Flow Visualization in Stirred Vessels: A Review of Experimental ...

REVIEW PAPER

FLOW VISUALIZATION IN STIRRED VESSELS

A Review of Experimental Techniques

P MAVROS

Department of Chemistry Aristotle University Thessaloniki Greece

Stirred vessels are being used not only in chemical processes for simple contacting orblending operations but also in novel conreggurations and processes as in mineralprocessing andor wastewater treatment with speciregc requirements like low shear or

regions in the vessel with high and low turbulence levels The techniques that are available forthe study of the macrow patterns induced by the various types of agitators eg classical pressureor velocity measurements with Pitot tubes or hot-wire anemometers and novel ones like laserDoppler velocimetry laser-induced macruorescence and particle image velocimetry are reviewedand their usefulness for particular situations is discussed

Keywords mixing agitation stirred vessel macrow visualization review laser LDV LDA PIVthermography trajectography macrow-follower

INTRODUCTION

Stirred vessels are widely used for various purposes oftencomprizing several phases

middot to combine miscible liquids or to disperse one immiscibleliquid into another

middot to disperse solid particles in a liquid often followed byanother process eg leaching macrotation chemicalreaction

middot to disperse a gas into a liquid usually followed either byabsorption andor by a chemical reaction between theliquid and the gaseous species or

middot to disperse a solid (eg a catalyst) and a gas into a liquidmedium to cause a reaction

For each particular application a different conreggurationis appropriate the design of stirred vessels has been theobject of numerous studies throughou t several decades andthe principal design rules are incorporated in standards ofvarious countries (ASME Code Section VIII DIN 28136among others)

However agitation is involved in other processes too

middot new applications like fermentation or crystallization ormiddot other processes which till now were not included in the

`classicalrsquo chemical process area like wastewater treat-ment mineral processing etc

In these processes the end product depends not only onthe physicochemical aspects of the particular process egits reaction kinetics but also on the pattern of speciescontacting on the level of energy dissipation the vessel

conregguration etc3254151155195205209 Attempting to inves-tigate andor optimize these processes necessitates there-assessment of the existing knowledge and even thedevelopment of novel conreggurations or equipment20219

The suitability of a particular agitator for a given mixingprocess depends on its capability to induce the macruid contentsof the vessel into vigorous circulation avoiding situationswhere regions of the macruid(s) are poorly mixed or not mixedat all while at the same time avoiding damaging the variousspecies dispersed in it which are sometimes shear-sensitiveeg cell cultures or crystals249106 208 It is thereforenecessary to determine for each type of impeller

1) the macrow pattern induced in an vessel as a function ofa) the internal vessel conregguration (bafmacres coils vessel

bottom form etc)b) the macruid properties (viscosity number of phases

densities etc)c) the location and mode of operation of the agitator

(clearance macrow-pumping direction)2) and the suitability of the impeller for a particular

application (eg low-shear or high-shear requirement)

Flow patterns induced by an agitator were a regrstindication of its suitability for a particular applicationInitially merely watching the macruid or possibly using somecoloured material to identify the major circulation patternswas sufregcient later simple measuring techniques like thePitot tube were used to quantify the velocity maps Thesetechniques allowed the identiregcation of the basic type ofcirculation established in a stirred vessel for example itwas found that a 6-blade `standardrsquo Rushton turbine (RT)would create two toroidally-shape d macrow loops in the vesselone in the lower and one in the upper part of the vesselwhile an axial impellerETHeg a marine propeller a pitched-blade turbine (PBT) among othersETHwould create essen-tially a single loop around the impeller

These patterns were widely accepted and incorporated inwidely-read references171240 the use of more sophisticated

113

0263plusmn876201$1000+000q Institution of Chemical Engineers

Trans IChemE Vol 79 Part A March 2001

techniques however allowed the detailed study of the macrowsin the various parts of the vessel and the results indicatedthat it may be necessary to re-deregne the macrow patternsinduced by the various impellers For example a detailedmacrow mapping using laser Doppler velocimetry showed thataxial impellers leave a substantial part of the macruid in theupper part of the vessel poorly agitated often with velocitieslower than 10 of the agitator tip speed154 and that with aRushton turbine the upper circulation loop is narrower thanexpected with the macruid in the region near the upper vesselwall agitated in a secondary macrow loop (Figure 1)

In the following sections the sophisticated macrow mappingmeasuring techniques that are nowadays available will bediscussed in conjunction with the oldersimpler ones Thesewill be separated in two categories

middot single-poin t measuring techniques which determine thevelocity (or one of the velocity vector components) at aset point within the vessel and

middot ensemble-measuring techniques which determine themacrow pattern simultaneously in a wider region of the bulkof the agitated macruid

SINGLE-POINT TECHNIQUES

Pitot Tubes

Velocimetry should not be considered as a noveltechnique in 1724 Henri de Pitot (1695plusmn1771) devized

the Pitot tube to measure water velocities in rivers and thiswas later developed for measuring macrows in closed conduitsvessels etc Its principle of operation is simple when macrow isdirected against an obstacle eg a tube it is demacrectedtowards the sides of the obstacle while the macrow pressure atthe obstacle tip (pt) rises above the ambient (mainstream)level (pa) By measuring the pressure difference at the tip ofthe obstacle and the mainstream macrow it is possible tocalculate the macrow velocity (u) using a simplireged Bernoulliequation

u

2 pt pa

r

r1

where r is the density of the macrowing macruid Special pressureprobes were developed of which the `Prandtlrsquo probe isprobably the most common a hole at the tip and one on theside of the probe measure both pressures at once Usuallythe two pressures are measured at the same U-manometerwhich is reglled with a macruid having a density rm different fromr (Figure 2) and equation 1 simplireges

u

2 rm r gh

r

s

2

Velocity however is a vector and probes have beendeveloped that are capable of determining simultaneouslytwo or even all three vector components (ur uz and uv) Inorder to avoid errors in pa measurement due to macruid motionthe hole size is drilled as small as possibleETHusually of theorder of tenths of a millimetre Novel designs of Pitot tubescomprise miniature piezoresistive pressure sensor chips forpressure measurement allowing for direct measurement ofpressure differences and availability of the velocity data inreadily-usable electronic form

The Pitot tube has been used to measure velocities instirred vessels96171217225 It should also be noted that it hasboth a disadvantage and an advantage

middot the probe is intrusive and this may affect the macrow patternespecially in small- and medium-size vessels

middot the tube is useful for measuring velocities in solid-liquid gas-liquid or gas-liquid-soli d dispersions217218 wherethe bubbles andor solid particles motion may interferewith other liquid-velocity determination techniques aswell as in large-scale vessel velocity measurementswhere other techniques eg laser Doppler velocimetrymay not be practicable

114 MAVROS


Figure 1 Illustration of the departure of `standardrsquo from actual macrowpatterns (a) `standardrsquo Rushton-turbine macrow pattern

240 (b) macrow pattern

determined by LDV154

Figure 2 Pitot tube89

Hot-wire Anemometry

Hot wire anemometry is another technique which wasused in the recent past to measure liquid velocities in stirredvessels and is still used for airgas velocity measurementsIt is based on the sensing and measurement of the rate ofcooling of a regne electrically heated wire3658 The wire isusually made of tungsten platinum or platinum-iridium itsdiameter is typically lt 5 mm with a length of 1 to 2 mm Bycombining several wires on the same probe (Figure 3) it ispossible to measure simultaneously all three components ofthe velocity vector

An alternative to wires is the hot-reglm sensor this is asmall-diameter solid non-conductive quartz cylinder onwhich a very thin layer of platinum is deposited When theprobe is to be used in liquids a quartz or alumina coating isapplied on top of the reglm in order to avoid erosion effectsdue to impinging particles which are dispersed in the liquid

Hot-wire anemometry has been used to study thecharacteristics of both steady and unsteady macrowregelds19373971130134135171206207226230235 Advances inthe understanding of the functional dependence of the heattransfer from the wire on velocity density temperature andmacrow angle led to greater measurement accuracy Accuratemeasurements may thus be obtained in a wide variety ofmacruids gases liquids conducting liquid metals etc andover a wide range of environmental conditions

Laser-Doppler Velocimetry

The development of the laser technology in the 1960sresulted in the emergence of a new measuring technique forvelocities the Laser Doppler Velocimetry (LDV)ETHwhichshould not be confused with anemometry which applies thesame measuring principles to the determination of velocitiesin gases LDV has an important advantage over previoustechniques since the probe lies outside the stirred vessel itdoes not interfere with the macrow pattern

The technique is rather simple1 a laser beam is split andthe two resulting coherent beams are made to cross at somepoint inside the stirred vessel (Figure 4) in the intersectionvolume parallel interference fringes are formed When asmall particle crosses this small volume it scatters lightwhich is captured by a photodetector By analysing thechange in the intensity macructuations on the photodetector it

is possible to determine the velocity of the particle crossingthe intersection volume59

In practice the frequency of one of the beams is slightlyshifted using a `Braggrsquo cell this change causes the fringepattern to pulsate at a steady frequency When a particlecrosses the fringe volume it affects this pulsating frequencyand this is registered by the photomultiplie r as a Dopplershift frequency fD since fD is related to the particle velocity(u) and the fringe spacing (df)

df

l

2 sin f3

(where 2f is the angle between the two beams and l is thelight wavelength) it is possible to determine the latter

u fD df 4

The velocity component measured by LDV is the one thatlies in the plane of the beams and which is normal to thebisector of the two laser beams By combining two sets ofdouble beams it is possible to determine at the same timetwo of the three velocity vector components (Figure 5)Also by installing the optical equipment on a traversingsystem (Figure 6) which allows the beam intersection to belocated at various places inside the stirred vessel velocitiesat various places may be determined fairly easily

The velocities which are determined by the LDV systemare usually stored as time series on a computer which iscoupled to the system Subsequent numerical analysis yieldsthe mean and the rms velocityETHsee Appendix 1ETHfor thevelocity vector component at the point of measurement

115FLOW VISUALIZATION IN STIRRED VESSLES


Figure 3 Schematics of (a) a 2-wire hot-wire95

and (b) a 3-wireanemometer probe

91

Figure 4 Intersection of two coherent laser beams

Figure 6 Typical experimental setup (1) laser (23) regber-optical module(4) torque measuring coupler (5) motor (6) photomultipliers (7) macrowvelocity analyser (8) oscilloscope (9) computer

154

Figure 5 Experimental setup for the determination of two of the threevelocity vector components

It should be noted here that for a velocity time series tobe useful it must have followed accurately the macrow historyfor a slow-changing macrow a few data are perhaps sufregcientbut for fast-changing macrows like the ones encountered in astirred vessel the frequency of sampling must be at leasttwice as large as the dominant frequency of the process190Figure 7(b) illustrates the case of a sub-sampled process themacrow history in this case is erroneous and not accuratelyrepresentative of the investigated macrow

Laser Doppler velocimetry has been used extensivelysince its appearance to measure velocities in stirred vesselsan extensive body of literature covers a variety of vessel-impeller conreggurations single-agitator systems tall con-regguration (H $ 2T) vessels where a second agitator isnecessary to agitate the upper part of the vessel contentsagitatorless systems Newtonian and non-Newtonian liquidsetc5plusmn81415172134383940 444549515457 6166707475798182

