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Direct numerical simulations (DNS) are performed to investigate the spatial evolution of flat-plate zero-pressure-gradient turbulent boundary layers over long streamwise domains ( $${>}300\delta _i$$ , with $$\delta _i$$ the inflow boundary-layer thickness) at three different Mach numbers, $2.5$ , $4.9$ and $10.9$ , with the surface temperatures ranging from quasiadiabatic to highly cooled conditions. The settlement of turbulence statistics into a fully developed equilibrium state of the turbulent boundary layer has been carefully monitored, either based on the satisfaction of the von Kármán integral equation or by comparing runs with different inflow turbulence generation techniques. The generated DNS database is used to characterize the streamwise evolution of multiple important variables in the high-Mach-number, cold-wall regime, including the skin friction, the Reynolds analogy factor, the shape factor, the Reynolds stresses, and the fluctuating wall quantities. The data confirm the validity of many classic and newer compressibility transformations at moderately high Reynolds numbers (up to friction Reynolds number $$Re_\tau \approx 1200$$ ) and show that, with proper scaling, the sizes of the near-wall streaks and superstructures are insensitive to the Mach number and wall cooling conditions. The strong wall cooling in the hypersonic cold-wall case is found to cause a significant increase in the size of the near-wall turbulence eddies (relative to the boundary-layer thickness), which leads to a reduced-scale separation between the large and small turbulence scales, and in turn to a lack of an outer peak in the spanwise spectra of the streamwise velocity in the logarithmic region.
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A uniform momentum zone--vortical fissure model of the turbulent boundary layer
Recent studies reveal that at large friction Reynolds number delta^+ the outer, inertially-dominated region of the turbulent boundary layer is composed of large scale zones of uniform momentum segregated by narrow fissures of concentrated vorticity. Experiments show that, when scaled by the boundary layer thickness, the fissure thickness is O(1/sqrt{delta^+}), while the dimensional jump in streamwise velocity across each fissure scales in proportion to the friction velocity u_tau. A simple model that exploits these essential elements of the turbulent boundary layer structure at large delta^+ is developed. First, a master wall-normal profile of streamwise velocity is constructed by placing a discrete number of fissures across the boundary layer. The number of fissures and their wall-normal locations follow scalings informed by analysis of the mean momentum equation. The fissures are then randomly displaced in the wall-normal direction, exchanging momentum as they move, to create an instantaneous velocity profile. This process is repeated to generate ensembles of streamwise velocity profiles from which statistical moments are computed. The modelled statistical moments are shown to agree remarkably well with those acquired from direct numerical simulations of turbulent channel flow at large delta^+. In particular, the model robustly reproduces the empirically observed sub-Gaussian behaviour for the skewness and kurtosis profiles over a large range of input parameters.
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- Award ID(s):
- 1437851
- PAR ID:
- 10075827
- Date Published:
- Journal Name:
- Journal of fluid mechanics
- ISSN:
- 1469-7645
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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