Labyrinth Weirs Crookston

Hosted by

Black & Veatch Corporation

GEI Consultants, Inc.

Kleinfelder, Inc.

MWH Americas, Inc.

Parsons Water and Infrastructure Inc.

URS Corporation

21st Century Dam Design —

Advances and Adaptations

31st Annual USSD Conference

San Diego, California, April 11-15, 2011

On the CoverArtist's rendition of San Vicente Dam after completion of the dam raise project to increase local storage and provide

a more flexible conveyance system for use during emergencies such as earthquakes that could curtail the region’s

imported water supplies. The existing 220-foot-high dam, owned by the City of San Diego, will be raised by 117

feet to increase reservoir storage capacity by 152,000 acre-feet. The project will be the tallest dam raise in the

United States and tallest roller compacted concrete dam raise in the world.

The information contained in this publication regarding commercial projects or firms may not be used for

advertising or promotional purposes and may not be construed as an endorsement of any product or

from by the United States Society on Dams. USSD accepts no responsibility for the statements made

or the opinions expressed in this publication.

Copyright © 2011 U.S. Society on Dams

Printed in the United States of America

Library of Congress Control Number: 2011924673

ISBN 978-1-884575-52-5

U.S. Society on Dams

1616 Seventeenth Street, #483

Denver, CO 80202

Telephone: 303-628-5430

Fax: 303-628-5431

E-mail: [email protected]

Internet: www.ussdams.org

U.S. Society on Dams

Vision

To be the nation's leading organization of professionals dedicated to advancing the role of dams

for the benefit of society.

Mission — USSD is dedicated to:

• Advancing the knowledge of dam engineering, construction, planning, operation,

performance, rehabilitation, decommissioning, maintenance, security and safety;

• Fostering dam technology for socially, environmentally and financially sustainable water

resources systems;

• Providing public awareness of the role of dams in the management of the nation's water

resources;

• Enhancing practices to meet current and future challenges on dams; and

• Representing the United States as an active member of the International Commission on

Large Dams (ICOLD).

Labyrinth Weirs 1667

THE DESIGN AND ANALYSIS OF LABYRINTH WEIRS

B.M. Crookston1 B.P. Tullis2

ABSTRACT

The experimental results of 32 physical models were used to develop a hydraulic design and analysis method for labyrinth weirs. Discharge coefficient data for quarter-round and half-round labyrinth weirs are presented for 6° ≤ sidewall angles ≤ 35°. The influence of cycle geometry, cycle configuration, spillway orientation and placement, nappe flow regimes, artificial aeration (vents, nappe breakers), and nappe stability on hydraulic performance are discussed. The validity of this method is presented by juxtaposing discharge coefficient data from this study and previously published labyrinth weir studies.

INTRODUCTION A labyrinth weir is a linear weir that is ‘folded’ in plan-view to increase the crest length for a given channel or spillway width. Due to the increase in crest length, a labyrinth weir provides an increase in discharge capacity for a given upstream driving head, relative to traditional linear weir structures. Labyrinth weirs are particularly well suited for spillway rehabilitation where dam safety concerns, freeboard limitations, and a revised and larger probable maximum flow have required replacement or modification of the spillway. An example of a labyrinth weir is presented in Figure 1.

Figure 1. Labyrinth Weir Schematic

There is great flexibility in the geometric design of labyrinth weirs. Yet, optimizing the many geometric variables in the hydraulic design of a labyrinth weir can be challenging. For example, the sidewall angle (α), total crest length (Lc), crest shape, number of cycles (N), the configuration of the labyrinth cycles, and the orientation and placement of a labyrinth weir must all be determined. Furthermore, the geometry of a labyrinth weir causes complex 3-dimensional flow patterns that must be considered. As the driving

1Postdoctoral Researcher, Utah Water Research Laboratory, Utah State Univ., 8200 Old Main Hill, Logan, Utah 84321, Phone: (435) 797-3171, Email: [email protected] 2Assoc. Prof., Utah Water Research Laboratory, Utah State Univ., 8200 Old Main Hill, Logan, Utah 84321, Phone: (435) 797-3194, Email: [email protected]

21st Century Dam Design — Advances and Adaptations 1668

head increases, flow efficiency declines, local submergence regions develop, flow separation may occur, the nappe aeration conditions change, and for certain flow conditions and geometries, the air cavity behind the nappe becomes unstable. In the past, physical models have proven to be highly useful tools to design and optimize labyrinth weirs. Previous Studies For this study, the basic equation developed for linear weirs is proposed to describe the head-discharge relationships of labyrinth weirs. It includes total head upstream measured relative to the crest, HT, and utilizes the centerline length of the crest, Lc, as the characteristic length (Equation 1).

