Generation Mechanism and Prediction Model for Low Frequency Noise Induced by Energy Dissipating Submerged Jets during Flood Discharge from a High Dam.

International Journal of

Environmental Research and Public Health Article

Generation Mechanism and Prediction Model for Low Frequency Noise Induced by Energy Dissipating Submerged Jets during Flood Discharge from a High Dam Jijian Lian 1, *, Wenjiao Zhang 1 , Qizhong Guo 2 and Fang Liu 1 1 2

*

State Key Laboratory of Hydraulic Engineering Simulation and Safety, Tianjin University, 92 Weijin Road, Nankai District, Tianjin 300072, China; [email protected] (W.Z.); [email protected] (F.L.) Department of Civil and Environmental Engineering, Rutgers, The State University of New Jersey, Piscataway, NJ 08854, USA; [email protected] Correspondence: [email protected]; Tel.: +86-22-2740-1123; Fax: +86-22-2740-1127

Academic Editors: Paul B. Tchounwou and Kim Natasha Dirks Received: 22 March 2016; Accepted: 4 June 2016; Published: 15 June 2016

Abstract: As flood water is discharged from a high dam, low frequency (i.e., lower than 10 Hz) noise (LFN) associated with air pulsation is generated and propagated in the surrounding areas, causing environmental problems such as vibrations of windows and doors and discomfort of residents and construction workers. To study the generation mechanisms and key influencing factors of LFN induced by energy dissipation through submerged jets at a high dam, detailed prototype observations and analyses of LFN are conducted. The discharge flow field is simulated using a gas-liquid turbulent flow model, and the vorticity fluctuation characteristics are then analyzed. The mathematical model for the LFN intensity is developed based on vortex sound theory and a turbulent flow model, verified by prototype observations. The model results reveal that the vorticity fluctuation in strong shear layers around the high-velocity submerged jets is highly correlated with the on-site LFN, and the strong shear layers are the main regions of acoustic source for the LFN. In addition, the predicted and observed magnitudes of LFN intensity agree quite well. This is the first time that the LFN intensity has been shown to be able to be predicted quantitatively. Keywords: LFN; high dam flood discharge; energy dissipation by submerged jets; vorticity fluctuation; prediction model

1. Introduction Noise pollution is a serious environmental problem to human beings, which has further been shown to be associated with reduced quality of life and wellbeing [1,2]. At present, most of the academic literature is related to high frequency noise sources from traffic, industry and human activities [3–5], while low frequency noise (LFN) is also considered annoying for humans [6]. The LFN found in living environments is mainly emitted from many artificial sources such as road vehicles, aircraft, and air movement machinery including wind turbines, compressors, and ventilation [7,8], and it is claimed that exposure to LFN has a negative impact on humans’ physiological and psychological health. The physiological problems include headaches, hormone changes, dizziness or vertigo, tinnitus and the sensation of aural pain or pressure, and the psychological impact can cause sleep disturbance, dysphoria, difficulty concentrating, irritability and fatigue [9,10]. In the field of hydraulic engineering in China, the majority of high dams were constructed in recent decades with the features of high water head, large flow capacity, a deep narrow valley and large flood discharge power. Issues such as energy dissipation and scour protection, vibration control Int. J. Environ. Res. Public Health 2016, 13, 594; doi:10.3390/ijerph13060594

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Int. J. Environ. Res. Public Health 2016, 13, 594

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of a hydraulic structure, vapor atomization protection, aeration for cavitation protection, and security warnings associated with high dam flood discharge have attracted significant attention and led to abundant technological achievements [11–14]. Some environmental problems from LFN have also recently been found around some hydropower stations during the flood discharge period. For instance, when the Xiangjiaba Hydropower Station (Zhaotong, at the border of Sichuan and Yunnan provinces, China) began to release flow through the dam orifices at a high water level on 10 October 2012, the roller shutter doors of some shops and the windows and doors of residential buildings experienced sustained vibration in downstream Shuifu County. The dominant frequencies of the LFN observed on-site were approximately 0–2 Hz. In a recent study [15], the impact of ground vibration induced by the flood discharge of Xiangjiaba on on-site roller shutter doors was eliminated by means of a vibration response analysis, and it was deduced that the doors shaking resulted from the resonant interaction between the flow-induced LFN and the door structures. Moreover, the windows of buildings located at the left abutment of the Ertan Hydropower Station (Panzhihua, Sichuan Province, China) oscillated noticeably when the flood was released. The windows and doors of residential buildings in a downstream village about 700–1500 m from the Huangjinping Hydropower Station (Kangding, Sichuan Province, China) experienced sustained vibrations when the flood was released. The LFN observed during the flood discharge period of both the Jinping Hydropower Station (Liangshan Yi Autonomous Prefecture, Sichuan Province, China) and Xiluodu Hydropower Station (Zhaotong, at the border of Sichuan and Yunnan provinces, China) had sound pressure levels (SPL) approximately 20–50 dB higher than the background noise, and the dominant LFN frequencies were between 0.5 Hz and 1.5 Hz. It is found that the inaudible LFN observed around these hydropower stations causes audible secondary noise from surrounding buildings. In Japan, there are some criteria specific to the vibration and rattle attributable to the effects of LFN from stationary sources in worksites, shops and neighborhood residences [16]. The lowest noise frequency listed in the criteria is 5 Hz with its reference SPL limit of 70 dB. For the flow-induced LFN, the LFN’s effects are extended to a lower frequency of about 0–2 Hz. Japanese scholars have conducted some research on flow-induced LFN. As Japan is a densely populated country and many hydropower stations are close to residents’ living quarters, the problems of LFN were noted earlier in Japan. Most of the research focused on the waterfalls formed by the discharge flow through the weir or dam’s floodgate. The oscillation of such waterfalls can cause LFN, which has an adverse impact on surrounding buildings and inhabitants [17–19]. In addition, since LFN is a low frequency wave, it has a low attenuation rate in air [17,20,21], which is difficult to control, and thus can spread over long distances, even tens of kilometers, to resonate with buildings. Among the previous studies, Nakamura [17] reported the phenomenon of LFN induced by flood discharge as early as 1978. Takebayashi [18] and Nakagawa [19] carried out systematic research on the mechanisms of self-excited oscillation of cavity-waterfall systems and the characteristics of the induced LFN based on site observations. Some control measures, such as placing deflectors, were put forward and applied effectively in the research. Ochiai et al. [22] studied various influencing factors of the SPL of the noise from windows and doors induced by LFN by a series of model tests. Saitoh et al. [23] studied the sound sources of the hydraulic jump through hydraulic model experiments on the hydraulic jump and cylinder nozzle, and they found that the noise energy at a high frequency of 500–600 Hz induced by the hydraulic jump was derived from bubble cloud oscillations. These research results indicate that LFN induced by flood discharge can cause environmental problems within large areas, and the generation of LFN closely correlates with the discharge flow regime. The problems of LFN can be controlled and reduced by adjusting the flow regime. The previous studies mainly focus on LFN induced by a relatively continuous waterfall of some water projects with low water head, small flow rate and a simple flow regime. However, for water projects that dissipate energy through multi-horizontal submerged jets, LNF energy can still be observed on site although a waterfall does not exist during flood discharge. Therefore, there must be some differences in the generation mechanisms of LFN between energy dissipation by the submerged jet of high dam flood discharge and the oscillation of


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the waterfall. An extensive literature search has not found any research reports on LFN induced by energy dissipation through the submerged jets of a high dam. The objective of this study was to identify the mechanisms and key influencing factors of LFN induced by energy dissipation through the submerged jets of a high dam. First, in light of the prototype observation results of LFN, the on-site spatial distribution and propagation laws of the induced LFN along the downstream are analyzed, and the correlation between LFN and the discharge flow regime is discussed. Next, the vortex sound model and numerical turbulent flow model for the flood discharge and energy dissipation of the high dam are presented as the theoretical bases. Then, the flow field’s distribution characteristics and effective regions of acoustic source for the LFN are studied and identified, according to the numerical simulation results of the gas-liquid turbulent flow model of flood discharge. The mathematical prediction model of the LFN intensity induced by the submerged jets is established based on the vortex sound model and turbulent flow model, and the prediction model is verified by prototype observation results. Finally, the findings are summarized, and the conclusions of this study are drawn. 2. Materials and Methods 2.1. Prototype Observation 2.1.1. Prototype The Xiangjiaba Hydropower Station is the third largest hydropower station in China and the sixth largest in the world. It is the last cascade on the Jinsha River and is adjacent to Shuifu County of Yunnan Province downstream, with the nearest distance being about 0.5 km [24]. The dam is 162 m in height, with a reservoir capacity of 5 ˆ 109 m3 and planned flood discharge rate of 41,200 m3 /s. The total installed capacity of the station is 6400 MW. The station consists of water-retaining structures, flood-releasing and sediment-flushing structures, a water diversion and power generation system, navigation structures, and irrigation water intakes. Because of the large scale of the flood discharge and energy dissipation and the requirement of the flood discharge and sediment flushing of the hydropower station, the water release structure was chosen as a gravity spillway dam, composed of 12 crest overflowing orifices and 10 mid-discharge orifices, as shown in Figure 1. However, after comparing a range of orifice layout schemes through a hydraulic model test, it was determined that the water release structure had to dissipate energy by the submerged jets and that the 12 crest overflowing orifices and the 10 mid-discharge orifices ought to be alternately arranged for the sake of balancing the unit width discharge, facilitating flood discharge and sediment flushing, decreasing the sluice gate’s size and reducing the influence of the discharge atomization on the surrounding town and enterprise [25]. There are two symmetrical energy dissipation areas separated by the middle guide wall. Int. J. Environ. Res. Public Health 2016, 13, 594

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Figure 1. Layout of the water release structures.

