Numerical simulation of flow reattachment length in a stilling basin with a step-down floor

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1 5 h Inernaonal Symposm on Hydralc Srcres Brsbane, Asrala, 5-7 Jne 04 Hydralc Srcres and Socey: Engneerng hallenges and Eremes ISBN DOI: 0.464/ql.04.3 Nmercal smlaon of flow reaachmen lengh n a sllng basn wh a sep-down floor Q. Xa, Z. L and X. Go Sae Key Laboraory of Smlaon and Reglaon of Waer ycle n Rver Basn, hna Inse of Waer Resorces and Hydropower Research Beng, hna E-mal:aqf@whr.com Absrac: A hydralc mp s a good energy dsspaor for eco-frendly dam consrcon. Usng a sllng basn wh a sep-down floor remarably decreases flow velocy on he floor as well as operaon rs. onsderng ha he nmber of hgh dams ha have adoped hs ype of energy dsspaor has recenly ncreased, hs sdy nvesgaes he relaonshp among reaachmen lengh, sep hegh, and flow deph and velocy on he sep by applyng a wo-phase flow nmercal smlaon ha combnes he renormalzaon grop -ε rblence model and he volme of fld mehod. Smlaon resls show ha he reaachmen lengh does no change wh he velocy on he sep nder ceran condons drng whch sep hegh and flow deph on he sep are varable. Fng crves are esablshed based on he dmensonless parameer of reaachmen lengh/sep hegh and sep hegh/flow deph on he sep. Keywords: energy dsspaon. hydralc mp, reaachmen lengh, nmercal smlaon, renormalzaon grop -ε rblence model. INTRODUTION Flood dscharge aomzaon drng energy dsspaon by a hydralc mp s mnmal and leaves nearly no mpac on he srrondng envronmen (Sn, 009). onsderng he crren eco-frendly rend n dam consrcon, a hydralc mp s a good ype of energy dsspaor. Drng he lae 0 h cenry, developed conres have sared sng hs ype of energy dsspaor n proecs ha amed o redce flood dscharge aomzaon o mnmze he mpac on he slope vegeaon (Gao, 008). In hna, some dams ha are hgher han 60 m, sch as he Xangaba Hydropower Saon (hegh: 6 m), he Gand Hydropower Saon (hegh: 68 m), and he Jn'anqao Hydropower Saon (hegh: 60 m), apply energy dsspaon by a hydralc mp n consderaon of envronmenal sses and geologcal condons. Hager (99) smmarzes he sllng basn ype, nclde USBR Sllng Basns, USE Sllng Basn, Bhavan Sllng Basn and VNIIG Sllng Basns. Therefore, ensrng he safe operaon of hese ypes of sllng basn s dffcl when radonal boom energy dsspaon s appled becase he mamm boom velocy s hgher han 40 m/s. The sllng basn wh a sep-down floor was recenly developed o address o he aforemenoned engneerng characerscs. Snce 000, a nmber of research nsons n hna have condced sdes on he hydralc characerscs of sllng basns wh a sep-down floor. The resls of model ess and nmercal smlaons ndcae ha a sep down sgnfcanly redces flow velocy and plsang pressre acng on he floor. Table lss some hgh dams ha se sllng basns wh a sep-down floor. The hegh of hese dams s ypcally beween 0 m and 60 m, he n dscharge on he sep s beween 00 m 3 /(s m) o 30 m 3 /(s m), and he Frode nmber s beween 5 and. A sllng basn wh a sepdown floor has a wde range of applcaons. In hs cone, he problem of flow reaachmen lengh was sded by sng nmercal smlaon. The flow reaachmen lengh downsream of a sep-down floor s a parameer ha ms be sded along wh oher sses sch as vore nensy, rern flow velocy, angle beween flows, as well as floor and pressre gradens n he flow mpac area. A sech map of he bacward-facng flow paern s gven n Fg.. A srong shear and vore flow srcre s formed when hgh-velocy waer flows hrogh he sep-down floor. The reaachmen pon s he area where he rblen dffson flow

