Influence of pressure gradients on wall pressure beneath a turbulent boundary layer

Abstract

This study investigates the effects of a pressure gradient on the wall pressure beneath equilibrium turbulent boundary layers. Excitation of the walls of a vehicle by turbulent boundary layers indeed constitutes a major source of interior noise and it is necessary to take into account the presence of a pressure gradient to represent the effect of the curvature of the walls. With this aim, large-eddy simulations of turbulent boundary layers in the presence of both mild adverse and mild favourable pressure gradients are carried out by solving the compressible Navier–Stokes equations. This method provides both the aeroacoustic contribution and the hydrodynamic wall-pressure fluctuations. A critical comparison with existing databases, including recent measurements, is conducted to assess the influence of a free stream pressure gradient. The analyses of wall-pressure spectral densities show an increase in the low-frequency content from adverse to favourable conditions, yielding higher integrated levels of pressure fluctuations scaled by the wall shear stress. This is accompanied by a steeper decay rate in the medium-frequency portion for adverse pressure gradients. No significant difference is found for the mean convection velocity. Frequency–wavenumber spectra including the subconvective region are presented for the first time in the presence of a pressure gradient. A scaling law for the convective ridge is proposed, and the acoustic domain is captured by the simulations. Direct acoustic emissions have similar features in all gradient cases, even if slightly higher levels are noted for boundary layers subjected to an adverse gradient.

Analytical models of the wall-pressure spectrum under a turbulent boundary layer with adverse pressure gradient

“…The experimental investigation of wall-pressure fluctuations dates back to the 50s (see the reviews of Bull (1996) and Cohen & Gloerfelt (2018)) and still proves challenging nowadays. For instance, Salze et al.…”

“…The experimental investigation of wall-pressure fluctuations dates back to the 50s (see the reviews of Bull (1996) and Cohen & Gloerfelt (2018)) and still proves challenging nowadays. For instance, Salze et al (2015) discussed the separation of the hydrodynamic and acoustic components of the spectrum of pressure fluctuations from the raw experimental data.…”

Simulation of Surface Pressure Fluctuations on an Airbus-A320 Fuselage at Cruise Conditions

“…Based on Eqs. (13)(14), a larger value of C τ slows the coherence decay. The streamwise coherence length increases by approximately 40% using the applied value of C τ compared to the one used in the incompressible flows.…”

“…A problem faced by measuring in wind tunnels at high flow velocity is the high background noise level, which contaminates the measured pressure spectra up to 2 kHz [10]. Numerical investigations on high-speed flows, however, only for low Reynolds number flows were carried out by Gloerfelt & Berland [11], Duan et al [12] and Cohen & Gloerfelt [13]. Results of in-flight tests were published by Bhat [14], Palumbo [15,16], Haxter & Spehr [17,18] and Klabes et al [19].…”

Optimized Runge-Kutta (LDDRK) schemes with non-constant-amplitude waves

“…Such optimized schemes are also starting to find favour outside of computational aeroacoustics, for example in Large Eddy Simulations [e.g. [13][14][15] Most of the optimized spatial and time-stepping schemes investigate the action of the scheme in the wavenumber/frequency domain. For example, the solution to the time-stepping problem dU/dt = F (U , t) for the p-stage low-storage Runge-Kutta scheme considered by Hu, Hussaini, and Manthey [11] is…”