Journal of the Korea Academia-Industrial cooperation Society (한국산학기술학회논문지)

The Korea Academia-Industrial cooperation Society (한국산학기술학회)
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A Study on the Estimation of Discharge in Unsteady Condition by Using the Entropy Concept

엔트로피 개념에 의한 부정류 유량 산정에 관한 연구

  • Choo, Tai Ho (Division of Civil Environmental Engineering, Pusan National University) ;
  • Chae, Soo Kwon (Division of Environmental Health and Safety, Eulji University)
  • 추태호 (부산대학교 사회환경시스템공학부) ;
  • 채수권 (을지대학교 보건환경안전학과)
  • Received : 2012.09.17
  • Accepted : 2012.12.06
  • Published : 2012.12.31
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Abstract

A discharge measurement is difficult in flood season which is especially important in the water resources field and the continuous discharge measurement for all rivers is impossible on the present system. So, the stage-discharge curve has been used for a long time to produce discharge data of rivers. However, there has been problems from a reliability angle due to the fact that this method uses only stage-discharge relationship, although the stage-discharge curve has the convenience. Therefore, a new mean velocity equation was derived by using Chiu's 2D velocity formula of the entropy concept in this paper. The derived equation reflected hydraulic characteristics such as the depth, gravity acceleration, hydraulic radius, energy slope, kinematic coefficient of viscosity, etc. and estimated also a maximum velocity. In addition, this method verified the relationship between a mean and maximum velocity and estimates an equilibrium state ${\phi}(M)$ well presenting properties of a river cross section as the results. The mean velocity was estimated by using the equilibrium state ${\phi}(M)$, and then the discharge was estimated. To prove this equation to be accurate, the comparison between the measured and estimated discharge is conducted by using the measured laboratory data in the unsteady condition flow showing loop state and the results are consistent. If this study is constantly carried out by using various laboratory and river data, this method will be widely utilized in water resources field.

수자원에서 특히 중요한 홍수기에 대한 유량 측정은 어려움이 있고 모든 하천에 대한 지속적인 유량측정은 현재 시스템상에서는 불가능하다. 그래서 유량의 생산을 위해서 그동안 수위유량 관계 곡선이 사용되어 왔다. 하지만 수위-유량 관계 곡선은 그 편리성에도 불구하고 수위와 유량만의 관계를 사용하므로 정확성 면에서 항상 문제가 있어왔다. 따라서 본 연구에서는 Chiu의 엔트로피 개념의 2차원 유속공식을 사용하여 새로운 평균유속공식을 유도하였다. 본 공식은 수심, 중력가속도, 동수경사, 에너지경사, 동점성 계수 등 하천의 수리적 특성을 잘 반영하고 최대유속도 산정할 수 있다. 또한 최대유속과 평균유속사이의 선형관계를 검증할 수 있었고 그 결과로써 하천단면의 특성을 잘 나타내는 평형상태의 ${\phi}(M)$을 산정하였다. 평형상태의 ${\phi}(M)$을 사용하여 평균유속을 산정하였고 이를 바탕으로 유량을 산정하였다. 본 공식의 검증을 위해서 고리형 특성을 보이는 부정류 상황에서의 실험실 측정 데이터를 사용하여 계산된 유량과 실측된 유량을 비교하였고 그 결과는 매우 잘 일치함을 알 수 있었다. 향후 다양한 실험실 데이터 및 하천 데이터를 이용하여 연구가 지속되어 진다면 수자원 분야에 널리 이용될 것으로 판단된다.