2 comes no conac wh he sllng basn floor, whereas he reaachmen lengh L s he dsance from he sep-down floor o he reaachmen pon. In hs sdy, downsream waer level s assmed o be sffcenly hgh, and ha e flow can form nder all condons. The smplfed D problem s sded by applyng a nmercal smlaon mehod. Table Ls of some large dams sng sllng basn wh sep-down floor Proec Mam Inflow ne Sep m of dam Inflow Frode dscharge hegh hegh nmber Fr 3 s - m- onry Ter Inda Shshens ~6.0 Rssa Gand hna Xangaba hna Ganynyan hna Mysone Myanmar Tngzo hna U0 0 d d h0 L Fg. The sech map of bacward-facng sep flow. MATHEMATIAL MODEL.. The volme of fld (VOF) model of a waer ar wo-phase flow In hs sdy, he VOF mehod was sed o rac he nerface. The fncons w(, y, ) and a(, y, ) represen he volme fracon of waer and ha of ar, respecvely, n he compaonal feld. A relaonshp s esablshed n each dscresed cell as follows: w a. () The governng eqaon of he waer volme fracon s epressed as: w w 0, () where s me; and and are velocy and coordnae componens ( =, ), respecvely. The nerface beween waer and ar was raced by solvng he connos Eq. (). The conny eqaon () shows ha he ransen solver was sed n he advecon feld of he VOF wo-phase model accordng o he nseady flow. The correc resls for he seady flow were obaned by gradal eraon of me.

3 .. Renormalzed grop (RNG) rblence -ε model The e flow s characerzed as a hgh-speed and ansoropc rblence, hs leadng o he selecon of he RNG -ε rblence model. The governng eqaons are as follows: onnos eqaon: 0 P, (3) Momenm eqaon: P, (4) eqaon: G, (5) ε eqaon: G *, (6) where and are he volme fracon average densy and moleclar vscos coeffcen, respecvely; s he velocy; P s he correced pressre; and s he rblen vscos coeffcen ha can be obaned by he rblen nec energy and he rblen dsspaon rae, and s epressed as. (7) The G n Eq. (6) s he rblen nec energy prodcon em ndced by he average velocy graden. I can be epressed as G, (8) *, (9) where S and S S S. The consans n he governng eqaon are lsed n Table. Table onsan n governng eqaon Nmercal mehod and bondary condon The compaonal feld was dscresed by a non-srcred cell and he conrol fne-volme mehod. A dfferenal eqaon was negraed no each conrol cell, and lnearzaon was sed o negrae eqaons. Each varable was hen obaned. The wo-order, pwnd fne-volme mehod was sed o measre volme fracon, momenm, and dffson va a rblen, nec-energy closed eqaon. Pressre and velocy were solved by sng he pressre mplc wh splng of operaor (PISO) algorhm. In hs algorhm, correced pressre

4 and velocy represen a hgh appromaed relaonshp ha s parclarly applcable o ransen problems. The PISO algorhm can mprove convergence n hghly dsored cells. The compaonal feld was smplfed no a D plane. Inle bondares nclded hose of waer and vapor. The former bondary condon was assgned he average velocy, whereas he laer bondary condon was assgned he pressre condon wh vales of n amospherc pressre. The ole bondares were assgned relaed fncons, sch as ar and waer, whereas laer fncon was for sac pressre dsrbon. The sold bondares were se wh a non-slp condon, and he vscos layer was formlaed by a sandard wall fncon. The nal bondary was flled wh waer. 3. SIMULATION RESULT AND ANALYSIS A oal of eamples were obaned by sng several facor combnaons ha nvolve waer deph above sep h 0 =,, and 6 m, sep hegh d =, 4, and 6 m, and average flow velocy above sep U 0 = 0, 5, 0, 30, and 40 m/s. The resls are lsed n Table 3 and llsraed n Fg.. To esablsh reglary among he nmercal resls, he smlaon resls were made dmensonless based on sep hegh d and on he average velocy above sep U 0. Epanson R se was defned as he rao of sep hegh d o waer deph above sep h 0, whereas R Ld was he rao of reaachmen L o sep hegh d. The dmensonless resls are lsed n Table 4. Eample Waer deph above sep Sep hegh Table 3 Resls of he nmercal smlaon Flow average velocy sbovesep s- Reaachmen lengh Eample Waer deph above sep Sep hegh Flow average velocy above sep s- Reaachmen lengh Fg. Smlaed resls of aachmen lengh

