Nonlinear mathematical model and method of solving the problem of isothermal flow of real fluid in a pipeline with a damper

The article presents a mathematical model of isothermal movement of a real liquid along a relief pipeline. The pipeline is characterized by a constant diameter, length, resistance coefficient and variable height of the axis above the horizon. The model is based on the quasi-one-dimensional, nonlinear model of N.E. Zhukovsky and volumetric deformation of the transported medium. The initial conditions are the pressure and velocity distributions along the pipeline. The boundary conditions of the problem take into account the change in the mass flow rate of liquid at the inlet and the intensity of liquid withdrawal after the air cap filled with real gas. By introducing an auxiliary function, equations are compiled relative to analogs of counter-running waves. Nonlinear equations are solved numerically using the finite difference method, and nonlinear boundary conditions are implemented using the tangent method. The role of the air cap in the processes of transition from one operating mode by mass flow is analyzed.