On the interaction of homogeneous shear turbulence and droplets of Taylor length-scale size

Our objective is to determine the effects of linear mean shear flow on the interaction of droplets with homogeneous turbulence. We performed DNS of 3130 finite-size droplets of diameter approximately equal to the Taylor lengthscale and with 5\% droplet volume fraction in homogeneous shear turbulence at initial Taylor-scale Reynolds number Re$_\lambda$=75. We studied the effects of varying the Weber number and the shear number on the droplet/turbulence interaction. Following the derivation of the turbulence kinetic energy (TKE) equation for two-fluid flow found in Dodd, Ferrante [J. Fluid Mechanics, Vol. 806, pp. 356-412], we derived the TKE equations for two-fluid flow in homogeneous shear turbulence. We will present the numerical methods we used to simulate two-fluid homogeneous shear turbulence, as well as the effects on droplet/turbulence interaction caused by the mean shear.