Figure 1. Layout of the water release structures. 2.1.2. Observation System and Conditions Since 2012, Tianjin University has organized prototype observations of LFN many times during the flood period of Xiangjiaba. The observation equipment of LFN on site consists of an infrasound microphone, a multi-channel digitizer and a computer. The infrasound microphone, which was fixed above the ground a little over 2 m, has a frequency range of 0.1–500 Hz and a sensitivity of 107 mv/Pa. The multi-channel digitizer connects the microphone with the computer, which supplies

Figure Int. J. Environ. Res. Public Health 2016, 13, 5941. Layout of the water release structures.

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2.1.2. Observation System and Conditions 2.1.2. Observation System and Conditions Since 2012, Tianjin University has organized prototype observations of LFN many times during Sinceperiod 2012, Tianjin University organizedequipment prototype of observations LFN many times during the flood of Xiangjiaba. Thehas observation LFN on siteofconsists of an infrasound the flood period of Xiangjiaba. The observation equipment of LFN on site consists of an infrasound microphone, a multi-channel digitizer and a computer. The infrasound microphone, which was microphone, a multi-channel and a computer. The infrasound microphone, which wasoffixed fixed above the ground a littledigitizer over 2 m, has a frequency range of 0.1–500 Hz and a sensitivity 107 above the ground a little over 2 m, has a frequency range of 0.1–500 Hz and a sensitivity of 107 mv/Pa. mv/Pa. The multi-channel digitizer connects the microphone with the computer, which supplies The multi-channel digitizer and connects microphone with the computer, to the power to the microphone savesthe data in high speed. The digitizerwhich has asupplies built-in power GPS, so the microphone andwork saveswell dataininthe high speed. hasthe a built-in GPS, so can work equipment can open air. The Withdigitizer regard to uncertainties inthe theequipment observed data from well in the open air. microphone With regard and to the uncertainties in the observed data from the self-noise of the the self-noise of the digitizer, the errors from the digitizer are small sufficiently to microphone and digitizer, the errors from the digitizer are small sufficiently to be neglected, and be neglected, and the maximum error from the microphone is below 2%, which corresponds tothe ±1 maximum error from the microphone is below 2%, which corresponds to ˘1 dB. dB. The observation thethe dam area,area, construction area and area of area Shuifu, The observationrange rangecovered covered dam construction areaurban and urban of placing Shuifu, 25 observation points in total in (T1–T25 in Figure 2). The2). observation work work was conducted at least placing 25 observation points total (T1–T25 in Figure The observation was conducted at twice at the same point under the same discharge conditions. The observation time period was set least twice at the same point under the same discharge conditions. The observation time period was as min. The observation frequency was setset asas1000 set3–6 as 3–6 min. The observation frequency was 1000Hz. Hz.Due Duetotothe thedaily, daily,traffic trafficand and industrial industrial noise in the noise in the county county [26,27], [26,27], especially especially with with respect respect to to the the LFN LFN generated generated by by the the surrounding surrounding living living environments [8,28,29], the observation work was carried out in the evening to avoid signal mixing or environments [8,28,29], the observation work was carried out in the evening to avoid signal mixing distortion and ensure, as much as possible, the validity of the flow-induced LFN data. Table 1 shows or distortion and ensure, as much as possible, the validity of the flow-induced LFN data. Table 1 the details of the observed discharge conditions of Xiangjiaba. shows the details of the observed discharge conditions of Xiangjiaba.

Figure 2. LFN observation point arrangement. Figure 2. LFN observation point arrangement. Table 1. Observed discharge conditions *. No.

Q (m3 /s)

Water Level Elevation (m)

Crest Overflowing Orifice

Upstream

Downstream

Number

Opening (m)

Number

Opening (m)

/ / C8–C11 C8–C11 C2–C5, C8–C11 C2–C5, C8–C11 C2–C5, C8–C11 C1–C6 C7–C12

/ / 1.5 1.5 1.5 1.7 3.0 3.0 2.0

/ M6, M8, M10 M6–M10 M1–M10 M1–M10 M1–M10 M1–M10

/ 3.3 1.5 1.5 1.5 1.9 2.0

M1–M10

1.2

1 2 3 4 5 6 7

0 1150 2760 3340 4470 5140 6370

/ 353.43 379.42 379.34 379.42 379.30 379.19

/ 267.71 269.81 270.52 271.27 271.87 272.77

8

6600

374.71

275.89

Mid-Discharge Orifice

* Q is the total discharge through the dam orifices. The discharge orifice’s number is named from the left bank to the right bank.

4 5 6 7

3340 4470 5140 6370

379.34 379.42 379.30 379.19

270.52 271.27 271.87 272.77

C8–C11 C2–C5, C8–C11 C2–C5, C8–C11 C2–C5, C8–C11 C1–C6 C7–C12

1.5 1.5 1.7 3.0 3.0 2.0

M1–M10 M1–M10 M1–M10 M1–M10

1.5 1.5 1.9 2.0

8 6600 374.71 275.89 M1–M10 1.2 Int. J. Environ. Res. Public Health 2016, 13, 594 5 of 24 * Q is the total discharge through the dam orifices. The discharge orifice’s number is named from the left bank to the right bank.

2.1.3. Prototype Observation Data 2.1.3. Prototype Observation Data

Figure 3 compares the time history and power spectral density (PSD) curves of the LFN observed Figure the 3 compares the discharge time history and power spectral 1) density (PSD) curves of thecondition LFN at T8 between no-releasing condition (Condition and the small discharge observed at T8 between the no-releasing discharge condition (Condition 1) and the small discharge (Condition 2) in Table 1. In this study, all of the PSD for the LFN is estimated using the autoregressive condition (Condition 2) in Table 1. In this study, all of the PSD for the LFN is estimated using the (AR) model with the Burg algorithm, which is one of the most frequently used parametric methods for autoregressive (AR) model with the Burg algorithm, which is one of the most frequently used processing various signals [30,31], and the order of the AR model is determined by the final prediction parametric methods for processing various signals [30,31], and the order of the AR model is errordetermined (FPE) criterion. shown, during the flood releaseAs period, the LFN the intensity increases greatly, by the As final prediction error (FPE) criterion. shown, during flood release period, and the theLFN LFNintensity energy presented in the PSD has an apparent peak frequency below 20 Hz. It is obvious increases greatly, and the LFN energy presented in the PSD has an apparent peak that frequency LFN is induced in Hz. the Itprocess of flood discharge. below 20 is obvious that LFN is induced in the process of flood discharge. Amplitude (Pa)

4 Q=0m3 /s

2

Q=1150m3 /s

0 -2 -4

0

10

20

30 Time (s)

40

50

60

0.8 Q=0m3 /s

PSD

0.6

Q=1150m3 /s

0.4 0.2 0

0

5

10 Frequency (Hz)

15

20

Figure 3. Comparisons of the time history and PSD curves of LFN.

Figure 3. Comparisons of the time history and PSD curves of LFN.

Spatial Distribution and Propagation Patterns

Spatial Distribution and Propagation Patterns

The spatial distribution patterns of the induced LFN along the downstream area were obtained

The spatial distribution the induced LFN along the downstream area were to obtained through statistical analysis.patterns The LFNofamplitude decreases gradually with increasing distance the through The LFN amplitude decreases with increasing to the dam statistical area underanalysis. all observed discharge conditions. Figuregradually 4 shows the contour map distance of the LFN observed under discharge Condition conditions. 8. In this condition, the LFN achieved theLFN damamplitude area under all observed Figure 4 shows theamplitude contour map of the maximum value, approximately 9.3 8. PaIn (113.3 dB), at the dam area.amplitude To evaluateachieved the human amplitude observed under Condition this condition, the LFN thehearing maximum and perception sensitivity for the LFN, the G-weighting (dB(G)) [32] is proposed as an appropriate value, approximately 9.3 Pa (113.3 dB), at the dam area. To evaluate the human hearing and perception metric for limitsthe forG-weighting LFN [33,34]. The maximum for the observed LFNfor was sensitivity fornoise the LFN, (dB(G)) [32] isG-weighting proposed asSPL an appropriate metric noise calculated as approximately 78.6 dB(G), well below the average 95 dB(G) hearing threshold [35] and limits for LFN [33,34]. The maximum G-weighting SPL for the observed LFN was calculated as the LFN limit of 85 dB(G) from Australian and Danish recommendations [36,37]. Therefore, it is approximately 78.6 dB(G), well below the average 95 dB(G) hearing threshold [35] and the LFN limit noted that, under the discharge conditions in Table 1, the LFN observed around Xiangjiaba has no of 85 dB(G) from Australian and Danish recommendations [36,37]. Therefore, it is noted that, under direct negative effect on local residents’ health in general. the discharge conditions in Table 1, the LFN observed around Xiangjiaba has no direct negative effect on local residents’ health in general. Int. J. Environ. Res. Public Health 2016, 13, 594

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Figure 4. Distribution of the LFN amplitude. Q = 6600 m³/s; the unit is Pa.

Figure 4. Distribution of the LFN amplitude. Q = 6600 m3 /s; the unit is Pa.

