Numerical Modeling of Fluid Transients by a Finite Volume Procedure for Rocket Propulsion Systems

This paper describes the application of a finite volume procedure for a fluid network to predict fluid transients following a rapid valve closure in a long cryogenic pipeline. The conservation equations of mass, momentum, energy, and the equation of state for real fluids are solved in the fluid network consisting of nodes and branches. In the present formulation, the speed of sound does not appear explicitly in the governing equations. Instead, the equation of state for a real fluid is solved in conjunction with the conservation equations to calculate the compressibility factor for modeling the wave propagation phenomenon. The numerical procedure is also capable of modeling the wave propagation due to phase change and gas-liquid mixture. The predicted history of pressure and velocity variation in a single pipe has been compared to the solution by the method of characteristics (MOC) for liquid oxygen (LO₂), liquid hydrogen (LH₂), and water (H₂O). The paper also presents the numerical solution of pressure surges for a gas-liquid mixture, condensation of vapor, and flow circuit with parallel branches and tailpipe.