.500 0.070 0.405 0.342 7.500 large 0.740 0.702 0.672 4 .582

CHAPTER 6. A PREDICTIVE MODEL.. 91

corresponding impeller speed and FI number have been taken again from [81]. Results o f Lu and Ju from eq. (6.26) and predictions o f the model eqs (6.17) and (6.23) can also be found together with the percentage difference between predictions of eq. (6.23) and (6.26).Cavity regime and RPD at flooding are also shown. FI numbers o f up to 0.07 are used since this is the highest FI number used by Lu and Ju during their measurements with the 9.6 and 14.4cm impellers. The mean gas fraction used in eq. (6.23) is the mean gas-fraction o f the whole tank while Lu and Ju found their correlation (6.25) using the gas fraction measured by them at the exit o f the impeller.

The model predictions are quite close to the correlation o f Lu and Ju. Differences even in the worst case are less than about 10% based on the lower value. With the big vessel model predictions are closer to the correlation o f Lu and Ju with differences of less than about 4%. It is expected that if mean gas fraction around impeller were used in model eq. (6.23) then differences between model predictions and correlation would be much smaller; gas-fraction around the impeller is much larger than the mean gas-fraction o f the whole tank especially when approaching the flooding point where lower part o f the vessel becomes void o f gas, [6, 34, 35]. It is important to note that if the impeller operates around the 3-3 region, which is usually the case for industrial scale operations, [26], then model predictions even with eq. (6.17) are very close to the correlation o f Lu and Ju.As the operation of the impeller approaches the flooding point the power of the gas coming out from the sparger is expected to become comparable with the power input from the shaft, [41]. In this region an energy balance has to take into account energy carried by the gas and the simple approach followed in deriving eq. (6.17) or eq. (6.23) may not be valid.

6.8 Conclusions

A simple model based on energy balance concepts has been derived to relate quantitatively the mean flow rate and mean velocity characteristics of the singlephase flow field to the two-phase flow field o f a stirred tank reactor agitated by an impeller, on the basis o f the Relative Power Demand and mean void fraction in the


vessel. It predicts that at the simplest case velocities vary as the one third power o f the energy input provided by the shaft power.

The model provides a basis for a straightforward and quick estimate of the two- phase liquid flow field if the corresponding single-phase flow field and Relative Power Demand are known. Knowledge of the mean void fraction in the vessel seems to improve predictions by a few percentage points. Application of the model is independent o f impeller and tank geometries or scale.

The model has been validated using an existing correlation from the literature for the variations in liquid impeller pumping capacity in aerated tanks agitated with Rushton impellers, and shown to be in fairly good agreement within regions checked.

Derivation of the model is subject to several assumptions; The fluid must be ofJ low viscosity, plewtonian, incompressible and the reactor must operate in the fully

turbulent regime. The two phases are treated, at the best case, as an homogeneous mixture considered as a fluid for which all the previously mentioned assumptions are valid. Fluid density is assumed to be approximately the same over inlet and outlet surfaces o f the control volumes for which energy balances are considered. This assumption is known to be inapplicable in two-phase stirred tanks, [6, 34]. However it has been shown that void-fraction and consequently two-phase mixture density variations affect predictions of the model within limits usually regarded as acceptable in engineering practice.

The model has to be validated for volumetric flow rates and mean velocities by velocity measurements taken at RPD as low as possible. This will be presented in the following chapters.

93

C h a p t e r 7

T H E F L O W F I E L D

I N A T W O - P H A S E S T R .

V e l o c i t y a n d t u r b u l e n c e m e a s u r e m e n t s .

7.1 Introduction

Velocity measurements in agitated tanks form a substantial part of the STR related literature. The reason is that information about mean and turbulent characteristics o f the flow field is necessary for calculating important mixing parameters like impeller pumping capacities, [53], mixing times, [80], or mass transfer and chemical reaction rates and yields, [6, 38, 35]. Moreover all o f the available stirred tank modelling methods need experimental velocity and/or turbulence data for either validation or input values, [17, 20, 22, 24, 50, 57].

Most o f the available research work in the literature concerns single-phase systems. Coherent structures formed behind impeller blades, (trailing vortex system), have been investigated together with steady and unsteady mean and turbulent flow field characteristics in the impeller discharge stream and in the bulk with several newtonian and non newtonian liquids, e.g. [12 ,15 ,18 , 46, 47, 52, 73, 89, 91, 90].

\CHAPTER 7. VELOCITY MEASUREMENTS. 94

Several velocity measurement methods have been used. Pitot tubes or photographic methods in early investigations, [63, 78], gave their place to more sophisticated methods like Hot Film or Hot Wire Anemometers, [31, 18], or one or two- component Laser Doppler Velocimetry. e.g. [52, 91, 2]. Laser Doppler Velocimetry, or Anemometry, has been proved to be particularly suitable for stirred tank velocity measurements where the flow field is very unstable, highly turbulent and highly recirculating. Moreover no probe disturbs the velocity at the point of measurement.

The research with two-phase gas-liquid stirred tanks is much less complete. Laser Doppler methods are hard to apply because a dense cloud o f gas bubbles formed by the dispersing action o f the impeller prevents laser beams reaching their intersection point, especially close to the impeller. As a result Laser Doppler methods have not been used for gas-liquid stirred tank velocity measurements with the only exception known to the present author that o f Mishra and Joshi, 1991, [40]. They used Laser Doppler techniques to get velocity measurements in a stirred tank equipped with an axial impeller under low gas load or in other words at high RPD. At this high RPD level according to the model developed in chapter 6 important features o f the flow changes may be missed. I f RPD is about 0.9 then the pumping capacity is reduced by only 3.5% which is well within the accuracy of the measuring method.

Another approach is to use Hot Film Anemometry. The only related work known to the present author is this of Lu and Ju, [29, 30, 31]. They used HFA - Hot Film Anemometer - to measure velocity components in a 0.288 m diameter tank stirred by Rushton type impellers. A discussion o f the problems associated with the use of HFA in stirred tanks can be found in [29]. The work was directed mainly towards calculating the pumping capacity o f the impeller. They found that their experimental data were correlated well with

Ql = 1.25*10-3 (Pg/V)°-412(D /T)1 -31 [2-(Q/D3)]0-28

This correlation has been shown to be in good agreement with the predictions of the model developed in chapter 6.

In this chapter new liquid velocity and turbulence measurements obtained by Laser Doppler techniques under conditions o f RPD as low as 0.55 will be presented. The

1 CHAPTER 7. VELOCITY MEASUREMENTS. 95

measurements which are believed to be the first o f this type presented in the open literature were made possible by working in a boiling system rather than in an aerated one. In these boiling conditions stable cavities are formed behind the impeller blades resulting in a lower RPD. The cavities are similar to those produced in aerated stirred reactors, [61]. At a given RPD in a boiling liquid the region around the impeller is much less obscured by small gas bubbles than in aerated systems. This facilitates Laser Doppler velocity measurements at the low relative power demand levels corresponding to the presence o f large cavities. Data obtained from these measurements will then be used in the next chapter to validate the model derived in chapter 6.

Data presented in this chapter by no means give a full detailed description of the two-phase liquid flow field in the impeller discharge stream and in the bulk. This might be a subject o f a thesis itself and it was not possible during the present investigation because o f equipment limitations. However the data are enough to produce a picture of the important changes when switching from single to two- phase operation and to give results for the validation o f the approach of the model presented in chapter 6.

7.2 Experimental arrangement and equipment.

A 0.45 m diameter stirred tank with a flat top and a standard dished bottom has been used for the measurements. The tank was made of a commercial glass-pipe section while the ends were made o f stainless steel 316. Dimensions and full description of the tank and the equipment used to measure torque, temperature and vapour rate can be found in paragraphs 3.2.2 and 4.3. The vapour generated in the vessel is condensed in a coil heat exchanger. The condensed flow is returned in the vessel as reflux. Picture 7.1 shows a view of the rig during the experiments.

Laser Doppler velocity measurements can be made in a horizontal plane through the side glass wall, fig. 7.1 and in a vertical plane through a purpose built glass window in the bottom dished cover.

CHAPTER 7. VELOCITY MEASUREMENTS. 96

Picture 7 .1 . View of th e experim ental rig.


Fig. 7.1. Schematic view of the tank.


A s in g le c o m p o n e n t H e -N e 5 m W la s e r f ro m S p e c tra -P h y s ic s w a s u s e d w ith a

s in g le c o m p o n e n t T S I f ib re -o p tic p ro b e s y s te m m o d e l 9 7 2 9 -2 -1 0 a n d b e a m

s h if t in g e q u ip m e n t T S I m o d e l 9 1 8 0 w o rk in g in b a c k s c a tte r m o d e . P r in c ip le s a n d

d e ta ils o f L a s e r D o p p le r V e lo c im e try c a n b e fo u n d in s ta n d a rd te x tb o o k s e .g . [1 6 ].

IF A 5 5 0 s ig n a l p ro c e s s o r h a s b e e n u s e d to fe e d w ith d a ta a m o d e l 140 0 L D A d a ta

a c q u is it io n in te r fa c e o f Z E C H e le c tro n ic s . S o f tw a re d e v e lo p e d b y C .T ro p e a a n d

r e v is e d d u r in g a re s e a rc h p ro g r a m fo r v e lo c ity a n d tu rb u le n c e m e a s u re m e n ts o f

b u b b ly f lo w s b y D r. T .P la k a , [5 1 ] w a s u s e d to r e tu rn m e a n a n d R M S -ro o t m e a n

s q u a re - o f v e lo c itie s in [m /s ] , a n d P D F -p ro b a b il i ty d is tr ib u tio n fu n c tio n - o f a ll th e

in s ta n ta n e o u s v e lo c itie s m e a s u re d in th e b e a m in te rse c tio n v o lu m e a f te r e a c h s e t o f

1 0 0 0 s a m p le s o f v e lo c ity m e a s u re m e n ts w a s c o m p le te d . A b lo c k d ia g ra m o f th e

L D A e q u ip m e n t a n d th e sp e c if ic a t io n s o f its c o m p o n e n ts c a n b e fo u n d in A p p e n d ix

3.

S ta n d a rd R u s h to n im p e lle rs o f 0 .2 4 a n d 0 .1 8 m d ia m e te r , a h o l lo w b la d e im p e lle r

o f 0 .1 8 m d ia m e te r d r iv e n w ith th e fa c e s c o n v e x in o rd e r to m a x im is e c a v ity

d e v e lo p m e n t a n d a n a x ia l 0 .2 m d ia m e te r d o w n w a rd s p u m p in g im p e lle r w e re u se d .

D im e n s io n s o f th e im p e lle rs c a n b e fo u n d in f ig . 4 .2 . T h e r ig c a n h a n d le a v a r ie ty

o f l iq u id s b u t e x p e r im e n ts w e re d o n e in f i l te re d ta p w a te r .

7 3 Measurements

V e lo c ity a n d tu rb u le n c e m e a s u re m e n ts w e re d o n e in tw o s ta g e s . A t f i r s t m e a n

v e lo c itie s a n d R M S v a lu e s w e re m e a s u re d in s in g le -p h a se c o n d it io n s a t 9 2 .5 °C .

T h e b a tc h te m p e ra tu re w a s k e p t s te a d y w ith in 0 .0 7 ° K w ith th e h e lp o f a th y r is to r

te m p e ra tu re c o n tro lle r . T w o -p h a s e liq u id v e lo c ity m e a s u re m e n ts w e re m a d e in th e

s e c o n d s ta g e a t a b o u t 10 0 ° C , d e p e n d in g o n th e a tm o s p h e r ic p re s s u re , k e e p in g a ll

th e p a ra m e te rs th e s a m e b u t a t f re e b o il in g c o n d itio n s .

L a s e r D o p p le r v e lo c ity m e a s u re m e n ts w e re d o n e th ro u g h th e s id e g la ss w a ll

b e c a u s e th e fo c a l le n g th o f th e f ib re -o p t ic p ro b e w a s n o t s u f f ic ie n t to a llo w it to b e

u s e d th ro u g h th e g la s s w in d o w o f th e d is h e d b o tto m c o v e r o f th e v e s s e l sh o w n in

f ig . 7 .1 . M e a s u re m e n ts w e re p e r fo rm e d in v e r t ic a l p la n e s a t 1 5 ° , 4 5 ° a n d 7 5 °

re la t iv e to th e b a f f le s , f ig . 7 .1 . T h e ta n g e n tia l a n d th e a x ia l c o m p o n e n ts w e re

m e a s u re d d ire c tly . T h e c u rv a tu re o f th e g la s s w a ll a n d th e fo c a l le n g th o f th e


f ib re -o p tic p ro b e p re v e n te d d ire c t m e a s u re m e n t o f th e ra d ia l v e lo c ity c o m p o n e n t

w h ic h w a s c a lc u la te d f ro m tw o d if fe re n t ta n g e n tia l m e a s u re m e n ts d o n e a t 1 5 °

a n g le s , f ig . 7 .1 , [6 9 ] . T h e a c c u ra c y o f th e ra d ia l v e lo c ity d a ta is a c c o rd in g ly n o t

a s g o o d a s th a t o f th e a x ia l a n d ta n g e n tia l c o m p o n e n ts . M o re d e ta ils o f th e

m e th o d a re g iv e n in A p p e n d ix 3 . T h e ta n g e n tia l c o m p o n e n t c o u ld a lso b e

c a lc u la te d in d ire c tly f ro m th e d a ta u s e d to c a lc u la te th e ra d ia l c o m p o n e n t a n d th e

r e s u l t c o u ld b e c o m p a re d w ith th a t o f th e d ire c tly m e a s u re d ta n g e n tia l v e lo c ity

c o m p o n e n t. T h is p ro v id e d a c h e c k o n th e a c c u ra c y o f th e ra d ia l v e lo c ity

c o m p o n e n t.

M e a s u re m e n ts w e re d o n e a t f ix e d p o s it io n s in sp a c e . P o s it io n in g e r ro r s o f th e

fo c a l p o in t w e re o v e rc o m e b y c a lib ra t io n o n a s te a d y o b je c t w h o s e p o s it io n w a s

k n o w n w ith in a c c u ra c y o f 0 .5 m m . T h e m e a s u re m e n t v o lu m e w a s a p p ro x im a te ly

1 .6 m m lo n g a n d o f 0 .11 m m d ia m e te r .

M e ta llic c o a te d s e e d in g p a r t ic le s o f 4 p m m e a n d ia m e te r a n d 2 6 0 0 k g /m 3 d e n s ity

w e re u s e d to im p ro v e s ig n a l q u a lity a n d d a ta ra te .

D u r in g th e f ir s t s ta g e s o f th e e x p e r im e n ta l in v e s tig a tio n a n a t te m p t w a s m a d e to

s e p a ra te s ig n a ls c o m in g f ro m b u b b le s a n d th o se o n e s c o m in g f ro m s e e d in g

p a r t ic le s a c c o rd in g to a p ro c e d u re d e v e lo p e d b y T .P la k a , [5 1 ] , w h ic h is s im ila r to

th a t o n e re p o r te d b y M is h ra a n d J o sh i, 1 9 9 1 , [4 0 ]. In th is w a y m e a s u re m e n t o f

b u b b le v e lo c ity to g e th e r w ith liq u id v e lo c ity w a s a tte m p te d . U n fo r tu n a te ly v e ry

fe w s ig n a ls o r ig in a te d f ro m th e b u b b le s , o f th e o rd e r o f 1% th a t f ro m th e liq u id , so

th e re w e re in s u f f ic ie n t d a ta to g e n e ra te r e l ia b le b u b b le v e lo c itie s . M o re o v e r th e

b u b b le v e lo c itie s w e re w e ll w ith in l iq u id v e lo c ity ra n g e . T h e a t te m p t to m e a s u re

b u b b le v e lo c itie s w a s th e re fo re a b a n d o n e d a n d a ll th e d a ta p re s e n te d in th is th e s is

c o n c e rn liq u id v e lo c itie s o n ly .

D a ta ra te w a s g e n e ra l ly o f th e o rd e r o f 3 0 0 to 4 0 0 s a m p le s p e r se c o n d . T h e

h ig h e s t d a ta r a te w a s o f th e o rd e r o f 1 0 0 0 sa m p le s / I " a c h ie v e d d u r in g s in g le

p h a s e o p e ra t io n o r d u r in g tw o -p h a s e o p e ra tio n fa r a w a y f r o m im p e lle r sw e p t

v o lu m e o r o u ts id e th e im p e lle r d is c h a rg e s tre a m u s u a lly a t R = 168 .5 a n d 1 9 8 .5

m m . T h e lo w e s t d a ta r a te u s e d , w a s a b o u t 100 s a m p le s /1" w h ic h w a s u s u a l d u r in g

tw o -p h a s e o p e ra tio n c lo s e to im p e lle r b la d e s i.e . a t R = 123 .5 m m w ith th e R u s h to n

2 4 0 m m d ia m e te r im p e lle r . E a c h v e lo c ity m e a s u re m e n t r e p re s e n t a t le a s t 2 0 0 0 0

in s ta n ta n e o u s v e lo c ity d a ta - s a m p le s - , m e a s u re d a t th e s a m e lo c a tio n d u r in g o n e

m e a s u re m e n t. E a c h m e a s u re m e n t w a s su p p o s e d to b e c o m p le te i f th e la s t f iv e

1 0 0 0 sa m p le -s e ts d if f e re d b y o n ly th e th ird d e c im a l d ig it.

\CHAPTER 7.VELOCITYMEASUREMENTS. 100

R e p ro d u c ib il i ty o f th e v e lo c ity d a ta a t th e s a m e lo c a tio n w a s c h e c k e d a t s e v e ra l

p o s itio n s . A sa m p le o f in d iv id u a l v e lo c ity m e a s u re m e n ts o f th e w o rs t c a se - lo w

d a ta ra te a n d m e a s u re m e n t p o in t v e ry c lo s e to th e im p e lle r b la d e s d u r in g tw o -p h a s e

o p e ra tio n - , is p re s e n te d in f ig . 7 .2 a . A t o th e r lo c a tio n s r e p ro d u c ib il i ty o f v e lo c ity

d a ta w a s b e t te r th a n th e o n e p r e s e n te d in f ig . 7 .2 b . T h e re fo re f o r m o s t o f th e d a ta

o n ly a s in g le in d iv id u a l v e lo c ity m e a s u re m e n t w a s u s e d f o r e a c h p o in t a n d a ll th e

d a ta p o in ts p re s e n te d in th e th e s is c o r r e s p o n d to s in g le m e a s u re m e n ts .

T h e v e lo c ity d a ta w e re c h e c k e d in te rm s o f th e m a s s b a la n c e s :

(p2 Z2 R2J { { v d R d z d t p (7 .1 )

(p i z i R i

a n d fo u n d to b e c o n s is te n t w ith in 6 % f o r m o s t o f th e c o n tro l v o lu m e s c h e c k e d .

Results and discussion.

7.4. The impeller discharge flow.

7 .4 .1 Rushton im pellers.

In m o s t o f th e p re v io u s in v e s tig a tio n s r e p o r te d in th e l i te ra tu re a s ta n d a rd g e o m e try

w ith l iq u id h e ig h t e q u a l to th e ta n k d ia m e te r h a s b e e n u s e d . T h is g e o m e try c o u ld

n o t b e u s e d d u r in g th e p re s e n t in v e s t ig a tio n b e c a u s e o f e q u ip m e n t l im ita tio n s ; th e

g la ss w a ll, b e c a u s e o f th ic k e n in g to w a rd s th e f la n g e s , w a s n o t su ita b le f o r la s e r

D o p p le r m e a s u re m e n ts o v e r th e w h o le h e ig h t. T h e re fo re th e c le a ra n c e c o u ld n o t

b e s m a lle r th a n th e 3 1 5 m m w h ic h w a s u s e d f o r th e m e a s u re m e n ts o f th e im p e lle r

d is c h a rg e s tre a m . T h is g a v e a s u b m e rg e n c e o f a b o u t 2 6 5 m m w h ic h is a p p ro p r ia te

f o r th e 0 .4 5 m d ia m e te r ta n k u se d . D e s p ite th e s ig n if ic a n t d if f e re n c e s in th e

g e o m e try o f th e ta n k , th e b a s ic f e a tu re s o f th e s in g le -p h a se f lo w f ie ld a re s im ila r to

th o s e fo u n d in th e l i te ra tu re ; m e a n v e lo c it ie s a n d R M S f lu c tu a tio n s sc a le w e ll w ith


im p e lle r s p e e d i f th e y a re n o rm a lis e d w ith im p e lle r tip sp e e d , [4 7 ] , f ig . 7 .3 a -d .

Im p e l le r v o lu m e tr ic f lo w ra te s a re c o m p a ra b le w ith th o se re p o r te d in lite ra tu re , f ig .

7 .4 a . T h e d if fe re n t e v o lu tio n o f v o lu m e tr ic f lo w a lo n g im p e lle r d is c h a rg e s tre a m

m a y b e a r e s u l t o f th e r e d u c e d e n tra in e m e n t b e c a u s e o f th e d if fe re n t g e o m e try o f

th e im p e lle r - ta n k sy s te m . T h e c h a ra c te r is t ic u p w a rd s h if t o f th e im p e lle r s tre a m

w h ic h is w id e ly re p o r te d in l i te ra tu re , [2 , 3 3 , 9 1 ] , c a n a lso b e fo u n d in o u r re su lts .

T u rb u le n c e in te n s ity is a n is o tro p ic in th e im p e lle r d is c h a rg e s tre a m , th is b e in g in

a g re e m e n t w ith th e re s u lts o f W u & P a tte rso n , [8 9 ] a n d Y a n n e s k is e t al, [9 1 ].

I n te re s t w ill n o w b e fo c u s e d o n th e r e la t iv e c h a n g e s w h ic h o c c u r in th e f lo w f ie ld

w h e n s w itc h in g f ro m s in g le to tw o -p h a s e o p e ra tio n .

60

«®aEE2 0

<aQ

-30

0 0.5 1 1.5 2 2.5Mean Velocity [m/a]

Fig. 7.2a. Consistency of individual measurement series, R=123.5mm Rushton 240mm imp.

Tangential measurement at +15o.

; : first mea|urement:;

* •&>

*

0

k

second measurement

* * * >kA * i* : A

=A :

* A* A *

_ J M ...-

_______ A * j *

Fig. 7.2b. Consistency of individual measurement series, R=123.5mm Rushton 240mm imp.

Tangential measurement at -15o.

60 -

5 3 0 - -

E2 o

A

A

first rnaajuremant:; second measurement

-A -

-A ^ * A

-30 -A *

A I * '

"i 1-- 1-- r-0.5 1.5Mean Velocity [m/s]

2.5

Dist

ance

fro

m im

pelle

r dis

c [m

m]

Dist

ance

fro

m Im

pelle

r dis

c [m

m]


3a Single-phase normalised tang.veloclties Rushton impeller, D=1B0mm, 45o, R=148.5mm

60

30 -

■30 -

3S0RPM■210RPM: : <?•: ■ 290QPM

(EA

O * □O A □ :! OAD I

f t------0---- ifc-□ P A

□ .1. AOO; OA

□ P

DA

t ! | j—0.1 0.2 0.3 0.4

Normalised velocity Vtang/Vtip

7.3c. Single-phase normalised tang. RMS Rushton impeller, D=180mm, 45o, R=148.5 mm

Normalised velocity RMS/Vtip

0.5

3b Single-phase normalised tang.veloclties Rushton Impeller, D=i80mm, 45o, R=l68.5mm

60 -

1 30 -

.30

:3s0pPM;210RPM|290QPM

GA : j :

(EBA : | :

o j S r i. . . ! 1

1 ! O A □ i

i □ A O ;

□ CA f i :

D A j j ! ;

0.1 0.2 0.3Normalised velocity Vtang/Vtip

0.4

7.3d. Slngle-phase normalised axial RMS Rushton impeller, D=180mm, 45o, R=148.5mm

60

30 -

-30 -

m

cm□

m>CD®o®

©-■—m n

m □m □ j

=o#d

—i------------ 1------------ 1------------ r~0.1 0.2 0.3 0.4

Normalised velocity RMS/Vtlp

0.5

0.5

Fig. 7.4a. Normalised radial flow ratesRushton impellers. This work with T =450,h=580

c=315, dished bottom, integr.from z=h/2 to -h/2

-m

□ ;

□ ;

n

- f A ° I •

x 'on

: ■

A ft \

2 -

1.5 -«<QZo 1

0.5 -

1.2 1.4 1.6 1.8 2.22R/D

:: i This work »K)RPM.0=iec :: :tljlo:work

TO.Work 0 ! M 0.19SRRM :; j '•: Flat bottom; Into.across stream : Flat bottom, ln^.2=-h/2 to lt/2.

2.4


7.4.1.1. Mean velocities.

In f ig u re s 7 .5 a -c to 7 .9 a -c m e a n v e lo c ity m e a s u re m e n ts in th e 4 5 ° p la n e fo r th e

R u s h to n 2 4 0 m m d ia m e te r im p e lle r a re sh o w n . L iq u id h e ig h t w a s 5 8 5 m m a n d

c le a ra n c e 3 1 5 m m . T h e im p e lle r w a s o p e ra t in g a t 195 R P M g iv in g a R e la tiv e

P o w e r D e m a n d -R P D - o f 0 ,7 0 w h e n b o ilin g .

F ig u re s 7 .5 a -c s h o w th e m e a n v e lo c ity m e a s u re m e n ts a t a ra d ia l d is ta n c e 123 .5

m m f ro m th e a x is o f ro ta t io n . T h is m e a n s o n ly 3 .5 m m f ro m th e im p e lle r b la d e 's

o u te r e d g e . D u r in g tw o -p h a s e o p e ra t io n w e ll d e v e lo p e d c l in g in g c a v itie s w e re

fo rm e d b e h in d im p e lle r b la d e s . S o m e tim e s th e c a v ity w h ic h w a s a tta c h e d to th e

b la d e p a s s e d th ro u g h th e fo c a l p o in t. V e lo c ity m e a s u re m e n ts o f f ig . 7 .5 a -c

r e p re s e n t liq u id v e lo c it ie s a t p o s i t io n s p a r t ia l ly b e in g b e tw e e n th e c a v ity a n d th e

su c c e e d in g b la d e . M e a s u re m e n ts a t th is p o s it io n w e re d if f ic u l t b e c a u s e la s e r

b e a m s h a d to c ro s s a r e g io n w ith m a n y v a p o u r b u b b le s . C o n s e q u e n tly th e d a ta ra te

w a s lo w e r th a n u s u a l, e s p e c ia l ly w h e n m e a s u r in g a t th e p o in ts w ith in th e im p e lle r

d is c h a rg e s tre a m . I t is e x p e c te d th a t r e s u l ts a t th is p o s i t io n c lo s e to th e im p e lle r

c o n ta in s ig n if ic a n t e r ro r . T h e e r ro r is a lso e x p e c te d to b e g re a te r f o r th e ra d ia l

v e lo c ity c o m p o n e n t w h ic h w a s n o t m e a s u re d d ire c tly b u t d e r iv e d f ro m

m e a s u re m e n ts a t d if f e re n t a n g le s in th e h o r iz o n ta l p la n e a s d e s c r ib e d in A p p e n d ix

3. In f ig u re 7 .5 c so lid tr ia n g le s a re a s m o o th e d re p re s e n ta t io n o f th e r a w tw o -

p h a s e d a ta , sh o w n in A p p e n d ix 3 . R a d ia l v e lo c ity c o m p o n e n ts s o m e tim e s b e c o m e

s m a lle r w h e n c h a n g in g f ro m s in g le to tw o -p h a s e f lo w a n d a lso c h a n g e d ire c tio n in

th e r e g io n s n e a r th e u p p e r a n d lo w e r b la d e e d g e s , w h ic h a re a t ± 2 4 m m e a c h s id e

o f th e z e ro p la n e . T h is re v e r s e f lo w e n te r in g th e im p e lle r m ig h t b e a re s u l t o f th e

c a v itie s b e h in d th e im p e lle r b la d e s . A s im ila r m o tio n o f th e l iq u id a d ja c e n t to th e

c a v ity c a n b e se e n in th e v id e o r e c o rd in g s o b ta in e d d u r in g c a v ity v isu a lis a tio n .

A x ia l v e lo c ity c o m p o n e n ts a lso c h a n g e w h e n o p e ra tin g in tw o -p h a s e m o d e w h ile

th e ta n g e n tia l o n e s r e m a in a p p ro x im a te ly th e sa m e , e x c e p t f o r th e tw o lo c a l

m a x im a , fig . 7 .5 a , w h ic h m a y b e c a u s e d b y th e p re s e n c e o f th e tw o ta ils o f th e

c lin g in g c a v itie s w h ic h lo c a lly a f f e c t th e l iq u id m o v e m e n t.

P ro c e e d in g fu r th e r d o w n s tre a m a ll v e lo c ity c o m p o n e n ts d e c lin e w ith a x ia l

v e lo c itie s c h a n g in g d ire c t io n n e a r th e w a ll , R = 1 9 8 .5 m m , f ig . 7 .9 b . T w o -p h a s e

l iq u id v e lo c it ie s a re g e n e ra l ly lo w e r th a n s in g le -p h a s e o n e s .

Dist

ance

fro

m im

pelle

r dis

c [m

m]

Dist

ance

fro

m im

pelle

r dis

c [m

m]

Dist

ance

fro

m im

pelle

r dis

c [m

m]


Flg.7.5a TANGENTIAL MEAN VELOCITIESRushton impeller, D=240mm, R=123.Smm, 45o

Mean Velocity [m/s]

Ftg.7.5b. Axial mean velocities Rushton Impeller, D=240mm, R=123.5mm, 45o

Mean Velocity [m/s]

Fig.7.5c. Radial mean velocities Rushton impeller, D=240mm, R=123.5mm, 4So

Mean Velocity [m/s]

Dist

ance

fro

m im

pelle

r dis

c [m

m]

Dist

ance

fro

m im

pelle

r dis

c [m

m]

Dist

ance

fro

m im

pelle

r dis

c [m

m]


Fig.7.6a. Tangential mean velocitiesRushton impeller, D=240mm, R=133.5mm, 45o

Mean Velocity [m/s]

Fig.7.6b. Axial mean velocities Rushton impeller, D=240mm, R=133.5mm, 45o

Mean Velocity [m/e]

Fig.7.6c. Radial mean velocities Rushton impeller, D=240mm, R=133.5mm, 4So

Mean Velocity [m/s]

Dist

ance

fro

m im

pelle

r dis

c [m

m]



Mean Velocity [m/s]

Fig.7.7b. Axial mean velocities Rushton impeller, D=240mm, R=148.5mm, 4So

Mean Velocity [m/s]

Fig.7.7c. Radial mean velocities Rushton impeller, D=240mm, R=148.5mm, 45o

Mean Velocity [m/e]

Dist

ance

fro

m im

pelle

r dis

c [m

m]

Dist

ance

fro

m Im

pelle

r dis

c [m

m]

Dist

ance

fro

m im

pelle

r dis

c [m

m]


Fig.8a. Tangential mean velocities Rushton impeller, D=240mm, R=l68.5mm, 45o

Mean Velocity [m/B]

Fig.7.Bb. Axial mean velocities Rushton impeller, D=240mm, R=16B.5mm, 45o

Mean Velocity [m/s]


Mean Velocity [m/s]

Dist

ance

fro

m im

pelle

r dis

c [m

m]

Dist

ance

fro

m im

pelle

r dis

c [m

m]

Dist

ance

fro

m im

pelle

r dis

c [m

m]


FJg.7.9a. Tangential mean velocitiesRushton impeller, D=240mm, R=198.Smm, 45o

Mean Velocity [m/s]

Fig.7.9b. Axial mean velocities Rushton impeller, D=240mm, R=198.Smm, 45o

Mean Velocity [m/s]

Fig.7.9c. Radial mean velocities Rushton impeller, Da240mm, R=198.Smm, 45o

Mean Velocity [m/s]

Dist

ance

fro

m im

pelle

r dis

c [m

m]

Dist

ance

fro

m im

pelle

r dis

c [m

m]

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Mean Velocity [m/s]

Flg.7.10c. Radial mean velocities Rushton Impeller, D=160mm, R=133.5mm, 45o

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I CHAPTER 7. VELOCITY MEASUREMENTS.

Flg.7.11a. Tangential mean velocitiesRushton impeller, D=180mm, R=148.5mm, 45o

Mean Veiocit


Mean Velocity [m/s]


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CHAPTER 7. VELOCITY MEASUREMENTS. I l l


Mean Velocity [m/s]

Fig.7.12b. Axial mean velocities Rushton impeller, Ds180mm, R=168.5mm, 45o

Mean Velocity [m/s]

Fig.7.12c. Radial mean velocities Rushton impeller, Da180mm, R=168.Smm, 45o

Mean Velocity [m/s]

I CHAPTER 7. VELOCITY MEASUREMENTS. 112

Q u a lita tiv e f e a tu re s o f th e s in g le p h a s e l iq u id f lo w a re s im ila r to th o s e re p o r te d in

th e l i te ra tu re . T h e u p w a rd d is c h a rg e o f th e f lo w h a s b e e n w id e ly re p o r te d , [4 7 , 9 1 ]

a n d is a r e s u l t o f th e m o re v ig o ro u s c irc u la t io n w h ic h o c c u rs in th e f re e s u r fa c e d

u p p e r p a r t o f th e ta n k . T h is u p w a rd s h if t in g o f th e f lo w is s l ig h tly e n h a n c e d d u r in g

tw o -p h a s e o p e ra tio n , f ig . 7 .6 a , f ig . 7 .7 a , p o s s ib ly b e c a u se o f th e b u o y a n c y e f fe c t o f

th e b u b b le s .

F ig u re 7 .1 0 a -c sh o w s v e lo c ity d a ta f o r th e R u s h to n 180 m m im p e lle r a t 4 3 .5 m m

f ro m th e im p e lle r b la d e s . W ith th e p re s e n t e q u ip m e n t i t w a s u n fo r tu n a te ly

im p o ss ib le to g e t v e lo c ity m e a s u re m e n ts c lo s e r to im p e lle r o u te r b la d e e d g e fo r

th is s m a lle r im p e lle r . T h e im p e lle r b la d e w id th is 3 6 m m , l iq u id h e ig h t 5 8 0 m m

a n d c le a ra n c e 3 1 5 m m . Im p e lle r s p e e d is 3 5 0 R P M a n d th e c o r re s p o n d in g

R e la tiv e P o w e r D e m a n d 0 .5 3 . T h e c a v itie s fo rm e d w e re la rg e c a v itie s . .

F ig u re 7 .1 0 c sh o w s a n u n u s u a l b e h a v io u r o f th e s in g le -p h a s e ra d ia l v e lo c ity

c o m p o n e n t w ith a lo c a l m in im u m n e a r th e im p e lle r d isc le v e l. T h is m in im u m

m a y b e a re s u l t o f th e w a y r a d ia l v e lo c it ie s w e re c a lc u la te d , A p p e n d ix 3 , c o m b in e d

w ith th e m a s s iv e p re s e n c e o f t in y a ir b u b b le s re s u lt in g f ro m th e s u r fa c e a e ra t io n a t

th is h ig h sp eed .

Fig. 7.1 Od. Trajectory of the bubbles and LDA beams.

CHAPTER 7.VELOCITYMEASUREMENTS. 113

B u b b le s w e re m a in ly d ra w n in th e tra i l in g v o r t ic e s b e fo re d is c h a rg e d in th e

im p e lle r d is c h a rg e s tre a m . B e c a u s e o f th is , th e re w e re p le n ty o f sm a ll b u b b le s

e s p e c ia l ly a t th e le v e l o f th e tra i l in g v o r t ic e s , th a t is a ro u n d ± 6 - 1 2 m m f ro m

im p e lle r d isc .

B e c a u s e o f th e p a r t ic u la r t ra je c to ry fo llo w e d b y th e b u b b le s d is c h a rg e d f ro m th e

tra il in g v o r tic e s , L D A m e a s u re m e n ts d o n e a t + 1 5 ° c o n s is te d , r e la tiv e ly to

m e a s u re m e n ts a t -1 5 ° , m a in ly o f l iq u id v e lo c ity d a ta f ro m th e s lo w e r liq u id la y e rs ,

[1 2 ] , fig . 7 .1 0 d , r e s u l t in g in m e a s u re d liq u id v e lo c itie s a t + 1 5 ° b e in g b ia s e d to

lo w e r v a lu e s f o r p o in ts ly in g w ith in th e tra il in g v o r tic e s i.e . a ro u n d 6 -1 2 m m f ro m

im p e lle r d isc . T h e b ia s e d lo w e r v e lo c it ie s a t + 1 5 ° re s u lte d v ia th e c a lc u la tio n

p ro c e d u re , A p p e n d ix 3 , in ra d ia l v e lo c itie s w h ic h w e re b ia s e d to h ig h e r v a lu e s .

T h is m a y b e th e r e a s o n o f th e tw o p e a k s o f th e s in g le -p h a se v e lo c ity p ro f i le o f f ig .

7. lO .c . E x c e s s b u b b le s in th e u p p e r p a r t o f th e v e s s e l e x p la in w h y th e h ig h e s t p e a k

o f th e s in g le -p h a s e ra d ia l v e lo c ity p ro f i le o f f ig . 7 .1 0 c is th e o n e a t th e to p ;

m e a s u re m e n t e r ro r w a s h ig h e r a t th e p o in ts ly in g w ith in th e u p p e r tra il in g v o r te x .

A s im ila r r e s u l t w a s a lso o b ta in e d in th e 15° a n d 7 5 ° v e r t ic a l p la n e s b e tw e e n th e

b a f f le s .

S ig n if ic a n t d if fe re n c e s c a n b e s e e n b e tw e e n th e tw o -p h a s e r a d ia l v e lo c itie s f ro m

th e 2 4 0 m m a n d th e 18 0 m m d ia m e te r R u s h to n im p e lle rs . T h e s e d if fe re n c e s m ig h t

b e an e f fe c t o f th e d if fe re n t c a v ity ty p e s fo rm e d d u r in g th e tw o e x p e r im e n ts . T h e

R u s h to n im p e lle r o f 2 4 0 m m d ia m e te r o p e ra tin g a t 195 R P M fo rm e d c lin g in g

c a v itie s . T h is m e a n s th a t th e re w a s s till e n o u g h ra d ia l o u tf lo w f ro m th e b la d e m id

p la n e . T ra il in g v o r t ic e s w e re s till th e re w ith liq u id ro ta t in g a ro u n d th e v o r te x a x e s

a n d d is c h a rg e d in th e m id p la n e o f th e im p e lle r b e tw e e n tra i l in g v o r tic e s . O n th e

o th e r h a n d la rg e c a v itie s w e re fo rm e d w ith th e 180 m m R u s h to n im p e lle r . L a rg e

c a v itie s r e s tr ic t ra d ia l o u tf lo w in th e im p e lle r d is c h a rg e s tre a m . T h is s e e m s to b e a

re a s o n fo r th e s ig n if ic a n t lo c a l m in im u m in th e R a d ia l tw o -p h a s e v e lo c itie s sh o w n

in f ig u re 7 .1 0 c a t a b o u t z = -6 m m . V a p o u r b u b b le s m a y a lso b e a r e a s o n f o r th e

tw o p e a k s o f th e tw o -p h a s e ra d ia l v e lo c ity p ro f i le a ro u n d ± 1 2 m m f ro m im p e lle r

d isc fo llo w in g th e s a m e re a s o n in g as w ith th e s in g le -p h a se d a ta . H o w e v e r th e lo c a l

m in im u m 6 m m u n d e r im p e lle r d isc le v e l se e m s to b e n o t v e r y e a s y to e x p la in b y

b ia s e d v e lo c ity m e a s u re m e n ts a n d p ro b a b ly h a s to b e e x p la in e d b y th e d if fe re n t

o u tf lo w c o n d itio n s fo rm e d b e c a u s e o f th e la rg e s ta b le c a v itie s a t ta c h e d b e h in d th e

im p e lle r b la d e s . T h e lo c a l m in im u m is s h if te d d o w n w a rd s b e c a u s e o f th e m o re

v ig o ro u s liq u id f lo w in th e u p p e r p a r t o f th e v e sse l. T h e c e n tra l s lo w liq u id re g io n

is q u ic k ly a c c e le ra te d b y th e m u c h fa s te r a d ja c e n t l iq u id la y e rs to re a c h th e m o re

c o m m o n ra d ia l v e lo c ity p ro f i le o f f ig u re 7 .1 1 c w h e re m a x im u m a t z = + 6 m m ,


fo l lo w in g th e r e a s o n in g m e n tio n e d b e fo re , m a y b e a lso a n e f fe c t o f th e w a y ra d ia l

v e lo c it ie s w e re c a lc u la te d .

T h e a b o v e e x p la n a tio n is b a s e d o n th e p re s e n t d a ta c o n c e rn in g tw o -p h a s e liq u id

f lo w in b o i l in g s t ir re d ta n k s . M o re d e ta ile d m e a s u re m e n ts in th e fu tu re m a y

r e q u ire a d if f e re n t a p p ro a c h to th e p h e n o m e n a .

T w o -p h a s e l iq u id v e lo c it ie s a re g e n e ra l ly lo w e r th a n th e c o r re s p o n d in g s in g le

p h a s e o n e s . T h e v e ry d if fe re n t v e lo c ity p ro f i le s c lo se to th e im p e lle r b o rd e r s

d e v e lo p in to p ro f i le s w h ic h a re n o t v e r y d if fe re n t in sh a p e f r o m th o se in s in g le

p h a s e o p e ra tio n b u t w ith g e n e ra l ly lo w e r v e lo c itie s . T h is s m o o th in g p ro c e s s n e e d s

a b o u t 1 .4 b la d e le n g th s , (o n e b la d e le n g th e q u a ls 0 .2 5 D ), fo r th e T /2 im p e lle r a n d

a b o u t 2 .4 b la d e le n g th s fo r th e 0 .4 T im p e lle r . T h e re a re n o t s u f f ic ie n t d a ta to

c o n c lu d e h o w c a v ita tio n re g im e a n d D /T ra t io in f lu e n c e th is d is ta n c e .

7.4.1.2 Root Mean Squares of velocity fluctuations.

R o o t M e a n S q u a re v e lo c ity f lu c tu a tio n m e a s u re m e n ts w e re d o n e a t th e s a m e t im e

as th e m e a n v e lo c ity m e a s u re m e n ts . A g a in ra d ia l R M S c o u ld n o t b e m e a s u re d

d ire c tly b u t h a d to b e c a lc u la te d f ro m th e tw o 15° a n g le m e a s u re m e n ts d o n e in th e

h o r iz o n ta l p la n e a n d f ro m th e ta n g e n tia l c o m p o n e n t, A p p e n d ix 3.

R M S v a lu e s p re s e n te d in th is th e s is a r is e f ro m b o th p e r io d ic a n d ra n d o m v e lo c ity

f lu c tu a tio n s - r e a l a n d p s e u d o tu rb u le n c e , [7 6 ].

F ig u re s 7 .1 3 a -c u p to 7 .1 7 a -c s h o w R M S d a ta fo r th e th re e v e lo c ity c o m p o n e n ts a t

th e 4 5 ° v e r t ic a l p la n e fo r th e 2 4 0 m m d ia m e te r R u s h to n im p e lle r . I t is e v id e n t th a t

ra d ia l R M S c o m p o n e n t d a ta s u f fe r f ro m la rg e sc a tte r w h ic h is a n e f fe c t o f th e w a y

th e y w e re c a lc u la te d . I t is v e ry d if f ic u lt to d ra w a n y c o n c lu s io n s f ro m d a ta o f fig .

7 .1 3 c . E v e n th e sh a p e o f th e r a d ia l R M S p ro f i le is n o t c o m p a ra b le in th e s in g le

a n d tw o -p h a s e m e a s u re m e n ts . H o w e v e r i t m ig h t b e sa id th a t i t fo llo w s th e g e n e ra l

f o rm o f th e ta n g e n tia l R M S p ro f ile .

O n th e o th e r h a n d th e a x ia l a n d ta n g e n tia l R M S d a ta fo rm d is t in c t c u rv e s . A n

im p o r ta n t o u tc o m e f ro m f ig u re s 7 .1 3 to 7 .1 7 is th a t th e R M S le v e ls m e a s u re d in

tw o -p h a s e o p e ra tio n a re g e n e ra l ly lo w e r th a n th e c o r re s p o n d in g o n e s m e a s u re d in

s in g le -p h a se .

A n o th e r im p o r ta n t f e a tu re o f th e R M S tw o -p h a s e p ro f i le s is th e a p p e a ra n c e o f tw o

p e a k s in th e ta n g e n tia l p ro f i le c lo s e s t to im p e lle r b la d e , f ig . 7 .1 3 a , w h ic h

c o r re s p o n d to th e tw o lo c a l m a x im a d e te c te d in th e m e a n v e lo c ity p ro f i le o f

f ig .7 .5 a . T h e p e a k s d is a p p e a r q u ic k ly w ith o n ly o n e sm a ll p e a k re m a in in g a t


R - 1 3 3 .5 m m . T h e s e tw o p e a k s m ig h t b e a r e s u l t o f th e tu rb u le n c e g e n e ra te d b y th e

c o m p e ti t iv e liq u id m o v e m e n t a ro u n d th e tw o ta ils o f th e c l in g in g c a v ity b e h in d

e a c h im p e lle r b la d e ; th e d is ta n c e b e tw e e n th e tw o p e a k s e q u a ls a p p ro x im a te ly th e

b la d e w id th , -4 8 m m -.

A n o th e r im p o r ta n t fe a tu re is th a t th e p e a k s in th e a x ia l R M S c o m p o n e n t s m o o th

o u t f a s te r in tw o -p h a s e o p e ra t io n th a n in s in g le -p h a se , f ig u re s 7 .1 3 b - 7 .1 5 b . T h is

u n d e r l in e s a g a in th a t th e tu rb u le n t m o v e m e n t o f th e liq u id is g e n e ra l ly w e a k e r in

tw o -p h a s e th a n in th e c o r re s p o n d in g s in g le -p h a s e o p e ra tio n . E x is te n c e o f th e tw o

p e a k s in th e a x ia l tw o -p h a s e R M S p ro f i le s h o w th a t th e re is s till v o r te x m o tio n

d u r in g c lin g in g c a v ita tio n .

S in g le -p h a s e R M S p ro f i le s d e m o n s tra te th e b a s ic fe a tu re s r e p o r te d in th e l i te ra tu re .

T h e sh a p e s o f th e a x ia l a n d ta n g e n tia l s in g le -p h a se R M S p ro f i le s a re in c lo se

a g re e m e n t w ith th o s e r e p o r te d in l i te ra tu re , [8 9 ].

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Flg.7.13a. Tangential RMS componentRushton Impeller, D=240mm, R=123.5mm, 45o

RMS [m/s]

Fig.7.13b. Axial RMS component Rushton impeller, D=240mm, R=123.Smm, 45o

RMS [m/s]

Fig.7.l3c. Radial RMS component Rushton impeller, D=240mm, R=123.Smm, 45o

RMS [m/s]

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Fig.7.14a. Tangential RMS componentRushton impeller, D=240mm, R=133.5mm, 45o

RMS [m/s]

Fig.7.14b. Axial RMS component Rushton Impeller, D=240mm, R=133.5mm, 45o

RMS [m/s]

Fig.7.14c. Radial RMS component Rushton impeller, D=240mm, R=133.5mm, 45o

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Fig.7.15a. Tangential RMS componentRushton impeller, D=240mm, R=148.5mm, 4So

RMS [m/s]

Fig.7.1Sb. Axial RMS component Rushton impeller, D=240mm, R=148.Smm, 45o

RMS [m/


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Fig,7.16a. Tangential RMS componentRushton impeller, D=240mm, R=168.5mm, 45o

RMS [m/s]

Fig.7.16b. Axial RMS component Rushton impeller, D=240mm, R=168.Smm, 45o

RMS [m/s]

Fig.7.16c. Radial RMS component Rushton impeller, D=240mm, R=168.Smm, 45o

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Singletphase

V i 'a

: Two-ghase

k aIV a i |

JffA A |......... /;:"■?.............. :...............:.............jk'

0 0.5 1 1.5 2 2.5RMS [m/s]

Fig.7.17b. Axial RMS component Rushton impeller, D=240mm, R=198.5mm, 45o

RMS [m/s]


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\CHAP TER 7. VELOCITY MEASUREMENTS. 121

Flg.7.18a. Tangential RMS componentRushton impeller, D=180mm, R=133.5mm, 45o

RMS [m/s]

Flg.7.18b. Axial RMS component Rushton impeller, D=180mm, R=133.Smm, 45o

RMS [mi

Flg.7.18c. Radial RMS component Rushton impeller, D=180fnm, R=133.5mm, 45o

RMS [m/s]

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RMS [m/s]

Fig.7.19b. Axial RMS component Rushton impeller, D=180mm, R=148.Smm, 4So

RMS [m/s]

Fig.7.19c. Radial RMS component Rushton Impeller, D=180mm, R=l48.5mm, 45o

RMS [m/s]

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Fig.7.20a. Tangential RMS component Rushton impeller, D=180mm, R=168.5mm, 4So

RMS [m/s]

Fig.7.20b. Axial RMS component Rushton impeller, Dsi80mm, R=168.5mm, 4So

RMS [m/s]

Fig.7.20c. Radial RMS components Rushton impeller, D=l80mm, R=168.5mm, 45o

RMS [m/s]


7 .4 .2 R eversed h o llo w blade im peller i.e . w ith the faces con vex

A h o llo w b la d e im p e lle r , f ig . 4 .2 , h a s b e e n u s e d to p ro d u c e so m e tw o -p h a s e

v e lo c ity a n d tu rb u le n c e d a ta f o r a d if f e re n t ra d ia l f lo w im p e lle r w ith a s lo w as

p o s s ib le R P D f o r g iv e n sp e e d ; it is k n o w n th a t a c o n v e x im p e lle r c a v ita te s m o re

e a s ily th a n a R u s h to n o r c o n c a v e ra d ia l im p e lle r , [5 8 ].

7.4.2.1. Mean velocities

F ig . 7 .2 1 a -c a n d 7 .2 2 a -c s h o w m e a n v e lo c ity d a ta fo r th e c o n v e x im p e lle r . L iq u id

h e ig h t is 5 8 0 m m , c le a ra n c e 3 1 5 m m a n d th e im p e lle r w a s o p e ra te d a t 3 5 0 R P M ,

g iv in g a n R P D o f 0 .5 7 w h e n b o ilin g .

B a s ic fe a tu re s o f th e d a ta in f ig . 7 .2 1 a -c a n d 7 .2 2 a -c a re s im ila r to th o se p ro d u c e d

b y R u s h to n im p e lle rs w ith g e n e ra l ly s m a lle r v e lo c itie s . I t is a g a in im p o r ta n t to

n o te th a t tw o -p h a s e v e lo c it ie s a re g e n e ra l ly lo w e r th a n s in g le -p h a s e o n e s . I t is

a lso c le a r th a t th e u p w a rd s s h if t o f th e v e lo c ity p ro f i le is e n h a n c e d d u r in g tw o -

p h a s e o p e ra tio n , p ro b a b ly b e c a u s e o f th e u p w a rd m o v e m e n t o f th e b u b b le s .

7.4.2.2. Root Mean Squares o f velocity fluctuations.

F ig s 7 .2 3 a -c a n d 7 .2 4 a -c s h o w th e R M S d a ta a t th e s a m e lo c a tio n s a s th e m e a n

v e lo c ity d a ta in f ig s 7 .2 1 a -c a n d 7 .2 2 a -c . T w o -p h a s e v a lu e s a re c o n s is te n tly lo w e r

th a n s in g le -p h a s e o n e s a n d lo w e r th a n th e c o r re s p o n d in g o n e s p ro d u c e d b y th e

R u s h to n im p e lle r .

Dist

ance

fro

m im

pelle

r dis

c [m

m]

Dist

ance

fro

m im

pelle

r dis

c [m

m]

Dist

ance

fro

m im

pelle

r dis

c [m

m]

CHAPTER ZVELOCITYMEASUREMENTS. 125

Fig.7.21a. Tangential mean velocities Convex Impeller, D=180mm, R=148.5mm, 45o

Mean Velocity [m/s]

Fig.7.21 b. Axial mean velocities Convex impeller, D=180mm, R=148.5mm, 45o

Mean Velocity [m/s]

Fig.7.21 c. Radial mean velocities Convex Impeller, D=180mm, R=148.5mm, 45o

Mean Velocity [m/s]

Dist

ance

fro

m im

pelle

r dis

c [m

m]

Dist

ance

fro

m im

pelle

r dis

c [m

m]

Dist

ance

fro

m Im

pelle

r dis

c [m

m]


Fig.7.22a. Tangential mean velocities Convex impeller, D=180mm, R=168.5mm, 45o

Mean Velocity [m/s]

Fig.7.22b. Axial mean velocities Convex impeller, D=180mm, R=168.5mm, 45o

Mean Velocity [m/s]

Flg.7.22c. Radial mean velocities Convex impeller, D=180mm, R=168.5mm, 45o

Mean Velocity [m/s]

Dist

ance

fro

m im

pelle

r dis

c [m

m]

Dist

ance

fro

m im

pelle

r dis

c [m

m]

Dist

ance

fro

m im

pelle

r dis

c [m

m]


Flg.7.23a. Tangential RMS component Convex impeller, D=180mm, R=148.5mm, 45o

RMS [m/s]

Fig.7.23b. Axial RMS component Convex impeller, D=180mm, R=148.5mm, 45o

RMS [m/s]

Fig.7.23c. Radial RMS component Convex impeller, D=180mm, R=148.5mm, 45o

RMS [m/s]

Dist

ance

fro

m im

pelle

r dis

c [m

mj

Dist

ance

fro

m Im

pelle

r dis

c [m

m]

Dist

ance

fro

m Im

pelle

r dis

c [m

m]

1 CHAPTER 7. VELOCITY MEASUREMENTS. 1 2 8

F!g.7.24a. Tangential RMS component Convex impeller, D=180mm, R=168.5mm, 45o

RMS [m/s]

Fig.7.24b. Axial RMS component Convex impeller, D=180mm, R=168.5mm, 45o

RMS [m/e]

Flg.7.24c. Radial RMS component Convex impeller, D=l80mm, R=168.5mm, 45o

RMS [m/s]


7.5 Flow in the bulk

S o m e v e lo c ity a n d R M S m e a s u re m e n ts w e re m a d e in th e b u lk o f th e ta n k to o b ta in

d a ta o n th e w a y th e im p e lle r d is c h a rg e s tre a m c h a n g e s a f f e c t th e f lo w f ie ld in th e

b u lk .

