Liquid-propellant rocket propulsion systems of the first stages of launch vehicles of medium, heavy, and super-heavy class usually include POGO-suppressors, which are one of the most widely used methods to eliminate launch vehicle longitudinal structural vibrations (POGO phenomena). However, until now, the theoretical studies and analysis of the effect of the POGO-suppressors’ installation in the feedlines of main liquid rocket engines on transient processes in systems during rocket engine starting have not been carried out due to the complexity of such analysis and the lack, first of all, reliable nonlinear models of cavitation phenomena in rocket engine pumps. A mathematical model for the start-up of a clustered rocket propulsion of the Cyclone-4M launch vehicle has been developed that takes into account the low-frequency dynamics of the POGO-suppressors and the asynchronous start-up timeline sequences of the rocket engines. The first stage of the launch vehicle propulsion system includes four RD-870 rocket engines. A nonlinear mathematical model of low-frequency dynamic processes of the POGO-suppressor with bellows separation of liquid and gaseous media is presented. A significant effect of cavitation in the pumps of engines and the POGO-suppressor installation to the LOX feedline on the propulsion system dynamic gains is shown. Based on the developed mathematical model of the clustered rocket propulsion start-up, the studies of the Cyclone-4M main engines’ start-up transients were carried out. The asynchronous start-up timeline sequences of the rocket engine and the places of installation of the POGO-suppressors in the LOX feedline branches to the RD-870 rocket engine – near the general feedline collector as standard placement or directly at the entrance to the engines – were investigated. The analysis of start-up transients in the oxidizer feed system of the considered propulsion (the time dependences of the flowrate and pressure at the engine inlet) showed the following. Firstly, while the synchronous start-up of the engines, the installation of the POGO-suppressors near the feedline collector makes it possible to eliminate all engine inlet overpressures that exist in the rocket propulsion system in case of the absence of the POGO-suppressors. Secondly, the RD-870 engine asynchronous start-up operation affects negatively the time dependences of the propellant flowrate and pressure at the engine inlet if the POGO-suppressors are located near the feedline collector. So, in the propulsion system’s start-up timeline interval 0.95 s - 1.35 s, for some computational variants of the initial moments of the engine operation start, an abnormally large drop in the LOX flow rate and the overpressures at the engine inlet is observed. The asynchronous start-up of the RD-870 engines with the installation of the POGO-suppressors at the engine inlet does not significantly change the start-up transients compared to the synchronous starting of the engines. Thirdly, thus, it is shown that the installation of the POGO-suppressors both at the engine inlet and at the RD-870 branches near the collector has a significant positive effect on the quality of start-up transient processes for the main engines of the 1st stage of the Cyclone-4M launch vehicle. Placing the POGO-suppressors at the engine inlets is not standard and is considered without reference to the propulsion system layout. Nevertheless, the POGO-suppressors installed at the inlet to the engines are an effective means of preventing overshoots and dips in the parameters of the liquid-propellant rocket engine, including the conditions of asynchronous starting of the liquid rocket engines in the clustered propulsion system. The results obtained can be used in mathematical modeling of the start-up of the first stage propulsion system either for multistage sustainer rockets used in parallel with booster rockets or for the clustered multi-engine rocket propulsion system containing POGO-suppressors.

To execute program motions, the space stages of liquid-propellant launch vehicles are equipped with restartable propulsion engines. On the shutdown of the propulsion engine of a space stage, the liquid propellant in the tank in microgravity conditions moves by inertia upwards as far as possible away from the intake. This results in the potential possibility of the pressurizing gas penetrating into the engine inlet in quantities that make an engine restart impossible. Because of this, motion parameter determination for a liquid moving in propellant tanks in microgravity conditions is a topical problem to be solved in the designing of liquid-propellant rocket engines. This paper presents a technique for the calculation of the parameters of motion of the gas-liquid interface in the propellant tanks of modern liquid-propellant launch vehicle space stages in microgravity conditions (between a start and a shutdown of their propulsion engines) taking into account the design features of in-tank propellant management devices. The technique is based on the use of the finite-element method, the volume-of-fluid method, and modern finite-element CAE systems. It allows one to determine the parameters of motion and the shape of the free liquid surface in the tank, the parameters of free gas inclusions formed in the liquid, and the efficiency of the in-tank propellant management devices in the passive portion of the launch vehicle flight for the normal operation of the propulsion system. For the conditions of motion of a prototype propellant tank with a liquid in a drop tower, which simulates microgravity, the motion of a liquid in a cylindrical tank was simulated numerically accounting for the deformation of its free surface. The computed motion parameters of the liquid and the gas-liquid interface agree with the experimental data. The technique developed will allow one to reduce the extent of testing of newly developed and upgraded launch vehicle space stages.

The steady trend towards the development of space stages capable of putting into orbit several spacecraft with a single launch vehicle (LV) by multiple restarts of the stage sustainer engine in microgravity calls for the solution of a complex of problems aimed at assuring the continuity of the liquid propellant components in the propulsion system feed lines. The aim of this paper is mathematical simulation of dynamic processes in the propellant feed system of LV space stages to assess its operability in microgravity in passive flight segments with an operating attitude control and stabilization system and at sustainer engine starts in periods with minimum tank filling levels. To solve these problems, the authors developed a methodology based on the finite-element method, the volume of fluid method, 3D CAE technologies, and the impedance method. The paper presents mathematical models of dynamic processes in a liquid-propellant LV space stage propulsion feed system that has a capillary propellant management system. The mathematical models of spatial oscillations of a LV space stage with a spacecraft developed with account for the design features of the in-tank devices and propellant feed systems made it possible to determine the mode shapes and the motion parameters of the free surfaces of the propellant components in the tanks (the oxidizer tank and the fuel tank) of the stage and identify flight regimes potentially dangerous in terms of the possibility of the pressurization gas or the substituent gas dissolved in the propellant components penetrating into the engine propellant lines. Quantitative estimates of the propellant management device operability in these regimes were obtained. The mathematical models of hydrodynamic processes in a space stage liquid propellant propulsion system presented in this paper allow one to identify sustainer engine start conditions in which the pressurization gas may penetrate in the engine propellant lines and determine the parameters of dynamic processes in a space stage feed system at sustainer engine starts and cutoffs. The mathematical model of low-frequency hydrodynamic processes in a space stage feed system at sustainer engine starts and cutoffs was tested using the results of experimental studies (on water) of space stage sustainer engine cutoffs, and the calculated oscillation frequencies and amplitudes were shown to be in satisfactory agreement with the experimental ones.