Valve noise at high pressure ratios

Erika Quaranta 1 and Malcolm Smith 2 ISVR Consulting University of Southampton Southampton, SO17 1BJ, UK

ABSTRACT

When high pressure air expands through an orifice it can be an intense noise source, which may be hazardous for nearby personnel if it occurs in an unexpected or uncontrolled way. This paper describes a set of measurements that were carried out to validate and calibrate a well-known semi-empirical prediction method. A number of valve mockups were tested over a range of mass flow rates with pressure ratios up to 11 Bar, so that the model could be used with confidence to extrapolate to higher pressures, larger valve sizes and higher mass flows.

Interpretation of the measured noise data is carried out using an isentropic analysis of the flow, assuming choked conditions in the orifice to infer a jet Mach number and mass flow rate for each test condition. Based on this inferred flow data the sound power scaled as expected with 8th power of jet Mach number.. It is also shown that for all valves the sound power varied as 1.5th power of mass flow rate in the higher range, which is in reasonable agreement with the law implicit in the semi-empirical model, and provided a good basis for extrapolating to larger devices.

1. INTRODUCTION

The noise of high pressure air expanding through an orifice, as occurs in blow-off and pressure release valves, can be an intense source of jet noise, which may be hazardous for nearby personnel.

Noise levels may be predicted using the valve noise model detailed by H. Heller and P. Franken in the reference textbook edited by Beranek [1], which describes three flow and noise source regimes as follows:

𝑀 𝑗𝑒𝑡 < 1 → turbulent mixing noise;

1 < 𝑀 𝑗𝑒𝑡 < 1.5 → turbulent mixing noise + shock noise;

𝑀 𝑗𝑒𝑡 >1.5 → shock noise.

𝑀 𝑗𝑒𝑡 is defined as the Mach number at the valve exit, depending on the pressure ratio (PR) of the total over the ambient pressure 𝑃 𝑡𝑜𝑡 𝑃 𝑎𝑚𝑏 Τ and ratio of specific heats γ, which is evaluated from the isentropic relation

1 E.Quaranta@soton.ac.uk 2 mgs@isvr.soton.ac.uk

𝛾−1

𝑀 𝑗𝑒𝑡 = ඨ 2 𝛾−1 ൥൬ 𝑃 𝑡𝑜𝑡

𝛾

−1൩ (1)

൰

𝑃 𝑎𝑚𝑏

In the first regime 𝑀 𝑗𝑒𝑡 < 1, when the turbulent mixing is the prevalent noise mechanism, the ratio

2 is proportional to 𝑀 𝑗𝑒𝑡

5 . This is be- cause the mass flow rate 𝑚 ሶ is linearly dependent on jet velocity 𝑢 𝑗𝑒𝑡 , so that 𝑊 𝑚𝑒𝑐 varies as 𝑢 𝑗𝑒𝑡

1

of acoustic power to mechanical stream power 𝑊 𝑚𝑒𝑐 =

2 𝑚 ሶ𝑢 𝑗𝑒𝑡

3 , whereas the acoustic power of turbulent mixing noise increases as the 8th power of 𝑢 𝑗𝑒𝑡 . The constant of proportionality depends on the ratio of jet density and temperature to ambient values. For ambient conditions the sound power level is

5 ൯+ 𝐿 𝑚𝑒𝑐 (2)

𝐿 𝑚𝑖𝑥 ሺdBሻ= 10 log ൫5e 5 𝑀 𝑗𝑒𝑡

𝑊 𝑚𝑒𝑐 𝑊 𝑟𝑒𝑓 ൰ and 𝑊 𝑟𝑒𝑓 is 1e-12 W.

where 𝐿 𝑚𝑒𝑐 = 10 log ൬

In the third regime 𝑀 𝑗𝑒𝑡 >1.5 the shock noise is prevalent. The ratio of the overall sound power radiated to the mechanical stream power in dB is linear dependent on PR, but the slope depends on the 𝑀 𝑗𝑒𝑡 range, being steeper for 𝑀 𝑗𝑒𝑡 < 2.5 and much less steep for 𝑀 𝑗𝑒𝑡 > 2.5 .

