Dynamic Modeling and Analysis of a High Pressure Regulator

Pressure regulator is a common device used to regulate the working pressure for plants and machines. In aerospace propulsion systems, it is used to pressurize liquid propellant rocket tanks at specified pressure for obtaining the required propellant mass flow rate. In this paper, a generalized model is developed to perform dynamic analysis of a pressure regulator so that constant pressure at outlet can be attained. A nonlinear mathematical model of pressure regulator is developed that consists of dynamic equation of pressure, temperature, equation of mass flow rate, and moving shaft inside regulator. The system of nonlinear and coupled differential equations is numerically simulated and computation of pressure and temperature is carried out for required conditions and given design parameters. Valve opening and mass flow rate are also found as a function of given inlet pressure and time. In the end, an analytical solution based on constant mass flow rate assumption is compared with nonlinear formulation. The results demonstrate a high degree of confidence in the nonlinear modeling framework proposed in this paper. The proposed model solves a real problem of liquid rocket propulsion system. For the real system under consideration, inlet pressure of regulator is decreased linearly from 150 bar to 60 bar and outlet pressure of nearly 15 bar is required from pressure regulator for the complete operating time of 19 s.