7 .5 .1 R ushton im peller

M e a s u re m e n ts w e re p e r fo rm e d in th e u p p e r p a r t o f th e v e s s e l w h e n a g ita te d b y th e

R u s h to n 1 8 0 m m im p e lle r . D a ta w e re o b ta in e d a t th e 4 5 ° p la n e b e tw e e n th e b a f f le s

f ro m z = 1 3 0 m m u p to z = 1 9 0 m m w h e re z is th e d is ta n c e f ro m im p e lle r m id p la n e ,

f ig . 7 .1 . L iq u id h e ig h t w a s 4 5 0 m m a n d th e im p e lle r w a s lo c a te d 15 0 m m f ro m th e

ta n k b o tto m i.e . w ith a c le a ra n c e o f T /3 . T h e im p e lle r w a s o p e ra te d a t 2 9 0 R P M

w h ic h g a v e a n R P D o f 0 .6 4 5 w h e n b o ilin g .

7.5.1.1 Mean velocities.

F ig u re s 7 .2 5 a -c s h o w th e m e a n v e lo c ity d a ta a t d if f e re n t ra d ia l d is ta n c e s f o r z= T 3 0

a n d 1 9 0 m m . I t is im p o r ta n t to n o te th a t, a s in th e im p e lle r d is c h a rg e s tre a m , tw o -

p h a s e liq u id m e a n v e lo c it ie s in th e b u lk a re g e n e ra lly lo w e r th a n s in g le -p h a s e o n e s .

T h e re c irc u la t io n p o in t, f ig . 7 .2 5 b , re m a in s a lm o s t u n a lte re d w h e n sw itc h in g f ro m

s in g le to tw o -p h a s e o p e ra tio n , its lo c a tio n m o v in g b y o n ly a fe w m ill im e tre s

to w a rd s th e ta n k a x is .

7.5.1.2 Root Mean Squares o f velocity fluctuations.

F ig u re s 7 .2 6 a -c s h o w R M S d a ta a t th e s a m e lo c a tio n s a s th e m e a n v e lo c ity d a ta o f

f ig s . 7 .2 5 a -c . Q u a lita tiv e a n d q u a n tita tiv e v a r ia tio n s a re s im ila r to th o se in th e

im p e lle r d is c h a rg e s tre a m . R a d ia l R M S d a ta a re a g a in v e ry s c a tte re d a s a r e s u l t o f

th e h ig h e r e r ro r g e n e ra te d b y th e w a y th e y w e re c a lc u la te d ; i t s e e m s d if f ic u lt to

d ra w a f irm c o n c lu s io n . H o w e v e r , th e y a p p e a r g e n e ra lly s im ila r to th e R M S

v a lu e s o f ta n g e n tia l a n d a x ia l c o m p o n e n ts .

velo

city

[m/s]

ve

locit

y [m

/s]

_ ve

locit

y [m

/s]

iCHAPTER /VELOCITYMEASUREMENTS. 130

Fig.7.£5«L Tangential m. velocities In the bulk Rushton Impeller, D=180mtn, 45o

Radial distance [mm]

Fig.7.25b.Axial mean velocities in the bulk Rushton impeller, D=180mm, 45o


Flg.7.25c.Radial mean velocities in the bulk Rushton Impeller, D=180mm, 45o


RMS

[m/s]

RM

S [m

/s]

..

..

RM

S


FIg.7.2£a. Torgenfictl RHS cowjponent In the bulk Rushton impeller, D=180mm, 45o

........

?^f90mm,^ngle-pha$e ; ZsIOOmm^two-ptiase : Zri30mm,^ngle-phae8

■; Z=1;30mmJvjO'phase

r....... i ..... -T -i 1 i .. ■ • * 1120 140 160 180 200 220


Fig.7.26b.Axial RMS component In the bulk Rushton impeller, D=l80mm, 45o


Fig.7.26c.Radlal RMS component in the bulk Rushton impeller, Ds=180mm, 45o



7.5.2 Axial downwards pumping impeller

V e lo c ity a n d R M S m e a s u re m e n ts w e re a lso p e r fo rm e d in th e b u lk o f th e ta n k

a g ita te d b y a p i tc h e d b la d e d o w n w a rd s p u m p in g tu rb in e . U n fo r tu n a te ly

m e a s u re m e n ts c o u ld n o t b e d o n e in th e im p e lle r d is c h a rg e s tre a m b e c a u s e o f

e q u ip m e n t l im ita tio n s ; th e fo c a l le n g th o f th e la s e r p ro b e w a s to o s h o r t to re a c h a n y

r e g io n in th e d is c h a rg e s tre a m o f th e im p e lle r p u m p in g e i th e r d o w n w a rd s o r

u p w a rd s . M e a s u re m e n ts w e re p e r f o r m e d in th e re g io n b e tw e e n th e im p e lle r a n d

th e w a ll o f th e ta n k o n th e 4 5 ° p la n e m id w a y b e tw e e n th e b a f f le s f ro m z = -4 0 to

z = + 4 0 m m , fig . 7 .2 7 . T h e im p e lle r d ia m e te r w a s 2 0 0 m m a n d im p e lle r w id th 4 8

m m , f ig . 4 .2 . Im p e l le r s p e e d w a s 3 5 0 R P M g iv in g a n R P D o f 0 .6 9 8 w h ile b o ilin g .

T h e liq u id h e ig h t w a s 5 8 0 m m a n d c le a ra n c e 3 3 0 m m .

7.5.2.1 Mean velocities

F ig u re s 7 .2 7 a -c sh o w m e a n v e lo c ity d a ta m e a s u re d a t d if f e re n t ra d ia l d is ta n c e s o n

th e 4 5 ° p la n e m id w a y b e tw e e n th e b a f f le s . F ig u re s s h o w d a ta o n ly fo r th e p o in ts

ly in g a t z = -4 0 , 0 a n d 4 0 m m f ro m th e im p e lle r h o r iz o n ta l m id p la n e , f ig . 7 .2 7 .

W h ils t th e e f fe c t o f tw o -p h a s e o p e ra t io n is n o t c le a r f o r th e ta n g e n tia l v e lo c ity

c o m p o n e n ts , th e a x ia l o n e s a g a in d e m o n s tra te th a t tw o -p h a s e o p e ra tio n re s u lts in a

d ra s tic re d u c tio n in th e a x ia l v e lo c itie s .

7.5.2.2 Root Mean Squares o f velocity fluctuations.

T h e re d u c tio n o f R M S v a lu e s w h e n o p e ra t in g in tw o -p h a s e m o d e in f ig s 7 .2 8 a -c , is

c o n s is te n t w ith R M S v a r ia t io n s o c c u r r in g in th e b u lk w h e n s t ir r e d b y th e R u s h to n

im p e lle r . T a n g e n tia l a n d a x ia l R M S c o m p o n e n ts a re e v id e n tly lo w e r in tw o -p h a s e

o p e ra t io n w h ile ra d ia l R M S d a ta a re v e r y s p re a d m a k in g d if f ic u lt to d ra w a n y

c o n c lu s io n s .

velo

city

[m/s]

ve

locit

y [m

/s]

velo

city

[m/s

]

\CHAPTER /VELOCITYMEASUREMENTS. 133

Fig.7.27a.Tangentlal mean velocities In the bulk PBT downwards pumping, D=200mm, 45o

2n40rmn,8jngle-phase j ;. Z^Ômmjjwo-pihase : J : Z=Ocnm ,e)ng le-phase; j ;: Z=0mm/Jjn>phas©!: ^ZiHomni.sJngip-phase:;2=-4Qmm<|wo^ph«se;

i l l !

1 1 |

▲ .... J _____

120 140 160 180 200 220Radial distance [mm]

Flg.7.27b.Axial mean velocities in the bulk PBT downwards pumping, D=200mm, 45o


Flg.7.27c.Radial mean velocities in the bulk PBT downwards pumping, D=200mm, 45o


velo

city

[m/s]

ve

loci

ty

[m/s]

ve

locit

y [m

/s]


Flg.7.28a. Tangential RMS component In the bulk PBT downwards pumping, Ds200mm, 45o

j j ;

; ! j

a — 4 ....... S = ^ —

i.......... — — ------ A:

-■ Z^4omm,sj{}glB-phasp • :; Z=40mmjjworphase;' ;Z==0mmi8l^gle-phase •

: Z=0mmi^6-ptrasB ;: : Z=-4pmrn^ngie-pha8e:

............................. 4............................. ..............................j............................. ......

-: Z=^40mmjtwo-phase :

i j . " - r ....... i 11 1 i i120 140 160 180 200 220


1

0.8

0.6

0.4

0.2

0

-0.2

■0.4

-0.6120 140 160 180 200 220


Fig.7.28c. Radial RMS component in the bulk PBT downwards pumping, D=200mm, 45o

1

0.8

0.6

0.4

0.2

0

■0.2

■0.4

■0.6120 140 160 180 200 220


Fig.7.28b. Axial RMS component In the bulk PBT downwards pumping, Ds200mm, 45o

G -

40mm,sungle-pha6S;: Z=40mmj|wa-phase: - : Z=Qmm,s^gle-pha8Q ■ : J Zkpmm.ôrphase; j Z=j-40mm,8^ngle-phase : Z=^40mntjfwo-p.hiase.:


7.6 Conclusions.

B a s ic fe a tu re s o f th e tw o -p h a s e l iq u id f lo w f ie ld in th e im p e lle r d is c h a rg e s tre a m

a n d in th e b u lk o f a b o il in g tw o -p h a s e m e c h a n ic a l ly a g ita te d s t ir re d ta n k h a v e b e e n

in v e s t ig a te d w ith th e h e lp o f L a s e r D o p p le r V e lo c im e try . U n fo r tu n a te ly

lim ita tio n s o f th e m e a s u r in g in s tru m e n ts u s e d in th is re s e a rc h w o rk d id n o t p e rm it

d ire c t m e a s u re m e n t o f a ll c o m p o n e n ts . R a d ia l m e a n a n d R M S v e lo c ity

c o m p o n e n ts h a d to b e c a lc u la te d f ro m o th e r m e a s u re m e n ts . B y c o m b in in g d a ta in

th is w a y a ll th re e m e a n a n d R M S v e lo c ity c o m p o n e n ts h a v e b e e n o b ta in e d fo r

s e v e ra l p o s it io n s in th e im p e lle r d is c h a rg e s tre a m a n d in th e b u lk .

N e a r th e im p e lle r b o u n d a r ie s m e a n a n d R M S v e lo c ity c o m p o n e n ts c h a n g e

d ra s tic a lly w h e n sw itc h in g f ro m s in g le to tw o -p h a s e o p e ra tio n b e c a u s e o f th e

s ta b le c a v itie s fo rm e d b e h in d im p e lle r b la d e s . D if fe re n t c a v ity re g im e s c re a te

d if f e re n t v e lo c ity p ro f i le s in th e v ic in i ty o f th e im p e lle r . C h a n g e s f ro m a v e lo c ity

p ro f i le u n d e r le s s d e v e lo p e d c a v ita t io n to o n e a s s o c ia te d w ith b ig g e r c a v itie s o f

d if f e re n t ty p e s e e m to b e g ra d u a l in th e s a m e w a y th a t c a v ity e v o lu tio n is a g ra d u a l

a n d c o n tin u o u s p ro c e s s . F a r a w a y f ro m im p e lle r b o u n d a r ie s tw o -p h a s e l iq u id

m e a n v e lo c ity a n d R M S p ro f i le s s m o o th o u t to w a rd s sh a p e s w h ic h lo o k lik e th e

u s u a l s in g le -p h a s e p ro f ile s . B e y o n d th a t d is ta n c e m e a n a n d R M S v e lo c ity v a lu e s

a re g e n e ra lly lo w e r th a n th o s e c o r re s p o n d in g to s in g le -p h a s e o p e ra tio n .

M e a s u re m e n ts d o n e a t s e v e ra l p o s it io n s in th e b u lk sh o w th a t th e re d u c tio n in

m e a n a n d R M S v e lo c itie s w h ic h o c c u r in tw o -p h a s e o p e ra t io n is g e n e ra l a n d n o t

l im ite d to th e im p e lle r re g io n .

M a in ly b e c a u s e o f th e in a c c u ra c ie s a s s o c ia te d w ith th e c a lc u la t io n o f th e r a d ia l

m e a n a n d R M S v e lo c ity c o m p o n e n t, re s u lts f ro m th is in v e s tig a tio n c a n n o t b e

c o n s id e re d a s d e f in itiv e . A m o re d e ta i le d in v e s tig a tio n e s p e c ia l ly o f th e r e g io n s

c lo se to th e im p e lle r b o u n d a r ie s m ig h t g iv e a c le a re r p ic tu re o f th e f lo w f ie ld s

a s s o c ia te d w ith th e d if fe re n t c a v ita tio n re g im e s w h ic h d e v e lo p d u r in g tw o -p h a s e

o p e ra tio n .

136

C h a p t e r 8

THE FLOW FIELD IN A TWO-PHASE STR.Validation of the model.

8.1 Introduction.

In c h a p te r 6 a s im p le m o d e l b a s e d o n e n e rg y b a la n c e s w a s d e r iv e d f o r th e

e s tim a tio n o f liq u id f lo w s g e n e ra te d b y im p e lle rs o p e ra t in g in tw o -p h a s e s t ir re d

ta n k s . I n p r in c ip le th e m o d e l c a n a ls o b e u s e d fo r th e e s t im a tio n o f liq u id m e a n

v e lo c it ie s in th e tan k . T h e m o d e l u s e s s in g le -p h a s e d a ta o f f lo w ra te s o r m e a n

v e lo c itie s a n d R e la t iv e P o w e r D e m a n d . I ts u s e fu ln e s s lie s in th e fa c t th a t s in g le

p h a s e e x p e r im e n ta l o r c a lc u la te d , u s in g se v e ra l C F D m e th o d s , d a ta , a re w id e ly

a v a ila b le in th e l i te ra tu re a n d c a n b e u s e d fo r th e e s t im a tio n o f th e tw o -p h a s e

p u m p in g c a p a c itie s o r l iq u id v e lo c it ie s i f R P D , a n d in s o m e c a se s th e m e a n g a s

f ra c tio n , in th e ta n k is k n o w n .

T h e m o d e l p re d ic t io n s h a v e b e e n s h o w n to b e in g o o d a g re e m e n t w ith c o r re la t io n s

a v a ila b le in th e l i te ra tu re f o r p u m p in g c a p a c itie s o f R u s h to n im p e lle rs o p e ra tin g in

tw o -p h a s e s t ir re d ta n k s , [3 1 ] .

CHAPTER 8. VALIDATION OF THE MODEL

I n th is c h a p te r th e m o d e l w il l b e v a l id a te d in te rm s o f b o th m e a n liq u id f lo w -ra te s

a n d m e a n liq u id v e lo c it ie s , u s in g d a ta o b ta in e d b y L a s e r D o p p le r V e lo c im e try a n d

p re s e n te d in th e p re v io u s c h a p te r . I n th is w a y th e in fo rm a tio n n e c e s s a ry to a s s e s s

th e lim ita tio n s a n d th e a p p lic a b ili ty o f th e m o d e l c a n b e o b ta in e d .

8.2 Flow rates

V o lu m e tr ic f lo w r a te s h a v e b e e n c a lc u la te d f ro m th e m e a s u re d m e a n v e lo c ity d a ta .

V o lu m e tr ic f lo w ra te ra t io s d u r in g tw o a n d s in g le -p h a se o p e ra t io n a t v a r io u s le v e ls

o f R e la t iv e P o w e r D e m a n d fo r d if f e r e n t im p e lle rs a re s h o w n in f ig . 8 .1 . T h e X

a x is c o r re s p o n d s to th e R P D , th e Y a x is to th e ra t io b e tw e e n th e tw o -p h a s e a n d

s in g le -p h a s e v o lu m e tr ic m e a n f lo w -ra te s th ro u g h a c e r ta in c o n tro l v o lu m e . T h e

so lid lin e c o r re s p o n d s to eq . (6 .1 7 ) . D e ta ils o f th e c o n tro l v o lu m e p o s it io n a n d

d im e n s io n s c a n b e fo u n d in ta b le 8 .1 . F lo w -ra te ra tio s in tw o a n d s in g le -p h a s e

o p e ra t io n w e re c a lc u la te d s e p a ra te ly fo r ta n g e n tia l ra d ia l a n d a x ia l v e lo c ity

c o m p o n e n ts fo r e v e ry c o n tro l v o lu m e . T h e n th e m e a n v a lu e o f th e th re e ra t io s w a s

u s e d in f ig . 8 .1 . I n th is w a y a ll th e th re e v e lo c ity c o m p o n e n ts c o n tr ib u te to th e

s a m e e x te n d in th e c a lc u la t io n o f tw o -p h a s e to s in g le -p h a s e ra t io -R e la tiv e M e a n

F lo w R a te - .

Fig.8.1 RPD vs Relative Mean Flow-Rate Drop

\CHAPTER 8. VALIDA TION OF THE MODEL 138

F ig . 8 .1 sh o w s th a t th e m o d e l p e r fo rm s a d e q u a te ly in o u r e x p e r im e n ts in b o il in g

w a te r e v e n w ith o u t ta k in g in to a c c o u n t g a s f ra c t io n e f fe c ts . A lth o u g h v a p o u r

f r a c t io n w a s n o t m e a s u re d d u r in g o u r e x p e r im e n ts , f ro m s im ila r g a s f ra c t io n

m e a s u re m e n ts in a e ra te d ta n k s i t c a n b e e s tim a te d th a t a t th is ra n g e o f R P D a n d

v a p o u r g e n e ra t io n ra te s , m e a n v a p o u r f r a c t io n in th e v e s s e l w o u ld b e a b o u t 4 %

re s u lt in g in an e x c e s s r e d u c t io n o f R e la t iv e M e a n F lo w R a te o f a b o u t o n ly 2 .5 -3 % .

Table 8.1. Details of the location of the control volumes.

Impeller hght clrc pine control control Mean T-P/ Mean RPDmm mm ang. volume volume Mean S-P flow-rates Value

from to [mm] from to[mm]Ri R2 Zi Z2 Rad.* Tang. Axia.

Rushton240mm

'585 315 15° 148.5 198.5 +54 -38 .965 .776 .796 .845 .71

Rushton240mm

585 315 45° 148.5 198.5 +54 -38 .915 .734 .95 .866 .71

Rushton240mm

585 315 75° 148.5 198.5 +54 -38 .975 .798 .888 .887 .71

Rushton180mm

580 315 15° 133.5 168.5 +54 -36 .864 .710 .885 .819 .53

Rushton180mm

580 315 45° 133.5 168.5 +54 -36 .998 .818 .83 .882 .53

Rushton180mm

580 315 750 133.5 168.5 +54 -36 .851 .700 .813 .788 .53

Rushton180mm

580 315 45° 148.5 168.5 +54 -36 .877 .780 .858 .838 .60

Rushton180mm

580 315 45° 148.5 168.5 +54 -36 .819 .976 .989 .928 .80

Convex180mm

580 315 15° 148.5 168.5 +54 -36 .785 .760 .755 .766 .56

Convex180mm

580 315 45° 148.5 168.5 +54 -36 .799 .783 .844 .793 .56

PBTdown200mm

580 330 45° 148.5 168.5 +40 -40 .600 1.03 .837 .823 .69

* Radial flow-rates were calculated over an angle of 3.6° around the vertical planes of 15°, 45° and 75° where measured radial velocities were supposed to remain const.

D e s p ite th e g o o d f i t f o r th e m e a n v a lu e o f th e f lo w -ra te s th e re a p p e a r to b e g re a te r

d is c re p a n c ie s w h e n e a c h v e lo c ity c o m p o n e n t f lo w -ra te is c o n s id e re d s e p a ra te ly ,

f ig . 8 .2 . I t s e e m s th a t w h ile a x ia l a n d ra d ia l R e la tiv e M e a n F lo w R a te s a re w e ll

b a la n c e d a ro u n d th e p re d ic t io n s o f m o d e l eq . (6 .1 7 ) , m e a s u re d ta n g e n tia l o n e s a re

g e n e ra l ly lo w e r. V a r io u s p a ra m e te rs su c h a s c a v ita tio n s tru c tu re a n d d is ta n c e f ro m

im p e lle r b o rd e r s m a y a f f e c t th e w a y v e lo c ity c o m p o n e n ts fo l lo w eq . (6 .1 7 ) .

CHAPTER 8. VALIDA TION OF THE MODEL

H o w e v e r a s a f i r s t a p p ro a c h e q . (6 .1 7 ) s e e m s to d e s c r ib e th e r e la t io n b e tw e e n th e

v o lu m e tr ic liq u id f lo w ra te s in s in g le a n d tw o -p h a s e o p e ra tio n s u ff ic ie n tly

a c c u ra te ly f o r m a n y p u rp o s e s .

Fig.8.2 RPD vs Relative Flow-Rate Drop

8.3 Mean velocities

M e a n v e lo c ity p re d ic t io n s w ill b e p re s e n te d to g e th e r w ith th e c o r re s p o n d in g tw o

a n d s in g le -p h a s e c o m p o n e n ts p r e s e n te d in th e p re v io u s c h a p te r . In th is w a y

c o m p a r is o n c a n b e m a d e b e tw e e n re la t iv e s iz e o f th e tw o -p h a s e v e lo c itie s -

p r e d ic te d a n d m e a s u re d - w ith th e s in g le -p h a s e v e lo c ity c o m p o n e n ts .

F ig u re s 8 .3 a -c sh o w m o d e l p re d ic t io n s f ro m eq . (6 .1 7 ) to g e th e r w ith tw o a n d

s in g le -p h a s e l iq u id m e a n v e lo c it ie s f o r th e 2 4 0 m m d ia m e te r R u s h to n im p e lle r a t

R = 1 4 8 .5 m m in th e im p e lle r d is c h a rg e s tre a m . P re d ic te d v e lo c it ie s a re re la t iv e ly

c lo s e to th o s e m e a s u re d .

F ig u re s 8 .4 a -c s h o w m e a s u re m e n ts a n d p re d ic t io n s a t th e s a m e lo c a tio n s b u t f o r

th e 1 8 0 m m R u s h to n im p e lle r . T h e c h a ra c te r is tic u p w a rd s ’s h if t in g ’ o f th e tw o -

p h a s e liq u id v e lo c it ie s in f ig u re 8 .4 c is n o t p re d ic te d b y th e m o d e l. T h is s h if t m a y

b e p a r t ia l ly a n e f fe c t o f b ia s e d v e lo c ity m e a s u re m e n ts , p a ra g ra p h 7 .4 .1 .1 , c a u s e d

p ro b a b ly b y th e m a s s iv e p re s e n c e o f b u b b le s r e le a s e d f ro m th e r e a r o f th e s ta b le

c a v itie s b e h in d th e im p e lle r b la d e s . T h is s h if t is n o t so o b v io u s w ith th e 2 4 0 m m

im p e lle r , p a r t ly b e c a u s e o f th e s tro n g e r l iq u id o u tf lo w a n d p a r t ly b e c a u s e im p e lle r

w a s o p e ra t in g a t a h ig h e r R P D w ith r a th e r sm a lle r v a p o u r c a v itie s p re s e n te d a n d in

a ll p ro b a b il i ty g e n e ra t in g le s s v a p o u r in th e v ic in ity o f th e im p e lle r .

Dist

ance

fro

m im

pelle

r dis

c [m

m]

Dist

ance

fro

m im

pelle

r dis

c [m

m]

Dist

ance

fro

m Im

pelle

r dis

c [m

m]

\CHAPTER 8. VALIDA TION OF THE MODEL

Fig.8.3a. Tangential mean velocitiesRushton impeller,D=240mm,R=148.5mm,45o,RPD=0.71

Mean Velocity [m/s]

Fig.8.3b. Axial mean velocities Rushton impeller,D=240mm,R=148,Smm,45o,RPD=0.71

Mean Velocity [m/s]

Fig.8.3c. Radial mean velocities Rushton impeller,D=240mm,R=148.Smm,45o,RPD=0.71

Mean Velocity [m/s]

Dist

ance

fro

m im

pelle

r dis

c [m

m]

Dist

ance

fro

m im

pelle

r dis

c [m

m]

Dist

ance

fro

m im

pelle

r dis

c [m

m]


Fig .8.4a. Tangential mean velocitiesRushton impeller,D=180mm,R=148.5mm,45o,RPD=0.53

Mean Velocity [m/s]

Fig.8.4b. Axial mean velocities Rushton impeller,D=180mm,R=148.Smm,45o,RPD=0.53

Mean Velocity [m/s]

Flg.8.4c. Radial mean velocities Rustiton impeller,D=180mm,R=148.5mm,45o,RPD=0.S3

Mean Velocity [m/s]

Dist

ance

fro

m im

pelle

r dis

c [m

m]

Dist

ance

fro

m im

pelle

r dis

c [m

m]

Dist

ance

fro

m Im

pelle

r dis

c [m

m]

CHAPTER 8. VALIDA TION OF THE MODEL 142

Flg.8.5a. Tangential mean velocitiesRushton impeller,D=240mm,R=198.5mm,45o,RPD=0.71

Mean Velocity [m/s]

Fig.8.5b. Axial mean velocities Rushton impeller,D=240mm,R=198.5mm,45o,RPD=0.71

Mean Velocity [m/s]

Fig.8.5c. Radial mean velocities Rushton impeller,D=240mm)Rsl98.5mm,45o,RPD=0.71

Mean Velocit

Dist

ance

fro

m im

pelle

r dis

c [m

m]

Dist

ance

fro

m im

pelle

r dis

c [m

m]

Dist

ance

fro

m im

pelle

r dis

c [m

m]

\CHAPTER 8. VALIDA TION OF THE MODEL 143

Flg.8.6a TANGENTIAL MEAN VELOCITIESRushton Impeller,D=240mm,R=123.5mm,4So,RPD=0.71

Mean Velocity [m/s]

Flg.8.6b. Axial mean velocities Rushton impeller,D=240mm,R=123.5mml45o,RPD=0.71

Mean Velocity [m/s]

Fig.8.6c. Radial mean velocities Rushton Impeller,D=240mm,R=123.5mm,45o,RPD=0.71

Mean Velocity [m/s]

velo

city

[m/s]

ve

locit

y [m

/s]

_ ve

locit

y [m

/s]

I CHAPTER 8. VALIDA TION OF THE MODEL 144

Fig.8.7s.Tangential mean velocities in the bulk Rushton impeller, D=180mm, 45o, RPD-0.64


pig.S.7b.Axlal mean velocities in the bulk Rushton Impeller, D=180mm, 45o, RPD=0.64


Flg.8.7c.Radial mean velocities in the bulk Rushton impeller, D=180mm, 45o, RPD=0.64


CHAPTER 8. VALID A TION OF THE MODEL

P re d ic tio n s o f th e m o d e l a re b e tte r w h e n m o v in g d o w n s tre a m , f ig . 8 .5 a -c , b u t th e y

a re w o r s t n e a r th e im p e lle r b o u n d a r ie s . F ig . 8 .6 a -c s h o w v e lo c ity d a ta a n d

p re d ic t io n s a t a d is ta n c e o n ly 3 .5 m m f a r f ro m im p e lle r tip . T h e v e lo c ity p ro f i le s o f

fig . 8 .6 .a -c r e p re s e n t m e a n v e lo c ity m e a s u re m e n ts d o n e in th e l iq u id d is c h a rg e d

b e tw e e n s u c c e s s iv e s ta b le c a v itie s . T h e p re s e n c e o f th e s ta b le c a v itie s c h a n g e

d ra s t ic a l ly th e f lo w p a tte rn o f th e tw o -p h a s e l iq u id f lo w -f ie ld r e s u lt in g in d if fe re n t

a re a s o f in a n d o u tf lo w in th e im p e lle r b o u n d a r ie s . U n d e r th e s e c o n d itio n s a

p re d ic t io n b a s e d o n eq . (6 .1 7 ) c a n n o t b e d o n e s in c e s u rfa c e s S j a n d S 2 a re q u ite

d if f e re n t in s in g le a n d tw o -p h a s e o p e ra tio n .

F ig u re s 8 .7 a -c s h o w h o w e f fe c tiv e ly th e m o d e l p e r fo rm s in th e b u lk , w e ll a w a y

f ro m th e im p e lle r . T h e c o n tro l v o lu m e in th is c a se is h a l f w a y b e tw e e n th e

im p e lle r a n d th e f re e su r fa c e , n e a r th e r e c irc u la t io n p o in t, in a r e g io n w h e re th e

lo c a l b u o y a n c y fo rc e s c a n b e e x p e c te d to b e c o m e m o re s ig n if ic a n t. M o d e l

p re d ic t io n s s e e m to b e su f f ic ie n tly a c c u ra te fo r a ll th e v e lo c ity c o m p o n e n ts .

U n fo r tu n a te ly th is s e e m s n o t to b e th e c a se fo r th e ra d ia l c o m p o n e n ts i f th e y a re

c o n s id e re d a t th e s a m e ra d ia l d is ta n c e e .g . R = 1 4 8 .5 m m , fig . 8 .8 . P re d ic tio n s o f

th e m o d e l a re n o w fa r f ro m th e m e a s u re m e n ts . T h is h a p p e n s b e c a u s e p o in ts o f f ig .

8 .8 a re a ro u n d th e re c irc u la t io n re g io n o f th e w e a k ra d ia l c o m p o n e n t. A t d is ta n c e

R = 198 .5 m m p re d ic t io n s a re a lso su f f ic ie n tly a c c u ra te fo r th e ra d ia l c o m p o n e n t,

f ig . 8 .9 .

Fig.8.8. Radial mean velocities in the bulk Rushton impeller,D=180mm,R=148.5mm,45o,RPD=0.645


Fig.8.9. Radial mean velocities in the bulk Rushton impeller,D=10Omm,R=198.5mml45o,RPD=O.64S

C o m p a r is o n o f f ig s 8 .7 b a n d 8 .8 c a n g iv e so m e in s ig h t in th e m o d e l c a p a b ilitie s .

T h e s tro n g a x ia l c o m p o n e n t in f ig . 8 .7 b c h a n g e s v e ry m u c h a s p re d ic te d b y th e

m o d e l. T h e r e c irc u la t io n p o in t o f th e a x ia l c o m p o n e n t is s h if te d o n ly fe w

m ill im e tre s to w a rd s th e ta n k a x is w h e n o p e ra t io n c h a n g e s to tw o -p h a s e m o d e . O n

th e o th e r h a n d th e r e c irc u la t io n p o in t o f th e ra d ia l c o m p o n e n t, w h ic h is m u c h

w e a k e r th a n a x ia l in th is r e g io n o f th e ta n k , is s h if te d n o t a f e w m illim e tre s b u t a

fe w c e n tim e tre s . C o n s e q u e n tly m o d e l p re d ic t io n s a re p o o r fo r th is r e g io n , f ig . 8 .8 ;

i t s e e m s th a t m o d e l d o e s n o t p e r fo rm w e ll in re g io n s c lo se to r e c irc u la t io n p o in ts

o f w e a k v e lo c ity c o m p o n e n ts th a t m a y c h a n g e p o s it io n w h e n s w itc h in g f ro m s in g le

to tw o -p h a s e o p e ra tio n . T h is fo llo w s d ire c tly f ro m th e d e r iv a tio n o f th e m o d e l

w h ic h re q u ire s th a t in le t a n d o u tle t c o n tro l v o lu m e s u rfa c e s S i a n d S 2 m u s t r e m a in

a n a lte re d .

8.4 Accuracy o f the model predictions

F ig . 8 .1 0 g iv e s a n id e a o f th e e r ro r c o n ta in e d in th e p re d ic t io n s o f m o d e l eq . (6 .1 7 )

in f ig s 8 .3 a -c a n d 8 .4 a -c . In f ig . 8 .1 0 th e X a x is r e p re s e n ts th e % e rro r ,

{[measured 2ph velocity - predicted 2ph velocity]E = (8 -1 )

measured 2ph velocity* 100

\CHAPTER 8. VALIDA TION OF THE MODEL

a n d th e Y a x is th e d im e n s io n le s s d is ta n c e f ro m im p e lle r d is c Z * = Z /(0 .2 * D /2 ) ,

w h e re 0 .2 D is th e b la d e w id th o f th e im p e lle r i.e . th e n u m b e r o f h a l f b la d e w id th s

f ro m th e im p e lle r m id p la n e . P re d ic t io n s o f v e lo c itie s a re m a d e a c c o rd in g to eq .

(6 .1 7 ) u s in g th e s in g le -p h a se v e lo c it ie s m e a s u re d a t th e s a m e lo c a tio n s .

Fig. 8.10. Comparison of the predicted & measured of figs 8.3 & 8.4.

-100 0 100

p e r c e n ta g e e r ro r

S c a tte r is n o t sm a ll b u t ta k in g in to a c c o u n t th e h ig h ly tu rb u le n t f ie ld a n d th e

s im p lic ity o f eq . (6 .1 7 ) th e m o d e l tu rn s o u t to b e a p o w e r fu l to o l; th e fe w h ig h -

e r ro r p o in ts a re o f m in o r im p o r ta n c e in te rm s o f v o lu m e f lo w ra te , n e a r ly 9 0 % o f

th e p o in ts a re a c c u ra te w ith in ± 4 0 % , 7 0 % o f th e p o in ts a re a c c u ra te w ith in 3 0 %

a n d 5 0 % o f th e p o in ts a re a c c u ra te w ith in 2 0 % .

F ig u re 8 .1 0 a sh o w s th a t th e p o in ts a re n e a r ly e v e n ly b a la n c e d in th e ir d is tr ib u tio n

a ro u n d th e p re d ic te d v a lu e s . I n f ig . 8 .1 0 a th e % m e a n re la t iv e a c c u ra c y is d e f in e d

asn

% m e a n re la tiv e a c c u ra c y = [ £ ( e) / n ] (8 .2 )n=l

and has been calculated over a ll the points o f fig. 8.10.


T h e c o e f f ic ie n t o f v a r ia tio n (c .v .) o f th e p o in ts o f fig . 8 .1 0 is p re s e n te d in fig .

8 .1 0 b . C o e f f ic ie n t o f v a r ia t io n is d e f in e d a s th e n o rm a lis e d ra t io o f th e s ta n d a rd

d e v ia tio n o f th e p re d ic tio n to th e m e a s u re d ( tru e ) v a lu e a n d c a n b e e v a lu a te d f ro m :

F lg .8 .1 0 a .% M ean rel. a c c u r a c y o f p re d ic t io n sMean velocities of figs. 8.3 and 8.4

Radial Axial Tangentialv e lo c ity c o m p o n e n ts

c .v . = [ £ ( | e I) / n ] (8 .3 )n -1

C o e ff ic ie n t o f v a r ia tio n u su a lly g iv e s a m e a s u re o f th e e x p e c te d a c c u ra c y o f a

m o d e l. F ro m fig . 8 .1 0 b it c o m e s o u t th a t fo r th e p re s e n t e x p e r im e n ts th e a c c u ra c y

o f th e m o d e l e v e n w ith eq . (6 .1 7 ) is b e tte r th a n 2 5 % fo r a x ia l a n d ta n g e n tia l

c o m p o n e n ts .

F lg .8 .1 0 b .C o e ffic ie n t o f v a r ia tio n (c.v .)Predictions of mean velocities figs 8.3&4

50 i------------------------------------------------------------------

40 -

Radial Axial Tangentialv e lo c ity c o m p o n e n ts


T h e s lig h tly s m a lle r a c c u ra c y o f th e ra d ia l c o m p o n e n t m a y b e a re s u l t o f th e h ig h e r

e r ro r a s so c ia te d w ith th e w a y ra d ia l v e lo c ity d a ta w e re c a lc u la te d ; th e e r ro r o f

ra d ia l v e lo c ity d a ta is a b o u t 5 % h ig h e r th a n th a t o f th e ta n g e n tia l a n d a x ia l v e lo c ity

d a ta w h ic h is e x a c tly th e e s t im a te d e x c e s s e r ro r a r is in g f ro m th e c a lc u la tio n

p ro c e d u re , A p p e n d ix 3. F ig u re s a re o f th e s a m e s ize fo r th e o th e r d a ta p o in ts o f th e

p re s e n t in v e s tig a tio n . I f e r ro r s a re w e ig h te d in te rm s o f v o lu m e tr ic f lo w ra te th e n

th e m o d e l p re d ic tio n s a p p e a r b e tte r , f ig . 8 .1 1 . In fig . 8.11 % m e a n re la tiv e e r ro rs

a n d c o e f f ic ie n t o f v a r ia tio n o f a ll th e v o lu m e tr ic f lo w ra te s c a lc u la te d in th e

d is c h a rg e s tre a m o f th e R u s h to n a n d c o n v e x im p e lle rs a re p re s e n te d . I t is sh o w n

th a t th e a c c u ra c y o f th e m o d e l eq . (6 .1 7 ) in p re d ic t in g tw o -p h a s e liq u id f lo w ra te s

in th e p re s e n t e x p e r im e n ts is a b o u t + 1 0 % .

30

20 -a>3(0>

0)E

0

F ig .8 .1 1 .A c c u ra c y o f m o d e l p re d ic t io n sMean values for flow-rates in the impeller

discharge stream

■ V mean relative error □ % coefficient of variation

10.52

-1.41

Radial Tangential AxialF lo w -ra te c o m p o n e n ts

8.5 Conclusions

T h e s im p le m o d e l d e r iv e d in c h a p te r 6 h a s b e e n v a lid a te d b y L a s e r D o p p le r

v e lo c ity m e a s u re m e n ts m a d e b o th in th e im p e lle r d is c h a rg e s tre a m a n d in th e b u lk .

E x p e r im e n ta l v a lid a tio n sh o w s th a t a p p lic a tio n o f th e m o d e l m u s t b e re s tr ic te d to

re g io n s f a r e n o u g h f ro m im p e lle r b o u n d a r ie s so th a t f lo w f ie ld c h a n g e s r e s u ltin g

f ro m th e p re s e n c e o f th e s ta b le c a v itie s fo rm e d b e h in d im p e lle r b la d e s a re

sm o o th e d o u t. M o d e l p re d ic t io n s a re a lso e x p e c te d to b e lia b le to e r ro r n e a r


r e c irc u la t io n re g io n s w ith w e a k v e lo c ity c o m p o n e n ts . E f fe c ts in d u c e d b y b u o y a n c y

a n d th e in f lu e n c e o f th e b u b b le s o n th e liq u id m o tio n c a n n o t b e p re d ic te d b u t

v e lo c ity m e a s u re m e n ts s h o w e d th a t l iq u id m o tio n is d o m in a n t w h e n o p e ra tin g fa r

f ro m f lo o d in g .

L iq u id tw o -p h a s e v e lo c ity m e a s u re m e n ts d o n e in b o il in g w a te r in th e im p e lle r

d is c h a rg e s tre a m o f ra d ia l im p e lle rs , s h o w e d th a t a t r e g io n s w h e re m o d e l e q u a tio n s

a re a p p lic a b le , m e a n liq u id f lo w r a te s a n d m e a n liq u id v e lo c it ie s a re p re d ic ta b le

w ith in a c c u ra c y o f 10% a n d 2 5 % re s p e c tiv e ly e v e n w ith o u t ta k in g v o id f r a c t io n

in to a c c o u n t. I t is e x p e c te d th a t a c c u ra c y w ill b e e n h a n c e d i f m e a n v o id f ra c t io n

c a n b e c o n s id e re d . T h e a c c u ra c y o f m o d e l p re d ic tio n s a re s im ila r a t p o in ts in th e

b u lk o f th e tan k .

I t is e x p e c te d th a t th e m o d e l c a n p ro v id e a q u ic k a n d fa ir ly a c c u ra te p re d ic t io n o f

th e m e a n liq u id f lo w ra te s a n d m e a n liq u id v e lo c itie s in tw o -p h a s e s tir re d ta n k s .

M o d e l p re d ic t io n s c a n b e u s e d a s in p u t v a lu e s in n u m e r ic a l c o d e s d e v e lo p e d fo r

tw o -p h a s e s t i r re d ta n k c a lc u la tio n s , e .g . [6 , 3 4 ].

151

C h a p t e r 9

CONCLUSIONS AND RECOMMENDATIONS

9.1 Conclusions.

S e v e ra l a sp e c ts o f th e tw o -p h a s e f lo w f ie ld o f B o ilin g M e c h a n ic a lly A g ita te d

S tir re d T a n k R e a c to rs h a v e b e e n in v e s tig a te d . A f ir s t s te p to w a rd s a g e n e ra l

m e th o d o f c o r re la t in g tw o -p h a s e f lo w f ie ld w ith s in g le -p h a se o n e in g a s - liq u id

s t i r re d ta n k s is p re s e n te d .

Cavitation regimes.

C a v ity fo rm a tio n s ta g e s in b o il in g s t ir r e d ta n k s h a v e b e e n d e te rm in e d u s in g

v is u a lis a tio n m e th o d s fo r b o th r a d ia l a n d a x ia l im p e lle rs . C a v ity fo rm a tio n is a

c o n tin u o u s p ro c e s s . S e v e ra l s ta g e s c a n b e c la s s if ie d in te rm s o f s e p a ra tio n e v e n ts .

T h e c a v ita tio n s ta g e s d e f in e d f o r R u s h to n im p e lle rs a re in a g re e m e n t w ith p re v io u s

in v e s tig a tio n s re p o r te d in th e l i te ra tu re . A x ia l p i tc h e d b la d e im p e lle rs d e v e lo p

c a v itie s w h ic h a re d if f ic u lt to c la s s ify in te rm s o f s e p a ra tio n e v e n ts o r a s s o c ia te d

c h a n g e s in f lo w p a tte rn s .

\CHAPTER 9. CONCLUSIONS 152

T h e P o w e r n u m b e r d ro p in b o il in g s t ir re d ta n k s is d ire c tly re la te d to th e c a v ity

e v o lu tio n p ro c e s s a n d h a s b e e n in v e s t ig a te d w ith th e h e lp o f a n e w ly d e v e lo p e d

d im e n s io n le s s g ro u p . T h is A g ita t io n C a v ita t io n - C a v a g i t a t i o n - n u m b e r h a s b e e n

d e r iv e d f ro m a tra d itio n a l c a v ita t io n n u m b e r b y u s in g p a ra m e te rs su ita b le f o r u s e

w ith s t ir re d ta n k s .

T h e R e la tiv e P o w e r D e m a n d -R P D - in b o il in g s t ir re d ta n k s h a s b e e n fo u n d to b e a

w e a k fu n c tio n o f v a p o u r g e n e ra t io n ra te , is n e a r ly in d e p e n d e n t o f th e lo c a tio n

w h e re v a p o u r is g e n e ra te d , is d ire c tly r e la te d to th e v a r io u s c a v ita tio n re g im e s

d e te c te d in b o ilin g re a c to r s a n d c a n b e a p p ro x im a te d s u f f ic ie n tly w e ll w ith in

r e g io n s o f p ra c tic a l in te re s t b y

R P D = A * C A g N B (9 .1 )

w h e re

C A g N - 2 * S * g / Vtip2

is th e C a v a g ita tio n n u m b e r w ith S th e s u b m e rg e n c e o f th e im p e lle r .

T h e c o n s ta n t A d e p e n d s o n th e im p e lle r ty p e . E x p o n e n t B d e p e n d s o n g e o m e tr ic a l

fa c to rs o f th e im p e lle r ta n k sy s te m .

A a n d B h a v e b e e n d e te rm in e d f o r s e v e ra l im p e lle r ta n k c o n f ig u ra tio n s f o r b o th

ra d ia l a n d a x ia l im p e lle rs .

A u n i f i e d a p p r o a c h t o c a v i t a t i o n p h e n o m e n a in b o i l i n g a n d

g a s s e d S T R .

C o m p a r is o n o f R e la tiv e P o w e r D e m a n d b e tw e e n b o il in g a n d g a s s e d s t ir re d ta n k s

sh o w e d th a t d if fe re n c e s in R P D , m a y r e f le c t d if fe re n c e s in th e p h y s ic a l

m e c h a n is m s c o n tro ll in g v a p o ro u s a n d g a s s e d c a v ity d e v e lo p m e n t. T h is p ro v id e s a

b a s is f o r a p h y s ic a l m o d e l w h ic h d e s c r ib e s c a v ita tio n p h e n o m e n a in b o th g a s s e d

a n d b o il in g s t ir r e d ta n k s . T h e m o d e l u s e s th e in te ra c tio n o f th e p re s s u re in s id e th e

c a v ity a n d th e p re s s u re f ie ld in th e l iq u id d u r in g sin g le-p h a se o p e ra tio n .

T h e m o d e l h a s b e e n v a lid a te d b y th e d e r iv a tio n o f a c a v ita tio n n u m b e r b a s e d o n

th e r e la t io n o f th e se p re s s u re s . T h is c a v ita tio n n u m b e r h a s b e e n sh o w n to

re p ro d u c e m o s t o f th e r e p o r te d tre n d s in R P D in b o th b o ilin g a n d g a s s e d sy s te m s .

P o w e r N u m b e r o f B o i l i n g S t i r r e d T a n k R e a c t o r s

1CHAPTER 9. CONCLUSIONS 153

A m o d e l f o r th e p r e d i c t i o n o f th e f l o w f i e l d in T w o - p h a s e S T R .

A s im p le m o d e l b a s e d o n e n e rg y b a la n c e s h a s b e e n d e r iv e d fo r th e e s tim a tio n o f

th e m e a n liq u id v o lu m e f lo w r a te s a n d th e m e a n v e lo c itie s in a tw o -p h a s e g a s -

liq u id s tir re d ta n k re a c to r . T h e m o d e l u s e s R P D a n d th e c o r re s p o n d in g s in g le

p h a s e d a ta to p re d ic t m e a n liq u id f lo w ra te s a n d m e a n liq u id v e lo c itie s in tw o -

p h a s e c o n d itio n s . K n o w le d g e o f m e a n g a s f ra c t io n im p ro v e s p re d ic tio n s . T h e

u s e fu ln e s s o f th e m o d e l lie s in th e f a c t th a t s in g le -p h a se e x p e r im e n ta l o r c a lc u la te d

f ro m se v e ra l C F D m e th o d s d a ta , w id e ly a v a ila b le in th e l i te ra tu re , c a n n o w b e u s e d

fo r th e e s tim a tio n o f th e liq u id tw o -p h a s e f lo w f ie ld in th e ta n k . A p p lic a tio n o f th e

m o d e l is l im ite d to s t ir re d ta n k s o p e ra t in g w ith lo w v is c o s ity n e w to n ia n liq u id s in

th e fu lly tu rb u le n t r e g im e f a r e n o u g h f ro m f lo o d in g p o in t, a n d is in d e p e n d e n t o f

im p e lle r - ta n k g e o m e try . S e v e ra l o th e r a s su m p tio n s a b o u t f lo w f ie ld c o m p a tib il i ty

a n d c o n tro l v o lu m e c h o ic e a re im p lie d .

M o d e l p re d ic t io n s h a v e b e e n s h o w n to b e in re a s o n a b le a g re e m e n t w ith lite ra tu re

d a ta a n d w ith d a ta o b ta in e d b y L a s e r D o p p le r v e lo c im e try m e th o d s in b o il in g

s t ir r e d ta n k s o p e ra tin g a t R P D as lo w a s 0 .5 5 .

T h e f l o w f i e l d in B o i l i n g S T R .

T h e tw o -p h a s e f lo w f ie ld o f a b o il in g s t ir re d ta n k h a s b e e n in v e s t ig a te d f o r th e f ir s t

t im e in th e o p e n l i te ra tu re b y L a s e r D o p p le r V e lo c im e try m e th o d s a t R P D as lo w

a s 0 .5 5 . A ll th e th re e c o m p o n e n ts o f th e m e a n v e lo c itie s a n d th e R M S o f th e

v e lo c ity f lu c tu a tio n s h a v e b e e n o b ta in e d fo r se v e ra l p o in ts in th e im p e lle r

d is c h a rg e s tre a m o f r a d ia l im p e lle rs a n d in th e b u lk o f th e ta n k . D a ta s h o w e d th a t:

- T h e f lo w f ie ld c h a n g e s d ra s tic a lly n e a r th e im p e lle r b o u n d a r ie s a s a re s u l t o f th e

s ta b le c a v itie s fo rm e d b e h in d im p e lle r b la d e s .

- T h e f lo w f ie ld n e a r im p e lle r b o u n d a r ie s d e p e n d s o n th e ty p e o f th e s ta b le c a v itie s

fo rm e d b e h in d im p e lle r b la d e s .

- C h a n g e s f ro m o n e f lo w f ie ld a s s o c ia te d w ith le ss d e v e lo p e d c a v ita tio n to a n o th e r

w ith m o re d e v e lo p e d c a v ita tio n se e m to b e g ra d u a l.

- A t so m e d is ta n c e d o w n s tre a m th e im p e lle r d is c h a rg e s tre a m f lo w f ie ld sm o o th e s

o u t to o n e w h ic h is g e n e ra l ly s im ila r to th a t o f s in g le -p h a se f lo w b u t w ith m e a n

a n d R M S v e lo c it ie s w h ic h a re g e n e ra l ly lo w e r th a n th o se o f th e s in g le -p h a s e f lo w

f ie ld a n d c a n b e p re d ic te d w ith in a c c e p ta b le e r ro r b y th e m o d e l.

CHAPTER 9. CONCLUSIONS 154

- B u lk f lo w -f ie ld v a r ia t io n s in re g io n s w h e re th e im p e lle r a c tio n d o m in a te s th e

f lo w a re s im ila r to th o se in th e d e v e lo p e d im p e lle r d is c h a rg e s tre a m . R e c irc u la t io n

re g io n s m a y c h a n g e lo c a tio n d u r in g tw o -p h a s e o p e ra tio n . C h a n g e s a re sm a ll w h e re

th e re a re s tro n g v e lo c ity c o m p o n e n ts a n d s ig n if ic a n t w h e re th e se a re w e a k .

- A t re g io n s w ith h ig h b u b b le c o n c e n tra tio n s , e .g . c o n f in e s o f th e im p e lle r a t lo w

R P D , b u b b le m o tio n s e e m s to a f fe c t l iq u id m o tio n so m e tim e s d ra s tic a lly . T h is

e f f e c t is e x p e c te d to b e c o m e s tro n g e r a p p ro a c h in g th e f lo o d in g p o in t, is n o t

p re d ic ta b le f ro m th e p re s e n t fo rm o f th e m o d e l, a n d is a lso d if f ic u lt to re s o lv e it

s a fe ly b e c a u s e o f th e e r ro r s a s s o c ia te d w ith th e m e a s u r in g m e th o d .

- O v e ra ll it c a n b e c o n c lu d e d th a t a s R P D fa lls , m e a n a n d R M S liq u id v e lo c itie s

g e n e ra l ly d e c lin e in th e tan k .

9.2 Recommendations for future work.

T h e re a re se v e ra l re s u lts o f th e p re s e n t w o rk w h ic h n e e d fu r th e r in v e s tig a tio n .

T h e c o r re la tio n o f R P D c h a n g e s in b o il in g sy s te m s , eq . (9 .1 ) , h a s b e e n fo u n d to b e

g e n e ra l ly a p p lic a b le a t le a s t fo r th e g e o m e tr ie s u se d . H o w e v e r e q . (9 .1 ) h a s b e e n

d e r iv e d u s in g o n ly f i l te re d ta p w a te r . T h e in f lu e n c e o f th e p h y s ic a l p ro p e r t ie s o f

th e f lu id s o n eq . (9 .1 ) s h o u ld b e e s ta b lish e d . M o re o v e r e q . (9 .1 ) sh o u ld in c lu d e

sc a le e ffe c ts . T o c a r ry o u t w o rk in la rg e sc a le b o ilin g re a c to r s is im p ra c tic a l fo r

a c a d e m ic re s e a rc h so c o lla b o ra t io n w ith in d u s try w o u ld b e n e c e s s a ry .

T h e c a v ita tio n n u m b e r d e f in e d f o r u s e in s tir re d ta n k s in c h a p te r 5 h a s p ro v e d to

d e m o n s tra te q u a lita tiv e ly m o s t o f th e fe a tu re s o f R P D c h a n g e s in g a s s e d s tir re d

ta n k s . F u r th e r re s e a rc h is n e e d e d to s h o w w h e th e r a c a v ita t io n n u m b e r o f th is

f o rm is su ita b le fo r c o r re la t in g R P D in g a s s e d s tir re d ta n k s a s a s in g le v a r ia b le o r

n o t.

T h e re la t io n b e tw e e n g a s s e d a n d b o il in g sy s te m s is a n im p o r ta n t to p ic fo r fu tu re

re s e a rc h a p p lic a tio n s w h ic h h a s im p lic a t io n s fo r m u c h o th e r w o rk u s in g a ir -w a te r

to s im u la te v a p o u r - l iq u id f lo w s .

