Journal of Korea Water Resources Association (한국수자원학회논문집)

Korea Water Resources Association (한국수자원학회)
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Free Surface Flow in a Trench Channel Using 3-D Finite Volume Method

  • Lee, Kil-Seong (Department of Civil and Environmental Engineering, Seoul National University) ;
  • Park, Ki-Doo (Department of Civil and Environmental Engineering, Seoul National University) ;
  • Oh, Jin-Ho (Department of Civil and Environmental Engineering, Seoul National University)
  • Received : 2011.03.05
  • Accepted : 2011.05.24
  • Published : 2011.06.30
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Abstract

In order to simulate a free surface flow in a trench channel, a three-dimensional incompressible unsteady Reynolds-averaged Navier-Stokes (RANS) equations are closed with the ${\kappa}-{\epsilon}$ model. The artificial compressibility (AC) method is used. Because the pressure fields can be coupled directly with the velocity fields, the incompressible Navier-Stokes (INS) equations can be solved for the unknown variables such as velocity components and pressure. The governing equations are discretized in a conservation form using a second order accurate finite volume method on non-staggered grids. In order to prevent the oscillatory behavior of computed solutions known as odd-even decoupling, an artificial dissipation using the flux-difference splitting upwind scheme is applied. To enhance the efficiency and robustness of the numerical algorithm, the implicit method of the Beam and Warming method is employed. The treatment of the free surface, so-called interface-tracking method, is proposed using the free surface evolution equation and the kinematic free surface boundary conditions at the free surface instead of the dynamic free surface boundary condition. AC method in this paper can be applied only to the hydrodynamic pressure using the decomposition into hydrostatic pressure and hydrodynamic pressure components. In this study, the boundary-fitted grids are used and advanced each time the free surface moved. The accuracy of our RANS solver is compared with the laboratory experimental and numerical data for a fully turbulent shallow-water trench flow. The algorithm yields practically identical velocity profiles that are in good overall agreement with the laboratory experimental measurement for the turbulent flow.

