Flow over Broad Crested Weirs: Comparison of 2D and 3D Models

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1 Journal of Cvl Engneerng and Archtecture 11 (2017) do: / / D DAVID PUBLISHING Flow over Broad Crested Wers: Comparson of 2D and 3D Models Shaymaa A. M. Al-Hashm 1, Huda M. Madhloom 1, 2, Rasul M. Khalaf 1, Thameen N. Nah 1 and Nadhr A. Al-Ansar 2 1. Department of Cvl Engneerng, Al-Mustansrayah Unversty, Baghdad 1001, Iraq; 2. Department of Cvl, Envronmental and Natural Resources Engneerng, Lulea Unversty of Technology, Lulea, Sweden Abstract: The flow over broad-crested wers was smulated by computatonal flud dynamc model. The water surface profle over broad crested wer was measured n a laboratory model and valdated usng two and three dmensonal Fluent programs. The Reynolds Averaged Naver-Stokes equatons coupled wth the turbulent standard (k-) model and volume of flud method were appled to estmate the water surface profle. The results of numercal model were compared wth expermental results to evaluate the ablty of model n descrbng the behavour of water surface profle over the wer. The results ndcated that the 3D requred more tme n comparson wth 2D results and the flow over wer changed from subcrtcal flow at the upstream (U/S) face of wer to crtcal flow over the crest and to supercrtcal flow at downstream (D/S). A reasonable agreement was notced between numercal results and expermental observatons wth mean error less than 2 %. Key words: Broad-crested wer, dscharge coeffcent, subcrtcal flow, numercal CFD, Fluent. Notaton B Wdth of the wer (m) C d The dmensonless coeffcent of dscharge (-) F The body force (N) g The gravtatonal acceleraton (ms -2 ) h exp. h num. The expermental head (m) The numercal head (m) The head over the U/S wer crest to the free h 0 surface (m) N The total number of ponts (-) p The pressure (pa) Q The dscharge (m 3 s -1 ) t u,j The tme (sec) The velocty n X and Y drecton α a The volume fractons of ar (-) α w The volume fractons of water (-) The densty (kgm -3 ) μ 0 μ t The dynamc vscosty (pas) The turbulence vscosty (pas) G k The producton of turbulent knetc energy (-) σ k and σ ε Are the turbulent Prandtl Numbers for k and respectvely (-) Correspondng author: Nadhr A. Al-Ansar, professor; research felds: water resources and envronment. E-mal: nadhr.alansar@ltu.se. 1. Introducton The broad crested wers are a hydraulc structures wdely used for depth control and flow measurement n feld and laboratory canals.the geometry descrbed as a flat-crested structure wth a length (L) of crest large enough compared to the flow thckness over the crest of the wer. The crest s broad when the streamlnes of the flow are parallel to the crest and the pressure dstrbuton s hydrostatc [1]. The general shape of broad crested wer s shown n Fg. 1. The dscharge equaton of the wer represented a functon of the head over wer crest and the geometrcal wer (Eq. (1)) [2]: 2 2 Q = C g 2 d ( h ) 3 0 B (1) 3 3 where; Q s the dscharge, C d s the dmensonless coeffcent of dscharge, g s the gravtatonal acceleraton, h 0 s the head over the U/S wer crest to the free surface, and B s the wdth of the wer.

2 770 Flow over Broad Crested Wers: Comparson of 2D and 3D Models Fg. 1 Defnton sketch of a broad-crested wer [3]. In recent years, the characterstc of flow over broad-crested wers has been ntroduced by many researches. Sarker and Rhodes [4] used the smple geometry of the rectangular broad-crested wer to test one dmensonal (1D) model of CFD (computatonal flud dynamcs) software wth complex regons of separated flow that affects ts hydrometrc performance n open channel flows. The results ndcated the upstream water depth was rapdly-vared flow profle over the crest for the gven flow rate. Ramamurthy, Tm and Rao [5] showed that the characterstcs of flow over broadcrested wers wth a squareedged and a roundnosed upstream corner vary wth the ratos H/L and R/p. The upstream head, H, the length L, the heght P, and the radus, R. Expermental data are presented to valdate the calculate results for the coeffcent of dscharge. Haun, Olsen and Feurch [6] calculated the water flow over a trapezodal broad-crested wer usng two CFD codes. Flow-3D used the VOF (volume of flud) method wth a fxed grd. SSIIM 2 used algorthm based on the contnuty equaton wth an adaptve grd. The result showed the accuracy of the model depends on the grd sze. Hager and Schwalt [7] recommended the broad-crested wer as a dscharge measurement structure. It satsfes some standard condtons based on expermental nvestgaton for surface profle, separaton profle, bottom pressure profle, and velocty profle close to the upper crest corner. The broadcrested wer s characterzed by nsenstvty to tal water submergence. Al-Hashm [8] studed the effect of nclnaton the U/S face of broad crested wers from 90º to 23º usng CFD model and laboratory data to ncrease the hydraulc performance of broad crested wers by reducng the effect of flow separaton. The results ndcated that the effcency of dscharge was ncreased wth slope of 23º about 22% hgher than the slope of 90º. The effect of the channel slope on the energy dsspaton (E%) over sngle step broad crested wers were smulated expermentally and numercally by usng 2D CFD [9]. The objectve of ths paper was to determne how well CFD (Fluent Verson 6.3) software could model the free-surface profle n 2D and 3D flow around the broad crested wer structure, wth a vew to ts better for modelng. The CFD model was carred out n comparson wth a physcal model operated over broad crested wer n a rectangular laboratory flume. 2. Physcal Model The expermental works were conducted at the hydraulc laboratory of Al-Mustansrayah Unversty, Baghdad, Iraq. The experments were carred out n a flume of 0.3 m deep, 0.3 m wde and 4.8 m long wth the front sde of glass (Fg. 2). A precse statc pont gauges (±0.1) were nstalled at the top of the centerlne of a flume for measurng water level. Water flow was suppled from a storage tank that contans an

