14th European Conference on Mixing Warszawa, 10-13 September 2012 INFLUENCE OF SOLIDS ON MACRO-INSTABILITIES IN A STIRRED

TANK

Matthias Eng, Anders Rasmuson

Chemical Engineering, Department of Chemical and Biological Engineering, Chalmers University of Technology, SE-412 96 Göteborg, Sweden

rasmuson@chalmers.se

Abstract. Measurements were conducted in a cylindrical tank stirred with a PBT in order to study the effect of varying amounts of suspended solids, up to 11.8 % by volume, on the frequency and amplitude of macro instabilities (MI). Solid glass particles of three different sizes were used in order to investigate the influence of the particle Stokes number. Measurements were made at 18 different locations in the vessel using Laser Doppler Anemometry (LDA) and were evaluated with the Lomb algorithm to obtain the frequency spectrum of the liquid flow. The results showed that the MI frequency is not influenced by the addition of solids. However, the MI amplitude was reduced by the addition of the solid phase although still detectable up to the highest concentration measured (11.8%vol.). In the studied system there seems to be a difference dependent on the particle Stokes number. Keywords: Macro-instabilities; Solid–liquid; LDA; Particle suspension, Stirred tank

1. INTRODUCTION Stirred tanks are widely used in the chemical process industry. Mean flows using

standard configurations are generally accepted to be well understood [1]. Instantaneous flow, on the other hand, is extremely complex; it varies due to predictable mechanics like axis rotation and blade passage of the impeller, and unpredictable high frequency phenomena, turbulence and low frequency quasi-stationary phenomena. These low frequency phenomena are usually referred to as macro instabilities (MI) and affect the flow pattern which in turn affects large scale mixing.

Early studies of vessels stirred with axial pumping impellers have identified MI phenomena as a consequence of double loop flow patterns [2,3]. A linear relationship between impeller speed and the frequency of the MI (fMI) has been found. Chapple and Kresta [4] have concluded that MI phenomena occur due to geometry, e.g. walls and baffles, and that these are linked to turbulence intensity. Kresta [5] has reported that two separate MI phenomena exist. One corresponds to blade passage frequencies (BPF) and the other corresponds to large scale structures of the flow. Galletti et al.[6] have found that the linear dependence between the frequency of the MI and the rotational speed of the stirrer exhibits different proportionality constants for low, intermediate and high Reynolds number flows. Roy et al. [7] have found, using PIV, that a significant amount of kinetic energy is observed to be associated with the low frequency dynamics of the trailing vortices during an MI cycle.

To the authors’ knowledge there are very few studies of the effects of solids on MI phenomena. Jahoda et al. [8] studied the effect of adding solids to a tank with a visual analyzing technique, and found a significant decrease in MI frequency at a solids loading above 10%w/w. Paglianti et al. [9] used a pressure transducer for detecting MI phenomena

95

and assefor one the instthese chbeen inva clearlsolid co

Theinfluencit is osuspenslayer wh

2. FLO

Figure 1

Theheight ewith a dB=T/15tank waThe conwith an is too stdifferenstudy. Tvessel cwindwaFigure was opeeven at

essed its appconcentrati

tabilities dehanges in mvestigated bly defined concentratione goal of tced by the pften menti

sion of solidhich forms

W CONFI

. Measureme

e flat bottomequal its diadiameter of 5=10mm. Thas made of nvex surfacoptical tech

teep, the tannt locations,The measurecentreline. Tard side of t1 shows theerated with high loadin

plicability aion. At a solecreased in macro flow by, e.g. [10,cloud heighns. this study ipresence of oned that

ds and imprnear the top

GURATIO

ent configura

med cylindameter T=H

f D=T/3 andhe impellerglass. The

ce of the cyhnique suchnk was plac, separated ements #00The measurethe baffle, we setup anda rotationa

ngs.

also to solidlids concentcomparisonstructures

,11,12]. Bitht coincided

is to investsolid particmacro ins

ove the mixp of a stirred

ON AND EX

ation of the m

drical tank hH. The suspd no hub. Tr rod, the b

bottom cleylindrical veh as LDV. Tced in a squ

into two v1 - #009 weements #01where the s

d the measual speed of 3

d-liquid systtration of 4n to the sinis the cloud

ttorf and Krd with the

tigate how cles Measurstabilities (xing due to d multi phas

XPERIME

mixing vesse

had a diamepension washe tank wa

blades and tearance of tessel is probTo prevent tuare glass tavertical rowere located 0 - #018 wstrongest in

urement loc30Hz=1080

tems. Their 0%w/w it w

ngle phase cd height ofresta [12] obdisappearan

MI phenorements of t(MI) couldtheir capabse tank.

