A contribution to the computation of transonic supersonic flows over blunt bodies

Stationary inviscid transonic supersonic flowfield around sphrese, ellipsoids and hemisphere-cylinders are calculated. The freestream Mach numbers considered are between $\text{M}{}_{\mathrm{\infty }}\text{= 1.02}$ and $\text{M}{}_{\mathrm{\infty }}\text{= 1.1}$. A special coordinate system is created which is adjusted to the subsonic stagnation point region for transonic freestream Mach numbers. The integration of the governing equations is carried out by means of a time-dependent finite-difference procedure. All the calculations discussed were stable and converged uniquely to the asymptotic stationary state. The influence of an artificial dissipation term added to the finite-difference scheme is studied. It is further shown, that in all cases the limiting characteristics come from the front part of the bodies. The results include bow shocks, sonic lines, characteristics, lines of constant pressure, density and Mach numbers. A comparison is made between such flow quantities which are calculable by analytical functions and the predicted ones. The quality of the results is checked by considering the conservation of the total enthalpy. For some examples the present solutions are compared with other theories and experimental data.