An experimental study of air-demand ratio in free-surface gated circular conduits Open Access

A_w

water flow cross-section area

B

water surface width

Fr

Froude number

g

acceleration of gravity

y_e

effective depth

L

conduit length

Q_a

air flow rate measured through the air vent

Q_a/Q_w

air-demand ratio (β)

Q_w

water flow rate in the conduit

V

water flow velocity at the gate location

φ

ratio of water flow cross-section area to the conduit cross-section area

When the gate of a high-head outlet conduit is partially opened, a high-velocity flow occurs downstream of the gate, resulting in subatmospheric pressures. Theoretically, these pressures could be as low as the vapor pressure of water and cause structural damage due to cavitation and vibration. To avoid severe subatmospheric pressures, the conduit is connected to the atmosphere via an air vent located downstream of the gate. The purpose of the air vent is to draw in the air so that the pressures downstream of the gate are at a safe level. An adequate air supply is vital to minimize structural damage from cavitation and vibration. The amount of air required depends on the entrainment and carrying capacity of the flow, while the drop in pressure behind the door is a function of the gate opening (Sharma 1976).

Sharma (1976) carried out several studies on air demand in high-head gated conduits. In this study, Sharma stated that for the air inlet, based on the water height at the bottom of the air vent, the air inlet here depends on the Froude number. Stahl & Hager (1999) made a series of studies on hydraulic jumping in circular conduits. Speerli (1999) suggested an equation for air demand in free surface tunnel flows. In recent years, Speerli & Hager (2000), Ozkan et al. (2006, 2009, 2010, 2014, 2015), Escarameia (2007), Oveson (2008), Safavi et al. (2008), Mortensen (2009), Unsal et al. (2008, 2009a, 2009b, 2014), Baylar & Batan (2010), Tuna et al. (2014), Hohermuth (2019), Hohermuth et al. (2020), Aydin et al. (2021), and Baylar et al. (2021, 2022), made various studies on the air-demand ratio (Q_a/Q_w) and aeration efficiency in gated conduits.

In this study in water engineering, gated conduits that have a wide application field and are shown as an alternative to the existing aeration systems in terms of aeration were used. In gated conduits operated as a free surface flow, the water velocity is increased due to contraction as it passes under the gate. This increase in velocity causes a pressure lower than atmospheric pressure to be formed downstream of the gate. This low pressure created causes air to enter the flow conduit through the air vents opened just downstream of the gated. The air vacuumed from the atmosphere is mixed with the water in the form of bubbles. In this study, the change in air-demand ratios depending on the Froude number was investigated for air vents at different locations, different gate openings (φ), and different lengths (L) in free-surface circular cross-section flow systems. The structure of this study consists of the Materials and Methods in the first part, the Experimental Results and Discussion in the second part, and the Conclusion and Recommendation in the third part.

Hydraulic structures can increase aeration efficiency by creating turbulent conditions when the volume of flow is transported to the thin air bubble. In this section, the aeration efficiency of the hydraulic structures used in the aeration processes of the water is examined with an emphasis on the aeration efficiency. Hydraulic structures, pressure flow systems, and free-flow systems are examined in two groups (Baylar et al. 2010).

In gated conduits, a pressure lower than the open-air pressure occurs at the air vent downstream of the gate, due to the high velocity created by the partial opening of the gate (Figure 1). With the effect of this low pressure, the air is vacuumed from the air vent. This vacuumed air causes the formation of a two-phase flow in the conduit. Due to this two-phase flow, accelerated oxygen transfer is provided (Unsal 2007).

Oveson stated that the Froude number can be used to describe the air demand in closed conduits with free surface flow, but comparisons should be made if the conduit geometries are not similar (Oveson 2008). In the literature, the Froude number has often been based on the vena contracta section. However, in this study, the Froude number was based on the effective depth in the conduit to avoid the problem of determining flow depth and velocity at the vena contracta section because the flow at the vena contracta section involves a high-velocity air-water mixture.

A physical experimental setup was built at Firat University Hydraulic Laboratory. Data were collected by modified setup configurations for the effect of physical variables on the air-demand ratio. All components used in the experimental setup are shown in Figure 2. The experimental setup consists of a storage tank, water pump, flow control valve, electromagnetic flowmeter, sluice gate, air vents, and circular conduit.

