Effect of Aeration on the Cavitation Characteristics of the Control Valve in Hydro-Driven Ship Lifts

: In hydro-driven ship lifts, plunger valves and ﬁxed cone valves are the most suitable structures for achieving accurate ﬂow control under a wide range of ﬂow conditions. In order to inhibit cavitation in these valve structures, experiments were conducted in which forced aeration was applied before the valve. The cavitation phenomena and aerated ﬂow regime were observed through a transparent glass pipe, and the cavitation noise characteristics were recorded using a hydrophone. The test results show that aeration can reduce the valve working cavitation number, albeit to a limited degree (<5%). Based on the sound velocity theory of aerated ﬂow and the experimental results, the relationship between the aeration concentration and the cavitation inhibition efﬁciency was obtained. When the aeration concentration is approximately 0.1%, cavitation can be signiﬁcantly inhibited via forced aeration before the valve. Once the aeration concentration reaches 0.9%, the cavitation inhibition efﬁciency becomes saturated. The research results presented in this paper provide a reference for the cavitation inhibition of industrial valves.


Introduction
The Yangtze River Golden Channel is the most important inland waterway in China, significantly contributing to the social and economic development of cities along the Yangtze River.In recent decades, inland navigation channels (such as the Yangtze River) have developed rapidly.On the one hand, these navigation channels have undergone large-scale restoration and construction, and their level and navigation capacity have significantly improved.On the other hand, important water conservancy projects (such as the Three Gorges Dam) are equipped with large-capacity ship lifts, which satisfy the demands of large ships passing through high dams.With the new demand for green development in rivers, the construction of ecological waterways has begun and achieved good results.Vegetation-based restoration methods (e.g., planting aquatic vegetation [1,2]) have been employed to protect floodplains and central bars from bed erosion, increasing the riverbed stability of navigation channels.For example, Liu and Shan [3] systematically studied the impact of vegetation on flow evolution and sediment transport, providing guidance for vegetation-based ecological restoration projects in navigation channels.At the same time, with the rapid development of inland shipping, the cargo capacity of ships gradually increases, corresponding to the increasing load requirements for ship lifts.This paper focuses on ship lifts, and the main goal of our study was to examine the impact of aeration on the cavitation characteristics of control valves in the lifts, which ensure the safe operation of ship lifts.
The Jinghong ship lift is the first HDSL in the world (Figure 1), with a maximum lifting height of 66.86 m.The core component of this HDSL is the control valve, which is Water 2023, 15, 4014 2 of 14 similar to the electric motor in an electric-driven ship lift and is the key to the safe and efficient operation of the ship lift [4].Thus, a high-performance control valve is required to control the flow rate accurately, with the potential to accommodate significant changes in flow conditions.At present, only plunger valves and fixed cone valves satisfy these requirements [5].Under high pressure differences, it is difficult to avoid cavitation in the control valve.Controlling the cavitation damage in the valve and pipeline is the key to the safe and efficient operation of HDSLs [6].
Water 2023, 15, x FOR PEER REVIEW The Jinghong ship lift is the first HDSL in the world (Figure 1), with lifting height of 66.86 m.The core component of this HDSL is the control v similar to the electric motor in an electric-driven ship lift and is the key to efficient operation of the ship lift [4].Thus, a high-performance control val to control the flow rate accurately, with the potential to accommodate signifi in flow conditions.At present, only plunger valves and fixed cone valves sa quirements [5].Under high pressure differences, it is difficult to avoid cav control valve.Controlling the cavitation damage in the valve and pipeline is safe and efficient operation of HDSLs [6].Research on cavitation in industrial valves has mainly focused on the in valve geometry [7][8][9] and valve operation mode [10].Chern [11] studied a glo and without a cage using a cavitation model and showed that the cage co cavitation in the vicinity of the cage and prevent the cavitation from erod body and downstream pipe.Jo [12] conducted a numerical study on reduc in a butterfly valve and found that a perforated plate was effective in suppre itation inside the pipe.Lee [13] designed the bottom plug used in three-w valves to minimize the cavitation effect, while Han [14] tested three typic poppet valves.The results revealed that a two-stage throttle valve can effecti the occurrence of cavitation, although the flow force of this valve type is muc for other valves.The optimization of the valve structure could effectively imp cavitation performance