Estimating friction errors in MOC analyses of unsteady pipe flows

Errors arising from the numerical treatment of friction in unsteady flows in small pipe networks are assessed for fixed-grid, method of characteristics analyses (MOC) with no interpolation. Although the results of the study are targeted at general unsteady flows, the underpinning analytical development is based on the behaviour of standing waves. This enables quantitative conclusions to be drawn about the sensitivity of MOC solutions to frequency. The development is undertaken first for a single pipe and then for networks, with and without a loop. The performance of MOC solutions is modelled with the aid of polynomial transfer matrices that are analogous to transfer function matrices available directly from partial differential equations of water hammer. It is found that, in a single pipe, the numerical errors tend to increase damping at all frequencies, but that, in networks, either increased or decreased damping may occur. The errors place both higher and lower limits on the frequencies that can propagate along a pipe in a numerical analysis. This contrasts with the physical case where only a lower limit exists. The work presented is part of a wider project with the long-term aim of automating the selection of numerical grid sizes in MOC analyses of unsteady flows.