Measurements on 5 1 Scale

7/31/2019 Measurements on 5 1 Scale

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Measurements on 5:1 Scale Abrasive Water Jet CuttingHead Models

P.S. Coray1, B. Jurisevic

2, M. Junkar

2and K.C. Heiniger

1

1Swiss Competence Centre of Water Jet Technology,Laboratory for Thermal and Fluid Engineering,

University of Applied Sciences Aargau, Northwestern Switzerland

2Laboratory for Alternative Technologies,

Faculty of Mechanical Engineering,University of Ljubljana, Slovenia

ABSTRACT

There is a vast potential market for high precision parts manufactured by abrasive water jet (AWJ)

machining, which calls for improvement of the current AWJ cutting methods. A reasonable approachis to use models which adjust machining parameters according to the workpiece properties, howeverdetailed knowledge of the physical behaviour of the cutting tool is required. The measurementspresented in this paper intend to extend the current knowledge of abrasive water jets, by determiningthe kinetic energy distribution of the abrasive particles and the structure of the jet in dependence of thecutting head parameters. Initially 5:1 scale models will be examined by using laser and phase doppleranemometry, force measurements and photographic methods. At a later stage comparativemeasurements and cutting experiments using real scale cutting heads will be performed. The work isstill in progress and mainly intermediate results and measurement methods are discussed in this paper.

Keywords: Multiphase-flow measurement, abrasive water jet, kinetic energy distribution.

NOMENCLATURE

AWJ Abrasive water jet

CD Discharge coefficient, -

Cdrag Drag coefficient, -

d Diameter, mm

E Energy, J

g Gravity, g = 9.81 m/s2

h Specific enthalpy, J / kg

L*

foc Dimensionless focussing tube length, L*

= Lfoc / dfoc

LDA Laser Doppler Anemometry

LIF Laser Induced Fluorescence

m Mass, kg

m Mass flow, kg/s

m*

abr Dimensionless abrasive mass flow, m*abr = mabr/mwater

PIV Particle Image Velocimerty

PTV Particle Tracking Velocimerty

Q, Q Heat flux, J / s

s Specific entropy, J / (kgK)

SF Scale factor (e.g. 5 for a 5:1 model)

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v Velocity, m/s

V, V Volume flow, m3/s

W W "Work flux", J / s

z Altitude, m

Density, kg/m3

Dynamic viscosity, kg/(ms) = Pas

Surface tension, kg/s2

= Pam

Subscripts:

abr Abrasive

air Air

air-water Relative to air-water (e.g. relative velocity)

air-abr Relative to air-abrasive

AP Abrasive particle

CV Control volumefoc Focusing tube

o Sapphire nozzle orifice

s Isentropic (e.g. in w.jet.s)

w.jet Water jet

water Water

Superscripts:

* Symbol for non-dimensional ratios.

' Symbol for a property of a scaled model.

Simplified time derivative symbol (e.g. m m )

1 INTRODUCTION

Most of today's commercially used abrasive water jet (AWJ) cutting machines operate in a rangewhere the achievable geometrical tolerances typically are greater than 0.1mm, with some companieslike Flow and OMAX already offering machining centres claiming to achieve tolerances up to0.05mm, an achievable accuracy also mentioned by Hashish in [7]. Improving the AWJ cuttingprocess in a way that parts can be manufactured more accurately and in smaller dimensions wouldenable AWJ manufacturing to be used in an even broader field of applications and to become morecompetitive compared to other manufacturing methods like laser cutting and electro-dischargemachining.

To achieve exacter parts, a machine with precise accuracy of motion, a precisely manufactured tool(cutting head) and optimally set machining parameters like water pressure, abrasive mass flow, motionof the tool relative to the workpiece, etc. is needed. Determining optimal cutting parameters is bestachieved by the use of models, which ideally make use of physical relationships between tool andworkpiece properties to establish a solution for a favourable cut. However in order to create suchmodels detailed knowledge and understanding of the different processes is required.

In this context it is the aim of this work, whose beginnings are presented in this paper, to contribute tothe understanding of the output characteristics of the tool in dependence of the tool geometry andinput parameters by Laser Doppler, reaction force, high speed imaging and if possible othermeasurement methods. It is planned to document the results in a non-dimensional way, allowing greatflexibility in modelling as the results would be transferable to different cutting head configurations. Tosimplify the initial measurements and to allow a greater spacial resolution, it was decided to conductthe first set of measurements on cutting head models scale 5:1 and at a later stage make comparativemeasurements on real scale nozzles. The ultimate goal would be the ability to measure the kineticenergy distribution of all three phases (air, water, abrasive) at the exit of the cutting tool, yet it has tobe noted that by using currently available methods a complete understanding is an infeasible aim.

