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Focusing on the continuous bends in Shapotou section of the Yellow River, this paper probes into the water level variation, planar flow field variation, longitudinal flow variation and secondary flow in the continuous bends. Specifically, a mathematical model for 3D turbulent flow was discretized by the finite-volume method based on unstructured grids, a numerical solution equation was set up under the unstructured grids, and the model was solved by the SIMPLE algorithm using unstructured non-staggered grids. Then, the calculation area was meshed into triangular grids, the grids were densified for the bends, and the vertical direction was divided into multiple layers by the equidistant layering method. The simulated results agree well with the measured value. The convex bank generally had a lower water level than the concave bank. In the first bend, the water level of the concave bank was 0.02m higher than that of the convex bank; in the second bend, the water level of the convex bank was 0.04m higher than the convex bank. The mainstream flow rate was biased towards the concave bank in the continuous bends. With the increase of the central angle in the second bend, the mainstream gradually moved to the convex bank and reached the bank at the tip of the bend. Besides, the surface-bottom vortex on the convex bank became increasingly obvious and intense, the short transition area between the two bends was significantly affected by the high flow rate area of the first bend, and scouring occurred near the convex bank at the inlet and the convex bank at the outlet. These results prove that the proposed model can accurately simulate the 3D bend water flow of natural rivers with complex boundaries; apart from planar spiral flow, the proposed model could simulate the sectional distribution of mainstream flow rate.
continuous bands, 3D water flow, unstructured grids, finite-volume method, numerical simulation
This paper is supported by the National Science Foundation of China (Grant No. 11761005); The Ningxia Natural Science Foundation (Grant No. 2018AAC03115).
[1] Song ZY. (2003). Generality of the Rozovskii's formulas on circulation at river bends. Advances in Water Science 14(2): 218-221. https://doi.org/10.3321/j.issn:1001-6791.2003.02.018
[2] Lv SJ, Feng MQ, Li CG. (2013). 3-D numerical simulation of flow in natural meandering channel. Hydro-Science and Engineering (5): 10-16. https://doi.org/10.3969/j.issn.1009-640X.2013.05.002
[3] Nakamura T, Yim SC. (2011). A nonlinear Three-dimensionl coupled Fluid-Sediment interaction model for large seabed deformation. Journal of Offshore Mechanics and Arctic Engineering-Transactions of the ASME 133(3): 1-14. https://doi.org/10.1115/1.4002733
[4] Pinto L, Fortunato AB, Zhang Y, Oliveira A, Sancho FEP. (2012). Development and validation of a three-dimensional morphodynamic modelling system for non-cohesive sediment. Ocean Modelling 57-58: 1-14. https://doi.org/10.1016/j.ocemod.2012.08.005
[5] Li CG, Yang C. (2013). Numerical simulation of three dimensional flow and sediment transport in ningxia shuidonggou reservoir. China Rural Water and Hydropower 12: 45-50. https://doi.org/10.3969/j.issn.1007-2284.2013.12.012
[6] Wang JH. (2011). Establishment and application of three-dimensional nonstructural wave and current coupling numerical model. PHD Thesis of Dalian University of Technology.
[7] Bai W, E XQ. (2003). Implement of SIMPLE algorithm based on unstructured colocated meshes. Chinese Journal of Computational Mechanics 20: 702-710. https://doi.org/10.3969/j.issn.1007-4708.2003.06.010
[8] Lai XJ, Qu ZJ, Zhou J, Shen MB. (2006). 3-D hydrodynamic model for shallow water on unstructured grids. Advances in Water Science 17(5): 693-699.
[9] Lei GD, Li WA, Ren YX. (2011). High-order unstructured-grid WENO FVM for compressible flow computation. Chinese Journal of Computational Physics 28(5): 633-640.
[10] Yue ZY, Cao ZX, Li YW. (2011). Unstructured grid finite volume model for two-dimensional shallow water flows. Chinese Journal of Hydrodynamics 26(3): 359-367. https://doi.org/10.3969/j.issn1000-4874.2010.03.013
[11] Huang MT, Tian Y. (2014). Three-dimensional lake hydrodynamic numerical modeling and its application to Lake Donghu. Chinese Journal of Hydrodynamics 29(1): 114-124. https://doi.org/10.3969/j.issn1000-4874.2014.01.015
[12] Aguizir A, Zantalla E, Ait Yassne Y, Selhaoui N, Bouirden L. (2016). Influence of the concentration of tellurium in tlie hardening mechanism of the lead-tellurium alloys for battery grids. Annales de Chimie: Science des Materiaux 40(3-4): 121-129
[13] Du M. (2005). Unstructured mesh generation and its application in 2D hydrodynamic model. Master Thesis of Tianjin University. https://doi.org/10.7666/d.y849139
[14] Shmitt FG. (2007). Direct test of a nonlinear constitutive equation for simple turbulent shear flows using DNS data. Comp-utation in Nonlinear Science and Numerical Simulation 12(7): 1251-1264. https://doi.org/10.1016/j.cnsns.2006.01.015
[15] Tao WQ. (1995). Numerical heat transfer. Xi'an: Xi'an Jiao Tong University Press.
[16] Olaiju OA, Hoe YS, Ogunbode EB. (2018). Finite element and finite difference numerical simulation comparison for air pollution emission control to attain cleaner environment. Chemical Engineering Transactions 63: 679-684. https://doi.org/10.3303/CET1863114
[17] Hsu C. (1981) A curvilinear-coordinate method for momentum, heat and mass transfer of irregular geometry. Ph D thesis, University of Minnesota.
[18] Rhie CM, Chow WL. (1983). A numerical study of the turbulent flow past an isolated airfoil with trailing edge separation. 3rd Joint Thermophysics, Fluids, Plasma and Heat Transfer Conference 21: 1525-1552. https://doi.org/10.2514/6.1982-998
[19] Liu SH, Zhao SL, Luo QS. (2007). Simulation of low concentration sediment-laden flow based on two-phase flow theory Ⅱ—Solution and verification. Journal of Wuhan University 4(4): 5-8. https://doi.org/10.3969/j.issn.1671-844.2007.04.002
[20] Li Y, Lv H. (2018). Numerical simulation of mass transfer of slug flow in microchannel. Chemical Engineering Transactions 65: 325-330. https://doi.org/10.3303/CET1865055