of the valve, but the universality of current designs In addition to optimizing the valve structure, aeration is another effec preventing cavitation.The most important factor affecting aeration is the aer tration.Many researchers have suggested that cavitation erosion can be sign igated when the air concentration near a wall is 1-2% and may be eliminated concentration reaches 5-7% [15].The aeration concentration at which cavit ited depends on the specimen materials.Rasmussen [16] suggested an aerat to avoid the cavitation erosion of an aluminum alloy specimen, while Russel [17] reported that an air concentration of 5.7% was suitable for a concrete s pressure in the cavitation region of a high-velocity flow with aeration incr of the formation of a compression wave after the flow has been aerated [18 Research on cavitation in industrial valves has mainly focused on the influence of the valve geometry [7][8][9] and valve operation mode [10].Chern [11] studied a globe valve with and without a cage using a cavitation model and showed that the cage could limit the cavitation in the vicinity of the cage and prevent the cavitation from eroding the valve body and downstream pipe.Jo [12] conducted a numerical study on reducing cavitation in a butterfly valve and found that a perforated plate was effective in suppressing the cavitation inside the pipe.Lee [13] designed the bottom plug used in three-way reversing valves to minimize the cavitation effect, while Han [14] tested three typical designs for poppet valves.The results revealed that a two-stage throttle valve can effectively suppress the occurrence of cavitation, although the flow force of this valve type is much higher than for other valves.The optimization of the valve structure could effectively improve the anti-cavitation performance of the valve, but the universality of current designs is poor.
In addition to optimizing the valve structure, aeration is another effective means of preventing cavitation.The most important factor affecting aeration is the aeration concentration.Many researchers have suggested that cavitation erosion can be significantly mitigated when the air concentration near a wall is 1-2% and may be eliminated when the air concentration reaches 5-7% [15].The aeration concentration at which cavitation is inhibited depends on the specimen materials.Rasmussen [16] suggested an aeration rate of 1% to avoid the cavitation erosion of an aluminum alloy specimen, while Russell and Sheehan [17] reported that an air concentration of 5.7% was suitable for a concrete specimen.The pressure in the cavitation region of a high-velocity flow with aeration increases because of the formation of a compression wave after the flow has been aerated [18].Theoretical analysis has determined the relationship between the aeration concentration (C) and the acoustic velocity of sound in water (v a ) [19].The air bubble size also affects the degree of cavitation inhibition [20][21][22].Smaller bubbles are more conducive to inhibiting cavitation erosion, whereas bigger bubbles float and break more easily, which reduces the aeration concentration on side walls [23].Small air bubbles tend to alleviate cavitation erosion, even at the same air concentration [24].Li made the prediction of aeration from data-driven and multi-gene genetic programming methods [25,26].These studies have had a strong guiding effect on the design of experimental models.
The aeration mode can be determined as either self-aeration or forced aeration.Selfaeration uses negative pressure to achieve natural aeration [27,28], such as in spillway aeration [29] and lock water valve aeration [30,31].Forced aeration requires an air compressor to achieve passive aeration.Self-aeration methods are relatively simple but cannot suppress the primary cavitation inside a valve.Forced aeration protects the pipeline after the valve, inhibits cavitation initiation, and protects the internal valve structure.
In conclusion, existing studies related to reducing cavitation erosion via aeration have mainly focused on microscopic aspects [32,33] and self-aeration [34].There have been few studies on macroscopic engineering applications and forced aeration.The specific effects of forced aeration on cavitation inhibition remain unclear.Studies have shown that forced aeration is necessary to protect the control valves in HDSLs [35], but large-scale aeration is not conducive to the stability of the shaft water surface.Thus, it is necessary to study the reasonable aeration concentration that can be achieved by forced aeration.In this study, forced aeration tests were conducted for the two types of industrial valves suitable for HDSLs.The cavitation characteristics in the valve segments at different opening degrees, flow rates, and aeration concentrations were studied.The structure of the flow field and the cavitation phenomenon were observed via high-speed photography [36][37][38].Analyses of the influence of aeration on the cavitation number and the relationship between the aeration concentration and cavitation inhibition efficiency are presented in this paper to provide a reference for similar engineering projects.