23232

Tcd HgLCQ = (1)

In Eq. (1), Q is the discharge of a labyrinth weir, Cd is a dimensionless discharge coefficient, g is the acceleration constant of gravity, and HT is defined as HT = V2/2g + h (V is the average cross-sectional velocity at the gauging location, h is the piezometric head upstream of the weir). Most of the design and performance information regarding labyrinth weirs has been developed from physical model studies, often for a specific prototype installation (e.g., Avon, Dungo, Hyrum, Keddara, Lake Brazos, Lake Townsend, Ute, and Woronora). A selection of notable research studies that have provided hydraulic design guidance for labyrinth weirs is presented in Table 1.

Table 1. Labyrinth Weir Design Methods Design Methods

( ) Authors Labyrinth Cycle Type†

Crest Shape‡

1 Taylor (1968), Hay and Taylor (1970) Tri, Trap, Rect Sh, HR 2 Darvas (1971) Trap LQR 3 Hinchliff and Houston (1984) Tri, Trap Sh, QR 4 Lux and Hinchliff (1985) Tri, Trap QR 5 Magalhães and Lorena (1989) Trap WES 6 Tullis et al. (1995) Trap QR 7 Melo et al. (2002) Trap LQR 8 Tullis et al. (2007) Trap HR 9 Lopes et al. (2008) Trap LQR

†Tri = Triangular, Trap = Trapezoidal, Rect = Rectangular ‡QR –Quarter-round (Rcrest = tw/2), LQR – Large Quarter-round (Rcrest = tw) HR – Half-round, Sh – Sharp, WES – Truncated Ogee (See Figure 1) Initial insights into labyrinth weirs come from Gentilini (1940) and Kozák and Sváb (1961), but the first study with sufficient information to design a labyrinth weir was conducted by Taylor (1968) and Hay and Taylor (1970). The Bureau of Reclamation (USBR) found discrepancies between the experimental results and design recommendations by Hay and Taylor (1970) and the results obtained from physical model studies of Ute Dam (Houston, 1982). From the research conducted by the USBR,


Hinchliff and Houston (1984) and Lux and Hinchliff (1985) provided valuable insights and new design guidelines. Based upon model studies for Avon and Woronora Dam, Darvas (1971) simplified labyrinth weir design by introducing an empirical discharge equation and a discharge coefficient. Magalhães and Lorena (1989) expanded upon this approach by presenting a dimensionless discharge coefficient and new experimental results and design curves, which were found to be systematically lower than Darvas’ (1971). Tullis et al. (1995) developed a design method based upon research conducted at the Utah Water Research Laboratory (UWRL) by Waldron, (1994), Tullis (1993), and Amanian (1987). To account for apex influences on discharge efficiency, Tullis et al. (1995) introduced an effective weir length, Le, as the characteristic weir length (instead of channel width, W, or Lc). Two significant contributions of this study were: the design method is presented as a table to be used in a spreadsheet program, and the design curves include a linear weir discharge curve that is useful for determining the hydraulic benefits of a labyrinth weir relative to a linear weir. This design method is favored by Falvey (2003); however, the α = 6° data is significantly lower than the adjacent curves and Willmore (2004) has noted the following discrepancies: the α = 8° data falls above the α = 9° presented by Waldron (1994), and a minor mathematical error was found in the geometric calculations. The supporting data for this method (quarter-round crest shape) is limited to 6° ≤ α ≤18° and provides linearly interpolated curves for α = 25° and 35°. Recently, Melo et al. (2002) expanded the work of Magalhães and Lorena (1989) by adding an adjustment parameter for labyrinth weirs located in a channel with converging channel sidewalls. Tullis et al. (2007) developed a dimensionless submerged head-discharge relationship (tailwater submergence) for labyrinth weirs. Lopez et al. (2008) provides design information regarding characteristic depths and energy dissipation of labyrinth weirs. Finally, an appreciable portion of published information on labyrinth weirs has been compiled by Falvey (2003). Labyrinth Weirs Located in a Reservoir Varying angles of the approach flow and flow convergence for labyrinth weirs situated in a reservoir may result in appreciable differences in weir efficiency [e.g. Prado Spillway, Copeland and Fletcher (2000)]. Depending on the site conditions and other contributing factors, the inlet section, spillway orientation and placement, and cycle configuration may significantly influence the flow capacity of a labyrinth spillway. Case studies for Boardman Dam (Babb, 1976) and Hyrum Dam (Houston, 1983) reported that curved abutment walls upstream of the labyrinth weir minimized the loss of efficiency caused by flow separation. The test program for a 2-cycle labyrinth weir for Hyrum Reservoir (Houston, 1983) included various weir orientations and placements (Normal, Inverse, Flush, and Partially Projecting, see Figure 2). For similar entrance conditions, it was reported that the Partially Projecting orientation increased discharge by 10.4% when compared to the Flush orientation and the Normal orientation had a 3.5% greater discharge than the Inverted orientation. However, Crookston and Tullis (2010) compared