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2 OVERVIEW OF MEASUREMENT METHODS AND PREVIOUSLY CONDUCTED

WORK

Himmelreich [1, 2] successfully used Laser-2-Focus (L-2-F) velocimetry to measure the velocitydistribution in the cross section of both 5:1 and 1:1 abrasive water jets for different cutting headgeometries and input conditions. Similarity laws and important non-dimensional numbers (Re, We, ...)were introduced and the similarity between the 5:1 model and real cutting heads discussed.Possibilities to distinguish between velocity signals from abrasive particles and from the water phase

were examined. Different intensities were not distinguishable from the photodetectors, so differencesin time of flight were used as a basis for distinguishing velocities of the different phases, a methodwhich however didn't allow to explicitly identify an individual signal as originating from an abrasiveparticle. Lightsheet photography was also carried out, however with limited results due to lack ofintensity and long shutter times.

Other researchers using pointwise measurement methods included Chen and Geskin [3] who used aLaser Transit Anemometer (similar to L-2-F) and Neusen et al. [4] who used a Laser DopplerVelocimeter (LDV, also called Laser Doppler Anemometer LDA). Both Chen and Neusen were onlyable to measure an average velocity in the centre of the jet.

Due to the many optical disturbances occurring in the abrasive water jet structure after the mixingprocess of water with abrasive and air, photographic methods appear to be limited to analysing thesurface and outline of the abrasive water jet without being able to depict the structures in the inside of

the jet. Nevertheless Sawamura et al. [5] used particle image velocimetry (PIV) to measure thevelocity of the water phase and particle tracking velocity (PTV) to measure the abrasive velocity.Their results however appear to be limited by high uncertainties. Claude et al. [6] used high speedphotography to measure the propagation velocity of the jet when it's turned on and to analyse thecontours of a developed jet. Chen and Geskin [3] made Schlieren images of the shock waves occurringwhen the surrounding air is accelerated to supersonic velocities. While photographing the jet structureafter the mixing process is strongly limited, imaging the mixing and acceleration process of abrasive,water and air inside the mixing chamber allows interesting insight into the interaction of the threephases. Hashish [7] observed the motion of the abrasive inside the mixing chamber and plugging ofthe abrasive flow when large particles are entrained. Osman et al. [8] made similar measurementsinside transparent abrasive cutting heads.

Methods based on electrical properties were used by Baar and Riess [9], who used a conductive-

correlative method, and by Hashish [7], Swanson et al. [10], Miller and Archibald [11], Dorle, Tylerand Summers [12] who all used coils and an abrasive substitution that would induce a signal whenpassing through the coils, thus allowing velocity determination by dividing the coil spacing by thetime a particle had to get from one coil to another. Of particular interest is the observation of Summers[12] who explained the temporal characteristics of a signal with the rotation of the particles. Asparticles appeared to rotate between 1'000 to 5'000'000 rpm this would imply a substantial amount ofkinetic energy being stored in the rotation of the abrasive particles. Unfortunately no further researchinto the rotation of particles is known to the authors of this paper, and it is not clear whether theoscillation can definitely be attributed to the particle's rotation and not to some other oscillationexcited in the electric circuit.

Other possibilities to determine the cutting tool characteristics include force measurements of whichexamples can be found in Claude et al. [6] who measured the jet reaction force and Momber A. [13]who measured the impact force on the workpiece. Impact count methods like the ones used by Isobe etal. [14] and Liu et al. [15] allow further insight into the cutting tool properties. The throw distance ofthe abrasive can also be used as an indirect measure for the kinetic energy of the abrasive as shown bySummers et al. [16]. Finally the use of X-Rays as a method to overcome the limits of an opticallydense spray for visible light was used by Neusen et al. [17] to determine the distribution of abrasiveacross the AWJ.

