대한토목학회논문집 (KSCE Journal of Civil and Environmental Engineering Research)

  • 제28권5B호
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  • Pages.575-589
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  • 2008
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  • 1015-6348(pISSN)
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  • 2799-9629(eISSN)
대한토목학회 (Korean Society of Civil Engeneers)
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단파의 전파에 따른 수위 및 유속변화의 특성에 관한 연구

Characteristics of Water Level and Velocity Changes due to the Propagation of Bore

  • 이광호 ((일)나고야대학 대학원 공학연구과 사회기반공학전공) ;
  • 김도삼 (한국해양대학교 건설환경공학부, (미)오레곤주립대학교) ;
  • 투고 : 2008.06.16
  • 심사 : 2008.08.28
  • 발행 : 2008.09.30
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초록

본 연구는 지진해일단파(tsunami bore) 혹은 조석단파(tidal bore)와 같은 단파의 동수역학적인 거동특성을 검토할 목적으로, 댐파괴류에서 단파의 형성과 동일한 방법, 즉 수조의 한쪽 끝단에 있는 고수위의 저수조(貯水槽) 게이트를 순간적으로 제거하는 방법으로 단파를 발생시킨다. 이러한 단파의 형성과 전파에 관한 수치시뮬레이션에 이상유(二相流)모델에 기초한 Navier-Stokes식을 적용하며, 이 때 비압축성 및 비혼합성의 액체와 기체흐름을 각각 고려한다. 기체와 액체의 접면을 VOF법으로 추적하고, Navier-Stokes방정식을 수치적으로 풀기 위하여 MCIP법을 적용한다. 1차원인 CIP법을 분할스텝기법을 사용하여 고차원으로 확장한 MCIP법은 수치확산이 매우 작고, 또한 안정된 스킴으로 알려져 있다. 게다가, 난류를 시뮬레이션하기 위하여 그의 유용성이 잘 알려져 있는 LES모델을 사용한다. 단파의 형성과 전파에 관한 수치해석결과를 검증하기 위하여 수리실험을 수행하였으며, 시간경과에 따른 수위변동과 평균유속변동에 대한 수치해석결과 및 실험결과를 비교하여 매우 양호한 상호대응관계를 확인할 수 있었다.

In the present work, we investigate the hydrodynamic behavior of a turbulent bore, such as tsunami bore and tidal bore, generated by the removal of a gate with water impounded on one side. The bore generation system is similar to that used in a general dam-break problem. In order to the numerical simulation of the formation and propagation of a bore, we consider the incompressible flows of two immiscible fluids, liquid and gas, governed by the Navier-Stokes equations. The interface tracking between two fluids is achieved by the volume-of-fluid (VOF) technique and the M-type cubic interpolated propagation (MCIP) scheme is used to solve the Navier-Stokes equations. The MCIP method is a low diffusive and stable scheme and is generally extended the original one-dimensional CIP to higher dimensions, using a fractional step technique. Further, large eddy simulation (LES) closure scheme, a cost-effective approach to turbulence simulation, is used to predict the evolution of quantities associated with turbulence. In order to verify the applicability of the developed numerical model to the bore simulation, laboratory experiments are performed in a wave tank. Comparisons are made between the numerical results by the present model and the experimental data and good agreement is achieved.

