Numerical simulations of turbulence modulation by dense particles in a fully developed pipe flow

Abstract

Turbulence modulation by disperse dense particles in a fully developed vertical pipe flow at Re τ =360 (based on the friction velocity, u τ , and the pipe diameter, D) is studied using direct numerical simulations (of the fluid). Particles smaller than the Kolmogorov length scale of turbulence are considered. The continuous and the disperse phases are treated using the Eulerian and Lagrangian approaches, respectively. The effects of varying particle parameters such as response time, volume fraction and settling velocity on fluid turbulence are investigated. A preliminary study with the inclusion of interparticle collision effects is also presented. Results indicate that when particles are not influenced by gravity, i.e., their settling velocity is zero, variation of either the volume fraction or the response time has negligible effects on the fluid streamwise mean velocity profile. However, it is observed that an increase in either the volume fraction or the response time augments the streamwise rms velocities and attenuates the radial and azimuthal rms velocities. Particles with settling velocity in the direction of the mean flow lead to a marginal increase in the streamwise mean velocities and a substantial increase in the streamwise rms velocities. The fluid radial and azimuthal rms velocities are also higher than those for the zero settling velocity case at the same particle volume fraction and response time. The pressure–strain term, in the presence of gravity, redistributes greater amount of energy from the streamwise direction to the cross-stream directions. Significant augmentation of turbulence at the dissipative scales can be seen in the energy spectra at certain radial locations. It is observed from the longitudinal energy spectra that turbulence augmentation is greatest at radial locations close to the pipe center and the pipe wall. Turbulence augmentation falls as we move away from these two boundaries. In case of azimuthal energy spectra, augmentation at medium and high wavenumbers is seen in the core region of the pipe. However, the azimuthal length scales become less responsive to particle fluctuations as we move towards the wall. In the presence of gravity, due to the reverse cascade [Phys. Fluids, A 5 (1993) 1203], turbulence augmentation at low wavenumbers is also observed. Collisions are seen to reduce the degree of particle migration to the wall. The effects of particle collisions on fluid turbulence are discussed.