Effect of Stokes number on energy modulation of the fluid in turbulent particle-laden channel flows

The effect of Stokes number on the kinetic energy (KE) budget in particle-laden turbulent channel flows is examined by conducting two-way coupled direct numerical simulations using the Eulerian-Lagrangian approach. The friction Reynolds number of the single phase channel flow is Re-tau = 180, the particle mass loading and volume fraction are phi(m) = 0.2, phi(v) approximate to 10(-4), and the Stokes numbers range from St(+) = 14-92. The statistics show that due to the presence of solid particles, the mean velocity is reduced in the vicinity of the wall but enhanced in the outer region, and the off-streamwise intensity of fluctuated velocity and the Reynolds stress are reduced in the whole channel. The analysis on the budgets of turbulent kinetic energy (TKE) finds that the presence of particles induces a significant reduction on both the production and dissipation rates. With increasing Stokes number St(+), both the production and dissipation rates exhibit non-monotonical trends, i.e., both initially decrease for St(+) < 40 and then transit to growth after St(+) > 40. This suggests that the particle-induced suppression on TKE production and dissipation is the strongest nearly at St(+) = 40. It is also found that particles act as an additional sink/source term in the budgets of both mean-flow kinetic energy (MKE) and TKE. In addition, we investigate the influence of St(+) on the "zero point" which indicates the balance of exchanging energy between the particle and fluid phases. It is shown that with increasing St(+), the "zero point" moves toward the wall, suggesting that the position of perfect following between particle and fluid is closer to the wall with larger St(+). The present results reveal the Stokes number effects on the spatial transport mechanisms of MKE, TKE in turbulent channel flows laden with inertial particles.