Physical modelling and scale effects of air-water flows on stepped spillways

Chanson et al. /.J Zhejiang Univ SCI 2005 64(3):243-250243Jourmal of Zhejiang University SCIENCEISSN 1009-3095http://www.zju.edu.cn/jzusJzUSE-mail: jzus@zju.edu.cnPhysical modelling and scale effects of air-water flowson stepped spillwaysCHANSON Hubert，GONZALEZ Carlos A.(Department of "Civil Engineering, The University of Queensland, Brisbane 4072, Australia)'E-mail: h.chanson@uq.cdu.auReceived Apr. l, 2004; revision accepted Jan. 20, 2005Abstract: During the last three decades, the introduction of new construction materials (e.g. RCC (Roller Compacted Concrete),strengthened gabions) has increased the interest for stepped channels and spillways. However stepped chute hydraulics is notsimple, because of different flow regimes and importantly because of very-strong interactions between entrained air and turbu-lence. In this study, new air-water flow measurements were conducted in two large-size stepped chute facilities with two stepheights in each facility to study experimental distortion caused by scale effects and the soundness of result extrapolation to pro-totypes. Experimental data included distributions of air concentration, air-water flow velocity, bubble frequency, bubble chordlength and air-water flow turbulence intensity. For a Froude similitude, the results implied that scale effects were observed in bothfacilities, although the geometric scaling ratio was only L,; =2 in each case. The selection of the criterion for scale efects is a criticalthough lttle scale effects were seen in terms of void fraction and velocity distributions. Overall the findings emphasize thatphysical modelling of stepped chutes based upon a Froude similitude is more sensitive to scale effects than classical smooth-invertchute studies, and this is consistent with basic dimensional analysis developed herein.Key words: Physical modelling, Scale effects, Stepped spillways, Air entrainment, Air-water flow measurementsdoi: 10.163 1/jzus.2005.A0243Document code: ACLC number: TU411INTRODUCTIONroller compacted concrete， with the constructiontechniques of gabion dams and with debris flowThe stepped channel design has been used forconveyance technique (Fig. l). During the last threemore than 3500 years. Greek and Minoan engineers decades, research in the hydraulics of stepped spill-were probably the first to design an overflow stepped ways has been very active with 2 books, 2 interna-weir and stepped storm waterways respectively tional workshops and over 35 international refereed(Chanson, 2001). Later, Roman, Moslem, Mughaljournal articles (Ohtsu and Yasuda, 1998; Minor andand Spanish designers used a similar technique. The Hager, 2000; Chanson, 2001). This was associatedsteps increase significantly the rate of energy dissi- with the completion of the world's largest steppedpation taking place on the channel face, reducing the sillways, in terms of design discharge capacity: e.g,size of the required downstream energy disipation Shuidong and Dachaoshan dams (Lin and Han, 2001).and the risks of scouring. Recently, new constructionFor a given stepped chute, waters flow as amaterials (e.g. RCC, strengthened gabions) have in- succession of free falling nappes (nappe flow regime)creased the interest for stepped channels and spill- at small discharges (Chanson, 1994; Chamani andways. The construction of stepped chutes is com-Rajaratnam, 1994; Toombes, 2002). For an interme-patible with the slipforming and placing methods ofdiate range of flow rates, a transition flow regime is .observed (Chanson and Toombes, 2004). Most pro-'Project supported by the National Council for Science and Tech-totype spillway中国煤化工es per unitnology of Mexico (CONACYT)width (i.e. skim:h the wat-MYHCNM HG.244 .Chanson et al. 1J Zhejiang Univ SCI 2005 6.4(3):243-250a)b)(c(d)Fig.1 Examples of stepped silways and waterwaysscheme. Stepped chute characteristics: h=0.43 m, 0= -59°, W=96 m, Gdes=1.15 m^/s; (b) Bucca weir (Australia) on 23 Dec.2001.Irigation water supply for sugar cane. Stepped chute