A Correction to the Barotropic Model of Gaseous Cavitation in Choked Converging-Diverging Nozzle Flows

The Barotropic Cavitation Model describes the behavior of a homogeneous mixture of liquid and gas bubbles (gaseous cavitation) as it traverses a converging-diverging (CD) nozzle. Its normal shock formulation makes reliable and accurate predictions of streamwise static pressure distribution from the nozzle inlet to just downstream of the throat and in the diverging section as the flow approaches the nozzle outlet. It fails in the intermediate portion of the divergence with maximum pressure prediction errors (as a fraction of nozzle inlet pressure) roughly equivalent to the back pressure ratio (as high as 0.46). A correction to the streamwise static pressure distributions predicted by the normal shock solution of the Barotropic Cavitation Model is proposed, applied and compared to experiments with aerated and non-aerated cavitation in several fluids. When used to simulate aerated cavitation of dodecane in a CD nozzle it predicts the location of first disagreement between the normal shock solution and experimental static pressure measurements within 4% of nozzle length. A polynomial curve fit between this predicted point (xcorr) and the normal shock location (xshock) then reduces maximum prediction error for static pressure in the correction region to no more than 0.11 (as a fraction of inlet pressure) for the aerated dodecane cases examined. For non-aerated gaseous cavitation in dodecane, water or JP8 jet fuel this error ratio does not exceed 0.13 and typical values are less than 0.07.