D e s p ite th e tu rb u le n t tw o -p h a s e f lo w f ie ld in a s t ir re d ta n k w ith its a s s o c ia te d sh o r t

te rm in s ta b ilitie s th e m o d e l d e r iv e d fo r th e p re d ic t io n o f tw o -p h a s e liq u id m e a n

CHAPTER 9. CONCLUSIONS 155

f lo w c h a ra c te r is tic s h a s b e e n fo u n d to p e r fo rm q u ite w e ll e n o u g h fo r e n g in e e r in g

a p p lic a tio n s . F u r th e r r e s e a rc h is n e e d e d to in v e s tig a te a ll th e p o s s ib le e x te n s io n s

a n d lim ita tio n s o f su c h a n a p p ro a c h in th e m o d e ll in g o f d is p e rs e d tw o -p h a s e

sy s te m s .

L a s e r D o p p le r V e lo c ity m e a s u re m e n ts h a v e p ro v id e d s ig n if ic a n t d a ta fo r th e tw o -

p h a s e l iq u id f lo w f ie ld in a b o i l in g re a c to r b u t th e y a re b y n o m e a n s c o m p le te . T h e

b a s ic re a s o n lie s in th e l im ita tio n s o f th e e q u ip m e n t u s e d w h ic h d id n o t p e rm it

d ire c t m e a s u re m e n t o f th e ra d ia l m e a n a n d R M S v e lo c ity c o m p o n e n ts . M o re o v e r

it w a s n o t p o s s ib le to p e r f o r m m e a s u re m e n ts v e ry c lo se to th e im p e lle r b la d e tip

w h ic h w o u ld h a v e re s o lv e d th e im p o r ta n t c h a n g e s w h ic h o c c u r in th e f lo w w h ile

c a v itie s o f d if f e r e n t ty p e s a re a t ta c h e d b e h in d im p e lle r b la d e s . I t is d e s ira b le to

o b ta in a fu ll p ic tu re o f th e tw o -p h a s e l iq u id f lo w f ie ld w ith b o th ra d ia l a n d a x ia l

im p e lle rs a t d if f e re n t R P D . D a ta f ro m su c h a n in v e s tig a tio n w o u ld b e v a lu a b le n o t

o n ly f o r th e d e s ig n o f g a s - l iq u id s t i r r e d ta n k s b u t fo r im p ro v in g k n o w le d g e in th e

w id e r f ie ld o f tw o -p h a s e f lu id d y n a m ic s .

156

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163

A p p e n d ix 1.

A n a l y s i s o f e n e r g y b a l a n c e e q u a t i o n f o r

t u r b u l e n t s y s t e m s - T h e s t r e s s t e n s o r i n

n e w t o n i a n f l u i d s .

The energy balance equation (6.1)

dE/dt + J p Vn dS + $ [x.Vn] dS + Ws — J p e V n d S + f ([dp e]/dt)dVS S S V

is quite general as it applies at any instant for a control volume independently of whether the flow is laminar or turbulent. In a turbulent system all quantities may be substituted by their mean and fluctuating components. Eq. (6.1) then becomes,

d(E+E')/dt + J (p+p’)(Vn+Vn,)dS + J [(f+ T 'M V n + V n ')] dS + (Ws+Ws’) = s s

J (p+p1) e (V n + V o 1) dS + J ([d(p+p') e]/dt)dV (A. 1.1)S V

If eq. (A. 1.1) is applied to a long-term steady-state situation and averaged over a sufficiently long time period then it becomes:

I (p+p')(Vn+Vn’)dS + } [(F+T’MVn+Vn’)] dS + (Ws+Ws’) =s s

APPENDIX 1. 164

j (p+p') 8 (Vn+Vn’) dS (A. 1.2)S

Interest will be focused firstly on the second term of the left hand-side of eq. (A. 1.2). In this term (t-Ht') is the stress tensor t at a time instant analysed in terms of its mean and fluctuating part. The relation between the stress tensor and velocity components in Cartesian co-ordinates for a newtonian fluid is given by, [1, 9, 55]:

Txx = (X -2/3p)0 + 2p (du/dx)

Tyy = (X -2/3p)0 + 2p (dv/dy)

xzz = (X -2/3p)0 + 2p (dw/dz) (A. 1.3)

Txy = xyx = p ( du/dy + dv/dx)

Tyz = Tzy = p ( dw/dz + dw/dx)

Txz = t z x = p ( du/dz + dw/dx)where

0 = du/dx + dv/dy + dw/dz

and p and X are the first and second viscosity coefficients, [55], or viscosity and volume viscosity respectively, [1, 9]. The pressure p has not been included in the normal stresses txx, Tyy, xzz, taking part in the energy balance in the first term of eq. (A. 1.2) as in [9]. Other textbooks include the pressure p in the equations which give normal stresses, [1,55]. In such a case the first term of eq. (A. 1.2) would be included in the second term. In a turbulent system eqs (A. 1.3) are still valid if the quantities are replaced with their instantaneous values. Applying the Reynolds decomposition to mean and fluctuating parts, eqs (A. 1.3) then become:

(xxx+xxx’) - (X -2/3p)(0+0’) + 2p {d(u+u')/dx}

(xxy+Txy) - (xyx+Tyx’) = p { d(u+u’)/dy + d(v+v')/dx) (A. 1.4)

where it has been assumed that viscosity does not change very much in time and space.If it is assumed that viscosity is very small, in other words X and p approach zero, then it follows from eqs (A. 1.4) that stress tensor components are very close to zero and consequently the second term in eq. (A. 1.2) is approximately zero.

APPENDIX 1. 165

Therefore if we restrict application of eq. (A. 1.2) to turbulent low viscosity systems the energy balance equation (A. 1.2) becomes:

I (pV)(Vn+W )dS + (Ws+Ws') = J (p+p') e (Vn+Vn') dS (A. 1.5)s s

In a turbulent system the internal energy per unit mass of fluid is:

s = l^C V + V y + g ^ + h ^ + CU+U1)

Substituting e in eq. (A. 1.5), assuming that density is not affected by the turbulent nature of the flow, is approximately constant over inlet and outlet surfaces and taking into account that the only significant velocity component for the calculation of energy fluxes in a control volume is the component vertical to the control volume surface we finally get:

{ (pVn)+(p'Vn')dS + Ws =s

If we assume that h' is small and in an adiabatic system LT is also small then

J (pV„)+(FW)dS + ws =s

p J {(l/2Vn3+3/2W "2̂ + l/2 V ^ )+ g (V n h )+ (V n U )}d S (A .I.7)

This is the final form of the energy balance equation for a newtonian low viscosity incompressible adiabatic turbulent system under the given assumptions.

It follows from the no slip condition that the surface integrals on other than the inlet and outlet control volume surfaces are zero. Assuming that Vj and V2 are the vertical to the inlet and outlet control volume surface velocities and integrating eq. (A. 1.7) over the inlet and outlet control volume surfaces we get:

APPENDIX 1. 166

Ws =

p2{ l/2 < v ;3> +3/2<v 7 2V;> + 1/2<VV3> + g<V2h2> + <V2U2> - <p2V2>/p2 -

<pVV2 >/p2 } - pj {l/2< V j3> +3/2<V /2Vj> + 1/2<V73> + g c V jh ^ + c V jU ^ -

<p1V 1>/p1 - <p1,V 1’> /p1 } (A. 1.8)

Assuming that p} « p2 eq. (A. 1.8) can be rewritten:

Ws =

p { l/2<Vy»-v;3> +g<V2h2-V1h1> - (<p2V2-p1V1>)/p}

+ p { 3/2<v 7 2V2 - + 1/2<V73-V?"3> - (<p7VV - P?V7,;>/p}

(A. 1.9)

In eq. (A. 1.9) the first term of the right hand-side is similar to eq. (6.7) and represents energy fluxes due to mean quantities while the second term of the right hand-side corresponds to energy transferred through the control volume surface by turbulent fluctuations. Depending on the nature of the flow this second term may be small if compared with the first term. As an example, in an energy balance around a heat exchanger where a liquid flow receives large amounts of heat, A may be much larger than the energy associated with velocity fluctuations so that ignoring turbulent fluctuations may result in a small error which usually is not taken into account, [68]. In the case of a stirred tank there are few cases in the literature where the relative amount of mean and fluctuating energy components has been calculated. Mahouast et al, 1989, [32], calculated from two-component Laser Doppler velocity measurements very close to the borders of the immediate swept volume of a Rushton impeller, that 25% of the power consumption of the impeller is contained in the fluctuations (turbulent+periodic).

If E is the part of the energy contained in the mean quantities and E' that in the fluctuations then eq. (A. 1.19) can be written as:

APPENDIX 1. 167

where according to [32], E * 3 E' just outside the borders of a Rushton impeller. Proceeding further downstream E' becomes smaller as it has been found that velocity fluctuations decline with distance from impeller tip, [32, 47, 89, 91]. Wu and Patterson 1989, [89], or Mahouast et al, 1989, [32], show that the kinetic energy contained in velocity fluctuations at a distance of about D/2 from impeller tip is about 1/3 that contained at the impeller tip. This means that at that distance only about 0.25*1/3= 8% of the energy content of the fluid is due to the turbulent fluctuations. These figures are expected to change towards smaller percentages of the fluctuating part for more streamlined impellers, [32], and may be different for other impeller-tank configurations.From the above analysis it is clear that turbulence plays an important role in the energy balance equation in a stirred tank near impeller boundaries becoming less important at more distant places in the tank.However it can be shown that in specific cases model equations (6.17), (6.20), (6.23) and (6.24) are not affected even if turbulent part of the energy balance equation is quite important.

For a specific control volume in a single-phase stirred tank the energy balance equation may be written as:

= Ejpk+ E V = EV + a*E^t = EV(l+a) (A.l .11)

where a*Elph = E’lph is the energy flux carried by the turbulent fluctuations and Elph the energy flux carried by the mean quantities.In a two-phase system it is again possible to resolve energy fluxes in two parts:

W V = EV+ E'2pi, = EV + b*EV = V ( H b ) (A. 1.12)

Dividing eqs (A. 1.11) and (A. 1.12) we get:

W ^ /W V = {EV/EV } (1 +a)/( 1 +b) (A. 1.13)

Equation (A. 1.13) shows that if the percentage of the energy flux carried through the control volume by turbulent fluctuations is approximately the same in both

Ws = E + E' (A .l .10)

APPENDIX 1. 168

single and two-phase systems, i.e. a » b , then model equations (6.17), (6.20), (6.23) and (6.24) remain analtered even if energy fluxes due to turbulent fluctuations form a substantial part of the total energy balance equation. Experimental data in chapter 7 have shown that RMS values during two-phase operation are generally lower than in a single phase one and seem to scale with RPD in the same way as mean velocities which confirms this assumption.

APPENDIX 2. 169

A p p en d ix 2.

D a t a a n d c a l c u l a t i o n s f o r R e l a t i v e P o w e r

D e m a n d i n B o i l i n g S t i r r e d T a n k R e a c t o r s .

2.1 Notation

All the data concerning Relative Power Demand of boiling Stirred Tank obtained during the present research work are presented in the tables of the present appendix. The notation which has been used is as follows:

Torq. Torque in [Nm] measured on the impeller shaft

Torq.real Torque absorbed by the impeller. Calculated from measuredtorque after subtraction of the torque absorbed by the teflon bearing at the bottom of the tank, in [Nm].

RPM Revolutions per minute measured on the impeller shaft.

Pu Uncavitated Power Number calculated from Torq. real andRPM measurements during "cold" conditions.

APPENDIX 2. 170

Pc Cavitated Power Number calculated from Torq. real and RPMmeasurements during boiling conditions.

Pc/Pu Relative Power Demand. Mean value of cold experimentsfound at the end of each cold experiment data set has been used as Pu.

ti Initial, at low speed, and final, at high speed, temperature in °C at the impeller level

1/CAgN Reciprocal of Cavagitation number as it has been defined ineq.4.3 corrected for temperature differences. This correction is discussed in details in the next paragraph.

l/CAgN*cor Reciprocal of Cavagitation number as it has been defined in eq. 4.3 corrected for temperature differences and for liquid depth only if submergence is smaller than 1.5 of impeller diameter D. Correction factor is cor = { (h-c)/1.5D}°-5

Patm Atmospheric pressure during the experiment in Torr.

2.2. Temperature correlation o f Cavagitation number.

In all the experiments done in boiling conditions a small temperature drop of the order of up to 0.4 °K was detected at impeller level probably because of enhanced heat transfer through the vessel wall due to vigorous agitation or because of air drawdown because of surface aeration. The measured liquid temperature was higher at low impeller speed falling with increased impeller speed. As was shown in chapter 4 it was necessary to correct the Cavagitation number from this small temperature drop in order to correlate results derived from different experiments. Typical temperature deviation data are shown in fig. A.2.1. In this figure temperature deviation at impeller level is shown as a function of impeller speed.

APPENDIX 2. 171

Fig. A.2.1 .Temperature evolution vs speedRushton impeller, d=180,h=450lc=150,

Vapour rate= 104dm3/min

RPM

For simplicity most data were approximated by a linear relationship, fig. A.2.1. Therefore temperature drop AT was calculated from initial and final RPM and temperatures using the following equation:

AT = (T initial - Tfinal) * [(RPM - RPMinitial)/(RPMfinal-RPMinitial)] (A.2.1)

Initial and final measured temperatures are given with each set of experimental data.Even small temperature deviations have a large effect on the vapour pressure used for the derivation of Cavagitation number in eq. (4.2). Literature tables give data of the thermophysical properties for water, [68]:

Table A.2.1 Thermophysical properties o f saturated water (M=18.015kg/kmol), from [68].

Temperature [°K] Saturated vapour pressure [bar]370 0.9040373.15 1.0133375 1.0815

Data of table A.2.1 show that around 100°C one tenth of a degree Celsi us corresponds to approximately 0.0036 bar vapour pressure change. Therefore the

APPENDIX 2. 172

cavagitation number has been corrected from vapour pressure changes because of temperature deviations as follows:

CAgN = 2* (S *pL *g + Ap) / (pl* V2tiP) .

= 2* [(h-c)*pL*g + 0.003578* AT* 100000/ 0.1]/(pl* V2tiP). (A.2.2)

Equation (A.2.2) with AT calculated from eq. (A.2.1) has been used to calculate Cavagitation number CAgN from the data presented in the present Appendix.

2.3. Relative Power Demand Data for the Radial and Axial impellers.

In the following tables the data for the calculation of the RPD of the radial & axial impellers are presented. Vessel diameter was 450 mm and working liquid filtered tap water. All the two-phase experiments were performed under atmospheric pressure. Impeller type, height, clearance, temperature at impeller level and vapour rate are given with each data set.

APPENDIX 2.

Data for the 240mm Rushton impellerhe igh t = 580m m c lea rance = 150m m

ti = 5 7 o CTorq .INm ] R P M Pu

0 .8 0 6 4 .5 0 5 .5 61 .0 0 7 1 .0 0 5 .7 31 .2 0 7 8 .5 0 5 .6 31 .4 0 8 6 .5 0 5.411 .6 0 9 0 .0 0 5.711 .8 0 9 7 .0 0 5 .5 32 .0 0 1 0 1 .0 0 5 .6 62 .4 0 1 1 1 .0 0 5 .6 32 .8 0 1 2 1 .0 0 5 .5 33 .2 0 1 2 9 .0 0 5 .5 63 .6 0 1 3 8 .0 0 5 .4 64 .0 0 1 4 5 .0 0 5 .5 04 .4 0 1 5 2 .0 0 5 .5 04 .8 0 1 5 9 .0 0 5 .4 95 .2 0 1 6 6 .0 0 5 .4 55 .6 0 1 7 2 .0 0 ’ 5 .4 76 .0 0 1 7 8 .0 0 5 .4 76 .4 0 1 8 4 .0 0 5 .4 66 .8 0 1 9 0 .0 0 5 .4 47 .2 0 1 9 5 .0 0 5 .4 77 .6 0 2 0 1 .0 0 5 .4 48 .0 0 2 0 6 .0 0 5 .4 58 .4 0 2 1 1 .0 0 5 .4 58 .8 0 2 1 6 .0 0 5 .4 59 .2 0 2 2 2 .0 0 5 .3 9

M ean value of Pu 5.60

APPENDIX 2. 174

Data for the 240mm Rushton impellerhe igh t= 580m m clea rance = 150m mVap ou r ra te= 104 .6 7d m 3 /m in , Patm = 7 5 8 To rrt = 1 0 0 .6 7 0 -1 0 0 .4 0 6 o CTorq.INm ] R PM Pc Pc/Pu

0 .8 0 6 4 .0 0 5 .7 9 1 .031 .00 7 1 .0 0 5 .8 8 1 .051 .20 7 7 .0 0 6 .0 0 1 .071 .40 8 5 .0 0 5 .7 5 1 .031 .60 9 0 .0 0 5 .8 6 1 .051 .80 9 7 .0 0 5 .6 7 1.012 .0 0 1 0 3 .0 0 5 .5 9 1 .002 .4 0 1 1 3 .0 0 5 .5 7 0 .9 92 .8 0 1 2 3 .0 0 5 .4 9 0 .9 83 .2 0 1 3 3 .0 0 5 .3 6 0 .9 63 .6 0 1 4 2 .0 0 5 .2 9 0 .9 44 .0 0 1 5 0 .0 0 5 .2 7 0 .9 44 .4 0 1 5 9 .0 0 5 .1 6 0 .9 24 .8 0 1 6 8 .0 0 5 .0 4 0 .9 05 .2 0 1 7 5 .0 0 5 .0 3 0 .9 05 .6 0 1 8 4 .0 0 4 .9 0 0 .8 86 .0 0 1 9 3 .0 0 4 .7 8 0 .8 56 .4 0 2 0 2 .0 0 4 .6 5 0 .8 36 .8 0 2 1 0 .0 0 4 .5 7 0 .8 27 .2 0 2 2 1 .0 0 4 .3 7 0 .7 87 .6 0 2 3 0 .0 0 4 .2 6 0 .7 68 .0 0 2 4 2 .0 0 4 .0 5 0 .7 28 .4 0 2 5 4 .0 0 3 .8 6 0 .6 98 .8 0 2 6 5 .0 0 3 .7 2 0 .6 69 .2 0 2 8 0 .0 0 3 .4 8 0 .6 29 .6 0 2 8 8 .0 0 3 .4 3 0.61

10 .0 0 3 0 1 .0 0 3 .2 7 0 .5 8he igh t= 580m m ,,clr. = 150m mti= 1 0 0 .6 5 -1 0 0 .3 8 0 O CPatm = 7 5 8 T o rr,V ap . rate = 67 .07dm 3/rr

0 .8 0 6 3 .0 0 5 .9 8 1 .071 .60 9 1 .0 0 5 .7 3 1 .022 .0 0 1 0 3 .0 0 5 .5 9 1 .002 .8 0 1 2 3 .0 0 5 .4 9 0 .9 84 .0 0 1 4 9 .0 0 5 .3 4 0 .9 55 .2 0 1 7 5 .0 0 5 .0 3 0 .9 06 .4 0 2 0 0 .0 0 4 .7 4 0 .8 58 .0 0 2 3 8 .0 0 4 .1 9 0 .7 5

1/C A gN0 .0 80 .0 90.110 .1 30 .1 50 .1 70 .1 90 .2 30 .2 70 .3 20 .3 60 .4 00 .4 50 .5 00 .5 40 .5 90 .6 50.710 .7 60 .8 40 .9 01.001 .091 .1 81.311 .381 .75

0 .0 70 .1 50 .1 80 .2 50 .3 60 .4 90 .611 .16

APPENDIX 2. 175

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APPENDIX 2.

Data for the 240mm Rushton impellerhe igh t = 588m m clea rance = 337m m t i= 1 1 .1 8 o CTorq.[Nm ] R PM Pu

0 .8 0 6 3 .0 0 5 .7 31 .0 0 7 1 .0 0 5 .6 41 .2 0 7 8 .0 0 5 .6 01 .4 0 8 4 .0 0 5 .6 41 .6 0 8 9 .0 0 5 .7 41 .8 0 9 5 .0 0 5 .6 72 .0 0 1 0 0 .0 0 5 .6 82 .4 0 1 1 2 .0 0 5 .4 42 .8 0 1 1 9 .0 0 5 .6 23 .2 0 1 2 7 .0 0 5 .6 43 .5 0 1 3 4 .0 0 5 .5 44 .0 0 1 4 2 .0 0 5 .6 44 .4 0 1 5 0 .0 0 5 .5 64 .8 0 1 5 7 .0 0 5 .5 35 .2 0 1 6 2 .0 0 5 .6 35 .6 0 1 7 0 .0 0 5.516 .0 0 1 7 5 .0 0 5 .5 76 .4 0 1 8 2 .0 0 5 .4 96 .8 0 1 8 8 .0 0 5 .4 77 .2 0 1 9 4 .0 0 5 .4 47 .6 0 2 0 0 .0 0 5 .4 08 .0 0 2 0 9 .0 0 5 .2 08 .4 0 2 1 5 .0 0 5 .1 68 .8 0 2 2 0 .0 0 5 .1 7

M ean va lue o f Pu 5 .6 3

APPENDIX 2. I l l

Data for the 240mm Rushton impellerhe igh t = 580m m c lea rance = 33 7m mVap ou r rate 1 0 4 .6 7d m 3/m in , Patm = 7 5 8 Torrt i= 1 0 0 .6 4 0 -1 0 0 .2 8 2 oC To rq .N m R PM Pc

0 .8 0 6 2 .0 0 6 .1 7Pc/Pu

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0 .1 31 /CAgN * cor.

0 .1 01 .00 7 0 .0 0 6 .0 5 1 .08 0 .1 6 0 .1 31 .20 7 6 .0 0 6 .1 6 1 .09 0 .1 9 0 .1 51 .40 8 3 .0 0 6 .0 3 1.07 0 .2 2 0 .1 81 .60 9 1 .0 0 5 .7 3 1 .02 0 .2 6 . 0 .211 .80 9 6 .0 0 5 .7 9 1 .03 0 .2 9 0 .2 42 .0 0 1 0 2 .0 0 5 .7 0 1.01 0 .3 2 0 .2 62 .4 0 1 1 4 .0 0 5 .4 8 0 .9 7 0 .3 9 0 .3 22 .8 0 1 2 5 .0 0 5.31 0 .9 4 0 .4 6 0 .3 83 .2 0 1 3 5 .0 0 5.21 0 .9 2 0 .5 3 0 .4 33 .6 0 1 4 7 .0 0 4 .9 4 0 .8 8 0 .6 2 0.514 .0 0 1 5 7 .0 0 4.81 0 .8 5 0 .6 9 0 .5 74 .4 0 1 6 8 .0 0 4 .6 2 0 .8 2 0 .7 8 0 .6 44 .8 0 1 8 1 .0 0 4 .3 4 0 .7 7 0 .8 8 0 .7 35 .2 0 1 9 2 .0 0 4 .1 8 0 .7 4 0 .9 8 0 .8 05 .6 0 2 0 6 .0 0 3.91 0 .7 0 1 .10 0 .9 06 .0 0 2 2 0 .0 0 3 .6 8 0 .6 5 1 .23 1.016 .4 0 2 3 1 .0 0 3 .5 6 0 .6 3 1 .33 1 .106 .8 0 2 4 4 .0 0 3 .3 9 0 .6 0 1 .4 6 1 .2 07 .2 0 2 5 3 .0 0 3 .3 4 0 .5 9 1 .55 1 .277 .6 0 2 6 7 .0 0 3 .1 6 0 .5 6 1 .69 1 .398 .0 0 2 8 0 .0 0 3 .0 3 0 .5 4 1 .83 1 .508 .8 0 3 0 1 .0 0 2 .8 4 0.51 2 .0 6 1 .69

1 0 .0 0 3 3 0 .0 0 2 .6 7 0 .4 7 2 .3 8 1 .961 0 .7 0 3 4 5 .0 0 2.61 0 .4 6 2 .5 5 2 .1 0

heig. = 580m i clr. = 337m m t i= 100 .617 -1

0 .8 00 0 .2 3 6 o C ,P a tm =

6 2 .0 07 5 8T o rr ,V ap .ra te = 67

6 .1 7 1 .10 0 .1 3 0 .1 01 .00 7 0 .0 0 6 .0 5 1 .08 0 .1 6 0 .1 31 .20 7 6 .0 0 6 .1 6 1 .09 0 .1 9 0 .1 51 .40 8 5 .0 0 5 .7 5 1 .02 0 .2 3 0 .1 91 .60 9 1 .0 0 5 .7 3 1 .02 0 .2 6 0 .211 .80 9 8 .0 0 5 .5 6 0 .9 9 0 .3 0 0 .2 42 .0 0 1 0 4 .0 0 5 .4 8 0 .9 7 0 .3 3 0 .2 72 .4 0 1 1 6 .0 0 5 .2 9 0 .9 4 0 .4 0 0 .3 32 .8 0 1 2 7 .0 0 5 .1 5 0.91 0 .4 7 0 .3 83 .2 0 1 3 8 .0 0 4 .9 8 0 .8 9 0 .5 4 0 .4 53 .6 0 1 4 8 .0 0 4 .8 7 0 .8 7 0.61 0 .5 04 .0 0 1 5 7 .0 0 4.81 0 .8 5 0 .6 8 0 .5 64 .4 0 1 6 7 .0 0 4 .6 8 0 .8 3 0 .7 5 0 .6 24 .8 0 1 8 0 .0 0 4 .3 9 0 .7 8 0 .8 6 0 .7 05 .6 0 2 0 5 .0 0 3 .9 5 0 .7 0 1 .06 0 .8 76 .4 0 2 3 0 .0 0 3 .5 9 0 .6 4 1 .29 1 .06

APPENDIX 2. 178

Data for the 240mm Rushton impeller7 .2 0 2 5 3 .0 0 3 .3 4 0 .5 9 1 .50 1 .238 .0 0 2 7 8 .0 0 3 .0 7 0 .5 5 1 .75 1 .439 .2 0 3 0 8 .0 0 2 .8 4 0 .5 0 2 .0 5 1 .69

1 0 .0 0 3 3 0 .0 0 2 .6 7 0 .4 7 2 .2 8 1 .88heig. = 580m mclr. = 337m mti = 1 0 0 .5 5 0 -1 0 0 .2 2 0 o C ,P a tm = 7 5 8 T orr, V ap .ra te = 27

0 .8 0 6 1 .0 0 6 .3 7 1 .13 0 .1 3 0 .1 01 .00 7 0 .0 0 6 .0 5 1 .08 0 .1 6 0 .1 31 .20 7 7 .0 0 6 .0 0 1 .07 0 .1 9 . 0 .1 52 .0 0 1 0 3 .0 0 5 .5 9 0 .9 9 0.31 0 .2 63 .2 0 1 3 6 .0 0 5 .1 3 0.91 0 .5 0 0.415 .2 0 1 9 0 .0 0 4 .2 7 0 .7 6 0 .8 8 0 .7 27 .2 0 2 5 0 .0 0 3 .4 2 0.61 1.41 1 .16

.1 0 .0 0 3 3 0 .0 0 2 .6 7 0 .4 7 2 .3 3 1.91

APPENDIX 2. 179

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APPENDIX 2. 180

Data fo r the R u sh ton 180m m im pe lle r H e ig h t= 45 0m m clea rance = 150m m ti = 5 3 .5 o C

R PM T o rq .tN m l1 2 6 .5 0 0 .8 01 4 3 .0 0 1 .0 01 5 5 .0 0 1 .2 01 6 9 .0 0 1 .401 8 1 .0 0 1 .6019 1 .0 0 1 .802 0 4 .0 0 2 .0 02 2 2 .0 0 2 .4 02 4 1 .0 0 2 .8 02 5 7 .0 0 3 .1 52 7 4 .0 0 3 .6 02 8 9 .0 0 4 .0 03 0 2 .0 0 4 .4 03 1 5 .0 0 4 .8 03 2 6 .0 0 5 .2 03 3 8 .0 0 5 .6 03 4 9 .0 0 6 .0 03 6 4 .0 0 6 .4 03 7 5 .0 0 6 .8 03 9 2 .0 0 7 .2 04 0 7 .0 0 7 .6 04 2 0 .0 0 8 .0 04 3 5 .0 0 8 .4 04 4 8 .0 0 8 .8 04 6 3 .0 0 9 .2 04 7 6 .0 0 9 .6 04 9 3 .0 0 1 0 .0 0

m ean co ld

Torq . real Pu0 .8 0 6 .0 61 .0 0 5 .9 31 .20 6 .0 51 .4 0 5 .9 41 .6 0 5 .9 21 .8 0 5 .9 82 .0 0 5 .8 22 .4 0 5 .9 02 .8 0 5 .8 43 .1 5 5 .7 83 .6 0 5.814 .0 0 5 .8 04 .4 0 5 .8 54 .6 5 5 .6 85 .0 3 5 .7 35 .4 0 5 .7 35 .7 7 5 .7 46 .1 4 5.616.51 5.616 .8 7 5 .4 27 .2 3 5 .2 97 .6 0 5 .2 27 .9 7 5 .1 08 .3 3 5 .0 38 .7 0 4 .9 29 .0 7 4 .8 59 .4 3 4 .7 0

num ber 5 .9 2

APPENDIX 2. 181

Data fo r the Rush ton 180m m im pe lle r H e ig h t= 45 0m m c lea rance = 150m mti = 1 0 0 .6 5 5 -1 0 0 .5 3 6 o C , Patm = 7 6 8 T o rrV ap ou r rate = 104 .67d m 3/m inR PM Torq .INm ] Tor.rea l

1 2 5 .0 0 0 .8 0 0 .8 01 4 3 .0 0 1 .00 1 .001 6 2 .0 0 1 .20 1 .201 7 6 .0 0 1 .40 1 .401 9 2 .0 0 1 .60 1 .6 02 0 7 .5 0 1 .80 1 .802 4 2 .0 0 2 .2 0 2 .2 02 7 1 .0 0 2 .5 0 2 .5 03 0 3 .0 0 2 .8 0 2 .8 03 3 8 .0 0 3 .2 0 3 .0 03 5 9 .5 0 3 .5 0 3 .2 53 9 0 .5 0 3 .8 0 3 .4 74 2 3 .0 0 4 .2 0 3 .7 94 4 1 .0 0 4 .5 0 4 .0 54 6 5 .0 0 4 .8 0 4 .2 94 9 0 .0 0 5 .2 0 4 .6 35 1 5 .0 0 5 .6 0 4 .9 75 2 8 .0 0 5 .8 0 5 .1 45 5 0 .0 0 6 .2 0 5 .4 9

V apou r rate = 67 .0 7 dm 3 /mt i= 1 0 0 .6 5 8 -1 0 0 .4 4 9 o CPatm = 7 6 8 To rr

1 2 5 .0 0 0 .8 0 0 .8 01 4 1 .0 0 1 .00 1 .001 6 3 .0 0 1 .20 1 .201 8 0 .0 0 1 .40 1 .401 9 4 .0 0 1 .60 1 .602 0 8 .0 0 1 .80 1 .8 02 2 3 .0 0 2 .0 0 2 .0 02 4 8 .0 0 2 .3 0 2 .3 02 7 6 .0 0 2 .6 0 2 .6 03 1 6 .0 0 3 .0 0 2 .8 53 3 7 .0 0 3 .3 0 3 .1 03 6 6 .0 0 3 .6 0 3 .3 34 0 2 .0 0 4 .0 0 3 .6 54 2 3 .0 0 4 .3 0 3 .8 94 4 6 .0 0 4 .6 0 4 .1 44 7 5 .0 0 5 .0 0 4 .4 74 9 2 .0 0 5 .3 0 4 .7 35 1 4 .0 0 5 .6 0 4 .9 85 3 9 .0 0 6 .0 0 5 .3 2

Pc Pc/Pu 1 /C A gN6 .4 0 1 .0 8 0 .2 46.11 1 .03 0 .315.71 0 .9 7 0 .4 05 .6 5 0 .9 5 0 .4 75 .4 2 0 .9 2 0 .5 55 .2 2 0 .8 8 0 .6 44 .6 9 0 .7 9 0 .8 64 .2 5 0 .7 2 1 .063.81 0 .6 4 1.313 .2 8 0 .5 5 1.613 .1 4 0 .5 3 1 .8 02 .8 5 0 .4 8 2 .1 02 .6 5 0 .4 5 2 .4 32 .6 0 0 .4 4 2 .6 22 .4 8 0 .4 2 2 .8 92.41 0 .41 3 .1 82 .3 4 0 .4 0 3 .4 82 .3 0 0 .3 9 3 .6 42 .2 7 0 .3 8 3.91

6 .4 0 1 .0 8 0 .2 46 .2 8 1 .0 6 0 .3 05 .6 4 0 .9 5 0 .3 95 .4 0 0 .91 0 .4 75.31 0 .9 0 0 .5 55 .2 0 0 .8 8 0 .6 25 .0 2 0 .8 5 0.714 .6 7 0 .7 9 0 .8 64 .2 6 0 .7 2 1 .063 .5 7 0 .6 0 1 .353 .41 0 .5 8 1 .523.11 0 .5 2 1 .772 .8 2 0 .4 8 2 .0 92 .7 2 0 .4 6 2 .2 92 .6 0 0 .4 4 2 .5 22 .4 8 0 .4 2 2 .8 22 .4 4 0 .41 3 .0 02 .3 5 0 .4 0 3 .2 42 .2 9 0 .3 9 3 .5 2

APPENDIX 2. 182

Data fo r the Rush ton 180m m im pe lle r5 5 8 .0 0

V apou r rate =6 .3 5

27 .31 dm 3/m in5 .6 2 2 .2 6 0 .3 8 3 .7 4

1 2 6 .0 0 0 .8 0 0 .8 0 6 .3 0 1 .06 0 .2 41 4 3 .0 0 1 .00 1 .00 6.11 1 .03 0.311 6 0 .0 0 1 .20 1 .20 5 .8 6 0 .9 9 0 .3 81 7 5 .0 0 1 .40 1 .40 5.71 0 .9 6 0 .4 51 9 0 .0 0 1 .6 0 1 .60 5 .5 4 0 .9 4 0 .5 22 0 4 .0 0 1 .80 1 .8 0 5 .4 0 0 .91 0 .6 02 1 8 .0 0 2 .0 0 2 .0 0 5 .2 6 0 .8 9 0 .6 83 9 8 .0 0 4 .0 0 3 .6 5 2 .8 8 0 .4 9 2 .0 34 7 5 .0 0 5 .1 0 4 .5 7 2 .53 0 .4 3 2 .7 85 5 1 .0 0 6 .3 5 5 .6 4 2 .3 2 0 .3 9 3 .5 9

V ap o u r rate = 104 .67d m 3/m in , t= 1 0 0 .4 3 3 -1 0 0 .2 2 3 , Patm = 76 2 T o rr1 2 4 .0 0 0 .8 0 0 .8 0 6 .5 0 1 .1 0 0 .2 31 3 8 .0 0 1 .00 1 .00 6 .5 6 1.11 0 .2 91 5 7 .0 0 1 .20 1 .2 0 6 .0 8 1 .03 0 .3 71 7 4 .0 0 1 .40 1 .40 5 .7 8 0 .9 8 0 .4 61 8 6 .0 0 1 .6 0 1 .60 5 .7 8 0 .9 8 0 .5 22 0 3 .0 0 1 .8 0 1 .80 5 .4 6 0 .9 2 0.612 1 6 .0 0 2 .0 0 2 .0 0 5 .3 6 0 .9 0 0 .6 92 7 3 .0 0 2 .5 0 2 .5 0 4 .1 9 0.71 1 .063 2 0 .0 0 3 .0 0 2 .9 6 3.61 0.61 1.413 6 4 .5 0 3 .5 0 3 .3 5 3 .1 5 0 .5 3 1 .794 0 5 .0 0 4 .0 0 3 .7 6 2 .87 0 .4 8 2 .1 54 4 1 .0 0 4 .5 0 4 .1 8 2 .69 0 .4 5 2 .5 04 7 5 .0 0 5 .0 0 4 .6 0 2 .55 0 .4 3 2 .8 45 0 7 .5 0 5 .5 0 5 .0 3 2 .4 4 0.41 3 .1 85 4 1 .0 0 6 .0 5 5 .5 0 2 .35 0 .4 0 3 .5 55 6 1 .0 0 6 .4 5 5 .8 6 2 .3 3 0 .3 9 3 .7 75 2 0 .0 0 5 .8 0 5 .3 0 2 .45 0 .41 3 .3 24 9 0 .0 0 5 .3 0 4 .8 7 2 .5 3 0 .4 3 3 .0 04 5 5 .0 0 4 .7 0 4 .3 5 2 .6 2 0 .4 4 2 .6 44 2 0 .0 0 4 .2 5 3 .9 8 2 .8 2 0 .4 8 2 .2 93 3 9 .5 0 3 .2 5 3 .1 6 3 .4 3 0 .5 8 1 .57

APPENDIX 2.

Data fo r the Rush ton 180m m im pe lle r h e ig h t= 450m m c learance = 225m m ti = 2 0 .6 3 o C

I Torq.[Nm ] Tor. real Pu1 2 4 .5 0 0 .8 0 0 .8 0 6 .1 91 3 8 .0 0 1 .00 1 .00 6 .3 01 5 3 .0 0 1 .20 1 .2 0 6 .1 51 6 4 .0 0 1 .40 1 .40 6 .2 41 7 6 .0 0 1 .60 1 .60 6 .1 91 8 6 .0 0 1 .80 1 .80 6 .2 41 9 6 .0 0 2 .0 0 2 .0 0 6 .2 42 1 1 .0 0 2 .3 0 2 .3 0 6 .1 92 2 2 .0 0 2 .6 0 2 .6 0 6 .3 32 3 9 .0 0 3 .0 0 3 .0 0 6 .3 02 7 1 .0 0 3 .6 0 3 .6 0 5 .8 82 8 6 .0 0 4 .0 0 4 .0 0 5 .8 63 0 9 .0 0 4 .6 0 4 .6 0 5 .7 83 1 9 .0 0 5 .0 0 4.91 5 .7 93 4 1 .0 0 5 .6 0 5 .4 6 5 .6 33 6 0 .0 0 6 .0 0 5 .8 2 5 .3 83 8 0 .0 0 6 .5 0 6 .2 7 5.213 9 9 .0 0 7 .0 0 6 .7 3 5 .0 74 2 0 .0 0 7 .5 0 7 .1 8 4 .8 84 4 6 .0 0 8 .0 0 7 .6 2 4 .5 94 6 9 .0 0 8 .5 0 8 .0 7 4 .4 05 0 5 .0 0 9 .0 0 8 .4 8 3 .9 9

in va lue o f co ld Pow er num ber 6 .2 0

APPENDIX 2. 184

Data for the Rushton 180mm impellerh e ig h t= 4 5 0 m m c lea rance = 225m mti= 1 0 0 .5 9 2 -1 0 0 .3 9 3 , Patm = 7 6 6 To rr V ap ou r ra te= 10 4 .6 7d m 3 /m in

M Torq.[Nm ] Tor. real Pc Pc/Pu 1/CAgN1 2 6 .0 0 0 .8 0 0 .8 0 6 .3 0 1 .02 0 .3 21 4 7 .0 0 1 .00 1 .00 5 .7 8 0 .9 3 0 .4 31 6 5 .5 0 1 .20 1 .20 5 .4 7 0 .8 8 0 .5 41 8 2 .0 0 1 .40 1 .40 5 .2 8 0 .8 5 0 .6 52 0 4 .0 0 1 .60 1 .60 4 .8 0 0 .7 7 0 .8 02 2 2 .0 0 1 .80 1 .80 4 .5 6 0 .7 4 0 .9 42 4 6 .0 0 2 .0 0 2 .0 0 4 .1 3 0 .6 7 1 .132 7 2 .0 0 2 .3 0 2 .3 0 3 .8 8 0 .6 3 1 .362 9 7 .0 0 2 .6 0 2 .5 0 3 .5 4 0 .5 7 1 .593 3 6 .0 0 3 .0 0 2 .8 0 3 .1 0 0 .5 0 1 .983 6 3 .0 0 3 .3 0 3 .0 4 2 .8 8 0 .4 6 2 .2 73 8 4 .0 0 3 .6 0 3 .2 9 2 .7 9 0 .4 5 2 .5 04 1 2 .0 0 4 .0 0 3 .6 2 2 .6 7 0 .4 3 2 .8 34 3 3 .0 0 4 .3 0 3 .8 7 2 .5 8 0 .4 2 3 .0 84 5 3 .0 0 4 .6 0 4 .1 2 2.51 0 .4 0 3 .3 34 7 6 .0 0 5 .0 0 4 .4 7 2 .4 6 0 .4 0 3 .6 34 9 7 .0 0 5 .3 0 4 .7 2 2 .39 0 .3 8 3 .9 05 1 3 .0 0 5 .6 0 4 .9 8 2 .3 6 0 .3 8 4 .1 25 3 8 .0 0 6 .0 0 5 .3 2 2 .3 0 0 .3 7 4 .4 65 6 4 .0 0 6 .3 0 5 .5 6 2 .1 8 0 .3 5 4 .8 3

i= 1 0 0 .6 0 1 -1 0 0 .3 2 4 o C (r Patm = 7 6 6 Torr, vapou r rate = 67 ,0 7 d n1 3 0 .0 0 0 .8 0 0 .8 0 5.91 0 .9 5 0 .3 41 4 7 .0 0 1 .00 1 .00 5 .7 8 0 .9 3 0 .4 31 6 7 .0 0 1 .20 1 .20 5 .3 8 0 .8 7 0 .5 41 8 1 .0 0 1 .40 1 .40 5 .3 4 0 .8 6 0 .6 32 0 1 .0 0 1 .60 1 .60 4 .9 5 0 .8 0 0 .7 62 1 9 .0 0 1 .80 1 .8 0 4 .6 9 0 .7 6 0 .8 82 3 9 .0 0 2 .0 0 2 .0 0 4 .3 7 0 .71 1 .032 6 1 .0 0 2 .3 0 2 .3 0 4 .2 2 0 .6 8 1 .202 9 0 .0 0 2 .6 0 2 .6 0 3 .8 6 0 .6 2 1 .453 2 5 .0 0 3 .0 0 2 .8 3 3 .3 5 0 .5 4 1 .763 5 4 .0 0 3 .3 0 3 .0 6 3 .0 5 0 .4 9 2 .0 43 7 6 .0 0 3 .6 0 3.31 2 .92 0 .4 7 2 .2 64 0 7 .0 0 4 .0 5 3 .6 8 2 .7 8 0 .4 5 2 .5 84 2 6 .0 0 4 .3 0 3 .8 9 2 .6 8 0 .4 3 2 .7 84 4 6 .0 0 4 .6 0 4 .1 4 2 .6 0 0 .4 2 3 .0 04 7 1 .0 0 5 .0 0 4 .4 8 2 .52 0 .41 3 .2 94 8 8 .0 0 5 .3 0 4 .7 4 2 .4 9 0 .4 0 3 .4 85 0 5 .0 0 5 .6 0 5 .0 0 2 .4 5 0 .3 9 3 .6 85 3 4 .0 0 6 .0 5 5 .3 8 2 .3 6 0 .3 8 4 .0 35 6 2 .0 0 6 .5 0 5 .7 6 2 .2 8 0 .3 7 4 .3 7

APPENDIX 2.

Data fo r the Rush ton 180m m im pe lle r h e ig h t= 4 5 0 m m ,c le a r . = 22 5m m

ti = 4 1 .3 oC , vapou r qu ided to the free su rface1 2 4 .5 0 0 .8 0 0 .8 0 6 .2 31 3 7 .0 0 1 .00 1 .00 6 .4 31 4 9 .0 0 1 .20 1 .20 6 .5 21 6 3 .0 0 1 .40 1 .40 6 .3 61 7 5 .0 0 1 .60 1 .60 6 .3 01 8 4 .5 0 1 .80 1 .80 6 .3 81 9 5 .0 0 2 .0 0 2 .0 0 6 .3 52 1 0 .0 0 2 .3 0 2 .3 0 6 .2 92 2 3 .0 0 2 .6 0 2 .6 0 6.312 4 0 .5 0 3 .0 0 3 .0 0 6 .2 62 6 4 .0 0 3 .6 0 3 .6 0 6 .232 7 8 .0 0 4 .0 0 4 .0 0 6 .2 42 9 9 .0 0 4 .6 0 4 .6 0 6.213 1 3 .0 0 5 .0 0 5 .0 0 6 .1 63 3 3 .0 0 5 .6 0 5 .5 3 6.013 4 5 .0 0 6 .0 0 5 .9 0 5 .9 83 6 8 .0 0 6 .5 0 6 .3 5 5 .653 8 8 .0 0 7 .0 0 6 .8 0 5 .4 54 0 7 .0 0 7 .5 0 7 .2 6 5 .294 2 3 .0 0 8 .0 0 7 .7 2 5.214 4 1 .0 0 8 .5 0 8 .1 8 5 .0 74 5 8 .0 0 9 .0 0 8 .6 4 4 .9 74 7 8 .0 0 9 .5 5 9 .1 5 4 .8 3an va lue o f Pu 6 .31

APPENDIX 2. 186

Data for the Rushton 180mm impellerhe igh t = 45 0m m ,c le a ran ce = 22 5m m , Patm = 7 5 0 Torr, vap .ra te= 10 4 .6 7d m 3/m in t i= 1 0 0 .0 3 4 -9 9 .8 3 9 o C , vapou r qu ided to the free su rface

8 1 .0 0 0 .4 0 0 .4 01 2 4 .0 0 0 .8 0 0 .8 01 4 2 .0 0 1 .00 1 .0 01 6 2 .0 0 1 .20 1 .2 01 7 5 .0 0 1 .40 1 .401 9 4 .0 0 1 .60 1 .602 1 2 .0 0 1 .80 1 .8 02 4 0 .0 0 2 .0 0 2 .0 02 7 2 .0 0 2 .3 0 2 .3 03 0 0 .0 0 2 .6 0 2 .6 03 4 2 .0 0 3 .0 0 2.913 6 2 .0 0 3 .3 0 3 .1 63 9 3 .0 0 3 .6 5 3 .4 44 1 5 .0 0 4 .0 0 3 .7 44 4 1 .0 0 4 .3 0 3 .9 84 6 1 .0 0 4 .6 0 4 .2 34 7 8 .0 0 5 .0 0 4 .6 05 0 3 .0 0 5 .3 0 4 .8 45 2 0 .0 0 5 .6 0 5 .1 05 6 0 .0 0 6 .0 0 5.41

h e ig h t= 4 5 0 m m , c lear. = 225m m ti = 1 0 0 .0 7 9 -9 9 .8 3 5 o C , Patm = 7 5 0 .5

1 2 6 .0 0 0 .8 0 0 .8 01 4 8 .0 0 1 .00 1 .001 6 9 .0 0 1 .20 1 .201 8 6 .0 0 1 .40 1 .402 0 4 .0 0 1 .60 1 .602 2 9 .0 0 1 .80 1 .802 5 2 .0 0 2 .0 0 2 .0 02 7 8 .0 0 2 .3 0 2 .3 03 0 4 .0 0 2 .6 0 2 .6 03 4 2 .0 0 3 .0 0 2.913 6 5 .0 0 3 .3 0 3 .1 53 8 6 .0 0 3 .6 0 3 .414 1 9 .0 0 4 .0 0 3 .7 34 4 5 .0 0 4 .3 0 3 .9 74 5 9 .0 0 4 .6 0 4 .2 44 8 6 .0 0 5 .0 0 4 .5 85 0 9 .0 0 5 .3 0 4 .8 35 2 4 .0 0 5 .6 0 5 .0 95 5 7 .0 0 6 .0 0 5 .4 2

7 .6 2 1.21 0 .1 36 .5 0 1 .03 0 .3 06 .2 0 0 .9 8 0 .3 95.71 0 .91 0 .5 05.71 0 .91 0 .5 85.31 0 .8 4 0 .7 05 .0 0 0 .7 9 0 .8 34 .3 4 0 .6 9 1 .053 .8 8 0 .6 2 1 .323.61 0 .5 7 1 .583 .1 0 0 .4 9 2 .0 03.01 0 .4 8 2 .2 22 .7 8 0 .4 4 2 .5 72.71 0 .4 3 2 .8 32 .5 6 0 .41 3 .1 52 .4 9 0 .3 9 3.412.51 0 .4 0 3 .6 32 .39 0 .3 8 3 .9 72 .3 6 0 .3 7 4.212 .1 6 0 .3 4 4 .7 8

*. = 104 .67d m 3/m in6 .3 0 1 .00 0 .3 25 .7 0 0 .9 0 0 .4 45 .25 0 .8 3 0 .5 65 .0 6 0 .8 0 0 .6 74 .8 0 0 .7 6 0 .7 94 .2 9 0 .6 8 0 .9 83 .9 3 0 .6 2 1 .163 .7 2 0 .5 9 1 .383 .5 2 0 .5 6 1.613 .1 0 0 .4 9 1 .982 .9 6 0 .4 7 2.212 .8 6 0 .4 5 2 .4 32 .6 6 0 .4 2 2 .7 92.51 0 .4 0 3 .0 92.51 0 .4 0 3 .2 52 .42 0 .3 8 3 .5 72 .33 0 .3 7 3 .8 52 .3 2 0 .3 7 4 .0 42 .1 8 0 .3 5 4 .4 6

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APPENDIX 2. 190Data for the hollow bladed 1 80mm impellerfaces o f blades concaveHeigth = 450mmclearance — 150mm

ti = 26.62oCRPM TorquelNm] Torq.reaUNn: Pu

164.00 0.80 0.80 3.57184.00 1.00 1.00 3.56204.00 1.20 1.19 3.45222.00 1.40 1.38 3.37239.00 1.60 1.57 3.31253.00 1.80 1.76 3.31267.00 2.00 1.95 3.29281.00 2.20 2.14 3.25297.00 2.40 2.32 3.16307.00 2.60 2.51 3.20319.00 2.80 2.70 3.19329.00 3.00 2.89 3.20,350.00 3.40 3.26 3.20372.00 3.80 3.63 3.15383.00 4.00 3.81 3.12403.00 4.40 4.18 3.09421.00 4.78 4.53 3.07452.00 5.57 5.27 3.10500.00 7.00 6.60 3.17546.00 8.45 7.95 3.20

Mean cold power number faces o f blades convex

3.40

ti = 26.82oC

135.00 0.80 0.80 5.27155.00 1.00 1.00 5.00190.00 1.40 1.40 4.66220.00 1.80 1.78 4.43231.00 2.00 1.98 4.45248.00 2.20 2.17 4.23257.00 2.40 2.36 4.29271.00 2.60 2.55 4.17291.00 3.00 2.93 4.15317.00 3.50 3.40 4.07338.00 4.00 3.88 4.08363.00 4.50 4.34 3.96386.00 5.00 4.81 3.88409.00 5.50 5.27 3.79450.00 6.50 6.20 3.68500.00 7.50 7.10 3.41545.00 8.40 7.90 3.20

Mean cold power number 4.64

APPENDIX 2. 191Data for the hollow bladed 1 80mm impellerfaces o f blades concaveHeigth = 450mmclearance = 150mmPatm = 750 Torrti = 100.159-99.947oC

M Torq.INm] Torq.reallNm Pc Pc/Pu 1/CAgN167.00 0.80 0.80 3.58 1.05 0.42180.00 1.00 1.00 3.87 1.14 0.48217.00 1.40 1.39 3.68 1.08 0.69251.00 1.80 1.76 3.50 1.03 0.90267.50 2.00 1.95 3.40 1.00 1.01304.00 2.40 2.32 3.13 0.92 1.28344.00 2.80 2.67 2.82 0.83 1.60363.00 3.00 2.84 2.70 0.79 1.76397.00 3.40 3.19 2.53 0.75 2.07428.00 3.80 3.54 2.42 0.71 2.36441.00 4.00 3.72 2.39 0.70 2.49474.00 4.40 4.06 2.26 0.66 2.83499.00 4.80 4.41 2.21 0.65 3.09515.00 5.00 4.57 2.15 0.63 3.26539.00 5.40 4.92 2.11 0.62 3.53567.00 5.80 5.25 2.04 0.60 3.85

faces o f blades convex ti= 100.194-100.025oC

154.00 0.80 0.80 4.21 0.91 0.36178.50 1.00 1.00 3.92 0.85 0.48233.00 1.40 1.38 3.17 0.68 0.79284.00 1.80 1.74 2.69 0.58 1.14312.00 2.00 1.91 2.45 0.53 1.36371.00 2.40 2.23 2.03 0.44 1.88416.00 2.80 2.56 1.85 0.40 2.32442.00 3.00 2.72 1.74 0.37 2.59473.00 3.40 3.06 1.71 0.37 2.92510.00 3.80 3.38 1.62 0.35 3.35525.00 4.00 3.55 1.61 0.35 3.52555.00 4.40 3.88 1.57 0.34 3.89581.00 4.75 4.17 1.54 0.33 4.22

APPENDIX 2. 192Data for the hollow bladed 1 80mm impellerfaces o f blades concave Height= 450mm clearance = 225mm

ti = 39.25oCRPM TorquelNm] Torq.reallNnr Pu

167.00 0.80 0.80 3.46187.00 1.00 1.00 3.46205.00 1.20 1.19 3.43226.00 1.40 1.38 3.26241.00 1.60 1.57 3.26255.00 1.80 1.76 3.27268.00 2.00 1.95 3.27283.00 2.20 2.14 3.22295.00 2.40 2.32 3.22308.00 2.60 2.51 3.19317.00 2.80 2.70 3.24329.00 3.00 2.89 3.22351.00 3.40 3.26 3.19369.00 3.80 3.63 3.22377.00 4.00 3.82 3.25395.00 4.40 4.20 3.24410.00 4.80 4.57 3.28422.00 5.00 4.75 3.22452.00 5.90 5.60 3.31504.00 7.40 7.00 3.32547.00 8.55 8.05 3.25

