3D Simulation of Flows Around Hydraulic Structures

Transcription

1 The 4 th Asian Conress of Fluid Mechanics - 4ACFM October 5-9, 0; Hanoi and Halon, Vietnam D Simulation of Flows Around Hydraulic Structures Tran Noc Anh, Shinichiro Onda, Nuyen Duc Hanh * and Nuyen Thanh Son * address of presentin authors: hanhnd.vnu@mail.com Abstract: Hydraulic structures have become popular tools for river trainin and bank protection. In many cases, roins or spur-dykes have had impressive effects on controllin sediment deposition for bank protection, or increasin water depth for naviation channels. Spur-dyke desins have enerally been based on D calculations of flow structure and sediment transport. In some rivers where flood sure could make a sinificant difference in water level resultin in an over-toppin phenomenon, these D aspects of flow structure may also cause additional harmful effects such as local scourin at the abutment, or river bank collapse. In these cases the D simulation of flow structure is needed to provide fundamental information for sediment transport and in order to examine solutions for these problems. This study deals with an application of a D hydraulic model based on RANS equations with turbulent closure usin a non-linear k- model, to simulate the flow structure around hydraulic structures. Basic flow equations with contravariant velocity in a eneralized curvilinear coordinate system are solved and a movin coordinate technique for vertical direction is used to calculate water surface variation. The simulation results were then compared with previous experimental results in the laboratory to show that this model is reasonably capable of reproducin results obtained in the field. Key Words: D flow simulation, hydraulic modelin, submered spur-dykes/roins. Introduction In meanderin rivers, hydraulic structures such as spur dykes (or roins) are common tools used to protect erodible banks, however, not all spur-dykes have worked as intended, particularly in rivers experiencin sinificant differences in water level; in such cases overtoppin can occur and cause harmful effects. In these cases, the complicated three-dimensional nature of flow around hydraulic structures must be taken into account. For active manaement of rivers, reliable prediction tools (models) are essential for comparison of the expected performance of alternative hydraulic structure desins. When somethin more usually usin an analytical solution is too difficult, physical and numerical models have been used to address sediment transport problems (Chanson, 999). Over the past few decades, problems related to flow and bed deformation processes around river hydraulic structures have been studied, mostly by physical modelin of spur-dykes, abutments, or bride piers. Spur-dykes and abutments have been found to be alike due to their relatively similar shapes. The investiations on this type of obstruction have been presented by Melville (99); Kwan and Melville (994); Lim (997); Rahman et al. (998); and Kuhnle et al. (999). The physical modelin experiments have also allowed close examination of flow characteristics and have been examined (Garde et al. 96; Melville 99), but the exact mechanism of how a submered spur-dyke impacts the surroundin flow behavior is still not fully understood. Numerical models are useful tools that can solve the basic equations of fluid hydrodynamics (Martin and McCutcheon, 999) and can be used for prediction and further examination of flow behavior. Fluid mechanics equations can be solved in one-dimensional, two-dimensional or three-dimensional (D) spatial schemes (Martin and McCutcheon, 999). Solvin these equations in their three-dimensional form is extremely difficult and has become feasible only as increased computer power makes numerical 94 Pae

2 solutions practical (Martin and McCutcheon, 999). Recently, several numerical models have been developed to calculate the phenomena around river hydraulic structures. However, the number of test cases used to validate these numerical models is not adequate in understandin their eneral applicability to river hydraulic structures (Naata et al., 005). This study deals with an application of a D hydraulic model based on Reynolds-averaed Navier-Stokes equations with a non-linear k- model for turbulent closure, to simulate the flow structure around hydraulic structures. The basic flow equations with contravariant velocity in a eneralized curvilinear coordinate system were solved and a movin coordinate technique in the vertical direction was used to calculate water surface variation. The simulation results were then validated aainst the laboratory experiment results of Tominaa et al. (000).. Numerical Method A D simulation was conducted usin the Reynolds averaed D flow equations with contravariant components of velocity vectors in a movin eneralized curvilinear coordinate system (Kimura el al., 004). These are described in Eqs ()-(4). [Continuity equation] V 0 [Momentum equation] V t [k equation] i k t [ equation] i V ( V i i F p l v v V i W ) V W k( V W ) k W il i i V W i i v v e D t i ik k V k m V k V k m () () () (4) l i ( V W ) W C ilv v V t k D t i C i k k (5) where i = eneralized curvilinear coordinate; V i = contravariant component of the velocity vector of flow; t = time; W i = contravariant component of the velocity vector of rid motion; p = pressure; = molecular dynamic viscosity; = density of water; k = turbulent enery; = turbulent enery dissipation rate; i and i = covariant and contravariant component of metric tensor; = det( i ); F i = contravariant component of ravitational acceleration; and i indicates a co-variant differential. A nd order non-linear k- model was adopted as a model which is appropriate for non-homoenous and anisotropic turbulent flows. This model has been applied to various flow fields, such as the swirlin flows around submered spur dikes (Kimura et al. 004). The constitutive equations are described in Eqs (6)-() as follows: i i i k v v Dt S k Dt Q Q Q (6) k D t C (7) Q Q Q S i l li S l S l (8a) i l k m i l S l S S ms k l (8b) i l l k m m i k l l (8c) i i i V V (9a) i i i V V (9b) f f (0a) 0.5 M, f M, f M k S, M max[ S, ] 0.0M S i S i k, i i M (0b) () 94 Pae

