Journal of Korea Water Resources Association (한국수자원학회논문집)

Korea Water Resources Association (한국수자원학회)
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Numerical Modeling of Free Surface Flow over a Broad-Crested Rectangular Weir

사각형 광정위어를 통과하는 자유수면 흐름 수치모의

  • Paik, Joongcheol (Department of Civil Engineering, Gangneung-Wonju National University) ;
  • Lee, Nam Joo (Department of Civil Engineering, Kyungsung University)
  • Received : 2015.01.26
  • Accepted : 2015.03.03
  • Published : 2015.04.30
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Abstract

Numerical simulations of free surface flow over a broad-crested rectangular weir are conducted by using the volume of fraction (VOF) method and three different turbulence models, the k-${\varepsilon}$, RNG k-${\omega}$ and k-${\omega}$ SST models. The governing equations are solved by a second-order accurate finite volume method and the grid sensitivity study of solutions is carried out. The numerical results are evaluated by comparing the solutions with experimental and numerical results of Kirkgoz et al. (2008) and some non-dimensionalized experimental results obtained by Moss (1972) and Zachoval et al. (2012). The results show that the present numerical model can reasonably reproduce the experimental results, while three turbulent models yield different numerical predictions of two distinct zones of flow separation, the first zone is in front of the upstream edge of the weir and the second is created immediately behind the upstream edge of the weir where the flow is separated to form the separation bubble. The standard k-${\varepsilon}$ model appears to significantly underestimate the size of both separation zones and the k-${\omega}$ SST model slightly over-estimates the first separation zone in front of the weir. The RNG k-${\varepsilon}$ model predicts both separation zones in overall good agreement with the experimental measurement, while the k-${\omega}$ SST model yields the best numerical prediction of separation bubble at the upstream edge of the weir.

표준 k-${\varepsilon}$, RNG k-${\omega}$ 그리고 k-${\omega}$ SST 난류 모형과 VOF (volume of fluid)기법을 이용하여 사각형 광정위어를 통과하는 난류 흐름의 수면 변화와 유속분포를 수치모의 하였다. 지배방정식은 2차 정확도의 유한체적기법을 이용하여 해석하였으며, 두 개의 서로 다른 격자해상도에서 계산을 수행하여 수치해석 결과의 격자 민감도를 분석하였다. 계산 결과를 Kirkgoz et al. (2008)의 실험 결과 그리고 Moss (1972) 및 Zachoval et al. (2012) 무차원화된 실험값과 비교 분석하여 적용한 수치모형의 정확도를 평가하였다. 수치모의 결과는 사각형 개수로에 설치된 광정위어 흐름의 실험결과들을 합리적으로 예측하고 있으면 적용한 난류모형에 따라서 두 개의 주요 흐름분리 영역에서 계산 결과에 차이가 있는 것으로 나타났다. 표준 k-${\varepsilon}$ 모형은 이들 두 개의 흐름분리영역의 크기를 과소산정하고 있으며, k-${\omega}$ SST 모형은 위어 전면부에서 발생하는 흐름분리 영역을 다소 과대 산정하는 것으로 나타났다. RNG k-${\varepsilon}$ 모형은 전반적으로 양호하게 두 흐름분리 영역을 예측하는 한편, k-${\omega}$ SST 모형은 위어 상류부 모서리에서 발생하는 박리거품의 발생 형태를 가장 잘 예측하는 것으로 나타났다.

