understanding of the noise caused by a gas displacement
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technical monograph 43 Fundamentals of Aerodynamic Noise in Control Valves Floyd D. Jury Technical Consultant Fisher Controls International, Inc. This paper provides a basic understanding of the mecha- nisms by which aerodynamic noise is generated in a control valve. A fundamental approach is taken to the description of these noise mechanisms and the terminology associated with noise. This terminology is consistent with that used in the IEC valve noise prediction standard.
Transcript
technicalmonograph
43
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Floyd D. Jury
Technical ConsultantFisher Controls International, Inc.
This paper provides a basic understanding of the mecha-nisms by which aerodynamic noise is generated in a controlvalve. A fundamental approach is taken to the description ofthese noise mechanisms and the terminology associated withnoise. This terminology is consistent with that used in theIEC valve noise prediction standard.
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THE CONTROL VALVE AS A NOISE SOURCE
Control valves are a major source of noise in anyindustrial environment. A well designed control valvecan reduce its noise to an acceptable level, but inorder to ensure that an appropriate valve selection ismade for any given application, one must understandhow and why control valves produce and control noise,and how the amount of noise produced by a controlvalve can be predicted before purchasing the valveand placing it in service.
INTRODUCTION TO NOISE
Sound is the physiological phenomenon which occurswhen fluctuations in air pressure register against oureardrums. Our brain then interprets these fluctuationsas sound. Not all air pressure fluctuations, however,result in sound being interpreted by the brain. Onlythose pressure fluctuations in the general frequencyrange of 20 Hz to 20,000 Hz, for individuals with goodhearing, are detected and interpreted by the brain assound.
Air pressure fluctuations which are outside the rangeof human hearing (audible range) simply do notregister in the brain as sound. For example, normalchanges in atmospheric pressure occur so graduallythat they are a much lower frequency than the audiblerange and therefore cannot be heard. For this, we canbe truly thankful. Likewise, there are some sounds,such as a dog whistle, which are sufficiently highenough in frequency that they are above the range ofhuman hearing. Most dogs, however, can hearfrequencies well above the audible range of humans.
Since sound is defined as air pressure fluctuationsagainst the eardrum, the implication seems to be thatif there is no ear, there is no sound. Every beginningphysics student sooner or later hears the question, “Ifa tree falls in the forest, and there is no one there tohear it; is there sound?” This type of philosophicalquestion may be fun to debate at cocktail parties, but itsheds little useful light. For example, imagine a controlvalve in a pipeline which is passing a large amount ofturbulent flow. The turbulent fluid downstream of thevalve produces vibrations in the pipe wall which in turndisturb the surrounding air causing air pressurefluctuations to eventually impinge upon the ear drum ofa person standing nearby the pipeline. The observer
might state that there is noise coming from the valve,yet there is no observer inside the valve or the flowingfluid to hear the noise. On the other hand, it is illogicalto believe that there is no noise inside the valve orflowing fluid, but somehow noise magically appearsoutside the pipeline. Therefore, this manuscript willtake a much more pragmatic approach to this issueand talk about noise inside the valve, the fluid, thepipeline, etc..
The amount of energy contained in the pressure wave(i.e., its sound power) also affects the ability of the earto register the pressure wave as sound. There aresome pressure waves whose energy levels are lowenough that it does not register as sound in the humanear. In other words, the pressure disturbance is belowthe human threshold of sound, or in common parlance,it is not loud enough for us to hear. In other words,how loud the noise sounds is a measure of the powerof the sound wave.
Although the term “loudness” is one that would feelvery comfortable to most of us, it is a term which willnot be used in this manuscript. “Loudness” has atechnical definition which is used in the field of archi-tecture, but has no significance within the scope of thisdiscussion. We may use relative terms indicating thatone noise is more (or less) loud than another, but wewill not attempt to quantify “loudness” as such.
The greater the power of the pressure wave distur-bance, the louder the sound; however, this is not alinear relationship. We cannot double the power of thesound wave and produce a sound which is twice asloud. In order to quantify how loud one sound iscompared to another, we will use either the SoundPower Level or Sound Pressure Level of the noisedisturbance. Both of these sound measurementquantities follow a logarithmic relationship which wewill define shortly. We measure both of these quanti-ties in units called “decibels” or “dB.” Measuring thingsin units of decibels (dB) is outside our range of normalexperience and may seem complex, or even magical,at first, but it is really quite straightforward once onelearns the basic principles involved. Dealing withdecibels is so fundamental to the field of valve noise itis essential that we have a good grasp of this type ofmeasurement. If you feel uncomfortable about yourunderstanding of decibels as a form of noise measure-ment, a review of Fisher Control’s Technical Mono-
3
graph, TM-42, “Understanding Decibels, (dB or notdB)” will allow you to talk about decibels like an expert.
The human ear does not possess the same sensitivityto noise at every frequency in the audible range.Sound at some frequencies tend to seem louder thansounds at other frequencies, even though the powerlevel of the sound waves are the same. For example,sounds at the high frequency end of the audible rangetypically do not seem as loud as sounds of the samepower level at middle range frequencies. Researchhas shown that the human ear is most sensitive tosounds at a frequency of 1000 Hz.
In order to have an equitable way to compare the effectof two sounds on the human ear, scientists havedeveloped a weighting scale (called “A-weighting”)which adjusts the dB sound level at other frequenciesto a level which would be the perceived equivalent to asound at 1000 Hz. To determine the amount ofadjustment, the power level of a sound at 1000 Hz isadjusted until it sounds equally as loud as the testnoise. The test noise is then assigned the value of thesound power level of the 1000 Hz sound, regardless ofthe actual power level of the test noise. These units ofadjusted power level are then listed as dB(A) or dBAand are typically used when dealing with governmentregulations which limit the amount of sound to whichhuman beings may be exposed. In other words, twosounds which appear to be equally loud would havethe same dB(A) number regardless of their frequencyor actual power level.
Naturally, we would expect that some of the things wehave discussed so far, such as the A-weighting,frequency sensitivity of the human ear, threshold ofhearing, and the audible range of sound, etc. will tendto be unique to a specific human being at a specificpoint in time. Since it is not possible to deal with noiseprediction on this individualistic basis, scientists havedeveloped a statistical representation of an average,27 year old, American male. So when anyone refers tohow noise affects the human ear, they are referencingthis statistically derived model.
Noise is simply unwanted sound. As you mightsuspect, there are many psychological, cultural, andcontextual factors which determine whether a particu-lar series of air pressure waves are called sound ornoise. Even the same sound experienced by the sameindividual may undergo different classification depend-ing upon the context in which the sound is heard. Forexample, the sound emanating from an aircraft engine
may be noise to some individuals, but it is sweet musicto the ears of a pilot flying a single-engine airplaneacross a large body of water. Since the primary focusof this manuscript is the unwanted sound produced bycontrol valves, nearly all future references will be tonoise.
Sound waves cannot radiate in a vacuum. They musthave some material medium to propagate the wave. Inorder for sound to get from its source of origin to thehuman ear, it must eventually pass through the air as apressure wave which registers against the humaneardrum. Before it can get to the ear, however, it mayhave to pass through one or more additional materialmedia. Any reduction in the eventual sound pressurefluctuations at the ear which is caused by the noisepassage through the different media, or the boundariesbetween these media is called “transmission loss.”
If we think of the valve as a point source of noisesending out spherical sound waves in all directions, wecan recognize that only the sound radiated in a direc-tion which can arrive at the observers ears is effectiveat producing perceived noise. Noise generated in thefluid at the valve must then be transmitted through thepipe due to vibration induced in the pipe wall. Due toreflections of the sound waves from the inner surfaceof the pipe, only the portion of the energy in the soundwave which produces a radial component against thepipe wall will be effectively transmitted through thepipe. The rest will be called “transmission loss.”Finally, as the pipe wall vibration induces pressurefluctuations in the air surrounding the pipe, thesesound waves must radiate outward to the observer.The type of waves generated would be classifiedprimarily as a “line” source which would radiate soundwaves radially outward from the surface of the pipe.Additional transmission losses occur through the air asthese waves expand and spread the noise energy overan ever-increasing surface area of the sound wave.Thus, additional transmission losses will occur whichare dependent upon the observer’s distance from thepipe.
NOISE LEVEL
When someone asks us how loud a given noise is, thefirst response should be, “As compared to what?”Typically, when we measure anything, we usuallymeasure it with respect to some reference level. Forexample, when we talk about a given pressure in avessel, we are actually talking about the pressure levelabove or below atmospheric pressure (i.e., the refer-
4
ence level). Likewise, with noise or sound we alsohave a reference level. In this manuscript, we will usethe letter (L) to represent noise “level.”
