The absorption of sound near abrupt axisymmetric area expansions

Sound incident onto an abrupt area expansion in an axisymmetric pipe is inv estigated analytically and experimentally. The incident sound field may syn chronize 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 en ergy, or vice versa. An acoustic analogy and a Green function, G, are used to determine the sound reflected and transmitted across the area change. On e finds that there is an optimal Strouhal number at which sound absorption is maximized and that this absorption can be enhanced by multiple reflectio ns 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 th e pipe expansion, lambda = a/b, where a is the radius of the small pipe, an d b is the radius of the larger pipe. For small lambda, the appropriate len gth scale is the pipe radius, a; whereas for lambda nearly equal to unity t he appropriate length scale is the step height b - a. Predictions are compa red with experiment. (C) 2001 Academic Press.