Angular Momentum and Moment of Enthalpy Integral Equations for Compressible Boundary Layers

It is a matter of basic observation and high engineering importance that boundary layer (BL) skin friction and surface heat flux are strongly augmented by turbulence. To enhance our understanding of this phenomenon in high-speed flows, the angular momentum integral (AMI) [Elnahhas & Johnson, 2022, J. Fluid Mech., 940, A36] and moment of temperature integral (MTI) [Kianfar et al., AIAA 2022-0944] equations are here extended to compressible BLs. The compressible AMI equation quantifies the skin friction coefficient (Cf) as the sum of a laminar Cf and augmentations due to the Reynolds stress, as well as other flow features such as mean wall-normal fluxes and freestream pressure gradients. A similar approach to the wall heat flux leads to the moment of enthalpy integral (MEI) equation, a quantitative relationship for how turbulence and other BL flow features influence the Stanton number of compressible BL flows. In this talk, the AMI and MEI equations will be applied to generate observations and insight from flat plate BL DNS having a range of edge Mach numbers and wall temperatures, using the Hypersonic Task-based Research (HTR) solver [Di Renzo et al., Comp. Phys. Comm. 255, 2020].