The performance losses in rocket nozzles due to the viscous effects have been studied. Special consideration was given to nozzles with high expansion ratios. The formulation of the boundary-layer equations used in this study includes the effects of transverse and longitudinal curvatures. The effects of longitudinal curvature manifest themselves as a centrifugal force term on the mean flow in the boundary layer and also on the turbulent shear stress model. The results indicate that although the longitudinal curvature creates a fairly strong pressure difference across the boundary layer, the effects on the performance are minimal. The results also show that in high expansion ratio nozzles, the viscous layer becomes very thick and the traditional boundary-layer assumptions cause significant error in the viscous loss calculations. Improvements to the method of evaluating thrust loss are presented.
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Kehtarnavaz et al. (1990) studied this question.
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