3 0. C min0.09, () 0.09M Eq. (0) was adusted by considerin the distribution of turbulent intensities in a simple shear flow in comparison with the previous experimental results (Kimura & Hosoda, 000). Eq. () was determined to satisfy the reliability in a simple shear flow and the sinular points in both D and D flow fields. The overnin equations were solved by applyin the finite volume method on a full-staered rid system. The QUICK scheme was used for the convection terms (Leonard, 979) and the central differencin is applied for the diffusion terms of the momentum equations. The hybrid central upwind scheme was applied to the k and equations. The pressure field was solved usin the iterative solution alorithm (SOLA) of Hirt et al. (975), and the wall function approach was applied for the wall boundary conditions for k and. The free surface elevation was calculated usin Eq. () (Takizawa et al. 99). h V t () where Δt = time increment and Δh = the chane in surface elevation durin Δt.. Application and Discussion The model was verified usin the laboratory experiment carried out by Tominaa et al. (000). In this experiment (Fiure ), two spur dikes were installed in the left side of an open rectanular channel, which was 8m lon, 0.m wide (B) and its bed slope (i) was /000. Fiure. The set up of the experimental model. The transverse lenth (l) of each spur dike was 0.05m; lonitudinal thickness of each spur dike (b) was 0.0m; and the distance between them (S) was 0.m. The spur dikes heiht (d) were 0.0, 0.0, 0.04, 0.05, 0.06m (submered cases) and 0.08m (emered case) correspondin to SD, SD, SD4, SD5, SD6 and SD8. The upstream inflow dischare (Q) and downstream water depth were kept constant as 4. l/s and 0.08m. All the above experiment conditions were simulated usin the developed model, within a rid consistin of x 6 x 7 cells in the lonitudinal, transverse and vertical directions of the channel (Fiure ) with a hiher resolution of cells nearest the modelled spur-dykes. Fiure. Computational rid: Upper: plan view (x-y) Lower: side view (x-z) Fiure shows time-averaed imaes of the velocity vector of flow in a steady state. The vertical lare-scale vortex eneration between the spur dikes was well reproduced by the simulations, includin the impacts of the increased spur dikes heiht, includin increased size of the vortex, increased velocity and movement of the vortex-core downstream. Simulations also replicated the flow behavior upstream of the first dike, where flow was split into two parts: one tendin upward from the dike crest and the other oin downward, potentially causin a horseshoe vortex and local scourin. These upstream vortices were intensified with the increase of the dike s heiht but almost disappeared in the emered case (SD8). Horizontal vortices were also reproduced well, as can be seen in the plan view of the velocity field at the half-depth of the spur dikes, shown in Fiure 4. The horizontal eddies occur in all cases of simulation and were stroner in SD6 and SD8, potentially lead to more severe local scourin at spur dykes toe. 944 Pae

4 Experiment Simulation Fiure. Velocity vector fields on Y-section. Left: measurement results; Riht: simulation results The velocity field in Fiure 5 demonstrates that the adverse flow was enerated near the channel bank with quite a stron over-toppin flow and vortices between spur dikes (Fiure 5 - upper), which miht be a reason for channel bank scourin near dike abutments, but this was not observed in the reion near the tip of the dikes (Fiure 5 - lower). At the same time, a downward flow was displayed in the front of the second spur dike s tip (Fiure 5), which miht also cause a local scour hole at the dyke s toe. These characteristics were confirmed by the occurrence of a lare eddy near the bed layer as shown in Fiure 6. Moreover, the harmonies of velocity distribution between measurement and simulation results are also revealed as shown in Fiure 7. All the above characteristics of flow structure were simulated in fair areement with the measurement results from Tominaa et al. (000), hence validatin the capacity of the numerical model in simulation of the D nature of flow fields around submered spur dikes. 945 Pae

5 Experiment Simulation Fiure 4. Velocity vector fields on Z-section. Left: measurement results; Riht: simulation results 946 Pae

