Improving the performance of the compound labyrinth weirs using an artificial ventilation approach Open Access

The following symbols are used in this paper:

A

Inside apex width

B

Length of labyrinth weir (Apron) in the flow direction

b1

Bottom width of the notch

D

Outside apex width

g

gravity acceleration

h

Depth of flow over the high stage of the weir crest

H′

total head over notch crest = h + V²/2 g

Lc

Total centerline length of labyrinth weir

lc

Centerline length of weir sidewall

P

Weir height

P′

Notch height

P1

Sensor in hole 1

P2

Sensor in hole 2

P3

Sensor in hole 3

Pr

Pressure head (m)

Q

Discharge over the weir

R_crest

Radius of crest shape

S

suction device

tw

Thickness of weir wall

V

with vented device

W

Width of channel

WV

without vented device

w

Width of a single labyrinth weir cycle

y_c

critical depth over a weir

α

Sidewall angle

γ

weight density

ΔL

Top width of the notch

ΔP

The notch depth

Labyrinth weirs are hydraulic structures used to increase discharge capacity (Crookston & Tullis 2013a, 2013b). Recently, compound labyrinth weirs could be used more efficiently than conventional labyrinth weirs for increasing discharge capacity (Idrees et al. 2016). The nape flow is a gravity-driven free-falling jet downstream of the labyrinth weir. It may exhibit different patterns of instability and behaviours (Crookston & Tullis 2012). However, pressure fluctuations behind nappe flow are considered the main reason for some phenomena such as potential nappe vibration, nappe instability, flow surging, and noise (Lodomez et al. 2019a, 2019b). These phenomena may not only affect the safety of the structure and discharge capacity of the labyrinth weir, but also cause problems from an environmental point of view. For example, the nappe oscillations produce a significant level of noise and acoustic pressure waves that increase the environmental and societal impacts of the structure. Also, unstable nappe occurs as a result of the change in the amount of air pressure behind the nappe flow. Therefore, it is necessary to clarify the mechanism of pressure distribution behind nappe flow and the effect it has on labyrinth weir performance. The Metropolitan Water, Sewage, & Drainage Board (1980) conducted a study on the labyrinth weir at Avon Dam. They evaluated the effectiveness of several countermeasures for nappe oscillations. Most countermeasures included adding crest roughness elements or low splitters. Sumi & Nakajima (1990) proved an effective mitigation technique that used spoilers at the gate crest to split the nappe and aerate the air pocket behind the nappe flow. Casperson (1993a) conducted a study on the nappe oscillations that occur in fountains in New Zealand. He derived equations to model the position of the nappe during vibration and approved the reason for the nappe instability. Casperson (1993b) found that the feedback mechanism was caused by the air cavities behind the nappe. Naudascher & Rockwell (1994) demonstrated pressure variations in the air cavity behind the nappe that were attributed to turbulent mixing air entrainment. Nago et al. (1994) showed the mechanism of the shifting nappe vibration mode. They also found that nappe vibration occurs even when the confined air chamber is open to the atmosphere. Also, Chanson (1996) found that nappe instability was likely to be linked to discontinuity of the pressure when the jet of water leaves the weir crest. Casperson (1996) investigated nappe oscillations that occur on a curved crest. Also, further studies were conducted to investigate the instability and vibration of the nappe flow of vertically falling water jets. These have been conducted by many researchers, such as Kyotoh (2002) and Schmid & Henningson (2002). Sato et al. (2007) studied the nappe oscillations. They did the work by the water sheet, and the dropping height of the experimental device was adjusted from 0.47 to 0.62 m, and the frequencies were measured between 5.3 and 17.4 Hz. They explained the causes of the occurrence of nappe vibration for three reasons: oscillation of air pressure behind the nappe; instability of the nappe itself; and