3 THE 5:1 MODEL

Fig. 1 gives a schematic overview of the 5:1 test stand and the measured input variables, which aretemperature, pressure and mass flow of water and air; the sand mass flow, air pressure in the mixingchamber inlet and the jet reaction force. The test stand consists of an abrasive feeder unit with a screwconveyor, a collimation tube, a variable cutting head consisting of a mixing chamber and focusing

tube and a Danfoss plunger pump capable of reaching pressures up to 15 MPa. For reaction forcemeasurements the usually firmly fixed cutting head and collimation tube hang loosely on a rope onlyguided by two PTFE bearings.

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Collimationtube

FF

p

T

m

E+H Pump

M

Sand

E+H

Mixing-

chamber

Focusingtube

p T

m

p

f

Abrasive Feeder

Nozzle

Water

Legend:

m ma s s flo w

T te mpe ra turep pressure

f freque ncy (m)

F force

Rope

Air

Fig. 1 Test stand scheme

A detailed sketch of one of the cutting heads used is shown in Fig. 2. Most geometrical dimensions arevariable, with only the specially manufactured sapphire nozzle kept at a constant nozzle diameter do of0.75mm. The focusing tubes have diameters dfoc=1.5, 2.3, 3 and 4.3mm with a maximum length of350mm (200 for dfoc=1.5). The focusing tube can be tilted to correct slight misalignment errors ofnozzle and focusing tube.

Fig. 2 Cutting head

The model is usually run at a pressure of (14.30.2) MPa, which yields a water mass flow of

(2.430.03) kg/min and an isentropic jet velocity (Chapter 4.3) of (1691) m/s.4 SIMILARITY AND CUTTING HEAD SYSTEM DEFINITION

4.1 Introduction

A very thorough overview about the important dimensionless numbers describing an abrasive water jetand a comparison of actually measured geometrically similar 1:1 (called prototype) and 5:1 (calledmodel) cutting heads is given in Himmelreichs PhD work [1]. Nevertheless an overview of the mostimportant parameters is given at this place.

The basic idea behind the laws of similarity is that similar models will have similar dimensionlessgeometric parameters, so the relationship between dependent and independent parameters would onlyhave to be determined once and then could be applied regardless of scale as a perfectly similar systemwould have similar dimensionless parameters. In real world applications however, it usually is notpossible to fulfil the criteria of complete similarity so some sort of compromise has to be achieved.

4.2 System definition and overview of the relevant dimensionless parameters

Fig. 3 shows a simplified overview of the system for which dimensionless numbers will be introduced.

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Equation (3), the Reynolds-number of the abrasive particles, is directly correlated with the drag actingon the abrasive.

4.2.2 Weber-similarity

The Weber-number (equation (4)) denotes the ratio of the inertia forces to the surface tension and is ofparticular importance for the breakup of the water jet and the formation of water droplets. More waterdroplets tend to increase the mass flow of air and the exchange of momentum with the abrasive, butalso tend to dissipate their kinetic energy much more than a compact water jet due to the increased

surface friction and the energy used for surface formation. Hence a jet which atomizes too early won'thave enough energy left for cutting.

Wew.jet

dw.jet

vw.jet

2

water

water

(4)

The condition for a similar Weber-number would be as follows:

Wew.jet

We 'w.jet

dw.jet

vw.jet

2

water

water

d 'w.jet

v 'w.jet

2'

water

'water

dw.jet

SFv

w.jet

SF

2

'water

'water

The condition

d 'w.jet

dw.jet

SF

would imply

v 'w.jet

vw.jet

SF , which is not possible for Reynolds-similar conditions except if the fluid properties and could be changed.

An enlarged model operated at Reynolds-similar conditions will thus have a lower Weber-numberthan the original. Hence one can expect the droplets to be larger than implied by the scale factor asthere is less kinetic energy left for atomization. This in turn alters the exchange of momentum. Wemake the simplifying assumption that the deviation of flow conditions between the enlarged modeland the original is neglectable if both model and original are operated in the same atomization regime,with the same disintegration mode, as shown in Fig. 4 with an x for the original and o for 5:1 model.

More information about the data in Fig. 4 can be found in [18]. It has to be noted that Fig. 4 strictlyisn't valid for the type of supercavitated nozzles used. Eventually validation and comparisonmeasurements on original 1:1 cutting heads will be unavoidable.

10 100 1 .103

1 .104

1 .105

1 .106

1 .103

0.01

0.1

1

10

Border between I (Raleigh) and II (Air influence)

Border between II and III

Border to complete atomization

Real 1:1 nozzle

5:1 Nozzle

Reynolds-number of the Liquid

Ohnesorge-nu

mber

RaleighMechanism

SecondaryAtomization

I

IIIII

Fig. 4 Modes of disintegration.

