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Abstract
This paper introduces a model for simulating the unsteady dynamics of sewer systems filling and emptying, offering greater accuracy and stability. This article presents two novel contributions: first, the HLLS scheme (Harten–Lax–van Leer + Source term) is adapted to ensure the preservation of stationary conditions not only in free surface flows, as originally conceived, but also in pressurized flows and mixed flow scenarios. Second, a new method is proposed for the treatment of open channel flow cells near pressurization or adjacent to pressurized cells to minimize spurious oscillations when utilizing the two-component pressure approach (TPA) model. To verify the new model's effectiveness, it was tested for various conditions against the outcomes of the Open Source Field Operation and Manipulation (OpenFOAM) computational fluid dynamics (CFD) model. Furthermore, to demonstrate the model's potential for simulating real systems, the model was applied to three sewer systems that closely resemble real-world conditions, each of which had been intentionally modified for confidentiality purposes. The results show that the improved model successfully maintains stationary conditions within a sloped pipe across various flow conditions, while also preventing spurious oscillations at mixed flow interfaces even when using a pressure wave speed of 1000 m s.
Disclosure statement
No potential conflict of interest was reported by the author(s).
Notation
| A | = | cross-sectional area of the flow (m2) |
| a | = | pressure wave speed (m s−1) |
| = | cross-sectional area of the flow corresponding to | |
| b | = | channel width as a function of elevation (η) and along-stream location (x) (m) |
| D | = | pipe diameter (m) |
| = | flux vector (m3 s−1 or m4 s−2) | |
| f | = | Darcy–Weisbach friction factor (−) |
| g | = | gravitational acceleration (m s−2) |
| = | represents hydrostatic pressure thrust (m4 s−2) | |
| = | represents lateral pressure force due to longitudinal width variation (m3 s−2) | |
| = | measure of the impact of the stationary wave associated to the source terms in the mass flux (first and second row of vector, respectively) (m2 s−1; m3 s−2) | |
| h | = | flow depth (m) |
| = | distance between the free surface and the centroid of the flow cross-sectional area (m) | |
| = | reference state depth (m) | |
| = | surcharging pressure head (m) | |
| k | = | sand-grain roughness height (m) |
| = | Manning's roughness coefficient (−) | |
| P | = | wetted perimeter (m) |
| Q | = | flow discharge (m3 s−1) |
| R | = | hydraulic radius (m) |
| = | source term vector (first and second row of vector, respectively) (m2 s−1; m3 s−2) | |
| = | energy line slope (−) | |
| = | left and right wave speed, respectively (m s−1) | |
| = | bed slope (−) | |
| T | = | free surface width (m) |
| t | = | time (s) |
| = | vector variable (first and second row of vector, respectively) (m2 s−1; m3 s−2) | |
| u | = | flow velocity (m s−1) |
| x | = | longitudinal coordinate (m) |
| δ | = | spatial difference between cell i + 1 and i (−) |
| ε | = | average height of surface irregularities (m) |
| ϕ | = | variable that is a function of the water depth and that is needed to calculate |
| η | = | local variable for integration over the depth (m) |
Data availability statement
All data and code that support the findings of this study are available from the corresponding author. The ITM model can be found at the website of the Illinois Transient Model (https://web.eng.fiu.edu/arleon/ITM.htm). The input files for the three actual sewer systems can be found at https://web.eng.fiu.edu/arleon/ITM/InputFiles/CASEA.inp, (https://web.eng.fiu.edu/arleon/ITM/InputFiles/CASEB.inp), and (https://web.eng.fiu.edu/arleon/ITM/InputFiles/CASEC.inp).