Standing acoustic waves in a low Mach number shear flow

Abstract

Acoustic shear flow interactions are studied in a rectangular cavity bounded by impermeable duct walls parallel to the flow direction and special perpendicular acoustic reflectors that permit the passage of a fully developed, low Mach number shear flow. Fourier-series-based asymptotic solutions are constructed to provide an explicit description of the evolution of an initially imposed axial standing wave disturbance. The bulk convective motion of the shear flow is shown to be responsible for periodic axial waveform deformations. Additionally, transverse and oblique standing acoustic waves as well as single-frequency bulk oscillations arise from the refraction of the imposed axial acoustic disturbance by the mean flow velocity gradient. Combinations of these disturbances give rise to irregular acoustic pressure signals in the duct. Certain refraction induced transverse and oblique acoustic modes are amplified under resonant conditions. It is shown that, in the parameter ranges of solid rocket engines, the refraction and bulk convection effects are small, in general.

Rayleigh streaming at large Reynolds number and its effect on shear flow

“…Baum & Levine (1987) used numerical methods to solve an initial boundary-value problem based on the Reynolds-averaged Navier-Stokes equations in order to reveal mechanisms for energy exchange between the acoustic and mean flow fields. Acoustic shear flow interactions in a rectangular duct were studied by Wang & Kassoy (1992), using the idealized model as a paradigm to demonstrate the complex response of an initially steady flow to an imposed longitudinal velocity disturbance.…”

Low order modeling of vortex driven self-sustained pressure pulsations in solid rocket motors

“…This results in an acoustic field dominated by standing waves (composed of traveling longitudinal plane waves of opposite direction and equal amplitude). In such a case the convective effects during wave propagation in one direction are compensated by the convective effects while traveling in the opposite direction (Morfey 1971;Wang and Kassoy 1992). At this point Howe 3 (Howe 1998) states without detailed argument that the only relevant term on the righthand side is r • (ω ⇥ v) and neglects all other source terms.…”

“…In a standing wave, convective effects on wave propagation of the incoming wave is partially compensated by the opposite convective effects on the outgoing wave. Hence, convective effects on acoustic wave propagation can in first-order be neglected (Wang and Kassoy 1992). However, convective effects are important to take into account for acoustic radiation losses at the nozzle (Culick 2006).…”