DOI QR코드

DOI QR Code

Effect of Corrected Hydrostatic Pressure in Shallow-Water Flow over Large Slope

대경사를 지나는 천수 흐름에서 수정된 정수압의 효과

  • 황승용 (한국건설기술연구원 수자원.환경연구본부 하천해안연구실)
  • Received : 2014.11.03
  • Accepted : 2014.11.10
  • Published : 2014.12.31

Abstract

This study suggests a new hydrostatic pressure distribution corrected for nonuniform flow over a channel of large slope. For analyzing shallow-water flows over large slope accurately, it is developed a finite-volume model incorporating the pressure distribution to the shallow water equations. Traveling speed of the hydraulic jump downstream a parabolic bump in the drain case is quite reduced by the weakened bottom gradient source term in the model with the pressure correction. In simulating the dam-break flow over a triangular sill, it is identified that the model with pressure correction could capture the water surface by the digital imaging measurements more than the model without that. Due to the pressure correction decreasing the reflected flows on and increasing overflows over the sill, there are good agreements in the experiment and the simulation with that. Therefore, this model is expected to be applied to such practical problems as flows in the spillway of dam or run-up on the beach.

대경사 수로의 부등류에 대해 적용될 수 있도록 수정된, 새로운 정수압 분포를 제시하였다. 이것을 천수방정식에 적용하여 대경사를 지나는 천수 흐름을 정확하게 해석할 수 있는 유한체적 모형을 개발하였다. 포물선형 융기의 배수에 대해 압력 수정이 고려된 모형에서 바닥 경사 생성항의 영향이 줄어들어 융기의 하류에서 도수의 진행 속도가 크게 감소되었다. 삼각형 턱을 지나는 댐 붕괴 흐름에 대한 모의에서 압력 수정항이 추가된 모형으로 디지털 영상분석에 의한 수면을 압력 수정이 고려되지 않은 경우에 비해 더 잘 포착할 수 있음을 확인하였다. 압력 수정항 덕분에, 턱에 반사되는 흐름은 줄어들고 월류는 늘어 모의 결과가 실험 결과에 잘 부합된다. 따라서 댐의 여수로나 해안의 처오름 등 실용적인 문제에 대한 이 모형의 적용성이 기대된다.

Keywords

References

  1. Aureli, F., Maranzoni, A., Mignosa, P., and Ziveri, C. (2008). "A weighted surface-depth gradient method for the numerical integration of the 2D shallow water equations with topography." Advances in Water Resources, Vol. 31, pp. 962-974. https://doi.org/10.1016/j.advwatres.2008.03.005
  2. Begnudelli, L., and Sanders, B.F. (2006). "Unstructured grid finite-volume algorithm for shallow-water flow and scalar transport with wetting and drying." Journal of Hydraulic Engineering, Vol. 132, pp. 371-384. https://doi.org/10.1061/(ASCE)0733-9429(2006)132:4(371)
  3. Bermudez, A., and Vazquez, M.E. (1994). "Upwind methods for hyperbolic conservation laws with source terms." Computers & Fluids, Vol. 23, pp. 1049-1071. https://doi.org/10.1016/0045-7930(94)90004-3
  4. Bouchut, F., Mangeney-Castelnau, A., Perthanme, B., and Vilotte, J.-P. (2003). "A new model of Saint Venant and Savage.Hutter type for gravity driven shallow water flows." Comptes Rendus de l'Academie des Sciences-Series I , Vol. 336, pp. 531-536.
  5. Chow, V.T. (1959). Open-channel hydraulics. McGraw-Hill.
  6. Dressler, R.F. (1978). "New nonlinear shallow-flow equations with curvature." Journal of Hydraulic Research, Vol. 16, pp. 205-222. https://doi.org/10.1080/00221687809499617
  7. Hwang, S.-Y. (2013). "Finite-volume model for shallowwater flow over uneven bottom." Journal of Korea Water Resources Association, Vol. 46, pp. 139-153 (in Korean). https://doi.org/10.3741/JKWRA.2013.46.2.139
  8. Hwang, S.-Y., and Lee, S.H. (2012). "An application of the HLLL approximate Riemann solver to the shallow water equations." Journal of Korea Society of Civil Engineers, Vol. 32, pp. 21-27 (in Korean).
  9. Keller, J.B. (2003). "Shallow-water theory for arbitrary slopes of the bottom." Journal of Fluid Mechanics, Vol. 489, pp. 345-348. https://doi.org/10.1017/S0022112003005342
  10. Lee, K.S., and Lee, S.-T. (1988). "Two-dimensional finite-volume unsteady-flow model for shocks." Journal of Korea Water Resources Association, Vol. 31, pp. 279-290 (in Korean).
  11. Liggett, J.A. (1994). Fluid mechanics. McGraw-Hill.
  12. Linde, T. (2002). "A practical, general-purpose, two-state HLL Riemann solver for hyperbolic conservation laws." International Journal for Numerical Methods in Fluids, Vol. 40, pp. 391-402. https://doi.org/10.1002/fld.312
  13. Savage, S.B., and Hutter, K. (1994). "The dynamics of avalanches of granular materials from initiation to runout. Part I: Analysis." Acta Mechanica, Vol. 86, pp. 201-223.
  14. Soares-Frazao, S. (2007). "Experiments of dam-break wave over a triangular bottom sill." Journal of Hydraulic Research, Vol. 45, pp. 19-26. https://doi.org/10.1080/00221686.2007.9521829
  15. Van Leer, B. (1979). "Towards the ultimate conservative difference scheme V. a second order sequel to Godunov's method." Journal of Computational Physics, Vol. 32, pp. 101-136. https://doi.org/10.1016/0021-9991(79)90145-1
  16. Van Leer, B. (2006). "Upwind and high-resolution method for compressible flow: from donor cell to residual-distribution schemes." Communications in Computational Physics, Vol. 1, pp. 192-206.
  17. Weiyan, T. (1992). Shallowwater hydrodynamics. Elsevier Science Publishers.