6 Experiment Simulation Fiure 5. Velocity vector fields on Y-section. Left: measurement results; Riht: simulation results Experiment Simulation Fiure 6. Velocity vector fields on Z-section. Left: measurement results; Riht: simulation results Fiure 7. Vertical and transversal distribution of velocity components at different planes 947 Pae

7 Conclusion A D numerical model has been described and applied for simulatin the flow structure around submered spur-dykes. The model uses a movin eneralized curvilinear rid allowin it to conform to a rane of curved channel and meanderin river terrains. The model simulations with different confiurations of submered spur-dykes compared favourably with experimental laboratory data. It was found that the vortex formed by overtoppin phenomena were reproduced well and this supports the further development of the model with the addition of sediment transport modules for more extensive application and investiation of practical river trainin structures. Acknowledements This study was partly financed by Vietnam National University, Hanoi within the framework of research proect QGTĐ..07 and by DANIDA within the framework of research proect -P04-VIE. The first author should like to acknowlede Dr Kate Crean and Dr Terence Chan, Monash University for their elaboration in revisin this manuscript. References [] Chanson, H. (999). The Hydraulics of Open Channel Flow: An Introduction. John Wiley and Sons Inc., New York [] Garde, P.J. et. al., (96). Study of Scour around Spur-Dikes. J. Hydraul. Div., Proceedins of ASCE, Vol. 87(6), pp. -7. [] Hirt, C. W., Nichols, B. D. & Romero, N. C. (975). SOLA - a Numerical solution alorithm for transient fluid flows. Los Alamos Scientific Report, LA-585. [4] Kimura, I. & Hosoda, T. (000). Numerical simulation of flows around a surface-mounted cube by means of a non-linear k- model. Proc. Of 9 th International Symposium on Flow visualization, Paper No.88, (CDROM). [5] Kimura, I., Hosoda, T., Onda, S. & Tominaa, A. (004). Computations of D turbulent flow structures around submered spur dikes under various hydraulic conditions. Greco, M., Carravetta, A. & Della Morte, R. (eds), Napoli: Balkema, River Flow 004 (), pp [6] Kuhnle, R. A., Alonso, C. V., and Shields, F. D., Jr. (999). Geometry of scour holes associated with 90 spur dikes. J. Hydraul. En., Vol. 5(9), pp [7] Kwan, T. F., and Melville, B. W. (994). Local scour and flow measurements at bride abutments. J. Hydraul. Res., Vol. (5), pp [8] Leonard, B.P. (979). A stable and Accurate Convective Modellin Procedure Based on Quadratic Upstream Interpolation. Comput. Meths. Appl. Mech. En. Vol.9, pp [9] Lim, S. Y. (997). Equilibrium clear-water scour around an abutment. J. Hydraul. En., Vol. (), pp [0] Martin, J. L. and McCutcheon, S. C. (999). Hydrodynamics and transport for water quality modellin. Lewis Publications, Boca Raton, Florida. [] Melville, B. W. (99). Local scour at bride abutments. J. Hydraul. En., Vol. 8(4), pp [] Naata et al. (005). Three-dimensional numerical model for flow and bed deformation around river hydraulic structures. Journal of Hydraulic Enineerin, Vol., No., pp [] Rahman, M. M., Naata, N., Muramoto, Y., and Murata, H. (998). Effect of side slope on flow and scourin around spur-dike-like structures. Proc., 7th Int. Symp. on River Sedimentation, Hon Kon, China, pp [4] Takizawa, A., Koshizuka, S. & Kondo, S. (99). Generalization of physical component boundary fitted co-ordinate (PCBFC) method for the analysis of free-surface flow. Int. J. Num. Methods in Fluids, Vol.(5): -7. [5] Tominaa A., Nakano A., Iima K. and Naasaka G. (000). Effects of relative dike hiht on flow structures in submered spur-dike zones. J. Applied Mechanics JSCE, Vol., pp Pae

8 Author Information Assoc. Prof. Dr. Tran Noc Anh. Center for Environmental Fluid Dynamics (CEFD), VNU-Hanoi University of Science, 4 Nuyen Trai, ThanhXuan, Hanoi, Vietnam. Assistant. Prof. Dr. Shinichiro Onda. Dept. of Urban Manaement, Kyoto University, Kyoto , Japan. BS. Nuyen Duc Hanh. Dept. of Hydroloy, VNU-Hanoi University of Science, 4 Nuyen Trai, ThanhXuan, Hanoi, Vietnam. Assoc. Prof. Dr. Nuyen Thanh Son. Dept. of Hydroloy, VNU-Hanoi University of Science, 4 Nuyen Trai, ThanhXuan, Hanoi, Vietnam. 949 Pae