Flow aeration, cavity processes and energy dissipation on flat and pooled stepped spillways for ...

23 Pages·2013·2.69 MB·English

EnvironFluidMech(2013)13:503–525
DOI10.1007/s10652-013-9277-4
ORIGINAL ARTICLE
Flow aeration, cavity processes and energy dissipation
on flat and pooled stepped spillways for embankments
PhilippGuenther · StefanFelder · HubertChanson
Received:15November2012/Accepted:9March2013/Publishedonline:27March2013
©SpringerScience+BusinessMediaDordrecht2013
Abstract Thedesignfloodsofseveralreservoirswererecentlyre-evaluatedandtherevised
spillwayoutflowcouldresultindamovertoppingwithcatastrophicconsequencesforsome
embankmentstructures.Hereinaphysicalstudywasperformedonflatandpooledstepped
spillwayswithaslopetypicalofembankments(θ=26.6◦)andfoursteppedconfigurations
were tested: a stepped spillway with flat horizontal steps, a pooled stepped spillway, and
twosteppedspillwayswithin-lineandstaggeredconfigurationsofflatandpooledsteps.The
focusofthestudywasontheflowaeration,air–waterflowproperties,cavityflowprocesses,
and energy dissipation performances. The results demonstrated the strong aeration of the
flow for all configurations. On the in-line and staggered configurations of flat and pooled
steps,theflowwashighlythree-dimensional.Theresidualheadandenergydissipationrates
atthesteppedchutedownstreamendwerecalculatedbaseduponthedetailedair–waterflow
properties.Theresultsshowedthattheresidualenergywasthelowestfortheflatsteppedweir.
Thedataforthesteppedspillwayconfigurationwithin-lineandstaggeredconfigurationsof
flat and pooled steps showed large differences in terms of residual head in the transverse
direction. Altogether the present results showed that, on a 26.6◦ slope stepped chute, the
designswithin-lineandstaggeredconfigurationsofflatandpooledstepsdidnotprovideany
advantageousperformancesintermsofenergydissipationandflowaeration,buttheywere
affectedbythree-dimensionalpatternsleadingtosomeflowconcentration.
Keywords Steppedspillways·Flowaeration·Cavityejectionprocesses·
Energydissipation·Pooledsteps·Residualhead·Physicalmodelling
B
PhilippGuenther·StefanFelder·HubertChanson( )
SchoolofCivilEngineering,TheUniversityofQueensland,Brisbane,QLD4072,Australia
e-mail:[email protected]
URL:http://www.uq.edu.au/∼e2hchans/
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1 Introduction
Worldwide the design floods of several reservoirs were re-evaluated and the revised spill-
way outflow was often larger than the original design one. The occurrence of such large
floods could result in dam overtopping with catastrophic consequences for embankment
structures when an insufficient storage and spillway capacity is available. During the last
decades, a number of overtopping protection systems were developed for embankment
structuresandearthfilldams.Theseincludeconcreteovertoppingprotectionsystems,tim-
ber cribs, sheet-piles, riprap and gabions, reinforced earth, minimum energy loss (MEL)
weirs, in-built spillway dams, embankment overflow stepped spillways and the precast
concrete block protection systems developed by the Russian engineers [2,9,10,26]. A
numberofembankmentdamsteppedspillwayswerebuiltwitharangeofdesignandcon-
struction techniques, including gabions, Reno mattresses, reinforced earth, pre-cast con-
crete slabs and roller compacted concrete (RCC) [5,6]. The stepped profile allows an
increased rate of energy dissipation on the spillway chute [6,27] and the design engi-
neers must assess accurately the turbulent kinetic energy dissipation down the staircase
chute, in particular for the large discharges per unit width corresponding to the skim-
ming flow regime. A characteristic feature of skimming flows is the high level of turbu-
lence and free-surface aeration [4,29,31]. The water flows down the steps as a coherent
free-stream skimming over the pseudo-bottom formed by the step edges, while the tur-
bulent recirculation in the step cavities is maintained through the transmission of shear
stressfromthefree-stream.Atthefree-surface,airiscontinuouslyentrainedandreleased,
and the resulting two-phase mixture interacts with the flow turbulence yielding some
intricate air–water structures associated with complicated energy dissipation processes
[15,24].
