Flow structure in front of the broad-crested weir

a Co esponding au ho : [email p o ec ed] Flow s uc u e in on o he b oad-c es ed wei Zbynk Zacho al1,a and Ladisla Rouša 2 1BUT, FCE, IWS, LWMR, 602 00 B no, Czech Republic 2BUT, FCE, IWS, 602 00 B no, Czech Republic Abs ac . The pape deals wi h esea ch ocused on desc ip ion o low s uc u e in on o b oad-c es ed wei . Based on expe imen al measu emen , he low s uc u e in on o he wei ( he eci cula ion zone o low and o nado o ices) and low s uc u e on he wei c es has been desc ibed. The de e mined low cha ac e has been simula ed using nume ical model and based on compa ing esul s he sui able model o u bulence has been ecommended. 1 In oduc ion Rec angula b oad-c es ed wei s a e equen ly used o he de e mina ion o discha ge [1]. Wei s a e moun ed in a p isma ic ec angula channel usually he same wid h B as wid h o wei b o su icien ly inc ease wa e su ace, ne e hless, do no in luence on maximum capaci y o channel. The wei c es is ho izon al wi h he wei hickness , he ups eam and downs eam aces a e e ical, he wei su ace is smoo h, he ups eam and downs eam wei edges a e sha p and he wei heigh is P (Figu e 1). The e o o moun ing hem is o ensu e a ee o e low in whole a ange o measu ing discha ges [2]. Rec angula b oad-c es ed wei s o m h ee eci cula ion zones o low [3]: ups eam [4], c es [5] and downs eam eci cula ion zones [3] (Figu e 1). The ups eam and c es eci cula ion zones ha e an in luence on a wei capaci y, he downs eam eci cula ion zone does no because he pa allel supe c i ical low is c ea ed on he wei c es [6]. 2 Flow s uc u e in on o he b oad- c es ed wei A di e en ela i e wei heigh s h/P, a di e en low s uc u e o ms in on o ups eam ace [7]. In a case o high wei s, he ups eam eci cula ion zone is no o med; in medium-high wei s, only he ups eam eci cula ion zone is o med; and in low wei s, he ups eam eci cula ion zone is o med and is supplemen ed by o nado o ices [8-11]. The c i e ia o he o ma ion o indi idual low s uc u es ha e been de e mined by Zacho al and Rouša [12]. Lu z P hu z ups eam eci cula ion zone c es eci cula ion zone L h poin o low s agna ion line o low s agna ion ups eam eci cula ion zone a ea o low s agna ion line o low s agna ion a ea o de eloping o eces bed s eamline a e age posi ion o o nado o ex axis Lc z hc z c es eci cula ion zone Figu e 1. Scheme o wei , low and no a ion o a iables. 3 Re iew o nume ical models o low o e b oad-c es ed wei The nume ical modelling o po en ial low o e b oad- c es ed wei was in es iga ed by, e.g., Moos [13], S ee ha an [14], Dias e al. [15]. Howe e , he po en ial low does no desc ibe eci cula ion zones o low, hence he esul s we e di e en . To achie e eliable esul s o DOI: 10.1051/ C Owned by he au ho s, published by EDP Sciences, 2015 / 021 201epjcon EPJ Web o Con e ences , 021 59 92 2 (2015) 1 1                      !"#! 7 7 A icle a ailable a h p://www.epj-con e ences.o g o h p://dx.doi.o g/10.1051/epjcon /20159202117 ansi low, hey mus ha e been composed by special ways [13]. The simula ion o o ical low o e ec angula wei was s udied by Bomba deli e al. [16]. They used 2D model o u bulen low o incomp essible iscous liquid. The low was desc ibed by Reynolds-a e aged Na ie –S okes equa ions (RANS). Tu bulence was sol ed by Reno malized G oup (RNG) k- ε model [17]. They compa ed esul s wi h measu emen s Hage and Schwal [18] and s a ed good ag eemen wi h a pa e n o wa e su ace e en in ange o he c es eci cula ion zone. Shake and Rhodes [19] simula ed wo phase low in 3D desc ibed by RANS equa ions supplemen ed wi h k- ε u bulence model [20] and wall unc ion. To de e mine wa e su ace hey