To analyze the attenuation rates of the flow-induced LFN in the process of propagation along the downstream city, the SPLs of 8 LFN observation points (dashed line in Figure 2) under all observed discharge conditions were calculated, as observed in Figure 5. Table 2 shows the SPL attenuation coefficients at different distances from the flood release and energy dissipation area. As a result, the SPLs near the dam area are greatly attenuated and have a maximum attenuation coefficient, 0.0347 dB/m, as a statistical average. The SPL attenuation coefficient gradually decreases

Figure 4. Distribution Int. J. Environ. Res. Public Health 2016, 13, 594 of the LFN amplitude. Q = 6600 m³/s; the unit is Pa.

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To analyze the attenuation rates of the flow-induced LFN in the process of propagation along To analyze the attenuation the flow-induced LFN in (dashed the process propagation along the the downstream city, the SPLsrates of 8ofLFN observation points lineofin Figure 2) under all downstream city, theconditions SPLs of 8 LFN (dashedinline in Figure 2) under all observed observed discharge wereobservation calculated,points as observed Figure 5. Table 2 shows the SPL discharge were calculated, as observed in Figure 5. Table 2 shows SPL attenuation attenuationconditions coefficients at different distances from the flood release and energy the dissipation area. As coefficients different release and energy dissipation area. As a result, a result, theatSPLs near distances the dam from area the are flood greatly attenuated and have a maximum attenuation the SPLs near the dam area are greatly attenuated and have a maximum attenuation coefficient, coefficient, 0.0347 dB/m, as a statistical average. The SPL attenuation coefficient gradually decreases 0.0347 dB/m, asdistance a statistical average. Theand SPLit attenuation gradually decreases with with increasing to the dam area, decreases tocoefficient 0.000459 dB/m for distances greater increasing than 2 km.distance to the dam area, and it decreases to 0.000459 dB/m for distances greater than 2 km. 120 T1

115

T2

110 SPL (dB)

3

Q (m /s) 1150 2760 3340 4470 5140 6370 6600

105 T3

100

T6 T9

95

T15 T18

90 85

0

500

1000

1500

2000

T22

2500

3000

Distance (m) Figure 5. SPL distribution along the downstream city. Figure 5. SPL distribution along the downstream city. Table 2. SPL attenuation coefficients at different propagation ranges *. Table 2. SPL attenuation coefficients at different propagation ranges *. Range Range

Dam area 2 kmkm

1150 1150 0.0434 0.0251 0.0434 0.0251 0.00594 0.00594 0.00236 0.00236 0.000324 0.000324

2760 2760 0.0336 0.0220 0.0336 0.0220 0.0108 0.0108 0.00190 0.00190 0.000368 0.000368

3340 3340 0.0322 0.0213 0.0322 0.0213 0.0118 0.0118 0.00276 0.00276 0.000397 0.000397

Q (m3/s) Q4470 (m3 /s) 4470 0.0356 0.0202 0.0356 0.0202 0.0124 0.0124 0.00319 0.00319 0.000777 0.000777

Statistical Average 5140 6370 6600 Statistical Average 5140 6370 6600 0.0274 0.0314 0.0386 0.0347 0.0224 0.0234 0.0206 0.0221 0.0274 0.0314 0.0386 0.0347 0.0224 0.0234 0.0206 0.0221 0.0112 0.0102 0.0106 0.0104 0.0112 0.00406 0.0102 0.00388 0.0106 0.0104 0.00360 0.00311 0.00360 0.00406 0.00388 0.00311 0.000416 0.000459 0.000416 0.000596 0.000596 0.000332 0.000332 0.000459

** The unitisisdB/m. dB/m. The unit

Correlation between LFN and Discharge Flow Regime Figure 6 shows the relationship between the RMS values of the LFN amplitude analyzed and the flow rate for several observation points in the downstream city area. In general, the LFN amplitude increases gradually with increasing Q, and the discharge operation conditions have some influence on the LFN amplitude. It is seen from Table 1 and Figure 6 that the joint discharge operation schemes of the crest overflowing orifices and mid-discharge orifices are advantageous for reducing the LFN amplitude. For instance, the LFN observed under Condition 4 (Q = 3340 m3 /s) has a higher amplitude than the LFN observed under Condition 5 (Q = 4470 m3 /s). The LFN amplitude observed under Condition 8 (Q = 6600 m3 /s) shows a significant decrease compared to the amplitude observed under Condition 7 (Q = 6370 m3 /s). As joint discharge operation schemes can avoid concentrated flow in the stilling basin, maintaining uniform and smooth flow in the stilling basin plays a significant role in reducing the LFN amplitude induced by flood discharge. Figure 7 shows the relationship between the analyzed dominant frequency of the LFN and the flow rate. As shown in the figure, the dominant frequencies of the LFN are concentrated between 0 Hz to 2 Hz and decrease gradually with increasing Q under the observed discharge conditions.

observed under Condition 7 (Q = 6370 m³/s). As joint discharge operation schemes can avoid observed under Condition 7 (Q = 6370 m³/s). As joint discharge operation schemes can avoid concentrated flow in the stilling basin, maintaining uniform and smooth flow in the stilling basin concentrated flow in the stilling basin, maintaining uniform and smooth flow in the stilling basin plays a significant role in reducing the LFN amplitude induced by flood discharge. Figure 7 shows plays a significant role in reducing the LFN amplitude induced by flood discharge. Figure 7 shows the relationship between the analyzed dominant frequency of the LFN and the flow rate. As shown the relationship between the analyzed dominant frequency of the LFN and the flow rate. As shown in the figure, the dominant frequencies of the LFN are concentrated between 0 Hz to 2 Hz of and Int.the J. Environ. Res.the Public Health 2016, 13, 594 24 in figure, dominant frequencies of the LFN are concentrated between 0 Hz to 2 Hz7 and decrease gradually with increasing Q under the observed discharge conditions. decrease gradually with increasing Q under the observed discharge conditions.

Amplitude RMS (Pa) Amplitude RMS (Pa)

1.2 1.2 1.0 1.0 0.8 0.8 0.6 0.6 0.4 0.4 0.2 0.2 0 0

2000 2000

4000 4000 3 Q (m3 /s) Q (m /s)

6000 6000

T7 T7 T8 T8 T9 T9 T10 T10 T11 T11 T12 T12 T13 T13 T14 T14 T15 T15 T16 T16 T17 T17 T18 T18 T20 T20 T21 T21 T22 T22 T23 T23 T24 T24 T25 T25

8000 8000

Dominant frequency (Hz) Dominant frequency (Hz)

Figure 6. Correlation between the LFN intensity and Q. Figure 6. 6. Correlation Correlation between between the the LFN LFN intensity intensity and and Q. Q. Figure

1.3 1.3 1.2 1.2 1.1 1.1 1.0 1.0 0.9 0.9 0.8 0.8 0.7 0.7 0.6 0.6

T7 T7 T8 T8 T9 T9 T10 T10 T11 T11 T12 T12 T13 T13 T14 T14 T15 T15 T16 T16 T17 T17 T18 T18 T20 T20 T21 T21 T22 T22 T23 T23 T24 T24 T25 T25

3000 3000

4000 4000

5000 6000 50003 6000 Q (m3 /s) Q (m /s)

7000 7000

8000 8000

Figure 7. Correlation between the LFN dominant frequency and Q. Figure 7. Correlation between the LFN dominant frequency and Q. Figure 7. Correlation between the LFN dominant frequency and Q.

2.2. Theoretical Model of Vortex Sound In acoustic research, Powell [38] and Howe [39,40] et al. studied the basic issues of the internal mechanism of fluid vocalization and the interaction between acoustic wave and turbulent flow in terms of vortex dynamic theory since the 1960s, and they established the vortex sound theory. Their research results indicated that the vortex is a significant acoustic source and that vortex sound theory is feasible and effective for identifying the generation mechanism of flow-induced noise at a low Mach number. In the turbulent flow field of flood discharge and energy dissipation from a high dam, various vortices always exist. In a stilling basin, the large amount of energy carried by high-velocity submerged jets is dissipated through strong turbulent mixing. Numerous low-frequency large coherent structures are present in the strong shear layers of the submerged jets, and they have evident vortical structures, high regularity and repeatability. The acoustic energy’s formation and transition coming from the interaction of the vortical structures, potential flow and solid boundaries cannot be neglected. Therefore, the vortex sound theory is applied to determine the mechanism for LFN induced by energy dissipation through submerged jets in this study. Assuming that the flow is incompressible and


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isentropic and based on the equations of continuity and motion, the vortex sound equation [38] can be deduced and simplified as: 1 B2 p (1) ∇2 p ´ 2 2 “ ´∇ ¨ ρ pω ˆ uq , c Bt where p is the acoustic pressure in the far field; c is the acoustic velocity; ρ is the density; ω is the vorticity vector; and u is the flow velocity vector. The equation shows that the vortex sound equation is a typical nonhomogeneous wave equation, with the differential expression of the acoustic wave’s propagation process in a nonhomogeneous fluid on the left and the acoustic source term of the vortex on the right. Equation (1) indicates that the flow-induced acoustic pressure is directly related to the sizes, variations and motion of the vortices. To predict the acoustic pressure, the general solution of Equation (1) for the far field is written as follows using the Green function method and the Helmholtz vortex equation, according to Möhring [41]: ppx, tq “ ρ

B Bt1

ż ` ˘ ` ˘ G x, t; y, t1 ¨ ω y, t1 d3 ydt1 ,

(2)

where x is the displacement vector of the predicted point in the far field and y is the displacement vector of the acoustic source point in the flow region. The Green function must satisfy ` ˘ ` ˘ ∇y G x, t; y, t1 “ ∇y ˆ G x, t; y, t1 . The integrand on the right side of Equation (2) only contains the vorticity variable ω, which identifies that the region with time-varying vorticity is the effective region of the acoustic source. Furthermore, because the flow velocity is not contained in the integrand, the acoustic pressure of the far field can be directly calculated by the effective vorticity fluctuation data. As G is a symmetric function, according to Powell’s deduction, G can be confirmed as: ` ˘ G x, t; y, t1 “

