Experimental and numerical investigation of supercritical flow in contraction and expansion of open channels
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ORIGINAL PAPER
Experimental and numerical investigation of supercritical flow in contraction and expansion of open channels Mohammad Reza Nikpour 1 & Payam Khosravinia 2 & Davod Farsadizadeh 3 Received: 15 August 2018 / Accepted: 9 November 2018 # Saudi Society for Geosciences 2018
Abstract Shock wave formation is very important in studies of supercritical flow. Based on increasing water height more than inlet flow depth, spreading over a wide range of downstream channel and making disturbances in water surface, formation and propagation of these waves are unfavorable in engineering. The present paper is an attempt to study the supercritical flow in contraction and expansion, and wave formation patterns. In this regard, the height and instantaneous velocity at different points of shock waves in contraction and free-surface wave profiles in expansion were measured for four different Froude numbers. In order to 3D simulation, turbulence models of k-ε RNG and RSM based on Fluent software were used. For calculating free-surface wave profiles using the k-ε RNG and RSM models, the mean relative errors were obtained as 30.3% and 98.2% in contraction: 13% and 2.58% in expansion, respectively. Also, the mean relative errors of the k-ε RNG and RSM models for wave velocity computation of contraction were calculated as 5.26% and 2.87%, respectively. The results indicated that RSM turbulence model performs better than k-ε RNG in simulating velocity profiles of shock waves. Keywords Shock waves . Contraction . Expansion . Transition . Supercritical flow . Turbulence model
Introduction In supercritical flows, cross waves are abundant at the surface of flow and this issue is the main distinction between supercritical and subcritical flows (Hager 1989). Cross waves formed in rapidly varied flows of open channels are similar to shock waves of ultrasonic gas flows. However, the characteristics of the shock waves are different in the liquids and gases. Cross waves formed in supercritical flows are also called shock waves (Chow 1959). Phenomenon such as convergence, divergence, rising and falling of bed, and bends along the channels with supercritical flows leads to sudden change in flow depth and velocity followed by formation of shock waves. In
* Payam Khosravinia [email protected] 1
Department of Water Engineering, Faculty of Agriculture, University of Mohaghegh Ardabili, Ardabil, Iran
2
Department of Water Sciences and Engineering, Faculty of Agriculture, University of Kurdistan, Sanandaj, Iran
3
Department of Water Engineering, Faculty of Agriculture, University of Tabriz, Tabriz, Iran
the supercritical flow studies, shock wave formation is of great importance. These waves form a turbulence pattern which affects significant distances of downstream (Chow 1959). Figure 1 shows the supercritical flow through a symmetric contraction. As it can be seen, when the supercritical flow reaches the beginning of the transition, the positive waves formed at points A and A/ and after collide at point B encounter to the points D/
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