Inrecentyears,theair–waterflowsonpooledsteppedspillwayswereresearchedinafew
studies (Table 1). André [1] and Ko˝kpinar [25] investigated the air entrainment processes
onflat,pooledandacombinationofflatandpooledstepswithchannelslopesof18.6◦ and
◦
30 . Thorwarth [33] researched the self-induced instabilities on pooled stepped spillways
withslopesof8.9◦ and14.6◦.RecentlyFelderetal.[22]conductedadetailedstudyofthe
air–water flow properties on a stepped spillway with flat, pooled and combination of flat
andpooledstepswithaslopeof8.9◦.Figure1ashowsaprototypepooledsteppedspillway.
Arelatedformofpooledsteppedchutesissomesteppedfishwaydesign.Figure1bshows
a fishway designed with a staggered combination of flat and pooled steps. This particular
structurecannotbeconsideredsuccessfulhowever,becausesomeflowconcentrationyielded
someveryhighvelocitiesatthedownstreamendofthefishpassagewhichweredetrimental
totheupstreamfishmigration.
Whilethepredictionofturbulentdissipationconstitutesacriticaldesignstage,themodern
literatureisskewedtowardssteepslopedesignswithflathorizontalsteps,typicalofmodern
gravitydams.Thispaperpresentssomenewphysicalexperimentsconductedinalargefacility
◦
with a channel slope of 26.6 (2H:1V) and step heights of 0.10 m. Such flow conditions
would be representative of some stepped storm waterways during flood events and could
be considered as a 2:1 to 20:1 scale study of the prototype chutes seen in Fig. 1. Four
steppedgeometriesweretested:flathorizontalsteps,pooledsteps,andin-lineandstaggered
configurationsofflatandpooledsteps(Fig.2).Thefocusofthepresentworkwas onthe
flow aeration, cavity ejection processes and energy dissipation performances. The results
emphasisethecomplicatednatureofturbulentair–waterflowsonsteppedspillways.Herein
theaimofthestudyisadetailedcharacterisationoftheturbulentflowpropertiessupported
bydetailedair–waterflowpropertiesintheskimmingflowregime.
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EnvironFluidMech(2013)13:503–525 505
Fig.1 Photographsofpooledsteppedstructures.aPooledsteppedspillwayofLePontdam(France)inJune
1998—Leftlookingdownstream,Rightlookingupstream.bFishwaystructureontheOkuraRiver(Japan)on
9October2012—Thesteppedchannelconsistsofastaggeredcombinationofflatandpooledsteps
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Fig.2 Definitionsketchofthesteppedconfigurations
2 Physicalmodellingandinstrumentation
2.1 Presentation
Inafree-surfaceskimmingflowdownasteppedspillway,adimensionalanalysisgivesaseries
of dimensionless relationships between the two-phase flow properties at a dimensionless
locationalongthechuteandthechannelcharacteristics,inflowpropertiesandfluidproperties
[8,13,19]:
(cid:2)
V u(cid:5) g L d F×d
C,√ , ,T × , xz, ab, c =
(cid:3) g×dc V int dc dc dc Vc (cid:4)
x y z w w l W d V×D g×μ4 W k(cid:5)
F , , , , , w, w, c,ρ × H, w, ,θ, s (1)
d d d h l d W h w μ ρ ×σ3 d d
c c c c w w c c
whereCisthevoidfraction,Vistheinterfacialvelocity,u’isaturbulentvelocityfluctuation,
d isthecriticalflowdepth,D isthehydraulicdiameter,qisthewaterdischargeperunit
c H
width,Wisthechannelwidth,histheverticalstepheight,listhesteplength,wisthepool
weirheightforapooledsteppedspillway,l isthehorizontalpoolweirlength,W isthe
w w
widthofthepooledandflatpartinthestaggeredandin-lineconfigurationsofflatandpooled
steps, g is the gravity acceleration, θ is the chute slope, u’ is the characteristic turbulent
velocity,T istheintegralturbulenttimescale,L istheintegralturbulentlengthscale,x,
int xz
y,zarerespectivelythelongitudinal,normalandtransversecoordinates,μ isthedynamic
w
viscosityofwater,ρ isthewaterdensity,σisthesurfacetensionbetweenairandwater,F
w
isthebubblecountrate,d isthecharacteristicbubblesizeandk ’istheequivalentsand
ab s
roughnessheightofthestepsurface.