The level of the noise is, of course, a function of thepower generated by the noise producing disturbance.We call this the “acoustic power” or “sound power” andwe designate it as (W
a). The standard noise reference
level is the lowest sound power which can just barelybe detected by the average person with averagehearing. This statistically derived threshold of hearingis called the “reference sound power” and is desig-nated as (W
o). Both W
o and W
a are typically measured
in units of Watts of power. The statistically derivedvalue for the reference sound power is W
o = 10-12
Watts.
As we increase the acoustic power we increase howloud the noise sounds to us, but not in a linear fashion.For example, if we were to double the sound power,we would not get a noise that sounds twice as loud.Due to this nonlinear nature, as well as due to the widerange of sounds to which the human ear can respond,it is convenient to use logarithms when dealing withnoise measurements. Likewise, it is typical to quantifyhow loud a noise is compared to a reference levelwhich is chosen as the threshold of hearing. Thus, theSound Power Level is defined as:
Lw = Log
10(W
a/W
o) (Units are “Bels”) (1)
The units of measurement for this noise level are“Bels;” named, of course, after Alexander GrahamBell, the grandfather of acoustic science. As it turnsout, however, the units of Bels are normally too largefor practical usage. Consequently, acoustic research-ers quickly began using a smaller unit of noise mea-surement called a “decibel (dB)” which equals one-tenth of a Bel. We can easily convert from Bels to dBas illustrated in the example below. Imagine a noiselevel such that
Lw = 8 Bels = (8 Bels)(10 dB/Bel) = 80 dB (2)
It is easy to conclude from this example, that if wewished to rewrite the equation (1) in terms of dB(decibel) units, it would become
Lw = 10 Log
10(W
a/W
o) (Units are “dB”) (3)
You will often see this equation incorrectly written asdB = 10 Log
10(W
a/W
o) which can be somewhat confus-
ing since it is actually using the units of measurement
as the name of the parameter being calculated. This issimilar to saying that m2 = (length)x(width) as the area(A) of a rectangle. We need to recognize that thisincorrect practice exists, but we should refrain fromperpetuating it.
COMPARING NOISE SOURCES
We don’t always want to compare a particular noisesource with the reference threshold of hearing. Some-times we may want to compare one noise source (W
1)
to a second noise source (W2). We can use our noise
level definition here as well; i.e., the following equationcan tell us how the noise power level of source (W
2)
compares to the noise power level of source (W1).
∆Lw = 10 Log
10(W
2/W
1) (Units are “dB”) (4)
If the answer is positive, it means that W2 is so many
dB louder than W1, and if the answer is negative, it
means that W2 is not as loud as W
1.
There is another comparison which is often of specialinterest to us. Let’s look at what would happen if wewere to actually double the power produced by thenoise source; i.e.,
∆Lw = 10 Log
10(W
2/W
1) = 10 Log
10(2W
1/W
1)
= 10 Log10
(2) = 10(0.301) = +3.01 ≅ +3 dB (5)
The usual custom, as inferred above, is to round the3.01 value to an even 3. In almost all noise controlproblems it makes little sense to deal with smallfractions of decibels. The precision of 0.1 dB is rarelyrequired and noise levels are nearly always best statedonly to the nearest decibel.
The above result means that if we started out with anoise level of 80 dB and we doubled the sound power,the noise level would increase only to 83 dB. By thesame token, if we were to cut the sound power in half,the noise level would decrease only to 77 dB.
COMBINING NOISE SOURCES
In a typical industrial environment, a control valve isseldom the only noise source present in a particularlocation; i.e., there are usually motors, compressors,turbines, other valves, other machines, etc. which arecontributing to the general noise level. Althoughcontrol valves can generate a significant amount ofnoise, they often are not the major noise source in agiven area. The noise level in a particular area is the
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result of combining the noise generated by eachsource in the vicinity. When doing this, however, it isimportant to recognize that dB’s don’t add; thepowers add.
Imagine that you are standing halfway between twoidentical valves installed in two different pipelines.Consider further that you measure a noise level of 60dB from each valve, when it is operating by itself. Now,you want to know what the noise level would be if youoperated both valves simultaneously. Since thepowers add (not the dB’s), we know that the totalresultant power would be twice as much as before.From the example above, we can see that the newnoise level would only be 63 dB, not 120 dB.
What happens when we combine noise sources of twodifferent levels? Consider the example of the twovalves above, but this time while one valve produces60 dB of noise by itself, the other produces 100 dB byitself. It turns out that 100 dB is so much louder than60 dB that the combination is essentially still 100 dB.We know that the result is really larger than 100 dB,but the difference between the resultant overall noiselevel and the noise generated by the 100 dB valve byitself is negligible. This may seem strange at first, butthe mystery should disappear when we consider thefollowing.
Recalling that powers add rather than dB’s, we cansolve equation (3) above in reverse to discover that100 dB represents a power of 0.01 Watt (Don’t forgetto take into account the reference power). On theother hand, 60 dB represents a power of only 0.000001Watt. When we combine these two noise sources toget a total of 0.010001 Watt we can see that there isindeed negligible difference between 0.010001 and0.01. These two examples allow us to develop twouseful rules of thumb:
RULE NO. 1: When a secondary noise source iscombined with a louder noise source, the overallresulting noise level cannot exceed 3 dB greater thanthe loudest source by itself. This maximum wouldoccur only when the secondary noise source becameequally as loud as the loudest primary source.
RULE NO. 2: When trying to reduce the overall noise,determine which noise sources are the loud, dominantones and correct them. Negligible improvement will beattained by eliminating a minor noise source. Eveneliminating one of two equal, dominant sources willonly result in a 3 dB improvement.
Table 1 below provides a practical aid in helping tocombine two different noise sources or to aid indetermining how much improvement would be gainedby quieting one of several different noise sources.
Table 1: Combining Two Point Noise Sources
dB Difference dB Difference BetweenBetween Two Sources Total Noise and Louder Source
You can use Table 1 to combine any number of noisesources. You can do this by combining any twosources, then combining the result with anothersource, etc. As an example of how this can be done,consider the following example:
EXAMPLE 1: Use table 1 to combine four point noisesources which generate noise levels of 102 dB, 96 dB,108 dB, and 102 dB respectively. Determine youranswer to the nearest dB.
ANSWER: First combine 102 dB and 102 dB to get105 dB. Next, combine this 105 dB with the 108 dB.The difference is 3 dB. From Table 1 then, 1.76 dBmust be added to 108 dB to get 109.76 dB. Thedifference between 109.76 dB and the remaining 96dB source is 13.76 dB. We could interpolate between0.17 dB and 0.22 dB in the table; however, to thenearest dB the combined noise level is 110 dB.
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SOUND POWER VERSUS SOUND PRESSURE
Although the acoustic power (Wa) generated by a noise
disturbance is related to how loud the noise sounds, itis not always easy to directly measure the soundpower. On the other hand, it is relatively easy tomeasure the noise induced air pressure disturbances(p
d) that exist in the vicinity of our ears. From a
pragmatic point of view, we are often more interestedin noise at the point where the noise pressure fluctua-tions impact our ears than we are at the actual sourceof the noise. All of this leads us to the conclusion thatit would be useful to understand how sound power andsound pressure are related to each other and to thenoise level.
It is a fundamental fact of nature that “power” is alwaysproportional to the square of the “potential.” In electri-cal systems, for example, we all know from our highschool physics that electrical power is proportional tothe square of the electrical potential (E). Likewise, theacoustic power is proportional to the square of thesound pressure. We can express this as an equationwhere C
1 is a constant of proportionality involving the
area (A), the density (ρ), and the speed of sound (c).
Wa = (A/ρc) (p
d)2 (6)
Wa = C
1(p
d)2 (7)
If we combine this fact with another fundamental factabout logarithms [Log Xa = aLog X], we can write twodifferent “level” equations which are simply two differ-ent ways of looking at what is essentially the samephenomenon.
Lpwr
= 10 Log10
(Wa/W
o) (3)
Lpres
= 20 Log10
(pd/p
o) = 10Log
10(p
a/p
o)2 (8)
NOTE: In both equations, the units are “dB”.
The statistically derived value for the reference soundpressure is p
o = 2x10-5 Pa.
NOTE: Lpres
is often written as Lp and is called “Sound
Pressure Level.”
Equation (8) tells us that if we double the soundpressure we will get a 6 dB increase in noise level;whereas equation (3) tells us that if we double thesound power we will get only a 3 dB increase in noiselevel. At first, this sounds inconsistent to some indi-viduals until they realize that we are not talking aboutthe same thing in these two cases.
