The Impact of Decreased Atmospheric Pressure on Forced Aeration of Discharged Flow

Abstract

To account for changes in the performance of spillway aerator structures of high-altitude dams, depressurization generalized model experiments and theoretical analyses were conducted in this study. Measurements were taken for ventilation hole air velocity, cavity subpressure, cavity length, and air concentration in crucial regions. The study proposed correction formulas for the aeration coefficient and water air concentration in aerator devices operating under low atmospheric pressure. The pressure range of the experiments was between 26.3 kPa and 101.3 kPa. The results indicated that with decreasing atmospheric pressure, ventilation hole air velocity, ventilation volume, cavity subpressure, and water air concentration all showed a decreasing trend. For every 15 kPa decrease in pressure, ventilation hole air velocity decreased by approximately 24%. When the atmospheric pressure dropped from 101.3 kPa to 26.3 kPa, the cavity subpressure decreased and eventually approached zero. The maximum reduction in air concentration was 14.9% in the cavity backwater area, 38.5% at the cavity end, and 38.3% in the downstream bubble escape segment. The proposed correction formulas could be used for a rapid estimation of ventilation volume and air concentration in low-pressure environments. This research provides a scientific basis for the design of aeration devices in water projects located in high-altitude regions.

1. Introduction

Cavitation damage caused by high-speed water flow can pose a serious threat to the safe operation of spillway structures. Spillway outlets of projects such as the Boulder Dam in the United States, the Liujiaxia Hydropower Station and the Ertan Hydropower Station in China, and the Aldeadavila Dam in Spain have all experienced severe cavitation damage during operation [1,2,3,4]. Currently, three main damage reduction measures are employed in engineering practices: reducing the incipient cavitation number through the optimization of the overflow boundary body shape and the control of the unevenness of the overflow surface; using materials with strong cavitation resistance; and using air entrainment to alleviate cavitation, aerating areas where cavitation is likely to occur in the water flow [5]. Extensive engineering practice has shown that aeration is one of the effective methods for preventing cavitation damage on overflow surfaces [6,7]. Due to its simple technical structure and noticeable effects, it is widely used in various high-head spillway structures. With the continuous development of water resources in China, the western high-altitude regions rich in hydropower resources are gradually becoming hotspots for hydropower development. An increasing number of high dams will be built in areas at altitudes of 3000 m and above. Besides characteristics such as high head and large flow, the environmental conditions of high altitude and low atmospheric pressure are gradually becoming a focus of attention for their impact on hydraulic safety, especially regarding cavitation in spillway structures. Due to the decrease in atmospheric pressure and reduction in cavitation number with increasing altitude, spillway structures are prone to cavitation and subsequent cavitation damage [8,9].

Under normal atmospheric pressure, researchers have conducted extensive research on using air entrainment to alleviate cavitation. Research directions mainly encompass the mechanisms of using air entrainment to alleviate cavitation [10,11], the characteristics of forced aeration in water flow [12,13,14,15], the design of aeration devices [16], the downstream bubble characteristics of aeration devices [17], and the scale effects of aeration ratios [18,19]. The ventilation volume is an important parameter for measuring the effectiveness of air entrainment devices. A significant amount of research has been conducted by previous researchers on the ventilation volume of aeration devices. There are numerous influencing factors, including incoming flow hydraulic characteristics, channel and aeration device geometry, and affected aeration phenomena [20,21,22]. However, relatively limited research has been conducted on aeration under low atmospheric pressure. Falvey [3] developed computer programs to support the design of aerator structures at different altitudes based on local atmospheric pressure. This approach has been applied to an altitude range of approximately 375 m to 2280 m. However, there was no generalized study of the extent and mechanisms of the impact of air pressure on aeration and cavity hydraulic characteristics. Currently, commonly used formulas for ventilation volume are mostly empirical formulas based on prototype or model data [12,23,24], without considering the influence of atmospheric pressure on ventilation volume.

