The absorption of sound near abrupt axisymmetric area expansions

Sound incident onto an abrupt area expansion in an axisymmetric pipe is investigated analytically and experimentally. The incident sound field may synchronize the unsteady shedding of vorticity at the lip of the expansion to produce an organized train of vortices. In the presence of a mean flow, the unsteady vorticity shed from the lip is convected downstream where it acts as a sink or source of sound, thereby converting acoustic into vortical energy, or vice versa. An acoustic analogy and a Green function, G, are used to determine the sound reflected and transmitted across the area change. One finds that there is an optimal Strouhal number at which sound absorption is maximized and that this absorption can be enhanced by multiple reflections from the duct ends. In addition, the appropriate distance to be used in the definition of the Strouhal number depends upon the diameter ratio of the pipe expansion, λ = a/b, where a is the radius of the small pipe, and b is the radius of the larger pipe. For small λ, the appropriate length scale is the pipe radius, a; whereas for λ nearly equal to unity the appropriate length scale is the step height b - a. Predictions are compared with experiment.