3 Flow over Broad Crested Wers: Comparson of 2D and 3D Models 771 electrcal pump. The dscharge was measured wth flow meter. The model of the broad-crested wer was made of well-polshed steel. The radus of curvature was desgned to 0.03 m to reduce the effects of separatons zone [9]. It was located at 0.9 m from the entrance of the flume to make the water surface levels stable and unform. The dmensons of the model were 0.15 m n heght (P), 0.3 m n wdth (B) and 0.36 m n length (L) as shown n Fg. 3. It was desgned accordng to practcal desgn recommendatons that have been stated as lmtaton condtons of broad-crested wers by ASTM Internatonal Desgnaton [2] as: h m or 0.05L; 0.05 h 0 /L 0.57; h 0 /P < 1.5; P 0.15 m; B 0.3 m or h 0 or L/5; and L 1.75h CFD Model Descrpton Numercal modelng of wers s very mportant n the engneerng work and t can be used nstead of physcal modelng to save cost, effort and tme due to the advances n computer technology [10]. CFD s a numercal tool that was used for smulatng flow by applyng Fluent software Verson 6.3 to solve 2D and 3D problems n open channels. The assumptons of flow over wers whch used to derve and solve usng numercal technques are fully turbulent, unsteady, ncompressble, and non-vscous. The dfferental equatons used n Fluent software are contnuty and RANS (Reynolds Averaged Naver-Stokes equatons). These are based on the prncples of conservaton of mass and Newton s Second Law. These equatons are descrbed by Eqs. (2) and (3) [10]: Fg. 2 Photograph showng the laboratory flume wth broad crested wer. Fg. 3 Schematc of the broad-crested wer and related notaton.

4 772 Flow over Broad Crested Wers: Comparson of 2D and 3D Models ρ + t x ( ρu ) = 0 (2) t where, s the densty, u,j s the velocty n X and Y drecton, x s the space, t s the tme, p s the pressure, μ = μ 0 + μ t, μ t s the turbulence vscosty and μ 0 s the dynamc vscosty, F s the body force and g s the acceleraton. The Fluent solves RANS equatons wth dfferent turbulence models; Standard k-, renormalzaton P u u ρ (3) x x x u j x j ( u ) + ( ρu ) = + μ + + ρg + F group (RNG) k-, and realzable k- [11]. In the present work, the standard (k-) turbulence model was employed. It has two advantages; there s strong curvature n the streamlnes and the acceleratng flow over the wer. The mathematcal equatons whch represent turbulent energy dsspaton and turbulent knetc energy rate are as follows [12]: t k x x μ k σ k x t ( ρk) + ( ρku ) = μ + + G ρε j k (4) t ε x ( ρε ) + ( ρεu ) = x j μ t ε μ + + G σ ε x 1ε ε G k k G 2ε 2 ε ρ k (5) where, the eddy vscosty t s: μ C 2 k ρ ε t = μ (6) G k s the producton of turbulent knetc energy. G 1ε, G 2ε and C are constants and equal to 1.44, 1.92, and 0.09, respectvely. σ k and σ ε are the turbulent Prandtl numbers for k and equal to 1.0 and 1.3, respectvely. VOF s one of the methods whch can be used to determne the water surface profle that represents the sharp nterface between the water and ar phases. VOF s the holds n the absence of any nter-phase mass transfer. When the program models the free surface between water and ar, a transport equaton s solved for the water phase [13]: α w t + x ( α u ) = 0 w (7) Only one such transport equaton needs to be solved snce the volume fracton of the other phase can be nferred from the constrant: α = 1 (8) a α w where, α w and α a are the volume fractons of water and ar, respectvely. The flow doman s dvded nto a grd consstng of many numbers of cells. In each cell, f t contans only ar, then α w = 0, when t contans only water, then α w = 1 and f t s contans ar and water, 0 α w 1. Accordng to the local volume fracton, the flow propertes n each cell are adjusted. The general shape of the model wth volume fracton s shown n Fg Geometry and Boundary Condtons The frst step n numercal model s generatng a mesh for the board crested wer havng the same dmenson of the expermental work. The mesh sze used n CFD can have an mportant effect on the smulaton tme and accuracy of the result. Gambt program was used to apply geometres and meshes. Fg. 5 shows the geometrcal mesh of the wer n 2D and Fg. 6 shows the geometrcal mesh of the wer n