Existing research indicates that as atmospheric pressure decreases, the distribution of gas nuclei in water undergoes changes, the surface tension coefficient of water increases, the cavitation number of the water flow decreases, and it becomes more difficult to generate backwater in the cavity [8,9,25,26]. Pang et al. [26], through the collection of gas nucleus images under different pressures, found that as the environmental air pressure decreased, the number of gas nuclei decreased, and the proportion of small-sized gas nuclei increased. Wang et al. [8], using the capillary method at different air pressures and water temperatures, measured surface tension. The results showed that at the same water temperature, lower air pressure corresponded to a larger surface tension coefficient. At a maximum vacuum pressure of 0.1 MPa, the surface tension of 20 °C water increased by approximately 18% compared to atmospheric pressure. Additionally, the influence of air pressure and temperature on the water surface tension was essentially independent as the air pressure decreased. Pang [9] utilized theoretical equations to calculate the variations in the critical pressure of a single gas nucleus under different atmospheric pressure conditions. The results demonstrated that under low atmospheric pressure, the incipient cavitation number of gas nuclei decreased, whereas the reduction in the flow cavitation number was significantly enhanced compared to that of the incipient cavitation number. For every increase in altitude of 500 m, the cavitation number of the water flow decreased by 2.5% to 3.5%. In high-altitude areas, the risk of cavitation and cavitation erosion increased in fast-flowing water. Wu [27] analyzed the changing patterns of air content in water under different atmospheric pressure and temperature conditions. As the atmospheric pressure decreases, the air content will also decrease. If there are differences in air content between the prototype and the model, the incipient cavitation numbers will also differ, leading to a scale effect. During experiments on a 1:35 scale model of a spillway at a hydropower station, Zhao and Hu [28] conducted observational comparisons and found that when the depressurization chamber reached a vacuum level of 93%, the cavity length decreased by approximately 10% compared to normal atmospheric pressure conditions. Using a computational fluid dynamics (CFD) numerical simulation, Pang et al. [29] calculated the cavity length in an aeration device under different atmospheric pressure conditions. The results indicated that as the atmospheric pressure decreases, the cavity length in high-velocity water flows becomes smaller. For each 10 kPa decrease in atmospheric pressure, the average cavity length decreased by approximately 1.7% to 2.9%. Xue et al. [30] conducted steady-state numerical simulations of a specific hydraulic turbine in high-altitude regions to analyze the effects of high-altitude environments on hydraulic machinery performance. They found that as the atmospheric pressure decreased, the low atmospheric pressure area of the elbow section of the draft became larger. Simultaneously, the cavitation coefficient of the hydraulic turbine increased with decreasing atmospheric pressure, making cavitation more likely to occur. In summary, research on the aeration characteristics in low atmospheric pressure environments is still in its initial stages, while the current calculation formulas for using air entrainment to alleviate cavitation have not yet provided regulations for the relevant hydraulic calculations and designs under low atmospheric pressure conditions.

Therefore, this paper presents depressurization generalization model experiments and theoretical analysis conducted with a primary focus on hydraulic characteristics such as ventilation hole air velocity, ventilation volume, and air concentration. Considering four discharges and six atmospheric pressures, a total of twenty-four sets of experimental conditions were established. This study investigated the ventilation characteristics of aeration devices under different low atmospheric pressure conditions and the downstream water air concentration characteristics. Furthermore, we proposed a correction method for using air entrainment to alleviate cavitation characteristics under low atmospheric pressure, with the aim of providing a scientific basis for the design of aeration devices in high-altitude hydraulic engineering projects.

