Buoyancy-generated variable-density turbulence

Because of the importance of turbulence mixing in many applications, a number of turbulence mixing models have been proposed for variable- density flows. These engineering models (one- point statistical models) typically include the transport of the turbulent kinetic energy and the turbulent energy dissipation rate (i.e., k - {epsilon} models). The model presented by Besnard, Harlow, Rauenzahn and Zemach (1992) (herein referred to as BHRZ) is a one-point model intended to describe variable-density turbulent flows. Transport equations for the Reynolds stress tensor, R{sub ij}, and the turbulent energy dissipation rate, the density-velocity correlation, a{sub i}, and the density-specific volume correlation, b are derived. This model employs- techniques and concepts from incompressible, constant- density turbulence modeling and incorporates ideas from two-phase flow models. Clark and Spitz (1994) present a two-point model for variable-density turbulence. Their derivation is based on transport equations that, are based 0481 on two-point- generalizations of R{sub ij}, a{sub ij}, and b. These equations are Fourier transformed with respect to the separation distance between the two points. Transport equations are derived for R{sub ij}, a{sub i}, b. As in the one-point model, this model contains many ad-hoc assumptions and unknown model coefficients that must be determined by comparison with experimental and numerical data. However, the two-point formalism requires fewer equilibrium assumptions then does a single-point model. Our primary concern in this paper lies in the nonlinear processes of turbulence and the influence of large density variations (not within the Boussinesq limit) on these processes. To. isolate the effects of variable-density on the turbulence we restrict our flow to be incompressible, statistically homogeneous buoyancy-generated. turbulence. To our knowledge there have not been any simulations reported for this problem