A COUPLED SECOND-ORDER GTS-MOC SOLUTION FOR TRANSIENT FLOWS IN COMPLEX PIPES

The classical method of characteristics (MOC) is often applied to numerically solve the transient flow equations of pressurized pipelines because of its simplicity and convenience, and the boundary conditions are easy to be coupled and solved. For complex pipeline systems, limited by the Courant number, the method often requires wave velocity adjustment or interpolation for solving, which may result in serious cumulative errors and numerical dissipation. The finite volume method Godunov type scheme (GTS) has good robustness to the internal Coulomb number of the pipeline, but the boundary condition adopts the exact Riemann invariant method, which is complicated to handle. Meanwhile, previous water hammer calculations usually only consider the steady-state moiré resistance, which underestimates the attenuation of transient pressure. In this paper, a coupled GTS-MOC model considering unsteady friction is proposed and derived to compute the internal control body of the pipe using the second-order GTS, which is handled by the coupled GTS-MOC method at the complex boundary. First, the exact Riemann invariant method and the MOC method are theoretically analyzed for the tandem and bifurcated pipe boundary conditions. The derivation results show that the results of the two boundary treatments are consistent in the transient flow solution for pipes with small Mach number (Ma), and the accuracy of the coupled format solution is verified by comparing and analyzing with the experimental results. Finally, the coupled format is compared with GTS and MOC, respectively. The results prove that the coupled format can achieve the same accuracy as GTS, and at the same time, the numerical dissipation exists in both the MOC linear interpolation method and the wave velocity adjustment method in the series pipeline system and increases more obviously with time, and the results of the coupled format have the accuracy and stability, which are more consistent with the exact solution.