Equation (7) reminds us that when we double thesound pressure, we actually quadruple the soundpower. Now, when we double the sound pressure inequation (8) we must quadruple the sound power inequation (3) in order to be consistent. Thus, in bothcases, we will get a 6 dB increase in noise level. Thisleads us to another rule:
RULE NO. 3: The noise level of any given noisedisturbance which exists in the environment will resultin exactly the same number of dB’s, regardless ofwhether we use the sound power or sound pressure todetermine it, as long as we remember and account forthe relationship described by equation (7).
CAUTION: Although equations (8) and (3) are closelyrelated to each other as we have indicated above, weshould be careful about concluding that these twoequations are always equal to each other because aswe shall shortly see, they are not.
The relationship between sound power and soundpressure is much like the relationship between massflow and pressure in a pipeline. As we proceed downa long pipeline, the mass flow is the same at everypoint even though the pressures will be different due tofriction losses, changes in pipe diameter, changes intemperature, etc. Likewise, sound power will be thesame as it “flows” outward from the source, but thesound pressure will vary at different distances from thesource. To illustrate, let’s take the simplest case of apoint source of noise.
If a sudden noise disturbance, such as an explosion,occurs at a point it will generate a spherically shapedsound pressure wave which emanates outward fromthe source in all directions. Even though the totalpower of the wave is the same at every point awayfrom the source, this total power is being spreaduniformly over an increasing surface area of thespherical wave. Thus, the Watts/m2 will decreasedramatically at any point on the spherical surface asthe surface area increases when we move further andfurther from the source.
Since the sound pressure at any point is proportional tothe Watts/m2 at that point, rather than the total power, itfollows that the sound pressure, which is what wetypically measure, will be different depending upon howfar away we are from the noise source. This situationis analogous to the phenomenon we witnessed aschildren when we tossed a rock into a quiet pond. Asthe rock entered the water it would produce a distur-
7
bance which generated a circular wave which traveledoutward from the source. As we watched, we wouldsee the amplitude of these waves decrease as theymoved further and further from the source. Eventhough the total power in each wave was staying thesame, it was getting dispersed over the rapidly increas-ing circumference of the wave circle. Eventually thistotal wave power would get so dispersed that therewould be no detectable amplitude of the wave left.
The dispersal of power and corresponding decrease insound pressure as we move away from the source isthe reason why it is important to have a standardreference point for measuring and comparing thesound pressure levels of noise sources. If we don’tmeasure them at the same distance from the sourceeach time, there would be no basis for comparison.The standard distance for measuring is typically onemeter from the source.
We can see now that equation (3) may tell us that thenoise power level at the source is perhaps 100 dB,while at the same time we may measure a soundpressure level at the one meter reference point of only85 dB. Of course, the sound pressure level would beeven less as we moved further from the source, eventhough the TOTAL sound power level would still be 100dB.
In valve noise studies, we are often talking aboutlooking at changes or reductions in noise levels. It isreassuring to note that a 10 dB reduction in noise isalways a 10 dB reduction whether we are talking aboutsound power level or sound pressure level. Forinstance, in the hypothetical example above, a 10 dBreduction in noise would reduce the sound power levelat the source from 100 to 90 dB, while the soundpressure level measurement at the standard referencepoint would be reduced from 85 dB to 75 dB.
One final point should be made about the differencesbetween sound power level and sound pressure level.Some people get very confused about this issue andtend to make their distinctions between the two casesbased on things such as the coefficient in front of theLog term (i.e., 10 or 20), or they make the distinctionbased on whether the equation contains a power term(W) or a pressure term (p). Neither of these distinc-tions by themselves can lead one to the correctconclusion. Equation no. (8) makes it clear that thecoefficient method is unreliable. The following rule ofthumb can assist you in making a definitive distinctionbetween sound power level and sound pressure level:
RULE NO. 4: If the log equation contains a powerterm ratio such as (W
1/W
2), the expression is most
certainly sound power level. If the log equation con-tains a pressure ratio and an area term; e.g., (p
12A
1/
p2
2A2), the expression is also sound power level,
because as equation (6) reminds us, the square of thepressure acting over a specific area is actually ameasure of power. Only when the log equationcontains a pressure ratio, but is stripped of the arearelationship can we consider the equation as soundpressure level. The following examples should help toillustrate this rule:
L = 10Log10
(W1/W
2) Sound power level
L = 10Log10
(p1
2/p2
2) Sound pressure levelL = 10Log
10(p
12A
1/p
22A
2) Sound power level
L = 10Log10
(p1/p
2)2 Sound pressure level
L = 20Log10
(p1/p
2) Sound pressure level
L = 10Log10
[(p1/p
2)2(A
1/A
2)] Sound power level
NOISE FREQUENCY AND WAVELENGTH
Sound, from the point of view of control valve noise,consists of pressure disturbances produced andpropagated by waves in solid or fluid media. Forpractical purposes, the most important type of wave isthe simple harmonic or sinusoidal wave shown inFigure 1. This is a snap-shot picture of one cycle of asimple harmonic sound wave.
Figure 1: Simple harmonic sound wave
For illustration purposes, we can think of this as asingle-frequency sound wave traveling through the airin the x-direction. The ordinate measures the ampli-tude of the air pressure disturbance above and belowthe ambient atmospheric pressure. It is this varyingpressure against our ear drums that registers assound.
Figure 1 only shows one complete cycle of the soundwave. The physical distance spanned by this onecomplete cycle is called the wavelength (λ). Actually,the distance between any two corresponding points on
8
the wave is the wavelength. Typically, the wavelengthis measured in meters (m).
The wave propagation corresponds to the motion ofthe whole sinusoidal figure to the right along the x-axiswith a velocity (c) which is the speed of sound in the air(meters/second).
The number of complete wavelengths (cycles) whichpass any given point on the x-axis per second is thefrequency (f) of the wave in cycles/sec (Hertz).
By concentrating on the dimensions of these funda-mental factors, we can logically combine them in sucha way as to derive the fundamental relationshipbetween wavelength (λ) and frequency (f). In otherwords,
(cycles/sec)(meters/cycle) = (meters/sec)
(f)(λ) = (c) which is often written as
f = c/λ (9)
Thus, we arrive at the logical conclusion that theshorter the wavelength of the sound, the higher thefrequency. As we shall see later, this is a fact which isof great importance in noise abatement using drilled-hole valve trim.
NOISE FREQUENCY SPECTRUM
Industrial noise, including control valve noise, is rarelya pure tone such as that shown in Figure 1. The noiseis usually made up of a whole band of frequencies,with varying sound power at each frequency. In orderto represent this type of noise, a noise frequencyspectrum is often used. Webster’s dictionary defines aspectrum as any collection of radiant energy arrangedin order of their wavelengths. In noise studies, it ismore conventional to deal with the frequency ratherthan the wavelength. Thus, the noise frequencyspectrum is a band of frequencies displayed in order oftheir frequencies. The audio spectrum, as was statedearlier, is typically defined as the band of frequenciesfrom 20 Hz to 20,000 Hz. These frequencies arenormally plotted along the horizontal axis of a chart,while the corresponding sound power for each fre-quency is plotted along the vertical axis as shown inFigure 2.
Noise Frequency Spectrum
0
2
4
6
8
0 100 200 300 400 500 600 700 800 900 1000
Frequency, Hz
Po
we
r,
Mic
row
att
s
Figure 2: Noise Frequency Spectrum
For the type of noise generated in a control valve, thenoise power spectrum tends to be more of a “haystack” shaped curve, such as shown in Figure 3, ratherthan the type of irregularly shaped curve shown inFigure 2.
NoisePowerLevel
Frequency (Hz)
fp
Figure 3: “Hay Stack” Noise Power Spectrum
Thus, as the noise being generated in the valvechanges, the power spectrum curve rarely changes itsbasic shape, but it may move up or down as the peaknoise power level changes, and it may move right orleft as the frequency (f
p) changes at which the peak
power occurs.
Strouhal, an early experimenter in turbulent flow,discovered that in general, the tone frequency of noisedue to turbulent flow was proportional to flow velocityand inversely proportional to some characteristicdimension. To turn this proportionality into an equa-tion, he invented what is known as the Strouhalnumber (S
T). Thus, the frequency equation becomes
fS U
DT vc
j= (10)
Since our noise studies typically deal with valve flow,the velocity we need becomes the velocity at the vena
9
contracta (Uvc
), and the characteristic dimensionassociated with that velocity becomes the diameter ofthe jet at the vena contracta (D
j).
When experimenters plotted noise power level versusfrequency as shown in Figure 3, it was discovered thatthe peak frequency of the “hay stack” noise spectrumtypically occurred around a Strouhal number of twotenths (i.e., S
T = 0.2).
