0263 ±8762/01/$10.00+0.00 q Institution of Chemical Engineers Trans IChemE, Vol. 79, Part A, March 2001 REVIEW PAPER FLOW VISUALIZATION IN STIRRED VESSELS A Review of Experimental Techniques P. MAVROS Department of Chemistry, Aristotle University, Thessaloniki, Greece S tirred vessels are being used not only in chemical processes for simple contacting or blending operations, but also in novel con®gurations and processes, as in mineral processing and/or wastewater treatment, with speci®c requirements, like low shear or regions in the vessel with high and low turbulence levels. The techniques that are available for the study of the ¯ow patterns induced by the various types of agitators, e.g., classical pressure or velocity measurements with Pitot tubes or hot-wire anemometers, and novel ones like laser Doppler velocimetry, laser-induced ¯uorescence and particle image velocimetry are reviewed and their usefulness for particular situations is discussed. Keywords: mixing, agitation ; stirred vessel; ¯ow visualization ; review; laser; LDV; LDA; PIV; thermography; trajectography ; ¯ow-follower. The suitability of a particular agitator for a given mixing process depends on its capability to induce the ¯uid contents of the vessel into vigorous circulation, avoiding situations where regions of the ¯uid(s) are poorly mixed or not mixed at all, while at the same time avoiding damaging the various species dispersed in it, which are sometimes shear-sensitive, e.g. cell cultures, or crystals2,49,106 ,20 8 . It is therefore necessary to determine, for each type of impeller: INTRODUCTION Stirred vessels are widely used for various purposes, often comprizing several phases: · to combine miscible liquids or to disperse one immiscible liquid into another; · to disperse solid particles in a liquid, often followed by another process, e.g., leaching, ¯otation, chemical reaction; · to disperse a gas into a liquid, usually followed either by absorption and/or by a chemical reaction between the liquid and the gaseous species; or · to disperse a solid (e.g., a catalyst) and a gas into a liquid medium, to cause a reaction. 1) the ¯ow pattern induced in an vessel, as a function of: a) the internal vessel con®guration (baf¯es, coils, vessel bottom form, etc.); b) the ¯uid properties (viscosity, number of phases, densities, etc.); c) the location and mode of operation of the agitator (clearance, ¯ow-pumping direction); 2) and the suitability of the impeller for a particular application (e.g., low-shear or high-shear requirement). For each particular application, a different con®guration is appropriate; the design of stirred vessels has been the object of numerous studies throughou t several decades, and the principal design rules are incorporated in standards of various countries (ASME Code Section VIII, DIN 28136, among others). However, agitation is involve d in other processes, too: · new applications, like fermentation or crystallization, or · other processes, which till now were not included in the `classical’ chemical process area, like wastewater treatment, mineral processing, etc. Flow patterns induced by an agitator were a ®rst indication of its suitability for a particular application. Initially, merely watching the ¯uid, or possibly using some coloured material to identify the major circulation patterns was suf®cient; later, simple measuring techniques, like the Pitot tube, were used to quantify the velocity maps. These techniques allowed the identi®cation of the basic type of circulation established in a stirred vessel: for example, it was found that a 6-blade `standard’ Rushton turbine (RT) would create two toroidally-shape d ¯ow loops in the vessel, one in the lower and one in the upper part of the vessel, while an axial impellerÐe.g., a marine propeller, a pitchedblade turbine (PBT), among othersÐwould create essentially a single loop around the impeller. These patterns were widely accepted and incorporated in widely-read references171,240 ; the use of more sophisticated In these processes, the end product depends not only on the physicochemical aspects of the particular process, e.g., its reaction kinetics, but also on the pattern of species contacting, on the level of energy dissipation , the vessel con®guration etc.32,54,151,155,195,205,209 . Attempting to investigate and/or optimize these processes necessitates the re-assessment of the existing knowledge and even the development of novel con®gurations or equipment20,219 . 