Closed-form model for three-dimensional vacuum plumes from a scarfed nozzle

A simple closed-form model for a three-dimensional vacuum plume is based upon satisfying mass and momentum conservation, while assuming a maximum density along the skewed thrust vector. Expansion at the nozzle lip is based on the local flow conditions around the nozzle periphery. The model can use either analytical or test-determined thrust vector coefficients. The present method was used to calculate the flowfield constants for a 10-deg half-angle conical nozzle and to calculate the plume flowfield for a typical ACS engine. For zero angles, the model collapses to an axisymmetric form, applicable up to the inviscid plume boundary angle.