Discussion of “Skimming, Nonaerated Flow on Stepped Spillways over Roller Compacted Concrete...
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Discussions and Closures Discussion of “Skimming, Nonaerated Flow on Stepped Spillways over Roller Compacted Concrete Dams” by Inês Meireles, Floriana Renna, Jorge Matos, and Fabián Bombardelli DOI: 10.1061/(ASCE)HY.1943-7900.0000591 Bo Wang 1 ; Ping Wu 2 ; Chao Wu 3 ; and Yun-Liang Chen 4 1 Associate Professor, State Key Laboratory of Hydraulics and Mountain River Engineering, Sichuan Univ., Chengdu, Sichuan 610065, China. E-mail: [email protected] 2 Lecturer, Institute of Architecture and Civil Engineering, Xihua Univ., Chengdu 610039, China. E-mail: [email protected] 3 Professor, State Key Laboratory of Hydraulics and Mountain River Engi- neering, Sichuan Univ., Chengdu, Sichuan 610065, China. E-mail: [email protected] 4 Associate Professor, State Key Laboratory of Hydraulics and Mountain River Engineering, Sichuan Univ., Chengdu, Sichuan 610065, China (corresponding author). E-mail: [email protected] The reach from the crest to the inception point of air entrainment on stepped spillways may become prone to cavitation damage because of the absence of air close to its bottom. Some methods for the bottom aeration of stepped spillways were proposed [e.g., Pfister et al. (2006) and Wang et al. (2008)]. A large number of hydraulic studies on the nonaerated region of the skimming flow have been conducted by the authors. The findings are useful for a designer. The discussers have investigated skimming flow (both the nonaer- ated region and the aerated region), and have some results to share with the authors. • The kinetic-energy correction coefficient α as a function of L=L i was suggested by the authors in the original paper’s Eq. (13). Another expression computing α was obtained by Meireles and Matos (2009). The value of α is calculated respectively from the previous formulas and shown in Fig. 1(a). The lines intersect at L=L i ¼ 0.622. For L=L i < 0.622, the value of α from Eq. (13) is smaller than that from the expression by Meireles and Matos (2009). For L=L i > 0.622, the contrary is the case. The kinetic-energy correction coefficient primarily depends on the cross- sectional distribution of velocity; the latter is impacted by the boundary. A standard Waterways Experiment Station (WES) spillway profile (composed of an upstream smooth region and 10 steps of increasing size) followed by steps with a slope of 53°, was adopted in the authors’ experiments. A broad-crested weir followed by steps (with constant width and height) with a slope of 26.6° was used in the tests by Meireles and Matos (2009). The discussers suggest that the expressions of α proposed by the authors and Meireles and Matos (2009) should be more suitable for application if the crest shape and the spillway slope are taken into consideration. The following expression is proposed for 0.36 ≤ L=L i ≤ 1: α ¼ 1 þ βðL=L i Þ tan θ ð1Þ where θ = spillway slope; and β = correction coefficient due to the crest shape. For a standard WES spillway profile, β ¼ 0.19. For a broad-crested weir, β ¼ 0.13. Differences in the values of α computed respectively from Eq. (1) and the original paper’ s Eq. (13) are not larger than 0.3%. When compared with the expression by Meireles and Matos (2009), differences do not exceed 1%. The results computed from Eq. (1) are in comparison with the experimental data by the authors and Meireles and Matos (2009), as shown in Fig. 1(b). • The flow accelerates down the spillway due to the force of gravity. The water depth will decrease and the interior turbu- lence will become more intense. When the boundary layer thickness has grown to the free surface, the air entrainment will take place. As a result, the depth decreases first and then increases along the chute. The experimental data by Sorensen (1985) supported this characteristic, and were used for the following analyses of the minimum depth and the correspond- ing location. The normalized water depth, d=d c , is plotted against the normalized distance L=L i , as shown in Fig. 2. The variable L i from Eq. (1) in the original paper and the observations by Sorensen (1985) were used respectively in Figs. 2(a and b). The value of L i from Eq. (1) is smaller than that from the observation, so the data points in Fig. 2(a) are farther from the vertical axis compared with those in Fig. 2(b). It is concluded that the minimum depth is located in the vicinity of the inception point. The conclusion can not be made from Fig. 2 that the 0.0 0.2 0.4 0.6 0.8 1.0 0.7 0.8 0.9 1.0 1.1 1.2 1.3 Study of Authors Meireles and Matos (2009) Eq. (1) (a) α L/L i 0.0 0.2 0.4 0.6 0.8 1.0 0.7 0.8 0.9 1.0 1.1 1.2 1.3 (b) Study of Authors Meireles and Matos (2009) Eq. (1) α L/L i Fig. 1. Evolution of the kinetic-energy correction coefficient in the nonaerated region: (a) comparison among expressions by the authors, Meireles and Matos (2009), and the discussers; (b) comparison among Eq. (1) and experimental data by the authors and Meireles and Matos (2009) © ASCE 07014011-1 J. Hydraul. Eng. J. Hydraul. Eng. 2014.140. Downloaded from ascelibrary.org by University of California, San Diego on 11/17/14. Copyright ASCE. For personal use only; all rights reserved.
