Study Of Compressible Flows With Nonlinear Eddy Viscosity Models

Computational Fluid Dynamics, which has the advantage of less cost and more detailed results, has been widely used in supersonic aerocrafts and supersonic engines development. Turbulence modeling, one of the key issues in numerical simulations, has been studied in the present research. The supersonic flow contains complex mechanisms such as the interactions between the shockwave and the turbulence, the shockwave and boundary layer and the separation of the boundary, traditional Linear Eddy Viscosity Models which were widely used in the engineering field cannot provide a precise result. To develop more precise turbulence model is one of the most important researches in CFD. The Nonlinear Eddy Viscosity Models can be easily combined into linear Eddy Viscosity Models'transport equation for its explicit characteristic. It based on the ideas which likened the behavior of a turbulent Newtonian fluid to the behavior of the laminar flow of a non-Newtonian fluid, replaces the usual Boussinesq-type linear eddy viscosity relationship between the Reynolds stress tensor and the mean strain rate with a higher-order expansion in terms of powers of the mean strain rate and rotation rate tensors. The models used the tensor terms developed by the Explicit Algebraic Stress Models as their higher-order expansions, then define the coefficients of the expansions by the results of the experiment and DNS of the classical flows. The Nonlinear Eddy Viscosity Models can be classified into second-order models and third-order models for the difference of their representations of the higher-order expansions.Most Eddy Viscosity Models contain a hypothesis that the divergence of velocity is zero, which cannot exist in the hypersonic flow. This paper develop SZL-P and CLS-P models which can be used in compressible flow by implying dilatational compressibility and unsteadiness of shockwave modifications to the low Reynolds k-εtransport equations which are used as scalar transport equations by two Nonlinear Eddy Viscosity Models, SZL second-order model and CLS third-order model. Numerical simulations were performed for supersonic back step flow, transonic channel flow and transonic bump flow. Comparing with result of experiments, the models developed in the present research showed better performance in predicting the shock's position, separation's length and the distribution of pressure, mean velocity, turbulence intensity and Reynolds shear stress in the near wall region.