Experimental Setup
The experiments were carried out in the multi-functional cavitation experiment hall of Nanjing Hydraulic Research Institute, China.This laboratory offers automated control of pumps, valves, and pressure and flow monitoring (Figure 2).The maximum capacity of the water pressure supply system was 1.5 MPa and the maximum flow rate was 0.15 m 3 /s.The experimental model combined a flow control system, aeration equipment, a test valve, a glass pipe, and a data acquisition system.As seen in Figure 3, there were two types of test valves: a plunger valve with an SZ 20-30% sleeve and a cone valve with a dome.The diameter of the test valves was 150 mm.The sensor layout and aeration ring design are shown in Figure 4. Based on recent research [39], we adopted a smaller, air-filled hole for aeration: the hole's diameter was 3 mm, and the number of holes was 32.The aeration concentration range was set to 0-4%.The sensor characteristics are listed in Table 1.
The aeration concentration (C) of each test is listed in Table 2.The maximum aeration concentration was about 4%.The aeration concentration is defined as: where Q a is the air flow (m 3 /h) and Q w is the water flow (m 3 /h).The typical experimental process involves adjusting the valve to the test opening degree, stabilizing the downstream pressure (P d ) at 60/120/180 kPa (P d in Table 2 is 180 kPa because the test results fluctuate less under a higher P d ), and then gradually increasing the upstream pressure (P u ) until primary cavitation occurs in the valve.The upstream and downstream control pressures need to be adjusted repeatedly.The criteria for identifying the primary cavitation state (σ i ) of the valve include intermittent pulses of cavitation noise, a sizzling sound inside the valve, and tiny visible cavitation bubbles in the water flow.Based on the primary cavitation state, P u was calculated according to the relative cavitation number σ/σ i = 0.4 (strong cavitation state), and then the upstream stable pressure was adjusted to this value.Once the flow field structure was stable, the cavitation noise and flow field structure were measured.Finally, forced aeration tests were conducted under different air flow rates (Q a = 0.1-3 m 3 /h), and the cavitation noise and flow field structure were repeatedly measured.The experiments were repeated at least three times, and experimental error was reduced by taking the mean value of multiple experimental results.The cavitation inhibition effect of forced aeration was explored by analyzing the flow field structure, cavitation number, and noise characteristics.The cavitation number σ is defined as [3]: (2 where P atm is the local atmospheric pressure; P sv is the local saturated vapor pressure; v is the average velocity in the reference section; P u is the upstream steady pressure; and P d is the downstream steady pressure.
Water 2023, 15, x FOR PEER REVIEW 4 of 15 a sizzling sound inside the valve, and tiny visible cavitation bubbles in the water flow.
Based on the primary cavitation state, Pu was calculated according to the relative cavitation number σ/σi = 0.4 (strong cavitation state), and then the upstream stable pressure was adjusted to this value.Once the flow field structure was stable, the cavitation noise and flow field structure were measured.Finally, forced aeration tests were conducted under different air flow rates (Qa = 0.1-3 m 3 /h), and the cavitation noise and flow field structure were repeatedly measured.The experiments were repeated at least three times, and experimental error was reduced by taking the mean value of multiple experimental results.
The cavitation inhibition effect of forced aeration was explored by analyzing the flow field structure, cavitation number, and noise characteristics.The cavitation number σ is defined as [3]: where Patm is the local atmospheric pressure; Psv is the local saturated vapor pressure; v is the average velocity in the reference section; Pu is the upstream steady pressure; and Pd is the downstream steady pressure.