Keywords

References

  1. Asgeir, P.O., Trond, R., "Accounting for rating curve imprecision in flood frequency analysis using likelihood-based method", Journal of Hydrology, Vol. 366, No. 1-4, pp. 89-100, 2009, Article(CrossRefLink) https://doi.org/10.1016/j.jhydrol.2008.12.014
  2. Chiu, C-L "Three-dimensional open channel flow", Journal of Hydraulic Division, ASCE, Vol. 104, No. 8, pp. 1119-1136. 1978.
  3. Chiu, C-L. "Entropy and probability concepts in Hydraulics", Journal of Hydraulic Engineering, ASCE, Vol. 113, No. 5, pp. 583-599. 1987, Article(CrossRefLink) https://doi.org/10.1061/(ASCE)0733-9429(1987)113:5(583)
  4. Chiu, C-L. "Entropy and 2-D velocity distribution in open channels", Journal of Hydraulic Engineering, ASCE, Vol. 114, No. 10, pp. 738-756. 1988, Article(CrossRefLink) https://doi.org/10.1061/(ASCE)0733-9429(1988)114:7(738)
  5. Chiu C.L., "Velocity distribution in oprn channel flow", Journal of Hydraulic Engineering, Vol. 115, No. 5. pp. 576-594, 1989, Article(CrossRefLink) https://doi.org/10.1061/(ASCE)0733-9429(1989)115:5(576)
  6. Choo, T. H., "A Method of Discharge Measurement using the Entropy Concept (I)-Based on the Maximum Velocity", Journal of The Korean Society of Civil Engineers, Vol. 22, No. 4B, pp.495-505, 2002.
  7. Choo, T. H., "Estimation of Energy Momentum Coefficients in Open Channel Flow by Chiu's Velocity Distribution Equation", M.S. Thesis, Dep. of Civ. Engrg., Univ. of Pittsburgh, Pittsburgh, 1990.
  8. Choo, T. H., "Velocity measuring method using the concept of entropy (II) - focusing on maximum velocity", Journal of Korean Society of Civil Engineers, Vol. 22, No. 4B, pp. 495-515, 2002.
  9. Choo, T. H., Kim, C. M., Ha, G. B., Yoon, H. C., "Estimation of discharge adapting changes of river environment", Korean society of hazard mitigation, Vol. 11, No. 5, pp. 241-246, 2011. https://doi.org/10.9798/KOSHAM.2011.11.5.241
  10. Choo, T. H., Lee, S. J., Park. S. W., Oh, R., S., "Estimation of River Discharge by probabilistic Velocity Function Considering Hydraulic Characteristics", Journal of Korea Water Resources Association, Vol. 29, No. 6B, pp. 537-542, 2009.
  11. Choo, T. H., Maeng, S. J., Yoon, H. C., Kim, D. M. and Kim, S. C., "A study on the derivation of a mean velocity formula from Chiu's velocity formula and bottom Shear stress, International Journal of Environmental Research, Vol. 6, No. 2, pp. 537-546, 2012, Article(CrossRefLink)
  12. Choo, T. H., Ok, C. Y., Kim, J. W., Maeng, S.J., "A study on the velocity distribution in closed conduit by using the entropy concept", Journal of Korean Society of Civil Engineers, Vol. 29, No. 4B, pp. 357-363, 2009.
  13. Coz, J. L., Hauet, A., Pierrefeu, G., Dramais, G., Camenen, B., "Performance of image-based velocimetry(LSPIV) applied to flash-flood discharge measurements in Mediterranean rivers", Journal of hydrology, 394, pp. 42-52, 2010, Article(CrossRefLink) https://doi.org/10.1016/j.jhydrol.2010.05.049
  14. Cunge, J.A., Holly, F.M., Jr., and Verwey A., "Practical aspects of computational river hydraulics", Pitman, Boston, Mass, 1980.
  15. Hauet, A., Creutin, J.-D., Belleudy, P., "Sensitivity study of large-scale particle image velocimetry measurement of river discharge using numerical simulation", Journal of Hydrology, Vol. 349, pp178-190, 2008, Article(CrossRefLink) https://doi.org/10.1016/j.jhydrol.2007.10.062
  16. Hwang, S. H., Kim, C. Y., Jung, S. W., Kim, W., "Improvement to the methods of discharge computation from float measurements", Proceedings of the Korea Water Resources association Conference 2006, pp. 852-857, 2006.
  17. Kim, C. Y., Kim, W., Kim, D. G., Lee, C. J., "Development of Electronic Float", Proceedings of the Korea Water Resources Association Conference 2007, pp. 508-512, 2007.
  18. Lee, C. J., Kim, W., Kim, C. Y., Kim, D. G., "Velocity and discharge measurement using ADCP", Journal of Korea water resources association, Vol. 38, No. 10, pp. 811-824, 2005. https://doi.org/10.3741/JKWRA.2005.38.10.811
  19. Leon, J. G., Calmant, S., Seyler, F., Bonnet, M-P., Cauhope, M., Frappart, F., Filizola, N., Fraizy, P. "Rating curves and estimation of average water depth at the upper Negro River based on satellite altimeter data and modeled discharges", Journal of Hydrology, Vol. 328, No. 3-4, pp. 481-496, 2006, Article(CrossRefLink) https://doi.org/10.1016/j.jhydrol.2005.12.006
  20. Moramarco, T., Saltalippi, C., and Singh, V. P., "Estimation of mean velocity in natural channel based on Chiu's velocity distribution equation", Journal of Hydrologic Engineering, Vol. 9, No. 1, pp. 42-50, 2004, Article(CrossRefLink) https://doi.org/10.1061/(ASCE)1084-0699(2004)9:1(42)
  21. Pierce, S. D., Barth, J. A., Smith, R. L., "Improving acoustic doppler current profiler accuracy with wide-area differential GPS and adaptive smoothing of ship velocity", Journal of Atmospheric and Oceanic Technology, Vol. 16, pp.591-596, 1999, Article(CrossRefLink) https://doi.org/10.1175/1520-0426(1999)016<0591:IADCPA>2.0.CO;2
  22. Song, T., "Velocity and turbulence distribution in non-uniform and unsteady open-channel flow", Ph. D. Dissertation, Dept. of Civil Engineering, Federal Institute of Technology Lausanne, EPFL, 1994, Article(CrossRefLink)
  23. Tokyay, T., Constantinescu, G., Castro, A. G., "Investigation of two elemental error sources in Boat-Mounted acoustic doppler current profiler measurements by large eddy simulations", ASCE, Journal of Hydraulic Engineering, Vol. 135, No. 11, pp. 875-887, 2009, Article(CrossRefLink) https://doi.org/10.1061/(ASCE)HY.1943-7900.0000083
  24. Xia, R., ''Relation between mean and maximum velocities in a natural river'', Journal of Hydraulic Engineering, Vol. 123, no. 8, pp. 720-723, 1997, Article(CrossRefLink) https://doi.org/10.1061/(ASCE)0733-9429(1997)123:8(720)