An Approximate Solution of Compressible Turbulent Boundary-Layer Development and Convective Heat Transfer in Convergent-Divergent Nozzles

Abstract A method has been derived for computing the development of the velocity boundary layer, the temperature boundary layer, and the local convective heat transfer in convergent-divergent nozzles. The method is based on approximate solutions of the integral momentum and integral energy equations for compressible turbulent boundary layers. To obtain the solutions, a flow model is adopted for which are prescribed the velocity and temperature profiles in the boundary layer, the skin-friction law, and the relation between heat and momentum transfer. The local heat-transfer coefficient is expressed as an explicit function of the boundary-layer thicknesses. The effects of nozzle size and throat radius of curvature on boundary-layer development and heat transfer are determined for certain similar nozzle contours in common use. The results of the solution are demonstrated by a sample calculation for a conventional rocket nozzle operating under typical conditions. The computed local heat fluxes were found to be in approximate agreement with those measured during rocket-motor tests using a nozzle of the same contour.