Nonlinear wave propagation in a water-filled, conical shock tube

Abstract

A conical shock tube is being developed for evaluating hull-mounted sonar transducers and related components for their vulnerability to exploding ordnance [J. F. Zalesak and L. B. Poché, Jr., Proc. 60th Shock and Vib. Symp. III, 73–76 (1989)]. A small explosive charge at the breech end generates a robust shock wave that travels down the tube and strikes the transducer at the muzzle end. Proper design of the water-filled shock tube requires an understanding of the nonlinear propagation of shock waves in a conical waveguide with nonrigid walls. This understanding is obtained by use of a numerical solution to the generalized Burgers’ equation [D. H. Trivett and A. L. Van Buren, J. Acoust. Soc. Am. 69, 943–949 (1981)]. Here the combined effects of nonlinearity, absorption, and dispersion are included in a stepwise calculation of the propagation. Results show that the effect of dispersion must be minimized to provide an acceptable shock waveform at the muzzle. Shock waves measured in a prototype shock tube are in good agreement with the theoretical predictions. [Work supported by ONR.]