´ 1 x¯ px ¨ yq x ˆ y, δ2 t ´ t1 ´ 2 3 c 12πc x

(3)

where δ is the Dirac delta function. Then, Equation (2) leads to: B3 ρ ppx, tq “ 12πc2 x3 Bt3

ż px ¨ yq x ˆ y ¨ ωd3 y,

(4)

where the vorticity values depend on the time t1 = t ´ x/c. As the attenuation of acoustic pressure during propagation is not included above, a sonar equation is obtained as: Pe SL ´ TL “ 20log10 ´ Pre f

ˆż

˙ αdL L

y

“ 20log10

P1 , Pre f

(5)

where SL is the RMS value of the SPL without regard to attenuation; TL is the SPL attenuation value; Pe is the RMS value of acoustic pressure calculated by Equation (4); Pref is the reference value of the acoustic pressure, set as 2 ˆ 10´5 Pa; α is the SPL attenuation coefficient; and P1 is the virtual value of the acoustic pressure finally achieved with regard to attenuation. The mathematical prediction model of LFN is generated using Equations (4) and (5), and the LFN intensity can be predicted by substituting the results of numerical simulation of the near-field turbulent flow into the prediction model. 2.3. Numerical Turbulent Flow Model 2.3.1. Gas-Liquid Turbulent Flow Model A large number of numerical simulation studies have shown that the k-ε turbulent flow model is a reasonable method for simulating the hydrodynamic characteristics of turbulent flow [42,43]. However, the RNG k-ε turbulent flow model, first developed by Yakhot and Orszag [44], can better simulate flow with high strain rate and large streamline curvature compared to the traditional k-ε turbulent flow


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model. The VOF method, proposed by Hirt and Nichols [45] in 1975 based on the MAC method, is also an effective way to calculate the complex free water surface [46]. Therefore, the RNG k-ε turbulent flow model and the VOF method are employed in this study to analyze the hydraulic parameters in the flow field of flood discharge and energy dissipation of a high dam. The major governing equations are listed below: Basic equations of turbulent flow: $ & B ρ ` B ρui “ 0 Bt B xi ¯´ ”´ ¯ı , Buj B ui k2 % B ui ` B ui u j “ ´ 1ρ B p ` 1ρ B µ ` C ` µ ε Bt Bxj B xi Bxj Bxj B xi

(6)

« ff B pρkq B pρkui q B Bk ` αk µe f f ` Gk ` ρε, “ Bt Bxi Bx j Bx j

(7)

« ff C˚ ε Bε B pρεq B pρεui q B ε2 αε µe f f ` 1ε Gk ´ C2ε ρ , ` “ Bt Bxi Bx j Bx j k k

(8)

k equation:

ε equation:

Gas-liquid VOF equation: #

α a “ 1 ´ αw , B αw B αw B t ` ui B x “ 0

(9)

i

¯ Bu ` B x j , Cµ = 0.0845, i αk = αε = 1.39, C1ε = 1.42, C2ε = 1.68, η 0 = 4.377, β = 0.012, and αw and aa are the volume fractions of water and air in a unit grid, respectively. 2

˚ “ C ´ where µe f f “ µ ` ρCµ kε , C1ε 1ε

η p1´η {η0 q , 1` βη 3

` ˘1{2 k η “ 2Eij ¨ Eij ε , Eij “

1 2

´

B ui Bxj

2.3.2. Simulation Domain and Boundary Conditions The numerical turbulent flow model established is for a 1:1 scale simplified spillway dam of Xiangjiaba, as shown in Figure 8, where X is along the flow direction. The calculation conditions of the numerical simulation are listed in Table 1. The simulation domain includes the water body extended 80-m into the reservoir; the spillway dam segments with the crest overflowing orifices and mid-discharge orifices, which are 132 m long; the 228 m long stilling basin; and the 40 m long tail-weir. Because the stilling basins of Xiangjiaba are symmetrical on two sides of the middle guide wall, the simulations are done on just a half portion of the discharge structures which is on one side of the middle guide wall in the transverse Z direction to reduce the numeration workload. The model is meshed by block-structured grids. For the main flood discharge and energy dissipation regions, such as the spillway dam area and the front of the stilling basins, the grid size is set as 1 m long ˆ 1 m wide ˆ 1 m high. In the remaining regions, the grid size is set as 2 m long ˆ 1 m wide ˆ 1 m high. Mesh refinement is applied on the overflow dam face, and the mesh refinement method adaptive to the variations of the pressure gradient and free water surface is employed during the calculation. The total number of grid units is approximately 3.52 million. Furthermore, based on the RNG k-ε turbulent flow model and the VOF method, the methods of finite volume, PISO and wall function are employed in the process of calculation. When setting the boundary conditions of the turbulent flow model, the upstream inlet and downstream outlet are set as the pressure inlet and pressure outlet, respectively, and the water levels of upstream and downstream are set equal to the measured values shown in Table 1. The top boundary of the model is all set as the air pressure inlet with the atmospheric pressure. The other boundary is set as a no-slip wall.

function are employed in the process of calculation. When setting the boundary conditions of the turbulent flow model, the upstream inlet and downstream outlet are set as the pressure inlet and pressure outlet, respectively, and the water levels of upstream and downstream are set equal to the measured values shown in Table 1. The top boundary the model all 13, set594 as the air pressure inlet with the atmospheric pressure. The10other Int. J. Environ.of Res. Public Healthis2016, of 24 boundary is set as a no-slip wall.

Figure 8. 8. Turbulent Turbulentflow flowmodel modeland andsimulation simulationdomain. domain. Figure

3. Results and Discussion 3. Results and Discussion From solving Powell’s equation in the above section, it is suggested that the region with the From solving Powell’s equation in the above section, it is suggested that the region with the time-varying vorticity is the effective region of acoustic source, and the mathematical prediction time-varying vorticity is the effective region of acoustic source, and the mathematical prediction model model of LFN is developed accordingly. The numerical turbulent flow model is also built as a feed of LFN is developed accordingly. The numerical turbulent flow model is also built as a feed to the to the LFN prediction model. In this section, the numerical calculation results from the turbulent LFN prediction model. In this section, the numerical calculation results from the turbulent flow model flow model and the vortex sound model are analyzed to verify the theoretical analysis results. The and the vortex sound model are analyzed to verify the theoretical analysis results. The flow field and flow field and vorticity fluctuation characteristics of the energy dissipation area are analyzed to vorticity fluctuation characteristics of the energy dissipation area are analyzed to identify the main identify the main regions of acoustic source for the LFN. The prediction model developed is used to regions of acoustic source for the LFN. The prediction model developed is used to calculate the LFN calculate the LFN intensity on site. intensity on site. 3.1. Verification and Validation of Turbulent Flow Model To evaluate the numerical uncertainty and discretization errors of the simulation results, the Grid Convergence Index (GCI) analysis based on the Richardson extrapolation method, which was outlined by Celik et al. [47,48], is adopted herein. Two additional refined grids are set to do the computations, which represent a relevant contribution to the numerical uncertainty. The three different grids consist of 3.52 (N1 ), 4.81 (N2 ) and 6.41 (N3 ) million cells respectively, which are called as the coarse, medium and fine grids. The GCI of the coarse and fine grids are calculated as follows: P 1.25e21 r21 P r21 ´1 1.25e32 P r32 ´1

$ & GCI 21 coarse “ % GCI 32 “ f ine

,

(10)

ˇ ˇ ˇ ˇ ˇ f ´f ˇ ˇ f ´f ˇ where P “ lnp1r q |ln |p f 3 ´ f 2 q { p f 3 ´ f 2 q| ` q pPq|, e21 “ ˇ 1 f 2 ˇ, and e32 “ ˇ 2 f 3 ˇ. Here P is the order 2 1 21 of accuracy; e is the relative error; r is the grid refinement factor; and f 1 , f 2 and f 3 denote the solutions at the coarse, medium, and fine levels, respectively. As Roach [49] recommended a minimum 10% change in point of the computational cost and time consumption, the grid refinement factor is set to r = 1.11. The variables, f 1 , f 2 and f 3 , are considered as the flow velocity magnitudes near the stilling basin floor for different grid sizes.


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Table 3 summarizes the numerical uncertainty assessment results for the turbulent flow model under Condition 8. All of the solutions for the velocity magnitudes show good mesh convergence behavior with errors of less than 2.5%, even to the coarse grid. Table 3. Numerical uncertainty assessment for the turbulent flow model *. Z (m)

X (m)

Velocity Magnitude (m/s) f1

f2

f3

44

155 170 185

2.628 2.516 2.182

2.610 2.498 2.171

54

155 170 185

2.773 2.509 2.411

2.763 2.511 2.400

32 GCI21 coarse GCIfine (%) (%)

r21

r32

p

e21

e32

2.599 2.491 2.176

1.11 1.11 1.11

1.11 1.11 1.11

4.28 8.79 7.73

0.0067 0.0072 0.0053

0.0043 0.0029 0.0024

2.33 1.49 1.19

0.96 0.24 0.24

2.768 2.509 2.395

1.11 1.11 1.11

1.11 1.11 1.11

5.79 2.51 8.56

0.0035 0.0009 0.0049

0.0019 0.0007 0.0020

0.95 0.49 1.04

0.29 0.29 0.18

* The solutions for the velocity magnitudes with Z = 44 m and Z = 54 m are at the midlines of the crest overflowing orifice and the mid-discharge orifice, respectively.