the structure of the weir acting as a vibrating system. Moreover, Nagamine et al. (2011) conducted an experimental study on a weir with a two-metre height to investigate nappe oscillation. They developed new equipment to muffle the low frequency of nappe oscillation. Crookston & Tullis (2013a, 2013b) investigated nappe instability, nappe vibrations, and nappe aeration conditions (clinging, aerated, partially aerated, and drowned) for labyrinth weirs with half- and quarter-round crests and a range of sidewall angle of 6° to 35°. They used artificial nappe aeration such as nappe breakers and vented nappe to show the effects of artificial nappe aeration on discharge capacity and nappe behaviour. They found that artificial nappe aeration using nappe breakers was better than using vented nappe. Also, for half-round crest shapes, the instability of the nappe was limited to the partially aerated nappe. When the nappe was vented, instability of the nappe happened to a smaller degree for α ≥20° in the partially aerated (half- and quarter-round crest shapes). Crookston et al. (2014); Anderson (2014) suggested that the nappe instability most likely arises at the weir crest. The horizontal bandings on the nappe created by the fluctuations are observed directly after the flow separation from the weir crest. De Rosa et al. (2014) conducted a theoretical study that showed the effect of the air pocket underneath the nappe with the nappe interface. They used a non-modal and a modal linear approach to investigate both the energy and the dynamics aspects. They found that the stability criterion of nappe depends on system stability if the time required to pass through the perturbation over the entire length of the domain is shorter than the period of the mass oscillator. Lodomez et al. (2016) presented the characteristics of the nappe vibrations obtained from sound analysis and images of a prototype-scale linear weir model. The main outcomes were the obvious relationship between the frequency of the sound and the frequency of horizontal stripes in the thin flow nappes. The various stages of the nappe-flow condition have been classified based on the ventilation of the space (cavity) behind the nappe flow (Abdalla & Shamaa 2016). Mudiyanselage (2017) studied the nappe flow for the aerated and nonaerated scenarios, building on the theory of Chanson (1996). Mudiyanselage (2017) found that the flow condition is aerated when the upper and lower nappe are subjected to atmospheric pressure. Further studies conducted by Girfoglio et al. (2017) showed the behaviour of nappe vibration by using a vertical thin sheet with an air pocket in the presence of surface tension effects. The outcomes demonstrated that experimental data from the literature were in agreement with the dynamics analysis. Also, Bousmar & Libert (2017) observed nappe oscillations in Papignies dam, which is a new structure for regulating water levels in Belgium, although using splitters 1.65-m spaced for nappe aeration. The tests that were conducted on the site demonstrated that short-spaced splitters (less than 1 m) are efficient to mitigate nappe oscillations. Recently, Anderson & Tullis (2018) developed mitigation techniques for nappe vibration. They used crest roughness modifications as an alternative device to the mitigation of the potential nappe vibration. Lodomez et al. (2019a, 2019b) conducted an experimental study to investigate the impact of size scale effects on nappe oscillations. They used two experimental aspects: a prototype-scale linear weir of 3-m drop height and a geometrically similar 1:3-scale model of 1-m drop height. The nappe oscillation has been evaluated using image and sound analyses. The results showed that the nappe oscillation phenomenon generally takes place over a fixed range of unit discharge. They also focus on the secondary effects of the crest profile and the fall height on the oscillation characteristics. Lodomez et al. (2020) conducted experimental work to assess nappe frequencies. They used two techniques for data analysis of images and sounds. They also proved that both techniques were effective by their application in the field.

