Wedge Aerator at the Bottom Outlet in Flat Tunnels

Wei, Wangru; Deng, Jun

doi:10.1061/(ASCE)HY.1943-7900.0002010

Open access

Technical Papers

Nov 14, 2022

Wedge Aerator at the Bottom Outlet in Flat Tunnels

Authors: Wangru Wei https://orcid.org/0000-0002-9513-6802 [email protected] and Jun Deng [email protected]Author Affiliations

Publication: Journal of Hydraulic Engineering

Volume 149, Issue 1

https://doi.org/10.1061/(ASCE)HY.1943-7900.0002010

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Abstract

Aerators are applied to provide air entrainment and cavitation erosion protections for high-speed flows. By traditional chute aerators in high-head bottom tunnels, it is difficult to maintain effective aeration protection for low-Froude-number and small-slope conditions. The present study explores a wedge aerator design at the bottom outlet, and detailed experimental data on the aeration cavity and the entrained air diffusion were obtained to assess the aeration protection performance. The wedge aerator separates the water flow from the bottom outlet into an upper free jet and a lower flow layer, creating a middle aeration cavity. The flowing lower layer can enhance the aeration cavity stability, ensuring the cross-sectional air diffusion generation downstream due to the flow collision interactions. The flow Froude number and vertical location are the main parameters affecting the air entrainment coefficient, cross-sectional air concentration distribution, and sufficient concentrations close to the chute floor. Optimized wedge aerators are proposed, indicating that the flow interior separation is an effective hydraulic design for bottom outlets in hydraulic engineering.

Introduction

Bottom tunnels to evacuate floods are a typical element of high-head dams. They consist of a pressurized conduit that connects an upstream reservoir to an open channel via a pressure gate that transforms the pressured flow into a free-surface flow. For water heads of 100–200 m, the velocity of the flow from the pressurized tunnel outlet into the open channel can reach

30 - 40 m / s

. Bottom outlets operating under high-velocity flows can cause cavitation erosion. A prototype bottom tunnel after a flood discharge operation is shown in Fig. 1; there is severe cavitation erosion on the sidewalls close to a radial gate, and the damaged area extends clearly downstream.

Fig. 1. Cavitation erosion damage on side-walls of a discharge tunnel. (Images by authors.)

Previously, aerator devices were the most effective way of controlling cavitation erosion (Peterka 1953; Rasmussen 1956; Russell and Sheehan 1974). However, if the chute connected to the bottom outlet usually has a small slope, the flow rollers rear of the air entrainment cavity retrogress and cause air duct choking, resulting in dangerous local cavitation damage. This makes it difficult to achieve adequate aeration protection using typical chute aerators (e.g., deflector or offset) located near the flat bottom outlet. Therefore, further research into the design of aerators for bottom outlets is required to improve gate outflow and flow aeration so that cavitation damage can be avoided.

A typical aerator consists of several transverse and vertical grooves around the chute walls that are connected to an air supply. Air is entrained into the water flow through the air cavity neighboring the water flow surface owing to the difference in atmospheric pressure. The cavity jet length, air entrainment coefficient, and air diffusion evolution near the wall are the main parameters used to describe the aerator efficiency. For bottom aerators, Pfister and Hager (2010a, b) investigated the optimum design parameters for an aerator, including the approach flow Froude number, deflector angle, and chute floor slope. Limits on the Froude number

{Fr}_{0}

were suggested to be

{Fr}_{0} = 6

for bottom offsets and

{Fr}_{0} = 4 - 5

for bottom deflectors with deflector angle

α = 6 - 11

. Steep chutes with a floor slope

φ > 30 °

were more efficient than those with a small slope, and these limits were reduced for steep chutes. Under adverse conditions such as low-Froude-numbers and small-chute slopes, the water jets flowing over the aerator are poorly aerated, and the water rollers on the floor of the chute move conversely to the air supply devices, filling the jet cavity (Laali and Michel 1984; Rutschmann and Hager 1990; Shi et al. 1983; Qian et al. 2014).