To further validate the turbulent numerical simulation model, the data among the physical model experiment, hydraulic prototype observation and numerical simulation results were compared. The measured and simulated results of the water surface profile of Condition 8 in the stilling basin are shown in Figure 9. The observed and simulated results of the time-average pressure distribution and Int. J. Environ. Res. Public Health 2016, 13, 594 12 of 25 flow velocity near the stilling basin floor of Condition 8 are shown in Figures 10 and 11, respectively. Int. J. Environ. Res. Public Health 2016, 13, 594

60

30 20

Y(m)

Y(m)

40

50

60

60

50

50

40

40 30

10 20 0 10 120 160 0 120

160

Measured Simulated Measured

200

240 280 320 Simulated 360 400 X(m) 200 240 280 320 360 400

Y(m) Y(m)

50

12 of 25

60

30

40

20

30

Measured Simulated

10 20

Measured

100

120

0 120

160 160

X(m)

200 200

Simulated 240 280 320 360 400 X(m) 240 280 320 360 400 X(m)

(b)

(a)

(b) (a) Figure 9. Comparisons of the water surface profile in the stilling basin between the measured (from Figure 9. Comparisons of the water surface profile in the stilling basin between the measured (from 9. Comparisons of the water surface(a) profile in the basin between the measured (from of the Figure physical model) and simulated results: Midline of stilling the crest overflowing orifice; (b) Midline the physical model) and simulated results: (a) Midline of the crest overflowing orifice; (b) Midline of the physical model) and simulated results: (a) Midline of the crest overflowing orifice; (b) Midline of the mid-discharge orifice. the mid-discharge orifice.

50 40 30

60 50 40

Observed Observed Simulated

Simulated

30

20 20 10 10 0 0 130130 140140 150 150 160 160 170 170 XX (m) (m) (a)(a)

180 180

190

Time-average (9.81kPa) Time-averagepressure pressure (9.81kPa)

60 Time-average pressure (9.81kPa)

Time-average pressure (9.81kPa)

the mid-discharge orifice.

60

60

Observed

50

Observed Simulated Simulated

50

40

40

30

30

20 20 10 10 00 130 130

140 150 150 160160 170170 180 180190 190 140 X (m) X (m)

(b)(b)

Figure 10. Comparisonsofofthe thetime-average time-average pressure pressure distribution the stilling basin floor between Figure 10.Comparisons Comparisons distributiononon Figure 10. of the time-average pressure distribution on the the stilling stilling basin basinfloor floorbetween between the observed (from the prototype) and simulated results: (a) Midline of the crest overflowing orifice; theobserved observed(from (fromthe theprototype) prototype) and and simulated simulated results: the results: (a) (a) Midline Midlineof ofthe thecrest crestoverflowing overflowingorifice; orifice; Midline of mid-dischargeorifice. orifice. (b) (b) Midline thethe mid-discharge (b) Midline ofofthe mid-discharge orifice.

4 0

-4

8

8 4 0 -4


Simulated

8

low velocity(m/s) velocity(m/s)

velocity(m/s)

low velocity(m/s)

8

4

4

0

0

-4


Simulated

140

150

160 X (m)

170

180

190

Ti

Ti

130

130

140

150

(a)

160 X (m)

170

180

190

(b)

Figure 10. Comparisons of the time-average pressure distribution on the stilling basin floor between observed (from the prototype) Int. J. the Environ. Res. Public Health 2016, 13, 594 and simulated results: (a) Midline of the crest overflowing orifice; 12 of 24 (b) Midline of the mid-discharge orifice.

8 Observed Simulated

4 0 -4 -8 130

140

150

160 X(m)

170

180

190

Flow velocity(m/s)

Flow velocity(m/s)

8

Observed Simulated

4 0 -4 -8 130

(a)

140

150

160 X(m)

170

180

190

(b)

Figure 11. Comparisons of the flow velocity near the stilling basin floor between the observed and Figure 11. Comparisons of the flow velocity near the stilling basin floor between the observed and simulated results: (a) Midline of the crest overflowing orifice; (b) Midline of the mid-discharge simulated results: (a) Midline of the crest overflowing orifice; (b) Midline of the mid-discharge orifice. orifice.

The figures of of thethe water surface profile, pressure distribution and The figures show showthat thatthe thesimulation simulationresults results water surface profile, pressure distribution flow flow velocity near the floor in good with thosewith from those the experiments and observations, and velocity near thearefloor are agreement in good agreement from the experiments and and the other conditions’ validation results are all consistent. As a result, it is feasible to itanalyze the observations, and the other conditions’ validation results are all consistent. As a result, is feasible hydraulic characteristics of the flow field by the numerical methods chosen in this study. to analyze the hydraulic characteristics of the flow field by the numerical methods chosen in this study. 3.2. Analyses of Numerical Modeling Results 3.2.1. FlowInt.Velocity Distribution J. Environ. Res. Public Health 2016, 13, 594

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Because the distribution of the flow field obtained by numerical calculation under every 3.2. Analyses of Numericalpatterns Modeling Results condition are similar, only the velocity contours on the sections along midlines of the crest overflowing 3.2.1. Flow Velocity Distribution orifice and mid-discharge orifice of Condition 8 are shown here in Figure 12. In Figure 12, the flow Because the distribution patterns of the flow field obtained by numerical calculation under velocity begins to increase after the water discharges from the reservoir through the orifices, and every condition are similar, only the velocity contours on the sections along midlines of the crest the maximum velocity reaches 39.67 m/s near end of the overflow damin surface. the high overflowing orifice and mid-discharge orifice the of Condition 8 are shown here Figure 12.Then, In Figure 12, thethe flowstilling velocity begins increase after the water discharges from the reservoir velocity flow enters basin toand forms submerged jets, where the waterthrough level rises locally. the orifices, and the maximum velocity reaches 39.67 m/sdistance near the end of the overflow dam other, surface.and a steady The multi-horizontal submerged jets maintain a certain in space from each Then, the high velocity flow enters the stilling basin and forms submerged jets, where the water level three-dimensional flow structure similar to a submerged hydraulic jump is developed with strong rises locally. The multi-horizontal submerged jets maintain a certain distance in space from each turbulenceother, and and shearing action. As a result, thestructure enormous energy carried by the high velocity flow is a steady three-dimensional flow similar to a submerged hydraulic jump is with strong and shearing As a result, the energy carried dissipated.developed Nevertheless, theturbulence kinetic energy of theaction. high-velocity jetsenormous cannot vanish until by the jets nearly the high velocity flow is dissipated. Nevertheless, the kinetic energy of the high-velocity jets cannot reach the middle of the stilling basin. vanish until the jets nearly reach the middle of the stilling basin.

Figure 12. Flow velocity contours of the midline sections of the crest overflowing orifice and

Figure 12.mid-discharge Flow velocity contours of the midline sections of the crest overflowing orifice and orifice. The unit is m/s. mid-discharge orifice. The unit is m/s. Figure 13 shows the instantaneous velocity vector distribution. Plenty of vortices of different sizes and strengths form and develop continuously around the high-velocity submerged jets in the Figure 13ofshows the instantaneous velocity vector distribution. Plenty zone the three-dimensional flow structure (submerged hydraulic jump) as a resultofofvortices the large of different flow velocityform gradient. sizes and strengths and develop continuously around the high-velocity submerged jets in the

Figure 12. Flow velocity contours of the midline sections of the crest overflowing orifice and mid-discharge orifice. The unit is m/s. Int. J. Environ. Res. Public Health 2016, 13, 594

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Figure 13 shows the instantaneous velocity vector distribution. Plenty of vortices of different sizes and strengths form and develop continuously around the high-velocity submerged jets in the zone of of thethe three-dimensional flow structure (submerged hydraulic jump) asas a result of of thethe large flow zone three-dimensional flow structure (submerged hydraulic jump) a result large velocity gradient. flow velocity gradient.

(a) 2016, 13, 594 Int. J. Environ. Res. Public Health

(b)

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Figure 13. and Flowthe velocity vector distribution in the energy dissipation area: (a) Midline of field the crest In structures, patterns of the vortex motion be found in an instantaneous flow Figure 13. Flow velocity vector distribution in thecan energy dissipation area: (a) Midline of the[51]. crest overflowing orifice; (b) Midline of the mid-discharge orifice. addition, the Q-criterion method relies on the derivatives overflowing orifice; (b) Midline of the mid-discharge orifice. of the velocity and is derived from the invariants of the velocity gradient tensor. The velocity gradient tensor A for incompressible flow can 3.2.2. Vortical Structures’ Characteristics be divided into two parts, S and W, respectively, for the symmetric and antisymmetric parts: 3.2.2. Vortical Structures’ Characteristics

When analyzing the characteristics of the vorticity field, the Eulerian method, such as the  ui ∂u j  field, 1  ∂vorticity 1  ∂u j ∂uEulerian When analyzing of =frequently the method,the such as the + utilized +  to the − i  , and visualize = S[50], Q-criterion developedthe by characteristics Hunt A etijal. identify vortical (11) ij + Wis ij ∂x j  and visualize the vortical xi  2  ∂to xi identify 2  ∂x j ∂utilized Q-criterion developed by Hunt et al. [50], is frequently structures, and the patterns of the vortex motion can be found in an instantaneous flow field [51]. where Sij is the strain rate tensor representing the irrotational motion, and Wij is the rotation tensor In addition, the Q-criterion method relies on the derivatives of the velocity and is derived from the representing the rotational motion. Q is the second invariant of Aij defined as: invariants of the velocity gradient tensor. The velocity gradient tensor A for incompressible flow can 1 be divided into two parts, S and W, respectively, the and antisymmetric parts: (12) Q = for Wij W Sij Sij , ij −symmetric 2 ¸ ¸ ˜ ˜ As a consequence, if the Q value1in some is 1positive, Bu j Bu j the Buirotational motion plays a Bui regions ` Wij “Figure 14 `displays`the visualization ´ , (11) ij “ Sij dominating role inAthose regions. 2 Bx j Bxi 2 Bxi Bx j results of the vortical

(

)

structures in the flow field of energy dissipation by the Q-criterion. To display the interaction of the more clearly the process of energythe dissipation, the contours theWQ value (Q > 0) of the wherevortices Sij is the strain rateintensor representing irrotational motion, of and ij is the rotation tensor midline sections of the crest overflowing orifice and mid-discharge orifice under Condition 8 are representing the rotational motion. Q is the second invariant of Aij defined as: presented in incremental time steps in Figure 15. At different discharge moments, the ˘ gradually along the overflow dam 1 `shear layers grow Q where “ W Sij , surface with increasing flow velocity, the vortical that are tubular in the horizontal(12) ij W ij ´ Sijstructures 2 axial direction (Z direction) begin to appear. At the end of the overflow dam surface and the beginning of the submerged the vortical structures shear layers to axial motion breakup.The As a consequence, if the Qjets, value in some regionsinisthe positive, the turn rotational plays a breakup becomes more evident when the submerged jets enter the stilling basin, and much more dominating role in those regions. Figure 14 displays the visualization results of the vortical structures structures different sizes strengths To aredisplay developed. It is seenof that the in the vortical flow field of energyofdissipation by theand Q-criterion. the interaction the vortices three-dimensional characteristics of the flow regime in the stilling basin are distinct, and the vortical more clearly in the process of energy dissipation, the contours of the Q value (Q > 0) of the midline structures in the flow field are unsteady, movable and intermittent under different discharge sections of the crest overflowing orifice and mid-discharge orifice under Condition 8 are presented in conditions. All of the visualization results show that the vortical structures are mainly located at the incremental time steps in Figure 15. beginning of the stilling basin, where the shearing motion of the flow is violent.

(a)

( b)

Figure 14. Instantaneous vortical structures in the energy dissipation area by Q = 10: (a) Condition 2;

Figure 14. Instantaneous vortical structures in the energy dissipation area by Q = 10: (a) Condition 2; (b) Condition 8. (b) Condition 8.


14 of 24


15 of 25

(a)

( b)

(c)

( d) Figure 15. Contours of the Q value (Q > 0) of the midline sections of the crest overflowing orifice and Figure 15. Contours of the Q value (Q > 0) of the midline sections of the crest overflowing orifice and mid-discharge orifice in incremental time steps: (a) t0 = 180 s; (b) t0 + 1 s; (c) t0 + 2 s; (d) t0 + 3 s. mid-discharge orifice in incremental time steps: (a) t0 = 180 s; (b) t0 + 1 s; (c) t0 + 2 s; (d) t0 + 3 s.

3.2.3. Correlation Analysis of Vorticity Fluctuating Characteristics and Acoustic Source At different discharge moments, the shear layers grow gradually along the overflow dam surface As the radiated acoustic where pressure the farstructures field is directly related to the vorticity fluctuation with increasing flow velocity, theinvortical that are tubular in the horizontal axial characteristics and vortex motions in the flow region according to previous theoretical deductions, direction (Z direction) begin to appear. At the end of the overflow dam surface and the beginning of the the dynamic of the vorticity in thelayers energy dissipation area are derived by numerical submerged jets,characteristics the vortical structures in the shear turn to axial breakup.The breakup becomes calculation this section to verify jets the deductions and estimate themuch location of the effective regionsofof more evidentinwhen the submerged enter the stilling basin, and more vortical structures acousticsizes source the LFN. 16 shows the vorticity contours of the midline sectionsofofthe the different andfor strengths areFigure developed. It is seen that the three-dimensional characteristics crest overflowing orifice and mid-discharge orifice of Condition 8. It is clearly observed that the flow regime in the stilling basin are distinct, and the vortical structures in the flow field are unsteady, distributions of the vorticity and velocitydischarge fields areconditions. approximately The vorticity intensity movable and intermittent under different All ofsimilar. the visualization results showis large in two regions, one located at the free surface of the overflow water, and the other one located that the vortical structures are mainly located at the beginning of the stilling basin, where the shearing at the strong shear motion of the flow is layers violent.around the submerged jets. Before the jets get into the stilling basin, the Z-component of the vorticity, representing the quantity of horizontal vortices in the shear layers, is 3.2.3. Correlation Analysis of Vorticity Fluctuating Acoustic Source maximum. When the horizontal vortices flow Characteristics into the stillingand basin, vertical vortices begin to develop, and the components of the vorticity in every direction tend toward uniformity. The As the radiated acoustic pressure in the far field is directly related to the vorticity fluctuation distributions of the vorticity field correspond to the identification results of the vortical structures in characteristics and vortex motions in the flow region according to previous theoretical deductions, Figures 14 and 15. the dynamic characteristics of the vorticity in the energy dissipation area are derived by numerical calculation in this section to verify the deductions and estimate the location of the effective regions of acoustic source for the LFN. Figure 16 shows the vorticity contours of the midline sections of the crest overflowing orifice and mid-discharge orifice of Condition 8. It is clearly observed that the distributions of the vorticity and velocity fields are approximately similar. The vorticity intensity is large in two regions, one located at the free surface of the overflow water, and the other one located


15 of 24

at the strong shear layers around the submerged jets. Before the jets get into the stilling basin, the Z-component of the vorticity, representing the quantity of horizontal vortices in the shear layers, is maximum. When the horizontal vortices flow into the stilling basin, vertical vortices begin to develop, and the components of the vorticity in every direction tend toward uniformity. The distributions of the vorticity field correspond to the identification results of the vortical structures in Figures 1416and 15. Int. J. Environ. Res. Public Health 2016, 13, 594 of 25 Int. J. Environ. Res. Public Health 2016, 13, 594

16 of 25

(a) (a)

( b) Figure 16. Vorticity contours in the energy dissipation area: (a) Midline of the crest overflowing (b) area: Figure 16. Vorticity contours in the energy dissipation (a) Midline of the crest overflowing orifice; orifice; (b) Midline of the mid-discharge orifice. The unit is s−1. ´1 . (b) Midline of the mid-discharge orifice. The unit is s Figure 16. Vorticity contours in the energy dissipation area: (a) Midline of the crest overflowing −1. orifice; (b) Midline of the mid-discharge The unit is To analyze the vorticity fluctuation orifice. characteristics ins the flow field, several monitoring points

have been setthe on vorticity the midline sections of the crest overflowing orifice mid-discharge orifice in the To analyze fluctuation characteristics in the flowand field, several monitoring points To analyze the vorticity fluctuation characteristics in the flow field, several monitoring points numerical models, as shownsections in Figure 17. Specifically, S1 and M1 are setand at the free surface oforifice the in havehave beenbeen set set on the midline of the crest overflowing orifice mid-discharge on the midline sections of the crest overflowing orifice and mid-discharge orifice in the overflow water; S2 as andshown M2 areinset under17. theSpecifically, high-velocityS1overflow water;set and the rest of the of the numerical models, Figure and at the free of surface numerical models, as shown in Figure 17. Specifically, S1 and M1 areM1 setare at the free surface the measuring points are set in the energy dissipation region of the submerged jets. the overflow S2 and andM2 M2are areset setunder underthe thehigh-velocity high-velocity overflow water; the of rest overflow water; water; S2 overflow water; and and the rest theof the measuring points areare setset in in thethe energy regionof ofthe thesubmerged submerged jets. measuring points energydissipation dissipation region jets.

Figure 17. Vorticity monitoring points on the midline sections of the crest overflowing orifice and mid-discharge orifice. Figure 17. Vorticity monitoring points on the midline sections of the crest overflowing orifice and Figure 17. Vorticity monitoring points on the midline sections of the crest overflowing orifice and mid-discharge orifice.values, RMS values and dominant frequencies of the vorticity fluctuation of The time-averaged

mid-discharge orifice. every monitoring point under all conditions were computed according to the transient monitoring The time-averaged values, RMS values and dominant frequencies of the vorticity fluctuation of data obtained through the numerical calculation. The results for Condition 8 are listed in Table 4. It is every monitoring point under all conditions were computed according to the transient monitoring shown that, for the monitoring points located at the free surface of overflow water (S1, M1), the data obtained through the numerical calculation. The results for Condition 8 are listed in Table 4. It is shown that, for the monitoring points located at the free surface of overflow water (S1, M1), the


