Numerical analysis of shallow-water flow over the square-edged broad-crested weir

Seung-Yong Hwang

doi:10.3741/JKWRA.2022.55.10.811

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2022 Vol.55, Issue 10 Preview Page Next Page

Review Article

Numerical analysis of shallow-water flow over the square-edged broad-crested weir 직각 광정 위어를 지나는 천수 흐름의 수치 해석

31 October 2022. pp. 811-821

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Abstract

Accuracy of a numerical model with the Hwang’s scheme of directly analyzing discontinuous topography could be enhanced by introducing a flux correction coefficient that accounted for the deviation of actual pressure from hydrostatic distribution acting on the front of discontinuous topography. The optimal coefficient was determined from 218 experimental runs for square-edged broad-crested weir and simulation with it showed good agreement with another two square-edged broad-crested weir experiments and an unsteady side-weir experiment. This enabled accurate numerical simulation of shallow-water flow over the discontinuous river structure, such as square-edged broad-crested weir, without alleviating discontinuous topography with refined meshes or imposing internal boundary conditions.

Keywords

Square-edged broad-crested weir

Discontinuous topography

Shallow-water flow

Numerical simulation

Hwang’s scheme

불연속 지형 전면에 작용하는 정수압 분포에 실제 압력과 차이를 해명하는 흐름률 보정 계수를 도입하여 불연속 지형을 직접 해석하는 Hwang의 기법이 적용된 수치 모형의 정확도를 높일 수 있었다. 218개 실험 시행으로 직각 광정 위어의 월류량에 가장 적합한 계수를 결정하였으며, 이것을 별도의 두 가지 직립 광정 위어 실험과 측면 위어 부정류 실험에 적용해보니 실험과 모의에서 월류량이 서로 잘 일치하였다. 이로써 조밀한 격자로 불연속 지형을 완화하거나 내부 경계를 부여하지 않고도 직각 광정 위어와 같은 불연속 하천 구조물을 지나는 천수 흐름의 정확한 수치 모의가 가능해졌다.

키워드

직각 광정 위어

불연속 지형

천수 흐름

수치 모의

Hwang의 기법

References

Batten, P., Lambert, C., and Causon, D.M. (1996). "Positively conservative high-resolution convection schemes for unstructured elements." International Journal for Numerical Methods in .Engineering, Vol. 39, No. 11, pp. 1821-1838. 10.1002/(SICI)1097-0207(19960615)39:11<1821::AID-NME929>3.0.CO;2-E

Bureau of Reclamation (Reclamation) (2001). Water measurement manual. A Water Resources Technical Publication, United States Department of the Interior, Washington, D.C., U.S.

Doeringsfeld, H.A., and Barker, C.L. (1941). "Pressure-momentum theory applied to the broad-crested weir." Transactions of the American Society of Civil Engineers, ASCE, Vol. 106, No. 1, pp. 934-946. 10.1061/TACEAT.0005353

Echeverribar, I., Morales-Hernández, M., Brufau, P., and García-Navarro, P. (2019). "Use of internal boundary conditions for levees representation: Application to river flood management." Environmental Fluid Mechanics, Vol. 19, No. 5, pp. 1253-1271. 10.1007/s10652-018-09658-6

García-Alén, G., García-Fonte, O., Cea, L., Pena, L., and Puertas, J. (2021). "Modelling weirs in two-dimensional shallow water models." Water, MDPI, Vol. 13, No. 16, 2152. 10.3390/w13162152

Goodarzi, E., Farhoudi, J., and Shokri, N. (2012). "Flow characteristics of rectangular broad-crested weirs with sloped upstream face." Journal of Hydrology and Hydromechanics, Vol. 60, No. 2, pp. 87-100. 10.2478/v10098-012-0008-1

Govinda Rao, N.S., and Muralidhar, D. (1963). "Discharge characteristics of weirs of finite-crest width." La Houille Blanche, Vol. 49, No. 5, pp. 537-545. 10.1051/lhb/1963036

Hager, W., and Schwalt, M. (1994). "Broad-crested weir." Journal of Irrigation and Drainage Engineering, ASCE, Vol. 120, No. 1, pp. 13-26. 10.1061/(ASCE)0733-9437(1994)120:1(13)

Hargreaves, D.M., Morvan, H.P., and Wright, N.G. (2007). "Validation of the volume of fluid method for free surface calculation: The broad-crested weir." Engineering Applications of Computational Fluid Mechanics, Taylor & Francis, Vol. 1, No. 2, pp. 136-146. 10.1080/19942060.2007.11015188

Henderson, F. (1966). Open channel flow, Macmillan Publishing Co., Inc., NY, U.S.

Horton, R.E. (1907). Weir experiments, coefficients, and formulas. Water-Supply and Irrigation Paper No. 200, Geological Survey, United States Department of the Interior, Washington, D.C., U.S.

Hwang, S.-Y. (2015). "A novel scheme to depth-averaged model for analyzing Shallow-water flows over discontinuous topography." KSCE Journal of Civil and Environmental Engineering Research, KSCE, Vol. 35, No. 6, pp. 1237-1246. 10.12652/Ksce.2015.35.6.1237

Hwang, S.-Y. (2019). "Flow resistance by discontinuous topography in simulating Shallow-water flow." KSCE Journal of Civil and Environmental Engineering Research, KSCE, Vol. 39, No. 1, pp. 175-181.

Hwang, S.-Y., and Kim, H.S. (2021). "Numerical simulation and laboratory experiment of flooding on a perpendicular floodplain with dam-break flows." KSCE Journal of Civil and Environmental Engineering Research, KSCE, Vol. 41, No. 3, pp. 219-227.

