INVESTIGATION OF TURBULENCE MODULATION IN SOLID- LIQUID SUSPENSIONS USING PARALLEL COMPETING REACTIONS AS PROBES FOR MICRO-MIXING EFFICIENCY

Transcription

1 14 th European Conference on Mixing Warszawa, 1-13 eptember 212 INVETIGATION OF TURBULENCE MODULATION IN OLID- LIUID UPENION UING PARALLEL COMPETING REACTION A PROBE FOR MICRO-MIING EFFICIENCY H. Unadkat, Z.K. Nagy and C. D. Rielly Department of Chemical Engineering, Loughborough University, Leicestershire, LE11 3TU, UK C.D.Rielly@lboro.ac.uk Abstract. The Bourne and the Villermaux competitive reaction chemistries were applied to study the effects of suspended particles on the yield of an undesired product and hence to infer their effects on local dissipation rates. Two-phase micro-mixing experiments were carried out in a 1 litre stirred vessel, agitated by a pitched-blade turbine, using four particle size ranges: 7-1, 2-3, 7-7 and 1 µm. Experiments were carried out with up to 1.7 vol % particles in the Bourne scheme and 3 vol % in the Villermaux scheme. Both reaction schemes gave qualitatively similar results, although stronger effects of added particles were obtained with the Bourne chemistry. The effect of 7-7 µm particles could not be distinguished from experimental error, but the other size ranges gave increased by-product yields and suppressed the dissipation rates. These results confirmed earlier two-phase PIV observations: smaller particles (7-1 and 2-3 µm) gave maximum suppression at ~1 vol%. Above this volume fraction, the level of suppression decreased and in some cases turbulence augmentation occurred, indicating that particle concentration, as well as size, is an important factor. Keywords: Micro-mixing; multiphase flows; turbulence; parallel reactions, stirred tanks. 1. INTRODUCTION The objective of this work was to quantify how micro-mixing rates are affected by the presence of solids in agitated suspensions and thereby to infer the effects of particles on turbulence dissipation rates. This was part of a broader study by Unadkat [1], where turbulence modulation by dispersed particles was investigated via fluorescent PIV experiments. Micro-mixing is the process of homogenization at the molecular scale, which has a direct influence on the course of chemical reactions, and consequently product distribution [2]. ince the degree of micro-mixing is governed by the local dissipation rate, chemical reactions may be used as molecular probes to infer how the presence of particles affects the product distribution, and consequently the dissipation rate. In the current study, two different parallel reaction schemes were implemented with inert dispersed particles in the fluid; i.e. the Bourne [3] and Villermaux [4] reaction schemes. 2. REACTION KINETIC 2.1 Bourne scheme The Bourne reaction scheme consists of two parallel reactions; an acid-base neutralisation and the alkaline hydrolysis of ethyl chloroacetate, as shown is eqns. (1) and (2) respectively. 1 NaOH + HCl k NaCl + H2O k NaOH CH ClCOOC H CH ClCOONa C H OH The kinetics of these reactions are well-established and rate constants are available from literature [- 7]. The current study considers the case where a small volume of concentrated sodium hydroxide solution is added to a larger volume of pre-mixed hydrochloric acid and ethyl chloroacetate solution in the tank. After completion of the feed addition, the product distribution of the sodium salt may be obtained from the residual concentration of ethyl chloroacetate, which was measured using GCM [1] Vc ( V + V ) c = V c ECA NAOH ECA NAOH NaOH (1) (2) (3) 479

2 where ECA denotes ethyl chloroacetate, V the liquid volume in the tank at the start of the reaction and V NaOH the total volume of sodium hydroxide fed to this mixture. When mixing is rapid and intense, the product distributions are determined only by the kinetics, hence =. On the other hand in a fully segregated regime, the kinetics become unimportant and =.. In partially segregated mixtures arising from insufficient micro-mixing, < < Villermaux scheme In the Bourne reaction scheme, ethyl chloroacetate is a toxic substance, which limits its application. Therefore many workers have preferred the Villermaux scheme: HBO+H 2 3 k HBO I + IO3 + 6H k 3I2 + 3H2O I2 + I k I3 ' k3 (4) () (6) Prior to mixing, the tank contains iodide ( I - ), iodate ( IO 3 ) in stoichiometric