An Approximate Analysis Of The Shock Structure In Underexpanded Plumes PDF Download

An approximate analytical model has been developed for computing the first cycle of the shock structure in plumes from underexpanded axisymmetric supersonic nozzles. The physical basis of the model is the same as that of the Abbett model, i.e., the Mach disk location is determined by the coupling of the flow in the vicinity of the Mach disk with the reaccelerating transonic flow downstream of the disk. The present model is based on a local compatibility condition for the flow just downstream of the Mach disk. To evaluate the local compatibility condition, the generalized shape of the slip line which originates at the shock triple point must be known. The Abbett method was used to compute slip line geometries for a number of plume flows; correlation equations for the slip line geometrical parameters were then developed. After the Mach disk is located, the supersonic flow outside of the slip line is computed for the prescribed slip line geometry. The approximate analytical model requires relatively small computation times and yields acceptably accurate flow-field solutions over the range of conditions for which the slip line correlation equations are valid.