The laws derived from the semi-empirical model are

𝐿 𝑠ℎ𝑜𝑐𝑘 ሺdBሻ= −40 + 37 log ൬ PR

2 ൰+ 𝐿 𝑚𝑒𝑐 if PR < 2.5 (3)

𝐿 𝑠ℎ𝑜𝑐𝑘 ሺdBሻ= −26 + 7 log ൬ PR

2.5 ൰ + 𝐿 𝑚𝑒𝑐 if PR > 2.5 (4)

where 𝐿 𝑚𝑒𝑐 is evaluated for 𝑢 𝑗𝑒𝑡 equal to the speed of sound.

However, when 1 < 𝑀 𝑗𝑒𝑡 < 1.5 both noise mechanisms must be included, and the total sound power is the resultant of the sum of the two contributions.

Whilst the noise model is well established for some applications, for the particular industrial noise problem under consideration there was a need for the model to be calibrated so it could be used with confidence to extrapolate to unusually high pressure ratios and flow rates.

2. METHODOLOGY FOR TESTING

2.1. Test rig

The flow noise rig was installed in the large anechoic chamber at the Institute of Sound and Vibration Research (ISVR). The chamber has a total volume of 295 m 3 and it is certified to be fully anechoic above 90 Hz. The ambient noise level inside the chamber is well below the noise floor of the instru- mentation. During the measurements all doors of the chamber were fully closed.

The valves were securely attached to the end of a 1m long instrumented duct placed in the centre of the chamber. The other end of this duct was attached to a 15m long thick-walled rubber hose which provided the connection to test facility’s 15 bar pressure reservoir through a remotely controllable valve.

A photograph of the test arrangement is shown in Figure 1, indicating how the duct and test valve were supported and the positioning of the microphones.

Figure 1: Test arrangement.

2.2. Acoustic Instrumentation and analysis

The main noise data were recorded using 5 Brüel & Kjær Type 4189 1/2 ” microphones. Four mi- crophones were placed 3 m away from the centre of the valves at polar angular positions of 10°, 30°, 60° and 90°. A microphone at 0° was not possible due to the jet of air. The 5th microphone was placed opposite the 90° microphone position at an azimuthal angle of 180° to provide a symmetry comparison.

The microphones were all more than 1 metre away from the wedges of the anechoic chamber and also had windshields installed. For tests with a 90° bend in the valve the microphone array was moved to new equivalent positions since rotating the test rig was difficult.

The microphones were connected to a Brüel & Kjær Pulse system, which was connected to a laptop running Brüel & Kjær Labshop analyser software. A microphone calibrator was placed on each of the microphones in order to verify and calibrate the measurement system. The analyser was used to acquire both 4 Hz constant bandwidth autospectra and 1/3 Octave band data based on 30s long re- cordings for each microphone and test case.

The spectra are converted to sound pressure levels (SPL) in dB using:

SPL = 10 log ቆ 𝑝 2

2 ቇ (5)

𝑝 𝑟𝑒𝑓

where 𝑝 𝑟𝑒𝑓 = 20e-6 Pa.

The microphones were calibrated at 1 kHz to 94 dB before the testing began. An RS temperature sensor was used to record the temperature inside the nozzle. The pressure sensors were used to meas- ure the static and total pressure for each pressure ratio inside the nozzle.

Overall sound power levels radiated into the downstream hemisphere have been evaluated as

4

2

𝐿 𝑤 = 10 log ൭෍ 𝑝 𝑖

𝐴 𝑖 ൱ (6)

2

𝑝 𝑟𝑒𝑓

𝑖=1

where the index i is over microphones 1 to 4 and 𝐴 𝑖 is the area of the spherical sector of radius R =3m relative to the microphone placed at the angle 𝛼 𝑖 , i.e.

