The turbulent convective heat transfer in a rocket nozzle has been numerically analysed by both the conventional integral equation method and the finite difference solution to the compressible N-S equation. The integral equation method originally performed by Bartz has been widely used, though the integral equation method depends on unreliable guesswork for the integral boundary layer thicknesses and it relies on semi-empirical data associated with the flat-plate skin friction coefficient or the flat-plate Stanton number. Whereas, the finite difference solution requires only to model the Reynolds stresses and the turbulent kinematic heat flux at a certain closure level.
The results of sample calculation of the boundary layer development and heat transfer in a rocket nozzle operating under typical conditions show that the boundary layer thicknesses reach minimum thicknesses slightly upstream of the nozzle throat and the maximum heat flux occurs very close to the throat. The heat transfer coefficient at the throat obtained by integral method is overpredicted by about 35% compared with experimental data, whereas overprediction by finite difference solution is about 20%.
Thus, it may be concluded that the finite difference solution to the N-S equation gives better result than the integral equation method. Developments of the thermal boundary layer thickness, displacement thickness, momentum thickness, energy thickness are also calculated. All these thicknesses are forms to have minimum values just before the throat area.
