Direct numerical simulation of ellipsoidal particles in turbulent channel flow

Abstract

This paper investigates the behaviour of elongated, axi-symmetric ellipsoidal particles, their interaction with turbulence, and the effects of the ellipsoids on turbulence in a turbulent channel flow with Re _τ = 150. The simulations are carried out with full four-way coupling using the point-source approach: the particles are affected by the fluid, the particles affect the fluid, and the particles can collide with each other or the wall using a realistic collision algorithm. The trajectories of the ellipsoids are tracked by solving the translational and rotational equations of motion in a Quaternion framework and are closed with hydrodynamic drag and torque laws. To specifically identify the effect of particle shape, simulations of single phase channel flow are compared to simulations with spherical particles and to simulations with ellipsoids. In all cases, the driving pressure drop, to establish a flow with Re _τ = 150, is kept constant. Both the spherical particles and the ellipsoidal particles have a Stokes number of 5. Although the volume fraction is very low, 0.00725 and 0.0219 % for the spheres and ellipsoids, respectively, there is some effect of the particles and the ellipsoids on the turbulence. Although the transport terms in the turbulent kinetic energy equation of the fluid are hardly affected, the turbulence kinetic energy itself decreases by 6.0 % for the flow laden with spherical particles and 4.8 % for the ellipsoidal particles. The homogeneous dissipation of turbulence kinetic energy by the fluid decreases due to the addition of particles, and the production also decreases. The particles dissipate turbulence kinetic energy of the fluid phase, predominantly in the near-wall region. Because there is a high average slip velocity in the stream-wise direction between the particles and the fluid in the near-wall region, the root mean square of the particle velocity is higher than that of the fluid velocity in this direction. In the other directions, the root mean square velocities of the particles are significantly lower than of the fluid. There is, however, a positive slip velocity between the particles and the fluid in the wall-normal direction, indicating that the particles move towards the wall with a higher momentum than that they return to the centre of the channel with. As a result, there is a 4–5 times higher concentration of particles near the wall than in the centre of the channel. As both the spherical and the ellipsoidal particles are very small, there is no major difference in their overall behaviour. However, in the near-wall region, there are some profound differences. The collision mechanism of ellipsoids with the walls is significantly different compared to spheres, the former predominantly inducing rotation resulting from a collision and the latter predominantly moving away from the wall after colliding. This is confirmed by the strong rotation as well as large root mean square of rotation of the ellipsoidal particles in the near-wall region. This results in a slight inward shift of the peak of the root mean square velocities of the fluid and the ellipsoidal particles as well as the peak in slip velocity, driving the momentum transfer, compared to the simulations with the spheres. Finally, the statistics of the orientation show that the ellipsoids align in the stream-wise direction in the near-wall region, because of the fluid boundary layer as well as the particle–wall collisions, but that there is no significant orientation of the ellipsoids outside of the near-wall region.