113 114 MAVROS Figure 2. Pitot tube8 9. the Pitot tube to measure water velocities in rivers and this was later developed for measuring ¯ows in closed conduits, vessels, etc. Its principle of operation is simple: when ¯ow is directed against an obstacle, e.g., a tube, it is de¯ected towards the sides of the obstacle, while the ¯ow pressure at the obstacle tip (pt ) rises above the ambient (mainstream) level (pa ). By measuring the pressure difference at the tip of the obstacle and the mainstream ¯ow, it is possible to calculate the ¯ow velocity (u) using a simpli®ed Bernoulli equation: r 2 pt pa u 1 r Figure 1. Illustration of the departure of `standard’ from actual ¯ow patterns: (a) `standard’ Rushton-turbine ¯ow pattern24 0; (b) ¯ow pattern determined by LDV15 4. techniques, however, allowed the detailed study of the ¯ows in the various parts of the vessel and the results indicated that it may be necessary to re-de®ne the ¯ow patterns induced by the various impellers. For example, a detailed ¯ow mapping, using laser Doppler velocimetry showed that axial impellers leave a substantial part of the ¯uid in the upper part of the vessel poorly agitated, often with velocities lower than 10% of the agitator tip speed154 , and that with a Rushton turbine the upper circulation loop is narrower than expected, with the ¯uid in the region near the upper vessel wall agitated in a secondary ¯ow loop (Figure 1). In the following sections, the sophisticate d ¯ow mapping measuring techniques that are nowadays available will be discussed, in conjunction with the older/simpler ones. These will be separated in two categories: · single-poin t measuring techniques, which determine the velocity (or one of the velocity vector components) at a set point within the vessel; and · ensemble-measuring techniques, which determine the ¯ow pattern simultaneously in a wider region of the bulk of the agitated ¯uid. SINGLE-POINT TECHNIQUES Pitot Tubes Velocimetry should not be considered as a novel technique; in 1724, Henri de Pitot (1695 ±1771) devized where r is the density of the ¯owing ¯uid. Special pressure probes were developed, of which the `Prandtl’ probe is probably the most common: a hole at the tip and one on the side of the probe measure both pressures at once. Usually the two pressures are measured at the same U-manometer, which is ®lled with a ¯uid having a density rm different from r (Figure 2), and equation 1 simpli®es: s 2 rm r gh u 2 r Velocity, however, is a vector, and probes have been developed that are capable of determining simultaneously two or even all three vector components (ur , uz and uv ). In order to avoid errors in pa measurement due to ¯uid motion, the hole size is drilled as small as possibleÐusually of the order of tenths of a millimetre. Novel designs of Pitot tubes comprise miniature piezoresistive pressure sensor chips for pressure measurement, allowing for direct measurement of pressure differences and availability of the velocity data in readily-usable electronic form. The Pitot tube has been used to measure velocities in stirred vessels96,171,217,225 . It should also be noted that it has both a disadvantage and an advantage: · the probe is intrusive , and this may affect the ¯ow pattern, especially in small- and medium-size vessels; · the tube is useful for measuring velocities in solid-liquid , gas-liquid or gas-liquid-soli d dispersions217,218 , where the bubbles and/or solid particles motion may interfere with other liquid-velocit y determination techniques, as well as in large-scale vessel velocity measurements, where other techniques, e.g. laser Doppler velocimetry, may not be practicable. Trans IChemE, Vol 79, Part A, March 2001 FLOW VISUALIZATION IN STIRRED VESSLES 115 Figure 3. Schematics of (a) a 2-wire hot-wire95 and (b) a 3-wire anemometer probe9 1. Hot-wire Anemometry Hot wire anemometry is another technique, which was used in the recent past to measure liquid velocities in stirred vessels, and is still used for air/gas velocity measurements. It is based on the sensing and measurement of the rate of cooling of a ®ne, electrically heated wire36,58 . The wire is usually made of tungsten, platinum, or platinum-iridium ; its diameter is typically < 5 mm, with a length of 1 to 2 