Discussion: Air entrainment and oxygen transfer in high-head gated conduits

The authors wish to thank the discusser for his interest in the paper (Kucukali, 2008). The authors would like to make some comments on several items raised by the discusser.

When the gate of a high-head outlet conduit is partly opened, a high-velocity flow occurs downstream of the gate resulting in subatmospheric pressures. Theoretically, these pressures can be as low as the vapour pressure of water and may lead to structural damage owing to cavitation and vibration. To avoid severe subatmospheric pressures the conduit is connected to the atmosphere through an air vent located downstream of the gate. The purpose of the air vent is to draw in air and thereby keep the pressures downstream of the gate at a safe level (Sharma, 1976). Therefore, in high-head gated conduits, air is frequently allowed to enter just downstream of the gate in order to

• (a) prevent or reduce cavitation damage

• (b) limit any vibrations and steady the flow.

Usually the air is entrained by the action of a hydraulic jump which forms just downstream of the structure.

Systematic studies of the air-entraining properties of hydraulic jumps in closed conduits were carried out by a large number of research workers: however, the comprehensive literature search did not identify any published analytical or physical studies of the dissolved oxygen levels in high-head gated conduits. The present authors (in the paper under discussion and Ozkan et al., 2006) carried out a series of laboratory experiments to study aeration efficiency in high-head gated conduit flow systems by using a simplified experimental configuration. The results indicated that high-head gated conduit flow systems had an extremely high aeration efficiency. Thus, using a simple high-head gated conduit flow system would significantly increase the solution of oxygen into the water. Recently, the authors have been carrying out laboratory studies to figure out the effects of conduit length, conduit shape and air vent diameter on aeration efficiency.

The experimental run consisted of establishing target values for gate opening h, flow velocity at the gate section V_w and slope of conduit s within the experimental conduit, followed by measurement of air entrainment rate Q_a, water temperature T, dissolved oxygen concentration upstream of the gate C_u and dissolved oxygen concentration downstream of the gate C_d. Experimental values of aeration efficiency E₂₀ were calculated from measured values using Equations 2 and 3. It was also observed from Figure 3 that the gate opening had an important effect on the ratio of the volumetric air entrainment rate to that of water Q_a/Q_w. The gate opening was not an important factor influencing E₂₀, however, as shown in Figure 4.

High-head gated conduits involve high-velocity air–water mixture flow; to avoid the problem of determining flow depths and velocities at the vena contracta section, the authors therefore considered flow velocities at gate section V_w instead of the dimensionless Froude numbers. In Figures 3, 4, 6 and 7, the horizontal axis was plotted as V_w. However, because air demand is related to the Froude number of the water flow, the Froude number can also be used instead of V_w as a main parameter. In this case, flow conditions at the vena contracta section downstream from the gate can be used as a reference to characterise the flow in the entire conduit. The contracted Froude number F_c relates to the section downstream from the gate, and F_c includes the contraction coefficient C_c. Therefore, the Froude number at the vena contracta section may be defined as

where V_c is the velocity at the vena contracta section, g is gravitational acceleration and h_c is flow depth at the vena contracta section.

Velocity at the vena contracta section is

where Q_w is water discharge and B is conduit width.

Flow depth at the vena contracta section is

where C_c is contraction coefficient and h is gate opening.