2. Research Methods

To simulate a series of low atmospheric pressures, experiments were conducted inside a depressurization chamber. The generalized model was based on a typical design of a tunnel spillway, which included a control section, a gentle slope section, a steep slope section, and a jet bucket section. The total length was 4.14 m, the net width was 0.188 m, and the height was 1.66 m. The arrangement of the model within the depressurization chamber is shown in Figure 1. A WES weir was used for the control section. The gentle slope section had a gradient of 3.0% and a length of 0.33 m. The steep chute section followed the gentle slope section and was composed of a parabolic curve, a straight line, and a counter-arc curve. To study the forced aeration characteristics under different low atmospheric pressure conditions, an aeration device was installed at the transition between the parabolic curve and the straight line. For the aeration device, a configuration combining a ramp and a slot was adopted, as shown in Figure 2. The slope of the ramp relative to the downstream straight section was 1:10, and the longitudinal length of the ramp was l = 20 cm. The total depth of the aeration slot was d = 4.5 cm, and the total length was 4.23 cm. The air vent hole was located within the chute and had a diameter of 3.0 cm.

Four experimental discharges Q (0.0740, 0.0528, 0.0354, 0.0199 m³/s) and six different atmospheric pressure conditions (the pressure range inside the depressurization chamber varied from 26.3 to 101.3 kPa in steps of 15 kPa) were employed in this study, resulting in a total of twenty-four experimental conditions. Vacuum degree refers to the degree of gas rarity in a vacuum state, expressed by the formula $P_{\mathrm{v}}=P_0-P_a$, where $P_a$ is the environmental pressure inside the vacuum chamber and $P_0$ is the atmospheric pressure in the external test laboratory of the vacuum chamber as shown in

Table 1. Vacuum degrees in the depressurization chamber under different atmospheric pressures.

Series	Atmospheric Pressure (kPa)	Simulating High Altitudes (m)	Depressurization Chamber Vacuum Degree (kPa)
1	101.3	0	0
2	86.3	1330	15.0
3	71.3	2900	30.0
4	56.3	4700	45.0
5	41.3	6950	60.0
6	26.3	10,000	75.0

for the vacuum degree inside the depressurization chamber. The test parameters are listed in

Table 2. Test parameters.

Series	Discharge (m3/s)	Incoming Flow Velocity (m/s)	Froude Number
1	0.0740	4.96	5.61
2	0.0528	4.63	5.99
3	0.0354	4.33	6.62
4	0.0199	4.19	8.41

.

Different measurement methods were employed to measure the ventilation hole air velocity, cavity length, cavity subpressure, and air concentration. The air velocity was measured using the KANOMAX multi-point air velocity measurement system (Andover, NJ, USA). The probe used was of the hot-wire type with a maximum range of 50 m/s and an accuracy of 2% full scale (F.S.). The probe with left and right ventilation holes was connected to a Model 1550 data acquisition system for automated measurements. The sampling frequency was 10 Hz, and the sampling duration was 120 s. The cavity length was determined through concentration measurements and observations. The downstream water air concentration under the aeration device was measured using a resistance-type air concentration meter. Four measurement points (C1, C2, C3, C4) were arranged on the bottom plate at distances of 24 cm, 40 cm, 48 cm, and 62 cm from the end of the aerator. The cavity subpressure was measured using an absolute pressure fluctuation sensor. Measurement point M1 was located in the middle of the aerator.

3. Forced Aeration Characteristics under Low Atmospheric Pressure

3.1. Ventilation Hole Air Velocity

The characteristic air velocity values of the ventilation holes under different atmospheric pressures are listed in

Table 3. Air velocity characteristic values of ventilation holes in aeration device under different atmospheric pressures (the discharge was Q = 0.0740 m³/s).

Atmospheric Pressure (kPa)	Feature Parameters (m/s)				Degree of Influence on the Average Value (%)
	Maximum Value	Minimum Value	RMS Value	Average Value
101.3	1.63	0.60	0.14	1.00
86.3	1.46	0.49	0.12	0.83	17.2
71.3	1.13	0.40	0.10	0.65	22.1
56.3	0.87	0.32	0.07	0.50	21.9
41.3	0.56	0.21	0.05	0.35	29.9
26.3	0.34	0.18	0.03	0.25	29.2