characteristics: h=0.6 m, 0= 63.49, W=130.8 m, 9es=55.4 m7/s. Note thetilting splitters installed at the crest to aerate the deflected nappe at low flows, reducing noise and vibrations to the structure; (C)Gabion stepped weir at Robina, Gold Coast (Australia) on 2 Apr. 1997, shortly after completion. Stepped weir characteristics:h=0.6 m, W=10.5 m, Reno mattress construction; (d) Artificial stepped waterway along Ruisseau Ravin de St Julien, inSt-Julien-Mont-Denis (France), on 11 Feb. 2004. Looking upstream with a slit check dam in background, the waterway isdesigned to carry safely debris flow around the townshipers skim as a coherent stream over the pseudo-bottomFlowformed by step edges (Figs.2 and 3). Skimming flowsare characterized by very-significant form losses andmomentum transfer from the main stream to the re-circulation zones (Chanson et al, 2002). There is anobvious analogy with skimming flows past large, CF.Velements and boundary layer flows past d-typeroughness (Knight and Macdonald, 1979; Djenidi etdeveloping shear layeral, 1999).Mixing layerStepped chute hydraulics is not simple, becauseFig.2 Skimming flow over a stepped chute: definitionof different flow regimes, but most importantly be- sketchcause of strong flow aeration, very-strong turbulence,and interactions between entrained air and turbulence(Chanson and Toombes, 2002). To date, lttle re- sis is supported by a series of systematic measure-search was conducted at the microscopic scale on the ments conducted in two large-size facilities with twocomplex nature of the flow and its physical modelling. step sizes each. The geometric scaling ratio was L, =2It is the purpose of this study to discuss similitude and in each case. TI中国煤化ierstandingscale effects affecting stepped chute flows. The analy- of scale effectsCwsfYHCNMH G.Chanson et al. /J Zhejiang Univ SCI 2005 6():243-250245entrained air bubble characteristics, and the geometryof the steps. Considering a skimming flow down astepped chute with flat horizontal steps at uniformequilibrium and for a prismatic rectangular channel, acomplete dimensional analysis yields a relationshipbetween the local air-water flow properties, and thefluid properties, physical constants, flow conditionsand step geometry:c,-V_ u'da(a)'Vgd'v'd'(1)=Fx:2:- 9w =:p. 9w.84 :d.W:a:'d d'Vgd'Pwμw'ρσ°h'n°hwhere C is the local void fraction; V is the local ve-locity; g is the gravity acceleration; d is the equivalentwater depth at uniform equilibrium; u' is a character-istic turbulent velocity; dab is a characteristic size ofentrained bubble; x is the coordinate in the flow di-b)rection measured from a step edge; y is the distanceFig.3 Photographs of skimming flows in Channel 2normal from the pseudo-bottom formed by the step(a) h=0.05 m, dJh=1.7; (b) h=0.10 m, dJ/h= 1.53edges; Gw is the water discharge per unit width; Pw andμw are the water density and dynamic viscosity re-spectively; σ is the surface tension between air andDIMENSIONAL ANALYSIS AND SIMILITUDEwater; W is the chute width; h is the step height; θ isthe angle between the pseudo-bottom and the hori-Basic analysiszontal, and ks' the skin roughness height (Fig.2). ForA dominant characteristic of sepped chute flows air-water flows, the equivalent clear water depth isis the strong flow aeration ('white waters') clearlydefined as:seen in prototype and laboratory (Fig.3). Theoreticalanalysis (and numerical study) is limited consideringd=j" (1-C)dythe large number of relevant equations: i.e, threebasic equations per phase plus a phase transfer equa-tion. Experimental investigations are also difficult butwhere Ygo is the depth where C=0.9. In Eq.(1) rightrecent advances in air-water flow instrumentationhand side, the 3rd, 4th and 5th dimensionless termsbrought new measuring systems enabling sccessful are Froude, Reynolds and Morton numbers respec-experiments (Chanson, 2002).tively, and the last four terms characterize the stepTraditionally model studies are performed withcavity shape and the skin friction effects on the cavitygeometrically similar models and the geometricwall. Note that any combination of dimensionlessscaling ratio L, is defined as the ratio of prototype to numbers is also dimensionless. One parameter amongmodel dimensions. Laboratory studies of air-waterthe Froude, Reynolds and Weber numbers may beflows require however the selection of an adequate replaced by the Morton number Mo=(g us )(ρwσ ) assimilitude.seen in Eq.