EVALUATION OF THE SCATTER OF LIQUID LAUNCH VEHICLE POGO OSCILLATION AMPLITUDES DUE TO THE INFLUENCE OF THE SCATTER OF INTERNAL FACTORS

Abstract

Almost all liquid launch vehicle developers faced the problem of ensuring stability in relation to POGO oscillations. The level of POGO amplitudes oscillations of the launch vehicle can be significantly affected by the scatter of internal factors. The study aims to create a mathematical model that can determine the range of POGO amplitudes in liquid launch vehicles. This will be demonstrated through the example of the Dnipro launch vehicle, which is affected by a variety of internal factors that cause its POGO amplitudes to vary. We developed the non-linear non-stationary mathematical model of POGO oscillations of the prototype of the Dnipro space launch vehicle. The model is built by taking into account the two lower vibration modes of the LV structure, two lower oscillation modes of the oxidizer feedline, and the first oscillation mode of the fuel feedline of the propulsion system. Modeling of dynamic processes was conducted in a combination of four liquid rocket engines based on the schematic of the staged rocket engine. The simulation takes into account cavitation phenomena in the engine pumps and delay times in the gas generators’ chambers. We have developed a method for determining the scatter of the POGO oscillations caused by the action of internal factors, which is based on the use of the LP uniformly distributed sequences. As internal factors, the frequencies, decrements, and shapes of LV structural oscillation modes, the values of pressurization of the propellant tanks, and the engines’ specific thrust impulses were considered. Based on the results of the calculations, the dependence of the POGO amplitudes in two regions of LV instability was determined, and the lower and upper enveloping curves for the POGO amplitudes were constructed. It is shown that the maximum POGO amplitudes oscillations in the first region of instability lie in the range from 0.23 g to 0.72 g and in the second region of instability — from 0 g to 0.60 g. Variants of combinations of internal factors, which provided the largest and smallest values of POGO amplitudes, were analyzed. This made it possible to determine the internal factors, the scatter of which has the greatest effect on the POGO amplitudes scatter: frequency, decrement, shape coefficients of oscillations of the oxidizer feedlines and the LV 1st mode structural longitudinal oscillations in the payload cross-section.