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Feb 2012

Volume 24, Issue 2, Articles (02xxxx)

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Phys. Fluids 24, 023101 (2012); http://dx.doi.org/10.1063/1.3684750 (21 pages)

R. Sattler, S. Gier, J. Eggers, and C. Wagner
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back to top Compressible Flows

Parametric study of cylindrical converging shock waves generated based on shock dynamics theory

Zhigang Zhai, Ting Si, Xisheng Luo, Jiming Yang, Cangli Liu, Duowang Tan, and Liyong Zou

Phys. Fluids 24, 026101 (2012); http://dx.doi.org/10.1063/1.3682376 (13 pages) | Cited 1 time

Online Publication Date: 8 February 2012

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In our previous work, the technique of generating cylindrical converging shock waves based on shock dynamics theory was proposed. In the present work, a further study is carried out to assess the influence of several parameters including the converging angle θ0, the incident planar shock Mach number M0, and the shock tube height h on the wall profile and the converging shock wave. Combining the high-speed schlieren photography and the numerical simulation with the shock dynamics theory, the characteristics of wall profiles, cylindrical converging shock waves, and thermodynamic properties for different controllable parameters are analyzed. It is found that these parameters have great effects on shapes of the wall profile and experimental investigation favors large values of M0 and h and moderate θ0. The experimental sequences of schlieren images indicate that the shocks moving in the converging part are of circular shapes, which further verifies the method in our previous work. In addition, the changes of the shock Mach number, pressure, temperature, and density are obtained quantitatively. The results show that higher pressure and temperature can be reached in the converging part at the same distance to the center of convergence for larger incident shock Mach numbers, larger shock tube heights, or smaller converging angles. All the database will be useful for understanding the shock focusing and further investigating the Richtmyer-Meshkov instability induced by the converging shock waves.
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47.40.Nm Shock wave interactions and shock effects
02.60.Cb Numerical simulation; solution of equations
47.60.Dx Flows in ducts and channels

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

Brian R. Seymour, Michael P. Mortell, and David E. Amundsen

Phys. Fluids 24, 026102 (2012); http://dx.doi.org/10.1063/1.3687611 (14 pages)

Online Publication Date: 29 February 2012

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For resonant oscillations of a gas in a straight tube with a closed end, shocks form and all harmonics are generated, see Chester [“Resonant oscillations in a closed tube,” J. Fluid Mech. 18, 44 (1964)]10.1017/S0022112064000040. 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 et al. [“Resonant oscillations of an inhomogeneous gas between concentric spheres,” Proc. R. Soc. London, Ser. A 467, 2149 (2011)]10.1098/rspa.2010.0576. 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 ≫ 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 → ∞ 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.
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47.40.Nm Shock wave interactions and shock effects
02.60.-x Numerical approximation and analysis
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