The mechanism reason for the cavity filling was deduced that the aerator geometry and flow conditions could lead to a high cavity subpressure, acting as the onset of the filling cavity. By summarizing prototype and model aerator performances (Chanson 1995), flow choking phenomena of chute aerator cavities were obvious for

{Fr}_{0} < 4

and

φ < 12 °

, and a minimum value of

{Fr}_{0} = 7 - 8

was proposed with a critical ratio of flow depth to offset height. Thus, the research gap in the aerator device for flat tunnels remains open, and the relevant flow pattern generating an effective air entrainment near the bottom outlet should be explored to advance the knowledge and technology.

In addition, as water flows with large depths release from a bottom aerator, neither free surface nor bottom cavity air entrainment can make the air diffuse immediately across the full flow section. The unaerated region in the center of the high-speed flow puts the sidewall at risk because the bottom aerator does not provide sufficient protection. To promote aerator applications, lateral deflectors or offsets combined with bottom devices have been designed. To optimize lateral aerators, the lateral cavity length should be less than the bottom cavity length; otherwise, unstable shock waves from the reattachment area between the lateral jet and the sidewalls can plug the air entrainment path and reduce the protection against cavitation erosion, as shown in Fig. 2.

Fig. 2. Model of an aerated flow with a combination of bottom and lateral deflector aerators.

Flat chutes have a relatively short bottom cavity, so it is difficult to obtain good aerated flow patterns downstream (Li et al. 2011; Wu et al. 2013; Xu et al. 2020). The flow pattern over the sidewall aerator is impressible for lateral deflector design parameters (Liu et al. 2007; Wang et al. 2006). Li et al. (2016) studied the evolution of sidewall pressure along the side cavity of a lateral aerator in a radial gate. Their results indicated that the sidewall pressure decreased as the radial gate operated, which could raise cavitation erosion risks of the sidewalls. These effects should be fully considered for full-section aeration and cavitation erosion protection on prototype bottom tunnels (Liu et al. 2006; Liu 2006). Thus, it is still necessary to design an appropriate aerator device for practical applications that can eliminate cavitation erosion for chutes with small slopes and bottom outlet sections.

For the design case of bottom outlets, the present study proposes a wedge aerator at the radial outlet connected to a flat chute. A series of hydraulic model tests were conducted to investigate the air entrainment and aerated flow features downstream from the wedge aerator, including the air diffusion and transport processes. Compared with the air entrainment generation of the wedge aerator with traditional aerators, the specific flow pattern for air–water flow is clarified to understand the mechanisms of the air diffusion process in bottom-outlet structures. Based on the aeration cavity and downstream air diffusion performances, the optimal height location for the wedge aerator is also discussed. These findings will help engineers designing bottom outlet and tunnel structures, improving the aeration protection for high-speed chute flows in high-head dams.

Experimental Setup

Experiments to examine the wedge aerator and corresponding air–water properties (Fig. 3) were conducted using a 0.25-m-wide rectangular chute model at the State Key Laboratory of Hydraulics and Mountain River Engineering, Sichuan University, China. A typical bottom outlet with a radial gate was connected to an 8-m-long open channel. The widths of the bottom outlet and open channel were identical. The chute had a constant slope of

α = 3 °

relative to the horizontal direction. Water flows were released from a pressurized outlet with a constant outlet height of

h_{0} = 0.23 m

. Approach Froude numbers of

{Fr}_{0} = V_{0} / (g h_{0})^{0.5}

were generated with various water discharge conditions, where

V_{0}

is the average flow velocity at the bottom outlet and

g

is the gravitational acceleration.

Fig. 3. Experimental photo and sketch of an aerated flow over a wedge aerator.

