The CFD simulation and an experimental study of hydrodynamic behaviour of liquid-solid flow

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1 The CFD simulation and an experimental study of hydrodynamic behaviour of liquid-solid flow J.Křišťál, V. Jiřičný and V.Staněk Institute of Chemical Process Fundamentals. Academy of Sciences of the Czech republic, Department of Diffusion and Separation Processes, Rozvojová 1, 16 02, Praha 6 - Suchdol Czech Republic, tel , kristal@icpf.cas.cz, jiricny@icpf.cas.cz. Abstract In the preliminary phase of our research, the CFD package Fluent is used to study the hydrodynamic behaviour of a multiphase flow in a rectangular channel. The focus is mainly on liquid-solid flow with particulate solid phase. The Eulerian-Eulerian multiphase model is used to compute unsteady flow in 2D geometry. The results are radial particle velocity profiles as a function of system parameters, e.g. particle size and density or electrolyte inlet velocity. In parallel with computer simulations the laboratory experiment are carried out in a small laboratory water model. Actual particle velocities are determined by using a highspeed camera and subsequent image processing. Experimental data are used to validate the CFD results. In this paper basic parameters of multiphase flow simulation and experimental determination of particle velocity profiles are described. Keywords: multiphase flow, CFD, liquid-solid, experimental particle velocity profiles Introduction Exact mathematical description of real multiphase flow is complex and for its formulation it is necessary to have deep knowledge of given issue. Elementary mathematical theories for basic relation for pressure and viscosity of solid phase deal with smooth, round separate particles. They do not account for the statistical size distribution or irregular shape of real particles. This is one of constraints for correct numerical prediction of real process. Surely a lot of empirical formulas are available but their validity is mostly limited to some specific problem. Therefore it is obvious to use some simplification. Results of such a simulation have to be compared with experimental data to confirm used assumption. Until recently the inability to simulate complex phase interactions was crucial limitation for wide use of numerical simulation as routine industrial technique. However in last few years, fast development of computers and simulation software made application of computational fluid dynamics (CFD) reasonable for everyday work. Liquid-solid multiphase flow can be found in various industrial applications. Many catalyzed reaction as fluidized catalyst cracking occur in fluidized bed reactors [1], some organics technologies [2] and electrowinning technologies [,] use the D electrodes, or storing and handling particulate materials include a silo discharging and also pneumatic transport. We deal with the D electrode design with external draft-tube (Fig. 1). Basically particles move down driven by gravity and electrodeposition takes place on particle surface. When particles leave the chamber trough the outlet nozzle, they are picked up by a stream of fresh electrolyte and carried upward through an external draft-tube. After reaching the top of the chamber they fall down on the bed. Particle behaviour in the whole apparatus can be divided in two main parts. Descending particle bed can be treated similarly to a silo with conical hopper during discharging and draft-tube as a riser of circulating fluidized bed. To achieve the

2 proper particle size distribution and also to prevent apparatus breakdown due to bed plugging, it is essential to retain the mass-flow of particles in descending particle bed. w 6 7 h α 1 2 Figure 1: Hydrodynamic cell, 1 electrolyte (water) inlet, 2 outlet nozzle, hopper, draft-tube, water outlets, 6 particle bed, 7 measurement regions, bed width w = 10 cm, bed height h = 2 cm, hopper slope angle α = 60, bed depth d = 1 cm Basic hydrodynamics During discharge of a particulate material from a silo, different flow patterns can occur. Jenike [] distinguishes between the mass-flow and funnel-flow. The mass-flow means the uniform motion of particles on the same vertical level, whereas funnel-flow means that the central part of the bulk is moving faster, forming funnel-like velocity profile. He also proposes one theory for predicting the flow pattern, deducing that the hopper slope angle and the angle of friction between particles and silo walls are the most important parameters. There are several ways to achieve the mass-flow in the whole silo. One of them is the choice of the suitable construction material for silo walls with corresponding value of the friction coefficient for the stored medium. This solution, however, narrows the range of available construction materials and also causes difficulties when properties of stored media are changed. Other possibility is the modification of silo geometry namely the selection of the proper hopper slope angle. But the appropriate values of this angle are relatively high and construction of such silo is not optimal when considering the space utilisation. Another possibility is the use of internal inserts forcing mass flow even when values of hopper slope angle or friction coefficient are not optimal. The effect of a passive insert on flow patterns in