mm. By combining several wires on the same probe (Figure 3), it is possible to measure simultaneously all three components of the velocity vector. An alternative to wires is the hot-®lm sensor: this is a small-diameter solid, non-conductiv e quartz cylinder, on which a very thin layer of platinum is deposited. When the probe is to be used in liquids, a quartz or alumina coating is applied on top of the ®lm, in order to avoid erosion effects due to impinging particles, which are dispersed in the liquid. Hot-wire anemometry has been used to study the characteristics of both steady and unsteady ¯ow ®elds19,37,39,71,130,134,135,171,206,207,226,230,23 5 . Advances in the understandin g of the functional dependence of the heat transfer from the wire on velocity, density, temperature, and ¯ow angle led to greater measurement accuracy. Accurate measurements may thus be obtained in a wide variety of ¯uids: gases, liquids, conducting liquid metals, etc., and over a wide range of environmental conditions. Laser-Doppler Velocimetry The development of the laser technology, in the 1960s, resulted in the emergence of a new measuring technique for velocities, the Laser Doppler Velocimetry (LDV)Ðwhich should not be confused with anemometry, which applies the same measuring principles to the determination of velocities in gases. LDV has an important advantage over previous techniques since the probe lies outside the stirred vessel, it does not interfere with the ¯ow pattern. The technique is rather simple1 : a laser beam is split, and the two resulting coherent beams are made to cross at some point inside the stirred vessel (Figure 4); in the intersection volume, parallel interference fringes are formed. When a small particle crosses this small volume, it scatters light which is captured by a photodetector. By analysing the change in the intensity ¯uctuations on the photodetector, it Figure 4. Intersection of two coherent laser beams. Trans IChemE, Vol 79, Part A, March 2001 Figure 5. Experimental setup for the determination of two of the three velocity vector components . is possible to determine the velocity of the particle crossing the intersection volume59 . In practice, the frequency of one of the beams is slightly shifted, using a `Bragg’ cell; this change causes the fringe pattern to pulsate at a steady frequency. When a particle crosses the fringe volume, it affects this pulsating frequency and this is registered by the photomultiplie r as a Doppler shift frequency, fD ; since fD is related to the particle velocity (u) and the fringe spacing (df ): l 3 df 2 sin f (where 2f is the angle between the two beams and l is the light wavelength), it is possible to determine the latter: u fD df 4 The velocity component measured by LDV is the one that lies in the plane of the beams and which is normal to the bisector of the two laser beams. By combining two sets of double beams, it is possible to determine at the same time two of the three velocity vector components (Figure 5). Also, by installing the optical equipment on a traversing system (Figure 6), which allows the beam intersection to be located at various places inside the stirred vessel, velocities at various places may be determined fairly easily. The velocities, which are determined by the LDV system, are usually stored as time series on a computer which is coupled to the system. Subsequent numerical analysis yields the mean and the r.m.s. velocity Ðsee Appendix 1Ðfor the velocity vector component at the point of measurement. Figure 6. Typical experimental setup: (1) laser; (2,3) ®ber-optical module; (4) torque measuring coupler; (5) motor; (6) photomultipliers; (7) ¯ow velocity analyser; (8) oscilloscope; (9) computer.15 4. 