Scaling of wall pressure and the peak of streamwise turbulence intensity in compressible wall flows

TL;DR

This paper derives scaling laws for wall-pressure fluctuations and turbulence intensity peaks in compressible wall flows, incorporating variable-property and compressibility effects through an expansion in Mach number.

Contribution

It introduces new scaling laws that include intrinsic compressibility effects, extending incompressible flow relations with calibrated higher-order terms.

Findings

Scaling laws accurately predict wall-pressure and turbulence intensity in various flows.

Higher-order terms effectively capture intrinsic compressibility effects.

The approach is validated across turbulent channel flows and boundary layers.

Abstract

This paper develops scaling laws for wall-pressure root-mean-square (r.m.s.) and the peak of streamwise turbulence intensity, accounting for both variable-property and intrinsic compressibility effects -- those associated with changes in fluid volume due to pressure variations. To develop such scaling laws, we express the target quantities as an expansion series in powers of an appropriately defined Mach number. The leading-order term is represented using the scaling relations developed for incompressible flows, but with an effective Reynolds number. Higher-order terms capture intrinsic compressibility effects and are modeled as constant coefficients, calibrated using flow cases specifically designed to isolate these effects. The resulting scaling relations are shown to be accurate for a wide range of turbulent channel flows and boundary layers.