ENTAL AP

el.

eter of T=1s axially ags equipped the baffles the impellerblematic wthe laser beank filled w

ws of 9 locain the vesseere located

nfluence of ations in th

0rpm to assu

paper presewas found thcase. Anothf solid suspbserved thance of MI p

omena in a this sort woud cause incbility to brea

PARATUS

150mm andgitated by a

with 4 baffwere mader was kept

when conduceams from h

with water. Mations, wereel bulk at hclose to theMI phenom

he mixing vure a good

ents only thhat the frequher attributepensions, what the appeaphenomena

mixing veuld be of increased offak up the cl

S

d was filleda 4 bladed 4fles with a w of steel, wconstant at

cting measuhaving an anMeasuremene conductedalf the radiue vessel wamena was evessel. The

particle sus

he results uency of e tied to hich has

arance of a at high

essel are nterest as f-bottom ear fluid

d up to a 45° PBT width of

while the t C=T/3. urements ngle that nts at 18 d in this us of the

all on the xpected. impeller spension

96

A c10μm sfollow tthat sollocation

3. DATThe

inherenthave analgorithrequire

Thefractiontypical vthe specfigure 2instabili

Figure 2

Thestrengthconditioconductinvestigbut the comparemethod needed suspensrate.

A sand themaximuamplitumaximudominananalysisconditio

commercialsilver coatethe liquid fllely the tracn a constant

TA INTERPe velocity dt in the flown unequal thm the Lomresampling e Lomb alg

n of each frvelocity mectrogram rep2 show the fity.

. Analysis of

e Lomb speh of a periodons it is noted at identgated instabmaximum ae the strenis needed

when invessions will ca

solution for e average bum amplituude of the um peak amnce of a pes techniqueons.

l LDV systeed hollow glow. An ovecers are detnumber of

PRETATIOdata collectew. LDV dattemporal d

mb techniqu of the dataorithm crearequency ineasurement present largflow veloci

f typical velo

ectrogram ldic phenom

ot suitable ttical physic

bility could amplitude dgth of instawhich is i

stigating susause less pe

this discrepackground

ude (green background

mplitude aneriodic phene to compa

em was useglass spherersize rejectected and 200,000 sam

ON AND Aed with the ta are not oistance bet

ue [13] is ab, and was th

ates a spectrn relation to

and the corge energy frity with dom

ocity data int

ets us identmenon is evato compare cal conditiobe identifie

did show a nabilities in independenspensions werfect condi

pancy is to noise of ealine) of a d noise (rend backgrounomena. Thare the stre

ed for all mres as tracetion was apall signals mples were

ANALYSISLDV were

obtained wiween measble to handherefore userogram in wo the flow rrespondingactions belominant low

to a frequenc

tify dominaaluated qual

the maximons, but wied at identinotable depdifferent s

nt on the mwith differenitions for th

use the ratach measurpeak decreed line). Inund noise ihe signal toength of in

measuremener particles,pplied to da

from solide acquired.

further analth a fixed tsured valuedle non equed throughowhich the amenergy. Fig

g Lomb speonging to a frequency

cy spectrogra

ant frequenclitatively be

mum peak aith differentical frequen

pendence onsuspensions

measuremennt concentrahe LDV con

io between rement. It weased due tn all furtheis used as o noise rationstabilities

nts. The flow, small enota acquisitio

d particles d

lyzed to obttemporal reses. In oppoually spacedout this workmplitude regure 2 showectrogram. Lcertain freqat 1.78Hz,

am.

cies in the etween diffeamplitude dt data-rates

ncies under n the data-ra with each

nt data-rate.ations of solnsequently

the maximwas recogno a low daer analysis a descriptioo was provdespite var

w was seedough to comon system tdischarged.

tain the freqsolution, an

osite to the d data and dk.

epresents thews a data pLarge ampliquency. Theidentified a

flow, but werent measudirectly. Tes of the LD

all test conate. To to beh other, an This is eslids, becauscause a low

mum peak amnized that wata-rate, so

the ratio on for the

ven to be a rying meas

ded with mpletely to assure

In each

quencies nd rather

Fourier does not

e energy plot of a itudes in e plots in as macro

when the urements sts were

DV. The nditions, e able to analysis

specially se denser wer data-

mplitude when the

did the between level of feasible

surement

97

4. RESULTS AND DISCUSSION

Figure 3. Lomb spectrograms for different locations with increasing concentration of 1mm particles.

