Empowering SWMM to capture waterhammer pressures in sewer flow pipe systems

US-SWMM5 is one of the most powerful hydraulic modelling software packages and it is widely used globally to analyze the response of sewer systems to hydrological events. Different software features such as the ability to incorporate or analyze sub-catchment flow hydrographs, snow melt flows, LID controls, unsteady flow of closed conduit and open channel for both prismatic and non-prismatic cross sectional areas, real time control logic (RTC), and range of control hydraulic structures, etc., allow the SWMM5 software users to simulate very complex sewer systems.  Moreover it has previously been shown that the Dynamic Wave Routine of SWMM5 can accurately incorporate and simulate transient flow in both open channel and closed conduit systems provided the channel or conduit is adequately discretized (i.e., broken down to an adequate number of short segments).

The only real limitation of the Dynamic Wave Routine is that it cannot account for the elastic feature of the flow or for a waterhammer effects in pressurized systems. This is often not an issue because mass oscillation generally dominates the flow regime in sewer systems and the elastic feature of the flow is not important. This is because the significant volume of storage and space in these types of systems prevents the liquid from being compressed or stretched in the conduit. This in turn generally eliminates the potential for waterhammer pressures. On the other hand, there are some cases in which the elastic feature of the flow is of great importance and the potential for significant waterhammer pressures is inevitable. An example of this is a scenario with two filling bores that move in opposite direction within a conduit, and the subsequent collision that may result in severe waterhammer pressures.

In order to overcome the aforementioned limitation, a few customized software packages have previously been developed by different individuals and/or organizations. Most of these software packages can accurately capture the waterhammer pressures, however due to numeral instability issues some of them are not able to account for acoustic wave velocity beyond 400 m/s; a limitation that ultimately compromises the analysis results for systems where this value is higher and/or dominant.

In general, there is little question about the superiority of these recently developed and customized software packages over the SWMM5 when it comes to accurately capturing waterhammer pressures. However, SWMM5 still stands out amongst the crowd because its many other power modeling features that are generally not available in the other software packages. For example, SWMM5 can incorporate any shape of conduit whereas most of the other software options can only account for circular and rectangular cross sections. Furthermore, SWMM5 allows the use of numerical larger time steps, which in turn significantly reduces the computational time.

The basic motivation behind this paper is the fact that mass oscillation flows dominate sewer systems hydraulics and that SWMM5 can accurately and holistically handle this type of flow in a significantly shorter computational time. The proposed approach for expanding on this capability is the simple idea of allowing SWMM5 to handle all components of the system except for any conduits in which waterhammer effects are expected or for those conduits that are deemed to be critical or of high interest. With that, a new computational engine has been developed and embedded in the SWMM5 code in order to calculate the flow hydraulics in selected conduits by the aid of the well-known Preissmann Slot Method. The new/modified engine includes a novel numerical method previously proposed by the authors of this paper and one that is based on a first order Godunov numerical scheme.

In this approach the numerical fluxes are calculated in such a way that adequate numerical viscosity is automatically added to the scheme when the pressurization of the conduit is imminent. The additional numerical viscosity removes the spurious numerical oscillation relevant to the Preissmann Slot Method and provides a non-oscillatory solution even for an acoustic wave velocity of more than 1000 m/s. Since the time step satisfying the numerical instability of the proposed numerical approach is significantly smaller than that used by SWMM5, a local time step approach is also employed in order to not impose such a small time step on the SWMM5 part of the solution. For every single time step for which SWMM5 updates the hydraulics for most of the system, the additional numerical engine calculates the hydraulic transient response for a number of local time steps in the selected conduits.

The initial results from the modified and customized SWMM5 model are shown to be in very good agreement with both experimental and analytical data. This paper presents a few example case studies and ultimately shows that with the powerful features of SWMM5, the proposed model enables the accurate and efficient calculation of transient flow in sewer systems for an acoustic wave velocity of more than 1000 m/s.