CALCULATING THE EFFECTS OF VARIATIONS IN COMPOSITION ON WAVE-PROPAGATION IN GASES

The equations of gas dynamics in one space dimension are solved whilst considering variations in gas composition and properties. A species continuity equation is derived and coupled in a single vector equation with the three usual conservation equations; the resulting system is solved directly in conservation law form using the two-step Lax-Wendroff technique. The effects of variable gas properties and composition on wave propagation are illustrated via the shock-tube, or Riemann, problem. Significant errors are introduced, in the cases investigated, by assuming that the fluid is a perfect gas of constant composition. Flux-corrected transport (FCT) and nonupwind total variation diminishing (TVD) approaches are evaluated as a means of mitigating the spurious oscillations produced at discontinuities by the classical Lax-Wendroff scheme; these oscillations can give rise to mass fraction values from the species equation which are greater than unity or less than zero. It is found that the FCT algorithm does. not suppress completely the oscillations at discontinuities and this corrupts the species transport calculations. The TVD algorithm eliminates the oscillations at shock waves and contact surfaces in the cases tested, thus maintaining the integrity of the species calculations. This is achieved at the expense of a 65% increase in computational effort over the constant gas property, constant composition case. The resolution of both the shock wave and contact surface can be improved significantly by the use of the artificial compression technique, but at an additional computational cost.