Equation(1)expressesthedimensionlessair–waterflowpropertiesatalocation(x,y,z)as
functionsoftherelevantdimensionlessparameters,includingFroudeandReynoldsnumbers.
InEq.(1),thedimensionlessdischar(cid:5)gedc/hisproportionaltoaFroudenumberdefinedin
termsofthestepheight:d /h=(q2/ g×h3)1/3.Hereinthesamefluidswereusedinmodel
c
andprototype:thatis,theMortonnumberMog×μ4/(ρ ×σ3)wasaninvariant[11,30,36].
w w
Similarly,thechuteslopeh/l,thechannelwidthW,thehorizontalpoolweirlengthl andthe
w
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Table1 Summaryofexperimentalstudiesofair–waterflowpropertiesonpooledsteppedspillwayconfigu-
rations
Reference θ(◦) Stepgeometry Flowconditions Instrumentation Comment
(1) (2) (3) (4) (5) (6)
Ko˝kpinar[25] 30 Flatsteps:h=6 Q=0.03–0.100 Double-tip W=0.5m,
cm,l=10.4cm m3/s, fiber-
Pooledsteps:h=6 Re=2.4×105– optical 64steps,
cm,l=10.4cm,w 8.0×105 probe
=3cm
Combinationof (Ø=0.08mm) lw=2.6cm
flat/pooledsteps:h=6
cm,l=10.4cm,w=3
cm
André[1] 18.6 Flatsteps:h=6cm,l Q=0.02–0.130 Double-tip W=0.5m,
=17.8cm m3/s, fiber-
Pooledsteps:h=6 Re=1.6×105–1.0×106 opticalprobe 42/64steps,
cm,l=17.8cm,w
=3cm
Combinationof (Ø=0.08mm) lw=2.6cm
flat/pooledsteps:h
=6cm,l=17.8cm,
w=3cm
30 Flat steps: h = 6
cm,l=10.4cm
Pooledsteps:h=6
cm,l=10.4cm,w
=3cm
Combination of
flat/pooled steps:
h=6cm,l=10.4
cm,w=3cm
Thorwarth[33] 8.9 Pooledsteps:h=5 Q=0.025–0.117 Double-tip W=0.5m,
cm,l=31.9cm,w m3/s, conductiv-
=0–5cm ityprobe
14.6 Pooledsteps:h=5 Re=2.0×105– (Ø=0.13mm) 22/26steps,
cm,l=19.2cm,w 9.3×105
=0–5cm
lw=1.5cm
Felderetal.[22] 8.9 Flat steps: Q=0.018–0.117m3/s,Re Double-tip W=0.5m,
h=5cm,l =1.4×105–9.3×105 conductiv-
=31.9cm ityprobe
Pooledsteps:h=w Q=0.027–0.117m3/s,Re (Ø=0.13mm) 21steps,
=5cm,l=31.9cm =2.2×105–9.3×105
Combination of Q=0.027–0.117m3/s,Re lw=1.5cm
flat/pooled steps: =2.2×105–9.3×105
h=w=5cm,l=
31.9cm
stepsurfaceskinroughnessk ’werekeptconstantduringtheexperiments.Someexperiments
s
were conducted in the centreline, and others at different transverse locations z/d . Hence
c
Eq.(1)couldbesimplifiedinto:
(cid:2) (cid:3) (cid:4)
C,√gV×dc,uV(cid:5),Tint× dgc,Ldxcz,ddacb,FV×cdc =F(cid:5) dxc,dyc,dzc,wh,wl ,WWw,dhc,Re
(2)
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Table1 continued
Presentstudy 26.6 Flat steps: Q=0.030–0.113 Double-tip W=0.52m,
h=10cm, m3/s,Re= conductiv-
l=20cm 2.3×105– ityprobe
8.7×105
Pooled steps: h = Q=0.013–0.130 (Ø = 0.25 mm); 10steps,
10cm,l=20cm, m3/s,Re= Arrayof2single-
w=3.1cm 1.0×105– tip conductivity
9.9×105 probes
In-line configura- Q=0.016–0.113 (Ø=0.35mm) lw=1.5cm
tion (Pooled and m3/s,Re=
flatstepsin-line):h 1.4×105–
=10cm,l=20cm, 8.7×105
w=3.1cm,Ww=
26cm
Staggeredconfigu- Q=0.030–0.113
ration(Pooledand m3/s,Re=
flatstaggered):h= 2.3×105–
10cm,l=20cm, 8.7×105
w=3.1cm,Ww=
26cm
Notesθ channelslope,hstepheight,lsteplength,wweirheight,lwpoolweirlength,W channelwidth,Q
waterdischarge,ReReynoldsnumberdefinedintermsofhydraulicdiameter,Wwwidthofpooledstepped
sectionsinin-linedandstaggeredconfigurations
whereReistheReynoldsnumber:Re = ρ ×V×D /μ .Thephysicalexperimentsare
w H w
traditionally conducted based upon an undistorted Froude similitude, although it is nearly
impossibletoachieveatruedynamicsimilarityofhigh-velocityair–waterflowsinsmallsize
laboratorymodelsbecauseofthenumberofrelevantdimensionlessparameters([8],pp.358-
263,[11]).Recentresultsdemonstratedthatthephysicalstudiesmustbeconductedinlarge
size facilities operatingat large Reynolds numbers tominimise viscous scaleeffects [19].
