Parameter Study on Pogo Stability of Liquid Rockets

Abstract

Nomenclature As = cross-sectional area of suction line, m 2 Ath = nozzle throat area, m 2 Cf = thrust coefficient, dimensionless g = standard gravitational acceleration, m=s hs = height of propellant in suction line, m ht = height of propellant in tank, m Is = inertance of propellant in suction line, s =m K = effective stiffness of accumulator which is defined as KaKp= Ka Kp , 1=m Ka = stiffness of the accumulator, 1=m 2 Kp = stiffness of pump cavitation, 1=m 2 k = the ratio between effective stiffness and stiffness of accumulator defined as K =Ka, dimensionless L = length, m Ms = 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 Rc = linearalized combustion resistance for propulsion flow perturbation, s=m 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 ’ = structural mode gain, dimensionless = circular natural frequency of the structure mode, 1=s ! = circular natural frequency of the propulsion mode, 1=s Subscripts