Four-equation model for unified prediction of turbulent mixing induced by interfacial instabilities

Abstract

Turbulent mixing induced by interfacial instabilities are generally predicted using the Reynolds-averaged Navier–Stokes (RANS) model in practical applications. Among RANS models, the advanced Besnard–Harlow–Rauenzahn (BHR) series stand out due to its capacity to characterize the mixing state, which is quite important for reaction rate calculation in fusion engineering. However, the present limitation of this model is its inability to unified predict mixing growth rates and profiles across diverse density ratios or types of turbulent mixing scenarios. To overcome these limitations, we extend the methodology in determining turbulence model coefficients to the four-equation framework. The extension concerns a refined four-equation model, particularly in modifying the dissipation term associated with the density-specific volume covariance, thereby greatly improving the model’s performance at high density ratios. Further, new self-similar profiles for various physical quantities are introduced by considering more realistic evolution. This enhancement is shown to yield more plausible predictions. Finally, leveraging the unique traits of the four-equation model, we utilize an ansatz of self-similarity to derive consistent model coefficients ensemble tailored to different turbulent mixing scenarios. With these enhancements, this model realizes unified predictions of mixing width and profiles across classical turbulent mixings and complex mixings, agreeing well with high-fidelity numerical simulations and experimental measurements. Given the model’s descriptive prowess of mixing state characteristics pertinent to engineering challenges, it has significant potential in the precise prediction of fusion reaction rate and assessments of fusion performance.