Assessment of Compressibility Corrections on Spalart–Allmaras Turbulence Model for High-Mach-Number Flows

Abstract

In this paper, various compressibility correction terms of the Spalart–Allmaras turbulence model are evaluated in hypersonic compressible flows. A unified transport equation containing six correction terms is equipped to investigate the separate and combined effects of the correction terms. The numerical results of the hypersonic flat-plate cases and corner cases are, respectively, calculated and compared with direct numerical simulation data and experimental data. By using the coarse-grained uncertainty metrics, errors on the profiles and wall coefficients are measured and analyzed in several cases. The results suggest that compressibility corrections should be applied when the strong cold-wall effect or the compressibility effect exists in the hypersonic flows. Catris and Aupoix’s correction (“Density Corrections for Turbulence Models,” Aerospace Science and Technology, Vol. 4, No. 1, 2000, pp. 1–11) and Séror, Rubin, Peigin, and Epstein’s correction (“Implementation and Validation of the Spalart–Allmaras Turbulence Model in Parallel Environment,” Journal of Aircraft, Vol. 42, No. 1, 2005, pp. 179–188) offer much more accurate predictions than other models in hypersonic corner cases. As the compressibility effect further increases, the conservation correction and Shur, Strelets, Zajkov, Gulyaev, Kozlov, and Sekundov’s compressibility correction (“Comparative Numerical Testing of One-and Two-Equation Turbulence Models for Flows with Separation and Reattachment,” 33rd Aerospace Sciences Meeting and Exhibit, AIAA Paper 1995-0863, 1995) drastically increase the prediction error of the profiles. The present work ends by emphasizing the importance of the individual and combined impacts of the correction terms for compressible flows at high Mach numbers, which may provide an understanding for developing further extensions of Spalart–Allmaras models.