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ASDSO Webinar August 20, 2013
Hydraulic Design of Labyrinth Weirs
2Hydraulic Design of Labyrinth Weirs 2
Dr. Blake P. Tullis
Utah State University
Dr. Brian M. Crookston
Schnabel Engineering
Standard Head-Discharge Relationships for Weirs
3
h
P
Energy Grade Line
V2/2g
V
Ht
Q =CLHt3/2
Q = discharge
C= discharge coefficient
L = weir length
Ht= total upstream head
Q =2
3C
dL 2gH
t
3/2
Q = discharge
Cd= dimensionless discharge coefficient
L = weir length
Ht= total upstream head
g= gravity
Hydraulic Design of Labyrinth Weirs 3
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How can we increase weir discharge capacity?
4
Q =2
3CdL 2gHt
3/2 Q =CLHt3/2
Ogee Crest vs. Broad Crested Weir
Hydraulic Design of Labyrinth Weirs 4
Increase discharge coefficient with improved crest shapes
How can we increase weir discharge capacity?
5
Q =2
3C
dL 2gH
t
3/2 Q =CLHt3/2
Labyrinth 200-600%L
Box-Inlet Drop200-400%L
Radial Weir111%L for 90
157%L for 180
Piano Key200-600%L
Hydraulic Design of Labyrinth Weirs 5
IncreaseL with non-linear or 3-D weirs
6
Radial Weirs
Hydraulic Design of Labyrinth Weirs 6
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7
Box-Inlet Drop Spillway
Hydraulic Design of Labyrinth Weirs 7
8
Fuse Gates
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9
Labyrinth Spillways
Hydraulic Design of Labyrinth Weirs 9
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10Hydraulic Design of Labyrinth Weirs 10
Labyrinth Weir Prototypes
Brazos Dam, Texas (USA)
Run-of-river labyrinth weir structure
11Hydraulic Design of Labyrinth Weirs 11
Labyrinth Weir Prototypes
Single-cycle labyrinth weir
Oneida, Pennsylvania (USA)
12Hydraulic Design of Labyrinth Weirs 12
Labyrinth Weir Prototypes
Yahoola Dam, Georgia (USA)
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13Hydraulic Design of Labyrinth Weirs 13
Labyrinth Weir Prototypes
Lake Townsend, North Carolina (USA)
Staged labyrinth weir
Lower-staged cycles
14Hydraulic Design of Labyrinth Weirs 14
Labyrinth Weir PrototypesArced Labyrinth Weir with integrated bridge piers and nappe breaker/vent pipes
Maguga Dam, Swaziland
15
Piano Key Weirs
Hydraulic Design of Labyrinth Weirs 15
L Etroit Dam (France)
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Hydraulic Design of Labyrinth Weirs 19
Hydraulic Design of Labyrinth Weirs 20
Hydraulic Design of Labyrinth Weirs 21
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22Hydraulic Design of Labyrinth Weirs
0.0
0.2
0.4
0.6
0.8
1.0
1.2
0 20 40 60 80 100
HT
(ft)
Q (cfs)
QR 1 cycle P=36in tw=4.5in w/P=2.66 L/W = 3.25
Discharge Capacity
232
3
2Tc)(d HgLCQ =
)nappe,flowapproach,,,shapecrest,,,,()( dTwd HHAPtfC =
Hydraulic Design of Labyrinth Weirs 23
Spreadsheet Design Method
Hydraulic Design of Labyrinth Weirs 24
Design Method
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Hydraulic Design of Labyrinth Weirs 25
Design Method
26
Discharge CoefficientsQuarter-Round Crests
Hydraulic Design of Labyrinth Weirs 26
27
Discharge CoefficientsHalf-Round Crests
Hydraulic Design of Labyrinth Weirs 27
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28
Discharge Coefficients
Hydraulic Design of Labyrinth Weirs 28
29
HT/P Limits
HT/P limited by experimental data
Crookston (2010) curve-fit equations trend-basedHT/P >1
Hydraulic Design of Labyrinth Weirs 29
Tullis et al. (1995) and Crookston
(2010)
Hydraulic Design of Labyrinth Weirs 30
dP
HaC
c
P
THb
Td +=
)(
HT/P Limits
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31
Crest Comparison
0.95
1.00
1.05
1.10
1.15
1.20
0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0
Cd-HR/Cd-QR
HT/P
6 degree
8 degree
10 degree
12 degree
15 degree
20 degree
35 degree
90 degree
Hydraulic Design of Labyrinth Weirs 31
Rating Curve Validation
Hydraulic Design of Labyrinth Weirs 32
Tullis et al. (1995)
