Numerical simulation of gas dynamics during operation of a wide-range rocket nozzle with a porous insert

When the rocket moves in the dense layers of the Earth’s atmosphere, classical nozzles operate in the jet overexpansion mode. In this mode, there is a partial decrease in the magnitude of the specific impulse. As a result, the amount of fuel consumed by the rocket engine increases. An increase in the efficiency of nozzle operation can be achieved by using designs of wide-range nozzles, in which case the replacement of a solid nozzle wall with a perforated one makes it possible to compensate for the loss of specific impulse. The paper presents a study of the effect of a porous insert on the operating modes of the nozzle. Numerical simulation was performed in the Ansys Fluent software package. At the first stage of the study, a geometric model of the computational zone is created which includes a two-dimensional model of the RD-107 rocket engine nozzle and a computational domain that simulates the external environment (air atmosphere). The calculation of the outflow of combustion products through the constructed nozzle at different pressures of atmospheric air is carried out. In the future, the classical nozzle is replaced by a nozzle with a porous insert, and the calculation is carried out at the same values of atmospheric pressure. The values of the specific impulse obtained in calculations with a classical and porous nozzle are compared. The amount of fuel saved when replacing a classic nozzle with a porous one is determined by the difference in the areas bounded by the curves on the plot of specific impulse versus the considered height above the Earth’s surface. Comparison of the values of the specific impulse of nozzles with an impenetrable wall and a porous insert made it possible to conclude that up to a height of 5.4 km the specific impulse of the nozzle with a perforated wall exceeds the values of the specific impulse of the classical nozzle. Evaluation of the effectiveness of the use of a gas-permeable insert in the nozzle design when the nozzle operates in dense layers of the Earth’s atmosphere showed that with the start of operation at a height of 0 km above sea level and up to the height at which the nozzle operates in the design mode – the value of the compensated specific impulse is 2.2 %. The results of the study can be applied in the design of nozzle devices of modern rocket engines operating in dense layers of the atmosphere

Darboux-integration of id\rho/dt=[H,f(\rho)]

A Darboux-type method of solving the nonlinear von Neumann equation $i\dot \rho=[H,f(\rho)]$, with functions $f(\rho)$ commuting with $\rho$, is developed. The technique is based on a representation of the nonlinear equation by a compatibility condition for an overdetermined linear system. von Neumann equations with various nonlinearities $f(\rho)$ are found to possess the so-called self-scattering solutions. To illustrate the result we consider the Hamiltonian $H$ of a one-dimensional harmonic oscillator and $f(\rho)=\rho^q-2\rho^{q-1}$ with arbitary real $q$. It is shown that self-scattering solutions possess the same asymptotics for all $q$ and that different nonlinearities may lead to effectively indistinguishable evolutions. The result may have implications for nonextensive statistics and experimental tests of linearity of quantum mechanics.Comment: revtex, 5 pages, 2 eps figures, submitted to Phys.Lett.A infinite-dimensional example is adde