Flow Coefficient
The variation in the flow coefficient with respect to the aeration concentration is shown in Figure 5.At different flow rates, the flow coefficient decreases with increasing aeration concentration, but the rate of decrease becomes slower.Under the same aeration concentration, a larger flow velocity produces a more obvious drop in the flow coefficient.From its definition, the flow coefficient is proportional to the flow rate and inversely proportional to the pressure difference.The test results show that the forced air intake in front of the valve produces a certain resistance to the incoming flow.This enforces a reduction in the flow rate over the valve, which enhances the pressure in front of the valve.The pressure behind the valve also increases, but to a lesser degree than that before the valve.Thus, the pressure difference continues to increase, and the flow coefficient continues to decline.With an increase in air content, the flow coefficient decreases continuously.This is because the pressure in front of the valve does not increase simultaneously with the increase in air content, and so the flow coefficient exhibits a relative decrease.Under the test conditions considered in this study, the maximum air content was 3 m 3 /h, the flow rate v ranged from 1.152 to 5.666 m/s, and the air content C varied from 0% to 4%.The maximum reduction in the flow coefficient was less than 5%, indicating that the air content has little effect on the flow coefficient.

Flow Coefficient
The variation in the flow coefficient with respect to the aeration concentration shown in Figure 5.At different flow rates, the flow coefficient decreases with increasin aeration concentration, but the rate of decrease becomes slower.Under the same aeratio concentration, a larger flow velocity produces a more obvious drop in the flow coefficien From its definition, the flow coefficient is proportional to the flow rate and inversely pr portional to the pressure difference.The test results show that the forced air intake in fro of the valve produces a certain resistance to the incoming flow.This enforces a reductio in the flow rate over the valve, which enhances the pressure in front of the valve.T pressure behind the valve also increases, but to a lesser degree than that before the valv Thus, the pressure difference continues to increase, and the flow coefficient continues decline.With an increase in air content, the flow coefficient decreases continuously.Th is because the pressure in front of the valve does not increase simultaneously with t increase in air content, and so the flow coefficient exhibits a relative decrease.Under t test conditions considered in this study, the maximum air content was 3 m 3 /h, the flo rate v ranged from 1.152 to 5.666 m/s, and the air content C varied from 0% to 4%.T maximum reduction in the flow coefficient was less than 5%, indicating that the air conte has little effect on the flow coefficient.

Wall Pressure
The variations in the pressure characteristics under different working conditions measuring point one (100 mm away from the valve port) with respect to the aeration co centration are shown in Figure 6.By comparing the dimensionless time-averaged pressu (Pav) on the pipe wall under different working conditions, it can be seen that little chan occurs as the aeration concentration increases.In contrast, the dimensionless tube wa pulsation pressure (Prms) exhibits an obvious dependence on the aeration concentratio

Wall Pressure
The variations in the pressure characteristics under different working conditions at measuring point one (100 mm away from the valve port) with respect to the aeration concentration are shown in Figure 6.By comparing the dimensionless time-averaged pressure (P av ) on the pipe wall under different working conditions, it can be seen that little change occurs as the aeration concentration increases.In contrast, the dimensionless tube wall pulsation pressure (P rms ) exhibits an obvious dependence on the aeration concentration when the valve opening is small and the average flow rate in the section is low.As the aeration concentration increases, the pressure pulsation coefficient continues to increase, but the rate of increase gradually slows.This is because the turbulence in the flow field is weak under small-opening and low-flow-velocity conditions, and air entrainment significantly increases the turbulence of the flow.The pressure characteristics on the walls behind the two types of valves are quite different, mainly because the flow field structure behind the plunger valve is quite different under different opening degrees, and the influence of aeration on the wall pressure characteristics is more obvious.However, the flow field structure of the cone valve with different opening degrees shows little difference, and the influence of aeration on the pressure characteristics on the wall is small.weak under small-opening and low-flow-velocity conditions, and air entrainment signif-icantly increases the turbulence of the flow.The pressure characteristics on the walls behind the two types of valves are quite different, mainly because the flow field structure behind the plunger valve is quite different under different opening degrees, and the influence of aeration on the wall pressure characteristics is more obvious.However, the flow field structure of the cone valve with different opening degrees shows little difference, and the influence of aeration on the pressure characteristics on the wall is small.As the concentration of entrained air increases, the turbulence intensity's rate of increase in the flow field decreases.Forced aeration before the valve affects the flow field structure behind the valve and increases the turbulence intensity of the water body.For a flow field with insufficient turbulence, air entrainment obviously increases the turbulence of the flow field and has a significant influence on the wall pressure.If the flow field is sufficiently turbulent, a small amount of aeration has a negligible effect on the flow field.The wall pressure characteristics of the cone valve are consistent with those of the plunger valve, indicating that the valve type has little influence on the aeration effect.

