Assessment of heat transfer and Mach number effects on high-speed turbulent boundary layers

Abstract

High-speed vehicles experience a highly challenging environment in which the freestream Mach number and surface temperature greatly influence aerodynamic drag and heat transfer. The interplay of these two parameters strongly affects the near-wall dynamics of high-speed turbulent boundary layers (TBLs) in a non-trivial way, breaking similarity arguments on velocity and temperature fields, typically derived for adiabatic cases. We present direct numerical simulations of flat-plate zero-pressure-gradient TBLs spanning three freestream Mach numbers $[2,4,6]$ and four wall temperature conditions (from adiabatic to very cold walls), emphasising the choice of the wall-cooling parameter to recover a similar flow organisation at different Mach numbers. We link qualitative observations on flow patterns to first- and second-order statistics to explain the decoupling of temperature–velocity fluctuations that occurs at reduced wall temperatures and high Mach numbers. For these cases, we discuss the formation of a secondary peak of thermal production in the viscous sublayer, which is in contrast with the monotonic behaviour of adiabatic profiles. We propose different physical mechanisms induced by wall-cooling and compressibility that result in apparently similar flow features, such as a higher peak in the streamwise velocity turbulence intensity, and distinct features, such as the separation of turbulent scales.

Turbulent drag reduction with streamwise-travelling waves in the compressible regime

“…To do so, the value of the diabatic parameter Θ is fixed across both the values of the Mach number and the control parameters of the StTW, implying that a fixed portion of bulk flow kinetic energy is converted into thermal energy, and that extra energy is spent for the cooling process. Using the diabatic parameter (or, equivalently, the Eckert number) has been recently considered by Cogo et al (2023) as a means to achieve a similar wall cooling across different values of the Mach number. Extending a Θ-based comparison to account for different values of Θ with flow control and drag reduction is an interesting future development of the present study.…”

“…with γ = c p /c v the heat capacity ratio, and r the recovery factor, a coefficient that, according to Shapiro (1953), for a turbulent flow over a flat surface is r = Pr 1/3 . Recent studies (Cogo et al 2023) have shown that a constant diabatic parameter, or equivalently, a constant Eckert number (Wenzel, Gibis & Kloker 2022), is the proper condition under which compressible flows at different Mach numbers should be compared. The parameter Θ represents the fraction of the available kinetic energy transformed into thermal energy at the wall (Modesti et al 2022), and the importance of wall cooling increases when Θ decreases.…”