The velocity was given by

V_{0} = q_{w} / (h_{0} - t)

, where

q_{w}

is the discharge per unit width, and

t

was the height of the wedge aerator. The water discharge

Q_{w}

was supplied by a water circulation system. Seven flow discharges were tested, and

V_{0}

ranged from 2.7 to

4.2 m / s

with

{Fr}_{0}

between 1.8 and 2.9. Thus, tests were conducted with low Froude numbers and small chute slope conditions. The

x - axis

was defined as the streamwise direction along the chute floor, starting at the roof of the bottom outlet. The

y - axis

was perpendicular to

x

, starting at

x = 0

.

For supercritical air–water flows in open channels, the scale effects of air–water properties relating to the hydraulic model were hard to avoid, and it was difficult to obtain similarity of air–water mixture properties from scale-physical models (Felder and Chanson 2017). To minimize scale effects of the air concentration of aerated open channel flows, limitations relative the approach flow Reynolds number

{Re}_{0} = V_{0} h_{0} / ν

and Weber number

{We}_{0} = (ρ V_{0}^{2} h_{0} / σ)^{0.5}

are suggested as

{1.0 \times 10}^{5}

and 140, respectively, where

ρ

is the water density,

σ

is the surface tension, and

ν

is the kinematic water viscosity (Pfister and Hager 2010a; Pfister and Chanson 2014; Heller 2011). In the present model tests, the limitations due to scale effects were respected with minimum values of

{Re}_{0} {= 4.7 \times 10}^{5}

and

{We}_{0} = 150

. Although experimental tests were carried out considering the scale limitations of the air–water flow, scaled models are prone to scale effects in the aeration properties (Falvey and Ervine 1988; Chanson 1996). The measurements paid particular attention to the air diffusion properties and were used to analyze the aeration efficiency of the wedge aerator.

The wedge aerator was set between the roof and the floor of the pressurized outlet. Smooth curves were used for the upper and lower solid walls, and an inclined side was used to fit the bottom outlet and radial gate configurations, as shown in Fig. 4. The length

L

of the wedge aerator was 31.5 cm, and the vertical height

t

was 4.5 cm. The inclined sides contained several air holes, which connected the aeration and air supply systems.

Fig. 4. Definition sketch with design parameters of a wedge aerator.

The approach water passing through the wedge aerator was divided into upper and lower flows with depths of

h_{1}

and

h_{2}

, respectively. The upper flow acted as a jet with two free surfaces, and the lower flow moved along the open channel. An aeration cavity was generated between the flows, and the air entrained by the wedge aerator was supplied via two lateral dropshafts on each side. The upper and lower flows reattached downstream at the end of the aeration cavity, and the impact interaction between them entrained air into the water, creating the cross-sectional air–water mixture. Air diffused to the floor and the free surface simultaneously. Air bubbles reaching the bottom floor and sidewalls could provide aeration protection. Moreover, the movement of the lower flow prevented the backwater from choking the aeration cavity and guaranteed free air flow below the upper flow. Furthermore, the angles between the upper and lower flows were small, which avoided splashing water and uncertain shock waves, and the free surface remained smooth because the air–water flow developed downstream.

The ratio

e = h_{2} / h_{0}

was used to represent the relative position above the floor. To obtain the optimal vertical location of the wedge aerator, six wedge aerator locations were arranged from 0.04 to 0.43 based on the entrained air diffusion performance close to the chute floor, and the maximum

h_{2} = 10 cm

. It was possible to control the two flows independently by changing

e

, and different

V_{0}

values could be tested with the same

e

. Thus, the effects of different

{Fr}_{1}

and

{Fr}_{2}

on wedge aerator performances were obtained for identical

V_{0}

conditions.

Several specific parameters for the air entrainment and downstream air diffusion were selected for the wedge aerator performance analyses. The aeration cavity length

L_{a}

was visually detected as the distance between

x = 0

and the reattachment point of the two flows. The cross-sectional air concentration distribution

C (y)

of the flow was measured using a phase-detection needle probe (CQY-Z8a Measurement Instrument, Institute of Water Resources and Hydropower Research, Beijing). The principle of the resistance-type probe was to determine the air concentration by detecting the clear water resistance and the aerated water resistance between the two electrodes. The sampling period for each measurement point was set to 120 s with a 100-Hz frequency. The time-averaged air concentration was calculated from the integration time, and the measurement accuracy was

\pm 10 %

if the sampling period exceeded 60 s.