116 MAVROS minute particles moving with the liquid. The velocity of the ¯uid is determined by the change in frequency of the emitted and re¯ected ultrasonic wave, and is related to the velocity of sound in the ¯uid medium and the angle v with respect to the propagation direction of the pulse. By transmitting a series of pulses and capturing the echoes, it is possible to determine almost simultaneously the ¯uid velocity at various depths (the number of `channels’ is ®xed by the instrumentation) . One drawback of this technique is the widening intensity lobe, which is related to the wavelength of the emitted wave and the radius of the transducer; this widening means that the deeper one measures from the surface of the transducer, the wider the region to which the determined average velocity applies. Another potential problem is the artifacts generated by moving surfaces within the measuring region94 . The technique has been used to determine the velocity maps in a stirred vessel for a hyperboloi d stirrer with D T/4 at a very low clearance (C T /40) 214 . ENSEMBLE MEASUREMENTS Figure 7. Illustration of the suitability of velocity sampling: (a) appropriate velocity sampling; (b) poor sampling. It should be noted, here, that for a velocity time series to be useful, it must have followed accurately the ¯ow history: for a slow-changing ¯ow, a few data are perhaps suf®cient, but for fast-changing ¯ows, like the ones encountered in a stirred vessel, the frequency of sampling must be at least twice as large as the dominant frequency of the process190 . Figure 7(b) illustrates the case of a sub-sampled process: the ¯ow history in this case is erroneous and not accurately representative of the investigated ¯ow. Laser Doppler velocimetry has been used extensively since its appearance to measure velocities in stirred vessels; an extensive body of literature covers a variety of vesselimpeller con®gurations; single-agitato r systems, tall con®guration (H $ 2T) vessels, where a second agitator is necessary to agitate the upper part of the vessel contents, agitatorless systems, Newtonian and non-Newtonian liquids etc.5 ± 8,14,15,17,2 1,34, 38 , 39 , 40 , 44 , 45 , 49, 51, 54, 57, 61, 66, 70, 74,75,79,81,82, Ensemble-measuring techniques encompass attempts to identify the pseudo-2-dimensiona l ¯ow pattern in a stirred vessel by capturing the velocities across a whole region, rather than at a single point. Simple Imaging Still pictures A still picture of the vessel is taken and the major circulation patterns are identi®ed from it, e.g.,191 . Streak lines An improvement of the technique has been the dispersion of small, neutrally-buoyan t particles in the liquid, so that their movement appears on the picture as streamlines (Figure 8). The illuminatio n of the vessel contents by a strong light source, e.g., a laser sheet, yields qualitative results regarding the major ¯ow patterns in the stirred vessel. The technique has been used to study the effect of various factors on the ¯ow pattern: ¯ow rates, impeller spacing, non-Newtonian liquid mixing, among others 102,105,138,148,150,213 ,231 . 8 4, 97 , 9 8, 99 , 1 00 ,1 01,1 03,10 7 ± 114 ,1 16 ,1 18,12 0,12 1,12 5,132 ,1 33 ,1 36,13 7, 139 ± 143,149,152 ± 154, 156, 157,158,160 ± 162,163 ,164,166,170,174,175,181, 1 83 ,1 87,18 8,18 9,193 ,194 ,1 96 ,1 97,19 9,20 2,21 0,21 2,217 ,2 18 ± 22 0,22 7,22 9, 232 ± 234,237,239 . One limitation of this technique is the need for the ¯uid to be transparent. This may not be the case in real-situation ¯uids, e.g. foodstuff; in such situations, it is necessary to perform the measurements in transparent model ¯uids, that have viscosity values and texture similar to the real ¯uid27 . Recently, measurements have also been reported for solid-liqui d systems with matching refractive index72 ± 73 ; the laser Doppler technique has also been extendedÐ termed `Phase Doppler Anemometry’ (PDA)Ðto measure both liquid velocities and particle or bubble sizes198,202,236 . Ultrasound Doppler Velocimetry Another non-intrusiv e technique, based on the Doppler effect, uses an ultrasound pulse, which is re¯ected by the Figure 8. Streak-line identi®cation of principal ¯ow patterns in stirred vessels: (a) tall (H = 2T) vessel with two HE-3 impellers9 ; (b) stirred vessel with a single Mixel TT impeller [P. Mavros, unpublishe d work]. Trans IChemE, Vol 79, Part A, March 2001 FLOW VISUALIZATION IN STIRRED VESSLES Prism derotation A very ingenious technique, using a set of prisms, has been developed to optically `freeze’ the rotating impeller, thus obtaining a stationary picture115 . The technique has been used to investigate the formation of cavities behind the blades of the various impellers; it has also been used to identify a region at the top of the blade, where the ¯ow separates from the blade, forming a bubble228 . Flow-Followers The use of a `¯ow-follower’ is another technique for the identi®cation of the ¯ow pattern. The meandering of a particular particle in the vessel is recorded and ¯ow