A New Unsteady-Based Turbulence Model to Predict Shear Layer Rollup and Breakdown

This paper documents the computational investigation of the unsteady rollup and breakdown of a turbulent separated shear layer. This complex phenomenon plays a key role in many applications, such as separated flow at the leading edge of an airfoil at off-design conditions; flow through the tip clearance of a rotor in a gas turbine; flow over the front of an automobile or aircraft carrier; and flow through turbulated passages that are used to cool turbine blades. Computationally, this problem poses a significant challenge in the use of traditional RANS-based turbulence models for the prediction of unsteady flows. To demonstrate this point, a series of 2-D and 3-D unsteady simulations have been performed using a variety of well-known turbulence models, including the “realizable” k-ε model, a differential Reynolds stress model, and a new model developed by the present authors that contains physics that account for the effects of local unsteadiness on turbulence. All simulations are fully converged and grid independent in the unsteady framework. A proven computational methodology is used that takes care of several important aspects, including high-quality meshes (2.5 million finite volumes for 3-D simulations) and a discretization scheme that will minimize the effects of numerical diffusion. To isolate the shear layer breakdown phenomenon, the well-studied flow over a blunt leading edge (Reynolds number based on plate half-thickness of 26,000) is used for validation. Surprisingly, none of the traditional eddy-viscosity or Reynolds stress models are able to predict an unsteady behavior even with modifications in the near-wall treatment, repeated adaption of the mesh, or by adding small random perturbations to the flow field. The newly developed unsteady-based turbulence model is shown to predict some important features of the shear layer rollup and breakdown.