Mathematical model of the propellant tank pressurization system with respect of heat exchange

The pressurization system for launch vehicle fuel tanks is designed to maintain excess pressure in the gas cushion of the tanks according to the calculated dependency, determined by the requirements for the supply of fuel components and the tank design. To achieve this, it is necessary to coordinate the operation of all elements of the pressurization system. This study considers a system comprising a single high-pressure vessel, a gas reducer, a fuel tank, and the connecting line. To maintain excess pressure in the tank’s gas cushion, pressurization gas is supplied, the flow rate of which depends on the parameters in the high-pressure vessel. The excess pressure in the gas cushion ensures a uniform flow of the component to the pumps or combustion chamber. Elements such as the gas reducer and the gas main are considered as a single conduit with an equivalent flow rate. Based on this system, a task is formulated where the elements are under different conditions. The problem requires determining the change in the flow rate of a component at the system’s outlet. The objective of the study was to develop a mathematical model of such a system. The proposed mathematical model includes a system of ordinary differential equations for the high-pressure vessel and the fuel tank, derived from the laws of conservation of mass, energy, and the equation of state for the pressurization gas. The operation of the gas reducer was considered with the possibility of changing the flow area of the gas outflow orifice over time. A simulation of the operation of the model pressurization system was carried out. It was found that with a constant cross-sectional area of the gas line, the deviation of the mass flow rate of the fuel component during the tank’s emptying was 4% of the nominal value. Using a linear law of area change reduced this deviation to 1%. Overall, the results indicate that the proposed method for calculating parameters in the tank is accurate and can be used in further missile design.