On Thermodynamics of Turbulence: Development of First Order Closure Models and Critical Evaluation of Existing Models

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. As a consequence, it is shown that the so-called “realizability-constraints” in [4, 5] which are often presented and applied to ensure physically sound solutions of the models in the literature, alone are not able to guarantee conformity with the irreversibility of the turbulent processes; they are only one among other conditions required by the second law of thermodynamics. On this basis the thermodynamic consistency of some existing nonlinear eddy-viscosity models as well as anisotropic models is analysed and discussed. It appears from this critical evaluation that many of the existing models are thermodynamically inadmissible.