Shock Examples

Here we describe the example shock problems.

Velocity and Mach conventions

The Fortran, C, Python, MATLAB, and Excel shock interfaces report stations [initial, incident, reflected], numbered [1, 2, 5] in legacy CEA. Speeds are positive magnitudes. The unshocked gas and reflecting wall are stationary in the laboratory frame.

  • velocity[0] = u1 is the upstream gas speed in the incident-shock frame, also the incident wave speed in the laboratory frame.

  • velocity[1] = u2 is the downstream gas speed in the incident-shock frame. The laboratory-frame gas speed is v2 = u1 - u2.

  • velocity[2] = u5 is the downstream gas speed in the reflected-shock frame. That gas is stationary at the wall, so u5 also equals the reflected wave-speed magnitude in the laboratory frame (the wave travels back toward the unshocked gas). The upstream reflected-frame gas speed is u5_p_v2 = u5 + v2. It is not u2.

Thus the reflected mass balance is rho2*(v2 + u5) = rho5*u5 and u5 = v2/(rho5/rho2 - 1). Mach is velocity/sonic_velocity in these respective shock frames, not a vector of laboratory-frame Mach numbers. The upstream reflected-shock Mach number would use (v2 + u5)/a2 with the appropriate upstream sound speed, not the reported downstream entry.

Sound speed is reported as sqrt(R*T*gamma_s/M). Initial and incident-frozen states use frozen heat capacities; equilibrium states use the equilibrium isentropic exponent. Reflected-frozen output retains the legacy incident-state frozen heat-capacity basis and molecular weight, evaluated with the reflected temperature in the sound-speed expression. For temperature-dependent heat capacities this can differ from a locally evaluated frozen sound speed; Mach uses the reported convention. Retained last-valid states use the same definition but remain unconverged and need not satisfy shock conservation.

M21 and M52 are molecular-weight ratios, not Mach-number ratios. The legacy M2/M1 and M5/M2 output labels and example variables retain this meaning. Mach ratios, if needed, must be formed from Mach explicitly, with due regard to the different reference frames.