84 97 98 99 100 101103107 plusmn 114 116 118120121125132 133 136137

139 plusmn 143149152 plusmn 154 156157158160 plusmn 162163 164166170174175181

183 187188189193 194 196 197199202210212217 218 plusmn 220227229

232 plusmn 234237239One limitation of this technique is the need for the macruid to

be transparent This may not be the case in real-situationmacruids eg foodstuff in such situations it is necessary toperform the measurements in transparent model macruids thathave viscosity values and texture similar to the real macruid27

Recently measurements have also been reported forsolid-liqui d systems with matching refractive index72plusmn 73the laser Doppler technique has also been extendedETHtermed `Phase Doppler Anemometryrsquo (PDA)ETHto measureboth liquid velocities and particle or bubble sizes198202236

Ultrasound Doppler Velocimetry

Another non-intrusiv e technique based on the Dopplereffect uses an ultrasound pulse which is remacrected by the

minute particles moving with the liquid The velocity ofthe macruid is determined by the change in frequency of theemitted and remacrected ultrasonic wave and is related to thevelocity of sound in the macruid medium and the angle v withrespect to the propagation direction of the pulse Bytransmitting a series of pulses and capturing the echoes itis possible to determine almost simultaneously the macruidvelocity at various depths (the number of `channelsrsquo is regxedby the instrumentation)

One drawback of this technique is the widening intensitylobe which is related to the wavelength of the emitted waveand the radius of the transducer this widening means that thedeeper one measures from the surface of the transducer thewider the region to which the determined average velocityapplies Another potential problem is the artifacts generatedby moving surfaces within the measuring region94

The technique has been used to determine the velocitymaps in a stirred vessel for a hyperboloid stirrer withD T4 at a very low clearance (C T 40)214

ENSEMBLE MEASUREMENTS

Ensemble-measuring techniques encompass attempts toidentify the pseudo-2-dimensiona l macrow pattern in a stirredvessel by capturing the velocities across a whole regionrather than at a single point

Simple Imaging

Still picturesA still picture of the vessel is taken and the major

circulation patterns are identireged from it eg191

Streak linesAn improvement of the technique has been the dispersion

of small neutrally-buoyan t particles in the liquid so thattheir movement appears on the picture as streamlines(Figure 8) The illumination of the vessel contents by astrong light source eg a laser sheet yields qualitativeresults regarding the major macrow patterns in the stirredvessel The technique has been used to study the effect ofvarious factors on the macrow pattern macrow rates impellerspacing non-Newtonian liquid mixing among

others102105138148150213231

116 MAVROS


Figure 7 Illustration of the suitability of velocity sampling (a) appropriatevelocity sampling (b) poor sampling

Figure 8 Streak-line identiregcation of principal macrow patterns in stirredvessels (a) tall (H = 2T) vessel with two HE-3 impellers

9 (b) stirred vessel

with a single Mixel TT impeller [P Mavros unpublished work]

Prism derotationA very ingenious technique using a set of prisms has

been developed to optically `freezersquo the rotating impellerthus obtaining a stationary picture115 The technique hasbeen used to investigate the formation of cavities behind theblades of the various impellers it has also been used toidentify a region at the top of the blade where the macrowseparates from the blade forming a bubble228

Flow-Followers

The use of a `macrow-followerrsquo is another technique for theidentiregcation of the macrow pattern The meandering of aparticular particle in the vessel is recorded and macrowpatterns are deduced from its trace Flow followers may besimple particles somehow made distinct eg by colour-ing207 and following its trajectory visually or using avideo126 or more sophisticated like the radio-frequencyemitting particle11159172 and the magnetic pill167 In thepast the recording was limited to the passage of theparticle from a specireged region eg the volume around theimpeller

The technique was used to observe the macrow or to measurecirculation times1260159 which were then used to validatetheoretical models147 or to calculate impeller character-istics60 Lately the technique called trajectography hasbeen extended to provide 3-D trajectories1013182224 and thusa better representation of the actual macrow in the vessel

A recent development of the technique is the radioactivetagging of a particle and monitoring its meanderingthroughou t the bulk of the dispersion in the vessel usingseveral radioactivity sensors located around the vessel127The technique (CARPTETHComputer Assisted RadioactiveParticle Tracking) has been used so far mainly to studymacrows in bubble columns eg3341 and crystallizers176 Analternative to this is the Positron Emission Particle Tracking(PEPT) technique104 developed by Parker and co-work-ers177plusmn 178 which has been used to study the macrow of viscousnon-Newtonian solutions agitated with an axial impeller56

An alternative to the `macrow followerrsquo is the `directionfollowerrsquo Short cotton tufts are positioned at various placesinside a stirred vessel and their position recorded The analysisof their movement yielded an estimate of the macrow stability interms of `direction coefregcientrsquo anda `switching probability rsquo31A further application of this techniqueETHsticking tufts at the

edge of the impeller bladesETHallowed the experimentaldetermination of the turbulence integral length scale239

Colour Change

One way of studying macrow patterns is to use somechemical to add a colour indicator in the transparent liquidand follow its macrow This technique using iodine plussodium thiosulfate for example in the presence of starch173was used to demonstrate that the macrow is slow in the upperpart of the stirred vessel

Another possibility is to use two reactants and anappropriate colour indicator As the vessel contents aremixed the colour changes and this indicates the macrowpattern7780 The technique is also widely used for measur-ing the mixing time A recent development combines thistechnique with tomography A light source illuminates thecontents of vessel a camera located normally to theilluminated plane records the illuminated raysheet andsubsequent treatment of the frames allows the reconstruc-tion of the mixing history3184

From these new techniques have emerged for the studyof macrow patternsrsquo particle image velocimetry laser-inducedmacruorescence thermography x-ray and resistance tomo-graphy to name a few

Thermography

A development of simple photography is the use of heat-sensitive thermochromic crystals dispersed in the liquidInitially since the temperature is the same throughou t thewhole liquid the crystals have all the same colour intensityWhen a quantity of heated liquid is introduced into thevessel its spreadETHand the associated macrow patternETHisshown as a disruption in the colour of the crystals This iscaptured by a colour video camera and the frames aresubsequently analysed digitally for the hue saturation andlightness of each pixel123plusmn 124

Figure 9 illustrates the evolution of the dispersion of asmall lump of liquid crystals heated 2 8 C above the bulktemperature in a lid-closed unbafmacred vessel123 From these(and subsequent pictures) it is possible to determine themixing time and more generally to investigate the effect ofthe vessel conregguration and operating conditions on theprocess of mixing



Figure 9 Hue contours illustrating the spreading of a small amount of tracer (heated liquid) in a stirred vessel Rushton turbine N 540 rpm123

Particle Image Velocimetry

The natural extension of the simple photographicrecording of streaks of particles moving in a stirred vesselis the comparison of two consecutive frames Pictures of aplane cutting through the vessel illuminated by a powerfullight source are taken at short intervals Analysing thedisplacement of each particle in the time between the twoshutter openings yields its 2-D velocity If sufregcient seedingparticles are present then a map of the macrow in theilluminated plane is obtained76119

The calculation of the particle velocities relies onsophisticated software In the case of low-density imageswith relatively few particles a program identifying speciregc

particles (`particle trackingrsquo) is sufregcient282947 48 for morecomplex macrows image correlation methods are used todetermine the individual particle vectors68 also 69222 fora review and regelds of application of PIV and33 for acomparison with particle tracking and computed tomogra-phy) The evolution of software has resulted in very detailedmacrow maps and even calculations of additional macrowcharacteristics eg of vorticity turbulence amongothers55180

Figure 10 illustrates the succession of results obtainedby PIV93 From the original picture (Figure 10(a)) thevelocity vectors are extracted From these it is then possibleto determine the macructuating component and the vorticity of

the macrow at this plane Figure 11 illustrates some `primitiversquoPIV results29 obtained in a stirred vessel with a 45 8 -pitched-blade turbine28 whereas Figure 12 illustrates resultsobtained with a more sophisticated apparatus and software

One interesting feature of PIV is that each recorded framerepresents a `freezersquo of the macrow in time The time averagingof consecutive maps generates the macrow map which ischaracteristic of the impeller and the vessel conregguration(Figure 12) each frame on the other hand is a transientimage of the macrow In that sense it exhibits non-stationaryphenomena like macrow instabilities By analysing consecu-tive frames it has been possible to calculate the majormacructuating frequency169 which was previously identireged154

and measured by LDV165PIV measurements have started being made for chemical-

process stirred vessels263335 168204 Novel extensions of thePIV technique include the holographic PIV238 whichcaptures the 3-D velocity distribution and digital photo-grammetry or three-dimensional particle tracking veloci-metry in which all three components of the velocity vectorare determined as a function of time1678

Laser-Induced Fluorescence

Some chemical substances become macruorescent whenexcited by a particular light source Several such species

118 MAVROS


Figure 10 Illustration of the macrow pattern results obtainable through PIV93

(a) Original picture (b) raw velocity vectors map 2015 velocity vectors have beenextracted by particle image tracking (c) instantaneous macructuating velocity vectors map this was obtained by interpolating the random sparse velocity vectorsin Figure 10b and then subtracting the ensemble average velocity (d) instantaneous vorticity map

exist eg macruorescein rhodamine B among others Thephenomenon was initially termed phototropism howeverthe current term is `photochromismrsquo and the dyes are termedphotochromic dyes

A laser beam illuminates a spotETHor a planeETHinside thestirred vessel the macruorescent dye that has been dissolved inthe liquid is excited within a few microseconds andbecomes macruorescent46 hence the name of the technique(Laser-Induced Fluorescence or LIF) The reverse reactionwhich brings the dye to its initial non-macruorescent conditionhas a half life ranging from a few seconds to several

minutes depending on the species128 A slightly differentapplication is the use of photochromic dyes to follow theevolution of macrow patterns192 A spot or line of a photo-sensitive dye is introduced in the liquid and suddenlyilluminated By following the movement of the dye spot orline using a high-speed camera and analysing subsequentlythe pictures it is possible to determine primary andsecondary macrows in vessels

Initially the technique was used for measuring point

concentrations 646583 117179 or temperatures4 since some ofthe photochromic dyes are also sensitive to heat LIF wasfurther developed to determine simultaneously concen-tration and velocity at a given point144 and the adventof laser sheet illumination allowed the determinationof whole-plane macrow patterns in various process ves-

sels1843858788129201211 Lately new photochromic dyesare being produced131 to allow long-term recording of macrowpatterns by `taggingrsquo the dye molecules67 Figure 13illustrates the use of two such dyes the persistence of thedye macruorescence and the possibility of following theevolution of mixing of two different liquid streams seemspromizing for stirred vessel mixing studies

Tomography

Most of the early macrow visualization techniques faced aconsiderable problem The presence of sometimes bulkyprobes disrupted the macrow pattern and resulted in erroneousor perhaps not quite accurate results This led to a search forvisualization techniques in other regelds which could also beuseful for chemical process vessels

During the 1970s x-ray tomography was developed formedical diagnosis An x-ray transmitter is positioned on one



Figure 12 Instantaneous digital PIV macrow patterns (a-d) and corresponding average velocity regeld (e average of 466 pictures) for a stirred vessel agitated witha Rushton turbine (T = 04 m D = 0138 m C = D 4 bafmacres N = 267 Hz) [M Perrard private communication]

Figure 11 Primitive PIV results obtained by image processing in a stirredvessel with a pitched-blade turbine

