^{1}and Nicholas S. Vlachos

^{1,a)}

### Abstract

The interaction of small heavy solid particles with turbulence near the wall of a vertical downward channel flow is investigated by using direct numerical simulation (DNS) and Lagrangian particle tracking. The interest is focused on the effect of the particles on the near-wall coherent structures obtained by conditional sampling of DNS results of a particle-laden turbulent channel flow. The coherent structures are detected from instantaneous flow fields by using the vortex definition of Jeong and Hussain [J. Fluid Mech.285, 69 (1995)]. The Reynolds number of the particle-free flow is based on the friction velocity and the wall half distance. The particle response time is 200 wall units and the average mass and volume fractions and , respectively. The particle diameter is smaller than the Kolmogorov length scale and the grid spacing, the latter being small enough to adequately resolve the smaller fluid flow scales. The feedback effect of the particles on the carrier phase is taken into account by a point-force model. Purely elastic interparticle collisions are also considered. For both particle-free and particle-laden flows, the dominant coherent structures in the near-wall region are elongated quasistreamwise vortices. The addition of particles results in a weaker mean structure, with larger diameter and longer streamwise extent. The qualitative characteristics of the velocity distributions around the mean coherent structures are similar, independent of the particles. However, the coherent velocityfluctuations in the wall-normal and spanwise directions considerably decrease, and the low-speed streak is damped by the particles. The educed results show that the particles create a torque of opposite sign to the rotation of the mean vortex, which in turn reduces the streamwise vorticity of the structure. Consequently, the magnitude of fluid pressure decreases and the redistribution of turbulent kinetic energy from the streamwise to the other velocity components is significantly reduced.

The authors wish to acknowledge the financial support of the Ministry of Education of Greece in the form of a fellowship to CDD of the program “Heracletos: Basic Research” (funded by the EU), under which part of this work was done.

I. INTRODUCTION

II. MATHEMATICAL FORMULATION

III. RESULTS AND DISCUSSION

A. Instantaneous flow fields

B. Conditional ensemble average flow fields

IV. CONCLUSIONS

### Key Topics

- Rotating flows
- 42.0
- Vortex dynamics
- 31.0
- Turbulent flows
- 27.0
- Particle laden flows
- 26.0
- Turbulent channel flow
- 15.0

## Figures

Mean streamwise velocity. Continuous line: fluid velocity of particle-free flow: dashed line: fluid velocity of particle-laden flow; symbols: particle velocity.

Mean streamwise velocity. Continuous line: fluid velocity of particle-free flow: dashed line: fluid velocity of particle-laden flow; symbols: particle velocity.

Fluid rms velocity fluctuations. Lines: particle-free flow; symbols: particle-laden flow.

Fluid rms velocity fluctuations. Lines: particle-free flow; symbols: particle-laden flow.

rms vorticity fluctuations. Lines: particle-free flow; symbols: particle-laden flow.

rms vorticity fluctuations. Lines: particle-free flow; symbols: particle-laden flow.

Mean and rms distributions of . Lines: particle-free flow; symbols: particle-laden flow.

Mean and rms distributions of . Lines: particle-free flow; symbols: particle-laden flow.

Cross correlations of with , , , and . Lines: particle-free flow; symbols: particle-laden flow.

Cross correlations of with , , , and . Lines: particle-free flow; symbols: particle-laden flow.

Top and side views of the mean coherent structure [(a) and (b)] for the particle-free flow, [(c) and (d)] for the particle-laden flow.

Top and side views of the mean coherent structure [(a) and (b)] for the particle-free flow, [(c) and (d)] for the particle-laden flow.

Ensemble-averaged coherent velocity fluctuations around the mean vortex at plane (a), (c), and (e) for the particle-free flow and (b), (d), and (f) for the particle-laden flow.

Ensemble-averaged coherent velocity fluctuations around the mean vortex at plane (a), (c), and (e) for the particle-free flow and (b), (d), and (f) for the particle-laden flow.

Coherent shear Reynolds stresses around the mean vortex at plane (a), (c), and (e) for the particle-free flow and (b), (d), and (f) for the particle-laden flow.

Coherent shear Reynolds stresses around the mean vortex at plane (a), (c), and (e) for the particle-free flow and (b), (d), and (f) for the particle-laden flow.

Coherent vorticity components around the mean vortex at plane (a), (c), and (e) for the particle-free flow and (b), (d), and (f) for the particle-laden flow.

Coherent vorticity components around the mean vortex at plane (a), (c), and (e) for the particle-free flow and (b), (d), and (f) for the particle-laden flow.

Coherent vorticity components and pressure fluctuations around the mean vortex at plane (a) for the particle-free flow, (b) for the particle-laden flow, (c) pressure variation with at , and (d) pressure variation with at and .

Coherent vorticity components and pressure fluctuations around the mean vortex at plane (a) for the particle-free flow, (b) for the particle-laden flow, (c) pressure variation with at , and (d) pressure variation with at and .

Components of fluid-particle energy exchange term around the mean vortex for the particle-laden flow at plane.

Components of fluid-particle energy exchange term around the mean vortex for the particle-laden flow at plane.

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