patterns are deduced from its trace. Flow followers may be simple particles, somehow made distinct, e.g. by colouring207 and following its trajectory visually or using a video126 , or more sophisticated, like the radio-frequency emitting particle11,159,172 and the magnetic pill167 . In the past, the recording was limited to the passage of the particle from a speci®ed region, e.g. the volume around the impeller. The technique was used to observe the ¯ow or to measure circulation times12,60,159 , which were then used to validate theoretical models147 or to calculate impeller characteristics 60 . Lately, the technique, called trajectography, has been extended to provide 3-D trajectories10,13,18 2,224 and thus a better representation of the actual ¯ow in the vessel. A recent development of the technique is the radioactive tagging of a particle and monitorin g its meandering throughou t the bulk of the dispersion in the vessel using several radioactivity sensors located around the vessel127 . The technique (CARPTÐComputer Assisted Radioactive Particle Tracking) has been used so far mainly to study ¯ows in bubble columns e.g.33,41 and crystallizers176 . An alternative to this is the Positron Emission Particle Tracking (PEPT) technique104 , developed by Parker and co-workers177 ± 178 , which has been used to study the ¯ow of viscous non-Newtonian solution s agitated with an axial impeller56 . An alternative to the `¯ow follower’ is the `direction follower’. Short cotton tufts are positione d at various places inside a stirred vessel and their positio n recorded. The analysis of their movement yielded an estimate of the ¯ow stability , in terms of `direction coef®cient’ and a `switching probability ’31 . A further application of this techniqueÐsticking tufts at the edge of the impeller bladesÐallowed the experimental determination of the turbulence integral length scale239 . Colour Change One way of studying ¯ow patterns is to use some chemical to add a colour indicator in the transparent liquid and follow its ¯ow. This technique, using iodine plus sodium thiosulfate for example in the presence of starch173 , was used to demonstrate that the ¯ow is slow in the upper part of the stirred vessel. Another possibility is to use two reactants and an appropriate colour indicator. As the vessel contents are mixed, the colour changes and this indicates the ¯ow pattern77,80 . The technique is also widely used for measuring the mixing time. A recent development combines this technique with tomography. A light source illuminates the contents of vessel, a camera located normally to the illuminated plane records the illuminated ray/sheet and subsequent treatment of the frames allows the reconstruction of the mixing history3,184 . From these, new techniques have emerged for the study of ¯ow patterns’ particle image velocimetry, laser-induced ¯uorescence, thermography, x-ray and resistance tomography, to name a few. Thermography A development of simple photography is the use of heatsensitive thermochromic crystals dispersed in the liquid. Initially, since the temperature is the same throughou t the whole liquid, the crystals have all the same colour intensity. When a quantity of heated liquid is introduced into the vessel, its spreadÐand the associated ¯ow patternÐis shown as a disruptio n in the colour of the crystals. This is captured by a colour video camera, and the frames are subsequently analysed digitally for the hue, saturation and lightness of each pixel123 ± 124 . Figure 9 illustrates the evolution of the dispersion of a small lump of liquid crystals, heated 28C above the bulk temperature in a lid-closed, unbaf¯ed vessel123 . From these (and subsequent pictures), it is possible to determine the mixing time, and more generally to investigat e the effect of the vessel con®guration and operating conditions on the process of mixing. Figure 9. Hue contours illustrating the spreading of a small amount of tracer (heated liquid) in a stirred vessel; Rushton turbine, N Trans IChemE, Vol 79, Part A, March 2001 117 540 rpm 12 3. 