𝐴 𝑖 = 2𝜋𝑅 2 ሾcosሺ𝛼 𝑖 − 𝛿ሻ−cosሺ𝛼 𝑖 + 𝛿ሻሿ

where 2δ is the angle between two microphones, thus δ = 15°.

2.3. Test items

Tests were conducted on 6 valves, which were simplified mockups of actual production valves. The valves were chosen to have a range of sizes and both straight through and L-ported in order to ver- ify and extend the valve model. The main characteristics of the components tested were:

Valve 1 : A straight through valve with a 12.5 mm bore and an expansion to 20.9 mm outlet.

Valve 2 : A straight through valve which was made from a pipe with internal diameter of 20.9 mm and a contraction to 13.5 mm screwed on the outlet.

Valve 3 : L-ported 3 way valve represented as a uniform 26.6 mm diameter pipe with a radiused elbow and a flange at the end.

Valve 3a : A straight-through version of Valve 3.

Valve 5 : L-ported valve of uniform diameter throughout, manufactured from a 48.7 mm internal diameter pipe, with a flange at the outlet.

Valve 6 : L-ported valve of uniform diameter throughout, manufactured from a 54 mm internal diameter pipe, with a flange at the outlet.

3. ANALYSIS OF RESULTS

For each valve, the SPL was acquired at various values of total pressure 𝑃 𝑡𝑜𝑡 , starting from a sub- sonic jet flow condition, and gradually increasing to achieve over 10 Bar. However, for valve 5 and 6, because of the higher mass flow rate, the maximum total pressure achieved was 8 and 6.7 Bar re- spectively.

In Table 1, estimated values of mass flow rate 𝑚ሶ 𝑒𝑥𝑖𝑡 and jet Mach number 𝑀 𝑗𝑒𝑡 are reported, for constant 𝑇 𝑡𝑜𝑡 = 300𝐾. They can only be accurately evaluated for choked conditions, i.e. 𝑀 𝑣𝑎𝑙𝑣𝑒 =1

𝛾 𝛾−1 , when the exit flow conditions are known by isentropic flow equations [2], and from Eq. 1 as

𝛾+1

corresponding to pressure ratio greater than ቀ

2 ቁ

𝛾 𝛾−1 𝑃 𝑒𝑥𝑖𝑡 = 1.893 𝑃 𝑒𝑥𝑖𝑡 (7)

𝛾+1

𝑃 𝑡𝑜𝑡 = ቀ

2 ቁ

𝑇 𝑡𝑜𝑡 = 𝑇൬1 + 𝛾−1

2 ൰= 1.2 𝑇 (8)

2 𝑀 𝑣𝑎𝑙𝑣𝑒

𝑢 𝑒𝑥𝑖𝑡 = 𝑐= ඥ𝛾𝑅𝑇 (9)

𝜌= 𝑃

𝛾𝑅𝑇 (10)

𝑚ሶ 𝑒𝑥𝑖𝑡 = 𝜌𝑢 𝑒𝑥𝑖𝑡 𝐴= 0.04 𝐴 𝑃 𝑡𝑜𝑡

(11)

ඥ𝑇 𝑡𝑜𝑡

where

𝑃 𝑒𝑥𝑖𝑡 = pressure at the valve exit;

𝑇 𝑡𝑜𝑡 = total temperature in the tank;

𝑇 = static temperature;

𝜌 = density;

𝑢 𝑒𝑥𝑖𝑡 = velocity at the valve exit which is equivalent to the speed of sound c ;

𝐴= throttle area;

𝛾= 1.4; 𝑅= 287 J/kg : gas constants for air.

Results of the overall sound power levels for each test condition are also presented in Table 1.

