Differential Equation-Based Specification of Turbulence Integral Length Scales for Cavity Flows

A new modeling approach has been developed that explicitly accounts for expected turbulent eddy length scales in cavity zones. It uses a hybrid approach with Poisson and Hamilton-Jacobi differential equations. These are used to set turbulent length scales to sensible expected values. For complex rim-seal and shroud cavity designs, the method sets an expected length scale based on local cavity width which accurately accounts for the large-scale wake-like flow structures that have been observed in these zones. The method is used to generate length scale fields for three complex rim-seal geometries. Good convergence properties are found and a smooth transition of length scale between zones is observed. The approach is integrated with the popular Menter Shear Stress Transport (MSST) RANS turbulence model and reduces to the standard Menter model in the mainstream flow. For validation of the model, a transonic deep cavity simulation is performed. Overall the Poisson-Hamilton-Jacobi model shows significant quantitative and qualitative improvement over the standard Menter RANS model for both velocity and Reynolds stress measurements. In its current development, the approach has been extended through the use of an initial stage of length scale estimation using a Poisson equation. This essentially reduces the need for user objectivity. A key aspect of the approach is that the length scale is automatically set by the model and not by the modeler. Notably, the current method is readily implementable in an unstructured, parallel processing computational framework.