Effects of Air Vent Size and Location Design on Air Supply Efficiency in Flood Discharge Tunnel Operations

Low-level outlets are important hydraulic structures in high-head dams for emergency flood discharge operations, sediment flushing, and water level control in reservoirs (Ma and Chi 2016; Kundzewicz et al. 2019). The high water head results in a high-velocity free-surface flow in the flood discharge tunnel, as shown in Fig. 1. The approach flow velocity through a pressurized low-level outlet can exceed $30\mathrm{m}/\mathrm{s}$, and the high-speed free-surface flow entrains and drags a lot of air downstream. Thus, air ventilation structures are designed to supply air into the flood discharge tunnel. In high-head dams, the water flow leads to a large air pressure drop and high air velocities in vents and tunnels. The air supply system is typically designed based on the tunnel geometry, air vent size, and operating flow hydraulic conditions (Campbell and Guyton 1953; Aydin 2002; Shao et al. 2016). Insufficient air discharge could result in cavitation erosion problems affecting the safety operation of low-level outlets (Falvey 1980; Volkart and Rutschmann 1991). Insufficient air discharge could result in cavitation erosion problems affecting the safety operation of low-level outlets (Falvey 1990). Moreover, an additional challenge may be the excessive wind noise in flood discharge operations. Although the tunnel operation safety was satisfied even at low air supply efficiency, the high air velocity with wind noise exceeding 85 dB threatened staff working conditions (Davies and Williams 1968; Falvey 1980). The feasible options included vent size variation and an additional vent to generate two combined working vents (Chen and Huang 1984; Luo 1984). A couple of combined working vents were installed downstream of a long flood discharge tunnel, such as the Rumei tunnel, Houziyan tunnel, and Lianghekou tunnel (Xu 2016; Du et al. 2021; Ma et al. 2022). More detailed recommendations for the vent design are required to improve the air supply performance in flood discharge tunnels.

For the air discharge estimation in flood discharge tunnels, a series of relations were developed based on different flow patterns, including spray flow, supercritical free surface flow, and hydraulic jump flow (Wisner 1967; Sharma 1973; Huang and Griffin 2014). Some valuable prototype investigations on high-head tunnels emphasized that the air supply was determined by flow patterns, tunnel layouts, and air vent loss coefficients (Lier and Volkart 1994; Volkart and Speerli 1994; Hohermuth et al. 2021a). In addition to flow parameter effects, such as the water discharge rate and flow Froude number, the effect of the ratio of the residual air area over the total tunnel cross-section was introduced (Sharma 1976; Speerli 1999; Tullis and Larchar 2011; Wright and Tullis 2014). Although the air space was a dependent variable in a certain closed tunnel (Goldring 1983), its effect on the air flow prediction was essential for the assessment on multiple hydraulic structures. Speerli and Hager (2000) suggested that the residual air area ratio should be larger than 30% to avoid slug flow filling the tunnel. Using numerical simulations, Song et al. (2022) suggested that the relative residual air area determined not only the air discharge but also air flow velocity distributions for different vent sizes. Wei et al. (2021) proposed a relation between the residual air area and average air velocity, which achieved the air discharge estimation of the prototype tunnel with velocities up to $30–50\mathrm{m}/\mathrm{s}$.

The air vent is usually set near the low-level outlet where the negative air pressure is minimal to supply air as much as possible (Fuentes and Garcia 1984; Speerli 1999; Edwini-Bonsu and Steffler 2006; Hohermuth 2019). Previous studies focused on the air discharge affected by approach water flow, air vent cross-section, and tunnel size conditions. Experimental observations showed that the air discharge decreased with decreasing cross-sectional area of the air vent (Rabben and Rouvé 1984; Safavi et al. 2008; Husain et al. 2014). To clarify the main factors determining the air discharge, Hohermuth et al. (2020) conducted a large-scale experimental model to obtain systemic air supply data, and the results emphasized the effects of air vent geometry and the loss coefficient. The increasing relative air vent size led to a larger air discharge, and this effect should be modified by the air vent loss coefficient. The specific loss coefficient increased with the differential negative pressure in the vent, reducing the air discharge especially for long tunnels. Combined with the related the prototype observations on the high-speed flood discharge (Hohermuth et al. 2021a), obvious changes of free surface drag effects indicated that the residual air area related to the tunnel and air ventilation geometries should be considered as a specific factor influencing the air supply performance. The tunnel length and slope were also considered for the air supply performance as they affected the negative pressure distributions in the bottom tunnel (Hohermuth 2017). Although the previous studies have provided some important understanding of the air supply in low-level outlets, investigations about the air supply efficiency affected by multiple air vents of different sizes have been limited so far.