Finally, although previous studies are available in the literature that used techniques to mitigate the pressure behind nappe flow, they focused on some of the techniques such as the reduction of the nappe width by using splitters, nappe breakers, and the variation of the crest roughness. But, these solutions are still inefficient to avoid nappe vibration, which affects the labyrinth weir performance of passing the discharges. The objective of the present study was to investigate the artificial ventilation approach to improve the performance of the compound labyrinth weirs. Also, the current study developed a better understanding of the mechanisms of nappe aeration when using ventilation devices. Therefore, it was attempted to further the practical understanding of the effect of the ventilation devices on the compound coefficient of discharge in the laboratory. This information will assist the designer in choosing the appropriate design of the compound labyrinth weir.

A rectangular laboratory flume with a length of 7 m, a width of 0.5 m, and a depth of 0.6 m was used for testing. In the present study, the horizontal bed slope of the flume was set to zero. The physical compound labyrinth weir was fixed on a horizontal platform base by using screws and silicon to prevent water leakage. The water was supplied from a tank with dimensions of 2.5 m × 1 m × 1 m that was located under the flume and recirculated through the channel with a 200-mm diameter supply pipe using two pumps connected in parallel. The capacity of each pump was 40 L/s, giving a total capacity of 80 L/s for both. The flume also contains one regulating gate downstream to control the tailwater elevation. A point gauge with an accuracy of ±0.2 mm was used to measure the water level over the weir. Wave suppressors were provided in upstream of the flume. Wave suppressors were used to control the flow and dissipate the surface disturbances. The flow rates for each test were controlled by a gate valve. A flow meter has been utilised to measure the discharge rates. The discharge rates ranged from 2 L∕s to 50 L∕s with an accuracy of ±1 L/s. The flow meter was installed in the main pipeline with a diameter of 150 mm.

The tests were carried out in three different scenarios: without a vent pipe, with a vent pipe, and with a suction pipe. After installing the labyrinth weir model and connecting all related facilities, the calibration process should be conducted to define the individual datum for each sensor of pressure. The calibration process was made by moving the sensor to yield a zero reading. These readings for three points were taken with no flow (Q = 0 m³/s) over the weir. Then, each tube that connects the sensor and the model must be flushed from the air by pumping water through each tube. When the tube is air free, the water in the flume can flow. The measurements taken at these points provide a base measurement that was used to determine the variation in pressure as a result of the increased flow. A high-speed camera, the Go-Pro Hero 4, was placed behind a sidewall weir. This location allows for observation during the test, and it does not affect measurements. Nappe-flow conditions were aerated or partially aerated without vent, aerated or partially aerated with vent, and aerated or partially aerated with suction. With the aid of Figure 4, the pressure measuring system diagram is described.

For each run, the water was pumped into the flume and the flow depths and transient pressures were measured. The average pressure was computed for each sensor. The pressure was measured again at three points after increasing the flow over the labyrinth weir by using a controlling valve. These processes were repeated for three cases (i.e. with vented (V) pipe, without vented (WV) pipe, and suction pipe (S)) and when nappe flow conditions were aerated and partially aerated. The measurements were obtained at a frequency (f) of 100 Hz during 150 s when the sampling time (1/f) was 0.01 or (10 ms/S). The pressure readings were collected from the data logger using the software, namely the Hioki pressure reader, to present the pressure data in Bar. Table 2 shows the results summary for physical model testing.

The accuracy of the results produced by using a scaled model may be affected when used at a prototype scale. Therefore, Chanson et al. (2002) recommended adopting a Reynolds number greater than 105 to avoid scale effects. As shown in Moody's diagram, the Reynolds number is independent of the friction factor in a wholly rough turbulent flow. In other words, energy dissipation is independent of the Reynolds number in a roughly turbulent flow. In the current study, the Reynolds number used ranges between (108,577 and 289,201) for sidewall angle (α = 10°) and half-round crest. Afterwards, the Reynolds number is large enough to avoid scale effects. Therefore, the flow condition is known as turbulent flow because the Reynolds number is greater than 10⁵.

Falvey (2003) describes the Weber number as a dimensionless parameter that is indicative of the ratio that exists between the forces of inertia and surface tension. Therefore, the Weber number is used to avoid the effect of surface tension forces, especially in models where the depths are small enough that this effect may be significant. Novak & Cabelka (1981) recommended a minimum Weber number of 11. In the present study, the results showed that the Weber number varies between 14 and 2,712. Therefore, the effect of surface tension allows it to be ignored.

In most free-surface modelling, satisfying only Froude similitude is typically sufficient due to the very limited influence of viscous and surface tension forces. Making scale effects associated with viscosity and surface tension nearly negligible, However, the scale effect depends on the surface tension force and viscosity of the water. Therefore, the impact of scale-up to prototype does not have a significant effect because it used the same fluid in the model and prototype, and thus the same viscosity. Also, the surface tension force is so low in a prototype that it can be neglected (Young 2018). Also, Heller (2011) showed that the Froude similitude resulted in a disjoint in the Reynolds and Weber numbers. These numbers generally remain large enough to limit excessive scaling errors.

In open channel flow, Froude similarity (i.e., gravitational force) is predominant. In general, researchers have endorsed various scale ratios. Pegram et al. (1999) indicated that prototype behaviour can be represented by a scale ratio of 1:20 or more and showed that the scale ratio of 1:15 was optimal. Furthermore, Boes & Hager (2003) stated that the scale ratio should be from 1:10 to 1:20 if smaller scale models can provide safe design information. In the present study, the scale was set to 1:20 to limit possible scale effects.

