An axisymmetric similarity solution for viscous-transonic nozzle flow

An axisymmetric viscous-transonic equation is presented. A nozzle-type similarity solution of this equation has been found, which describes the initial stages in the development of shock waves downstream of a converging-diverging nozzle throat. This solution is an extension of a two-dimensional solution found previously (Sichel 1966). By an appropriate choice of an arbitrary scaling constant solutions were found such that there is essentially a weak normal shock near the axis with effects of wall and shock-wave curvature occurring only at a sufficiently large radius. The upstream and downstream asymptotic behaviour of these viscous-transonic nozzle solutions has been investigated.