To provide practical references for air vent designs for low-level outlets, the present study focuses on the air supply efficiency for different vent layouts, using systematic hydraulic model tests. Single air vent sizes, locations, and two combined working vents are considered for different approach flow conditions. According to the differences in air supply efficiency, the effects of a single air vent and two working air vents on the air discharge are determined. Based on the quantitative estimation for the air discharge, the principles of air vent parameters are discussed, incorporating the assessment of prototype air ventilation and flood discharge operations.

A physical model of a typical flood discharge tunnel with a low-level outlet was built at the State Key Laboratory of Hydraulics and Mountain River Engineering, Sichuan University (Fig. 2). The gate chamber, flume, and air vents were made of acrylic glass. Using a pump for water discharge supply with a maximum capacity of $0.3{\mathrm{m}}^3/\mathrm{s}$, the low-level outlet was set with a pump pipe, and the outlet height $h_w$ operated in a range from 0.08 m to 0.20 m. A rectangular flume was connected to the outlet with a length of $L_t=16\mathrm{m}$, as shown in Fig. 3. The tunnel slope was $\alpha =2°$. The tunnel had a constant width of $W_t=0.25\mathrm{m}$, which was the same as the outlet width. The water discharge $Q_w$ was measured by a thin rectangular weir downstream. The approach water flow velocity was computed by $V_w=Q_w/(h_w{W}_t)$. A series of detachable plates was set as the tunnel roof, which were fixed by a series of screw bolts, allowing for a continuous variation in the tunnel height. A single air vent or two air vents were set at the tunnel roof with a 0.25 m width, and the air vent size in flow direction was variable.

The air vent height was 2 m height, about 5–10 times of the tunnel height. The air velocity in the vent was measured along the center line from 1.5 m to 0.5 m using a thermal anemometer (GM8903, China) with an accuracy of $0.001\mathrm{m}/\mathrm{s}$ (Fig. 3). Four gauging points at the vent cross-section $y=0.5\mathrm{m}$ were set, and the specific positions from the upstream vent sidewall were $x=0.005\mathrm{m}$, 0.055 m, 0.125 m, and 0.175 m, respectively. For each measurement point, the sampling frequency and duration was 1 Hz and 120 s, respectively, to obtain a relatively stable value of the air flow velocity. Fig. 4 shows measurement results of air flow velocities in the tested air vents. According to the measured cross-sectional air velocities in the air vent, the cross-sectional distributions are close to uniform and there is no obvious trend. This is mainly because the air flow velocity is low in the model vent within the boundary layer induced by the smooth acrylic glass. Most $v_a$ values fluctuate within $\pm 20\%$ of $v_{a\text{-}\mathrm{center}}$. Thus, the air discharge through the air vent was computed from the product of $v_{a\text{-}\mathrm{center}}$ and the vent cross-section square. It should be noted that compared to the experimental model, air vents in prototype flood discharge tunnels are significantly longer, and the head loss in long air vents needs to be considered.

