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Experimental study of skimming flow on stepped spillways
downstream of Piano Key Weirs
Maria Ines Falcao Reis
Supervisors:Prof. Dr. Jorge de Saldanha Goncalves MatosDr. Maria Teresa Fontelas dos Santos Viseu
Instituto Superior Tecnico, Lisboa, Portugal
October 2015
Abstract
The present investigation is focused on the hydraulics of stepped spillways downstream of a pianokey weir (PKW). Based on a set of air concentration and velocity data gathered on a 1:0.75 slopingchute built at the LNEC, and adapted for the present investigation, the head-discharge relationshipis evaluated, along with main skimming flow properties on the symmetry axes of the inlet and outletkeys of the chute, namely: air concentration distribution, velocity distribution, mean air concentra-tion, mean water velocity, bulked flow depth, and equivalent clear water depth. A brief study of thehydraulic jump on the stilling basin is conducted, based on piezometric head data acquired on thestilling basin floor. The experimental data acquired in the present study are compared with thoseobtained by other authors in the same stepped chute, downstream of a WES weir.Keywords: stepped spillway, piano key weir, skimming flow, air entrainment
1. IntroductionDuring the 20th century, the construction of dams witnessed a significant rate of growth, in parallel withthe development of the society and the construction technology. The hydraulic-operational safety of damsmay be of particular relevance, depending on their size, typology, and type of occupation of the valleydownstream of those large infrastructures.
Even though the number of accidents in dams in operation is relatively small to date, an importantpart of those has been caused by the insufficient release capacity of their spillways. The increasing concernin dam safety and improvement in the technical knowledge (e.g., hydrologic data and flood estimation)has frequently lead to an increase in the design flood of several dam spillways.
The French consulting company Hydrocoop, in colaboration with the University of Biskra (Algeria),has recently developed a new type of labyrinth weir geometry, the Piano Key Weir (PKW), that wasproven to be more than or as efficient as a labyrinth weir, whereas it can be installed at the crest ofconcrete gravity dams, due to its small footprint (Figure 1).
Figure 1: Piano Key Weir of Marlace dam (France): downstream view (Photograph J. Matos, Nov. 2013)
1
The present study aims to deepen the knowledge of the skimming flow on a stepped spillway down-stream of a PKW, including the development of the air concentration and velocity distribution, andcharacteristic flow depths. Further it comprises the study of the rating curve of the PKW as well as thepressure head data on the floor of the stilling basin, where a free hydraulic jump takes place.
2. Main types of Piano Key WeirsThe Piano Key Weir (PKW) is a particular case of the labyrinth weir that uses up and/or downstreamsoverhangs. The horizontal rectangular shape of the labyrinth allows to increase the length of the crest fora certain weir width. Because it is a labyrinth shaped weir, the PKW is also a potential solution for damprojects that require a high discharge capacity with a small head above crest and allows the increase ofits reservoir storage capacity. The first PKW used as a solution of rehabilitation of an existing dam wasdesigned by the french engineer Francois Lemperiere, in 2001. In 2006 the first PKW was built for therehabilitation of the Goulours dam by the Electricit de France (EDF). EDF has, since then, developeddifferent projects using PKW for the rehabilitation of dams in France, namely Saint-Marc, Gloriettes,Etroit and Malarce dams (Laugier et al., 2009, Pinchard et al., 2011, Erpicum et al., 2011, Leite Ribeiroet al., 2013).
The PKW structure can be described as being made of a basic structure, the parapet walls and thenoses (Figure 2). The inlet key is the alveoli that is opened to downstream and is sided by two lateralwalls and the downstream crest. The outlet key is the alveoli that is opened to the downstream face andis also sided by two lateral walls but by the upstream crest. The base structure is made of ”PKW units”,where its parameters are the total width of the weir (W ), the total developed crest length (L) and thestructure Nu. The unit represents the smallest extension of a complete structure, made by a completeinlet key with two side walls and half of an outlet key on both sides. All of the parameters related to thePKW unit are defined with the index u, whilst the indexes i, o and s are associated, respectively, to theinley key, outlet key and to the side wall. Therefore, the main parameters that define the geometry ofthe PKW unit are the unit width, Wu, the width of both the inlet and outlet keys, that is Wi and Wo,the heigh of each key Pi and Po and the slope associated to each one.
