Compressibility effects in near-wall turbulence

It is difficult to envision an industrial application where turbulent flows interacting with solid walls do not play a critical role. While understanding these flows at low speeds is already challenging, the complexity increases significantly when the flow speed exceeds the speed of sound or when heat transfer through the walls is intense. These so-called compressible flows are at the core of many engineering applications including aerospace vehicles, combustors, high-speed propulsion systems, gas turbines and other power-generating technologies. Understanding the physics governing these flows is essential for developing accurate predictive models, which in turn enable the improved design of engineering systems.

Compressible wall-bounded turbulent flows involve two distinct effects: those related to heat transfer, commonly referred to as variable-property effects, and those arising from density changes of fluid elements in response to changes in pressure, termed intrinsic compressibility (IC) effects. While the former can occur across all flow speeds, the latter becomes significant only at high Mach numbers. In the past, variable-property effects have been extensively studied; in contrast, the influence of intrinsic compressibility has received limited attention. This gap is largely attributed to Morkovin’s hypothesis, which asserts that IC effects can be neglected in wall-bounded flows under certain conditions. The present work revisits this assumption and directly addresses the question posed by Otto Zeman in 1993: “are the (intrinsic) compressibility effects significant in reality, and can they be isolated in experiments and verified?” To isolate such effects, we perform direct numerical simulations (DNS) of fully developed high-Mach-number channel flows, in which the energy equation is augmented with an external heat source to maintain approximately constant mean thermophysical properties, thereby eliminating variable-property effects.

This thesis is divided in two parts. The first part uses these tailored flow cases to investigate the physics associated with IC effects. We demonstrate that IC effects significantly influence various turbulence statistics—an influence previously misattributed to variable-property effects. The underlying mechanism is as follows: pressure-induced expansions and contractions of the near-wall fluid oppose sweeps and ejections, leading to a weakening of quasi-streamwise vortices. The weakened vortices reduce the energy transferred from the streamwise to the wall-normal velocity components, thereby modulating turbulence statistics.

The second part builds on these insights to develop scaling laws and predictive models applicable to a wide range of channel flows and zero-pressure-gradient boundary layers. Specifically, we derive scaling laws for wall pressure fluctuations, the peak of streamwise turbulent stress, and the mean velocity profile—accounting for both variable-property and intrinsic compressibility effects. The mean velocity scaling is then further exploited to derive predictive models that estimate skin friction and heat transfer coefficients, and to propose compressibility corrections for Reynolds-averaged Navier- Stokes (RANS) turbulence models. These corrected models demonstrate significantly improved accuracy over the state-of-the-art and hold strong potential for enhancing the modeling of complex, real-world engineering systems.