While most previous experimental studies were conducted in rectangular conduits, the channels in this study have circular cross-sections. A 2 m long plexiglass (acrylic) transparent pipe with an inner diameter of 19 cm and an outer diameter of 20 cm was used as a circular conduit. In addition, to be able to see the effect of the length, 2 PVC conduits, with 2 m, and 20 cm diameter were used. To regulate the flow regime, a metal pipe of the same dimensions was made on the upstream side of the gate.

In this study, gate opening values at different rates (2.5, 5, and 10%) were used to increase the air-demand ratio. Figure 3 shows the conduit gate with different opening ratios used in the experiments.

To determine the air-demand ratio in different locations, 5 air vents were opened at different distances downstream of the conduits. Air vent diameters were taken as D = 14 mm by the airflow meter, considering the measurement precision and convenience. The distance between each air vent center was also taken as 4xD = 56 mm (Figure 2).

The amount of air sucked from the air vents was measured separately by changing the flow rate values for different gate opening rates. To measure air velocity in the air vent, a calibrated digital airflow measuring instrument (TESTO Model-435) was used. This measurement was accomplished by locating the anemometer at the center of the air vent. Each air velocity measurement was taken over 60 seconds or longer. After obtaining a value for the air velocity, the airflow rate through the air vent was calculated. The anemometer used for air velocity measurements was accurate to ±(0.2 m/s +1.5% of mv). Care was taken to ensure that the anemometer was always perpendicular to the flow direction in the air to ensure the most accurate measurements possible.

Since the water in the experimental setup was continually circulated, a water tank one side of which was glass with 0.75 m width, 1.5 m height, and 1.5 m length was used. In this system, continuous water is provided to the water tank outside to provide water for the experiments. The water used in the experiments was continually changed to prevent pollution from possibly to effect aeration performance. Then a certain volume of water was continuously circulated. A water pump at the bottom of the water tank was used to take the water from the tank and send it to the conduit, a control valve to set the desired flow value, and a 100 mm diameter electromagnetic flowmeter with a digital display and 0.01 L/sec measurement sensitivity was used to determine the flow rate passing through the system.

The atmosphere pressure and environment temperature, where the experiments were performed, were 677 mm Hg and 22 °C, respectively.

The experiments to determine the optimum aeration location in free-surface flow conditions in gated conduits were first started from a 2 m long pipe for a gate opening ratio of 2.5%. The velocity of the air drawn from 5 different air vents, each at a different distance, was measured with an anemometer, with one air vent open, respectively. These measurements were repeated for the 4 and 6 m lengths and for the different 5 and 10% gate openings.

Before starting the experiments, the air of the system was completely evacuated using the vent air vent opened at the top of the metal conduit, which was made to correct the water regime, to discharge the previously accumulated air in the system, which would affect the test results.

While the flow rate of air entering the conduit was calculated, approximately 1-minute measurement was performed using an anemometer; as a result of this, the average air velocity was found. The air-demand ratio was calculated by multiplying the average velocity value by the area of the air vent.

This study aims to search the most suitable location for the maximum air-demand ratio (Q_a/Q_w). For this, the air-demand ratio in a free-surface circular conduit and especially the effect of Froude number and conduit length (L) on the air demand ratio were examined. This objective was achieved by establishing a physical experimental setup, conducting experiments, obtaining data, analyzing data, and presenting the results.

Figures 4, 5 and 6(a)–6(c) show the variation of Q_a/Q_w depending on the change of Froude number for the gate opening rates of 2.5, 5, and 10%, respectively. These changes were examined separately for air vents at 5 different distances downstream of the conduit gate. In addition, the change in the Q_a/Q_w depending on the length of the conduit for the air vents is seen.

It is seen that Q_a/Q_w increases with the increase of the Froude number in all of the air vents. It was observed that there was no significant change in the airflow rates passing through each of the 5 air vents for the same gate opening and conduit length. The reason for this is the increased pressure difference between the upstream and downstream sides of the gate with increasing the Froude number. The increased pressure difference caused the increased airflow through the air vent (Ozkan et al. 2015).

