Numerical Investigation of Flow Patterns in Rectangular Shallow Reservoirs

Abstract

In this study, the capability of a two-dimensional shallow-water numerical model to simulate the symmetric and asymmetric flows that can take place in rectangular shallow reservoirs with different lateral expansion ratios and dimensionless lengths is investigated. Numerically, the main difficulty is to properly reproduce the transition between symmetric and asymmetric flows. For a large lateral expansion ratio, the use of two protocols of simulation highlighted a high sensitivity of the simulated flow pattern to the initial condition. Comparison between simulated results and experimental data showed a good agreement for the critical shape parameter (combination of the lateral expansion ratio and the dimensionless length) between symmetric and asymmetric flows. A good agreement was also found for the value of the shorter reattachment length of asymmetric flows. For small lateral expansion ratios, the agreement was not so good. The model was used for even larger lateral expansion ratios in order to numerically extend the experimental dataset. This predictive work showed that the shape parameter, whose expression was only based on experiments carried out for small lateral expansion ratios, was also relevant for larger values. Moreover, the predicted values of the shorter reattachment length were also consistent with a regression only based on experimental results.

Maximum energy dissipation to explain velocity fields in shallow reservoirs

“…Fig. 4 of Dufresne et al, 2011), this feature is not captured in our simple model set-up. This, however, does not hamper the model's ability to deliver realistic transitions between symmetric and asymmetric flow patterns, as shown in Section 3.…”

“…In connected studies, the same group (Camnasio, Erpicum, Archambeau, Pirotton, & Dewals, 2014;Dewals, Kantoush, Erpicum, Pirotton, & Schleiss, 2008;Dufresne, Dewals, Erpicum, Archambeau, & Pirotton, 2011) as well as others (Kantoush, 2008;Peng, Zhou, & Burrows, 2011;Secher et al, 2014;Zhou, Liu, Shafiai, Peng, & Burrows, 2010) successfully simulated the observed flow patterns using the 2D shallow-water equations on a high resolution grid. For a given reservoir geometry, they showed that the flow pattern consistently evolved to a stable symmetric or asymmetric state in accordance with observations.…”

Can the collapse of a fly ash heap develop into an air-fluidized flow? — Reanalysis of the Jupille accident (1961)

“…The time step is adaptive and computed based on the Courant-Friedrichs-Lewy (CFL) stability criterion, with a CFL number equal to 0.5. It takes values of the order of 10 -3 -10 -2 s. This finite volume model has already proven its validity and efficiency for the analysis of natural and artificial floods (Ernst et al, 2010;Erpicum et al, 2010a;Dewals et al, 2011), as well as numerous other applications including complex turbulent flows (Dewals et al, 2008;Erpicum et al, 2009;Roger et al, 2009;Dufresne et al, 2011).…”

Reservoir sedimentation

“…The Darcy-Weisbach standard formulation was used for the friction modelling (Dufresne et al, 2011) and the bottom roughness was set to k s = 0.1 mm (representative of the polyvinylchloride state during the experiments).…”

“…and the flow modellers have successfully demonstrated that these flow features can be reproduced using an operational numerical model, where only the friction modelling is adjustable (Dewals et al, 2008, Dufresne et al, 2011, Peng et al, 2011, Camnasio et al, 2013, Khan et al, 2013, many questions remain regarding meandering flows.…”