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참고문헌

  1. Abdolmaleki, A., Thiagarajan, K.P., and Morris-Thomas, M.T. (2004) Simulation of the dam break problem and impact flows using a Navier-Stokes slover. 15th Australasian Fluid Mech. Conference, pp. 13-17
  2. Akanbi, A.A. and Katopodes, N.D. (1988) Model for flood propagation on initially dry land. J. of Hydraulic Engineering, ASCE, Vol. 114, No. 7, pp. 689-706 https://doi.org/10.1061/(ASCE)0733-9429(1988)114:7(689)
  3. Akiyama, M. and Aritomi, M. (2002) Advanced numerical analysis of two-phase flow dynamics -multi-dimensional flow analysis-. Corona Publishing Co., LTD. Tokyo, JAPAN
  4. Amsden, A.A. and Harlow, F.H. (1970) The SMAC method : a numerical technique for calculating incompressible fluid flow. Los Alamos Scientific Laboratory Report LA-4370, Los Alamos, N.M.
  5. Arnason, H. (2005) Interactions between an incident bore and a free-standing coastal structure. Ph.D Dissertation, University of Washington, USA
  6. Dalrymple, R.A., Grilli, S.T., and Kirby, J.T. (2006) Tsunamis and challenges for accurate modeling. Advances in Comput. Oceanography, Vol. 19, No. 1, pp. 142-151
  7. Dressler, R.F. (1952) Hydraulic resistance effect upon the dambreak functions. J. of hydraulic Research, Vol. 49, No. 3, pp. 217-225
  8. Dressler, R.F. (1954) Comparison of theories and experiments for hydraulic dam-break wave. Int. Assoc. Sci. Pubs., Vol. 38, No. 3, pp. 319-328
  9. Garcia-Navarro, P., Alcrudo, F., and Saviron, J.M. (1992) 1-D open channel flow simulation using TVD-MacCormack scheme. J. of Hydraulic Engineering, ASCE, Vol. 118, No. 10, pp. 1359-1372 https://doi.org/10.1061/(ASCE)0733-9429(1992)118:10(1359)
  10. Gharangik, A. and Chaudhry, M.H. (1991) Numerical simulation of hydraulic jump. J. of Hydraulic Engineering, ASCE, Vol. 117, No. 9, pp. 1195-1211 https://doi.org/10.1061/(ASCE)0733-9429(1991)117:9(1195)
  11. Glaister, P. (1988) Approximate Riemann solutions of shallow water equations. J. Hydraulic Research, Delft, The Netherlands, Vol. 26, No. 3, pp. 293-306 https://doi.org/10.1080/00221688809499213
  12. Gotoh, H. Sakai, T., and Hayashi, M (2002) Lagrangian model of drift-timbers induced flood by using moving particle semiimplicit method. J. of Hydroscience and Hydraulic Engineering, JSCE, Vol. 20, No. 1, pp. 95-102
  13. Guard, P.A. and Baldock, T.E. (2007) The influence of seaward boundary conditions on swash zone hydrodynamics. Coastal Engineering, Vol. 54, pp. 321-331 https://doi.org/10.1016/j.coastaleng.2006.10.004
  14. Harlow, F.H. and Welch, J.E. (1965) Numerical calculation of time-dependent viscous incompressible flow of fluid with a free surface. Phys. Fluids, Vol. 8, pp. 2182-2189 https://doi.org/10.1063/1.1761178
  15. Harten, A. (1983) High resolution schemes for hyperbolic conservation laws. J. Comput. Phys., Vol. 49, pp. 357-393 https://doi.org/10.1016/0021-9991(83)90136-5
  16. Hirt, C.W and Nichols, B.D. (1981) Volume of fluid(VOF) method for the dynamics of free boundaries. J. Comput. Phys., Vol. 39, pp. 201-225 https://doi.org/10.1016/0021-9991(81)90145-5
  17. Hornung, H.G., Willert, C., and Turner, S. (1995) The flow field downstream of a hydraulic jump. J. of Fluid Mech., Vol. 287, pp. 299-316 https://doi.org/10.1017/S0022112095000966
  18. Hu, K., Mingham, C.G., and Causon, D.M. (1998) A bore-capture finite volume method for open-channel flows. Int. J. Numer. Methods in Fluids, Vol. 28, pp. 1241-1261 https://doi.org/10.1002/(SICI)1097-0363(19981130)28:8<1241::AID-FLD772>3.0.CO;2-2
