Secondary Flow Induced by a Transverse Resonant Acoustic Field in a Circular Duct

Abstract

The flow field resulting from the interaction of a finite amplitude standing acoustic field and a viscous fluid was investigated analytically and experimentally. For an adiabatic wall, an analytical solution was obtained for the velocity field over the entire duct cross section. The solution predicts standing vortices in the duct cross section: their number is proportional to the resonance mode number. Similar secondary flow behavior has been found by Maslen and Moore who considered the case of an isothermal duct. The analysis is strictly valid for a characteristic Reynolds number of the order of magnitude one compared to δ, where δ ≃ 10−3 . Measurements of the resonant pressure field and photographs of the induced secondary motion, using smoke as a tracer, qualitatively substantiated the analysis. Experimental data were obtained at values of the characteristic Reynolds number varying from 4.5 to 15.3.