proportions, and borate ions ( HBO 2 3 ), to which the limiting reagent sulphuric acid is added. The kinetics of this reaction scheme are still uncertain [8], but the analysis of the results is well-established [9]. The degree of micro-mixing is characterized by a segregation index : ( ) 2 n 2 ni + n - I 2 I 2 3 where Y = = n n + + H H and Y T = 6n 6n + n - IO3, - - IO3, H2BO3, It follows that when mixing is perfect, no iodine is produced; hence Y = and =. Under totally segregated conditions Y = Y T and = 1, whereas for imperfect mixing < < 1. The concentration of triiodide was obtained via spectrophotometry, using the absorption peak at 33 nm [1]; the extinction coefficient of the triiodide ion was found to be 2686 m 2 mol -1. All other concentrations in eqn.(7) may be obtained using the reaction stoichiometry and the thermodynamic equilibrium for reaction (6). 3. EPERIMENTAL METHOD Experiments were carried out in a baffled stirred tank of diameter T = 11 mm, equipped with a 4 pitched-blade turbine (PBT) of diameter D= T / 3, at a clearance of C = T / 4 from the base. The four baffles had a width of T / 1. The feed location was in the discharge stream, where the highest degree of turbulence modulation by the particles was detected in the PIV study of Unadkat [1]. The feed was positioned at z/ T =.178 and r/ T =.129; the pipe was made from 1 mm i.d. stainless steel. Inert glass spheres of density 2 kg m -3 were added to the reactive mixture as the dispersed phase. Four particles sizes were employed (7-1, 2-3, 7-7 and 1 µm diameter) and different volume fractions were employed depending on the impeller speed of the PBT, which determined the suspension homogeneity. The Bourne reaction scheme was conducted using the standard solutions employed previously in the literature [3, 11, 12]. The Villermaux scheme was implemented using concentrations studied by Fournier et al. [4]; detailed experimental procedures are discussed by Unadkat [1]. The Villermaux scheme may be used with multiple additions of acid: the first addition was into a single phase liquid flow, whereas in subsequent additions of acid the solids volume fraction was slowly increased. In this way, the first run became a single-phase benchmark and subsequent runs examined two-phase conditions with increasing volume fraction of solids, but all were conducted in precisely the same feed and tank geometry. 4. PRELIMINARY EPERIMENT 4.1 Critical feed time At high feed rates, the product distribution is adversely affected by macro-mixing and the presence of large scale concentration gradients [3, 1]. Therefore, it is desirable to add the feed slowly enough to be in the micro-mixing controlled regime. Figs. 1 and show that the by-product yield reduces as the feed time is increased, up to a critical feed time, after which it becomes constant. For the Bourne reaction scheme at rpm ( ε =.4 W kg -1 ), Fig. 1 shows is approximately constant for t >12 s, corresponding to a feed rate of 1 ml min -1 (a repeat point differs by 3% which is typical of the experimental error); further experiments with the Bourne scheme used a feed time t = 12 s. The product distribution at the critical feed time is =.6, similar to ~.7 reported by Bourne 48 (7)

3 and Yu [3] for a feed in the discharge stream at the same Da = 1.2, where the Damköhler number is the ratio of characteristic micro-mixing and chemical reaction times. Therefore, the single phase product distribution is reliable, and may be used a basis of comparison in the two-phase experiments. Results for the Villermaux scheme at 8 and 1 rpm in Fig. 1, indicate a critical feed time of 3 s (corresponding to a feed rate of 2 ml min -1 ); t = 3 s was fixed for subsequent experiments. The segregation indexes obtained in experiments at 1 rpm are lower than those at 8 rpm ( ε =.34 W kg -1 ), since micro-mixing is faster. At 1 rpm and t > 3 s, =.13, which is similar to ~. reported by Fournier et al. [4] for a feed in the discharge stream at the same average power per unit volume. Consequently, the single phase segregation index is considered to be a reliable estimate, at both impeller speeds rpm 1 rpm.8.7 s Feed time (s) Fig. 1 Effect of feed time on product distribution at: rpm, Bourne scheme, 8 and 1 rpm, Villermaux scheme 4.2 Choice of impeller speed Two-phase micro-mixing experiments should be