Journal of Wetlands Research (한국습지학회지)

Korean Wetlands Society (한국습지학회)
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The Estimation of Shear Stress in Uniform and Nonuniform Flow by the Entropy Concept

엔트로피 개념을 이용한 개수로에서 등류 및 부등류 흐름의 전단응력 산정

  • Choo, Yeon Moon (School of Civil, Environmental and Architectural Engineering, Korea University) ;
  • Choo, Tai Ho (Department of Civil and Environmental Engineering, Pusan National University) ;
  • Yang, Da Un (Department of Civil and Environmental Engineering, Pusan National University) ;
  • Kim, Joong Hoon (School of Civil, Environmental and Architectural Engineering, Korea University)
  • 추연문 (고려대학교 건축사회환경공학부) ;
  • 추태호 (부산대학교 사회환경시스템공학과) ;
  • 양다운 (부산대학교 사회환경시스템공학과) ;
  • 김중훈 (고려대학교 건축사회환경공학부)
  • Received : 2017.04.20
  • Accepted : 2017.05.08
  • Published : 2017.05.31
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Abstract

Shear stress is one of the most important mechanical factors used in various fields and is important for the design of artificial channels. Current shear stresses have been used in the past, but there are factors that are difficult to actually measure or calculate, such as bed shear stress and energy slope in the equation used. In particular, the energy slope is a very difficult factor to estimate, and it is difficult to estimate the slope and flow velocity of the boundary layer although the energy slope can be used to obtain the shear stress distribution. In addition, the bed shear stress among the shear stress distribution is very difficult to measure directly, and the research is somewhat slower than the velocity. In this study, we have studied the simple calculation of the average flow velocity and the shear stress distribution using entropy M without reflecting the energy gradient, and we used existing laboratory data to demonstrate the utility of the applied equation. The stress distribution in the graphs was comparatively analyzed. In the case of the uniform flow and the non-uniform flow, the correlation coefficient was almost identical to 0.930-0.998.

전단응력은 여러 분야에서 사용하는 매우 중요한 역학 인자 중 하나이며, 인공수로의 설계를 위해서 중요하다. 현재 전단응력은 과거에 정해진 계산법을 사용하고 있지만, 사용되는 식에서 바닥전단응력과 에너지경사와 같이 실제로 측정하거나 계산하기 어려운 요소들이 존재한다. 특히, 에너지경사는 산정하기 매우 어려운 인자이며, 전단응력분포를 구하기위해서는 에너지경사가 있어야만 산정할 수 있지만, 경계층의 유속기울기와 유속을 측정하는 것은 현실적으로 어려운 부분이다. 또한 전단응력분포 중 바닥전단응력은 직접 측정하기 매우 어렵고, 유속에 비해 연구가 다소 더딘 실정이다. 전단응력분포를 정확하게 산정할 수 있다면, 바닥전단응력과 에너지경사를 손쉽게 산정할 수 있다. 본 연구에서는 에너지경사를 반영하지 않고 엔트로피 M을 이용하여 평균유속과 전단응력분포를 간단히 산정하는 연구를 진행하였고, 적용한 식의 효용성을 증명하기 위해 기존의 실험실 실측 자료를 사용하였다. 이는 그래프를 통해 응력분포를 나타내어 비교분석을 하였으며, 등류와 부등류에서 각각 결정계수는 0.930-0.998까지로 거의 일치하였다.

