Numerical method for calculating the nozzle thrust of a wide-range rocket engine

A numerical method for calculating the thrust of a wide-range rocket engine nozzle has been developed. This type of engine is equipped with an annular nozzle with a flat central body and is designed to operate in the upper atmosphere and in vacuum. The nozzle forms a jet converging to the axis of symmetry due to which a more compact torch of the working fluid is formed. Nozzles of this type have important design advantages over conventional external expansion nozzles. They are more compact, simpler in terms of cooling, but they have increased losses in the bottom region due to the presence of a flat bottom near the central body. Therefore, the design of such engines needs parametric optimization. Currently, for engines equipped with an annular nozzle with a flat central body, there are no validated methods that would allow parametric optimization. The characteristics of the jet, the loss of specific impulse, and the magnitude of thrust for a given type of nozzle depend on three main parameters: the area of the bottom region of the central body, the area of  the throat section, and the angle of rotation of the inner edge of the nozzle to the axis of symmetry. The gas flow in the bottom region is accompanied by complex shock-wave processes that require a lot of time for numerical calculations. To optimize the design of the nozzle, it is required a simple engineering method to calculate the thrust of the nozzle according to its main parameters. The calculation of the nozzle thrust is based on the integral distribution of pressure forces over its surface obtained by performing numerical calculations in a wide range of external pressure. The Reynolds-averaged Navier-Stokes equations closed by the SST-modification of the k-ω turbulence model are solved. Based on the results of numerical simulation, the calculated coefficients for one-dimensional engineering dependencies are determined; they make it possible to calculate the speed and pressure in a random section of the combustion chamber and engine nozzle. A simple engineering method for calculating the thrust of the chamber nozzle of a wide-range rocket engine has been developed. The technique is verified by comparison with the results of a numerical experiment. The problem of parametric optimization of the rocket engine combustion chamber, capable to operate in a wide range of altitudes, was solved, and it is of interest to the space industry. The developed method of calculation makes it possible to carry out a wide range analysis of the influence of the ratio of geometric dimensions, regime parameters on the thrust of the combustion chamber and nozzles of a wide-range rocket engine, and to estimate the thrust value at different engine operating heights.

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