the hydraulic performance of a Normal and Inverse oriented α = 6° labyrinth weir in a channel application and found no change in hydraulic performance. In general, labyrinth weir cycles follow a linear configuration; however, the discharge efficiency of the weir may be improved by orienting the cycles to the approaching flow. According to Falvey (2003), the efficiency of Prado Spillway could have been increased by arcing the cycle configuration. Examples of curved or arced labyrinth spillways are: Avon (Darvas, 1971), Kizilcapinar (Yildiz and Uzecek, 1996), and Weatherford (Tullis, 1992). Page et al. (2007) recently conducted a study for María Cristina Dam (Castellón, Spain). Two labyrinth weir physical models (1/50th scale, P~140-mm) for the emergency spillway were examined: a 9-cycle labyrinth with 4 cycles following an arced configuration, and a 7-cycle labyrinth that featured 5 arced cycles. Predicted discharges by Magalhães and Lorena (1989), Lux and Hinchliff (1985) and Tullis et al. (1995) design methods were systematically higher than the physical model results. However, the 7-cycle arced configuration provided the greatest orientation improvement of cycle to the approaching flow and was found to be the more efficient design. The objective of this study is to improve the design and analyses of labyrinth weirs by: investigating the operation and performance of specific weir geometries using physical modeling, consolidating available labyrinth weir information and data, and further developing current design methodologies.

Figure 2. Labyrinth Weir Orientations, Placements, and Cycle Configurations


EXPERIMENTAL METHOD 32 physical models of labyrinth weirs were fabricated and tested at the Utah Water Research Laboratory (UWRL), located in Logan, Utah, USA (Crookston, 2010). Labyrinth weirs were fabricated from High Density Polyethylene (HDPE) sheeting and were tested in a laboratory flume (1.2 m x 14.6 m x 1.0 m) and an elevated headbox (7.3 m x 6.7 m x 1.5 m deep). The models were installed on an elevated horizontal platform (level to ±0.4-mm). The flume facility featured a ramped upstream floor transition, which was reported by Willmore (2004) to have no influence on discharge capacity. Sidewall effects in the rectangular flume were considered to be negligible, based upon the findings of Johnson (1996). In the headbox, the discharge channel downstream of the weir was relatively short (~10 cm) and terminated with a free overfall. The radius for the rounded inlet was set to the cycle width (Rabutment = w). Details of the physical model test program are summarized in Table 2 and Figure 2. Model test flow rates were determined from calibrated orifice meters in the flume supply piping, differential pressure transducers, and a data logger. Point velocity measurements (U) were made using a 2-dimensional acoustic Doppler velocity probe. Weirs were tested with and without a nappe aeration apparatus consisting of an aeration tube for each labyrinth sidewall. The test program also evaluated the performance of wedge-shaped nappe breakers in a variety of locations (upstream apex, weir sidewall, downstream apex). Experimental data were collected under steady-state conditions. A large number of head-discharge data points were collected for all tested weir geometries, and a system of checks was established wherein at least 10% of the data were repeated to ensure accuracy and determine measurement repeatability. Q measurements were recorded for 5 to 7

Table 2. Physical model test program

Model α θ P Lc-cycle Lc-cycle/w w/P N Crest Type . Orientation† ( ) (°) (°) (mm) (mm) ( ) ( ) ( ) ( ) ( ) ( ) 1 6 0 304.8 4,654.6 7.607 2.008 2 HR Trap Inverse

2-3 6 0 304.8 4,654.6 7.607 2.008 2 QR HR Trap Normal 4 6 0 203.2 3,075.5 7.607 2.008 5‡ HR Trap Projecting

5-7 6 10, 20, 30 203.2 3,075.5 7.607 2.008 5‡ HR Trap Arced & Projecting 8 6 0 203.2 3,075.5 7.607 2.008 5 HR Trap Flush 9 6 0 203.2 3,075.5 7.607 2.008 5 HR Trap Rounded Inlet

10-11 8 0 304.8 3,544.9 5.793 2.008 2 QR HR Trap Normal 12-13 10 0 304.8 2,879.1 4.705 2.008 2 QR HR Trap Normal 14-15 12 0 304.8 2,435.1 3.980 2.008 2 QR HR Trap Normal

16 12 0 203.2 634.6 4.705 2.008 5‡ HR Trap Projecting 17-19 12 10, 20, 30 203.2 634.6 4.705 2.008 5‡ HR Trap Arced & Projecting