HereinthestudywasperformedbaseduponanundistortedFroudesimilarityandtheexper-
imentalflowconditions(Table1)wereselectedtoachievelargedimensionlessdischarges
correspondingtoReynoldsnumbersrangingfrom1×105to1×106.
2.2 Physicalfacilityandinstrumentation
NewexperimentswereperformedattheUniversityofQueenslandonalargesizestepped
spillway model with a slope of 26.6◦. The experimental facility was newly designed. The
stepped spillway consisted of 10 steps with step height h = 10 cm, and step length of l =
20cm.ThechutehadawidthW=0.52m.Thestepsweremadeoutofplywoodandthe
channelwallsoutofperspex.Constantflowratesweresuppliedbyalargeupstreamintake
basinwithasizeof2.9m×2.2mandadepthof1.5m.Asmoothinflowwassuppliedby
a1.01mlongsmoothsidewallconvergentwitha4.23:1contractionratio.Attheupstream
end of the test section, the flow was controlled by a broad-crested weir with height of 1
m, width W = 0.52 m, length L = 1.01m and an upstream rounded corner (r = 0.08
crest
m).Thebroad-crestedweirwaspreviouslytestedandsomedetailedvelocityandpressure
measurements[20]providedthedischargecalibrationcurveusedinthepresentstudy:
(cid:6)
(cid:3) (cid:4) (cid:3) (cid:4)
Q H 2 3
= 0.92+0.153× 1 × g× ×H 0.02≤H /L ≤0.3 (3)
1 1 crest
W L 3
crest
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EnvironFluidMech(2013)13:503–525 509
Fig. 3 Photographs of the stepped configurations including in-line and staggered stepped arrangements
(Bottom) View from upstream looking downstream (a, Left) Flat stepped arrangement (b, Right) Pooled
steppedarrangement(c,Left)In-linesteppedarrangement(d,Right)Staggeredsteppedarrangement
where Q is the water discharge and H is the upstream total head measured using a point
1
gauge.
Atthedownstreamend,thesteppedchutewasfollowedbyasmoothhorizontalraceway
ending with an overfall into the recirculation sump pit. The flow was supercritical in the
horizontalracewayanddidnotinterferewiththesteppedchuteflow.
Theair–waterflowmeasurementswereconductedwitheitheratwo-tipphase-detection
intrusive probe (∅ = 0.25mm,(cid:4)x = 7.2mm,(cid:4)z = 1.5mm) or an array of two single-
tipphase-detectionprobes(∅ = 0.35mm)separatedbyarangeofwell-definedtransverse
distances3.5< (cid:4)z<81mm.Herein(cid:4)xisthelongitudinaldistancebetweenprobesensors
and(cid:4)zisthetransversedistancebetweensensors.Theprobesensorswereexcitedbyanair
bubbledetector(Ref.UQ82.518)andsampledat20kHzpertipfor45s.Allconductivity
probetipsweremountedonatrolleyandtheirelevationinthedirectionperpendiculartothe
pseudo-bottomformedbythestepedges(i.e.y-direction)wascontrolledbyafineadjustment
screw-drivemechanismequippedwithaMitutoyoTMdigitalruler(accuracy<0.1mm).
Further observations were conducted with a HD video camera SonyTM HDR-XR160E
(StandardHQHDquality25fps),twodSLRcameraPentaxTMK-7andCanonTM450D.More
detailsontheexperimentalfacility,instrumentationandexperimentaldatawerereportedin
[23].