For each test condition, approximately 120 air concentration measurement points were obtained at eight cross-sections. The first point was set 5 mm above the floor to obtain the bottom air concentration

C_{b}

. The air entrainment coefficient

β

was used to describe the aeration capacity of the wedge aerator. It was defined as

β = Q_{a} / Q_{w}

, where

Q_{a}

is the air quantity deduced from the first section close to the attachment point, which does not account for air entrainment along the upper free surface by the upper flow.

Results and Discussion

Cavity Characteristics of a Wedge Aerator

The typical flow patterns of two wedge aerator designs are shown in Fig. 5. Along the approach flow direction, the wedge aerators deflected the water and produced a free jet above a flow moving forward along the open channel. The thickness of the aeration cavity between the two flows gradually decreased in the streamwise direction. The upper jet reattached to the lower flow at a certain reattachment location, which generated a considerable layer of air–water mixture in the middle of the combined flow. The flow downstream from the reattachment section was fully aerated as a typical air–water flow.

Fig. 5. Longitudinal section of typical aerated flow patterns generated by the wedge aerator.

The effects of wedge aerator vertical positions for different

{Fr}_{0}

conditions were observed in the cavity areas. For

e = 0.04

with a low

{Fr}_{0} = 1.8

, unstable flow rollers were observed and the cavity was partially choked. The recirculating water could fill back to the wedge aerator intermittently. For a large

e = 0.43

with identical

{Fr}_{0} = 1.8

, a longer cavity was observed due to the cast capacity improvement of the upper jet flow; moreover, the partially choking phenomenon got weakened. As the approach

{Fr}_{0}

increased to 2.9, the aeration cavity became stable, ensuring an effective cavity length. Besides, the aeration cavity became more stable with increasing

e

, but air diffusion toward the chute floor was weak and there was a layer of unaerated water closed to the bottom floor downstream. Thus, the lower flow layer played a key role in stabilizing the aeration cavity and simultaneously restricted the fully cross-sectional air diffusion. Both of the aeration effects should be considered for the wedge aerator design to avoid insufficient air entrainment and low air concentration because these might provoke local cavitation erosion damage.

The air entrainment cavity length between the wedge aerator and the reattachment point

L_{a}

was used as a characteristic parameter of the two separated flows. The values of

L_{a} / t

are plotted in Fig. 6(a). As the approach

e

increased, the cavity length increased for all of the tested

{Fr}_{0}

values. According to the cavity-generation mechanism, the cavity length is determined by the upper-flow ejection combined with its reattachment interaction with the lower flow. Thus, the upper-flow Froude number

{Fr}_{1} = V_{0} / (g h_{1})^{0.5}

is an essential factor. Two effects govern

{Fr}_{1}

: (1) the water-head energy represented by

V_{0}

; and (2) the relative flow proportion, dependent on the position of the wedge aerator. The cavity length can be expressed as an approximately linear relationship

L_{a} / t = 2.25 \cdot ({Fr}_{1} - 1)

with

R^{2} = 0.869

, as shown in Fig. 6(b).

Fig. 6. Effects of wedge aerator design on cavity length $L_{a}$ : (a) effect of $e$ ; (b) effect of ${Fr}_{1}$ ; and (c) comparison with the literature.