Also, Figure 5 showed the existence of negative pressures on the downstream face of the weir in the sensor (P2) for the case where nappe conditions were aerated and with existing ventilation devices, as shown in Figure 5(b) for the vent device and Figure 5(c) for the suction device. In addition, for a given flow rate, the pressures differ along the vertical face of the weir sidewall. As shown in Figure 5, increasing the H′_t/p′ value raises the average pressure in all sensor readings (P1, P2, and P3) and nappe conditions (WV, V, and S). The high difference in pressure values was noticed in P2 and P3 when increasing discharge. But in P1, the pressure values slightly increased when the discharge was increased.

Comparing the pressure values at three points behind nappe flow, the results showed that the pressure values in P3 were greater than those in P1 and P2 for a given H′_t/p′. This difference is because of the location of the sensor in P3, which is near the water circulation zone behind the nappe. It occurs because of the nappe flow hitting the base of the weir. Therefore, the pressure values in P3 were higher and more positive than the pressure values in P1 and P2. Figure 5 shows that when H′_t/p′ was 0.10 for nappes without ventilation devices, 0.14 for nappes with vent pipes, and 0.18 for nappes with suction devices, the pressure values in P1 were greater than those in P2. This difference is because of the existing confined air behind the nappe when the nappe is fully aerated. Furthermore, the pressure in P1 is sub-atmospheric while the pressure in P2 is negative.

Although artificial ventilation is used, average negative pressures were recorded in some of the test points. However, the pressure readings oscillated, and the instantaneous pressures exceeded the sub-atmospheric pressure limits, meaning that cavitation could still occur. In the positions of P1 and P2, a compound labyrinth weir may operate with slight negative pressure for H′_t/p′ values between 0.1 and 0.2.

Also, Figure 7 demonstrated the effects of a fluctuating variation of negative and positive pressures in the air cavities. These pressure differences produce pulses that push and pull the nappe. In particular, these differences provide a vibration feedback loop that agrees with the outcomes of Naudascher & Rockwell (1994). However, the irregular supply of air to the air pocket causes vibrations of the resultant nappe. If the frequencies of the nappe and air pocket both exist, there is a significant effect, and this effect may be disastrous for the structure as a whole. To prevent these undesirable effects, therefore, artificial ventilation devices behind nappe have been used, and doing so completely removes the air cavities. In the position of P3, the turbulent water behind the nappe was replaced by air cavities (Figure 7(c)). An unstable air cavity also produces oscillating pressures at the downstream face of the weir. Therefore, the ventilation devices reduce the pressure behind the nappe and produce a more stable nappe. Figure 7 shows clear differences between nappe vibration occurring at low and high discharges. Vibration occurring at a range of high discharges (approximately 0.03–0.05 m³/s) is typically intense and noticeable when nappe flow is partially aerated and WV. At high flow, the nappe trajectory refers to the vibrating condition relative to the nonvibrating condition because of developing sub-atmospheric pressures in the confined air region. The results showed that the nappe trajectory is drawn toward air cavities, and the time required for nappe vibration to occur under high flow was random.

At low flow (approximately 0.005–0.03 m³/s) when nappe flow is aerated and WV, nappe vibration characteristics were displayed in different conditions. Rather than being sustained at a low-flow condition, the high intensity of nappe vibration caused a distinct cyclical nappe vibration process, including high capacity waves with a low frequency. As flow passed over the weir crest, the nappe would become nonvibrating (stable) with a constant nappe trajectory. The pressure in the confined air cavities beneath the nappe would also gradually increase, and this is attributed to the supply of enclosed air pockets from the air-entrained behind the nappe. It primarily occurs where the nappe hits the base of the weir. When the pressure differential became large enough, the nappe would begin producing large, fluctuating, and flapping nappe waves, most observable close to the region of impact with the base of the weir. The flapping nappe waves reduce the pressure behind the nappe. Once the nappe returned to stable conditions, the cycle was repeated. Noise and pressure were related to the low flow of the nappe vibration compared with the nappe vibration at higher flow.

