Numerical simulation study on noise pollution of the pressurized gas system in pumped storage power station

To Investigate the noise pollution caused by pneumatic whistling during the blowdown operation of a pressurized gas storage system in a pumped storage power station, the flow field and sound field distribution of the gas storage tank under blowdown operation are analyzed in detail through full-channel unsteady numerical simulation of the gas storage tank and its supporting facilities. Subsequently, a comprehensive analysis of the noise issue in the gas cylinder was conducted. While investigating the mechanism of noise generation based on the distribution of noise intensity, the precise location of the noise source was pinpointed, providing a reference for the stability research of the exhaust pressurized water system.


Introduction
After years of development, pumped storage technology has become the most mature, reliable, economical, and efficient physical energy storage facility [1,2] .In the short term, pumped storage can still occupy the large-scale and large-capacity energy storage market [3] with its low cost and sound operation mechanism.Through the rapid and frequent conversion between various working conditions, the pumped storage power station can complete the important tasks of smoothing load, peaking and valley filling, and greatly improve the comprehensive utilization efficiency and power supply safety and reliability of conventional power systems and energy systems [4] .The pressurized gas system not only undertakes the task of the unit governor and the water inlet valve oil pressure device to fill the air but also is the core of the pumping storage unit to realize phase regulating operation and start the pump condition.The system facilitates rapid start-up and smooth operation of the unit by injecting medium-pressure compressed air into the rotor chamber to pressurize the water level below the turbine, allowing the turbine to rotate in the air [5] .In this system, high-pressure air stored in the air reservoir expands and releases rapidly during exhaust pressurization and waste discharge conditions, which leads to an increase in the flow losses of the gas within the tank, resulting in a rapid decrease in temperature [6,7] .Because of the problem of pneumatic howling, it will also produce a considerable degree of noise pollution [8] .However, it is not yet clear what the flow field and noise distribution mechanisms are during the waste discharge conditions of the pressurized gas system's air reservoir.Figure 1 illustrates the basic configuration of the high pressure air tank and its ancillary equipment.The sewage discharge condition for the pressurized gas system's air storage tank refers to the process where, during routine maintenance, the waste discharge valve of the storage tank is briefly opened to expel the accumulated impurities settled at the bottom of the tank.The characteristic of this process is its short duration (typically less than 5 seconds) and high pressure (with tank pressure reaching up to 8 MPa).During the construction of an extraction and storage power station, in the installation and debugging of the high pressure air tank, it was found that there was an obvious noise problem in the gas tank under the blowdown condition, and the strong noise caused obvious discomfort to the field staff.Therefore, this paper conducts numerical simulations of the waste discharge conditions of compressed air storage tanks in pressurized gas systems, investigating the distribution of the internal flow field within the tank and the mechanisms of noise generation.This research offers scientific guidance for the stability design of such systems.

Figure 1.
The structure of the gas tank and its blowdown device in the pressurized gas system of a pumped storage power station.

Simulation scheme
2.1.Turbulence modeling and theoretical acoustics 2.1.1.Turbulence model.The fundamental principle behind LES is the decomposition of the turbulent flow field into specific scales of resolution.For pulsations larger than the resolution scale, the N-S equation is directly used to solve the problem, while for pulsations smaller than the resolution scale, the model is closed in solving equations.The difference in flow at different scales is realized by filtering.The basic form of the N-S equation is as follows [9] : t -Time, s;  -density, kg/m 3 ; u -velocity, m/s; p -pressure, Pa.For numerical simulations involving compressible gases, the use of the SST (Shear-Stress Transport) model is currently the mainstream choice within the RANS (Reynolds-Averaged Navier-Stokes) methods.Its governing equations are as expressed in Equation (2) and Equation (3).This method integrates the results from the κ-ω model in the low-speed regions with the κ-ε model results in high-speed regions through a blending function F1, showing good adaptability to flow fields with large velocity gradients.
where e P is the actual sound pressure;  P is the reference sound pressure, in the formula, 2×10 -5 Pa is taken ,which is the threshold of hearing for humans.
The expression for the sound intensity level is: ) lg( 10 where I is the actual sound intensity ; ref I is the reference sound intensity, in the formula, 10 -12 W/m 2 is taken.

