Aeration is the process of bringing water and air into close contact in order to increase dissolved oxygen concentration. The concentration of dissolved oxygen is an important indicator of water quality because aquatic life lives on the dissolved oxygen in the water. The hydraulic structures can be accepted as the key components in increasing dissolved oxygen concentration because of the strong turbulent mixing associated with substantial air bubble entrainment at these structures. Closed conduit is a classic example of a hydraulic structure where aeration occurs. This work focused on determining the effect of conduit length on air-demand ratio and aeration efficiency in free-surface gated circular conduits. Experimental results showed that the Froude number had an important effect on the air-demand ratio and the aeration efficiency. The effect of the conduit length on the air-demand ratio and the aeration efficiency changed depending on the Froude number. It was demonstrated from the results that a free-surface gated circular conduit flow system had high efficiency in transferring oxygen from air bubbles to water. Moreover, a formula for the aeration efficiency was presented relating the aeration efficiency to the conduit length and the Froude number.

NOTATION

     
  • A

    surface area associated with transfer volume

  •  
  • C

    mean concentration of dissolved gas in water within control volume

  •  
  • Cd

    dissolved oxygen concentration downstream of hydraulic structure

  •  
  • Cs

    saturation concentration of dissolved oxygen at standard atmospheric pressure

  •  
  • Cu

    dissolved oxygen concentration upstream of hydraulic structure

  •  
  • D

    conduit diameter

  •  
  • dC/dt

    rate of change in concentration

  •  
  • E

    aeration efficiency

  •  
  • E20

    aeration efficiency at 20°C

  •  
  • Fr

    Froude number based on effective depth in conduit

  •  
  • g

    acceleration of gravity

  •  
  • KL

    liquid film coefficient

  •  
  • L

    conduit length

  •  
  • Qa

    air flow rate measured through air vent

  •  
  • Qw

    water flow rate in conduit

  •  
  • t

    time

  •  
  • T

    water temperature

  •  
  • V

    water flow velocity at gate location

  •  
  • ye

    effective depth

  •  
  • β

    air-demand ratio ()

  •  
  • φ

    ratio of water cross-sectional flow area to conduit cross-sectional area

  •  
  • volume of liquid into which mass of gas dm diffuses in time dt

INTRODUCTION

The ecological quality of water depends largely on the amount of oxygen the water can hold. The higher the level of dissolved oxygen the better the quality of the water system. By measuring dissolved oxygen, scientists determine the quality of water and the healthiness of an ecosystem. Oxygen enters water by entrainment of air bubbles. This process has been termed aeration. Aeration is used for water quality enhancement in sewage treatment plants and in polluted rivers and lakes. Hydraulic structures can increase aeration efficiency by creating turbulent conditions where air bubbles are carried into the bulk of the flow. Gated conduits are a particular instance of this (Figure 1).
Figure 1

Free-surface gated conduit flow.

Figure 1

Free-surface gated conduit flow.

Gated conduits are hydraulic structures that involve high-velocity air-water flow. In large dams, they are commonly used for reservoir drawdown, sediment flushing, river diversion and environmental flow releases. In a gated conduit, a high-speed flow issuing from the gate drags and entrains a lot of air. If the air demand of the flow is not supplied, pressure reduction downstream of the gate causes cavitation. Usually an air vent is installed just downstream of the gate to supply enough air to the flow. Air that is entrained into the water is instantly forced downstream in the form of fine air bubbles. These fine air bubbles that create a large air-water surface area facilitate the solution of oxygen. The diffusion of oxygen into the water is usually greater in systems with fine air bubbles than systems with coarse air bubbles. This occurs because fine air bubbles present a greater surface area to the surrounding water than coarse air bubbles. Oxygen diffuses into the water at the surface, so a large surface area facilitates greater oxygen absorption.

Kalinske & Robertson (1943), Campbell & Guyton (1953), Sharma (1976), Stahl & Hager (1999), Speerli (1999), Speerli & Hager (2000), Ozkan et al. (2006, 2008, 2010, 2014), Escarameia (2007), Oveson (2008), Safavi et al. (2008), Mortensen (2009), Unsal et al. (2008, 2009) and Tuna et al. (2014) studied the air-demand ratio () and aeration efficiency (E20) in closed conduits and outlet works. However, the comprehensive literature search did not identify any published analytical or physical studies of the aeration efficiency in free-surface gated circular conduits. This paper reports an experimental investigation of a free-surface gated circular conduit flow system, including the effects of the Froude number (Fr) and conduit length (L) on the air-demand ratio and the aeration efficiency.

