Steve Scott1, Yafei Jia2 and Sam S.Y. Wang3
1Research Hydraulic Engineer, Coastal & Hydraulic Engineering Laboratory of ERDC, US Army Corps of Engineers, Waterway Experimental Station.
2Research Associate Professor, National Center for Computational Hydroscience and Engineering, The University of Mississippi, MS 38655.
E-mail: jia@ncche.olemiss.edu.
3F.A.P.Barnard Distinguished Professor, Director, NCCHE,
E-mail: wang@ncche.olemiss.edu.
Abstract: More and more 3D numerical hydrodynamic models have been applied to hydraulic research and engineering design studies, due to the fact that numerical modeling is more cost effective. However, questions have been raised about the uncertainties of the numerical models’ applicability to investigate real world problems, even if these models have been verified by using rigorous approaches. This paper presents a validation test of a three dimensional numerical model, CCHE3D, using 3D field data measured in the Mississippi River. The numerical study is focused on a curved channel reach, Victoria Bendway, in which many submerged dikes were constructed to improve the channel navigation condition. To support the study, 3D velocity data were collected using ADCP across the channel. The CCHE3D model was applied to study the secondary flow and investigate the effectiveness of these submerged weirs for improving navigation. The simulated flow field and the measured data showed good agreement, thus the model’s applicability to simulate natural river processes was confirmed.
Keywords: numerical modeling, simulation, verification, natural river
Applicability of numerical models to real world flow problems study has been questioned, because of the numerous unknowns in natural channel flow environments. Recently, the CCHE3D model, developed at the National Center for Computational Hydroscience and Engineering, was applied to study the effectiveness of hydraulic structures (submerged weirs) for improving navigation in Victoria Bendway, Although the CCHE3D model has been verified by using analytical approaches and comparison to physical experimental data (Jia and Wang, 1999, 2000), it is important to validate the model to natural river. Because the uncertainties of boundary conditions and channel morphology are much higher than those of analytical solutions and physical experiments, the validation was an important test to determine the model’s capability in real world problem applications. The simulated velocity field is compared with a vast amount of data collected in this reach. Excellent agreements between the simulation and field data enhanced our confidence on the applicability of this 3D model to study flows in natural channels with structures. The validation results with submerged weirs are reported in this paper.
Model description
CCHE3D is a free surface, three-dimensional numerical simulation model for unsteady turbulent flows developed at the NCCHE. Based on a special finite element method, Efficient Element Method, it is capable of handling flows and sediment transport in complex channel domain and irregular bed topography. Staggered grid and convective interpolation functions are adopted to eliminate node to node oscillations. Solutions with both dynamic pressure and hydrostatic pressure assumption are available. Several turbulence closure models and sediment transport models are included. This model has been verified by analytical methods and many sets of data from physical model experiments. Recently, CCHE3D was applied to simulate the near field flow around a submerged dike of physical experimental scale (Jia, and Wang, 2000). A realistic three-dimensional flow field, including horse shoe vortex and 3D recirculation, were obtained.
Victoria BendWay is located at the confluence of the White River, between the State of Arkansas and Mississippi. The discharge in the Mississippi River upstream of the VBW is influenced by the White River. Victoria bendway is a highly curved bend, with a ratio of the radius of curvature to the channel width varying from 1 to 3 approximately, depend on the river stage. It has a 108o heading change and a radius of 1280 m. It is expected that the secondary current would be very strong in such a channel, which create a navigation hazard to navigating barges.
Six submerged weirs were constructed along the concave side of VBW in 1995, oriented upstream with angle from 69 to 76 degrees between the weirs and the bend longitudinal line. Post-construction surveys indicate deposition at the upstream reach of the weir field and scouring throughout the rest of the weir system. Three long spur dikes were constructed on the flood plain or point bar of the VBW. The effect of these dikes is to converge the flow to the main channel, therefore the point bar is protected from erosion, and the channel is re-aligned to enhance navigation.
A comprehensive survey of this reach was conducted in 1998. The data were measured by acoustic devices with bed elevation referenced to a Cartesian coordinate system. In addition to the bed elevations, velocity data were taken in VBW using Acoustic Doppler Current Profiler instrumentation on June 11 and June 12, 1998.
Figure 1. shows bathymetry of the VBW and the cross-sections for measuring the velocity field. The weirs constructed in the main channel are clearly visible. At each survey point, three dimensional velocities were measured along a vertical line with a number of points ranging from 5 to more than 100, depending on the flow depth. The depth-averaged velocity is shown in the figure as vectors along the survey paths. The velocity data measured on June 11, 1998 has 17 sections with total 2210 points while the data taken in June 12, 1998 includes 17 sections with a total of 2494 points.
