A turbulence model for steady and unsteady boundary layers in strong pressure gradients

Abstract

A new turbulence model designed 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 an understanding of the flow physics obtained from recent experimental observations. The turbulent shear stress is given by a mixing length model, but the variation of the mixing length in the outer region is not constant; it varies according to an integral form of the turbulence kinetic-energy equation. This approach allows for the history effects of the turbulence to be taken into account in an approximate but rational way. The form of the near-wall mixing length model is derived based on the rigorous 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 is increasing as separation is approached, a model accounting for this contribution is incorporated. The model is calibrated using available experimental data. These data also 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 gradient up to separation. Improved predictions compared to those obtained with other turbulence models were demonstrated. The general and rational approach that led to the derivation of the model allows the straightforward extension of the model in the region of separation. The further extension to steady and unsteady, three-dimensional cases is indicated.