Here, X and Y are the coordinates of the crest profile origin at the highest point of the crest. h is the water head without approach velocity head, and K and n depend on the slope of the upstream face. For the vertical upstream face, K = 2 and n = 1.85.

According to the statistical indicators presented in Table 3, the RMSE and MAE indexes showed the difference between the observed and estimated data. The RE were 1.065%, 4.218%, and 0.552% for three cases of nappe ventilation, such as without a vent, with a vent, and with a suction device, respectively. As seen from the RMSE and MAE indexes, they were closer to zero for three cases of nappe ventilation. The results indicated better agreement.

Pressure distribution behind nappe flow is important because it reflects what is occurring in this region of changes in the pressures between upper and lower nappe surfaces. Moreover, it is important to determine the size and location of the pressure regions that influence the trajectory of the nappe. Hence, its effect on the hydraulic characteristics of the compound labyrinth weir. Also, knowing about pressure distribution aids the designer in selecting the H′_t/p′ with the appropriate C_dc.

The coefficients in Equation (8) are provided in Table 4. Also, Table 4 includes four statistical measures of R2, RE, RMSE and MAE for each set of coefficients. These statistical measures were used to evaluate the accuracy of the results. The statistical indicators demonstrated the difference between the observed and estimated compound coefficient of discharge (C_dc). The observed (C_dc) was obtained from the experimental tests and the estimated (C_dc) was obtained from Equation (8). For sensor 1 (P1), the RE was 1.455, 1.814, and 1.447 for three cases of nappe ventilation (WV, V, and S device), respectively. For sensor 2 (P2), the RE was 2.023, 2.569, and 2.141 for three cases of nappe ventilation (WV, V, and S device), respectively. For sensor 3 (P3), the RE was 3.368, 3.323, and 2.371 for three cases of nappe ventilation (WV, V, and S device), respectively. As seen from the RMSE and MAE indexes, they were closer to zero for three sensors and three cases of nappe ventilation. The results indicated good agreement.

It is important to discuss the effect of ventilation devices on discharge coefficient and pressure behind nappe flow for compound labyrinth weirs. Depending on the outcomes of this work, the following conclusions were drawn:

• At higher H′_t/P′ values, the air cavities behind the nappe were unstable and varied temporally and spatially.

• The nappe flow was initially relatively tranquil and then developed to be unstable.

• When nappe flow was not vented, negative pressures were measured on the downstream face of the weir in the sensor (P2).

• A compound labyrinth weir was observed in both sensors (P1) and (P2) that operated with slight negative pressure when H′_t/P′ values were between 0.1 and 0.2.

• In all sensor readings at P1, P2, and P3, H′_t/P′ values were increased when the average pressure values increased.

• In both sensors (P2 and P3), the high difference in pressure values was noticed when increasing the discharge, while the pressure in a sensor (P1) slightly increased.

• The pressure values in a sensor (P3) were greater than those in both sensors (P1 and P2) for a given H′_t/P′.

• The pressure values in the sensor (P3) were greater when using a vented pipe device.

• A suction pump was the best device to increase the coefficient of discharge and reduce pressure behind the nappe.

• The compound coefficient of discharge was not linear and had the greatest value at low pressure behind nappe.

• The compound coefficient of discharge (C_dc) using the suction device and the vent device was greater than the compound coefficient of discharge (C_dc) without using the vent device by 10% and 4.5%, respectively.

• An empirical equation has been provided to predict the compound coefficient of discharge when pressure data behind nappe flow are available.

Although the methods and information for the compound labyrinth weir were obtained in the present study, it is generally recommended that future work uses numerical methods to verify the physical model. This information must be taken into account for site-specific conditions that may exist outside the scope of the current study. The benefit of using ventilation devices is to reduce pressure risk behind nappe flow and increase discharge capacity over compound labyrinth weirs under the smallest possible head. In addition, it will give valuable insights into the operation and performance of the compound labyrinth weir.

The authors would like to express their sincere thanks and gratitude to the Government and the Ministry of Higher Education and Scientific Research in Iraq for providing financial support for the study. They also express their sincere thanks to the School of Engineering/Deakin University for the use of the new test facility. They appreciate the technical assistance provided by laboratory staff at the School of Engineering (Deakin University).

All relevant data are included in the paper or its Supplementary Information.

The authors declare there is no conflict.