3D Simulation of Flow over Flip Buckets at Dams.

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1 Journal of Amercan Scence, 2011;7(6) 3D Smulaton of Flow over Flp Bucets at Dams M. Jorabloo 1, R. Maghsood 2, H. Sarardeh 3 1 Assstant Professor, Garmsar Branch, Islamc Azad Unversty, Garmsar, Iran. 2 Department of Engneerng, Sabzevar Branch, Islamc Azad Unversty, Sabzevar, Iran. 3 Hydraulc Structures Dvson, Water Research Insttute (WRI), Tehran, Iran. orabloo.mehd@yahoo.com Abstract: In the present numercal study, by usng the Fluent software, the ablty of t to predct the comple flow condtons s presented. In ths purpose, epermental data over a flp bucet n dfferent hydraulc condtons were selected. To smulate the turbulence phenomenon, -ε Standard turbulence model was selected. Moreover to predct et surface the VOF free surface model was employed. Fnally by comprsng the numercal model and avalable epermental results, a good agreement was observed. [M. Jorabloo, R. Maghsood, H. Sarardeh. 3D Smulaton of Flow over Flp Bucets at Dams. Journal of Amercan Scence 2011;7(6): ]. (ISSN: ).. Keywords: Flp Bucet; Fluent Software; VOF Free Surface Model; -ε Standard Turbulence Model. 1. Introducton The energy dsspater structure for a spllway could be a flp bucet because t s generally the most economcal soluton. Improvng n desgn parameters of a flp bucet wll protect the talrace from scourng of mpacted et. Analyss of flow wth free surface whch passes over a curved boundary by the gravty force s a challengng problem n hydrodynamcs. From 1933 tll 1954, Unted State Bureau of Reclamaton (USBR) regardng to hydraulc model tests, covered a complete range of bucet szes and tal water elevatons, were conducted to verfy the bucet dmensons and detals and to establsh general relatons between bucet sze, dscharge capacty, heght of fall, and the mamum and mnmum tal water depth lmts. Analytcal studes on potental flows past spllway flp bucets were done by many researchers such as: Sao and Hubbard (1953), Tnney et al. (1961), Orlov (1968) Sao et al. (1988). Xe-Qng Xu and Xao-Xa Sun (1990), by usng the fnte element method, obtaned pressure dstrbuton over spllway and flow bucet. Vscher and Hager (1998) proposed that flp bucets are used when energy has to be dsspated for a flow velocty larger than about m/s. Roman Juon and Wll H. Hager (2000) and Valentn Heller et al. (2005) and Remo Stener et al. (2008) performed some nvestgatons on flp bucets, ncludng scale effects n hydraulc models, bucet pressure dstrbuton, and nappe traectores wth and wthout the presence of deflectors. Regardng to the prevous researches, n the present study by usng the FLUENT Software, flow over the flp bucets at dams was numercally studed. 2. Epermental Data Collected Selected epermental tests for ths numercal study were conducted n a smooth channel by Roman Juon and Wll H. Hager (2000). The selected test cases nclude eght fed-bed cases. All epermental tests were conducted n a flume wth 499 mm wde and 700 mm deep wth a total length of 7 m (Fgure 1). Fgure 1. Schematc vew of the selected epermental setup: (a) Sde vew (b) Plan vew In the Fgure 1, notfcaton numbers are as 1) Jet bo, 2) Approach channel, 3) Flp bucet, 4) Downstream channel, 5) Start of chute. Other parameters are gven n Table 1 (F 0 =V 0 /(gh 0 ) 1/2 ). The channel had a PVC nvert and rght wall and a left glass wall. The flp bucet conssted of a 1 m long approach channel wth a bucet of radus R and deflecton angle β. The approach channel was nserted 250 mm above the orgnal channel nvert. 931 edtor@amercanscence.org

