Hydraulic jump in stilling basin with vertical end sill

Transcription

1 International Journal of Phical Science Vol. (), pp. -9, Januar, Available online at ISSN 99-9 Academic Journal Full Length Reearch Paper Hdraulic jump in tilling bain with vertical end ill A. Alikhani, R. Behrozi-Rad and M. Fathi-Moghadam 3 * Department of Civil Engineering, Qom Univerit, Qom, Iran. School of Water Science Engineering, Shahid Chamran Univerit, Ahvaz, Iran. 3 School of Water Science Engineering, Shahid Chamran Univerit, Ahvaz, Iran. Accepted 6 November, 9 Stilling bain with dentiated or continuou ill are frequentl ued a energ diipater downtream of hdraulic tructure. In thi tud, experiment are conducted to evaluate effect of a ingle vertical continuou ill and it poition on control of depth and length of a forced jump in tilling bain without conidering tailwater depth which i variable and totall controlled b downtream river condition. A ill with five different height wa placed at three different longitudinal ditance along a caled model of a tilling bain. The hdraulic characteritic of the jump were meaured and compared with the claical hdraulic jump under variable dicharge. Reult of experiment confirmed ignificant effect of the ill on diipation of energ. A new relationhip wa developed between ill height and poition, equent depth ratio, and length of tilling bain. The advantage of the propoed relationhip in practice i it capabilit to deign tilling bain where tailwater depth i unpredictable Ke word: Hdraulic jump, baffle block, equent depth. INTRODUCTION Kinetic energ of water over the pillwa mut be diipated in order to prevent evere couring of downtream riverbed and failure of downtream tructure. The hut block and ill with different configuration are ued in the tilling bain to diturb water and diipate large amount water energ through formation of a hdraulic jump. To enure proper performance and energ diipation, the bain hould be deigned to reduce the equent depth of the hdraulic jump and keep it le than the tailwater depth. Otherwie jump will weep out of the bain and downtream couring will be unavoidable. To reduce the equent depth particularl where the tailwater depth i too mall (normall where downtream of the tructure i teep), a continuou ill can control and tabilize the jump, thu reducing the bain length. Sill height, poition and configuration (where more than one ill i ued) have coniderable impact on the jump and diipation of water energ. Hager (99) claified the jump over a vertical ill into A-jump, B-jump, minimum B-jump, C-jump and D-jump. The A-jump i claical hdraulic jump which i charac- *Correponding author. dramiralikhani@qom.ac.ir. Tel: terized b the maximum equent depth ratio (where ill i far awa to affect the jump). B decreaing the tailwater depth, toe of jump move toward the ill and a B-jump occur in which the flow i coniderabl modified b ill and the treamline pattern become curved over ill. Alo the height of bottom roller grow and a urface boil appear at the rear ill ide, et without ignificantl changing the free urface profile. A the tailwater depth decreae more, the ditance between the toe of the jump and uptream ill face i further reduced and the curved flow pattern over the ill i amplified. Morever, the urface current tart to plunge behind the ill, et without reaching the channel bottom. A further characteritic of uch flow, referred to a minimum B-jump, i the formation of a econd roller at the downtream ill zone and a C-jump i characterized b having the maximum difference between the depth of flow over the ill and the tailwater depth. D-jump initiate when flow i diturbed more and roller wave can reach the bed and couring become expectable. When tailwater depth i low, D- jump ma appear ooner than normal condition allow. Ohtu et al. () preented the upper limit of the inflow Froude number for undular-jump formation in mooth rectangular channel. It ha been found that the formation of undular jump depend not onl on the inflow Froude number but on the boundar-laer develop-