used Volume o luid (VOF) me hod [21]. They ound good ag eemen wi h low and wa e su ace le el, only hey no ed di e ences in posi ion o he c es eci cula ion zone and in pos i ion o a nappe. Ha gea es e al. [22] simula ed wo phase 2D low (one case 3D) and es ed h ee di e en u bulence models k- ε , RNG k- ε and Reynolds S ess Model (RSM) [23]. RNG k- ε and RSM u bulence models simula ed low mo e eliable han k- ε . They de e mined ha 3D model does no p o ide in compa ison wi h 2D model a imp o emen in pa e n o wa e su ace. The g ea es di icul ies hey saw in simula ion o hyd aulic jump and a ea ion o low. Hsu and Ozdemi [24] modeled he same low as Ha g ea es and concen a ed on compa ison wi h RNG k- ε and RSM u bulence models. They s a ed ha model RSM yields be e esul s o wa e su ace le el. Ki kgoz e al. [11] deal wi h 2D modelling. They compa ed nume ically sol ed po en ial low ield, nume ically sol ed low ield wi h he use o RANS equa ions and k- ω [25] and k- ε ubulence models wi h measu ed by me hod Pa icle Image Velocime y (PIV) [26]. They ecommended RANS app oach wi h k- ω u bulence model. Adegbulugbe [27] ca ied ou a s udy o he ela ed e i ica ion as Ha g ea es e al. [22]. He claimed ha he mos accu a e esul s we e ob ained using wi h RNG k- ε u bulence model. 4 Expe imen Fo compa ing was chosen he wei desc ibed by Zacho al e al. [29]. The wei was made o o ganic glass, was moun ed in o a ec angula lume, wi h wei heigh P = 0.250 m, wid h b = 1.003 m and hickness = 0.500 m. The eloci y ield measu emen s was conduc ed wi h a combina ion o Ul asonic Veloci y P o ile (UVP) Moni o and PIV. The eloci y ield was measu ed a inle channel by UVP Moni o [29] and in on o he wei and on he wei c es by PIV [5]. The shape o eci cula ion zones was isualiza ed by dye and by pa icles added in o low. The ea e , he low s uc u e was displayed by pa icles mo ing on he bo om. The le el o wa e su ace was measu ed by a poin gauge and he discha ge was de e mined by calib a ed iangula sha p-c es ed wei . 5 Nume ical model 5.1 Selec ed app oach The a ie y o app oaches may be used o sol ing low s uc u e in on o he ec angula b oad-c es ed wei . E e y app oach b ings wi h i a ce ain deg ee o simpli ica ion and, he eby e o desc ip ion compa ed wi h eali y. The equi emen s o he esul s de e mine he choice o empo al and spa ial schema iza ion. Fo sol ing s eady o e low om a mac oscopic iew desc ibed by pa e n o wa e su ace and by ime- a e aged eloci y ield he models we e used based on RANS equa ions and La ge eddy simula ion (LES) model wi h Smago insky subg id-scale (SGS) model. The modelling o eci cula ion zones no a ec ed side walls was pe o med by 2D and o nado o ex by 3D due o hei spa ial cha ac e . Fo modelling u bulence wi h RANS app oach he i s o de models we e selec ed based on u bulence iscosi y: one laye models S anda d k- ε , RNG k- ε , S anda d k- ω models and wo laye Shea S ess T anspo (SST) model [28]. Fu he , he second o de models we e used based on Reynolds s ess anspo equa ion [23]: Baseline (BSL) Reynolds S ess (RS) and Speziale-Sa ka -Ga ski (SSG) RS [30]. Fo sol ing he so wa e we e used ANSYS-CFX (3D, 2D) (Figu e 2) – wo phase low, ANSYS-Flo an (2D) (Figu e 3) – one phase low and Flow-3D (2D) (Figu e 4) – one phase low. 5.2 Calcula ion Fluid domain geome y included he inle channel, he wei and a pa o ou le channel wi h ee nappe. The inle channel leng h was so long o de elop eloci y p o ile. A inle bounda y he hyd os a ic p essu e dis ibu ion was se o a dep h es ablished om he measu emen s and a cons an eloci y. A ou le bounda y he ee ou low was se . The walls we e hyd aulically smoo h. The hal domain