conducted at high enough speeds for the particles to be suspended, however the yield sensitivities decline at high N. In Fig. 2 for the Bourne kinetics, is much reduced at higher N. As a compromise, two-phase experiments were carried out at 1 rpm ( ε =.4 W kg ), allowing 7-1 µm particles to be suspended up to 1.7 vol% and 2-3 µm up to 1.2 vol%. imilarly, Fig. 2 shows the sensitivity of the segregation index, to the mean power dissipation rate, for the Villermaux scheme. An impeller speed of 8 rpm 1 ( ε.6 W kg ) = was selected for the two-phase Villermaux experiments, where reasonable sensitivity of the yield was attained and all particle sizes were suspended up to 3 vol%. These upper volume fraction limits were determined by visual inspection of the suspension quality, using the Zweitering criterion. Unadkat [1] demonstrated that particle concentration gradients exist under these conditions, with higher than average volume fractions close to the feed pipe. Due to the higher impeller speed, the Villermaux scheme was more suitable than the Bourne scheme (under these chemical conditions) to study two-phase flows, where particles need to be suspended. Furthermore, the yield in the Bourne scheme is quite low: =.6 compared to Y =.18 or =.2 in the Villermaux scheme, both at rpm Feed time (s) s <ε> (W kg -1 ).1. 1 <ε> (W kg -1 ) Fig. 2 The sensitivity of product distribution to the mean dissipation rate for the Bourne scheme and Villermaux scheme 481

4 . REULT AND DICUION In both reaction schemes, results are expressed as the percentage change in the segregation index compared to the single phase experiment, shown in eqn.(8). A positive percentage change in the segregation index would arise from turbulence augmentation; conversely a negative change would arise from turbulence suppression. δ s = s L s L s L (Villermaux) or δ = L L L (Bourne) (8) Here subscripts L and L, represent the liquid only and liquid-solid cases, respectively. For each set of experiments the first run is always the benchmark, liquid only case, and hence the change is zero..1 Villermaux scheme Fig. 3 shows the results of micro-mixing experiments with 3 μm particles up to 3 vol %. Four repeated experiments are shown; the discrepancies could arise from even a small difference in the location of the feed position each time the experiment is reconfigured, e.g. a deviation of 1 mm in the feed position could change the local turbulence by up to %, and the degree of turbulence modulation at that position may also be variable. Notwithstanding this difference, all of the trend lines appear to follow the same pattern: particles dampen turbulence at lower concentrations, but increase turbulence at larger concentrations; the transition occurs at approximately 1 vol %. If it is true that the behaviour changes for a given particle size, with respect to concentration, this may explain the many contradictions reported in literature, which are often carried out for single volume fractions [13, 14]. Turbulence augmentation Turbulence augmentation Turbulence suppression vol% 3 μm particles Turbulence suppression vol% 3 μm particles Fig. 3 Percentage change in segregation index relative to a single phase experiment, in the presence of 3 μm particles up to 3% increasing from % and increasing from 1% At low particle concentrations, Gore and Crowe s theory [] may be applied to interpret the turbulence suppression by 3 µm particles, for which d p / L <.1; turbulence augmentation is not expected in this case. However, this theory does not take into account the effects of particle concentration. Careful analysis of the experimental errors in [1] show a maximum error of % and hence the changes are considered significant: the percentage change in yield observed in the two-phase experiments with 3 μm particles is double the maximum error, at around 1%. Furthermore, alternative explanations, such as the effects of oxidation of potassium iodide, or an increase in the fluid viscosity due to the presence of particles would have the opposite effect on to what has been observed at higher vol %. Fig. 3 shows a similar trend for runs over different particle concentrations, starting arbitrarily either above or below 1 vol%; regardless of the start point of the experiment, particles suppressed turbulence for < 1 vol % and augmented it >1 vol %. In a dilute