2 6 Int. J. Ph. Sci. Figure. Forced hdraulic jump in tilling bain with a continuou ill. ment at the toe of the jump under condition in which the effect of the apect ratio and the Renold number on the flow condition are negligible. Furthermore, Debabeche and Achour (7) tudied the effect of a continuou ill on hdraulic jump in a triangle channel. Deng et al. (7) repreented the prototpe meaurement of preure fluctuation for hdraulic jump while a tud deal with tatitical anali of preure fluctuation at the bottom of patial hdraulic jump with abrupt lateral expanion wa conducted b Yan et al., (6). The effect of the channel expanion ratio and inflow condition on the power pectral and dominant frequenc were examined. Preure data were recorded for different Froude number ranging from and channel expanion ratio ranging from A numerical imulation of minimum B-jump in horizontal rectangular channel having an abrupt drop i given b Toka et al. (8). Before that, A-tpe jump at a poitive tep wa imulated numericall b Altan-Sakara and Toka (). Review of literature reveal that previou tudie on forced hdraulic jump b large rel on tailwater depth downtream of the tilling bain. For the ame flow and jump condition, tailwater depth can be different a it i highl controlled b lope and cro ection of river downtream of the bain. The purpoe of thi tud i to propoe deign criteria for etimation of the tilling bain length without conideration of tailwater. Thi i done b creating and teting forced hdraulic jump uing a ingle continuou ill with variable height and poition in a caled model of a tilling bain. MATERIALS AND METHOD Theor Conider a tilling bain at the end of a chute in which a rectangular continuou ill located a ditance of L B from the entrance i ued to develop a forced hdraulic jump (Figure ). The effective hdraulic parameter are hown in the figure. 3 and x coordinate the point for maximum depth of flow over the ill and ditance from the beginning of the bain. The following functional relationhip among ignificant parameter i ued to characterize the forced hdraulic jump due to the preence of a continuou ill in a rectangular tilling bain. f ( h,,, 3, v, x, L, L, i, g, ρ, µ ) = B j () Where; h i the height of ill, and v are depth and average velocit of the upercritical tream at ditance x uptream of the ill, i the equent depth of jump (or in fact flow depth immediatel after ill for a forced jump), 3 i maximum flow depth uptream of the ill. L B i the length of the tilling bain or ditance from the beginning of the tilling bain to the uptream face of the ill, L j i the length of the hdraulic jump, i i channel lope, g i gravit, ρ and µ are water denit and vicoit repectivel. Auming a horizontal tilling bain (i = ) and full turbulent flow independent of Renold number, the dimenionle parameter are ummarized a: f h 3 x LB,,,,, F = Lj According to Belanger Equation, the equent depth ratio for a claical hdraulic jump i given b, ( ) + 8 Y = = F (3) Where; F follow, i the equent depth of claical hdraulic jump. For., the equent depth ratio can be approximated a Y = F (4) Baed on experimental obervation of Hager (99), the following relation wa found when a continuou ill i located in front of the hdraulic jump. Y = = Y Y Where the ill effect compared to a claical jump (Y ) i expreed b the following relationhip. β Y = α S (6) The coefficient (, ) depend on the tpe of hdraulic jump. () ()

3 Alikhani et al. 7 (a) LB=93.3 mm 3/ F h/lb=.7 h/lb=.4 h/lb=. h/lb=.8 h/lb=.3 (b) B=33 mm 3/ 3 Claical Hdraulic Jump 6 8 F h/lb=. h/lb=. h/lb=. h/lb=. h/lb=. (c) LB=67 mm 3/ 3 Claical Hdraulic Jump 6 8 F h/lb=.4 h/lb=.8 h/lb=. h/lb=.6 "Claical Hdraulic Jump" h/lb=. Figure. Variation of maximum depth ratio with ill height ratio. According to Equation 6, the maximum amount of Y can be obtained b increaing the height of the ill. If the height of the ill (h) become larger than a limit value S L, the ill flow i changed into weir flow. The following relationhip i uggeted for the limited value of S L (Hager (99). S.64 L = F (7) 6 For a given F, the relative height of ill mut be maller than S L. Thi condition mut