Towards a robust and efficient v 2 - f implementation with application to transonic bump flow

1. Motivation and objectives In the last few years, Durbin’s v-f turbulence model has been extensively tested for subsonic and transonic flows using different numerics for the discretization of the equations and for their solution. Three versions of the model have been successively developed. The original model, Durbin (1995), includes a non-trivial wall boundary condition for the quantity f , which represents the pressure-strain term and is obtained from an elliptic relaxation equation. It also requires the distance to no-slip walls, albeit for the determination of the coefficient C 1 which regulates the production of dissipation of turbulent kinetic energy in the equation. The version developed by Parneix & Durbin (1997) defines a new expression for the coefficient C 1 substituting the distance to the wall with the ratio v2/k. Lien & Durbin (1996) developed another version of the model with a trivial wall boundary condition for f to improve the numerical robustness of the model, in particular for codes which solve equation by equation in a segregated manner. An extensive, systematic comparison of each version has been conducted in Kalitzin (1999a) and Lien & Kalitzin (2000) for external flow around airfoils, wings, and over a bump. The conclusion of these studies was that all three versions predict in general very similar results for the potential flow region and most of the boundary layer. However, the C 1(v/k) definition causes an overprediction of the boundary layer growth rate in high Reynolds number flows with strong adverse pressure gradients. Forcing f to zero at no-slip walls has been found to delay transition. This is often desirable in transitional flow predictions, as RANS models generally trigger transition too far upstream. However, it has also been found responsible for a significant overprediction of skin friction in flow recovery regions, for example downstream of shock induced separation. The present report is a continuation of this validation effort. It also describes the current implementation of Durbin’s v-f turbulence model in the turbomachinery code TFLO, CITS (2000). This RANS code will be used in the framework of the Accelerated Strategic Computing Initiative (ASCI) at the Center for Integrated Turbulence Simulations (CITS) for large scale computations of flow through the compressor and turbine of an aircraft engine. This requires a robust and efficient implementation of the model. A three-factored scheme which is able to handle the wall boundary conditions of the original model has been developed for this purpose, and its description is included in the report.