29

side of the body and a receiver sensor on the othercapturing the signal passing through the body and examin-ing its attenuation yields an estimate of the (line integral)local mass density distributio n along the signal path Byrotating the emitter-receiver system around the body andusing appropriate software it is possible to reconstruct thetomographic image of the cross-section being observed andif the whole system is translated along the body examined itis also possible to obtain 3-D tomographic data Theassistance of computers meant that the technique wasknown as Computer-Assisted Tomography (CAT) or simplyComputer Tomography (CT)30

The technique has been applied in stirred vessels to studythe macrow in opaque non-Newtonian liquids for which othermacrow visualization techniques were not successful52plusmn 53eg to study the development of cavities and caverns inviscous macruids62 plusmn63191203

A more important development of process tomographywas the emergence of electrical impedance electricalcapacitance or electrical resistance tomography electrodesare macrush-mounted on the inside walls of the vessel(Figure 14) and an electrical property is measured by allof them simultaneously eg resistance in the case ofelectrically-conducting liquids capacitance for non-con-ducting macruids etc216 Again the signals from the varioussensors are combined into slices or `tomogramsrsquo (Figure15(a)) and a set of such images may be used to obtain a 3-Drepresentation of the macrow inside the vessel (Figure 15(b))The technique has been used to investigate the macrow invarious process vessels for various two-phase sys-

tems222342 5086122145146185200215221223 The tomo-graphic technique for the reconstruction of the macrow insidevessels has also been applied recently with a visual

technique using two dyes2425184186

CONCLUSIONS

Several experimental techniques ranging from the simpleones which rely on visual observation to sophisticated onesencompassing special tools sensors and software (digitalPIV LIF LDV etc) are today available for visualizing macrowpatterns in stirred vessels as well as other chemical processvessels Laser Doppler velocimetry (LDV) and ParticleImage Velocimetry (PIV) have evolved into relatively easy-to-use techniques and if the measurements are carefullyperformed they provide considerable information about thethree-dimensional macrow generated by the various impellersThe tomographic techniques on the other hand especiallythe ones based on the electrical properties of the stirred macruidsystem look promizing since they seem appropriate forboth lab- and large-scale vessels

120 MAVROS


Figure 13 Illustration of the use of two macruorescent dyes (green disodium macruorescein red orange rhodamine-B) to investigate the impact of a liquid jet(green) on a liquid layer (red)

90

Figure 14 Positioning of the electrodes on the inside walls of a stirredvessel

92

APPENDIX 1

One of the beneregts of LDV is the availability of the macrowhistory for a given point in terms of a time series of singledouble or sometimes all three of the velocity vectorcomponents uij where ìrsquo refers to the vector component(rzv) while `jrsquo refers to the j-th value in the time seriesThis instantaneous j-th velocity measurement is consideredas consisting of a mean (Aringui) and a macructuating term (uij)

uij Aringui uij A1

where the mean is calculated as the average of allmeasurements

Aringui

1

N

XN

j 1

uij i r z v A2

The average of the macructuating term is the rms value of thevelocity

uirms u 2i

12 1

N

XN

j 1

uij Aringui2

Aacute 12

i r z v

A3

The mean and macructuating velocity terms may now be usedto determine several characteristics of the stirred vessel macrowpatterns The variability of the macrow as measured by therms velocities may be illustrated by the intensity ofturbulence (I) which is the ratio of the rms to the meanvelocity

Iu 2

r u 2z u 2

v12

u2r u2

z u2v

12A4

while the turbulent kinetic energy (k) is

k1

2u 2

r u 2z u 2

v A5

One of the important features of a particular vesselconregguration is the pattern of energy dissipation sincethis is related to the performance of the stirred vessel as areactor Some of it is dissipated inside the impeller-sweptvolume but the main part is dissipated within the bulk of thestirred macruid The local value of energy dissipation (e) isrelated to the macructuating velocity

e Cu 3

LA6

where C is a constant and L a characteristic lengthRegarding C several values have been used by variousworkers ranging from 051 to 72 It is perhaps better todetermine it by integrating the results over the wholevolume of the vessel and equating this to the power drawnby the agitator (P) assuming that C is independent oflocation L is a length scale associated to the impellerdiameter (L Da with values of a ranging from 6 to125) a length scale of D10 has been reported as givingaccurate results for the Rushton turbine Alternatively L isrelated to a mean velocity value and the Eulerian integraltime scale (ti)

Li Aringuiti A7

where ti is calculated as the integral of the autocorrelationfunction

ti

hellipyen

0

Ri dt A8

and Ri is calculated from

Ri

ui t ui t Dt

u 2i

A9

Finally for u in equation (A6) we may use either one of therms velocitiesETHin that case the corresponding velocityvector autocorrelation is used to determine the lengthscaleETHor a combination of all available eg k12 In allcases an approximate map of energy dissipation rates isobtained and this characterizes the suitability of a particularimpeller andor vessel conregguration for a given task

NOMENCLATURE

a factordf fringe spacingD impeller diameter mfD Doppler frequency HzI turbulence intensityk turbulent kinetic energy m2 splusmn2

L length scale mpa ambient (mainstream) pressure Papt tip pressure PaR autocorrelation functiont time su velocity m s

plusmn1

u macructuating velocity m splusmn1



Figure 15 Illustration of the electrical resistance tomography technique (a) a set of `tomogramsrsquo for various positions along the z-axis (b) resulting 3-Dmacrow pattern (in this case dispersion of gas into a stirred liquid)

92

Greek letterse energy dissipation rate m

2s

plusmn3

l light wavelength mr liquid density kg m

plusmn3

t integral time scale sf half-angle between two laser beams 8

Indicesm manometer liquidr radialz axialv tangential

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ndEd (Taylor amp Francis

Washington DC) pp 175plusmn2992 Aloi L E and Cherry R S 1996 Cellular response to Agitation

Characterized by Energy-Dissipation at the Impeller Tip Chem EngSci 51 1523plusmn1529

3 Al-Saeedi J N and Pike R W 1997 `Spatial Reconstruction ofConcentration Distribution for a Fast Reaction in a Stirred ChemicalReactor using Tomography and suitable 3-D reconstruction methodrsquoin Bertrand J and Villermaux J (Eds) ReAcirccents ProgreAacutes en GeAcircniedes ProceAcircdeAcircs (Lavoisier Paris) 11 (51) pp 357plusmn364

4 AndreAcirc C David R Villermaux J and Gence J N 1991`Measurement of Concentration Fluctuations during Mixing in aStirred Tank and in a Channel Flow by Laser Induced FluorescenceSpectroscopyrsquo Proceedings 7th Europ Conf Mixing (Brugge 18plusmn20Sept) (EFCE-KVIV Antwerpen) pp 43plusmn50

5 Armenante P M Chou C-C and Hemrajani R R 1994`Comparison of Experimental and Numerical Fluid VelocityDistribution Proregles in an Unbafmacred Mixing Vessel provided with aPitched-Blade Turbinersquo Proceedings 8th Europ Conf Mixing(Cambridge 21plusmn23 Sept) (IChemE Rugby) pp 349plusmn356

6 Armenante P M Luo C G Chou C C Fort I and Medek J1997 Velocity proregles in a closed unbafmacred vesselETHComparisonbetween experimental LDV data and numerical CFD predictionsChem Eng Sci 52 3483plusmn3492

7 Armstrong S G and Ruzkowski S 1988 `The Flow Field in theDischarge StreamofDisk Turbinesrsquo inProceedings 6th EuropeanConfMixing (Pavia 24plusmn26 May 1988) (AIDIC-BHRA Pavia) pp 1plusmn6

8 Bakker A and Van den Akker H E A 1994 Single-phase macrow instirred reactors Chem Eng Res Des 72A 583plusmn593

9 Bakker A Fasano J B and Myers K J 1994 Èffects of FlowPattern on the Solids Distribution in a Stirred Tankrsquo Proceedings 8thEurop Conf Mixing (Cambridge 21plusmn23 Sept) (IChemE Rugby)pp 1plusmn8

10 Barillon B and JeAcirczeAcircquel P H 2000 `Characterization ofConvective Mixing in Industrial Precipitation Reactors by Real-Time Processing of Trajectography Datarsquo in Van den Akker H E Aand Derksen J J (Eds) Proceedings 10

thEurop Conf Mixing

(Delft 2plusmn5 July) (Elsevier Amsterdam) pp 329plusmn33611 Van Barneveld J Smit W Oosterhuis N M G and Pragt H J

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15 Baudou C Xuereb C Costes J Ranchin G and Bertrand J 1997`Laser Doppler measurement s of Flow Field and Turbulent FlowParameters in a Stirred Tank equipped with two Industrial Propellersrsquoin Bertrand J and Villermaux J (Eds) ReAcirccents ProgreAacutes en GeAcircniedes ProceAcircdeAcircs (Lavoisier Paris) 11 (51) pp 11plusmn18

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thEurop Conf

Mixing (Delft 2plusmn5 July) (Elsevier Amsterdam) pp 35plusmn4419 Bertrand J and Couderc J P 1985 Evaluation of the power

consumption in agitation of viscous Newtonian or pseudoplasti cliquids by two-bladed anchor or gate agitator Chem Eng Res Des 63259plusmn263

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22 Bolton G T Korchinsky W J and Waterfall R C 1999Ìnvestigating Liquid-Liquid Mixing by Electrical CapacitanceTomographyrsquo in H Benkreira (Ed) Fluid Mixing 6 (IChemESymp Ser no 146) (IChemE Rugby) pp 159plusmn164

23 BombacIuml A and ZIuml un A 2000 Gas-reglled cavity structures and localvoid fraction distribution in vessel with dual-impellers Chem Eng Sci55 (15) 2995plusmn3001

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thEurop Conf Mixing (Delft 2plusmn5 July) (Elsevier

Amsterdam) pp 25plusmn3426 Bugay S Line A and Roustan M 1997 Èfregciency of particle

image velocimetry (PIV) technique to analyse the mixing in agitatedtanksrsquo in Bertrand J and Villermaux J (Eds) ReAcirccents ProgreAacutes enGeAcircnie des ProceAcircdeAcircs (Lavoisier Paris) 11 (51) pp 27plusmn34

27 Chandrasekaran M Marcroft H Bakalis S and Karwe M V1997 Applications of laser Doppler anemometry in understandingfood processing Trends in Food Science amp Technology 8 369plusmn375

28 Chang T P K Watson A T and Tatterson G B 1985 Imageprocessing of tracer motions as applied to mixing and turbulent macrowI The technique Chem Eng Sci 40 269plusmn275

29 Chang T P K Watson A T and Tatterson G B 1985 Imageprocessing of tracer motions as applied to mixing and turbulent macrowII Results and discussion Chem Eng Sci 40 277plusmn285

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39 Costes J Alran C and Couderc J P 1988 CaracteAcircristiques du

122 MAVROS


courant de refoulement drsquoune turbine de Rushton Mesures paraneAcircmometrie thermique et Doppler aAacute laser Entropie 24 (140) 20plusmn29

40 Derksen J J Stockmann J H and Van den Akker H E A 1997`Three-dimensiona l laser Doppler anemometry in a stirred tankrsquo inBertrand J and Villermaux J (Eds) ReAcirccents ProgreAacutes en GeAcircnie desProceAcircdeAcircs (Lavoisier Paris) 11 (51) pp 81plusmn88

