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Labyrinth weirs provide higher discharge capacity than conventional weirs, with the ability to pass large flows at comparatively low heads. Labyrinth weirs are primarily used as spillways for dams where the spillway width is restricted. In recent years, many research investigations have considered the hydraulic performance of labyrinth weirs, particularly as dependent on the geometric features. The previous work has improved the design basis for such weirs. However, their design still requires experimentally derived and generalized performance curves. It is especially important to observe the behavior of the weir nappe to ensure the design provides hydraulic optimization and to account for pressure fluctuations, possible vibrations, resonance effect, noise and flow surging. In the present study, discharge coefficients were experimentally determined for both circular labyrinth weirs and sharp crested trapezoidal labyrinth weirs of varying side wall angle (α). Additional studies were completed with nappe breakers included to reduce the impact of vibration on the labyrinth weirs. In general, the test data indicated that nappe breakers placed on the trapezoidal labyrinth weirs and circular labyrinth weirs reduced the discharge coefficient by up to 4% of the un-amended weir.

Labyrinth weirs provide an effective means to increase the spillway discharge capacity of dams and are often considered for renovation projects required due to an increase in expected flood inflow to the reservoir of an existing dam. Due to the complex design of the overflow structure, the labyrinth spillway discharge capacity is affected by many factors including weir geometry and approach channel conditions [

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 (L_{c}), 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. The flow rate passing over the labyrinth is dependent on the crest length, which can be controlled by modifying the number of folds. The relationship between lengthand discharge is not linear, however, except for very small heads. As the water level above the labyrinth weir increases, four stages of nappe shape occur: fully aerated, partially aerated, transition and submerged. The thickness of nappe and depth of the tail water do not affect the discharge capacity of the labyrinth weir in the fully aerated flow condition. In this case, the labyrinth weir acts as a vertical cross section of the linear weir. As the water level above the labyrinth weir increases and the tail water rises, the nappe becomes partially aerated (adhering to the weir wall) and the discharge coefficient is reduced [

The jet of water that passes over a weir is referred to as the nappe. Nappe aeration conditions for a variety of linear weirs have been previously investigated and documented [

Schwartz [

In addition to literature regarding the nappe vibration mechanism, several studies have focused on nappe vibration mitigation. Nappe vibration can be attributed to three different factors: instability of the nappe itself, fluctuation of air pressure behind the nappe, and the structure acting as a vibrating system [

At high heads, nappe instability may also require remedial action, depending on the corresponding noise levels and fluctuation frequency. Yildiz and Uzucek [

Over the past 50 years, extensive research on the influence of geometric and hydraulic parameters on the hydraulic behavior of labyrinth weirs, particularly on the discharge capacity, has been completed. Taylor [

where C_{d} is the discharge coefficient; h is the depth of flow over the weir crest and P is the weir height.

Additional work by Darvas [

Lux [

where Q is the discharge over labyrinth weir; C_{d} is the discharge coefficient; H_{t} is the total upstream head measured relative to the weir crest; Wc is the channel width and P is the weir height.

Magalhaes and Lorena [_{d}) of labyrinth weirs as function of L/w and H_{t}/P parameters. They defined discharge capacity of labyrinth weirs with Equation (3).

Tullis et al. [_{t}/P) for side wall angles (α) of 6˚ to 18˚. Additional curves for weir side angles of 25˚ and 35˚ were obtained by extrapolation. Tullis et al. [

Labyrinth weirs are also used as side weirs to increase the outflowing discharge. Emiroglu et al. [

Khode et al. [

Carollo et al. [

Crookston and Tullis [

Crookston and Tullis [

Anderson and Tullis [

Information regarding nappe aeration conditions (clinging, aerated, partially aerated, and drowned), nappe instability, and nappe vibrations for trapezoidal labyrinth weirs on a horizontal apron with quarter-and half-round crests (6˚ ≤ α ≤ 35˚) was presented by Crookston and Tullis [

While all these documented studies have provided significant insights to the behavior of labyrinth weirs under specific conditions, the general theory remains: the capacity of labyrinth weir is a function of the upstream total head, the effective crest length, and the coefficient of discharge. The discharge coefficient depends on the total head, weir height, thickness, crest shape, apex configuration, and angle of side wall. While viscosity and surface tension are also significant variables, their influence is limited at velocities of sufficient magnitude and by appropriate model geometries [

The purpose of this study is to systematically investigate the discharge capacity of sharp-crested trapezoidal and circular labyrinth weir with and without nappe breaker, using a broad range of experiments, and considered together with the other effective dimensionless parameters.

