Abstract
This paper aimed to justify the performance of a non-oscillatory TPA-based model proposed by the authors for capturing transient mix flow in sewer systems consisting of a variety of pipe shapes. The model utilizes a first-order Godunov Finite volume numerical scheme in which a Harten–Lax–van Leer (HLL) Riemann solver was used for calculating the fluxes at the cells’ boundaries. The spurious numerical solution associated with the transient mix flow analysis is suppressed by enhancing the numerical viscosity of the scheme when the pipe pressurization is imminent. Due to the lack of experimental data for systems with pipe shapes other than circular and rectangular, a hypothetical pipe system for which analytical solutions exist was employed to verify the model performance. The results reveal that for all pipe shapes considered, the model provides oscillation-free solutions even at a high acoustic speed of 1400 m/s. It is also observed that the numerical results are in perfect agreement with the analytical solution. The obtained results conclude that the proposed model can be utilized to capture transient responses of sewer systems with any pipe shape.
Highlights
Sewer pipe systems rarely run under steady-state flow conditions as the inflows into such systems change with time
By splitting the pressure term in the momentum equation, Vasconcelos et al [17] proposed a novel approach, the two-component pressure approach (TPA), which can capture negative pressures during transient mixed-flow analysis. Both Preissmann slot method (PSM) and TPA, generate spurious numerical oscillation when the flow regime changes from open channel to pressurized flow
Malekpour and Karney [14] proposed an approximate Harten– Lax–van Leer (HLL) solver that can remove the numerical oscillation in the PSM even when the acoustic speed exceeds 1000 m/s; the validity of his method has been independently confirmed by others [20]
Summary
Sewer pipe systems rarely run under steady-state flow conditions as the inflows into such systems change with time. During pressurization, the available storage in the partially filled conduit can accommodate the transient flow energy and does not allow the energy to be stored in the pipe and liquid as strain and compression energy [1] In such conditions, the elastic feature of the flow does not play an important role even if the pace of the transient is high, and the inertia and mass oscillation mainly govern the transient flow. By splitting the pressure term, Vasconcelos et al [17] proposed a novel approach, the two-component pressure approach (TPA), which can capture negative pressures during transient mixed-flow analysis Both PSM and TPA, generate spurious numerical oscillation when the flow regime changes from open channel to pressurized flow. Malekpour and Karney [14] proposed an approximate HLL solver that can remove the numerical oscillation in the PSM even when the acoustic speed exceeds 1000 m/s; the validity of his method has been independently confirmed by others [20]
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