^{1,a)}and Efstathios E. Michaelides

^{2,b)}

### Abstract

A newly developed direct numerical simulation method has been used to study the dynamics of nonisothermal cylindrical particles in particulate flows. The momentum and energy transfer equations are solved to compute the effects of heat transfer in the sedimentation of particles. Among the effects examined is the drag force on nonisothermal particles, which we found strongly depends on the Reynolds and Grashof numbers. It was observed that heat advection between hotter particles and fluid causes the drag coefficient of particles to significantly increase at relatively low Reynolds numbers. For Grashof number of 100, the drag enhancement effect diminishes when the Reynolds number exceeds 50. On the contrary, heat advection with colder particles reduces the drag coefficient for low and medium Reynolds number for Grashof number of . We used this numerical method to study the problem of a pair of hot particles settling in a container at different Grashof numbers. In isothermal cases, such a pair of particles would undergo the well-known drafting-kissing-tumbling (DKT) motion. However, it was observed that the buoyancy currents induced by the hotter particles reverse the DKT motion of the particles or suppress it altogether. Finally, the sedimentation of a circular cluster of 172 particles in an enclosure at two different Grashof numbers was studied and the main features of the results are presented.

I. INTRODUCTION

II. DIRECT NUMERICAL SIMULATION FOR HEAT ADVECTION

A. Momentum interaction between the fluid and the particles

III. SIMULATION RESULTS AND DISCUSSION

A. The sedimentation of a circular particle in an infinite channel: A validation test

B. The sedimentation of a circular particle in an enclosure

C. The DKT motion with energy exchange

D. The sedimentation of a circular cluster of particles

IV. CONCLUSIONS

### Key Topics

- Sedimentation
- 38.0
- Heat transfer
- 22.0
- Reynolds stress modeling
- 21.0
- Convection
- 20.0
- Kinematics
- 12.0

## Figures

Conceptual model of two circular particles suspended in a fluid.

Conceptual model of two circular particles suspended in a fluid.

The lateral position of a particle setting in an infinite channel at and . In both cases , , and density ratio .

The lateral position of a particle setting in an infinite channel at and . In both cases , , and density ratio .

Schematic diagram of a cylindrical particle settling in an enclosure (not to scale).

Schematic diagram of a cylindrical particle settling in an enclosure (not to scale).

(a) Drag coefficient on a cylindrical particles vs Reynolds number (based on the terminal velocity) for , 100, and at . The results have been normalized by the terminal velocity of particle. (b) Dimensionless terminal velocity of cylindrical particles vs a Reynolds number defined in terms of the reference velocity, , for , 100, and at .

(a) Drag coefficient on a cylindrical particles vs Reynolds number (based on the terminal velocity) for , 100, and at . The results have been normalized by the terminal velocity of particle. (b) Dimensionless terminal velocity of cylindrical particles vs a Reynolds number defined in terms of the reference velocity, , for , 100, and at .

Particle position at from its release for . From left to right: (a) Velocity vector map and vorticity for isothermal flow ; (b) temperature contour for a hot particle, and ; (c) temperature for a cold particle, and .

Particle position at from its release for . From left to right: (a) Velocity vector map and vorticity for isothermal flow ; (b) temperature contour for a hot particle, and ; (c) temperature for a cold particle, and .

The vertical settling velocity of two particles at and for relative density ratio and .

The vertical settling velocity of two particles at and for relative density ratio and .

Snapshots of the relative position of the particles and temperature contours for and . From left to right: , drafting; , kissing; , tumbling; , moving in separate directions.

Snapshots of the relative position of the particles and temperature contours for and . From left to right: , drafting; , kissing; , tumbling; , moving in separate directions.

Vertical settling velocity of two particles at and for relative density ratio and .

Vertical settling velocity of two particles at and for relative density ratio and .

Snapshots for , relative density ratio , and . Top, from left to right: , 84, 168, and 252. Bottom, left to right: , 448, 560, and 700.

Snapshots for , relative density ratio , and . Top, from left to right: , 84, 168, and 252. Bottom, left to right: , 448, 560, and 700.

Snapshots for , relative density ratio , and . From left to right: , 56, 182, and 266.

Snapshots for , relative density ratio , and . From left to right: , 56, 182, and 266.

Snapshots at , 2.5, 5, 7.5, 10, and for relative density ratio and .

Snapshots at , 2.5, 5, 7.5, 10, and for relative density ratio and .

Snapshots at , 2.5, 5, 7.5, 10, and for relative density ratio and .

Snapshots at , 2.5, 5, 7.5, 10, and for relative density ratio and .

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