Mathematical modelling of start-up transients at clustered propulsion system with POGO-suppressors for CYCLON-4M launch vehicle

Abstract

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.