Keywords

References

  1. Alfrink, B.J., and van Rijn, L.C. (1983). Two-equation turbulence model for flow in trenches. Journal of Hydrologic Engineering, Vol. 109, pp. 941-958. https://doi.org/10.1061/(ASCE)0733-9429(1983)109:7(941)
  2. Basara, B., and Younis, B.A. (1995). Prediction of turbulent flows in dredged trenches. Journal of Hydraulic Research, Vol. 33, pp. 813-824. https://doi.org/10.1080/00221689509498553
  3. Beam, R.M., and Warming, R.F. (1978). An implicit finite-difference algorithm for hyperbolic systems in conservation-law form. Journal of Computational Physics, Vol. 22, pp. 87-110.
  4. Beddhu, M., and Tayloe, L.K. (1994). A time accurate calculation procedure for flow with a free surface using a modified artificial compressibility formulation. Applied Mathematics and Computation, Vol. 65, pp. 33-48. https://doi.org/10.1016/0096-3003(94)90164-3
  5. Casulli, V. (1999). A semi-implicit finite difference method for non-hydrostatic, free-surface flows. International Journal for Numerical Methods in Fluids, Vol. 30, pp. 425-440. https://doi.org/10.1002/(SICI)1097-0363(19990630)30:4<425::AID-FLD847>3.0.CO;2-D
  6. Casulli, V., and Busnelli, M.M. (2001). Numerical simulation of the vertical structure of discontinuous flow. International Journal for Numerical Methods in Fluids, Vol. 37, pp. 23-43. https://doi.org/10.1002/fld.162
  7. Casulli, V., and Cheng, R.T. (1992). Semi-implicit finite difference methods for three-dimensional shallow water flow. International Journal for Numerical Methods in Fluids, Vol. 15, pp. 629-648. https://doi.org/10.1002/fld.1650150602
  8. Casulli, V., and Stelling, G.S. (1998). Numerical simulation of three dimensional, quasi-hydrostatic free-surface flows. Journal of Hydraulic Engineering, ASCE, Vol. 124, No. 7, pp. 678-686. https://doi.org/10.1061/(ASCE)0733-9429(1998)124:7(678)
  9. Chorin, A. (1967). Numerical solution of Navier-Stokes equations for an incompressible fluid. Bulletin of the American Mathematical Society, Vol. 73, No. 6, pp. 928-945. https://doi.org/10.1090/S0002-9904-1967-11853-6
  10. Chow, V.T. (1956). Open-channel Hydraulics. New York, McGraw-Hill.
  11. Ferziger, J.H., and Peric, M. (1996). Computational Methods for Fluid Dynamics, Springer-Verlag, Berlin Heidelberg.
  12. Hoffmann, K.A., and Chiang, S.T. (1993). Computational Fluid Dynamics for Engineers, Engineering Education System.
  13. Huang, W., and Spaulding, M. (1995). 3D model of estuarine circulation and water quality induced by surface discharges. Journal of Hydraulic Engineering, Vol. 121, pp. 300-311. https://doi.org/10.1061/(ASCE)0733-9429(1995)121:4(300)
  14. Kaliaktsos, C.H., Pentaris, A., Koutsouris, D., and Tsangais, S. (1996). Application of an artificial compressibility methodology for the incompressible flow through a wavy channel. Communications in Numerical Methods in Engineering, Vol. 12, pp. 359-369. https://doi.org/10.1002/(SICI)1099-0887(199606)12:6<359::AID-CNM992>3.0.CO;2-4
  15. Kocyigit, M.B., Falconer, R.A., and Lin, B. (2002). Three-dimensional numerical modeling of free surface flows with non-hydrostatic pressure. International Journal for Numerical Methods in Fluids, Vol. 40, pp. 1145-1162. https://doi.org/10.1002/fld.376
  16. Lee, J.W., Teubner, M.D., Nixon, J.B., and Gill, P.M. (2006a). A 3-D non-hydrostatic pressure model for small amplitude free surface flows. International Journal for Numerical Methods in Fluids, Vol. 50, pp. 649-672. https://doi.org/10.1002/fld.1054
  17. Lee, J.W., Teubner, M.D., Nixon, J.B., and Gill, P.M. (2006b). Applications of the artificial compressibility method for turbulent open channel flows. International Journal for Numerical Methods in Fluids, Vol. 51, pp. 617-633. https://doi.org/10.1002/fld.1137
  18. Li, T. (2003). Computation of turbulent free-surface flows around modern ships. International Journal for Numerical Methods in Fluids, Vol. 43, pp. 407-430. https://doi.org/10.1002/fld.580
  19. Lin, F.B., and Sotiropoulos, F. (1997). Assessment of artificial dissipation models for three-dimensional incompressible flow solutions. Journal of Fluids Engineering, Vol. 119, No. 2, pp. 331-340. https://doi.org/10.1115/1.2819138
  20. Lu, Q., and Wai, O.W.H. (1998). An efficient operator splitting scheme for three-dimensional hydrodynamic computations. International Journal for Numerical Methods in Fluids, Vol. 26, pp. 771-789. https://doi.org/10.1002/(SICI)1097-0363(19980415)26:7<771::AID-FLD672>3.0.CO;2-7
  21. Madsenm, P.A., and Schaffer, H.A. (2006). A discussion of artificial compressibility. Coastal Engineering, Vol. 53, pp. 93-98. https://doi.org/10.1016/j.coastaleng.2005.09.020
  22. Mahadevan, A., Oliger, J., and Street, R. (1996). A non-hydrostatic mesoscale ocean model. Part II: numerical implementation. Journal of Physical Oceanography, Vol. 26, pp. 1881-1900. https://doi.org/10.1175/1520-0485(1996)026<1881:ANMOMP>2.0.CO;2
  23. Rodi, W. (1984). Turbulence Models and their Application in Hydraulics-A State of the Art Review, IAHR.
  24. Stansby, P.K., and Zhou, J.G. (1998). Shallow-water flow solver with non-hydrstatic pressure: 2D vertical plane problems. International Journal for Numerical Methods in Fluids, Vol. 28, pp. 541-563. https://doi.org/10.1002/(SICI)1097-0363(19980915)28:3<541::AID-FLD738>3.0.CO;2-0
  25. van Rijn, L.C. (1982). The Computation of the Flowand Turbulence Field in Dredged Trenches.: Delft Hydraulics Laboratory.
  26. Yuan, H., and Wu, C.H. (2004). An implicit three-dimensional fully non-hydrostatic model for free-surface flows. International Journal for Numerical Methods in Fluids, Vol. 46, pp. 709-733. https://doi.org/10.1002/fld.778
  27. Zhou, J.G., and van Kester, J. (1999). An aribitary Lagrangian-Eulerian $\sigma$ (ALES) model with non-hydrostatic pressure for shallow water flows. Computer Methods in Applied Mechanics and Engineering, Vol. 178, pp. 199-214. https://doi.org/10.1016/S0045-7825(99)00014-6