This Technical Note presents the results of a large set of laboratory tests and tries to determine the conditions that ensure the existence of a water cushion that is not expelled by the impingement of a nappe (effective cushion). Second, values of mean dynamic pressures at the stagnation point of nonsymmetric plunge pools downstream of arch dams are assessed

Dolz, Jose

Puertas, J.

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TECHNICAL NOTESDownloaded from ascelibrary.org by Univ Politec Catalunya on 06/25/20. Copyright ASCE. For personal use only; all rights reserved.ensure theicPlunge Pool Pressures Due to a Falling Rectangular JetJ. Puertas1 and J. Dolz2Abstract: This Technical Note presents the results of a large set of laboratory tests and tries to determine the conditions thatexistence of a water cushion that is not expelled by the impingement of a nappe~effective cushion!. Second, values of mean dynampressures at the stagnation point of nonsymmetric plunge pools downstream of arch dams are assessed.DOI: 10.1061/~ASCE!0733-9429~2005!131:5~404!CE Database subject headings: Hydraulic jets; Laboratory tests; Hydraulic pressure; Dams, arch.s forgularn ofct anae, sonergyandmallerhich.thengac-ppe.n isnapps de-f ahion.en thefd inula totdnt;ns;fl toforveryetseail:hoolain.sionste bygingviewer 13,5/5-IntroductionFree overflow spillways are frequently constructed as outletarch dams. These structures generate high-velocity rectanjets, or nappes, impacting downstream. To avoid direct actiothe nappe on the riverbed it is common practice to construauxiliary structure ~downstream cofferdam!, which createsplunge pool. This pool receives the impact of the falling nappwhen the nappe reaches the riverbed, it has lost most of its ei.e., its scouring capacity.The nappe absorbs a certain amount of air during its fall,the thickness of the compact core of the nappe becomes sdue to gravity. A certain degree of turbulence is reached, wdepends on the velocity of the water in the nappe~Ervine et al1997! and on outlet conditions.The thickness of the water cushion in the plunge pool ismain point of this Technical Note. Aki, referred by Cui GuaTao et al.~1985!, provided a classification of water cushionscording to their behavior when receiving the impact of a naTwo different situations can be pointed out. First, the cushionot deep enough to absorb the nappe and the energy of theis great enough to expel the cushion, so a hydraulic jump iveloped in the stilling basin near the cofferdam@Fig. 1~b!#. Sec-ond @Fig. 1~a!#, the cushion is able to avoid the formation ojump, and a certain amount of energy is absorbed by the cusA separation is proposed based upon the relationship betwethicknesses of the cushionshd and the nappesBd. The goodness othis definition of the separation line will be discussed.Studies of the pressure field on a plunge pool floor starte1Professor, Univ. Da Coruña, Civil Engineering School~ETS I.Caminos!, Campus de Elviña, 15192 A Coruña, Spain. E-mjpuertas@udc.es2Professor, Univ. Politècnica de Catalunya, Civil Engineering Sc~ETS I. Caminos!, Campus Nord. Módulo D-1, 08034 Barcelona, SpE-mail: j.dolz@upc.esNote. Discussion open until October 1, 2005. Separate discusmust be submitted for individual papers. To extend the closing daone month, a written request must be filed with the ASCE ManaEditor. The manuscript for this technical note was submitted for reand possible publication on May 10, 2002; approved on Septemb2004. This technical note is part of theJournal of Hydraulic Engineer-ing, Vol. 131, No. 5, May 1, 2005. ©ASCE, ISSN 0733-9429/200404–407/$25.00.404 / JOURNAL OF HYDRAULIC ENGINEERING © ASCE / MAY 2005 J. Hydraul. Eng., 2005, ,ethe 1960s. A classic reference is the study by Cola~1966! who,based on the momentum conservation law, proposed a formevaluate the mean dynamic pressure at the stagnation poin~thepoint where the nappe reaches the floor!. The parameters involveand the structure of the equation wereDPmax= Crv2B2hs1dwhereDPmax=mean dynamic pressure at the stagnation poir=water density;C=coefficient to be fit by experimental meav=velocity of the water when reaching the pool;B=thickness othe nappe; andh=thickness of the cushion, which is set equathe cofferdam height.The coefficientC has been calculated by several writersvery heterogeneous experimental facilities and conditionsheterogeneous~Cola 1966; Hartung and Häusler 1973; Ervineal. 