Abstract
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.
Highlights
In order to accurately simulate turbomachinery flows it is often necessary to include the effects of real engine geometry features such as rim-seals and shroud cavities
Reductions in error of 30% and 38% are observed when compared with the standard Menter and k − ε RANS models respectively
7 CONCLUSIONS A new turbulence modeling approach is presented that uses Poisson and Hamilton-Jacobi differential equations to set turbulence length scales in cavity flow zones based on expected scales
Summary
In order to accurately simulate turbomachinery flows it is often necessary to include the effects of real engine geometry features such as rim-seals and shroud cavities. When performing design based calculations involving an optimization procedure, it is typical to run many thousands of iterative simulations It is not currently feasible within the industrial environment to run fully unsteady calculations, especially when there are multiple cavities and stages included. Cavity meshes can contain as many grid nodes as the primary geometry itself, and if low velocities are encountered, this can lead to long run times, especially in unsteady simulations It is common in the early-to-mid design stage to run comparatively low-order steady calculations, for optimization studies where many thousands of geometries/configurations are tested. Inspired by this need, Gangwar [4] and Lukovic [5] explored deterministic stress modeling of idealized cavity flows. The approach is called the Poisson-Hamilton-Jacobi approach (PHJ) and is readily applicable to unstructured flow solvers, providing a natural and elegant way to impose integral wake scales in detached flow zones whilst preserving accurate modeling of near-wall scales on attached boundary layers
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