4.2.3 Froude-similarity

The ability of the airflow to "drag along" abrasive particles to the inlet of the mixing chamber againstthe force of gravity can be described by the Froude-number, which is the ratio of inertia to gravityforces. For similar abrasive transportation capability the drag coefficient would have to remain similaras in the following equation:

Cdrag

APd

AP

3

6g

air

1

2vair-water

2dAP

2

4

which in a simplified form results in the Froude number:

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Frv

air-water

2

g dAP

(5) - Froude number

Again Reynolds- and Froude-similarity cannot be achieved at the same time. For this reason, the 5:1model used is built in a way that the transport of abrasive to the mixing chamber makes increased useof the gravitational potential energy to compensate for the reduced capability of the air to drag alongthe abrasive against the force of gravity.

4.2.4 Other dimensionless numbers

Of further importance are the mass flow ratios mabr*

mabr

mwater

and mair*

mair

mwater

as they influence the

exchange of momentum between water and abrasive. The characteristic density number *

used byHimmelreich [1] is useful as a measure for similar momentum exchange in situations where the

abrasive densities between model and prototype are different. *

is the ratio of the abrasive density tothe average fluid density in the focusing tube and is calculated as follows:

* AP

air-water

with air-waterwater

Vwater air

Vair

Vair

Vwater

Further dimensionless numbers like the Mach- and Galilei-number are currently considered less

important (though not necessarily absolutely neglectable) and are not further discussed in this paper.4.2.5 Varied parameters

Among the most important parameters to be varied are:

the dimensionless length of the focussing tube Lfoc*

Lfoc

dfoc

the diameter ratios dfoc*

dfoc

dw.jet

and dAP*

dAP

dw.jet

,which to reduce the number of measurements can

be combined to d*

dAP

0.5 dfoc

dw.jet

with denominator of d*

being a measure for the gap between

the focussing tube wall and the water jet.

the mass flow ratio mabr*

mabr

mw.jet

and geometric parameters of the mixing chamber which in turn affect the dimensionless mass flow

of air mair*

mair

mw.jet

4.3 Isentropic velocity

The conditions to be able to use the Bernoulli-Equation (equation 6) to calculate the velocity of thewater jet are: Steady state conditions, incompressible flow, no friction, neglectable gravity forces andflow along streamlines, no heat transfer.

vw.jet.Bernoulli

2 p

water

(6) - Bernoulli equation

For high pressure water-jets the condition of incompressibility is not fulfilled as at 400MPa the waterdensity increases by 13% compared to water at ambient pressure.

A thermodynamical approach to solve for the ideal expansion velocity of the water is to use the energybalance (equation 7) set over a control volume as in Fig. 5.

Control Volume

p1, T

1, v

1

p2

Fig. 5 Control volume over a simplified nozzle

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dECV

dtW

CVQ

CVm h

1

1

2v

1

2g z

1h

2

1

2v

2

2g z

2 (7) - Energy balance

Assuming steady state conditions, adiabatic walls, constant entropy, isentropic expansion, neglectingthe potential and kinetic energy at the inlet simplifies equation (7) to equation (8), the isentropicvelocity.

v2.s

p1

,T1

, p2

2 h1

p1

,T1

h2

p2

,T2.s (8) - Isentropic velocity

The enthalpies can be determined from a database of thermodynamic properties of water. Theisentropic temperature T2.s can be determined from the condition of constant entropy s1=s2. Detailsabout the equations applied above can be found in thermodynamics literature like [19].

Comparing the calculated isentropic velocities for an initial temperature of T1=25C with an equationfor the waterjet velocity given by Hashish in [7] yields excellent agreement (Fig. 6).

0 100 200 300 4000

200

400

600

800

1000

Jet velocity according to M. Hashish

Isentropic velocity

Bernoulli velocity

Pressure MPa

Velocitym/s

Fig. 6 Jet velocity comparison

5 LDA / PDA MEASUREMENTS

5.1 Setup and principle

A detailed overview of the principle underlying LDA / PDA (also called LDV / PDPA) measurementsis given in [20]. Basically the method utilises two coherent laser beams which cross in the focal pointof a lens and there define a control volume of which the frequency of light from the two laser beamsreflected from a particle passing through the control volume is directly correlated with the velocity ofthe particle. For "perfectly" spherical particles (i.e. small water droplets) the phase shift of thereflected light measured from two different angles contains information about the size of the particles.