20 12 0 203.2 634.6 4.705 2.008 5 HR Trap Flush 21 12 0 203.2 634.6 4.705 2.008 5 HR Trap Rounded Inlet

22-23 15 0 304.8 1,991.4 3.254 2.008 2 QR HR Trap Normal 24 15 0 152.4 1,991.4 3.254 4.015 2 QR Trap Normal 25 15 0 152.4 995.7 3.254 2.008 4 QR Trap Normal 26 15 0 304.8 995.7 3.254 1.019 4 QR Trap Normal

27-28 20 0 304.8 1,548.1 2.530 2.008 2 QR HR Trap Normal 29-30 35 0 304.8 983.5 1.607 2.008 2 QR HR Trap Normal 31-32 90 - 304.8 1,223.8 1.000 4.015 - QR HR - - †Linear cycle configuration was used for all model orientations unless ‘Arced’ is specified ‡Based upon the outlet labyrinth cycle geometry


minutes with the data logger to determine an average flow rate, and h (±.15 mm) was determined with a stilling well equipped with a point gauge. A dye wand was used to observe the unique and complex local flow patterns associated with labyrinth weir flow. Digital photography and high-definition (HD) digital video recording were used extensively to document the hydraulic behaviors of the tested labyrinth weirs. Observations also noted nappe aeration conditions and behavior, nappe stability, nappe separation point, nappe interference, areas of local submergence, and any harmonic or recurring hydraulic behaviors for all α tested.

EXPERIMENTAL RESULTS Discharge Rating Curves Equation 1 was selected to determine the discharge of labyrinth weirs. Cd is a dimensionless discharge coefficient, influenced by weir geometry, flow conditions, and aeration conditions of the nappe (clinging, aerated, partiallyaerated, drowned). Cd data are presented in terms of HT/P for non-vented trapezoidal labyrinth weirs (Normal or Inverse weir orientations) for 6° ≤ α ≤ 35° in Figure 3 (quarter-round crest shape) and Figure 4 (half-round crest shape). Data for α = 90° (linear weirs) are included for comparison. In Figure 3, slight increases in efficiency for the α = 90°, 35°, and 20° at HT/P ~ 0.25 were caused by the abrupt removal of the air cavity behind the nappe. In Figure 4, the sudden decrease in weir efficiency varies (caused by the weirs shifting out of the clinging nappe aeration regime) but is present for all tested half-round weirs (e.g., HT/P ~ 0.3 for α = 15°).

Figure 3. Cd vs HT/P for Quarter-round Trapezoidal Labyrinth Weirs


Figure 4. Cd vs HT/P for Half-round Trapezoidal Labyrinth Weirs Cd data for the half-round and quarter-round crest shapes indicate that the half-round shape is appreciably more efficient for HT/P ≤ 0.4. This is because a crest that is rounded on the downstream face helps the flow stay attached (clinging flow) to the weir wall, thus increasing flow efficiency. If the flow detaches (momentum, debris, etc.), the gains in efficiency are lost. The hydraulic efficiency gained from a half-round crest shape diminishes as HT/P increases; there should be no appreciable gains for HT/P > 1.0. Labyrinth Weir Orientation, Placement, and Cycle Configuration The labyrinth weir orientations and cycle configurations tested in this study are summarized in Figure 2 and Table 2. To quantify differences in hydraulic efficiency, Cd values from each model were juxtaposed to the Cd values from a labyrinth weir located in a channel with a Normal orientation. The ratio of Cd-res (tested spillway models located in a reservoir) to Cd-Channel (Normal orientation located in a channel) vs HT/P for α = 6° and α = 12° are presented in Figures 5 and 6. The abrupt increase in efficiency seen in Figure 5 (B) at HT/P ~ 0.25 is caused by the reference weir (Normal orientation in a channel, See Figure 4) abruptly shifting from the clinging to the aerated nappe flow condition, causing an abrupt decrease in Cd. There was no abrupt change in Cd for the α = 6° normally oriented weir or in the models tested in the reservoir. The Normal and Inverse spillway orientations were observed to have no discernable performance difference. The Projecting and Rounded Inlet [Figure 6 (A)] also performed similarly at low values of HT/P to weirs tested in the channel. However, as flow rates increased, local submergence, wakes, and flow convergence caused ~5% decrease in hydraulic efficiency. Observations found that Rabutment = w was sufficient to prevent flow separation that occurred for the Flush orientation, which was found to be ~10% less