5 The smlaed resls n Table 3 were obaned based on he hypohess ha he downsream flow was sffcenly deep for he oflow from he sep o become a sbmerged e flow. Based on he nown waer deph, he reaachmen lengh was shown o be proporonal o sep hegh. Tha s, f he sep hegh s hgh, hen reaachmen s long. The waer flow feld nder dfferen hegh seps when he waer deph above he sep was m and he average flow velocy was 0 m/s s shown n Fg. 3. However, Fg. shows ha waer flow velocy above he sep nearly had no effec on reaachmen lengh when he sep hegh and he man waer deph above he sep were nown. Meanwhle, dfferen flow felds behnd he sep when he waer deph above he sep was m and he sep hegh was 4 m are presened n Fg. 5. The reaachmen lengh dd no change wh he velocy above he sep even f he sep hegh and he waer deph above he sep become nown becase of he followng reasons. () The waer flow behnd he sep became a e flow. Moreover, he velocy graden of he e bondary and he relave saonary feld ncreased, hs reslng n ncreasng shear sress. () A closed area was formed by he boom bondary of he hgh-speed flow and he facade of he sep along wh he sllng basn boom becase of he waer flowng nder he sep. Gven he characerscs of hgh-speed waer flow, a vore flow srcre was formed when a par of he waer became nvolved n he hgh-speed man waer flow. The velocy graden of he vore flow srcre ncreased wh ncreasng velocy; hs ndcng ncreases n pressre graden and n he adsorpon for he man flow. The wo ressances nrodced a hs pon wh a spermposed force cancelled o he ncreasng nera ndced by ncreasng velocy, hs reslng n a response of he reaachmen lengh o velocy change. The dmensonless nmercal resls lsed n Table 4 show ha he Frode nmber Fr above he sep s beween.0 and 9.0, and ha he rao of he reaachmen lengh o he sep hegh s beween and 3. The vale of d/h 0 s beween and, whch s common n engneerng saons, whereas he vales of L/d have scaered o a ceran degree. However, he errors wh he average vale of L/d are ypcally smaller han 5%. Fg. 6, whch was llsraed accordng o he relaonshp beween L/d and d/h 0 n all engneerng saons, shows a crve well-fed by a qadrac polynomal wheren all calclaed pons have clear dsrbon reglary. When he vale of d/h 0 s nearly 4, he vale of L/d reaches mnmm. Table 4 Dmensonless resl of he nmercal smlaon Eample F r Rse=d/h 0 R Ld =L/d Eample F r R se =d/h 0 R Ld =L/d d=m d=4m d=6m Fg.3 Flow dsrbon nder dfferen sep hgh When h 0 =m and U 0 =0m/s

6 h 0 =m h 0 =m h 0 =6m Fg. 4 Flow dsrbon nder dfferen flow dephs when d 0 = 6 m and U 0 = 0m/s velocy=5m/s velocy=0m/s velocy=30m/s velocy=40m/s Fg. 5 Flow dsrbon nder dfferen veloces when h 0 = m and d = 4 m 4. ONLUSION Hydralc dsspaon performs well n eco-frendly dam consrcon. The problem of hgh speed a he boom of he floor, whch hreaens engneerng safey, s solved by seng a sep n fron of he sllng basn. Recenly, a nmber of hgh dam proecs have been se n a sllng basn wh a sep-down floor. Ths sdy sed a wo-phase flow nmercal mehod combned wh he RNG -ε rblence model and he VOF mehod o nvesgae he relaonshp among reaachmen lengh, sep hegh, as well as waer deph and velocy above he sep. The nmercal smlaon resls show ha when he sep hegh s nown, he reaachmen lengh s proporonal o he waer deph above he sep. onversely, when he waer deph above he sep s nown, he reaachmen lengh s proporonal o he sep hegh. However, when he sep hegh and he waer deph above he sep are nown, he velocy change n he sep nearly has no effec on he reaachmen lengh. Meanwhle, he dmensonless he nmercal smlaon resls shows ha a qadrac relaonshp s ehbed by he rao of he reaachmen lengh o he sep hegh L/d, and ha rao d/h 0 can be obaned. Ths rao reaches mnmm when d/h 0 = 4.

7 L/d 4 3 y = R = d/h 0 Fg. 6 Relaon beween L/d and d/h 0 5. REFERENES Sn Shange (009), Smmary of research on flood dscharge and energy dsspaon of hgh dams n hna, J. hna Inse of Waer Resorces and Hydropower Research, 7(): Gao Jzhang, Dong Xngln, L Jgang (008). Research and applcaon of eco-frendly energy dsspaon echnology-nernal energy dsspaon. J. Hydralc Engneerng, 39(0):76-8. Hager WH (99). Energy dsspaors and hydralc mp, Klwer Academc Pblcaons, Dordrech, The Neherlands. pp Sn Shange, L Haao, Xa Qngf, Wang Xaosong (005). Sdy on sllng basn wh sep-down floor for energy dsspaon of hydralc mp n hgh dams. J. Hydralc Engneerng, 36(0): heng Xang, hen Yongchan, Lo ln (006). Nmercal smlaon of flow on sepped spllway. J. Scence n hna Ser. E Technologcal Scences, 36(): Flen Inc, Flen 6. User s Gde,Febrary, 003. Dong Zhyong (997), Impngng es, Ocean Press, Beng (n hnese). Y hangzhao (993), Trblen Jes, Hgher Edcaon Press, Beng (n hnese).