As stated earlier, measurements were conducted at 18 positions in the vessel. The test

conducted at different impeller speeds showed a linear connection between MI frequency and impeller speed with a resulting non dimensional MI frequency (Strouhal) of St=0.06. At an impeller speed of 30Hz this leads to an MI frequency of 1.78Hz. The linear behaviour and St=0.06 is in good agreement with previous studies, such as Montes et al. [14] who identified St=0.0575 and Bruha et al. [15]. The MI could be recognized all over the mixing vessel, but the dominance varied between different vessel location, which is in accordance with the findings by Kilander et al. [16].

Figure 3 shows the Lomb spectrograms from the suspension with 1mm particles. One measurement position close to the baffle (#015) and one measurement position in the vessel bulk (#006) were chosen to be presented in the figure. The results are representable for all other measurements. It can be seen that the macro instability peak stays constant at the same frequency for all concentrations investigated; this differs from the results found by Jahoda et al.[8] and Paglianti et al. [9]. Jahoda et al. [8] identified a decrease in MI frequency, from St=0.08 to St=0.04, with an increase in solid concentration. Paglianti et al. [9], as well,

98

present experim

Butdominandecreasemeasura

Figure 4 The

MI strenstrengthparticle positionmacro ithe largwas definteractidetermi

D in m1

1.52

Table 1.

At observeconcentto keepappearsstrong ppenetratfluctuat

1

1

1

1

sign

al to

noi

se ra

tio

a decrease mental condit while the nce of the Mes with incrable concen

4. Amplitude

e suspensionngth, but ra

h. Figure 4 concentrati

ns. Betweeninstability ther particles fined by relion in the foned, while t

mm Rela

5

Particle rela

around 3%ved. The cloutration. Thep the particl cut off fromperiodic flutes the cloutes periodica

0

2

4

6

8

10

12

14

16

0% 1%

in MI frequitions differvalue of th

MI in relatioreasing soli

ntration.

of the MI w

n with 2mmather an inc

shows theion. Each p

n 3%vol andhan in the sis connecte

lating the pfocus of the the smaller

Stoke

axation time o0.150.350.62

axation time

vol the formud height que kinetic eneles lifted ism the mixin

uctuations. Oud and tranally in stren

% 2% 3%volu

uency in ther between thhe frequencon to the baid concentra

with increasin

m particle ocrease at mo signal to n

point in the d 6%vol thesingle phased to the lararticle relaxpresent stuparticles ha

l

pkes wi=ττ

of particle in56 51 24

and Stokes N

mation of a uickly decreergy of the s taken fromng flow. ThOnly the upsports parti

ngth as a par

% 4% 5%metric conc

eir study wihe studies, ty of the Mackground nation, it cou

ng particle co

n the other oderate connoise ratio chart is obt

e 2mm partie case. It isrger Stokes xation time

udy. For the ad values of

pp 18

ith =ρ

τ

n s Recip

Number.

clear cloudeased to 1/2flow is not

m the fluidhe cloud heipwards jet ficles to the rt of the ma

% 6% 7%centration of

ith a 40%w/he results m

MI stays connoise. Evenuld still be c

oncentration.

hand did noncentrations

of the mactained by avicle suspenss expected tnumber. Thto the time2mm partic

f 0.2 and 0.6

l

p D and

8

2

τμ

procal of MI0.56180.56180.5618

d height at 22 of the vest sufficient td flow, so tight is not sfrom the wiupper part

acro instabil

% 8% 9%solid particl

/w system. may not be cnstant one cn though theclearly iden

ot show a cfollowed b

cro instabilveraging ovsion was feathat the difhe Stokes nue scale of thcles a value6 respective

MIl f

1=τ

freq. in s

2/3 of the vssel height wto lift all pathat the flostationary, bindward sidof the vess

lity.

% 10% 11es

1 mm1,5 m2 mm

However, scontradictorcan identify e strength ontified at the

constant decby a decreaslity with inver all 18 matured by a fferent behaumber (Equhe MI, becae of Stokes=ely (Table 1

Stokes Nu0.2780.6251.111

vessel heighwhen increaarticles. The

ow above thbut charactede of the basel. The jet

% 12%

mmmm

since the ry.

a lower f the MI

e highest

crease of se of MI

ncreasing measured

stronger aviour of uation 1) ause this =1.1 was ).

