Translated Titles

Simulation of Curved Channel Flow Using a Semi-3D Model with Orthogonal Curvilinear Coordinate System





Key Words

垂直水平分離 ; 擬似三維 ; 彎道水流 ; 正交曲線座標系統 ; σ 座標系統 ; 隱式雙階分割操作趨近法 ; vertical-horizontal splitting ; semi-3D ; bend flow ; orthogonal curvilinear coordinate system ; sigma coordinate system ; implicit two-step split-operator



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Chinese Abstract

本研究以垂直水平分離(VHS)演算的方法發展一擬似三維水理模式,探討彎 道流場之水理現象。在水平部份,利用深度平均的控制方程式計算水位與水平 兩方向的水深平均流速值;在垂直部份,先假設任一深度的流速等於水深平均 流速加上一擾動量,帶入三維控制方程式後再扣除深度平均控制方程式即可得 水平兩方向擾動量在垂向(水深方向)的控制方程式;綜合水平與垂直的計算結 果,即可計算不同深度之水平兩方向的流速值。在座標系統上,水平方向與垂 直方向分別採用正交曲線座標與σ 座標系統,使模式能便利處理不規則的渠道 與底床邊界。在計算步驟上,水平部份採用雙階分割操作趨近法,將水理控制 方程式分割成延散步驟(包含移流項與擴散項)和傳播步驟(包含底床剪應力項與 壓力項)求解,增進模式在實用上的彈性。數值差分上,水平與垂直部分皆採用 隱式法求解,使模式可用較大之演算間距。最後,本研究分別採用緩彎、急彎 及連續彎來模擬彎道流場,並與實驗值與水深平均二維模式模擬結果比較,展 示本模式在不同彎道型態、彎道長度、二次流強度及彎道反曲的情況下,皆能 模擬出合理的結果。

English Abstract

This study develops a semi-3D model based on a vertical-horizontal splitting (VHS) method to analyze the flow in open-channel bends. In horizontal, the surface elevation and depth-averaged velocity components are computed by 2D depth-averaged model. In vertical, assume the 3D velocity profile of Navier-Stokes equations is equal to the depth-averaged velocity plus the deviation of velocity profile, and then the vertical governing equations can be derived by subtracting the 2D depth-averaged equations to the 3D Navier-Stokes equations. In order to fit the complex geometry in both side wall and bed slope of channel, the orthogonal curvilinear coordinate system is used in horizontal gird, and sigma coordinate system is used in vertical grid. As for the numerical solution procedure, the two-step split-operator approach, which includes dispersion process (advection and diffusion terms) and propagation process (bed shear stress and pressure terms), is adopted to solve the 2D depth-averaged flow equations to improve the application flexibility. Implicit difference methods are adopted to relax the time step restriction allowing large time steps. Finally, three sets of experimental data including mildly curved, sharply curved and meandering channel are used to demonstrate the capability and accuracy of the semi-3D model, and the results of 2D depth-averaged model are also compared. The simulation results of semi-3D model show well agreement with experimental data considering different curved channels, bend lengths, secondary current and transverse mixing conditions.