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44 Ditl P ForIumlt I and Stejc V 1994 `Flow in an agitated vesselequipped with multiple impellerrsquo Proceedings 8th Europ ConfMixing (Cambridge 21plusmn23 Sept) (IChemE Rugby) pp 147plusmn154

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48 Dracos Th 1996 `Particle tracking velocimetry (PTV)rsquo in DracosTh (Ed) Three-Dimensional Velocity and Vorticity Measuring andImage Analysis Techniques (Kluwer Academic Publishers Dor-drecht) pp 155plusmn160

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thEurop Conf

Mixing (Delft 2plusmn5 July) (Elsevier Amsterdam) pp 353plusmn36056 Fangary Y S Seville J P K and Barigou M 1999 `Flow studies

in stirred tanks by positron emission particle tracking (PEPT)rsquo inBenkreira H (Ed) Fluid Mixing 6 (IChemE Symp Ser no 146)pp 23plusmn34

57 Fei W Y Wang Y D Wan Y K 2000 Physical modelling andnumerical simulation of velocity regelds in rotating disc contactorvia CFD simulation and LDV measurement Chem Eng J 78 131plusmn139

58 Fingerson L M and Freymuth P 1996 `Thermal anemometersrsquo inGoldstein R J (Ed) Fluid Mechanics Measurements 2

ndEd

(Taylor amp Francis Washington DC) pp 115plusmn17359 Fingerson L M and Menon R K 1998 `Laser Doppler

velocimetryrsquo in Johnson R W (Ed) The Handbook of FluidDynamics (CRC Press- Springer Boca Raton FL) pp 351plusmn3518

60 ForIumlt I and Medek J 1988 `Hydraulic and energetic efregciency ofimpellers with inclined bladesrsquo Proceedings 6th Europ Conf Mixing(Pavia 24plusmn26 May) (BHRA Cranregeld) pp 51plusmn56

61 ForIumlt I VoznyAcirc M and ForstovaAcirc B 1991 `Distribution of turbulencecharacteristics in agitated system with axial high-speed impeller and

bafmacresrsquo Proceedings 7th Europ Conf Mixing (Brugge 18plusmn20 Sept)(EFCE-KVIV Antwerpen) pp 33plusmn41

62 Galindo E and Nienow A W 1992 Mixing of highly viscoussimulated Xanthan fermentation broths with the Lightnin A315impeller Biotechnol Prog 8 233plusmn239

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66 Geisler R K and Mersmann A B 1988 `Local velocitydistribution and power dissipation rate of suspensions in stirredvesselsrsquo Proceedings 6th Europ Conf Mixing (Pavia 24plusmn26 May)(BHRA Cranregeld) pp 267plusmn272

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68 Grant I and Pan X 1997 The use of neural techniques in PIV andPTV Measurement Science amp Technology 8 1399plusmn1405

69 Grant I Particle image velocimetryETHA review 1997 ProceedingsInst Mech Eng Part C-J of Mech Eng Sci 211 55plusmn76

70 Guiraud P Costes J Bertrand J and Bousquet J 1991 `Localmeasurements of liquid and solid velocities and of particle sizes instirred suspensions with a phase Doppler particle analyserrsquoProceedings 7th Europ Conf Mixing (Brugge 18plusmn20 Sept)(EFCE-KVIV Antwerpen) pp 443plusmn450

71 GuEgravenkel A A and Weber M E 1975 Flow phenomena in stirredtanks Part I The impeller stream Part II The bulk of the tankAIChEJ 21 931plusmn949

72 Haam S J and Brodkey R S 2000 Motions of dispersed beadsobtained by particle tracking velocimetry measurements Part II Int JMultiphase Flow 26 (9) 1419plusmn1438

73 Haam S J Brodkey R S ForIumlt I Klaboch L Placnik M andVanecek V 2000 Laser Doppler anemometry measurements in anindex of refraction-matched column in the presence of dispersedbeads Part I Int J Multiphase Flow 26 (9) 1401plusmn1418

74 Harvey A D Wood S P and Leng D E 1997 Experimental andcomputational study of multiple impeller macrows Chem Eng Sci 52 (9)1479plusmn1491

75 Hasal P Montes J-L Boisson H-Cand ForIumlt I 2000 Macro-instabilities of velocity regeld in stirred vessel detection and analysisChem Eng Sci 55 (2) 391plusmn401

76 Hassan Y A 1998 `Multiphase macrow measurements using particleimage velocimetryrsquo in Johnson R W (Ed) The Handbook ofFluid Dynamics (CRC Press- Springer Boca Raton FL) pp 361plusmn3615

77 Hiby J W 1988 `Decolouring of chemical indicators applicationsand limitationsrsquo Proceedings 6th Europ Conf Mixing (Pavia 24plusmn26May) (BHRA Cranregeld) pp 123plusmn128

78 Hinsch K D and Hinrichs H 1996 `Three-dimensiona l particlevelocimetryrsquo in Dracos Th (Ed) Three-Dimensiona l Velocity andVorticity Measuring and Image Analysis Techniques (KluwerAcademic Publishers Dordrecht ) pp 129plusmn152

79 Hirata Y and Aoshima Y 1994 `Flow characteristics and powerconsumption in an agitated shear-thinning plastiv macruidrsquo Proceedings8th Europ Conf Mixing (Cambridge 21plusmn23 Sept) (IChemERugby) pp 415plusmn422

80 Hirata Y and Ito R 1988 `Characteristics of macrow and mixing invessel with rotating multistaged disksrsquo Proceedings 6th Europ ConfMixing (Pavia 24plusmn26 May) (BHRA Cranregeld) pp 109plusmn114

81 Hirata Y Nienow A W and Moore I P 1991 `LDA studies ofvelocity distributions and cavern sizes in a yield stress macruid agitatedby a Rushton turbinersquo Proceedings 7th Europ Conf Mixing (Brugge18plusmn20 Sept) (EFCE-KVIV Antwerpen) pp 167plusmn172

82 Hirata Y Nienow A W and Moore I P T 1994 Estimationof cavern sizes in a shear-thinning plastic macruid agitated by aRushton turbine based on LDA measurements J Chem Eng Jap27 235plusmn237

83 Hirofuji Y Inoue T and Nagase Y 1991 `Micromixing begaviourin a batch vessel with several impellers using alkali-macruorescent dye



systemsrsquo Proceedings 7th Europ Conf Mixing (Brugge 18plusmn20Sept) (EFCE-KVIV Antwerpen) pp 57plusmn65

84 Hockey R M and Nouri J M 1996 Turbulent macrow in a bafmacredvessel stirred by a 60-degrees pitched blade impeller Chem Eng Sci51 4405plusmn4421

85 Hoefsloot H C J Willemsen S M Hamersma P J and IedemaP D 2000 `Mixing of two liquids with different rheologicalbehaviour in a lid driven cavityrsquo in Van den Akker H E A andDerksen J J (Eds) Proceedings 10th Europ Conf Mixing (Delft 2plusmn5 July) (Elsevier Amsterdam) pp 109plusmn116

86 Holden P J Wang M Mann R Dickin F J and Edwards R B1998 Imaging stirred-vessel macromixing using electrical-resistancetomography AIChEJ 44 780plusmn790

87 Houcine I Vivier H Plasari E David R and Villermaux J1994 `Comparison of mixing action of several stirrers by laser sheetvisualization and image processingrsquo Proceedings 8th Europ ConfMixing (Cambridge) IChemE Symp Ser No 136 pp 97plusmn104

88 Houcine I Vivier H Plasari E David R and Villermaux J1996 Planar laser induced macruorescence technique for measurementsof concentration regelds in continuous stirred tank reactors Experi-ments in Fluids 22 95plusmn102

89 httpnishmitedu 2006TextbookNodeschap04node13html90 httpwebegrmsuedutmualCHuckringhtml91 httpwwwaoevtedumacrowdataprojectsvortex92 httpwwwceumistacukcentresptcentreertmixhtm93 httpwwwengwarwickacuk espbcpivhtm94 httpwwwsignal-processingcom app_notes interfaceshtm95 httpwwwtsicom96 Jaworski Z and ForIumlt I 1991 Energy dissipation rate in a bafmacred

vessel with pitched blade turbine impeller Collect Czech ChemCommun 56 1856plusmn1867

97 Jaworski Z and Nienow A W 1993 Àn LDA study of thehydrodynamic s of caverns formed in a yield stress macruid agitated by ahydrofoil impellerrsquo paper H62 presented at CHISA 93 (PragueAug)

98 Jaworski Z and Nienow A W 1994 `LDA measurements of macrowregelds with hydrofoil impellers in macruids with different rheologicalpropertiesrsquo Proceedings 8th Europ Conf Mixing (Cambridge 21plusmn23Sept) (IChemE Rugby) pp 105plusmn112

99 Jaworski Z Dyster K N Moore I P T Nienow A W andWyszynski M L 1997 `The use of angle resolved LDA data tocompare two differential turbulence models applied to sliding meshCFD macrow simulations in a stirred tankrsquo in Bertrand J andVillermaux J (Eds) ReAcirccents ProgreAacutes en GeAcircnie des ProceAcircdeAcircs(Lavoisier Paris) 11 (51) pp 187plusmn194

100 Jaworski Z ForIumlt I and Marisko V 1991 `Turbulent macrow andmixing in a vessel with a proregled blade impellerrsquo Proceedings 7thEurop Conf Mixing (Brugge 18plusmn20 Sept) (EFCE-KVIV Antwer-pen) pp 193plusmn197

101 Jaworski Z Nienow A W and Dyster K N 1996 An LDA studyof the turbulent-macrow regeld in a bafmacred vessel agitated by an axialdown-pumping hydrofoil impeller Can J Chem Eng 74 3plusmn15

102 Jaworski Z Pacek A W and Nienow A W 1994 On macrow close tocavern boundaries in yield stress macruids Chem Eng Sci 49 3321plusmn3324

103 Jeurissen F Wijers J and Thoenes D Ìnitial mixing of feedstreams in agitated vesselsrsquo Proceedings 8th Europ Conf Mixing(Cambridge 21plusmn23 Sept) (IChemE Rugby) pp 235plusmn242 (1994)

104 Jones J R and Bridgwater J 1998 A case-study of particle mixingin a plowshares mixer using positron emission particle tracking Int JMin Proc 53 29plusmn38

105 Ju W Huang X Wang Y Shi L Zhang B and Yuan J 2000Àn investigation of the macrow of viscoelastic macruid in a stirred vesselrsquoin Van den Akker H E A and Derksen J J (Eds) Proceedings 10

th

Europ Conf Mixing (Delft 2plusmn5 July) (Elsevier Amsterdam)pp 313plusmn320

106 JuEgravesten P Paul G C Nienow A W and Thomas C R 1998Dependence of Penicillium chrysogenum growth morphology vacuolation and productivity in fed-batch fermentations on impellertype and agitation intensity Biotechnol Bioeng 59 762plusmn775

107 Keller D B A 1985 `To determine the velocity distribution aroundan impeller in a stirred tank using laser Doppler anemometryrsquo inProceedings Int Conf Laser AnemometryETHAdvances and Applica-tions (Manchester Dec 1985) pp 85plusmn98

108 Kemoun A Lusseyran F Mahouast M and Mallet J 1994Èxperimental determination of the complete Reynolds stress tensor

in macruid agitated by a Rushton turbinersquo Proceedings 8th Europ ConfMixing (Cambridge 21plusmn23 Sept) (IChemE Rugby) pp 399plusmn406

