MATHEMATICAL MODEL OF A GAS PIPELINE OF THE ROCKET ENGINES PNEUMATIC SYSTEMS AS A LUMPED-PARAMETER SYSTEM

Gas pipelines are key elements in systems for transporting and supplying compressed gas in various technical systems, including supercharging fuel tanks of liquid rocket engines and other pneumatic systems. The main function of the pipeline is to ensure the transmission of gas with the required pressure and flow parameters from a high-pressure source to the consumer. This paper considers the pipeline as an independent object of modelling, connecting the high-pressure cylinder and the gas cushion of the fuel tank. To describe dynamic processes in pipelines, models with lumped parameters are often used, where physical elements of the system, such as pipelines, tanks and local resistances (nipples, adapters, jets), are described by a set of capacities and resistances. This approach allows to reduce the problem to a system of ordinary differential equations, adequately reflecting the behaviour of the system at an acceptable level of simplifications. Therefore, the purpose of this work is to build a mathematical model of the pipeline based on the laws of conservation of mass, energy, quantity of motion and the equation of state of gas. To correctly describe the interaction of the system elements, the solution of the Riemann problem is used, which allows to determine the gas parameters in the places where the pipeline is connected to other elements of the pneumatic system. During the study of the system operation a test problem was formulated and solved. The distribution of the main flow parameters in the pneumatic system was determined, and it was found that the mass flow rate calculated on the basis of the solution of the Riemann problem differs from the flow rate calculated by the Saint-Venant-Wenzel formula by no more than 10%. This is due to the fact that the losses in local resistances, which are the connection points of the system elements, are not taken into account. This issue will be investigated in further work.