Kinetic energy balance in turbulent particle-laden channel flow

Abstract

The present study investigates the influence of particle additives on the transfer, conversion, and dissipation of kinetic energy (KE) of a turbulent gas–solid channel flow. We derived the equations of KE, mean-flow KE, and turbulent KE (TKE) of the particle-laden flow and further performed two-way coupled direct numerical simulations of channel flow laden with four-million particles with Stokes number St = 30 (corresponding to a mass loading ratio of around one) with an Eulerian–Lagrangian approach. We found that, in the unladen flow, more than half of the input energy is directly dissipated in the mean flow, whereas the rest is converted to maintain the turbulence. By contrast, in the laden flow, both mean dissipation and energy supply are comparable with the unladen flow. However, the turbulence production is greatly reduced in the particle-laden flow. Another sink term due to the presence of the particle–fluid interactions corresponds to the rest loss of the total energy supply. The results reveal the particle-induced redistribution of mean KE, which is transferred from the mean flow to particles in the channel core, whereas the flow gains energy from particles in the near-wall region. In total, there is a loss of the mean-flow energy due to the presence of the inertial particles. Regarding TKE balance, the particles, gaining energy from the mean flow, transfer the energy to the fluid across the channel, which contributes around one third of the TKE source. The present results provide a general picture of KE balance of a particle-laden channel flow.