Shock wave/boundary layer interaction in hypersonic turbulence flows can cause significant changes in key parameters such as aerodynamic force and aerothermal environment, therefore drawing extensive attention in the design and optimization of high-speed vehicles. The most widely used approach for turbulent simulation of such vehicles is RANS modelling with eddy viscosity models. Many studies have focused on the modification and improvement of the turbulence models to obtain better prediction in such flows. Nevertheless, studies on the RANS equations, particularly those on the role of the Turbulent Kinetic Energy(TKE) in the transport equations of mean variables, are rare. We investigate the influence of three TKE terms on the RANS equations using the k-ω SST model in the simulation of a hollow cylinder-flare flow of Mach number 7.05. The action mechanism of each individual TKE term on the prediction of hypersonic shock wave boundary layer interaction is analyzed qualitatively and quantitatively. The results show that these TKE terms have a significant impact on the flow prediction in the Shock Wave/Boundary Layer Interaction (SWBLI) area, particularly on the size of the separation region. Omission of one TKE term could lead to shrink of the separation bubble to only 40% of that without omission; in contrast, ignoring another TKE term would enlarge the separation length by more than 30%. The theoretical analysis of the mean momentum and energy equations indicates that this strong influence is mainly introduced by the significant change of the effective mean pressure field when the TKE terms are ignored. This will, consequently, lead to a change in the adverse pressure gradient near the separation point, resulting in a clear variation in the predicted length of flow separation.
ZHANG Haoyuan
,
SUN Dong
,
QIU Bo
,
ZHU Yandan
,
WANG Anling
. Influence of turbulent kinetic energy on shock wave/boundary layer interaction[J]. ACTA AERONAUTICAET ASTRONAUTICA SINICA, 2022
, 43(7)
: 125504
-125504
.
DOI: 10.7527/S1000-6893.2021.25504
[1] DOLLING D S. Fifty years of shock-wave/boundary-layer interaction research:what next?[J]. AIAA Journal, 2001, 39(8):1517-1531.
[2] COAKLEY T J, HORSTMAN C C, MARVIN J G, et al. Turbulence compressibility corrections:NASA Technical Memorandum 108827[R]. Washington, D.C.:NASA, 1994.
[3] RUBESIN M W. Extra compressibility terms for Favre-averaged two-equation models of inhomogeneous turbulent flows:NASA Contractor Report[R]. Washington, D.C.:NASA, 1990.
[4] VUONG S T, COAKLEY T J. Modeling of turbulence for hypersonic flows with and without separation:AIAA-1987-0286[R]. Reston:AIAA, 1987.
[5] KRIST S L, BIEDRON R T, RUMSEY C L. CFL3D user's manual (version 5.0)[S]. Hampton:NASA, 1998.
[6] GREENSHIELDS C J, WELLER H G, GASPARINI L, et al. Implementation of semi-discrete, non-staggered central schemes in a colocated, polyhedral, finite volume framework, for high-speed viscous flows[J]. International Journal for Numerical Methods in Fluids, 2010, 63(1):1-21.
[7] WILCOX D C. Turbulence modeling for CFD[M]. 3rd ed. La Canada:DCW Industries, Inc, 2006.
[8] ZHANG H, CRAFT T J, IACOVIDES H. The formulation of the RANS equations for supersonic and hypersonic turbulent flows[J]. The Aeronautical Journal, 2021, 125(1285):525-555.
[9] SUTHERLAND W. The viscosity of gases and molecular force[J]. Philosophical Magazine, 2009(36):507-531.
[10] POLING B E, PRAUSNITZ J M, O'CONNELL J P. The properties of gases and liquids[M]. 5th ed. New York:Mcgraw-Hill, 2004.
[11] KIM K H, KIM C, RHO O H. Methods for the accurate computations of hypersonic flows[J]. Journal of Computational Physics, 2001, 174(1):38-80.
[12] VAN ALBADA G, VAN LEER B, ROBERTS W W. A comparative study of computational methods in cosmic gas dynamics[J]. Astronomy and Astrophysics, 1982, 108:76-84.
[13] MENTER F R, KUNTZ M, LANGTRY R. Ten years of industrial experience with the SST turbulence model[J]. Turbulence, Heat and Mass transfer, 2003, 4(1):625-632.
[14] MENTER F R. Two-equation eddy-viscosity turbulence models for engineering applications[J]. AIAA Journal, 1994, 32(8):1598-1605.
[15] KUSSOY M I, HORSTMAN C C. Documentation of two-and three-dimensional hypersonic shock wave/turbulent boundary layer interaction flows:NASA Technical Memorandum 101075[R]. Washington, D.C.:NASA, 1989.
[16] CORATEKIN T, VAN KEUK J, BALLMANN J. Performance of upwind schemes and turbulence models in hypersonic flows[J]. AIAA Journal, 2004, 42(5):945-957.
[17] GEORGIADIS N J, RUMSEY C L, HUANG G P. Revisitingturbulence model validation for high-Mach number axisymmetric compression corner flows:AIAA-2015-0316[R]. Reston:AIAA, 2015.
[18] OLSEN M, COAKLEY T, LILLARD R. The lag model applied to high speed flows:AIAA-2005-0101[R]. Reston:AIAA, 2005.
[19] 刘景源. SST湍流模型在高超声速绕流中的改进[J].航空学报, 2012, 33(12):2192-2201. LIU J Y. An improved SST turbulence model for hypersonic flows[J]. Acta Aeronautica et Astronautica Sinica, 2012, 33(12):2192-2201(in Chinese).
[20] GEORGIADIS N, YODER D. Recalibration of theshear stress transport model to improve calculation of shock separated flows:AIAA-2013-0685[R]. Reston:AIAA, 2013.
[21] HOLDEN M, WADHAMS T, MACLEAN M,et al. Experimental studies of shock wave/turbulent boundary layer interaction in high Reynolds number supersonic and hypersonic flows to evaluate the performance of CFD codes:AIAA-2010-4468[R]. Reston:AIAA, 2010.
[22] 孙东,刘朋欣,沈鹏飞,等.马赫数6柱-裙激波/边界层干扰直接模拟[J].航空学报, 2021, 42(12):124681. SUN D, LIU P X, SHEN P F, et al. Direct numerical simulation of shock wave/turbulent boundary layer interaction in hollow cylinder-flare configuration at Mach number 6[J]. Acta Aeronautica et Astronautica Sinica, 2021, 42(12):124681(in Chinese).