14th European Conference on Mixing Warszawa, 10-13 September 2012 RELATION BETWEEN PARTICLE RISING BEHAVIOR AND LIQUID

FLOW AROUND THE BOTTOM OF A STIRRED VESSEL

Ryuta Misumia, Takuji Sasakib, Hayato Katob, Kazuhiko Nishia, Meguru Kaminoyamaa

a Yokohama National University, Faculty of Engineering, 79-5, Tokiwadai, Hodogaya-ku,

Yokohama 240-8501, Japan b Yokohama National University, Graduate School of Engineering, 79-5, Tokiwadai,

Hodogaya-ku, Yokohama 240-8501, Japan

r-misumi@ynu.ac.jp

Abstract. The mechanism of particle rising behavior from a bottom in a stirred vessel is not understood sufficiently. Using Computational Fluid Dynamics (CFD) coupled with the Lagrangian simulation of particle motion, this study clarified the relation between particle rising behavior from a vessel bottom and liquid flow just above a bottom in stirred vessels of three types (with and without baffles, and different impeller height) having different mean flow patterns. Results show that a common relation exists between particle rising behavior and liquid flow around the bottom in the stirred vessels of three types. The relation is summarized as the following process. (i) Stagnant regions of horizontal fluid flow just above the vessel bottom are induced depending on the type of stirred vessel. (ii) Bottom particles are swept and piled up around the stagnant region. (iii) Upward fluid flows are induced above the stagnant region. (iv) The particles are included in the upward liquid flow and are suspended throughout the whole vessel. Keywords: Solid–liquid mixing, CFD, Crystallization, Flow pattern, Distinct Element Method (DEM)

1. BACKGROUND Solid–liquid mixing is used frequently in many industrial processes. The main purpose of

these processes is suspension of solid particles in liquid and the enhancement of mass transfer between particles and liquid. Many models have been proposed to explain the mechanism of ‘complete suspension’ of solid particles in a stirred vessel. These models mainly describe the relation between the particle motion and ‘turbulent eddies’ just around the vessel bottom [e.g. 1]. Nevertheless, the relation between particle rising behavior from a bottom surface and ‘mean liquid flow’ in a stirred vessel is not understood sufficiently, mainly because of difficulties in characterizing detailed particle behaviors experimentally. However, Computational Fluid Dynamics (CFD), coupled with the Lagrangian simulation of particle motion, is a very useful and powerful technique to quantify the particle behavior [e.g., 2, 4, 7]. In this study, the relation between particle rising behaviors and mean liquid flow pattern just around the vessel bottom were investigated using Euler–Lagrangian simulations of particle behaviors [3, 5, 6] rising from a vessel bottom.

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Figure 1. Coordinate system and computational domain for a stirred vessel.

2. NUMERICAL SIMULATION Figure 1 presents a coordinate system and computational domain for a stirred vessel. A

cylindrical stirred vessel filled with water was of 100 mm inner diameter D and 100 mm liquid level H. The vessels were flat-bottom cylindrical vessels with four baffle plates (B = 0.1 D) or without a baffle. A six-blade, paddle-type impeller of 50-mm diameter d and 10 mm axial width b was submerged at h = H / 10 to H / 3. The impeller rotational speed, n, was 6 s-1.

The mass and momentum conservation equations for the liquid phase were solved using a scheme based on the MAC method. Large Eddy Simulation (LES) was used for turbulence simulation. The Lagrangian particle motion equations for each particle were calculated based on the instantaneous local fluid velocity obtained using the LES simulation. Contact forces acting on particles were calculated based on the Distinct Element Method (DEM). Particles taken up for suspension corresponded to glass beads with particle diameter dp of 100 μm, density ρp of 2,500 kg/m3, and particle number N of 50,000.

For the LES simulation coupled with DEM, we used commercial CFD software “R-Flow (Rflow Co. Ltd.)” [2, 4, 5] with some user subroutines.

