Dynamics of cylindrical converging shock waves interacting with aerodynamic obstacle arrays

Abstract

Cylindrical converging shock waves interacting with an array of aerodynamic obstacles are investigated numerically for diverse shock strengths and for different obstacle configurations in air in standard conditions. The considered number of obstacles N is 4, 6, 8, 16, and 24. Obstacles are lenticular airfoils with thickness-to-chord ratios tc of 0.07, 0.14, and 0.21. The distances of the airfoil leading edge from the shock focus point rLErLEref are 1, 2, and 2.5, where rLEref=7 is the dimensionless reference distance from the origin. Considered impinging shock Mach numbers Ms are 2.2, 2.7, and 3.2 at the reference distance from the origin. The reference experimental configuration (N=8,tc=0.14,rLE=7,Ms=2.7) was proposed by Kjellander et al. [“Thermal radiation from a converging shock implosion,” Phys. Fluids 22, 046102 (2010)]. Numerical results compare fairly well to available one-dimensional models for shock propagation and to available experimental results in the reference configuration. Local reflection types are in good agreement with the classical criteria for planar shock waves. The main shock reshaping patterns are identified and their dependence on the shock strength and obstacle configuration is exposed. In particular, different shock patterns are observed after the leading edge reflection, which results in polygonal shock wave with N, 2N, 3N, and 4N sides. The largest temperature peak at the origin is obtained for the 8- and the 16-obstacle configurations and for the smallest thickness to length ratio, 0.07, located at distance from the origin of 2rLEref. In terms of compression efficiency at the origin, the 16-obstacle configuration is found to perform slightly better than the reference 8-obstacle configuration—with an efficiency increase of about 2%-3%, which is well within the model accuracy—thus confirming the goodness of the obstacle arrangement proposed by Kjellander and collaborators.