Topic Category 工學院 > 土木工程系所
工程學 > 土木與建築工程
  1. 國立交通大學土木工程研究所博士論文。
  2. (205), Center for Research in Water Resources, University of Texas at Austin.
  3. free surface flows by a Multilayer Saint-Venant model” Internat. J. Numer.
  4. simulation of flow in sharp open-channel bends with horizontal and developed
  5. circulation studies of the South Atlantic Bight” Journal of Geophysics Research,
  6. de Vriend, H.J., and Koch, F.G. (1977), “Flow of water in a curved open channel
  7. Falconer, R.A. (1980), “Numerical modeling of tidal circulation in harbors” J
  8. Waterway Port Coast Ocean Div; 106: 31-48
  9. Falconer, R.A., and Lin, B. (1996), “Three-dimensional modelling of water quality in
  10. modelling of open-channel flow with submerged vegetation” IAHR Journal of
  11. Hydraulic Research, No. 3.
  12. finite-volume, nonhydrostatic, parallel coastal-ocean simulator” Ocean
  13. Ge, L., and Sotiropoulos, F. (2005), “3D unsteady RANS modeling of complex
  14. with vertical eddy viscosity prescribed in two layers” Geophysics, Vol.24.
  15. Hsieh, T.Y., and Yang, J.C. (2004), “Implicit Two-Step Split-Operator Approach for
  16. Modeling Two-Dimensional Open Channel Flow” J. Hydro-science and
  17. Approach for Shallow Water Free Surface Flow Computation” Communications
  18. in Numerical Methods in Engineering, 24(12), 1699-1722. (SCI, EI)
  19. Li, B., and Fleming, C. A. (2003), “Three-dimensional hydrodynamic model for free
  20. Li, C.W., and Gu, J. (2001), “3d layered-integrated modelling of mass exchange in
  21. semi-enclosed water bodies” Journal of Hydraulic Research, Vol.39, No.4, pp.
  22. Lien, H.C., Hsieh T.Y., and Yang J.C. (1999a), “Use of two-step split-operator
  23. Lin, M.Y., and Huang, L.H. (2008), “Velocity profiles of nonlinear shallow-water
  24. flows” Journal of the Chinese Institute of Engineers, 31(1), 105-120.
  25. Muin, M., and Spaulding, M.L. (1997), “Three-Dimensional Boundary-fitted
  26. Muneta, B.N., and Shimizu, Y. (1994), “Numerical analysis model with spur-dikes
  27. numerical model of lateral-intake inflows” J.Hydr. Engrg., ASCE, 125(2),
  28. Rozovskii, I.L. (1957), “Flow of Water in Bends of Open Channels” Ac. Sc. Ukr.
  29. Simons, T.J. (1974), “Verifications of numerical models of Lake Ontario, I:
  30. Subramanya, K. (2001), “Flow in Open Channels” Second Edition.
  31. Wang, K.H. (1994), “Characterization of Circulation and Salinity Change in
  32. Xia, C., and Jin, Y.C. (2007), “Multilayer Depth-Averaged Flow Model with Implicit
  33. Ye, J., and McCorquodale, J.A. (1998), “Simulation of curved open channel flows by
  34. hydrodynamic model in curvilinear coordinates with collocated grid” Int. J.
  35. Numer. Methods Fluids 28 (1998) 1109.
  36. Yeh, K. C., and Kennedy, J. F. (1993), “Moment model of nonuniform channel-bend
  37. Zeng, J., Constantinescu, G., Blanckaert, K., and Weber, L. (2008), “Flow and
  38. Resource Research, VOL. 44, W09401, doi: 10.1029/ 2007WR006303
  39. 謝德勇(1994),「二維彎道水理模式之研究」,國立交通大學土木工程研究所碩
  40. 士論文。
  41. 連和政(1999),「二維水深平均模式應用於彎道水流與泥沙運移模擬之研究」,
  42. 謝德勇(2003),「二維水理、污染傳輸及沉滓運移模式之研發與應用」,國立交
  43. 通大學土木工程研究所博士論文。
  44. Almquist, C.W., and Holley, E.R. (1985), “Transverse mixing in meandering
  45. laboratory channels rectangular and naturally varying cross-section” Tech. Rep.
  46. Audusse, E., Bristeau, M.O., and Decoene, A. (2008), “Numerical simulations of 3D
  47. Methods Fluids 56, no. 3, 331–350.
  48. Blanckaert, K., and de Vriend, H.J. (2003), “Non-linear modeling of mean flow
  49. redistribution in curved open channels” Water Resources Res., AGU, 39(12).
  50. Blanckaert, K., Glasson, L., Jagers, H.R.A., and Sloff, C.J. (2003), “Quasi-3D
  51. bed topography” Proc., Int. Symp. On Shallow Flows, G.H. Jirka and W.S.J.
  52. Uijttewaal, eds., Delft Univ. of Technology, Delft, The Netherlands, I, 93-100.
  53. Blumberg, A.F., and Mellor, G.L. (1983), “Diagnostic and prognostic numerical
  54. 88(C8):4579-4592
  55. with a fixed plane bed” Report on experimental and theoretical investigations
  56. R675-V M1415 part I, Delf Univ. of Technology, Delf, The Netherlands.
  57. the Humber Estuary” Water Research 31 5, pp. 1092–1102.