109 Kemoun A Lusseyran F Skali-Lami S Mahouast M Mallet JLartiges B S Lemelle L and Bottero J Y 1997 `Hydrodynami cregeld dependence of colloidal coagulation in agitated reactorsrsquo inBertrand J and Villermaux J (Eds) ReAcirccents ProgreAacutes en GeAcircnie desProceAcircdeAcircs (Lavoisier Paris) 11 (52) pp 33plusmn40

110 Klaboch L PtaAcirccIumlnotildeAcirck M Lamka J and ForIumlt I 1988 Àpplication ofthe laser Doppler anemometry for determination of velocity regeld inthe cylindrical bafmacred system with pitched-blade impellersrsquo Proceed-ings 6th Europ Conf Mixing (Pavia 24plusmn26 May) (BHRA Cranregeld)pp 35plusmn42

111 Komori S and Murakami Y 1988 `Turbulent mixing in anunbafmacred stirred tank with double impellersrsquo Proceedings 6th EuropConf Mixing (Pavia 24plusmn26 May) (BHRA Cranregeld) pp 63plusmn68

112 Koutsakos E Nienow A W and Dyster K N 1990 `Laseranemometry study of shear thinning macruids agitated by a Rushtonturbinersquo IChemE Symp Ser No 121 pp 51plusmn73

113 Kresta S M and Wood P E 1993 The macrow regeld produced by apitched blade turbine characterization of the turbulence andestimation of the dissipation rate Chem Eng Sci 48 1761plusmn1774

114 Kresta S M and Wood P E 1993 The mean macrow regeld produced bya 45 8 pitched blade turbine changes in the circulation pattern due tooff bottom clearance Can J Chem Eng 71 45plusmn53

115 Kuboi R Nienow A W and Allsford K 1983 A multipurposestirred tank facility for macrow visualization and dual impeller powermeasurement Chem Eng Commun 22 29plusmn39

116 Kuncewicz C Heim A and Pietrzykowski M 1997 À model oflaminar liquid macrow for macrat bladed paddlesrsquo in Bertrand J andVillermaux J (Eds) ReAcirccents ProgreAacutes en GeAcircnie des ProceAcircdeAcircs(Lavoisier Paris) 11 (51) pp 113plusmn120

117 Kurada S Rankin G W and Sridhar K 1994 Flow visualizationusingphotochromic dyesETHa review Opticsamp Lasers Eng 20 177plusmn192

118 Kusters K A Wijers J G and Thoenes D 1991 `Numericalparticle tracking in a turbine agitated vesselrsquo Proceedings 7th EuropConf Mixing (Brugge 18plusmn20 Sept) (EFCE-KVIV Antwerpen)pp 429plusmn441

119 Lai W T 1996 `Particle image velocimetry a new approach inexperimental macruid researchrsquo in Dracos Th (Ed) Three-DimensionalVelocity and Vorticity Measuring and Image Analysis Techniques(Kluwer Academic Publishers Dordrecht ) pp 61plusmn92

120 Lamberto D J Alvarez MMand Muzzio F J 1999 Experimentaland computational investigation of the laminar macrow structure in astirred tank Chem Eng Sci 54 (7) 919plusmn942

121 Lawler J V Armstrong R C Brown R A and Muller S J 1986Laser Doppler velocimetry measurements of velocity-regelds andtransitions in viscoelastic macruids J Non-Newtonian Fluid Mechanics20 51plusmn92

122 Lech M Polednia E and Werszler A 2000 Measurement of solidmean particle size using tomography Powder Technol 111 (3) 186plusmn191

123 Lee K C and Yianneskis M 1997 `Measurement of temperatureand mixing time in stirred vessels with liquid crystal thermographyrsquo in Bertrand J and Villermaux J (Eds) ReAcirccents ProgreAacutes en GeAcircniedes ProceAcircdeAcircs (Lavoisier Paris) 11 (51) pp 121plusmn128

124 Lee K C and Yianneskis M 1997 A liquid crystal thermographictechnique for the measurement of mixing characteristics in stirredvessels Chem Eng Res Des 75A 746plusmn754

125 Lee K C and Yianneskis M 1998 Turbulence properties of theimpeller stream of a Rushton turbine AIChEJ 44 13plusmn24

126 Lee W K and Bryanston-Cross P J 1997 A real-time videoencoded particle imaging tracking technique for velocity measure-ment Optics amp Lasers in Engineering 27 (6) 621plusmn636

127 Legoupil S Pascal G Chambellan D and Bloyet D 1996Determination of the detection process in an experimental tomographfor industrial macrow visualization using radioactive tracers IEEE TransNuclear Science 43 751plusmn760

128 Lemoine F Antoine Y Wolff M and LeboucheAcirc M 1998Èxperimental investigation on thermal turbulent diffusion in a heatedjet using optical methodrsquo in Proceedings 11th Int Heat TransferConf Heat Transfer 98 (Kyongju Korea Aug 23-28) vol 4pp 113plusmn118

129 Lemoine F Wolff M and LeboucheAcirc M 1996 Simultaneousconcentration and velocity-measurement s using combined laser-induced macruorescence and laser-Doppler velocimetryETHApplicationto turbulent transport Exp in Fluids 20 319plusmn327

124 MAVROS


130 Lemonis G and Dracos Th 1996 `Determination of 3-D velocityand vorticity vectors in turbulent macrows by multi-hotwire anemome-tryrsquo in Dracos Th (Ed) Three-Dimensional Velocity and VorticityMeasuring and Image Analysis Techniques (Kluwer AcademicPublishers Dordrecht) pp 1plusmn42

131 Lempert W R Magee K Ronney P Gee K R and Haugland RP 1995 Flow tagging velocimetry in incompressible macrow usingphoto-activated nonintrusive tracking of moleculr motion (PHAN-TOMM) Exper In Fluids 18 249plusmn257

132 Ljungqvist M and Rasmuson A 1997 `Hydrodynamic s of open andclosed stirred vesselsrsquo in Bertrand J and Villermaux J (Eds)ReAcirccents ProgreAacutes en GeAcircnie des ProceAcircdeAcircs (Lavoisier Paris) 11 (51)pp 97plusmn104

133 Ljungqvist M and Rasmuson A 1998 A comparison of thehydrodynamic s of open and closed stirred vessels Chem Eng Comm165 123plusmn150

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135 Lu W M and Ju S J 1987 Local gas holdup mean liquid velocityand turbulence in an aerated stirred tank using hot-reglm anemometryChem Eng J and Biochem Eng J 35 9plusmn17

136 Lu WM and Lee CM 1995 Turbulent macrow in mechanical stirredvessels with multiple impeller 1 Single phase macrow J Chin Inst ChemEng 26 399plusmn409

137 Magni F Costes J Bertrand J and Couderc J-P 1988 `Study bylaser Doppler anemometry of the macrow induced by a Rushton turbine ina stirred tank Inmacruences of the geometry of the tank bottom and of theposition of the turbinersquo Proceedings 6th Europ Conf Mixing (Pavia24plusmn26 May) (BHRA Cranregeld) pp 7plusmn14

138 Mahmoudi S M and Yianneskis M 1991 `The variation of macrowpattern and mixing time with impeller spacing in stirred vessels withtwo Rushton impellersrsquo Proceedings 7th Europ Conf Mixing(Brugge 18plusmn20 Sept) vol I pp 17plusmn24

139 Mahmoudi S M S Rutherford K Lee K C and Yianneskis M1994 À study of the turbulence characteristics of dual-impellermixing systemsrsquo Proceedings 8th Europ Conf Mixing (Cambridge21plusmn23 Sept) (IChemE Rugby) pp 137plusmn145

140 Mahouast M 1991 `Reynolds stresses and stirring regimes of aRushton turbinersquo Proceedings 7th Europ Conf Mixing (Brugge 18plusmn20 Sept) (EFCE-KVIV Antwerpen) pp 51plusmn56

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142 Mahouast M David R and Cognet G 1987 Characterization ofhydrodynami c and concentration regelds in a continuous fed standardstirred tank Entropie 133 7plusmn17

143 Mahouast M David R and Cognet G 1988 `Periodic phenomenagenerated in the discharge macrow by a Rushton turbine in a CSTR andinvestigation of the Reynolds stressesrsquo Proceedings 6th Europ ConfMixing (Pavia 24plusmn26 May) (BHRA Cranregeld) pp 23plusmn28

144 Mahouast M Nardin P El Rhassouli A and Rondot D 1991`Concentration measurements in a stirred tank using macruorescencespectroscopy and image processingrsquo Proceedings 7th Europ ConfMixing (Brugge 18plusmn20 Sept) (EFCE-KVIV Antwerpen) pp 187plusmn192

145 Mann R Dickin F J Wang M Dyakowski T Forrest A EHolden P J Williams R A and Edwards R B 1997`Visualization of stirred vessel mixing at plant scale using electricalresistance tomographyrsquo in Bertrand J and Villermaux J (Eds)ReAcirccents ProgreAacutes en GeAcircnie des ProceAcircdeAcircs (Lavoisier Paris) 11 (51)pp 3plusmn10

146 Mann R Dickin F J Wang M Dyakowski T Williams R AEdwards R B Forrest A E and Holden P J 1997 Application ofelectrical resistance tomography to interrogate mixing processes atplant scale Chem Eng Sci 52 2087plusmn2097

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148 Manning S A and Jameson G J 1991 À study of ventilated gascavities on disc-turbine bladesrsquo Proceedings 7th Europ Conf Mixing(Brugge 18plusmn20 Sept) (EFCE-KVIV Antwerpen) pp 225plusmn231

149 Mao D M Feng L F Wang K and Li Y L 1997 The mean macrowregeld generated by a pitched blade turbineETHchanges in the circulationpattern due to impeller geometry Can J Chem Eng 75 307plusmn316

150 Marcant B Seidlitz F Plasari E and Villermaux J 1997 `Directmeasurement of the generalized mixing model parameters by laser

sheet visualizationrsquo in Bertrand J and Villermaux J (Eds) ReAcirccentsProgreAacutes en GeAcircniedesProceAcircdeAcircs (Lavoisier Paris) 11 (51) pp 349plusmn356

151 Marmo L Manna L Chiampo F Sicardi S and Bersano G1996 Inmacruence of mixing on the particle size distribution of anorganic precipitate J Crystal Growth 166 1027plusmn1034

152 Mavros P and Baudou C 1997 Quantiregcation of the performanceof agitators in stirred vessels Deregnition and use of an agitation indexChem Eng Res Des 75A 737plusmn745

153 Mavros P Naude I Xuereb C and Bertrand J 1997 LaserDoppler velocimetry in agitated vessels Effect of continuous liquidstream on macrow patterns Chem Eng Res Des 75A 763plusmn776

154 Mavros P Xuereb C and Bertrand J 1996 Determination of 3-Dmacrow regelds in agitated vessels by laser-Doppler velocimetry Effect ofimpeller type and liquid viscosity on liquid macrow patterns Chem EngRes Des 74A 658plusmn668

155 Merchuk J C 1991 Shear effects on suspended cells Adv BiochemEng 44 65plusmn95

156 Mewes D and Renz R 1991 `Jet mixing of liquids in storagetanksrsquo Proceedings 7th Europ Conf Mixing (Brugge 18plusmn20 Sept)(EFCE-KVIV Antwerpen) pp 131plusmn136