In contrast to other chute aerators, including deflectors and offsets, there is a flow layer below the aeration cavity. When this lower flow layer is thin (

e < 0.1

), Fig. 6(c) shows that the cavity length with a wedge aerator

L_{a}

will be shorter than that with other aerators

L_{cal}

, as calculated by Pfister and Hager (2010a). This is mainly because the thin lower flow is insufficient to stabilize the cavity, and the choking effect caused by a small chute slope is unavoidable. Even for a low location with

e = 0.04

, the aeration cavity does not disappear and

L_{a} / L_{cal}

remains at approximately 0.6–0.8. As the lower flow layer increases with

e = 0.1 - 0.2

,

L_{a} / L_{cal}

is approximate 0.8–1.0, which indicates that the wedge aerator cavity with small

{Fr}_{0}

and flat chute conditions is as effective as traditional aerator cavities. For a relatively thick flow (

e > 0.2 - 0.3

),

L_{a}

increases gradually, reaching approximate 1.2 times of

L_{cal}

for

e = 0.4 - 0.5

. This indicates that the thick lower flow can maintain the air entrainment efficiency of the wedge aerator.

The effects of

e

and

{Fr}_{1}

on the air entrainment coefficient

β

are shown in Fig. 7. As

{Fr}_{1}

increases,

β

gradually increases, which can be expressed as linear relations for different

e

conditions. Compared with the conditions

e < 0.1

and

0.3 < e < 0.5

, the operation cases for

e = 0.1 - 0.3

produced a relatively large

β

of approximately 0.3–0.6 with approximately the same

{Fr}_{1}

. It is known from existing literature that

β

is primarily a function of the Froude number and chute aerator parameters (Rutschmann and Hager 1990; Hager and Pfister 2009); however, for bottom outlets with low Froude numbers and flat slope conditions, the value of

β

deduced by Pfister and Hager (2010b) is negative, representing the failure of traditional aerators. Because

β

mainly represents the air entrainment capacity of the local reattachment point, it is strongly affected the impingement of the flow and the level of turbulence. The wedge aerator is more efficient in terms of air entrainment than the traditional chute aerator for bottom-outlet aeration protection.

Fig. 7. Comparisons of air entrainment coefficient affected by a wedge aerator: (a) effect of ${Fr}_{1}$ ; and (b) effect of $e$ .

This investigation also showed that the height location of the wedge aerator has two effect aspects on the flow pattern and aeration performances. With the increase of

e

, the impingement of the upper flow reduces with a decrease of the flow depth, which makes the air entrainment intensity of the reattachment area get weak. Simultaneously, the stability of the lower flow strengthens with an increase in

e

, avoiding the air entrainment cavity choking due to the breakup of the thin flow layer. This enhances the air entrainment efficiency, retaining sufficient entrained air transport downstream. This coupling effect of the wedge aerator design indicates the parameter

e

is suggested as 0.1–0.2 to ensure optimum aerator performance. Present model tests showed that both small

e < 0.1

and large

0.3 < e < 0.5

lead to a potential of air entrainment reduction for relevant flow discharge operations.

Air Concentration Characteristics

The air concentration profiles for the flow downstream from the reattachment point for a representative case,

{Fr}_{0} = 2.9

, are shown in Fig. 8. The dimensionless depth perpendicular to the chute floor is

y / y_{90}

, where

y_{90}

is the flow surface with local air concentration

C = 0.90

. The two cross sections at

(x - L_{a}) / h_{0} = 0.0

and 0.8 immediately downstream from the attachment point had high air concentrations of 0.4–0.6 at the specific flow depths where the wedge aerator was set. The air concentrations were considerably reduced in both the upper and lower flows compared with the air–water mixture layer.

Fig. 8. Cross-sectional air concentration distributions downstream generated by a wedge aerator for ${Fr}_{0} = 2.9$ : (a) $e = 0.04$ ; (b) $e = 0.22$ ; and (c) $e = 0.43$ .

In the upper flow, a clear water core, where

C = 0

, reached approximately

(x - L_{a}) / h_{0} = 8.2 - 12.5

and, combined with upper free-surface air entrainment and bubble rise diffusion, it ultimately disappeared at

(x - L_{a}) / h_{0} > 12.5

. Air penetration to the floor was limited for different values of

e

. Further downstream from the air–water mixture development, the terminal

C

profile became fully aerated with a local

C > 0.01

for

e = 0.04

and 0.22, and unaerated water in the lower flow was not eliminated for large

e = 0.43

. For thick lower flows, it is difficult to transfer a small amount of air bubbles a long distance downstream. According to the typical characteristics of uniformly developed air–water flows (Hager 1991; Chanson 1996; Kramer and Hager 2005), the

C_{mean}

of a chute with a constant slope is approximately 0.10 for the present model. Compared with the uniform air concentration distribution of Chanson (1996), it takes about a long development distance

(x - L_{a}) / h_{0} > 20

for the model air concentration profile developing to uniform air–water flows.