Table 1: Test matrix with calculated mass flow rate, jet Mach number and overall sound power

level.

nozzle diameter D

𝑷 𝒕𝒐𝒕 𝑷 𝒂𝒎𝒃

(kg/s) 𝑴 𝒋𝒆𝒕 Sound power

𝒎ሶ 𝒆𝒙𝒊𝒕

Valve No.

(dB re 1pW)

(mm)

1.39 - 0.70 111.9 1.79 0.050 0.95 115.8 2.45 0.069 1.20 122.0 4.97 0.140 1.70 111.4 8.74 0.246 2.07 128.3 11.47 0.325 2.24 134.0

1 12.5

1.53 - 0.81 103.8 1.85 0.061 0.98 110.3 2.26 0.075 1.14 115.9 5.97 0.197 1.82 134.0 11.03 0.364 2.22 137.3

2 13.5

1.61 - 0.85 121.1 2.09 0.269 1.08 126.4 3.96 0.508 1.55 137.6 5.31 0.681 1.75 142.0 11.07 1.420 2.22 147.0

3 26.6

1.42 - 0.73 108.3 1.96 0.251 1.03 119.0 4.39 0.564 1.62 141.0 5.65 0.725 1.79 141.4 10.38 1.332 2.18 144.9

3a 26.6

1.58 - 0.84 127.5 2.25 0.971 1.14 134.5 3.81 1.647 1.53 143.6 5.99 2.583 1.83 149.9 8.04 3.470 2.02 151.7

5 48.7

1.52 - 0.80 127.1 2.14 1.135 1.10 134.4 3.72 1.978 1.51 144.6 4.30 2.284 1.61 146.0 5.37 2.851 1.76 150.1 6.68 3.546 1.90 151.6

6 54

Some typical spectra for the microphone placed at 30° are presented in Figure 2. The peak fre- quency of subsonic jet noise would increase with velocity, as 𝑓 𝑝𝑒𝑎𝑘 = ሺ𝑆 𝑢 𝑒𝑥𝑖𝑡 ሻ/𝐷 based on the Strouhal number (non-dimensional frequency) 𝑆 = 0.2, while the shock noise spectrum for choked valves peaks at lower frequencies, as exit velocity does not increase over the speed of sound and the Strouhal number decreases with PR as reported in [1]. This is broadly confirmed by the experimental spectra, even if there is no significant shift in frequency especially for the higher PRs.

Figure 2: Sound spectra for the microphone at 30°.

4. COMPARISON WITH THE VALVE MODEL

The sound power levels have been compared with predicted values evaluated using the semi-empiri- cal model proposed in Beranek [1] and explained in detail in the Section 1. Results were plotted versus PR (Figure 3), 𝑀 𝑗𝑒𝑡 (Figure 4) and 𝑚ሶ 𝑒𝑥𝑖𝑡 (Figure 5). The predicted levels were evaluated using different noise data laws depending on 𝑀 𝑗𝑒𝑡 , therefore the lines have different slopes depending on the 𝑀 𝑗𝑒𝑡 range.

Generally, noise level increases with the valve size, but results can be grouped in 3 sets: a) valve 1 and 2, b) valve 3 and 3a, c) valve 5 and 6. Variations within each set are negligible, suggesting that the global valve size is the overall dominant parameter, while detailed valve design does not signifi- cantly affect the noise level.

However, the anomaly of valve 1 might be due to the different design from the other valves. Valve 2, 3, 3a, 5 and 6 all have converging nozzles, while valve 1 nozzle was converging then diverging. This means that the throttle is not at the exit, but inside the valve, so that choking condition is at the throttle, but the flow in the jet is supersonic [2]. 𝑀 𝑗𝑒𝑡 as defined for an isentropic expansion is not applicable. For increasing PR a normal shock is formed inside the diverging nozzle and Mach exit is

subsonic. This explains why at PR = 4.97 the noise level drops. Then, increasing PR further, the noise increases again but with a higher power law then the other valves.