3 silo was studied numerically [6,7]. As a result it was shown that such insert can induce massflow even for the silo with degree slope hopper. In case of D electrodes it is profitable to ensure mass-flow because of first-in-first-out flow pattern. If the funnel-flow occurs some particles may stay in the bed much longer than others and thus cause malfunction of apparatus (dendrite formation). The particle behaviour in a draft-tube can be described as a liquid-solid fluidized bed with particle velocity higher than the terminal velocity. It is similar to the raiser of liquid-solid circulating fluidized bed [8]. Its hydrodynamic regime is characterized by non-uniform radial distribution of liquid velocity, particle velocity and particle hold-up in the bed (draft-tube), different from the conventional fluidization regime where the radial flow structure is more uniform. When designing the draft-tube it is important to provide sufficient particle circulation velocity to retain continuous feed of particles into the particle bed. CFD simulations In this part of our work CFD package Fluent was used to study only the hydrodynamic behaviour of a liquid-solid flow in a rectangular channel. Main region of interest was the particle bed, where radial particle velocity profiles were computed as a function of system parameters, e.g. particle size and density or electrolyte inlet velocity. Concerning high volume fractions of a solid phase the Eulerian-Eulerian multiphase model and the standard k-ε turbulence model were used. The unsteady problem formulation was used to simulate the start-up of the apparatus. Time step values were between and s depending on type of used mesh. For first approximations only 2D model of hydrodynamic cell was used and because the depth of the cell is only 1 cm, it seemed to be correct assumption. Two different types of computational grid were used. Firstly it was unstructured triangular grid (Fig. 2) with approx cells and later structured tetragonal grid (Fig. ) with approx. 000 cells. Few different modifications of structured grid were used to investigate its effect on the flow field in the cell. These modifications involved refining the mesh in region of particle bed and different cell layout in hopper and upper part of draft-tube. Figure 2: Unstructured triangular grid Figure : Structured tetragonal grid

4 Water was used as a continuous primary phase. Three different materials were used as a solid phase. It was glass, copper and lead with densities of 2 00, and kg/m respectively [9]. Particles were small spheres with 1, 2 and mm in diameter. Experimental set-up Actual particle velocities were determined to validate CFD results. Experiments were carried out in a small laboratory water model (Fig. ). It consisted of a hydrodynamic cell itself, a centrifugal pump with a water tank and pipelines, a particle separator, an ultrasonic flowmeter and a pressure indicator. Water was circulated with centrifugal pump through the flowmeter to the cell and back to the water tank in a closed loop. If any particles got accidentally out of the cell they were caught in the separator and after the measurement they were returned to the bed. The maximum water flow rate was 22 l/min with the corresponding velocity of 2. m/s at the hydrodynamic cell inlet. Flow rate values taken from the flowmeter were used for evaluating of the particle velocity profiles whereas the pressure in the apparatus served only as a reference point. The motion of particles was recorded by a high speed camera. Recorded frames were transferred to a PC via the SCSI interface and later processed Figure : Experimental apparatus, 1 water tank, 2 pump, flowmeter, hydrodynamic cell (side view), particle separator, 6 high speed camera, 7 computer Main geometrical parameters of the cell were pack bed width (w = 10 cm), height (h = 2 cm) and depth (d = 1 cm), outlet position, draft-tube and outlet nozzle dimensions and a hopper slope angle (α = 60 ). These parameters were kept constant for all the measurements. The effect of phase properties on particle velocity profiles was monitored. The phase properties considered were fluid inlet rate, particle size and density. Tap water was used as the primary continuous phase. Two different materials, glass and lead, were used as the secondary particulate phase. Particles were regular spheres with constant diameter of 2. and 1.7 mm for glass and lead respectively. Densities were identical with ones used in simulations.

5 Experimental data evaluation The main region of interest was a rectangular sector of the particle bed located about cm above the hopper. Close-up images of this area were captured with Kodak Motion Corder Analyzer SR-Ultra-C. The motion of particles in this region was recorded with 12 frames per second and every fifth frame was transferred to the personal computer. In this rate approx. 10 s record was stored in the camera internal memory. The motion of particles in the drafttube was recorded in region about 0 cm above the base level, where the draft tube is almost strictly vertical. Because of the high particle velocity in this region the recording rate was 1000 fps and each frame was transferred to PC. In this case the length of recording time was approx. s. For the image post-processing National Instruments program Vision Builder was used. In every run of batch processing the following steps were undergone. After some initial image adjustments two well-defined non-moving edges were detected to represent the reference coordinate system. Then by pattern matching technique the shifted particle was detected in consequent images. Its distances from given edges and corresponding angles were saved as a result of Caliper measuring tool. These values were used for evaluation of the particle trajectory and position in the bed. Time value for velocity calculation was taken from frame index and frame rate. Combining all these data the radial particle velocity profile was evaluated. Experimental particle velocity profiles for lead particles were evaluated for four different water inlet velocities and for two water velocities in case of glass particles. The velocities were 1.2, 1., 1.7 and 1.9 m/s for lead and 0.7, 0.9 and 1.2 m/s for glass particles. These values were chosen from the range where the apparatus operated properly (no jerky motion takes place and particles did not leave the cell together with water). Operating pressure in the cell was 0 kpa. Results CFD simulation of given multiphase system were computed for different water inlet velocities. Also different particle sizes were concerned. Chosen results were compared with experimental velocity profiles. For better identification the profiles are interpolated with parabolas. In Fig. are shown particle velocity profiles for different outlet size to particle diameter ratio. This geometrical parameter is very important for proper apparatus operation. If this value is smaller than there is high possibility that the doming can occur and the particle flow in the cell can be blocked. In agreement with published data [10] the descending particle velocity is increasing with growing outlet size to particle diameter ratio (D/d P ). In other words smaller particles move faster. In comparison with experimental data the computed velocities are approximately three times higher. Fig. 6 documents effect of water inlet velocity on particle flow in the particle bed. In accordance with experiments the computed particle velocity increases with increasing inlet flowrate. In this case the difference between simulation and experiment is slightly more triple. Experiments also show that for the higher particle density, the effect of inlet flowrate is smaller. The effect of polydispersion of particulate phase is just the same.