was sol ed because longi udinal symme y. The e e ence p essu e was ze o. The numbe o elemen s depended on used so wa e and dimension, o 2D model i was app oxima ely om 1·105 (Flow-3D, ANSYS-Flo an) o 5·105 (ANSYS- CFX) and o 3D model 5·106. The calcula ions we e pe o med in ange o discha ges 0.040 m3/s, 0.070 m3/s and 0.130 m3/s. Ma e ial p ope ies o wa e we e: densi y 998 kg/m3 and iscosi y 1·10-6 m2/s. All coe icien s o u bulence models we e le unchanged. The mesh was s uc u ed wi h ec angula elemen s. 5.3 E alua ed pa ame e s The e alua ed pa ame e s we e he o e low head h a a gi en discha ge, he leng h o c es eci cula ion zone Lc z, he heigh o c es eci cula ion zone hc z, he leng h o ups eam eci cula ion zone Lu z, he heigh o ups eam eci cula ion zone hu z and he a e age posi ion o o nado o ex axis L . EPJ Web o Con e ences 02117-p.2 6 Resul s The measu ed alues o e alua ed pa ame e s calcula ed o he discha ge 0.070 m3/s a e shown in Table 1. The esul s 2D calcula ions a e p esen ed in he o m o eloci y ields o all e alua ed discha ges sol ed by all so wa e. Table 1. E alua ed pa ame e s [uni s in m], 2D, Q = 0.070 m3/s. Model h Lc z h c z L u z h u z Measu ed 0.131 0.108 0.022 0.140 0.140 S anda d k- ε ANSYS-Flo an ANSYS-CFX Flow-3D 0.132 0.129 0.129 0.050 0.100 0.087 0.006 0.019 0.013 0.087 0.142 0.198 0.067 0.075 0.103 RNG k- ε ANSYS-Flo an ANSYS-CFX Flow-3D 0.130 0.130 0.127 0.068 0.130 0.081 0.008 0.020 0.012 0.072 0.148 0.144 0.060 0.106 0.084 S anda d k- ω ANSYS-Flo an ANSYS-CFX 0.129 0.132 0.057 0.069 0.006 0.011 0.139 0.165 0.061 0.111 SST ANSYS-Flo an ANSYS-CFX 0.128 0.130 0.074 0.114 0.015 0.020 0.360 0.162 0.113 0.111 BSL RS ANSYS-CFX 0.129 0.123 0.020 0.197 0.128 SSG RS ANSYS-CFX 0.129 0.143 0.021 0.230 0.114 LES (Smago insky SGS) Flow-3D 0.128 0.092 0.015 0.317 0.116 Figu e 2. ANSYS-CFX, 2D, k- ε , 0.070 m3/s, eloci y ield. Figu e 3. ANSYS-Flo an, 2D, k- ε , 0.040 m3/s, eloci y ield Figu e 4. Flow-3D, 2D, k- ε , 0.130 m3/s, eloci y ield. Figu e 5. To nado o ex. Figu e 6. ANSYS-CFX, 2D, SST, 0.070 m3/s, s eamlines. Figu e 7. ANSYS-CFX, 3D, SST, 0.070 m3/s. EFM 2014 02117-p.3 . 7 Conclusions F om he esul s in Table 1 is e iden ha alues o e alua ed pa ame e s change wi h used so wa e and u bulence model. P ac ically, all one laye models based on u bulen iscosi y unde es ima e a size o eci cula ion zones. The mos eliable esul s o hem RNG k- ε u bulence model p o ide. The models based on Reynolds s ess anspo equa ion o e es ima e he leng h o eci cula ion zones in di ec ion o low. Two laye s model SST p o ides he mos eliable esul s om all used models (Figu e 6). LES model o e es ima es he leng h o ups eam eci cula ion zone. O e es ima ion o he leng h o ups eam eci cula ion zone may be caused by a ac ha he nume ical model due o small numbe o elemen s does no simula e o ices a ising nea he bed in on o he ups eam eci cula ion zone [12]. The alues o esul s in Table 1 a e signi ican ly dependen on he elemen size which i is mainly e lec ed a he heigh o c es eci cula ion zone. The bes esul s a e achie ed wi h he la ges numbe o elemen s which explains he di e ences in esul s wi h used so wa e. The sol ed o e low head was p ac ically o all models sligh ly smalle han measu ed. E o o i s de e mina ion is in all cases up o 3 %. The co ec modelling o he heigh o he c es eci cula ion zone is essen ial o de e mina e he o e low head. The e o e, i is ecommended o use a leas 8 elemen s along i s heigh . In he case o using a smalle numbe o elemen s he modelled c es eci cula ion zone is smalle . In he case o using a la ge numbe o elemen s ha ing no signi ican e inemen i s heigh . The co