Energy equations for gas-liquid turbulent flows with phase change

Abstract

In this work, we derive the equations of turbulence kinetic energy (TKE), mean-flow kinetic energy (MFKE) and mean internal energy (MIE) for gas-liquid interfacial flows with phase change for the first time. We present the equations for a fully compressible flow in gas or liquid phase which allows us to study the effects of global volume changes away from the interface. We then take the interface into account and present the energy equations for the gas-liquid interfacial flow allowing for local volume changes at the gas-liquid interface. These equations allow us to explain the pathways of energy exchange between the gas and liquid phase while highlighting the effects of local volume changes at the interface due to phase change. We explain the role of the phase change in the energy interactions through phase change free energy. We relate the rate of change of phase change free energy to the powers of mass flux, momentum flux and heat flux due to phase change. This link allows us to explain how evaporation or condensation affects the temporal evolution of energies for compressible gas-liquid flows with phase change. We rewrite these energy equations for droplet-laden homogeneous shear turbulence with phase change (DLHST-PC), and droplet-laden decaying homogeneous isotropic turbulence with phase change (DLHIT-PC). Furthermore, we explain the role of interfacial surface energy through the power of surface tension.