2 Journal of Amercan Scence, 2011;7(6) Table 1. Selected Epermental Parameters R (cm) F 0 H 0 Test Test Test Test Test Test Test Test Numercal Modelng In ths secton the turbulence model whch used n the present research s descrbed. In Reynolds averagng for the velocty components: u = u + u (1) Where u and u are the mean and fluctuatng velocty components. Substtutng epressons of ths form for the flow varables nto the nstantaneous contnuty and momentum equatons and smplfyng (and droppng the over bar on the mean velocty, u ): ρ + ( ρuu ) = 0 (2) t t ( ρ u ) + ( ρu u )= p u u u l + μ + 2 δ + ( ρu u ) (3) 3 l where equatons 1 and 2 are called Reynoldsaveraged Naver-Stoes (RANS) equatons that ρ u u s called Reynolds stresses, must be modeled. by usng the Boussnesq hypothess (Hnze, 1975) relate the Reynolds stresses to the mean velocty gradents: u u u ρuu μt ρ μt δ 2 (4) = The Boussnesq hypothess s used n the -ε models. In the present wor the Standard -ε model (Launder and Spaldng, 1972) was used to smulate the turbulence phenomenon. For Modelng the effectve vscosty: 2 μt = ρc (5) μ ε where C µ s a constant, s the turbulence netc, and ε s the turbulence rate of dsspaton. The transport equatons for the Standard -ε model are as follow: ( ρ ) + ( ρu )= t t ( ρ ) ( ρu ) + = t μ t μ + + G + Gb ρε Y (6) M σ ( ρε ) + ( ρεu )= 2 μ t ε ε ε μ + C1 ε ( G + C3 εgb ) C2ε ρ + σ (7) ε Standard constants of -ε model are lsted n Table 2 and were used n the model. Table 2. Standard -ε turbulence model constants C 1ε C 2ε C μ σ σ ε Standard -ε The volume of flud (VOF) method was employed as a powerful computatonal tool for the analyss of free surface flow (Hrt and Nchols, 1981). The tracng of the nterface(s) between the phases s accomplshed by the soluton of a contnuty equaton for the volume fracton of one (or more) of the phases. In the present research, both structured and unstructured mesh was used (Fgure 2). (a) (b) Fgure 2. Computatonal grd n the vcnty of flp bucet: (a) 3D vew, (a) Sde vew. Boundary condtons whch were employed n ths nvestgaton are (Fgure 3): Two dfferent nlets were needed to defne the water flow (Inlet 1) and ar flow (Inlet 2) n the model doman. These nlets were defned as stream-wse velocty nlets that requre the values of velocty. To estmate the effect of walls on the flow, emprcal wall functons nown as standard wall functons (Launder and Spaldng, 1974) were used. The upper boundary above the ar phase was 932 edtor@amercanscence.org

3 Journal of Amercan Scence, 2011;7(6) specfed as a symmetry condton, whch enforces a zero normal velocty and a zero shear stress. Fgure 3. Soluton doman and boundares for modeled flp bucet Other consderatons n ths smulaton n ths secton are presented. The PRESTO pressure dscretzaton was selected because ths scheme was showed the best convergence n ths smulaton. The momentum and turbulent netc energy equatons were dscredted by frst order upwnd. The PISO pressurevelocty couplng algorthm was also used. Usng unsteady and free surface equatons requred fne grd spacng and small ntal tme steps. To do so, a senstvty analyss was performed on grd spacng and fnally a number of meshes equal to were selected as the best result. Tme steps were selected equal to to Due to model runs, soluton convergence and water-surface profles were montored. The value of VOF parameter was selected equal to 0.5 whch s a common practce for volume fracton results (Fluent Manual, 2005 and Dargah, 2006). 4. Verfcaton Before employng the numercal model, t s necessary to ensure about the accuracy of the numercal model. For ths purpose, epermental cases whch were mentoned n the prevous secton were employed. To evaluate the free surface, the frst case was selected regardng the avalable flume data. Estng epermental results to valdate the numercal smulaton predctons ncluded water surface profles and pressure dstrbutons. To calculate the et traectory by defnng α as the taeoff angle and V as the taeoff velocty, the traectory geometry z() may be descrbed for free et flow as z = z0 + tanα g ( 2V cos α ) (9) By consderng the flow depth across the flp bucet remans constant, taeoff flow depth at =0 and so z o =h o for the upper nappe and z o =0 for the lower nappe. The taeoff velocty V s V o at h o 5 cm. By ntroducng the normalzed coordnates relatng to the upper (subscrpt O) nappe profle as Z O = (z O - h o )/(z M =h o ) and X = 2 ( h F 0 0 ) where z M, s the mamum (subscrpt M) nappe elevaton above the taeoff elevaton, results n 2 X Z α 1 0 = tan X (10) 2 cos 2 α Fgure 4 shows the numercal results n comparson wth epermental data Z O (X) for varous flow confguratons and produces agreement wth equaton 10 provded α =20 o s ftted. The data for the lower (subscrpt U) nappe traectory were analyzed correspondngly usng Z U =z U /z M and 2 ( ) a) Test 1 b) Test 2 c) Test 3 d) Test 4 X = h F edtor@amercanscence.org

4 Journal of Amercan Scence, 2011;7(6) e) Test 5 f) Test 6 b) Test 2 g) Test 7 c) Test 3 h) Test 8 Fgure 4. Water surface profles for flow over Flp- Bucet (left dagram upper nappe profle, rght dagram lower nappe profle) The dstrbuton of pressures at the bottom along the flp bucet s an mportant desgn parameter for statc purposes. It s equal to the sum of the statc approach pressure head h o plus a dynamc porton. Fgure 5 shows the comparson between epermental and numercal results. Normalzed parameter H P = (h P - h o )/(h PM - h o ) where h P and h PM are the total and mamum pressure heads, respectvely, plotted along the normalzed stream wse coordnate X P =/(Rsnβ), where =0 s located at the taeoff pont, and Rsnβ s the stream wse flp-bucet length. d) Test 4 e) Test 5 a) Test 1 f) Test edtor@amercanscence.org