All parameter combinations were tested for three approach water velocities, namely, $V_w=3.1\mathrm{m}/\mathrm{s}$, $4.1\mathrm{m}/\mathrm{s}$, and $4.7\mathrm{m}/\mathrm{s}$. The approach flow depth or the outlet height was varied from 0.13 m to 0.18 m. A series of relative areas of the air flow in the tunnel cross-section were controlled with $S_{at}/S_t=0.25$, 0.30, 0.40, 0.50, 0.625, and 0.675, by adjusting the tunnel height $h_t$. For different approach flow depths, the air layer height above the flow free surface varied from 0.03 m to 0.25 m. To investigate the effects of vent layouts on the air supply discharge, in the present experimental tests, a single air vent and two combined working vents were used. For single air vent effects, the vent length size $b_{a1}$ and distance location to the bottom outlet $L_{a1}$ conditions were tested. Seven $b_{a1}$ sizes ranged from 0.03 m to 0.25 m with $L_{a1}=0,2\mathrm{m}$, and 4 m. For the two air vent tests, the upstream air vent was set near the gate chamber ($L_{a1}=0$) with a minimum size design $b_{a1}=0.03\mathrm{m}$. The second air vent was set 4 m downstream ($L_{a2}=4\mathrm{m}$) with size ranging from 0.03 to 0.27 cm. All these flow and air vent conditions led to a total of 225 runs with free surface flows in the tunnel.

According to different flow patterns in tunnels, air flow discharges transported by water flows were formulated using different equations (Rabben 1984; Huang and Griffin 2014). For this study, the flow Froude number $Fr=V_w/{(g{h}_w)}^{0.5}$ ranged from 2.07 to 5.30, which indicated that the supercritical flow was satisfied for each test run. The total air discharge for a free-flow tunnel contains the air discharge entrained into the water and the air flow above the free surface (Qian et al. 2017; Hohermuth et al. 2021b). For the present flow conditions with a small chute slope, the flow velocity was too small for significant free surface aeration. The rectangular outlet design ensured the stable water flow as a stratified free-surface flow, which prevailed for large gate opening operations. This avoided the effects of different water flow patterns (e.g., spray flow, foam flow, hydraulic jump flow, or pressurized flow) on the air supply efficiency. The previous investigation suggested that the tunnel was long with the ratio of $L_t/h_t$ was greater than 36.5, for which the air was mainly supplied from the air vent (Gongchun and Chupei 1987). If the tunnel was short with the $L_t/h_t$ was less than 27.5, a considerable amount of air was supplied from the tunnel end and the counter-current air flow generated above the free surface flow. The present tunnel length ranged from 40 to 92.5, indicating that the air discharge was supplied by vents and the counter-current could be neglected for the air vents considered herein.

For prototype low-level outlet operations, the flow velocity can reach up to $30\mathrm{m}/\mathrm{s}$, and the order of magnitude of tunnel sizes ranges from ${10}^{-2}{\mathrm{m}}^2$ to ${10\mathrm{m}}^2$. Table 1 summarizes bottom tunnel parameters from 14 prototype dam projects, and an assessment analysis of the air vent size principle from the present experiments is shown in Fig. 11. To assess the air supply efficiency for different prototype tunnels, there are some simplifications and assumptions. First, the gate opening is used as the flow depth $h_w$ to calculate $S_{at}$ within the stratified free-surface flow pattern. This is a simplification of the flow pattern in long flood discharge tunnels. It should be noted that the flow characteristics of low-level outlets vary from the vena contracta (near the gate chamber) to developing flow and fully developed flow until the end of the tunnel. The effects of flow development on the dragged air are not considered in the present study. Second, the effects of shock waves and counter-current air flow near the gate chamber are neglected, and the flow is assumed to be stable without considering intensive flow depth fluctuations along the long flood discharge tunnel. Third, because of the complex vent designs in prototype tunnels, it is hard to obtain accurate vent loss coefficients; thus, the calculations are conducted without considering vent loss coefficients. The $S_{a1}/S_{at}$ ranges from 0.02 to 0.68 with $V_w=9.50–30.0\mathrm{m}/\mathrm{s}$, and the values of $Q_{aC}$ are deduced by the methods of Wei et al. (2021). Eq. (1) captures the overall data trend of the air supply efficiency in prototype low-level outlets. For a specific single vent design with $S_{a1}/S_{at}\le 0.5$, most of the prototype data are enveloped by the predicted trend lines within $\pm 50\%$ of Eq. (1). The effects of vent size on the air discharge are considered reasonable, and an underestimated design of the single vent size can result in low air supply efficiency. The present comparison with prototype air supply performance demonstrates that for a single air vent near the bottom outlet, a specific size design with $S_{a1}/S_{at}>0.5$ can mainly ensure an air supply efficiency $Q_{a1}/Q_{aC}>0.8$. Both the air drag and air entrainment capacities for prototype high-speed flows are higher than those of scaled model flows, and an underestimation of the air supply efficiency for flood discharge tunnels should be considered as well.

