Direct numerical simulation of hypersonic turbulent boundary layers. Part 2. Effect of wall temperature

Abstract

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.

DNS of a spatially evolving hypersonic turbulent boundary layer at Mach 8

“…(6) for M8T2. This result is consistent with the results proposed by Duan et al [9], who investigated the effects of the wall temperature at Mach 5 under an isothermal wall with T w approximating to T r (or T w /T r ≈5.4). For an extremely cold wall, the present case, the maximum mismatch between eq.…”

“…is approximately -0.6 through most of the boundary layer for y + >100, and similar results have been reported [7,9,21].…”

“…Thus, the transition peak lies at x≈9. The second segment, starting from the transition peak, approximately covers the range (9,13), where the average slope of the friction coefficient (shown as the dashed dot line in Figure 3) decreases dramatically. In the last segment, the flow further evolves into a fully developed turbulence at about x>13.…”

“…The results demonstrate that Morkovin's hypothesis and the strong Reynolds analogy (SRA) are still valid for 6  Ma  for a different wall temperature. Recently, Martin [8] and Duan et al [9][10][11] proposed a series of investigations on the compressible turbulence boundary layer over a flat-plate by the temporal evolving DNS, to assess the effects of wall temperature, Mach number and high enthalpy on the Morkovin's hypothesis and SRA. In general, when Ma ∞ =5, Morkovin's hypothesis is still considered valid for different wall temperatures.…”

Direct Numerical Simulation of Supersonic Turbulent Boundary Layer with Spanwise Wall Oscillation

“…However, high values of velocity fluctuations can be seen beyond the peak for the present case. According to the study of Duan et al [40], with a higher Mach number and lower wall temperature, the velocity fluctuations get larger values after the peak. Therefore, the higher values of RMS velocity fluctuations are attributed to the cold wall condition adopted in the present research.…”