Cavitation Phenomena
Typical post-valve cavitation phenomena are shown in Figure 7 for a valve opening degree of 0.3.The main type of cavitation across both valves is foggy cavitation.The sym- As the concentration of entrained air increases, the turbulence intensity's rate of increase in the flow field decreases.Forced aeration before the valve affects the flow field structure behind the valve and increases the turbulence intensity of the water body.For a flow field with insufficient turbulence, air entrainment obviously increases the turbulence of the flow field and has a significant influence on the wall pressure.If the flow field is sufficiently turbulent, a small amount of aeration has a negligible effect on the flow field.The wall pressure characteristics of the cone valve are consistent with those of the plunger valve, indicating that the valve type has little influence on the aeration effect.

Cavitation Phenomena
Typical post-valve cavitation phenomena are shown in Figure 7 for a valve opening degree of 0.3.The main type of cavitation across both valves is foggy cavitation.The symmetrical runner design of the plunger valve causes cavitation bubbles to converge in a spiral rope at the center of the pipe.The flow oscillates back and forth in an unstable flow field structure, and the impact on the pipe wall is strong.After the foggy cavitation gathers into a rope, the cavitation is harder to suppress.The rectification and limitation of the dome make the flow regime more uniform after the cone valve, with the cavitation bubbles evenly distributed in the flow.After aeration, the flow field structure behind the plunger valve is gradually destroyed.When Qa = 0.10 m 3 /h (0.1% of the mainstream), the dynamic process of small air bubbles converging into the spiral rope cavitation can be observed.The incorporation of air bubbles gradually thickens the spiral rope cavitation.However, the limitation imposed by water flow convergence leads to an increasing number of scattered air bubbles in the water flow.When Qa = 1.20 m 3 /h (1.5% of the mainstream), there are too many air bubbles in the water flow, and the multiple strands of spiral rope cavitation mix with each other, making the flow pattern very unstable.
Comparison experiments indicate that the flow field structure after the cone valve is relatively stable, with no significant changes as the level of aeration increases.With a low level of aeration, fine, needle-like air bubbles are evenly distributed in the water flow.As Flow Q a =0.0After aeration, the flow field structure behind the plunger valve is gradually destroyed.When Q a = 0.10 m 3 /h (0.1% of the mainstream), the dynamic process of small air bubbles converging into the spiral rope cavitation can be observed.The incorporation of air bubbles gradually thickens the spiral rope cavitation.However, the limitation imposed by water flow convergence leads to an increasing number of scattered air bubbles in the water flow.When Q a = 1.20 m 3 /h (1.5% of the mainstream), there are too many air bubbles in the water flow, and the multiple strands of spiral rope cavitation mix with each other, making the flow pattern very unstable.Comparison experiments indicate that the flow field structure after the cone valve is relatively stable, with no significant changes as the level of aeration increases.With a low level of aeration, fine, needle-like air bubbles are evenly distributed in the water flow.As the air content increases, the number of air bubbles in the water flow obviously increases and the visibility of the water flow gradually decreases, but the flow field structure after the cone valve remains relatively unchanged.

Working Cavitation Number
The variation in the working cavitation number under test conditions with respect to the aeration concentration is shown in Figure 8 (∆σ = σ a − σ, where σ a is the cavitation number with aeration).Forced aeration has a certain blocking effect on the flow before the valve, resulting in a decrease in the valve overflow capacity.Increasing the aeration concentration enhances both P u and P d , although the former grows faster than the latter, so the working cavitation number decreases.Under the experimental conditions in this study, the maximum air content was 3 m 3 /h, the flow velocity ranged from 1.152 to 5.666 m/s, and the air concentration range was 0-4%.The maximum reduction in the working cavitation number was less than 5%, which indicates that the air content has little influence on the working cavitation number.
Water 2023, 15, x FOR PEER REVIEW 10 valve, resulting in a decrease in the valve overflow capacity.Increasing the aeration centration enhances both Pu and Pd, although the former grows faster than the latte the working cavitation number decreases.Under the experimental conditions in study, the maximum air content was 3 m 3 /h, the flow velocity ranged from 1.152 to m/s, and the air concentration range was 0-4%.The maximum reduction in the wor cavitation number was less than 5%, which indicates that the air content has little influ on the working cavitation number.