118 MAVROS Figure 10. Illustration of the ¯ow pattern results obtainable through PIV9 3. (a) Original picture; (b) raw velocity vectors map: 2015 velocity vectors have been extracted by particle image tracking; (c) instantaneous ¯uctuating velocity vectors map: this was obtained by interpolating the random sparse velocity vectors in Figure 10b and then subtracting the ensemble average velocity; (d) instantaneous vorticity map. Particle Image Velocimetry The natural extension of the simple photographi c recording of streaks of particles moving in a stirred vessel is the comparison of two consecutive frames. Pictures of a plane cutting through the vessel, illuminated by a powerful light source, are taken at short intervals. Analysing the displacement of each particle in the time between the two shutter openings yields its 2-D velocity. If suf®cient seeding particles are present, then a map of the ¯ow in the illuminated plane is obtained76,119 . The calculation of the particle velocities relies on sophisticate d software. In the case of low-density images, with relatively few particles, a program identifyin g speci®c particles (`particle tracking’) is suf®cient28,29,47 ,4 8 ; for more complex ¯ows, image correlation methods are used to determine the individua l particle vectors68 , also 69,222 for a review and ®elds of application of PIV, and33 for a comparison with particle tracking and computed tomography). The evolution of software has resulted in very detailed ¯ow maps and even calculations of additional ¯ow characteristics, e.g. of vorticity, turbulence, among others 55,180 . Figure 10 illustrates the succession of results obtained by PIV 93 . From the original picture (Figure 10(a)), the velocity vectors are extracted. From these it is then possible to determine the ¯uctuating component and the vorticity of the ¯ow at this plane. Figure 11 illustrates some `primitive’ PIV results 29 obtained in a stirred vessel with a 458-pitchedblade turbine28 , whereas Figure 12 illustrates results obtained with a more sophisticate d apparatus and software. One interesting feature of PIV is that each recorded frame represents a `freeze’ of the ¯ow in time. The time averaging of consecutive maps generates the ¯ow map which is characteristic of the impeller and the vessel con®guration (Figure 12); each frame, on the other hand, is a transient image of the ¯ow. In that sense it exhibits non-stationary phenomena, like ¯ow instabilities . By analysing consecutive frames, it has been possible to calculate the major ¯uctuating frequency169 , which was previously identi®ed154 and measured by LDV165 . PIV measurements have started being made for chemicalprocess stirred vessels26,33,35 ,168,204 . Novel extensions of the PIV technique include the holographi c PIV238 , which captures the 3-D velocity distribution , and digital photogrammetry or three-dimensional particle tracking velocimetry, in which all three components of the velocity vector are determined as a function of time16,78 . Laser-Induced Fluorescence Some chemical substances become ¯uorescent when excited by a particular light source. Several such species Trans IChemE, Vol 79, Part A, March 2001 FLOW VISUALIZATION IN STIRRED VESSLES Figure 11. Primitive PIV results obtained by image processing in a stirred vessel with a pitched-blade turbine2 9. exist, e.g. ¯uorescein, rhodamine B, among others. The phenomenon was initially termed phototropism ; however, the current term is `photochromism ’ and the dyes are termed photochromi c dyes. A laser beam illuminates a spotÐor a planeÐinside the stirred vessel; the ¯uorescent dye, that has been dissolved in the liquid, is excited within a few microseconds and becomes ¯uorescent46 , hence the name of the technique (Laser-Induced Fluorescence, or LIF). The reverse reaction, which brings the dye to its initial non-¯uorescent condition, has a half life ranging from a few seconds to several 119 minutes, depending on the species128 . A slightly different application is the use of photochromic dyes to follow the evolution of ¯ow patterns192 . A spot or line of a photosensitive dye is introduced in the liquid and suddenly illuminated. By following the movement of the dye spot or line, using a high-speed camera and analysing subsequently the pictures, it is possible to determine primary and secondary ¯ows in vessels. Initially, the technique was used for measuring point concentrations 64,65,83 ,117,179 or temperatures4 , since some of the photochromi c dyes are also sensitive to heat. LIF was further developed to determine simultaneously concentration and velocity at a given point144 , and the advent of laser sheet illuminatio