5 Journal of Amercan Scence, 2011;7(6) g) Test 7 h) Test 8 Fgure 5. Comparson between computed and measured pressure head dstrbutons at bottom Conclusons: One way to dsspate of the energy n large dams s usng flp bucet at the termnal of over fall spllways. Improvng n desgn parameters of a flp bucet wll protect the talrace from scourng of mpacted et. Numercal modelng and analyss of flow wth free surface whch passes over a curved boundary by the gravty force s a challengng problem n hydrodynamcs. In the present research by usng Fluent software, a flp bucet structure was numercally smulated. To smulate the geometry and verfy the results, epermental tests whch were conducted n a smooth channel by Roman Juon and Wll H. Hager (2000) were selected. -ε Standard turbulence model and VOF free surface model were employed n the model. The results et traectory propertes and pressures n the bottom and ts good agreement wth analytcal and epermental data n eght cases showed the ablty of Fluent numercal model n modelng the flow over the flp bucets. Correspondng Author: Dr. Mehd Jorabloo Department of Engneerng Islamc Azad Unversty, Garmsar Branch, Garmsar, Iran. E-mal: orabloo.mehd@yahoo.com References 1. B. E. Launder and D. B. Spaldng., 1972, Lectures n Mathematcal Models of Turbulence, Academc Press, London, England. 2. B. E. Launder and D. B. Spaldng.,1974, The numercal computaton of turbulent flows., Computer Methods n Appled Mechancs and Engneerng, 3, pp Dargah, B., 2006, Epermental study and 3D numercal smulatons for a free-overflow spllway, J. Hydraulc Engneerng, 132 (9), 899, /(ASCE), Fluent Manual, 2005, Manual and user gude of Fluent Software., Fluent Inc. 5. Hrt, C.W. and Nchols, B.D., 1981, Volume of flud methods for the dynamcs of free boundares, Journal of Computatonal Physcs, 39, pp J.O. Hnze., 1975, Turbulence, McGraw-Hll Publshng Co., New Yor. 7. K. C. Kar and S. V. Patanar., 1989, Pressure-based calculaton procedure for vscous flows at all speeds n arbtrary confguratons., AIAA Journal, 27, pp L Shuguarg and Lang Zhengang, 1988, Gravty-affected potental flows past spllway flp bucets.,journal of Hydraulc Engneerng, Paper No , Vol. 114, No Orlov, V. T., 1968, Calculaton of free surface profle and pressure dstrbuton along a crcular arc connectng slopng and horzontal segments., Transactons of All Unon Scentfc Research Insttute of Hydraulc Engneerng, No. 87 (Russan). 10. Petera, A. J., 1983, Hydraulc desgn of stllng basns and energy dsspators., 7th Ed., Engrg. Monograph 25, Bureau of Reclamaton, U.S. Department of the Interor, Denver. 11. R. I. Issa., 1986, Soluton of mplctly dscretzed flud flow equatons by operator splttng., J. Comput. Phys., 62, pp Remo Stener & Valentn Heller & Wll H. Hager and Hans-Erwn Mnor, 2008, Deflector S Jump Hydraulcs, ASCE, Journal of hydraulc engneerng, Vol. 134, No. 5, Sao, T. T., and Hubbard, P. G., 1953, Deflecton of ets, Pt I: symmetrcally placed V-shaped obstacle Free streamlne analyss of transtonal flow and et deflecton., J. S. McNown and C. S. Yh, eds., State Unv. of Iowa, Iowa Cty, Iowa. 14. Tnney, R. E.et al, 1961, Free streamlne theory for segmental et deflector, J. Hydr. Dv., ASCE, 87(HY5), edtor@amercanscence.org

6 Journal of Amercan Scence, 2011;7(6) 15. Valentn Heller &Wll H. Hager and Hans- Erwn Mnor 2005, S Jump Hydraulcs, ASCE, Journal of hydraulc engneerng, Vol. 131, No. 5, Valentn Heller & Wll H. Hager, 2000, Flp bucet wthout and wth deflectors., ASCE, Journal of hydraulc engneerng, Vol. 126, No. 11, Vscher, D. L., and Hager, W. H., 1998, Dam hydraulcs, Wley, Chchester, England, and New Yor. 18. Xe-Qng Xu and Xao-Xa Sun, 1990, Flow n spllways wth gradually vared curvature, Journal of Engneerng Mechancs, Paper No , Vol. 116, No Young D.L., 1982, Tme-dependent multmateral flow wth large flud dstorton, In: K.W. Morton and M.J. Banes, eds. Numercal methods for flud dynamcs. New Yor: Academc Press, pp /31/ edtor@amercanscence.org