BACKGROUND

Oxygen is a highly volatile compound with a gas-water transfer rate that is controlled entirely by the liquid phase. Thus, the change in oxygen concentration over time in a parcel of water as the parcel travels through a hydraulic structure can be expressed as: 
formula
1
where C is dissolved oxygen concentration, dC/dt is rate of change in concentration, KL is liquid film coefficient for oxygen, A is surface area associated with transfer volume ∀, Cs is saturation concentration and t is time. Equation (1) does not consider sources and sinks of oxygen in the water body because their rates are relatively slow compared to the oxygen transfer occurring typically at hydraulic structures due to the increase in free-surface turbulence and the large quantity of air that is normally entrained into the flow. Cs is constant and determined by the water-atmosphere partitioning. Thus, the aeration efficiency E may be defined as (Gulliver et al. 1990) 
formula
2
where Cu and Cd are dissolved oxygen concentrations upstream and downstream of a hydraulic structure, respectively. For E > 1 the water is supersaturated (i.e., Cd > Cs) whereas for E = 1 the full oxygen transfer up to the saturation value is reached, and no transfer would correspond to E = 0. The aeration efficiency is adjusted to 20 °C as (Gulliver et al. 1990) 
formula
3
where E20 is aeration efficiency at a water temperature of T = 20 °C, and 
formula
4

EXPERIMENTAL

A physical experimental setup of a circular, gated closed conduit was built at Firat University Hydraulic Laboratory. Setup configurations were modified and data were collected to aid in the study of physical variables on air-demand ratio and aeration efficiency. All testing was performed in a physical experimental setup shown in Figure 2. The experimental setup consisted of a mixing/storage tank, DO meter, water pump, flow control valve, electromagnetic flow meter, sluice gate, air vent, circular conduit and measuring tank.
Figure 2

General view of experimental setup.

Figure 2

General view of experimental setup.

Most of the previous experimental works were conducted in rectangular conduits, whereas conduits usually have circular cross-sections. In the present study, a 190 mm diameter pipeline with adjustable length was used. The conduit length L varied from 2 to 6 m in 2 m increments. Froude numbers (Fr) were between 3.15 and 43.79. The Froude number was calculated by using Equation (5) using the effective depth (ye) in the conduit. 
formula
5
where V is the water velocity at the gate, g is acceleration of gravity and ye, effective depth, is the water cross-sectional flow area divided by the water surface width. 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.
The ratio of the water cross-sectional flow area to the conduit cross-sectional area (φ) was selected as 2.5% (see Figure 3).
Figure 3

Cross-section of gate.

Figure 3

Cross-section of gate.

An air vent was installed immediately downstream of the gate. The air vent consisted of 14 mm inside-diameter pipes that had a length of 150 mm. The sluice gate lip angle was 45°. As water entered the flume under the sluice gate, a vacuum (air entrainment) occurred at the air vent of the free-surface conduit. An anemometer (Testo Model 435) was used to measure air velocity in the air vent. This measurement was accomplished by locating the anemometer at the center of the air vent. Each air velocity measurement was taken over a period of 60 seconds or longer. After obtaining a value for the air velocity, the air flow 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 direction of flow in the air vent to provide the most accurate measurements possible. Water flow rates were measured using a calibrated electromagnetic flow meter.

A calibrated dissolved oxygen meter (WTW Model Oxi 330i) was used to measure both the dissolved oxygen and the water temperature. The dissolved oxygen (DO) meter was calibrated using procedures following those recommended by the manufacturer. The sensor of the DO meter was immersed in the water to a depth of 0.20 m. Clean tap water was used throughout the experiments. The water in the storage tank was deoxygenated using the sodium-sulfite method. Cobalt chloride catalyzed the reaction between molecular oxygen and sodium sulfite. Each experiment was started by filling the storage tank and adding sodium sulfite (Na2SO3) and cobalt chloride (CoCl2). A stirrer was used to mix sodium sulfite and cobalt chloride with the water, until the DO was reduced to approximately 0. The aeration efficiency values were calculated from Equation (2) and then adjusted to 20 °C with Equation (3).