Experiments on the discharge capacity and flow characteristics of the labyrinth weirs were carried out using a model located in the hydraulic laboratory of Firat University, Elazig, Turkey. The experimental set-up includes sump, pumping system, discharge tank, rectangular flume, digital flowmeter and labyrinth weir. Water is recirculated through 250 mm diameter of supply line using two 75 HP pumps. Water for experimental setup is taken from the supply line by means of a pipe with 150 mm diameter. The discharge was measured by means of a Siemens electromagnetic flow-meter installed in the supply line. Water was supplied to the main channel (2 m wide and 0.80 m height this channel length is 3.0 m) through a supply pipe from the sump (volume of 15 m^{3}) with flow controlled by a gate valve (

To measure the nappe height, water depth was measured accurately using Mitutoyo digital point gauges (accurate to ±0.01 mm) just upstream of the weirs. Level measurements were taken at a distance from the weir equal to five times the nappe height. For flow rate measurements, Nortek brand acoustic three-axis velocimeter was used.

In the experiments, the weir heights were taken as 100 mm, 150 mm and 200 mm and apex width (A) was taken as 80 mm. Sharp-crested shapes is provided for all models. All experiments were performed according to free flow conditions.

The flow over labyrinth weir is three dimensional and does not readily fit into mathematical description and hence the discharge function is found through experimental studies and analysis. The crest coefficient depends on the total head, weir height, thickness, crest shape, apex configuration and angle of side wall. To simplify the analysis, the effect of viscosity and surface tension could be neglected by selecting model and velocity of sufficient magnitude. The discharge over labyrinth weir can be expressed as:

where Q is the discharge over a labyrinth weir; C_{d} is the discharge coefficient of the labyrinth weir; L is the effective length of labyrinth weir; H_{t} is the total head (

Head over labyrinth weir was measured for different value of discharges in the range of 14.7 L/s to 136.9 L/s. In this range, the head over the labyrinth weir varied from 10 to 90 mm. The model of linear weir is also tested in the same flume for the purpose of comparison. In the experiments, the characteristics of different types of the weirs which are tested in the experiments are given in

The objective of this research is to further the understanding related to the mechanisms that cause nappe vibration, document the occurrence conditions, and investigate mitigation techniques for trapezoidal and circular labyrinth weirs.

Model | W_{c} (cm) | P (cm) | L (cm) | N | A (cm) | L_{c}/w | Type of Weir |
---|---|---|---|---|---|---|---|

1_{ } | 196 | 10 | 196 | - | - | - | Linear Weir, a = 90˚^{ } |

2_{ } | 196 | 10 | 294 | 3 | 8 | 1.50 | Trapezoidal Labyrinth Weir, a = 37˚^{ } |

3_{ } | 196 | 10 | 345 | 3 | 8 | 1.76 | Trapezoidal Labyrinth Weir, a = 30˚^{ } |

4_{ } | 196 | 10 | 427 | 3 | 8 | 2.18 | Trapezoidal Labyrinth Weir, a = 23˚^{ } |

5_{ } | 196 | 10 | 534 | 3 | 8 | 2.73 | Trapezoidal Labyrinth Weir, a = 18˚ |

6_{ } | 196 | 10 | 621 | 3 | 8 | 3.17 | Trapezoidal Labyrinth Weir, a = 15˚ |

7_{ } | 196 | 10 | 774 | 3 | 8 | 3.95 | Trapezoidal Labyrinth Weir, a = 12˚ |

8_{ } | 196 | 15 | 196 | - | - | - | Linear Weir, a = 90˚ |

9_{ } | 196 | 15 | 294 | 3 | 8 | 1.50 | Trapezoidal Labyrinth Weir, a = 37˚ |

10_{ } | 196 | 15 | 345 | 3 | 8 | 1.76 | Trapezoidal Labyrinth Weir, a = 30^{o} |

11_{ } | 196 | 15 | 427 | 3 | 8 | 2.18 | Trapezoidal Labyrinth Weir, a = 23˚ |

12_{ } | 196 | 15 | 534 | 3 | 8 | 2.73 | Trapezoidal Labyrinth Weir, a = 18˚ |

13_{ } | 196 | 15 | 621 | 3 | 8 | 3.17 | Trapezoidal Labyrinth Weir, a = 15˚ |

14_{ } | 196 | 15 | 774 | 3 | 8 | 3.95 | Trapezoidal Labyrinth Weir, a = 12˚ |

15_{ } | 196 | 20 | 196 | - | - | - | Linear Weir, a = 90˚ |

16_{ } | 196 | 20 | 294 | 3 | 8 | 1.50 | Trapezoidal Labyrinth Weir, a = 37˚ |

17_{ } | 196 | 20 | 345 | 3 | 8 | 1.76 | Trapezoidal Labyrinth Weir, a = 30^{o} |

18_{ } | 196 | 20 | 427 | 3 | 8 | 2.18 | Trapezoidal Labyrinth Weir, a = 23˚ |

19_{ } | 196 | 20 | 534 | 3 | 8 | 2.73 | Trapezoidal Labyrinth Weir, a = 18˚ |

20_{ } | 196 | 20 | 621 | 3 | 8 | 3.17 | Trapezoidal Labyrinth Weir, a = 15˚ |

21_{ } | 196 | 20 | 774 | 3 | 8 | 3.95 | Trapezoidal Labyrinth Weir, a = 12˚ |

22_{ } | 196 | 10 | 294 | 3 | 8 | 1.50 | Circular Labyrinth Weir |

23_{ } | 196 | 15 | 294 | 3 | 8 | 1.50 | Circular Labyrinth Weir |

24 | 196 | 20 | 294 | 3 | 8 | 1.50 | Circular Labyrinth Weir |

Experiments are carried out on six trapezoidal labyrinth weir models having side wall angles of 12˚, 15˚, 18˚, 23˚, 30˚ and 37˚, circular labyrinth weir models and a linear weir models having sharp crested shape similar to labyrinth weirs models. On all these models, head-discharge measurements are taken for weir height of P = 10, 15 and 20 cm. In addition, experiments were repeated by placing nappe breakers on all models of the labyrinth weirs. A total of 24 different configurations were examined in these experiments.

Discharge coefficient for labyrinth weirs was computed using equation (Equation (4)). Discharge coefficients of labyrinth side weirs have much higher values than the conventional weirs. The effect of crest shape on the discharge coefficient is very significant for the same channel width and crest length.

In this study, the nappe breakers installed on the crest spaced at a regular interval is a remedy used on prototype spillways to eliminate nappe oscillation. The nappe breakers create a break in the continuous lateral nappe profile, venting the confined air pocket (if one exists) behind the nappe to atmospheric pressure. Anderson, A.A. [

From these experiments, the variation of C_{d} for trapezoidal labyrinth weirs with H_{t}/P is plotted for P = 10, 15 and 20 cm in _{d} for trapezoidal labyrinth weirs with nappe breakers is plotted in _{d} for circular labyrinth weirs with and without nappe breakers is plotted together in

Also, the variation of discharge coefficient (C_{d}) with head to weir height (H_{t}/P) for trapezoidal labyrinth weirs (a = 37˚, L = 294 cm, N = 3, P = 10 - 15 - 20 cm) and circular labyrinth weirs (L = 294 cm, N = 3, P = 10 - 15 - 20 cm) which have the same crest length is plotted in _{t}/P. Similarly, to establish a relationship between L_{c}/w with C_{d} the observed data are plotted and shown in

To represent the data of the equation form, correlation analysis is carried out for the observed data for each model, separately. The 5th degree polynomial provides a reasonable fit between C_{d} and H_{t}/P. Thus, discharge coefficient (C_{d}) of sharp-crested labyrinth weir with and without nappe breaker is expressed as:

The values of C_{d}, A_{0} to A_{5}, and R^{2} are shown in Tables 2-4.

According trapezoidal labyrinth weir test data in _{d}) depending on side wall angels (12˚, 15˚, 18˚, 23˚, 30˚, 37˚) in the range from 0.1 to 0.5 of H_{t}/P. The effect of nappe breakers on discharge coefficient is a negligible level for α = 12˚ in the range from 0.1 to 0.5 of H_{t}/P. Similarly, the test data showed that the nappe breakers which have 12˚, 15˚, 18˚, 23˚, 30˚, 37˚ side wall angles reduced the discharge coefficient by 3.50% to 3.80%. As shown in

The discharge coefficient values of labyrinth weir compared well with those of Woronora Dam, Boardman Dam, and Avon Dam. Moreover, the results of the present study compared well with those of Tullis et al. [

Labyrinth weirs can pass large flows at comparatively low heads. The crest shape is one of the most important factors which affect the discharge capacity for labyrinth weirs. According to this experimental study, it has found that the trapezoidal labyrinth weirs are hydraulically more efficient than the circular labyrinth weirs and linear weirs from the perspective of ease of construction and the discharge capacity.

