Direct numerical simulation of supersonic and hypersonic turbulent boundary layers at moderate-high Reynolds numbers and isothermal wall condition

Abstract

We study the structure of high-speed zero-pressure-gradient turbulent boundary layers up to friction Reynolds number $Re_{\tau } \approx 2000$ using direct numerical simulation of the Navier–Stokes equations. Both supersonic and hypersonic conditions with nominal free-stream Mach numbers $M_{\infty }=2$ , $M_{\infty }=5.86$ and heat transfer at the wall are considered. The present simulations extend the database currently available for wall-bounded flows, enabling us to explore high-Reynolds-number effects even in the hypersonic regime. We first analyse the instantaneous fields to characterize the structure of both velocity and temperature fluctuations. In all cases elongated strips of uniform velocity and temperature (superstructures) are observed in the outer portion of the boundary layer, characterized by a clear association between low-/high-speed momentum and high/low temperature streaks. The results highlight important deviations from the typical organization observed in the inner region of adiabatic boundary layers, revealing that the near-wall temperature streaks disappear in strongly non-adiabatic flow cases. We also focus on the structural properties of regions of uniform streamwise momentum (De Silva, Hutchins & Marusic, J. Fluid Mech., vol. 786, 2016, pp. 309–331) observed in turbulent boundary layers, confirming the presence of such zones in the high-speed regime at high Reynolds number and revealing the existence of similar regions for the temperature field. The accuracy of different compressibility transformations and temperature–velocity relations is assessed extending their range of validation to moderate/high Reynolds numbers. Spanwise spectral densities of the velocity and temperature fluctuations at various wall distances have been calculated revealing the energy content and the size of the turbulent eddies across the boundary layer. Finally, we propose a revised scaling for the characteristic length scales, that is based on the local mean shear computed according to the recent theory by Griffin, Fu & Moin [Proc. Natl Acad. Sci. USA, vol. 118 (34)].

Linear-model-based study of the coupling between velocity and temperature fields in compressible turbulent channel flows

“…In fact, the multi-physics coupling is more prominent in compressible wall turbulence than incompressible flows to some extent. For example, very recently, several studies have reported that the alterations of the wall thermal boundary condition can remarkably modify the temperature and velocity streaks in supersonic/hypersonic turbulent boundary layers (Hirai et al 2021;Cogo et al 2022;Huang et al 2022). Hence, the present study can provide an effective tool to quantify these variations.…”

Linear response analysis of supersonic turbulent channel flows with a large parameter space

“…2018) and from DNS of the energy spectrum at different (Modesti & Pirozzoli 2016; Yao & Hussain 2020; Cogo et al. 2022; Cheng & Fu 2022 b ). As discussed in figure 6, the large-scale structure corresponding to the outer peak results mainly from the kinematic part of the forcing, not the thermodynamic part.…”

An algebraic non-equilibrium turbulence model of the high Reynolds number transition region

“…A similar interpretation is provided in [32], which cites results from [33]: "[...]which argued that the excess of turbulent production in the log layer feeds inactive motions that do not contribute to the turbulent shear stress, but transfer energy to other locations of the flow. ".…”