(a) (b)
Figure 2: Fundamental parameters of Piano Key Weirs (adapted from Pralong et al., 2011)
There are four types of PKW spillways known as type A, type B, type C and type D. The PKW typeA selected for the present work includes upstream and downstream projections.
2.1. Rating of the discharge spillways of type PKWThe main characteristics of the PKW that influence the rating curve are n = L/W ; Hu/P and Wi/Wo.
With respect to the experimental setup, there are two approaches to estimate the rating curve ofthe PKW. The first is to estimate the rating coefficient of the PKW and to include this value directlyon the rating equation for broad crested weir (Ouamane et al., 2006, Kabiri-Samani and Javaheri, 2012,Anderson and Tullis, 2012), or, secondly, to compare the rating value of the PKW with the theoreticalvalue of broad crested weir (Leite Ribeiro et al., 2012), as follows:
2
r =Qp
Qs(1)
whereQs = 0, 42W
√2g H1,5 (2)
Based on the results of their study, Leite Ribeiro et al. (2012) obtained:
r = 1 + 0, 24 δ (3)
where:
δ =
((L−W )Pi
WH
)0,9
(4)
3. Experimental set-up3.1. Preliminary remarksA facility assembled at the National Laboratory of Civil Engineering (LNEC), in Portugal, in the frame-work of previous research (Matos, 1999, Meireles, 2004, Renna, 2004), was readapted for this experimentalstudy. The installation comprised initially a 2.90 m high (from crest to toe), 1.00 m wide, stepped chute,with a slope of 1V:0.75H, 8 cm high steps, and a 5.00 m long and 1.00 m wide stilling basin. In thepresent study, the WES crest weir was replaced by a PKW (Figure 3).
For the rating curve, the flow rates varied between 0.08 to 0.20 m2/s, whereas for the study of theflow along the chute, the tested discharges were 0.08 and 0.14 m2/s.
A conductivity probe and a backflushing Pitot tube developed and calibrated by the U.S. Bureau ofReclamation were tested and calibrated to measure the air concentration and the water velocity in theLNEC chute. Further details on the instrumentation can be found in Reis (2015), as well as in Matos(1999), Matos and Frizell (1997, 2000), Meireles (2004), and Renna (2004).
Flow depths along the chute were also measured by means of visual observation through the sidewalls.The main geometric characteristics of the PKW used in the present research are included in Table 1.
Table 1: Main geometric characteristics of the PKW used in the present research (parameters as perFigure 2).
Wu W L B Bo
BiWi Wo Ts P Bo Bi
Wi
Wo
PWu
2Ts
LLW
(m) (m) (m) (m) (-) (m) (m) (m) (m) (m) (m) (-) (-) (-) (-)0,39 1,00 4,29 0,67 1,00 0,22 0,15 0,012 0,20 0,13 0,13 1,50 0,51 0,014 4,29
4. Results4.1. DefinitionsThe local air concentration C is defined as the time-averaged value of the volume of air per unit volumeof air and water. The equivalent clear water depth is defined as:
h =
∫ Y90
0
(1 − C) dy (5)
where y is measured perpendicular to the spillway surface and Y90 is the depth where the local airconcentration is 90%. A depth averaged mean air concentration in a vertical (or in a cross-section, fortwo-dimensional flow) can then be defined from:
h = (1 − C)Y90 (6)
The average water velocity in a vertical is defined as:
U =
∫ Y90
0V dy
Y90(7)
In a two-dimensional flow, Equation (7) can be rewritten as:
U =q
h(8)
3
Figure 3: Experimental facility assembled at the LNEC: a) general view of the spillway; b) side view ofthe WES weir (Cardoso, 2007); c) side view of the Piano Key Weir.
4.2. Rating CurveThe rating curve of the PKW obtained in the present study is presented in Figure 4a), along with therating curve data obtained by Matos (1999), Meireles (2004) and Cardoso (2007) in the same experimentalfacility, but with a WES weir. The water depth was measured with a point gauge located at a distancegreater than 1 m from the upstream face of the weir, hence corresponding to a distance six times largerthan the maximum head.
The results show that rating curve of the PKW is practically linear, being much more efficient thanthat of a WES weir, as shown in previous studies. For identical flow depth above the crest, the dischargeon a PKW is much higher (two to three times) than that for a WES weir.