Comparing with the semi-empirical model (solid lines), in the middle PR range the agreement is very good, apart from valve 1, but at the highest PRs, for the biggest valves (5 and 6) the model generally underpredicts the noise, while for the smallest valve (2) it overpredicts the level. The dif- ference is most significant for the smallest valves, being about 4 dB, while is only 2 dB for the biggest valves.

The major discrepancy between the semi-empirical model and the experimental data is at the low- est PRs when the valve is not choked and only the turbulent mixing noise (Eq. 2) is included in the model. The slope of the experimental data follows more the intermediate regime and this is consistent for all valve sizes, suggesting that at lower PRs when 𝑀 𝑗𝑒𝑡 < 1 but approaching 1, the turbulent mix- ing noise model is not suitable to account for the actual total noise mechanism especially for bigger valves.

Figure 3: Experimental overall levels per valve (dashed lines) compared with the valve

model (solid lines) plotted versus PR.

Figure 4: Experimental overall levels per valve (dashed lines) compared with the valve

model (solid lines) plotted versus 𝑀 𝑗𝑒𝑡 .

Figure 5: Experimental overall levels per valve (dashed lines) compared with the valve

model (solid lines) plotted versus 𝑚ሶ 𝑒𝑥𝑖𝑡 .

5. IMPLICATIONS FOR EXTRAPOLATION

The classical 8th power scaling law based on 𝑀 𝑗𝑒𝑡 defined for jet noise can be applied to the overall levels plotted in Figure 4. Because 𝑀 𝑗𝑒𝑡 does not account for valve size, three different trendlines have been fitted to the data corresponding to the three main sizes, as shown in Figure 6.

However, because 𝑚ሶ 𝑒𝑥𝑖𝑡 depends on the valve size, it is possible to fit a single trendline to inter- polate over all the valves for the highest values, as shown in Figure 7. In this case the best fit slope for the trendline follows the power law of 1.5, so that the line plotted in Figure 7 is:

𝐿 𝑤 = 145 + 1.5 ∗10 logሺ𝑚ሶ 𝑒𝑥𝑖𝑡 ሻ (12)

This 1.5 power law is a small adjustment to the power law of 1.7 that can be derived from the shock noise model at the highest 𝑀 𝑗𝑒𝑡 as described in [1].

Figure 6: Fitting a trendline per valve size type using a power law of 8.

Figure 7: Fitting a trendline using a power law of 1.5 to extrapolate at the higher 𝑚ሶ 𝑒𝑥𝑖𝑡 over

all the valves.

6. CONCLUSIONS

Tests of six valves were carried out over a range of flow conditions shown in Table 1. These data may be interpolated to give noise levels for specific flow conditions. The main question addressed by the paper is how these data compare with the semi-empirical model available in the literature and if the model can be extended to extrapolate the noise level to higher PR and mass flow.

Analysis of the noise spectra showed that in choked conditions the peak frequency broadly de- creases with PR, as predicted by the model. Noise levels vary with the classical law of the 8th power of jet Mach number for valves 2-6. However, valve 1 behaved differently because the nozzle is con- verging–diverging, so that choking occurs inside the valve rather than at the exit. For the other valves the detailed shape does not affect the overall noise level, which only depends on the main nozzle diameter.

Considering data for all the valves, at the lowest mass flow rate, when approaching the choking condition, the turbulent mixing mechanism does not seem to be sufficient to give the correct scaling law. In the higher range a scaling law of sound power increasing as mass flow rate to the power 1.5 has been derived. This is a small adjustment to the valve model described in the literature, but seems to be more appropriate to extrapolate to higher PR for all valve types.

7. REFERENCES

1 Beranek, L. Noise and vibration control , Institute of Noise and Control Engineering, Wash- ington DC, USA, 1988 2 Cantwell, B.J. Fundamentals of Compressible Flow , Stanford University CA, USA, 3 Octo- ber 2018.