  58. 66
  59. Fischer-Antze, T., Stösser, T., Bates, P., and Olsen, N. R. B. (2001) “3D numerical
  60. Flokstra, C. (1977), “The closure problem for depth-averaged two-dimensional
  61. flows” Proc., 18th Congr. Of the Int. Assn. For Hydr. Res., 247-256.
  62. French, R.H. (1986), Open Channel Hydraulics. McGraw-Hill Book Company,
  63. Singapore, 705 pp.
  64. Fringer, O.B., Gerritsen, M., and Street, R. L. (2006), “An unstructured-grid,
  65. Modelling, 14 (3-4), 139-278.
  66. hydraulic engineering flows. I: Numerical model” J Hydraul Eng 131 (9), pp.
  67. 800–808.
  68. Gross, E.S., Koseff, J.R., and Monismith, S.G. (1999), “Three-dimensional salinity
  69. simulations of South San Francisco Bay” Journal of Hydraulic Engineering 125
  70. (11): 1199-1209.
  71. Heaps, N.S., and Jones, J. (1981), “Three dimensional model for tides and surges
  72. Herzfeld, M., Waring, J., Parslow, J., Margvelashvili, N., Sakov, P., and
  73. Andrewartha, J. (2010), SHOC: Sparse Hydrodynamic Ocean Code, Scientific
  74. Manual. CSIRO Marine Research.
  75. Hydraulic Engineering, 22(2), 113-139.
  76. Hung, M.C., Hsieh, T.Y., Tsai, T.L., and Yang, J.C. (2008), “A Layer-Integrated
  77. Jin, X., and Kranenburg, C. (1993), “Quasi-3D Numerical Moderling of
  78. Shllow-Water Circulation” J. of Hydr. Eng., 119(4), pp. 458-472.
  79. Lardner, R.W., and Cekirge, H.M. (1988), “A new algorithm for three-dimensional
  80. 67
  81. tidal and storm surge computations” Appl. Math. Modeling, Vol. 12, 471-481
  82. surface flow” Journal of Hydraulic Research, Volume 41, No 4, pp. 367-377.
  83. 403-411.
  84. approach for 2D shallow water flow computation” Int. J. Numer. Methods in
  85. Fluids, 30, 557-575.
  86. Lien, H.C., Hsieh, T.Y., Yang, J.C., and Yeh, K.C. (1999b), “Bend-flow simulation
  87. using 2D depth-averaged model” J. Hydr. Engrg., ASCE, 125(10), 1097-1108.
  88. Circulation Model” J. Hydraulic Engineering, ASCE, Vol. 123, No. 1
  89. Considering the vertical flow velocity distribution” JSCE, Journal of Hydraulic,
  90. Coastal and Environmental Engineering, 497, 31-39.
  91. Neary, V.S., Sotiropoulos, F., and Odgaard, A.J. (1999), “Three-dimensional
  92. pp.126-140.
  93. Nicholas, A.P., McLelland, S.J. (2004), “Computational fluid dynamics modelling of
  94. three-dimensional processes on natural river floodplains” Journal of Hydraulic
  95. Research, 42(2), 131-143.
  96. Queutey, P., and Visonneau, M. (2007), “An Interface Capturing Method for
  97. Free-Surface. Hydrodynamic Flows” Computers & Fluids, Vol. 36, Issue 9, pp.
  98. 1481-1510
  99. SSR; Isr. Progr. Sc. Transl., Jerusalem, (1961).
  100. 68
  101. circulation in spring and early summer” J. Phys. Oceanogr. 4, 507-523.
  102. Song, Y.T., and Hou, Y.T. (2006), “Parametric vertical coordinate formulation for
  103. multiscale, Boussinesq, and non-Boussinesq ocean modeling” Ocean Modeling,
  104. 11, 298-332.
  105. Spalding, D.B. (1972), “A novel finite difference formulation for differential
  106. expressions involving both first and second derivatives” Int. J. Numer. Methods
  107. Eng., 4, 551-559.
  108. Galvestion Bay” J. of Engineering Mechanics, ASCE, 120(3), 557-579.
  109. Wu, Y., and Falconer, R.A. (2000), “A mass conservative 3-D numerical model for
  110. predicting solute fluxes in estuarine waters” Advances in Water Resources 23,
  111. pp. 531–543.
  112. Interfaces” J. Hydr. Engrg. 133, 1145
  113. 3D hydrodynamic model” J. Hydr. Engrg., ASCE, 124(7), 687-698.
  114. Ye, J., McCorquodale, J.A., and Barron, R.M. (1998), “A three-dimensional
  115. flow. I: Fixed beds” J. Hydr. Engrg., ASCE, 119(7),776–795.
  116. Yen, B.C. (1965), “Characteristics of Subcritical Flow in a Meandering Channel”
  117. Institute of Hydraulic Research, the University of Iowa, Iowa City, Iowa.
  118. Zhang, X.F., Lu, X.H., Dong, B.J., and Hu, C.H. (2011), “A quasi-3D mathematical
  119. bend flow model in non-orthogonal curvilinear coordinate system” J. Hydr.
  120. Engrg., 1, 268
  121. bathymetry in sharp open-channel bends: Experiments and predictions” Water
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