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Characteristics of Hydraulic Shock Waves in an Inclined Chute Contraction – Numerical Simulations

Published online by Cambridge University Press:  05 May 2011

C.-D. Jan ,
C.-J. Chang ,
J.-S. Lai  and
W.-D. Guo
C.-D. Jan*
Affiliation:
Department of Hydraulic and Ocean Engineering and Sustainable Environment Research Center, National Cheng Kung University, Tainan, Taiwan 70101, R.O.C.
C.-J. Chang*
Affiliation:
Department of Hydraulic and Ocean Engineering, National Cheng Kung University, Tainan, Taiwan 70101, R.O.C.
J.-S. Lai*
Affiliation:
Hydrotech Research Institute, Disaster Research Center, National Taiwan University, Taipei, Taiwan 10617, R.O.C
W.-D. Guo*
Affiliation:
Hydrotech Research Institute, National Taiwan University, Taipei, Taiwan 10617, R.O.C.
*
*Professor
** Ph.D. candidate
***Associate Research Fellow
****Postdoctoral Researcher
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Abstract

This paper presents the results of numerical simulations on the characteristics of hydraulic shockwaves in an inclined chute contraction. A two-dimensional numerical hydraulic simulation model is used to simulate the hydraulic shockwaves, based on the finite-volume multi-stage (FMUSTA) scheme proposed by Guo et al. [1]. This numerical model has been proved having good ability in simulating hydraulic shockwaves through the comparison with the exact solution of idealized shockwaves in a horizontal contraction provided by Ippen and Dawson [2], and the comparison with experimental results provided in the companion paper by Jan et al. [3]. The simulated shockwave parameters such as the shock angle, maximum shockwave height and maximum shockwave position for various conditions are compared with those calculated by the empirical relations obtained in the companion paper. The numerical results validate the applicability of these empirical relations and also extend their applicability to higher approach Froude numbers.

Keywords

Shock waveChute contractionNumerical simulationFMUSTA scheme.
Type
Articles
Information
Journal of Mechanics , Volume 25 , Issue 1 , March 2009 , pp. 75 - 84
Copyright
Copyright © The Society of Theoretical and Applied Mechanics, R.O.C. 2009

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References

1.Guo, W. D., Lai, J. S. and Lin, G. F., “Finite-Volume Multi-Stage Schemes for Shallow-Water Flow Simulations,” International Journal for Numerical Methods in Fluids, 57, pp. 171–204 (2008).Google Scholar
2.Ippen, A. and Dawson, J., “Design of Channel Contractions-High Velocity Flow in Open Channels,” Trans., ASCE, 116, pp. 326–346 (1951).Google Scholar
3.Jan, C. D., Chang, C. J., Lai, J. S. and Guo, W. D., “Characteristics of Hydraulic Shock Waves in an Inclined Chute Contraction-Experiments,” Journal of Mechanics (Accepted and to be published in 2009).CrossRefGoogle Scholar
4.Hirsch, C., Numerical Computation of Internal and External Flows, John Wiley and Sons, New York (1990).Google Scholar
5.Toro, E., Riemann solvers and numerical methods for fluid dynamics, Springer-Verlag, Berlin (1997).CrossRefGoogle Scholar
6.Roe, P., “Approximate Riemann Solvers, Parameter Vectors, and Different Schemes,” J. Comput. Phys., 43, pp. 357–372 (1981).Google Scholar
7.Steger, J. and Warming, R., “Flux Vector Splitting of the Inviscid Gas Dynamic Equations with Application to Finite Difference Methods,” J. Comput. Phys., 40, pp. 263–293 (1981).CrossRefGoogle Scholar
8.Osher, S. and Solomone, F., “Upwind Difference Schemes for Hyperbolic Systems of Conservation Laws,” Mathematics and Computers in Simulation, 38, pp. 339–374 (1982).Google Scholar
9.Causon, D. M., Mingham, C. G. and Ingram, D. M., “Advances in Calculation Methods for Supercritical Flow in Spillway Channels,” Journal of Hydraulic Engineering, ASCE, 125, pp. 1039–1050 (1999).CrossRefGoogle Scholar
10.Wang, J. W. and Liu, R. X. A., “Comparative Study of Finite Volume Methods on Unstructured Meshes for Simulation of 2D Shallow Water Wave Problems,” Mathematics and Computers in Simulation, 53, pp. 171–184 (2000).Google Scholar
11.Erduran, K. S., Kutija, V. and Hewett, C. J. M., “Performance of Finite Volume Solutions to the Shallow Water Equations with Shock-Capturing Schemes,” International Journal for Numerical Methods in Fluids, 40, pp. 1237–1273 (2002).Google Scholar
12.Hus, M. H., Su, T. H. and Chang, T. J., “Optimal Channel Contraction for Supercritical Flows,” Journal of Hydraulic Research, IAHR, 42, pp. 639–644 (2004).Google Scholar
13.Tan, W. Y., Shallow Water Hydrodynamics, Elsevier, New York (1992).Google Scholar
14.Toro, E.Shock-Capturing Methods for Free-Surface Shallow Water Flows, John Wiley and Sons, New York (2001).Google Scholar
15.Lin, G. F., Lai, J. S. and Guo, W. D., “High-Resolution TVD Schemes in Finite Volume Method for Hydraulic Shock Wave Modeling,” Journal of Hydraulic Research, IAHR, 43, pp. 376–389(2005).Google Scholar
16.Lai, J. S., Lin, G. F. and Guo, W. D., “An Upstream Flux-Splitting Finite-Volume Scheme for 2D Shallow Water Equations,” International Journal for Numerical Methods in Fluids, 48, pp. 1149–1174 (2005).CrossRefGoogle Scholar
17.Guo, W. D., Lai, J. S. and Lin, G. F., “Hybrid Flux-Splitting Finite-Volume Scheme for the Shallow Water Flow Simulations with Source Terms,” Journal of Mechanics, 23, pp. 399–414 (2007).Google Scholar
18.Leveque, R. J., “Balancing Source Terms and Flux Gradients in High-Resolution Godunov Methods: The Quasi-Steady Wave-Propagation Algorithm,” Journal of Computational Physics, 146, pp. 346–365 (1998).Google Scholar
19.Zhou, J. G., Causon, D. M., Mingham, C. G. and Ingrams, D. M., “The Surface Gradient Method for the Treatment of Source Terms in the Shallow Water Equations,” Journal of Computational Physics, 168, pp. 1–25 (2001).Google Scholar