3. RESULTS AND DISCUSSION

3.1 The case of h = H / 3 with four baffle plates Figure 2 portrays a particle sedimentation pattern on a vessel bottom and directions of

horizontal fluid flow for h = H / 3 with four baffle plates. Figure 3 depicts a contour of the time-averaged vertical fluid velocity Vf, z immediately above the vessel bottom (z = 0.9 mm). The liquid flows from the front face of each baffle plate discharge in two directions, and mutually collide, forming a twisted criss-cross stagnant area running from the four baffle plates (a figure of horizontal fluid vectors is omitted here). The particles on the bottom are swept by the horizontal flows, forming a twisted criss-cross sedimentation pattern running from the four baffle plates along the stagnant area of liquid flow (Figure 2). Along this stagnant area, upward liquid flows are also induced (Figure 3). Consequently, the particles are piled up along the stagnant area, and some particles are sucked upward by the liquid flow.

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Figure 2. Particle sedimentation pattern on the bottom (0.0 < z < 0.3 mm, h = H / 3 with four baffles).

Figure 3. Distribution of Vf,z just above the bottom (z = 0.9 mm, h = H / 3 with four baffles).

Figure 6. Particle sedimentation pattern on the bottom (0.0 < z < 0.3 mm, h = H / 10 with four baffles).

Figure 7. Distribution of particles moving upward around the bottom (0.3 < z < 4.0 mm, h = H / 10 with four baffles).

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Figure 4. Horizontal fluid velocity vectors, Vf, r-θ just above the bottom (z = 0.9 mm, h = H / 10 with four baffles).

Figure 5. Distribution of Vf,z just above the bottom (z = 0.9 mm, h = H / 10 with four baffles).

3.2 The case of h = H / 10 with four baffle plates

For h = H / 10 with four baffle plates, the mean flow pattern and particle motion differ from the case of h = H / 3 with four baffle plates. Figure 4 portrays the time-averaged fluid velocity vectors Vf, r-θ in the vicinity to the vessel bottom (n = 6 s-1, z = 0.9 mm). Figure 5 depicts the distribution of the time average vertical fluid velocity Vf, z just above the vessel bottom (n = 6 s-1, z = 0.9 mm). These figures show that the liquid flows discharged from the impeller reach the bottom directly and then flow toward the vessel wall with some elevation.

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Figure 10. Particle sedimentation pattern on the bottom (0.0 < z < 0.3 mm, h = H / 3 without baffles).

Figure 8. Horizontal fluid velocity vectors, Vf, r-θ just above the bottom (z = 0.9 mm, h = H / 3 without baffles).

Figure 9. Distribution of Vf,z just above the bottom (z = 0.9 mm, h = H / 3 without baffles).

Figure 11. Distribution of particles moving upward around the bottom (0.3 < z < 4.0 mm, h = H / 3 without baffles).

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The discharged flows collide with weak down-flow at around the vessel wall; then they proceed upward along the wall.

Figure 6 shows the particle sedimentation pattern on the bottom. Figure 7 shows the distribution of particles moving upward around the bottom. The particles on the bottom are swept toward the wall by the discharged flow from the impeller. Then they are piled up along the stagnant area near the vessel wall. Upward liquid flows are induced along this stagnant area. Subsequently the particles are sucked upward by the flow along the wall.

3.3 The case of h = H / 3 without baffles Figure 8 portrays the time-averaged fluid velocity vectors Vf, r-θ near the vessel bottom (n

= 6 s-1, z = 0.9 mm) in the case of h = H / 3 without baffles. Figure 9 shows the distribution of the time-averaged vertical fluid velocity, Vf, z just above the vessel bottom (n = 6 s-1, z = 0.9 mm). In this case, at the impeller equipped height, liquid flows discharged from the impeller tip reach the vessel wall forming a counter-clockwise rotating flow (figure is omitted). Around the bottom, the rotating flow focuses to the center of bottom (Figure 8); then it induces upward flow at the center of the bottom (Figure 9).

Figure 10 exhibits the particle sedimentation pattern on bottom (0.0 < z < 0.3 mm). Figure 11 displays the distribution of particles moving upward around the bottom (0.3 < z < 4.0 mm). The particles on the bottom are swept toward the center of vessel bottom by the rotating flow. Then they are piled up at the center of the bottom where the horizontal liquid flow is stagnant (Figure 10). Upward liquid flows are induced above the stagnant region. Subsequently the particles are sucked upward by the flow (Figure 11) similarly to the pattern observed in the vessel with baffles.

