Instability of two-phase mixing layers: analysis of exact and approximate base flows from boundary layer theory

Abstract

The utility of composite error-function velocity profiles for the modeling of gas–liquid shear layers is examined by comparing temporal stability results from such approximate error-function profiles with results from the exact velocity profiles based on the two-fluid boundary layer equations. The stability analysis is restricted to two-dimensional perturbations. The two-fluid boundary layer equations are solved numerically using a shooting method in each fluid layer. The composite error-function profile is constructed by matching displacement thicknesses with the exact solution. With given fluid properties, the displacement thicknesses depend on the asymptotic velocity ratio of the liquid and gas stream in the laboratory frame. For different sets of fluid properties, the maximum growth rates of the Kelvin–Helmholtz instability show good numerical agreement between the exact and the approximate velocity profiles, especially when the asymptotic velocities of the gas and liquid phase are close.