عنوان مقاله [English]
نویسندگان [English]چکیده [English]
Modelling 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, modelling 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. The shallow water equations (SWEs), on the other hand, are a well-known system of conservation laws that generally require less computational resources in particular for areas of the flow where the fluid depth is assumed small compared to the entire width. Herein, the shallow water equations (SWEs) with the assumption of hydrostatic pressure is 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 is utilized. Moreover, an ODE system of equations is utilized to anticipate the flow action through the manhole. Then these equations are coupled with each other to unify the approaches.
STAR-CD software is 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, although at considerable computational expense.
To calculate the error between SWEs results and STAR-CD solution, Root Mean Square Error (RMSE) method is 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; RMSE is a measure of how spread out these residuals 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 is studied. This test case is important as it shows the ability of the proposed method in modelling multiple wave interactions over the dry-state. Then a ?D sewer network consisting of one manhole and an underground channel is considered and flowing water inside the system is modelled.
For all test cases, the achieved numerical results were compared with those of the ?D 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) is defined based on the height of manhole and underground channel, manhole width and the velocity of the water entering the manhole. Moreover, many experiments are performed by changing the mentioned effective parameters to create a range for the manhole number. This range shows that the defined numerical solver gives accurate predictions if the MN is satisfied. Results are shown that if MN ? ?.??, the error obtained using RMSE method will be less than one percent and tends to zero.
The simulation results show that in all investigated cases, a good agreement is observed between the solutions of the proposed method and the Navier-Stokes solver. This is despite observing some inherent drawbacks such as inability to capture cavities and model free-fall problems in the SWEs solutions.