for typical discharges. Air velocity changed with atmospheric pressure under different discharges, as shown in Figure 3. The root mean square proportion of air velocity to the average air velocity under different pressures ranged from 13.3% to 15.3%, showing no significant trend with changes in atmospheric pressure. This suggested that changes in atmospheric pressure did not noticeably impact the turbulence of the air entrainment. There was a strong linear positive correlation between atmospheric pressure and the air velocity through the air vent holes. As shown in Figure 3, the air velocity through the air vent holes notably declined with decreased atmospheric pressure. With the use of a linear fit with a y-intercept of 0, the R² value approached 0.99. At a discharge of 0.0740 m³/s, for every 15 kPa decrease in pressure, the air velocity decreased by approximately 17.2% to 29.2%, with an average reduction of about 24.1%. At a discharge of 0.0528 m³/s, the air velocity decreased by around 16.9% to 32.8%, with an average reduction of about 25.0%. At a discharge of 0.0354 m³/s, the air velocity decreased by approximately 17.5% to 35.7%, with an average reduction of about 25.4%. Finally, at a discharge of 0.0199 m³/s, the air velocity decreased by about 17.9% to 34.8%, with an average reduction of approximately 23.9%.

The ventilation volume of the flip bucket is equal to the sum of the air supply from the ventilation holes on both sides. If the ventilation volume is insufficient, the anti-cavitation protection effect is poor, while if the ventilation volume is saturated, it can lead to adverse flow conditions. Under various operating conditions, the ventilation volume decreased significantly with the decrease in atmospheric pressure. The probable reasons for this are as follows: (i) In low atmospheric pressure conditions, the gas density was lower compared to normal atmospheric pressure. This led to an increase in the average distance between air molecules and a reduction in the thermal motion of air molecules, resulting in inadequate air intake through the ventilation holes. (ii) There was a reduction in the air pressure gradient force. The horizontal air pressure gradient force served as the primary driving force behind wind formation and could be calculated using Equation (1).

$$G=-\frac{1}{\rho }\nabla P$$

(1)

where $-\nabla P$ is the pressure gradient, with its direction pointing from high pressure to low pressure.

For aeration devices, high pressure refers to the atmospheric pressure, while low pressure pertains to the pressure within the cavity. Air flows from the high-pressure region to the low-pressure region, creating airflow within the ventilation holes. Hence, its characteristics are closely linked to the cavity subpressure. The measurement results from point M1, the cavity subpressure, and the air pressure gradient force under different atmospheric pressures are listed in

Table 4. Cavity subpressure values and pressure gradient forces under different atmospheric pressures.

Measurement Point		Atmospheric Pressure (kPa)
		101.3	86.3	71.3	56.3	41.3	26.3
M1	Measurement Value (kPa)	101.108	86.166	71.230	56.259	41.275	26.294
	Subpressure Value(kPa)	0.192	0.134	0.070	0.041	0.025	0.006
Pressure gradient force (N/kg)		0.908	0.728	0.458	0.339	0.281	0.106

. The ventilation volume decreased with the reduction in discharge. The trend of changes in ventilation volume and cavity subpressure was essentially consistent with the variation in the incoming discharge. The larger the subpressure inside the cavity under the water jet, the stronger the intake capacity of the ventilation hole. Taking the air pressure gradient force from point M1 to the ventilation hole as an example, lower atmospheric pressure resulted in decreased air density and cavity subpressure. However, since the decrease in cavity subpressure was much greater than that in atmospheric air density, the air pressure gradient force noticeably diminished with decreased atmospheric pressure.

3.2. Cavity Length

The length of the cavity is an important parameter in the design of an aeration device. Both the ventilation volume and the effective protection length of the aeration device are influenced by it. The longer the cavity, the greater the ventilation volume, the more fully the water flow is aerated, and the longer the aeration protection distance. The variation in cavity length under different atmospheric pressures is shown in Figure 4.