A-WEIGHTING OF NOISE LEVEL (dB(A))
In literature concerning noise, we often encounter theterms dBA or dB(A). These terms both refer to what isknown as A-weighted noise, but dB(A) is the preferreddesignation. Weighting a noise measurement consistsof modifying a measured sound pressure level bysome weighted factor which is a function of frequency.The A-weighting factors are intended to adjust actual,measured sound pressure levels at each frequencyband to the sensitivity of the human ear.
The numerical value of the A-weighting factor at anyfrequency is determined by how loud a noise soundscompared to how loud a 1000 Hz tone appears to be.In other words, at 1000 Hz, the A-weighting factor isunity (1.0). The sound pressure level of a 1000 Hztone is adjusted until it appears to be equally as loud asthe unknown noise source. If the sound pressure levelof the 1000 Hz tone measures 105 dB when that matchoccurs, we say the unknown source “sounds like” 105dB, regardless of what its sound pressure level wouldmeasure. For example, if we listen to a sound at 50Hz, which to us appears to be just as loud as the 105dB was at 1000 Hz, we say the 50 Hz tone sounds like105 dB regardless of the measured sound pressurelevel. In this case we would say that the 50 Hz A-weighted noise level is 105 dB(A).
If two or more sounds at different frequencies soundequally loud, they are the same dB(A), regardless ofwhat their individual sound pressure levels may be.Government standards are written in terms of dB(A)since they are really more concerned about how loudthe noise actually sounds, rather than with what thesound pressure level actually is.
A-weighting of noise level is a much more significantfactor for hydrodynamic noise (noisy liquid flow) thanfor aerodynamic noise (noisy gas flow). The reason forthis has to do with the sensitivity of the human ear.The response of the human ear to noise is fairly flat inthe frequency range of 600 Hz to 10,000 Hz. This
means that in this frequency range there is negligibledifference between the actual measured soundpressure level and the A-weighted noise level.
Since aerodynamic noise in a valve is generatedprimarily in this same frequency range of 600 Hz to10,000 Hz, the A-weighting factor is essentially unity.Thus, whether we predict the noise level in dB or indB(A), we will arrive at approximately the samenumber when we are dealing with aerodynamic noise.
On the other hand, hydrodynamic noise in a valve canhave appreciable energy at frequencies below 600 Hz.Because the human ear is much less sensitive to noiseat these lower frequencies than it is at 1000 Hz, the A-Weighting factor is going to be considerably less thanunity. Therefore, when dealing with hydrodynamicnoise, it is extremely important to take into account theA-weighting factor.
GOVERNMENT STANDARDS FORNOISE EXPOSURE
Society values people and their health and welfare. Inour democracy, it is considered to be the proper role ofgovernment to ensure each citizen’s health and welfarethrough various regulations and programs. When itbecame apparent to various governments in the 1960’sthat industrial noise pollution was becoming a seriousproblem, federal and state governments began devel-oping legislation to establish standards and penaltieswhich are intended to protect people from noisepollution.
ALLOWABLE SOUND PRESSURE LEVEL (dBA)
405060708090
100110120
0 1 2 3 4 5 6 7 8
Hours
dBA
Figure 4: Federal Noise Regulation
10
Figure 4 shows the allowable sound pressure levelwhich the USA government will allow an individual tobe exposed to for any given duration. The allowablenoise level can be louder if the individual is only goingto be exposed briefly than if he or she must work a full8-hour shift in the noisy environment. Notice also thatthe standard uses A-weighted sound levels (dB(A))since the actual sound pressure level is not as impor-tant as how loud it actually sounds to the human ear.
There are three elements of noise standards which areessential considerations when dealing with industrialnoise problems. These are people, noise level, andexposure time. If there are no people involved, there isno problem as far as the government standards areconcerned. So, one way to address the issue is tofence off and isolate noisy equipment from people. Inairports, for example, the majority of people areisolated from the jet noise either by fences, noisebarriers, or by the insulated walls of the terminalbuilding. Employees who can’t be completely isolatedwear ear protectors to insulate their ears from damag-ing noise. Since the amount of hearing damage doneby noise is a function of how long an individual isexposed to the noise, various governments havedeveloped regulations which relate noise level toexposure time.
THE CONTROL VALVE AS A NOISE GENERATOR
Noise is the result of energy dissipation in the controlvalve. The major sources of control valve noise aremechanical vibration of components, hydrodynamicnoise, and aerodynamic noise.
MECHANICAL NOISE
Vibration of valve components is a result of randompressure fluctuations within the valve body and/or fluidimpingement upon the movable or flexible parts.Noise that is a by-product of vibration of valve compo-nents is usually of a secondary concern and may evenbe beneficial since it warns that conditions exist whichcould produce valve failure. Mechanical vibration hasfor the most part been eliminated by improved valvedesign and is generally considered a structural prob-lem rather than a noise problem. Accordingly, me-chanical noise is not addressed by the IEC noisestandard.
HYDRODYNAMIC VALVE NOISE
The major source of hydrodynamic noise (i.e., noiseresulting from liquid flow) is cavitation which is caused
by implosion of vapor bubbles formed in the cavitationprocess. Cavitation occurs in valves controlling liquidswhen the service conditions are such that at somepoint within the valve the pressure drops below thevapor pressure causing bubbles to form, while thestatic pressure downstream of the valve is greater thanthe vapor pressure causing the vapor bubbles toimplode and release energy.
As the fluid velocity increases due to the restrictionformed by the valve trim parts, vapor bubbles areformed in the region of minimum static pressure(highest velocity) and are subsequently collapsed orimploded as they pass downstream into the pressurerecovery region. Noise is produced by the energydissipation of the imploding bubbles. Noise producedby cavitation in a valve has a broad frequency range,however, it can have appreciable energy at frequenciesbelow 600 Hz. Cavitation noise is often described as arattling sound similar to that which would be anticipatedif gravel were in the fluid stream.
Cavitation may produce severe damage to the solidboundary surfaces that confine the cavitating fluid.Generally speaking, noise produced by cavitation is ofsecondary concern. In addition, test results and fieldexperience indicate that noise levels from non-cavitat-ing liquid applications are quite low and generallywould not be considered a noise problem.
AERODYNAMIC VALVE NOISE
The major source of aerodynamic valve noise (i.e.,noise resulting from gas flow) is a by-product of aturbulent gas stream. A control valve controls gas flowby converting potential (pressure) energy into turbu-lence. Most of the energy is converted into heat;however, a small portion of this energy is convertedinto sound. It is possible to determine an acousticalefficiency factor (η) which indicates how much of theinitial energy in the flowing medium is converted intosound. This acoustical efficiency factor varies as thevalve service conditions change, and this changes theflow patterns through the valve. The IEC valve noiseprediction standard defines five different flow regimeswhich affect the acoustical efficiency factor. Since theconditions which exist in each of these flow regimesresult in slightly different noise generation mecha-nisms, it is important that we understand the flowregimes that have been defined by the standard.
11
IEC FLOW REGIMES
As the pressure drop across the valve increases, theflow energy intensifies and the flow patterns changeand the noise generation mechanisms change accord-ingly. For purposes of the IEC noise standard, fivedifferent flow regimes are defined. The boundaries ofthese regimes are defined by the relationship of thevalve outlet absolute pressure (p
contracta pressure at critical flow conditions (pVCC
), thevalve outlet absolute pressure at a break point (p
2B),
and the valve outlet absolute pressure where theregion of constant acoustical efficiency begins (p
2CE).
The break point pressure (p2B
) occurs at the pointwhere the shock cell-turbulent interaction mechanismbegins to dominate the noise spectrum over theturbulent-shear mechanism. Both p
2B and p
2CE will be
discussed in more detail later.
The concept of flow regimes can best be understoodusing a graphical illustration of the flow through acontrol valve. For purposes of simplification, a controlvalve at any flow opening can be represented by asimple restriction in the line as shown in Figure 5.
Vena Contracta
p1 p1
p2
p1 p2
Figure 5: Valve Pressure Profile
As the flow passes through the physical restriction,there is a necking down, or contraction, of the flowstream. The minimum cross-sectional area of the flowstream occurs at a point called the vena contracta,which is just a short distance downstream of thephysical restriction. It is important that we understandthe interchange between the kinetic energy (energy ofmotion) and the potential energy (pressure energy inthis case) of a fluid that is flowing through a valve orother restriction. To maintain a steady flow of gasthrough the valve, the velocity must be greatest at thevena contracta where the cross-sectional area is theleast. This increase in velocity, or kinetic energy,
comes about at the expense of the pressure, orpotential energy as illustrated in Figure 5.
The pressure profile along the valve shows a sharpdecrease in the pressure as the velocity increases.The pressure will decrease to a minimum at the venacontracta where the velocity is the greatest. Whathappens downstream of the vena contracta is afunction of several things, including the general flowefficiency of the valve style and other external processconditions. Typically, however, there will be a decreasein velocity and a corresponding increase in pressure asthe fluid stream expands into a larger area. Of course,the pressure downstream of the valve never recoverscompletely to the pressure that existed upstream. Thepressure recovery downstream of the valve is oftencalled “recompression.”