Cavitation Noise Characteristics
The cavitation noise collected during the tests reflects certain time domain chara istics.As this study focused on the constant cavitation characteristics, the time do signal of cavitation noise was converted into a frequency domain signal using a Fo transform.All complex waveforms can be regarded as the synthesis of several sine w and any periodic function can be formed by the superposition of multiple sine waves different amplitudes and phases.Thus, the collected noise signal can be represented where ωi is the frequency of the test signal, φi is the initial phase angle of the test si and i = 1, 2, 3, …, n.
The following Fourier transform was applied to convert the cavitation noise tim main features into frequency domain features: Cavitation noise is an important index in determining the strength of cavitation main characteristic parameters of cavitation noise include the noise sound pressure and the noise sound pressure level (SPL), which are related according to:

Cavitation Noise Characteristics
The cavitation noise collected during the tests reflects certain time domain characteristics.As this study focused on the constant cavitation characteristics, the time domain signal of cavitation noise was converted into a domain signal using a Fourier transform.All complex waveforms can be regarded as the synthesis of several sine waves, and any periodic function can be formed by the superposition of multiple sine waves with different amplitudes and phases.Thus, the collected noise signal can be represented as: where ω i is the frequency of the test signal, ϕ i is the initial phase angle of the test signal, and i = 1, 2, 3, . .., n.
The following Fourier transform was applied to convert the cavitation noise time domain features into frequency domain features: Water 2023, 15, 4014 10 of 14 Cavitation noise is an important index in determining the strength of cavitation.The main characteristic parameters of cavitation noise include the noise sound pressure (SP) and the noise sound pressure level (SPL), which are related according to: where P r is the reference sound pressure, usually taken as 2 × 10 −5 Pa.The variation in SPL under typical test conditions with different aeration concentrations is shown in Figure 9.The SPL value is very high in the frequency domain without aeration.When a small amount of air is added, the SPL value decreases rapidly.With a further increase in the air concentration, the downward trend of SPL obviously slows down, and finally drops to the background noise level of the water flow.The dominant frequency of the SPL is about 6 kHz.The maximum SPL (SPL max ) in the dominant frequency under different aeration concentrations is shown in Figure 10.  Figure 10 shows that the variations in SPLmax with aeration are similar at differen velocities.When C ≈ 0.1%, SPLmax drops rapidly by more than 60%; with increasing aer tion concentration, the rate of decline in SPLmax is significantly reduced.When C ≈ 0.9% SPLmax has dropped to a stable value and remains largely unchanged with further in creases in the aeration concentration.This indicates that, when C ≈ 0.1%, cavitation can b significantly inhibited, and when C ≈ 0.9%, the cavitation inhibition effect induced b forced aeration has become saturated.
Aeration changes the propagation velocity of sound waves in water flow [18].Th theoretical relationship between the acoustic velocity of aerated flow and the aeration co    Figure 10 shows that the variations in SPLmax with aeration are similar at diff velocities.When C ≈ 0.1%, SPLmax drops rapidly by more than 60%; with increasing tion concentration, the rate of decline in SPLmax is significantly reduced.When C ≈ SPLmax has dropped to a stable value and remains largely unchanged with furth creases in the aeration concentration.This indicates that, when C ≈ 0.1%, cavitation c significantly inhibited, and when C ≈ 0.9%, the cavitation inhibition effect induc forced aeration has become saturated.