5 Flow over Broad Crested Wers: Comparson of 2D and 3D Models 773 Fg. 4 General shape of mesh n volume of flud method. Fg. 5 Mesh and boundary condtons of 2D broad crested wer usng Gambt program. Fg. 6 Mesh and boundary condtons of 3D broad crested wer usng Gambt program.

6 774 Flow over Broad Crested Wers: Comparson of 2D and 3D Models 3D. The cell szes around the upstream corner of the wre are reduced whch conssted of 22,962 quadrlateral cells. The cell sze around the downstream corner of the wer crest ncreases gradually wth dstance from the walls. The open channel boundary condtons were appled to the CFD model pressure nlet at the man channel nlet, the symmetry at the boundares whch are open to the atmosphere, the pressure outlet at the man channel outlet. Also wall boundary was used to specfy the sold surfaces. The pressure nlet boundary condton represents an opton whch ensures easy descrpton of the bottom and the surface water levels of the man channel and also the velocty of the channel flow. The boundary condtons of for 2D and 3D used n ths study are shown n Fgs. 5 and Results and Dscusson A broad crested wer has been smulated usng Fluent n 2D and 3D to test the accuracy of the results for water surface profle. The numercal results were compared wth the expermental results n XY plot n Fg. 7, where, X s the length of the flume and Y s the depth of flow. The results showed n 2D and 3D that the depth of flow level was nearly stable tll (0.7 m) from the nlet of the flume. The depth of flow start decreased at the U/S edge of the broad crested wer and contnues n decrease to the D/S edge of the wer. The flow condton was subcrtcal flow at U/S edge, crtcal flow at wer crest, and supercrtcal flow at D/S edge n both smulaton 2D and 3D. The water surface profle, velocty vectors and pressure dstrbuton over wer n 2D and 3D are shown n Fgs. 8-13, respectvely. It can be seen that there s a smlar behavor for the dstrbuton of the velocty and water surface profle over the wer n both 2D and 3D smulaton wth smple dfferences. The values of pressure are approxmately the same for both 2D and 3D smulaton. 6. Senstvty Analyss The RE (relatve error) percentage, RMSE (root mean square errors) and MAE (mean absolute errors) were used to evaluate the accuracy of results for water surface profle. The RE, RMSE and MAE are defned as [14]: Fg. 7 Water surface profles over wer.

7 Flow over Broad Crested Wers: Comparson of 2D and 3D Models 775 Fg. 8. Free surface profles over wer n 2D smulaton. Fg. 9 Velocty dstrbuton vectors over wer n 2D smulaton.

8 776 Flow over Broad Crested Wers: Comparson of 2D and 3D Models Fg. 10 Dstrbuton of pressure over wer n 2D smulaton. Fg. 11 Free surface profles over wer n 3D smulaton.

9 Flow over Broad Crested Wers: Comparson of 2D and 3D Models 777 Fg. 12 Velocty dstrbuton vectors over wer n 3D smulaton. Fg. 13 Dstrbuton of pressure over wer n 3D smulaton. Table 1 Relatve error between numercal and expermental results at x = 0.7 m. Model work 2D 3D CFD CFD H exp. (cm) H num. (cm) RE% RMSE% MAE%