Calculation setup and grid independence verification
To simulate the purging process of the pressurized gas system in a specific pumped-storage power station, this study carried out simulation experiments and the catchment model utilized is depicted in Figure 2. The simulation adopted a comprehensive channel model that included all pipeline structures from the high-pressure gas tank to the exhaust end wall.
In light of the current lack of internal flow data for the pressure vessels in the pressurized gas system of pumped storage power stations, this paper refers to data provided by literature [10] to verify the appropriateness of the selected turbulence model.Based on the air reservoir size and exhaust conditions in literature [10] , numerical simulations are carried out with structured meshes of 4.5 million to 6 million nodes.The results show that when the internal pressure of the gas is greater than 0.35 MPa, the data from this paper fits well with the literature [10] , but when the gas pressure is less than 0.35 MPa, there is a large deviation in the data.Taking into account the fact that the absolute pressure in the pressurized gas system significantly exceeds the range of low-pressure exhaust and that data from high-pressure regions demonstrates a high degree of consistency, it has been determined that the simulation approach outlined in this paper will be utilized to simulate both the medium and highpressure exhaust scenarios of the pressurized gas system.
Furthermore, the outcomes from simulations employing various mesh configurations exhibit fundamental consistency, suggesting that a grid consisting of 5 million nodes is sufficient to fulfil the verification tasks in compliance with the criteria for grid independence.In Yang's work [10] , the total volume of the gas tank is 13.07 L. When 5 million structured grids are used, the height of the wall grid is 0.01 mm, the growth index of the boundary layer grid is 1.3, the average resolution of the highspeed basin is 4 mm, and the average resolution of the low-speed basin is 20 mm.Taking into account that the exhaust and pressurization water dynamics within the pressurized gas system are in accordance with the specific attributes of the problem that this verification simulation tackles, the established rules for grid distribution are anticipated to adhere to the requirements of grid independence for modeling the pressurized gas system as well.Hence, the finalized simulation of the pressurized gas system utilizes a mesh comprising 6.05 million nodes.

Blowdown condition boundary settings
In the blowdown condition scenario, the blowdown pipeline's stop valve is closed while the vent pipeline's stop valve and the solenoid valve are open.The compressed air with an initial pressure of 8 MPa is discharged from the high-pressure gas tank along the pipeline to the exhaust side wall, and discharged into the outside environment through the bottom outlet of the wall.The ambient temperature outside the gas tank is 20 ℃, considering the natural convection of air over the exterior wall surfaces, the heat transfer coefficient is approximately 50 W/m 2 •K.The simulation process and the setting of boundary conditions are aligned with the actual scenario (the vent pipeline cut-off valve is closed, and the sewage pipeline cut-off valve, along with the solenoid valve, are both in a fully open state).An interface surface is added during the simulation to emulate the opening and closing of the valves by toggling the interface.An interface surface is placed at the outlet of the blowdown pipeline's stop valve, designating the upstream pipeline as "Upstream Pipeline" and the downstream pipeline as "Downstream Pipeline.".
To solve the aerodynamic noise within the system, CFD is used to calculate the noise sources, followed by applying the FEM to solve the internal acoustic field.LES is employed for noise source calculation with a computational time step of 0.00005 seconds and a total computation duration of 0.6 seconds.In the acoustic field calculation, the internal fluid physical properties correspond to those of ideal air, while the system enclosure's material properties are identical to those of 304 stainless steel, which include a Young's modulus of 194 GPa, a Poisson's ratio of 0.3, a density of 7.93 g/cm³, and a thickness of 5 mm.The analysis frequency range is 0-10000 Hz.Within this range, an analysis is conducted every 50 Hz from 0 to 600 Hz, every 200 Hz from 600 to 6000 Hz, and every 400 Hz from 6000 Hz to 11000 Hz.

Air tank measurement point configuration
To explore the flow state of compressed air in the process of blowdown, several data monitoring points are arranged in the system.The monitoring points used to record changes in gas tank data are shown in Figure 3. Measurement points are arranged along the axial line of the air tank's vertical direction, with the distance between the measuring points 350 mm.The digital number of the measuring points is shown in Figure 3, and the recording parameters mainly include pressure data (P), temperature data (T), and density data (D).

