Turbulence Model for Steady and Unsteady Boundary Layers in Strong Pressure Gradients

Abstract

A new turbulence model for two-dimensional, steady and unsteady boundary layers in strong adverse pressure gradients is described. The model is developed in a rational way based on understanding of the flow physics obtained from experiments. The turbulent shear stress is given by a mixing length model, but the mixing length in the outer region is not a constant times the boundary layer thickness; it varies according to an integral form of the turbulence kinetic energy equation. This approach accounts for the history effects of the turbulence. The form of the near-wall mixing length model is derived based on the distribution of the shear stress near the wall, and it takes into account the pressure and convection terms which become important in strong adverse pressure gradients. Since the significance of the normal stresses in turbulent kinetic energy production increases as separation is approached, a model accounting for this contribution is incorporated. Experimental data indicate a change in turbulence structure near and through separation. Such a change can be significant and is accounted for here using an empirical function. The complete model was tested against steady and unsteady, two-dimensional experimental cases with adverse pressure gradients up to separation. Improved predictions compared to those obtained with other turbulence models were demonstrated.