0.8

0.9

1

1.1

1.2

1.3

1.4

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7

Cd-

Res

/ Cd-

Cha

nnel

HT/P

α=6° Normal in Channel

α=6° θ=0° Projecting




α=6° θ=0° Flush

α=6° θ=0° Rounded Inlet

0.8

0.9

1

1.1

1.2

1.3

1.4

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7

Cd-

Res

/ Cd-

Cha

nnel

HT/P

α=12° Normal in Channel





α=12° θ=0° Flush

α=12° θ=0° Rounded Inlet

Figure 5. Comparison of Labyrinth Weir Orientations for α = 6°(A) and α = 12° (B)

Figure 6. Example of Flow Passing from O1 and O5 to I1 and I4

efficient than the Normal orientation. Flow separation at the abutment affected cycles I1, I5, and O1, O2, O5 and O6). An arced cycle configuration [Figure 6 (B)] improved the orientation of each cycle to the approaching flow that reduced surface turbulence, flow separation, and local submergence at the upstream apexes of O1, O2, O4 and O5. This improvement provided increases in hydraulic efficiency ranging from 10% to over 25% for the α = 12°. It is important to verify that the downstream channel width (W’) does not limit the discharge capacity of an arced labyrinth spillway. During testing, the point of flow control shifted from the labyrinth weir to the chute inlet (downstream), greatly limiting the efficiency of the arc cycle angles θ = 20° and θ = 30° for HT/P ≥ 0.5. Nappe Aeration Behavior and Stability Nappe aeration behavior and nappe stability influence the hydraulic performance of labyrinth weirs. Four different aeration conditions were observed during labyrinth weir


testing: clinging, aerated, partially aerated, and drowned. Aeration conditions are influenced by the crest shape, HT, the momentum and trajectory of the flow passing over the crest, the depth and turbulence of flow behind the nappe, and the pressure behind the nappe (sub-atmospheric for non-vented or atmospheric for vented nappes). A labyrinth weir will transition from clinging to aerated, to partially aerated, and finally to drowned as HT increases. Not all labyrinth weir geometries will produce all four aeration conditions. Sub-atmospheric pressures develop on the downstream face of the weir when the nappe is clinging and may exist for a non-vented aerated condition. As HT increases, the nappe will transition to a partially aerated nappe because the air cavity behind the nappe becomes unstable, due to the fluctuating and turbulent water surface behind the nappe. An unstable air cavity oscillates between labyrinth weir apexes, increasing or decreasing the length of sidewall that is aerated and/or the air cavity may repeatedly be completely removed and then replaced. An unstable air cavity also causes fluctuating pressures at the downstream face of the weir. Further increases in HT produce a drowned aeration condition, characterized by a large, thick nappe with no air cavity. Table 3 presents the range of HT/P that was observed for each nappe aeration condition for quarter-round and half-round labyrinth weirs. Nappe instability is characterized by a nappe whose trajectory oscillates and aeration condition (e.g., clinging, aerated, partially aerated, drowned) changes without any change in flow rate to the labyrinth weir. Nappe instability is a low frequency phenomenon that causes the formation and removal of the air cavity behind the nappe, which produces an audible, strong flushing noise. There are little to no discernable indicators that nappe instability will occur or is about to commence, but the phenomena intensity decreases and eventually disappears as HT increases. HT/P ranges for nappe instability are provided in Table 4. It is suggested that these ranges be avoided, as vibrations, pressure fluctuations, and noise may reach sufficient levels as to be undesirable or harmful. Artificial aeration by vent or nappe breakers minimizes but does not prevent nappe instability.

Table 3. Nappe Aeration Flow Conditions for Labyrinth Weirs Half-Round (HT/P) Quarter-Round (HT/P) α

(°) Clinging Aerated Partially Aerated Drowned Clinging Aerated Partially

Aerated Drowned

6 <0.165 0.165-0.298 0.298-0.405 >0.405 <0.050 0.051-0.256 0.256-0.319 >0.319 8 <0.165 0.165-0.312 0.312-0.465 >0.465 <0.050 0.057-0.288 0.288-0.364 >0.364

10 <0.219 0.219-0.283 0.283-0.505 >0.505 <0.050 0.061-0.293 0.293-0.479 >0.479 12 <0.250 - 0.250-0.530 >0.530 <0.050 0.061-0.275 0.275-0.510 >0.510 15 <0.306 - 0.306-0.560 >0.560 <0.050 0.052-0.256 0.256-0.508 >0.508 20 <0.363 - 0.363-0.599 >0.599 <0.050 0.053-0.240 0.240-0.515 >0.515 35 <0.411 0.140-0.185 0.411-0.460 >0.460 <0.050 0.059-0.232 0.232-0.515 >0.515

Table 4. Unstable Nappe HT/P Regions for Labyrinth Weirs α (°) 6 8 10 12 15 20 35 Quarter-Round (HT/P) none none none 0.30-0.35 0.27-0.47 0.22-0.53 0.22-0.70 Half-Round (HT/P) none none 0.33-0.33 0.33-0.39 0.33-0.58 0.36-0.60 0.41-0.46