Mean cold power number 3.40faces o f blades convexti = 36.85oC

145.00 0.80 0.81 4.68161.00 1.00 1.01 4.70178.00 1.20 1.21 4.59196.00 1.40 1.40 4.39210.00 1.60 1.59 4.35227.00 1.80 1.78 4.17243.00 2.00 1.97 4.02252.00 2.20 2.16 4.11268.00 2.40 2.35 3.95279.00 2.60 2.54 3.94288.00 2.80 2.73 3.97301.00 3.00 2.92 3.89320.00 3.40 3.30 3.88340.00 3.80 3.67 3.83352.00 4.00 3.86 3.76370.00 4.40 4.23 3.73391.00 4.80 4.60 3.63400.00 5.00 4.79 3.61455.00 5.90 5.59 3.26509.00 6.80 6.38 2.97552.00 7.65 7.14 2.83


APPENDIX 2. 193Data for the hollow bladed 1 80mm impellerfaces o f blades concave Heights 450mm clearance = 225mm Patm = 750 Torr ti = 100.151-99.862

RPM Torq.tNm] Torq.real[Nm Pc Pc/Pu 1 /CAgN 1/CAgN*cor157.00 0.80 0.80 4.06 1.19 0.53 0.41181.00 1.00 1.00 3.83 1.13 0.69 0.53218.00 1.40 1.39 3.64 1.07 0.95 0.74254.00 1.80 1.76 3.41 1.00 1.24 0.97277.00 2.00 1.94 3.16 0.93 1.44 1.12316.00 2.40 2.30 2.88 0.85 1.80 1.40350.00 2.80 2.66 2.71 0.80 2.13 1.66375.00 3.00 2.83 2.51 0.74 2.39 1.86393.00 3.40 3.20 2.59 0.76 2.58 2.01426.00 3.80 3.55 2.44 0.72 2.94 2.29443.00 4.00 3.72 2.37 0.70 3.13 2.43471.00 4.40 4.06 2.29 0.67 3.45 2.68499.00 4.80 4.41 2.21 0.65 3.78 2.94512.00 5.00 4.58 2.18 0.64 3.93 3.06536.00 5.40 4.92 2.14 0.63 4.22 3.29563.00 5.80 5.26 2.07 0.61 4.56 3.55570.00 5.95 5.39 2.07 0.61 4.65 3.61

faces o f blades convex ti = 100.139-99.932oC

160.00 0.80 0.81 3.96 0.86 0.57 0.44195.00 1.00 1.00 3.28 0.71 0.82 0.64253.00 1.40 1.36 2.66 0.58 1.31 1.02307.00 1.80 1.71 2.27 0.49 1.84 1.43334.00 2.00 1.88 2.11 0.46 2.12 1.65371.00 2.40 2.23 2.03 0.44 2.54 1.98412.00 2.80 2.57 1.89 0.41 3.03 2.36425.00 3.00 2.75 1.90 0.41 3.20 2.49460.00 3.40 3.08 1.82 0.40 3.64 2.83489.00 3.80 3.43 1.79 0.39 4.03 3.13508.00 4.00 3.59 1.74 0.38 4.29 3.34538.00 4.40 3.92 1.69 0.37 4.71 3.66567.50 4.80 4.25 1.65 0.36 5.13 3.99578.00 4.90 4.32 1.62 0.35 5.28 4.11

APPENDIX 2. 194Data for the hollow bladed 180mm impellerfaces o f blades concave Height= 580mm clearance = 150mm

ti = 23.7oCRPM TorquelNm] Torq.reallNrr Pu

158.00 0.80 0.80 3.84181.50 1.00 1.00 3.65216.00 1.40 1.39 3.57250.00 1.80 1.76 3.38265.00 2.00 1.95 3.33279.00 2.20 2.14 3.30291.00 2.40 2.33 3.30302.00 2.60 2.52 3.31316.00 2.80 2.70 3.24327.00 3.00 2.89 3.24350.00 3.40 3.26 3.19369.00 3.80 3.63 3.20380.00 4.00 3.82 3.17399.00 4.40 4.19 3.16418.00 4.80 4.56 3.13425.00 5.00 4.75 3.15450.00 5.55 5.25 3.11500.00 6.80 6.40 3.07548.00 8.20 7.70 3.07


faces o f blades convex ti = 23.8oC

140.00 0.80 0.80 4.89156.00 1.00 1.00 4.93194.00 1.40 1.40 4.46220.00 1.80 1.78 4.42234.00 2.00 1.98 4.33259.00 2.40 2.36 4.21280.00 2.80 2.74 4.19289.00 3.00 2.93 4.21311.00 3.40 3.31 4.10328.00 3.80 3.69 4.11337.00 4.00 3.88 4.09361.00 4.50 4.35 4.00379.00 5.00 4.82 4.02397.00 5.50 5.29 4.03452.00 7.00 6.70 3.93500.00 8.55 8.15 3.91526.00 9.45 9.00 3.90


APPENDIX 2. 195Data for the hollow bladed 180mm impellerfaces o f blades concave Height=580mm clearance = 150mm Patm = 734 Torr ti = 99.790-99.578oC

RPM Torq.INm] Torq.real[Nm Pc Pc/Pu 1/CAgN161.00 0.80 0.80 3.86 1.09 0.28185.00 1.00 1.00 3.66 1.04 0.36212.00 1.40 1.39 3.86 1.09 0.47241.00 1.80 1.77 3.81 1.08 0.60255.00 2.00 1.96 3.77 1.07 0.66284.00 2.40 2.34 3.62 1.02 0.81311.00 2.80 2.71 3.50 0.99 0.96328.00 3.00 2.89 3.35 0.95 1.06358.00 3.40 3.25 3.17 0.90 1.25391.00 3.80 3.60 2.94 0.83 1.47407.00 4.00 3.78 2.85 0.81 1.58438.50 4.40 4.12 2.68 0.76 1.81467.50 4.80 4.47 2.56 0.72 2.03482.00 5.00 4.64 2.50 0.71 2.15516.00 5.50 5.07 2.38 0.67 2.42570.00 6.30 5.74 2.21 0.62 2.89

faces o f blades convex ti = 99.73-99

151.00 0.80 0.80 4.38 0.95 0.24170.00 1.00 1.00 4.32 0.94 0.30207.50 1.40 1.39 4.04 0.88 0.45250.50 1.80 1.76 3.51 0.76 0.64272.00 2.00 1.95 3.29 0.71 0.75320.00 2.40 2.30 2.80 0.61 1.01366.00 2.80 2.64 2.46 0.53 1.30387.00 3.00 2.81 2.34 0.51 1.44442.00 3.40 3.12 1.99 0.43 1.84474.50 3.80 3.46 1.92 0.42 2.09495.00 4.00 3.61 1.84 0.40 2.26526.00 4.40 3.95 1.78 0.39 2.52556.00 4.80 4.28 1.73 0.38 2.79579.00 5.10 4.52 1.68 0.37 3.00

APPENDIX 2. 196Data for the hollow bladed 180mm impellerfaces o f blades concaveHeight=450mmclearance = 190mm

ti = 36.86oCRPM TorquetNm] Torq.reallNrr Pu

170.00 0.80 0.80 3.33192.00 1.00 1.00 3.27210.00 1.20 1.19 3.25228.00 1.40 1.38 3.20242.00 1.60 1.57 3.23259.00 1.80 1.76 3.15273.00 2.00 1.95 3.14288.00 2.20 2.13 3.09300.00 2.40 2.32 3.10313.00 2.60 2.51 3.08322.00 2.80 2.70 3.13335.00 3.00 2.88 3.09356.00 3.40 3.25 3.09373.00 3.80 3.63 3.14382.00 4.00 3.82 3.15399.00 4.40 4.19 3.17415.00 4.80 4.56 3.19423.00 5.00 4.75 3.20451.00 5.75 5.45 3.23502.00 7.25 6.85 3.27545.00 8.45 7.95 3.22

Mean cold power number 3.33feces o f blades convexti = 36.92oC

145.00 0.80 0.80 4.58161.00 1.00 1.00 4.65182.00 1.20 1.20 4.38197.00 1.40 1.40 4.34215.00 1.60 1.59 4.14227.00 1.80 1.78 4.16240.00 2.00 1.97 4.12255.00 2.20 2.16 4.00266.00 2.40 2.35 4.00277.50 2.60 2.54 3.97288.00 2.80 2.73 3.97300.00 3.00 2.92 3.91318.00 3.40 3.30 3.93337.00 3.80 3.68 3.90346.00 4.00 3.87 3.89366.00 4.40 4.24 3.81384.00 4.80 4.61 3.77396.00 5.00 4.80 3.68454.00 6.00 5.70 3.33502.00 6.80 6.40 3.06553.00 7.75 7.23 2.85


APPENDIX 2. 197Data for the hollow bladed 180mm impellerfaces o f blades concaveHeight= 450mm clearance = 190mm Patm = 750Torr ti = 100.134-99.892oC RPM Torq.[Nm] Torq.realfNm Pc Pc/Pu 1/CAgN 1/CAgN*coi

159.00 0.80 0.80 3.95 1.19 0.46 0.42178.00 1.00 1.00 3.94 1.18 0.56 0.52216.00 1.40 1.39 3.71 1.11 0.81 0.74251.00 1.80 1.76 3.50 1.05 1.06 0.98271.00 2.00 1.95 3.31 0.99 1.21 1.12313.00 2.40 2.31 2.94 0.88 1.57 1.45344.00 2.80 2.67 2.82 0.85 1.85 1,71366.00 3.00 2.84 2.65 0.79 2.06 1 -90400.00 3.40 3.19 2.49 0.75 2.40 2.22421.50 3.80 3.55 2.50 0.75 2.62 2.43441.00 4.00 3.72 2.39 0.72 2.83 2.62469.00 4.40 4.07 2.31 0.69 3.14 2.91496.00 4.80 4.41 2.24 0.67 3.45 3.19510.00 5.00 4.58 2.20 0.66 3.61 3.34534.00 5.40 4.93 2.16 0.65 3.90 3.61562.00 5.80 5.26 2.08 0.62 4.24 3.92572.00 5.90 5.34 2.04 0.61 4.37 4.04

faces o f blades convex ti = 100.173-99.98oC

146.00 0.80 0.80 4.69 1.01 0.39 0.36171.00 1.00 1.00 4.27 0.92 0.52 0.48233.00 1.40 1.38 3.17 0.68 0.93 0.86290.00 1.80 1.73 2.57 0.55 1.39 1.29312.00 2.00 1.91 2.45 0.53 1.59 1.47365.00 2.40 2.24 2.10 0.45 2.11 1.95402.00 2.80 2.59 2.00 0.43 2.50 2.32419.00 3.00 2.76 1.96 0.42 2.70 2.50454.00 3.40 3.10 1.88 0.40 3.10 2.87482.00 3.80 3.44 1.85 0.40 3.45 3.19502.00 4.00 3.60 1.78 0.38 3.70 3.42538.00 4.40 3.92 1.69 0.36 4.17 3.86568.00 4.80 4.25 1.65 0.35 4.57 4.23579.00 5.00 4.42 1.65 0.35 4.72 4.37

APPENDIX 2. 198

Data for the 225mm 6biade 45o axial impellerheight=450mm clearance = 150mm downwards pumping

ti = 49.6oC Torq.INm] RPM

0.80 122.001.00 139.001.20 152.001.40 167.001.60 176.001.80 188.002.00 198.002.45 221.002.80 236.003.30 253.003.60 267.004.00 281.004.40 294.004.80 308.005.20 322.005.60 333.006.00 344.006.40 356.007.00 375.008.15 400.008.90 422.00

Mean value of Pu

Torq.real[Nm Pu0.80 2.131.00 2.051.20 2.061.40 1.991.60 2.051.80 2.022.00 2.032.45 1.992.80 2.003.30 2.053.58 1.993.96 1.994.35 2.004.74 1.985.12 1.965.51 1.975.89 1.986.28 1.976.85 1.937.97 1.988.68 1.93

2.02

APPENDIX 2. 199

Data for the 225mm 6biade 45o axial impellerheight=450mm clearance = 150mm downwards pumpingvapour rate = 104dm3/mindownwards t = 100.775-100.524oC,Patm = 765TorrTorquelNm] RPM Torq..real[Nm Pc/Pu

0.80 124.00 0.80 1.051.00 144.00 1.00 0.981.20 161.00 1.20 0.941.40 175.00 1.40 0.921.60 191.00 1.60 0.891.80 204.00 1.80 0.872.00 217.00 2.00 0.862.40 240.00 2.40 0.842.80 266.00 2.80 0.803.20 292.00 3.15 0.753.60 318.00 3.53 0.714.00 349.00 3.89 0.654.40 380.00 4.25 0.594.80 404.00 4.61 0.575.20 436.00 4.96 0.536.10 503.00 5.72 0.466.90 553.00 6.41 0.42

vapour rate = 67dm3/mindownwards, ti= 1 00.749-100.530oC

0.80 121.00 0.80 1.111.00 131.00 1.00 1.181.40 166.00 1.40 1.031.80 193.00 1.80 0.982.50 231.00 2.50 0.953.40 285.00 3.36 0.844.00 333.00 3.91 0.714.80 380.00 4.65 0.655.20 417.00 4.99 0.586.00 478.00 5.68 0.50

vapour rate = 27.3 dm3/mindownwards, ti= 100.700-100.,443oC

0.80 122.00 0.80 1.091.20 150.00 1.20 1.081.40 165.00 1.40 1.041.65 176.00 1.65 1.082.05 202.00 2.05 1.023.20 268.00 3.18 0.894.25 317.00 4.18 0.845.00 355.00 4.88 0.785.90 423.00 5.68 0.646.85 483.00 6.52 0.56

1/CAgN 0.36 0.49 0.60 0.70 0.83 0.94 1.05 1.27 1.53 1.81 2.11 2.48 2.89 3.21 3.67 4.69 5.50

0.340.400.630.831.161.702.252.853.354.24

0.350.530.630.710.911.512.032.463.314.11

APPENDIX 2. 200

Data for the 225mm 6blade 45o axial impellerheight= 450mm clearance = 225mm downwards pumping

ti = 48.49oCTorq.INm] RPM Torq.real Pu

0.80 111.00 0.80 2.581.00 123.00 1.00 2.621.20 136.00 1.20 2.581.45 150.00 1.45 2.561.60 157.00 1.60 2.581.80 168.00 1.80 2.532.00 177.00 2.00 2.532.40 195.00 2.40 2.513.20 232.00 3.20 2.364.00 269.00 3.98 2.184.90 306.00 4.84 2.056.30 382.00 6.14 1.67

Mean value of Pu 2.58

APPENDIX 2. 201

Data for the 225mm 6blade 45o axial impellerheight=450mm clearance = 225mm downwards pumping

vapour rate — 104dm3/min ti = 100.644-100.535oC, Patm = 763.5TorrTorquelNm] RPM Torq.reallNrr Pc/Pu 1/CAgN

0.80 112.00 0.80 1.01 0.391.00 128.00 1.00 0.97 0.511.20 145.00 1.20 0.90 0.661.45 160.00 1.45 0.90 0.801.60 174.00 1.60 0.84 0.941.80 182.00 1.80 0.86 1.032.15 202.00 2.15 0.84 1.252.50 226.00 2.50 0.78 1.552.85 260.00 2.85 0.67 2.023.10 284.00 3.06 0.60 2.383.55 343.00 3.45 0.46 3.384.00 388.00 3.83 0.40 4.234.75 432.00 4.51 0.38 5.145.30 471.00 4.99 0.36 6.015.75 509.00 5.36 0.33 6.90

vapour rate== 67dm3/minti= 100.555-100.454oC

0.80 112.00 0.80 1.01 0.391.30 141.00 1.30 1.04 0.621.97 180.00 1.97 0.96 0.992.40 200.00 2.40 0.95 1.213.00 229.00 3.00 0.91 1.573.65 262.00 3.65 0.84 2.034.05 292.00 4.00 0.74 2.494.45 322.00 4.37 0.67 2.994.70 352.00 4.58 0.59 3.534.70 381.00 4.54 0.50 4.094.80 413.00 4.59 0.43 4.755.20 442.00 4.94 0.40 5.395.60 471.00 5.29 0.38 6.056.10 505.00 5.72 0.36 6.87

APPENDIX 2.

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APPENDIX 2. 203

Data fo r th e 2 2 5 m m 6b lade 4 5 o ax ia l im pe lle r h e ig h t= 4 5 0 m m c lea rance = 150m m

upwards pumping

ti = 4 9 .6 4 o CTorq.[Nm ] R PM

0 .8 0 1 2 5 .5 01 .00 1 4 1 .0 01 .25 1 5 7 .0 01 .40 1 6 7 .0 01 .60 1 7 7 .0 01 .80 1 8 8 .0 02 .0 0 2 0 0 .0 02 .4 5 2 2 0 .0 03 .2 0 2 4 9 .0 04 .1 0 2 8 5 .0 04 .6 5 3 0 2 .0 05 .6 0 3 3 2 .0 06 .6 5 3 6 0 .0 0

M ean va lue o f Pu

To rq .rea l Pu0 .8 0 2 .0 21 .00 2 .0 01 .25 2.011 .40 1 .991 .60 2 .0 31 .80 2 .022 .0 0 1 .992 .4 5 2.013 .2 0 2 .0 54 .0 6 1 .984 .5 9 2 .0 05.51 1 .986 .5 2 2 .0 0

2 .01

APPENDIX 2. 204

Data for the 225mm 6blade 45o axial impeller he igh t= 45 0m m c lea rance = 150m m

upwards pumpingvapou r rate = 1 0 4 d m 3 /m in Patm = 76 5 T o rr

t i= 1 0 0 .6 7 7 -1 0 0 .3 2 6 o CTo rque lN m ] R PM Torq .rea l[N m Pc/Pu

0 .8 0 1 2 4 .0 0 0 .8 0 1 .061 .00 1 4 0 .0 0 1 .0 0 1 .041 .20 1 5 5 .0 0 1 .20 1 .021 .40 1 6 8 .0 0 1 .40 1.012 .0 0 1 9 8 .0 0 2 .0 0 1 .042 .8 0 2 4 3 .0 0 2 .8 0 0 .9 73 .2 0 2 7 2 .0 0 3 .1 7 0 .8 75 .0 0 3 4 9 .0 0 4 .8 9 0 .8 26 .0 0 4 1 8 .0 0 5 .7 9 0 .6 77 .5 0 5 2 8 .0 0 7 .0 7 0 .5 2

V ap ou r rate:= 67dm 3/m inti = 1 0 0 .6 8 8 -1 0 0 .2 8 3 o C

0 .8 0 1 2 1 .0 0 0 .8 0 1.111 .20 1 5 1 .0 0 1 .2 0 1 .071 .60 1 7 8 .0 0 1 .6 0 1 .032 .0 0 2 0 0 .0 0 2 .0 0 1 .022 .4 0 2 1 9 .0 0 2 .4 0 1 .022 .8 0 2 3 8 .0 0 2 .8 0 1.013 .2 0 2 5 8 .0 0 3 .2 0 0 .9 84 .1 0 3 0 5 .0 0 4 .0 4 0 .8 84 .9 5 3 3 5 .0 0 4 .8 6 0 .8 85 .6 5 3 7 3 .0 0 5.51 0.816 .1 0 4 1 3 .0 0 5 .8 9 0 .7 07 .7 0 5 0 2 .0 0 7 .3 3 0 .5 98 .1 0 5 4 0 .0 0 7 .6 4 0 .5 3

Upwards pumpingV ap ou r rate == 27dm 3/m int i= 1 0 0 .5 8 2 -1 0 0 .3 0 0 o C

0 .8 0 1 1 7 .0 0 0 .8 0 1 .191 .00 1 3 3 .0 0 1 .0 0 1 .151 .20 1 4 5 .0 0 1 .20 1 .161 .40 1 6 0 .0 0 1 .40 1.111 .60 1 7 5 .0 0 1 .6 0 1 .061 .8 0 1 8 5 .0 0 1 .8 0 1 .072 .0 0 1 9 5 .0 0 2 .0 0 1 .072 .4 0 2 1 8 .0 0 2 .4 0 1 .032 .8 0 2 3 7 .0 0 2 .8 0 1.013 .2 0 2 5 2 .0 0 3 .2 0 1 .033 .7 0 2 7 2 .0 0 3 .6 7 1.014 .0 0 2 8 4 .0 0 3 .9 6 1 .004 .4 5 3 0 5 .0 0 4 .3 9 0 .9 65 .6 0 3 5 4 .0 0 5 .4 8 0 .8 9

1/C A gN0 .3 60 .4 60 .5 70.660 .9 21.311 .59 2 .4 0 3 .2 04 .5 9

0 .3 40 .5 20 .7 00.861.011 .171 .351 .802.112 .5 22 .9 84 .0 94 .5 8

0 .3 20.410 .4 80 .5 70.660 .7 30 .8 00 .9 81 .131 .251 .421 .531 .722 .1 9

APPENDIX 2. 205

Data for the 225mm 6blade 45o axial impellerhe igh t = 45 0m m c learance = 225m m Upwards pumping

ti = 4 8 .3 o CTorq.[Nm ] R PM To rq .rea l Pu

0 .8 0 1 1 2 .0 0 0 .8 0 2 .5 31 .0 0 1 2 5 .0 0 1 .0 0 2 .5 41 .2 0 1 3 8 .0 0 1 .2 0 2 .5 01 .4 0 1 5 0 .0 0 1 .4 0 2 .4 71 .65 1 6 2 .0 0 1 .6 5 2 .5 01 .80 1 7 0 .0 0 1 .8 0 2 .4 72 .0 0 1 8 0 .0 0 2 .0 0 2 .4 52 .4 0 1 9 7 .0 0 2 .4 0 2 .4 63 .6 5 2 4 6 .0 0 3 .6 5 2 .3 95 .4 0 3 0 0 .0 0 5 .3 5 2 .3 66 .9 0 3 4 0 .0 0 6 .8 0 2 .3 48 .0 5 3 8 1 .0 0 7 .8 9 2 .1 6

M ean va lue o f Pu. 2 .51

APPENDIX 2. 206

Data for the 225mm Gblade 45o axial impellerh e ig h t= 4 5 0 m m c learance = 225m mUpwards pumping

vapou r rate = 104dm 3/m inti = 1 0 0 .6 3 0 -1 0 0 .3 0 6 o C Patm = 7 6 3 .5 T o rr

TorquetN m ] R P M Torq .rea l[N m Pc/Pu 1 /C A gN0 .8 0 1 1 1 .0 0 0 .8 0 1 .06 0 .3 91 .00 1 2 4 .5 0 1 .00 1 .05 0 .4 81 .20 1 3 9 .0 0 1 .20 1.01 0 .5 81 .40 1 5 0 .0 0 1 .40 1 .02 0 .6 71 .60 1 6 3 .0 0 1 .60 0 .9 8 0 .7 81 .8 0 1 7 4 .0 0 1 .80 0 .9 7 0 .8 72 .0 0 1 8 6 .0 0 2 .0 0 0 .9 4 0 .9 82 .4 0 2 0 8 .0 0 2 .4 0 0.91 1 .192 .8 5 2 2 6 .0 0 2 .8 5 0.91 1 .3 83 .2 0 2 4 8 .0 0 3 .2 0 0 .8 5 1 .623 .6 5 2 7 5 .0 0 3 .6 2 0 .7 8 1 .934 .1 5 3 0 4 .0 0 4 .0 9 0 .7 2 2 .2 84 .4 5 3 2 1 .0 0 4 .3 7 0 .6 9 2 .4 94 .8 0 3 4 9 .0 0 4 .6 9 0 .6 3 2 .8 65 .3 0 3 9 5 .0 0 5 .1 2 0 .5 4 3 .4 95 .9 5 4 3 1 .0 0 5.71 0 .5 0 4.016 .7 0 4 8 5 .0 0 6 .3 6 0 .4 4 4 .8 2

Vapou r rate = 67dm 3/m it i= 1 0 0 .6 2 0 -1 0 0 .2 3 1 oC

0 .8 0 1 1 5 .0 0 0 .8 0 0 .9 9 0 .4 21 .42 1 5 0 .0 0 1 .42 1 .03 0 .6 62 .0 0 1 8 2 .0 0 2 .0 0 0 .9 9 0 .9 22 .6 5 2 1 4 .0 0 2 .6 5 0 .9 4 1.213 .2 5 2 4 2 .0 0 3 .2 5 0.91 1 .493 .8 5 2 7 0 .0 0 3 .8 2 0 .8 6 1 .774 .4 0 3 0 0 .0 0 4 .3 5 0 .7 9 2 .1 04 .8 0 3 3 0 .0 0 4.71 0.71 2 .4 45 .2 0 3 6 0 .0 0 5 .0 7 0 .6 4 2 .7 95 .5 0 3 9 2 .0 0 5 .3 3 0 .5 7 3 .1 86 .0 0 4 2 6 .0 0 5 .7 7 0 .5 2 3 .6 06 .4 5 4 5 6 .0 0 6 .1 7 0 .4 8 3 .9 95 .9 5 4 2 0 .0 0 5 .7 3 0 .5 3 3 .5 35 .2 0 3 6 0 .0 0 5 .0 7 0 .6 4 2 .7 94 .4 0 3 0 0 .0 0 4 .3 5 0 .7 9 2 .1 03 .4 5 2 4 8 .0 0 3 .4 5 0 .9 2 1 .552 .3 5 1 9 8 .0 0 2 .3 5 0 .9 8 1 .071 .25 1 4 2 .0 0 1 .25 1.01 0 .6 0

APPENDIX 2. 207

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APPENDIX 2. 221

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222

A p p e n d i x 3

Data o f the Velocity Measurements.

3 . 1 C a l c u l a t i o n o f t h e R a d i a l v e l o c i t y c o m p o n e n t s

Radial mean and RMS velocity components have been calculated according to the method of Tropea, 1983, [69]. If three measurements are performed with the orientation 9 = 0 and 0 = ±0], fig. A.3 .1, then:

V-9] -V+9]vrad= ------------ (A.3 .1)

28010]

and

V'2rad = t t y 2**! + V'2 9j -2V(2tangcos201)| / 2sin20 1 (A.3 .2)

In our experiments 9] = 15°.

Equations (A.3 .1) and (A.3 .2) give the radial mean and RMS velocity component.

APPENDIX 3. 223

V-15°

Fig. A .3 .1 . The measurements done for the calculation of Radial mean and RM S

velocity component.

3 . 2 E r r o r s a s s o c i a t e d w i t h t h e c a l c u l a t i o n p r o c e d u r e .

If we take into account that mean velocity data contain an error of about 5% then from the formulae used to calculate radial mean velocity component & radial component of RMS velocity fluctuations it follows out that the errors associated with the calculation of these quantities are:

TABLE A.3.1

QUANTITY % ERRORMean Radial velocity component around 10%Radial component of RMS vel. flucuat. around 40%

APPEND IX 3. 224

Results in table A.3.1 explain the scatter of the Radial RMS velocity data seen in the figures of chapter 7. It is also evident that small inaccuracies in the measurement of the V+15° and V-15° velocity components may result in very disordered data curves of the radial velocity component. This effect was enhanced at regions with higher error probabilities i.e. near the impeller blades where massive presence of bubbles reduce data rate and at regions with steep velocity gradients. However smoothing was necessary only with the data used to calculate the radial velocity component at R= 123.5 mm with the Rushton 240 mm impeller. This was done by using a least square approximation of the measured data of the V+i5° and V-15° velocity components as shown in fig. A.3 .2 .

Pig. A.3.2. Approximation of velocity data Rushton Impeller, D=240mm, R=123.5mm, 45o

V+15o velocity component

3 . 3 T h e L a s e r D o p p l e r e q u i p m e n t u s e d .

A block diagram of the laser system used in this work is shown in fig. A.3.3 .Specifications of the equipment are as follows:Laser beam generator from Spectra-Physics.Beam characteristics:5mWHeNe, wavelength 632.8 nm.TSI 9720-2-10 fiber optic probe.

APPENDIX 3. 225

1 . L a s e r g e n e r a t o r2 . O p t ic s - b e a m s p i i t in g3 . F r e q u e n c y s h i f t in g A. O p t ic f i b e r s5 . L a s e r p r o b e

6 . P h o to m u l t ip l i e r s y s t e m 9 1 6 07 . IFA 5 5 0 s i g n a l p r o c e s s o r8 . O s c i l o s c o p e9 . C o m p u te r

Fig. A .3 .3 . The iaser Doppler Anemometer used in this work.

Optical characteristics.Internal beam spacing 15 mm.Working distance in air 102 mm.

in water 135mm.Velocity components measured................................ oneMeasuring volume in air

Diameter........................................... 0.11 mmLength 1.6 mm

Number of fringes (beam of 514.5nm wavelength).......... 25Frequency shift.................................................... yesFibres.Transmiting fiber................. Polarization preserving, single-mode type.Receiving fiber.................... Multimode, graded-index type.Cable length.........................10 m.Power throughput efficiency.... 45% typical with lOmW input power.TSI Frequency Shifting system.Brag cell shifting up to 5 MHz.TSI IFA 550 Signal Processor.Frequency range

Low...................... 1kHz

APPENDIX 3. 226

High...................... 15MHzHigh-limit filters ....3, 1 MHz

300.100.30.10.3.1 kHz 300, 100 Hz

Low-limit filters................. 15,10,3,1 MHz300.100.30.10.3.1 kHz

Input voltage rangeLow........................0.1 mVHigh....................... 1.0 V

Time resolution.................. 2 nsFixed number of cycles......... 8(on which time measurement is based).

3 . 4 D a t a o f t h e v e l o c i t y m e a s u r e m e n t s .

In the following tables all the data obtained during the present research work can be found. Column designations are as follows:Z[mm] Vertical distance in mm from impeller midplane, fig.7 .1.V+ 15 measured mean velocity on the tang.-rad. plane at +15o angle,

fig.A.3 .1, in [m/sec].V-15 measured mean velocity on the tang.-rad. plane at -15o angle,

fig.A.3 .1, in [m/sec].angle angle in rads of the mean tang.-rad. velocity component, angle x in

fig.A.3 .1.Vradial calculated from eq. (A.3 .1) mean radial velocity component

in [m/sec].Vaxial measured mean axial velocity component in [m/sec].Vtangent. measured mean tangential velocity component in [m/sec],RMS+15o measured RMS velocity component on the tang.-rad. plane at

+15o angle, fig.A.3 .1, in [m/sec].RMS-15© measured RMS velocity component on the tang.-rad. plane at

-15o angle, fig.A.3 .1, in [m/sec].RMStang measured RMS tangential velocity component in [m/sec],RMSrad calculated RMS radial velocity component in [m/sec].

APPENDIX 3. 227

RMSax measured RMS axial velocity component [m/sec].The radial distance R of the measurement point from the axis of rotation in [mm], the angle of the plane of measurements relative to the baffles in [°], RPM and RPD are given for each set of measurements.

All the velocity measurements were performed in the 450 mm diameter vessel. Working liquid was filtered tap water. Table A.3.2 shows liquid height, impeller clearance and RPD for all the configurations used during the experiments.

Table A.3 .2 .Impeller type region of

measur.height[mm]

clear.[mm]

RPD

Rushton 240mm impellerstream

585 315 0.71


580 315 0.53


580 315 0.60


580 315 0.80

Rushton 180mm bulk 450 150 0.64

Hollow blade convex impellerstream

580 315 0.56

PBT downwards bulk 580 330 0.69

APPENDIX 3. 228

ZImm] V+ 15o V -15o angle Vradial Vaxial V tangent.R = 123 ,5m m , 15o ,195 R P M ,s in g le -p h a se .

Mean velocity data for the Rushton 240mm impellerT = 450m m , h = 585mm, c= 315m m , velocity [m/s]

5 4 ,0 0 0 0 ,2 8 6 0 ,3 6 6 0 ,1 6 8 0 ,1 5 5 -0 ,2 4 7 0 ,3 3 73 8 ,0 0 0 0 ,3 6 7 0 ,4 2 7 0 ,0 1 3 0 ,1 1 6 -0 ,1 1 8 0 ,4 3 73 0 ,0 0 0 0 ,3 6 7 0 ,4 2 7 0 ,0 1 3 0 ,1 1 6 0 ,1 7 0 0 ,5 8 52 4 ,0 0 0 0 ,5 0 0 0 ,7 5 4 0 ,3 8 5 0 ,491 0 ,1 7 0 0 ,8 9 41 8 ,0 0 0 1 ,052 1 ,2 3 8 0 ,0 3 3 0 ,3 5 9 0 ,5 3 5 1 ,0871 1 ,0 0 0 1 ,5 8 0 2 ,231 0 ,3 0 6 1 ,2 5 8 0 ,391 1 ,7236 ,0 0 0 1,551 2 ,1 8 8 0 ,3 0 5 1,231 0 ,2 4 0 2 ,1 2 70 ,0 0 0 1,571 2 ,0 9 6 0 ,2 2 9 1 ,0 1 4 0 ,2 6 9 1 ,887

-6 ,0 0 0 1 ,5 5 6 1 ,8 4 2 0 ,0 4 3 0 ,5 5 3 0 ,3 0 9 1 ,7 5 0-1 2 ,0 0 0 1 ,1 5 0 1 ,8 4 2 0 ,4 5 0 1 ,337 0 ,3 2 7 1 ,2 0 0-1 8 ,0 0 0 0 ,7 9 6 0 ,8 8 7 -0 ,0 6 3 0 ,1 7 6 0 ,3 2 7 0 ,9 2 5-3 0 ,0 0 0 0 ,591 0 ,6 0 5 -0 ,2 1 8 0 ,0 2 7 0 ,2 0 9 0 ,5 4 0-3 8 ,0 0 0 0 ,281 0 ,3 2 6 0 ,0 0 8 0 ,0 8 7 0 ,2 2 4 0 ,3 1 3

123 ,5m m , 1 5 o ,1 9 5 R P M ,tw o -•phase,RPD = 0 ,7 0 55 4 ,0 0 0 0 ,2 2 8 0 ,311 0 ,2 6 0 0 ,1 6 0 -0 ,251 0 ,2 5 33 8 ,0 0 0 0 ,3 3 6 0 ,3 5 4 -0 ,1 6 5 0 ,0 3 5 -0 ,2 6 3 0 ,3 2 62 4 ,0 0 0 0 ,6 6 7 0 ,7 8 0 0 ,0 2 2 0 ,2 1 8 -0 ,0 0 2 0 ,8 3 31 8 ,0 0 0 1 ,3 8 9 1 ,415 -0 ,2 2 7 0 ,0 5 0 0 ,5 3 9 1 ,5 0 01 2 ,0 0 0 1,961 2 ,1 0 4 -0 ,131 0 ,2 7 6 0 ,5 2 6 2 ,0 3 4

6 ,0 0 0 1 ,6 6 5 2 ,1 9 6 0 ,2 1 2 1 ,0 2 6 0 ,4 6 9 2 ,0 9 00 ,0 0 0 1 ,569 2 ,1 1 3 0 ,2 4 2 1,051 0 ,1 4 5 1,961

-6 ,0 0 0 1,591 1 ,5 9 3 -0 ,2 5 9 0 ,0 0 4 0 ,1 5 0 1 ,6 2 0-1 2 ,0 0 0 1 ,3 1 7 1 ,2 2 8 -0 ,3 9 2 -0 ,1 7 2 0 ,2 9 0 1 ,2 3 4-1 5 ,0 0 0 1 ,112 1 ,1 7 6 -0 ,1 5 8 0 ,1 2 4 1 ,0 0 0-1 8 ,0 0 0 0 ,8 1 6 0 ,7 3 5 -0 ,4 5 4 -0 ,1 5 6 0 ,361 0 ,8 0 0-2 4 ,0 0 0 0 ,4 4 0 0 ,4 3 7 -0 ,2 7 5 -0 ,0 0 6 0 ,4 9 5 0 ,4 2 0-3 0 ,0 0 0 0 ,2 8 9 0 ,3 2 0 -0 ,0 7 4 0 ,0 6 0 0 ,3 3 0-3 8 ,0 0 0 0 ,2 8 7 0 ,301 -0 ,1 7 3 0 ,0 2 7 0 ,3 6 9 0 ,2 8 8

APPENDIX 3. 229

Z[mm] V+ 15o V -15o angle Vradial Vaxial V tangent.R = 13 3 ,5m m , 15o , 1 9 5 R P M , sing le-pha:

Mean velocity data for the Rushton 240mm impellerT =450m m , h = 585mm, c= 315m m , velocity [m/s]

5 4 ,0 0 0 0 ,2 9 7 0 ,3 5 5 0 ,0 5 9 0 ,1 1 2 -0 ,1 6 2 0 ,3 3 03 8 ,0 0 0 0 ,3 6 6 0 ,4 2 5 0 ,0 1 0 0 ,1 1 4 -0 ,1 1 2 0 ,4 0 73 0 ,0 0 0 0 ,3 5 4 0 ,4 9 5 0 ,2 9 3 0 ,2 7 2 -0 ,0 5 2 0 ,4612 4 ,0 0 0 0 ,4 2 4 0 ,6 1 6 0 ,3 4 2 0 ,371 0 ,5 6 31 8 ,0 0 0 0 ,6 7 5 1 ,1 0 0 0 ,4 6 7 0 ,821 0 ,4 9 7 1 ,0 0 01 1 ,0 0 0 1 ,157 1 ,7 8 4 0 ,4 1 0 1,211 0 ,4 4 4 1 ,522

6 ,0 0 0 1 ,3 0 2 1,961 0 ,3 8 4 1 ,273 1 ,7 9 60 ,0 0 0 1 ,2 8 6 1 ,909 0 ,3 6 7 1 ,2 0 4 0 ,1 7 3 1 ,7 5 5

-6 ,0 0 0 1 ,2 1 2 1 ,5 6 0 0 ,1 7 6 0 ,6 7 2 0 ,2 6 2 1 ,5 0 7-1 2 ,0 0 0 0 ,8 2 3 0 ,9 6 3 0 ,0 2 3 0 ,2 7 0 0 ,241 0 ,9 0 3-2 4 ,0 0 0 0 ,3 3 4 0 ,4 1 0 0 ,1 0 2 0 ,1 4 7 0 ,381-3 8 ,0 0 0 0 ,271 0 ,3 3 9 0 ,1 3 2 0 ,131 0 ,2 5 3 0 ,3 1 5

133 ,5m m , 15o , 1 9 5R P M , tw o -phase5 4 ,0 0 0 0 ,2 0 4 0 ,2 9 0 0 ,3 1 4 0 ,1 6 6 -0 ,1 9 3 0 ,2 2 93 8 ,0 0 0 0 ,3 4 0 0 ,3 5 8 -0 ,1 6 6 0 ,0 3 5 0 ,2 9 93 0 ,0 0 0 0 ,3 5 0 0 ,4 4 0 0 ,1 4 0 0 ,1 7 4 -0 ,171 0 ,3 7 52 4 ,0 0 0 0 ,4 3 0 0 ,6 3 6 0 ,3 6 3 0 ,3 9 8 0 ,041 0 ,5 2 51 8 ,0 0 0 0 ,8 0 8 1 ,0 6 4 0 ,2 1 0 0 ,4 9 5 0 ,4 6 8 0 ,9 4 01 2 ,0 0 0 1 ,1 2 8 1,721 0 ,3 9 9 1 ,1 4 6 0 ,501 1 ,4 4 6

6 ,0 0 0 1 ,1 3 5 1 ,6 5 5 0 ,3 4 6 1 ,005 0 ,3 1 0 1 ,5 5 00 ,0 0 0 1 ,0 9 2 1,551 0 ,3 1 3 0 ,8 8 7 0 ,1 8 8 1 ,3 9 8

-6 ,0 0 0 0 ,9 3 0 1 ,2 5 5 0 ,2 4 5 0 ,6 2 8 0 ,2 3 8 0 ,841-1 2 ,0 0 0 0 ,7 0 5 0 ,9 2 3 0 ,2 0 2 0 ,421 0 ,2 4 7 0 ,5 5 0-2 4 ,0 0 0 0 ,3 1 0 0 ,331 -0 ,1 4 0 0 ,041 0 ,2 8 6 0 ,3 2 6-3 8 ,0 0 0 0 ,2 5 0 0 ,2 7 2 -0 ,1 0 6 0 ,0 4 3 0 ,2 9 9 0 ,2 5 2

4 8 ,5m m , 15o, 19 5 R P M , s ing le -phase 5 4 ,0 0 0 0 ,3 0 9 0 ,351 -0 ,0 2 9 0 ,081 -0 ,0 4 2 0 ,3 5 23 8 ,0 0 0 0 ,4 0 7 0 ,4 3 7 -0 ,1 3 0 0 ,0 5 8 -0 ,0 6 6 0 ,4 4 03 0 ,0 0 0 0 ,4 5 6 0 ,6 0 0 0 ,2 0 9 0 ,2 7 8 -0 ,0 1 7 0 ,5 4 62 4 ,0 0 0 0 ,6 2 7 0 ,7 8 8 0 ,1 4 0 0 ,311 0 ,7611 8 ,0 0 0 0 ,8 7 0 1 ,2 6 0 0 ,3 3 8 0 ,7 5 3 0 ,271 1 ,1 0 01 2 ,0 0 0 1 ,0 5 4 1 ,6 6 7 0 ,4 3 7 1 ,1 8 4 0 ,3 6 4 1 ,4 0 3

6 ,0 0 0 1 ,0 5 4 1 ,7 2 5 0 ,4 7 2 1 ,2 9 6 1 ,4 4 60 ,0 0 0 0 ,961 1 ,547 0 ,4 5 5 1 ,1 3 2 0 ,1 4 6 1 ,3 0 5

APPENDIX 3. 230

Mean velocity data for the Rushton 240mm impeller T = 450mm, h = 585mm, c=315mm, velocity [m/s]Zlmm] V+ 15o V -15o angle Vradial Vaxial V tangent.

-6 ,0 0 0 0 ,7 7 3 1 ,1 0 7 0 ,3 2 4 0 ,6 4 5 1 ,0 4 4-1 2 ,0 0 0 0 ,4 9 3 0 ,7 2 3 0 ,3 5 3 0 ,4 4 4 0 ,2 0 3 0 ,6 8 5-1 8 ,0 0 0 0 ,3 0 8 0 ,4 8 2 0 ,4 2 6 0 ,3 3 6 0 ,4 3 6-2 4 ,0 0 0 0 ,3 0 3 0 ,3 8 5 0 ,1 5 7 0 ,1 5 8 0 ,3 4 4-3 8 ,0 0 0 0 ,2 0 2 0 ,3 2 5 0 ,4 5 5 0 ,2 3 8 0 ,2 0 4 0 ,2 7 3

148 ,5m m , 15o, 19 5 R PM ,tw o -•phase.5 4 ,0 0 0 0 , 193 0 ,3 0 6 0 ,4 4 0 0 ,2 1 8 -0 ,0 6 9 0 ,2 3 53 8 ,0 0 0 0 ,2 5 3 0 ,3 4 3 0 ,251 0 ,1 7 4 -0 ,0 6 5 0 ,2 9 73 0 ,0 0 0 0 ,2 8 0 0 ,4 3 2 0 ,411 0 ,2 9 4 0 ,0 1 5 0 ,4 2 51 8 ,0 0 0 0 ,6 1 6 0 ,9 3 0 0 ,3 8 7 0 ,6 0 7 0 ,3 4 6 0 ,7 7 21 2 ,0 0 0 0 ,871 1 ,395 0 ,4 5 0 1 ,0 1 2 0 ,3 6 6 1 ,1 5 7

6 ,0 0 0 0 ,991 1 ,4 0 6 0 ,3 1 2 0 ,8 0 2 0 ,2 3 4 1 ,2 1 50 ,0 0 0 0 ,931 1 ,1 9 9 0 ,1 7 7 0 ,5 1 8 0 ,1 1 0 1 ,1 0 8

-6 ,0 0 0 0 ,6 9 6 0 ,9 1 6 0 ,2 0 9 0 ,4 2 5 0 ,1 0 0 0 ,8 8 0-1 2 ,0 0 0 0 ,4 7 6 0 ,5 7 8 0 ,0 8 5 0 ,1 9 7 0 ,1 3 2 0 ,6 0 2-2 4 ,0 0 0 0 ,2 8 9 0 ,3 4 9 0 ,0 7 6 0 ,1 1 6 0 ,1 8 5 0 ,3 1 3-3 8 ,0 0 0 0 ,2 2 2 0 ,2 8 2 0 ,1 5 6 0 ,1 1 6 0 ,1 6 5 0 ,2 4 4

168 ,5m m , 1 5 o ,1 9 5 R P M ,,s ing le -phase .5 4 ,0 0 0 0 ,2 9 9 0 ,371 0 ,1 2 0 0 ,1 3 9 0 ,1 0 3 0 ,3 4 33 8 ,0 0 0 0 ,4 9 4 0 ,6 5 5 0 ,2 2 0 0 ,311 0 ,1 1 5 0 ,5 8 52 4 ,0 0 0 0 ,8 9 3 1 ,2 7 0 0 ,3 1 5 0 ,7 2 8 0 ,2 2 6 1 ,1 1 61 2 ,0 0 0 1 ,0 0 8 1 ,5 6 6 0 ,4 1 8 1 ,0 7 8 0 ,3 0 8 1 ,299

0 ,0 0 0 0 ,7 5 2 1 ,2 7 7 0 ,5 0 6 1 ,0 1 4 0 ,1 3 3 1 ,0 5 5-1 2 ,0 0 0 0 ,4 6 0 0 ,7 5 5 0 ,4 7 4 0 ,5 7 0 0 ,1 0 2 0 ,6 2 0-2 4 ,0 0 0 0 ,2 5 3 0 ,3 9 2 0 ,4 1 6 0 ,2 6 9 0 ,1 0 5 0 ,3 1 9-3 8 ,0 0 0 0 ,1 6 8 0 ,2 3 4 0 ,2 8 8 0 ,1 2 8 0 ,1 1 2 0 ,2 3 4

168 ,5m m , 15o , 195 R P M ,tw o --phase.5 4 ,0 0 0 0 , 193 0 ,2 7 8 0 ,331 0 ,1 6 4 0 ,0 2 5 0 ,2 4 53 8 ,0 0 0 0 ,2 6 2 0 ,401 0 ,4 0 2 0 ,2 6 9 0 ,0 7 8 0 ,3 3 92 4 ,0 0 0 0 ,4 2 6 0 ,6 4 8 0 ,3 9 5 0 ,4 2 9 0 ,1 9 4 0 ,5 8 61 2 ,0 0 0 0 ,6 7 6 1 ,145 0 ,5 0 4 0 ,9 0 6 0 ,2 3 7 0 ,9 4 70 ,0 0 0 0 ,651 1 ,0 3 2 0 ,4 4 0 0 ,7 3 6 0 ,1 2 8 0 ,9 1 7

-1 2 ,0 0 0 0 ,4 2 2 0 ,6 4 9 0 ,4 0 7 0 ,4 3 9 0 ,1 4 7 0 ,551-2 4 ,0 0 0 0 ,2 6 2 0 ,3 5 4 0 ,2 4 7 0 ,1 7 8 0 ,1 0 3 0 ,3 1 2-3 8 ,0 0 0 0 ,1 8 3 0 ,2 1 7 0 ,0 4 5 0 ,0 6 6 0 ,0 6 7 0 ,1 7 4

APPENDIX 3. 231

Mean velocity data for the Rushton 240mm impeller T =450mm, h=585mm, c=315mm, velocity [m/s]Z[mm] V + 15o V -15o angle Vradial Vaxial V tangent.

R= 198,5mm, 15o,195RPM,single-phase54,000 0,253 0,167 -0,914 -0,166 0,423 0,17138,000 0,310 0,322 -0,191 0,023 0,405 0,32124,000 0,456 0,560 0,103 0,201 0,360 0,52512,000 0,524 0,796 0,394 0,525 0,270 0,6660,000 0,370 0,795 0,675 0,821 0,056 0,563

-12,000 0,303 0,535 0,540 0,448 -0,106 0,303-24,000 0,149 0,306 0,649 0,303 -0,152 0,235-38,000 0,094 0,133 0,308 0,075 -0,216 0,095

R = 198,5mm, 15o, 195RPM,two-phase.54,000 0,144 0,114 -0,671 -0,058 0,386 0,17138,000 0,194 0,389 0,634 0,377 0,336 0,29124,000 0,321 0,656 0,646 0,647 0,340 0,43512,000 0,351 0,659 0,588 0,595 0,211 0,5440,000 0,348 0,688 0,624 0,657 -0,013 0,497

-12,000 0,279 0,450 0,457 0,330 -0,057 0,345-24,000 0,139 0,201 0,336 0,120 -0,143 0,196-38,000 0,146 0,082 -1,070 -0,124 -0,222 0,128

APPENDIX 3. 232

Mean velocity data for the Rushton 240mm impeller T = 450mm, h = 585mm, c = 315mm, velocity[m/s]Z[mm] V +15o V-15o angleY Vradial Vaxial VtangentialR = 12 3 ,5 m m , 4 5 o , 1 9 5 R P M , s ing le -phase .

