Implementation and Validation of Quadratic Constitutive Relation in One-Equation k-kL Turbulence Model

Abstract

Computational Fluid Dynamics (CFD) has been widely used in modern engineering analysis of products and systems involving fluid flow. In majority of applications, the flow is turbulent; however accurate prediction of turbulent flow remains a challenging problem to date. Considering both the accuracy and cost of simulations, the most widely used approach for simulation of turbulent flows is to solve the Reynolds Averaged Navier-Stokes equations (RANS) in conjunction with a turbulence model which models the Reynolds stresses using the Boussinesq approximation that relates the Reynolds stress tensor to strain tensor via an eddy viscosity. In past many decades, a linear relationship between Reynolds Stress tensor and strain tensor has been employed in almost all turbulence models. Linear eddy viscosity models have shown good results for wide variety of flows; however in many cases they have been found to be inadequate. Therefore, the nonlinear Quadratic Constitutive Relation (QCR) has been suggested to improve the accuracy of simulations. In this thesis, QCR is implemented for a recently developed one-equation k-kL turbulence model by Shuai and Agarwal, and is tested by comparing its accuracy with linear eddy viscosity models and one-equation Algebraic Reynolds Stress Model (ARSM) developed by Wen and Agarwal. The computational results for k-kL-QCR for several benchmark cases from NASA TMR are compared to other widely used turbulence models with QCR, such as Spalart-Allmaras model (SA), Wray-Agarwal model (WA) and SST k-ω model. It is shown that one-equation k-kL-QCR model shows good accuracy against experimental data with less computational cost for both incompressible and compressible transonic and supersonic flow cases