Figure 4b) includes the head-discharge curve of the PKW obtained in the present study, as well as thehead-discharge curve estimated from the method proposed by Leite Ribeiro et al. (2012) (Equations 1 to4). The results from Leite Ribeiro et al. (2012) are close to those obtained at the LNEC facility, exceptfor low flow rates. For heads greater than 30% of the design head of the WES weir (H ≈ 0, 06m), therelative differences between the flow rates measured at LNEC and those estimated from Leite Ribeiro etal. (2012) are lower than 6%, for identical head above the weir crest.
4.3. Air concentration distribution and mean air concentrationOn the basis of visual observation of the flow along the spillway (Figure 5), downstream of a PKW,along with the anaysis of the air concentration profile data aquired in several verticals, for 80 and 140l/s, three distinct flow reaches can be observed along the spillway: i) an initial reach (reach I), shortlydownstream of the PKW, where free jets resulting from the flow on the inlet keys hit the spillway chuteshortly downstream, whereas the flow from the outlet key evolves towards an air-water skimming flow;ii) a second reach (reach II), shortly downstream, where a three-dmensional (3D) skimming flow occupiesthe entire width of the cross-section; iii) a third reach (reach III), where the 3D nature of the skimmingflow is mitigated, hence the flow tends to become 2D.
In Figures 6 and 7, the air concentration distribution along the spillway is plotted as a function ofthe normalized distance to the pseudo-bottom (y/Y90), for Q = 80 and 140 l/s. Therein the results fromWood’s (1985) advection-diffusion model for the air bubbles in the uniform regime of high velocity flowover conventional (smooth) chutes are also included.
The results show that the air concentration profiles in the symmetry axis of the inlet key are clearly
4
0
2
4
6
8
10
12
14
16
18
20
0 40 80 120 160
h (
cm
)
Q (l/s)
Matos (1999) Meireles (2004) Cardoso (2007)
PKW data (2015) Linear (PKW) Power (WES)
(a)
0,00
0,03
0,05
0,08
0,10
0,13
0,15
0,18
0 0,05 0,1 0,15 0,2
H (
m)
Q (m³/s)
Present study (2015) Eqs 1 to 4
(b)
Figure 4: Rating curves: (a) PKW (present study) and WES weir (Matos, 1999, Meireles, 2004, andCardoso, 2007); (b) PKW (present study), against the application of the formulae proposed by LeiteRibeiro et al. (2012).
24
15
17
19
21
(a)
19
24
22
21
(b)
Figure 5: Flow in the chute downstream of the PKW: front view for (a) Q = 80 l/s; (b) Q = 140 l/s.
different from those gathered in the outlet key, namely in the upstream reach of the spillway (Figures 6and 7, for Q = 80 and 140 l/s, respectively). In the layers near the pseudo-bottom (y < 3cm) usptreamof step 24, the values of the air concentration in the symmetry axis of the outlet key are always largerthan those for the inlet key, regardlesss of the discharge. Further downstream, namely on steps 27, 30and 32, the air concentration profiles on both keys are fairly similar, leading to the conclusion that the3D nature of the flow is strongly mitigated. However, for Q = 80 l/s, the air concentration data in thesymmetry axis of the inlet key are in general larger than those for the outlet key, and similar to the resultsfrom Woods (1985) model, in uniform flow. For Q = 140 l/s, the air concentration profiles on steps 27,30 and 32 are still distant from those corresponding to unifom flow on smooth chutes. It is judged thatthe intersection of the air concentration profiles on the downstream reach of the spillway is due to thecross-waves and 3D flow generated in the vicinity of the PKW.
In Figure 8, the air concentration distribution in the symmetry axes of both inlet and outlet keys isplotted as a function of the normalized distance to the pseudo-bottom (y/Y90), for 140 l/s. The resultsobtained from Matos (1999), in identical experimental facility, but with a WES weir, are also includedin the same figure. The following observations can be drawn:
- On step 19, the air concentration profiles are considerably different; for a given distance to thepseudo-bottom, the air concentration in the symmetry axis of the inlet key is considerably lower
5
0,0
0,5
1,0
1,5
2,0
2,5
0,0 0,2 0,4 0,6 0,8 1,0
y /Y
90
C
Q = 80 l/s Step 15
Step 17
Step 19
Step 21
Step 24
Step 27
Step 30
Step 32
Wood (1985)
(a)
0,0
0,5
1,0
1,5
2,0
2,5
3,0
3,5
4,0
0,0 0,2 0,4 0,6 0,8 1,0
y /Y
90
C
Q = 80 l/s Step 15
Step 17
Step 19
Step 21
Step 24
Step 27
Step 30
Step 32
Wood (1985)
(b)
Figure 6: Normalized air concentration distribution along the chute, for Q = 80 l/s: (a) in the symmetryaxis of the inlet key; (b) in the symmetry axis of the outlet key.
