Devising a method to design supersonic nozzles of rocket engines by using numerical analysis methods

Abstract

The object of research is supersonic nozzles of liquid-propellant rocket engines. The work considers the problem of the lack of an effective method for profiling the supersonic contour of the nozzle, which will generate maximum thrust. For its solution, a method is proposed, the essence of which is approximating the nozzle contour with a power-law polynomial and determining the values of its coefficients by solving a multidimensional minimization problem using numerical modeling methods. The expression for the axial component of the thrust with the opposite sign at the specified values of atmospheric pressure and radius at the nozzle section was chosen as the objective function in this paper. Using the proposed method, contours of optimal nozzles were obtained based on polynomials of powers 2, 3, and 4, which were compared with nozzles obtained by the generally accepted Rao method. The maximum value of the relative deviation modulus calculated during the comparison did not exceed 3 %, which allows us to assert the correctness of the obtained results. The existence of such a discrepancy is explained by the difference in the numerical modeling method used. In contrast to the method of characteristics common in similar problems, the method of finite volumes of the Godunov type was used in the work. This has made it possible to reduce the sensitivity of the calculation to initial and boundary conditions and make decisions regardless of the flow regime of combustion products. In addition, the use of the extended cells method for the integration of finite volumes at the boundary of the calculation domain significantly reduced the total time of solving the problem of profiling the contour of the optimal nozzle