(1)

umber 8 5 1

ht can be asing the e energy he cloud erized by affles [1] t as well

99

6. CONCLUSIONS The peak height received from the Lomb spectrogram was not meaningful enough to

make a quantitative interpretation of the MI amplitude under different solid loading conditions. The relative peak amplitude, defined as the ratio between absolute amplitude and the average strength of the background signal, was introduced in this study. This relative amplitude value appeared much less sensitive to changes in the data rate and made it possible to determine the significance of the macro instability frequency in relation to the general flow.

The results showed that the MI amplitude, but not the frequency, was influenced by the addition of solids. The general tendency observed was that with increasing solid concentration, a decrease in MI dominance could be observed. Nevertheless, macro instability could still be identified under the maximal measurable solid concentration of 11.8%vol. At nearly all locations the amplitude of the MI frequency remained significantly higher than the background noise.

Particles of three different diameters were used to investigate the possible impact of the particle Stokes number. Particles with a diameter of 1mm and 1.5mm showed a steady, albeit slow decrease in MI dominance. However, for the particles with a diameter of 2mm the results showed an increase in MI dominance at a solid loading between 3%vol and 6%vol.

7. REFERENCES [1] P. Hasal, J. Montes, H. Boisson, and I. Fort, 2000. “Macro-instabilities of velocity field in stirred vessel: detection and analysis,” Chemical Engineering Science, 55(2), pp. 391-401. [2] S. M. Kresta and P. E. Wood, 1993. “The Mean Flow Field Produced by a 45 Pitched Blade Turbine: Changes in the Circulation Pattern Due to Off Bottom Clearance” The Canadian Journal of Chemical Engineering, 71, 42-53. [3] O. I. Bruha, I. Fořt, and P. Smolka, 1994. “Flow transition in an axially agitated system,” in Proceedings of the VIII European Conference on Mixing (IChEME Symposium Series), p. 121. [4] D. Chapple and S. M. Kresta, 1994. “The effect of geometry on the stability of flow patterns in stirred tanks,” Chemical engineering science, 49(21), pp. 3651-3660. [5] S. Kresta, 1998. “Turbulence in stirred tanks: Anisotropic, Approximate, and Applied,” The Canadian Journal of Chemical Engineering, 76, 563-576. [6] C. Galletti, a. Paglianti, K. C. Lee, and M. Yianneskis, 2004. “Reynolds number and impeller diameter effects on instabilities in stirred vessels,” AIChE Journal, 50(9), pp. 2050-2063. [7] S. Roy, S. Acharya, and M. D. Cloeter, 2010. “Flow structure and the effect of macro-instabilities in a pitched-blade stirred tank,” Chemical Engineering Science, 65(10), pp. 3009-3024. [8] M. Jahoda, V. Machon, L. Vlach, and I. Fort, 2002. “Macro-instabilities of a suspension in an axially agitated mixing tank,” Acta Polytechnica, no. 42, pp. 3-7. [9] A. Paglianti, G. Montante, and F. Magelli, 2006. “Novel experiments and a mechanistic model for macroinstabilities in stirred tanks,” AIChE Journal, 52(2), pp. 426-437. [10] M. T. Hicks, K. J. Myers, and A. Bakker, 1997. “Cloud height in solids suspension agitation,” Chemical Engineering Communications, 160, pp. 137-155. [11] W. Bujalski et al., 1999. “Suspensions and liquid homogenisation in high solids concentration stirred chemical reactors,” Trans. IChemE, 77, pp. 241 - 247. [12] K. Bittorf and S. Kresta, 2003. “Prediction of Cloud Height for Solid Suspensions in Stirred Tanks,” Chemical Engineering Research and Design, 81(5), pp. 568-577. [13] N. R. Lomb, 1976. “Least-square frequency analysis of unequally spaced data”, Astrophysics and Space Science, 39, pp. 447-462. [14] J. Montes, H. Boisson, and I. Fort, 1997. “Velocity field macro-instabilities in an axially agitated mixing vessel,” Chemical Engineering Journal, 67(2), pp. 139-145. [15] O. I. Bruha, I. Fořt, and P. Smolka, 1993. “Large scale unsteady phenomena in a mixing vessel,” Acta Polytechnica, 33, pp. 27-34. [16] J. Kilander, F. J. E. Svensson, and A. Rasmuson, 2006. “Flow instabilities, energy levels, and structure in stirred tanks,” AIChE J., 52 (12), pp. 4039–4051.

100