Random-choice solutions for weak spherical shock-wave transitions of n-waves in air with vibrational excitation

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 weresolvedd 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 randmness in the variation of the shock thickness remains. It is shown that a computer simulation is possible by using a proper coice 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.