An Iterative Method For Solving The Problem Of Pipeline Transportation Of Gas Along A Relief Track

Аннотация

A numerical method developed to solve the problem of pipeline transport of real gas, when a pressure change in time is specified at the inlet, and a change in the mass flow of gas is output. Unlike other works, the height of the axis of the gas pipeline varies depending on the distance. Using the new desired natural logarithm of the reduced gas density, the degree of unknowns in the momentum conservation equation reduced, according to which the directional pressure change is due to the local and convective components of the gas inertia force, the quadratic law of resistance and gravity. Using this equation and the equation of conservation of mass, the equations compiled for traveling along the stream and against the flow of waves. For the numerical solution of the system of equations, an implicit scheme is used and the directions of propagation of the forward and backward waves are taken into account. Simple dependences are proposed to approximate the boundary condition for pressure, and to satisfy the boundary condition for mass flow, a transcendental equation is constructed with respect to the inlet flow rate. To solve the latter, a sequential approximation algorithm based on the Newton tangent method has been developed. Due to the nonlinearity of convective terms and the resistance force, an iterative process is organized for a fixed time step. As an initial condition, it is proposed to use a numerical solution of the momentum conservation equation in a stationary setting at a constant gas mass flow rate. The results of computational experiment for various options of the route and indicators of the object are presented.