Weak spherical shock-wave transitions of N-waves in air with vibrational excitation

The effects of vibrational excitation on the shock-wave transitions of weak, spherical N-waves which are generated by using sparks and exploding wires as sources are studied by solving numerically the compressible Navier-Stokes equations, with a vibrational-relaxation equation for oxygen. An explosion from a small pressurized sphere filled with air is used to simulate the N-waves from the actual sources. The effects of artificial viscosity appearing in finite-difference schemes are eliminated and accurate profiles of the shock transitions are obtained by using the random-choice method with an operator-splitting technique. It is shown that a computer simulation can be made by using a proper choice of initial parameters to obtain the variations of N-wave overpressure and half-duration with distance from the source. It is also shown that the calculated rise times simulate both spark and exploding-wire data. In addition to the vibrational-relaxation time of oxygen, both the duration (N-wave effect) and the attenuation rate (nonstationary effect) of a spherical N-wave are found to be important factors controlling its rise time.