A model problem for a supersonic gas jet from a moon

Some celestial bodies such as planets, moons and comets (here referred to as moons for simplicity) emit jets of material at speeds that in some instances are large enough to escape gravity. Previous investigations have shown this problem to be highly complex, e.g. involving multi-phase flows, phase changes, radiation and gas rarefaction effects. In order to learn from exploring a manageable parameter space, and to provide a limiting case, the present study considers a much simpler model situation in which the material of the jet is an inviscid, non-heat-conducting, perfect gas that issues radially at the surface of the moon with sonic velocity. Theoretical considerations show that the escape velocity of a gas is much smaller than that of a solid body. An analytical solution is obtained for the maximum height reached by a jet in steady flow. A computational parameter study of unsteady, inviscid, axisymmetric flow, including the effect of an atmosphere, provides a rich picture of the features and behaviour of the model jet. The deficit of the computed maximum steady-state penetration height below the isentropic theoretical value may be explained by the effect of the atmosphere and of dissipation in shock waves that occur in the computed flows. Many of the features of the gas jet are qualitatively mirrored in an experiment using a water flow analogy in which the gravitational field is simulated by a surface of suitable shape.