Willmore (2004) QR Crest Shape
Validation
Rating Curve Validation
Hydraulic Design of Labyrinth Weirs 33
Validation
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0
Cd()
HT/P
6 de gr ee H R Cr oo ks to n 8 d eg re e HR C roo ks to n 1 0 d eg re eH R Cr oo ks to n 1 2 d eg re e H R Cr oo kst on
1 5 de gr ee HR C ro ok st on 2 0 de gr ee H R Cr oo kst on 3 5 de gr ee HR C ro ok st on 7 d eg re e HR W il lm or e
8 d eg re eH R Wi ll mo re 1 0 d eg re e H R Wi ll mo re 1 2 d eg re eH R Wi ll mo re 1 5 d eg re e H R Wi ll mo re
2 0 de gr ee H R W il l mo re 3 5 de gr ee H R Wi ll mo r e
Willmore (2004) HR Crest Shape
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Rating Curve Validation
Hydraulic Design of Labyrinth Weirs 34
Validation
35
Nappe Behavior
Hydraulic Design of Labyrinth Weirs 35
36
Nappe Behavior
Hydraulic Design of Labyrinth Weirs 36
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37
Nappe Behavior
Hydraulic Design of Labyrinth Weirs 37
38Hydraulic Design of Labyrinth Weirs 38
Nappe Behavior
39Hydraulic Design of Labyrinth Weirs 39
Nappe Vibration
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Hydraulic Design of Labyrinth Weirs 43
44
Nappe Interference & Local
Submergence
Hydraulic Design of Labyrinth Weirs 44
45
Nappe Interference & Local
Submergence
Hydraulic Design of Labyrinth Weirs 45
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46
Nappe Interference & Local
Submergence
Hydraulic Design of Labyrinth Weirs 46
47Hydraulic Design of Labyrinth Weirs 47
( ) 03916.07-E155.5038.2307.1
1+
=
P
H
B
BTint
48
Nappe Interference & Local
Submergence
Hydraulic Design of Labyrinth Weirs 48
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49Hydraulic Design of Labyrinth Weirs 49
Q & A Break
50
Labyrinth Weir Submergence
Hydraulic Design of Labyrinth Weirs 50
51
Labyrinth Weir Submergence
Hydraulic Design of Labyrinth Weirs 51
Ogee crest weir, Iowa River,
Iowa City (USA)
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52
Labyrinth Weir Submergence
Hydraulic Design of Labyrinth Weirs 52
Tailwater submergence definition: S=H* /Hd
Key Terms:
Ho: free-flow upstream total head (relative to crest elevation)
ho: free-flow upstream water depth (relative to crest elevation)
H*: submerged upstream total head (relative to crest elevation)
h*: submerged upstream water depth (relative to crest elevation)
Hd: downstream total head (relative to crest elevation)
hd: downstream water depth (relative to crest elevation)
s = h* /hdAlternative Tailwater submergence definition:
53
Labyrinth Weir Submergence
Hydraulic Design of Labyrinth Weirs 53
Modular Submergence Limit (H*=Ho)
Free-flow conditions
no longer apply (H*Ho)
54
Labyrinth Weir Submergence
Hydraulic Design of Labyrinth Weirs 54
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55
Labyrinth Weir Submergence
Hydraulic Design of Labyrinth Weirs 55
Submerged Labyrinth WeirHead-Discharge Calculations
Inputs: Q(hydrology)Hd(HEC-RAS)
Calculate Qvs.HT(Ho)Using design method
CalculateHd/HoDetermineH*/Housing Submergence Curve
H*=(H*/Ho)*Ho
Output: (Q,Ho) submerged rating curve data point
56
Discharge Efficiency vs. Labyrinth Weir Cycle Geometry
Cycle Efficiency ()
1. Cddecreases with decreasing
*smaller Cd = smaller unit discharge
Hydraulic Design of Labyrinth Weirs 56
2.L increases with decreasing
*assuming cycle width w remains constant
*assuming no longitudinal footprint restrictions
57
0.0
0.5
1.0
1.5
2.0
2.5
3.0
3.5
4.0
4.5
0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0
'=Cd()Lc-cycle/w
HT/P
6 de gr ee H R 8 de gr ee HR
1 0 de gr ee H R 1 2 de gr e e HR
1 5 de gr ee H R 2 0 de gr e e HR
3 5 de gr ee H R 9 0 de gr e e HR
Cycle Efficiency ()
' =CdLcycle
w
shows relative change in efficiency between values for a given HT/P
Hydraulic Design of Labyrinth Weirs 57
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. 0
.