flow, the particle motion is governed by the surface and body forces exerted by the fluid, but in a dense flow the motion will be affected by particle-particle collisions. These mean vol % values would not normally be considered as dense, but here the particles were not suspended homogeneously. At higher particle vol %, a cloud of particles could cause a momentum flux which behaves like a Reynolds stress [16]. Alternatively, the dispersed phase will have a fluctuating kinetic energy, due to particle-particle collisions, e.g. the granular temperature effect [16]. Fig. 4 suggests turbulence suppression due to the presence of 7 µm solids, but the effects are small and indistinguishable from the % errors. DNA simulations [17] to study modulation of isotropic turbulence by particles with.1< t < (defined relative to the Kolmogorov time scale), suggest that particles with t =.2 modified the TKE and its dissipation rate spectra in such a way 482

5 that these properties remained close to the particle-free case. These were denoted ghost particles [17], so it is plausible that 7 µm particles have no detectable effect on the turbulence. 1 1 Turbulence augmentation vol% 7 μm particles Fig. 4 Percentage change in segregation index relative to a single phase experiment, in the presence up to 3 vol%, Villermaux scheme: 7 μm particles, 1 μm particles Finally, repeated experiments with the 1 µm particles show great consistency. In Fig. 4, all results indicate turbulence suppression and the percentage change in yield increases continuously with respect to particle concentration. The level of change observed in the two-phase experiments (12-13% at 3 vol% particles) exceeds the change which may be attributed to experimental error (~%). Ferrante and Elghobashi [17] showed that particles with t > 1 decrease the TKE and dissipation rate. pecifically, particles with t = were found to dampen the TKE by 3% at concentrations low as.1 vol%, which finding supports the current results that large particles suppress turbulence..2 Bourne scheme Fig. shows that the 1 and 3 µm particles have the effect of damping the turbulence, for the Bourne scheme. At concentrations below 1 vol %, particles increasingly suppress the dissipation rate with respect to concentration. Fig. shows that not only does the level of suppression decrease for concentrations > 1 vol%, but in some cases turbulence augmentation occurs, such that the percentage changes in yield became positive (Villermaux scheme: Fig. 3). The 1 µm particles have a much greater effect than the 3 µm particles at the same vol %, suggesting that particle size is an important factor. At.7 vol%, they caused a change in yield of -27 and -9 %, respectively. Results from the Villermaux experiments included four repeated experiments with the 3 µm particles, but only one set is displayed in Fig. for clarity. The trends are in very good agreement with the Bourne scheme, as are the percentage changes in yield. In most cases, at equivalent concentrations, the levels of changes agree within % which was evaluated to be the experimental error in the Villermaux scheme with repeated feed injections. Differences up to 1% would not be unusual, as this was found to be the maximum error in yield between identical experiments for the Bourne experiments. Notwithstanding the deviations, the pattern of turbulence damping is evident below ~1 vol %, and reduction in suppression above 1 vol %. Again 1 µm particles have a greater impact on the dissipation rate. An alternative interpretation for the difference in percentage changes between the two size classes may be due to particle number, which is inversely linked to size. For smaller sizes, there are more particles per unit volume than for larger size at the same volume fraction. The theory of Gore and Crowe [], suggests that the most energetic eddies are able to impart their energy to more particles, which would reduce the turbulence intensity of the carrier phase to a greater extent. At higher concentrations where collisions become important, the smaller particles would have a higher collision frequency due to the larger number, thereby increasing the granular temperature of the particles, which is transferred back to the fluid. or -1 Turbulence suppression vol% 1 μm particles Bourne rpm 3 μm Villermaux 8 rpm 3 μm Bourne rpm 1 μm Villermaux 8 rpm 1 μm vol% 1 or 3 μm particles Fig. Percentage change in yield in the presence of 1 or 3 μm particles 483

