Numerical Investigation of Flow Field in the Skewed Compound Channel

Introduction
A compound channel consists of one main channel with a deeper flow in the middle and one or two floodplains around the main channel by looser flow depth. The difference between velocity in the main channel and floodplains in compound channels creates a strong shear layer at interface between the main channel and floodplains. Also, because of the three-dimensional (3D) structure of flow, the Investigation of flow characteristics in compound channels is completely complicated. In non-prismatic compound channels, due to the mass exchange between subsections, the study of flow is more complex. Therefore, the prediction of flow behavior in the non-prismatic compound channel is an important subject for river and hydraulic engineers. The skewed compound channel is one kind of non-prismatic compound channels. In compound channel with skewed floodplains, one of the floodplains is divergent and the other is convergent. The flow patterns in skewed compound channels have been studied experimentally by many researchers (James and Brown, 1977; Jasem, 1990; Elliott, 1990; Ervine and Jasem, 1995; Chlebek, 2009; Bousmar et al., 2012). However, numerical studies on flow characteristics in skewed compound channels were rarely performed. In this research, by using the computational fluid dynamics (CFD) and two turbulence models of the RNG and LES, the velocity, boundary shear stress distributions, secondary current circulation, and water surface profile in a compound channel with skewed floodplains has been numerically investigated.
Methodology
In this research, modeled compound channel is similar to the experimental channel using by Chlebek (2009) at the hydraulic laboratory of Birmingham University, Department of Civil Engineering. The experimental studies were performed in a straight flume of 17 m long, 1.198 m wide, 0.4 m depth, and with an average bed slope of 2.003×10-3 (Fig. 1). By using the PVC material, the cross-section of this flume was made compound shape, a rectangular main channel of 0.398 m wide and 0.05 m deep in middle, and two floodplains with 0.4 m wide around the main channel (Fig. 2). The skewed compound channel was made by isolated floodplains using L-shaped aluminum profiles. Experiments were conducted at the skewed angle of 3.81° and four relative depths of 0.205, 0.313, 0.415, and 0.514. The lateral distributions of depth-averaged velocity and boundary shear stress were measured at six sections along the skewed compound channel (see Fig. 3), using a Novar Nixon miniature propeller current meter and Preston tube of 4.77 mm diameter, respectively.
For numerical simulation of the flow field in the skewed compound channel, the FLOW-3D computational software was used. Also, the renormalization group (RNG) and large eddy simulation (LES) turbulence models were selected. Two mesh blocks were utilized for gridding, mesh block 1 by coarser mesh size at the upstream of the skewed portion of the channel, and mesh block 2 by smaller mesh size for skewed part (Fig. 5). The flow field is numerically simulated by three computational meshes (fine, medium, and coarse mesh size). Details of griding for different computational meshes are summarized in Table 2. Finally, the medium mesh by 1653498 cells was selected. For boundary conditions, using volume flow rate condition for inlet, outflow condition for the outlet, symmetry condition for water surface area and the interface of two mesh blocks, and wall condition for lateral boundaries and floor (see Fig. 8 and Table 3).
Results and Discussion
The results of numerical simulation show that the RNG turbulence model, can predict the depth-averaged velocity and boundary shear stress distributions in the skewed compound channel fairly well (Figs. 9 and 10). In addition, in the skewed compound channel, the mean velocity and boundary shear stress on the diverging floodplain is more than these values on the converging floodplain at the same section. The longitudinal discharge distribution on floodplains of the skewed compound channel is linear, and the numerical modeling can compute these values very well (Figs. 11 and 12). By moving along the skewed part of the channel, areas with more flow velocity move toward the diverging floodplain. Also, the position of the maximum velocity, instead of the main channel centerline, move to the interface between the main channel and diverging floodplain, too (see Figs. 13 and 14). The lateral flow that leaves the converging floodplain, caused by changing the geometry of the channel along the skewed portion, created a secondary flow circulation in the main channel near the converging floodplain. Also, by going to the end of the skewed compound channel, this secondary flow becomes stronger (Figs. 15 and 16). For prediction of water surface profile in the skewed compound channel, two turbulence models of RNG and LES can compute the water depth along the channel fairly well, especially the RNG turbulence model (Fig. 17). In addition, the error analysis by using experimental data and numerical results are investigated. For error analysis, mean absolute error (MAE), mean absolute percentage error (MAPE), root mean square error (RMSE), and the coefficient of determination (R2) were calculated by using the equations of (12) to (15), respectively. These computation errors between numerical simulation results and experimental studies data are presented in Table 5 and are showed in Figs. 18 and 19.
Conclusion
In this research, the flow field in compound channel with skewed floodplains was numerically simulated. The FLOW-3D software and two turbulence models of the RNG and the LES were used to model the depth-averaged velocity, boundary shear stress distributions, and discharge distribution at different sections of skewed compound channel. The results of simulations indicate that comparing with the LES turbulence model, the RNG turbulence model are able to predict the velocity and bed shear stress distributions quite well especially in the first half of the skew portion. Also, by increasing the flow relative depth, the accuracy of numerical modeling is increased to compute different flow characteristics, but in water surface profile, by increasing the relative depth, the precision of simulation decreases (see Fig. 18).