Transcript of Discussion of “Skimming, Nonaerated Flow on Stepped Spillways over Roller Compacted Concrete...
Discussions and Closures
Discussion of “Skimming, NonaeratedFlow on Stepped Spillways over RollerCompacted Concrete Dams” byInês Meireles, Floriana Renna,Jorge Matos, and Fabián BombardelliDOI: 10.1061/(ASCE)HY.1943-7900.0000591
Bo Wang1; Ping Wu2; Chao Wu3; and Yun-Liang Chen4
1Associate Professor, State Key Laboratory of Hydraulics and MountainRiver Engineering, Sichuan Univ., Chengdu, Sichuan 610065, China.E-mail: [email protected]
2Lecturer, Institute of Architecture and Civil Engineering, Xihua Univ.,Chengdu 610039, China. E-mail: [email protected]
3Professor, State Key Laboratory of Hydraulics and Mountain River Engi-neering, Sichuan Univ., Chengdu, Sichuan 610065, China. E-mail:[email protected]
4Associate Professor, State Key Laboratory of Hydraulics and MountainRiver Engineering, Sichuan Univ., Chengdu, Sichuan 610065, China(corresponding author). E-mail: [email protected]
The reach from the crest to the inception point of air entrainment onstepped spillways may become prone to cavitation damage becauseof the absence of air close to its bottom. Some methods for thebottom aeration of stepped spillways were proposed [e.g., Pfisteret al. (2006) and Wang et al. (2008)]. A large number of hydraulicstudies on the nonaerated region of the skimming flow have beenconducted by the authors. The findings are useful for a designer.The discussers have investigated skimming flow (both the nonaer-ated region and the aerated region), and have some results to sharewith the authors.• The kinetic-energy correction coefficient α as a function
of L=Li was suggested by the authors in the original paper’sEq. (13). Another expression computing α was obtainedby Meireles and Matos (2009). The value of α is calculatedrespectively from the previous formulas and shown inFig. 1(a). The lines intersect at L=Li ¼ 0.622. For L=Li <0.622, the value of α from Eq. (13) is smaller than thatfrom the expression by Meireles and Matos (2009). ForL=Li > 0.622, the contrary is the case. The kinetic-energycorrection coefficient primarily depends on the cross-sectional distribution of velocity; the latter is impactedby the boundary. A standard Waterways Experiment Station(WES) spillway profile (composed of an upstream smoothregion and 10 steps of increasing size) followed by stepswith a slope of 53°, was adopted in the authors’ experiments.A broad-crested weir followed by steps (with constant widthand height) with a slope of 26.6° was used in the tests byMeireles and Matos (2009). The discussers suggest thatthe expressions of α proposed by the authors and Meirelesand Matos (2009) should be more suitable for applicationif the crest shape and the spillway slope are taken intoconsideration. The following expression is proposed for0.36 ≤ L=Li ≤ 1:
α ¼ 1þ βðL=LiÞtan θ ð1Þwhere θ = spillway slope; and β = correction coefficient dueto the crest shape. For a standard WES spillway profile,
β ¼ 0.19. For a broad-crested weir, β ¼ 0.13. Differencesin the values of α computed respectively from Eq. (1) andthe original paper’s Eq. (13) are not larger than 0.3%.When compared with the expression by Meireles and Matos(2009), differences do not exceed 1%. The results computedfrom Eq. (1) are in comparison with the experimental databy the authors and Meireles and Matos (2009), as shownin Fig. 1(b).
• The flow accelerates down the spillway due to the force ofgravity. The water depth will decrease and the interior turbu-lence will become more intense. When the boundary layerthickness has grown to the free surface, the air entrainmentwill take place. As a result, the depth decreases first and thenincreases along the chute. The experimental data by Sorensen(1985) supported this characteristic, and were used for thefollowing analyses of the minimum depth and the correspond-ing location.The normalized water depth, d=dc, is plotted against the
normalized distance L=Li, as shown in Fig. 2. The variableLi from Eq. (1) in the original paper and the observations bySorensen (1985) were used respectively in Figs. 2(a and b).The value of Li from Eq. (1) is smaller than that from theobservation, so the data points in Fig. 2(a) are farther fromthe vertical axis compared with those in Fig. 2(b). It is concludedthat the minimum depth is located in the vicinity of the inceptionpoint. The conclusion can not be made from Fig. 2 that the
0.0 0.2 0.4 0.6 0.8 1.00.7
0.8
0.9
1.0
1.1
1.2
1.3
Study of Authors Meireles and Matos (2009) Eq. (1)
(a)
α
L/Li
0.0 0.2 0.4 0.6 0.8 1.00.7
0.8
0.9
1.0
1.1
1.2
1.3
(b)
Study of Authors Meireles and Matos (2009) Eq. (1)
α
L/Li
Fig. 1. Evolution of the kinetic-energy correction coefficient in thenonaerated region: (a) comparison among expressions by the authors,Meireles and Matos (2009), and the discussers; (b) comparison amongEq. (1) and experimental data by the authors and Meireles andMatos (2009)
© ASCE 07014011-1 J. Hydraul. Eng.