The pressure differential that exists across the valve iscalled the ∆p (delta p) of the valve. This ∆p is ameasure of the amount of energy that was dissipatedin the valve. Useful energy is lost in the valve becauseof turbulence and friction. The energy is dissipatedprimarily as heat and some noise. The greater the ∆pfor a given flow area, the greater the energy dissipatedin the valve.
The amount of energy dissipated in the valve isinfluenced greatly by the design of the valve and itsflow efficiency. If the valve design minimizes theamount of energy dissipated in turbulence and friction,there will be more energy left over for recovery in theform of downstream pressure. Such a valve would berelatively streamlined and would be classified as a highrecovery valve. In contrast, a low recovery valvedissipates more energy due to turbulence and frictionand consequently has a greater ∆p for the same flow.
Two important points can be made here. First of all,the recovery properties described above are aninherent characteristic of the valve design and can thusbe assigned a fixed index number (F
L) called the
“recovery factor” of the valve. This will be discussed inmore detail later. The second point is that it would bea mistake to believe that there is always a relationshipbetween the ∆p and the flow through the valve.
Regardless of the recovery characteristics of the valve,the amount of gas flow is determined primarily by thedensity of the gas, the flow area at the vena contracta,and the flow velocity at the vena contracta. Therefore,assuming the case of constant inlet pressure, if theflow area is constant, such as would be the case when
12
the valve is wide open, any increase in flow must comefrom an increase in velocity at the vena contracta.
Due to the interchange of energy from one form toanother, an increase in velocity at the vena contractaresults in a lower vena contracta pressure (p
vc). This
train of logic leads to the conclusion that the pressuredifferential (p
1 - p
vc) between the inlet and the vena
contracta is directly related to the flow rate. The largerthis pressure differential, the greater the flow. Whilethis statement remains true, there is a limit to theamount of flow that can be achieved.
In a normal control valve design, it is impossible for thecompressible gaseous fluid to achieve a velocitygreater than the speed of sound at the vena contracta.Thus, when sonic velocity is reached at the venacontracta, there will be no further increase in velocity,there will be no further increase in flow, and there willbe no further decrease in the vena contracta pressure.This condition is referred to as either “choked flow” or“critical flow.”
At the point where critical flow is first reached, thepressure at the vena contracta is designated as (p
VCC);
i.e., the absolute vena contracta pressure at criticalflow conditions, and the downstream pressure wherethis occurs is designated as (p
2C); i.e., the valve outlet
absolute pressure at critical flow conditions.
External process conditions may force the valve outletpressure (p
2) to drop below the valve outlet critical
pressure (p2C
). This increase in ∆p across the valvewill result in additional energy dissipation (and there-fore produce more noise), but it will not increase theflow through the valve nor the velocity at the venacontracta. Regardless of what happens to p
2, the
pressure differential (p1 - p
vc) will always be directly
related to the flow.
Still assuming a constant absolute inlet pressure (p1),
we can look now at how the flow regimes are definedas a function of valve outlet absolute pressure (p
2).
FLOW REGIME I: (p2 ≥≥≥≥≥ p2C)
Figure 6 illustrates the definition of flow Regime I (i.e.,for the operating condition where p
2 ≥ p
2C). In Regime
I, the flow is subsonic. Since p2 has not yet reached
the critical pressure, the velocity at the vena contractais less than the speed of sound. In this regime, the gasis partially recompressed and the amount of pressurerecovery depends, of course, on the design of thevalve. Therefore, it is only to be expected that the
valve recovery factor (FL) will play a role in determining
the amount of sound power generated by the valve.
Vena Contracta
p1 p1
p2C
pVCC
p2B
p2CE
p2Regime I
Regime II
Regime III
Regime IV
Regime V
p1 p2
Laminar Core
Turbulent mixing region
Figure 6: Flow Regime I
Note in Figure 6, that under this non-choked flowcondition, there is a jet core which is essentiallylaminar flow in nature. Although, the jet core itself canbe quite uniform, it is surrounded by an area of intenseturbulence. Under non-choked flow conditions,aerodynamic noise is primarily a result of the Reynoldsstresses or shear forces created in the flow stream asa result of rapid deceleration and expansion of thefluid. The principal area of noise generation is in thisshear/mixing region where the flow field is character-ized by extreme turbulence and mixing. This noisegeneration mechanism is known as “turbulent shearflow.”
FLOW REGIME II: (p2C > p2 ≥≥≥≥≥ pVCC)
Vena Contracta
p1 p1
p2C
pVCC
p2B
p2CE
p2
Regime I
Regime II
Regime III
Regime IV
Regime V
p1 p2
Normal Shock
Shear turbulence region
Figure 7: Flow Regime II
13
Figure 7 illustrates the definition of flow Regime II (i.e.,for the operating condition where p
2C > p
2 ≥ p
VCC). In
Regime II the flow is sonic. Since p2 has dropped
below the critical pressure, the velocity at the venacontracta has reached the speed of sound. In thisregime, some recompression still exists; however, itdecreases as p
2 drops lower and lower in this regime.
Note in Figure 7, that under this choked flow condition,the laminar jet core has disappeared and a normalshock is formed at the vena contracta. This is essen-tially a stationary shock region that the flow must passthrough. As the flow passes through the normalshock, it rapidly dissipates energy as it goes from sonicvelocity to a subsonic velocity in a very short distance.Much of this dissipation of energy goes into noise.This noise generation mechanism is known as, “shock-turbulence interaction.”
Downstream from this normal shock, there is still aregion of even more intense turbulence than in RegimeI. This, of course, is due to the greater pressure drop.Because some recompression does exist, the pres-sure drop across the valve will still have some effect onthe amount of noise generated due to increasedturbulence, even though it does nothing to increase theflow since choked flow already exists at the venacontracta. As p
2 drops lower and lower in this flow
regime, the amount of noise power produced in-creases proportionately until it reaches a maximum atthe boundary between Regimes II and III. At thisboundary, the ∆p across the valve will no longer havean effect on the amount of energy available in the fluidstream; however, it will have an effect upon the acous-tic efficiency (η) which continues to increase theamount of acoustic power converted from the streampower.
Under these choked flow conditions in Regime II,aerodynamic noise is still primarily a result of theReynolds stresses or shear forces created in theshear-turbulence region downstream of the normalshock, but there is some contribution from the shock-turbulence interaction. As p
2 drops lower and lower
into Regime II, the normal shock begins to “protrude”further downstream. As it does so, more and morereflected waves are spawned from the shock and thereis an increase in interaction between these reflectedwaves and the turbulent mixing region which increasesthe acoustic efficiency (η
2) somewhat; however, the
flow-shear turbulence mechanism continues to domi-nate.
FLOW REGIME III: (pVCC >>>>> p2 ≥≥≥≥≥ p2B)
Vena Contracta
p1 p1
p2C
pVCC
p2B
p2CE
p2
Regime I
Regime II
Regime III
Regime IV
Regime V
p1 p2
Shock Cells
Reflected shock waves
Shear turbulence
Figure 8: Flow Regime III
Figure 8 illustrates the definition of flow Regime III (i.e.,for the operating condition where p
VCC > p
2 ≥ p
2B). In
Regime III the flow is still basically sonic in a macrosense; however, there will be regions of localizedsupersonic flow. Since p2 has now dropped below thevena contracta critical pressure, there is no furtherpressure recovery, or recompression.
Note in Figure 8, that multiple shock cells have formed.Surrounding these shock cells, there is still a region ofintense turbulence where some noise is generated asbefore, but now the shock-turbulence interactionbegins to come more into play. Notice the presence ofthe reflected shock waves which have broken awayfrom the shock cells and pass through the region ofturbulent mixing. As these reflected shock waves passthrough and interact with the turbulence, additionalenergy is dissipated and more noise is produced. Thisis an expansion of the mechanism known as “shock-turbulence interaction.” Only a single shock wave isshown here, but in reality there will be whole families ofthese reflected shock waves formed as p
2 continues to
decrease.