Variation of the nappe pressure between sub-atmospheric pressure and atmospheric pressure causes vibrations, oscillations and noise. Although the negative pressures under water nappe partially increase the discharge ca-

Model | A_{0} | A_{1} | A_{2} | A_{3} | A_{4} | A_{5} | R^{2} |
---|---|---|---|---|---|---|---|

Trapezoidal, α = 12˚ | 0.4598 | 2.8255 | −17.296 | 40.718 | −43.59 | 17.273 | 0.9799 |

Trapezoidal, α = 15˚ | 0.4600 | 3.4773 | −19.171 | 42.242 | −43.039 | 16.438 | 0.9848 |

Trapezoidal, α = 18˚ | 0.5638 | 2.1933 | −12.876 | 29.283 | −30.857 | 12.090 | 0.9738 |

Trapezoidal, α = 23˚ | 0.6417 | 0.9673 | −4.0152 | 5.7463 | −3.8338 | 0.8922 | 0.9608 |

Trapezoidal, α = 30˚ | 0.6395 | 1.5467 | −8.3233 | 17.937 | −18.184 | 6.9522 | 0.9620 |

Trapezoidal, α = 37˚ | 0.6537 | 1.6113 | −8.6152 | 18.076 | −17.719 | 6.5955 | 0.9790 |

Linear | 0.6991 | 0.9370 | −3.4166 | 2.4939 | 1.8340 | -1.9528 | 0.9665 |

pacity of the labyrinth weirs, effects of vibration and resonance may cause problems that could threaten the safety of the structure.

Alleviation of these effects and to minimize the dynamic effects on structures can be possible with the nappe breakers which are placed on the labyrinth weirs. While it has been targeted to minimize these dynamic effects

Model | A_{0} | A_{1} | A_{2} | A_{3} | A_{4} | A_{5} | R^{2} |
---|---|---|---|---|---|---|---|

Trapezoidal, α = 12˚ | 0.4731 | 2.8739 | −17.689 | 40.762 | −42.397 | 16.331 | 0.9823 |

Trapezoidal, α = 15˚ | 0.5175 | 2.5002 | −15.434 | 36.535 | −39.287 | 15.580 | 0.9664 |

Trapezoidal, α = 18˚ | 0.6117 | 1.0411 | −7.3097 | 18.299 | −21.211 | 8.9806 | 0.9631 |

Trapezoidal, α = 23˚ | 0.6343 | 1.0339 | −5.7465 | 11.886 | −11.710 | 4.3669 | 0.9419 |

Trapezoidal, α = 30˚ | 0.6901 | 0.7188 | −5.7036 | 15.169 | −17.800 | 7.5301 | 0.9320 |

Trapezoidal, α = 37˚ | 0.6870 | 1.0889 | −7.8546 | 19.953 | −22.336 | 9.1109 | 0.9284 |

Model | A_{0} | A_{1} | A_{2} | A_{3} | A_{4} | A_{5} | R^{2} |
---|---|---|---|---|---|---|---|

Circular | 0.6416 | 2.2646 | −15.683 | 38.676 | −41.490 | 16.310 | 0.9239 |

Circular with nappe breakers | 0.6687 | 1.4221 | −10.630 | −27.15 | −27.158 | 10.482 | 0.9454 |

with nappe breakers which are placed on circular and trapezoidal labyrinth weirs, it also has been examined the effects on discharge coefficient in this experimental study. The values for coefficient of discharge can be suitably obtained from the design curves and the regression equation generated through this study for trapezoidal and circular labyrinth weirs with/without nappe breakers.

The values for discharge coefficient of trapezoidal labyrinth weirs with and without nappe breakers can be suitably obtained from the design curves and the regression equations generated through this study for α between 12˚ and 37˚.

For trapezoidal labyrinth weirs, with H_{t}/P in the range from 0.1 to 0.5, the nappe breakers reduced the discharge coefficient C_{d} by 0.5% - 4% depending on side wall angles (12˚, 15˚, 18˚, 23˚, 30˚, 37˚). The reduction in discharge coefficient for nappe breakers on circular labyrinth weir is about 2 %.

Of course, given unlimited width, greater efficiencies (discharge per head) will be obtained for a linear weir. However, the trapezoidal provides much greater weir length in confined space with only limited reductions in efficiency (reduction in C_{d}). The circular weir is the least efficient of those investigated.

The nappe breakers located on the weir crest have proven to be an effective countermeasure by several researchers, but specific spacing of nappe breakers for a weir of a given height and width has not been determined and would be a valuable focus of future research, along with further investigation of the aspect ratio of flow depth to nappe width conducive to nappe vibration. A better understanding of the causes and preventative measures of nappe vibration will aid engineers in the design of dam spillways structures.

Funding for this study was provided by the Scientific Research Project Department of Firat University in Turkey, Project No: 1610. The authors gratefully acknowledge the assistance of Mr. Javad Roostaei in the preparation of Figures and Tables for this manuscript.

Omer Bilhan,M. Emin Emiroglu,Carol J. Miller, (2016) Experimental Investigation of Discharge Capacity of Labyrinth Weirs with and without Nappe Breakers. World Journal of Mechanics,06,207-221. doi: 10.4236/wjm.2016.67017