0,0
0,5
1,0
1,5
2,0
2,5
0,0 0,2 0,4 0,6 0,8 1,0
y /Y
90
C
Q = 140 l/s Step 19
Step 21
Step 24
Step 27
Step 30
Step 32
Wood(1985)
(a)
0,0
0,5
1,0
1,5
2,0
2,5
0,0 0,2 0,4 0,6 0,8 1,0
y /Y
90
C
Q = 140 l/s Step 19
Step 21
Step 24
Step 27
Step 30
Step 32
Wood(1985)
(b)
Figure 7: Normalized air concentration distribution along the chute, for Q = 140 l/s: (a) in the symmetryaxis of the inlet key; (b) in the symmetry axis of the outlet key.
than that for the outlet key, for 0.3 < y/Y90 < 0.7, and larger than that obtained by Matos (1999),for y/Y90 < 0.6.
- On step 21, the air concentration profile in the symmetry axis of the inlet key is close to that obtainedby Matos (1999), and considerably lower than that for the oulet key; a different situation occurs onstep 24, where the air concentration profile in the symmetry axis of the outlet key approaches thatobtained by Matos (1999). It is judged that this behaviour is a consequence of the cross-waves and3D flow downstream of the PKW.
- In step 27 and further downstream, the air concentration obtained by Matos (1999) lies in generalbetween those obtained on the outlet and inlet keys. This result is to be expected, considering thatthe relative influence of the weir type on the flow conditions on the spillway tends, in general, todecrease with distance.
Figure 9 shows the mean air concentration along the spillway, in the symmetry axes of both inlet andoutlet keys, for Q = 80 and 140 l/s, along with the data from Matos (1999). The results show that:
- The mean air concentration in the symmetry axis of the outley key is initially greater than that onthe symmetry axis of the inlet key, namely usptream of step 24, for Q = 80 l/s, and step 27, for Q
6
0,0
0,5
1,0
1,5
2,0
2,5
0,0 0,2 0,4 0,6 0,8 1,0
y/Y
90
C
Step 19
Outlet Key Inlet Key Matos (1999)
0,0
0,5
1,0
1,5
2,0
2,5
0,0 0,2 0,4 0,6 0,8 1,0
y/Y
90
C
Step 21
Outlet Key Inlet Key Matos (1999)
0,0
0,5
1,0
1,5
2,0
2,5
0,0 0,2 0,4 0,6 0,8 1,0
y/Y
90
C
Step 24
Outlet Key Inlet Key Matos (1999)
0,0
0,4
0,8
1,2
1,6
2,0
0,0 0,2 0,4 0,6 0,8 1,0
y/Y
90
C
Step 27
Outlet Key Inlet key Matos (1999)
0,0
0,4
0,8
1,2
1,6
2,0
0,0 0,2 0,4 0,6 0,8 1,0
y/Y
90
C
Step 30
Outlet Key Inlet Key Matos (1999)
0,0
0,4
0,8
1,2
1,6
2,0
0,0 0,2 0,4 0,6 0,8 1,0
y/Y
90
C
Step 32
Outlet Key Inlet Key Matos (1999)
Figure 8: Normalized air concentration distribution along the chute, in the symmetry axes of the inletand outlet keys, for Q = 140 l/s; comparison with the results presented by Matos (1999), for the sameinstallation and discharge, downstream of a WES weir.
= 140 l/s. The situation is inverted downstream of those steps, due to the cross-waves and 3D flowdownstream of the PKW.
- The mean air concentration in the symmetry axis of the outley key tends to decrease down thespillway, in particular for Q = 80 l/s, inasmuch as observed for skimming flow downstream of WESweirs. The intersection of the jets with origin at the PKW, and the resulting high turbulence levels,is believed to explain the high air concentration in the usptream reach of the outlet key (Figure 5).
