Improved buoyancy-drag model based on mean density profile and mass conservation principle

Abstract

Rayleigh–Taylor (RT) and Richtmyer–Meshkov (RM) turbulent mixing occur frequently in various natural phenomena and practical engineering applications. Accurate prediction of the evolution of mixing width, which comprises the bubble mixing width (BMW) and spike mixing width (SMW), holds significant scientific and engineering importance. Over the past several decades, buoyancy-drag models have been widely used to predict this evolution, but these models exhibit several limitations. In this paper, we propose a new buoyancy-drag model that incorporates additional physical constraints. The new model posits that the evolutions of the BMW and SMW are interrelated and mutually dependent. Consequently, we innovatively introduce the principle of mass conservation to link the evolution of SMW to that of BMW. The BMW is modeled using an ordinary differential equation (ODE) that includes inertial force, drag, and buoyancy terms. Accurate modeling of the inertial force term requires knowledge of the mean density profile, which we analytically derived for any density ratio by improving the previous density-ratio-invariant mean-species profile theory. The form and coefficient of the drag term were determined inversely by imposing the constraint that the ODE must predict the physical evolution of RM mixing. For the buoyancy term, we accounted for the entrainment phenomenon by introducing a density-ratio-dependent buoyancy coefficient additionally. The specific form of this coefficient was derived by requiring that the ODE predict the physical evolution of RT mixing as the density ratio approaches 1. Using a single set of coefficients, the new model successfully predicted the physical evolution of the mixing width across different density ratios and acceleration histories. This study enhances both the accuracy and robustness of the buoyancy-drag model.