6 6. CONCLUION The Bourne and Villermaux reaction schemes produced comparable results and changes in yield could be detected in the presence of 1 and 3 µm particles. Below ~1 vol %, the particles dampened turbulence, causing a negative percentage change in by-product yield, whereas above ~1 vol %, the level of suppression decreased, and in the Villermaux experiments turbulence augmentation became evident at ~3 vol % for 3 µm particles. The theory of Gore and Crowe [] correctly predicts the initial turbulence damping by these particles, according to the dp / L ratio. Their criterion [] was based on experimental observations up to a maximum of.2 vol% particles in the flow and does not account for the change in turbulence modulation regime at higher solids concentrations. The 1 µm particles had a considerably larger effect on the fluid turbulence compared to the 3 µm particles in both reactions schemes, indicating that particle size or alternatively number is important. In the Villermaux experiments, 7 µm particles did not show consistent changes in yield, and the observed fluctuations were within experimental error %. It is possible they behaved as ghost particles [17]. The 1 µm particles repeatedly showed turbulence damping of the continuous phase. Their respective dp / L ratio being greater than.1 opposes the hypothesis of Gore and Crowe []. However, the micro-mixing experiments validate earlier PIV observations by Unadkat [1] that both small and large particles suppress the dissipation rate at low concentrations at least. The results presented highlight the need for more comprehensive theories of turbulence modulation which take into account effects of size and concentration to predict the levels of change. 7. REFERENCE [1] Unadkat, H., 21. Investigation of turbulence modulation in solid-liquid suspensions using FPIV and micromixing experiments, PhD Thesis, Dept Chemical Engineering, Loughborough University. [2] Baldyga, J. & Bourne, J. R., Turbulent mixing and chemical reactions, John Wiley & ons Ltd, West ussex, England. [3] Bourne, J. R. & Yu,., 1994). Investigation of micro-mixing in stirred tank reactors using parallel reactions, Ind. Eng. Chem. Res., 33, 4. [4] Fournier, M. C., Falk, L. & Villermaux, J., A new parallel competing reaction system for assessing micro-mixing efficiency - experimental approach, Chem. Eng. ci., 1(22), [] Yu,., (1993), Micro-mixing and parallel reactions, Ph.D Thesis, ETH Zurich. [6] Eigen, M., & DeMaeyer, L., 19. Untersuchungen uber die kinetic der neutralization, Z. Elektro Chem., 9(1), [7] Nolan, G. J. & Amis, E.., The rates of alkaline hydrolysis of ethyl aplha-haloacetates in pure and mixed solvents, J. Phys. Chem., 6(9), 6. [8] Bourne, J. R., 28. Comments on the iodide/iodate method for characterising micro-mixing, Chem. Eng. J., 14, [9] Guichardon, P., Falk, L. & Villermaux, J., 2. Characterisation of micro-mixing efficiency by the iodide/iodate reaction system Part 2: Kinetic study, Chem. Eng. ci., (19), [1] Guichardon, P. & Falk, L., 2. Characterisation of micro-mixing efficiency by the iodide/iodate reaction system Part 1: experimental procedure, Chem. Eng. ci.,, [11] Baldyga, J., Henczka, M. & Makowski, L., 21. Effects of mixing on parallel chemical reactions in a continuous-flow stirred tank reactor, Chem. Eng. Res. Des., 79(Part A), [12] Bhattacharya,. & Kresta,. M., 24. urface feed with minimum by-product formation for competitive reactions, Chem. Eng. Res. Des., 82(A9), [13] Micheletti, M. & Yianneskis, M., 24. tudy of fluid velocity characteristics in stirred solidliquid suspensions with a refractive index matching technique, P. I. Mech. Eng. E-J. Pro., 218(4), [14] Virdung, T. & Rasmuson, A. C., 28. olid-liquid flow at dilute concentrations in an axially stirred vessel investigated using particle image velocimetry, Chem. Eng. Commun., 19(1), [] Gore, R. A. & Crowe, C. T., Effect of particle size on modulating turbulent intensity, Int. J. Multiphase Flow, (2), [16] Crowe, C. T., Troutt, T. R. & Chung, J. N., Numerical models for two-phase turbulent flows, Ann. Rev. Fluid Mech., 28, [17] Ferrante, A. & Elghobashi,., 23. On the physical mechanisms of two-way coupling in particle-laden isotropic turbulence, Phys. Fluids, 14(2),