.
. 0
. 0
. 0
. 0
.
.
. 0
Straight Weir
15Labyrinth
0.00
0.50
1.00
1.50
2.00
2.50
0 0.2 0.4 0.6 0.8 1 1.2
H/P
CycleEfficiency(CdxL/W)
Straight Weir
15Labyrinth
Cycle Efficiency ()15-degree labyrinth vs. linear weir
Cd
Ht/PHydraulic Design of Labyrinth Weirs 58
59
Debris / Sediment
Hydraulic Design of Labyrinth Weirs 59
60
Biological Growth on Crest
Hydraulic Design of Labyrinth Weirs 60
Labyrinth weir crest shape: ogee crest profile
Run-of-the-river dam: crest always wet
Ogee crest profile used to keep nappe attached (clinging flow): improve discharge efficiency
Algal growth on the crest caused the nappe to separate from crest: benefit of ogee crest not fully realized
Biological growth on the crest likely not an issue for spillways that are typically dry (emergency spillway, etc.)
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62
High Headwater Ratios
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CFD
Hydraulic Design of Labyrinth Weirs 63
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0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0
Cd(15)
HT/P
Model1
Model2
CFD Model
Crookston (2010) Curve Fit
Hydraulic Design of Labyrinth Weirs 64
High Headwater Ratios
Hydraulic Design of Labyrinth Weirs 65
High Headwater Ratios
Hydraulic Design of Labyrinth Weirs 66
HT/P 2.1
dP
HaC
c
P
THb
Td +=
)(
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Hydraulic Design of Labyrinth Weirs 67
Configurations/Abutments
Hydraulic Design of Labyrinth Weirs 68
Configurations/Abutments
69
Arced Labyrinth Weir Geometry
Hydraulic Design of Labyrinth Weirs 69
Arced Labyrinth Weirs
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Hydraulic Design of Labyrinth Weirs 70
Arced Labyrinth Weirs
Hydraulic Design of Labyrinth Weirs 71
Reservoir vs. In-channel
0.80
0.85
0.90
0.95
1.00
1.05
1.10
1.15
1.20
0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7
Cd-Res
/Cd-Channel
HT/P
=12 Normal in Channel =12Ar ced Projecting, =10
=12Flush =12Pr ojecting (Linear, =0)
=12 Rounded Inlet
72
Residual Energy
Lopes, Matos, and Melo (2006, 2008)
0
0.5
1
1.5
2
2.5
0 25 50 75 100 125 150 175 200
Unit Discharge, q (l/s/m)
Hds/P
L/W = 2
L/W = 3
L/W = 4
L/W = 5
Drop (Chanson, 1994)
Hydraulic Design of Labyrinth Weirs 72
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P = 6 inches
P = 12 inches
P = 36 inches
Hydraulic Design of Labyrinth Weirs 73
Scale Effects
Partially Aerated
Hydraulic Design of Labyrinth Weirs 74
Scale Effects
75Hydraulic Design of Labyrinth Weirs 75
Q & A Break
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Sectional Model Studies
Hydraulic Design of Labyrinth Weirs 76
Sectional Model Studies
Hydraulic Design of Labyrinth Weirs 77
Full-Width Model Studies
Hydraulic Design of Labyrinth Weirs 78
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When is a Model Recommended
Hydraulic Design of Labyrinth Weirs 79
Prototype hydraulic/geometric conditions fall outside published design conditions
Wall height effects (w/P)
Approach flow angle
Approach flow topography and abutments
Energy dissipation
Wall thickness & apex details
Arced Labyrinth Weir Model
Hydraulic Design of Labyrinth Weirs 80
Approach Channel Details
Arced Labyrinth Weir Model
Hydraulic Design of Labyrinth Weirs 81
Approach Channel Details
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Labyrinth Weir Model
Hydraulic Design of Labyrinth Weirs 82
Significant Approach Flow Angle
Advantages/Limitations
Physical Model Very visual
Quick changes
Handles complex flow
patterns
Scale Effects
Cost/construction schedule
Data limited to specific
measurement locations
Calibration (roughness
models)
Lab space/flow capacity