RESULTS AND DISCUSSION

The present study investigated the air-demand ratio () and aeration efficiency (E20) in free-surface gated circular conduits, and in particular, the effect of the Froude number (Fr) and conduit length (L) on the air-demand ratio and the aeration efficiency.

In the first part of this study, the influence of conduit length (L) on the air-demand ratio () was investigated. The results indicated that increased as the Froude number increased in all experiments, as shown in Figure 4. 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 air flow through the air vent. Moreover, it was observed from Figure 4 that at Froude numbers lower than 20, there was no effect of the conduit length on . However, at Froude numbers greater than 20, increased with increasing conduit length.
Figure 4

Variation in air-demand ratio with the Froude number for L [m] = (a) 2, (b) 4, (c) 6.

Figure 4

Variation in air-demand ratio with the Froude number for L [m] = (a) 2, (b) 4, (c) 6.

In the second part of this study, the influence of conduit length (L) on the aeration efficiency (E20) was investigated. The results indicated that E20 increased as the Froude number increased in all experiments, as shown in Figure 5. The reason for this is the increased air-demand ratio () with increasing the Froude number. Moreover, it was observed from Figure 5 that at Froude numbers lower than 15, there was no effect of the conduit length on E20. However, at Froude numbers greater than 15, E20 increased with increasing conduit length.
Figure 5

Variation in aeration efficiency with the Froude number for L [m] = (a) 2, (b) 4, (c) 6.

Figure 5

Variation in aeration efficiency with the Froude number for L [m] = (a) 2, (b) 4, (c) 6.

The results indicated that the free-surface gated circular conduit flow system had high aeration efficiency. The primary reason for this high aeration efficiency is that air is entrained into the flow in the form of a large number of fine bubbles. These air bubbles greatly increased the surface area available for mass transfer and hence the aeration efficiency.

An empirical correlation predicting aeration efficiency (E20) was developed for free-surface gated circular conduit flows including 23 data points with a correlation coefficient R2 = 0.97 as 
formula
6

where E20 is aeration efficiency at 20 °C, L is conduit length and Fr is Froude number based on effective depth in conduit.

The measured aeration efficiency values were compared with those predicted with Equation (6). A very good agreement between the measured values and the values computed from the empirical correlation was obtained. Further confidence in the correlation can be seen in Figure 6.
Figure 6

Measured values of aeration efficiency versus computed values from Equation (6).

Figure 6

Measured values of aeration efficiency versus computed values from Equation (6).

CONCLUSIONS

This study was performed in an effort to better understand air-demand ratio and aeration efficiency of gated circular conduits with free-surface flow condition. For this purpose, a series of experiments was conducted in a free-surface gated circular conduit. The following conclusions can be drawn from the present study:

  • (a) The Froude number had an important effect on the air-demand ratio and the aeration efficiency. The air-demand ratio and the aeration efficiency increased with increasing the Froude number.

  • (b) The effect of the conduit length on the air-demand ratio and the aeration efficiency changed depending on the Froude number.

  • (c) At Froude numbers lower than 20, there was no effect of the conduit length on the air-demand ratio. However, at Froude numbers greater than 20, the air-demand ratio increased with increasing conduit length.

  • (d) At Froude numbers lower than 15, there was no effect of the conduit length on the aeration efficiency. However, at Froude numbers greater than 15, the aeration efficiency increased with increasing conduit length.

  • (e) The free-surface gated circular conduit flow system was very effective for oxygen transfer. Therefore, this system can be used as a highly effective aerator in aeration processes.

  • (f) A regression equation was obtained with a very high correlation coefficient, showing the effect of the conduit length and the Froude number on the aeration efficiency.

  • (g) Great care must be taken when scaling results from models of two-phase flows as size-scale effects may exist. Previous studies have shown that scale effects of air entrained within closed conduits are negligible. However, scaling of aeration data to prototype size is virtually impossible, largely due to the relative invariance of bubble size. Various model sizes may be necessary to determine the significance of size-scale effects of aeration efficiency in circular closed conduits between the different-sized structures.

  • (h) Additional research is needed to better understand the effect of conduit geometry on aeration efficiency.

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