Numerical Investigation of Separation Control for Flow Over a Wall Mounted Hump

Abstract

This work describes the development of a high-order k turbulence model and application to flow over a wall-mounted hump. The high-order turbulence model is validated for a flat plate and subsequently applied to the more complex wall-mounted hump for conditions with and without flow control. Results for the hump flow are compared to previous numerical and experimental data. The turbulence model is incorporated into an implicit parallel flow solver that is based on an approximately-factored time-integration method coupled with spatial fourth- and sixth-order compact-dierence formulations and a high-order filtering strategy. Both a second-order and high-order version of the k turbulence model were included in the compact solver. Validation using flow over a flat plate demonstrated that use of a second-order turbulence model dominates the solution even when high-order compact dierencing is used for the flow equations. This validation also demonstrated that significant computational savings are possible since less mesh resolution is required when using a high-order turbulence model. Comparison of the high-order compact solver and turbulence model with a second- order flow solver and turbulence model were also performed for the wall-mounted hump. Qualitative agreement was achieved with experimental data for both high- and low-order schemes. High-order solutions on a coarse grid agreed very well with second-order solutions on a considerably finer grid. Significant net computational savings were realized for both cases by using high-order compact schemes for the flow equations and the turbulence model.