Direct Numerical Simulation (DNS) of turbulent spatially-developing boundary layers is performed over an isothermal flat plate at several flow regimes: incompressible, supersonic (Mach 2.5), and hypersonic (Mach 5). Similar low Reynolds numbers are considered in all cases with the purpose of assessing flow compressibility on low/high order flow statistics and on the dynamics of coherent structures of Zero Pressure Gradient (ZPG) flows. Turbulent inflow information is generated by following the concept of the rescaling-recycling approach introduced by Lund et al. (J. Comp. Phys. 140, 233-258, 1998); although, the proposed methodology is extended to high-speed flows. Furthermore, a dynamic approach
is employed to connect the friction velocities at the inlet and recycle stations (i.e., there is no need of an empirical correlation as in Lund et al.). The Mach number effect has been mainly identified as significant changes in peak values of the streamwise velocity fluctuations. The vertical transport of Reynolds shear stresses is slightly away from the wall in the near wall region for the hypersonic case. Zones of low speed fluid exhibits a much more elongated shape in incompressible
flow as compared with the compressible counterpart. Furthermore, low speed streaks exhibit a contorted, twisted and stretched form in incompressible flow while they are shorter and more isotropic in the supersonic flow.
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Asymptotic behaviour at the wall in compressible turbulent channels
The asymptotic behaviour of Reynolds stresses close to walls is well established in incompressible flows owing to the constraint imposed by the solenoidal nature of the velocity field. For compressible flows, thus, one may expect a different asymptotic behaviour, which has indeed been noted in the literature. However, the transition from incompressible to compressible scaling, as well as the limiting behaviour for the latter, is largely unknown. Thus, we investigate the effects of compressibility on the near-wall, asymptotic behaviour of turbulent fluxes using a large direct numerical simulation (DNS) database of turbulent channel flow at higher than usual wall-normal resolutions. We vary the Mach number at a constant friction Reynolds number to directly assess compressibility effects. We observe that the near-wall asymptotic behaviour for compressible turbulent flow is different from the corresponding incompressible flow even if the mean density variations are taken into account and semi-local scalings are used. For Mach numbers near the incompressible regimes, the near-wall asymptotic behaviour follows the well-known theoretical behaviour. When the Mach number is increased, turbulent fluxes containing wall-normal components show a decrease in the slope owing to increased dilatation effects. We observe that $R_{vv}$ approaches its high-Mach-number asymptote at a lower Mach number than that required for the other fluxes. We also introduce a transition distance from the wall at which turbulent fluxes exhibit a change in scaling exponents. Implications for wall models are briefly presented.
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- Award ID(s):
- 2031913
- NSF-PAR ID:
- 10338466
- Date Published:
- Journal Name:
- Journal of Fluid Mechanics
- Volume:
- 933
- ISSN:
- 0022-1120
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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- Free Publicly Accessible Full Text
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Accepted Manuscript1.0
- Journal Article:
- https://doi.org/10.1017/jfm.2021.1087