be atified for the propoed deign criteria of thi tud. Experiment Experiment were conducted on a /3 cale model of Galabar dam pillwa in the Reearch Intitute of the Minitr of Power of Iran. Thi wa done to develop the deign criteria for etimation of tilling bain length for the forced jump a reult of a continuou ill at the end of a horizontal bain. A ingle ill with five height of 6.7, 3.3,., 6.7, and 33.3 cm wa teted at 3 ditance of 93.3, 33, and 67 cm from beginning of the bain. Tet were conducted with man dicharge around the deigned dicharge baed on and return ear and PMF (Probable Maximum Flood) which were previoul etimated to be.7, 33.8, and 9.9 m 3 ec - repectivel. RESULTS AND DISCUSSIONS The main purpoe of thi tud wa the development of deign criteria for etimating the tilling bain length where a continuou ill i located at the downtream end of the bain. Since tailwater depth i variable and completel dependent on downtream condition, the advantage of the preent work i elimination of the tailwater depth from the anali. Figure (a) illutrate the variation of the maximum depth ratio 3 / with Froude number for the forced hdraulic jump due to a continuou ill at L B = 93.3 cm with five height. Similar i repeated in Figure b and c for L B = 33 and 67 cm. For imilar inflow, the reult of maximum depth ratio 3 / for forced hdraulic jump in thi tud i ignificantl higher than thoe for free hdraulic jump calculated from Belanger equation (Equation 3). In addition, Figure 3(a) - 3(c) demontrate the variation of the equent depth ratio / with Froude number for the forced hdraulic jump due to a continuou ill for fifteen ratio of h/l B. An invere reult wa obtained when the were compared with the equent depth ratio of free hdraulic jump from Equation 3 for the ame flow condition. Thi how ignificant effect of the ill on the reduction of flow depth after it. All figure prove an increae in the maximum depth and a decreae in the equent depth if the ill height i increaed for a particular L B. Although maller ill poition howed to have more effect on increaing of 3 and reducing of, more experiment are required to find the mot effective ill ditance. However, ill poition larger than 67 cm did not how a ignificant effect on and 3. The experiment revealed that both and 3 repon-

4 8 Int. J. Ph. Sci. (a) LB=93.3 mm / 3 S = h/ Karki & Kumar 99 Hager et al. 986 Ohtu 98 Rand 96 Current Stud Ohtu et al F h/lb=.4 h/lb=. (b) LB=33 mm / h/lb=.8 h/lb=.3 Claical Hdraulic Jump LB/h= F h/lb=. h/lb=. h/lb=. h/lb=. h/lb=. (c) LB=67 mm / Claical Hdraulic Jump 6 8 F h/lb=.4 h/lb=. h/lb=.6 h/lb=. Claical Hdraulic Jump h/lb=.8 Figure 3. Variation of equent depth ratio with ill height ratio. ded to ratio of h/l B much better than h or L B alone, and Fr Figure 4. Comparion of the reult with previou tudie (from Ohtu et al., 996) for ratio of h/l B le than. no ignificant effect wa oberved on both and 3. Reult of thi tud for a relation between Froude number (F ) and ill height ratio (h/ ) are compared with previou tudie (from Ohtu et al., 996) in Figure 4. Previou tudie b large have been concentrated on condition to initiate an incipient jump b regular end ill. For thi reaon, while reult are concurred with previou tudie for lower Froude number and about incipient condition, the are in line with Karki' reult deviate from other tudie at higher Froude number. Main reaon for deviation i the tallne of the ill and control of flow with higher Froude number in horter ditance. However, effect due to difference in cale and boundar flow condition might be ground for divergence of the reult in Figure 4. DESIGN CRITERIA FOR SILL-CONTROLLED STILLING BASIN The reult in thi tud in concurrence with previou tudie proved coniderable effect of ill height and poition in reduction of the equent depth and length of the tilling bain. Thu, proper deign of the ill height and it location have ignificant contribution to cot effectivene of a tilling bain. Baed on the experiment reult, a relationhip between the mot effective dimenionle parameter in Equation i contructed to help deign of a illcontrolled tilling bain. Figure how the relationhip between inflow Froude number, ratio of L B / and h/ a main parameter to expre inflow condition, tilling bain and ill geometr repectivel. Figure enable the deign of an end ill-controlled tilling bain (etimation of L B and h), once the inflow condition and F are known. Diagram are contructed o that b electing a bain length of L B, the