Labyrinth Design and Analyses The recommended procedure for designing a labyrinth weir is presented in “Labyrinth Weirs” (Crookston, 2010), which can be conveniently implemented in a spreadsheet-based computer program. This method utilizes a design table; the top section of the table includes the user-defined hydraulic conditions (Q, HT, Hd) or requirements for the labyrinth weir. Next, the footprint size, weir height, crest shape, and other labyrinth weir geometric parameters are entered to begin optimizing the labyrinth weir layout. A place is provided in the design table where a nappe aeration device may be specified. The remaining portion of the design table computes remaining geometric parameters (Lc, w, N, etc.) and the hydraulic performance based on previously defined geometric parameters and the head-discharge requirements, including the submerged head-discharge relationship developed by Tullis et al. (2007). B and N may easily be changed between independent and dependent variables from the equations provided in the design table. Cd(90°) (linear weir) and the required weir length to match the design head-discharge condition are reported, for comparison. This design table is supplemented with the design tools developed for arced and linear labyrinth weirs in a reservoir application. After determining a cycle geometry from the afore mentioned table, Figure 5 is utilized to make adjustments to the discharge rating curve, depending on desired labyrinth weir orientation or cycle configuration. For example, site conditions may require a labyrinth spillway to be projecting into the reservoir. The increase in discharge capacity resulting from an arced cycle configuration can be determined. Optimizing a labyrinth weir geometric design can be difficult. One complication is shown in Figures 3 and 4; Cd decreases with decreasing α, yet increasing the weir length compensates for reduction in flow efficiency. To aid in the selection of α, cycle efficiency, ε’ (ε’=CdLc-cycle/w), which is representative of the discharge per cycle, is presented in Figure 7 (A) and 7 (B) (quarter-round and half-round, respectively) as a function of HT/P. Maximum ε’ values occur at low HT/P (as delineated by the dashed line); ε’ increases as α decreases; and the benefits of smaller α angles decrease with increasing HT/P. Therefore, cycle efficiency is a useful design tool because it facilitates the comparison of hydraulic performance of several acceptable spillway designs against other significant spillway factors, such as construction costs associated with increasing or decreasing the weir length and apron size. Data Verification The performance of this design method has been validated through two comparisons. First, the laboratory flume experimental results of this study were compared to the experimental results of Willmore (2004), which were in very close agreement. The comparison was then extended to the experimental results from 10 physical model studies for prototype labyrinth weir structures, presented in Table5. The agreement between Cd values calculated from this study and predicted Cd values indicate that there is good agreement between the proposed design method and the reported model studies.


Figure 7. Cycle Efficiency vs HT/P for Quarter-round (A) and Half-round (B) Labyrinth Weirs

However, there are varying levels of agreement for multiple HT/P values for a single structure, indicating that sources of uncertainty associated with physical modeling may be present, such as different model sizes, experimental methods, entrance configurations, etc. For Table 5, an average difference of 1.4% with a standard deviation of 3.3% was calculated.

CONCLUSION New information for labyrinth weir design, including reservoir applications, is presented

Table 5. Comparison Between the Results Obtained from Hydraulic Model Tests for Labyrinth Weir Prototypes and the Proposed Design Method

Q HT/P α N Cd Cd Diff. Name Source (m3/s) ( ) (°) ( ) Eq. 1 Fig. 3&4 (%) 1 Avon Darvas (1971) 1790.0 0.932 27.50 10 0.4867 0.4590 5.88%

387.0 0.652 19.44 2 0.4995 0.4937 1.16% 2 Boardman Babb (1976) 386.8 0.507 18.21 2 0.5129 0.5381 -4.80% 120.7 0.200 15.20 4 0.6041 0.6001 0.67% 303.1 0.400 15.20 4 0.5364 0.5223 2.66% 3 Dungo Magalhães &

Lorena (1989) 576.0 0.558 15.20 4 0.4542 0.4583 -0.89% 350.0 0.442 15.20 3 0.5208 0.5046 3.16% 4 Harrezza Magalhães &

Lorena (1989) 220.8 0.400 15.20 3 0.5195 0.5223 -0.54% 5 Hyrum Houston (1983) 256.3 0.458 9.85 2 0.4097 0.3990 2.63%

6 Keddara Magalhães & Lorena (1989) 250.0 0.703 14.90 2 0.4078 0.4053 0.63%

239.0 0.400 13.00 4 0.4649 0.4887 -5.01% 7 Mercer CH2M-Hill (1973) 135.4 0.233 13.37 4 0.5892 0.5716 3.04% 94.3 0.400 13.30 2 0.5066 0.4935 2.63% 8 São