The typical prototype flood discharge tunnel in Nuozhadu Dam, China, is used for the analysis of two combined working air vents upstream. The dam is a rock-fill dam with a height of 261.5 m. Two low-level outlets for flood discharge operations are set separately on the two sides of the dam, as shown in Fig. 12. The bottom tunnel slope is $\alpha =11.5°$. The radial gate is used to control the gate opening (considered as the approach flow depth). During cumulate 920-h flood discharge operations, high wind noise was monitored exceeding over 100 dB due to the high air velocities in the air vent system of the bottom tunnel (Deng 2017). Although the operational safety of the tunnel is satisfied at the observed air supply efficiency, the high air velocity phenomena resulting in adverse staff working conditions is the reason for an air supply assessment leading to an air vent reconstruction. In terms of the ventilation system, two air vents with two circular cross-sections are set upstream. The diameters of the vent conduit are 6.8 m and 2.0 m, respectively. The upstream air vent is set close to the gate with $S_{a1}=36.30{\mathrm{m}}^2$, and the second vent with $S_{a2}=3.14{\mathrm{m}}^2$ is set $L_{a2}=126.9\mathrm{m}$ downstream. Four recent flood discharges, during which air discharge was measured, are shown in Table 2. The water head is approximately 107.2–109.7 m with $V_w=28.2–37.1\mathrm{m}/\mathrm{s}$. The basic water flow conditions are $\mathsf{F}=4.06–4.88$ with $L_{a2}/(b_{a1}+b_{a2})=14.4$.

Due to the water flow velocity increasing from $28.2\mathrm{m}/\mathrm{s}$ to $37.1\mathrm{m}/\mathrm{s}$, the measured air discharge in the upstream air vent rises from 1,310.4 to $\mathrm{1,756.8}{\mathrm{m}}^3/\mathrm{s}$, as shown in Fig. 13(a), and the measured air discharge in the downstream air vent rises from ${68.1\mathrm{m}}^3/\mathrm{s}$ to $83.4{\mathrm{m}}^3/\mathrm{s}$. For the second air vent, the low air supply efficiency is mainly due to the small size and the location away from the gate chamber. Based on the flow velocity conditions, the maximum air supply level is calculated, resulting in the air discharge $Q_{aC}$ ranging from 1,434.3 to $\mathrm{2,367.8}{\mathrm{m}}^3/\mathrm{s}$. The air supply efficiency of the two combined working vents is still low. This mainly causes the high air velocity and large wind noise phenomena during the flood discharge operation monitor (Devenport et al. 2018; Xiong et al. 2018). For a high velocity $V_w=37.1\mathrm{m}/\mathrm{s}$, the design parameters of air vent sizes $S_{a1}/S_{at}$ and $S_{a2}/S_{at}$ are 0.352 and 0.030, respectively. These results illustrate that the air vent size is small for the air discharge replenishment on the basis of present air vent design principles. Using the air supply discharge calculation methods of the free surface flow pattern in literature (Table 3), the various results show that the data scatter is large over one order of magnitude. (The contraction flow $F{r}_C$ is approximately deduced by the gate opening.) The relative error of Sharma (1973) is smaller than that of Campbell and Guyton (1953). Given two vent loss coefficient values $\zeta =0.1$ and $\zeta =1.0$, the results of Hohermuth (2019) infer that the air discharge is sensitive to the vent and tunnel geometrical parameters. Note that the Froude numbers for the prototype flows are below 5 and thus are outside of the application range of these approaches. Speerli (1999) suggested to use the water head $H_E$ as the dominate flow parameter. The various prediction methods indicate that for the prototype low-level outlets, the scale effects of dominant factors related to the air phase properties, including high energy head, air vent loss coefficient, and air–water mixture structure, likely play a role in the underestimation of air supply performance in flood discharge tunnels.

