Asymptotic solutions for shocked resonant acoustic oscillations between concentric spheres and coaxial cylinders

作者：Seymour Brian R^*; Mortell Michael P; Amundsen David E

来源：Physics of Fluids, 2012, 24(2): 026102.

DOI：10.1063/1.3687611

• confined flow
• fluid oscillations
• Mach number
• numerical analysis
• shock waves

For resonant oscillations of a gas in a straight tube with a closed end, shocks form and all harmonics are generated, see Chester [%26quot;Resonant oscillations in a closed tube,%26quot; J. Fluid Mech. 18, 44 (1964)]. When the gas is confined between two concentric spheres or coaxial cylinders, the radially symmetric resonant oscillations may be continuous or shocked. For a fixed small Mach number of the input, the flow is continuous for sufficiently small L, defined as the ratio of the inner radius to the difference of the radii, see Seymour [%26quot;Resonant oscillations of an inhomogeneous gas between concentric spheres,%26quot; Proc. R. Soc. London, Ser. A 467, 2149 (2011)]. However, shocks appear in the resonant flow for either larger values of L or larger input Mach number. A nonlinear geometric acoustics approximation is used to analyse the shocked motion of the gas when L %26gt;%26gt; 1. This approximation and the exact numerical solution are compared for the shocked wave profiles and shock strengths, and the approximation is valid for surprisingly small values of L. The flow in the plane wave case for a straight tube is recovered in the limit L -%26gt; infinity for both the spherical and cylindrical cases, providing a check on the results. The shocked solutions given here complement those continuous solutions previously derived from a dominant first mode approximation.

• 出版日期2012-2