The currently used system utilises a 2D Dantec Dynamics Fibre PDA and BSA P80 system with60mm transmitter and receiver probes and a Coherent Argon-Ion laser. The receiver probe is alignedin a scattering angle of 70 to the transmitter probe and the size of the control volume is (0.25 x 0.092x 0.092) mm. Two velocities, one along the axis of the jet and one perpendicular to both the jet axis

and the optical axis of the transmitter are measured simultaneously.5.2 Limitations / Difficulties

In order to get good, clearly defined signals, the particles reflecting the light would have to be smallerthan the size of the control volume. While most water droplets are small enough to fulfil this criteria,the 5:1 quartz sand particles used in a size range of 0.5-1mm are certainly not. Test velocitymeasurements on sand particles poured through a funnel have shown that the LDA is actually able tomeasure the sand velocity although the resulting signal was rather noisy. It also has to be kept in mind,that the measured velocity for large particles will correspond to their surface velocity, which isinfluenced by the rotation of the particles.

A central limitation and difficulty is the ability to identify an incoming signal as originating from anabrasive particle or from the water phase. Chen [3] argued that the intensity of the signal could be used

as a criteria to distinguish a signal as originating from an abrasive particle, Himmelreich [1] howevermentioned that the sensitivity of the photo detectors he used was insufficient for such a distinction.With the current LDA system used for the 5:1 measurements presented in this paper only an averageintensity (photo multiplier anode current) over time can be measured, thus intensity again cannot beused to identify signals from an abrasive particle. An alternative possibility is to compare the

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velocities of the validated water droplets with the velocities of all signals (validated and non validated)as shown in Fig. 7. (N.B. a non validated signal doesn't imply that it's not from the water phase as evenwhen the abrasive is turned off the droplet validation rate is seldom higher than 30-60%).

40 60 80 100 120 140

400

800

1200

1600

All counts

Diameter Validated Counts (scaled up)

Velocity m/s

"C

ounts"

Fig. 7 Velocity histogram 5:1 AWJ m*abr=0.33

For the test conditions no apparent difference in velocity distribution was recognisable. This could beexplained with the long focusing tube used (L

*foc=82), which could be the reason for a strong mixing

of the different phases. Himmelreich [1] measured the time of flight distribution for different focussingtube lengths and observed two distinct maximas in time of flight for shorter focussing tubes, whichgradually merged into one distribution for longer focussing tubes as shown above. Another criteria forthe origin of a velocity signal could be its transit time (TT), which is a measure for the duration of thesignal and for the time a particle had to cross the control volume. At a given velocity only a very largeparticle (compared to the control volume size) would have a longer transit time than a smaller particle.However, making use of this as a criteria for identification of the abrasive particles failed, as hightransit times were typically observed at high velocities as shown in Fig. 8 for measurements with andwithout abrasive and even for the velocities of the validated diameters.

0 20 40 60 80 100 120 140 160

0.15

0.3

All TT

1%< < 5% of all TT counts (i.e. lower TT)

99%> >95% of all TT counts (i.e. higher TT)

Velocity m/s

NormalisedCounts

Fig. 8 Velocity distributions for different transit times

In all cases where the signal origin cannot be clearly distinguished and other indicators like the onesdescribed above have to be used, a major uncertainty is the bias caused by an unequal numberdistribution of signals originating from the abrasive and water particles. The volume of a 0.5mm sand

particle would be equal to that of more than 15'000 20m water droplets, which without consideringall other effects would imply a higher data rate of velocity signals from water than from sand.Quantifying the probability and frequency (rate) of detection for the water and abrasive phase isgenerally a very difficult task, as there is a plethora of effects which would have to be considered (likefor example that a sand particle can only be detected as long as it doesn't completely cover or shadeout the control volume or that the measurement volume appears larger for a large sand particle than fora small water droplet etc.).

