Random Choice Solutions for Weak Spherical Shock-Wave Transitions of N-Waves in Air with Vibrational Excitation.
Interim technical rept.,
TORONTO UNIV DOWNSVIEW (ONTARIO) INST FOR AEROSPACE STUDIES
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In order to clarify the effects of vibrational excitation on shock-wave transitions of weak, spherical N-waves, which were generated by using sparks and exploding wires as sources, the compressible Navier-Stokes equations were solved numerically, including a one-mode vibrational-relaxation equation. A small pressurized air-sphere explosion was used to simulate the N-waves generated from the actual sources. By employing the random-choice method RCM with an operator-splitting technique, the effects of artificial viscosity appearing in finite-difference schemes were eliminated and accurate profiles of the shock transitions were obtained. However, a slight randomness in the variation of the shock thickness remains. It is shown that a computer simulation is possible by using a proper choice of initial parameters to obtain the variations of the N-wave overpressure and half-duration with distance from the source. The calculated rise times are also shown to simulate both spark and exploding-wire data. It was found that, in addition to the vibrational-relaxation time of oxygen, both the duration and the attenuation rate of a spherical N-wave are important factors controlling its rise time. The effects of the duration and the attenuation rate of a spherical N-wave on its rise time, which are designated as the N-wave effect and the nonstationary effect, respectively, are discussed in more detail pertaining to Lighthills analytical solutions and the RCM solutions for nonstationary plane waves and spherical N-waves. Author