3-D hydrodynamic model using the spectral method in the vertical direction for bend flow simulations

doi:10.16511/j.cnki.qhdxxb.2018.26.032

Download: PDF(3150 KB)
Export: BibTeX | EndNote | Reference Manager | ProCite | RefWorks

Abstract The traditional depth-averaged 2-D hydrodynamic models for bend flow simulations assume velocity profiles for the secondary flow terms in the momentum equations which are unable to adjust to dynamic conditions. More flexible three-dimensional models are not very efficient. A simplified 3-D model using a spectral method in the vertical direction was developed with the flow velocity components modeled by orthogonal polynomials in the vertical direction using polynomial coefficient equations obtained using the weighted residuals method with the advection terms defined at the vertical Gauss points by the semi-Lagrangian scheme. Simulated flow structures in a sharp bend open channel match well with measured data for polynomials having degrees larger than 1 with reasonable flow structures. The mean error of the predicted main flow location is less than 7%, equivalent to other 3-D hydrodynamic models. The eddy viscosity is solved in a simple way with consideration of the turbulence anisotropy between the vertical and horizontal directions. Since this method does not have a vertical grid, the calculational efficiency is proved to be to 2-D models.

Keywords spectral method 3-D hydrodynamic model secondary flow bend flow anisotropy

Issue Date: 17 October 2018

	Service

	E-mail this article
	E-mail Alert
	RSS
	Articles by authors

	YANG Fei
	FU Xudong

Cite this article:

YANG Fei,FU Xudong. 3-D hydrodynamic model using the spectral method in the vertical direction for bend flow simulations[J]. Journal of Tsinghua University(Science and Technology), 2018, 58(10): 914-920.

URL:

http://jst.tsinghuajournals.com/EN/10.16511/j.cnki.qhdxxb.2018.26.032 OR http://jst.tsinghuajournals.com/EN/Y2018/V58/I10/914

[1] ENGELUND F. Flow and bed topography in channel bends[J]. Journal of the Hydraulics Division, 1974, 100(3):1631-1648.
[2] KIKKAWA H, IKEDA S, KITAGAWA A. Flow and bed topography in curved open channels[J]. ASCE, 1976, 102(9), 1327-1342.
[3] BLANCKAERT K. Saturation of curvature-induced secondary flow, energy losses, and turbulence in sharp open-channel bends:Laboratory experiments, analysis, and modeling[J]. Journal of Geophysical Research:Earth Surface, 2009, 114(F3), F03015.
[4] BLANCKAERT K, DE VRIEND H J. Nonlinear modeling of mean flow redistribution in curved open channels[J]. Water Resources Research, 2003, 39(12):1-6.
[5] BLANCKAERT K, DE VRIEND H J. Meander dynamics:A nonlinear model without curvature restrictions for flow in open-channel bends[J]. Journal of Geophysical Research:Earth Surface, 2010, 115(F4), F04011.
[6] HOSODA T, NAGATA N, KIMURA I, et al. A depth averaged model of open channel flows with lag between main flows and secondary currents in a generalized curvilinear coordinate system[J]. Advances in Fluid Modeling and Turbulence Measurements. 2002:63-70.
[7] ONDA S, HOSODA T, KIMURA I. Depth averaged model considering transformation of downstream velocity in curved channel in generalized curvilinear coordinate system and its verification[J]. Annual Journal of Hydraulic Engineering, 2006, 50:769-774.
[8] KIMURA I, ONDA S, HOSODA T, et al. Computations of suspended sediment transport in a shallow side-cavity using depth-averaged 2-D models with effects of secondary currents[J]. Journal of Hydro-environment Research, 2010, 4(2):153-161.
[9] YANG F, KIMURA I, SHIMIZU Y, et al. Computations of open channel flows in a shallow sharp bend using depth-averaged 2D models with secondary flow effects[J]. Journal of Japan Society of Civil Engineers, 2016, 72(2):505-513.
[10] BERNARD R S, SCHNEIDER M L. Depth-averaged numerical modeling for curved channels[R/OL].[2017-12-15]. https://www.researchgate.net/publication/235054674_Depth-Averaged_Numerical_Modeling_for_Curved_Channels.
[11] UCHIDA T, FUKUOKA S. Numerical calculation for bed variation in compound-meandering channel using depth integrated model without assumption of shallow water flow[J]. Advances in Water Resources, 2014, 72:45-56.
[12] ODGAARD, J A. Meander flow model:I. Development[J]. Journal of Hydraulic Engineering, 112(12), 1117-1136, 1986.
[13] IKEDA S, NISHIMURA T. Flow and bed profile in meandering sand-silt rivers[J]. Journal of Hydraulic Engineering, 1986, 112(7):562-579.
[14] JOHANNESSON H, Parker G. Secondary flow in mildly sinuous channel[J]. Journal of Hydraulic Engineering, 1989, 115(3):289-308.
[15] CANUTO C, HUSSAINI M Y, QUARTERONI A et al. Spectral Methods in Fluid Dynamics[M]. New York:Springer Verlag, 1988.
[16] KIMURA I, HOSODA T, ONDA S. Numerical simulator on full staggered boundary fitted coordinate system for the analysis of 3D turbulent flows in open channels[J]. Yokkaichi University Journal of Environmental and Information Sciences, 2002, 5(1-2):145-170.(in Japanese)
[17] EWING R E, WANG H. A summary of numerical methods for time-dependent advection-dominated partial differential equations[J]. Journal of Computational and Applied Mathematics, 2001, 128(1), 423-445.
[18] JANG C L, SHIMIZU Y. Numerical simulation of relatively wide, shallow channels with erodible banks[J]. Journal of Hydraulic Engineering, 2005, 131(7):565-575.
[19] YANG F, FU X. Eulerian-Lagrangian method based on streamline[C]//Proceeding of 2013 IAHR World Congress. Chengdu, China, 2013:1-10.
[20] ZHANG Y, BAPTISTA A M, MYERS E P. A cross-scale model for 3D baroclinic circulation in estuary-plume-shelf systems:I. Formulation and skill assessment[J]. Continental Shelf Research, 2004, 24(18):2187-2214.
[21] BLANCKAERT K. Flow and turbulence in sharp open-channel bends[D]. Switzerland:Ecole Polytechnique Fe'de'rale Lausanne, 2002.
[22] ZENG J, CONSTANTINESCU G, BLANCKAERT K, et al. Flow and bathymetry in sharp open-channel bends:Experiments and predictions[J]. Water Resource Research, 2008, 44(9), W09401.
[23] VAN BALEN W, BLANCKAERT K, UIJTTEWAAL W S J. Analysis of the role of turbulence in curved open-channel flow at different water depths by means of experiments, LES and RANS[J]. Journal of Turbulence, 2010, (11), N12.