The results indicated that, in the atmospheric pressure range of 101.3 to 41.3 kPa, the cavity length showed an increasing trend as the atmospheric pressure decreased. For every 15 kPa decrease in atmospheric pressure, the cavity length increased by an average of 1.68%. The growth amplitude was correlated with the change in the cavity negative pressure. As the atmospheric pressure decreased, the reduction in the cavity negative pressure was more significant, leading to a larger growth amplitude in the cavity length. The subpressure in the cavity exerts a downward drag force on the water flow, and the larger the subpressure, the shorter the cavity [31]. As seen from the previous section’s results, the subpressure in the cavity showed a significant decrease with the decrease in atmospheric pressure. When the atmospheric pressure dropped below 41.3 kPa, the subpressure inside the cavity was almost equal to the ambient atmospheric pressure. Neglecting the effects of air resistance and surface tension, at this point, the ejected water could be considered to be only subject to the force of gravity. Therefore, the length of the cavity tended to increase as the atmospheric pressure dropped, and the extent of growth was related to the decrease in negative pressure within the cavity.

3.3. Correction of Aeration Coefficient under Low Atmospheric Pressure

The calculation of the ventilation volume in aeration devices is a crucial issue in the study of using air entrainment to alleviate cavitation. It also serves as the basis for the rational arrangement of aeration devices. Through dimensional analysis, the widely applicable formula for calculating ventilation volume in aeration devices takes the form of Equation (2). The empirical formulas proposed by Bruschin [12] and Pan et al. [32] were of the above form.

$$q_a=KvL$$

(2)

where $q_a$ is the ventilation volume per unit width, K is the aeration coefficient, v is the average velocity at the flip bucket, and L is the length of the cavity.

The aeration coefficient K value is currently widely regarded as a constant related to the dimensions of the aeration device. Existing preliminary research indicated that the impact of atmospheric pressure on cavity length is relatively minor. Therefore, changes in atmospheric pressure have a significant effect on the aeration coefficient K value, necessitating adjustments; otherwise, significant errors will arise. The relationship between these two factors at different discharges is illustrated in Figure 5. Decreased atmospheric pressure resulted in lower air density, while K exhibited a linear decrease.

Through regression analysis of 20 sets of test data with different discharges and atmospheric pressures, and incorporating corrections based on variations in cavity length, the modified calculation Equation (3) for the aeration coefficient $K\prime$ accounting for low atmospheric pressure was derived.

$$K\prime =0.935\frac{p}{p_0}{K}_0$$

(3)

where p is the atmospheric pressure; p₀ is the standard atmospheric pressure; K₀ is the aeration coefficient at standard pressure.

To verify the effect of the correction equation, experiments were conducted by lowering the flip bucket height by 1 cm from Figure 2; the correction Equation (3) was substituted into Equation (2), and the data comparison between the corrected value of the calculated ventilation volume and the test value is plotted in Figure 6. The maximum error did not exceed 10%, indicating the accuracy of the rapid estimation of the ventilation volume in aeration devices under low atmospheric pressure.

Currently, in high-altitude areas, especially those above 3000 m, there are relatively limited prototype observational data for hydraulic engineering. To verify Equation (3), model test data (scale 1:40) and prototype data from the Baihetan Hydropower Station spillway model were compared. The Baihetan Hydropower Station has a maximum dam height of 289 m, an altitude of 825 m, an environmental air pressure of approximately 91.6 kPa, a normal reservoir water level of 825 m, and a discharge of 3900 m³/s. The calculated results are presented in

Table 5. Comparison of calculated values from equation (3) with experimental model values.

Upstream Flow Velocity (m/s)	Prototype qa	Model Test qa	Model Test Error (%)	Calculation of qa Using Equation (3)	Calculation Error (%) Using Equation (3)
25	16.2	19.38	19.60	16.48	1.72

. The error between the model test results of the single-width aeration flow and the prototype measured data under normal pressure was 19.60%. However, when using the corrected Equation (3), the error of the calculated single-width aeration flow was only 1.72%, demonstrating higher accuracy.