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Figure 12. Sketch of particle rising behavior and liquid flow around the vessel bottom; (left) h = H / 3 with four baffles, (right) h = H / 10 with four baffles.

3.4 Relation between particle rising behavior and liquid flow around the bottom Figure 12 shows a sketch of the relation between particle rising behavior and liquid flow

around the bottom in the cases of h = H / 3 with four baffles (left) and h = H / 10 with four baffles (right). The relation is summarized as the following process. (i) A stagnant region of horizontal fluid flow is induced just above the vessel bottom depending on the type of stirred vessel; a twisted criss-cross shap (h = H / 3), along the vessel wall (h = H / 10) and at around the center of vessel bottom (h = H / 3 without baffle). (ii) The particles are swept and piled up around the stagnant region. (iii) Upward fluid flows are also induced above the stagnant region. (iv) The particles are included in the up-ward liquid flow and are suspended to the whole vessel.

The important point that the authors must mention is that this relation exists in a closed flow field system such as that of a stirred vessel in which the time-averaged flow pattern is stable and the upward flow rate and downward flow rate must be conserved.

4. CONCLUSIONS This study clarified the relation between particle rising behavior from a vessel bottom and

liquid flow just above a bottom under three types of stirred vessel (with and without baffles, and different impeller heights) having different main flow patterns. Results show that a common relation exists between particle rising behavior and liquid flow around the bottom in stirred vessels of three types: the particles on the bottom are swept and piled up around the stagnant region which differ from each stirred vessel; then particles are included in upward liquid flow that is induced above the stagnant region, after which they are suspended throughout the whole vessel.

ACKNOWLEDGEMENTS

The authors acknowledge advice given by Mr. H. Takeda of Rflow Co. Ltd. and assistance by Y. Masui, and T. Miura of Yokohama National University. This study was supported financially by Grants-in-Aid from the Salt Science Research Foundation (Nos. 0711 and 0813), the Excellent Young Researchers Oversea Visit Program from JSPS, and Grants-in-Aid for Young Scientists (B) from MEXT (Nos. 16760121, 19760112 and 23760147).

5. REFERENCES

[1] Baldi G., Conti R., Alaria E., 1978. “Complete Suspension of Particles in Mechanically Agitated Vessels”, Chem. Eng. Sci., 33, 21-15. [2] Derksen J. J., 2003. “Numerical Simulation of Solids Suspension in a Stirred Tank”, AIChE J., 49, 2700-2714. [3] Misumi R., Masui Y., Nakanishi R., Nishi K., Kaminoyama M., 2009. “Lagrangian Numerical Simulation of Particle Collision and Suspension in a Stirred Vessel”, Proc. Eighth World Cong. of Chem. Eng. (Montreal, 23–27 Aug.), Canada, No. 1724.

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[4] Misumi R., Nakamura N., Nishi K., Kaminoyama M., 2004. “Effects of Instantaneous Slip Velocity and Solute Distribution on the Dissolution Process of Crystal Particles in a Stirred Vessel”, J. Chem. Eng. Japan, 37, 1452-1460. [5] Misumi R., Nakanishi R., Masui Y., Nishi K., Kaminoyama M., 2008. “Lagrangian Numerical Simulation of Crystal Particle Impact in a Stirred Vessel”, Proc. Second Asian Conf. on Mixing (Yonezawa, 7-9 Oct.), Japan, pp. 269-275. [6] Misumi R., Sasaki T., Miura T., Nishi K., Kaminoyama M., 2011. “Lagrangian Simulation of Solid Particles Motion from a Vessel Bottom”, Proc. Int. Symp. on Mixing in Ind. Proce. 7, (Beijing, 18-22 Sep.), Japan, pp. 86-87. [7] Rielly C. D., Marquis A. J., 2001. “A Particle’s Eye View of Crystallizer Fluid Mechanics”, Chem. Eng. Sci., 56, 2475-2493.

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