2.3 Signalprocessing
Therawdatarecordedwiththedouble-tipconductivityprobeyieldedthevoidfractionC,
the bubble count rate F, the interfacial velocity V, and the turbulence intensity Tu. For all
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Fig.4 Skimmingflowregimeonflatandpooledsteppedspillways.aFlatsteps,Q=0.114m3/s,dc/h=
1.7,Re=8.8×105.bPooledsteps,Q=0.100m3/s,dc/h=1.56,Re=7.7×105
experiments, the void fraction, bubble frequency and particle chord sizes were calculated
baseduponasingle-thresholdtechniquewithathresholdsetat50%oftheair–waterrange
[34].Theinterfacialvelocity,turbulenceintensityandintegralturbulentscaleswerecalcu-
latedusingsomecorrelationtechnique[7,12].
Thedataforthearrayofthetwosingle-tipprobesprovidedthetransverseintegralturbulent
timeandlengthscalesT andL .Anintegrationofthemaximumcross-correlationvalues
int xz
(R ) betweentherawdataofthetwosingle-tipprobeswithvariousspacing(cid:4)zgavethe
xz max
integralturbulentlengthscale[12]:
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EnvironFluidMech(2013)13:503–525 511
Fig.5 Three-dimensionalskimmingflowsdownthein-lineandstaggeredconfigurationsofflatandpooled
steps(a,Left)In-lineconfiguration,Q=0.098m3/s,dc/h=1.54,Re=7.6×105(b,Right)Staggeredconfig-
uration,Q=0.090m3/s,dc/h=1.45,Re=6.9×105
z=z((R(cid:7)xz)max=0)
L = (R ) ×dz (4)
xz xz max
z=0
Thecorrespondingintegralturbulenttimescalewasalsocalculated:
z=z((R(cid:7)xz)max=0)
1
T = × (R ) ×T ×dz (5)
int L xz max xz
xz
z=0
whereT isthecross-correlationintegraltimescalecalculatedinanintegrationfromthe
xz
maximumofthecross-correlationfunctionuntilthefirstcrossing.
2.4 Experimentalinvestigations
Theexperimentalstudywasconductedforfoursteppedspillwayconfigurations(Figs.2,3).
Thesewereasteppedspillwaywithflathorizontalsteps,apooledsteppedspillwaywithweir
heightw=0.031m,andtwosteppedspillwayswithin-lineandstaggeredconfigurationsof
flatandpooledsteps(w=0.031m).Thein-linesteppedspillwayconfigurationconsistedof
pooledandflatstepsin-lineforhalfthechannelwidth(W =W/2=0.26m).Thestaggered
w
pooledsteppedspillwayconfigurationwascharacterisedbyalternatingflatandpooledsteps.
Ontheflatandpooledsteppedspillways,theair–waterflowmeasurementswereconducted
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Fig.6 Definitionsketchesof
sidewallstandingwavesand
shockwavesinsteppedchutes
within-lineandstaggered
configurationsofflatandpooled
steps.aIn-lineconfigurationof
flatandpooledsteps.bStaggered
configurationofflatandpooled
steps
on the channel centreline. For the in-line and staggered configurations, the measurements
wereperformedatthreetransverselocations:z/W=0.25,0.5(centreline)and0.75.
Theflowpatternswereobservedforawiderangeofdischarges:0.002≤Q≤0.155m3/s.
Theair–waterflowmeasurementswereperformedfordischargeswithin0.013≤Q≤0.130
m3/scorrespondingtoReynoldsnumbersbetween1×105 and1×106.Mosttwo-phase
flowexperimentswereconductedinthetransitionandskimmingflowregimes(seebelow).
3 Flowpatterns
Thevisualobservationsofflowpatternswereconductedforallsteppedspillwayconfigura-
tionsforabroadrangeofdischarges.Forsomelowdischarges,theair–waterflowsonthe
pooledsteppedspillwayexhibitedsomesmallinstabilitieslinkedwithsomeflowpulsations.
Theflowprocessesonthesteppedspillwayswithin-lineandstaggeredconfigurationsofflat
andpooledstepsshowedsomestronglythree-dimensionalair–waterflowfeaturesincluding
standingsidewallwavesandsupercriticalshockwaves.
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