Research Note pubs.acs.org/IECR
Simulation of Settling of Solid Particles Due to Sudden Impeller Stoppage Madhavi V. Sardeshpande and Vivek V. Ranade* Industrial Flow Modeling Group, Chemical Engineering and Process Development Division, National Chemical Laboratory, Pune−411 008, India ABSTRACT: Stirred tank reactors (STRs), which are used in process industries (for a variety of operations, such as catalytic reactions, dissolution of a solid, crystallization, and so on), often involve handling of solid−liquid (−gas) systems. The solid suspension and the quality of the suspension are key issues in the design and operation of such stirred reactors. Despite extensive experimental work over previous decades, comprehensive understanding and reliable methods to predict the solids suspension and the quality of the suspension are not yet available. Advances in computational fluid dynamics (CFD) and new experimental techniques offer potentially effective ways of understanding solids suspension in stirred tanks. The present work highlights the potential of using transient measurements by way of the dynamic settling of solid particles because of the sudden stoppage of an impeller to evaluate CFD models. Sudden impeller stoppage results in significantly different conditions, in terms of the ratio of particle diameter to Kolomogorov length scale (dp/λ), as well as the solids volume fraction experienced by solid particles. Therefore, experimental data under such sudden impeller stoppage offer a better way to evaluate the influence of prevailing turbulence and solids volume fraction on effective drag and therefore offer a more-stringent test to CFD models than steady-state profiles. Besides facilitating the development of computational models, the experimental and simulation studies of sudden impeller stoppage also provide useful data to gain insight into the behavior of the stirred tank after abrupt impeller stoppage due to sudden power failure.
1. INTRODUCTION Stirred vessels are widely used in chemical and allied industry to carry out a large number of multiphase applications (reactions, precipitations, emulsions, etc.) and recipes involving solid suspensions. In such solid−liquid stirred vessels, knowledge of solids distribution within the vessel (suspension quality) is an important parameter required for reliable design, optimum performance, and scaleup of the reactors. Complex interactions of impeller-generated flow, turbulence, and solids loading play a crucial role in determining the quality of the solid suspension. Despite significant research efforts, prediction of the design parameters to ensure an adequate solid suspension is still an open problem for design engineers. Recent advances in computational fluid dynamics (CFD) and the availability of fast computational resources have made it possible to develop CFD models to “a priori” simulate flow field in stirred vessels.1 However, unlike single-phase flow, which can be predicted with reasonable confidence,2 the computational models capable of predicting real-life turbulent multiphase flows involving complex geometries and with a wide range of space and time scales are yet to be well-established. If such models are developed for simulating solid−liquid flow in stirred vessels and are adequately validated by comparing results with the experimental data, these can be used for simulating suspension quality and for the optimal designing of solid−liquid stirred vessels. Several attempts of developing CFD models for simulating solid−liquid flow in stirred vessels have been made.3−6 However, most of these CFD models were evaluated by comparing simulated results of solids volume fraction profiles averaged over reactor cross section with the experimental data. © 2012 American Chemical Society
Unfortunately, comparison of such cross-sectionally averaged solid volume fraction profiles is not an effective way to discriminate and evaluate the flow models (and various submodels used to construct such flow models). There are relatively few studies available related to the measurement of local solid velocity profiles.7−9 Such measurements are often quite difficult, with significant error bars associated with the measured quantities. Therefore, it is essential to devise better methods to evaluate and assess the usefulness of the CFD models. Recently, Sardeshpande et al.6 proposed the use of hysteresis observed in the behavior of the cloud height of suspended solid particles in stirred vessels, with respect to impeller speed, for this purpose. The results indicated that it may be useful to explore the possibility of dynamic experiments to evaluate the usefulness of CFD models. Therefore, in this work, the dynamic settling of suspended solid particles because of the sudden stoppage of a rotating impeller was studied. The quantitative dynamic solids settling data were obtained, which may be used to gain better insight as well as to evaluate CFD models. Besides facilitating the development of computational models, the experimental and simulation studies of sudden impeller stoppage also provide useful data to gain insight into the behavior of stirred tanks after abrupt impeller stoppage due to sudden power failure. The simulated results of the CFD model of Sardeshpande et al.6 were compared with the Received: Revised: Accepted: Published: 4112
December 10, 2011 February 21, 2012 February 28, 2012 February 28, 2012 dx.doi.org/10.1021/ie2028987 | Ind. Eng. Chem. Res. 2012, 51, 4112−4118
Industrial & Engineering Chemistry Research
Research Note
speed camera) the solid bed height at the side wall of the tank, with respect to the slurry settling time, and the time at which this bed height became constant was considered to be the settling time for that particular impeller speed. Images of the settled bed and the bed height were measured at the vessel wall. Note that the bed which settled at the vessel bottom is radially nonuniform. Therefore, the bed height at the vessel wall may change, relative to the impeller speed, even for the same volume fraction of solids in the vessel. Despite such a nonuniform bed, the experimental methodology used in this work is adequately accurate for identifying the solids settling time (since it depends on the temporal profile of the bed height at the vessel wall and not on its absolute value). Reproducibility of the settling of cloud of particles was verified by repeating all experiments at least three times.