Domingos Magalhães & Lorena (1989) 160.0 0.511 13.30 2 0.4726 0.4462 5.75%

9 Standley Lake Tullis (1993) 1539.4 0.648 8.51 13 0.3155 0.2980 5.71%

10 Townsend Tullis & Crookston (2008) 2717.2 0.554 11.40 7 0.3917 0.3956 -1.01%


based upon the results of physical modeling in a rectangular flume and a reservoir facility. Q is calculated based on the traditional weir equation (Equation 1), utilizing Lc as the characteristic length and HT. A comparison (Table 5) of the proposed design method to other physical model studies found an average difference of 1.4%, indicating that the information and tools presented herein will accurately design and analyze a labyrinth weir spillway. The dimensionless discharge coefficient, Cd, is presented in Figures 3 and 4 as a function of HT/P for quarter-round and half-round labyrinth weirs (6° ≤ α ≤ 35°) and linear weirs. The experimental results indicate that the efficiency gained from a half-round crest shape (relative to a quarter-round crest) is more significant for HT/P ≤ 0.4. Cycle efficiency, ε’, is offered to examine the discharge capacity of different labyrinth weir geometries with either a quarter-round [Figure 7 (A)] or half-round [Figure 7 (B)] crest shape. ε’ illustrates the relationship between the decrease in discharge efficiency associated with decreasing α and the increase in discharge caused by the increase in crest length. The hydraulic performance of the following orientations and configurations were examined: Normal, Inverse, Projecting, Flush, Rounded Inlet, and Arced (see Figure 2). An arced labyrinth weir maximizes discharge efficiency (~10%-25%), and rounded abutments (Rounded Inlet) were found to appreciably improve the hydraulic efficiency of the Flush orientation. No performance difference was found between a Normal and Inverse orientation. Nappe aeration conditions and nappe stability should also be considered in the hydraulic and structural design of labyrinth weirs. Tables 3 and 4 give the ranges of HT/P for each aeration condition and the ranges of nappe instability. Regions where the nappe is unstable should be avoided as the fluctuating pressures at the weir wall, noise, and vibrations may be undesirable. Nappe ventilation by means of aeration vents or nappe breakers diminished but did not eliminate nappe instability. From the experimental results, it is recommended that 1 vent be placed per sidwall and 1 breaker be centered on each downstream apex. It is recommended that a labyrinth weir design be verified with a physical or numerical model study, as it would include site-specific conditions that may be outside the scope of this study and may provide valuable insights into the performance and operation of the labyrinth weir.

ACKNOWLEDGEMENTS This study was funded by the State of Utah and the Utah Water Research Laboratory.

NOTATION A Inside apex width α Sidewall angle B Length of labyrinth weir (Apron) in flow direction


Cd Discharge coefficient, data from current study Cd(90°) Discharge coefficient for linear weir Cd-channel Discharge coefficient specific to a labyrinth weir located in a channel Cd-res Discharge coefficient specific to a labyrinth weir located in a reservoir D Outside apex width ε’ Cycle efficiency g acceleration constant of gravity h depth of flow over the weir crest Hd Total head downstream of a labyrinth weir HT Unsubmerged total upstream head on weir HT/P Headwater ratio Lc Total centerline length of labyrinth weir lc Centerline length of weir side wall Lc-cycle Centerline length for a single labyrinth weir cycle Lc-cycle/w Magnification ratio, M Le Total effective length of labyrinth weir N Number of labyrinth weir cycles P Weir height Q Discharge over weir Rcrest Radius of crest shape Rabutment Radius of rounded abutment tw Thickness of weir wall θ Cycle arc angle U Local flow velocity V Average cross-sectional flow velocity upstream of weir W Width of channel W’ Width of the arced labyrinth spillway w Width of a single labyrinth weir cycle w/P Cycle width ratio

REFERENCES

Amanian, N. (1987). “Performance and design of labyrinth spillways.” M.S. thesis, Utah State University, Logan, Utah. Babb, A. (1976). “Hydraulic model study of the Boardman Reservoir Spillway.” R.L Albrook Hydraulic Laboratory, Washington State University, Pullman, Wash. CH2M-Hill, (1973). “Mercer Dam Spillway model study.” Dallas Oregon, March International Report. Copeland, R. and Fletcher, B. (2000). “Model study of Prado Spillway, California, hydraulic model investigation.” Report ERDC/CHL TR-00-17, U.S. Army Corps of Engineers, Research and Development Center. Crookston, B. M. 2010. Labyrinth weirs. Ph.D. Dissertation. Utah State University, Logan, Utah.


