Abstract
A challenge in the study of turbulent boundary layers (TBLs) is to understand the non-equilibrium relaxation process after sep-aration and reattachment due to shock-wave/boundary-layer interaction. The classical boundary layer theory cannot deal with the strong adverse pressure gradient, and hence, the computational modeling of this process remains inaccurate. Here, we report the direct numerical simulation results of the relaxation TBL behind a compression ramp, which reveal the presence of intense large-scale eddies, with significantly enhanced Reynolds stress and turbulent heat flux. A crucial finding is that the wall-normal profiles of the excess Reynolds stress and turbulent heat flux obey a β-distribution, which is a product of two power laws with respect to the wall-normal distances from the wall and from the boundary layer edge. In addition, the streamwise decays of the excess Reynolds stress and turbulent heat flux also exhibit power laws with respect to the streamwise distance from the corner of the compression ramp. These results suggest that the relaxation TBL obeys the dilation symmetry, which is a specific form of self-organization in this complex non-equilibrium flow. The β-distribution yields important hints for the development of a turbulence model.
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Acknowledgements
This work was supported by the National Natural Science Foundation of China (Grant Nos. 11452002, 11372008, and 11521091), and the Aeronautical Science Foundation of China (Grant No. 2014ZA71001). The authors thank XinLiang Li (Institute of Mechanics, Chinese Academy of Sciences) for his help on the DNS, which was performed on TianHe-1 at the National Supercomputer Center in Tianjin, China.
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Hu, Y., Bi, W., Li, S. et al. β-distribution for Reynolds stress and turbulent heat flux in relaxation turbulent boundary layer of compression ramp. Sci. China Phys. Mech. Astron. 60, 124711 (2017). https://doi.org/10.1007/s11433-017-9072-8
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DOI: https://doi.org/10.1007/s11433-017-9072-8