AENSI Journals Advances in Environmental Biology ISSN:1995-0756 EISSN: 1998-1066 Journal home page: http://www.aensiweb.com/aeb.html PAIDEffect of Sudden Area Expansion on Formation of Cross-Waves in Downstream of Bottom Outlet Tunnel of Dams 1 Ali Fallah Maraghi, 2 Mahmood Reza Mollaei Nia and 3 Hassan Abdi 1 Master Student, Civil Engineering, Zabol University, Zabol, Iran. 2 Associate Professor, Civil Engineering, Zabol University, Zabol, Iran. 3 Senior Research Engineering, SEPASAD Corporation, Tehran, Iran. A R T I C L E I N F O Article history: Received 25 April 2014 Received in revised form 20 May 2014 Accepted 26 May 2014 Available online 22 June 2014 ey words: Aeration, Air-water flow, Cavitation, Numerical modeling, k-ε turbulence model. A B S T R A C T Investigation of the air vents in the bottom outlet tunnel of dams due to prevention of vibration and cavitation is an important issue. The air above the water surface should be transmitted through tunnel easily. In the present study, the effect of area expansion after step on formation of cross-waves in downstream tunnel is investigated. The aeration ratio values in the numerical simulation, in the gate openings of 20%, 60%, and 100% are compared with that of physical model results. Numerical results showed a good agreement with experiments. In this study, two-phase turbulent flow is simulated using the -ε model. In addition, for implementation of two-phase flow, the volume of fluid scheme is used. 2014 AENSI Publisher All rights reserved. To Cite This Article: Ali Fallah Maraghi, Mahmood Reza Mollaei Nia and Hassan Abdi., PAIDEffect of Sudden Area Expansion on Formation of Cross-Waves in Downstream of Bottom Outlet Tunnel of Dams. Adv. Environ. Biol., 8(10), 21-26, 2014 INTRODUCTION Gated tunnels are used in dams for various purposes such as regulating the reservoir water surface in impounding, drawdown of the reservoir, sediment flushing and flood release [1]. Bottom outlets are relatively short for arch or gravity dams and considerably long for embankment and diversions dams. To reduce the length of pressurized reach, a long bottom outlet is normally divided into a pressurized portion controlled with a high head gate and an outlet tunnel that discharges a supercritical flow into the atmosphere [2]. In downstream of the gate, high-speed water flow as well as motion of air cause negative pressure. Negative pressure can increase possibility of cavitation and vibration. To prevent these phenomena, usually an air vent is installed immediately downstream of the gate for aeration and prevention of cavitation [3]. alinske and Robertson [4], Campbell and Guyton [5], Peterka [7], USCE [6], Sharma [8] and also Speerli and Hager have physically investigated that flow under gate in bottom outlet of dams. Modeling of Cavitation by experimental studies is very helpful in raising our knowledge in the high-velocity air-water flow; however, these approaches are more time consuming and expensive than the numerical approaches [9]. Jian-min et al. ] 10 [ investigated three-dimensional numerical simulation of aerated flows downstream sudden fall aerator expansion in a tunnel. They compared cavity length and pressure on the sidewall with experimental data. Many researchers have examined the phenomenon of cavitation in dams; for instance, Nikseresht et al. [9] estimated cavitation index values for both aerated and non-aerated flow. Shamsai and Soleymanzadeh [11], olachian et al. [12], Jalalabadi, and Nouri [13] are some other researchers that investigated flow in bottom outlet of dams in recent years. In the present paper, the possibility of rooster tail formation in downstream of gate is studied. Furthermore, this research indicates whether flow aeration in bottom outlet of ROUDBR LORESTAN dam has been sufficient. In this study, complex two-phase turbulent flow was simulated using the -ε model. In addition, for implementation of two-phase flow, the volume of fluid scheme (VOF) was used. Numerical Modeling: The -Epsilon Model: is the turbulence kinetic energy and is defined as the variance of the fluctuations in velocity. It has 2 2 2 2 dimensions of ( LT ), for example, m / s. is the turbulence eddy dissipation (the rate at which the Corresponding Author: Ali Fallah Maraghi, Master Student, Civil Engineering, Zabol University, Zabol, Iran. E-mail: ali.fallah89@yahoo.com
22 Ali Fallah Maraghi et al, 2014 2 3 m / s. 2 3 velocity fluctuations dissipate), and k has dimensions of per unit time ( LT ); for example, The k model introduces two new variables into the system of equations. The continuity equation is then: ( U j ) 0 (1) t x j and the momentum equation becomes: Ui P U U i j ( U U ) [ ( )] S t x x x x x i j eff M j i j j i wheres M is the sum of body forces, eff is the effective viscosity accounting for turbulence, and p is the modified pressure as defined in (2) 2 2 U P P eff ( ) 3 3 x (3) The k model, like the zero equation model, is based on the eddy viscosity concept, so that: (4) eff t where t is the turbulence viscosity. The k model assumes that the turbulence viscosity is linked to the turbulence kinetic energy and dissipation via the relation: 2 (5) t C where C is a constant. The values of k and come directly from the differential transport equations for the turbulence kinetic energy and turbulence dissipation rate: ( ) t ( U ) [( ) ] P P t x x x j b j j j ( ) ( U ) [( ) ] ( C P C P ) t x x x t j 1 2 b j j j (6) (7) P where C 1, C 2, k and are constants. p represent the influence of the buoyancy forces, which are described below. pkb and b p is the turbulence production due to viscous forces, which is modeled using: k U U j U 2 U U ( i ) i (3 ) x x x 3 x x t t j i j For incompressible flow, U / x is small and the second term on the right side of equation 8 does not contribute significantly to the production. For compressible flow, U / velocity divergence, such as at shocks [14]. (8) x is only large in regions with high Mesh Generation: The solution to a flow problem (velocity, pressure, etc.) is defined at nodes inside each cell. The accuracy of a CFD solution is governed by the number of cells in the grid. In general, the larger the number of cells, the better the solution accuracy. Both the accuracy of a solution and its cost in terms of necessary computer hardware and calculation time are dependent on the fineness of the grid [16]. In this study, the software ANSYS was firstly used for generating the mesh. Due to the complexity of the geometry as well as the software inability to create fine mesh for this geometry, Gambit 2.4.6. Software was
