Coupled Second-Order GTS-MOC Scheme for Transient Pipe Flows with an Entrapped Air Pocket

The fix-grid method of characteristic (MOC) has been the main numerical scheme for modeling the transient pipe flows with an entrapped air pocket, where the Courant number Cr usually equals one (i.e., Cr=1) to ensure its accuracy and stability. However, Cr=1 cannot always be guaranteed in each pipe of real pipe systems; thus, the MOC needs to be approximated by interpolation or wavespeed adjustment. This could lead to large accumulated numerical errors and serious shape distortion of simulated pressure curves. To address this problem, an alternative coupled scheme, which combines the second-order Godunov-type scheme (GTS) and the MOC, is developed. Specifically, the conservation equations with unsteady friction of the water column are numerically solved by the GTS, and the moving air-water interface is modeled and captured by the coupled GTS-MOC scheme. The simulated pressure curves by the GTS-MOC scheme are compared with both MOC results and laboratory experiments. The proposed scheme with unsteady friction can better reproduce the experimental pressure oscillations, and is more robust and efficient than the MOC. The MOC scheme with Cr<1 and coarse grids causes more obvious numerical dissipation during an intensive transient induced by relatively high inlet pressure, in which more high-frequency waves occur.