Hwang, S.-Y., and Lee, S.H. (2012). "An application of the HLLL approximate Riemann solver to the shallow water equations." KSCE Journal of Civil and Environmental Engineering Research, KSCE, Vol. 32, No. 1B, pp. 21-27.

Jun, K.S. (1996). "A study on unsteady flow model including weir flow simulation." Journal of Korea Water Resources Association, KWRA, Vol. 29, No. 2, pp. 153-165.

Kim, S. (2013). Analysis on flood-control effect of side-weir detention basin considering the flow pattern over the weir. Master's Thesis, Myongji University.

Kirkgoz, M.S., Akoz, M.S., and Oner, A.A. (2008). "Experimental and theoretical analyses of two-dimensional flows upstream of broad-crested weirs." Canadian Journal of Civil Engineering, CSP, Vol. 35, No. 9, pp. 975-986. 10.1139/L08-036

Lee, H. (2020). "Implicit discontinuous Galerkin scheme for discontinuous bathymetry in shallow water equations." KSCE Journal of Civil Engineering, KSCE, Vol. 24, No. 9, pp. 2694-2705. 10.1007/s12205-020-2409-8

Lee, K.S., and Lee, S.-T. (1998). "Two-dimensional finite-volume unsteady-flow model for shocks." Journal of Korea Water Resources Association, KWRA, Vol. 31, No. 3, pp. 279-290.

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, No. 3-4, pp. 391-402. 10.1002/fld.312

Morales-Hernández, M., Murillo, J., and García-Navarro, P. (2013). "The formulation of internal boundary conditions in unsteady 2-d shallow water flows: Application to flood regulation." Water Resources Research, Vol. 49, No. 1, pp. 471-487. 10.1002/wrcr.20062

Moss, W.D. (1970). Flow over a square-edged broad-crested weir. Doctoral dissertation, University of Surrey, Guildford Surrey, U.K.

Paik, J., and Lee, N.J. (2015). "Numerical modeling of free surface flow over a broad-crested rectangular weir." Journal of Korea Water Resources Association, KWRA, Vol. 48, No. 4, pp. 281-290. 10.3741/JKWRA.2015.48.4.281

Press, W.H., Flannery, B.P., Teukolsky, S.A., and Vetterling, W.T. (1992). Numerical recipes in c: The art of scientific computing, second edition, Cambridge University Press, NY, U.S.

Prokof'ev, V.A. (2005). "Two-dimensional horizontal numerical model of open flow over a bed with obstacles." Water Resources, Vol. 32, No. 3, pp. 252-264. 10.1007/s11268-005-0034-z

Rafter, G.W. (1900). "On the flow of waer over dams." Transactions of the American Society of Civil Engineers, ASCE, Vol. 44, pp. 220-398. 10.1061/TACEAT.0001434

Ramamurthy, A.S., Tim, U.S., and Rao, M.V.J. (1988). "Characteristics of square-edged and round-nosed broad-crested weirs." Journal of Irrigation and Drainage Engineering, ASCE, Vol. 114, No. 1, pp. 61-73. 10.1061/(ASCE)0733-9437(1988)114:1(61)

Sarker, M.A., and Rhodes, D.G. (2004). "Calculation of free-surface profile over a rectangular broad-crested weir." Flow Measurement and Instrumentation, Vol. 15, No. 4, pp. 215-219. 10.1016/j.flowmeasinst.2004.02.003

Schubert, J.E., and Sanders, B.F. (2012). "Building treatments for urban flood inundation models and implications for predictive skill and modeling efficiency." Advances in Water Resources, Vol. 41, pp. 49-64. 10.1016/j.advwatres.2012.02.012

Tracy, H.J. (1957). Discharge characteristics of broad-crested weirs. Geological Survey Circular 397, Geological Survey, United States Department of the Interior, Washington, D.C., U.S. 10.3133/cir397

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, No. 1, pp. 101-136. 10.1016/0021-9991(79)90145-1

Vanden-Broeck, J.-M., and Keller, J.B. (1986). Weir flows. MRC Technical Summary Report, 2919, Mathematics Research Center, University of Wisconsin-Madison, WI, U.S. 10.21236/ADA167495

Weiyan, T. (1992). Shallow water hydrodynamics, Elsevier Science Publishers, Amsterdam, The Netherland.

Willmott, C.J., Robeson, S.M., and Matsuura, K. (2012). "A refined index of model performance." International Journal of Climatology, Vol. 32, No. 13, pp. 2088-2094. 10.1002/joc.2419

Zhou, J.G., Causon, D.M., Ingram, D.M., and Mingham, C.G. (2002). "Numerical solutions of the shallow water equations with discontinuous bed topography." International Journal for Numerical Methods in Fluids, Vol. 38, No. 8, pp. 769-788. 10.1002/fld.243

Zhou, J.G., Causon, D.M., Mingham, C.G., and Ingram, D.M. (2001). "The surface gradient method for the treatment of source terms in the shallow-water equations." Journal of Computational Physics, Vol. 168, No. 1, pp. 1-25. 10.1006/jcph.2000.6670

Information

Publisher :KOREA WATER RESOURECES ASSOCIATION
Publisher(Ko) :한국수자원학회
Journal Title :Journal of Korea Water Resources Association
Journal Title(Ko) :한국수자원학회 논문집
Volume : 55
No :10
Pages :811-821
Received Date : 2022-09-14
Revised Date : 2022-09-28
Accepted Date : 2022-09-30
DOI :https://doi.org/10.3741/JKWRA.2022.55.10.811

Journal of Korea Water Resources Association ISSN:2799-8746(Print) 2799-8754(Online) 한국수자원학회 논문집

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