Development and Application of Quadratic Constitutive Relation and Transitional Crossflow Effects in the Wray-Agarwal Turbulence model

Computational Fluid Dynamics (CFD) has now become an almost indispensable tool for modern engineering analysis of fluid flow over aircrafts, turbomachinery, automobiles, and many other industrial applications. Accurate prediction of turbulent flows remains a challenging problem. The most popular approach for simulating turbulent flows in complex industrial applications is based on the solution of the Reynolds-Averaged Navier-Stokes (RANS) equations. RANS equations introduce the so called “Reynolds or turbulent stresses” which are generally modeled using the Boussinesq approximation known as “Turbulence modeling.” Despite their development over a century, the turbulence models used with RANS equations still need much improvement. The first part of this research introduces the Quadratic Constitutive Relations (QCR), which is a nonlinear approach to approximating the turbulent stresses in eddy-viscosity class of turbulence models. In Boussinesq approximation, turbulent stresses are assumed to be linearly proportional to the strain with eddy viscosity being the proportionality constant. In recent years it has been found that linear eddy viscosity models are not accurate for prediction of vortical flows and wall bounded flows with mild separation with regions of recirculating flows. Such flows occur in junctions of aerodynamic surfaces e.g. the wing-body junction and in inlets and ducts with corners. The accurate prediction of these flows is needed for design improvements and better product performance. To remedy some of the shortcomings of the linear eddy-viscosity models, the Quadratic Constitutive Relation (QCR) for eddy viscosity is investigated to test its capability for predicting non-equilibrium turbulence effects. QCR is implemented in Spalart-Allmaras (SA), SST k-ω and Wray-Agarwal (WA) turbulence models and is applied to several applications involving large recirculating regions. It is demonstrated That QCR improves the results compared to linear eddy viscosity models. Another shortcoming of RANS models is their inability to accurately predict regions of transitional flow in a flow field. Many flow regions in industrial applications contain the transitional flow regime e.g. flows over aircraft wings and fuselages, past wind turbines and in gas turbines engines to name a few. The second part of this research has been on the development of a transitional model by suitably combining a correlation based intermittency-γ equation with the WA turbulence model; this new model is designated as Wray-Agarwal-γ (WA-γ) transition model. The WA-γ is extensively validated by computing a number of benchmark cases. The WA-γ model is also extended to include the crossflow-instability induced transition which is a dominant mode of transition in flows involving three-dimensional boundary layers, e.g. flow past swept wings and ellipsoids. This modified WA-γ model is validated using a benchmark test case for analyzing crossflow-induced transition