In flow Regime III, there is no difference in the acousticefficiency from that in Regime II. The only majordifference in noise generation is the effects of ∆p whichwas prevalent in Regime II, but has now disappearedin Regime III. Noise is produced by both flow-shearturbulence and shock-turbulence interaction, with thelatter increasing in importance as the boundary (calledthe “break point”) between Regimes III and IV is
14
approached.FLOW REGIME IV: (p2B > p2 ≥≥≥≥≥ p2CE)
Vena Contracta
p1 p1
p2C
pVCC
p2B
p2CEp2
Regime I
Regime II
Regime III
Regime IV
Regime V
p1 p2
Mach disk
Shear turbulence
Figure 9: Flow Regime IV
Figure 9 illustrates the definition of flow Regime IV (i.e.,for the operating condition where p
2B > p
2 ≥ p
2CE). In
Regime IV, p2 has now dropped below the break point
pressure, which by definition is that pressure belowwhich the shock-turbulence interaction mechanismbegins to dominate the noise spectrum over theturbulent-shear mechanism. Turbulent-shear noisegeneration is still present, of course, but it pales insignificance compared to the shock cell-turbulenceinteraction noise generation.
Note in Figure 9, that the multiple shock cells havedisappeared, and have been replaced by what is calledthe “Mach disk.” You can visualize the Mach disk as astationary shock wave with a much more intenseenergy gradient through which the flow must pass,dissipating energy into noise as it does so. The flow atthe vena contracta is still choked sonic flow, but theflow in the Mach cone between the vena contracta andthe Mach disk is locally supersonic.
Flow Regime IV is basically a transition region. Thereis a slight decrease in the acoustic efficiency as ittransitions from the high Mach number dependence inRegime III to the constant value in Regime V.
FLOW REGIME V: (p2CE > p2)
Vena Contracta
p1 p1
p2C
pVCC
p2B
p2CE
p2
Regime I
Regime II
Regime III
Regime IV
Regime V
p1 p2
Mach disk
Shear turbulence
Figure 10: Flow Regime V
Figure 10 illustrates the definition of flow Regime V (i.e.,for the operating condition where p
2CE > p
2). In flow
Regime V, p2 has now dropped below a pressure,beyond which there will essentially be no further in-crease in acoustical efficiency. Shock-turbulenceinteraction mechanism continues to dominate the noisespectrum, even though the turbulent-shear mechanismis still present.
Note in Figure 10, that there is little difference in the flowstructure except that the Mach disk has grown slightly indiameter over that shown in Figure 9; however, there islittle significance that can be attached to this from anoise generation point of view. The growth in the Machdisk is due to the somewhat higher local pressure whichexists in the Mach disk area as it exits into the lowerpressure downstream region. As before, the flow at thevena contracta is still choked sonic flow, but the flow inthe Mach cone between the vena contracta and theMach disk is locally supersonic.
Once the flow has entered Regime V where the acousticefficiency remains constant, there will be no furtherincrease in valve noise generation, regardless of howlow we drop p
2.
LOW NOISE VALVE DESIGNS
The IEC noise standard basically recognizes threedifferent categories of noise reducing trim. These are
o Single stage, multiple flow passage trimo Single flow path, multistage pressure reduction trim
15
o Multi-path, multistage trimThe IEC noise standard develops a noise calculationprocedure and equations which are intended to applyto any standard valve construction. When special lownoise trims are used in valves, the general calculationprocedure and most of the equations still apply,however, these special trims need some specialconsideration. Here we will not discuss the specialtechniques used in the standard. This paper will onlydeal with the theory behind why these trims providenoise reduction.
SINGLE STAGE, MULTIPLE FLOW PASSAGE TRIM
“Single stage” means that the flowing fluid goes fromthe upstream pressure condition at the valve inlet (p
1)
to the downstream pressure condition at the valveoutlet (p
2) in one step, or stage. This is the typical
arrangement in most conventional control valves.
“Multiple flow passage” means that the flowing fluid, ingoing from the valve inlet to the valve outlet, passesthrough several flow openings rather than just oneorifice. There are a couple of restrictive conditions onthis definition, however, which are important to remem-ber.
First of all, the flow passages must be sufficientlyseparated in distance so that there can be no interac-tion between the jets emanating from each flowopening. Secondly, the calculation procedures of thestandard require that all of the multiple flow passageshave the same hydraulic diameter (d
H). “Hydraulic
diameter” is just a term used to account for the factthat each flow opening might have some unusual orirregular shape other than circular. Hydraulic diameterthen simply becomes the diameter of a circular holethat has the same area as the irregularly shaped flowpassage. In the case of a drilled-hole cage, thehydraulic diameter would simply be the diameter ofeach identical hole.
The question we will attempt to answer here is, “Howdo these single-stage, multiple flow passage designsreduce valve noise?” The answer may surprise you.At one time, it was widely believed that passing theflow through several holes instead of one would reducethe noise power level. The following quote is from anearly article on noise reduction which attempted toexplain this phenomenon. “The acoustic power of asingle flow restriction increases as a function of (C
g)2.
Changing the area by a factor of 2 results in a corre-sponding 6 dB change of power level, whereas, the
power level is changed only 3 dB when the number ofequal noise sources is changed by a factor of two.Thus noise reduction to be derived from utilization ofmany small restrictions rather than a single or fewlarge restrictions is self-evident.”
The reader should clearly understand that we nowknow that the explanation in the previous quote ISNOT CORRECT! In fact, the amount of acousticalpower generated by several small holes is preciselythe same as that generated by one equivalent largehole!
The considerable success of drilled-hole cages innoise reduction is not due to a reduction of the internalnoise power level, but due to the fact that the noisegenerated by the smaller holes has been shifted to ahigher frequency where it is no longer as serious aproblem to human hearing or the pipework.
Reviewing the shape of the typical “hay stack” noisepower spectrum in Figure 3 will help us understandhow this works. The peak power frequency (f
p) for a
single hole flow opening often falls into a lower audiblerange (e.g., 200 - 6000 Hz) where the ear is moresensitive to sounds than it is to the upper end of theaudible spectrum. By using several smaller holes topass the same flow, the peak power frequency ismoved to a much higher frequency. Thus, it is appar-ent from the “hay stack” curve that by moving the peakfrequency higher, the power level is decreased in thelower frequency range. Therefore, even though themaximum power level is still the same, the dB(A) levelis reduced because of the reduced sensitivity of thehuman ear at the higher frequencies.
This phenomenon produces an additional benefit aswell with regard to pipe transmission loss. For atypical pipeline, the greatest coupling between thedynamic characteristics of the pipe and the internalnoise field will occur in the 1000 Hz to 6000 Hz fre-quency range. Thus, by moving the peak frequency ofthe internal power higher, we reduce the amount ofenergy that is effective in exciting pipe vibrations andtherefore reduce the radiated noise.
Let’s now investigate how the use of a drilled-holecage accomplishes this shift in peak power frequency.When a pressure wave exits from a flowing jet, thewavelength of that pressure wave is primarily deter-mined by the diameter of the jet orifice. The wavefrequency, of course, is just the inverse of the wave-length. Thus, we can see that a small hole will pro-
16
duce a shorter wavelength (and therefore a higherfrequency) than will a larger hole. It’s as simple asthat! In fact, theory tells us that for a simple drilledhole cage noise trim, the amount of noise reduction isrelated directly to the number of holes; i.e., the moreholes, the greater the noise reduction capability.
In addition, experience in the gas production, petro-chemical and other industries has demonstrated thatacoustic energy in high capacity, gas pressure reduc-ing systems can cause severe piping vibrations, and inextreme cases have led to piping fatigue failures. Byshifting the peak frequency of the internal powerhigher, we reduce the amount of energy that is effec-tive in exciting pipe vibrations, and since stress isdirectly proportional to the level of vibration, there is areduction in the potential for fatigue damage in thesystem. Thus, the use of many smaller holes in thedrilled hole cage allows us to win two ways; less noiseand less pipe fatigue.
Fisher Control’s research performed on both internaland external large-scale piping systems lead torecommended guidelines for maximum valve noiselevels designed to ensure safe levels of pipe stressdue to acoustic vibrations. These guidelines, whichare summarized in Figure 11, were published in an ISApaper in 19861 . Figure 11 gives a recommendedSound Pressure Level (for standard weight pipe)measured at the standard location of 1.0 meter fromthe pipe wall as a function of the nominal pipe diameterin inches.
109110111112113114115116
0 5 10 15 20 25 30 35 40
Pipe Diameter (in.)
Allo
wab
le S
PL
at
1.0
Met
er (
dB
)
Figure 11: Recommended Maximum Valve NoiseLevels for Structural Integrity of the Piping System
SINGLE FLOW PATH, MULTISTAGEPRESSURE REDUCTION TRIM
“Single flow path, multistage” means that the sameflow stream passes through each of the multiple************************************************************************************************
1 Dr. Allen C. Fagerlund, “Recommended MaximumValve Noise Levels,” Advances in Instrumentation, Vol.41-Part 3, Proceedings of the ISA/86 Internal Confer-ence and Exhibit, Houston, Texas, October 13-16,
1986.pressure reduction stages sequentially in series. Thismeans that the outlet pressure of the first stagebecomes the inlet pressure to the second stage, andso on down the line. In its simplest sense, this isequivalent to placing two or more control valves inseries to reduce the pressure drop across each valve,rather than taking the entire pressure drop (p
1 - p
2)
across one valve. It would help to keep that perspec-tive when reviewing the following explanation of howmultistaging helps reduce the noise.