Aeration changes the propagation velocity of sound waves in water flow [18 theoretical relationship between the acoustic velocity of aerated flow and the aeration   Figure 10 shows that the variations in SPL max with aeration are similar at different velocities.When C ≈ 0.1%, SPL max drops rapidly by more than 60%; with increasing aeration concentration, the rate of decline in SPL max is significantly reduced.When C ≈ 0.9%, SPL max has dropped to a stable value and remains largely unchanged with further increases in the aeration concentration.This indicates that, when C ≈ 0.1%, cavitation can be significantly inhibited, and when C ≈ 0.9%, the cavitation inhibition effect induced by forced aeration has become saturated.Aeration changes the propagation velocity of sound waves in water flow [18].The theoretical relationship between the acoustic velocity of aerated flow and the aeration concentration is presented in Equation (6). Figure 11 shows the theoretical curve of acoustic velocity with respect to the aeration concentration in the plunger valve.The acoustic velocity decreases rapidly with increasing aeration concentration, and the trend is very similar to that of SPL max in the dominant frequency.This indicates that reducing cavitation using forced aeration is closely related to the decrease in the acoustic velocity.
where v a is the acoustic velocity of sound in water, and ρ w is the density of water.
Water 2023, 15, x FOR PEER REVIEW 12 Based on the comparison of theoretical acoustic velocity and SPLmax in the dom frequency, the cavitation inhibition efficiency η is defined as follows: where η is the cavitation inhibition efficiency; SPLmax is the maximum sound pressure in the dominant frequency without aeration; SPLa is the sound pressure level in the inant frequency with aeration; and SPLamin is the minimum sound pressure level i dominant frequency with aeration.
Based on the test results obtained in this study, the empirical formula relatin cavitation inhibition efficiency by aeration and the aeration concentration is present Equation (8).As the cavitation inhibition efficiency is not only affected by acoustic v ity, correction factor of m = 1.08 is introduced.
( ) A fitting curve based on Equation ( 8) is compared with the experimental valu Figure 12.The cavitation noise in both valves is significantly suppressed by aeration der the same aeration concentration, η is higher in the cone valve than the plunger for C < 0.3%, which indicates that a small amount of aeration produces a more obv inhibition effect on cavitation in the cone valve.When C > 0.3%, this effect is no lo obvious.Because the flow regime after the plunger valve is complex, cavitation bu may form a slender region of spiral cavitation, which reduces the effect of aeration.H the cavitation inhibition efficiency of aeration in the plunger valve is lower.Larger v of Qa damage the flow field structure after the plunger valve, which enhances the m   Based on the comparison of theoretical acoustic velocity and SPL max in the dominant frequency, the cavitation inhibition efficiency η is defined as follows: where η is the cavitation inhibition efficiency; SPL max is the maximum sound pressure level in the dominant frequency without aeration; SPL a is the sound pressure level in the dominant frequency with aeration; and SPL amin is the minimum sound pressure level in the dominant frequency with aeration.
Based on the test results obtained in this study, the empirical formula relating the cavitation inhibition efficiency by aeration and the aeration concentration is presented in Equation (8).As the cavitation inhibition efficiency is not only affected by acoustic velocity, a correction factor of m = 1.08 is introduced.
A fitting curve based on Equation ( 8) is compared with the experimental values in Figure 12.The cavitation noise in both valves is significantly suppressed by aeration.Under the same aeration concentration, η is higher in the cone valve than the plunger valve for C < 0.3%, which indicates that a small amount of aeration produces a more obvious inhibition effect on cavitation in the cone valve.When C > 0.3%, this effect is no longer obvious.Because the flow regime after the plunger valve is complex, cavitation bubbles may form a slender region of spiral cavitation, which reduces the effect of aeration.Hence, the cavitation inhibition efficiency of aeration in the plunger valve is lower.Larger values of Q a damage the flow field structure after the plunger valve, which enhances the mixing effect of cavitation bubbles and air bubbles.Therefore, the difference in the corrosion reduction effects of aeration between the two types of valves is reduced.