ec modelling o he ups eam eci cula ion zone has signi ican ly less an in luence on he o e low head han he c es eci cula ion zone. To nado o ex (Figu e 5) was able o simula e (Figu e 7), i s posi ion is in a ange o measu ed alues [12]. The low in a ea o o nado o ex is de eloped du ing he simula ion p ocess as he las . The e o e, he su icien numbe o simula ion is necessa y o pe o m. Fo de e mining o he o e low head has negligible e ec . Fo p ac ical use in de e mining o he o e low head a known discha ge and ice e sa is possible due o he ela i ely small demands on mesh and high accu acy de e mina ion o low cha ac e o ecommend RANS app oach and a wo laye SST u bulence model. Acknowledgmen s Acknowledgmen s a e due o p ojec s FAST-S-14-2203 - Cha ac e is ics o subme gence o low ec angula b oad- c es ed wei s and FAST-S-13-2010 T anspo o pa icles o e he ec angula b oad-c es ed wei . Re e ences 1. ISO 3846 (2008) 2. M. G. Bos, Discha ge measu emen s uc u es. (ILRI, Wageningen, 1989) 3. W. H. Hage , Discha ge measu emen s uc u es. (EPFL, Lausanne, 1986) 4. S. Mulle , P. Gui aud, A. Line, J. Hyd aul. Res., 49, 2 (2011) 5. Z. Zacho al, I. Mis o á, L. Rouša , J. Šulc, P. Zubík, J. Hyd ol. Hyd omech., 60, 4, 288-298 (2012) 6. Z. Zacho al, M. Knéblo á, L. Rouša , J. Rumann, J. Šulc, J. Hyd ol. Hyd omech., 62, 2, 145-149 (2014) 7. Z. Zacho al, P. Zubík, I. Mis o á, L. Rouša , Expe imen ální ýzkum a nume ické modelo ání úpla u za ná odní h anou peli u se ši okou ko unou obdélníko ého p ezu. (BUT, B no, 2012) 8. N. Raja a nam, D. Mu alidha , J. Hyd aul. Res., 9, 2 (1971) 9. O. Baud, W. H. Hage , J. En i. Eng., 126, 2 (2000) 10. C. A. Gonzalez, H. Chanson, Flow Meas. Ins ., 18 (2007) 11. M. S. Ki kgoz, M. S. Akoz, A. A., One , Canadian J. Ci il Eng., 35, 9, 975-986 (2008) 12. Z. Zacho al, L. Rouša , T anspo dno ých spla enin pes peli p a oúhlého p ezu se ši okou ko unou. (BUT, B no, 2014) 13. Moss, W. D., J. Fluid Mech., 52, 2, 307-320 (1972) 14. P. M. S ee ha an, Analy ical and expe imen al in es iga ion o low measu emen by long-based wei s in he ec ilinea and cu ilinea anges. (The Ha ield Poly echnic, Ha ield 1983) 15. F. Dias, J. B. Kelle , J.-M. Vanden-B oeck, Phys. Fluids, 31, 8, 2071-2076 (1988) 16. F. A. Bomba deli, M. H. Ga cía, M. E. Caisley. Hyd oIn o ma ics 4 h (2000) 17. V. Yakho , S. A. O szag, Phys. Re iew Le e s, 57, 14 (1986) 18. W. H. Hage , M., J. Schwal , I ig. D ainage Eng. 120, 1, 13-26 (1994) 19. M. A. Sa ke , D. G. Rhodes, Flow Meas. Ins umen ., 15, 4, 215-219, (2004) 20. B. E. Launde , D. B. Spalding, Compu e Me hods Appl. Mech. Eng., 3, 2, 269-289 (1974) 21. C. W. Hi , B. D. Nichols, J. Comp. Phys. 39 (1981) 22. D. M. Ha g ea es, H. P. Mo an, N. G. W igh , Eng. Appl. Comp. Fluid Mech., 1, 2, 136-146. (2007) 23. B. E. Launde , G. J. Reece, W. Rodi, J. Fluid Mech., 68, 3, (1975) 24. T. Hsu, E. C. Ozdemi , S udy o complex lows h ough SFWMD cul e s uc u es by CFD modeling. Uni e si y o Flo ida (2007) 25. D. C. Wilcox, AIAA J., 26, 11, 1299-1310 (1988) 26. R. J. Ad ian, Annual Re . Fluid Mech., 23, 261-304 (1991) 27. A. O. Adegbulugbe, A compu a ional luid dynamic alida ion s udy o he p edic ion and analysis o ee su ace low o e a b oad c es ed wei . (The Uni e si y o Leeds, Leeds, 2010) 28. F. R. Men e , Two-Equa ion Eddy-Viscosi y Tu bulence Models o Enginee ing Applica ions (NASA, 1992) 29. Z. Zacho al, J. Pa$ílko á, L. Rouša , 26 h Symposium on Anemome y, Ins . Hyd omech. ASCR, Li ice, 113-119 (2012) 30. C. G. Speziale, S. Sa ka , T. B. Ga ski, Modeling he p esu e-s ain co ela ion o u bulence – an in a ian dynamical sys ems app oach (NASA, 1990) EPJ Web o Con e ences 02117-p.4