- The mean air concentration in the symmetry axis of the inlet key decreases in a initial spillwayreach, whereas it increases further downstream (e.g., downstream of steps 21, for Q = 80 l/s, and24, for 140 l/s).
- The mean air concentration obtained by Matos (1999) are in general limited by those obtained in
7
the outlet and inlet keys, being fairly close to these in the reaches downstream of steps 19, for Q =80 l/s, and 24, for Q = 140 l/s).
- The mean air concentration near the downstream end of the spillway reach under analysis (≈0.5− 0.6) is relatively close to that obtained on uniform flow over a smooth chute of identical slope(≈ 0.6). Hence one may expect that uniform flow conditions might be attained in the spillway,shortly downstream of the reach under analysis.
Further the comparison of Figures 9a) and 9b) indicate that the development trend of the mean airconcentration along the spillway is significantly different on the inlet and outlet key axes and praticallyindependent of the discharge.
0,0
0,1
0,2
0,3
0,4
0,5
0,6
0,7
0,8
10 12 14 16 18 20 22 24 26 28 30 32 34
Step number
Q = 80 l/s
Outlet key Inlet key Matos (1999)
(a)
0
0,1
0,2
0,3
0,4
0,5
0,6
0,7
0,8
10 12 14 16 18 20 22 24 26 28 30 32 34
Step number
Q = 140 l/s
Outlet Key Inlet Key Matos (1999)
(b)
Figure 9: Mean air concentration along the chute, in the symmetry axis of the outlet and inlet keys; com-parison with the results presented by Matos (1999), for the same installation and discharge, downstreamof a WES weir: a) Q = 80 l/s; b) Q = 140 l/s.
4.4. Characteristic flow depthsThe representative flow depths along the spillway are plotted in Figures 10 and 11, for Q = 80 and 140l/s. In Figure 10, the minimum and maximum flow depths obtained by visual observation through thesidewalls are also included. Taking into account that the PKW near the walls is antisymmetric, one mayinfer that the flow depths near the walls are of the same order of magnitude that those correspondingto the flow in the symmetry axis of the inlet or outlet keys. Figure 10 shows that the flow depths arevery large in the vicinity of the PKW, due to its peculiar geometry. The measurement of the flow depthsin reach I was very difficult, because of the significant turbulence and air entrainment. Downstreamof step 15, for Q = 80 l/s, or in all tested steps (for Q = 140 l/s), the characteristic flow depth liesbetween the minimum and maximum flow depths estimated by visual observation. This result is in lineof the findings of Matos (1999) and Meireles (2004), in identical stepped spillway, but downstream ofa WES weir. Figure 10 also shows that the equivalent clear water depth is much lower than the othercharacteristic depths, due to the large air entrainment and flow bulking.
In Figure 11, the equivalent clear water depth (h) and the characteristic flow depth (Y90) in thesymmetry axes of both keys are plotted, for Q = 80 and 140 l/s. The data gathered by Matos (1999) arealso plotted. Therein it can be observed that:
- The values of h e Y90 in the symmetry axis of the inlet key are initially greater than those for theoutlet key, and subsequently lower (e.g., downstream of step 21, for Q = 80 l/s);
- In the symetry axis of the inlet key, both h and Y90 tend to decrease significantly in a initial reach,and follow an almost constant trend further downstream;
- The h and Y90 values presented in Matos (1999) are of the same magnitude as those obtained inthe symmetry axes of the inlet and outlet keys, in the downstream end of the spillway reach; theyare, however, closer to the those obtained in the symmetry axis of the inlet key.
8
0
2
4
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8
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14
16
18
20
22
24
26
10 12 14 16 18 20 22 24 26 28 30 32 34 36 38 40 42 44
Ch
arac
teri
stic
flo
w d
ep
ths
(cm
)
Step number
Outlet Key
Y90 Ymin (OBS) Ymax (OBS) Ymean (OBS) h (Eq. 6)
(a)
0
2
4
6
8
10
12
14
16
18
20
22
24
26
10 12 14 16 18 20 22 24 26 28 30 32 34 36 38 40 42 44
Ch
arac
teri
stic
flo
w d
ep
ths
(cm
)
Step number
Inlet Key
Y90 Ymin (OBS) Ymax (OBS) Ymean (OBS) h (Eq. 6)
(b)
Figure 10: Characteristic flow depths along the chute, in the symmetry axes of the inlet and outlet keys,for Q = 80 l/s: (a) outlet key; (a) inlet key.
