DOI QR코드

DOI QR Code

흐름저항응력 및 초기수심에 따른 댐붕괴류의 수리특성

Hydraulic Characteristics of Dam Break Flow by Flow Resistance Stresses and Initial Depths

  • 투고 : 2014.08.01
  • 심사 : 2014.10.17
  • 발행 : 2014.11.30

초록

댐붕괴에 의해 발생하는 홍수파는 초기수심의 깊이에 따라서 하류부로 전달되는 수리학적 특성이 다르게 나타나며, 수치모의 시 흐름저항응력은 충격파의 전파 속도, 도달 거리 및 접근 수심 등에 영향을 미친다. 본 연구에서는 천수방정식을 SU/PG 기법으로 이산화한 모형을 개발하고 해석해를 이용하여 모형을 검증한 후, 초기수심 및 흐름저항응력에 따른 댐붕괴류의 전파특성을 분석하였다. 바닥마찰력을 적용한 경우 수심은 상대적으로 컸으나 충격파의 도달거리는 짧게 나타났다. Coulomb 응력을 적용한 경우 댐붕괴 후면에서의 유속이 상대적으로 작게 나타났으나, 충격파가 도달하는 영역에서는 바닥마찰력을 적용한 값과 흐름저항응력을 고려하지 않은 값 사이의 유속을 보였다. 또한 초기수심에 관계없이 흐름 저항응력을 고려하지 않은 경우의 불연속면에서의 Fr 수가 1.0에 가장 근사하였다. 초기수심이 얕은 경우 Coulomb 응력에 의한 모의결과가 난류응력을 적용한 경우에 비해 우수한 모의결과를 도출하였으나, 초기수심이 깊어지는 경우 흐름저항항의 영향력이 소멸되므로 반대의 양상이 나타났다.

The flood wave generated due to dam break is affected by initial depth upstream since it is related with hydraulic characteristics propagating downstream, and flow resistance stress has influence on the celerity, travel distance, and approaching depth of shock wave in implementing numerical simulation. In this study, a shallow water flow model employing SU/PG scheme was developed and verified by analytic solutions; propagation characteristics of dam break according to flow resistance and initial depth were analyzed. When bottom frictional stress was applied, the flow depth was relatively higher while the travel distance of shock wave was shorter. In the case of Coulomb stress, the flow velocity behind the location of dam break became lower compared with other cases, and showed values between no stress and turbulent stress at the reach of shock wave. The value of Froude number obtained by no frictional stress at the discontinuous boundary was the closest to 1.0 regardless of initial depth. The adaption of Coulomb stress gave more appropriate results compared with turbulent stress at low initial depth. However, as the initial depth became increased, the dominance of flow resistance terms was weakened and the opposite result was observed.