5.3 LDA velocity measurement results

Fig. 9 shows the measured velocity distribution at the exit of the focussing tube with and withoutabrasive. It can be seen that the distribution resembles the velocity distribution of a pipe flow, anobservation also made by Himmelreich [1] for longer focussing tubes. The error bars show thestandard deviation of the velocity histograms at the respective points. The third dotted curve is the

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result of scaling down the water velocity distribution by a factor obtained by the law of exchange ofmomentum (equation 9), with the difference between the dotted curve and the velocity with abrasivebeing a measure for the amount of dissipation. It has to be kept in mind however, that a bias due todifferent measurement data rates would result in a deviation from the measured velocity distribution tothe actual velocity distribution of the abrasive particles.

vdotted

vwater.1

mwater.1

mair.1

mabr.2

mwater.2

mair.2

(9) reduced velocity via the law of momentum exchange

2 1.5 1 0.5 0 0.5 1 1.50

0.25

0.5

0.75

1

With abrasiveStandard deviation limits

Just water (without abrasive)Standard deviation limits

Estimated velocity by law of momentum exchange

Dimensionless Radius in y r/rfoc

D

imensionlessAxialVelocityv/vs

orificeboundary d

0

focussing tubeboundary d

foc

Fig. 9 Axial velocity distribution at the exit of the focussing tube

The average radial velocity distribution in the cross section of the focussing tube is in the range of the

possible misalignment error (i.e. close to zero). More interesting are the fluctuations, which in thecentre region of the focussing tube are in the range of 4% of the axial velocities and in the borderregion reach up to 10% of the axial velocity (Fig. 11). Another effect is a strong reduction in the LDAdata rate (number of measured valid velocity signals per time) by more than an order of magnitude.This is caused by the increased disturbances when adding abrasive to the waterjet, an effect that canalso be seen in the noisy signal and the low data validation rate.

Fig. 10 LDA measured data rate

2 1.5 1 0.5 0 0.5 1 1.50

5

10

15

20

With abrasive

Just water (without abrasive)


Ratioofradia

ltoaxialvelocity%

2 1.5 1 0.5 0 0.5 1 1.50

5000

1 .104

1.5 .104

2 .104

2.5 .104

With abrasive

Just water (without abrasive)


DatarateCh1#/s

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Fig. 11 Ratio of the radial to the axial velocity in the focussing tube

6 IMAGING

6.1 Setup and principle

In order to get an idea of the structure of the 5:1 jet and the applicability of imaging methods, the jet

was photographed with an SCO 4QuikE intensified fast shutter (ICCD) camera used with shutter timesbetween 0.1s and 0.5s. Two different light sources in form of a halogen lamp, used for back lightilluminated pictures, and a laser light sheet, fed by a continuous Argon-Ion Laser in multi line mode,(Fig. 12) were used.

4 Quik E

Laser Light Sheet

HalogenLamp

Fig. 12 ICCD Camera Setup

6.2 Results and Discussion

Fig. 13 shows the picture of the waterjet without abrasive as it exits the focussing tube. It is apparent,that the disintegration of the jet is at an advanced stage, a fact that is contributed to by the rather longfocusing tube (length 350mm, nozzle distance ~400mm). For this reason photographs of the jetwithout the mixing chamber and focusing tube installed were taken (Fig. 17-19), and it wasdetermined that in free air the achievable nozzle distance for a more or less coherent jet wasapproximately 300mm. Adding abrasives to the flow (m

*abr = 0.33) as in Fig. 14 resulted in a much

denser jet with many small droplets and a foggy curtain making it impossible to locate the abrasiveparticles. These pictures show, that the AWJ really is a three phase flow with a high degree of mixingbetween the three phases.

Illuminating the jet with a laser light sheet as in Fig. 15 & 16 showed discrete intense spots on thepicture, which probably could be used to determine velocities with the particle tracking method. Withthe abrasive turned on, there was a strong source of reflection directly at the side of the waterjet wherethe laser light sheet entered the jet. Again the jet / spray was to dense to spot any abrasives.

Images showing the jet. The markers indicate the focussing tube walls and jet orifice diameter do.

Fig. 13 No abrasive, halogen backlight Fig. 14 W. abrasive, halogen backlight

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Fig. 15 No abr. - light sheet (negative image) Fig. 16 W. abr. - light sheet (negative image)

Fig. 17 50mm nozzle distance Fig. 18 250mm nozzle distance Fig. 19 400mm nozzle distance

7 REACTION FORCE MEASUREMENT

The advantage of reaction force measurements is, that the direction of the flow in and out of thecontrol volume over which the condition of static equilibrium has to be fulfilled is much more knownand well definable than for impact force measurements.