5 4 0 ,1 5 7 0 ,2 1 3 0 ,2 5 2 0 ,1 0 8 -0 ,2 6 3 0 ,1 8 34 6 ,0 0 0 0 ,141 0 ,1 7 4 0 ,111 0 ,0 6 4 -0 ,2 0 9 0 ,1 9 03 8 ,0 0 0 0 ,1 6 9 0 ,2 2 7 0 ,2 3 8 0 ,1 1 2 -0 ,0 6 4 0 ,1 9 83 3 ,0 0 0 0 ,2 6 2 0 ,3 0 2 -0 ,0 0 3 0 ,0 7 7 0 ,0 9 9 0 ,2 5 62 4 ,0 0 0 0 ,4 6 7 0 ,6 9 5 0 ,3 7 0 0 ,4 4 0 0 ,3 1 5 0 ,9112 1 ,0 0 0 1,091 1 ,4 9 8 0 ,2 6 9 0 ,7 8 6 0 ,6 7 0 1 ,2 6 31 1 ,0 0 0 1 ,6 5 5 2 ,3 7 2 0 ,3 2 5 1 ,3 8 5 0 ,3 4 4 2 ,0 4 4

6 ,0 0 0 1 ,6 1 9 2 ,3 5 2 0 ,341 1 ,4 1 6 0 ,251 2 ,1 2 20 ,0 0 0 1 ,699 2 ,321 0 ,2 6 2 1 ,202 0 ,3 0 2 2 ,0 2 9

-6 ,0 0 0 1 ,6 1 3 1 ,8 4 0 -0 ,021 0 ,4 3 9 0 ,2 2 0 1 ,7 1 8-1 2 ,0 0 0 1 ,202 1 ,3 3 4 -0 ,0 7 0 0 ,2 5 5 0 ,2 6 0 1 ,2 9 4-1 8 ,0 0 0 0 ,7 0 4 0 ,7 7 2 -0 ,0 9 2 0 ,131 0 ,2 4 9 0 ,7 6 5-2 6 ,0 0 0 0 ,3 1 2 0 ,4 6 9 0 ,3 8 2 0 ,3 0 3 0 ,1 1 2 0 ,2 7 7-3 0 ,0 0 0 0 ,2 3 0 0 ,2 5 8 -0 ,051 0 ,0 5 4 0 ,1 3 0 0 ,2 3 4-3 8 ,0 0 0 0 ,1 2 4 0 ,1 3 9 -0 ,0 5 2 0 ,0 2 9 0 ,2 7 6 0 ,1 3 5

123 ,5m m ,,45o , 195 R PM ,tw o --phase,RPD = 0 ,7 0 55 4 ,0 0 0 0 ,1 5 0 0 ,2 1 9 0 ,3 4 7 0 ,1 3 3 -0 ,3 3 8 0 ,1 9 54 7 ,0 0 0 0 ,1 4 0 0 ,2 2 3 0 ,4 4 5 0 ,1 6 0 0 ,0 0 0 0 ,1 9 84 6 ,0 0 0 0 ,1 5 0 0 ,2 3 0 0 ,4 0 4 0 ,1 5 5 -0 ,291 0 ,0 0 03 8 ,0 0 0 0 ,1 6 0 0 ,2 3 5 0 ,3 5 5 0 ,1 4 5 -0 ,2 7 5 0 ,2 0 63 3 ,0 0 0 0 ,2 0 5 0 ,2 3 5 -0 ,0 1 3 0 ,0 5 8 -0 ,2 4 9 0 ,2 2 03 1 ,0 0 0 0 ,3 5 0 0 ,2 8 8 -0 ,6 1 0 -0 ,1 2 0 0 ,0 0 0 0 ,0 0 02 8 ,0 0 0 0 ,6 0 9 0 ,4 2 3 -0 ,8 5 4 -0 ,3 5 9 -0 ,1 5 3 0 ,3 8 22 5 ,0 0 0 0 ,9 1 8 0 ,8 3 7 -0 ,4 3 2 -0 ,1 5 6 0 ,0 0 0 0 ,8 6 22 4 ,0 0 0 0 ,7 2 0 0 ,9 5 6 0 ,2 2 2 0 ,4 5 6 0 ,1 6 9 0 ,0 0 02 3 ,0 0 0 1 ,0 4 4 0 ,9 9 9 -0 ,3 4 4 -0 ,0 8 7 0 ,0 0 0 1 ,0 2 72 0 ,0 0 0 1 ,4 1 9 1 ,3 9 5 -0 ,2 9 4 -0 ,0 4 6 0 ,4 1 2 1 ,6 0 51 6 ,0 0 0 1 ,4 9 5 1 ,7 0 8 -0 ,0 1 9 0 ,411 0 ,6 5 6 1 ,5 1 21 1 ,0 0 0 1 ,843 2 ,3 3 6 0 ,1 5 3 0 ,9 5 2 0 ,5 5 2 2 ,1 0 7

6 ,0 0 0 1 ,733 2 ,2 6 0 0 ,1 9 6 1 ,0 1 8 0 ,3 7 0 2 ,0 7 70 ,0 0 0 1 ,9 4 5 2 ,171 -0 ,0 6 0 0 ,4 3 7 0 ,141 1,981

-3 ,0 0 0 2 ,0 8 7 2 ,1 6 7 -0 ,1 9 2 0 ,1 5 5 0 ,0 0 0 0 ,0 0 0-6 ,0 0 0 1 ,852 1 ,6 3 9 -0 ,4 8 6 -0 ,411 0 ,1 0 4 1 ,7 0 4-9 ,0 0 0 1 ,2 1 2 1 ,633 0 ,2 4 3 0 ,8 1 3 0 ,0 0 0 0 ,0 0 0

-1 2 ,0 0 0 1 ,202 1 ,2 3 5 -0 ,211 0 ,0 6 4 0 ,2 2 6 1 ,2 8 7-1 5 ,0 0 0 1 ,3 0 4 1 ,1 6 8 -0 ,4 6 4 -0 ,2 6 3 0 ,0 0 0 1 ,5 8 2-1 8 ,0 0 0 0 ,9 7 5 0 ,7 2 8 -0 ,7 5 8 -0 ,4 7 7 0 ,3 6 0 1,281-2 0 ,0 0 0 0 ,6 2 2 0 ,5 9 3 -0 ,351 -0 ,0 5 6 0 ,0 0 0 0 ,0 0 0-2 2 ,0 0 0 0 ,5 1 0 0 ,4 8 6 -0 ,351 -0 ,0 4 6 0 ,4 1 7 0 ,4 8 9-2 4 ,0 0 0 0 ,3 4 5 0 ,3 2 2 -0 ,3 9 0 -0 ,0 4 4 0 ,0 0 0 0 ,0 0 0-2 6 ,0 0 0 0 ,1 9 6 0 ,2 0 9 -0 ,1 4 3 0 ,0 2 5 0 ,381 0 ,1 6 3-3 0 ,0 0 0 0 ,1 1 4 0 ,1 6 6 0 ,3 4 4 0 ,1 0 0 0 ,3 8 4 0 ,1 5 0-3 6 ,0 0 0 0 ,1 4 6 0 ,1 5 8 -0 ,1 1 6 0 ,0 2 3 0 ,3 7 7 0 ,1 3 5-3 8 ,0 0 0 0 ,1 0 9 0 ,1 6 7 0 ,4 0 3 0 ,1 1 2 0 ,0 0 0 0 ,1 4 8

APPENDIX 3. 233

Mean velocity data for the Rushton 240mm impellerT= 450m m , h = 585mm , c= 315m m , velocity[m/s]Z[mm] V + 15o V 15o angleY Vradisl Vaxial VtangentialR = 13 3 ,5m m , 4 5 o , 1 9 5 R P M , - • *

5 4 ,0 0 0 0 ,1 2 2 0 ,1 7 0 0 ,2 8 8 0 ,0 9 3 -0 ,2 6 7 0 ,1 4 53 8 ,0 0 0 0 ,1 6 8 0 ,1 5 3 -0 ,4 3 4 -0 ,0 2 9 -0 ,1 5 3 0 ,1 2 23 0 ,0 0 0 0 ,1 8 3 0 ,2 5 6 0 ,2 9 4 0 ,141 -0 ,001 0 ,2 0 92 4 ,0 0 0 0 ,3 0 7 0 ,4 8 6 0 ,4 3 8 0 ,3 4 6 0 ,3 0 7 0 ,4 5 61 8 ,0 0 0 0 ,7 8 0 1 ,1 2 2 0 ,3 2 9 0 ,661 0 ,7 6 4 1 ,0 6 41 2 ,0 0 0 1 ,2 3 2 2 ,0 8 2 0 ,5 0 2 1 ,6 4 2 0 ,5 5 2 1 ,6 1 2

6 ,0 0 0 1 ,3 2 6 2 ,211 0 ,4 8 9 1 ,7 1 0 0 ,291 1 ,8 0 40 ,0 0 0 1 ,4 4 8 2 ,1 3 6 0 ,3 6 0 1 ,3 2 9 0 ,2 0 5 1 ,767

-6 ,0 0 0 1 ,3 1 8 1 ,6 8 2 0 ,1 6 3 0 ,7 0 3 0 ,2 5 9 1 ,4 8 4-1 2 ,0 0 0 1 ,0 5 8 1 ,0 0 0 -0 ,3 6 7 -0 ,1 1 2 0 ,2 8 2 0 ,8 0 8-1 8 ,0 0 0 0 ,2 9 4 0 ,4 2 2 0 ,3 2 7 0 ,2 4 7 0 ,2 8 2 0 ,4 1 4-3 0 ,0 0 0 0 ,0 0 5 0 ,1 6 3 1 ,031 0 ,3 0 5 0 ,2 9 6 0 ,1 1 8-3 8 ,0 0 0 0 ,0 4 4 0 ,141 0 ,8 3 7 0 ,1 8 7 0 ,0 9 8

R = 133 ,5m m , 5o , 19 5 R P M , tw o -phase5 4 ,0 0 0 0 ,1 2 5 0 ,1 8 4 0 ,3 5 7 0 ,1 1 4 -0 ,3 0 8 0 ,1 5 94 6 ,0 0 0 0 ,131 0 ,1 8 5 0 ,3 0 6 0 ,1 0 4 -0 ,2 6 3 0 ,1 7 23 8 ,0 0 0 0 ,1 4 7 0 ,201 0 ,2 6 3 0 ,1 0 4 -0 ,2 3 2 0 ,1 7 93 3 ,0 0 0 0 ,1 7 4 0 ,1 9 5 -0 ,0 5 3 0 ,041 -0 ,1 7 0 0 ,1 8 22 8 ,0 0 0 0 ,2 6 5 0 ,3 3 8 0 ,1 6 3 0 ,141 -0 ,0 5 6 0 ,2 8 22 4 ,0 0 0 0 ,4 2 3 0 ,5 7 9 0 ,2 6 5 0 ,301 0 ,1 5 7 0 ,5 5 82 0 ,0 0 0 0 ,8 4 2 0 ,9 6 2 -0 ,0 1 8 0 ,2 3 2 0 ,361 0 ,8 7 41 6 ,0 0 0 1,091 1 ,3 4 6 0 ,1 1 0 0 ,4 9 3 0 ,5 7 6 1 ,1 7 61 1 ,0 0 0 1 ,2 1 9 1,831 0 ,381 1 ,182 0 ,5 3 7 1 ,5 3 9

6 ,0 0 0 1 ,2 1 6 1 ,8 6 3 0 ,4 0 3 1 ,2 5 0 0 ,2 9 8 1 ,6 7 00 ,0 0 0 1 ,139 1 ,6 7 2 0 ,3 5 4 1 ,0 3 0 0 ,1 3 5 1 ,4 0 5

-6 ,0 0 0 0 ,9 2 0 1 ,1 9 4 0 ,1 8 9 0 ,5 2 9 0 ,1 5 8 1 ,0 3 0-9 ,0 0 0 0 ,9 3 3 1 ,0 1 7 -0 ,1 0 2 0 ,1 6 2 0 ,0 0 0 0 ,8 9 0

-1 2 ,0 0 0 0 ,9 4 7 0 ,8 4 0 -0 ,4 8 2 -0 ,2 0 7 0 ,231 0 ,7 5 4-1 5 ,0 0 0 0 ,6 6 0 0 ,6 5 5 -0 ,2 7 6 -0 ,0 1 0 0 ,0 0 0 0 ,6 9 4-1 8 ,0 0 0 0 ,3 9 8 0 ,3 9 0 -0 ,3 0 0 -0 ,0 1 5 0 ,2 6 2 0 ,4 2 0-2 2 ,0 0 0 0 ,2 0 7 0 ,2 0 5 -0 ,2 8 0 -0 ,0 0 4 0 ,2 7 0 0 ,0 0 0-2 6 ,0 0 0 0 ,0 9 5 0 ,1 5 8 0 ,4 8 7 0 ,1 2 2 0 ,2 7 3 0 ,1 1 6-3 0 ,0 0 0 0 ,0 6 9 0 ,1 3 2 0 ,6 0 2 0 ,1 2 2 0 ,2 9 3 0 ,1 1 2-3 6 ,0 0 0 0 ,0 9 7 0 ,1 2 7 0 ,2 0 2 0 ,0 5 8 0 ,3 3 3 0 ,0 0 0-3 8 ,0 0 0 0 ,101 0 ,1 3 3 0 ,2 1 0 0 ,0 6 2 0 ,1 1 9

1 4 8 ,5 m m ,4 5 o , 195R PM ,rsing ie -phase5 4 ,0 0 0 0 ,0 8 5 0 ,1 4 0 0 ,4 7 8 0 ,1 0 6 -0 ,2 3 3 0 ,1 1 23 8 ,0 0 0 0 ,1 1 7 0 ,141 0 ,0 7 2 0 ,0 4 6 -0 ,1 4 5 0 ,1 1 63 0 ,0 0 0 0 ,1 9 8 0 ,3 5 2 0 ,5 4 6 0 ,2 9 8 -0 ,0 2 8 0 ,2 6 22 4 ,0 0 0 0 ,4 9 7 0 ,6 8 4 0 ,2 7 2 0 ,361 0 ,2 4 7 0 ,7111 8 ,0 0 0 0 ,9 8 5 1 ,2 5 3 0 ,1 5 8 0 ,5 1 8 0 ,5 2 0 1,1811 2 ,0 0 0 1 ,1 6 4 1 ,7 1 0 0 ,3 5 5 1 ,055 0 ,4 4 5 1 ,4 9 7

6 ,0 0 0 1 ,1 9 6 1 ,8 4 2 0 ,4 0 9 1 ,2 4 8 0 ,3 0 0 1 ,5 2 20 ,0 0 0 1 ,1 0 9 1 ,6 8 9 0 ,3 9 7 1 ,1 2 0 0 ,171 1 ,4 3 3

APPENDIX 3. 234

Mean velocity data for the Rushton 240m m impellerT =450m m , h = 585mm, c= 315m m , vek>crty[m/s]Z[mm] V +15o V-15o angleY Vradial Vaxial Vtangential

-6 ,0 0 0 0 ,971 1 ,223 0 ,1 4 3 0 ,4 8 7 0 ,231 1 ,0 5 6-1 2 ,0 0 0 0 ,571 0 ,6 4 0 -0 ,0 5 2 0 ,1 3 3 0 ,2 5 0 0 ,5 4 8-1 8 ,0 0 0 0 ,1 9 3 0 ,2 5 8 0 ,2 3 2 0 ,1 2 6 0 ,2 5 5 0 ,241-3 0 ,0 0 0 0 ,0 1 8 0 ,1 1 4 0 ,9 5 6 0 ,1 8 5 0 ,3 1 3 0 ,0 6 4-3 8 ,0 0 0 0 ,0 3 5 0 ,1 0 3 0 ,811 0 ,131 0 ,3 0 2 0 ,0 5 9

R = 1 4 8 ,5 m m ,4 5 o ,1 9 5 R P M ,tw o -p h a se .5 4 ,0 0 0 0 ,091 0 ,1 7 5 0 ,6 0 5 0 ,1 6 2 -0 ,2 4 9 0 ,1 3 54 6 ,0 0 0 0 ,0 6 8 0 ,1 8 8 0 ,7 9 0 0 ,2 3 2 -0 ,2 1 8 0 ,1 3 83 8 ,0 0 0 0 ,1 7 3 0 ,1 6 2 -0 ,3 8 4 -0 ,021 -0 ,1 6 0 0 ,1413 0 ,0 0 0 0 ,1 6 6 0 ,2 7 6 0 ,4 8 7 0 ,2 1 3 -0 ,0 2 4 0 ,2 2 02 4 ,0 0 0 0 ,3 5 2 0 ,5 0 0 0 ,3 1 3 0 ,2 8 6 0 ,1 6 2 0 ,4611 8 ,0 0 0 0 ,691 0 ,9 8 9 0 ,3 2 3 0 ,5 7 6 0 ,3 5 5 0 ,8 1 61 2 ,0 0 0 0 ,9 7 4 1 ,3 8 6 0 ,3 1 6 0 ,7 9 6 0 ,3 7 5 1 ,1 9 0

6 ,0 0 0 0 ,9 2 8 1 ,475 0 ,4 4 2 1 ,0 5 7 0 ,2 6 0 1 ,2 7 80 ,0 0 0 0 ,8 4 7 1 ,202 0 ,3 1 2 0 ,6 8 6 0 ,1 2 2 1 ,0 5 4

-6 ,0 0 0 0 ,5 8 9 0 ,7 6 9 0 ,1 9 8 0 ,3 4 8 0 ,1 0 8 0 ,6 8 9-1 2 ,0 0 0 0 ,2 8 5 0 ,4 5 7 0 ,451 0 ,3 3 2 0 ,1 5 6 0 ,3 8 8-1 8 ,0 0 0 0 ,1 0 3 0 ,2 3 7 0 ,7 1 2 0 ,2 5 9 0 ,1 9 7 0 ,1 8 5-2 4 ,0 0 0 0 ,0 5 9 0 ,1 1 6 0 ,621 0 ,1 1 0 0 ,2 5 7 0 ,0 6 8-3 0 ,0 0 0 0 ,0 3 5 0 ,1 0 3 0 ,811 0 ,131 0 ,271 0 ,0 5 9-3 8 ,0 0 0 0 ,0 4 0 0 ,1 0 7 0 ,7 7 8 0 ,1 2 9 0 ,2 8 5 0 ,0 7 0

R = 16 8 ,5 m m ,4 5 o , 19 5 R PM ,s in g le -p ha se5 4 ,0 0 0 0 ,0 4 6 0 ,1 4 6 0 ,8 3 4 0 ,1 9 3 -0 ,1 6 2 0 ,0 7 33 8 ,0 0 0 0 ,1 2 5 0 ,2 1 8 0 ,5 3 0 0 ,1 8 0 -0 ,0 6 7 0 ,1 7 73 0 ,0 0 0 0 ,3 8 0 0 ,4 7 7 0 ,1 3 8 0 ,1 8 7 0 ,0 0 0 0 ,4 5 32 4 ,0 0 0 0 ,7 5 7 0 ,9 0 0 0 ,0 5 0 0 ,2 7 6 0 ,2 1 7 0 ,8 5 81 8 ,0 0 0 0 ,9 9 7 1 ,3 2 5 0 ,2 2 3 0 ,6 3 4 0 ,0 0 0 1 ,1 3 51 2 ,0 0 0 1 ,0 8 4 1 ,5 8 0 0 ,3 4 5 0 ,9 5 8 0 ,3 5 2 1 ,3 6 56 ,0 0 0 0 ,9 9 5 1 ,5 3 3 0 ,4 0 9 1 ,039 0 ,0 0 0 1 ,3 0 80 ,0 0 0 0 ,9 0 2 1 ,3 2 2 0 ,3 5 2 0 ,811 0 ,2 0 6 1 ,143

-6 ,0 0 0 0 ,6 6 4 0 ,9 5 3 0 ,3 2 6 0 ,5 5 8 0 ,0 0 0 0 ,8 2 3-1 2 ,0 0 0 0 ,401 0 ,5 2 2 0 ,1 9 3 0 ,2 3 4 0 ,2 0 2 0 ,4 4 4-2 4 ,0 0 0 0 ,0 4 0 0 ,1 4 2 0 ,8 6 3 0 ,1 9 7 0 ,2 2 7 0 ,0 9 2-3 8 ,0 0 0 0 ,0 0 9 0 ,0 7 5 0 ,9 8 0 0 ,1 2 8 0 ,2 5 4 0 ,0 4 5

R = 16 8 ,5 m m ,4 5 o , 195 R P M ,tw o -p h a se .5 4 ,0 0 0 0 ,0 8 5 0 ,1 6 2 0 ,5 9 9 0 ,1 4 9 -0 ,1 4 3 0 ,1213 8 ,0 0 0 0 ,131 0 ,2 5 4 0 ,611 0 ,2 3 8 -0 ,0 7 0 0 ,1 6 42 4 ,0 0 0 0 ,3 8 6 0 ,6 5 3 0 ,5 0 3 0 ,5 1 6 0 ,1 7 9 0 ,5 0 61 2 ,0 0 0 0 ,7 5 9 1 ,1 8 8 0 ,4 2 6 0 ,8 2 9 0 ,2 6 7 0 ,9 5 0

6 ,0 0 0 0 ,7 4 8 1 ,1 8 3 0 ,4 3 7 0 ,8 4 0 0 ,2 0 3 0 ,9 8 40 ,0 0 0 0 ,6 4 9 0 ,9 5 7 0 ,3 5 9 0 ,5 9 5 0 ,1 8 4 0 ,8 2 0

-6 ,0 0 0 0 ,4 6 3 0 ,6 2 3 0 ,241 0 ,3 0 9 0 ,171 0 ,5 2 9-1 2 ,0 0 0 0 ,2 4 4 0 ,3 5 6 0 ,3 4 7 0 ,2 1 6 0 ,2 0 8 0 ,3 0 3-2 4 ,0 0 0 0 ,0 3 4 0 ,131 0 ,881 0 ,1 8 7 0 ,2 4 2 0 ,0 6 8

APPENDIX 3. 235

Mean velocity data for the Rushton 240mm impeller T =450mm, h = 585mm, c=315mm, veto city [m/s]Z[mm] V +15o V-15o angleY Vradial Vaxial Vtangential

-3 8 ,0 0 0 0 ,0 2 4 0 ,1 0 8 0 ,9 1 0 0 ,1 6 2 0 ,2 4 0 0 ,0 5 7

CO CO Ol

3 3 r4 5 o ,1 9 5 R P M , s ing le -phase5 4 ,0 0 0 0 ,341 0 ,3 5 4 -0 ,1 9 2 0 ,0 2 5 0 ,3 2 4 0 ,4 2 93 8 ,0 0 0 0 ,4 7 7 0 ,5 7 2 0 ,0 6 4 0 ,1 8 4 0 ,3 4 5 0 ,5 7 72 4 ,0 0 0 0 ,6 6 5 0 ,941 0 ,3 0 8 0 ,5 3 3 0 ,3 4 8 0 ,7 6 51 2 ,0 0 0 0 ,6 8 6 1 ,0 4 5 0 ,3 9 7 0 ,6 9 4 0 ,2 3 6 0 ,9 2 7

0 ,0 0 0 0 ,5 9 2 0 ,8 4 0 0 ,3 1 2 0 ,4 7 9 0 ,051 0 ,7 5 0-1 2 ,0 0 0 0 ,3 6 7 0 ,5 6 4 0 ,4 0 7 0 ,381 -0 ,0 5 5 0 ,5 0 5-2 4 ,0 0 0 0 ,2 0 5 0 ,3 4 6 0 ,501 0 ,2 7 2 -0 ,0 7 9 0 ,3 2 5-3 8 ,0 0 0 0 ,1 9 5 0 ,2 2 5 -0 ,001 0 ,0 5 8 -0 ,1 3 8 0 ,2 2 0

198 ,5m m ,,4 5 o ,1 9 5 R P M ,tw o -p h a se .5 4 ,0 0 0 0 ,2 5 2 0 ,3 0 5 0 ,0 7 9 0 ,1 0 2 0 ,3 2 5 0 ,2 8 73 8 ,0 0 0 0 ,3 0 8 0 ,441 0 ,3 2 3 0 ,2 5 7 0 ,2 8 0 0 ,3 6 72 4 ,0 0 0 0 ,4 4 0 0 ,6 6 2 0 ,3 8 3 0 ,4 2 9 0 ,3 1 6 0 ,5 6 51 2 ,0 0 0 0 ,4 7 7 0 ,7 9 3 0 ,4 8 7 0 ,6 1 0 0 ,1 6 0 0 ,6 5 0

0 ,0 0 0 0 ,4 1 8 0 ,6 5 4 0 ,4 2 6 0 ,4 5 6 0 ,031 0 ,591-1 2 ,0 0 0 0 ,3 3 6 0 ,5 2 5 0 ,4 2 5 0 ,3 6 5 -0 ,0 5 9 0 ,4 2 7-2 4 ,0 0 0 0 ,2 0 5 0 ,2 9 7 0 ,3 3 8 0 ,1 7 8 -0 ,0 9 6 0 ,2 9 5-3 8 ,0 0 0 0 ,1 5 7 0 ,2 3 7 0 ,3 8 7 0 ,1 5 5 -0 ,1 1 8 0 ,2 0 7

APPENDIX 3. 236

im] V + 1 5 o V -1 5 o 12 3 ,5 m m ,7 5 o , l 9 5 R PM ,s in g le -p ha se

sn g ie V rad ia l V ax ia l V tangen tia i

5 4 ,0 0 0 0 ,2 7 0 0 ,3 1 3 0 ,0 0 7 0 ,0 8 3 -0 ,4 0 0 0 ,2 9 74 6 ,0 0 0 0 ,2 9 0 0 ,3 2 5 -0 ,0 5 3 0 ,0 6 8 0 ,3 0 03 8 ,0 0 0 0 ,3 4 3 0 ,3 5 3 -0 ,2 0 8 0 ,0 1 9 -0 ,1 4 2 0 ,3 5 63 0 ,0 0 0 0 ,4 2 0 0 ,5 0 0 0 ,0 5 2 0 ,1 5 5 0 ,1 2 7 0 ,5 2 02 4 ,0 0 0 0 ,5 3 8 0 ,7 1 4 0 ,221 0 ,3 4 0 0 ,2 3 3 0 ,7 5 61 8 ,0 0 0 0 ,9 0 0 1 ,2 4 5 0 ,2 7 9 0 ,6 6 6 0 ,5 8 0 1 ,2 0 01 1 ,0 0 0 1 ,4 6 2 2 ,1 1 8 0 ,3 3 8 1 ,2 6 7 0 ,4 4 2 1 ,733

6 ,0 0 0 1 ,5 5 7 2 ,2 2 0 0 ,3 1 8 1,281 0 ,2 4 5 2 ,0 4 00 ,0 0 0 1 ,6 0 7 2 ,131 0 ,2 2 0 1 ,012 0 ,2 1 7 1 ,9 1 3

-6 ,0 0 0 1,611 1 ,8 3 8 -0 ,021 0 ,4 3 9 0 ,2 8 4 1 ,7 4 0-1 8 ,0 0 0 0 ,6 6 5 0 ,741 -0 ,0 6 3 0 ,1 4 7 0 ,1 9 6 0 ,9 0 4-2 4 ,0 0 0 0 ,4 8 7 0 ,4 9 2 -0 ,2 4 3 0 ,0 1 0 0 ,1 8 3 0 ,4 8 8-3 8 ,0 0 0 0 ,2 4 3 0 ,2 4 5 -0 ,2 4 7 0 ,0 0 4 0 ,2 7 6 0 ,2 6 5

APPENDIX 3. 237

nm] V+ 15o V-15o angle Vradiai V axial Vtangentia!= 1 2 3 ,5 m m ,7 5 o ,1 9 5 R P M ,tw o -p h a se ,R P D = 0 ,7 0 5

5 4 ,0 0 0 0 ,2 2 3 0 ,2 8 9 0 ,1 8 7 0 ,1 2 8 -0 ,3 6 3 0 ,2 5 73 8 ,0 0 0 0 ,2 7 8 0 ,3 1 5 -0 ,0 3 3 0 ,071 -0 ,2 9 9 0 ,2 9 93 0 ,0 0 0 0 ,3 9 0 0 ,4 0 4 -0 ,1 9 6 0 ,0 2 7 -0 ,2 6 2 0 ,5 0 02 7 ,0 0 0 0 ,4 7 5 0 ,4 7 7 -0 ,2 5 4 0 ,0 0 4 -0 ,1 6 0 0 ,4 4 52 4 ,0 0 0 0 ,6 5 0 0 ,6 8 4 -0 ,1 6 7 0 ,0 6 6 -0 ,0 3 7 0 ,8 7 22 1 ,0 0 0 0 ,9 9 2 0 ,9 5 0 -0 ,3 4 2 -0 ,081 0 ,2 2 5 1 ,0 9 41 8 ,0 0 0 1 ,275 1 ,4 0 8 -0 ,0 7 9 0 ,2 5 7 0 ,4 3 4 1 ,2 5 41 5 ,0 0 0 1 ,5 0 0 1 ,8 2 5 0 ,0 8 8 0 ,6 2 8 0 ,5 3 0 1 ,7 5 01 2 ,0 0 0 1 ,6 2 5 2 ,2 0 7 0 ,2 5 4 1 ,1 2 4 0 ,5 3 0 2 ,0 0 5

6 ,0 0 0 1 ,6 5 0 2 ,3 4 9 0 ,3 1 6 1 ,3 5 0 0 ,4 0 7 2 ,1 3 20 ,0 0 0 1 ,525 2 ,1 5 2 0 ,3 0 5 1,211 0 ,1 3 8 1,891

-6 ,0 0 0 1 ,3 2 0 1 ,6 7 5 0 ,1 5 5 0 ,6 8 6 0 ,1 1 6 1 ,5 3 5-9 ,0 0 0 1 ,175 1 ,4 0 0 0 ,0 5 3 0 ,4 3 5 0 ,1 6 5 1 ,3 5 0

-1 2 ,0 0 0 1 ,0 2 5 1 ,1 0 0 -0 ,131 0 ,1 4 5 0 ,2 0 0 1 ,1 1 9-1 5 ,0 0 0 0 ,8 6 0 0 ,8 6 0 -0 ,2 6 2 0 ,0 0 0 0 ,2 5 4 1 ,2 7 3-1 8 ,0 0 0 0 ,6 8 0 0 ,6 0 0 -0 ,491 -0 ,1 5 5 0 ,3 0 0 0 ,8 5 6-2 1 ,0 0 0 0 ,5 2 5 0 ,4 3 7 -0 ,591 -0 ,1 7 0 0 ,3 9 4 0 ,5 7 0-2 4 ,0 0 0 0 ,4 4 0 0 ,3 3 3 -0 ,7 3 9 -0 ,2 0 7 0 ,3 8 0 0 ,3 5 0-3 0 ,0 0 0 0 ,2 4 7 0 ,261 -0 ,1 5 9 0 ,0 2 7 0 ,431 0 ,2 5 0-3 8 ,0 0 0 0 ,2 2 8 0 ,2 4 0 -0 ,1 6 6 0 ,0 2 3 0 ,4 4 3 0 ,2 2 0

= 133 ,5m m , 75o , 1 9 5 R P M , sing le-pha:5 4 ,0 0 0 0 ,2 5 6 0 ,2 9 3 -0 ,0 1 5 0 ,071 -0 ,4 1 4 0 ,2813 8 ,0 0 0 0 ,3 2 0 0 ,3 5 8 -0 ,0 5 6 0 ,0 7 3 0 ,3 0 83 0 ,0 0 0 0 ,3 6 0 0 ,3 8 8 -0 ,1 2 3 0 ,0 5 4 -0 ,1 2 2 0 ,3 6 42 4 ,0 0 0 0 ,4 4 4 0 ,5 5 6 0 ,1 3 4 0 ,2 1 6 0 ,0 4 5 0 ,4 9 41 1 ,0 0 0 1 ,1 5 6 1 ,765 0 ,3 9 9 1 ,1 7 6 0 ,3 7 9 1 ,4 8 5

6 ,0 0 0 1 ,283 2 ,0 5 5 0 ,4 5 0 1,491 0 ,2 9 6 1 ,7 4 20 ,0 0 0 1 ,3 1 8 1,971 0 ,3 7 6 1,261 0 ,1 9 3 1 ,6 9 7

-6 ,0 0 0 1,231 1 ,5 1 9 0 ,111 0 ,5 5 6 0 ,2 8 7 1,371-1 5 ,0 0 0 0 ,4 6 6 0 ,5 3 9 0 ,0 0 3 0 ,141 0 ,2 7 4 0 ,5 2 4-2 4 ,0 0 0 0 ,3 5 7 0 ,3 4 6 -0 ,3 2 0 -0 ,021 0 ,2 8 6 0 ,301-3 8 ,0 0 0 0 ,2 1 4 0 ,271 0 ,1 5 2 0 ,1 1 0 0 ,3 5 2 0 ,2 2 0

133 ,5m m , 75o , 1 9 5 R P M , tw o -phase5 4 ,0 0 0 0 ,2 1 8 0 ,2 7 5 0 ,1 4 6 0 ,1 1 0 -0 ,331 0 ,2414 6 ,0 0 0 0 ,2 2 7 0 ,2 8 2 0 ,1 2 2 0 ,1 0 6 0 ,2 3 03 8 ,0 0 0 0 ,2 5 9 0 ,3 0 7 0 ,0 4 5 0 ,0 9 3 -0 ,2 5 9 0 ,2 7 83 0 ,0 0 0 0 ,3 0 0 0 ,3 4 9 0 ,0 1 3 0 ,0 9 5 -0 ,1 8 0 0 ,3 7 02 4 ,0 0 0 0 ,4 3 7 0 ,5 7 4 0 ,2 0 6 0 ,2 6 5 0 ,0 2 5 0 ,5 2 81 8 ,0 0 0 0 ,7 0 0 1 ,1 1 2 0 ,4 4 2 0 ,7 9 6 0 ,4 2 7 0 ,9 2 51 2 ,0 0 0 1 ,1 2 0 1 ,8 4 4 0 ,4 7 7 1 ,3 9 9 0 ,531 1 ,4 6 6

6 ,0 0 0 1 ,187 1 ,8 0 8 0 ,3 9 7 1 ,2 0 0 0 ,3 1 7 1 ,6 5 20 ,0 0 0 1 ,0 7 3 1 ,6 3 0 0 ,3 9 4 1 ,0 7 6 0 ,1 4 3 1,401

-6 ,0 0 0 0 ,8 4 0 1,201 0 ,3 2 2 0 ,6 9 7 0 ,1 7 4 1 ,0 7 0-1 2 ,0 0 0 0 ,7 7 8 0 ,8 4 5 -0 ,1 0 9 0 ,1 2 9 0 ,2 5 4 0 ,7 4 8

APPENDIX 3. 238

Z[m m ] V+ 15o ¥-15o angle Vradial ¥ axial ¥tangential-1 8 ,0 0 0 0 ,4 0 9 0 ,4 7 7 0 ,0 1 7 0 ,131 0 ,3 0 7 0 ,4 7 5-2 4 ,0 0 0 0 ,2 6 6 0 ,2 8 5 -0 ,1 3 4 0 ,0 3 7 0 ,2 5 9-3 0 ,0 0 0 0 ,201 0 ,2 3 8 0 ,0 4 3 0 ,071 0 ,3 7 8 0 ,2 1 0-3 8 ,0 0 0 0 ,1 9 9 0 ,1 9 9 -0 ,2 6 2 0 ,0 0 0 0 ,3 5 6 0 ,1 9 5

R = 1 4 8 ,5m m ,75o , 19 5 R PM ,s in g le -p ha se 5 4 ,0 0 0 0 ,2 2 5 0 ,2 8 3 0 ,141 0 ,1 1 2 -0 ,3 4 9 0 ,2 5 73 8 ,0 0 0 0 ,2 6 9 0 ,3 2 0 0 ,051 0 ,0 9 9 0 ,0 0 0 0 ,2913 0 ,0 0 0 0 ,3 0 9 0 ,4 1 7 0 ,2 4 5 0 ,2 0 9 -0 ,1 6 6 0 ,3812 4 ,0 0 0 0 ,5 0 3 0 ,6 4 9 0 ,1 8 0 0 ,2 8 2 0 ,0 3 9 0 ,6 5 21 8 ,0 0 0 0 ,8 0 0 1 ,2 0 0 0 ,3 7 9 0 ,7 7 3 0 ,2 6 8 1 ,0 9 51 2 ,0 0 0 1 ,0 5 9 1 ,6 5 3 0 ,4 2 3 1 ,1 4 8 0 ,3 1 9 1 ,3 6 3

6 ,0 0 0 1 ,0 9 9 1 ,7 2 9 0 ,4 3 2 1 ,217 0 ,2 4 7 1 ,4 6 20 ,0 0 0 1 ,0 4 6 1 ,6 0 4 0 ,4 0 4 1 ,0 7 8 0 ,1 4 8 1 ,3 6 4

-6 ,0 0 0 0 ,8 1 0 1 ,0 7 5 0 ,221 0 ,5 1 2 0 ,0 0 0 1 ,0 7 7-1 2 ,0 0 0 0 ,5 4 2 0 ,6 9 6 0 ,1 7 3 0 ,2 9 8 0 ,2 0 6 0 ,6 5 5-1 8 ,0 0 0 0 ,251 0 ,3 6 9 0 ,3 5 6 0 ,2 2 8 0 ,0 0 0 0 ,361-2 4 ,0 0 0 0 ,2 1 2 0 ,2 8 7 0 ,2 4 9 0 ,1 4 5 0 ,2 9 4 0 ,2 5 6-3 8 ,0 0 0 0 ,1 6 6 0 ,2 4 5 0 ,3 6 0 0 ,1 5 3 0 ,3 9 5 0 ,191

R = 14 8 ,5 m m ,7 5 o ,1 9 5 R P M , tw o -phase . 5 4 ,0 0 0 0 ,191 0 ,2 6 3 0 ,2 7 3 0 ,1 3 9 -0 ,2 7 7 0 ,2 3 24 6 ,0 0 0 0 ,1 8 3 0 ,2 6 2 0 ,3 2 3 0 ,1 5 3 -0 ,2 0 2 0 ,2 4 53 8 ,0 0 0 0 ,2 7 5 0 ,2 9 5 -0 ,1 3 2 0 ,0 3 9 -0 ,1 8 2 0 ,2 6 43 0 ,0 0 0 0 ,2 6 2 0 ,3 8 9 0 ,3 6 8 0 ,2 4 5 -0 ,0 7 4 0 ,3 3 02 4 ,0 0 0 0 ,3 7 3 0 ,5 9 4 0 ,4 4 4 0 ,4 2 7 0 ,1 2 4 0 ,4 7 31 8 ,0 0 0 0 ,6 4 9 0 ,971 0 ,3 7 6 0 ,6 2 2 0 ,3 3 8 0 ,8 0 01 2 ,0 0 0 0 ,901 1 ,4 2 7 0 ,4 3 9 1 ,0 1 6 0 ,3 8 2 1 ,187

6 ,0 0 0 0 ,921 1 ,483 0 ,4 5 6 1 ,0 8 6 0 ,2 8 0 1 ,2 9 40 ,0 0 0 0 ,7 7 3 1 ,2 4 7 0 ,4 5 7 0 ,9 1 6 0 ,1 1 3 1 ,0 6 6

-6 ,0 0 0 0 ,541 0 ,8 4 9 0 ,4 2 9 0 ,5 9 5 0 ,1 1 2 0 ,7 4 5-1 2 ,0 0 0 0 ,371 0 ,501 0 ,2 4 6 0 ,251 0 ,4 7 2-1 8 ,0 0 0 0 ,2 1 3 0 ,3 3 3 0 ,4 2 5 0 ,2 3 2 0 ,2 2 8 0 ,3 3 0-2 4 ,0 0 0 0 ,1 8 5 0 ,2 5 5 0 ,2 7 4 0 ,1 3 5 0 ,2 3 5-3 0 ,0 0 0 0 ,1 4 3 0 ,2 3 5 0 ,4 7 6 0 ,1 7 8 0 ,3 3 3 0 ,2 0 0-3 8 ,0 0 0 0 ,1 4 9 0 ,2 1 4 0 ,3 2 7 0 ,1 2 6 0 ,3 6 3 0 ,191

16 8 ,5 m m ,7 5 o ,1 9 5 R P M , s ing le -phase 5 4 ,0 0 0 0 ,2 4 9 0 ,2 9 3 0 ,0 3 2 0 ,0 8 5 -0 ,2 2 3 0 ,2 4 93 8 ,0 0 0 0 ,2 6 9 0 ,3 8 8 0 ,3 3 3 0 ,2 3 0 -0 ,1 6 3 0 ,3 3 62 4 ,0 0 0 0 ,5 9 7 0 ,861 0 ,3 3 2 0 ,5 1 0 0 ,0 2 0 0 ,7 6 81 2 ,0 0 0 0 ,9 4 0 1 ,475 0 ,4 2 9 1 ,0 3 4 0 ,2 5 0 1 ,2 4 40 ,0 0 0 0 ,8 2 9 1 ,3 5 5 0 ,4 7 0 1 ,0 1 6 0 ,151 1 ,1 1 9

APPENDIX 3. 239

Z[mm] V+ 15o V-15o angle Vradial V axial Vtangential-1 2 ,0 0 0 0 ,4 2 6 0 ,681 0 ,4 4 8 0 ,4 9 3 0 ,1 7 8 0 ,5 8 5-2 4 ,0 0 0 0 ,1 9 3 0 ,2 8 7 0 ,3 6 9 0 ,1 8 2 0 ,1 9 6 0 ,2 2 6-3 8 ,0 0 0 0 ,1 3 7 0 ,2 1 0 0 ,4 0 4 0 ,141 0 ,2 5 2 0 ,2 0 5

16 8 ,5 m m ,7 5 o , 195R PM ,r tw o -phase .5 4 ,0 0 0 0 ,191 0 ,2 5 6 0 ,2 3 5 0 ,1 2 6 -0 ,1 5 2 0 ,2 1 33 8 ,0 0 0 0 ,1 9 8 0 ,341 0 ,5 1 9 0 ,2 7 6 -0 ,0 5 5 0 ,2 6 02 4 ,0 0 0 0 ,3 8 7 0 ,6 6 6 0 ,5 1 8 0 ,5 3 9 0 ,1 6 9 0 ,5 5 41 2 ,0 0 0 0 ,8 0 6 1 ,1 7 9 0 ,3 5 0 0 ,721 0 ,3 0 3 0 ,9 5 4

6 ,0 0 0 0 ,7 5 7 1 ,2 2 5 0 ,461 0 ,9 0 4 0 ,2 1 3 1 ,0 3 60 ,0 0 0 0 ,6 3 0 1 ,0 5 7 0 ,4 9 5 0 ,8 2 5 0 ,1 5 9 0 ,8 6 2

-6 ,0 0 0 0 ,4 6 0 0 ,7 7 5 0 ,4 9 9 0 ,6 0 9 0 ,6 4 5-1 2 ,0 0 0 0 ,3 1 9 0 ,4 5 8 0 ,3 2 7 0 ,2 6 9 0 ,2 3 7 0 ,4 2 4-2 4 ,0 0 0 0 ,1 7 9 0 ,2 8 8 0 ,4 5 5 0 ,211 0 ,2 5 2 0 ,2 1 6-3 8 ,0 0 0 0 ,1 3 6 0 ,2 0 3 0 ,3 7 4 0 ,1 2 9 0 ,2 9 7 0 ,171

19 8 ,5 m m ,7 5 o , 195R PM ,,s ing le -phase5 4 ,0 0 0 0 ,3 9 4 0 ,4 2 2 -0 ,1 3 4 0 ,0 5 4 0 ,3 5 4 0 ,4 2 93 8 ,0 0 0 0 ,5 3 6 0 ,6 4 8 0 ,0 7 8 0 ,2 1 6 0 ,2 7 4 0 ,6 2 52 4 ,0 0 0 0 ,6 1 9 0 ,8 7 7 0 ,3 1 0 0 ,4 9 8 0 ,3 5 5 0 ,8 0 61 2 ,0 0 0 0 ,6 5 5 1,031 0 ,4 3 2 0 ,7 2 6 0 ,1 5 7 0 ,8 7 20 ,0 0 0 0 ,6 0 9 0 ,9 5 3 0 ,4 2 6 0 ,6 6 5 -0 ,0 2 8 0 ,8 1 7

-1 2 ,0 0 0 0 ,501 0 ,631 0 ,1 4 3 0 ,251 -0 ,1 1 9 0 ,5 4 5-2 4 ,0 0 0 0 ,2 8 6 0 ,381 0 ,2 2 7 0 ,1 8 4 -0 ,1 6 7 0 ,3 5 0-3 8 ,0 0 0 0 ,241 0 ,3 4 8 0 ,3 3 4 0 ,2 0 7 -0 ,2 7 9 0 ,2 7 8

1 9 8 ,5 m m ,75 o , 19 5R P M r tw o -phase .5 4 ,0 0 0 0 ,3 3 7 0 ,3 3 3 -0 ,2 8 4 -0 ,0 0 8 0 ,3 4 3 0 ,3 4 63 8 ,0 0 0 0 ,3 2 4 0 ,5 0 0 0 ,411 0 ,3 4 0 0 ,3 4 3 0 ,4 4 62 4 ,0 0 0 0 ,5 0 6 0 ,7 1 9 0 ,3 1 4 0 ,411 0 ,3 1 3 0 ,6 2 51 2 ,0 0 0 0 ,4 5 9 0 ,8 3 4 0 ,5 6 3 0 ,7 2 4 0 ,1 7 6 0 ,6 8 9

0 ,0 0 0 0 ,5 0 4 0 ,8 3 6 0 ,4 8 4 0 ,641 -0 ,021 0 ,6 3 4-1 2 ,0 0 0 0 ,3 7 4 0 ,5 5 8 0 ,3 7 3 0 ,3 5 5 -0 ,1 0 9 0 ,4 6 3-2 4 ,0 0 0 0 ,3 2 8 0 ,3 8 6 0 ,0 3 3 0 ,1 1 2 -0 ,1 3 6 0 ,3 5 6-3 8 ,0 0 0 0 ,3 2 0 0 ,2 6 8 -0 ,581 -0 ,1 0 0 -0 ,191 0 ,3 4 0

APPENDIX 3. 240

RMS data for the 240mm Rushton impeller, T = 450mm,h = 585mm,c = 315mm Z[mm] RMS+150 RMS-150 RMStang RMSrad RMSaxR = 12 3 ,5 m m , 15o , 1 9 5 R P M , sing le -phase .

5 4 .0 0 0 .2 2 6 0 .2 8 2 0 .2 7 2 0 .2 3 6 0 .2 6 73 8 .0 0 0 0 .3 1 9 0 .3 7 6 0 .3 4 8 0 .3 5 8 0 .4413 0 .0 0 0 0 .4 7 5 0 .4 7 0 0 .4 5 0 0 .7 1 6 0 .7 7 42 4 .0 0 0 0 .6 6 4 0 .7 0 8 0 .6 2 5 1 .2 6 2 0 .7 2 41 8 .0 0 0 0 .771 0 .5 9 4 0 .6 1 0 1 .3 7 4 1 .0 2 81 1 .0 0 0 0 .7 6 0 0 .8 8 9 0 .8 2 4 0 .8 6 8 0 .801

6 .0 0 0 0 .7 9 8 1 .0 0 6 0 .8 4 7 1.521 0 .5 7 70 .0 0 0 0 .7 9 6 0 .9 4 8 0 .8 9 0 0 .6 3 6 0 .5 3 6

-6 .0 0 0 0 .801 0 .8 3 0 0 .8 0 0 1 .0 0 8 0 .6 1 4-1 2 .0 0 0 0 .7 2 0 0 .8 0 0 0 .7 3 0 1 .1 0 6 0 .6 8 5-1 8 .0 0 0 0 .6 1 7 0 .6 2 4 0 .6 4 0 0 .2 0 7 0 .6 2 5-2 4 .0 0 0 0 .6 1 4 0 .5 5 5 0 .5 3 8 1 .0 4 0 0 .5 6 0-3 0 .0 0 0 0 .4 4 0 0 .4 7 5 0 .4 5 5 0 .4 9 6 0 .4 5 0-3 8 .0 0 0 0 .2 8 9 0 .3 2 6 0 .311 0 .2 6 4 0 .3 7 6

123 ,5m m , 15o, 1 9 5 R P M , tw o -phase , R PD = 0 .7 0 55 4 .0 0 0 0 .2 2 6 0 .2 3 9 0 .2 4 3 0 .1 2 2 0 .2 3 93 8 .0 0 0 0 .3 1 5 0 .2 8 8 0 .2 7 4 0 .5 6 0 0 .2 9 72 4 .0 0 0 0 .6 0 6 0 .701 0 .7 4 8 1 .1 7 6 0 .7 2 41 8 .0 0 0 0 .9 4 6 0 .8 5 3 0 .8 9 0 1 .0 3 8 0 .9 1 91 2 .0 0 0 0 .8 8 6 0 .9 1 6 0 .8 7 9 1 .1 6 6 0 .7 9 4

6 .0 0 0 0 .8 0 3 0 .8 7 4 0 .8 1 0 1 .1 7 3 0 .6 9 60 .0 0 0 0 .7 8 9 0 .8 1 0 0 .8 0 6 0 .7 0 4 0 .5 6 4

-6 .0 0 0 0 .9 5 4 0 .7 7 8 0 .8 2 5 1 .3 5 3 0 .631-1 2 .0 0 0 0 .9 5 5 0 .7 2 9 0 .8 0 6 1 .3 1 4 0 .6 7 8-1 8 .0 0 0 0 .7 5 2 0 .6 2 6 0 .6 6 0 1 .0 3 9 0 .5 9 3-2 4 .0 0 0 0 .6 3 5 0 .4 7 4 0 .4 5 0 1 .3 6 6 0 .481-3 0 .0 0 0 0 .3 0 3 0 .341 0 .3 7 5 0 .6 3 7 0 .3 5 0-3 8 .0 0 0 0 .2 4 9 0 .2 6 9 0 .2 5 7 0 .2 8 8 0 .271

R as 133 ,5m m , 15o, 195 R P M ,s in g le -p h a se5 4 .0 0 0 0 .281 0 .2 9 63 8 .0 0 0 0 .3 5 2 0 .3 6 63 0 .0 0 0 0 .4 4 5 0 .4 8 82 4 .0 0 0 0 .5 2 5 0 .6 2 71 1 .0 0 0 0 .7 0 7 0 .8 9 7

0 .2 7 4 0 .4 4 5 0 .2 6 40 .3 4 8 0 .4 8 8 0 .3 8 50 .4 5 7 0 .5 8 9 0 .6 0 30 .6 1 7 0 .5 5 7 1 .0 3 40 .8 2 0 0 .6 0 9 0 .8 7 4

APPENDIX 3. 241

RMS data for the 240mm Rushton impeller, T=450mm,h = 585mm,c= 315mm Z[mm] RMS+15o RMS-150 RMStang RMSrad RMSax

6 .0 0 0 0 .7 5 2 0 .9 9 0 0 .9 1 2 0 .2 1 9 0 .7 0 50 .0 0 0 0 .8 0 9 0 .9 2 9 0 .9 1 2 0 .5 0 8 0 .5 8 3

-6 .0 0 0 0 .8 0 7 0 .821 0 .861 0 .6 5 8 0 .7 0 5-1 2 .0 0 0 0 .6 6 9 0 .6 8 2 0 .6 7 4 0 .6 9 7 0 .6 4 3-2 4 .0 0 0 0 .4 1 7 0 .4 5 0 0 .4 4 2 0 .2 9 7 0 .4 3 5-3 8 .0 0 0 0 .291 0 .301 0 .301 0 .2 1 5 0 .291

133 ,5m m , 15o, 19 5 R P M , tw o -phase , RPD = 0 ,7 0 55 4 .0 0 0 0 .2 2 6 0 .2 2 9 0 .2 3 7 0 .0 9 8 0 .2 2 83 8 .0 0 0 0 .2 6 5 0 .2 7 0 0 .2 5 7 0 .3 8 5 0 .2 9 53 0 .0 0 0 0 .3 5 0 0 .3 7 5 0 .3 6 0 0 .3 9 9 0 .4 0 62 4 .0 0 0 0 .4 3 4 0 .4 9 4 0 .4 9 7 0 .461 0 .6 4 71 8 .0 0 0 0 .6 8 8 0 .6 7 0 0 .6 5 5 0 .9 5 3 0 .7 8 31 2 .0 0 0 0 .7 6 4 0 .8 5 0 0 .8 1 9 0 .6 3 8 0 .651

6 .0 0 0 0 .6 9 9 0 .7 7 2 0 .7 8 0 0 .6 1 5 0 .5 6 30 .0 0 0 0 .6 9 7 0 .6 9 6 0 .7 1 7 0 .2 8 6 0 .6 9 9

-6 .0 0 0 0 .6 4 3 0 .5 6 6 0 .6 5 0 0 .6 3 8 0 .8 3 7-1 2 .0 0 0 0 .5 7 2 0 .5 6 5 0 .5 8 2 0 .3 2 7 0 .7 0 8-2 4 .0 0 0 0 .331 0 .3 8 3 0 .3 3 5 0 .591 0 .4 2 0-3 8 .0 0 0 0 .2 5 8 0 .2 6 8 0 .2 4 3 0 .4 5 9 0 .2 4 2

148 ,5m m , 15o, 1 9 5R P M , sing le -phase5 4 .0 0 0 0 .3 1 2 0 .3 0 4 0 .2 9 8 0 .4 2 4 0 .2 6 93 8 .0 0 0 0 .4 1 7 0 .3 6 4 0 .371 0 .6 0 8 0 .3 8 03 0 .0 0 0 0 .5 1 5 0 .5 1 2 0 .5 3 7 0 .2 8 3 0 .6 0 02 4 .0 0 0 0 .6 8 0 0 .6 6 0 0 .6 7 4 0 .6 1 3 0 .8 3 01 8 .0 0 0 0 .7 4 5 0 .7 6 2 0 .7 7 0 0 .4 6 8 0 .9 4 01 2 .0 0 0 0 .811 0 .8 6 5 0 .8 6 7 0 .1 5 6 0 .8 8 4

6 .0 0 0 0 .7 4 8 0 .911 0 .8 4 2 0 .7 0 4 0 .7 7 50 .0 0 0 0 .7 5 9 0 .8 5 7 0 .8 3 4 0 .3 0 7 0 .6 8 3

-6 .0 0 0 0 .7 0 8 0 .7 4 9 0 .8 1 5 1 .1 5 0 0 .6 0 0-1 2 .0 0 0 0 .5 4 8 0 .6 0 3 0 .6 1 0 0 .4 7 7 0 .5 9 0-1 8 .0 0 0 0 .4 2 6 0 .4 2 5 0 .4 2 3 0 .4 5 9 0 .5 1 5-2 4 .0 0 0 0 .3 2 9 0 .3 6 0 0 .3 2 9 0 .5 1 7 0 .4 5 2-3 8 .0 0 0 0 .2 7 7 0 .2 8 8 0 .2 8 3 0 .2 7 6 0 .2 4 5

R = 148 ,5m m , 15o , 19 5 R P M ,tw o -p h a se , RPD = 0 ,7 0 55 4 .0 0 0 0 .2 4 6 0 .2 6 2 0 .2 4 7 0 .3 3 8 0 .2 2 43 8 .0 0 0 0 .271 0 .261 0 .2 8 6 0 .2 8 7 0 .3 0 0

APPENDIX 3. 242

RMS data for the 240mm Rushton impeller, T=450mm,h = 585mm,c=315mm Z[mm] RMS+15o RMS-15o RMStang RMSrad RMSax

3 0 .0 0 0 0 .3 3 2 0 .3 7 8 0 .3 9 0 0 .4 7 9 0 .4 5 71 8 .0 0 0 0 .5 9 5 0 .631 0 .6 5 3 0 .5 7 0 0 .6 8 01 2 .0 0 0 0 .7 3 5 0 .7 8 5 0 .7 7 3 0 .5 5 6 0 .6 4 4

6 .0 0 0 0 .781 0 .7 6 4 0 .7 9 5 0 .3 2 7 0 .6 4 00 .0 0 0 0 .7 6 8 0 .6 8 4 0 .7 4 7 0 .3 5 0 0 .5 9 9

-6 .0 0 0 0 .6 4 9 0 .6 1 3 0 .6 5 0 0 .2 5 3 0 .6 2 0-1 2 .0 0 0 0 .5 0 9 0 .4 7 6 0 .5 3 2 0 .5 6 3 0 .5 3 5-2 4 .0 0 0 0 .321 0 .3 2 4 0 .3 2 4 0 .301 0 .3 2 5-3 8 .0 0 0 0 .2 5 8 0 .2 6 3 0 .2 6 3 0 .2 2 3 0 .2 2 7

168 ,5m m , 1 5 o ,1 9 5 R P M , sing le -phase5 4 .0 0 0 0 .351 0 .3 2 7 0 .3 5 0 0 .1 0 7 0 .3 1 73 8 .0 0 0 0 .5 0 6 0 .5 4 2 0 .5 3 7 0 .2 9 5 0 .4 6 92 4 .0 0 0 0 .7 9 4 0 .7 8 8 0 .8 3 8 0 .6 6 4 0 .7 2 61 8 .0 0 0 0 .7 9 0 0 .8 1 5 0 .8 2 3 0 .4 2 7 0 .7 8 21 2 .0 0 0 0 .7 8 7 0 .8 4 3 0 ,8 0 8 0 .9 1 3 0 .771

0 .0 0 0 0 .7 0 2 0 .7 8 0 0 .7 4 5 0 .6 9 9 0 .6 7 8-1 2 .0 0 0 0 .5 6 4 0 .5 7 9 0 .5 6 9 0 .6 0 6 0 .4 9 2-2 4 .0 0 0 0 .361 0 .381 0 .3 5 4 0 .5 5 7 0 .3 5 4-3 8 .0 0 0 0 .2 9 0 0 .301 0 .3 0 4 0 .1 3 0 0 .2 5 0

168 ,5m m , 15o, 19 5 R P M ,tw o --phase,RPD = 0 ,7 0 55 4 .0 0 0 0 .2 9 6 0 .2 6 8 0 .2 7 0 0 .4 1 8 0 .2313 8 .0 0 0 0 .3 3 9 0 .3 2 5 0 .3 2 8 0 .3 8 4 0 .3 6 42 4 .0 0 0 0 .5 1 3 0 .511 0 .511 0 .5 2 6 0 .5 5 01 2 .0 0 0 0 .6 4 8 0 .7 1 4 0 .6 9 6 0 .4 3 9 0 .6 1 0

0 .0 0 0 0 .6 4 0 0 .6 6 7 0 .6 6 7 0 .4 2 6 0 .5 6 9-1 2 .0 0 0 0 .511 0 .5 1 5 0 .5 1 9 0 .421 0 .4 5 0-2 4 .0 0 0 0 .3 2 8 0 .3 4 3 0 .3 3 7 0 .3 1 5 0 .2 9 7-3 8 .0 0 0 0 .2 7 3 0 .2 7 6 0 .2 6 6 0 .3 7 3 0 .241

198 ,5m m , 15o , 195 R PM ,s in g le -p ha se . 5 4 .0 0 0 0 .391 0 .3 7 8 0 .3 8 8 0 .3 3 3 0 .3 9 23 8 .0 0 0 0 .4 3 3 0 .4 9 4 0 .4 5 9 0 .5 3 5 0 .5 1 92 4 .0 0 0 0 .5 6 0 0 .5 8 4 0 .5 5 4 0 .7 8 2 0 .5 6 21 2 .0 0 0 0 .5 8 6 0 .6 0 5 0 .6 0 4 0 .4 6 3 0 .6 1 6

0 .0 0 0 0 .5 0 2 0 .6 2 6 0 .5 6 7 0 .5 7 3 0 .5 4 8-1 2 .0 0 0 0 .4 7 4 0 .5 4 7 0 .4 8 5 0 .7 9 6 0 .4 6 5-2 4 .0 0 0 0 .3 7 5 0 .4 4 9 0 .4 3 8 0 .3 4 3 0 .4 1 9-3 8 .0 0 0 0 .3 3 7 0 .321 0 .3 5 0 0 .2 9 9 0 .3 3 0

APPENDIX 3. 243

RMS data for the 240mm Rushton impeller, T =450mm,h = 585mm,c=315mm Z[mm] RMS+150 RMS-15o RMStang RMSrad RMSaxR = 198 ,5m m , 15o , 19 5 R P M ,tw o -p h a se ,R P D = 0 ,7 0 5

5 4 .0 0 0 0 .3 5 4 0 .3 4 0 0 .321 0 .6 0 3 0 .3 4 93 8 .0 0 0 0 .4 0 3 0 .4 6 3 0 .3 9 8 0 .7 7 8 0 .4 3 52 4 .0 0 0 0 .4 6 2 0 .5 5 8 0 .481 0 .8 3 4 0 .5 2 01 2 .0 0 0 0 .5 0 9 0 .5 4 0 0 .5 1 0 0 .6 9 8 0 .5 4 2

0 .0 0 0 0 .4 6 8 0 .581 0 .5 1 8 0 .6 4 6 0 .4 9 0-1 2 .0 0 0 0 .4 3 5 0 .4 8 9 0 .471 0 .3 2 8 0 .4 4 0-2 4 .0 0 0 0 .3 9 9 0 .4 0 5 0 .3 6 4 0 .7 5 3 0 .4 0 7-3 8 .0 0 0 0 .2 9 9 0 .3 2 5 0 .3 3 8 0 .3 6 8 0 .3 2 7

APPENDIX 3. 244

Z[mm] RMS+150 RMS-15o RMStang. RMSrad. RMSax.R = 12 3 ,5m m , 45 o , 19 5 R P M , s ing le -phase .