It is understood that the suction formed downstream of the gate in free surface conduit flows does not show a local change. It is thought that the air sucked from the air vents is formed by the drag effect of the water. To demonstrate this situation, measurements were made for 2.5 and 5% gate opening when all air vents were open, and graphs of these measurements are given in Figures 7 and 8(a)–8(c). It was observed that the air-demand ratio of each vent did not change even if all air vents were open. Since it was determined that the air-demand ratio did not change when all the air vents were open, no experiment was performed for 10% gate opening.

When all experimental series were examined, it was seen that the air-demand ratio reached the maximum value at the gate opening rate of 2.5%. The air-demand ratio decreased as the gate opening rate increased. There was an inverse proportion between the gate opening rate and the air-demand ratio. The reason for this was that the pressure difference between the gate upstream and downstream decreased as the gate opening rate increased and a weak hydraulic jump occurred due to the decrease in the Froude number (Aydin et al. 2021; Baylar et al. 2022).

Air-demand ratios increased slightly as the conduit lengths increased for three gate opening ratios (2.5, 5, and 10%). It is seen that the largest air-demand ratio for conduit lengths of 2, 4, and 6 m for a gate opening of 2.5% are 0.20, 0.22, and 0.28, respectively. Likewise, these values were 0.14, 0.17, and 0.17 at 5% gate opening and 0.10, 0.14, and 0.19 at 10% gate opening, respectively. In the conduit length of 2 m, the lowest air-demand ratio values were observed. The reason for this was that the air inlet from downstream of the conduit was high in short conduit lengths. Similar to this study, Baylar et al. (2022) determined that there is a lower air-demand rate in short conduit lengths.

It has been observed that the air-demand ratio for each air vent increases in direct proportion with the increase of the Froude number, with the cover openings fixed (Figures 9–11(a)–11(e)). However, considering the conduit lengths, it has been observed that the air-demand ratio increases with the increase in conduit lengths, especially at high Froude values. The decrease in the air inlet from the outlet mouth to the inside of the conduit with the lengthening of the conduit and the fuller flow of the cross-section due to the jump is thought to be the reason for this increase.

It is observed that the air-demand ratios, which are sucked from all air vents, increase as the conduit length increases, with the cover openings remaining constant (Figures 9–11(a)–11(e)). It is thought that increasing the conduit length causes a decrease in the amount of air entering the conduit flow from the downstream part, and therefore, the low pressure downstream of the gate increases the air sucked from the air vents.

Extreme care should be taken when scaling results from two-phase flow models as there can be size scale effects. Previous studies have shown that the percentage of air entrainment is not affected by the size of the model. However, scaling aeration data to prototype size is nearly impossible, largely due to the relative invariance of bubble size. Various model sizes may be required to determine the significance of size scale effects of oxygen transfer efficiency in closed conduits between different-sized structures.

In this study, air-demand ratios were investigated for each air vent by opening air vents at regular intervals downstream of the gate and the most suitable location for maximum air inlet was aimed. For this purpose, air-demand ratios depending on flow rates were determined for different gate openings and different lengths of conduits. As a result, we can say the following;

• It was observed that with the increase of Froude number in all air vents, the air-demand ratio also increased, but the air vent location did not significantly affect the air-demand ratio.

• It is thought that the suction air flow rate is caused by the drag effect of the water.

• In all conduit cross-sections, the air-demand ratio decreased as the gate opening rate increased.

• For all gate opening ratios, it is seen that the air-demand ratios increase with the increase in conduit lengths in almost all of the air vents.

• The highest air-demand ratio (Q_a/Q_w = 0.28) took at the conduit length of 6 m and the gate opening ratio of 2.5%.

• It was observed that the air-demand ratio of each air vent did not change even if all air vents were open.

The following recommendations are made to the researchers for further study of the current research subject:

• It is a separate research topic whether the oxygen transfer increases at the same rate as the increase in the amount of sucked air.

• Experiments should be carried out to determine the effect of gate design on the air demand ratio and oxygen transfer efficiency.

• Tests should be performed to determine whether the location, shape, and number of air vents influence the air-demand ratio and oxygen transfer efficiency.

• Tests should be conducted to determine whether conduit slope affects air-demand ratio and oxygen transfer efficiency.

• In high-head conduits, the effect of the location of the air vent on the air-demand rate should be investigated.

The authors would like to thank the referees for their valuable comments, which improve and strengthen the presentation of this manuscript.

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

The authors declare there is no conflict.