4. The Effect of Atmospheric Pressure on the Air Concentration in Water

Air concentration is defined as the ratio of the volume of air to the volume of the air–water mixture in the aerated water flow. It is generally considered that when the air concentration in water is in the range of 1.5% to 2.5%, the damage caused by solid boundary cavitation is significantly reduced. When it reaches 3% to 5%, the damage from cavitation can be avoided. Experiments conducted by Peterka showed that when the air concentration in water close to the channel bottom was 2%, it significantly alleviated cavitation damage to solid boundary walls, and when the air concentration reached 7.4%, cavitation damage completely disappeared [33]. Russell and Sheehan conducted experimental research on the surface cavitation of concrete under different air concentrations. The results of the experiments indicated that an air concentration of 2.8% was sufficient to prevent cavitation damage to the concrete surface. Even in situations where severe air-entrained damage to the concrete surface was anticipated, an air concentration of 5% was enough to avoid cavitation damage [34]. Due to the decreased atmospheric pressure, there is a significant reduction in the ventilation volume of the aeration devices. This is bound to result in a weakening effect on the air concentration in the downstream water bodies, which is unfavorable for using air entrainment to alleviate cavitation.

The variation trend of the air concentration in characteristic downstream water bodies of the aeration device under different operating conditions with changes in atmospheric pressure is depicted in Figure 7.

The results indicated that the air concentration within the cavity remained constant regardless of changes in atmospheric pressure under different discharge conditions (Figure 7a). However, the air concentration at the other measurement points decreased with lower atmospheric pressure. When the atmospheric pressure decreased from 101.3 kPa to 26.3 kPa, the minimum reduction in air concentration in the cavity backwater area was 1.72%, and the maximum reduction was 14.9%. The minimum reduction in air concentration at the end of the cavity was 32.7%, and the maximum reduction could reach 38.5%. The minimum reduction in air concentration in the bubble escape section downstream of the cavity was 25.8%, and the maximum reduction could reach 38.3%.

Under various discharge conditions, with a uniform decrease in atmospheric pressure, there was a turning point in the extent of reduction in air concentration in the water at the end of the cavity’s backwater region (Figure 7b). In the range of atmospheric pressure from 101.3 kPa to 71.3 kPa, for every 15 kPa decrease in atmospheric pressure, the air concentration only decreased by an average of 0.10%, showing a minor reduction. In the range of atmospheric pressure from 56.3 kPa to 26.3 kPa, for every 15 kPa decrease in atmospheric pressure, the air concentration decreased by 0.48% to 1.71%. Across different discharges, the average reduction was about 1.1%, indicating a relatively larger reduction.

The air concentration at the end of the cavity exhibited a favorable linear relationship with atmospheric pressure (Figure 7c). With every 15 kPa decrease in atmospheric pressure, the air concentration decreased by approximately 0.34% to 0.54%, accounting for around 6.5% to 7.7% of the air concentration at normal atmospheric pressure.

Under different discharge conditions, with a uniform decrease in atmospheric pressure, there is a turning point in the extent of reduction in air concentration in the water within the cavity’s downstream bubble escape section (Figure 7d). When atmospheric pressure was within the range of 101.3 kPa to 86.3 kPa, a significant reduction in the water air concentration was observed. With a 15 kPa decrease in atmospheric pressure, the air concentration decreased by 0.18% to 0.34% under various discharge conditions. This reduction accounted for about 11.7% to 15.3% of the air concentration at normal atmospheric pressure, with an average proportion of 13.7%. When atmospheric pressure was within the range of 86.3 kPa to 26.3 kPa, there was a favorable linear relationship between air concentration and atmospheric pressure. For every 15 kPa decrease in atmospheric pressure, the air concentration decreased by about 0.04% to 0.10% under different discharges. This reduction accounted for about 3.3% to 6.3% of the air concentration at normal atmospheric pressure, with an average proportion of 4.4%. And in this region, the rate of decline in the air concentration along the path was relatively fast under low air pressure. The decrease in atmospheric pressure may lead to a quicker reduction in the downstream along-path air concentration to below the minimum erosion-free air concentration, which is unfavorable for aeration protection. By assessing the correlation between the air concentration and atmospheric pressure in different characteristic regions of the water bodies, it can be inferred that air concentration decreases at lower atmospheric pressure, and the reduction trend varies depending on the initial air concentration. Specifically, when the water air concentration is higher, as the atmospheric pressure decreases, the reduction in air concentration initially shows a small decrease and then shows a larger decrease. Conversely, as the atmospheric pressure decreases, the reduction in air concentration exhibits an initial larger decrease followed by a smaller decrease when the water air concentration is lower. The current understanding of the air concentration decreasing with decreasing atmospheric pressure is as follows: Due to the decrease in atmospheric pressure, the surface tension of the water increases, making turbulent fragmentation more difficult. As a result, the exchange between the flowing water and the surrounding medium decreases during motion, resulting in a reduction in air entrainment. Turbulent diffusion is the fundamental reason for air entrainment. With decreased atmospheric pressure and increased surface tension, water particles require greater turbulent energy to overcome surface tension. Therefore, it is more challenging to achieve air entrainment under low atmospheric pressure.

The air concentration in the water of the downstream bubble escape region of the cavity is a crucial basis for analyzing the effectiveness of aeration device protection. As the air concentration in this area is often low, the impact of decreased atmospheric pressure on it is relatively significant. Based on regression analysis from depressurization generalized modeling experiments, considering the effect of atmospheric pressure, a correction formula for the air concentration C in the downstream bubble escape section of the aeration device cavity has been formulated as Equation (4).

$$C=\{\begin{array}{ll}0.0573(p_0-p)C_0& 86.3\le \mathrm{p}<101.3\\ \left[0.8978-0.0025\left(p_0-p\right)\right]C_0& 26.3\le \mathrm{p}<86.3 \end{array}$$

(4)

where C₀ is the air concentration in the water under normal atmospheric pressure, which can be obtained through model experiments, numerical simulations, or empirical formulas based on prototype observations; p is the atmospheric pressure; p₀ is the standard atmospheric pressure.

5. Conclusions

In this study, depressurized generalized model experiments comprising six different atmospheric pressure conditions and four discharges were conducted, resulting in a total of twenty-four operating conditions. This research aimed to investigate the variations in ventilation hole air velocity, ventilation volume, and air concentration under low atmospheric pressure conditions. Additionally, a low-pressure correction method for the aeration coefficient and water air concentration was proposed. The main conclusions are as follows:

(1)

There is a favorable linear relationship between atmospheric pressure and the airflow velocity of the ventilation hole. With a decrease in atmospheric pressure, the airflow velocity and ventilation volume through the hole decreased. For every 15 kPa decrease in atmospheric pressure, the air velocity decreased by an average of 24.6%. Additionally, with the decrease in atmospheric pressure, the subpressure in the cavity significantly decreased, and there was a trend of increasing cavity length.

(2)

When the atmospheric pressure decreased from 101.3 kPa to 26.3 kPa, the maximum reduction in air concentration in the cavity backwater area was 14.9%. The minimum reduction in air concentration at the end of the cavity was 32.7%, and the maximum reduction could reach 38.5%. The minimum reduction in air concentration in the bubble escape section downstream of the cavity was 25.8%, and the maximum reduction could reach 38.3%. As the atmospheric pressure decreased, there was a trend of decreasing air concentration in the water, and the extent of this decrease depended on the initial air concentration. When the water air concentration was higher, the reduction was initially small, followed by a more significant decrease. Conversely, when the water air concentration was lower, the reduction showed an initially larger decrease followed by a smaller decrease.

(3)

A low-atmospheric-pressure correction method for the aeration coefficient and water air concentration in the bubble escape section has been proposed. This method can be applied for the rapid estimation of ventilation volume and air concentration in aeration devices under low atmospheric pressure.