Dynamics of turbulence kinetic energy in droplet-laden homogeneous shear turbulence

Our objective is to study the effects of droplets on the turbulence kinetic energy (TKE) in homogeneous shear turbulence via direct numerical simulation (DNS). The main difference with the study of droplet-laden decaying isotropic turbulence by Dodd & Ferrante (J. Fluid Mech., 2016) is the presence of the mean shear in the flow which results in the production term for the TKE equation. We performed DNS of 1260 non-evaporating droplets of diameter approximately equal to twice the Taylor lengthscale of turbulence at the time the droplets are released, and with 5% droplet volume-fraction in homogeneous shear turbulence at an initial Re_λ,0 = 40 using a mesh of 1200 × 600 × 600 grid points. For the cases studied, we varied the initial We_rms from 0.02 to 0.5 while keeping the density and viscosity ratios constant, ρ_d/ρ_c = 10 and μ_d/μ_c = 10. The results show that increasing We_rms causes a decrease in TKE production, and that for We_rms = 0.02 and We_rms = 0.5, the TKE production is larger and smaller, respectively, than that of the droplet-free case. The underlying physical mechanisms for such dynamics will be discussed.