5 4 .0 0 0 0 .2 3 2 0 .2 5 7 0 .2 4 3 0 .2 6 9 0 .2 9 44 6 .0 0 0 0 .2 5 6 0 .2 9 9 0 .2 9 5 0 .2 3 6 0 .3 2 63 8 .0 0 0 0 .3 0 9 0 .3 7 6 0 .3 4 8 0 .2 8 5 0 .4 8 33 3 .0 0 0 0 .3 8 6 0 .4 7 5 0 .4 2 0 0 .5 8 3 0 .6 8 32 4 .0 0 0 0 .6 2 5 0 .7 4 7 0 .7 0 6 0 .3 7 2 0 .9 2 22 1 .0 0 0 0 .6 6 4 0 .6 9 4 0 .6 3 5 1 .1 2 7 0 .9 6 41 3 .0 0 0 0 .8 1 4 0 .9 6 8 0 .9 4 0 0 .6 0 6 0 .731

6 .0 0 0 0 .8 1 2 1 .1 2 2 0 .9 5 3 1 .2 9 2 0 .5 2 20 .0 0 0 0 .8 1 8 1 .0 4 7 0 .9 4 9 0 .7 9 6 0 .5 5 6

-6 .0 0 0 0 .8 3 4 0 .9 3 0 0 .8 5 2 1 .2 4 0 0 .6 5 6-1 2 .0 0 0 0 .8 3 8 0 .7 3 7 0 .7 7 0 1 .0 1 9 0 .7 6 4-1 8 .0 0 0 0 .6 4 8 0 .7 4 9 0 .7 1 5 0 .4 4 9 0 .7 2 9-2 6 .0 0 0 0 .4 2 8 0 .5 0 9 0 .4 8 5 0 .1 5 8 0 .6 4 0-3 0 .0 0 0 0 .3 6 5 0 .4 0 7 0 .3 8 6 0 .3 9 5 0 .5 7 2-3 8 .0 0 0 0 .2 8 7 0 .3 3 3 0 .3 0 8 0 .3 4 8 0 .4 0 6

R = 123 ,5m m , 45 o , 1 9 5 R P M , tw o -phase , RPD = 0 ,7 0 55 4 .0 0 0 0 .2 0 7 0 .2 2 6 0 .2 0 6 0 .3 3 2 0 .2 3 44 6 .0 0 0 0 .2 1 6 0 .2 3 9 0 .241 0 .1 8 5 0 .2 6 53 8 .0 0 0 0 .2 6 2 0 .3 0 2 0 .2 7 7 0 .3 5 3 0 .3413 3 .0 0 0 0 .3 3 4 0 .381 0 .3 5 0 0 .4 5 8 0 .4 6 03 1 .0 0 0 0 .5 4 5 0 .4 3 6 0 .4 5 8 0 .8 4 5 0 .5 8 02 5 .0 0 0 0 .8 5 7 0 .7 7 2 0 .8 3 3 0 .5 1 62 4 .0 0 0 0 .7 1 9 0 .7 9 3 0 .8 4 6 1 .1 9 0 0 .8 3 22 3 .0 0 0 0 .9 9 9 0 .8 0 7 0 .8 6 0 1 .4 1 72 0 .0 0 0 0 .9 9 7 0 .8 7 7 0 .9 6 0 0 .5 6 9 0 .8 5 51 6 .0 0 0 0 .9 1 4 0 .8 9 2 0 .8 7 3 1 .2 4 9 0 .8 7 31 1 .0 0 0 0 .8 8 2 0 .8 5 6 0 .8 4 4 1 .1 6 4 0 .6 9 9

6 .0 0 0 0 .7 6 8 0 .9 0 0 0 .8 3 3 0 .8 8 5 0 .5 7 80 .0 0 0 0 .851 0 .8 8 7 0 .8 0 2 1 .5 2 3 0 .5 3 9

-6 .0 0 0 0 .9 4 6 0 .8 5 3 0 .8 1 8 1.671 0 .6 2 7-1 2 .0 0 0 0 .9 5 5 0 .8 0 9 0 .871 1.061 0 .701-1 5 .0 0 0 0 .9 2 2 0 .8 6 5 1 .017 1 .5 7 3-1 8 .0 0 0 0 .9 4 7 0 .6 8 9 1 .0 1 0 1 .9 9 3 0 .7 2 5-2 2 .0 0 0 0 .6 6 2 0 .6 4 0 0 .6 5 0 0 .6 6 6 0 .7 3 3-2 4 .0 0 0 0 .5 3 3 0 .5 2 9 0 .5 2 0 0 .6 6 6-2 6 .0 0 0 0 .3 6 5 0 .4 2 8 0 .3 9 0 0 .4 9 3 0 .5 2 7-3 0 .0 0 0 0 .2 8 8 0 .3 5 6 0 .3 3 7 0 .1 2 9 0 .4 1 2-3 6 .0 0 0 0 .2 6 6 0 .2 7 7 0 .2 5 9 0 .4 0 8 0 .3 3 2-3 8 .0 0 0 0 .2 3 0 0 .2 5 5 0 .2 5 0 0 .0 9 8

R = 133 ,5m m , 45 o , 1 9 5 R P M , s ing le -phase5 4 .0 0 0 0 .2 2 9 0 .2 3 4 0 .2 3 4 0 .1 9 4 0 .2 6 73 8 .0 0 0 0 .3 3 3 0 .3 5 3 0 .321 0 .5 6 8 0 .4 0 73 0 .0 0 0 0 .3 8 5 0 .4 9 0 0 .4 3 2 0 .5 4 7 0 .6 2 42 4 .0 0 0 0 .5 5 2 0 .6 1 7 0 .6 3 6 0 .7 2 0 0 .8 8 41 8 .0 0 0 0 .7 6 5 0 .7 5 4 0 .8 2 5 0 .9 3 2 1 .0 6 0

APPENDIX 3. 245

Z[mm] R M S+15o RMS-15o RMStang. RMSrad. RMSax.1 2 .0 0 0 0 .7 8 2 1 .0 3 5 0 .8 9 9 1 .1 4 2 0 .791

6 .0 0 0 0 .7 5 8 1 .0 8 5 0 .9 3 6 0 .9 3 4 0 .5 4 20 .0 0 0 0 .8 2 3 1.041 0 .9 4 0 0 .9 1 5 0 .581

-6 .0 0 0 0 .9 3 4 0 .961 0 .9 4 5 0 .9 8 3 0 .7 6 3-1 2 .0 0 0 0 .9 1 5 0 .8 0 0 0 .751 1.781 0 .8 1 7-1 8 .0 0 0 0 .4 9 4 0 .5 7 5 0 .5 8 7 0 .7 1 4 0 .6 4 0-3 0 .0 0 0 0 .3 0 8 0 .351 0 .3 3 5 0 .2 5 4 0 .3 7 8-3 8 .0 0 0 0 .2 5 2 0 .281 0 .2 6 0 0 .3 4 9

13 3 ,5 m m ,4 5 o , 195 R P M ,tw o -p h a se ,R P D = 0 ,7 0 55 4 .0 0 0 0 .1 9 5 0 .1 9 8 0 .2 0 7 0 .1 4 3 0 .2214 6 .0 0 0 0 .2 1 4 0 .2 3 2 0 .2 2 4 0 .211 0 .2 4 73 8 .0 0 0 0 .2 3 7 0 .2 7 2 0 .2 5 8 0 .211 0 .3 0 53 3 .0 0 0 0 .2 9 4 0 .3 3 8 0 .3 1 6 0 .3 2 7 0 .4 0 52 8 .0 0 0 0 .4 2 5 0 .4 7 8 0 .4 1 0 0 .8 4 4 0 .5 6 52 4 .0 0 0 0 .5 2 3 0 .5 9 3 0 .6 3 0 0 .9 2 8 0 .7 3 52 0 .0 0 0 0 .8 1 2 0 .7 1 6 0 .7 7 0 0 .7 0 0 0 .8 0 81 6 .0 0 0 0 .8 9 4 0 .821 0 .8 1 0 1 .3 6 3 0 .7 7 61 1 .0 0 0 0 .7 8 6 0 .8 8 6 0 .871 0 .3 1 0 0 .6 8 3

6 .0 0 0 0 .7 3 3 0 .8 7 8 0 .8 5 5 0 .6 4 6 0 .6 0 20 .0 0 0 0 .7 4 9 0 .8 2 4 0 .7 6 0 1 .1 0 0 0 .6 1 6

-6 .0 0 0 0 .7 2 6 0 .6 4 3 0 .6 4 5 1 .1 0 7 0 .7 2 7-1 2 .0 0 0 0 .8 5 3 0 .6 3 0 0 .6 3 4 1 .6 7 2 0 .7 6 9-1 5 .0 0 0 0 .721 0 .6 1 3 0 .7 2 0 0 .7 3 2-1 8 .0 0 0 0 .5 4 8 0 .5 2 0 0 .5 3 6 0 .5 0 8 0 .6 3 4-2 6 .0 0 0 0 .2 6 7 0 .341 0 .3 0 7 0 .2 9 6 0 .391-3 0 .0 0 0 0 .2 4 8 0 .2 9 5 0 .2 6 6 0 .351 0 .3 0 7-3 8 .0 0 0 0 .2 1 3 0 .2 2 7 0 .2 1 7 0 .2 6 0 0 .2 5 3

1 4 8 ,5 m m ,4 5 o , 1 9 5 R P M , s ing le -phase5 4 .0 0 0 0 .2 1 9 0 .2 3 2 0 .2 2 8 0 .1 8 9 0 .2 5 33 8 .0 0 0 0 .3 6 8 0 .3 3 5 0 .311 0 .7 0 8 0 .3 7 63 0 .0 0 0 0 .4 9 2 0 .5 5 0 0 .5 2 4 0 .4 9 0 0 .6 1 42 4 .0 0 0 0 .7 7 8 0 .7 8 5 0 .8 4 8 0 .9 4 8 0 .8 6 91 8 .0 0 0 1 .0 0 5 0 .9 3 3 0 .9 8 0 0 .8 1 2 1 .0 1 31 2 .0 0 0 0 .9 5 0 0 .981 0 .9 7 4 0 .8 4 0 0 .8 2 2

6 .0 0 0 0 .8 5 8 1 .0 1 4 0 .9 4 0 0 .9 2 9 0 .6 4 60 .0 0 0 0 .8 6 4 1 .0 1 2 0 .9 2 6 1 .1 2 8 0 .6 9 8

-6 .0 0 0 0 .8 9 0 0 .9 3 2 0 .9 1 3 0 .8 8 6 0 .7 4 2-1 2 .0 0 0 0 .7 5 2 0 .6 9 6 0 .6 9 9 1 .0 1 6 0 .6 8 4-1 8 .0 0 0 0 .4 9 4 0 .4 6 4 0 .4 5 5 0 .7 3 8 0 .5 4 2-3 0 .0 0 0 0 .2 6 0 0 .281 0 .2 6 5 0 .3 4 0 0 .2 6 9-3 8 .0 0 0 0 .2 4 0 0 .2 4 4 0 .231 0 .3 6 2 0 .2 5 9

14 8 ,5 m m ,4 5 o ,1 9 5 R P M , tw o -phase , R PD = 0 ,7 0 55 4 .0 0 0 0 .201 0 .2 0 7 0 .2 0 2 0 .2 3 0 0 .2 1 84 6 .0 0 0 0 .201 0 .2 2 2 0 .2 1 7 0 .1 1 6 0 .2 5 3

APPENDIX 3. 246

Z[mm] RM S+150 RMS-15o RMStang. RMSrad. RMSax.3 8 .0 0 0 0 .3 6 9 0 .2 5 4 0 .2 4 9 0 .7 9 6 0 .3 3 33 0 .0 0 0 0 .3 9 8 0 .3 9 9 0 .401 0 .3 6 2 0 .4 9 32 4 .0 0 0 0 .5 7 2 0 .5 7 3 0 .6 1 7 0 .6 4 0 0 .6 6 41 8 .0 0 0 0 .751 0 .7 7 5 0 .7 5 6 0 .8 5 6 0 .7 1 71 2 .0 0 0 0 .8 1 9 0 .8 7 3 0 .8 6 2 0 .5 8 8 0 .6 8 8

6 .0 0 0 0 .7 9 3 0 .8 6 5 0 .8 7 2 0 .5 5 9 0 .6 8 30 .0 0 0 0 .7 9 7 0 .8 2 4 0 .8 1 0 0 .8 1 9 0 .6 5 0

-6 .0 0 0 0 .7 2 5 0 .6 7 0 0 .701 0 .6 5 5 0 .6 1 3-1 2 .0 0 0 0 .5 2 7 0 .5 4 8 0 .5 4 9 0 .341 0 .5 3 8-1 8 .0 0 0 0 .3 5 2 0 .3 7 6 0 .3 9 6 0 .4 5 2 0 .4 4 6-2 4 .0 0 0 0 .2 8 2 0 .2 8 7 0 .2 6 4 0 .4 8 7 0 .3 3 7-3 0 .0 0 0 0 .2 0 7 0 .2 4 2 0 .2 3 0 0 .1 4 2 0 .2 5 6-3 8 .0 0 0 0 .1 9 9 0 .2 0 0 0 .1 9 3 0 .2 7 4 0 .2 2 616 8 ,5 m m ,4 5 o ,1 9 5 R P M , s ing le -phase5 4 .0 0 0 0 .251 0 .2 5 0 0 .2 4 8 0 .2 8 3 0 .2713 8 .0 0 0 0 .441 0 .4 0 8 0 .4 4 2 0 .1 6 4 0 .4 4 43 0 .0 0 0 0 .7 0 8 0 .6 3 7 0 .7 2 0 0 .6712 4 .0 0 0 0 .9 1 7 0 .8 5 8 0 .9 0 6 0 .5 8 2 0 .7 7 81 8 .0 0 0 0 .9 7 4 0 .9 5 4 0 .9 4 2 1.2311 2 .0 0 0 0 .9 5 8 0 .9 6 7 0 .9 5 9 1 .0 1 0 0 .781

6 .0 0 0 0 .8 8 9 0 .9 4 0 0 .9 4 9 0 .2 2 20 .0 0 0 0 .8 9 0 0 .9 3 0 0 .9 2 7 0 .6 3 2 0 .7 1 9

-6 .0 0 0 0 .8 3 2 0 .8 6 5 0 .8 5 4 0 .7 7 0-1 2 .0 0 0 0 .701 0 .6 8 9 0 .671 0 .9 7 0 0 .5 9 8-2 4 .0 0 0 0 .3 3 2 0 .3 5 2 0 .3 4 2 0 .3 4 4 0 .3 7 7-3 8 .0 0 0 0 .2 2 7 0 .2 2 7 0 .2 2 5 0 .2 5 3 0 .2 5 516 8 ,5 m m ,4 5 o ,1 9 5 R P M ,tw o -p h a se ,R P D = 0 ,7 0 55 4 .0 0 0 0 .2 1 8 0 .2 2 8 0 .2 2 9 0 .111 0 .2 4 63 8 .0 0 0 0 .3 2 4 0 .3 4 5 0 .3 1 4 0 .5 4 7 0 .3 6 72 4 .0 0 0 0 .6 3 5 0 .641 0 .6 0 5 0 .9 8 9 0 .6 4 01 2 .0 0 0 0 .7 8 4 0 .8 0 7 0 .801 0 .7 1 6 0 .6 5 56 .0 0 0 0 .7 8 6 0 .8 1 0 0 .7 9 6 0 .8 2 7 0 .6 2 30 .0 0 0 0 .7 6 4 0 .8 1 3 0 .7 8 2 0 .8 7 9 0 .6 1 6

-6 .0 0 0 0 .6 9 2 0 .6 7 3 0 .6 8 7 0 .6 1 8 0 .5 5 4-1 2 .0 0 0 0 .5 6 3 0 .5 1 9 0 .5 3 6 0 .6 1 2 0 .4 5 8-2 4 .0 0 0 0 .2 8 0 0 .2 6 2 0 .2 6 6 0 .3 3 5 0 .2 8 9-3 8 .0 0 0 0 .2 0 7 0 .2 0 4 0 .2 0 2 0 .2 4 9 0 .2 1 519 8 ,5 m m ,4 5 o , 19 5 R P M , s ing le -phase .5 4 .0 0 0 0 .451 0 .4 1 3 0 .4 5 6 0 .3 2 4 0 .4 3 03 8 .0 0 0 0 .591 0 .5 6 6 0 .6 0 6 0 .3 4 2 0 .5712 4 .0 0 0 0 .6 9 4 0 .7 1 4 0 .6 8 4 0 .9 4 0 0 .6 7 01 2 .0 0 0 0 .7 3 8 0 .7 5 9 0 .7 4 8 0 .7 5 7 0 .6 4 2

0 .0 0 0 0 .7 0 3 0 .7 3 2 0 .731 0 .4 9 6 0 .5 8 8-1 2 .0 0 0 0 .5 7 3 0 .5 9 4 0 .6 2 3 0 .5 6 7 0 .4 9 6-2 4 .0 0 0 0 .4 3 8 0 .4 4 5 0 .5 1 5 0 .8 8 5 0 .3 9 8-3 8 .0 0 0 0 .3 4 0 0 .3 3 2 0 .3 5 3 0 .2 2 4 0 .3 1 7

APPENDIX 3. 247

Z[mm] RMS+15o RMS-15© RMStang. RMSrad. RMSax.R = 198,5111111,450,19 5 R P M ,tw o -p h a s e ,R P D = 0 ,7 0 5

5 4 .0 0 0 0 .3 5 5 0 .3 4 4 0 .3 6 3 0 .1 0 7 0 .3 7 83 8 .0 0 0 0 .4 3 0 0 .4 4 3 0 .4 2 5 0 .5 7 4 0 .4312 4 .0 0 0 0 .5 5 0 0 .5 5 2 0 .5 2 7 0 .8 1 5 0 .5 2 41 2 .0 0 0 0 .5 7 8 0 .6 0 2 0 .5 7 4 0 .781 0 .5 3 0

0 .0 0 0 0 .5 4 7 0 .5 9 3 0 .5 6 8 0 .6 0 4 0 .5 0 9-1 2 .0 0 0 0 .4 5 7 0 .4 8 0 0 .4 8 8 0 .1 9 6 0 .4 4 9-2 4 .0 0 0 0 .3 8 7 0 .3 8 0 0 .3 9 5 0 .1 5 0 0 .3 7 0-3 8 .0 0 0 0 .331 0 .3 2 2 0 .3 3 4 0 .1 9 5 0 .2 9 8

APPENDIX 3. 248

Z[mm] RMS+15o RMS-15o RMStang. RMSrad. RMSax.R = 123 ,5m m , 75 o , 1 9 5 R P M , s ing le -phase .

5 4 .0 0 0 0 .2 0 3 0 .2 2 5 0 .2 1 5 0 .2 0 4 0 .2 4 03 8 .0 0 0 0 .281 0 .3 3 4 0 .3 1 9 0 .0 6 9 0 .4 5 33 0 .0 0 0 0 .0 0 0 0 .7 3 32 4 .0 0 0 0 .5 6 5 0 .681 0 .7 7 5 1 .5 8 8 0 .8911 8 .0 0 0 0 .0 0 0 1 .0 2 81 1 .0 0 0 0 .7 0 8 0 .9 0 6 0 .821 0 .6 9 3 0 .8 0 2

6 .0 0 0 0 .7 5 4 1 .0 4 0 0 .9 0 3 0 .9 8 0 0 .5 8 40 .0 0 0 0 .771 0 .951 0 .8 7 4 0 .7 4 0 0 .5 6 2

-6 .0 0 0 0 .7 7 9 0 .8 2 3 0 .7 9 8 0 .8 4 6 0 .6 2 6-1 8 .0 0 0 0 .6 0 2 0 .6 1 5 0 .7 2 0 1.301 0 .6 3 5-2 4 .0 0 0 0 .4 7 3 0 .5 1 5 0 .5 2 4 0 .4 1 8 0 .5 7 6-3 8 .0 0 0 0 .2 4 6 0 .2 7 5 0 .2 7 5 0 .1 9 3 0 .3 9 9

123 ,5m m , 75o , 1 9 5 R P M , tw o -phase , RPD = 0 ,7 0 55 4 .0 0 0 0 .1 9 2 0 .2 0 0 0 .1 9 9 0 .1 4 9 0 .2 2 03 8 .0 0 0 0 .2 5 8 0 .2 6 7 0 .2 5 7 0 .3 3 0 0 .3 2 03 0 .0 0 0 0 .3 6 0 0 .391 0 .341 0 .6 9 9 0 .4 5 52 7 .0 0 0 0 .5 1 5 0 .491 0 .4 2 6 1 .1 1 92 4 .0 0 0 0 .5 2 9 0 .6 2 2 0 .8 2 0 2 .0 9 5 0 .6 7 82 1 .0 0 0 0 .7 9 9 0 .761 0 .8 0 7 0 .1 3 01 8 .0 0 0 0 .871 0 .8 5 6 0 .7 9 7 1.511 0 .8411 2 .0 0 0 0 .8 4 8 0 .9 0 0 0 .8 3 7 1 .2 8 7 0 .7 2 5

6 .0 0 0 0 .6 8 9 0 .8 7 0 0 .7 8 4 0 .7 9 5 0 .5 8 30 .0 0 0 0 .7 3 7 0 .8 5 6 0 .781 1 .0 1 4 0 .5 2 9

-6 .0 0 0 0 .7 6 4 0 .7 8 7 0 .7 4 3 1 .1 3 6 0 .6 0 0-9 .0 0 0 0 .6 7 9 0 .7 8 5 0 .7 3 9 0 .6 5 9 0 .5 9 2

-1 2 .0 0 0 0 .731 0 .6 9 7 0 .7 3 6 0 .2 6 4-1 5 .0 0 0 0 .8 3 5 0 .621 0 .9 0 6 1 .8 3 0 0 .591-1 8 .0 0 0 0 .5 9 4 0 .5 7 6 0 .7 5 4 1 .6 7 6-2 1 .0 0 0 0 .4 9 0 0 .5 2 9 0 .6 1 8 1 .1 9 9 0 .5 4 0-2 4 .0 0 0 0 .5 2 7 0 .4 3 3 0 .4 3 7 0 .901-3 0 .0 0 0 0 .2 6 8 0 .3 2 9 0 .3 3 3 0 .4 4 8 0 .3 4 8-3 8 .0 0 0 0 .2 2 2 0 .2 4 8 0 .2 2 9 0 .311 0 .2 8 9

133 ,5m m , 75o , 1 9 5 R P M , sing le -phase5 4 .0 0 0 0 .1 9 7 0 .2 2 0 0 .2 2 6 0 .2 4 6 0 .2 3 33 8 .0 0 0 0 .3 3 2 0 .3 0 3 0 .2 8 7 0 .6013 0 .0 0 0 0 .4 0 2 0 .4 4 2 0 .3 9 7 0 .6 8 5 0 .5 8 82 4 .0 0 0 0 .4 5 4 0 .5 6 9 0 .5 2 2 0 .4 0 0 0 .8 2 91 1 .0 0 0 0 .6 6 4 0 .8 9 0 0 .7 8 7 0 .7 5 9 0 .8 2 6

APPENDIX 3. 249

Z[mm] RMS+150 RMS-150 RMStang. RMSrad. RMSax.6 .0 0 0 0 .7 8 6 1 .0 0 2 0 .8 6 6 1 .2 8 8 0 .6 3 60 .0 0 0 0 .7 5 6 0 .9 6 5 0 .8 8 9 0 .4 5 7 0 .6 0 2

-6 .0 0 0 0 .8 0 6 0 .8 4 2 0 .8 4 3 0 .4 9 3 0 .7 4 8-1 5 .0 0 0 0 .5 0 4 0 .5 5 9 0 .531 0 .5 4 9 0 .6 5 3-2 4 .0 0 0 0 .3 4 6 0 .4 1 4 0 .3 8 8 0 .2 7 6 0 ,4 6 2-3 8 .0 0 0 0 .2 4 2 0 .2 5 2 0 .2 4 6 0 .261 0 .3 1 2

= 133 ,5m m , 75o , 1 9 5R P M , tw o -phase . RPD = 0 ,7 0 55 4 .0 0 0 0 .2 0 0 0 .1 9 7 0 .1 9 0 0 .2 9 2 0 .2 2 44 6 .0 0 0 0 .1 9 7 0 .2 0 6 0 .7 7 93 8 .0 0 0 0 .2 4 8 0 .2 4 2 0 .2 3 7 0 .3 3 7 0 .2 9 63 0 .0 0 0 0 .2 9 2 0 .3 5 5 1 .2 5 6 0 .4 5 32 4 .0 0 0 0 .4 1 7 0 .4 9 7 0 .4 6 5 0 .361 0 .6 7 81 8 .0 0 0 0 .6 0 7 0 .6 7 8 2 .4 8 6 0 .7 9 61 2 .0 0 0 0 .6 8 6 0 .8 6 7 0 .7 8 8 0 .6 8 9 0 .6 2 3

6 .0 0 0 0 .6 4 8 0 .821 0 .7 9 3 0 .7 7 0 0 .5 4 40 .0 0 0 0 .6 3 6 0 .741 0 .7 2 7 0 .4 9 4 0 .5 9 3

-6 .0 0 0 0 .5 5 6 0 .5 6 4 2 .1 6 4 0 .7 0 5-1 2 .0 0 0 0 .6 0 9 0 .531 0 .5 2 4 1 .0 2 4 0 .7 1 4-1 8 .0 0 0 0 .3 8 0 0 .4 3 4 1 .5 7 6 0 .6 1 3-2 4 .0 0 0 0 .3 0 2 0 .3 5 7 0 .3 0 9 0 .5 5 0-3 0 .0 0 0 0 .2 4 7 0 .2 6 6 0 .9 9 2 0 .3 0 2-3 8 .0 0 0 0 .2 1 4 0 .2 2 0 0 .2 0 0 0 .3 8 2 0 .2 5 8

1 4 8 ,5 m m ,75 o , 195 R PM ,s in g le -p hase .5 4 .0 0 0 0 .2 0 7 0 .2 0 0 0 .2 0 9 0 .1 0 0 0 .2 4 33 8 .0 0 0 0 .2 8 9 0 .2 6 2 0 .2 8 0 0 .2 0 93 0 .0 0 0 0 .3 8 3 0 .4 3 9 0 .4 0 2 0 .5 3 2 0 .5 4 92 4 .0 0 0 0 .6 0 6 0 .6 3 4 0 .6 3 4 0 .3 7 8 0 .8 0 31 8 .0 0 0 0 .0 0 0 0 .9 6 21 2 .0 0 0 0 .8 0 7 0 .8 8 2 0 .8 7 8 0 .2 6 4 0 .8 9 5

6 .0 0 0 0 .7 5 6 0 .9 2 3 0 .8 5 5 0 .6 6 6 0 .7 4 30 .0 0 0 0 .7 7 8 0 .9 1 6 0 .8 5 0 0 .8 4 7 0 .7 1 8

-6 .0 0 0 0 .7 3 2 0 .7 7 3 0 .8 2 6 1.021-1 2 .0 0 0 0 .6 1 7 0 .6 2 7 0 .6 2 6 0 .5 6 4 0 .6 4 7-1 8 .0 0 0 0 .3 9 4 0 .421 0 .4 1 5 0 .2 8 8-2 4 .0 0 0 0 .2 9 0 0 .2 9 6 0 .3 0 7 0 .1 7 6 0 .3 7 4-3 8 .0 0 0 0 .2 0 0 0 .2 1 3 0 .2 0 3 0 .251 0 .2 5 3

R = 148 ,5m m , 75o , 1 9 5 R P M ,tw o -p h a se , RPD = 0 ,7 0 55 4 .0 0 0 0 .1 9 2 0 .201 0 .1 9 3 0 .241 0 .2 3 74 6 .0 0 0 0 .1 9 8 0 .1 9 5 0 .1 9 5 0 .2 1 6 0 .3 0 6

APPENDIX 3. 250

ZEmm] RM S+150 RMS-15o RMStang. RMSrad. RMSax.3 8 .0 0 0 0 .3 3 9 0 .2 4 5 0 .2 3 5 0 .7 3 3 0 .3 2 63 0 .0 0 0 0 .3 3 5 0 .3 7 6 0 .3 4 5 0 .4 8 5 0 .4 7 62 4 .0 0 0 0 .4 7 6 0 .5 5 2 0 .4 6 9 0 .9 5 0 0 .6 3 318 .0 0 0 0 .6 1 6 0 .6 9 7 0 .6 2 5 1 .0 0 9 0 .7 1 81 2 .0 0 0 0 .7 1 4 0 .8 1 2 0 .781 0 .481 0 .6 4 2

6 .0 0 0 0 .7 0 3 0 .8 0 6 0 .8 0 0 0 .6 1 3 0 .6 2 70 .0 0 0 0 .651 0 .7 7 4 0 .7 3 8 0 .221 0 .6 0 3

-6 .0 0 0 0 .561 0 .6 3 8 0 .6 0 0 0 .611 0 .6 2 4-1 2 .0 0 0 0 .4 6 9 0 .4 6 4 0 .4 8 9 0 .2 8 6-1 8 .0 0 0 0 .3 2 0 0 .3 3 7 0 .3 7 5 0 .5 8 9 0 .441-2 4 .0 0 0 0 .2 5 7 0 .2 8 5 0 .2 6 3 0 .3 6 9-3 0 .0 0 0 0 .1 9 8 0 .2 3 0 0 .2 2 0 0 .1 1 6 0 .2 7 3-3 8 .0 0 0 0 .1 8 9 0 .2 0 4 0 .1 8 5 0 .3 1 7 0 .2 4 5168 ,5m m , 7 5 o ,1 9 5 R P M , sing le -phase5 4 .0 0 0 0 .251 0 .2 3 5 0 .2 4 9 0 .1 3 7 0 .2 6 83 8 .0 0 0 0 .3 7 8 0 .4 0 3 0 .3 7 6 0 .5 5 6 0 .4 2 02 4 .0 0 0 0 .6 9 7 0 .7 2 2 0 .7 2 3 0 .4 8 6 0 .7 5 51 2 .0 0 0 0 .8 2 0 0 .8 9 9 0 .8 3 7 1 .1 3 7 0 .8 2 8

0 .0 0 0 0 .7 6 7 0 .8 7 5 0 .8 1 9 0 .8 7 4 0 .7 2 7-1 2 .0 0 0 0 .5 8 2 0 .6 4 5 0 .6 0 5 0 .7 3 2 0 .5 7 9-2 4 .0 0 0 0 .3 4 0 0 .2 8 6 0 .2 8 5 0 .5 8 5 0 .3 6 6-3 8 .0 0 0 0 .2 2 5 0 .2 0 7 0 .2 2 0 0 .1 5 4 0 .2 4 5

1 4 8 ,5 m m ,7 5 o ,1 9 5 R P M ,tw o -p h a se ,R P D = 0 ,7 0 55 4 .0 0 0 0 .2 3 2 0 .2 1 5 0 .2 0 6 0 .3 9 5 0 .2 3 33 8 .0 0 0 0 .2 9 9 0 .3 3 0 0 .2 9 0 0 .5 5 6 0 .3 8 62 4 .0 0 0 0 .5 0 9 0 .5 7 9 0 .5 6 9 0 .271 0 .6 2 31 2 .0 0 0 0 .7 0 2 0 .7 4 5 0 .7 2 5 0 .7 0 7 0 .651

6 .0 0 0 0 .7 0 0 0 .7 7 0 0 .7 5 5 0 .3 7 9 0 .6 0 80 .0 0 0 0 .6 7 3 0 .7 9 0 0 .6 9 7 1 .1 2 8 0 .5 9 6

-1 2 .0 0 0 0 .4 8 2 0 .5 7 5 0 .5 0 0 0 .8 4 8 0 .4 7 7-2 4 .0 0 0 0 .2 6 8 0 .2 8 3 0 .2 6 9 0 .3 5 5 0 .3 1 0-3 8 .0 0 0 0 .2 1 2 0 .2 0 3 0 .1 9 4 0 .3 4 5 0 .2 3 3

1 9 8 ,5 m m ,7 5 o ,1 9 5 R P M , s ing le -phase .5 4 .0 0 0 0 .4 2 4 0 .3 8 3 0 .4 0 3 0 .4 1 8 0 .4 1 23 8 .0 0 0 0 .5 0 8 0 .5 1 6 0 .5 4 5 0 .4 7 3 0 .5012 4 .0 0 0 0 .5 8 4 0 .6 3 0 0 .6 3 0 0 .141 0 .6 3 31 2 .0 0 0 0 .6 5 7 0 .6 8 0 0 .6 6 2 0 .7 5 5 0 .6 6 00 .0 0 0 0 .6 7 3 0 .7 0 8 0 .7 0 5 0 .4 4 7 0 .6 0 0

-1 2 .0 0 0 0 .6 1 0 0 .5 5 5 0 .5 8 0 0 .6 2 5 0 .4 7 8-2 4 .0 0 0 0 .4 1 4 0 .401 0 .4 3 0 0 .3 0 9 0 .421-3 8 .0 0 0 0 .3 5 3 0 .3 8 3 0 .3 3 6 0 .6 7 3 0 .3 7 3

APPENDIX 3. 251

Z[mm] RMS+15o RMS-15o RMStang.R = 19 8 ,5 m m ,7 5 o ,1 9 5 R P M , tw o -phase , RPD = 0 ,7 0 5

5 4 .0 0 0 0 .3 4 83 8 .0 0 0 0 .3 9 62 4 .0 0 0 0 .5 5 41 2 .0 0 0 0 .551

0 .0 0 0 0 .5 7 0-1 2 .0 0 0 0 .4 7 5-2 4 .0 0 0 0 .3 7 3-3 8 .0 0 0 0 .3 2 4

0 .3 2 7 0 .3 5 90 .4 2 4 0 .4 1 60 .5 7 5 0 .5 4 90 .5 7 5 0 .5 9 00 .5 9 3 0 .5 4 90 .4 9 7 0 .4 8 80 .3 5 7 0 .4 0 00 .2 9 8 0 .3 3 3

RMSrad. RMSax.

0 .3 0 5 0 .3 4 50 .3 1 9 0 .4 5 40 .7 4 9 0 .5 1 50 .3 3 8 0 .5510 .9 2 3 0 .5 3 00 .4 5 9 0 .4 7 50 .4 8 9 0 .3 4 00 .3 1 3 0 .2 8 8

APPENDIX 3. 252

Mean velocity data for the 180mm Rushton impeller. Velocities in [m/s]T = 450mm, h = 580mm, c=315mmZlmm] V+ 15o V-15o angleY Vradial Vaxial Vtang.R = 13 3 ,5m m , 15o , 3 5 0 R P M , s ing le -phase

5 4 ,0 0 0 0 ,2 0 4 0 ,2 7 0 0 ,2 1 7 0 ,1 2 8 -0 ,1 6 7 0 ,2 6 33 6 ,0 0 0 0 ,2 2 9 0 ,3 3 7 0 ,3 5 7 0 ,2 0 9 -0 ,1 7 0 0 ,2 7 52 4 ,0 0 0 0 ,3 3 4 0 ,5 4 9 0 ,4 7 6 0 ,4 1 5 -0 ,051 0 ,6 4 21 8 ,0 0 0 0 ,7 8 3 0 ,9 7 2 0 ,1 2 0 0 ,3 6 5 0 ,2 3 2 0 ,8 1 01 2 ,0 0 0 1 ,2 0 0 1 ,9 4 0 0 ,4 6 0 1 ,4 3 0 0 ,7 5 2 1 ,293

6 ,0 0 0 1 ,3 9 9 2 ,1 8 9 0 ,4 2 6 1 ,5 2 6 0 ,721 1 ,7420 ,0 0 0 1,831 2 ,201 0 ,0 6 8 0 ,7 1 5 0 ,5 0 2 1 ,8 2 8

-6 ,0 0 0 1 ,4 0 0 1 ,7 1 0 0 ,0 9 4 0 ,5 9 9 0 ,5 1 2 1 ,5 2 8-1 2 ,0 0 0 0 ,8 0 0 1 ,4 7 0 0 ,5 7 2 1 ,2 9 4 0 ,4 0 2 0 ,8 7 4-1 8 ,0 0 0 0 ,4 6 6 0 ,7 0 0 0 ,381 0 ,4 5 2 0 ,351 0 ,5 5 0-2 4 ,0 0 0 0 ,2 4 9 0 ,4 3 5 0 ,531 0 ,3 5 9 0 ,3 0 3 0 ,3 7 3-3 6 ,0 0 0 0 ,1 9 5 0 ,3 0 4 0 ,4 2 2 0 ,211 0 ,2 9 2 0 ,2 6 2

133 ,5m m , 15o, 3 5 0 R P M , tw o -p h a se ,R PD = 0 ,5 3 75 4 ,0 0 0 0 ,1 9 5 0 ,2 3 2 0 ,051 0 ,071 -0 ,2 1 2 0 ,1 6 73 6 ,0 0 0 0 ,1 8 0 0 ,2 7 0 0 ,3 7 9 0 ,1 7 4 -0 ,1 7 9 0 ,1 9 22 4 ,0 0 0 0 ,4 1 6 0 ,5 2 0 0 ,131 0 ,201 0 ,171 0 ,3 8 21 8 ,0 0 0 0 ,7 4 5 0 ,8 4 9 -0 ,0 2 3 0 ,201 0 ,9 1 91 2 ,0 0 0 0 ,7 9 7 1 ,5 2 8 0 ,6 0 3 1 ,4 1 2 0 ,6 9 8 1 ,0 8 0

6 ,0 0 0 0 ,8 2 8 1 ,6 7 0 0 ,6 3 7 1 ,627 0 ,6 2 8 1 ,2 4 70 ,0 0 0 1 ,5 0 6 1 ,5 4 6 -0 ,2 1 3 0 ,0 7 7 0 ,3 7 8 1 ,4 0 0

-6 ,0 0 0 1 ,0 8 5 1 ,2 2 9 -0 ,0 3 4 0 ,2 7 8 0 ,3 1 0 1 ,1 9 4-1 2 ,0 0 0 0 ,6 0 6 1 ,1 4 5 0 ,5 9 3 1,041 0 ,2 9 0 0 ,611-1 8 ,0 0 0 0 ,3 4 9 0 ,7 2 9 0 ,6 5 9 0 ,7 3 4 0 ,4 7 8-2 4 ,0 0 0 0 ,1 9 6 0 ,3 3 2 0 ,5 0 4 0 ,2 6 3 0 ,2 2 2 0 ,2 5 5-3 6 ,0 0 0 0 ,1 6 5 0 ,241 0 ,3 4 8 0 ,1 4 7 0 ,2 2 6 0 ,1 5 0

148 ,5m m , 15o, 3 5 0 R P M , sing le -phase5 4 ,0 0 0 0 ,2 3 4 0 ,2 8 5 0 ,0 9 0 0 ,0 9 9 -0 ,0 8 8 0 ,2 7 23 6 ,0 0 0 0 ,2 3 6 0 ,3 6 4 0 ,411 0 ,2 4 7 -0 ,0 9 8 0 ,3 1 22 4 ,0 0 0 0 ,3 6 6 0 ,6 1 7 0 ,5 0 0 0 ,4 8 5 0 ,0 0 0 0 ,5 5 51 8 ,0 0 0 0 ,7 0 8 0 ,9 9 4 0 ,2 9 8 0 ,5 5 3 0 ,1 0 8 0 ,7 6 51 2 ,0 0 0 0 ,8 5 4 1 ,3 3 4 0 ,4 2 4 0 ,9 2 7 0 ,2 8 5 1 ,0 8 9

6 ,0 0 0 1 ,0 5 0 1 ,6 1 3 0 ,4 0 6 1 ,0 8 8 0 ,3 8 3 1 ,2 8 30 ,0 0 0 1 ,027 1 ,6 1 9 0 ,4 3 4 1 ,1 4 4 0 ,3 1 9 1 ,3 6 2

-6 ,0 0 0 0 ,9 0 6 1 ,4 7 6 0 ,4 6 7 1,101 0 ,3 0 5 1 ,1 6 0-1 2 ,0 0 0 0 ,6 8 2 0 ,9 5 6 0 ,2 9 6 0 ,5 2 9 0 ,291 0 ,8 0 6-1 8 ,0 0 0 0 ,4 3 9 0 ,6 9 4 0 ,4 3 7 0 ,4 9 3 0 ,2 7 0 0 ,5 4 0-2 4 ,0 0 0 0 ,2 9 9 0 ,5 0 4 0 ,4 9 9 0 ,3 9 6 0 ,2 5 4 0 ,3 7 3-3 6 ,0 0 0 0 ,1 8 9 0 ,3 0 8 0 ,4 6 7 0 ,2 3 0 0 ,2 2 3 0 ,2 5 0

R = 148 ,5m m , 15o , 3 5 0 R P M , tw o -p h a se ,R P D = 0 ,5 3 75 4 ,0 0 0 0 ,1 9 4 0 ,2 4 3 0 ,1 3 5 0 ,0 9 5 -0 ,1 3 4 0 ,2 0 83 6 ,0 0 0 0 ,201 0 ,3 0 5 0 ,3 9 3 0 ,201 -0 ,111 0 ,1 9 32 4 ,0 0 0 0 ,2 8 9 0 ,5 5 6 0 ,6 0 6 0 ,5 1 6 0 ,0 5 6 0 ,5 0 91 8 ,0 0 0 0 ,5 4 9 0 ,9 4 2 0 ,5 1 5 0 ,7 5 9 0 ,7 9 0

APPENDIX 3. 253

Mean velocity data for the 180mm Rushton impeller. Velocities in [m/s]T=450mm, h = 580mm, c=315mmZ[mm] V+ 15o V-15o angleY Vradial Vaxial Vtang.

1 2 ,0 0 0 0 ,5 5 4 1 ,0 9 5 0 ,6 2 4 1 ,0 4 5 0 ,3 0 9 0 ,8 1 06 ,0 0 0 0 ,7 4 2 1 ,2 2 4 0 ,4 7 9 0 ,931 0 ,3 5 7 0 ,8 7 50 ,0 0 0 0 ,6 4 5 1 ,1 0 5 0 ,5 1 4 0 ,8 8 9 0 ,2 7 8 0 ,9 5 0

-6 ,0 0 0 0 ,5 4 2 0 ,9 2 5 0 ,511 0 ,7 4 0 0 ,1 9 9 0 ,8 4 0-1 2 ,0 0 0 0 ,4 2 8 0 ,641 0 ,3 7 8 0 ,411 0 ,1 8 7 0 ,4 8 3-1 8 ,0 0 0 0 ,3 1 7 0 ,4 5 0 0 ,3 1 3 0 ,2 5 7 0 ,3 3 4-2 4 ,0 0 0 0 ,2 0 2 0 ,3 2 6 0 ,4 5 8 0 ,2 4 0 0 ,1 6 4 0 ,2 1 7-3 6 ,0 0 0 0 ,1 7 8 0 ,2 3 4 0 ,2 0 8 0 ,1 0 8 0 ,1 6 4 0 ,1 6 4

168 ,5m m , 15 o ,3 5 0 R P M ,rsing le -phase5 4 ,0 0 0 0 ,2 5 3 0 ,2 9 7 0 ,0 2 8 0 ,0 8 5 0 ,0 1 0 0 ,2 6 73 6 ,0 0 0 0 ,2 8 0 0 ,4 3 7 0 ,4 2 3 0 ,3 0 3 0 ,0 1 3 0 ,3 6 22 4 ,0 0 0 0 ,3 9 2 0 ,6 8 0 0 ,5 2 5 0 ,5 5 6 0 ,0 6 9 0 ,6 1 41 2 ,0 0 0 0 ,7 0 4 1 ,0 9 6 0 ,421 0 ,7 5 7 0 ,1 8 4 0 ,9 6 2

0 ,0 0 0 0 ,7 5 9 1 ,3 2 9 0 ,5 3 3 1 ,101 0 ,1 8 7 1,071-1 2 ,0 0 0 0 ,5 4 6 0 ,9 7 0 0 ,5 4 5 0 ,8 1 9 0 ,1 4 0 0 ,7 7 6-2 4 ,0 0 0 0 ,341 0 ,5 6 9 0 ,4 9 0 0 ,4 4 0 0 ,1 8 8 0 ,4 2 8-3 6 ,0 0 0 0 ,2 2 5 0 ,3 4 6 0 ,4 0 7 0 ,2 3 4 0 ,191 0 ,2 6 0

168 ,5m m , 15 o ,3 5 0 R P M ,,tw o -phase , R P D = 0 ,5 3 75 4 ,0 0 0 0 ,1 9 6 0 ,2 3 7 0 ,0 7 8 0 ,0 7 9 -0 ,0 1 8 0 ,1 8 93 6 ,0 0 0 0 ,2 0 3 0 ,3 7 0 0 ,5 6 6 0 ,3 2 3 -0 ,0 1 0 0 ,2 5 02 4 ,0 0 0 0 ,2 6 8 0 ,5 6 3 0 ,6 6 2 0 ,5 7 0 0 ,1 0 2 0 ,4 0 91 2 ,0 0 0 0 ,3 8 7 0 ,8 9 7 0 ,7 1 6 0 ,9 8 5 0 ,1 8 3 0 ,6 5 5

0 ,0 0 0 0 ,4 4 8 0 ,9 0 6 0 ,6 3 9 0 ,8 8 5 0 ,1 7 3 0 ,6 8 0-1 2 ,0 0 0 0 ,3 3 3 0 ,6 1 5 0 ,5 7 6 0 ,5 4 5 0 ,1 2 8 0 ,4 3 7-2 4 ,0 0 0 0 ,1 8 8 0 ,351 0 ,5 8 4 0 ,3 1 5 0 ,1 4 0 0 ,2 1 2-3 6 ,0 0 0 0 ,1 6 9 0 ,2 9 4 0 ,5 2 7 0 ,241 0 ,0 9 5 0 ,191

APPENDIX 3. 254

Mean velocity data for the 180mm Rushton impeller. Velocities in m/s.T = 450mm, h = 580mm, c=315mm

Z[mm] V + 15o V-15o angleY Vradial Vaxia! Vtangent.5m m , 4 5 o , 3 5 0 R P M , sing le -phase54 0 ,1 4 5 0 ,2 1 3 0 ,3 5 5 0 ,131 -0 ,3 6 2 0 ,1 6 93 6 0 ,1 4 2 0 ,201 0 ,3 0 9 0 ,1 1 4 -0 ,2 7 0 0 ,1 5 024 0 ,1 5 7 0 ,3 3 5 0 ,6 7 2 0 ,3 4 4 -0 ,111 0 ,3 1 018 0 ,451 0 ,6 2 6 0 ,2 8 3 0 ,3 3 8 0 ,0 8 5 0 ,6 9 712 0 ,921 1 ,3 9 4 0 ,3 9 0 0 ,9 1 4 0 ,3 9 7 1 ,1 5 5

6 1 ,2 3 4 1 ,8 8 8 0 ,4 0 2 1 ,263 0 ,5 4 5 1 ,6650 1 ,4 5 6 1 ,9 7 8 0 ,2 5 4 1 ,0 0 8 0 ,381 1 ,8 0 4

-6 1 ,2 2 6 1 ,5 8 3 0 ,181 0 ,6 9 0 0 ,3 7 8 1 ,6 3 5-12 0 ,5 9 9 1 ,1 3 2 0 ,5 9 3 1 ,0 3 0 0 ,3 7 9 0 ,821-18 0 ,3 0 0 0 ,521 0 ,5 2 6 0 ,4 2 7 0 ,3 6 3 0 ,3 9 8-24 0 ,1 0 9 0 ,2 4 5 0 ,7 0 0 0 ,2 6 3 0 ,3 9 7 0 ,2 0 4-36 0 ,0 9 6 0 ,1 8 4 0 ,6 0 3 0 ,1 7 0 0 ,3 9 5 0 ,1 2 5

R = 133 ,5m m , 45 o , 3 5 0 R P M , tw o -p ha se5 4 ,0 0 0 0 ,1 3 2 0 ,1 9 3 0 ,3 4 9 0 ,1 1 8 -0 ,331 0 ,1 6 43 6 ,0 0 0 0 ,1 5 0 0 ,1 8 4 0 ,101 0 ,0 6 6 -0 ,2 2 9 0 ,1 4 22 4 ,0 0 0 0 ,2 3 3 0 ,3 8 7 0 ,4 8 6 0 ,2 9 8 -0 ,0 1 3 0 ,5 5 01 8 ,0 0 0 0 ,5 6 2 1,031 0 ,571 0 ,9 0 6 0 ,2 0 7 1 ,0 7 01 2 ,0 0 0 0 ,8 2 0 1 ,6 5 9 0 ,6 3 9 1,621 0 ,4 2 3 1,121

6 ,0 0 0 0 ,8 2 3 1 ,5 6 5 0 ,5 9 7 1 ,433 0 ,4 7 0 1 ,3 7 50 ,0 0 0 1 ,2 1 6 1 ,521 0 ,1 3 2 0 ,5 8 9 0 ,2 9 5 1,461

-6 ,0 0 0 1 ,0 3 3 1 ,1 0 7 -0 ,1 3 3 0 ,1 4 3 0 ,2 8 8 1 ,1 2 9-1 2 ,0 0 0 0 ,4 4 3 1 ,1 3 7 0 ,761 1,341 0 ,2 9 0 0 ,5 7 2-1 8 ,0 0 0 0 ,2 8 0 0 ,3 9 2 0 ,2 9 5 0 ,2 1 6 0 ,3 1 6 0 ,3 6 0-2 4 ,0 0 0 0 ,1 2 3 0 ,2 0 5 0 ,4 8 9 0 ,1 5 8 0 ,3 2 9 0 ,1 8 3-3 6 ,0 0 0 0 ,1 1 5 0 ,1 5 5 0 ,2 4 3 0 ,0 7 7 0 ,3 5 0 0 ,0 9 5