Because the air diffusion typically appears near the chute floor where cavitation damage is a concern, the downstream air transport was examined using the bottom air concentration

C_{b}

close to the chute floor. Figs. 9 and 10 show representative tests with

e < 0.3

; no air was detected for

e = 0.43

under the present flow conditions. The value of

C_{b}

is large at the reattachment point because of the aeration cavity and strong air–water mixture rollers. When

e = 0.04

and 0.13,

C_{b}

was approximately 0.3–0.6, indicating that the lower flow was highly fragmented when it was impacted by the upper flow. With a slight increase in

e

to 0.22,

C_{b}

decreased below 0.05, showing the stabilization of the lower flow and intensive constraint of the air penetration capacity.

Fig. 9. Effect of ${Fr}_{0}$ on the $C_{b}$ decay downstream: (a) $e = 0.04$ ; (b) $e = 0.13$ ; and (c) $e = 0.22$ .

Fig. 10. Effect of $e$ on the $C_{b}$ decay downstream: (a) ${Fr}_{0} = 1.8$ ; (b) ${Fr}_{0} = 2.5$ ; and (c) ${Fr}_{0} = 2.9$ .

Along the downstream flow,

C_{b}

decreased notably for

(x - L_{a}) / h_{0} > 5 - 10

owing to air detrainment and flow reorganization downstream along the flat chute. For a certain

e

, the bottom aeration level improved and the

C_{b}

decay trends became smooth as the approach

{Fr}_{0}

increased. This is mainly because a high approach flow velocity can maintain the air transport capacity along the floor, overcoming the air bubble buoyancy and air detrainment effects. When

e < 0.22

, local

C_{b} > 0

was almost detected for

(x - L_{a}) / h_{0} > 5 - 10

, which is believed to provide the longest possible effective protection distance and reduce serious cavitation damage after the wedge aerators.

A comparison with the traditional bottom aerator is shown in Fig. 11(a), and a factor

f_{0} = (x / L_{a} - 1) {Fr}_{0}^{- 2} [h_{0} / (h_{0} + s {)]}^{- 1.3} (\sin α)^{0.4}

was used to normalized with the bottom air concentration decay (Pfister and Hager 2010b). The parameter

s

is the aerator height for traditional aerator, and for the wedge aerator, it is defined as

s = t + h_{2}

, which includes the moving layer depth of the lower flow. For the present small chute slope condition (

α = 3 °

), the value of

C_{b}

decreases obviously as the air–water flow develops downstream. However, for small

e = 0.04 - 0.09

of the wedge aerator,

C_{b}

can remain a long development distance. Compared with the traditional chute aerator, the reattachment interaction between the upper and lower flows generated by the wedge aerator can improve the air diffusion close to the chute floor. The decreasing trend of

C_{b}

gets rapid with the increase of

e

, and a similar

C_{b}

trend with the traditional chute aerator is obtained for

e = 0.22

. This indicates that a large

e

with a thick lower flow depth and weak aeration performance restrains the air diffusion along the chute floor.

Fig. 11. Streamwise air diffusion close to the bottom floor: (a) comparison with the traditional chute aerator of Pfister and Hager (2010b); (b) effect of ${Fr}_{2}$ on $L_{b}$ ; and (c) effects of $β$ and $e$ on $L_{b}$ .