157 Michelet S Mahouast M Kemoun A and Mallet J 1997`Turbulence in the discharge of a Rushton turbine and Taylorrsquoshypothesisrsquo in Bertrand J and Villermaux J (Eds) ReAcirccents ProgreAacutesen GeAcircnie des ProceAcircdeAcircs (Lavoisier Paris) 11 (51) pp 89plusmn96

158 Michelet S Mallet J and Mahouast M 1999 `Direct measurementof the turbulent macro-scales in a stirred vessel by two-point LDArsquo inBenkreira H (Ed) Proceedings Symp Fluid Mixing 6 (IChemESymp Ser no 146) (IChemE Rugby) pp 3plusmn13

159 Middleton J C 1979 `Measurement of circulation within largemixing vesselsrsquo Proceedings 3rd Europ Conf Mixing (York 4-6Apr) (BHRA Cranregeld) pp 15plusmn36

160 Mishra V P and Joshi J B 1991 `LDA measurements of macrow instirred gas-liquid reactorsrsquo Proceedings 7th Europ Conf Mixing(Brugge 18plusmn20 Sept) (EFCE-KVIV Antwerpen) pp 217plusmn224

161 Mishra V P and Joshi J B 1993 Flow generated by a disc turbinePart III Effect of impeller diameter impeller location and comparisonwith other radial macrow turbines Chem Eng Res Des 71 563plusmn573

162 Mishra V P Kumar P and Joshi J B 1994 `LDA measurement sof macrow generated by multiple pitched blade turbine impellersrsquoProceedings 8th Europ Conf Mixing (Cambridge 21plusmn23 Sept)(IChemE Rugby) pp 465plusmn472

163 Mishra V P Kumar P and Joshi J B 1998 Flow generated by adisc turbine in aqueous solutions of polyacrylamide Chem Eng J 7111plusmn21

164 Montante G Lee K C Brucato A and Yianneskis M 1999 Anexperimental study of double-to-single-loop transition in stirredvessels Can J Chem Eng 77 649plusmn659

165 Montes J L Boisson H C ForIumlt I and Jahoda M 1997 Velocityregeld macro-instabilities in an axially agitated mixing vessel ChemEng J 67 139plusmn145

166 Morud K E and Hjertager B H 1996 LDA measurements andCFD modelling of gas-liquid macrow in a stirred vessel Chem Eng Sci51 233plusmn249

167 Mukataka S Kataoka H and Takahashi J 1981 Circulation timeand degree of macruid exchange between upper and lower regions in astirred vessel with a dual impeller J Ferment Technol 59 303plusmn307

168 Myers K Reeder M F Bakker A and Dickey D S 1997 Àparametric study of the performance of the Prochem Maxmacro Timpellerrsquo in Bertrand J and Villermaux J (Eds) ReAcirccents ProgreAacutesen GeAcircnie des ProceAcircdeAcircs (Lavoisier Paris) 11 (52) pp 115plusmn122

169 Myers K J Ward R W and Bakker A 1997 A digital particle imagevelocimetry investigation of macrow regeld instabilities of axial-macrowimpellers J Fluids Eng -Transactions of the ASME 119 (3) 623plusmn632

170 Nagase Y Hirofuji Y and Imiya M 1988 `Mixing power and macrowof reciprocating impellers of triangular cross sectionrsquo Proceedings6th Europ Conf Mixing (Pavia 24plusmn26 May) (BHRA Cranregeld)pp 97plusmn102

171 Nagata S 1975 Mixing Principles and Applications (KodanshaTokyo)

172 Nikiforaki L Lee K C and Yianneskis M 1999 `Circulation timemeasurements with miniature radio frequency identiregcation devicesrsquoin Benkreira H (Ed) Fluid Mixing 6 (IChemE Symp Ser no 146)(IChemE Rugby) pp 47plusmn57

173 Nomura T Uchida T and Takahashi K 1997 Enhancement ofmixing by unsteady agitation of an impeller in an agitated vessel JChem Eng Japan 30 875plusmn879



174 Nouri J M and Whitelaw J H 1990 Flow characteristics of stirredreactors with Newtonian and non-Newtonian macruids AIChEJ 36627plusmn629

175 Nouri J M Yianneskis M and Whitelaw J H 1987 `The scalingof the macrow regeld with impeller size and rotational speed in a stirredtankrsquo in Proceedings 2nd Intl Conf Laser AnemometryETHAdvancesand Applications (Strathclyde Sept) paper no 35 pp 489plusmn500

176 Pant H J 2000 Flow rate measurements in a draft tube bafmacrecrystallizer using a radioactive macrow follower technique AppliedRadiation and Isotopes 53 (6) 999plusmn1004

177 Parker D J and McNeil P 1996 Positron emission tomography forprocess applications Meas Sci Technol 7 287plusmn296

178 Parker D J Broadbent C J Fowles P Hawkesworth M R andMcNeil P 1993 Positron emission particle trackingETHa techniquefor studying macrow within engineering equipment Nucl Instr Meth PhysRes A326 592plusmn607

179 Patterson G K Bockelmann W and Quigley J 1982 `Measure-ment of mass transfer rates velocity and concentration macructuations inan industrial stirred tankrsquo Proceedings 4th Europ Conf Mixing(Leeuwenhorst The Netherlands 27plusmn29 April) (BHRA Cranregeld)pp 303plusmn313

180 Perrard M LeSauze N Xuereb C and Bertrand J 2000`Characterization of the turbulence in a stirred tank using particleimage velocimetryrsquo in Van den Akker H E A and Derksen J J(Eds) Proceedings 10

thEurop Conf Mixing (Delft 2plusmn5 July)

(Elsevier Amsterdam) pp 345plusmn352181 Pettersson M and Rasmuson A C 1997 Application of 3-

dimensional phase Doppler anemometry to mechanically agitatedcrystallizers Chem Eng Res Des 75A 132plusmn141 Correction in ChemEng Res Des 75A p U1 (1997)

182 Pitiot P and Falk L 2000 `Characterization of macrow and mixing inan open system by a trajectography methodrsquo in Van den Akker H EA and Derksen J J (Eds) Proceedings 10

thEurop Conf Mixing

(Delft 2plusmn5 July) (Elsevier Amsterdam) pp 337plusmn344183 Plion P Costes J and Couderc J P 1985 `Study by laser

Doppler anemometry of the macrow induced by a propeller in a stirredtankETHinmacruence of bafmacresrsquo in Proceedings 5th European ConferenceMixing (WuEgraverzburg Jun 10plusmn12 1985) (BHRA Cranregeld UK) pp 341plusmn353

184 Rahimi M Buchmann M Mann R and Mewes D 2000Ìnterpretation of macro- and micro-mixing measured by dual-wavelength photometric tomographyrsquo in Van den Akker H E Aand Derksen J J (Eds) Proceedings 10

thEurop Conf Mixing

(Delft 2plusmn5 July) (Elsevier Amsterdam) pp 377plusmn384185 Rahimi M Senior P R and Mann R 1999 Ìmage-reconstruction

3-D visual modelling of stirred vessel mixing for an inclined-bladeimpellerrsquo in Benkreira H (Ed) Fluid Mixing 6 (IChemE Symp Serno 146) (IChemE Rugby) pp 135plusmn145

186 Rahimi M Senior P R and Mann R 2000 Visual 3-D modellingof stirred vessel mixing for an inclined-blade impeller Chem Eng ResDes 78A (3) 348plusmn353

187 Ranade V V and Joshi J B 1989 Flow generated by pitched bladeturbines 1 Measurements using Laser Doppler anemometer ChemEng Comm 81 197plusmn224

188 Ranade V V Mishra V P Saraph V S Deshpande G B andJoshi J B 1992 Comparison of axial macrow impellers using a LaserDoppler anemometer Ind amp Eng Chem Res 31 2370plusmn2379

189 Reed X B Jr Princz M and Hartland S 1977 `Laser Dopplermeasurements of turbulence in a standard stirred tankrsquo in Proceed-ings 2

ndEurop Conf Mixing (Cambridge 30 Marchplusmn1

s tApr)

(BHRA Cranregeld) pp B11plusmnB126190 Resch F J and Abel R 1975 Spectral analysis using Fourier

transform techniques Int J Numer Methods Eng 9 869plusmn902191 Rigby G D Evans G M and Jameson G J 1997 `Cavity

formation behind ventilated impeller bladesrsquo in Bertrand J andVillermaux J (Eds) ReAcirccents ProgreAacutes en GeAcircnie des ProceAcircdeAcircs(Lavoisier Paris) 11 (52) pp 231plusmn238

192 Roesner K G 1997 Flow-regeld visualization by photochromi ccoloring Mol Cryst Liq Cryst 298 243plusmn250

193 RousAEligar I and Van den Akker H E A 1994 `LDA measurements ofliquid velocities in sparged agitated tanks with single and multipleRushton turbinesrsquo Proceedings 8th Europ Conf Mixing (Cambridge21plusmn23 Sept) (IChemE Rugby) pp 89plusmn96

194 Roussinova V and Kresta S M 2000 Ànalysis of macro-instabilities (MI) of the macrow regeld in a stirred tank agitated with axialimpellersrsquo in Van den Akker H E A and Derksen J J (Eds)

Proceedings 10th Europ Conf Mixing (Delft 2plusmn5 July) (ElsevierAmsterdam) pp 361plusmn368

195 Roustan M Meziane A and Faup G 1988 `Circulation anddispersion of gas-liquid induced by agitators with horizontal axes in aclosed loop open channelrsquo Proceedings 6th Europ Conf Mixing(Pavia 24plusmn26 May) (BHRA Cranregeld) pp 381plusmn388

196 Rutherford K Lee K C and Yianneskis M 1994 The interactionof the trailing vortex streams from Rushton turbine blades inProceedings 7th Symp Applications of Laser techniques to FluidMechanics (Lisbon Portugal) vol 1 pp 1021plusmn1027

197 SchaEgravefer M HoEgravefken M and Durst F 1997 Detailed LDVmeasurements for visualization of the macrow-regeld within a stirred-tank reactor equipped with a Rushton turbine Chem Eng Res Des75A 729plusmn736

198 SchaEgravefer M WaEgravechter P and Durst F 2000 Èxperimentalinvestigation of local bubble size distributions in stirred vesselsusing phase Doppler anemometryrsquo in Van den Akker H E A andDerksen J J (Eds) Proceedings 10

thEurop Conf Mixing (Delft 2plusmn

5 July) (Elsevier Amsterdam) pp 205plusmn212199 SchaEgravefer M Yianneskis M WaEgravechter P and Durst F 1998 Trailing

vortices around a 45-degrees pitched-blade impeller AIChEJ 441233plusmn1246

200 Schmitz D and Mewes D 2000 Tomographic imaging of transientmultiphase macrow in bubble columns Chem Eng J 77 (1plusmn2) 99plusmn104

201 Schoenmakers J H A Wijers J G and Thoenes D 1997`Determination of feed stream mixing rates in agitated vesselsrsquo inBertrand J and Villermaux J (Eds) ReAcirccents ProgreAacutes en GeAcircnie desProceAcircdeAcircs (Lavoisier Paris) 11 (52) pp 185plusmn192