A review of the acoustic efficiency factors (ηn) in the
IEC standard shows that the acoustic efficiencyincreases proportionately to some higher power of thevelocity (i.e., the Mach number), ranging from 3.6 toapproximately 6.6 depending upon the flow regime.The point to be made here is that noise generation isvery sensitive to the flow velocity. For purposes ofsimplification and to illustrate the basic principle, let’sassume that the acoustic efficiency is equal to the 4th
power of the velocity. Actually, this is not too far fromthe case in flow Regime I where the exponent isactually 3.6. Based upon this simplifying assumption,we can continue.
We already know that the flow (and therefore thevelocity) is proportional to the square root of thepressure drop across the flow restriction. Thus, if wereduce the pressure drop by a factor of two, we canreduce the noise power level by a factor of four (-6 dB).This means that if we take the total pressure dropequally across two valves instead of one, the noisegenerated by each valve will be 6 dB less than if all thepressure drop was taken across one valve. We know,however, that when we combine two equal noisesources, the total noise power level is only 3 dBgreater than either of the noise sources alone. Thismeans that we have a net gain in noise reduction of 3dB.
Dividing the pressure drop equally across more thantwo stages will, of course, reduce the noise even more.For example, if we divide the flow equally across 4valves in series, we will reduce the noise power level ofeach valve by a factor of sixteen (-12 dB). When wecombine valves 1 and 2 we will get a 3 dB increase fora total of -9 dB. Likewise, we will get the same - 9 dBwhen we combine valves 3 and 4 together. Now if wecombine these two groups of valves together, we willget another 3 dB increase for a total noise level
17
reduction of - 6 dB for all four valves.
By following this same logic, we can show that eachtime we double the number of equal stages, we will getan additional 3 dB reduction in noise. We are rapidlyapproaching the point of diminishing returns if we haveto double the number of restrictions in series for each3 dB improvement. When we place all of the multiplerestriction stages inside a single valve, however, weget a dramatic improvement in the picture.
Each restriction still produces its share of noise, just asit would if it were a separate valve; however, the noisegenerated by all the interior stages will have a moredifficult time radiating to the environment since thenoise must pass through the rigid metal structure ofthe valve body in order to reach the observer. Only thejet from the orifice of the final stage will be able toeffectively radiate sound waves directly into the flowstream at the outlet of the valve, where it can then beradiated through the pipe wall to the observer. Thus, ifwe have a valve with an 8 stage trim, the noise powerlevel produced by the final stage would only be 1/64 (1/82) of the noise from a single valve. This wouldprovide a noise reduction of 18 dB (10log
101/64)
instead of only the 9 dB we would get with 8 separatevalves.
In reality, however, the picture may not always be thisrosy, since a small amount of the noise generated bysome of the interior stages may get introduced into theflow stream and carried downstream into the pipe atthe valve outlet, but this is likely to be relatively minorand the general principle holds. That is why the noisecalculations in the standard only consider the pressuredrop across the final stage of the multistage trim.
One final note should be made. The multistageconcept discussed so far is not the same thing as whathas been called the “tortuous path” method of noisereduction. The true multistage design has a series ofrestrictions, each followed by its own pressure recov-ery chamber; whereas, the “tortuous path” design issimply one long restriction which depends upon frictionand flow-direction changes to dissipate the flowenergy. It could be thought of as the equivalent ofplacing a series of elbows in a pipeline to absorb thepressure drop rather than placing a simple restrictionin the line. The “tortuous path” method is an attempt toabsorb the pressure drop over the flow path withoutdramatically increasing the velocity and therefore thenoise producing turbulence. While this method can
provide some noise reduction, it is not as effective asthe true multistage method.
MULTI-PATH, MULTISTAGE TRIM
This configuration is simply a combination of the twoprevious methods and the noise reduction is likewise acombination of the two phenomena.
PIPE REDUCERS AND EXPANDERS (SWAGES)
Pipe reducers and expanders, which are often called“swages” are often lumped together under the generalterm of “fittings.” It should be understood that thephenomena of valve noise generation discussed so farassumes that there are no swages attached to thevalve.
Due to the fluid velocity changes which take place inthe swage fittings, these swages are sources of noisegeneration in themselves. Thus, when a valve is fittedwith swages at the inlet and outlet, there are reallythree noise sources; i.e., the inlet reducer, the valve,and the outlet expander. Each of these sources mustbe treated as a separate noise source and the resultscombined using Table 1 to determine the total noisecoming from the combination of valve and fittings. TheIEC noise standard offers a fittings compensationfactor to account for the attached fittings; however, thistechnique places severe and unreasonable velocitylimitations on the outlet of the assembly. It is better totreat these fittings as separate noise generatingentities.
FLUID VELOCITY CONSIDERATIONS
Fluid velocity at the outlet of the valve has a significanteffect upon the noise produced by the downstreamturbulence. At the time this manuscript was written,the IEC standard had no provision for predicting noiselevels for valve installations where the outlet velocityexceeds Mach 0.3. In order to maintain realisticinstallation costs, however, it is not always possible tolimit valve outlet velocities to this range. For example,a control valve may be selected in a size smaller thanthe adjacent piping for economic reasons; however,the piping size is still subject to the normal selectionprocess involving gas density and mass flow. Withpressure reducing valves, for example, this invariablyleads to a downstream pipe that is larger than thevalve size, thus dictating the use of a pipe expanderwith resulting higher velocities in the valve outlet andexpander.
18
Intense turbulence, caused primarily by the differencebetween the gas velocity in the valve outlet andexpander and the larger downstream pipe, creates itsown noise source which can often exceed the noiselevel of the valve itself.
There are techniques available to accurately predictcontrol valve noise at high exit velocities, and work isbeing done to incorporate these techniques into a laterrevision of the standard.
NOISE TRANSMISSION LOSSES
Even though the control valve may be producing noisepower in the fluid stream at the valve outlet, it is of littleconcern to us until it actually reaches the ears of ahuman observer in the vicinity of the valve. The firsthurdle that the noise must overcome is to somehowget from pressure disturbances in the fluid stream topressure disturbances in the air surrounding thepipeline. To do this, of course, the noise energy in thefluid stream must cause the pipe wall to vibrate insome manner so as to disturb the surrounding air andproduce sound waves that will impact on the observer.
How effectively the noise power in the fluid stream canestablish vibration of the pipe wall depends upon manyfactors. It will be most effective when the fluid noisepower at any frequency coincides with a resonantfrequency of the pipe. This implies that the noisepower spectrum, and in particular the peak frequency,is an important consideration. Likewise, the geometryand material properties of the pipe will also have aneffect on its resonant frequencies and whether they willmatch up with the fluid noise frequencies.
There are basically three frequencies that we need todiscuss in order to better understand the acousticcoupling between the fluid in the pipe and the pipe wall.These three frequencies are the Acoustic CutoffFrequency (f
C), the Ring Frequency (f
r), and the First
Coincidence Pipe Frequency (fO). These three fre-
quencies always obey the following relationship:
fC ≤ f
O ≤ fr (11)
CUTOFF FREQUENCY
The cutoff frequency (fC) is basically a property of the
flowing fluid. It is the lower limit of energy transmissionto the pipe wall since below this frequency there is verylittle radial displacement of the pipe. When the wave-
length of the acoustic wave in the fluid is roughly equalto or longer than twice the diameter of the pipe, thewave moves down the pipeline essentially as a normal,plane wave at the speed of sound (c
2) in the fluid, as
illustrated in Figure 12.
c2
Figure 12: Normal Plane Wave
Since this normal sound wave is perpendicular to thepipe wall, it has little ability to transmit any energy tothe pipe wall. Therefore, below the cutoff frequency(f
C), where the wavelength is somewhat greater than
the pipe diameter, there will be essentially no acousticcoupling with the pipe and no sound will be transmittedto the outside observer. We would say that the trans-mission “loss” is very high.
FIRST COINCIDENCE PIPE FREQUENCY
The first coincidence pipe frequency (fO) is actually a
property of both the flowing fluid and the pipe. As thenoise frequencies become greater than the cutofffrequency, the wavelengths become shorter and theacoustic wave patterns in the fluid become much morecomplex. The shorter wavelengths attempt to radiatein all directions and so begin to propagate outwardtoward the pipe wall at some angle from the centerline.These waves then strike the pipe wall at an angle,reflecting off the wall and passing across the pipe tothe opposite wall. As these acoustic waves propagateby reflection down the pipeline, they tend to proceed ina spiral wave pattern.
