Evolution of mixing width induced by general Rayleigh-Taylor instability

Abstract

Turbulent mixing induced by Rayleigh-Taylor (RT) instability occurs ubiquitously in many natural phenomena and engineering applications. As the simplest and primary descriptor of the mixing process, the evolution of mixing width of the mixing zone plays a notable role in the flows. The flows generally involve complex varying acceleration histories and widely varying density ratios, two dominant factors affecting the evolution of mixing width. However, no satisfactory theory for predicting the evolution has yet been established. Here a theory determining the evolution of mixing width in general RT flows is established to reproduce, first, all of the documented experiments conducted for diverse (i.e., constant, impulsive, oscillating, decreasing, increasing, and complex) acceleration histories and all density ratios. The theory is established in terms of the conservation principle, with special consideration given to the asymmetry of the volume-averaged density fields occurring in actual flows. The results reveal the sensitivity or insensitivity of the evolution of a mixing front of a neighboring light or heavy fluid to the degree of asymmetry and thus explain the distinct evolutions in two experiments with the same configurations.

Nonequilibrium and morphological characterizations of Kelvin–Helmholtz instability in compressible flows

“…Therefore, we present here an interface-tracking method through tracking the leftmost and the rightmost positions with |∆ * m,n | ≥ |∆ * m,n | th , where |∆ * m,n | th is a threshold of |∆ * m,n |. Essentially, the mixing zone width and its growth rate are of great significance in the study of the hydrodynamic instability and turbulent mixing [29,[103][104][105][106][107][108]. The time evolution of w mixing , revealing the mixing extent and efficiency, is an important parameter to quantitatively study the development of KHI.…”

Progress on Understanding Rayleigh–Taylor Flow and Mixing Using Synergy Between Simulation, Modeling, and Experiment

“…A generalized buoyancy-drag model was developed by incorporating conservation of mass and momentum and a symmetry factor to account for density variations [143]. A parabolic velocity profile was assumed, and the local rate of advance of the mixing fronts was approximated by a volume-averaged rate.…”

“…Copyright 2000 by AIP Publishing.)Fig. 18Validation of current theory for problems with constant acceleration and at all density ratios (Reproduced with permission from Ref [143]…”

Methodology for determining coefficients of turbulent mixing model

“…Consequently, given the value of any one undetermined variable, the others can be uniquely determined. Considering that (i) the drag coefficient C D has a more clear physical meaning, and (ii) the value of C D has been widely investigated in either buoyancy-drag model (Dimonte 2000;Zhang et al 2016) or K-L model (Dimonte & Tipton 2006;Morgan & Greenough 2016), in this paper we leave the one degree of freedom to C D . Now given α b , α KH , θ, ΔE k /ΔPE, s, γ and C D , the final expressions to calculate the model coefficients are collected, in an order that each coefficient can be determined explicitly one by one, as…”