23 Ali Fallah Maraghi et al, 2014 finally used. After obtaining the required grid and determining the boundaries of the flow field, the file is read by ANSYS CFX software. The space of three-dimensional numerical modeling increases computing time; therefore, due to the geometric symmetry of the model, the symmetry condition was used for modeling. For modeling, the powerful six-core system with high processing power was used. The parallel system, with distributing nods between each processing, uses all computer power. The number of optimum mesh, according to tunnel length through the gate and comparing results for different conditions, 1600000 cells were considered. In addition, in order to assess the grid sensitivity, 3380000 cells were used for the opening 100 of the gate. Since the difference in results is less than 5%, 1.6 million cells were finally used because of reducing the numerical calculations time. Figure 1 shows generated mesh in Gambit software. Fig. 1: A view of the mesh generated in three-dimensional numerical model of the tunnel in the gate opening 100% Determining the Initial and Boundary Conditions: For the wall of conduit, wall boundary condition is applied where the wall velocity is zero. In main conduit, inlet boundary condition is pressure. Since the input section consists entirely of water phase, the air phase fraction is considered zero and water phase fraction is considered one in this boundary. The aerator is connected to the atmosphere; therefore, the zero pressure boundary condition is applied to the air duct input. By putting the total pressure equal to zero, required air was injected into the system through aerator. As a result, velocity head increases with reduction of the static pressure head till total pressure boundary condition is met to be zero. Governing boundary condition is shown in Figure 2. Fig.2: A view of the boundary conditions in the numerical model of bottom outlet RESULTS AND DISCUSSION Comparing the Efficiency of the Aeration in Different Condition of Opening Gate: In figure 3, aeration ratio was compared with numerical and experimental of the past investigations. As shown in this figure, aeration coefficient values obtained from numerical and physical models results are closer Sharma (1976) studies.
24 Ali Fallah Maraghi et al, 2014 Fig. 3: Comparison of measured aeration ratio plotted against gate opening Figure 4 shows aerator flow rate on physical and numerical models for different opening of the gate. As shown in this figure, the amount of air flow in numerical and physical models in low and high opening gate have the greatest difference. Fig. 4: Comparison of the air flow rate on physical and numerical model Figure 5 displays Froude number for different condition of opening gate. As shown in this figure, the amount of Froude number reduces during opening of the gate. Fig. 5: Froude number for different gate openings
25 Ali Fallah Maraghi et al, 2014 The Flow Pattern: In gated tunnels where the flow condition changes from pressurized to free surface, determining flow pattern and water surface profile is a main concern. In this regard, investigating the possibility of rooster tail formation is a major issue. Rooster tail formation causes the blockage of the air passage above the free surface; therefore, it prevents circulation of air from the tunnel outlet. Rooster tail formation depends on flow condition and geometry of the tunnel [17]. Figure 6 depicts formation of cross waves in the tunnel for gate opening 100% in the physical model and the numerical model. As can be seen, in both sides of the tunnel, water tails go upward and contact into the tunnel ceiling and create undesirable conditions. (a) (b) Fig. 6: Rooster tail formation in unmodified model (a) physical model; (b) Numerical model (a) (b) Fig. 7: Removing rooster tail in modified model (a) physical model; (b) Numerical model To fix this problem, the width of the tunnel at the tunnel cross section is reduced from 66 cm to 20 cm. Figure7 shows the numerical and physical modeling of water surface profiles. Improved physical model shows that in the 100% gate opening, water flow will not go higher than both sides of the wall and there is sufficient space above the tunnel. Thus discharge conditions are safe. In this case, the numerical results are consistent with the results of the physical model. Conclusion: In this study, ANSYS CFX software was used to model the flow in the bottom outlet of ROUDBAR LORESTAN dam. In this research, aeration flow rate values at different opening service gate in the numerical model were compared with the physical model and the results of other investigators. Comparison of numerical and physical model showed suitability and efficiency of the numerical model in simulation of water and air twophase flow. This study also examined the pattern of flow and the possibility of rooster tail formation in discharge tunnel. The results indicate that in order to remove the undesired waves in the downstream tunnel, expansion width after the section of step should be reduced. ACNOWLEDGEMENT The authors wish to acknowledgement the cooperation of SEPASAD Corporation in Tehran for making available the needed data to carry out present study. Last but not least, I would like to appreciate Dr. Hossein Ebrahimpour omleh, High Performance and Intelligent Systems Research Centre in the University of ashan.
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