Keywords

References

  1. Cho, H.J., and Kang, H.S. (2011). "An estimation of discharge coefficient considering the geometrical shape of broad crested side weir." Journal of Korea Water Resources Association, Vol. 44, No. 12, pp. 955-965. https://doi.org/10.3741/JKWRA.2011.44.12.955
  2. Gonzalez, C.A., and Chanson, H. (2007). "Experimental measurements of velocity and pressure distribution on a large broad-crested weir." FlowMeasurement and Instrumentation, Vol. 18, No. 3-4, pp. 107-113.
  3. Hager, W.H., and Schwalt, M. (1994). "Broad-crest weir." Journal of Irrigation and Drainage Engineering, Vol. 120, No. 1, pp. 13-26. https://doi.org/10.1061/(ASCE)0733-9437(1994)120:1(13)
  4. Im, J.H., Jin, S.W., and Song, J.W. (2009). "Study on estimation for discharge coefficient of diagonal weir." Journal of Korea Water Resources Association, Vol. 42, No. 5, pp. 375-383. https://doi.org/10.3741/JKWRA.2009.42.5.375
  5. Ippen, A.T. (1950). Engineering Hydraulics, New York, John Wiley and Sons, Inc, p. 526-527.
  6. Jasak, H., Weller, H.G., and Gosman, A.D. (1999). "High resolution NVD differencing scheme for arbitrarily unstructured meshes." International Journal for Numerical Methods in Fluids, Vol. 31, pp. 431-449. https://doi.org/10.1002/(SICI)1097-0363(19990930)31:2<431::AID-FLD884>3.0.CO;2-T
  7. Jasak, H. (2009). "OpenFOAM: Open source CFD in research and industry." International Jounral of Naval Architecture and Ocean Engineering, Vol. 1, No. 2, pp. 89-94. https://doi.org/10.3744/JNAOE.2009.1.2.089
  8. Kirkgoz, M.S., Akoz M.S., and Oner, A.A. (2008). "Experimental and theoretical analyses of two-dimensional flows upstream of broad-crested weirs." Can. J. Civil Engineering, Vol. 35, pp. 975-986. https://doi.org/10.1139/L08-036
  9. Kim, D.G., and Kim, Y.G. (2007) "Analysis of the flow over broad crested side weir by using three-dimensional numerical simulation." Journal of Korea Water Resources Association, Vol. 40, No. 3, pp. 277-286. https://doi.org/10.3741/JKWRA.2007.40.3.277
  10. Lewith, E.H. (1978). Hydraulics ad Fluid Mechanics, 10th Edition, London, 1978.
  11. Menter, F.R. (1994). "Two-equation eddy-viscosity turbulence models for engineering applications." AIAA Journal. Vol. 32, No. 8, pp. 1598-1605.
  12. Moss, W.D. (1972). "Flow separation at the upstream edge of a square-edge broad-crested weir." Journal of Fluid Mechanics, Vol. 52, pp. 307-320. https://doi.org/10.1017/S0022112072001430
  13. Park, M., and Rhee, D.S. (2010). "Development of discharge formula for broad crested side weir." Journal of Korea Water Resources Association, Vol. 43, No. 6, pp. 525-531. https://doi.org/10.3741/JKWRA.2010.43.6.525
  14. Sarkar, M.A., and Rhodes, D.G. (2004). "Calculation of free-surface profile over a rectangular broad-crested weir." FlowMeasurement and Instrumentation, Vol. 15, pp. 215-219.
  15. USBR (2001). Water measurement manual. A water resources technical publication. U.S. Department of the Interior, Bureau of Reclamation, Third edition revised, p. 485.
  16. Weller, H.G. (2008). "A new approach to VOF-based interface capturing methods for incompressible and compressible flows. Technical Report No. TR/HGW/04.
  17. Wilcox, D.C. (1988). "Reassessment of the scale-determining equations for advanced turbulence models." AIAA Journal, Vol. 26, No. 11, pp. 1299-1310. https://doi.org/10.2514/3.10041
  18. Yakhot, V., Orszag, S.A., Thangam, S., Gatski, T.B., and Speziale, C.G. (1992). "Development of turbulence models for shear flows by a double expansion technique." Physics of Fluids A. Vol. 4, No. 7, pp. 1510-1520.
  19. Zachoval Z., Mistrova, I., Rousar, Sulc, J., and Zubik, P. (2012). "Zone of flow separation at the upstream edge of a rectangular broad-crested weir." Journal of Hydrology and Hydromechanics, Vol. 40, No. 4, pp. 288-298.

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