Optimum Pressure Ratio in a Turbojet Engine: Mathematical Expression to Determine the Pressure Ratio Required for Optimization of the Specific Thrust

With the resurgence of interest in blended wing body aircraft, flight test vehicles are being designed to perform scaled model testing of the concept. Consequently, there is a demand for high-efficiency turbojet engines in the sub-1000 N-thrust range. Since very few engines have been manufactured specifically for these flight test vehicles, RC scale/hobby engines have been the solution of choice. These engines are famously known for their low efficiency; therefore, further improvement is required. The pressure ratio of a turbojet engine plays a major role in its efficiency and performance. The effects of pressure ratio have been explored fairly extensively and often require an iterative process because of the complexity of the equations and the number of variables. This publication investigates the derivation of a mathematical expression to determine the optimum pressure ratio to maximize the specific thrust of a turbojet engine. Mathematical expressions in place of iterative processes accelerate the time it takes to perform an optimization. Mathematical expressions for the optimum total pressure across the compressor to maximize the specific thrust are developed for two scenarios. In the first scenario, the engine components, including the compressor, combustor, and turbine, are assumed to possess isentropic efficiencies of one hundred percent. In the second scenario, these efficiencies are not assumed to be perfect, and a pressure loss exists across the combustor. These expressions are obtained by differentiating the net specific thrust with respect to the total compressor pressure ratio. The results are validated by calculating the net specific thrust for varying pressure ratios and then manually identifying the optimum value. The results of this exercise serve as a starting point for selecting total compressor pressure ratios in a clean sheet turbojet design.