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minimum depth is certainly located upstream of the inceptionpoint. The reason is that the depth measurements made bySorensen (1985) were at the tips of steps 6, 15, 24, 33, 42, 51,59 (toe), consequently the minimum depth listed in Table 2 ofthe paper by Sorensen (1985) is not certainly but close to theactual values.
The minimum depth dmin and the location Lmin from theobservations by Sorensen (1985) are shown in Figs. 3 and 4,respectively, excluding the results of Run C-10 becauseits minimum depth is not located in the stepped region.For 2.2 < lnð1=dcÞ < 3.9 or 0.6 < lnð1=F�Þ < 3.1, dmin can bepredicted by
lnð1=dminÞ ¼ 0.9 lnð1=dcÞ þ 0.82 ð2Þor
lnðdmin=kÞ ¼ 0.6 lnðF�Þ − 0.46 ð3Þ
For 1.7 < F� < 21.8, the data suggest
Lmin=h ¼ 7e0.07F� ð4Þ
In Eqs. (3) and (4), the roughness Froude numberF� ¼ qw=ðg sin θk3Þ1=2, where qw = unit discharge, g = accelerationdue to gravity, θ = spillway slope, and k = roughness heightperpendicular to pseudobottom, defined as k ¼ h cos θ.
The authors have conducted a large number of experi-mental studies on the depth at the inception point as well asthe location and have obtained relevant expressions. It maybe interesting to compare the minimum depth and the depth
at the inception point together with their corresponding loca-tions. The discussers would appreciate the authors’ commentson this issue.
Acknowledgments
The discussers acknowledge the financial supports of theNational Natural Science Foundation of China (Grant No.
0 4 8 12 160.0
0.5
1.0
1.5
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L/Li=1
d/d c
L /Li
C-1C-2C-3C-4C-5C-6C-7C-8C-9C-10
0 4 8 12 160.0
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1.5
(b)
L/Li=1
d/d c
L /Li
C-1C-2C-3C-4C-5C-6C-7C-8C-9C-10
Fig. 2. Evolution of the normalized water depth along the steppedspillway: (a) Li from Eq. (1) in the original paper; (b) Li from theobservation by Sorensen (1985)
0 1 2 3 4 50
1
2
3
4
5
(a)
ln (
1/d m
in)
Sorensen (1985) Eq. (2)
ln (1/dc)
0 1 2 3 4 5-0.5
0.0
0.5
1.0
1.5
2.0
(b)
ln (d
min/k
)
Sorensen (1985) Eq. (3)
ln (F*)
Fig. 3. Minimum depth of the skimming flow: (a) variation with thecritical depth; (b) variation with the roughness Froude number
0 5 10 15 20 250
5
10
15
20
25
30
35
F*
L min/h
Sorensen (1985) Eq. (4)
Fig. 4. Location of the minimum depth
© ASCE 07014011-2 J. Hydraul. Eng.
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51209155 and 51109149) and the Research Fund for the Doc-toral Program of Higher Education of China (20110181120093).
References
Meireles, I., and Matos, J. (2009). “Skimming flow in the nonaerated regionof stepped spillways over embankment dams.” J. Hydraul. Eng.,10.1061/(ASCE)HY.1943-7900.0000047, 685–689.
Pfister, M., Hager, W. H., and Minor, H. E. (2006). “Bottom aerationof stepped spillways.” J. Hydraul. Eng., 10.1061/(ASCE)0733-9429(2006)132:8(850), 850–853.
Sorensen, R. (1985). “Stepped spillway hydraulic model investigation.”J. Hydraul. Eng., 10.1061/(ASCE)0733-9429(1985)111:12(1461),1461–1472.
Wang, B., Wu, C., Hu, Y. H., and Mo, Z. Y. (2008). “Discussion of ‘bottomaeration of stepped spillways.’” J. Hydraul. Eng., 10.1061/(ASCE)0733-9429(2008)134:8(1180), 1180–1181.
© ASCE 07014011-3 J. Hydraul. Eng.
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