A kinetic-model analysis of the source expansion flow into vacuum

A third-order hierarchy kinetic model, which resembles the Boltzmann equation up to the lower 20 moments in terms of the collisional integral, is employed to describe the dynamics of an expansion flow into a vacuum. Attention is given to the distribution associated with the inverse radial velocity. A smooth transition is obtained from the equilibrium at the sonic point to the non-equilibrium conditions downstream. The moment method and Krook models are presented by way of comparison, and it is noted that the former exhibits deviation from the hierarchy model for greater Knudsen numbers, while the Krook model is found to be in good agreement with the hierarchy model for a wide range of Knudsen numbers.