experimental data. The experimental results, CFD models, and simulated results presented in this work will be useful for extending our understanding of solid suspensions in stirred vessels. The observed results are discussed later in section 4 of this paper.
2. EXPERIMENTAL SECTION A fully baffled, flat-bottom cylindrical reactor (diameter of T = 0.7 m and aspect ratio = (H/T) − 1) with a six-bladed downpumping pitched-blade turbine was used for experimentation. The impeller off-bottom clearance (C) was measured from the center of impeller blade (C = T/3). All experiments were carried out with tap water as a liquid phase (ρl = 1000 kg/m3) and glass beads 250 μm in diameter as solid particles (ρs = 2500 kg/m3). A schematic representation of the experimental setup is shown in Figure 1. Experiments were carried out for one solids
3. COMPUTATIONAL MODEL The solid−liquid flow in stirred vessels was modeled using a multiple reference frame approach to represent impeller rotation and the Eulerian−Eulerian approach to represent dispersed two-phase flow.11 Appropriate representation of the interaction between solid particles and continuous liquid phase in the form of interphase drag force and turbulent dispersion of solid particles often determines the usefulness of the model in simulating key aspects of solid−liquid flow in stirred vessels.5,12−16 In stirred vessels, suspended solid particles experience significantly higher turbulence (generated by rotating impellers). It is essential to account for the influence of this turbulence prevailing in the continuous phase on effective drag on particles. Recently, Khopkar et al.5 evaluated the two alternative proposals proposed by Brucato et al.12 and Pinelli et al.,13 using a two-dimensional CFD-based model problem. They have observed that the predicted results deviate from the trends estimated by correlation of Pinelli et al.13 However, the predicted results show reasonable agreement with estimation based on the correlation by Brucato et al.12 They correlated their results using the same form of the equation [drag solely depends on the ratio of particle diameter to Kolomogorov length scale (dp/λ) for a range of solid holdup values (5% < α < 25%)] and reported a different (lower) proportionality constant. Sardeshpande et al.6 used this interphase drag formulation and simulated hysteresis in cloud height, with respect to impeller speed. In this work, we used the drag model used by Sardeshpande et al.6 to simulate the dynamic settling of solid particles due to a sudden stoppage of impeller rotation:
Figure 1. Schematic view of experimental setup for dynamic settling for suspended solids.