1997!. The values ofC are in the range of 5–8 for thewriters.Fig. 1. ~a! Effective cushion and~b! noneffective cushion131(5): 404-407 hichdis-lutelybeenirectlytethisof, thennotrfaceyperi-cts insat is-con-hion.ppern iso-e ba-htsthe-ut, ashion,e0°, soclud-e pa-v-ooludewheng fallunitfu-noteisendsetri-pat-whosep ishethetheare,thecush-mustd byationgsa sub-ofDownloaded from ascelibrary.org by Univ Politec Catalunya on 06/25/20. Copyright ASCE. For personal use only; all rights reserved.A certain turbulence level is achieved in the nappes, wcould be calculated as a function of the fall height and thecharge, as the water level in the upper resrervoir was absostable. However, no direct measurements of turbulence havedone. Also the aeration degree of the nappes has not been dmeasured. Ervine et al.~1997! provides information to calculaturbulence effects on falling nappes. Most of the papers ontopic dealt with symmetric pools~upstream and downstreamthe jet!. If one considers the free overflow over an arch dampool often is not symmetric.Franzetti ~1980! did experimental work with a model of aarch dam, which had a fall height of 1.6 m. The nappe wasvery thick, so some of the results may be affected by the sutension, which compacts the nappe. The “C” values obtained bFranzetti are in the range of only 2.15–5.74. Franzetti’s exments are quite similar to those presented here.Some other papers deal with turbulence and aeration effefalling jets, as the one by Canepa and Hager~2003!. These effectare not considered in this Technical Note.This study has tried to analyze, for nonsymmetric pools:• The conditions that ensure the existence of a cushion thnot expelled by the impingement of the nappe~effective cushion!; and• The mean dynamic pressure at the stagnation point whensidering a nonbroken nappe impinging on an effective cusExperimental MethodologyExperimental FacilitiesThe experimental equipment used in this research was• A structure based on two orthoedric basins, where the uone spills the water to the lower one, in which the cushioformed and pressures are measured~Fig. 2!. The spillway~1.2 m wide! is straight, in order to work under twdimensional conditions. The vertical distance between thsins may be varied in order to work with different fall heigsh+Hd from a value of 2 up to 5.5 m. The thickness ofcushion and the discharge may also be varied: 0øhø0.8 m,0.02 m2/søqø0.2 m2/s.• A set of piezoresistive sensors~from 4 up to 6! ~Fig. 2!, whichmeasure at a frequency of 40 Hz for 1 min~2,400 measurements per test!.Tests to ensure two-dimensional character were carried owell as tests to ensure the effect of the length of the cuswhich, according to Armengou~1991!, happens to be null if thFig. 2. Experimental facilities. Upper and lower basin. Setsensors.cushion has a minimum length. This length has been set at 3.2 m.J J. Hydraul. Eng., 2005, The impact angle between the nappe and the slab is nearly 9no effect of the angle has been taken into account.Dimensional AnalysisIn order to apply the results of this research to structures ining a falling nappe, we used nondimensional parameters. Thrameters involved@Fig. 1~a!# ~taking into account pressure, graity, and inertia forces! areDp/gH ~Dynamic pressure recorded on a point of the pfloor versus fall height.Dp=p−gh!;h/H ~cushion thickness versus fall height!; andq/Î2gH3=B/H ~Nappe thickness versus fall height; Fronumber. It can be considered as an ideal nappe thicknessneglecting turbulence and aeration effects.!Ten large arch dams in Spain have been analyzed, coverinheights from 37 up to 135 m, in order to obtain their meanH andq values. The mean fall height is about 89 m, and the meandischarge is about 10.9 m2/s ~6.5 up to 23.53!. The mean value oB is 0.26 m ~0.18 up to 0.46!, and the mean value ofB/H is0.0034~B/H about 1.6e−3–8.6e−3!. As cushion heights are usally not under 4 m, and concrete-lined pools are usuallydeeper than 8–12 m, expected values forh/H are in the rang0.04–0.13, and the values forB/h are about 0.025–0.085. Thrange has been widely covered in the experimental work.ResultsThe behavior of the cushion when a nappe is impinging depon its thickness. As has been mentioned above for nonsymmcal plunge pools without any influences from recirculationterns, a separation line can be established between poolsshape remain unaltered and pools in which a hydraulic jumdeveloped@Figs. 1~a and b!