(1) where the W eber number was replaced.The relevant parameters needed for any dimen-Further simplifcations may be derived bysional analysis include the fluid properties and considering the depth-averaged air-water flowphysical constants, the channel geometry and inflow properties. F中国煤化工uniformconditions, the air-water flow properties including the equilibrium,'YHCNMHG.246Chanson et al. 1J Zhejiang Univ SCI 2005 6.4(3):243-250Uwd. guo,.d.nusually, the same fluids (air and water) are used inF);今=0 (3) model and prototype, and the Morton number be-| Vgdμw°ρσ'mem'h' hh|comes an invariant.where Uw is the mean flow velocity (Uw=qw/d) andDiscussionCmean is the depth- averaged void fraction:Few studies tested systematically the validity ofa Froude similitude with geometric similarity usingsame fluids in model and prototype (Table 1). TheseCmemn =一J Cdy(4) were based upon a Froude similitude with undistortedgeometric scale and sometimes two-dimensionalmodels. Results are summarized in Table 1 (Column 3)In fe-surface flows, most laboratory studies are indicating conditions to avoid scale efects.based upon a Froude similitude (Henderson, 1966;BaCaRa (1991) described a systematic labora-Chanson, 2004). But cavity recirculation and motory investigation of M'Bali dam spillway with modelmentum exchanges between cavity and stream flowscales of L,= 10, 21.3, 25 and 42.7. (No protoype testare dominated by viscous effects suggesting the need was conducted.) For the smallest models (L,=25 andfor a Reynolds similitude, while the entrapment of air 42.7), the flow resistance was improperly reproduced.bubbles and the mechanisms of air bubble breakup Chanson et al.(2002) re-analyzed more than 38 modeland coalescence are dominated by surface tensionstudies and 4 prototype investigations with channeleffects implying the need for a Weber similitude. For slopes ranging from 5.7° up to 559, and with Reynoldsgeomtrically-similar models, it is impossible to sat- numbers between 3E+4 and 2E+8. They concludedisfy simultaneously Froude, Reynolds and Weber that physical modelling of flow resistance may besimilarities unless L,=1. In small size models (L,> >1)，conducted based upon a Froude similitude if labora-the air entrainment process may be affected by sig- tory flow conditions satisfy h>0.020 m and Re>1E+5.nificant scale effects. Wood (1991) and Chanson They added that true similarity of air entrainment was(1997) presented comprehensive reviews. Kobus achieved only for model scales L,<10. However de-(1984) ilustrated some applications.tailed studies of local air-water flow properties, in-Despite very simplistic assumptions, Eq.(1), and cluding present results, yielded more stringent condi-even Eq.(3), demonstrate that dynamic similarity of tions suggesting the impossibility to achieve dynamicstepped chute flows is impossible with geometrically similarity, even in large-size models (Table 1). In thesimilar models, unless working at full-scale, because present study, a Froude similitude was used as forof the large number of relevant parameters. Note that, most open channel flow studies and past studies.Table 1 Summary of systematic studies on stepped chute flows based upon a Froude similitudeStudyDefinition of scale effctsLimiting conditionsExperimental flow conditionsto avoid scale efectsBaCaRaFlow resistance andL,<25Model studies: θ-53.10, h=0.06, 0.028,(1991)energy dissipation0.024, 0.014 m, L,=10, 21.3, 25, 42.7BoesVoid fraction andRe>1E+5Model studies: θ 30° and 50°, W=0.5 m, h=0.023(2000)velocity distributionsto 0.093 m, L,=6.6, 13, 26 (30°)/6.5, 20 (50°)Chanson et al. Flow resistancePrototype and model studies: θ-5° to 50°, W=0.2 to(2002)15 m, h=0.005 to 0.3 m, 3E+4