In order to use available resources efficiently, a two dimensional depth integrated model, CCHE2D, was first applied to compute the flow in an extended channel (33.866km, about 4 times longer than the 3D simulation channel) so that adequate boundary conditions (discharge, flow direction and surface elevation distributions across the in and outlet sections of the 3D channel) for the 3D model could be determined. The 2D simulation was also used as a tool to calibrate roughness of the channel. The 3D computation is for the flow in the bend with a mesh size of 123 (transversal) x 322 (longitudinal) x 11 (vertical); the extended 2D channel included both up and downstream of the VBW with a mesh size of 123x622. The bathymetry data for 1998 were used for these meshes. The following table summarizes the flow conditions and structures in the channel.
Fig.1 Bathymetry of
Victoria Bendway and velocity survey lines, depth-averaged velocities are shown.
Table 1 Some flow conditions of victoria bendway
|
Discharge (m3/s) |
Manning’s n |
Roughness Height (m) |
Submerged weirs (left bank) |
Spur dikes (right bank) |
|
12,600.0 |
0.047 |
0.5 |
6 |
3 |
The discharge is consistent with the measured velocity data, and the calibrated Manning’s coefficient n=0.047 is reasonable considering the number of structures built in this channel reach. The calibrated Manning’s coefficient is then transformed to equivalent roughness height for the three-dimensional model by using Sticker’s function
(1)
where d is the equivalent roughness height, A is an empirical constant (A=19 according to Chien and Wan, 1999).
The CCHE3D hydrodynamic model for three-dimensional free surface turbulent flow was applied to simulate the flow field in this channel. The three-dimensional Reynolds equations, continuity equation and free surface kinematics equation are solved. Mixing length turbulence model was applied as the closure scheme. Hydrostatic pressure option of the model was used. Because the computational mesh points were different from those of the velocity survey, interpolation was performed to obtain numerical solution at the measurement points. Inverse distance interpolation was used to compute the velocity from the four vertices of a mesh cell containing a measurement point. In the vertical direction, interpolation was based on the relative depth because the flow depth at the four mesh vertices and the measurement point are not the same.
Figure 2 demonstrates the simulated flow field near the free surface of the channel. The river stage was high, the point bar and the third dike on the right bank side were submerged. The second dike on the point bar was exposed. One can see the flow velocity variation along the channel due to the existence of the dike and weir structures. Because water depth is small over the submerged weirs and was deepened between weirs due to scouring, the flow accelerates over the submerged weirs and decelerates between them.
Because there were more than 4500 survey points, it is impossible and unnecessary to show all the comparisons in the paper. Instead, only comparisons at selected points are presented. For practical reasons, the points chosen are along the main channel. Figure 3 shows the locations of the velocity validation points along the main channel, one point for each survey section. Some of them are located in scour holes between weirs, and others are very close to the weirs. Due to space limitation, only comparisons of even number of these points (section 2, 4, 6, …) are presented here in Figure 4.
Most of the comparisons show excellent agreement between data and simulation. In general, measured data indicates fluctuation and variation along vertical lines. The simulation results are of smooth curves because the numerical model simulates mean turbulent flow field while the measured velocities are taken in highly turbulent and unsteady natural conditions. Results indicate that the velocity profiles are quite normal in most areas in the channel, with velocity magnitude increasing with distance from the bed. The velocity profiles become highly irregular near the weirs, especially behind them. It can be seen that in measuring points 8, 16, and 26, the measured velocities indicate stronger variations along the vertical (Figure 4). These sections are located (Figure 3) either near the abrupt bed change, close to the weir, or in the scour hole of a weak zone. In these locations, the secondary flow is very strong. The upper and lower part of the flow often have different directions, due to the effect of the submerged weirs on the flow pattern in the curved channel. Mesh refinement would enable the model to further improve the prediction of flow characteristics around these weirs.
Fig.4 Comparisons of simulated velocity and measurement at selected points
CCHE3D has been comprehensively tested following a procedure developed by the ASCE Task Committee on 3D Free-Surface Flow Model Verification and Validation. According to this procedure, all models should be tested using analytic solution, physical model measurements, and field data. In the present study, the field data collected at Victoria Bendway on the Mississippi River is used to conduct a site-specific validation of the CCHE3D simulation model. The reasonable agreements between the results and field data have exceeded the model developers’ expectations, particu-larly the consistency and the trend of the flow fields predicted. The magnitude and direction of the predicted velocities are within the margin error of field measurements. This successful validation test indicated that the CCHE3D model is capable of providing realistic solutions to real world practical problems in hydraulic engineering.
Acknowledgements
This investigation is conducted under contract agreement No.DACW 42-00-P-0456 with the US Army Corps of Engineers, Waterway Experimental Station.
References
Chien, N. and Wan, Z. 1999, Mechanics of Sediment Transport, ASCE press, ASCE, 1801 Alexander Bell Drive, Reston, Virginia 20191-4400.
Jia, Y., and Wang, S.S.Y., 1999, “Simulation of horse-shoe vortex around a bridge pier”, Proceedings of the International Water Resources Engineering Conference”. CD-ROM.
Jia, Y., and Wang, S.S.Y., 2000, ”Numerical Study of Turbulent Flow around Submerged Spur Dikes”, Accepted, 2000 International Conference of Hydroscience and Engineering.