10 778 Flow over Broad Crested Wers: Comparson of 2D and 3D Models 100 N hexp. hnum. RE = N = (9) 1 hexp. 1 N 2 RMSE = = ( h ) exp. h 1 num. (10) N 1 N MAE = = h exp. h 1 num. (11) N where, h exp. s the expermental head; h num s the numercal head; N s the total number of ponts; and s the number of ponts. Table 1 shows a good agreement between the expermental and numercal results at x = 0.7 m. The percent of error between expermental and 2D numercal model was 2.5, 0.6 and 0.6 n RE%, RMSE% and MAE%, respectvely. Whle, the percent of error between expermental and numercal model for 3D smulaton was 2.1, 0.5 and 0.5 n RE%, RMSE% and MAE%, respectvely. The error percentage between 2D and 3D s very small. So we can consder that 2D and 3D gve the same results. The smulaton tme of 3D s much longer than 2D under the same condtons. Therefore, 2D can be appled to solve the dffcult flud problem wth good accuracy. 7. Conclusons The Fluent wth VOF method and standard (k-) turbulence model were used to dscusses the accuracy of 2D and 3D to predct the mportant flow varables over abroad crested wer. By usng expermental data as valdaton data, t s possble to buld mathematcal model wth acceptable levels. The smulaton results of 2D and 3D have a good agreement wth expermental work. The most mportant fndngs were: The results showed that the water level s approxmately stable untl x = 0.7 m from the nlet of the flume and the flow varaton from subcrtcal flow at the U/S of wer to crtcal flow over crest, then the flow became supercrtcal at D/S; The relatve errors of water level at pont x = 0.7 m for broad crested wer between expermental and 2D result were 2.5, 0.6 and 0.6 n RE%, RMSE% and MAE%, respectvely. Whle the relatve error values between expermental and 3D numercal models were 2.1, 0.5 and 0.5 n RE%, RMSE% and MAE%, respectvely; The 3D results have values approxmately close to the 2D results but wth longer smulaton tme. The numercal model proved that 2D model can be used to nvestgate the behavor of water surface profle over a wer n reasonable tme and t wll be less expensve. Ths work can be used n future for desgnng wers wthout conductng laboratory tests to study the overtoppng of other hydraulc structure such as dams. Acknowledgments The authors would lke to thank Al-Mustansryah Unversty, Baghdad, Iraq ( Baghdad-Iraq, where the experments were carred out at the labs of the unversty and Lulea Unversty of Technology for ts support n the present work. Refrences [1] Chow, V. T Open Channel Hydraulcs. New York: McGraw-Hll. [2] ASTM Internatonal Desgnaton Standard Gude for Selecton of Wers and Flumes for Open-Channel Flow Measurement of Water. Unted States. [3] Hosen, S. H., and Afshar, H Flow over a Broad-Crested Wer n Subcrtcal Flow Condtons, Physcal Study. Journal of Rver Engneerng 2: [4] Sarker, M. A., and Rhodes, D. G Calculaton of Free-Surface Profle over a Rectangular Broad-Crested Wer. Flow Measurement and Instrumentaton 15 (4): [5] Ramamurthy, A. S., Tm, U. S., and Rao, M. J Characterstcs of Square-Edged and Round-Nosed Broad-Crested Wers. Journal of Irrgaton and Dranage Engneerng 114: [6] Haun, S., Olsen, N. R. B., and Feurch, R Numercal Modelng of Flow over Trapezodal Broad-Crested Wer. Engneerng Applcatons of Computatonal Flud Mechancs 5 (3):

11 Flow over Broad Crested Wers: Comparson of 2D and 3D Models 779 [7] Hager, W. H., and Schwalt, M Broad-Crested Wer. Journal of Irrgaton and Dranage Engneerng 120 (1): Accesed November 8, [8] Al-Hashm, A. S., Sadeq, A., and Huda, M Determnaton of Dscharge Coeffcent of Rectangular Broad-Crested Wer by CFD. In The 2nd Internatonal Conference of Buldngs, Constructon and Envronmental Engneerng (BCEE2-2015), Berut, October 17-18: [9] Al-Hashm, S. A., Madhloom, H. M, Nah, T. N., and Al-Ansar, N Channel Slope Effect on Energy Dsspaton of Flow over Broad Crested Wers. Engneerng 8 (12). Accessed November 8, [10] Lu, C., Hute, A., and Wenju, M Numercal and Expermental Investgaton of Flow over a Semcrcular Wer. Acta Mechancs Snca 18: [11] Wlcox, D. C Turbulence Modelng for CFD. La Canada Flntrdge: DCW Industres Inc. [12] Launder, B., and Spaldng, B. D The Numercal Computaton of Turbulent Flow. Computer Methods n Appled Mechancs and Engneerng 3: Accessed November 8, [13] Hrt, C. W., and Nchols, B. D Volume of Flud (VOF) Method for the Dynamcs of Free Boundares. Journal of Computatonal Physcs 39: Accessed November 8, [14] Wllmott, C. J., and Matsuura, K Advantages of the Mean Absolute Error (MAE) over the Root Mean Square Error (RMSE) n Assessng Average Model Performance. Clmate Research 30: