In this paper, we perform direct numerical simulation (DNS) of turbulent boundary layers at Mach 5 with the ratio of wall-to-edge temperature Tw/Tδ from 1.0 to 5.4 (Cases M5T1 to M5T5). The influence of wall cooling on Morkovin's scaling, Walz's equation, the standard and modified strong Reynolds analogies, turbulent kinetic energy budgets, compressibility effects and near-wall coherent structures is assessed. We find that many of the scaling relations used to express adiabatic compressible boundary-layer statistics in terms of incompressible boundary layers also hold for non-adiabatic cases. Compressibility effects are enhanced by wall cooling but remain insignificant, and the turbulence dissipation remains primarily solenoidal. Moreover, the variation of near-wall streaks, iso-surface of the swirl strength and hairpin packets with wall temperature demonstrates that cooling the wall increases the coherency of turbulent structures. We present the mechanism by which wall cooling enhances the coherence of turbulence structures, and we provide an explanation of why this mechanism does not represent an exception to the weakly compressible hypothesis.

In this paper, we perform direct numerical simulations (DNS) of turbulent boundary layers with nominal free-stream Mach number ranging from 0.3 to 12. The main objective is to assess the scalings with respect to the mean and turbulence behaviours as well as the possible breakdown of the weak compressibility hypothesis for turbulent boundary layers at high Mach numbers (M > 5). We find that many of the scaling relations, such as the van Driest transformation for mean velocity, Walz's relation, Morkovin's scaling and the strong Reynolds analogy, which are derived based on the weak compressibility hypothesis, remain valid for the range of free-stream Mach numbers considered. The explicit dilatation terms such as pressure dilatation and dilatational dissipation remain small for the present Mach number range, and the pressure–strain correlation and the anisotropy of the Reynolds stress tensor are insensitive to the free-stream Mach number. The possible effects of intrinsic compressibility are reflected by the increase in the fluctuations of thermodynamic quantities (p′rms/pw, ρ′rms/ρ, T′rms/T) and turbulence Mach numbers (Mt, M′rms), the existence of shocklets, the modification of turbulence structures (near-wall streaks and large-scale motions) and the variation in the onset of intermittency.

In this paper, the effects of freestream Mach number on the statistics and large-scale structures in compressible turbulent boundary layers are investigated using direct numerical simulations(DNS). DNS of turbulent boundary layers with nominal freestream Mach number ranging from 3 to 8 are performed. The validity of Morkovin's scaling, strong Reynolds analogy, and Walz's equation are assessed. We find that many of the scaling relations used to express compressible boundary layer statistics in terms of incompressible boundary layers still hold for the range of freestream Mach number considered. Compressibility effects are enhanced with increasing freestream Mach number but remain insignificant, and the turbulence dissipation remains primarily solenoidal. Moreover, the variation of near-wall streaks, iso-surface of the swirl strength, and hairpin packets with freestream Mach numbers demonstrates that increasing freestream Mach number decreases the coherency of turbulent structures. Nomenclature M Mach number, dimensionless ρ Density, kg/m 3 T Temperature, K δ Boundary layer thickness, mm θ Momentum thickness, mm δ * Displacement thickness, mm u τ Friction velocity, m/s H Shape factor, H = δ * /θ, dimensionless Re θ Reynolds number, Re θ ≡ ρ δ u δ θ µ δ , dimensionless Re δ2 Reynolds number, Re δ2 ≡ ρ δ u δ θ µw , dimensionless Re τ Reynolds number, Re τ ≡ ρwuτ δ µw , dimensionless Cf Skin friction, dimensionless Superscripts + inner wall units Subscripts δ Boundary layer edge

The characterization of the turbulence structure using statistical analysis 1 and a geometric packet-finding algorithm 2 is explored. We follow structures which have been identified by the geometric packet-finding algorithm, using automated object segmentation and feature tracking software, 3, 4 and observe how these structures and their associated wall signatures evolve in time. Using a direct numerical simulation database, we begin to assess the turbulence structure given by each method and the evolution of this structure. * Student Member AIAA. † Student Member AIAA. ‡ Member AIAA.

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