0,0
0,5
1,0
1,5
2,0
2,5
3,0
3,5
4,0
4,5
10 12 14 16 18 20 22 24 26 28 30 32 34
h (
cm)
Step number
Outlet Key Inlet Key Matos (1999)
(a)
0
1
2
3
4
5
6
7
8
9
10
10 12 14 16 18 20 22 24 26 28 30 32 34
Y9
0 (
cm)
Step number
Outlet Key Inlet Key Matos (1999)
(b)
Figure 11: Characteristic flow depths along the chute, in the symmetry axes of the inlet and outlet keys,for Q = 80 l/s; (a) equivalent clear water depth; (b) characteristic flow depth Y90 ; comparison with theresults presented by Matos (1999), for the same installation and discharge, downstream of a WES weir.
4.5. Velocity distributionThe normalized velocity distribution on self-aerated chute flow can be given as (Wood, 1991, Chanson,1996, 2001):
V
V90=
(y
Y90
) 1N
(9)
where y is measured perpendicular to the spillway surface, Y90 is the depth where the local airconcentration is 90%, V the local water velocity at the distance y and V90 is the velocity for y = Y90:
Figure 12 includes the normalized velocity distribution data obtained in the present study for theinlet and outlet keys and the respective regression equation (as per Equation 9), as well as the results byMatos (1999). The following conclusions can be drawn:
- In the upstream reach of the spillway, the velocity profiles in the symmetry axes of the outlet andinlet keys are very dissimilar (steps 15, 19), and become similar in the downstream reach (steps 30,32);
- In downstream reach of the spillway, the velocity profiles in the symmetry axes of the outlet and
9
inlet keys are similar to those obtained by Matos (1999) (step 30), whereas the values obtained inthe outlet key approach those of Matos (1999) on a larger chute extension (e.g., from step 19).
0,0
0,2
0,4
0,6
0,8
1,0
0,0 0,2 0,4 0,6 0,8 1,0
y/Y
90
V/V90
Step 15 N (Outlet) = 12,7
N (Inlet) = 9,5
Outlet Key
Trendline(Outlet)
Inlet Key
Trendline(Inlet)
Matos (1999)
Trendline(Matos 1999)
0,0
0,2
0,4
0,6
0,8
1,0
0,0 0,2 0,4 0,6 0,8 1,0
y/Y
90
V/V90
Step 19 N (Outlet) = 5,8 N (Inlet) = 2,7
Outlet Key
Trendline(Outlet)
Inlet Key
Trendline(Inlet)
Matos (1999)
Trendline(Matos 1999)
0,0
0,2
0,4
0,6
0,8
1,0
0,0 0,2 0,4 0,6 0,8 1,0
y/Y
90
V/V90
Step 30 N (Outlet) = 3,5 N (Inlet) = 2,6
Outlet Key
Trendline(Outlet)
Inlet Key
Trendline(Inlet)
Matos (1999)
Trendline(Matos 1999)
0,0
0,2
0,4
0,6
0,8
1,0
0,0 0,2 0,4 0,6 0,8 1,0
y/Y
90
V/V90
Step 32 N (Outlet) = 4,1 N (Inlet) = 4,7
Outlet Key
Trendline(Outlet)
Inlet Key
Trendline (Inlet)
Figure 12: Normalized velocity distribution along the chute, in the symmetry axes of the inlet and outletkeys, for Q = 80 l/s; comparison with the results presented by Matos (1999), for the same installationand discharge, downstream of a WES weir.
4.6. Hydraulic jump in the stilling basinMeasurements of pressure heads along the stilling basin floor were collected for discharges ranging from80 to 140 l/s. Piezometric taps were installed on the stilling basin floor and connected to a piezometricpanel to obtain pressure heads along the complete stilling basin and the downstream region. The locationof the piezometric taps can be found in Reis (2015).