Keywords

References

  1. Chiu, CL, Lin, GF(1983) Computation of 3-D flow and shear in open channels. J. Hydraul. Eng., 109, pp. 1424-1440. https://doi.org/10.1061/(ASCE)0733-9429(1983)109:11(1424)
  2. Chiu, CL, Chiou, JD(1986) Structure of 3-D flow in rectangular open channels. J. Hydraul. Eng., 112, pp. 1050-1067. https://doi.org/10.1061/(ASCE)0733-9429(1986)112:11(1050)
  3. Chiu, CL(1987) Entropy and probability concepts in hydraulics. J. Hydraul. Eng., 113, pp. 583-599. https://doi.org/10.1061/(ASCE)0733-9429(1987)113:5(583)
  4. Chiu, CL(1988) Entropy and 2-D velocity distribution in open channels. J. Hydraul. Eng., 114, pp. 738-756. https://doi.org/10.1061/(ASCE)0733-9429(1988)114:7(738)
  5. Chiu, CL(1991) Application of entropy concept in openchannel flow study. J. Hydraul. Eng., 117, pp. 615-628. https://doi.org/10.1061/(ASCE)0733-9429(1991)117:5(615)
  6. Chiu, CL(1993) Application of probability and entropy concepts in pipe-flow study. J. Hydraul. Eng., 119, pp. 742. https://doi.org/10.1061/(ASCE)0733-9429(1993)119:6(742)
  7. Chiu, CL, Tung, NC(2002) Maximum velocity and regularities in open-channel flow. J. Hydraul. Eng., 128, pp. 390-398. https://doi.org/10.1061/(ASCE)0733-9429(2002)128:4(390)
  8. Chiu, CL, Hsu, SM(2006) Probabilistic approach to modeling of velocity distributions in fluids flows. J. Hydraul. Eng., 316, pp. 28-42.
  9. Choo, TH(1990) Estimation of energy momentum coefficients in open channel flow by Chiu's velocity distribution equation. Dissertation, University of Pittsburgh.
  10. Cui, H, Singh, VP(2012) Two-dimensional velocity distribution in open channels using the Tsallis entropy. J. Hydrol. Eng., 18, pp. 331-339.
  11. Cui, H, Singh, VP(2013) One-dimensional velocity distribution in open channels using Tsallis entropy. J. Hydrol. Eng., 19, pp. 290-298.
  12. Cui, H, Singh, VP(2013) Suspended sediment concentration in open channels using Tsallis entropy. J. Hydrol. Eng., 19, pp. 966-977.
  13. Einstein, HA(1942) Formulas for the transportation of bed load. Trans. ASCE., pp. 561-597.
  14. Ghosh, SN, Knight, DW(1973) Discussion. Boundary shear distribution in channels with varying wall roughness. Proc. Inst. Civ. Eng., 55, pp. 503-511.
  15. Hu, CH(1985) The effect of the width/depth ratio and side-wall roughness on velocity profile and resistance in rectangular open-channels. MS thesis, Tsinghua Univ., Beijing.
  16. Johnson, JW(1942) The Importance of Side Wall Friction in Bed-load Investigation. Proc. Civ. Eng., 12, pp. 339-331.
  17. Keulegan, GH(1938) Laws of turbulent flow in open channels. US: National Bureau of Standards, 21.
  18. Knight, DW, Macdonald, JA(1979) Hydraulic resistance of artificial strip roughness. J. Hydraul. Div., 105, pp. 675-690.
  19. Knight, DW, Macdonald, JA(1979) Open channel flow with varying bed roughness. J. Hydraul. Div., 105, pp. 1167-1183.
  20. Knight, DW(1981) Boundary shear in smooth and rough channels. J. Hydraul. Div., 107, pp. 839-851.
  21. Knight, DW(1982) Boundary shear stress distributions in open channel and closed conduit flows. Proc. Euro. Mech., 156, pp. 33-40.
  22. Knight, DW, John, DD(1983) Flood plain and main channel flow interaction. J. Hydraul. Eng., 109, pp. 1073-1092. https://doi.org/10.1061/(ASCE)0733-9429(1983)109:8(1073)
  23. Knight, DW, Patel, HS(1985) Boundary shear in smooth rectangular ducts. J. Hydraul. Eng., 111, pp. 29-47. https://doi.org/10.1061/(ASCE)0733-9429(1985)111:1(29)
  24. Leighly, JB(1932) Toward a theory of the morphologic significance of turbulence in the flow of water in streams. University of California Press, 6.
  25. Lundgren, H, Jonsson, IG(1964) Shear and velocity distribution in shallow channels. J. Hydraul. Div., 90, pp. 1-21.
  26. Michael, AD(2004) The no-slip condition of fluid dynamics. Springer Netherlands, pp. 285-296.
  27. Noutsopoulos, GC, Hadjipanos, PA(1982) Discussion of Boundary shear in smooth and rough channels by D.W. Knight. J. Hydr. Div., 108, pp. 809-812.
  28. Patel, HS(1984) Boundary shear in rectangular and compound ducts. PhD Thesis. The University of Birmingham.
  29. Shannon, CE(1948) The mathematical theory of communications, I and II. Bell Syst. Tech. J., 27, pp. 379-423. https://doi.org/10.1002/j.1538-7305.1948.tb01338.x
  30. Singh, VP(1997) The use of entropy in hydrology and water resources. Hydrol. Process., 11, pp. 587-626. https://doi.org/10.1002/(SICI)1099-1085(199705)11:6<587::AID-HYP479>3.0.CO;2-P
  31. Singh, VP, Hao, L(2011) Entropy theory for distribution of one-dimensional velocity in open channels. J. Hydro. Eng., 16, pp. 725-735. https://doi.org/10.1061/(ASCE)HE.1943-5584.0000363
  32. Song, T(1995) Velocity and turbulence distribution in nonuniform and unsteady open-channel flow.