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The time-averaged values, RMS values and dominant frequencies of the vorticity fluctuation of every monitoring point under all conditions were computed according to the transient monitoring Int. J. Environ. Res.through Public Health 13, 594 17 of 25 data obtained the2016, numerical calculation. The results for Condition 8 are listed in Table 4. It is shown that, for the monitoring points located at the free surface of overflow water (S1, M1), time-averaged values of the fluctuation are larger, whereas the RMS values are smaller, and the time-averaged values of vorticity the vorticity fluctuation are larger, whereas the RMS values are smaller, the dominant frequency does not exist. The points located at the strong shear layers around the and the dominant frequency does not exist. The points located at the strong shear layers around the high-velocity submerged jets (S4, S5, S7, M4, M6, and M8) have the vorticity fluctuation with larger high-velocity submerged jets (S4, S5, S7, M4, M6, and M8) have the vorticity fluctuation with larger RMS values values and and dominant dominant frequencies frequencies of of 0–2 0–2 Hz. Hz. RMS Table 4. 4. Analyses Analyses of of the the vorticity vorticity monitoring monitoring data. data. Table Midline Section of Crest Overflowing Orifice Midline Section of Crest Overflowing Orifice RMS Dominant Monitoring Time-Averaged RMS Dominant Value Frequency Monitoring Time-Averaged −1) Point Value (s Frequency Value ´1 − 1) (Hz) (s Point Value (s ) (Hz) (s´1 ) S1 15.143 0.663 / S1 15.143 0.663 / S2 3.022 0.031 / S2 3.022 0.031 / S3S3 1.828 0.812 // 1.828 0.812 S4S4 18.737 1.149 1.000 18.737 1.149 1.000 S5S5 11.686 1.599 0.960 11.686 1.599 0.960 1.518 0.680 S6S6 1.518 0.680 // 8.948 1.839 1.020 S7S7 8.948 1.839 1.020 2.036 1.056 S8S8 2.036 1.056 //

Midline Section of Mid-Discharge Orifice RMS Dominant Monitoring Time-Averaged RMS Dominant Value Frequency Monitoring Time-Averaged Point Value (s−1) Value−1 Frequency (Hz) (s ) Point Value (s´1 ) (Hz) (s´1 ) M1 30.021 1.656 / M1 30.021 1.656 / M2 7.986 0.394 / M2 7.986 0.394 / M3 0.654 0.243 / M3 0.654 0.243 / M4 20.610 2.530 1.060 M4 20.610 2.530 1.060 M5 1.630 0.665 M5 1.630 0.665 / / M6 10.589 1.162 0.875 M6 10.589 1.162 0.875 M7 1.791 0.967 / / M7 1.791 0.967 M8 6.045 1.812 0.425 M8 6.045 1.812 0.425 Midline Section of Mid-Discharge Orifice

the vorticity vorticity fluctuation fluctuation Contrastive analyses were conducted between the monitoring data of the the prototype prototype observation observation data of the the LFN LFN under under the the same same condition. condition. Figure Figure 18 18 compares compares the the and the time-history curves curvesandand autocorrelation PSD between monitoring pointprototype S5 andobservation prototype time-history autocorrelation PSD between monitoring point S5 and observation point T8 under 8. As a consequence, the vorticitydata fluctuation from the point T8 under Condition 8. Condition As a consequence, the vorticity fluctuation from thedata strong shear strong(S4, shear (S4, S5,and S7, M8) M4, have M6, and M8) have approximately the same periodic pattern with layers S5,layers S7, M4, M6, approximately the same periodic pattern with the prototype the prototype observation observation data of LFN. data of LFN. 1.5

LFN

LFN Sx (f)

Amplitude (Pa)

5

0

-5

0

10

20

30

40

1 0.5 0

50

0

2

4

6

8

10

5

Vorticity fluctuation Sy (f)

Amplitude (s -1 )

6

Vorticity fluctuation

0

4 2

-5 0

0

10

20 30 Time (s)

40

50

0

2

(a)

4 6 Frequency (Hz)

8

10

(b)

Figure 18. Comparisons between the vorticity monitoring point S5 and the prototype observation Figure 18. Comparisons between the vorticity monitoring point S5 and the prototype observation point point T8: (a) Time-history curve; (b) Autocorrelation PSD. T8: (a) Time-history curve; (b) Autocorrelation PSD.

Additionally, for clearly quantifying the correlation between the vorticity fluctuation and LFN, the spectral correlation coefficient ρF [52] is defined as: n

 F (k )F (k ) x

ρF =

k =1 n

 k =1

Fx2

y

,

n

(k ) k =1

Fy2

(k )

(13)


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Additionally, for clearly quantifying the correlation between the vorticity fluctuation and LFN, the spectral correlation coefficient ρF [52] is defined as: n ř

Fx pkq Fy pkq , ρ F “ d k “1 n n ř ř Fy2 pkq Fx2 pkq Int. J. Environ. Res. Public Health 2016, 13, 594

k “1

(13)

k“1

18 of 25

where Fx and Fy represent the module of the Fourier spectrum of the vorticity fluctuation and where Fx and Fy represent the module of the Fourier spectrum of the vorticity fluctuation and the the observed observedLFN, LFN,respectively. respectively.Figure Figure displays statistical results spectral correlation 1919displays thethe statistical results of of thethe spectral correlation coefficients between every monitoring point of the vorticity fluctuation and the prototype observation coefficients between every monitoring point of the vorticity fluctuation and the prototype point T8 underpoint all conditions. is seen that values points inpoints the strong F at the ρF at the monitoring in observation T8 under allItconditions. It the is seen that of theρvalues ofmonitoring shear S5,layers S7, M4, M8)M6, areand relatively which can be up to average thelayers strong(S4, shear (S4,M6, S5, and S7, M4, M8) arelarger, relatively larger, which can0.762. be upThe to 0.762. values ρF of the monitoring points in the strong the layers crest overflowing orifice and the monitoring points shear in the layers strongof shear of the crest overflowing Theof average values of ρF of the orifice and the mid-discharge orifice are 0.681 and 0.601, respectively. mid-discharge orifice are 0.681 and 0.601, respectively.

1 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0

ρF

ρF

1 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0 S1 S2 S3 S4 S5

Condition 8 Condition 7 Condition 6 Condition 5 Condition 4 Condition 3

S6

Observation point

S7

S8

(a)

M1 M2 M3 M4 M5 M6 M7 M8

Condition 8 Condition 7 Condition 6 Condition 5 Condition 4 Condition 3 Condition 2

Observation point

( b)

Figure 19. Statistical distribution of the spectral correlation coefficients between the vorticity

Figure 19. Statistical distribution of the spectral correlation coefficients between the vorticity monitoring points and the prototype observation point: (a) Midline of the crest overflowing orifice; monitoring points and the prototype observation point: (a) Midline of the crest overflowing orifice; (b) Midline of the mid-discharge orifice. (b) Midline of the mid-discharge orifice.

The analysis results of the vorticity fluctuating characteristics above verify the close correlation between the vorticity in the fluctuating strong shearcharacteristics layers around the high-velocity jets The analysis resultsfluctuation of the vorticity above verify thesubmerged close correlation and the flow-induced LFN propagated to the far field. In addition, combined with the identification between the vorticity fluctuation in the strong shear layers around the high-velocity submerged jets of the vorticalLFN structures above,to it the is concluded during the energy dissipation process of andresults the flow-induced propagated far field. that, In addition, combined with the identification the submerged jets, a large number of turbulent low-frequency large-scale vortical structures come of results of the vortical structures above, it is concluded that, during the energy dissipation process existence in the strong shear layers around the submerged jets because of the large velocity the into submerged jets, a large number of turbulent low-frequency large-scale vortical structures come into gradient, and the LFN is generated in the intensive interactions of the vortical structures. Therefore, existence in the strong shear layers around the submerged jets because of the large velocity gradient, the strong shear layers around the submerged jets are judged as the main regions of acoustic source and the LFN is generated in the intensive interactions of the vortical structures. Therefore, the strong for the LFN.

shear layers around the submerged jets are judged as the main regions of acoustic source for the LFN. 3.3. Verification of the Mathematical Prediction Model of LFN

3.3. Verification of the Mathematical Prediction Model of LFN According to the mathematical prediction model of LFN (Equations (4) and (5)) built

According to prediction model simulation of LFN (Equations and (5))acoustic built theoretically theoretically in the the mathematical previous section, the numerical results of(4) the main source in the previous section, the numerical simulation results of the main acoustic source regions in the flow regions in the flow field are put into the prediction model to calculate the LFN intensity of prototype fieldobservation are put into the T1, prediction to at calculate the dissipation LFN intensity of prototype observationThe point point which ismodel located the energy region under all conditions. T1, comparisons which is located at the dissipation region underobservation all conditions. The comparisons between between theenergy prediction results and prototype results are listed in Table 5. the prediction results and prototype observation results are listed in Table 5.


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Table 5. Comparisons of results from the prediction model and prototype observation of LFN *. Prototype Observation Results

Condition 2 3 4 5 6 7 8

Prediction Model Results

LFN (Pa)

SPL (dB)

Frequency (Hz)

LFN (Pa)

SPL (dB)

Frequency (Hz)

8.57 9.49 10.72 10.38 10.54 11.87 13.08

112.64 113.53 114.59 114.30 114.44 115.47 116.31

1.117 1.022 0.978 0.899 0.833 0.894 1.178

8.84 9.99 11.54 10.62 11.08 12.93 13.46

112.91 113.97 115.23 114.50 114.87 116.21 116.56

1.150 1.125 0.933 0.895 0.975 1.261 1.250

* The values of the LFN intensity and SPL in the table are the RMS values.