6 Radial position [cm] Particle velocity [cm/s] Figure : Different outlet size to particle diameter ratio, lead, v inlet = 2 m/s D/d P : 9. (exp) 1 7. Radial position [cm] Particle velocity [cm/s] Water inlet velocity: 0.9 m/s (exp) 0. m/s 0.6 m/s 0.9 m/s Figure 6: Different inlet velocities, glass, d P = 2. mm

7 Comparison of computed velocity profiles for particle with different density is shown in Fig. 7. As expected for particles with the lower density the lower water inlet velocity is sufficient for the same particle velocity in the bed. Also the funnel-flow is not so developed for lighter particles. The lower experimental values for glass particles are caused by air bubbles present in the particle bed. These bubbles come from silo loading when some air remains dispersed in the bed. They rise up, coalesce and break-up and thus their size varies with time. When it exceeds certain value the buoyancy force becomes significant and glass particles may be slowed down. For particles with higher densities this effect is negligible. Radial position [cm] Particle velocity [cm/s] Particle density: 2 00 kg/m kg/m kg/m Figure 7: Different particle density, vinlet = 2 m/s, d P = 1 mm Conclusions As the aim of this phase of this work was to predict particle velocity profiles in rectangular channel by a CFD simulation and compare them with experimental profiles, the results are satisfactory. Simulation captured important trends in influence of system parameters (particle size and density, inlet velocity of carrier phase) on particle velocity. However quantitative agreement is not so good, simulation show faster moving particles then experiments. This trend occurs in all simulation results and probably it is due to neglecting the shear stress between front and rear walls and particles. Numerical results also show that type and shape of computational grid are not elementary parameters. They have only small affect on flow pattern in the cell, at least in tested range of mesh parameters. The experiments further show that techniques used for particle velocity profiles determination and experimental data evaluations are convenient. The experimental results for given apparatus show that for particles with higher density it is necessary to provide the higher inlet water velocities to ensure particle circulation, as expected. Moreover particle motion in both packed beds and draft-tube is strongly affected by cell geometry and entire apparatus

8 construction. From experimental results it can be seen that in the cell with tested geometry only funnel-flow is present. Comparison with experimental data offers acceptable semi quantitative validation of CFD model, but for electrochemical application the results are not optimal. Acknowledgement The authors are grateful for the financial support from GACR 10/0/H11. References [1] Froment G. F., Bischoff K. B., Chemical reactor analysis and design, John Wiley & Sons, New York, 1990 [2] Jiricný V., Stanek V.: Production of D-arabinose in a pilot-plant fluidized bed electrochemical reactor. J. Appl. Electrochem. 2, (199) [] Jiřičný V., Siu S., Roy A., Evans J. W.: Regeneration of zinc particles for zinc-air fuel cells in a spouted-bed electrode. J. Appl. Electrochem. 0, (2000) [] Jiřičný V., Roy A., Evans J.W.: Copper Electrowinning using Spouted-Bed Electrodes: Part I., Metallurgical and Materials Transactions B B, (2002) [] Jenike A.W.: Quantitative Design of Mass Flow Bins, Powder Technol. 1, (1967) [6] Ding S. et al.: Finite Element Investigations of the Effects of a Passive Insert on Flow Patterns in Silos, Proceedings of 1th International Congress of Chemical and Process Engineering CHISA 2002, 2 29 August 2002, Prague, Czech Republic. [7] Ding S. et al.: Simulations of Silo Discharge Flow Patterns and Predictions of Loads on Walls and Inserts, Proceedings of 1th International Congress of Chemical and Process Engineering CHISA 2002, 2 29 August 2002, Prague, Czech Republic. [8] Liang W.: Flow Characteristic of the Liquid-Solid Circulating Fluidized Bed, Powder Technol. 90, (1997) [9] Jirkovský R., Tržil J.: Chemické a laboratorní tabulky, nakl. Práce, Praha 197. [10] Reisner W.: The Behaviour of Granular Materials in Flow Out of Hoppers. Powder Technol. 1, (1967/68)