202 SIumledivyAcirc V Ditl P Severa M and Rieger F 1999 `Dimensionlessmacrow characteristics in mixed suspension obtained by LDAPDArsquo inBenkreira H (Ed) Fluid Mixing 6 (IChemE Symp Ser no 146)(IChemE Rugby) pp 373plusmn381

203 Serrano-Carreon L and Galindo E 1997 `Studies on caverndevelopment in mixing a yield stress macruid in a pilot-scale proto-fermenterrsquo in Bertrand J and Villermaux J (Eds) ReAcirccents ProgreAacutesen GeAcircnie des ProceAcircdeAcircs (Lavoisier Paris) 11 (51) pp 161plusmn168

204 Sharp K V Kim K C and Adrian R J 1998 `Dissipationestimation around a Rushton turbine using particle image velocime-tryrsquo Proceedings 9th Int Symp Applications of Laser techniques toFluid Mechanics (Lisbon) 10 pp

205 Shimizu K Nagasawa H and Takahasi K 1995 Effect of off-bottom clearance of a turbine type impeller on crystal size distributionof aluminum potassium sulfate in a batch crystallizer J CrystalGrowth 154 113plusmn117

206 Soliman M and Bertrand J 1986 Àgitation by helical ribbons Powerconsumption mixing time and local velocitiesrsquo Proceedings III WorldCongress Chemical Engineering (Tokyo) pp 398plusmn400

207 Solomon J Elson T P Nienow A W and Pace G W 1981Cavern sizes in agitated macruids with a yield stress Chem Eng Commun11 143plusmn164

208 Spicer P T Keller W and Pratsinis S E 1996 The effect ofimpeller type on macroc size and structure during shear-inducedmacrocculation J Colloid Interface Sci 184 112plusmn122

209 Stanley S J and Smith D W 1995 Measurement of turbulent macrowin standard jar test apparatus J Env Eng 121 902plusmn910

210 Tiljander P Ronnmark B and Theliander H 1997 Characteriza-tion of 3 different impellers using the LDV technique Can J ChemEng 75 787plusmn793

211 Unger D R and Muzzio F J 1999 Laser-induced macruorescencetechnique for the quantiregcation of mixing in impinging jets AIChEJ45 (12) 2477plusmn2486

212 van der Molen K and Van Maanen H R E 1978 Laser Dopplermeasurements of the turbulent macrow in stirred vessels to establishscaling rules Chem Eng Sci 33 1161plusmn1168

213 Voncken R M Goetzee W J J and Beek W J 1978 `Circulationmacrow and mixing at low Reynolds numbersrsquo Proceedings Int SympMixing (Mons 21plusmn24 Feb) pp A51plusmn19

214 WaEgravechter P Steidl W HoEgravefken M and Durst F 1996 Àpplicationof the ultrasound velocity measuring technique to stirred vesselmacrowsrsquo in Takeda Y and Ravoux J-F (Eds) Proceedings 1

s tIntern

Symp Ultrasonic Doppler Methods in Fluid Mechanics and FluidEngineering (Paul Scherer Institute Villigen Switzerland 9plusmn11Sept) vol II pp 31plusmn62

215 Wang M Dorward A Vlaev D and Mann R 2000 Measure-ments of gasplusmnliquid mixing in a stirred vessel using electricalresistance tomography (ERT) Chem Eng J 77 (1plusmn2) 93plusmn98

126 MAVROS


216 Wang M Mann R and Dickin F J 1999 Electrical resistancetomographic sensing systems for industrial applications Chem EngCommun 175 49plusmn70

217 Wang X and Qian N 1989 Turbulence characteristics of sediment-laden macrow J Hydr Eng 115 781plusmn800

218 Wang X and Qian N 1992 Velocity proregles of sediment-ladenmacrow Int J Sediment Res 7 27plusmn58

219 Weetman R J 1991 `Development of transitional macrow mixingimpellerrsquo Proceedings 7th Europ Conf Mixing (Brugge 18plusmn20Sept) (EFCE-KVIV Antwerpen) pp 25plusmn31

220 Werner F and Mersmann A 1997 `New equations for thedetermination of the local speciregc power input Eloc and themacroscale of turbulence Amacroc from measured rms-values u macroc inNewtonian and shear-thinning power law macruidsrsquo in Bertrand J andVillermaux J (Eds) ReAcirccents ProgreAacutes en GeAcircnie des ProceAcircdeAcircs(Lavoisier Paris) 11 (51) pp 129plusmn136

221 West R M Jia X and Williams R A 2000 Parametric modellingin industrial process tomography Chem Eng J 77 (1plusmn2) 31plusmn36

222 Westerweel J Fundamental s of digital particle image velocimetryMeasurement Science amp Technology 8 1379plusmn1392

223 Williams R A Jia X and McKee S L 1996 Development ofslurry mixing models using resistance tomography Powder Tech 8721plusmn27

224 Wittmer S Falk L Pitiot P and Vivier H 1998 Characterizationof stirred vessel hydrodynamic s by three-dimensiona l trajectographyCan J Chem Eng 76 600plusmn610

225 Wolf D and Manning F S 1966 Impact tube measurement of macrowpatterns velocity proregles and pumping capacities in mixing vesselsCan J Chem Eng 44 137plusmn142

226 Wong C W and Huang C T 1988 `Flow characteristics andmechanical efregciency in bafmacred stirred tanks with turbine impellersrsquoProceedings 6th Europ Conf Mixing (Pavia 24plusmn26 May) (BHRACranregeld) pp 29plusmn34

227 Wu H and Patterson G K 1989 Laser-Doppler measurement s ofturbulent-macrow parameters in a stirred mixer Chem Eng Sci 442207plusmn2221

228 Wu J Pullum L Yunken R and Welsh M C 1997 Rapiddiagnosis of macrow separation around an axial impeller in a mixingvessel Experiments in Fluids 22 519plusmn522

229 Wu P P Feldkamp J R Hem S L and White J L 1986Monitoring particle interactions in aqueous suspensions by regber opticDoppler anemometry J Colloid Interf Sci 110 398plusmn409

230 Xuereb C Riba J P Bertrand J and Bousquet J 1991 Àpplicationof hot reglm anemometry technique in an agitated tower tank reglled with anon-Newtonian solutionrsquo Proceedings 7th Europ Conf Mixing(Brugge 18plusmn20 Sept) (EFCE-KVIV Antwerpen) pp 145plusmn152

231 Yianneskis M 1991 `The effect of macrow rate and tracer insertiontime on mixing times in jet-agitated vesselsrsquo Proceedings 7th EuropConf Mixing (Brugge 18plusmn20 Sept) vol I pp 121plusmn128

232 Yianneskis M Popiolek Z and Whitelaw J H 1987 Anexperimental study of the steady and unsteady macrow characteristicsof stirred reactors J Fluid Mech 175 537plusmn555

233 Youcereg A Anne-Archard D Boisson H C and Sengelin M1997 On the inmacruence of liquid elasticity on mixing in a vesselagitated by a two-bladed impeller Trans ASME 119 616plusmn622

234 Youcereg A Anne-Archard D Boisson H C Sengelin M andBertrand J 1992 ÈAcirc tude numerique et experimentale de lrsquoeAcirccoule-ment drsquoun macruide visco-eAcirclastique autour drsquoun agitateur bipale en cuveagiteAcircersquo in Bertrand J (ed) Proceedings Forum drsquoAgitationIndustrielle (Toulouse 27plusmn29 Jan 1992) ENSIGC Toulousepp I1plusmnI8

235 Youcereg A Gaudu R Bertrand J Anne-Archard D and SengelinM 1992 `Mechanical agitation of viscoelastic macruids by a two-bladedstirrerrsquo Proceedings 1992 IChemE Research Event (ManchesterUK) pp 377plusmn379

236 Yu Z and Rasmuson EcircAC 1999 Projected area of measurementvolume in phase-Dopple r anemometry and application for velocitybias correction and particle concentration estimation Exp in Fluids27 189plusmn198

237 Zannoud N Guiraud P Costes J and Bertrand J 1991 `Locallaser measurement s of velocities and concentrations in two contin-uous systems a tubular jet-stirred reactor and a stirred vesselrsquoProceedings 7th Europ Conf Mixing (Brugge 18plusmn20 Sept) (EFCE-KVIV Antwerpen) pp 173plusmn180

238 Zhang J Tao B and Katz J 1997 Turbulent macrow measurement ina square duct with hybrid holographic PIV Exp in Fluids 23 373plusmn381

239 Zhou G and Kresta S 1996 Distribution of energy betweenconvective and turbulent macrow for three used impellers Chem Eng ResDes 74A 379plusmn389

240 Zlokarnik M and Judat H 1988 `Stirringrsquo in Elvers BRavenscroft M Rounsaville J F and Schulz G (Eds) UllmannrsquosEncyclopedia of Industrial Chemistry 5th Ed (VCH Weinheim) volB2 pp 251-2533

ACKNOWLEDGEMENTS

Thanks are due to Professor A W Nienow for his valuable commentsand suggestions Thanks also to the European Union for the partial regnancialsupport of this work (contract BRITE-EURAM BRRT CT97 5035) and tothe IChemE (UK) Lavoisier Publishers (Paris France) Elsevier (TheNetherlands) and VCH (Germany) copyright holders for their permissionto reproduce Figures 1(a) 8(a) 9 and 11

ADDRESS

Correspondenc e concerning this paper should be addressed toDr P Mavros Department of Chemistry Aristotle University GR-54006Thessaloniki Greece

The manuscript was received 14 February 2000 and accepted forpublication after revision 31 October 2000



techniques however allowed the detailed study of the macrowsin the various parts of the vessel and the results indicatedthat it may be necessary to re-deregne the macrow patternsinduced by the various impellers For example a detailedmacrow mapping using laser Doppler velocimetry showed thataxial impellers leave a substantial part of the macruid in theupper part of the vessel poorly agitated often with velocitieslower than 10 of the agitator tip speed154 and that with aRushton turbine the upper circulation loop is narrower thanexpected with the macruid in the region near the upper vesselwall agitated in a secondary macrow loop (Figure 1)

In the following sections the sophisticated macrow mappingmeasuring techniques that are nowadays available will bediscussed in conjunction with the oldersimpler ones Thesewill be separated in two categories

middot single-poin t measuring techniques which determine thevelocity (or one of the velocity vector components) at aset point within the vessel and

middot ensemble-measuring techniques which determine themacrow pattern simultaneously in a wider region of the bulkof the agitated macruid

SINGLE-POINT TECHNIQUES

Pitot Tubes

Velocimetry should not be considered as a noveltechnique in 1724 Henri de Pitot (1695plusmn1771) devized

the Pitot tube to measure water velocities in rivers and thiswas later developed for measuring macrows in closed conduitsvessels etc Its principle of operation is simple when macrow isdirected against an obstacle eg a tube it is demacrectedtowards the sides of the obstacle while the macrow pressure atthe obstacle tip (pt) rises above the ambient (mainstream)level (pa) By measuring the pressure difference at the tip ofthe obstacle and the mainstream macrow it is possible tocalculate the macrow velocity (u) using a simplireged Bernoulliequation

u

2 pt pa

r

r1

where r is the density of the macrowing macruid Special pressureprobes were developed of which the `Prandtlrsquo probe isprobably the most common a hole at the tip and one on theside of the probe measure both pressures at once Usuallythe two pressures are measured at the same U-manometerwhich is reglled with a macruid having a density rm different fromr (Figure 2) and equation 1 simplireges

u

2 rm r gh

r

s

2

Velocity however is a vector and probes have beendeveloped that are capable of determining simultaneouslytwo or even all three vector components (ur uz and uv) Inorder to avoid errors in pa measurement due to macruid motionthe hole size is drilled as small as possibleETHusually of theorder of tenths of a millimetre Novel designs of Pitot tubescomprise miniature piezoresistive pressure sensor chips forpressure measurement allowing for direct measurement ofpressure differences and availability of the velocity data inreadily-usable electronic form