키워드

참고문헌

  1. Akin, J.E., and Tezduyar, T.E. (2004). "Calculation of the advective limit of the SUPG stabilization parameter for linear and higher-order elements." Computer Methods in Applied Mechanics and Engineering, Vol. 193, No. 21, pp. 1909-1922. https://doi.org/10.1016/j.cma.2003.12.050
  2. Bova, S.W., and Carey, G.F. (1996) "A symmetric formulation and SU/PG scheme for the shallow-water equations." Advances in Water Resources, Vol. 19, No. 3, pp 123-131. https://doi.org/10.1016/0309-1708(95)00040-2
  3. Chanson, H. (2006). Analytical solutions of laminar and turbulent dam break wave. River Flow 2006, Edited by Ferreira, Alves, Leal and Cardoso, Taylor & Francis Group, London, ISBN 0-415-40815-6.
  4. Dressler, R.F. (1952). Hydraulic resistance effect upon the dam-break functions. National Bureau of Standards.
  5. Hungr, O. (1995). "A model for the runout analysis of rapid flow slides, debris flows, and avalanches." Canadian Geotechnical Journal, Vol. 32, No. 4, pp. 610-623. https://doi.org/10.1139/t95-063
  6. Jeong, W.C., and Park, Y.J. (2011). "A study on simulation of dam-break wave using two-dimensional finite volume model." Journal of Korea Water Resources Association, Vol. 44, No. 3, pp. 249-262. https://doi.org/10.3741/JKWRA.2011.44.3.249
  7. Kim, B.H., Han, K.Y., and Ahn, K.H. (2009a). "Propagation analysis of dam break wave using approximate Riemann solver." Journal of the Korean Society of Civil Engineers, Vol. 29, No. 5B, pp. 429-439.
  8. Kim, D.H., and Cho, Y.S. (2005). "An improved surface gradient method for the computation of hyperbolictype shallow-water equations on irregular bathymetry." Journal of the Korean Society of Civil Engineers, Vol. 25, No. 3B, pp. 223-229.
  9. Kim, H.J., Kim, J.M., and Cho, Y.S. (2009b). "Numerical analysis of dam-break flow in an experimental channel using cut-cell method." Journal of the Korean Society of Civil Engineers, Vol. 29, No. 2B, pp. 121-129.
  10. Mangeney, A., Heinrich, P., and Roche, R. (2000). "Analytical solution for testing debris avalanche numerical models. Pure and Applied Geophysics, Vol. 157, No. 6-8, pp. 1081-1096. https://doi.org/10.1007/s000240050018
  11. Medina, V., Hurlimann, M., and Bateman, A. (2008). "Application of FLATModel, a 2D finite volume code, to debris flows in the northeastern part of the Iberian Peninsula." Landslides, Vol. 5, No. 1, pp. 127-142. https://doi.org/10.1007/s10346-007-0102-3
  12. Mungkasi, S., and Roberts, S.G. (2011). "A new analytical solution for testing debris avalanche numerical models." ANZIAM Journal, Vol. 52, pp. C349-C363.
  13. Murillo, J., and Garcia-Navarro, P. (2012). "Wave Riemann description of friction terms in unsteady shallow flows: Application to water and mud/debris floods. Journal of Computational Physics, Vol. 231, No. 4, pp. 1963-2001. https://doi.org/10.1016/j.jcp.2011.11.014
  14. Naef, D., Rickenmann, D., Rutschmann, P., and McArdell, B.W. (2006). "Comparison of flow resistance relations for debris flows using a one-dimensional finite element simulation model." Natural Hazards and Earth System Science, Vol. 6, No. 1, pp. 155-165. https://doi.org/10.5194/nhess-6-155-2006
  15. Ritter, A. (1892). "Die Fortpflanzung der Wasserwelle." Vereine Deutscher Ingenieure Zeitswchrift, Vol. 36, pp. 947-954.
  16. Seo, I.W., and Song, C.G. (2010). "Development of 2D finite element model for the analysis of shallow water flow." Journal of the Korean Society of Civil Engineers, Vol. 30, No. 2B, pp. 199-209.
  17. Seo, I.W., Kim, Y.D., and Song, C.G. (2014). "Validation of Depth-Averaged Flow Model Using Flat-Bottomed Benchmark Problems." The Scientific World Journal, Vol. 2014, Article ID 197539, 18 pages.
  18. Song, C.G., and Seo, I.W. (2012). "Numerical simulation of convection-dominated flow using SU/PG scheme." Journal of the Korean Society of Civil Engineers, Vol. 32, No. 3B, pp. 175-183.
  19. Stoker, J.J. (1957). Water Waves: The Mathematical Theory with Application. Interscience Publishers, New York.
  20. Toro, E.F. (2001). Shock-capturing Methods for Freesurface Shallow Water Flows. Wiley, New York.
  21. Whitham, G.B. (1955). "The effects of hydraulic resistance in the dam-break problem." Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences, Vol. 227, No. 1170, pp. 399-407. https://doi.org/10.1098/rspa.1955.0019

피인용 문헌

  1. Numerical Simulation of Dam Break Flow using EFDC Model and Parameter Sensitivity Analysis vol.31, pp.4, 2016, https://doi.org/10.14346/JKOSOS.2016.31.4.143