  19. Hunt, B. (1982) Asymptotic solution for dam-break problem. J. of Hydraulic Engineering Division, ASCE, Vol. 109, No. 12, pp. 1698-1706
  20. Hunt, B. (1987) A perturbation solution of the flood-routing problem. J. of Hydraulic Research, Vol. 25, No. 2, pp. 215-234 https://doi.org/10.1080/00221688709499300
  21. Hunt, J., Wray, A., and Moin, P. (1988) Eddies, stream, and convergence zones in turbulent flows. Center for Turbulence Research Rep., CTR-S88, p. 193
  22. Jha, A.K., Akiyama, J., and Ura, M. (1995) First- and second-order flux difference splitting schemes for dam-break problem. J. of Hydraulic Engineering, ASCE, Vol. 121, No. 12, pp. 877-884 https://doi.org/10.1061/(ASCE)0733-9429(1995)121:12(877)
  23. Katopodes, N.D. and Strelkoff, R. (1978) Computing two-dimensional dam-break flood waves. J. of Hydraulic Division, ASCE, Vol. 104, No. 9, pp. 1269-1288
  24. Kunugi, T. (2000) MARS for multiphase calculation. CFD J., Vol. 9, No. 1, IX-563
  25. Lesieur, M., Metais, O., and Comte, P. (2005) Large-eddy simulations of turbulence. Cambridge University Press, New York, N.Y.
  26. Madsen, P.A., Simonsen, H.J., and Pan, C.H. (2005) Numerical simulation of tidal bores and hydraulic jumps. Coastal Engineering, Vol. 52, pp. 409-433 https://doi.org/10.1016/j.coastaleng.2004.12.007
  27. Miyata, H. and Nishimura, S. (1985) Finite-difference simulation of nonlinear waves generated by ships of arbitrary three-dimensional configuration. J. Comput. Phys., Vol. 60, pp. 391-436 https://doi.org/10.1016/0021-9991(85)90028-2
  28. Mohapatra, P.K. and Chaudhry, M.H. (2004) Numerical solution of Boussinesq equations to simulate dam-break flows. J. of Hydraulic Engineering, ASCE, Vol. 130, No. 2, pp. 156-159 https://doi.org/10.1061/(ASCE)0733-9429(2004)130:2(156)
  29. Mohapatra, P.K., Eswaran, V., and Bhallamudi, S.M. (1999) Two-dimensional analysis of dam-break flow in vertical plane. J. of Hydraulic Engineering, ASCE, Vol. 125, No. 2, pp. 183-192 https://doi.org/10.1061/(ASCE)0733-9429(1999)125:2(183)
  30. Mollis, T. and Mollis, F. (1998) Space-time conservation method applied to Saint Venant equations. J. of Hydraulic Engineering, ASCE, Vol. 124, No. 5, pp. 501-508 https://doi.org/10.1061/(ASCE)0733-9429(1998)124:5(501)
  31. Nakamura, T. and Yabe, T. (1999) Cubic interpolated propagation scheme for solving the hyper-dimensional Vlasov-Poisson equation in phase space. Comput. Phys. Commun., Vol. 120, pp. 122-154 https://doi.org/10.1016/S0010-4655(99)00247-7
  32. Nichols, B.D. and Hirt, C.W. (1971) Improved free surface conditions for numerical incompressible flow computations. J. Comput. Phys., Vol. 8, pp. 434-448 https://doi.org/10.1016/0021-9991(71)90022-2
  33. Pohle, F.V. (1952) Motion of water due to breaking of a dam and related problems. USNBS, Vol. 521, No. 8, pp. 47-53
  34. Ramsden, J.D. (1993) Tsunami : Forces on a vertical wall caused by long waves, bores, and surges on a dry bed. Ph.D. Dissertation, California Institute of Technology
  35. Ramsden, J.D. (1996) Forces on a vertical wall due to long waves, bores, and dry-bed surges. J. of Waterway, Port, Coastal, and Ocean Engineering, ASCE, Vol. 122, No. 3, pp. 134-141 https://doi.org/10.1061/(ASCE)0733-950X(1996)122:3(134)
  36. Rao, V.S. and Latha, G. (1992) A slope modification method for shallow water equations. Int. J. Numer. Methods in Fluids, Vol. 14, pp. 189-196 https://doi.org/10.1002/fld.1650140206
