Document Type: Research Paper


1 Department of Water Engineering, University of Mohaghegh Ardabili, Ardabil, Ardabil, 9132220485, Iran

2 Department of Water Sciences and Engineering, University of Kurdistan, Sanandaj, Kurdistan, 9120977875, Iran

3 Department of Water Engineering, University of Tabriz, Tabriz, East Azerbaijan , 9143135801, Iran


Formation of shock waves has an important role in supercritical flows studies. These waves are often occurring during passage of supercritical flow in the non-prismatic channels. In the present study, the effect of length of contraction wall of open-channel for two different geometries (1.5 m and 0.5 m) and fixed contraction ratio was investigated on hydraulic parameters of shock waves using experimental model (models 1 and 2). For achieving to this goal, values of height and instantaneous velocity were measured in various points of shock waves observed in contractions for four Froude Numbers. In general, non-uniform distribution of velocity and turbulence intensity profiles were completely clear. Comparing results of models 1 and 2, show that the height and velocity values of formed waves in the model 2 is so much more than the model 1. Also, motion of the shock waves was accompanied with longitude gradient decrease of turbulence kinetic energy. The results of the present research can be very useful for designer engineers.

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[1]     O. F. Jimenez, and M. H. Chaudhry, “Computation of supercritical free-surface flows”, Journal of Hydraulic Engineering, Vol. 114, No. 4. pp. 377-395,(1988).


[2]     W. H. Hager, “Supercritical flow in channel junction”. Journal of HydraulicEngineering, Vol. 115, No. 5. pp. 595-616,(1989).


[3]     F. Feurich, and N. R. B. Olsen, “Finding Free Surface of Supercritical Flows- Numerical Investigation”. Journal Engineering Applications of Computational Fluid Mechanics, Vol. 6, No.2.pp.307-315, (2012).



[4]     D. M. Causon, C. G. Mingham, and D. M. Ingram, “Advances in calculation methods for supercritical flow in spillway channels” Journal of HydraulicEngineering, Vol. 125, No. 10. pp. 1039-1050,(1999).


[5]     V. T. Chow, Open Channel Hydraulics, McGraw-Hill Publisher, Michigan, (1959).


[6]     R. J. Fennema, and H. M. Chaudhry, “Explicit methods for 2-D transient free-surface flows”, Journal of Hydraulic Engineering, Vol. 116, No. 8. pp. 1013-1035,(1990).


[7]     S. M. Bhallamudi, and M. H. Chaudhry, “Computation of flows in open-channel transitions”, Journal of Hydraulic Research, Vol. 30, No. 1. pp. 77-93, (1992).


[8]     A. Valiani, and V. Caleffi, “Brief analysis of shallow water equations suitability to numerically simulate supercritical flow in sharp bends”.  Journal of Hydraulic Engineering, Vol. 131, No. 10. pp. 912-916, (2005).


[9]     S. C. Jain. “Nonunique water-surface profiles in open channels”. Journal of Hydraulic Engineering, Vol. 119, No. 12, pp.1427-1434.(1993).


[10]  S. Krüger, and P. Rutschmann, “Modeling 3D supercritical flow with extended shallow-water approach”, Journal of HydraulicEngineering, Vol. 132, No. 9, pp. 916-926, (2006).


[11]   S. K. Mazumder, and W. H. Hager, “Supercritical expansion flow in Rouse modified and reversed transitions”, Journal of HydraulicEngineering, Vol. 119, No. 2, pp. 201-219, (1993).


[12]   A. Stamou, D. Chapsas, and G. Christodoulou, “3-D numerical modeling of      supercritical     flow      in     gradual

expansions”, Journal of Hydraulic Research, Vol. 46, No. 3, pp. 402-409, (2008).


[13]   M. Hessaroeyeh, and A. Tahershamsi, “Analytical model of supercritical flow in rectangular chute bends”, Journal of Hydraulic Research, Vol. 47, No. 5, pp. 566-573, (2009).


[14]  M. R. Jaefarzadeh, A. Shamkhalchian, and M. Jomehzadeh, “Supercritical flow profile improvement by means of a convex corner at a bend inlet”, Journal of Hydraulic Research, Vol. 50, No. 6, pp. 623-630, (2012).


[15]  M. Montazeri Namin, R. Ghazanfari-Hashemi, and M. Ghaeini-Hessaroeyeh, “3D numerical simulation of supercritical flow in bends of channel”, Int. ConferenceMechanical, Automotive and Materials Engineering, Dubai, United Arab Emirates, pp. 167-171, (2012).


[16]   M. Kolarević, L. Savić, R. Kapor, and N. Mladenović, Supercritical flow in circular pipe bends. Fme Transactions, Vol. 42, No. 2, pp.128-132. (2014).


[17] S. Kocaman, and H. Ozmen-Cagatay, Investigation of dam-break induced shock waves impact on a vertical wall. Journal of Hydrology, Vol. 525, pp. 1-12. (2015).


[18]  R. Ghostine, I. Hoteit, J. Vazquez, A. Terfous, A. Ghenaim, and R. Mose, Comparison between a coupled 1D-2D model and a fully 2D model for supercritical flow simulation in crossroads. Journal of Hydraulic Research, Vol. 53, No. 2, pp. 274-281. (2015).