The reference protection length

L_{b}

was extracted from the tested data and is considered to be the streamwise distance from the reattachment point to the last point where an effective

C_{b} > 0

is measured. Because the air transport is strongly influenced by the lower flow layer, the present experimental results indicate a positive correlation between

L_{b} / h_{2}

and

{Fr}_{2}

, following a simple power function, as shown in Fig. 11(b). An optimal design for

e

with a wide

{Fr}_{2}

operation range can increase the protection length for the chute floor. Combing the aeration performance

β

and wedge aerator parameter

e

, an approximately linear relationship between

L_{b} / h_{2}

and

β / e^{2}

is obtained in Fig. 11(c).

Besides the individual effect of the lower flow, the parameters included the governing effects of approach flow conditions, including the

V_{0}

and the

{Fr}_{1}

. For a specific wedge aerator with a constant

h_{2}

design, the efficiency of the air entrainment and aeration protection can be improved by increased flow velocities and upper flow depths, and the relevant factors are usually given for a certain bottom tunnel by design and economic options. Consequently, for the bottom tunnel with a small slope, the wedge aerator operates more effectively in terms of the bottom air concentration close to the chute floor than the traditional chute aerator because the turbulent air transport with the moving lower flow is sufficient.

Discussions of an Optimal Location

For a bottom outlet connected to a flat chute, the efficiency of a wedge aerator at location

e

is described by three factors: (1) aeration cavity stability, (2) the air entrainment coefficient, and (3) the cross-sectional air concentration distribution, especially the distance of cavitation damage protection. First, a minimum value of

e

is necessary to achieve a stable cavity shape. For low flow Froude numbers,

e

should be greater than 0.1 to provide a sufficient flow layer below the aeration cavity to eliminate possible filling water from the cavity. Second, when

e

exceeds 0.2, the lower flow is relatively thick for air bubble penetration toward the floor of the flat chute. As shown in Fig. 12(a), besides the obvious effect of high

{Fr}_{0}

conditions on the sufficient air entrainment, an optimal

e

of 0.1–0.2 can provide large values of

C_{mean}

and substantial air entrained into the flow. This can result in a

C_{mean}

larger than the uniform value, promoting the air diffusion and transport across the entire flow cross section, as shown in Fig. 12(b).

Fig. 12. Assessments of an optimal $e$ for wedge aerator: (a) $C_{mean} [(x - L_{a}) / h_{0} = 0.8]$ ; (b) $C (y / y_{90})$ ; and (c) $L_{b}$ .

Simultaneously, the decreased air concentration detrainment rate benefits the distinctive sidewall aeration protection. Moreover, Fig. 12(c) emphasizes that the contradiction between the

e

design and the two separate flows along reference length

L_{b}

results in an optimal

e

of

0.1 - 0.2

. Values of

e

smaller or larger than the optimal value cannot provide remarkable aeration efficiency, resulting in unavoidable unaerated regions of the flow near the sidewalls or floor, and increasing the risk of serious cavitation damage.

The results of this investigation were entirely based on hydraulic model data, and they provide a hydraulic solution for aeration protection applications. The range of approach Froude numbers was

1.8 \leq 2.9

with a constant chute slope of

α = 3 °

, and the air–water flow downstream was

x / h_{0} = 500 - 600

. The geometrical designs of the wedge aerator were fixed to the radial outlet gate of the bottom chute. Assuming that air bubbles entrained into the water flow were larger in the Froude scale model than in the prototype tunnels, the air detrainment rate dominated by rising bubbles will be higher, and the proposed optimization of the wedge aerator can be used as a safe guideline. Apart from the specific air concentration required for cavitation erosion protection, practical experience (Chen et al. 2003 , 2001; Yin et al. 2021) shows that a small quantity of entrained air bubbles appear close to the walls, which is more important than the specific air concentration value.

Further research should focus on the effects of detailed wedge aerator designs, including geometrical parameters of boundary curves. The experiments conducted in the present study were limited to the bottom-outlet area with no comprehensive transition from the outlet gate to the long tunnel. Their combination of the wedge aerator with other chute aerators is recommended in further research, especially in large hydraulic models and prototype bottom tunnels.