Conclusions
The working conditions of the control valve in HDSLs are very difficult, and v cavitation is inevitable.To ensure the safety of the valve and pipeline, this study ducted forced aeration tests on two types of industrial valves that are suitable for the erational requirements of HDSLs.The main conclusions are as follows: (1) The test results show that forced aeration in front of the valve produces a ce resistance to the incoming flow, resulting in flow reduction.The aeration conce tion in this study was less than 4%, and the reduction in the flow coefficient was than 5%, indicating that aeration has little effect on the flow coefficient.(2) In flow fields with insufficient turbulence, aeration obviously increases the lev turbulence, which has a significant influence on the wall pressure.If the turbul in the flow field is sufficiently strong, a small amount of aeration has a negli effect on the flow field.(3) The main cavitation type across both valves was foggy cavitation.The flow reg after the plunger valve is complex, and cavitation bubbles may form a slender re of spiral cavitation.The flow field structure after the cone valve is simpler, w stable, uniform flow regime containing evenly distributed cavitation bubbles tha easier to suppress.(4) Aeration reduces the working cavitation number, but its influence is limited.In study, the reduction in the valve working cavitation number was less than 5%.(5) Aeration can significantly inhibit valve cavitation.The test results show that wh ≈ 0.1%, the cavitation can be inhibited.When C ≈ 0.9%, the suppres of valve cavitation by forced aeration before the valve becomes saturated.An em ical formula relating the cavitation inhibition efficiency and the aeration conce tion was obtained.
This research was based on the constant flow test condition.Valve opening and ing is an unsteady process, and the rule of aeration in this dynamic process needs t studied further.In summary, from a macroscopic view, the flow field structure of the two types of valves is quite different, and a small amount of aeration has little impact on the flow field structure, while a large amount of aeration may destroy the flow field structure.From a microscopic view, a small amount of aeration can significantly inhibit valve cavitation, but a large amount of aeration cannot further improve the cavitation inhibition effect.

Conclusions
The working conditions of the control valve in HDSLs are very difficult, and valve cavitation is inevitable.To ensure the safety of the valve and pipeline, this study conducted forced aeration tests on two types of industrial valves that are suitable for the operational requirements of HDSLs.The main conclusions are as follows: (1) The test results show that forced aeration in front of the valve produces a certain resistance to the incoming flow, resulting in flow reduction.The aeration concentration in this study was less than 4%, and the reduction in the flow coefficient was less than 5%, indicating that aeration has little effect on the flow coefficient.(2) In flow fields with insufficient turbulence, aeration obviously increases the level of turbulence, which has a significant influence on the wall pressure.If the turbulence in the flow field is sufficiently strong, a small amount of aeration has a negligible effect on the flow field.(3) The main cavitation type across both valves was foggy cavitation.The flow regime after the plunger valve is complex, and cavitation bubbles may form a slender region of spiral cavitation.The flow field structure after the cone valve is simpler, with a stable, uniform flow regime containing evenly distributed cavitation bubbles that are easier to suppress.(4) Aeration reduces the working cavitation number, but its influence is limited.In this study, the reduction in the valve working cavitation number was less than 5%.(5) Aeration can significantly inhibit valve cavitation.The test results show that when C ≈ 0.1%, the cavitation can be significantly inhibited.When C ≈ 0.9%, the suppression of valve cavitation by forced aeration before the valve becomes saturated.An empirical formula relating the cavitation inhibition efficiency and the aeration concentration was obtained.
This research was based on the constant flow test condition.Valve opening and closing is an unsteady process, and the rule of aeration in this dynamic process needs to be studied further.

Figure 1 .
Figure 1.A schematic drawing of the Jinghong HDSL.

Figure 1 .
Figure 1.A schematic drawing of the Jinghong HDSL.

Figure 5 .
Figure 5. Variation in flow coefficient with aeration concentration.

Figure 5 .
Figure 5. Variation in flow coefficient with aeration concentration.

Figure 6 .
Figure 6.Variation in wall pressure with aeration concentration.

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15, x FOR PEER REVIEW 9 of 15

Figure 11 .
Figure 11.Comparison of theoretical acoustic velocity and SPLmax in the dominant frequency.

Figure 11 .
Figure 11.Comparison of theoretical acoustic velocity and SPL max in the dominant frequency.

Figure 12 .
Figure 12.Fitting relationship of η and C.