Abstract
The derivation of a two-equation turbulence model consistent with the second law of thermodynamics that takes into account the effects of buoyancy to within the Boussinesq approximation is presented. The equations of conservation of mass, balance of momentum, conservation of energy, and entropy inequality are averaged, and the corresponding balance laws for the mean turbulent buoyant flow field are developed. The physical constraints imposed by the second law of thermodynamics are used to formulate the constitutive equations (or closure assumptions) for the turbulent stress tensor, the heat flux vector, and the energy flux vector. It is shown that the model has the capability of predicting nongradient heat diffusion. The new model contains empirical constants that are determined via comparison of analytical solutions of limiting turbulent flows with experimental data. Furthermore, with certain simplifications the model equations reduce to those of the common k-ϵ model for turbulence with added buoyancy terms.
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