Practical Applications

Aerator devices should be designed so that the cavitation erosion damage is avoided in high-speed chute flows. If the chute slope is small or the flow kinetic energy is low, the aerator performance is poor because the flow rollers rear of the aeration cavity retrogresses and cause air duct choking. The present wedge aerator provides an acceptable hydraulic design applied to low flow Froude numbers with

{Fr}_{0} = 1.8 - 2.9

and a flat bottom tunnel with

α = 3 °

. The aeration protection efficiency of the wedge aerator is primarily affected by the vertical location and approach flow conditions. The optimized design of the wedge aerator can effectively ensure the air entrainment capacity and eliminate the air supply device choking.

Conclusions

The experimental tests in this study represent a basic investigation of a wedge aerator for a bottom outlet of a flat flood discharge tunnel. The hydraulic model accounts for air–water flow patterns and air diffusion downstream of the wedge aerator. These efforts focused on aeration performance, which is commonly characterized by the cavity length, air entrainment coefficient, cross-sectional air distribution, and bottom air transport along the floor. The relative position

e

is a governing factor of wedge aerators, and its relation to aeration parameters was described at the reattachment point and various cross sections.

In contrast to traditional aerators, a wedge aerator was set at the bottom outlet to separate the approach flow into two parts, an upper free jet and a moving lower flow layer, and air entrainment occurred through the middle aeration cavity. Even a thin lower flow with a small

e

is helpful in terms of protecting the cavity from the choking effect caused by the small tunnel slope. As

e

and the approach flow Froude number increased, the aeration cavity length increased owing to improved upper jet projection and cavity stability. An optimal

e

of 0.1–0.2 can provide a large air entrainment coefficient, indicating that the reattachment and impingement interactions between the two separated flows can affect local aeration without specifying the air diffusion development.

In terms of the air concentration distributions and bubble transport along the floor, the optimal

e

can promote the entrained air diffusion across the full section, eliminating the clear water region on the walls and the floor. Furthermore, the moving lower flow provides kinetic energy, which can strengthen the air transport downstream, overcoming the air detrainment process. The present exploration indicates that the local flow interior separation and collision interaction by artificial devices is an optional hydraulic design to eliminate the choking flow and improve the aeration protection for bottom-outlet operations in hydraulic engineering. Besides, the streamwise and lateral air–water diffusions affected by two separated flow interactions were different to the previous aerated flows, and further experimental works in this area are needed to expand the understanding of the specific air–water mixture mechanism.

Data Availability Statement

All data, models, and code generated or used during the study appear in the published article.

Acknowledgments

This work was funded by the National Science Foundation of China (Grant Nos. 51979182 and 51979183).

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Published In

Journal of Hydraulic Engineering

Volume 149 • Issue 1 • January 2023

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This work is made available under the terms of the Creative Commons Attribution 4.0 International license, https://creativecommons.org/licenses/by/4.0/.

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Received: Sep 15, 2021

Accepted: May 23, 2022

Published online: Nov 14, 2022

Published in print: Jan 1, 2023

Discussion open until: Apr 14, 2023

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Wangru Wei https://orcid.org/0000-0002-9513-6802 [email protected]

Associate Professor, State Key Laboratory of Hydraulics and Mountain River Engineering, Sichuan Univ., Chengdu 610065, China. ORCID: https://orcid.org/0000-0002-9513-6802. Email: [email protected]

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Jun Deng [email protected]

Professor, State Key Laboratory of Hydraulics and Mountain River Engineering, Sichuan Univ., Chengdu 610065, China (corresponding author). Email: [email protected]

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Wedge Aerator at the Bottom Outlet in Flat Tunnels

Abstract

Introduction

Experimental Setup

Results and Discussion

Cavity Characteristics of a Wedge Aerator

Air Concentration Characteristics

Discussions of an Optimal Location

Practical Applications

Conclusions

Data Availability Statement

Acknowledgments

References

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Abstract

Introduction

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Practical Applications

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Acknowledgments

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