n allowed the determination of whole-plane ¯ow patterns in various process vessels18,43,85,87,88,129,201,21 1 . Lately, new photochromi c dyes are being produced131 to allow long-term recording of ¯ow patterns, by `tagging’ the dye molecules67 . Figure 13 illustrates the use of two such dyes, the persistence of the dye ¯uorescence and the possibility of following the evolution of mixing of two different liquid streams seems promizing for stirred vessel mixing studies. Tomography Most of the early ¯ow visualization techniques faced a considerable problem. The presence of sometimes bulky probes disrupte d the ¯ow pattern and resulted in erroneous or perhaps not quite accurate results. This led to a search for visualization techniques in other ®elds, which could also be useful for chemical process vessels. During the 1970s, x-ray tomography was developed for medical diagnosis. An x-ray transmitter is positione d on one Figure 12. Instantaneous digital PIV ¯ow patterns (a-d) and correspondin g average velocity ®eld (e; average of 466 pictures) for a stirred vessel agitated with a Rushton turbine (T = 0.4 m, D = 0.138 m, C = D, 4 baf¯es, N = 2.67 Hz) [M. Perrard, private communication] . Trans IChemE, Vol 79, Part A, March 2001 120 MAVROS Figure 13. Illustration of the use of two ¯uorescent dyes (green: disodium ¯uorescein; red/ orange: rhodamine-B) to investigate the impact of a liquid jet (green) on a liquid layer (red)90. side of the body, and a receiver sensor on the other, capturing the signal passing through the body and examining its attenuation yields an estimate of the (line integral) local mass density distributio n along the signal path. By rotating the emitter-receiver system around the body and using appropriate software, it is possible to reconstruct the tomographic image of the cross-section being observed, and if the whole system is translated along the body examined, it is also possible to obtain 3-D tomographic data. The assistance of computers meant that the technique was known as Computer-Assisted Tomography (CAT) or simply Computer Tomography (CT)30 . The technique has been applied in stirred vessels to study the ¯ow in opaque non-Newtonian liquids, for which other ¯ow visualization techniques were not successful52 ± 53 , e.g., to study the development of cavities and caverns in viscous ¯uids62 ± 63,191,203 . A more important development of process tomography was the emergence of electrical impedance, electrical capacitance or electrical resistance tomography: electrodes are ¯ush-mounte d on the inside walls of the vessel (Figure 14), and an electrical property is measured by all of them simultaneously, e.g., resistance in the case of electrically-conductin g liquids, capacitance for non-conducting ¯uids, etc.216 . Again, the signals from the various sensors are combined into slices, or `tomograms’ (Figure 15(a)), and a set of such images may be used to obtain a 3-D representation of the ¯ow inside the vessel (Figure 15(b)). The technique has been used to investigate the ¯ow in various process vessels for various two-phase systems22,23,42 ,50,86,122,145,146,185,200,215,221,22 3 . The tomographic technique for the reconstruction of the ¯ow inside vessels has also been applied recently with a visual technique, using two dyes24,25,184,186 . CONCLUSIONS Figure 14. Positioning of the electrodes on the inside walls of a stirred vessel 9 2. Several experimental techniques, ranging from the simple ones which rely on visual observation, to sophisticated ones encompassing special tools, sensors and software (digital PIV, LIF, LDV, etc.) are today available for visualizing ¯ow patterns in stirred vessels, as well as other chemical process vessels. Laser Doppler velocimetry (LDV) and Particle Image Velocimetry (PIV) have evolved into relatively easyto-use techniques, and if the measurements are carefully performed, they provide considerable information about the three-dimensiona l ¯ow generated by the various impellers. The tomographic techniques, on the other hand, especially the ones based on the electrical properties of the stirred ¯uid system, look promizing, since they seem appropriate for both lab- and large-scale vessels. Trans IChemE, Vol 79, Part A, March 2001 FLOW VISUALIZATION IN STIRRED VESSLES 121 Figure 15. Illustration of the electrical resistance tomography technique: (a) a set of `tomograms’, for various positions along the z-axis; (b) resulting 3-D ¯ow pattern (in this case, dispersion of gas into a stirred liquid)9 2. APPENDIX 1 One of the bene®ts of LDV is the availability of the ¯ow history for a given point, in terms of a time series of single, double or sometimes all three of the velocity vector components uij , where `i’ refers to the vector component (r,z,v), while `j’ refers to the j-th value in the time series. This instantaneous j-th velocity measurement is considered as consisting of a mean (Åui ) and a ¯uctuating term (uij ): uij uÅ i A1 uij where the mean is calculated as the average of all measurements: N 1X uÅ i u , i r, z, v A2 N j 1 ij The average of the ¯uctuating term is the r.m.s. value of the velocity: Á !1/2 N 1X 2 2 1/2 ui,rms ui u uÅ i , i r, z, v N j 1 ij A3 The mean and ¯uctuating velocity terms may now be used to determine several characteristics of the stirred vessel ¯ow patterns. The variability of the ¯ow, as measured by the r.m.s. velocities, may be illustrated by the intensity of turbulence (I), which is the ratio of the r.m.s. to the mean velocity: I u 2r u 2r u 2z u 2z u 2v u 1/2 2 1/2 v A4 where C is a constant and L a characteristic length. Regarding C, several values have been used by various workers, ranging from 0.51 to 7.2. It is perhaps better to determine it by integrating the results over the whole volume of the vessel and equating this to the power drawn by the agitator (P), assuming that C is independent of location. L is a length scale associated to the impeller diameter (L D/a, with values of a ranging from 6 to 12.5); a length scale of D/10 has been reported as giving accurate results for the Rushton turbine. Alternatively, L is related to a mean velocity value and the Eulerian integral time scale (ti ): Li uÅ i ti A7 where ti is calculated as the integral of the autocorrelation function: …¥ Ri dt ti A8 0 and Ri is calculated from: Ri ui t ui t u Dt 2 i Finally, for u in equation (A6), we may use either one of the r.m.s. velocities Ðin that case, the corresponding velocity vector autocorrelation is used to determine the length scaleÐor a combination of all available, e.g. k1/2 . In all cases, an approximate map of energy dissipation rates is obtained, and this characterizes the suitabilit y of a particular impeller and/or vessel con®guration for a given task. while the turbulent kinetic energy (k) is: 1 2 u u 2z u 2v A5 2 r One of the important features of a particular vessel con®guration is the pattern of energy dissipation, since this is related to the performance of the stirred vessel as a reactor. Some of it is dissipated inside the impeller-swept volume, but the main part is dissipated within the bulk of the stirred ¯uid. The local value of energy dissipation (e) is related to the ¯uctuating velocity: NOMENCLATURE k e C u3 L Trans IChemE, Vol 79, Part A, March 2001 A6 A9 a df D fD I k L pa pt R t u u factor fringe spacing impeller diameter, m Doppler frequency, Hz turbulence intensity turbulent kinetic energy, m2 s ± 2 length scale, m ambient (mainstream) pressure, Pa tip pressure, Pa autocorrelation function time s velocity m s ± 1 ¯uctuating velocity m s ± 1 122 Greek e l r t f MAVROS letters energy dissipation rate, m2 s ± 3 light wavelength, m liquid density, kg m ± 3 integral time scale, s half-angle between two laser beams, 8 Indices m manometer liquid r radial z axial v tangential REFERENCES 1. Adrian, R. J., 1996, `Laser velocimetry’, in R. J. Goldstein (Ed.), Fluid Mechanics Measurements, 2nd Ed., (Taylor & Francis, Washington, D.C.), pp. 175±299. 2. Aloi, L. 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(VCH, Weinheim), vol. B2, pp. 25.1-25.33. ACKNOWLEDGEMENTS Thanks are due to Professor A. W. Nienow for his valuable comments and suggestions. Thanks also to the European Union for the partial ®nancial support of this work (contract BRITE-EURAM BRRT CT97 5035) and to the IChemE (UK), Lavoisier Publishers (Paris, France), Elsevier (The Netherlands) and VCH (Germany), copyright holders, for their permission to reproduce Figures 1(a), 8(a), 9 and 11. ADDRESS Correspondenc e concerning this paper should be addressed to Dr. P. Mavros, Department of Chemistry, Aristotle University, GR-54006 Thessaloniki, Greece. The manuscript was received 14 February 2000 and accepted for publication after revision 31 October 2000.