R = 14 8 ,5 m m , 4 5 o , 3 5 0 R P M , sing le -phase5 4 ,0 0 0 0 ,1 1 2 0 ,1 9 6 0 ,5 3 2 0 ,1 6 2 -0 ,3 1 3 0 ,1 6 33 6 ,0 0 0 0 ,101 0 ,2 0 3 0 ,6 3 5 0 ,1 9 7 -0 ,2 1 5 0 ,1512 4 ,0 0 0 0 ,1 9 2 0 ,4 0 7 0 ,6 6 8 0 ,4 1 5 -0 ,0 6 2 0 ,3 9 21 8 ,0 0 0 0 ,4 7 6 0 ,7 2 8 0 ,401 0 ,4 8 7 0 ,1 1 2 0 ,5 8 31 2 ,0 0 0 0 ,7 3 6 1 ,1 3 8 0 ,4 1 3 0 ,7 7 7 0 ,2 0 5 0 ,9 7 6

6 ,0 0 0 0 ,9 4 0 1 ,4 7 3 0 ,4 2 8 1 ,0 3 0 0 ,3 3 9 1 ,1 7 20 ,0 0 0 0 ,9 5 3 1,511 0 ,4 4 0 1 ,0 7 8 0 ,2 8 4 1 ,3 3 3

-6 ,0 0 0 0 ,8 4 5 1 ,3 1 9 0 ,4 2 3 0 ,9 1 6 0 ,2 8 9 1 ,0 8 6-1 2 ,0 0 0 0 ,5 4 8 0 ,8 2 6 0 ,3 8 5 0 ,5 3 7 0 ,2 9 9 0 ,7 3 6-1 8 ,0 0 0 0 ,3 2 9 0 ,5 1 6 0 ,4 2 9 0 ,361 0 ,3 1 5 0 ,4 6 5-2 4 ,0 0 0 0 ,1 3 3 0 ,3 0 6 0 ,7 1 2 0 ,3 3 4 0 ,3 4 6 0 ,2 0 8-3 6 ,0 0 0 0 ,0 6 6 0 ,1 6 6 0 ,7 5 3 0 ,1 9 3 0 ,3 7 2 0 ,1 2 6

R = 14 8 ,5 m m ,4 5 o ,3 5 0 R P M ,tw o -p h a se ,R5 4 ,0 0 0 0 ,1 0 3 0 ,1 8 9 0 ,571 0 ,1 6 6 -0 ,2 5 4 0 ,1 3 33 6 ,0 0 0 0 ,1 0 9 0 ,2 1 6 0 ,6 2 6 0 ,2 0 7 -0 ,1 6 5 0 ,1 4 92 4 ,0 0 0 0 ,2 0 7 0 ,4 8 6 0 ,7 2 2 0 ,5 3 9 0 ,0 5 8 0 ,4 7 21 8 ,0 0 0 0 ,511 0 ,8 8 8 0 ,5 2 6 0 ,7 2 8 0 ,1 5 0 0 ,5 9 8

APPENDIX 3. 255

Mean velocity data for the 180mm Rushton impeller. Velocities in m/s. T =450mm, h = 580mm, c - 315mm

Ztmm] V+ 15o V-15o angleY Vradial Vaxial Vtongerrt.1 2 ,0 0 0 0 ,5 4 5 1 ,0 6 3 0 ,6 1 5 1,001 0 ,2 4 2 0 ,841

6 ,0 0 0 0 ,5 6 3 1 ,2 0 5 0 ,6 7 3 1 ,2 4 0 0 ,2 7 9 0 ,9 0 90 ,0 0 0 0 ,621 1 ,0 7 7 0 ,5 2 5 0 ,881 0 ,2 4 2 0 ,9 9 6

-6 ,0 0 0 0 ,5 2 0 0 ,911 0 ,5 3 3 0 ,7 5 5 0 ,2 1 0 0 ,8 2 6-1 2 ,0 0 0 0 ,3 4 2 0 ,5 1 5 0 ,3 8 4 0 ,3 3 4 0 ,2 3 3 0 ,4 0 9-1 8 ,0 0 0 0 ,1 7 2 0 ,3 3 2 0 ,6 0 8 0 ,3 0 9 0 ,2 5 0 0 ,2 7 0-2 4 ,0 0 0 0 ,0 8 0 0 ,2 2 3 0 ,7 9 3 0 ,2 7 6 0 ,3 0 2 0 ,1 3 5-3 6 ,0 0 0 0 ,051 0 ,1 4 7 0 ,8 0 4 0 ,1 8 5 0 ,2 9 6 0 ,0 9 5

168 ,5m m ,r4 5 o ,3 5 0 R P M ,,s ing le -phase5 4 ,0 0 0 0 ,1 2 0 0 ,1 6 8 0 ,2 9 5 0 ,0 9 3 -0 ,1 8 3 0 ,1 3 53 6 ,0 0 0 0 ,1 1 5 0 ,2 5 4 0 ,691 0 ,2 6 9 -0 ,0 9 5 0 ,1 9 62 4 ,0 0 0 0 ,251 0 ,4 9 0 0 ,6 1 6 0 ,4 6 2 0 ,0 2 3 0 ,4 0 21 2 ,0 0 0 0 ,5 9 2 1 ,0 4 2 0 ,5 3 7 0 ,8 6 9 0 ,2 0 2 0 ,8 0 5

0 ,0 0 0 0 ,7 1 9 1 ,2 1 2 0 ,4 9 9 0 ,9 5 2 0 ,221 0 ,9 3 6-1 2 ,0 0 0 0 ,4 8 8 0 ,8 0 3 0 ,4 7 7 0 ,6 0 9 0 ,1 9 4 0 ,5 9 5-2 4 ,0 0 0 0 ,2 0 3 0 ,3 4 4 0 ,5 0 4 0 ,2 7 2 0 ,2 7 5 0 ,2 5 8-3 6 ,0 0 0 0 ,101 0 ,1 7 9 0 ,5 4 3 0 ,151 0 ,2 8 7 0 ,1 5 8

168 ,5m m ,,4 5o ,3 50R P M ,r tw o -phase , R P D = 0 ,5 3 75 4 ,0 0 0 0 ,0 9 5 0 ,1 7 6 0 ,5 7 8 0 ,1 5 6 -0 ,1 6 3 0 ,1 1 23 6 ,0 0 0 0 ,1 0 2 0 ,2 3 8 0 ,7 1 9 0 ,2 6 3 -0 ,0 5 3 0 ,1 7 92 4 ,0 0 0 0 ,2 0 8 0 ,4 9 0 0 ,7 2 3 0 ,5 4 5 0 ,0 7 9 0 ,4 1 51 2 ,0 0 0 0 ,3 6 6 0 ,8 4 0 0 ,711 0 ,9 1 6 0 ,2 0 3 0 ,6 5 7

0 ,0 0 0 0 ,3 7 3 0 ,8 3 8 0 ,7 0 0 0 ,8 9 8 0 ,171 0 ,6 4 8-1 2 ,0 0 0 0 ,2 5 7 0 ,4 8 6 0 ,5 9 3 0 ,4 4 2 0 ,1 6 7 0 ,3 6 5-2 4 ,0 0 0 0 ,091 0 ,2 4 0 0 ,7 7 2 0 ,2 8 8 0 ,211 0 ,1 1 9-3 6 ,0 0 0 0 ,0 5 6 0 ,1 2 9 0 ,7 1 2 0 ,141 0 ,2 2 4 0 ,0 9 3

APPENDIX 3. 256

im ] V+ 15o V -15o angle Y Vradial Vaxial Vtang.13 3 ,5 m m , 75o , 3 5 0 R P M , s ing le -phase5 4 ,0 0 0 0 ,1 9 4 0 ,2 4 7 0 ,1 6 0 0 ,1 0 2 -0 ,3 8 5 0 ,2 2 53 6 ,0 0 0 0 ,2 2 0 0 ,2 9 5 0 ,2 3 6 0 ,1 4 5 -0 ,3 0 7 0 ,2 4 62 4 ,0 0 0 0 ,2 9 3 0 ,4 5 4 0 ,4 1 6 0 ,311 -0 ,131 0 ,3 7 51 8 ,0 0 0 0 ,5 4 3 0 ,7 6 5 0 ,3 0 3 0 ,4 2 9 0 ,1 8 3 0 ,7 8 01 2 ,0 0 0 1 ,022 1 ,5 8 4 0 ,4 1 6 1 ,0 8 6 0 ,7 2 0 1 ,3 4 4

6 ,0 0 0 1 ,3 9 9 2 ,0 9 5 0 ,3 7 7 1 ,345 0 ,7 6 4 1 ,9130 ,0 0 0 1 ,7 6 3 2 ,0 4 9 0 ,011 0 ,5 5 3 0 ,541 2 ,0 7 2

-6 ,0 0 0 1 ,1 6 0 1 ,6 3 2 0 ,301 0 ,9 1 2 1 ,6 7 0-1 2 ,0 0 0 0 ,7 8 5 1 ,1 5 0 0 ,3 5 2 0 ,7 0 5 0 ,3 6 5 0 ,9 1 9-1 8 ,0 0 0 0 ,3 9 2 0 ,6 0 9 0 ,4 1 8 0 ,4 1 9 0 ,521-2 4 ,0 0 0 0 ,2 1 0 0 ,3 4 6 0 ,4 7 8 0 ,2 6 3 0 ,3 3 5 0 ,2 9 4-3 6 ,0 0 0 0 ,1 5 0 0 ,2 4 0 0 ,4 4 9 0 ,1 7 4 0 ,3 7 5 0 ,1 9 8

133 ,5m m , 7 5o , 3 5 0 R P M , tw o -p h a se ,R P D == 0 ,5 3 75 4 ,0 0 0 0 ,1 3 5 0 ,2 0 2 0 ,3 7 7 0 ,1 2 9 -0 ,3 2 2 0 ,1 6 53 6 ,0 0 0 0 ,1 6 0 0 ,2 2 0 0 ,271 0 ,1 1 6 -0 ,2 3 9 0 ,1 7 52 4 ,0 0 0 0 ,2 4 7 0 ,3 9 5 0 ,4 4 9 0 ,2 8 6 0 ,0 0 8 0 ,3 6 01 8 ,0 0 0 0 ,4 9 6 0 ,7 2 3 0 ,3 4 6 0 ,4 3 9 0 ,3 0 4 0 ,6 0 91 2 ,0 0 0 0 ,6 2 6 1,271 0 ,6 4 2 1 ,2 4 6 0 ,6 1 0 1 ,052

6 ,0 0 0 0 ,7 5 9 1 ,4 6 4 0 ,6 0 7 1 ,3 6 2 0 ,5 8 0 1 ,1 8 80 ,0 0 0 1 ,3 3 0 1 ,4 2 3 -0 ,1 3 6 0 ,1 8 0 0 ,3 6 0 1 ,293

-6 ,0 0 0 0 ,9 3 0 1 ,1 0 2 0 ,0 4 4 0 ,3 3 2 1 ,1 6 5-1 2 ,0 0 0 0 ,4 5 7 0 ,7 3 6 0 ,4 5 6 0 ,5 3 9 0 ,2 5 2 0 ,6 2 4-1 8 ,0 0 0 0 ,3 0 3 0 ,4 0 0 0 ,2 1 4 0 ,1 8 7 0 ,3 7 9-2 4 ,0 0 0 0 ,1 7 4 0 ,261 0 ,3 7 9 0 ,1 6 8 0 ,2 8 2 0 ,2 3 3-3 6 ,0 0 0 0 ,141 0 ,1 8 8 0 ,2 2 8 0 ,091 0 ,3 2 5 0 ,1 6 4

148 ,5m m , 7 5o , 3 5 0 R P M , sing le -phase5 4 ,0 0 0 0 ,1 9 6 0 ,271 0 ,2 7 8 0 ,1 4 5 -0 ,3 1 3 0 ,2 1 43 6 ,0 0 0 0 ,2 0 2 0 ,2 9 6 0 ,3 5 2 0 ,1 8 2 -0 ,2 4 2 0 ,2 5 22 4 ,0 0 0 0 ,3 5 2 0 ,5 0 0 0 ,3 1 3 0 ,2 8 6 -0 ,0 3 8 0 ,4 8 71 8 ,0 0 0 0 ,6 4 7 0 ,9 0 6 0 ,2 9 5 0 ,5 0 0 0 ,121 0 ,7111 2 ,0 0 0 0 ,831 1 ,2 8 7 0 ,4 1 5 0 ,881 0 ,3 6 6 1 ,0 9 0

6 ,0 0 0 1 ,0 7 0 1 ,5 5 9 0 ,3 4 5 0 ,9 4 5 0 ,4 2 3 1 ,2 8 80 ,0 0 0 1 ,0 5 0 1 ,572 0 ,3 7 7 1 ,0 0 8 0 ,3 6 4 1 ,4 4 4

-6 ,0 0 0 0 ,971 1 ,3 6 8 0 ,3 0 3 0 ,7 6 7 1,271-1 2 ,0 0 0 0 ,6 2 4 0 ,9 9 2 0 ,4 4 3 0 ,711 0 ,3 0 4 0 ,7 8 6-1 8 ,0 0 0 0 ,3 7 4 0 ,5 8 2 0 ,4 2 0 0 ,4 0 2 0 ,5 3 4-2 4 ,0 0 0 0 ,2 3 8 0 ,3 9 5 0 ,4 8 5 0 ,3 0 3 0 ,3 1 7 0 ,331-3 6 ,0 0 0 0 ,1 5 5 0 ,2 5 9 0 ,491 0 ,201 0 ,3 5 5 0 ,2 1 8

148 ,5m m , 75o , 3 5 0 R P M , tw o -phase , RPD == 0 ,5 3 75 4 ,0 0 0 0 ,1 4 2 0 ,1 7 7 0 ,1 2 7 0 ,0 6 8 -0 ,261 0 ,1 6 83 6 ,0 0 0 0 ,1 5 0 0 ,2 5 7 0 ,5 1 4 0 ,2 0 7 -0 ,1 8 8 0 ,2 0 02 4 ,0 0 0 0 ,2 4 0 0 ,4 6 6 0 ,6 1 2 0 ,4 3 7 0 ,0 3 6 0 ,3 7 21 8 ,0 0 0 0 ,4 8 0 0 ,8 3 8 0 ,5 3 0 0 ,6 9 2 0 ,2 1 0 0 ,6 3 21 2 ,0 0 0 0 ,4 8 6 0 ,9 8 4 0 ,6 4 0 0 ,9 6 2 0 ,2 8 8 0 ,7 9 36 ,0 0 0 0 ,5 9 7 1 ,1 3 2 0 ,5 9 5 1 ,0 3 4 0 ,3 3 0 0 ,861

APPENDIX 3. 257

lm] V+ 15o V -15o angle Y Vradial Vaxial Vtang.0 ,0 0 0 0 ,6 0 3 1 ,0 5 6 0 ,5 3 3 0 ,8 7 5 0 ,2 6 4 0 ,9 5 3

-6 ,0 0 0 0 ,6 2 2 0 ,8 2 9 0 ,2 2 7 0 ,4 0 0 0 ,8 2 8-1 2 ,0 0 0 0 ,3 4 6 0 ,6 2 0 0 ,5 5 2 0 ,5 2 9 0 ,1 9 5 0 ,4 8 8-1 8 ,0 0 0 0 ,2 4 5 0 ,3 9 7 0 ,4 6 2 0 ,2 9 4 0 ,3 4 4-2 4 ,0 0 0 0 ,1 9 2 0 ,2 6 7 0 ,2 8 6 0 ,1 4 5 0 ,2 2 3 0 ,2 5 0-3 6 ,0 0 0 0 ,1 3 7 0 ,2 1 5 0 ,4 2 9 0 ,151 0 ,2 8 0 0 ,171

R = 1 6 8 ,5 m m ,7 5 o ,3 5 0 R P M , sing le -phase5 4 ,0 0 0 0 ,1 8 2 0 ,2 4 9 0 ,2 6 4 0 ,1 2 9 -0 ,1 9 5 0 ,2 1 73 6 ,0 0 0 0 ,2 3 3 0 ,3 4 3 0 ,3 5 7 0 ,2 1 3 -0 ,1 2 7 0 ,2 7 92 4 ,0 0 0 0 ,341 0 ,5 7 6 0 ,501 0 ,4 5 4 0 ,0 1 6 0 ,5 0 91 2 ,0 0 0 0 ,6 2 5 1 ,0 5 6 0 ,5 0 2 0 ,8 3 3 0 ,2 2 6 0 ,8 8 4

0 ,0 0 0 0 ,6 9 6 1 ,2 3 9 0 ,5 4 7 1 ,0 4 9 0 ,2 0 2 1 ,0 5 3-1 2 ,0 0 0 0 ,5 3 6 0 ,8 8 5 0 ,4 8 0 0 ,6 7 4 0 ,1 7 8 0 ,7 4 3-2 4 ,0 0 0 0 ,2 8 9 0 ,4 4 9 0 ,4 1 8 0 ,3 0 9 0 ,2 0 9 0 ,3 7 4-3 6 ,0 0 0 0 ,181 0 ,2 6 9 0 ,3 6 9 0 ,1 7 0 0 ,2 4 7 0 ,2 2 6

1 6 8 ,5 m m ,7 5 o ,3 5 0 R P M ,tw o -p h a se ,R P D = 0 ,5 3 75 4 ,0 0 0 0 ,1 3 9 0 ,2 0 4 0 ,3 5 4 0 ,1 2 6 -0 ,1 7 3 0 ,1 7 33 6 ,0 0 0 0 ,1 7 9 0 ,3 0 4 0 ,5 0 6 0 ,241 -0 ,0 9 5 0 ,1 8 52 4 ,0 0 0 0 ,2 4 8 0 ,4 7 5 0 ,6 0 3 0 ,4 3 9 0 ,0 3 8 0 ,4 0 41 2 ,0 0 0 0 ,3 7 4 0 ,8 0 2 0 ,6 7 4 0 ,8 2 7 0 ,1 6 3 0 ,6 2 5

0 ,0 0 0 0 ,3 8 0 0 ,8 6 7 0 ,7 0 8 0 ,941 0 ,1 6 0 0 ,6 7 9-1 2 ,0 0 0 0 ,2 9 4 0 ,5 2 5 0 ,5 4 9 0 ,4 4 6 0 ,1 3 2 0 ,4 3 0-2 4 ,0 0 0 0 ,1 8 5 0 ,3 0 6 0 ,4 8 2 0 ,2 3 4 0 ,1 8 4 0 ,2 3 8-3 6 ,0 0 0 0 ,1 5 0 0 ,2 4 3 0 ,4 6 2 0*180 0 ,2 1 4 0 ,1 7 4

APPENDIX 3. 258

Rm s data fo r the 180m m Rush ton im pe lle rZIm m] R M S + 1 5 R M S -1 5 R M S ta n g R M S rad R M S ax R = 13 3 .5m m , 15 o ,3 5 0 R P M , s ing le -phase

54 0 .241 0 .2 5 5 0 .251 0 .2 0 3 0 .2 7 436 0 .2 9 2 0 .2 7 9 8 0 .2 8 2 0 .3 3 6 0 .2 924 0 .4 8 7 0 .5 0 7 0 .6 8 8 1 .7 0 4 0 .5 4 718 0 .9 3 8 0 .8 7 9 0 .9 2 5 0 .6 4 6 0 .8 4 512 1 .165 1 .2 3 3 1 .1 1 9 2 .0 0 9 1.141

6 1 .2 1 2 1 .2 3 8 1 .2 4 3 0 .9 4 0 1 .060 1.3 1 .2 33 1 .247 1 .518 0 .9 5

-6 1 .2 15 1 .1 5 9 1 .1 7 4 1 .359 0 .8 6 7-12 0 .9 6 6 1 .1 5 9 0 .8 9 6 2 .4 1 0 0 .6 7-18 0 .6 7 4 0 .7 3 5 0 .5 2 5 1 .893 0 .5 0 8-24 0 .3 7 5 0 .3 7 7 0 .3 9 6 0 .271 0 .3 6 7-36 0 .2 8 3 0 .2 7 2 0 .2 7 9 0 .2 5 7 0 .2 6 8

R = 13 3 ,5 , 15o , 3 5 0R P M ,tw O -ph ase , RPD = 0 ,5 3 754 0 .2 2 5 0 .2 1 4 0 .2 0 6 0 .3 5 9 0.213 6 0 .2 9 0 .2 4 5 0 .2 8 0 .1 2 7 0 .25124 0 .6 6 0 .521 0.51 1 .2 8 6 0 .7 0 218 0 .9 1 9 0 .7 6 0 .8 9 7 0 .7 6 912 0 .8 6 4 0 .9 5 8 0 .8 6 9 1 .3 8 0 0 .9 6

6 0 .8 4 7 0 .9 1 2 0 .9 1 4 0 .2 6 9 0 .9 9 30 1 .127 0 .8 8 6 0 .9 7 3 1 .467 0 .8 5

-6 1 .2 4 6 0 .8 6 9 0 .9 4 3 2 .2 0 0 0 .7 4 6-12 0 .7 3 3 0 .9 6 9 0 .6 7 8 2 .1 4 9 0 .5 3 6-18 0 .5 0 7 0 .8 1 3 0 .6 5 5 0 .9 3 6-24 0 .31 0 .3 0 2 0 .3 6 9 0 .7 0 6 0 .3 0 9-36 0 .2 3 9 0 .2 3 8 0 .2 0 3 0 .5 2 5 0 .1 8 6

i,5m m , 15 o ,3 5 0 R P M ,rsing le -phase54 0 .2 7 6 0 .271 0 .2 8 9 0 .2 1 6 0 .2 4 43 6 0 .3 1 9 0 .3 1 3 0 .3 3 4 0 .251 0 .3 3 824 0 .5 3 4 0 .5 5 4 0 .5 7 7 0 .4 6 7 0 .5 9 218 0 .8 0 4 0 .8 1 8 0 .7 3 9 1 .488 0 .7 3 812 0 .8 9 0 .941 0 .901 1 .1 0 2 0 .8 6 5

6 0 .9 7 5 1 .0 0 6 0 .9 6 7 1 .275 0 .8 8 20 0 .9 6 3 1 .0 0 3 0 .9 8 3 0 .9 8 6 0 .81

-6 0 .921 0 .9 6 5 0 .9 3 4 1 .0 6 4 0 .7 0 9-12 0 .8 2 6 0 .8 1 3 0 .7 8 7 1 .183 0 .6 0 8-18 0 .6 2 3 0 .6 1 7 0 .6 2 3 0 .5 7 7 0 .4 7 9-24 0 .4 4 6 0 .471 0 .4 5 9 0 .4 5 4 0 .3 8 8-36 0 .3 2 5 0 .3 1 6 0 .3 0 5 0 .4 8 8 0 .2 9 4

t,5mm, 15 o ,350 R P M ,r tw o -phase , RPD = 0 ,5 3 754 0 .2 5 8 0 .2 4 7 0 .2 3 0 .4 6 4 0 .1 9 63 6 0 .3 4 7 0 .3 0 6 0 .281 0 .7 0 6 0 .3 2 624 0 .4 6 8 0 .5 0 6 0 .6 4 3 1 .4 8 8 0 .5 618 0 .7 4 9 0 .7 8 0 .7 9 9 0 .4 0 412 0 .6 9 4 0 .731 0 .6 9 6 0 .9 1 5 0 .7 4 2

6 0.81 0 .7 4 4 0 .6 7 9 1 .615 0 .7 8 20 0 .7 4 4 0 .711 0 .7 6 5 0 .4 9 6 0 .6 9 4

-6 1 .045 0 .6 7 8 0 .8 1 8 1 .5 0 4 0 .5 8 7

APPENDIX 3. 259

data for the 180m m !Rush ton im pe lle rn] R M S + 1 5 R M S -1 5 R M S tan g R M S rad R M S ax

-12 0 .5 7 8 0 .5 5 4 0 .5 2 6 0 .9 6 5 0 .4 8 7-18 0 .481 0 .4 2 6 0 .4 4 5 0 .5 6 9-24 0 .3 2 6 0 .3 2 2 0 .3 1 6 0 .4 2 0 0 .2 8 8-36 0 .2 5 9 0 .2 5 9 0 .2 4 3 0 .4 2 3 0 .1 9 8

68 ,5m m , 1 5 o ,3 5 0 R P M54 0 .3 1 3 0 .3 0 7 0 .3 1 4 0 .2 4 8 0 .2 8 53 6 0 .3 9 2 0 .4 1 7 0 .3 9 0 .571 0 .3 8 524 0 .5 5 4 0 .581 0 .5 9 8 0 .4 1 3 0 .612 0 .741 0 .7 5 4 0 .7 6 3 0 .4 8 3 0 .7 4 4

0 0 .7 8 8 0 .8 0 8 0 .7 9 2 0 .8 7 8 0 .7 0 3-12 0 .6 6 7 0 .7 1 6 0 .721 0 .3 0 5 0 .5 8 6-24 0 .491 0 .511 0 .4 9 6 0 .5 6 7 0 .4 4 5-36 0 .3 7 0 .381 0 .3 5 5 0 .5 9 2 0 .3 2 3

68 ,5m m , 15 o ,3 5 0 R P M ,tw o -phase , RPD = 0,!53754 0 .2 8 3 0 .2 9 6 0 .2 5 9 0 .5 6 3 0 .2 1 236 0 .4 0 .381 0 .3 5 3 0 .7 3 6 0 .3 4 924 0 .4 6 6 0 .4 8 5 0 .4 8 4 0 .3 3 7 0 .5 0 912 0 .5 6 6 0 .5 8 4 0 .5 9 4 0 .1 5 0 0 .5 9

0 0 .5 7 6 0 .5 7 3 0 .5 8 8 0 .3 3 4 0 .5 4 2-12 0 .4 9 0 .5 0 7 0 .4 7 5 0 .7 5 4 0 .4 2 3-24 0 .3 4 7 0 .3 5 0 .3 4 7 0 .3 6 9 0 .2 7 8-36 0 .2 9 9 0 .2 9 5 0 .2 7 7 0 .4 9 8 0 .2 1 7

APPENDIX 3. 260

Z[mm]

0 .0

R M S + 1 5 R M S -1 5 R M S tang R M S rad R M S a xl. 5 m m ,4 5 o ,3 5 0 R P M , sing le -phase

54 0 .2 0 8 0 .2 1 7 0 .2 1 8 0 .1 1 2 0 .2 3 536 0 .3 0 7 0 .2 4 7 0 .2 3 6 0 .6 1 9 0 .2 9 224 0 .4 4 6 0 .441 0 .5 3 7 1 .039 0 .5 7 418 0 .7 8 0 .7 3 5 0 .8 9 6 1 .615 0 .8 0 212 1.111 1 .1 2 3 1.151 0 .4 1 7 1 .025

6 1 .208 1 .219 1 .2 4 8 0 .5 3 9 1 .0 1 21 .255 1 .2 2 6 1 .273 0 .6 3 6 0 .9 1 7

-6 1 .1 8 2 1 .1 7 2 1 .2 8 6 1 .5 3 4 0 .8 2 9-12 0 .9 1 7 1 .065 0 .9 7 9 1 .1 8 0 0 .7 0 5-18 0 .621 0 .6 3 9 0 .6 1 6 0 .801 0 .5 4 4-24 0 .3 9 6 0 .351 0 .3 8 4 0 .1 9 0 0 .3 8-36 0 .2 4 2 0 .2 5 5 0 .2 4 3 0 .3 1 6 0 .2 7 2

l,5 ,4 5o , 3 5 0 R P M ,tw o -p h a se ,R P D = 0 ,5 3 754 0 .1 8 4 0 .1 9 0 .1 9 3 0 .0 5 8 0 .2 0 736 0 .3 5 6 0 .2 2 5 0 .2 2 6 0 .7 8 3 0 .2 9 22 4 0 .4 8 5 0 .501 0 .5 1 7 0 .3 0 6 0 .6 2 218 0 .791 0 .9 6 6 0.71 2 .1 4 8 0 .8 0 812 0 .8 7 9 1 .0 6 2 0 .8 9 7 1 .7 2 6 0 .901

6 0 .8 6 2 0 .881 0 .9 5 6 1 .179 0 .9 1 50 1 .033 0 .9 1 3 1 .0 3 5 0 .8 5 6 0 .8 0 2

-6 1.01 0 .8 7 0 .9 9 7 0 .7 6 2 0 .6 9 4-12 0 .6 9 4 1 .04 0 .7 1 8 2 .1 1 8 0 .5 1 9-18 0 .5 8 0 .5 2 9 0 .621 0 .8 7 8 0 .3 8 6-24 0 .3 4 4 0 .2 9 6 0 .3 4 0 .2 7 0 0 .2 9 3-36 0 .2 5 3 0 .2 0 .1 9 0 .5 2 3 0 .2 1 6

R = 1 4 8 ,5 m m ,4 5 o ,3 5 0 R P M ,s in g le -p h a se54 0 .2 1 4 0 .2 1 5 0 .2 0 5 0 .3 1 9 0 .2 2 836 0 .2 9 6 0 .2 9 4 0 .2 8 0 .4 5 5 0 .3 5 624 0 .5 4 0 .5 4 0 .6 2 6 1.051 0 .6 2 818 0 .781 0 .7 7 6 0 .7 5 9 1 .012 0 .8 1 712 0 .9 4 4 0 .9 6 7 0 .9 6 9 0 .7 4 4 0 .8 9 7

6 1 .022 1 .0 3 6 1 .0 3 7 0 .911 0 .90 1.021 1 .0 5 4 1 .0 8 6 0 .5 9 5 0 .8 4 7

-6 0 .9 8 7 1 .0 3 3 1 .0 8 4 1 .063 0 .7 5 7-12 0 .8 4 4 0 .8 6 0 .8 7 9 0 .2 7 5 0 .6 5 6-18 0 .6 7 2 0 .6 6 2 0 .6 9 3 0 .2 1 7 0 .5 3 2-24 0 .4 5 2 0 .4 5 7 0 .4 7 2 0 .1 3 8 0 .4 2 3-36 0 .2 6 3 0 .2 4 8 0 .2 6 6 0 .101 0 .3 0 4

(,5mm,,4 5 o ,3 5 0 R P M ,tw o -p h a se , RPD = 0 ,5 3 754 0 .1 9 5 0 .2 0 .1 9 0 .2 8 2 0 .2 1 43 6 0 .3 2 0 .2 6 3 0 .2 6 0 .5 8 2 0 .3 4 224 0 .4 6 7 0 .5 5 2 0 .6 6 2 1 .4 8 4 0 .6 0 418 0 .7 6 4 0 .7 9 3 0 .6 9 8 1 .50512 0 .7 2 8 0 .7 4 8 0 .771 0 .3 8 4 0 .7 5 7

6 0 .7 2 6 0 .7 6 4 0 .7 3 4 0 .8 8 7 0 .7 6 30 0 .771 0 .7 4 0 .831 1 .0 4 6 0 .7 1 4

-6 0 .7 1 9 0 .7 6 4 0 .7 9 8 0 .8 0 9

APPENDIX 3. 2 61

R M S + 1 5 R M S -1 5 R M S tan g R M S rad R M S a x-12 0 .6 0 .5 6 7 0 .5 5 2 0 .9 1 8 0 .4 9 9-18 0 .4 4 9 0 .451 0 .4 2 0 .7 5 2-24 0 .2 9 9 0 .3 2 0 .2 9 2 0 .4 9 4 0 .2 7 6-36 0 .2 0 2 0 .2 1 6 0 .2 0 7 0 .2 3 7 0 .2 1 5

R = 1 6 8 ,5m m , 4 5 o ,3 5 0 R P M , s ing le -phase54 0 .2 2 3 0 .241 0 .2 4 9 0 .2 4 3 0 .2513 6 0 .3 3 7 0 .3 4 2 0 .3 5 8 0 .2 5 4 0 .4 4 924 0 .5 4 2 0 .5 6 2 0 .5 8 9 0 .531 0 .6 3 512 0 .7 7 5 0 .831 0 .7 6 6 1 .2 1 0 0 .8010 0 .8 5 3 0 .8 7 3 0.81 1 .4 0 8 0 .7 4 2

-12 0 .751 0 .7 6 9 0 .7 2 1 .185 0 .6 5 6-24 0 .5 1 8 0 .521 0 .4 9 2 0 .811 0 .461-36 0 .3 2 8 0 .3 0 7 0 .3 4 4 0 .3 7 6 0 .3 4 9

1,5m m , 4 5 o ,3 5 0 R P M , tw o -phase , R PD = 0 ,5 3 754 0 .221 0 .2 0 9 0 .2 0 3 0 .3 4 2 0 .2 43 6 0 .3 1 6 0 .331 0 .3 0 8 0 .4 9 2 0 .4 0 324 0 .4 7 4 0 .4 9 9 0 .5 6 6 0 .9 6 3 0 .5 5 312 0 .5 9 0 .6 0 6 0 .6 2 2 0 .2 2 2 0 .6 6 90 0 .5 9 9 0 .6 0 7 0 .6 1 2 0 .4 6 0 0 .6 0 6

-12 0 .5 0 6 0 .5 0 2 0 .4 8 4 0 .7 2 8 0 .471-24 0 .3 2 2 0 .341 0 .3 0 .6 2 3 0 .3 4 2-36 0 .2 2 6 0.21 0 .2 2 0 .1 9 0 0 .2 4 5

APPENDIX 3. 262

Z[mm] R M S + 1 5 o R M S -1 5 o R M S tan g R M S rad R M S a x R = 1 3 3 .5 m m ,7 5 o ,3 5 0 R P M ,s in g le -p h a se

54 0 .1 8 7 0 .1 9 6 0 .2 0 .0 9 7 0 .2 1 53 6 0 .2 3 8 0 .2 1 2 0 .1 9 8 0 .461 0 .2 4 624 0 .4 2 9 0 .4 5 7 0 .4 5 0 .3 3 5 0 .5 4 718 0 .7 3 4 0 .7 5 4 0 .8 6 5 1 .4 6 9 0 .8 3 412 1 .0 5 8 1 .1 2 8 1 .1 2 2 0 .5 6 4 1 .062

6 1 .17 1 .19 1 .2 2 6 0 .3 8 4 1 .0 0 80 1 .258 1 .1 8 6 1 .249 0 .7 6 4 0 .8 8 6

-6 1 .1 1 5 1 .1 1 3 1 .1 9 3 1 .139-12 0 .9 4 4 0 .991 0 .9 3 8 1 .3 1 4 0 .6 4 7-18 0 .6 0 6 0 .681 0 .6 9 3 0 .6 9 7-24 0 .3 5 0 .3 4 5 0 .3 8 0 .4 5 7 0 .3 6 3-36 0 .1 9 6 0 .2 0 3 0 .1 9 7 0 .2 3 2 0 .2 4 8

i,5m m , 7 5 o ,3 5 0 R P M ,.tw o-phase, RPD = 0 ,5 3 754 0 .1 6 3 0 .1 6 7 0 .1 6 8 0 .1 1 6 0 .1 8 83 6 0 .2 4 5 0 .1 8 9 0 .1 8 7 0 .4 7 7 0 .2 5 52 4 0 .391 0 .4 5 2 0 .4 7 7 0 .7 0 9 0 .5 9 918 0 .6 8 8 0 .6 7 5 0 .6 4 7 1 .050 0 .8 1 812 0 .7 2 9 0 .8 7 8 0 .8 4 9 0 .5 6 5 0 .9 4 2

6 0 .7 7 8 0 .8 6 3 0 .8 5 5 0 .3 2 4 0 .9 2 20 1 .067 0 .8 7 0 .901 1 .685 0 .8 3 8

-6 0 .9 2 7 0 .8 2 0 .9 1 8 0 .5 5 2-12 0 .6 2 0 .6 7 6 0 .6 8 7 0 .5 4 2 0 .541-18 0 .451 - 0 .4 4 0 .4 9 8 0 .701-24 0 .2 5 2 0 .251 0 .31 0 .6 2 8 0 .2 7 8-36 0 .1 7 3 0 .1 5 9 0 .1 5 6 0 .2 7 0 0 .1 9 5

1,5mm, 75o , 3 5 0 R P M ,s in g le -p h a se54 0 .1 9 5 0 .2 2 9 0 .1 9 2 0 .4 0 2 0 .2 1 93 6 0 .2 6 3 0 .2 2 9 0 .2 6 4 0 .251 0 .3 2 824 0 .5 1 7 0 .5 0 .5 6 7 0 .7 8 5 0 .60118 0 .7 6 0 .7 8 5 0 .7 3 8 1.151 0 .7 7 312 0 .8 7 5 1 .07 0 .9 2 6 1 .522 0 .8 5 5

6 0 .961 0 .9 8 9 0 .9 7 9 0 .9 1 9 0 .8 3 90 0 .9 7 5 0 .991 1 .0 1 7 0 .1 4 2 0 .7 7 4

-6 0 .9 3 8 0 .9 7 2 0 .9 7 9 0 .5 1 9-12 0 .7 8 5 0 .8 4 6 0 .8 0 5 0 .9 5 7 0 .5 9 8-18 0 .5 6 2 0 .6 0 5 0 .631 0 .6 7 5-24 0 .4 0 6 0 .4 1 9 0 .4 1 8 0 .3 2 7 0 .3 8 3-36 0 .2 3 2 0 .2 2 6 0 .2 2 9 0 .2 2 9 0 .2 5 6

1,5mm, 7 5 o ,3 5 0 R P M ,tw o -phase , RPD = 0 ,5 3 754 0 .1 6 2 0 .1 6 3 0 .161 0 .1 8 2 0 .1 7 23 6 0 .2 3 6 0 .221 0 .2 2 8 0 .2 3 7 0 .3 0 224 0 .4 0 2 0 .461 0 .4 8 3 0 .6 7 6 0 .5 6 618 0 .6 6 5 0 .7 0 2 0 .6 4 3 1 .105 0 .6 9 912 0 .6 5 2 0 .7 1 6 0 .7 2 3 0 .5 3 0 0 .7 4 6

6 0 .6 8 9 0 .7 3 7 0 .7 0 4 0 .8 3 3 0 .7 7 90 0 .7 0 5 0 .6 8 8 0 .7 8 1 .109 0 .7 0 7

-6 0 .751 0 .6 6 4 0 .7 7 6 0 .9 4 2

APPENDIX 3. 263

R M S + 1 5 0 R M S -1 5 o R M S tan g R M S rad R M S a x-12 0.51 0 .5 1 5 0 .5 3 8 0 .3 3 2 0 .4 8 6-18 0 .3 7 4 0 .3 7 7 0 .4 3 9 0 .761-24 0 .3 2 4 0 .2 7 3 0 .2 7 2 0 .5 5 6 0 .2 9 7-36 0 .1 8 0 .1 6 8 0 .1 7 5 0 .161 0 .1 9 4

R = 1 6 8 ,5m m , 7 5 o ,3 5 0 R P M , s ing le -phase54 0 .2 2 5 0 .2 0 7 0 .2 1 5 0 .2 3 2 0 .2 43 6 0 .321 0 .331 0 .3 1 3 0 .4 7 2 0 .3 9 324 0 .491 0 .5 3 3 0 .5 4 9 0 .5 2 7 0 .6 1 712 0.71 0 .7 6 7 0 .7 5 3 0 .5 0 6 0 .7 4 6

0 0 .7 4 7 0 .8 2 9 0 .8 2 8 0 .5 0 4 0 .7 1 7-12 0 .6 5 7 0 .7 1 4 0 .7 1 7 0 .3 6 5 0 .6 0 7-24 0 .481 0 .4 5 2 0 .4 6 0 .5 5 2 0 .4 5 3-36 0 .2 7 3 0 .2 5 2 0 .2 6 4 0 .2 4 4 0 .3 0 6

:,5 m m ,7 5 o ,3 5 0 R P M ,tw o -p h a se , RPD = 0 ,5 3 754 0 .1 8 4 0 .1 8 8 0 .1 7 9 0 .2 6 5 0 .1 9 93 6 0 .281 0 .2 7 7 0 .2 4 4 0 .5 7 7 0 .3 0 624 0 .3 9 7 0 .4 3 7 0 .4 7 5 0 .7 3 5 0 .5 0 712 0 .5 2 8 0 .5 7 4 0 .5 8 6 0 .4 9 3 0 .6 0 50 0 .5 2 2 0 .5 7 5 0 .5 9 0 .5 8 9 0 .5 6 4

-12 0 .4 4 9 0 .4 5 0 .4 6 8 0 .1 8 5 0 .4 3 3-24 0 .2 9 4 0 .2 7 5 0 .2 7 9 0 .3 5 4 0 .311-36 0 .1 9 3 0 .181 0 .1 7 8 0 .2 8 5 0 .221

APPENDIX 3. 264

Mean velocity data of the 180mm Rushton impeller. Velocities in m/s.T =450mm, h = 580mm, c=315mm

ZImm] V+ 15o V-15o angleY Vradial Vaxial Vtangent.S ing le -phase , 2 1 0 R P M , 4 5 o , 1 4 8 .5 m m

5 4 .0 0 0 0 .0 5 8 0 .1 1 7 0 .6 3 7 0 .1 1 4 -0 .1 9 2 0 .0 9 03 6 .0 0 0 0 .0 2 4 0 .0 9 9 0 .8 9 5 0 .1 4 5 -0 .1 4 7 0 .0 6 22 4 .0 0 0 0 .0 7 4 0 .2 0 0 0 .781 0 .2 4 3 -0 .0 9 4 0 .1 2 81 8 .0 0 0 0 .1 6 5 0 .3 7 2 0 .7 0 2 0 .4 0 0 -0 .0 2 9 0 .2 8 21 2 .0 0 0 0 .3 3 0 0 .5 9 4 0 .5 5 6 0 .5 1 0 0 .0 2 8 0 .441

6 .0 0 0 0 .4 4 2 0 .8 1 9 0 .5 7 8 0 .7 2 8 0 .0 9 2 0 .6 7 40 .0 0 0 0 .481 0 .9 0 6 0 .5 9 0 0 .821 0 .0 9 5 0 .701

-6 .0 0 0 0 .421 0 .7 6 6 0 .5 6 4 0 .6 6 6 0 .101 0 .6 1 0-1 2 .0 0 0 0 .3 1 0 0 .5 4 4 0 .5 3 5 0 .4 5 2 0 .1 2 3 0 .4 5 8-1 8 .0 0 0 0 .1 6 5 0 .3 0 4 0 .5 7 4 0 .2 6 9 0 .1 4 8 0 .2 4 8-2 4 .0 0 0 0 .0 7 3 0 .1 7 8 0 .7 3 9 0 .2 0 3 0 .1 8 5 0 .1 1 9-3 6 .0 0 0 0 .0 1 6 0 .091 0 .9 4 4 0 .1 4 5 0 .1 9 5 0 .0 4 0

gle-phase, 2 1 0 R P M ,4 5 o , 168 .5 m m5 4 .0 0 0 0 .0 4 7 0 .0 6 4 0 .2 5 7 0 .0 3 3 -0 .1 1 7 0 .0 7 43 6 .0 0 0 0 .0 4 9 0 .1 2 2 0 .7 4 8 0 .141 -0 .0 9 9 0 .0 7 42 4 .0 0 0 0 .1 1 3 0 .251 0 .6 9 4 0 .2 6 7 -0 .0 4 4 0 .1 6 91 2 .0 0 0 0 .2 6 7 0 .5 2 0 0 .6 1 4 0 .4 8 9 0 .051 0 .4 3 00 .0 0 0 0 .3 4 9 0 .7 3 7 0 .6 6 6 0 .7 5 0 0 .0 8 8 0 .5 4 4

-1 2 .0 0 0 0 .2 4 2 0 .541 0 .6 9 7 0 .5 7 8 0 .0 7 5 0 .3 9 0-2 4 .0 0 0 0 .0 8 9 0 .2 1 3 0 .731 0 .2 4 0 0 .1 2 9 0 .1 3 7-3 6 .0 0 0 0 .0 2 3 0 .0 7 9 0 .8 5 5 0 .1 0 8 0 .1 5 5 0 .0 3 8

g le-phase , 2 9 0 R P M , 1 4 8 .5 m m , 45o .5 4 .0 0 0 0 .0 7 2 0 .1 3 8 0 .6 0 3 0 .1 2 8 -0 .2 4 2 0 .1 0 63 6 .0 0 0 0 .0 4 6 0 .1 5 7 0 .8 5 3 0 .2 1 4 -0 .1 8 0 0 .1 0 42 4 .0 0 0 0 .2 7 3 0 .3 9 6 0 .3 4 0 0 .2 3 8 0 .0 5 2 0 .3 4 01 8 .0 0 0 0 .4 7 6 0 .7 4 8 0 .431 0 .5 2 5 0 .1 1 0 0 .6 1 61 2 .0 0 0 0 .6 9 6 1 .2 1 7 0 .5 3 2 1 .0 0 6 0 .211 0 .9 1 9

6 .0 0 0 0 .7 3 0 1 .2 8 5 0 .5 3 7 1 .072 0 .241 1 .0 0 80 .0 0 0 0 .6 8 4 1 .2 4 5 0 .5 6 5 1 .0 8 4 0 .2 1 0 0 .9 6 5

-6 .0 0 0 0 .5 2 7 0 .9 7 9 0 .5 8 0 0 .8 7 3 0 .1 8 6 0 .7 5 8-1 2 .0 0 0 0 .3 4 3 0 .6 0 2 0 .5 3 5 0 .5 0 0 0 .1 8 6 0 .4 7 5-1 8 .0 0 0 0 .1 4 2 0 .3 3 4 0 .7 2 3 0 .371 0 .2 2 2 0 .2 4 6-2 4 .0 0 0 0 .0 4 5 0 .1 6 6 0 .8 7 2 0 .2 3 4 0 .2 4 3 0 .1 0 0-3 6 .0 0 0 0 .0 1 7 0 .0 9 2 0 .9 3 8 0 .1 4 5 0 .2 8 6 0 .0 4 9

S ing le -phase , 2 9 0 R P M , 1 6 8 .5 m m , 4 5 o5 4 .0 0 0 0 .0 5 4 0 .121 0 .6 9 8 0 .1 2 9 -0 .1 6 5 0 .0 8 23 6 .0 0 0 0 .0 5 9 0 .1 8 0 0 .8 2 2 0 .2 3 4 -0 .1 1 8 0 .1 1 22 4 .0 0 0 0 .2 3 9 0 .4 6 6 0 .6 1 5 0 .4 3 9 0 .0 0 0 0 .3 2 21 2 .0 0 0 0 .4 9 2 0 .8 9 3 0 .5 6 2 0 .7 7 5 0 .1 6 6 0 .7 2 4

0 .0 0 0 0 .5 0 0 0 .9 5 7 0 .6 0 2 0 .8 8 3 0 .1 3 9 0 .7 3 9-1 2 .0 0 0 0 .2 6 6 0 .5 5 7 0 .661 0 .5 6 2 0 .121 0 .4 0 3-2 4 .0 0 0 0 .0 6 5 0 .2 0 5 0 .8 3 2 0 .2 7 0 0 .1 8 0 0 .1 1 9-3 6 .0 0 0 0 .0 2 8 0 .1 0 4 0 .8 7 3 0 .1 4 7 0 .2 2 0 0 .0 5 2

APPENDIX 3. 265

Mean velocity data for the 180mm Rushton impeller. Velocities in [m/s].Z[mml V + 1 5 o V -1 5 o angle Y Vradial Vaxial Vtang.Two-phase, 210RPM, 45o, 1 4 8 .5mm,RPD = 0 .8 0 2

5 4 .0 0 0 0 .0 5 3 0 .0 8 7 0 .4 7 5 0 .0 6 6 -0 .1 8 4 0 .0 8 53 6 .0 0 0 0 .0 5 6 0 .1 2 2 0 .6 8 3 0 .1 2 8 -0 .1 1 6 0 .0 9 82 4 .0 0 0 0 .1 7 7 0 .3 3 0 0 .5 8 3 0 .2 9 6 0 .0 0 2 0 .2 3 81 8 .0 0 0 0 .3 3 3 0 .4 7 5 0 .3 1 9 0 .2 7 4 0 .0 7 8 0 .3 5 81 2 .0 0 0 0 .4 4 3 0 .6 9 6 0 .4 3 0 0 .4 8 9 0 .1 4 0 0 .5 8 3

6 .0 0 0 0 .4 5 2 0 .7 9 2 0 .5 3 4 0 .6 5 7 0 .1 6 4 0 .6 4 70 .0 0 0 0 .4 2 9 0 .7 9 5 0 .5 7 8 0 .7 0 7 0 .1 3 2 0 .6 2 6

-6 .0 0 0 0 .3 6 0 0 .5 6 9 0 .4 3 7 0 .4 0 4 0 .1 2 0 0 .4 3 9-1 2 .0 0 0 0 .2 5 4 0 .3 6 6 0 .331 0 .2 1 6 0 .1 2 0 0 .321-1 8 .0 0 0 0 .1 3 2 0 .2 2 9 0 .5 2 5 0 .1 8 7 0 .1 3 8 0 .1 9 8-2 4 .0 0 0 0 .0 8 2 0 .141 0 .5 1 7 0 .1 1 4 0 .1 6 8 0 .111-3 6 .0 0 0 0 .0 4 5 0 .1 0 5 0 .7 1 9 0 .1 1 6 0 .1 9 4 0 .0 7 9

T w o -p h a se ,2 10 R PM , 4 5o , 1 6 8 .5m m ,R PD = 0 .8 0 25 4 .0 0 0 0 .051 0 .0 9 0 0 .5 3 9 0 .0 7 5 -0 .1 3 7 0 .0 7 63 6 .0 0 0 0 .0 5 0 0 .1 4 3 0 .8 0 2 0 .1 8 0 -0 .0 5 2 0 .1012 4 .0 0 0 0 .1 6 6 0 .331 0 .6 3 0 0 .3 1 9 0 .0 4 3 0 .2 5 41 2 .0 0 0 0 .2 8 9 0 .5 3 5 0 .5 7 8 0 .4 7 5 0 .0 8 5 0 .4 3 30 .0 0 0 0 .3 1 6 0 .5 8 7 0 .5 8 0 0 .5 2 4 0 .0 6 7 0 .4 5 9

-1 2 .0 0 0 0 .1 8 5 0 .3 5 2 0 .5 9 8 0 .3 2 3 0 .0 9 5 0 .2 6 0-2 4 .0 0 0 0 .0 6 9 0 .1 7 5 0 .7 5 6 0 .2 0 5 0 .1 1 6 0 .1 0 9-3 6 .0 0 0 0 .0 3 0 0 .0 9 5 0 .8 3 3 0 .1 2 6 0 .1 3 7 0 .0 6 0

T w o -phase , 148 .5m m , 2 9 0 R P M , 4 5 o ,R P D = 0 .6 0 95 4 .0 0 0 0 .0 6 9 0 .1 3 2 0 .6 0 2 0 .1 2 2 -0 .2 3 7 0 .1 0 83 6 .0 0 0 0 .051 0 .1 3 9 0 .7 8 5 0 .1 7 0 -0 .1 5 0 0 .1 0 72 4 .0 0 0 0 .1 7 6 0 .3 3 9 0 .6 0 6 0 .3 1 5 0 .0 0 9 0 .2611 8 .0 0 0 0 .2 6 5 0 .5 5 6 0 .6 6 2 0 .5 6 2 0 .1 2 2 0 .4311 2 .0 0 0 0 .4 6 0 1 .0 5 4 0 .7 1 0 1 .148 0 .1 9 8 0 .6 7 2

6 .0 0 0 0 .4 5 7 0 .971 0 .6 6 9 0 .9 9 3 0 .231 0 .7 4 40 .0 0 0 0 .4 6 0 0 .9 5 0 0 .6 5 2 0 .9 4 7 0 .1 6 2 0 .7 5 0

-6 .0 0 0 0 .3 9 0 0 .6 8 6 0 .5 3 7 0 .5 7 2 0 .1 5 9 0 .5 3 0-1 2 .0 0 0 0 .3 3 0 0 .4 2 0 0 .1 5 9 0 .1 7 4 0 .1 5 2 0 .3 5 4-1 8 .0 0 0 0 .1 3 5 0 .2 3 0 0 .5 0 9 0 .1 8 4 0 .1 7 8 0 .2 1 2-2 4 .0 0 0 0 .0 6 3 0 .1 4 7 0 .7 1 9 0 .1 6 2 0 .2 2 3 0 .1 0 3-3 6 .0 0 0 0 .0 2 6 0 .1 0 6 0 .8 9 3 0 .1 5 5 0 .2 3 8 0 .0 6 7

o-phase, 10S .Sm m ^ O O R PM ,,4 5o ,R PD = 0 .6 0 95 4 .0 0 0 0 .0 7 4 0 .1 2 2 0 .4 7 9 0 .0 9 3 -0 .1 4 6 0 .1 0 33 6 .0 0 0 0 .0 5 9 0 .1 7 7 0 .8 1 7 0 .2 2 8 -0 .1 0 0 0 .1 2 72 4 .0 0 0 0 .1 5 2 0 .361 0 .7 2 7 0 .4 0 4 0 .031 0 .2 7 81 2 .0 0 0 0 .2 8 7 0 .6 8 9 0 .7 3 2 0 .7 7 7 0 .1 2 8 0 .5 1 00 .0 0 0 0 .3 1 0 0 .7 0 6 0 .7 0 7 0 .7 6 5 0 .1 0 3 0 .5 3 2

-1 2 .0 0 0 0 .1 7 9 0 .3 8 5 0 .6 7 6 0 .3 9 8 0 .1 0 5 0 .2 8 7-2 4 .0 0 0 0 .0 5 7 0 .1 7 8 0 .8 2 9 0 .2 3 4 0 .1 3 2 0 .131-3 6 .0 0 0 0 .0 1 9 0 .1 0 9 0 .9 4 5 0 .1 7 4 0 .1 6 4 0 .051

APPENDIX 3. 266

Mean velocity data of the 180mm Rushton impeller. Velocities in m/s.T = 450m m , h = 580mm, c= 315m m

Zlmm] V + 1 5o V-15o angleY Vradial Vaxial Vtangent.

