Time‐Marching Approach for Pipe Steady Flows

Abstract

The time‐marching approach (TMA) for determining steady‐state flows as the asymptotic limit of transient flows in pipelines has been improved. It is shown that the rate of convergence to steady state is increased by reducing the spectral radius of a coefficient matrix of a state‐vector equation, which is composed of the basic equations and boundary conditions linearized about the steady condition. A generalized TMA theory using the method of characteristics has been formulated and the spectral radius is minimized by changing system parameters to imaginary ones by using the energy and mass conservation equations. In addition, a practical method was designed to efficiently handle TMA in large pipelines without having to calculate eigenvalues. The TMA has been extended to accurately estimate friction factors using an explicit approximation to the Colebrook‐White formula.