عنوان مقاله [English]
نویسندگان [English]چکیده [English]
Urban flooding is generally caused by some unexpected phenomena such as dam failure, torrential rainfall or tsunami waves moving toward the urban areas. Numerical methods have been used for many years to model the inundation problems over urban areas. Computational and mathematical approaches can be employed for several reasons. First, they can be considered as a reliable approach that allows modellers or engineers to predict the flooding extent into the cities and mitigate the hazardous effects on civilians, infrastructure facilities and constructions. Second, the experimental and geophysical data obtained for the previous inundations around the world are regional and strongly depend on the geographical and local conditions for the inundated area, and therefore cannot be applied for the other districts. Finally, the numerical simulation can be used for the large computational domains and can help to design the flood capacity for the conveyance channels or underground pipe networks devised for collecting free-surface flows within the cities. Modeling of water waves within a sewer network is a contemporary research area where the main goal is developing an accurate sewer design and planning tools. The prediction models should ideally be able to simulate the unsteady flow regime within the sewer network as well as the flow field created inside the manholes which link the surface flows to the sewer system. Manhole is one of the sewer network components which conveys surface flow to underground network. Inspection of the flow behavior when propagates and enters the sewer network is therefore momentous.
In general, modeling of such flows is only possible by means of Navier-Stokes equations with free surface capability. However, for a large domain and three-dimensional problem, the computational demands are rather high and prohibitive. Besides, the shallow water equations (SWEs) are a well-established set of conservation laws that approximate the hydrodynamics of flows in shallow water domains, where the depth is small compared to the overall plan dimensions. The SWEs are depth-averaged with the assumption of hydrostatic pressure and are much more computationally efficient for simulation of inundation over large areas. Herein, the shallow water equations (SWEs) were used as a proper substitution for Navier-Stokes equations to predict the wave movement. In order to solve the SWEs, a modified wave propagation algorithm with complex wave interaction capability over a dry-state was utilized. Moreover, an ODE system of equations was utilized to anticipate the flow action through the manhole. Then, these equations were coupled with each other to unify the approaches. STAR-CD software was utilized to validate the results of abovementioned approach. The STAR-CD is the commercial Navier-Stokes solver based on the VOF (volume of fluid) approach which models free-surface motion quite generally, despite considerable computational expense. To calculate the error between SWEs results and STAR-CD solution, Root Mean Square Error (RMSE) method was used. RMSE is the standard deviation of the residuals (prediction errors). Residuals are a measure of how far from the regression line data points are. In other words, it shows how concentrated the data is around the line of best fit.
First, to test the ability of the proposed approach, the interaction of dam break flow with two surcharged flows released on a dry bed was studied. This test case was important as it shows the ability of the proposed method in modelling multiple wave interactions over the dry-state. Then a 1D sewer network consisting of one manhole and an underground channel was considered and flowing water inside the system was modelled. For all test cases, the achieved numerical results were compared with those of the 3D Navier-Stokes solver, STAR-CD, which was setup to use the two-phase VOF solver for capturing free-surface. In addition, a dimensionless number named Manhole Number (MN) was defined based on the height of manhole and underground channel, manhole width and the velocity of the water entering the manhole. Moreover, many experiments were performed by changing the mentioned effective parameters to create a range for the manhole number. This range showed that the defined numerical solver gives accurate predictions if the MN is satisfied. Results were shown that if MN ≤ 0.98, the error obtained using RMSE method will be less than one percent and tends to zero.
The simulation results indicated that in all investigated cases, a good agreement was observed between the solutions of the proposed method and the Navier-Stokes solver. This was despite observing some inherent drawbacks such as inability to capture cavities and model free-fall problems in the SWEs solutions.