Two-equation Turbulence Model Applied Research

In modern aircraft design, there is an urgent requirement for accurate, efficient and easy-use aerodynamic data and computational analysis tools. However, the Euler codes cannot satisfy all the demands for simulating the complex flow-fields. It's necessary to solve Navier-Stokes (NS) equations to give viscous effects, more accurate and more detailed information of flow-fields. Although being superior over the other methods in terms of physical realism, the RANS methods, however, involve one major weakness-the effects of the turbulent motion of the mean flow are unknown and must be modeled. The influence of turbulence is seen as a new term in the equations. This term is the divergence of a second-order correlation tensor of the fluctuating parts of each velocity component. This correlation tensor is known as the Reynolds stress tensor, and it is the object that needs to be modeled. The main focus of this study is on two-equation turbulence models.The two-equation turbulence models can be thought to consist of two more or less separate parts: the scale determining model, which provides scalar information about the turbulence, and the constitutive model, which determines the Reynolds stress tensor. If the two-equation turbulence models employ a linear relationship between the Reynolds stress and the mean strain-rate tensors, this relationship is known as the generalized Boussinesq model, the two-equation models can be extended for a wider range of applicability by developing more advanced nonlinear algebraic relations between the stress tensor and the mean-velocity gradient and the turbulent scales, this is known as explicit algebraic stress models (EASM).The NS solver is developed from Euler equation code by adding viscous terms and two-equation turbulence models. In order to get a better result, the improved Jameson second and forth artificial dissipation is used, the implicit residual averaging and local time step techniques are employed to accelerate the convergence processing. We studied four eddy viscosity models (EVM) and three nonlinear EASM models in detail.The two-equation turbulence models are validated through simulating the flow fields over flat plate, airfoils and ONERA M6 wing. The capabilities of different turbulence models are accessed in this study.