Parameter Study on Pogo Stability of Liquid Rockets

Abstract

Nomenclature A s= cross-sectional area of suction line, m 2 A th = nozzle throat area, m 2 C f = thrust coefficient, dimensionless g = standard gravitational acceleration, m=s 2 h s = height of propellant in suction line, m h t = height of propellant in tank, m I s = inertance of propellant in suction line, s 2 =m 2 K = effective stiffness of accumulator which is defined as K a K p =K a K p , 1=m 2 K a = stiffness of the accumulator, 1=m 2 K p = stiffness of pump cavitation, 1=m 2 k = the ratio between effective stiffness and stiffness of accumulator defined as K =K a , dimensionless L = length, m M s = modal mass of structure mode, kg i, j, n = index, dimensionless m 1 = pump gain, dimensionless N = number of thrust chambers, dimensionless p = oscillatory pressure, Pa R c = linearalized combustion resistance for propulsion flow perturbation, s=m 2 w = weight displacement of flow, N = mass flow gain factor of a pump, s = the propulsion modal damping coefficient, dimensionless = dimensionless mass flow gain factor of a pump defined as , dimensionless = couple strength between the structure mode and the propulsion system, dimensionless = frequency ratio between the propulsion mode and the structure mode, dimensionless = the structure damping ratio, dimensionless = density of the propellant, kg=m 3 ' = structural mode gain, dimensionless = circular natural frequency of the structure mode, 1=s ! = circular natural frequency of the propulsion mode, 1=sSubscripts c = combustion chamber p = pump s = suction line t = tank

Modeling and Stability Analysis of Pogo Vibration in Liquid-Propellant Rockets with a Two-Propellant System

“…On the other hand, lowering the combustion resistance R oc makes the coupling strength o1 decrease, but the coefficient o becomes larger, which is advantageous for holding Pogo stability. The phenomenon is in contrast to the results of Zhao et al, 17) because the coupling strength between single propulsion and the rocket structure system is independent of the combustion resistance discussed in this paper.…”

“…Finally, the influences of the original parameters of the oxidant pipeline system, fuel pipeline system and rocket structure system on Pogo stability are clearly revealed. The higher propulsion combustion resistance makes it much easier for the Pogo system to lose stability, which is different from the results of Zhao et al 17) The reason is that the coupling strength between a single propulsion system and rocket structure system is independent of the combustion resistance discussed in this literature. It is provided that a reference for reducing longitudinal vibration in liquid-propellant rockets and furtherly researching the characteristics of Pogo vibration.…”

“…16) So some effective methods have been developed by pioneers in China based on the Rubin and Oppenheim methods. Zhao et al 17) derived the governing equations of the closed-loop system with a simple coupling between a longitudinal struc-ture mode and a reduced single-propellant system, and investigated the role of physical factors on Pogo stability. According to rational function fitting of the transfer function and rocket three-dimensional tank modeling, Xu et al 18) proposed a new Pogo stability analysis method that proved to be highly correct and efficient in comparison to traditional methods.…”

A method for deriving a non-singular state-space formulation based on Rubin's model for Pogo analysis

“…Zhao et al. 12 analysed Pogo in parameter space using a simplified single-propellant single-engine model. Xu et al.…”

“…Ordonneau 5 proposed a numerical method for Pogo analysis using the transfer matrix method. Zhao et al 12 analysed Pogo in parameter space using a simplified single-propellant single-engine model. Xu et al 13 consider the flexibility of the tank and the importance of the outflow near the tank outlet, developing an three-dimensional tank model.…”