#. The frontier proposed by Aki, whiccan be found in Cui Guang Tao et al.~1986!, depends on threlationship B/h, where h=thickness of the cushion andB=thickness of the nappe as it enters the cushion.This relationship does not take into account that bothheight of the falling nappe and the discharge contribute topower provided to the cushion. The parameterB cannot explainthis phenomenon, asB is a relationship betweenq andH1/2B =qÎ2gHs2dThe parameters involved in the creation of a hydraulic jumpon the one hand,H andq: the higher they are, the more energynappe will have; and on the other hand, the thickness of theion. Thus the parameter that could explain the separationhave the following structure:haqbHgs3dThe forces involved in the ejection of the water cushion causethe nappe seem to be analogous to that involved in the formof a hydraulic jump in a channel@Fig. 1~b!#. When considerinthe momentum equation, and assumingF1 andF2 to be the forcegenerated by the pressures in a supercritical regime and incritical regime, respectively,F1 − F2 = rQsv2 − v1d s4dIf we acceptF2@F1 andv1@v2, we haveOURNAL OF HYDRAULIC ENGINEERING © ASCE / MAY 2005 / 405131(5): 404-407 fol-or-ingg toll thefndot ane re-ing-ationfectseanst beion,n theutms ofonlythee ofp istheto bestag-ethise ex-enceex-ear, arestedsh-eredzeroanpointearDownloaded from ascelibrary.org by Univ Politec Catalunya on 06/25/20. Copyright ASCE. For personal use only; all rights reserved.F2 > rQv1 s5dIf the pressure distribution is considered as hydrostatic thelowing relations holds:rgh2/2 = rqv1 s6dIf the water velocity along the floor is considered linearly proptional to the velocity of the water in the nappe, then the followrelationship holds:gh2/2 = AqÎ2gH s7dOr, in terms of nondimensional numbersN =S hHD2BH=h2qÎ2gH= 4A s8dThe N parameter gives a relationship between forces tryineject and forces trying to maintain the cushion. It satisfies aexpected conditions of the parametersq, h, andH, and the sign otheir exponents. Nevertheless,N does not consider turbulence aaeration effects. When these effects may be neglected,N is con-sidered to be an accurate parameter to explain whether or neffective cushion exists in asymmetrical plunge pools whercirculation patterns are considered of no influence to the imping nappe.Pressure measurements have been done at some locclearly downstream of the stagnation line, where dynamic efare negligible, in order to validate this fomulation. The mpressure registered in a point downstream of the nappe muaboutgh if a water cushion exists. If there is no effective cushthe pressure registered will be quite lower thangh.As can be seen in Fig. 3, there is a relationship betweevalues ofN and the values ofp/gh. The areas with and withoan effective cushion are separated by the lineN=0.6. If N has avalue of over 0.6, the cushion is considered effective.The presence of a cushion makes a great difference in terenergy dissipation. If there is a cushion, energy is lost notduring the fall, but also in the cushion itself before reachingfloor. Eddies are formed and their movement dissipates somthe energy. If the cushion is not effective, and a hydraulic jumformed, little energy is lost in the cushion before impactingfloor, and the dynamic pressures on the floor are expectedhigher for the same height and discharge.As mentioned before, the mean dynamic pressure at theFig. 3. Relationship betweenN and the quotient between the mepressure recorded and the expected hydrostatic pressure, atdownstream of the stagnation linenation point, Cola~1966!, can be written as406 / JOURNAL OF HYDRAULIC ENGINEERING © ASCE / MAY 2005 J. Hydraul. Eng., 2005, sDPmax= Crv2B2hs9dThis expression includes the termh, i.e., the thickness of thcushion. If the cushion is not effective,h is not a relevant termand the expression by Cola would be inappropriate. To verifystatement, a test has been carried out. Cola’s formula can bpressed asDpmaxgH= CBhs10dThe expressionDpmaxgH= A + CBHhHs11dhas been tested with a Student “t” test with a 