Hydraulic Design of Labyrinth Weirs
ASDSO Webinar August 20, 2013
Dr. Blake P. Tullis
Dr. Brian M. Crookston
Utah State University
Schnabel Engineering
[email protected]
[email protected]
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Standard Head-Discharge Relationships for Weirs Q = CLH t3/2
2 Q = Cd L 2gH t3/2 3
Q = discharge
Q = discharge
C = discharge coefficient
Cd = dimensionless discharge coefficient
L = weir length
L = weir length
Ht = total upstream head
Ht = total upstream head
V2/2g
g= gravity
Energy Grade Line Ht
h
V P
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How can we increase weir discharge capacity?
2 Q = Cd L 2gH t3/2 3
Q = CLH t3/2
Increase discharge coefficient with improved crest shapes Ogee Crest
vs.
Broad Crested Weir
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How can we increase weir discharge capacity?
2 Q = Cd L 2gH t3/2 3
Q = CLH t3/2
Increase L with non-linear or 3-D weirs
Radial Weir
Box-Inlet Drop
111% L for 90° 157% L for 180°
200-400% L
Labyrinth
200-
600% L
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Piano Key 200-600% L
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Radial Weirs
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Box-Inlet Drop Spillway
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Fuse Gates
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Labyrinth Spillways
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Labyrinth Weir Prototypes Run-of-river labyrinth weir structure
Brazos Dam, Texas (USA)
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Labyrinth Weir Prototypes Single-cycle labyrinth weir
Oneida, Pennsylvania (USA)
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Labyrinth Weir Prototypes
Yahoola Dam, Georgia (USA)
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Labyrinth Weir Prototypes Staged labyrinth weir Lower-staged cycles
Lake Townsend, North Carolina (USA)
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Labyrinth Weir Prototypes Arced Labyrinth Weir with integrated bridge piers and nappe breaker/vent pipes
Maguga Dam, Swaziland Hydraulic Design of Labyrinth Weirs
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Piano Key Weirs
L’ Etroit Dam (France)
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Labyrinth Research Timeline Falvey (2003)
Taylor (1968) Hay & Taylor (1970)
Darvas (1971)
Megalhães & Lorena (1989)
Lux & Hinchliff (1985)
Houston (1983)
Tullis et al (1995)
Tullis et al (2007)
Crookston & Tullis (2012a,b,c)
Lopes et al.
Crookston & Tullis
(2006, 2008)
(2013a,b) Crookston (2010)
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Terminology
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Discharge Capacity 2 32 Q = C d ( α ° ) Lc 2 g H T 3 C d (α ° ) = f (α , t w , P, A, crest shape, H T , H d , approach flow , nappe) 1.2 QR 1 cycle P=36in tw=4.5in w/P=2.66 L/W = 3.25
1.0
HT (ft)
0.8
0.6
0.4
0.2
0.0 0
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40
Q (cfs)
60
80
100
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Spreadsheet Design Method
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Design Method
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Design Method
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Discharge Coefficients Quarter-Round Crests
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Discharge Coefficients Half-Round Crests
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Discharge Coefficients
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HT/P Limits HT/P limited by experimental data Crookston (2010) curve-fit equations trend-based HT/P >1
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Tullis et al. (1995) and Crookston HT/P(2010) Limits C d (α °) = a
Hydraulic Design of Labyrinth Weirs
HT P
H b T P
c
+d
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Crest Comparison 1.20
6 degree 8 degree 10 degree 12 degree
1.15
15 degree 20 degree
Cd-HR / Cd-QR
35 degree 90 degree
1.10
1.05
1.00
0.95 0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
HT/P
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Rating Validation Curve Validation Tullis et al. (1995) Willmore (2004)
QR Crest Shape
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Rating Validation Curve Validation Willmore (2004)
HR Crest Shape
0.9 0.8 0.7 0.6 0.5
Cd(α°) 0.4 0.3 0.2 0.1 0 0.0
6 degree HR Crookston
8 degree HR Crookston
10 degree HR Crookston
12 degree HR Crookston
15 degree HR Crookston
20 degree HR Crookston
35 degree HR Crookston
7 degree HR Willmore
8 degree HR Willmore
10 degree HR Willmore
12 degree HR Willmore
20 degree HR Willmore
35 degree HR Willmore
0.1
0.2
0.3
0.4
0.5
0.6
0.7
15 degree HR Willmore
0.8
0.9
1.0
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Rating Validation Curve Validation
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Nappe Behavior
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Nappe Behavior
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Nappe Behavior
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Nappe Behavior
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Nappe Vibration
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Nappe Vibration
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Nappe Instability
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Nappe Instability
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Nappe Interference & Local Submergence
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Nappe Interference & Local Submergence
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Nappe Interference & Local Submergence
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1.307 Bint 1 α° H + 0.03916 = 2.038 (5.155E - 7 ) T B P
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Nappe Interference & Local Submergence
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Q & A Break
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Labyrinth Weir Submergence
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Labyrinth Weir Submergence
Ogee crest weir, Iowa River, Iowa City (USA) Hydraulic Design of Labyrinth Weirs
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Labyrinth Weir Submergence Tailwater submergence definition: S = H * /H d
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)
Alternative Tailwater submergence definition:
s = h * /hd
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Labyrinth Weir Submergence Modular Submergence Limit (H*=Ho)