Analysis of simulation results of the gas tank flow field
Figure 4 illustrates the parameter changes at the measurement points within the air storage tank as well as the cross-sectional parameters of the tank outlet under the purging conditions, wherein the pressure inside the gas tank continues to decrease during the discharge time, and at the end of the discharge condition, the average pressure of the gas tank decreases from the initial 8 MP to 7.94 MP.From a macro perspective, the measured values of all measuring points at the same time are basically the same, indicating that in the whole discharge process, there is no severe pressure gradient inside the tank, which means that the expansion process of the gas inside the tank is very gentle, or the expansion degree is limited.The mean temperature within the tank experiences a marginal decline, with the tank' s cooling pace during the blowdown phase being approximately 0.09 ℃/s.Since the tank's air density is predominantly influenced by its pressure, the progression of the tank's density mirrors the spatial pressure trends, diminishing from an initial value of 95.1 kg/m 3 to 94.5kg/m 3 as the blowdown occurs.However, there are still some spatial differences in the distribution of pressure in the gas tank: The lowest pressure is measured at the tank outlet, and as the height of the measurement points increases, the pressure data firstly rises and then gradually declines.This is because the cross-section at the outlet of the gas tank is reduced, and the air pressure is increased.Meanwhile, the velocity of the other measuring points is basically the same.According to Bernoulli's theorem, the pressure decreases progressively with increasing height.In the process of blowdown, except for the high velocity of the section of the gas tank outlet and the measuring point 1 near the outlet, the velocity of the remaining positions in the tank is almost 0. It indicates that the flow of the gas tank is relatively stable except for other positions near the outlet, and the flow state remains extremely low speed (as shown in Figure 5).

Analysis of simulation results of gas tank sound field
The arrangement of measuring points at the outlet of the gas tank is shown in Figure 3 (Measuring Point 1). Figure 6 is the frequency response diagram of sound intensity at measuring points.The figure illustrates that at a frequency of 150 Hz, the sound intensity level hits its maximum, with a reading of 103.7 dB along the X-axis and 106.8 dB along the Y-axis.Figure 7 clearly shows that, the peak frequency of sound pressure level at the outlet of the gas tank is also 150 Hz, reaching 139.1 dB, and the frequency spectrum is evenly distributed between 200 and 10000 Hz.The distribution cloud diagram of the total sound intensity level for the gas tank at a 150 Hz frequency is depicted in Figure 8.It can be seen that the gas tank outlet is the main noise source of the gas tank.

Conclusions
In this paper, LES is employed to perform full passage transient numerical simulations on the air storage tanks of pressurized gas systems and their affiliated waste discharge facilities under waste discharge operational conditions at a certain pumped storage power station.Near-field noise analysis techniques are employed to examine the aerodynamic noise distribution in air storage tanks under conditions of waste discharge.
Results indicate that during the waste discharge operation of the pressurized gas systems, except for the vicinity of the outlet, the other positions of the gas tank are kept in an extremely low flow state, and the average temperature, pressure, and density of the gas tank are slightly reduced.However, the noise issue within the tank is quite severe, with high sound intensity levels at 150 Hz.The main noise source is identified as being at the outlet of the air storage tank.These problems may compromise the safe and steady functioning of the pressurized gas systems and negatively influence the health of the onsite personnel, necessitating resolution through additional optimization.

ij
is the Kronecker function of tensor calculation, containing the Reynolds stress term.averaging modeling is applied to the Reynolds stress terms, it is known as the Reynolds-Averaged Navier-Stokes (RANS) method.

Figure 2 .
Figure 2. Draining Condition and Blowdown Condition Full-Channel Simulation Mesh.

Figure 3 .
Figure 3. Schematic diagram of measuring points of the gas tank.

Figure 4 .
Figure 4. Variation curve of parameters of measuring points inside the gas tank with time under blowdown condition (unit: kg/m 3 ).

Figure 5 .
Figure 5. Velocity cloud diagram of the cylinder shaft section (Unit: m/s).

Figure 6 .
Figure 6.Sound intensity level at the air storage tank outlet measurement point 1(unit: dB).

Figure 7 .
Figure 7. Sound pressure level at the air storage tank outlet measurement point 1 (unit: dB).

Figure 8 .
Figure 8. Sound intensity level contour map of the air storage tank at 150 Hz frequency.
) This paper analyzes the aerodynamic noise of the system, focusing primarily on the aspects of sound pressure level and sound intensity level.Since the range of sound intensity heard by the human ear is very wide, using the absolute values of sound pressure or sound intensity to judge the level of sound is very inconvenient.Therefore, this article introduces two indicators: sound pressure level and sound intensity level.Sound pressure level can be expressed as follows: and  are constants;  is turbulence frequency; 1 F is a mixed function.2.1.2.Acoustic theory.