5 Alikhani et al. 9 ACKNOWLEDGEMENTS F =4 =6 =8 = The author acknowledge the Shahid Chamran Univerit of Ahwaz and Qom Univerit of Iran a well a the Reearch Intitute of the Minitr of Power of Iran for facilitation of the experiment LB / Figure. Deign diagram for jump in ill-controlled tilling bain ( = h/ ). required ill height (h) can be predicted. The predicted ill height (h) hould be checked to be le than the Froude number baed parameter S L calculated from Equation 7. Thi ma require everal etimation of L B. Baed on the extenive teting and obervation in thi tud, it i recommended to elect initial tilling bain length L B baed on the following relationhip. ( ) LB ( ) 3 (8) For L B maller than 3( - ), the jump plunged downtream of the ill and couring ma be unavoidable, while for larger value than ( - ) the effect of the ill wa not ignificant. Figure and the propoed deign criteria are baed on inflow Froude number ranging from 4 to around and = h / from to 8. CONCLUSION Experiment were conducted on a /3 cale model of a dam pillwa and tilling bain to propoe a deign criteria for forced hdraulic jump a a reult of ingle continuou ill at the end of tilling bain. The objective wa to etimate the efficient ill height and ditance to reduce jump and bain length, thu cot. Deign criteria i baicall developed for B-jump with inflow Froude number F = 4- and h/ = - 8. However, an over deign of ill height to about % and 3% will facilitate it for C-jump and D-jump repectivel. Comparion of forced jump reult of thi tud with free jump relationhip confirm up to 3% reduction in length of tilling bain where ill i there to control the jump. The advantage of the propoed method i it implicit in practice and it capabilit to etimate ill height and bain length for mot flow tpe without conidering tailwater depth which i controlled b lope and river condition downtream of the bain. Notation: F ; approaching Froude number, g ; acceleration due to gravit, h ; height of ill, i ; channel lope, L ; length of tilling bain, L ; length of B hdraulic jump, L r ; length of roller for claical hdraulic jump, µ ; water vicoit, ρ ; water denit, ; relative ill height, v ; average velocit of upercritical flow, x ; ditance from toe of the jump to uptream ill face, ; depth of upercritical flow, ; equent depth of forced hdraulic jump, ; equent depth of claical hdraulic jump, 3 ; maximum depth of flow over the ill, t ; tailwater depth, Y ; equent depth ratio for forced hdraulic jump, Y ; equent depth ratio for claical hdraulic jump, Y 3 ; maximum depth ratio for forced hdraulic jump, Y ; depth effect of ill. REFERENCE Altan-Sakara AB, Toka ND (). Numerical imulation of A-tpe hdraulic jump at poitive tep. Canadian J. Civil Eng. 7(4): doi:.39/cjce Debabeche M, Achour B (7). Effect of ill in the hdraulic jump in a triangular channel. J. Hdraul. Re. 4(): Deng Z, Guench GR, Richmond MC, Weiland MA, Caron TJ (7). Prototpe meaurement of preure fluctuation in The Dalle Dam tilling bain, J. of Hdraul. Re. 4(): Hager WH (99). Energ diipator and hdraulic jump, Kluwer Academic Publication, Dordrecht, The Netherland. P: iipator+and+hdraulic+jump%e%8%9d,&ource=gb_ummar _&cad=. Ohtu I, Yauda Y, Gotoch H (). Hdraulic condition for undular jump formation. J. Hdraul. Re. 39(): Ohtu I, Yauda Y, Hahiba H (996). Incipient jump condition for flow over a vertical ill. J. of Hdraulic Eng., ASCE (8): doi:.6/(asce) (996):8(46). Toka ND, Altan-Sakara AB, Eki E (8). Numerical imulation of minimum B-jump at abrupt drop. Inter. J. for Numerical Method in Fluid, 6 (9):6 63. doi:./fld.. Yan Z, Zhou C, Lup S (6). Preure fluctuation beneath patial hdraulic jump. J. Hdrodn. 8(6): doi:.6/ S- 68(7)6- doi:.6/s68(7) 6-. j