The comparison results indicate that the LFN amplitudes, dominant frequencies and variation laws predicted theoretically are approximately consistent with those of the prototype observation. The predicted amplitudes gradually increase with increasing flow rate, and the dominant frequencies of the LFN predicted are concentrated between 0 Hz and 2 Hz. Depending on the prediction results of T1 and the SPL attenuation rate in Table 2, the LFN amplitudes of several observation points (T2, T3, T6, T9, T15, T18, and T22) downstream were estimated. Figure 20 compares the normalized PSD of T1 and the LFN amplitudes along the downstream between the observed and predicted LFN data under all conditions. It is shown that the variation tendencies of the LFN amplitudes of the observed and predicted LFN are nearly the same, while the predicted LFN amplitudes of some points are a little larger than the observed data. In order to evaluate the proposed prediction model, the power spectral entropy, derived from Shannon entropy [53] as a common method [54,55], is introduced here to quantify and compare the uncertainties and complexities of PSD estimation between the observed and predicted LFN data. The power spectral entropy is defined as [54,55]: HF “ ´

fÿ “20

p p f q log pp p f qq,

(14)

f “0.1

O where p p f q “ s p f q

f“ ř20

s p f q , s(f ) is the spectral component, the base of the logarithm is two, and

f “0.1

the unit of HF is bits. In current work, because the infrasound microphone’ minimum measuring threshold is 0.1 Hz and the on-site LFN energy is generally below 20 Hz, the power spectral entropy is estimated based on the PSD within 0.1–20 Hz in Equation (14). In essence, the greater the spectral entropy, the more irregular the PSD distribution. The power spectral entropy between the observed and predicted LFN data of T1 under all conditions are shown in Figure 21. It is seen that the power spectral entropy of the observed and predicted LFN data are very close, and the power spectral entropy of the observed LFN are always a little larger than those of the predicted LFN. The average power spectral entropy of the observed and predicted LFN data are 2.632 and 2.540, respectively, and the difference in the average values is approximately 0.0923. A comparison of the results reveals that the PSD between the observed and predicted LFN data has uncertainties and complexities of nearly the same degree.


19 of 24


20 of 25

(a)

(b)

(c)

(d)

Figure 20. Cont.


20 of 24


21 of 25

(e)

( f)

( g) Figure 20. Comparisons of the normalized PSD of T1 and the LFN amplitudes along the downstream

Figure 20. Comparisons of the normalized PSD of T1 and the LFN amplitudes along the downstream between the observed and predicted data: (a) Condition 2; (b) Condition 3; (c) Condition 4; (d) between the observed and predicted data:7; (g) (a)Condition Condition Condition 5; (e) Condition 6; (f) Condition 8. 2; (b) Condition 3; (c) Condition 4; (d) Condition 5; (e) Condition 6; (f) Condition 7; (g) Condition 8.

Moreover, the spectral correlation coefficients ρF between the observed and predicted LFN data of T1 were calculated through Equation (13). As observed in Figure 22, the values of ρF under all conditions are relatively large, at approximately 0.645–0.717. Thus, according to the analyses of the uncertainties of PSD and the spectral correlation coefficients, it can be seen that the mathematical prediction model is feasible and reasonable for preliminary estimation of the LFN intensity induced by energy dissipation through the submerged jets of a high dam.

Int. J. Environ. Res. Public Health 2016, 13, 594 Int. J. Environ. Res. Public Health 2016, 13, 594 Int. J. Environ. Res. Public Health 2016, 13, 594

21 of 24 22 of 25 22 of 25

3.2 3.2

Power Powerspectral spectralentropy entropy

3.0 3.0 The average difference=0.0923 The average difference=0.0923

2.8 2.8 2.6 2.6 2.4 2.4

Observed Observed Average value (Observed) Average value (Observed) Predicted Predicted Average value (Predicted) Average value (Predicted)

2.2 2.2 2.0 2.0 1.8 1.8

22

33

44 55 66 Condition Number Condition Number

77

88

Figure 21. Comparisons of the power spectral entropy between the observed and predicted LFN Figure 21. 21. Comparisons Comparisonsofofthe the power spectral entropy between the observed and predicted LFN Figure power spectral entropy between the observed and predicted LFN data. data. data.

1.0 1.0 0.9 0.9

ρρ FF

0.8 0.8 0.7 0.7 0.6 0.6 0.5 0.5 0.4 0.4 0.3 0.3 0.2 0.2 0.1 0.1 0.0 0.0

22

33

44 55 Number 66 Condition Condition Number

77

88

Figure 22. Spectral correlation coefficients between the observed and predicted LFN data. Figure 22. Spectral correlation coefficients coefficients between between the the observed observed and and predicted predicted LFN LFN data. data.

4. Conclusions Conclusions 4. 4. Conclusions In this this study, study, extensive extensive prototype prototype observations observations and and analyses analyses of of low low frequency frequency noise noise (LFN) (LFN) In In this study, extensive prototype observations and analyses of low frequency noise (LFN) induced induced by by the the process process of energy energy dissipation dissipation through through the the submerged submerged jets jets of aa high high dam dam are are carried carried induced by the process of energyofdissipation through the submerged jets of a high of dam are carried out. It is out. It is found that the LFN amplitude reaches the maximum value near the dam area, which is out. It that is found that amplitude the LFN amplitude reaches the maximum neararea, the dam whichthe is found the LFN reaches the maximum value nearvalue the dam whicharea, is below below the the hearing hearing threshold threshold and and the the LFN LFN limits. limits. In In general, general, the the observed LFN LFN has no no directly directly below hearing threshold and the LFN limits. In general, the observed LFNobserved has no directlyhas negative effect negative effect on local residents’ health. The sound pressure level (SPL) attenuation coefficient of negative effect on local residents’ health. The sound pressure level (SPL) attenuation coefficient of on local residents’ health. The sound pressure level (SPL) attenuation coefficient of LFN decreases LFN decreases gradually with increasing distance to the dam area, reaching maximum in the vapor LFN decreases gradually with increasing distance the dam area, reaching in the vapor gradually with increasing distance to the dam area, to reaching maximum in the maximum vapor atomization area atomization area area near near the the overflow overflow dam. dam. The The flow-induced flow-induced LFN LFN intensity intensity has has aa close close relationship relationship atomization near the overflow dam. The flow-induced LFN intensity has a close relationship with the discharge with the the discharge discharge operation operation schemes schemes and and flow flow regimes regimes in in the the stilling stilling basin, basin, and and maintaining maintaining with operation schemes and flow regimes in the stilling basin, and maintaining uniform and smooth flow uniform and smooth flow patterns in the stilling basin using the joint discharge operation scheme uniform in and the discharge stilling basin using scheme the jointhas discharge operation scheme patterns thesmooth stilling flow basinpatterns using theinjoint operation the benefit of reducing the has the the benefit benefit of of reducing reducing the the LFN LFN intensity. intensity. has LFN intensity. The results results from from numerical numerical simulation simulation of of the the flow flow field field characteristics characteristics of of energy energy dissipation dissipation by by The The results from numerical simulation of the flow field characteristics of energy dissipation by the the submerged submerged jets jets indicate indicate that that the the vortical vortical structures structures are are mainly mainly located located at at the the beginning beginning of of the the the submerged jets indicate that the vortical structures are mainly located at the beginning of the stilling stilling basin where the shearing motion of the flow is violent. The results from correlation analysis stillingwhere basinthe where the shearing of the is violent. The results from correlation analysis basin shearing motion motion of the flow is flow violent. The results from correlation analysis of the of the vorticity fluctuation characteristics and acoustic source indicate that the vorticity fluctuation of the vorticity fluctuation characteristics and acoustic indicate that the vorticity fluctuation vorticity fluctuation characteristics and acoustic sourcesource indicate that the vorticity fluctuation from from the the strong strong shear shear layers layers around around the the high-velocity high-velocity submerged submerged jets jets have have larger larger RMS RMS values, values, where where from the strong shear layers around the high-velocity submerged jets have larger RMS values, where the the vorticity vorticity fluctuation fluctuation data are are highly highly correlated correlated to the the on-site LFN LFN data. data. Besides, Besides, the the strong shear shear the vorticity fluctuation data data are highly correlated to theto on-siteon-site LFN data. Besides, the strong strong shear layers layers are the main regions of acoustic source for the LFN. The mathematical prediction model of the layers are the main regions of acoustic source for the LFN. The mathematical prediction model of the


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are the main regions of acoustic source for the LFN. The mathematical prediction model of the LFN intensity for energy dissipation by the submerged jets is established by combining the vortex sound theory and turbulent flow model, and the model is verified by the prototype observations. The intensity and dominant frequency of the predicted and observed LFN data show satisfactory agreement. This study for the first time provides the reference data, theoretical foundation and prediction method for addressing the environmental problem of LFN induced by energy dissipating submerged jets during flood discharge from a high dam. In further studies, the specific and scientific discharge operation schemes for reducing the LFN intensity around the station should be built using the current models, which will provide an operation guide and improvements for the station in engineering practices. The theoretical and numerical methods adopted in this study should be applied to other similar engineering projects on LFN issues for further verification of the universality of the prediction model and optimization of the model parameters. Moreover, further problems, such as the propagation and attenuation patterns of LFN and the effects of the water surface wave on the LFN energy, should be studied systematically. Acknowledgments: This work was supported by the National Natural Science Foundation of China under Grant No. 51379140 and 51579173. Author Contributions: Jijian Lian conceived the study and contributed to the design of the study. Wenjiao Zhang completed the modeling and numerical analysis works and prepared the manuscript. Qizhong Guo conducted the analysis and contributed to presenting the methods. Fang Liu and Wenjiao Zhang contributed to the prototype observation data collection and analyses. All authors reviewed and approved the final manuscript. Conflicts of Interest: The authors declare no conflict of interest.

Abbreviations The following abbreviations are used in this manuscript: LFN SPL PSD AR model FPE Q GCI

Low frequency noise Sound pressure level Power spectral density Autoregressive model Final prediction error Total discharge through the dam orifices (m3 /s) Grid Convergence Index

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