Numerical Model Easy streamline visualization
Data available anywhere in
domain
Easily stored
Cost/simulation time
Calibration to physical model
data required
Results vary with user-
defined boundary conditions
and turbulence simulation
model selection
Hydraulic Design of Labyrinth Weirs 83
CompositeModeling
84
Non-Linear Weirs with Footprint Restrictions
Hydraulic Design of Labyrinth Weirs 84
Piano Key Weirs
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85
Non-Linear Weirs with Footprint Restrictions
Hydraulic Design of Labyrinth Weirs 85
Piano Key Weirs
PK Weir History
Lemprire 2003, 2005, 2009
Laugier 2007, 2009
Ribeiro et al 2007, 2009
Machiels et al 2009
Anderson and Tullis 2012
Abdorreza et al. 2012
Labyrinth PK-Weir Workshops
Belgium 2011
New Delhi, India May 2012
Hydraulic Design of Labyrinth Weirs 86
Discharge
Cd=f (HT,L, Wi, Wo,B, P, Tw, Ramp Angle, Parapet)
Hydraulic Design of Labyrinth Weirs 87
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PK Weir Submergencechannel applications
free-flow PK weir local submergencetailwater submergence
Dabling and Tullis (2012)
Piano Key Weir Submergence in Channel Applications
Journal of Hydraulic Engineering
Hydraulic Design of Labyrinth Weirs 88
PK vs. Labyrinth Weir
1.00
1.50
2.00
2.50
3.00
3.50
4.00
4.50
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
H/P
CdxL/W
PK 6
8 10
12 15
20 RL
Cycleefficiency
Hydraulic Design of Labyrinth Weirs 89
PK vs. Labyrinth WeirGeometries required for
equivalent discharge
Changes in discharge and weir dimensions
with channel width constrained
Q-specific
Q-specific
Hydraulic Design of Labyrinth Weirs 90
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Select References for Labyrinth and PK Weirs
1. Crookston, B. M. and B. P. Tullis (?). Hydraulic Design and Analysis of Labyrinth Weirs. J. Irrigation
and Drainage (two companion papers-under review).
2. Crookston, B. M. and B. P. Tullis (2012). Arced Labyrinth Weirs. J. Hydraulic Engineering, 138(6),
pp. 555-562, DOI: 10.1061/(ASCE)HY.1943-7900.0000553.
3. Anderson, R. M. and B. P. Tullis (2012). Comparison of Piano Key and Rectan gular Labyrinth WeirHydraulic. J. Hydraulic Engineering (in press), doi:10.1061/(ASCE)HY.1943-7900.0000509.
4. Crookston, B. M. and B. P. Tullis (2012). Discharge Efficiency of Reservoir-Application-Specific
Labyrinth Weirs. J. of Irrigation and Drainage, 138(6), 564-568 , doi: 10.1061/(ASCE)IR.1943-
4774.0000451.
5. Dabling, M. and B. P. Tullis (2012). Piano Key Weir Submergence in Channel Applications .J.
Hydraulic Engineering (in press), doi:10.1061/(ASCE)HY.1943-7900.0000563 .
6. Crookston, B. M. and B. P. Tullis (2012). Labyrinth Weirs: Nappe Interference and Local
Submergence.J. Irritation and Drainage, 138(6), pp. 555-562, doi: 10.1061/(ASCE)IR.1943-
4774.0000466.
7. Anderson, R. M. and B. P. Tullis (2012). Piano Key Weir: Reservoir vs. Channel Applications. J.
Hydraulic Engineering (in press), doi:10.1061/(ASCE)IR.1943-4774.0000464.
8. Erpicum, S., F. Laugier, J. L. Boillat, M. Pirotton, B. Reverchon, and A. J. Schleiss (2011).Labyrinth
and Piano Key Weirs. CRC Press, New York, NY.
9. Falvey. H. (2003).Hydraulic Design of Labyrinth Weirs. ASCE, Reston, VA.
10.Tullis, J. P, N. Amanian, and D. Waldron ( 1995). Design of Labrinth Weir Spillways. J. Hydraulic
Engineering, 121(3), 247-255.
Hydraulic Design of Labyrinth Weirs 91
State of Utah
Utah State University-Utah Water Research Lab
Ricky Anderson
Nathan Christensen
Tyler Seamons
Schnabel Engineering
Dave Campbell
Greg Paxson
Freese & Nichols
Idaho State University
Dr. Bruce Savage
92
Acknowledgements
Hydraulic Design of Labyrinth Weirs 92
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