  37. Ritter, A. (1892) Die fortpflanzung der wasserwellen, Zeitschrift des Vereines deutscher Ingenieurer. Vol. 36, No. 33, pp. 947-954
  38. Rudman, M. (1997) Volume-tracking methods for interfacial flow calculations. Int. J. Numer. Methods in Fluids, Vol. 24, pp. 671-691 https://doi.org/10.1002/(SICI)1097-0363(19970415)24:7<671::AID-FLD508>3.0.CO;2-9
  39. Sakkas, J.G. and Strelkoff, T. (1973) Dam-break flood in a prismatic dry channel. J. of Hydraulic Engineering Division, ASCE, Vol. 99, No. 12, pp. 2195-2216
  40. Savic, L.J. and Holly, F.M. (1993) Dambreak flood waves computed by modified Gonunov method. J. Hydr. Res., Delft, The Netherlands, Vol. 31, No. 2, pp. 187-204
  41. Smagorinsky, J. (1963) General circulation experiments with the primitive equations. Mon. Weath. Rev., Vol. 91, No. 3, pp. 99-164 https://doi.org/10.1175/1520-0493(1963)091<0099:GCEWTP>2.3.CO;2
  42. Stansby, P.K., Chegini, A., and Barnes, T.C.D. (1998) The initial stages of dam-break flow. J. of Fluid Mech., Vol. 374, pp. 407-424 https://doi.org/10.1017/S0022112098009975
  43. Stoker, J.J. (1957) Water waves. Interscience, Wiley, New York, N.Y., pp. 331-341
  44. Strelkoff, T. (1986) Dam-break flood waves. Megatrends in Hydraulic Engineering, Albertson, M. L. and Papadakis, C. N. Editors, California State University, pp. 257-266
  45. Svendsen, I.A. and Madsen, P.A. (1984) A turbulent bore on a beach. J. of Fluid Mech., Vol. 148, pp. 73-96 https://doi.org/10.1017/S0022112084002251
  46. Takewaki, H., Nishiguchi, A., and Yabe, T. (1985) The cubic-interpolated pseudo-particle (CIP) method for solving hyperbolictype equations. J. of Comput. Phys., Vol. 61, pp. 261-268 https://doi.org/10.1016/0021-9991(85)90085-3
  47. Tome, M.F. and McKee, S. (1994) GENSMAC : A computational marker and cell method for free-surface flows in general domains. J. Comput. Phys., Vol. 110, No. 1, pp. 171-186 https://doi.org/10.1006/jcph.1994.1013
  48. Tonkin, S., Yeh, H, Kato, F., and Sato, S. (2003) Tsunami scour around a cylinder. J. of Fluid Mech., Vol. 496, pp. 165-192 https://doi.org/10.1017/S0022112003006402
  49. Wang, Z. and Shen, H.T. (1999) Lagrangian simulation of one-dimensional dam-break flow. J. of Hydraulic Engineering, ASCE, Vol. 125, No. 11, pp. 1217-1220 https://doi.org/10.1061/(ASCE)0733-9429(1999)125:11(1217)
  50. Whitham, G.B. (1955) The effect of hydraulic resistance in the dam-break problem. Proceedings Series A, Royal Society of London, pp. 226-227
  51. Wu, C., Huang, G., and Zheng, Y. (1999) Theoretical solution of dam-break shock wave. J. of Hydraulic Engineering, ASCE, Vol. 125, No. 11, pp. 1210-1215 https://doi.org/10.1061/(ASCE)0733-9429(1999)125:11(1210)
  52. Yeh, H.H. (1991) Vorticity-generation mechanism in bores. Proceedings of Royal Society, London A, Vol. 432, pp. 215-231
  53. Yeh, H.H. and Ghazali, A. (1986) Nearshore behavior of bore on a uniformly sloping beach. 20th ICCE, ASCE, pp. 877-888
  54. Yeh, H.H. and Ghazali, A. (1988) On bore collapse. J. Geophys., Vol. 93, pp. 6930-6936 https://doi.org/10.1029/JC093iC06p06930
  55. Yeh, H.H., Ghazali, A., and Marton, I. (1989) Experimental study of bore run-up. J. of Fluid Mech., Vol. 206, pp. 563-578 https://doi.org/10.1017/S0022112089002417
  56. Ying, X., Khan, A.A., and Wang, S.S.Y. (2004) Upwind conservative scheme for the Saint Venant equations. J. of Hydraulic Engineering, ASCE, Vol. 130, No. 10, pp. 977-987 https://doi.org/10.1061/(ASCE)0733-9429(2004)130:10(977)