Differential equation-based specification of turbulence integral length scales for cavity flows

Jefferson-Loveday, Richard J.

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 wakelike 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 (SST) Reynolds-averaged Navier–Stokes (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 and k–ε two-equation turbulence models. In some instances, it is comparable or more accurate than high-fidelity large eddy simulation (LES). 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. Notably, the current method is readily implementable in an unstructured, parallel processing computational framework.

Citation

Jefferson-Loveday, R. J. (2017). Differential equation-based specification of turbulence integral length scales for cavity flows. Journal of Engineering for Gas Turbines and Power, 139(6), https://doi.org/10.1115/1.4035602

• Journal Article Type: Article
• Acceptance Date: Nov 23, 2016
• Publication Date: Feb 7, 2017
• Deposit Date: Feb 15, 2017
• Publicly Available Date: Feb 15, 2017
• Journal: Journal of Engineering for Gas Turbines and Power
• Print ISSN: 0742-4795
• Electronic ISSN: 0742-4795
• Publisher: American Society of Mechanical Engineers
• Peer Reviewed: Peer Reviewed
• Volume: 139
• Issue: 6
• DOI: https://doi.org/10.1115/1.4035602
• Public URL: https://nottingham-repository.worktribe.com/output/847229
• Publisher URL: https://gasturbinespower.asmedigitalcollection.asme.org/article.aspx?articleid=2596196
• Related Public URLs: http://proceedings.asmedigitalcollection.asme.org/proceeding.aspx?articleid=2554779