Simulation of Curved Open Channel Flows by 3D Hydrodynamic Model

A mathematical model of three-dimensional (3D) free surface flows has been applied to simulate the curved channel flows and mass transport. In the horizontal plane, a channel-fitted curvilinear coordinate system is used, whereas in the vertical plane, the σ-transformation is adopted to track the free surface and variable bed topography. To reduce the numerical diffusion, the second-order upwind scheme of Roe is incorporated to discretize the convection terms. The standard k-e model has been modified to take account of some anisotropic effects appearing in shallow curved channels, i.e., streamline curvature and the damping effects of free surface and solid walls. The governing equations are solved in a collocated grid system by a fractional three-step implicit algorithm. Two test cases from curved flumes have been studied: (1) A 270° channel bend with a sloped outer bank; and (2) a meandering channel with mass transport. The results are compared with the available data, which shows generally good agreement.

[1]  Jian Ye,et al.  Depth-averaged hydrodynamic model in curvilinear collocated grid , 1997 .

[2]  Yasuyuki Shimizu,et al.  Three-Dimensional Computation of Flow and Bed Deformation , 1990 .

[3]  Saeed Farokhi,et al.  On Turbulent Flows Dominated by Curvature Effects , 1992 .

[4]  N. N. Yanenko,et al.  The Method of Fractional Steps , 1971 .

[5]  B. Lakshminarayana,et al.  Turbulence modeling for three-dimensional shear flows over curved rotating bodies , 1984 .

[6]  S. Majumdar.  Role of underrelaxation in momentum interpolation for calculation of flow with nonstaggered grids , 1988 .

[7]  Y. L. Lau,et al.  TRANSVERSE MIXING IN MEANDERING CHANNELS WITH VARYING BOTTOM TOPOGRAPHY , 1977 .

[8]  S. Patankar.  Numerical Heat Transfer and Fluid Flow , 2018, Lecture Notes in Mechanical Engineering.

[9]  P. Roe.  Approximate Riemann Solvers, Parameter Vectors, and Difference Schemes , 1997 .

[10]  B. Launder,et al.  The numerical computation of turbulent flows , 1990 .

[11]  W. Rodi,et al.  Calculation of Secondary Currents in Channel Flow , 1982 .

[12]  P. Bradshaw,et al.  Turbulence Models and Their Application in Hydraulics. By W. RODI. International Association for Hydraulic Research, Delft, 1980. Paperback US $15. , 1983, Journal of Fluid Mechanics.

[13]  D. Cokljat,et al.  Second-Order Closure Study of Open-Channel Flows , 1995 .

[14]  Wolfgang Rodi,et al.  Calculation of flow and pollutant dispersion in meandering channels , 1985, Journal of Fluid Mechanics.

[15]  A. Demuren.  A numerical model for flow in meandering channels with natural bed topography , 1993 .

[16]  A. Jacob Odgaard,et al.  MEANDER FLOW MODEL. I: DEVELOPMENT , 1986 .

[17]  J. P. V. Doormaal,et al.  ENHANCEMENTS OF THE SIMPLE METHOD FOR PREDICTING INCOMPRESSIBLE FLUID FLOWS , 1984 .

[18]  B. Launder,et al.  Lectures in mathematical models of turbulence , 1972 .

[19]  C. H. Priddin,et al.  The calculation of turbulent boundary layers on spinning and curved surfaces , 1977 .

[20]  G. Stelling,et al.  On the approximation of horizontal gradients in sigma co‐ordinates for bathymetry with steep bottom slopes , 1994 .

[21]  Yung-Chi Chang,et al.  Lateral Mixing in Meandering Channels , 1984 .

[22]  H. D. Vriend,et al.  Velocity redistribution in curved rectangular channels , 1981, Journal of Fluid Mechanics.

[23]  Wolfgang Rodi,et al.  Calculation of Annular and Twin Parallel Jets Using Various Discretization Schemes and Turbulence-Model Variations , 1981 .

[24]  Dennis N. Assanis,et al.  Evaluation of various high-order-accuracy schemes with and without flux limiters , 1993 .

[25]  Wolfgang Rodi,et al.  CALCULATION OF STRONGLY CURVED OPEN CHANNEL FLOW , 1979 .

[26]  Howard H. Chang.  Fluvial Processes in River Engineering , 1988 .

[27]  Ayodeji O. Demuren,et al.  Calculation of turbulence-driven secondary motion in ducts with arbitrary cross section , 1989 .

[28]  J Ye,et al.  Three-dimensional numerical modelling of mass transport in curved channels , 1997 .

[29]  G. Parker,et al.  Velocity Redistribution in Meandering Rivers , 1989 .

[30]  Yee-Chung Jin,et al.  Flow near sloped bank in curved channel , 1990 .