By plotting the prototype data in Fig. 13(b), detailed comparisons with the design equations are evaluated. For the air vent near the low-level outlet, the air supply efficiency does not reach the maximum level for the four cases, and the air supply efficiency from the two combined working vents is not obviously affected due to the relative small vent size. The present experimental results estimate the predictions of $Q_{at}/Q_{aC}$ within an approximately 50% error. The data deviations of the predicted air discharge mainly result from three aspects. First, the high speed velocity of tunnel flows may cause the scale effects of air–water flows on the free surface drag capacity. Although the high flow velocity leads to a large air discharge in prototype tunnels, the strong breakup free surface with small air–water mixture structures may reduce the air flow drag performance (Jiang et al. 2020). This coupling effect on the air supply efficiency remains unclear. Second, the specific bottom gate types, such as radial and slide gates, can lead to different flow disturbances in prototype tunnels once the pressurized water flow is released into the chute section (Vischer and Hager 1998; Speerli and Hager 2000). The shock waves and flow recirculation phenomena can cause a differential pressure near the gate area (Safavi et al. 2008). The local pressure variation is sensitive for the air supply in tunnels for a constant flow condition. Third, the air velocity distribution in prototype vents is nonuniform due to the rough walls and curving conduits. The effects of height, length, curve type, and roughness factors of air vents on the potential air supply could not be determined from the present data.

The present analysis concentrates on the air supply efficiency in association with preliminary ventilation design parameters for low-level outlets. For the free surface flow pattern in a long bottom tunnel, the vent parameter range includes relative size $S_a/S_{at}=0.12–3.0$, relative length $L_{a1}/h_a=0–70$ for the single vent, and two vent size $b_{a2}/b_{a1}=1–9$ and relative interval $L_{a2}/(b_{a1}+b_{a2})=6.7–33.3$. Although the present prediction cannot include high aeration and complex flow patterns, the quantitative assessment is able to provide a reasonable reference for the air supply design. The relative air vent size should be appropriate, $S_a/S_{at}>0.5$ as a general recommendation for a high air supply efficiency. The air discharge decreases as the air vent is set downstream of the tunnel and $L_{a1}/h_a>10$ should be avoided for the single vent location. Additional air vents designed downstream can replenish the air supply. The relative interval between the two vents is suggested as $L_{a2}/(b_{a1}+b_{a2})<8$ due to the air supply efficiency reduction for the combined working vents.

It should be noted that the present analysis on the efficient air supply of air vents is under low flow Froude number conditions ($\mathsf{F}=2.07–5.30$) and applies for the stratified free-surface flow pattern in flood discharge tunnels. The deviations of the comparison with prototype data shows the limitations of current investigations, including the multiple influence factors of spray flow properties and air vent loss coefficients. Detailed measurements of air supply properties in prototype low-level outlets are essential to promote the understanding of the flood discharge tunnel system.

In the present study, the air supply by air ventilation devices is systematically studied by experimental models. The effects of air vent sizes, locations, and two combined working operations on the air supply efficiency are presented. The following conclusions can be drawn.

The air discharge through a single vent increases with vent size until the maximum air supply level is reached. For the single vent set downstream away from the low-level outlet, the air supply efficiency decreases for identical vent geometry conditions. For two combined working vents, the downstream vent can replenish air discharge into the tunnel if the size of upstream air vent is small. The air supply efficiency of the two vents is lower than that of the single air vent with an identical size. These effects are summarized in the model-based design equations. Based on the available comparison with prototype air discharge data, the present analyses are able to assess the prototype air ventilation design. For a relatively high air supply efficiency of the flood discharge tunnel, the design recommendations are suggested as relative air vent $S_a/S_{at}>0.5$, $L_{a1}/h_a<10$ and two combining working vents $L_{a2}/(b_{a1}+b_{a2})<8$. Further prototype measurements of air supply for low-level outlets are needed to understand the model limitation and improve the accurate prediction method.

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

The authors gratefully acknowledge the suggestions provided by the reviewers and technical paper revisions by editors. The paper was completed within the research projects funded by the National Natural Science Foundation of China (Grant Nos. 51979182 and 51939007).