The Pitot tube has been used to measure velocities instirred vessels96171217225 It should also be noted that it hasboth a disadvantage and an advantage

middot the probe is intrusive and this may affect the macrow patternespecially in small- and medium-size vessels

middot the tube is useful for measuring velocities in solid-liquid gas-liquid or gas-liquid-soli d dispersions217218 wherethe bubbles andor solid particles motion may interferewith other liquid-velocity determination techniques aswell as in large-scale vessel velocity measurementswhere other techniques eg laser Doppler velocimetrymay not be practicable

114 MAVROS


Figure 1 Illustration of the departure of `standardrsquo from actual macrowpatterns (a) `standardrsquo Rushton-turbine macrow pattern

240 (b) macrow pattern

determined by LDV154

Figure 2 Pitot tube89

Hot-wire Anemometry









df

l

2 sin f3


u fD df 4







91



154




84 97 98 99 100 101103107 plusmn 114 116 118120121125132 133 136137


183 187188189193 194 196 197199202210212217 218 plusmn 220227229











Simple Imaging





others102105138148150213231

116 MAVROS








Flow-Followers






Colour Change




Thermography

















118 MAVROS










Tomography







29






CONCLUSIONS


120 MAVROS



90


92

APPENDIX 1


uij Aringui uij A1


Aringui

1

N

XN

j 1

uij i r z v A2


uirms u 2i

12 1

N

XN

j 1

uij Aringui2

Aacute 12

i r z v

A3


Iu 2

r u 2z u 2

v12

u2r u2

z u2v

12A4


k1

2u 2

r u 2z u 2

v A5


e Cu 3

LA6


Li Aringuiti A7


ti

hellipyen

0

Ri dt A8


Ri

ui t ui t Dt

u 2i

A9


NOMENCLATURE



plusmn1





92


2s

plusmn3


plusmn3



REFERENCES













thEurop Conf Mixing










thEurop Conf

























122 MAVROS



















thEurop Conf





ndEd















































th



























124 MAVROS




























































thEurop Conf Mixing




thEurop Conf Mixing








s tApr)






























s tIntern



126 MAVROS



























ACKNOWLEDGEMENTS


ADDRESS





Hot-wire Anemometry









df

l

2 sin f3


u fD df 4







91



154




84 97 98 99 100 101103107 plusmn 114 116 118120121125132 133 136137


183 187188189193 194 196 197199202210212217 218 plusmn 220227229











Simple Imaging





others102105138148150213231

116 MAVROS








Flow-Followers






Colour Change




Thermography

















118 MAVROS










Tomography







29






CONCLUSIONS


120 MAVROS



90


92

APPENDIX 1


uij Aringui uij A1


Aringui

1

N

XN

j 1

uij i r z v A2


uirms u 2i

12 1

N

XN

j 1

uij Aringui2

Aacute 12

i r z v

A3


Iu 2

r u 2z u 2

v12

u2r u2

z u2v

12A4


k1

2u 2

r u 2z u 2

v A5


e Cu 3

LA6


Li Aringuiti A7


ti

hellipyen

0

Ri dt A8


Ri

ui t ui t Dt

u 2i

A9


NOMENCLATURE



plusmn1





92


2s

plusmn3


plusmn3



REFERENCES













thEurop Conf Mixing










thEurop Conf

























122 MAVROS



















thEurop Conf





ndEd















































th



























124 MAVROS




























































thEurop Conf Mixing




thEurop Conf Mixing








s tApr)






























s tIntern



126 MAVROS



























ACKNOWLEDGEMENTS


ADDRESS







84 97 98 99 100 101103107 plusmn 114 116 118120121125132 133 136137


183 187188189193 194 196 197199202210212217 218 plusmn 220227229











Simple Imaging





others102105138148150213231

116 MAVROS








Flow-Followers






Colour Change




Thermography

















118 MAVROS










Tomography







29






CONCLUSIONS


120 MAVROS



90


92

APPENDIX 1


uij Aringui uij A1


Aringui

1

N

XN

j 1

uij i r z v A2


uirms u 2i

12 1

N

XN

j 1

uij Aringui2

Aacute 12

i r z v

A3


Iu 2

r u 2z u 2

v12

u2r u2

z u2v

12A4


k1

2u 2

r u 2z u 2

v A5


e Cu 3

LA6


Li Aringuiti A7


ti

hellipyen

0

Ri dt A8


Ri

ui t ui t Dt

u 2i

A9


NOMENCLATURE



plusmn1





92


2s

plusmn3


plusmn3



REFERENCES













thEurop Conf Mixing










thEurop Conf

























122 MAVROS



















thEurop Conf





ndEd















































th



























124 MAVROS




























































thEurop Conf Mixing




thEurop Conf Mixing








s tApr)






























s tIntern



126 MAVROS



























ACKNOWLEDGEMENTS


ADDRESS







Flow-Followers






Colour Change




Thermography

















118 MAVROS










Tomography







29






CONCLUSIONS


120 MAVROS



90


92

APPENDIX 1


uij Aringui uij A1


Aringui

1

N

XN

j 1

uij i r z v A2


uirms u 2i

12 1

N

XN

j 1

uij Aringui2

Aacute 12

i r z v

A3


Iu 2

r u 2z u 2

v12

u2r u2

z u2v

12A4


k1

2u 2

r u 2z u 2

v A5


e Cu 3

LA6


Li Aringuiti A7


ti

hellipyen

0

Ri dt A8


Ri

ui t ui t Dt

u 2i

A9


NOMENCLATURE



plusmn1





92


2s

plusmn3


plusmn3



REFERENCES













thEurop Conf Mixing










thEurop Conf

























122 MAVROS



















thEurop Conf





ndEd















































th



























124 MAVROS




























































thEurop Conf Mixing




thEurop Conf Mixing








s tApr)






























s tIntern



126 MAVROS



























ACKNOWLEDGEMENTS


ADDRESS
















118 MAVROS










Tomography







29






CONCLUSIONS


120 MAVROS



90


92

APPENDIX 1


uij Aringui uij A1


Aringui

1

N

XN

j 1

uij i r z v A2


uirms u 2i

12 1

N

XN

j 1

uij Aringui2

Aacute 12

i r z v

A3


Iu 2

r u 2z u 2

v12

u2r u2

z u2v

12A4


k1

2u 2

r u 2z u 2

v A5


e Cu 3

LA6


Li Aringuiti A7


ti

hellipyen

0

Ri dt A8


Ri

ui t ui t Dt

u 2i

A9


NOMENCLATURE



plusmn1





92


2s

plusmn3


plusmn3



REFERENCES













thEurop Conf Mixing










thEurop Conf

























122 MAVROS



















thEurop Conf





ndEd















































th



























124 MAVROS




























































thEurop Conf Mixing




thEurop Conf Mixing








s tApr)






























s tIntern



126 MAVROS



























ACKNOWLEDGEMENTS


ADDRESS











Tomography







29






CONCLUSIONS


120 MAVROS



90


92

APPENDIX 1


uij Aringui uij A1


Aringui

1

N

XN

j 1

uij i r z v A2


uirms u 2i

12 1

N

XN

j 1

uij Aringui2

Aacute 12

i r z v

A3


Iu 2

r u 2z u 2

v12

u2r u2

z u2v

12A4


k1

2u 2

r u 2z u 2

v A5


e Cu 3

LA6


Li Aringuiti A7


ti

hellipyen

0

Ri dt A8


Ri

ui t ui t Dt

u 2i

A9


NOMENCLATURE



plusmn1





92


2s

plusmn3


plusmn3



REFERENCES













thEurop Conf Mixing










thEurop Conf

























122 MAVROS



















thEurop Conf





ndEd















































th



























124 MAVROS




























































thEurop Conf Mixing




thEurop Conf Mixing








s tApr)






























s tIntern



126 MAVROS



























ACKNOWLEDGEMENTS


ADDRESS










CONCLUSIONS


120 MAVROS



90


92

APPENDIX 1


uij Aringui uij A1


Aringui

1

N

XN

j 1

uij i r z v A2


uirms u 2i

12 1

N

XN

j 1

uij Aringui2

Aacute 12

i r z v

A3


Iu 2

r u 2z u 2

v12

u2r u2

z u2v

12A4


k1

2u 2

r u 2z u 2

v A5


e Cu 3

LA6


Li Aringuiti A7


ti

hellipyen

0

Ri dt A8


Ri

ui t ui t Dt

u 2i

A9


NOMENCLATURE



plusmn1





92


2s

plusmn3


plusmn3



REFERENCES













thEurop Conf Mixing










thEurop Conf

























122 MAVROS



















thEurop Conf





ndEd















































th



























124 MAVROS




























































thEurop Conf Mixing




thEurop Conf Mixing








s tApr)






























s tIntern



126 MAVROS



























ACKNOWLEDGEMENTS


ADDRESS





APPENDIX 1


uij Aringui uij A1


Aringui

1

N

XN

j 1

uij i r z v A2


uirms u 2i

12 1

N

XN

j 1

uij Aringui2

Aacute 12

i r z v

A3


Iu 2

r u 2z u 2

v12

u2r u2

z u2v

12A4


k1

2u 2

r u 2z u 2

v A5


e Cu 3

LA6


Li Aringuiti A7


ti

hellipyen

0

Ri dt A8


Ri

ui t ui t Dt

u 2i

A9


NOMENCLATURE



plusmn1





92


2s

plusmn3


plusmn3



REFERENCES













thEurop Conf Mixing










thEurop Conf

























122 MAVROS



















thEurop Conf





ndEd















































th



























124 MAVROS




























































thEurop Conf Mixing




thEurop Conf Mixing








s tApr)






























s tIntern



126 MAVROS



























ACKNOWLEDGEMENTS


ADDRESS






2s

plusmn3


plusmn3



REFERENCES













thEurop Conf Mixing










thEurop Conf

























122 MAVROS



















thEurop Conf





ndEd















































th



























124 MAVROS




























































thEurop Conf Mixing




thEurop Conf Mixing








s tApr)






























s tIntern



126 MAVROS



























ACKNOWLEDGEMENTS


ADDRESS






















thEurop Conf





ndEd















































th



























124 MAVROS




























































thEurop Conf Mixing




thEurop Conf Mixing








s tApr)






























s tIntern



126 MAVROS



























ACKNOWLEDGEMENTS


ADDRESS






















th



























124 MAVROS




























































thEurop Conf Mixing




thEurop Conf Mixing








s tApr)






























s tIntern



126 MAVROS



























ACKNOWLEDGEMENTS


ADDRESS































































thEurop Conf Mixing




thEurop Conf Mixing








s tApr)






























s tIntern



126 MAVROS



























ACKNOWLEDGEMENTS


ADDRESS






























ACKNOWLEDGEMENTS


ADDRESS





Flow Visualization in Stirred Vessels: A Review of Experimental ...

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Transcript of Flow Visualization in Stirred Vessels: A Review of Experimental ...