Abstract
In this paper, we use an averaged entropy inequality and employ it together with an entropy principle to develop thermodynamically consistent rate-dependent turbulence models and governing equations at the first order level for describing the turbulence. In particular, a thermodynamically consistent evolution equation of the dissipation rate of the turbulent kinetic energy is presented in contrast to other recent works [1–3]. The domain of validity of the model is defined by the restrictions placed upon the model parameters imposed by the entropy inequality, so that only physically realizable processes can be described.
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