F

mwater.in

, vwater.in

mabr

, vabr.in

mout

, vout

ControlVolume

Fig. 20 Reaction force

ControlVolume

Freaction

min, v

inmout

, vout

mout

, vout

Fig. 21 Impact force

Applying Newton's second axiom to a control volume yields:

Fd

dtv dV

d v

dtdV v v dA

or with the assumptions and simplifications of steady state flow conditions, averaged velocities,frictionless bearings, excluded gravity forces and with from a point of view where the control volumeis a non-accelerated inertial system, yields equation 10, which can be found in fluid mechanicsliterature like [21].

FCV

vCV.out

mCV.out

vCV.in

mCV.in (10) - balance of momentum

Applying equation (10) to the system in Fig. 21 to determine the jet reaction force causes greatdifficulties, as the flow out of the control volume is not well defined and changes with the cutgeometry, so there are too many unknowns for the equation to be solved. Equation (10) applied to the

system in Fig. 20 in axial direction however allows direct determination of a momentum averaged jetvelocity:

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vw.jet.momentum

Faxial

mwater

mabr

mair

(11) - momentum averaged velocity

At the time of writing this paper the force measurement system of the 5:1 model still had somedifficulties, mainly due to a drift which was probably due to a connection pipe. Nevertheless, theeffect of turning the abrasive on and off can be seen in Fig. 22&23, where the reaction force decreaseswhen the abrasive is turned on (indicated with an arrow). The force shown is the force gravitysuperimposed to the reaction force, which acts in the other direction.

6 6.5 7 7.5 8 8.170.8

171

171.2

171.4

171.6

5

Force

time / min

Force/N

Fig. 22 Force w/wo abr, m*abr=0.33

8.3 9.2 10.1 11170.1

170.4

170.7

171

Force

time / min

Force/N

Fig. 23Force w/wo abr, m*abr=0.16

8 OTHER METHODSNon of the applied methods allowed the unambiguous measurement of the abrasive particle velocities,and of all the known methods only the ones measuring current induced by particles moving thoughcoils appear to work reliably. An optical method to measure the velocity of the abrasive particleswould be to use fluorescent particles with a sort of LIF (laser induced fluorescence) method. Afterexcitation by a high power laser light the particles emit light at a higher wavelength which can beseperated from the laser light by means of an optical filter, allowing the application of a particletracking algorithm. Using fluorescent particles was already suggested by Himmelreich in [1] but hecouldn't pursuit utilising the method as for the high price of such particles. The authors intend tocommence work on utilising either UV excitable sand, which occurs naturally, or fluorescent colouredsand particles for AWJ measurements in the near future.

A method which could lead to very interesting results is the use of flash x-ray photography, which asfar as the authors know wasn't applied for abrasive waterjets yet, but could give some very interestingresults. An overview of the technique can be found under [22].

9 CONCLUSIONS

From this paper, which has given an overview of different measurement methods applied to a 5:1 scalemodel of an abrasive waterjet, the following conclusions can be drawn:

Similarity between 5:1 and 1:1 scale AWJ models is never complete. For Reynolds-similar flow theWeber- and Froude-similarity, which both are critical for the AWJ process, cannot be fulfilled.

The isentropic jet velocity, which can be determined by solving the energy balance over the nozzle,shows excellent agreement with an equation presented by Hashish [7].

Using the LDA / PDA measurement methods, allows measurement of the 5:1 AWJ velocity at high

spacial resolution, however the difference between signals from the abrasive- and water particlescannot yet be distinguished.

High speed imaging methods allow the characterisation of the AWJ to some degree, however theAWJ is too dense to make out any abrasive in the image. It can be seen, that the AWJ flow of thetest conditions is a three phase flow with a strong degree of mixing between the three phases.

Reaction force measurements allow the estimation of an average AWJ velocity for comparison withother measurements. It was also shown, that doing the same with impact force measurements isvery difficult and dependant of the cut geometry.

Promising methods that could be applied in the future are the LIF / PTV method utilisingfluorescent abrasive particles and perhaps flash x-ray photography.

ACKNOWLEDGEMENTSThe authors would like to thank the CTI Swiss Innovation Promotion Agency, WaterJet Holding AGAarwangen, Switzerland and MVT AG Nidau, Switzerland for support and funding.

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Measurements on 5 1 Scale