S in g le-p h ase , B U L K flo w m easu rem e nts, 2 9 0 R P M , 4 5 o , 1 3 3 .5 m m1 9 0 .0 0 0 0 .2 0 4 0 .1 3 1 -0 .9 4 5 -0 .14 1 -0 .3 3 2 0 .1 8 71 7 0 .0 0 0 0 .2 0 7 0 .1 3 0 -0 .9 6 8 -0 .1 4 9 -0 .3 5 8 0 .1 7 41 5 0 .0 0 0 0 .1 7 9 0 .1 8 0 -0 .25 1 0 .0 0 2 -0 .3 8 0 0 .1 6 51 3 0 .0 0 0 0 .1 7 0 0 .1 8 5 -0 .1 0 5 0 .0 2 9 -0 .4 1 1 0 .1 7 7

S in g le-ph ase , 1 4 8 .5 m m1 9 0 .0 0 0 0 .2 5 3 0 .1 9 0 -0 .7 5 0 -0 .1 2 2 -0 .2 1 3 0 .2 4 11 7 0 .0 0 0 0 .2 3 4 0 .2 0 4 -0 .5 1 2 -0 .0 5 8 -0 .2 5 0 0 .2 1 11 5 0 .0 0 0 0 .1 8 7 0 .1 9 5 -0 .1 8 4 0 .0 1 5 -0 .2 6 0 0 .2 0 41 3 0 .0 0 0 0 .1 6 8 0 .1 9 0 -0 .0 3 6 0 .0 4 3 -0 .3 1 4 0 .1 8 6

S in g le-ph ase , 16 8 .5 m m1 9 0 .0 0 0 0 .2 8 8 0 .2 2 2 -0 .7 1 2 -0 .1 2 8 -0 .07 1 0 .2 8 01 7 0 .0 0 0 0 .2 3 8 0 .2 1 9 - 0 .4 1 6 -0 .0 3 7 -0 .0 7 5 0 .2 2 71 5 0 .0 0 0 0 .2 0 2 0 .1 9 8 -0 .2 9 9 -0 .0 0 8 -0 .1 4 6 0 .2 1 31 3 0 .0 0 0 0 .1 7 5 0 .1 8 5 -0 .1 5 9 0 .0 1 9 -0 .1 7 4 0 .1 6 8

S in g le-ph ase , 1 9 8 .5 m m

1 9 0 .0 0 0 0 .2 6 0 0 .2 1 4 -0 .6 0 9 -0 .0 8 9 0 .3 2 3 0 .2 2 21 7 0 .0 0 0 0 .2 2 9 0 .2 2 0 -0 .3 3 6 -0 .0 1 7 0 .3 3 1 0 .2 0 91 5 0 .0 0 0 0 .1 9 3 0 .1 8 0 -0 .3 9 1 -0 .0 2 5 0 .2 9 8 0 .2 1 31 3 0 .0 0 0 0 .2 1 6 0 .1 9 4 -0 .4 5 9 -0 .0 4 3 0 .3 2 5 0 .1 8 6

APPENDIX 3. 267

Mean velocity data for the 180mm Rushton impeller. Velocities in [m/s].Zlmm] V+ 15o V -15o angle Y Vradiat Vaxial Vtang.

T w o -p h a se ,B U LK -FLO W m easu rem en ts ,2 9 0 R P M , 45o , 1 3 3 .5m m ,R PD = 0 .6 4 51 9 0 .0 0 0 0 .191 0 .1 1 0 -1 .0 4 9 -0 .1 5 6 -0 .2 7 0 0 .1511 7 0 .0 0 0 0 .1 9 7 0 .1 1 0 -1 .0 7 5 -0 .1 6 8 -0 .3 0 3 0 .1 7 21 5 0 .0 0 0 0 .1 7 3 0 .141 -0 .6 2 5 -0 .0 6 2 -0 .3 1 4 0 .1 7 31 3 0 .0 0 0 0 .1 6 6 0 .1 5 0 -0 .4 4 9 -0 .031 -0 .341 0 .1 5 6

Tw o -phase , 1 4 8 .51 9 0 .0 0 0 0 .2 2 6 0 .161 -0 .8 2 2 -0 .1 2 6 -0 .1 6 7 0 .1 9 51 7 0 .0 0 0 0 .2 2 3 0 .1 5 4 -0 .861 -0 .1 3 3 -0 .2 0 0 0 .1 9 81 5 0 .0 0 0 0 .1 9 3 0 .1 6 4 -0 .5 5 6 -0 .0 5 6 -0 .2 0 8 0 .1 8 01 3 0 .0 0 0 0 .1 4 3 0 .1 5 6 -0 .101 0 .0 2 5 -0 .2 6 5 0 .1 4 6

T w o -phase , 168 .5m m 1 9 0 .0 0 0 0 .2 6 2 0 .1 9 2 -0 .7 8 4 -0 .1 3 5 -0 .0 4 4 0 .2 4 31 7 0 .0 0 0 ~ 0 .2 2 7 0 .1 4 7 -0 .9 3 6 -0 .1 5 5 -0 .0 7 4 0 .1 9 01 5 0 .0 0 0 0 .171 0 .1 6 3 -0 .351 -0 .0 1 5 -0 .1 2 0 0 .1 8 41 3 0 .0 0 0 0 .1 3 0 0 .1 4 9 -0 .0 1 3 0 .0 3 7 -0 .1 1 2 0 .1 4 9

Tw o -phase , 1 98 .5m m 1 9 0 .0 0 0 0 .2 1 6 0 .1 8 2 -0 .5 7 0 -0 .0 6 6 0 .3 0 0 0 .2 0 81 7 0 .0 0 0 0 .1 7 3 0 .1 7 0 -0 .2 9 4 -0 .0 0 6 0 .3 0 4 0 .1 9 21 5 0 .0 0 0 0 .1 7 6 0 .1 6 7 -0 .3 5 9 -0 .0 1 7 0 .3 1 2 0 .1 7 51 3 0 .0 0 0 0 .1 5 8 0 .1 3 8 -0 .5 0 9 -0 .0 3 9 0 .3 3 6 0 .1 6 9

APPENDIX 3. 268

Z[mm]ata for the 180mm Rushton impeller

RMS+15 RMS-15 RMStang RMSrad RMS axM ,R = 148 .5m m , 45 o , s ing le -phase

54 0 .161 0 .1 6 6 0 .1 6 3 0 .1 7 0 5 8 5 0 .1 83 6 0 .2 4 9 0 .2 5 3 0 .2 3 8 0 .3 8 9 3 6 1 0 .2 7 22 4 0 .531 0 .5 2 6 0 .5 3 0 .5 0 7 2 3 9 0 .5 5 518 0 .6 7 2 0 .7 1 6 0 .7 0 6 0 .5 0 4 8 4 4 0 .6 8 412 0 .7 7 2 0 .8 3 2 0 .8 0 2 0 .8 1 0 3 3 3 0 .751

6 0 .7 8 9 0 .8 4 9 0 .8 0 7 0 .9 7 7 7 3 4 0 .7 0 70 0 .781 0 .8 2 7 0 .7 9 8 0 .8 8 7 8 0 1 0 .6 5

-6 0 .7 0 9 0 .7 8 4 0 .7 4 6 0 .7 6 7 2 3 5 0 .6 0 4-12 0 .6 1 9 0 .6 6 2 0 .6 4 7 0 .5 4 8 2 5 1 0 .5 2-18 0 .4 4 9 0 .4 8 6 0 .4 8 7 0 .1 8 8 6 1 8 0 .4 1 8-24 0 .3 1 9 0 .3 3 5 0 .3 1 6 0 .4 5 4 3 1 1 0 .3 0 9-36 0 .1 7 9 0 .1 8 8 0 .1 8 5 0 .1 6 2 0 9 8 0.21

2 9 0 R P M ,R = 1 6 8 .5 m m ,4 5 o , s ing le -phase54 0 .1 7 7 0 .1 8 5 0 .1 8 0 .1 9 5 0 0 8 0 .1 8 83 6 0 .2 8 0 .3 0 .291 0 .2 7 8 3 8 9 0 .3 2 62 4 0 .4 6 9 0 .531 0 .5 0 2 0 .4 8 6 2 4 5 0 .5 4 212 0 .6 2 5 0 .6 5 7 0 .6 3 7 0 .6 9 7 0 6 8 0 .6 3 6

0 0 .6 3 5 0 .6 8 4 0 .6 7 2 0 .4 6 0 5 2 5 0 .5 9 9-12 0 .5 2 2 0 .5 7 3 0 .5 5 7 0 .4 0 4 1 2 6 0 .4 9 7-24 0 .3 4 3 0 .361 0 .341 0 .4 8 0 9 2 4 0 .3 5-36 0 .2 0 8 0 .2 0 7 0 .2 0 5 0 .2 3 9 6 3 2 0 .2 2 7

VI,R = 1 4 8 .5m m ,45o ,s in g le -p hase5 4 0 .1 2 4 0 .1 2 4 0 .1 2 8 0 .0 3 6 5 5 6 0 .1 4 23 6 0 .1 4 6 0 .1 4 4 0 .1 4 9 0 .0 6 8 2 6 7 0 .1 7 324 0 .2 7 2 0 .2 8 6 0 .3 0 5 0 .3 6 4 5 7 3 0 .3 0 918 0 .3 9 5 0 .4 3 0 .4 3 2 0 .2 3 3 7 4 8 0 .4 2 312 0 .5 1 8 0 .561 0 .5 3 2 0 .6 4 0 2 2 8 0 .5 1 3

6 0 .5 7 6 0 .6 2 2 0 .6 1 5 0 .3 1 0 0 9 1 0 .5 0 70 0 .5 8 5 0 .6 3 8 0 .6 0 3 0 .7 2 6 7 7 4 0.51

-6 0 .5 6 7 0 .5 9 9 0 .5 9 6 0 .3 6 0 8 7 8 0 .4 8 5-12 0 .5 1 6 0 .5 4 2 0 .5 5 6 0 .3 5 4 4 9 0 .4 4 8-18 0 .3 9 9 0 .4 2 4 0 .4 3 7 0 .3 6 0 1 3 4 0 .3 6 4-24 0 .2 9 5 0 .3 0 8 0 .3 0 .3 2 2 6 4 5 0 .2 8 9-36 0 .1 6 3 0 .1 4 0 .1 5 5 0 .0 9 9 9 2 5 0 .1 8 3

M, R == 168 .5m m ,45o ,s in g le -p h a se54 0 .1 4 2 0 .1 4 9 0 .1 3 7 0 .2 3 4 0 9 0 .1 4 63 6 0 .1 8 5 0 .1 8 6 0 .1 9 5 0 .1 2 6 2 2 6 0 .2 1 924 0 .3 0 9 0 .3 2 9 0 .3 2 0 .3 0 7 1 7 0 .3 3 512 0 .4 3 5 0 .4 7 6 0 .4 6 9 0 .1 9 9 7 9 8 0 .4 4 5

0 0 .481 0 .5 2 6 0 .4 9 9 0 .5 6 9 1 2 5 0 .4 6 7-12 0 .4 2 2 0 .4 8 3 0 .4 5 0 .5 0 0 0 6 9 0 .4 1 7-24 0 .3 0 .3 3 0 .3 1 4 0 .3 3 3 6 8 4 0 .3 1 7-36 0 .191 0 .1 9 8 0 .1 8 8 0 .2 6 9 5 2 2 0 .2 2 8

Bulk, 2 9 0 R P M , H = 4 5 0 ,c = 15 0 ,4 5 o , R = 133 .5m m19 0 0 .2 0 6 0 .2 2 4 0 .2 0 4 0 .3 3 4 1 1 0 .1 9 61 7 0 0 .1 9 5 0 .2 1 9 0 .21 0 .1 6 6 0 5 6 0 .2 0 8

APPENDIX 3. 269

RMS data for the 180mm Rushton impellerZ[mm] RMS+15 RMS-15 RMStang RMSrad RMS ax

1 5 0 0 .2 0 5 0 .2 0 6 0 .21 0 .1 2 7 2 4 7 0 .1 9 213 0 0 .1 9 8 0 .2 0 2 0 .2 0 3 0 .1 5 2 3 8 3 0 .1 9 3

B u lk ,2 9 0 R P M ,H = 4 5 0 ,c = 15 0 ,4 5 o ,R = 148 .5m m19 0 0 .2 1 2 0 .2 1 4 0 .2 1 4 0 .1 9 8 5 8 6 0 .2 1 317 0 0 .2 1 6 0 .2 1 2 0 .2 1 5 0 .1 9 9 7 0 1 0 .2 1 715 0 0 .2 0 6 0 .2 1 8 0 .2 0 7 0 .2 7 3 2 4 2 0 .2 1 613 0 0 .1 9 5 0 .2 1 5 0 .2 0 5 0 .2 0 8 6 0 9 0 .2 1 4

B u lk ,2 9 0 R P M ,H = 4 5 0 , c = 15 0 ,4 5 o ,R = 168 .5m m19 0 0 .2 2 0 .2 2 6 0 .2 3 4 0 .1 4 1 9 6 4 0 .2 2 317 0 0 .2 1 5 0 .2 2 9 0 .2 3 7 0 .2 1 4 1 9 7 0 .22115 0 0 .2 0 8 0 .2 3 3 0 .2 2 4 0 .1 7 1 1 2 6 0 .2 1 313 0 0 .2 0 7 0 .2 2 9 0 .2 0 6 0 .3 4 6 6 9 4 0 .2 1 8

B u lk ,2 9 0 R P M ,H = 4 5 0 ,c = 15 0 ,4 5 o ,R = 198 .5m m19 0 0 .2 4 7 0 .2 2 9 0 .2 3 9 0 .2 2 6 2 9 5 0 .2 6 517 0 0 .2 3 4 0 .2 6 3 0 .2 3 8 0 .3 6 8 8 3 6 0 .2 7 915 0 0 .2 3 8 0 .2 2 9 0 .261 0 .3 6 6 8 5 4 0 .2 8 513 0 0 .2 3 4 0 .2 4 8 0 .2 4 7 0 .1 3 4 2 7 8 0 .2 9 6

APPENDIX 3. 270

RMS data for the 180mm Rushton impellerZ[mm] RMS+15 RMS-15 RMStang RMSrad RMS axTw o -phase , 2 9 0 R P M , R PD = 0 .6 0 9 , R = 1 4 8 .5 m m ,4 5 o

54 0 .1 5 2 0 .1 5 8 0 .1 5 9 0 .0 8 1 6 4 3 0 .1 5 93 6 0 .211 0 .2 1 9 0 .2 0 9 0 .2 8 6 1 7 7 0 .3 2 624 0 .4 4 8 0 .4 2 6 0 .4 3 5 0 .4 6 5 9 0 4 0 .5 0 918 0 .5 3 5 0 .5 7 6 0 .5 5 5 0 .5 6 7 9 6 8 0 .6 0 212 0 .6 9 2 0 .8 2 6 0 .6 7 1 .5 5 3 8 6 5 0 .6 5 7

6 0 .6 4 3 0 .6 9 2 0 .6 7 9 0 .4 8 8 7 1 5 0 .6 70 0 .6 4 3 0 .7 1 3 0 .6 9 4 0 .4 1 4 9 9 3 0 .611

-6 0 .6 3 2 0 .6 2 6 0 .5 9 3 1 .0 0 4 2 4 3 0 .5 6 5-12 0 .6 0 .5 0 8 0 .5 1 8 0 .9 3 5 9 6 0 .4 3 7-18 0 .411 0 .3 5 8 0 .4 2 5 0 .5 4 6 1 7 7 0 .3 2 8-24 0 .2 7 0 .2 3 7 0 .2 4 5 0 .3 5 6 8 5 3 0 .2 6 6-36 0 .1 5 8 0 .1 7 6 0 .1 4 7 0 .3 4 1 4 2 0 .171

ia se ,2 9 0 R P M ,R P D = 0 .6 0 9 ,R = 1 6 8 .5 m m ,4 5 o54 0 .1 6 6 0 .1 7 2 0 .1 5 6 0 .2 9 5 8 7 5 0.18136 0 .2 3 9 0 .2 4 8 0 .2 5 4 0 .1 1 4 7 3 0 .3 1 524 0 .3 7 6 0 .4 1 7 0 .4 1 4 0 .1 8 4 5 7 6 0 .4 7 712 0 .5 2 3 0 .5 2 7 0 .5 2 4 0 .5 3 8 7 9 1 0 .5 5 7

0 0 .5 3 5 0 .5 3 8 0 .5 4 7 0 .3 5 9 7 3 3 0 .5 2 9-12 0 .4 2 4 0 .4 4 4 0 .4 4 8 0 .1 3 3 6 5 4 0 .4 1 6-24 0 .2 7 7 0 .251 0 .2 4 7 0 .4 3 9 5 6 0 .2 8 8-36 0 .1 8 0 .1 7 4 0 .1 7 9 0 .1 4 6 7 8 7 0 .2 1 8

ia se ,2 1 0 R P M , RPD == 0 .8 0 2 , R = 1 4 8 .5 m m ,4 5 o54 0 .1 2 7 0 .1 2 8 0 .1 2 7 0 .1 3 4 2 8 5 0 .1413 6 0 .2 0 4 0 .1 9 5 0 .1 9 9 0 .2 0 7 0 6 9 0 .2 5 824 0 .3 9 8 0 .4 2 6 0 .4 0 .5 5 5 3 2 5 0 .4 5 418 0 .571 0 .5 2 2 0 .5 0 6 0 .9 4 9 3 8 4 0 .5 2 412 0 .6 4 7 0 .611 0 .6 3 4 0 .5 5 9 0 3 6 0 .5 5 8

6 0 .6 3 3 0 .6 5 0 .6 5 0 .5 0 9 6 0 8 0 .5 7 50 0 .6 0 .6 6 8 0 .6 4 6 0 .4 5 3 0 7 4 0 .5 2 3

-6 0 .5 9 3 0 .5 5 9 0 .5 3 4 0 .9 9 2 6 8 5 0 .471-12 0 .4 9 7 0 .4 5 8 0 .481 0 .4 3 2 3 8 5 0 .381-18 0 .3 4 8 0 .3 2 4 0 .3 7 8 0 .5 5 0 1 2 1 0 .2 8 5-24 0 .2 4 7 0 .221 0 .2 1 5 0 .4 1 9 6 4 3 0 .2 3 2-36 0 .1 3 0 .1 4 2 0 .1 3 5 0 .1 5 1 0 2 3 0 .1 4 8

ia se ,2 1 0 R P M ,R P D = 0 .8 0 2 ,R = 1 6 8 .5 m m ,4 5 o54 0 .1 4 4 0 .1 4 9 0 .1 4 6 0 .1 5 3 5 9 9 0 .1 5 43 6 0 .2 2 2 0 .2 2 6 0 .2 3 0 .1 1 0 8 8 4 0 .2 8 324 0 .3 5 8 0 .3 7 0 .3 5 7 0 .4 5 0 9 2 0 .4 0 812 0 .471 0 .4 5 2 0 .4 8 4 0 .2 8 6 3 1 4 0 .471

0 0 .4 7 4 0 .4 5 0 .4 8 2 0 .2 1 7 6 4 8 0 .4 4 3-12 0 .3 7 5 0 .3 9 6 0 .3 7 2 0 .5 4 1 0 0 8 0 .3 3 5-24 0 .2 4 6 0 .2 3 9 0 .2 1 8 0 .4 6 4 8 9 8 0 .2 3 6-36 0 .1 4 7 0 .1 4 6 0 .1 5 2 0 .0 3 7 4 2 5 0 .171

Bulk, Tw o -phase , RPD = 0 .6 4 5 , 4 5 o , R = 133 .5m m19 0 0 .2 0 6 0 .1 9 8 0 .2 0 .2 2 8 5 6 3 0 .1 8 617 0 0 .1 9 3 0 .1 9 3 0 .1 9 9 0 .0 6 7 0 0 6 0 .1 8 2

APPENDIX 3.

RMS data for the 180mm Rushton impellerZ[mm] RMS+15 RMS-15 RMStang RMSrad RMS ax

15 0 0 .191 0 .1 8 3 0 .1 9 6 0 .1 1 3 1 4 9 0 .1 8 5130 0 .1 8 0 .181 0 .1 8 4 0 .1 2 1 7 1 7 0 .1 8 5

Bulk, Tw o -phase , R PD = 0 .6 4 5 , 4 5 o , R = 148 .5m m190 0 .211 0 .1 9 5 0 .2 0 5 0 .1 7 5 4 9 6 0 .1 9 8170 0 .2 0 8 0 .2 0 7 0 .2 0 4 0 .2 5 1 2 3 7 0 .1 9 7150 0 .1 9 0 .191 0 .2 0 4 0 .1 9 4 6 3 8 0 .1 8 2130 0 .1 9 4 0 .1 8 7 0 .1 8 2 0 .2 8 3 8 5 4 0 .1 9 5

Bulk, Tw o -phase , RPD = 0 .6 4 5 , 4 5 o , R = 168 .5m m19 0 0 .2 1 8 0 .211 0 .2 1 3 0 .2 3 4 7 8 6 0 .2 0 2170 0 .2 1 6 0 .2 1 3 0 .2 1 8 0 .1 5 7 9 8 7 0 .201150 0 .1 9 7 0 .2 0 8 0 .2 1 3 0 .1 3 8 9 5 1 0 .1 9 5130 0 .2 0 3 0 .1 9 3 0 .2 0 6 0 .0 7 3 7 4 8 0 .1 9 7

Bulk, Tw o -phase , RPD = 0 .6 4 5 , 4 5o , R = 198 .5m m190 0 .2 1 3 0 .21 0 .2 1 3 0 .1 8 9 4 6 5 0 .2 5 3170 0 .2 3 0 .2 0 4 0 .2 1 6 0 .2 3 5 8 8 7 0 .231150 0 .2 0 8 0 .211 0 .2 1 4 0 .1 3 1 8 3 4 0 .2 5 4130 0.21 0 .2 2 0 .2 0 7 0 .3 0 5 9 7 4 0 .2 2 8

APPENDIX 3. 272

Convex 180mm impeller velocity measurements.Z[mm] V + 1 5 V-15 angle x V radial Vaxial VtangentialSingle-phase, 148.5m m , 15o

5 2 .0 0 0 0 .1 4 5 0 .1 9 2 0 .2 1 8 0 .091 -0 .2 7 4 0 .1 7 93 6 .0 0 0 0 .1 8 8 0 .2 5 8 0 .2 6 8 0 .1 3 5 -0 .2 1 8 0 .2 1 82 4 .0 0 0 0 .3 0 5 0 .4 5 7 0 .3 7 8 0 .2 9 4 -0 .0 5 7 0 .3 7 21 8 .0 0 0 0 .3 9 5 0 .6 7 8 0 .5 1 6 0 .5 4 7 0 .021 0 .5 4 01 2 .0 0 0 0 .4 9 3 0 .9 2 4 0 .5 8 7 0 .8 3 3 0 .1 4 4 0 .7 4 0

6 .0 0 0 0 .5 8 6 1 .1 0 9 0 .5 9 4 1 .0 1 0 0 .1 8 0 0 .8 1 80 .0 0 0 0 .5 9 7 . 1 .101 0 .5 7 5 0 .9 7 4 0 .1 7 7 0 .8 7 5

-6 .0 0 0 0 .5 3 3 1 .0 1 9 0 .601 0 .9 3 9 0 .1 9 5 0 .7 8 2-1 2 .0 0 0 0 .4 4 8 0 .8 3 0 0 .5 7 8 0 .7 3 8 0 .1 7 8 0 .6 0 4-1 8 .0 0 0 0 .3 2 3 0 .5 6 0 0 .5 2 4 0 .4 5 8 0 .2 0 5 0 .4 5 4-2 4 .0 0 0 0 .2 5 2 0 .3 9 9 0 .4 3 8 0 .2 8 4 0 .2 2 9 0 .3 2 8-3 6 .0 0 0 0 .1 8 6 0 .2 6 2 0 .3 0 3 0 .1 4 7 0 .301 0 .2 1 6

Tw o -phase , 148 .5m m , 15o ,R PD = 0 .5 65 2 .0 0 0 0 .1 0 8 0 .1 5 7 0 .3 4 2 0 .0 9 5 -0 .221 0 .1 2 73 6 .0 0 0 0 .1 4 7 0 .1 9 2 0 .1 9 8 0 .0 8 7 -0 .141 0 .1 7 02 4 .0 0 0 0 .2 3 6 0 .4 1 6 0 .5 3 9 0 .3 4 8 0 .0 4 3 0 .3 4 71 8 .0 0 0 0 .3 3 3 0 .6 5 3 0 .6 1 9 0 .6 1 8 0 .1 5 0 0 .5 3 31 2 .0 0 0 0 .3 9 8 0 .8 6 9 0 .6 8 4 0 .9 1 0 0 .2 0 5 0 .6 6 7

6 .0 0 0 0 .4 5 2 0 .9 4 0 0 .6 5 6 0 .9 4 3 0 .1 9 6 0 .6 8 80 .0 0 0 0 .4 3 0 0 .8 6 3 0 .6 3 4 0 .8 3 6 0 .1 3 8 0 .6 6 3

-6 .0 0 0 0 .3 3 0 0 .671 0 .6 4 3 0 .6 5 9 0 .1 4 0 0 .5 3 7-1 2 .0 0 0 0 .2 7 0 0 .4 6 4 0 .5 1 7 0 .3 7 5 0 .151 0 .401-1 8 .0 0 0 0 .1 9 5 0 .3 0 6 0 .4 2 9 0 .2 1 4 0 .2 4 2-2 4 .0 0 0 0 .1 4 4 0 .231 0 .4 5 2 0 .1 6 8 0 .1 9 0 0 .1 8 7-3 6 .0 0 0 0 .1 2 0 0 .1 7 9 0 .3 7 3 0 .1 1 4 0 .2 2 4 0 .1 6 2

jle -phase ,5 2 .0 0 0

16 8 .5 m m ,15o 0 .141 0 .2 0 3 0 .3 3 0 0 .1 2 0 -0 .1 7 7 0 .1 8 0

3 6 .0 0 0 0 .231 0 .2 7 7 0 .0 6 4 0 .0 8 9 -0 .1 0 2 0 .2 3 32 4 .0 0 0 0 .2 7 0 0 .4 9 6 0 .5 7 2 0 .4 3 7 0 .001 0 .3 8 91 2 .0 0 0 0 .361 0 .8 0 2 0 .6 9 4 0 .8 5 2 0 .111 0 .5 9 4

0 .0 0 0 0 .4 2 5 0 .9 1 9 0 .6 7 9 0 .9 5 4 0 .1 0 2 0 .6 9 2-1 2 .0 0 0 0 .3 4 0 0 .7 2 2 0 .6 6 9 0 .7 3 8 0 .1 0 8 0 .5 6 3-2 4 .0 0 0 0 .251 0 .4 2 8 0 .5 1 0 0 .3 4 2 0 .1 4 8 0 .3 1 8-3 6 .0 0 0 0 .191 0 .2 7 9 0 .3 4 8 0 .1 7 0 0 .2 0 4 0 .2 4 2

> phase , 168 .5m m , 15o ,R PD 5 2 .0 0 0 0 .111

= 0 .5 6 0 .1 4 6 0 .2 0 8 0 .0 6 8 -0 .1 3 8 0 .1 2 9

3 6 .0 0 0 0 .1 6 2 0 .2 1 6 0 .2 2 8 0 .1 0 4 -0 .0 6 0 0 .1 7 22 4 .0 0 0 0 .2 2 7 0 .4 2 5 0 .5 8 6 0 .3 8 3 0 .0 4 6 0 .3 3 61 2 .0 0 0 0 .3 2 4 0 .7 1 2 0 .6 8 8 0 .7 5 0 0 .1 2 6 0 .5 4 50 .0 0 0 0 .3 1 0 0 .701 0 .7 0 3 0 .7 5 5 0 .0 8 6 0 .5 2 8

-1 2 .0 0 0 0 .2 3 3 0 .4 4 4 0 .5 9 9 0 .4 0 8 0 .0 9 5 0 .3 2 8-2 4 .0 0 0 0 .161 0 .2 4 5 0 .3 9 6 0 .1 6 2 0 .1 2 9 0 .1 9 5-3 6 .0 0 0 0 .1 3 5 0 .1 9 6 0 .341 0 .1 1 8 0 .1 4 6 0 .1 5 9

APPENDIX 3. 273

Convex 180mm impeller velocity measurements.Z[mm] V + 1 5 V-15 angle x V radial Vaxial Vtangential,Single-phase, 148.5m m ,45o

5 2 .0 0 0 .0 6 2 0 .1 2 0 0 .6 1 0 0 .1 1 2 -0 .2 7 0 0 .0 8 93 6 .0 0 0 .111 0 .1 3 4 0 .0 7 5 0 .0 4 4 -0 .1 9 0 0 .1 0 62 4 .0 0 0 .1 8 4 0 .371 0 .6 3 7 0 .361 0 .0 5 7 0 .2 6 318 .0 0 0 .3 0 3 0 .5 8 2 0 .6 0 5 0 .5 3 9 0 .4 3 41 2 .0 0 0 .4 1 9 0 .8 8 5 0 .6 6 6 0 .9 0 0 0 .1 3 3 0 .6 5 4

6 .0 0 0 .5 1 9 1.051 0 .6 4 0 1 .0 2 8 0 .7 6 50 .0 0 0 .5 2 5 1 .0 7 0 0 .6 4 4 1 .053 0 .1 6 0 0 .8 1 0

-6 .0 0 0 .4 7 3 0 .9 6 0 0 .641 0 .941 0 .1 8 9 0 .7 3 6-1 2 .0 0 0 .3 5 0 0 .731 0 .6 5 9 0 .7 3 6 0 .181 0 .5 4 5-1 8 .0 0 0 .2 2 4 0 .471 0 .6 6 3 0 .4 7 7 0 .361-2 4 .0 0 0 .1 2 8 0 .2 7 8 0 .6 8 2 0 .2 9 0 0 .2 2 5 • 0 .1 9 4-3 6 .0 0 0 .0 4 0 0 .1 0 0 0 .7 5 0 0 .1 1 6 0 .2 8 6 0 .0 6 3

Tw o -phase , 148 .5m m , 45 o , RPD = 0 .5 65 2 .0 0 0 0 .0 6 6 0 .1 2 2 0 .5 7 6 0 .1 0 8 -0 .2 2 5 0 .0 9 43 6 .0 0 0 0 .1 1 0 0 .1 3 9 0 .1 4 8 0 .0 5 6 -0 .1 4 2 0 .0912 4 .0 0 0 0 .1 9 5 0 .3 5 8 0 .571 0 .3 1 5 0 .0 1 0 0 .2 7 91 8 .0 0 0 0 .2 8 3 0 .5 9 8 0 .6 6 6 0 .6 0 9 0 .5311 2 .0 0 0 0 .3 6 0 0 .8 3 9 0 .7 1 8 0 .9 2 5 0 .1 5 6 0 .611

6 .0 0 0 0 .4 0 9 0 .9 0 6 0 .6 9 2 0 .9 6 0 0 .6 3 50 .0 0 0 0 .3 5 7 0 .8 0 0 0 .6 9 8 0 .8 5 6 0 .1 1 8 0 .5 8 9

-6 .0 0 0 0 .3 0 2 0 .5 9 5 0 .6 2 2 0 .5 6 6 0 .1 2 2 0 .4 4 6-1 2 .0 0 0 0 .1 7 0 0 .3 7 4 0 .6 8 9 0 .3 9 4 0 .1 6 5 0 .2 4 5-1 8 .0 0 0 0 .0 6 0 0 .1 9 4 0 .8 3 9 0 .2 5 9 0 .1 4 5-2 4 .0 0 0 0 .0 4 3 0 .1 3 5 0 .831 0 .1 7 8 0 .2 0 3 0 .0 6 5-3 6 .0 0 0 0 .021 0 .0 8 6 0 .8 9 4 0 .1 2 6 0 .2 3 6 0 .0 8 4

jie -phase5 2 .0 0 0

, 1 6 8 .5m m , 45 o 0 .0 5 0 0 .1 1 7 0 .7 2 0 0 .1 2 9 -0 .1 5 5 0 .0 8 9

3 6 .0 0 0 0 .101 0 .191 0 .5 9 3 0 .1 7 4 -0 .1 2 5 0 .1 2 42 4 .0 0 0 0 .1 6 6 0 .4 0 5 0 .7 4 0 0 .4 6 2 0 .0 0 7 0 .2811 2 .0 0 0 0 .3 4 2 0 .7 6 3 0 .6 9 6 0 .8 1 3 0 .0 8 6 0 .5 3 50 .0 0 0 0 .3 8 6 0 .8 8 4 0 .7 1 0 0 .9 6 2 0 .0 9 7 0 .6 5 3

-1 2 .0 0 0 0 .2 6 5 0 .6 5 0 0 .7 4 2 0 .7 4 4 0 .1 2 3 0 .4 8 0-2 4 .0 0 0 0 .141 0 .2 8 6 0 .641 0 .2 8 0 0 .1 4 9 0 .1 9 2-3 6 .0 0 0 0 .0 4 6 0 .1 3 3 0 .8 0 5 0 .1 6 8 0 .1 9 5 0 .1 0 5

> phase ,5 2 .0 0 0

168 .5m m , 4 5 o ,R P D = 0 .5 6 0 .0 4 7 0 .1 2 9 0 .7 8 7 0 .1 5 8 -0 .1 3 9 0 .0 7 4

3 6 .0 0 0 0 .1 1 2 0 .171 0 .3 9 9 0 .1 1 4 -0 .0 3 5 0 .1112 4 .0 0 0 0 .1 8 4 0 .3 9 0 0 .6 6 8 0 .3 9 8 0 .0 5 2 0 .2811 2 .0 0 0 0 .2 8 0 0 .6 9 5 0 .7 4 7 0 .8 0 2 0 .1 3 2 0 .4 6 4

0 .0 0 0 0 .2 5 8 0 .6 3 6 0 .7 4 4 0 .7 3 0 0 .1 0 6 0 .4 5 3-1 2 .0 0 0 0 .1 2 6 0 .321 0 .7 5 8 0 .3 7 7 0 .1 0 4 0 .2 3 2-2 4 .0 0 0 0 .0 2 0 0 .151 0 .9 7 3 0 .2 5 3 0 .1 2 4 0 .0 6 9-3 6 .0 0 0 0 .0 1 5 0 .081 0 .9 3 7 0 .1 2 8 0 .1 6 5 0 .0 4 5

APPENDIX 3. 274

RMS data for the convex 180mm impeller, h = 580mm,c=315mm Z[mm] RMS +15 RMS-15 RMStang RMSrad RMS axS ing le -phase , 3 5 0 R P M , 1 5o ,R = 1 4 8 .5 m m

52 0 .1 8 0 .1 6 7 0 .1 7 8 0 .0 9 3 0 .1 9 63 6 0 .2 6 2 0 .2 3 3 0 .2 4 7 0 .2 6 0 0 .2 9 22 4 0 .4 4 2 0 .4 3 5 0 .4 3 0 .5 4 3 0 .5 1 518 0 .5 0 7 0 .5 4 9 0 .5 2 5 0 .5 7 4 0 .5 9 912 0 .5 7 7 0 .6 2 5 0 .6 0 7 0 .5 1 9 0 .671

6 0 .6 2 5 0 .6 4 7 0 .6 0 5 0 .971 0 .6 8 20 0 .6 2 9 0 .641 0 .6 3 3 0 .6 6 3 0 .6 7

-6 0 .5 8 4 0 .6 4 4 0 .6 1 5 0 .611 0 .6 2 3-12 0 .5 6 6 0 .601 0 .5 6 0 .8 4 8 0 .5 4 2-18 0 .4 6 0 .5 0 6 0 .4 9 5 0 .2 7 9 0 .4 8 8-24 0 .3 8 5 0 .3 9 8 0 .3 7 9 0 .5 3 7 0 .3 9 3-36 0 .2 4 7 0 .2 3 0 .2 2 9 0 .3 4 6 0 .261

hase, RPD = 0 .5 6 , 3 5 0 R P M , 1 5 o ,R = 148 .5m m52 0 .1 4 2 0 .1 4 7 0 .1 5 0 .0 4 0 0 .1 5 336 0 .2 6 7 0 .211 0 .2 1 6 0 .4 6 3 0 .2 7 324 0 .3 9 7 0 .4 2 8 0 .421 0 .2 7 4 0 .5 0 718 0 .491 0 .5 4 9 0 .5 4 3 0 .2 4 0 0 .5 9 412 0 .5 1 5 0 .6 1 6 0 .5 8 2 0 .3 0 7 0 .6 4 8

6 0 .5 5 3 0 .5 9 9 0 .5 5 0 .8 6 5 0 .6 1 20 0 .5 2 7 0 .5 7 8 0 .5 6 8 0 .2 7 0 0 .5 7 8

-6 0 .4 7 7 0 .5 4 3 0 .5 2 3 0 .2 9 9 0.51-12 0 .411 0 .4 6 0 .4 7 0 .4 8 6 0 .4 1 4-18 0 .2 8 6 0 .31 0 .3 0 2 0 .2 4 0-24 0 .2 0 3 0 .2 1 6 0 .2 0 5 0 .2 6 6 0 .2 2 9-36 0 .1 4 8 0 .1 4 3 0 .1 4 4 0 .1 6 5 0 .1 5 2

•phase, 3 5 0 R P M , 1 5 o ,R = 16 8 .5 m m52 0 .2 0 .191 0 .1 9 7 0 .1 7 4 0 .2 1 836 0 .3 4 4 0 .2 9 2 0 .2 7 0 .7 1 0 0 .3 4 424 0 .4 1 3 0 .4 3 4 0 .4 2 9 0 .3 4 0 0 .5 0 812 0 .4 8 9 0 .5 4 0 .5 1 4 0 .531 0 .611

0 0 .5 1 5 0 .5 6 0 .5 4 8 0 .371 0.61-12 0 .4 8 2 0 .5 0 9 0 .5 0 7 0 .2 9 6 0 .5 3 9-24 0 .3 7 8 0 .3 7 3 0 .3 8 0 .3 0 6 0 .4 0 5-36 0 .2 6 3 0 .2 7 0 .2 4 3 0 .4 8 8 0 .2 8 3

iase, RPD = 0 .5 6 , 3 5 0 R P M , 15o ,R = 168 .5m m52 0 .1 6 4 0 .1 5 9 0 .1 6 0 .181 0 .1 6 73 6 0 .2 9 6 0 .2 4 0 .2 3 3 0 .5 7 3 0 .2 9 324 0 .3 6 7 0 .3 8 8 0 .391 0 .0 1 9 0 .4 3 412 0 .4 3 8 0 .4 6 0 .4 7 8 0 .4 1 4 0 .5 1 3

0 0 .4 3 6 0 .461 0 .4 5 5 0 .3 4 9 0 .4 7 3-12 0 .3 5 2 0 .3 9 2 0 .3 7 4 0 .3 5 2 0 .381-24 0 .2 1 6 0 .2 1 6 0 .2 2 8 0 .1 6 6 0 .2 3 9-36 0 .1 5 5 0 .151 0 .161 0 .1 0 7 0 .1 8 6

APPENDIX 3. 275

R M S data fo r the co n ve x 18 0m m im pe lle r, h = 58 0 m m ,c = 3 1 5m mZ lm m ] R M S + 1 5 R M S -1 5 R M S ta n g R M S rad R M S axS ing le -phase , 3 5 0 R P M , 4 5 o ,R = 14 8 .5m m

52 0 .1 8 2 0 .1 7 7 0 .1 7 5 0 .2 3 4 0 .23 6 0 .3 1 4 0 .2 5 0 .2 5 0 .5 7 6 0 .3 2 32 4 0 .4 4 6 0 .4 5 3 0 .4 2 3 0 .7 2 4 0 .51118 0 .5 2 7 0 .5 5 5 0 .5 2 7 0 .7 1 012 0 .5 6 9 0 .6 4 6 0.61 0 .591 0 .6 5 7

6 0 .6 0 9 0 .6 5 2 0 .6 2 4 0 .7 2 00 0 .6 1 5 0 .6 4 8 0 .6 2 7 0 .6 9 4 0 .6 8

-6 0 .6 0 7 0 .661 0 .6 2 7 0 .7 3 2 0 .6 0 9-12 0 .5 6 2 0 .631 0 .601 0 .5 4 6 0 .5 7 5-18 0 .4 9 7 0 .561 0 .5 1 9 0 .6 6 4-24 0 .4 1 9 0 .431 0 .411 0 .5 8 7 0 .3 8 8-36 0 .2 5 3 0 .2 4 7 0 .2 4 3 0 .3 3 3 0 .2 6 3

Tw o -phase , RPD = 0 .5 6 , 3 5 0 R P M , 4 5 o ,R = 148 .5m m52 0 .141 0 .1 4 7 0 .1 4 2 0 .1 7 0 0 .1 5 53 6 0 .3 1 2 0 .231 0 .2 1 5 0 .6 9 4 0 .2 6 524 0 .401 0 .4 2 7 0 .4 2 2 0 .2 8 4 0 .4 718 0 .4 7 7 0 .5 2 5 0 .5 9 4 1 .0 7 612 0 .5 2 3 0 .5 9 5 0 .561 0 .5 4 8 0 .6 0 9

6 0 .5 5 8 0 .5 6 5 0 .5 4 4 0 .7 6 50 0 .5 1 6 0 .5 7 4 0 .5 4 4 0 .5 7 0 0 .5 3 6

-6 0 .4 8 6 0 .5 4 0 .5 0 7 0 .5 9 9 0 .4 8 5-12 0 .3 8 8 0 .4 6 2 0 .4 0 4 0 .6 6 6 0 .3 7 8-18 0 .2 8 2 0 .3 0 4 0 .2 8 5 0 .3 9 0-24 0 .2 2 5 0 .2 0 9 0 .2 8 6 0 .6 6 0 0 .2 3 2-36 0 .1 5 3 0 .1 5 4 0 .1 5 7 0 .0 9 2 0 .1 5 8

S ing le -phase , 3 5 0 R P M , 4 5 o ,R = 16 8 .5 m m52 0 .1 9 7 0 .1 9 7 0 .1 9 2 0 .2 5 7 0 .2 0 43 6 0 .3 0 8 0 .3 0 2 0 .2 7 9 0 .5 5 2 0 .3 2 224 0 .4 1 5 0 .4 5 0 .4 4 2 0 .2 7 6 0.5112 0 .5 1 7 0 .5 5 9 0 .5 3 9 0 .5 3 0 0 .5 9 2

0 0 .5 3 2 0 .5 7 8 0 .5 5 9 0 .5 0 4 0 .6 1 7-12 0 .5 1 6 0 .5 6 8 0 .5 3 2 0 .6 7 3 0 .5 2 7-24 0 .4 0 .4 2 7 0 .4 0 7 0 .4 9 8 0 .4 2 9-36 0 .2 9 0 .2 8 8 0 .2 8 8 0 .3 0 3 0 .3 1 8

Tw o -phase , RPD = 0 .5 6 , 3 5 0 R P M , 4 5 o ,R = 168 .5m m52 0 .1 5 7 0 .1 5 8 0 .1 5 2 0 .2 2 0 0 .1 6 936 0 .3 0 2 0 .2 5 9 0 .2 5 3 0 .5 3 8 0.3124 0 .381 0 .3 9 3 0 .3 8 5 0 .4 1 5 0 .4 3 312 0 .4 3 7 0 .4 6 5 0 .4 7 6 0 .341 0 .50 0 .431 0 .4 6 6 0 .4 5 2 0 .4 0 2 0 .451

-12 0 .3 6 5 0 .3 7 0 .3 8 2 0 .1 2 7 0 .361-24 0 .2 1 7 0 .2 3 8 0 .2 1 4 0 .3 6 9 0 .2 3 7-36 0 .1 6 6 0 .1 6 2 0 .1 5 7 0 .241 0 .1 6 9

APPENDIX 3. 276

Velocity measurements of the 45o, 200mm, PBT, downwards pumping T=450mm, D = 200mm, h = 580mm, c=330mm, RPD = 0.698Zimm] V+1 5 V-15 angle x V radial Vaxial Vtangential,S ing le -phase , 1 4 8 .5m m ,45o

4 0 .0 0 0 -0 .1 1 2 -0 .1 4 5 0 .1 8 5 -0 .0 6 4 -0 .5 2 7 -0 .1 2 92 0 .0 0 0 -0 .1 0 2 -0 .1 4 2 0 .2 8 7 -0 .0 7 7 -0 .5 1 6 -0 .1 4 9

0 .0 0 0 -0 .1 6 6 -0 .1 5 5 -0 .3 8 9 0 .021 -0 .451 -0 .1 7 8-2 0 .0 0 0 -0 .2 2 0 -0 .0 6 4 -1 .3 7 9 0 .301 -0 .3 9 6 -0 .1 6 4-4 0 .0 0 0 -0 .2 4 4 -0 .1 0 5 -1 .2 4 0 0 .2 6 9 -0 .2 2 0 -0 .1 8 2

T w o -p h a se ,1 4 8 .5m m ,45o4 0 .0 0 0 -0 .0 8 4 -0 .2 0 2 0 .7 3 3 -0 .2 2 8 -0 .3 4 8 -0 .1 2 72 0 .0 0 0 -0 .1 4 6 -0 .161 -0 .081 -0 .0 2 9 -0 .3 4 4 -0 .121

0 .0 0 0 -0 .1 7 3 -0 .2 1 3 0 .1 0 7 -0 .0 7 7 -0 .4 1 2 -0 .1 9 6-2 0 .0 0 0 -0 .1 7 0 -0 .1 9 8 0 .0 1 5 -0 .0 5 4 -0 .3 4 0 -0 .1 6 3-4 0 .0 0 0 -0 .221 -0 .1 8 4 -0 .5 9 0 0 ,071 -0 .2 3 9 -0 .2 0 9

S ing le -phase , 16 8 .5 m m ,4 5 o4 0 .0 0 0 -0 .091 -0 .201 0 .691 -0 .2 1 3 -0 .1 8 8 -0 .1 4 62 0 .0 0 0 -0 .1 0 4 -0 .1 5 5 0 .3 7 2 -0 .0 9 9 -0 .2 8 6 -0 .1 4 7

0 .0 0 0 -0 .1 5 0 -0 .1 2 4 -0 .6 0 2 0 .0 5 0 -0 .2 1 8 -0 .1 1 9-2 0 .0 0 0 -0 .1 3 9 -0 .0 5 4 -1 .2 8 6 0 .1 6 4 -0 .1 8 8 -0 .1 9 4-4 0 .0 0 0 -0 .3 1 0 -0 .0 4 3 -1 .4 9 2 0 .5 1 6 0 .0 3 3 -0 .2 3 0

T w o -phase , 1 6 8 .5m m ,45o4 0 .0 0 0 -0 .091 -0 .201 0 .691 -0 .2 1 3 -0 .1 5 5 -0 .1 6 92 0 .0 0 0 -0 .121 -0 .1 6 3 0 .2 4 3 -0 .081 -0 .1 3 8 -0 .1 4 0

0 .0 0 0 -0 .131 -0 .1 9 3 0 .3 5 8 -0 .1 2 0 -0 .1 6 0 -0 .1 8 2-20 .0 00 -0 .1 7 0 -0 .1 4 5 -0 .5 5 0 0 .0 4 8 -0 .0 5 7 -0 .1 9 0•40 .000 -0 .2 2 3 -0 .1 4 3 -0 .9 4 6 0 .1 5 5 -0 .0 6 6 -0 .1 8 6

S ing le -phase , 1 9 8 .5m m ,45o4 0 .0 0 0 -0 .1 3 7 -0 .1 9 2 0 .2 9 6 -0 .1 0 6 0 .8 5 6 -0 .2 7 92 0 .0 0 0 -0 .1 2 5 -0 .1 8 3 0 .351 -0 .1 1 2 0 .9 4 5 -0 .161

0 .0 0 0 -0 .2 4 4 -0 .2 5 0 -0 .2 1 7 -0 .0 1 2 0 .9 0 2 -0 .2 2 0-20 .0 00 -0 .3 0 4 -0 .1 8 8 -0 .9 8 3 0 .2 2 4 0 .9 6 5 -0 .281■40.000 -0 .3 9 4 -0 .2 6 7 -0 .8 8 4 0 .2 4 5 0 .9 3 0 -0 .3 3 6

Tw o -phase , 19 8 .5 m m ,4 5 o4 0 .0 0 0 -0 .1 6 3 -0 .2 0 7 0 .1 5 6 -0 .0 8 5 0 .5 6 7 -0 .1 8 82 0 .0 0 0 -0 .2 3 4 -0 .2 5 8 -0 .0 8 2 -0 .0 4 6 0 .601 -0 .1 6 0

0 .0 0 0 -0 .2 4 6 -0 .2 1 0 -0 .5 4 8 0 .0 7 0 0 .6 2 9 -0 .2 0 4-2 0 .0 0 0 -0 .1 8 3 -0 .1 3 5 -0 .7 7 5 0 .0 9 3 0 .7 5 5 -0 .2 1 7-4 0 .0 0 0 -0 .2 7 5 -0 .2 0 9 -0 .7 3 3 0 .1 2 8 0 .7 0 0 0 .2 2 6

APPENDIX 3. 277

RMS values for the 200mm PBT downwards pumping

Z[mm] RMS +15 RMS-15 RMStang RMSrad RMS axS ing le -phase , bu lk, 4 5 o , R = 19 8 .5 m m

4 0 0 .4 7 9 0 .521 0 .4 5 3 0 .9 3 8 0 .5 3 420 0 .4 7 2 0 .4 7 6 0 .4 6 2 0 .6 1 7 0 .5 3 7

0 0 .4 6 3 0 .4 4 7 0 .4 6 6 0 .2 5 9 0 .5 1 5-20 0 .4 4 7 0 .4 7 3 0 .4 6 9 0 .3 1 3 0 .5 1 6-40 0 .4 6 9 0 .4 8 0 .481 0 .3 7 3 0 .5 7

S ing le -phase , bu lk, 4 5o , R = 168 .5m m4 0 0 .4 7 0 .4 3 7 0 .4 8 0 .3 6 7 0 .5 1 620 0 .4 6 8 0 .4 8 9 0 .4 6 5 0 .6 3 9 0 .4 8 7

0 0 .4 7 2 0 .4 4 3 0 .4 8 5 0 .3 8 5 0 .511-20 0 .4 3 3 0 .4 2 6 0 .4 4 0 .2 4 0 0 .4 5 6-40 0 .4 7 8 0 .4 4 7 0 .4 3 2 0 .7 7 3 0 .5 7 9

S ing le -phase , bu lk, 4 5 o , R = 148 .5m m4 0 0 .4 5 3 0 .4 7 0 .4 6 3 0 .441 0 .4 3 620 0 .4 5 7 0 .4 1 5 0 .4 5 6 0 .2 2 8 0 .4 6 6

0 0 .4 3 8 0 .4 3 4 0 .4 3 7 0 .4 2 2 0 .4 4 5-20 0 .41 0 .4 1 8 0 .4 0 8 0 .4 9 0 0 .3 8 9-40 0 .4 6 4 0 .4 1 5 0 .4 4 5 0 .3 6 7 0 .5 6 8

Tw o-phase , RPD = 0 .6 9 8 ,bu lk , 4 5 o , R = 198 .5m m4 0 0 .3 2 2 0 .3 5 2 0 .3 4 5 0.202 0 .4 0 420 0 .3 2 5 0 .3 2 3 0 .3 5 5 0 .4 3 4 0 .4 0 2

0 0 .3 6 0 .3 7 0 .341 0 .6 0 8 0 .4 0 9-20 0 .3 5 8 0 .3 5 4 0 .3 5 8 0 .3 2 7 0 .4 2-40 0 .3 7 4 0 .3 8 7 0 .3 4 9 0 .6 8 2 0 .4 0 9

Tw o -phase , RPD = 0 .6 9 8 ,bu lk, 4 5 o , R = 168 .5m m40 0 .3 7 9 0 .3 7 5 0 .3 5 9 0 .5 7 2 0.4120 0 .371 0 .3 4 3 0 .3 4 6 0 .4 8 8 0.41

0 0 .3 6 3 0 .3 4 8 0 .3 7 8 0 .3 2 0 0 .4 7-20 0 .3 3 9 0 .3 4 9 0 .3 5 7 0 .091 0 .4 0 2-40 0 .381 0 .3 4 9 0 .3 7 3 0 .2 3 4 0 .4 4 4

Tw o -phase , RPD = 0 .6 9 8 ,bu lk , 4 5 o , R = 148 .5m m4 0 0 .3 5 7 0 .341 0 .3 7 3 0 .3 4 4 0 .3 5 820 0 .3 7 9 0 .3 6 2 0 .361 0 .4 8 5 0 .3 7 2

0 0 .3 6 6 0 .3 4 8 0 .3 6 7 0 .1 6 7 0 .3 2 3-20 0 .3 6 7 0 .3 3 7 0 .3 6 2 0 .1 6 7 0 .3 7 2-40 0 .3 6 6 0 .3 5 6 0 .3 7 6 0 .1 5 3 0 .4 4 2

Documents

University of Surreyepubs.surrey.ac.uk/844581/1/10149064.pdf · ABSTRACT The flow field in two-phase boiling and gas-liquid Stirred Tank Reactors, STR, was examined in relation to