As the acoustic wave in the fluid goes spiraling downthe pipeline, the radial component of this wave tends toinduce a corresponding wave in the pipeline which alsospirals down the pipe at the same speed as theacoustic wave spiral. Aside from the spiraling nature,this wave in the pipe is really a bending or flexure wavesimilar to what would occur in a flat sheet of metal ifwe grabbed it by the end and shook it rapidly up anddown. Imagine for a moment, that we have removed anarrow section of the pipe wall for some distance alongthe pipe as shown in Figure 13.
As we imagine this strip to be narrower and narrower,the curvature becomes less predominant and we canfurther stretch our imagination to think of this as simplya thin, narrow, relatively long strip of “flat” metal.
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If we were to grab the left end of this long strip andshake it rapidly up and down one time, we wouldexpect to see something similar to a sine wave thatwould travel at some speed down the length of thestrip, just exactly analogous to the kind of waves weused to make with jump ropes when we were kids.
Figure 13: Strip section of the pipe wall along thelength of the pipe
What we have excited in the strip is the fundamental(lowest) frequency mode which results basically in asecond-order, spring-mass oscillation of the strip. Ifwe were to shake the strip more vigorously in arandom manner, we could probably excite some of thehigher frequency modes which would result in evenmore complex wave shapes in the strip. For right now,however, we are interested only in this lowest fre-quency, fundamental mode of the pipe strip. Werecognize, of course, that this fundamental modefrequency is a function of the pipe material and geom-etry.
Let’s stretch our imaginations slightly further to think ofthis strip not as a long straight strip down the pipe, butas a spiral strip down the pipe which spirals at thesame rate down the pipe as the acoustic wave insidethe pipe. Thus, the radial component of the acousticwave continuously excites this strip causing it to wantto vibrate. The frequency, however, with which theacoustic wave excites the strip will determine just howeffective the vibration response will be. We know fromexperience that, because of the wide band of acousticfrequencies, there will most likely always be a fre-quency component of the acoustic wave that preciselymatches the lowest frequency mode of the strip. Asthe spiraling wave continuously excites the lowestfrequency mode of this strip, the amplitude of pipe wallmotion will be the greatest. This means that the noisetransmission through the pipe will be the greatest, orthe transmission “loss” will be at a minimum. Thefrequency of the acoustic wave where this occurs is
called the “first coincidence pipe frequency, (fO).”
Webster’s dictionary defines “coincidence” as, “Condi-tion, fact, or instance of coinciding; correspondence.”In our case, the acoustic wave speed as it spirals downthe pipe exactly coincides with the bending wavespeed down the pipe.
RING FREQUENCY
Figure 14: Ring section of pipe
Let’s now imagine a very short section along the lengthof the pipe. What we would have would resemble a“ring” as shown in Figure 14. If we were to apply astatic transverse force to the pipe as shown in Figure14, the deformation will be predicted by treating thepipe as a hollow beam with a particular bendingstiffness determined by the radius and wall thickness.When the stresses in the pipe are analyzed, we willfind that there will be nearly uniform compressivestresses through the wall thickness on the side of thepipe where the force is applied, and nearly uniformtensile stresses through the wall thickness on theopposite side of the pipe. The tensile stress on theopposite side of the pipe occurs due to the compres-sion wave which transmits the effect of the forcearound the circumference of the pipe ring.
If the force is now changed to an oscillating force, suchas we would see from the radial component of theacoustic wave, we would find that the stresses will varywith time since it takes the compression wave aroundthe circumference of the ring a finite amount of time totravel to the other side of the ring. If the frequency ofexcitation is very low, then the picture at any instant willclosely resemble the static case, where the stressesare opposite in sense on opposite sides of the pipe.
As the frequency of excitation increases, the speed of
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the compression wave around the circumference ofthepipe ring will begin to come into play. For a particularfrequency of excitation, the wave will arrive at theopposite side of the pipe out of phase with the drivingforce. At this frequency the traveling wave will arrive inphase with the driving force back at the point ofexcitation, due to a delay of exactly one period of thewave cycle. This “in phase” reinforcement feedbackcauses an amplification effect which greatly magnifiesthe movement of the pipe wall, thus amplifying theamount of sound transmitted; i.e., a minimum trans-mission “loss.”
The frequency where this resonant amplificationoccurs is call the “ring frequency (f
r)” and is defined by
the condition where the wavelength (λ) of the com-pression wave is exactly equal to the circumference(πD
i) of the pipe ring.
TRANSMISSION LOSS SPECTRUM
fofc fr
Transmission Loss
(dB)
Frequency, (Hz)
Slope equals 20 dB/Decade
Slope equals 13 dB/Decade
Figure 15: Pipe Transmission Loss Spectrum
Since our perspective is noise reduction, we usuallytalk in terms of transmission losses instead of trans-mission efficiency. As we have just implied, thistransmission loss for the pipe will vary with frequencyas shown in Figure 15. Below the cutoff frequency (f
C),
the transmission loss is very large (essentially infinite)since there is no radial component of the normal shockwave to excite the pipe wall.
As the frequency approaches the first coincidence pipefrequency (f
O), the acoustic waves begin to develop
some radial component to stimulate the pipe wall andnoise transmission becomes more and more efficient;i.e., the transmission loss decreases at a rate of 20 dBper decade of frequency to a minimum value preciselyat the first coincidence pipe frequency.
As the frequency increases from the first coincidencepipe frequency (f
O) toward the ring frequency (f
r), the
transmission loss increases slightly due to the complexpropagation path of the spiral acoustic waves. Therate of increase in this region is 13 dB per decade offrequency.
At frequencies above the ring frequency (fr), the
wavelengths become significantly shorter compared tothe pipe dimensions and the structure begins torespond more and more like a flat plate. In this region,the transmission losses begin to increase more rapidly(20 dB per decade) with frequency.
SUMMARY
Obviously, this has been a rather simplified approachto an extremely complex topic; however, an elementaryunderstanding and appreciation of the theory behindaerodynamic noise generation and transmission allowsone to make a fully informed decision regarding theselection of a control valve for any given noise applica-tion. There are a number of common errors that canbe avoided through application of this basic knowl-edge.
For example, when comparing noise quotations for avalve assembly, we recognize that it is important tomake certain that we are comparing apples to apples.One quotation may be limited to just the valve, whilethe other may include the attached swages. Knowingthat the swages may be the dominant noise source,and that the lower noise generated by the valve willhave minimal effect on the overall noise level, we canavoid paying too much for an expensive noise controltrim that will have neglible effect on the overall noiselevel.
Likewise, we might want to seriously consider thewisdom of buying an expensive noise control trim for avalve that is going to be installed next to a much largernoise source, such as a compressor, etc. Remember,even if the noise of the valve is equal to the other noisesource, the valve will only increase the overall noiselevel by 3 dB. A valve vendor might take advantage ofthis fact by promising a lower valve noise level thancan actually be achieved, knowing that the likelihood ofverification is slim. The best defense against this tacticis to verify the stated valve noise prediction via the IECnoise prediction standard.
The general rule of thumb for controlling the noise level
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in a given space is to identify the dominant noisesources and eliminate or reduce them. Only then is itlogical to put precious resources into reducing valvenoise.Finally, an understanding of pipe transmission losstheory helps us realize that controlling the frequency ofthe noise being generated is perhaps even moreimportant than the noise power. There are threeimportant benefits to the frequency shifting method ofnoise control.
First, much of the high frequency noise will fall outsidethe audible range where it has neglible effect onhumans. Secondly, the high frequency noise isconcentrated mainly in the region of the frequencyspectrum where the transmission loss is very high (seethe right side of Figure 15). In this region, very little ofthe noise that is generated will get into the outsideenvironment where humans will be located. Finally,the reduced coupling between the internal sound fieldand the pipewall at these high frequencies means thatthere are reduced levels of stress in the piping struc-ture which will help to prevent fatigue damage.
As in many other areas, knowledge is the best defenseagainst waste and inefficiency.
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The contents of this publication are presented forinformational purposes only, and while every effort hasbeen made to ensure their accuracy, they are not to beconstrued as warranties or guarantees,express or implied,regarding the products or services described herein ortheir use or applicability. We reserve the right to modify orimprove the designs or specifications of such products atany timewithout notice.
Fisher, Fisher-Rosemount, and Managing The Process Betterare marks of the Fisher-Rosemount Group of companies.All other marks are the property of their respective owners.
Fisher Controls International, Inc.205 South Center StreetMarshalltown, Iowa 50158Phone: (641) 754-3011Fax: (641) 754-2830Email: [email protected]: www.fisher.com