Crookston, B.M. and Tullis, B. (2010). “Hydraulic performance of labyrinth weirs.” Proc. of the Int. Junior Researcher and Engineer Workshop on Hydraulic Structures (IJREWHS ’10). Edinburgh, U.K. Darvas, L. (1971). “Discussion of performance and design of labyrinth weirs, by Hay and Taylor.” J. of Hydr. Engrg., ASCE, 97(80), 1246-1251. Falvey, H. (2003). Hydraulic design of labyrinth weirs. ASCE, Reston, Va. Gentilini, B. (1940). “Stramazzi con cresta a planta obliqua e a zig-zag.” Memorie e Studi dell Instituto di Idraulica e Construzioni Idrauliche del Regil Politecnico di Milano, No. 48 (in Italian). Hay, N., and Taylor, G. (1970). “Performance and design of labyrinth weirs.” J. of Hydr. Engrg., ASCE, 96(11), 2337-2357. Hinchliff, D., and Houston, K. (1984). “Hydraulic design and application of labyrinth spillways.” Proc. of 4th Annual USCOLD Lecture. Houston, K. (1982). “Hydraulic model study of Ute Dam labyrinth spillway.” Report No. GR-82-7, U.S. Bureau of Reclamation, Denver, Colo. Houston, K. (1983). “Hydraulic model study of Hyrum Dam auxiliary labyrinth spillway.” Report No. GR-82-13, U.S. Bureau of Reclamation, Denver, Colo. Johnson, M. (1996). “Discharge coefficient scale effects analysis for weirs.” Ph.D. dissertation, Utah State University, Logan, Utah. Kozák, M. and Sváb, J. (1961). “Tort alaprojzú bukók laboratóriumi vizsgálata.” Hidrológiai Közlöny, No. 5. (in Hungarian). Lopes, R., Matos, J., and Melo, J. (2008). “Characteristic depths and energy dissipation downstream of a labyrinth weir.” Proc. of the Int. Junior Researcher and Engineer Workshop on Hydraulic Structures (IJREWHS ‘08), Pisa, Italy. Lux III, F. (1985). “Discussion on ‘Boardman labyrinth crest spillway.’” J. of Hydr. Engrg., ASCE, 111(6), 808-819. Lux III, F. and Hinchliff, D. (1985). “Design and construction of labyrinth spillways.” 15th Congress ICOLD, Vol. IV, Q59-R15, Lausanne, Switzerland, 249-274. Magalhães, A., and Lorena, M. (1989). “Hydraulic design of labyrinth weirs.” Report No. 736, National Laboratory of Civil Engineering, Lisbon, Portugal.


Melo, J., Ramos, C., and Magalhães, A. (2002). “Descarregadores com soleira em labirinto de um ciclo em canais convergentes. Determinação da capacidad de vazão.” Proc. 6° Congresso da Água, Porto, Portugal. (in Portuguese). Page, D., García, V., and Ninot, C. (2007). “Aliviaderos en laberinto. presa de María Cristina.” Ingeniería Civil, 146(2007), 5-20 (in Spanish). Taylor, G. (1968). “The performance of labyrinth weirs.” Ph.D. thesis, University of Nottingham, Nottingham, England. Tullis, B. and Crookston, B.M. (2008). “Lake Townsend Dam spillway hydraulic model study report.” Utah Water Research Laboratory, Logan, Utah. Tullis, B. and Young, J. (2005). “Lake Brazos Dam model study of the existing spillway structure and a new labyrinth weir spillway structure.” Hydraulics. Report No. 1575. Utah Water Research Laboratory. Logan, Utah. Tullis, B., Young, J., & Chandler, M. (2007). “Head-discharge relationships for submerged labyrinth weirs.” J. of Hydr. Engrg., ASCE, 133(3), 248-254. Tullis, P. (1992). “Weatherford Spillway model study.” Hydraulic Report No. 311, Utah Water Research Laboratory, Logan, Utah. Tullis, P. (1993). “Standley Lake service spillway model study.” Hydraulic Report No. 341, Utah Water Research Laboratory, Logan, Utah. Tullis, P., Amanian, N., and Waldron, D. (1995). “Design of labyrinth weir spillways.” J.of Hydr. Engrg., ASCE, 121(3), 247-255. Waldron, D. (1994). “Design of labyrinth spillways.” M.S. thesis, Utah State University, Logan, Utah. Willmore, C. (2004). “Hydraulic characteristics of labyrinth weirs.” M.S. report, Utah State University, Logan, Utah. Yildiz, D., and Uzecek, E. (1996). “Modeling the performance of labyrinth spillways.” Hydropower, 3:71-76.

Labyrinth Weirs Crookston

Documents

Transcript of Labyrinth Weirs Crookston