Free-flow conditions no longer apply (H*≠Ho)
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Labyrinth Weir Submergence
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Labyrinth Weir Submergence Submerged Labyrinth Weir Head-Discharge Calculations Inputs: Q (hydrology) H d (HEC-RAS)
Calculate Q vs. HT (H o) Using design method
Calculate Hd/H o Determine H*/Ho using Submergence Curve Figure to determin
Repeat
H*= (H*/Ho)* Ho Output: (Q, Ho) submerged rating curve data point
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Discharge Efficiency vs. Labyrinth Weir Cycle Geometry Cycle Efficiency (ε’) 1. Cd decreases with decreasing α *smaller Cd = smaller unit discharge 2. L increases with decreasing α *assuming cycle width w remains constant *assuming no longitudinal footprint restrictions
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Cycle Efficiency (ε’) ε'=
Cd Lcycle w
4.5 6 degree HR
8 degree HR
10 degree HR
12 degree HR
15 degree HR
20 degree HR
35 degree HR
90 degree HR
4.0
ε'=Cd(α°)Lc-cycle/w
3.5 3.0 2.5 2.0 1.5 1.0 0.5 0.0 0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
HT/P
ε’ shows relative change in efficiency between α values for a given HT/P
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Cycle Efficiency (ε’) 15-degree labyrinth vs. linear weir
2.50
Cycle Efficiency (Cd x L/W)
2.00
0.90 0.80
1.50
1.00
0.50
Straight Weir 15º Labyrinth
0.70 0.60
0.00 0
0.50
0.2
0.4
0.6
0.8
1
1.2
H/P
Cd
0.40 0.30 0.20
Straight Weir 15º Labyrinth
0.10 0.00
Ht/P
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Debris / Sediment
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Biological Growth on Crest
• 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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High Headwater Ratios
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CFD
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High Headwater Ratios 0.7
0.6
0.5
0.4
Cd(15°) 0.3
0.2 Model 1 Model 2
0.1 CFD Model Crookston (2010) Curve Fit
0.0 0.0
0.2
0.4
0.6
0.8
1.0
1.2
1.4
1.6
1.8
2.0
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High Headwater Ratios
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HT/P ≤ 2.1 C d (α °) = a
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HT P
H b T P
c
+d
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Configurations/Abutments
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Configurations/Abutments
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Arced Labyrinth Weirs
Arced Labyrinth Weir Geometry
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Arced Labyrinth Weirs
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Reservoir vs. In-channel 1.20 1.15
Cd-Res / Cd-Channel
1.10 1.05 1.00 0.95 0.90 α=12° Normal in Channel
0.85
α=12° Arced Projecting, θ=10°
α=12° Flush
α=12° Projecting (Linear, θ=0°)
α=12° Rounded Inlet
0.80 0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
HT/P Hydraulic Design of Labyrinth Weirs
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Residual Energy 2.5
2
Hds/P
1.5
1 L/W = 2 L/W = 3 L/W = 4 L/W = 5 Drop (Chanson, 1994)
0.5
0 0
25
50
75
100
125
150
175
200
Unit Discharge, q (l/s/m)
Lopes, Matos, and Melo (2006, 2008) Hydraulic Design of Labyrinth Weirs
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Scale Effects P = 6 inches P = 12 inches
P = 36 inches Hydraulic Design of Labyrinth Weirs
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Scale Effects Partially Aerated
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Q & A Break
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Sectional Model Studies
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Sectional Model Studies
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Full-Width Model Studies
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When is a Model Recommended 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
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Arced Labyrinth Weir Model Approach Channel Details
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Arced Labyrinth Weir Model Approach Channel Details
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Labyrinth Weir Model Significant Approach Flow Angle
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Advantages/Limitations 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
Composite Modeling
Physical Model • • •
• Numerical Model • • •
Easy streamline visualization Data available anywhere in domain Easily stored
•
Cost/simulation time
•
Calibration to physical model data required
•
Results vary with userdefined boundary conditions and turbulence simulation model selection
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Non-Linear Weirs with Footprint Restrictions Piano Key Weirs
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Non-Linear Weirs with Footprint Restrictions Piano Key Weirs
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PK Weir History • • • • • •
Lempérière 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
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Discharge Cd = f (HT, L, Wi, Wo, B, P, Tw, Ramp Angle, Parapet)
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PK Weir Submergence channel applications
free-flow PK weir
local submergence
tailwater submergence
Dabling and Tullis (2012) “Piano Key Weir Submergence in Channel Applications” Journal of Hydraulic Engineering Hydraulic Design of Labyrinth Weirs
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PK vs. Labyrinth Weir 4.50
3.50
PK
6º
8º
10º
12º
15º
20º
RL
3.00 CdxL/W
Cycle efficiency
4.00
2.50
2.00
1.50
1.00 0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
H/P
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PK vs. Labyrinth Weir Geometries required for equivalent discharge
Changes in discharge and weir dimensions with channel width constrained
Q-specific
Q-specific
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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 Rectangular Labyrinth Weir Hydraulic.” 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.19434774.0000451. 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.19434774.0000466. 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.
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Acknowledgements 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
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