90% confidlevel for the hypothesisA=0 for both the data from effectivcushion experimentsN.0.6d and the data from noneffective eperimentssNø0.6d. The plot of these data is as follows~Fig. 4!.The statistics of the fits, whose interest is to confirm if a lintrend without intercept can be considered as a fitting curveshown in Table 1.The values from effective cushion tests are properly adjuby a linear regression without intercept~Cola’s theory! sC=3.8d.The fits with all the data or with the data from noneffective cuions do not show this behavior if the above figures are consid~the confidence interval for the intercept does not include thevalue!.sFig. 4. Relationship betweenDpmax/gH and B/h for data with~a! and without~b! an effective cushion. Poor agreement to a lintrend of the right-hand data may be observed.Table 1. Confidence Intevals for Linear Trends BetweenDpmax/gHandB/hFactor R2 Confidence intervalATotal 0.55 0.023 0.058Without effective cushion 0.3 0.011 0.15With effective cushion 0.75 −0.02 0.006131(5): 404-407 data.la’shaveola isppesionst thens.e andll oftabil-aterppesda.PhDenoagem-de-a din-Downloaded from ascelibrary.org by Univ Politec Catalunya on 06/25/20. Copyright ASCE. For personal use only; all rights reserved.Thus, two behaviors may be observed, one for each set ofThe data from effective cushions seem to fit quite well to Coexpression, while the data from noneffective cushions do nota good adjustment. This may be explained by the fact thath hasno influence in the second case and so the expression by Cnot suitable for this set of data.ConclusionsThe main conclusions of this research on vertically falling naare• A frontier can be established between effective water cushand noneffective water cushions, based on the so-calledN pa-rameter: forN,0.6 a hydraulic jump developes, forN.0.6nappe diffuses through the cushion.• The expression by Cola for mean dynamic pressures astagnation point is only useful for effective water cushioThe value obtained for the constantsCd is about 3.8.The present research did not account for nappe turbulencaeration and eventual plunge pool recirculation currents. Athese phenomena might have a significant influence on the sity of the nappe upon impact and thus the efficiency of the wcushion. To account for these effects in prototype falling nafurther research must be done.NotationThe following symbols are used in this technical note:~All parameters have been evaluated using SI unit system!A 5 Generic parameter;B 5 thickness of the nappe;C 5 Cola’s linear trend coefficient;J J. Hydraul. Eng., 2005, D 5 jet diameter;F 5 generic force;g 5 acceleration due to gravity;H 5 fall height;h 5 thickness of cushion;p 5 pressure;Q 5 discharge;q 5 unit discharge;R2 5 determination coefficient;r 5 distance to the jet center~for circular jets!;v 5 water velocity;g 5 specific gravity of water;Dp 5 dynamic pressure; andr 5 water density.ReferencesArmengou, J.~2001!. “Vertido libre por coronación en presas bóveAnálisis del campo de presiones en el cuenco amortiguador.”thesis, Universitat Politècnica de Catalunya.Canepa, S., and Hager, W.~2003!. “Effect of jet air content on plungpool scour.”J. Hydraul. Eng., 129~5!, 358–365.Cola, R. ~1966!. “Diffusione di un getto piano verticale in un bacid’aqua d’altezza limitata.”Energ. Elettr., ~11!, 649–667.Cui, Guang Tao, Lin, Ji Yong, and Liang, Xing Rong,~1985!. “Efeito doimpacto, no leito do rio, da lamina descarregada sobre una barrabobada”[portuguese translation from the chinese, J. A. PintoCampos, LNEC, Lisboa]. Shuili xuebao, Beijing, ~8! 58–63.Ervine, D. A., Falvey, H. T., and Whiters, W.~1997!. “Pressure fluctuations on plunge pool floors.”J. Hydraul. Res., 35~2!, 257–284.Franzetti, S.~1980!. “Pressione idrodinamichi sul fondo di una vascsmorzamento.”Energ. Elettr., ~6!, 280–285.Hartung, F., and Häusler, E.~1973!. “Scours, stilling basins and dowstream protection under free overfall jets and dams.”Trans., 11thCongress on Large Dams, Madrid, Spain, Q.41, R.3., 39–56.OURNAL OF HYDRAULIC ENGINEERING © ASCE / MAY 2005 / 407131(5): 404-407 

Plunge pool pressures due to a falling rectangular jet

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Plunge pool pressures due to a falling rectangular jet

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