Comparison of empirical correlations for the estimation of conjugate heat transfer in a thrust chamber

Due to high temperatures and pressures in the thrust chamber, regenerative cooling along with film cooling is one of the basic requirements for safe operation. This is ensured by controlling the rate of heat transfer from the walls of chamber through the coolant flow rate. For optimum performance of thrust chamber using efficient combustion, specific heat transfer rates through the nozzle section are required to guarantee the structure integrity of the chamber. Analytical procedures for the thermal design of thrust chambers are fairly limited and designers have to rely on empirical relationships and/or computational methods to calculate the heat transfer rates. Experimental correlations are usually used to predict heat transfer through the internal wall however the exact mechanism of heat transfer is not fully understood. Here a comparison of analytical and empirical approaches has been made for a simplified geometry consisting of two concentric shells. The simplified geometry allows direct application of analytical approach and provides a test ground for the empirical approaches. Results for heat flux and hot side wall temperatures are also compared with a coupled numerical simulation using commercial software Fluent. While estimations for cooling fluid outlet temperature and temperature of outer wall of coolant shell are also compared with the experimental data. The comparison indicates that the analytical method for the heat transfer calculation matches the numerical simulations and experimental data reasonably well.