loading (7% v/v). The impeller speed was varied over the range from 220 rpm to 445 rpm (corresponding to an impeller Reynolds number of Re ≈ (1.5−3) × 105), whereas just the suspension speed was 445 rpm for a solids loading of 7% v/v. Visual observation of the cloud of suspended particles indicated that the cloud height was not uniform along the radial direction. This may be because of the inherently unsteady flow in stirred vessels.10 The range of the cloud height variation (i.e., maximum and minimum) was noted and the arithmetic mean of the upper and lower limits of this range was reported as the mean cloud height. The dynamic settling of suspended solids study was characterized using a high-speed camera, as shown in Figure 1. The camera was used to record the height of the solid bed being accumulated on the side wall of the vessel while settling. The video was recorded at a speed of 30 frames per second for duration of 60 s (with the camera at a fixed position). A black-colored cloth was used as a background, and illumination (using halogen lamp) was arranged from the front side. For every experiment, the impeller was rotated at a specific speed for at least 10 min to ensure that a quasi-steady state of the solids suspension corresponding to that of the impeller speed is achieved. After achieving the quasi-steady state of solid suspension, the power to the impeller was abruptly switched off. It was observed that the impeller stopped completely within 1 s after switching off the power. We monitored (with the high-
⎡ ⎛ d ⎞3⎤ ⎢ 5⎜ p ⎟ ⎥ − CD = C D0 1 + 8.76 × 10 ⎢ ⎝ λ ⎠ ⎥⎦ ⎣
(1)
It was thought to be desirable to include a factor that accounts for the influence of the solids volume fraction on effective drag. The simulated results of Khopkar et al.5 were reexamined to quantify the influence of drag and the following equation was proposed: ⎡ ⎛ d ⎞3⎤ ⎢ −5⎜ p ⎟ ⎥ CD = C D0 1 + 8.76 × 10 ⎢ ⎝ λ ⎠ ⎥⎦ ⎣ × max[(1 − 2.65εs), 0.2] 4113
(2)
dx.doi.org/10.1021/ie2028987 | Ind. Eng. Chem. Res. 2012, 51, 4112−4118
Industrial & Engineering Chemistry Research
Research Note
order to understand the limiting conditions, we have carried out simulations of decaying flow after switching off the impeller by using the standard k−ε model as well as completely eliminating the turbulence model (using the molecular viscosity like laminar flow). Both of these models indicate that the volume-averaged velocity (averaged over the entire tank) is still ∼0.03 m/s by the time all the solids are settled. Please note that, before switching off the impeller, the volume-averaged velocity was 0.37 m/s and the impeller Reynolds number (Re) was ∼3 × 105. The flow in stirred vessels is typically simulated with turbulent models beyond an impeller Reynolds number of 300−500. Ranade17 had used the standard k−ε model to simulate flow generated by the Rushton turbine, even for an impeller Reynolds number as low as 35 and above, and had demonstrated good agreement with the published experimental data. With this background, it can be safely assumed that the flow in a stirred vessel is turbulent, even with a 2-fold reduction in Re from 3 × 105 (corresponding to the volume-averaged velocity of ∼0.004 m/s). Considering that the volume-averaged velocity by the time solids are settled is much greater than 0.004 m/s, we have used the turbulence models to simulate transient profiles. Therefore, settling simulations were carried out with the fully turbulent model discussed by Sardeshpande et al.6 Simulated results were used to extract transient data on a simulated cloud height. The cloud height computations were based on circumferential averages of the solids volume fraction calculated at five different radial locations (see Sardeshpande et al.6 for more details). Note that, in reality, the cloud height at any location is indeed fluctuating. It is possible, in principle, to model these fluctuations by relating them to the local turbulent kinetic energy. In the present work, however, no such attempt has been made. The primary objective of the work was to examine whether effective drag correlations developed for the steady-state suspension of solids can be applied to simulate transient behavior. The scope was restricted to capturing transient profiles of mean cloud height. Therefore, the cloud height fluctuations were not considered and are not discussed in this manuscript. The mean cloud height was calculated as an average of cloud heights at five radial locations. For each of these radial locations, the circumferential average of cloud height was calculated based on the results of CFD simulations. It is essential to establish an equivalence and basis for comparing simulated results with the experimental data. In this work, it was difficult to estimate the solids settling time directly from simulations as it was measured in the experiments. Therefore, in order to establish the equivalence between simulations and experiments, a criterion based on a simulated volume-averaged solids velocity profile was defined to estimate the solids settling time from simulations at one particular impeller speed. The same criterion was then applied for all of the rest of the simulations to evaluate the performance of the computational model in terms of simulating the solids settling time. This is a usual practice when direct and one-to-one comparison is not possible between simulated and experimental results. The volume-weighted average of velocity of water and the velocity of the solids in the vessel were monitored/recorded during the transient simulations. In numerical simulations, the solids settling time was defined based on the decaying velocities of solid particles. The settling time was defined as a time at which the volume-averaged solids particle velocity becomes
