On the analytical solution for the cylindrical supersonic free jet

Abstract

Based on linear potential theory, the problem of steady supersonic flow inside a cylindrical free jet is treated by analytical methods. The presence of shocks in the flow leads to non-uniform convergence of the obtained series, manifesting itself in strong oscillations of the truncated infinite series solutions (also known as the Gibbs phenomenon), which makes the theoretical solution unsuitable for proper numerical computation. This severe difficulty is overcome by an analytical method based on Kummer's series transformation, which completely eliminated the disturbing oscillations. The resulting free jet solutions is discussed, and it is shown that the cylindrical jet exhibits a rather complicated cellular structure. The comparison with experiment shows excellent agreement, thus proving that linear theory can indeed adequately describe the flow field of supersonic jets.