For each discharge, the upstream end of the hydraulic jump was located next to the chute toe, at theimpact point of the flow. For the tested range of discharges, the Froude number at the upstream end ofthe hydraulic jump varied between 4.5 and 6.0, corresponding to a stable hydraulic jump, according toPeterka (1958).
In Figure 13, the mean pressure head is plotted as a function of the distance along the basin, measuredfrom the spillway toe. Also included in the same figure are the data obtained by Meireles (2004), inidentical facility but with a WES weir at the entrance of the spillway. The differences between theexperimental data gathered by the author and that by Meireles (as well as by Matos, 1999, not shownherein) are in general very small, leading to the conclusion that the energy dissipation is not greatlyinfluenced by the type of weir crest (WES or PKW), for the tested range of geometric conditions andflow rates.
5. ConclusionsThe aim of the present study was, essentially, to provide a contribution to the understanding of theskimming flow in stepped spillways downstream of Piano Key Weirs (PKW).
The following conclusions can be drawn from this experimental study:
10
0
10
20
30
40
50
0,0 0,5 1,0 1,5 2,0 2,5 3,0 3,5 4,0
p/γ
(cm
)
s (m)
Q = 80 l/s Q = 100 l/s
Q = 120 l/s Q = 140 l/s
Q = 80 l/s (Meireles 2004) Q = 100 l/s (Meireles 2004)
Q = 140 l/s (Meireles 2004)
Figure 13: Hydraulic jump: mean pressure head along the basin floor.
- The rating curve of the PKW is practically linear, being much more efficient than that of a WESweir; the empirical approach developed by Leite Ribeiro et al. (2012) fits well to the head-dischargedata acquired in the present investigation, but for low flow rates.
- The air concentration profiles in the symetry axis of the inlet key are clearly different from thosegathered in the outlet key, namely in the upstream reach of the spillway. Further downstream,the air concentration profiles on both keys are fairly similar, leading to the conclusion that the 3Dnature of the flow is strongly mitigated.
- The development of the mean air concentration along the spillway is significantly influenced by thekey axis (inlet or outlet), and pratically independent of the discharge.
- The mean air concentration in the symetry axis of the outley key tends to decrease down the spillway,inasmuch as observed downstream of WES weirs; in the symetry axis of the inlet key, the mean airconcentration decreases in a initial spillway reach, whereas it increases further downstream; also,the mean air concentration data obtained by Matos (1999) are in general limited by those obtainedin the outlet and inlet keys.
- The mean air concentration near the downstream end of the spillway reach under analysis is rela-tively close to that obtained on uniform flow over a smooth chute of identical slope.
- The values of the equivalent clear water depth (h) and characteristic flow depth (Y90) in the symetryaxis of the inlet key are initially greater than those for the outlet key, and subsequently lower; inthe downstream end of the spillway reach, the h and Y90 values presented in Matos (1999) are ofthe same magnitude as those obtained in the symetry axis of the inlet and outlet keys.
- In the upstream reach of the spillway, the velocity profiles in the symmetry axis of the outlet andinlet keys are very dissimilar, whereas they become similar in the downstream chute reach; also inthis reach, the velocity profiles in the symmetry axis of the outlet and inlet keys are similar to thoseobtained by Matos (1999).
- The differences between the pressure head data acquired herein at the floor of the hydraulic jumpstilling basin and those obtained by Meireles (2004) are in general very small, leading to the con-clusion that the energy dissipation is not significantly influenced by the type of weir crest (WES orPKW), for the range of tested geometric conditions and flow rates.
The research undertaken in the framework of the present dissertation may be broaden and deepen,namely by embrancing: (i) analysis of the flow properties for a wider range of discharges, verticals, andnearer the donwstream end of the chute; (ii) study of the flow conditions for other step heights (e.g., 4 cmor 2 cm); (iii) study of the residual energy from the hydraulic jump pressure head data; (iv) developmentof empirical models in order to estimate the flow conditions down the spillway; (v) study of the flow
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conditions on a smooth spillway donwstream of PKW; (vi) analsysis of the flow conditions in smoothand stepped spillways downstream of other types of PKW; (vii) study of the performance of other energydissipators (e.g., USBR type III stilling basins, roller buckets, ski jumps).
AcknowledgementsThe author gratefully acknowledge Professor Jorge Matos (IST) and Dr. Maria Teresa Viseu (LNEC) forall the support and supervision of her M.Sc. thesis.
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