This led to the following conclusions: First, one has to realize, that vapor bubbles within the liquid implode where the
C O N T R O L & S M A RT V A LV E S
A fresh look How to estimate cavitation noise Estimating cavitation noise on valves has vexed many experts due to the apparent complexity of the phenomena. The problem has been tackled by private firms[1] and even resulted in an IEC standard 60654-8-4[2]. While turbulence noise produced with water in control valves can be predicted fairly accurately, since it follows standard hydrodynamic and acoustic laws, cavitation still challenges established wisdom. Current methods are either too complicated or not accurate enough. By Dr. Hans D. Baumann, P.E.
This writer also studied the phenomena for many years[3] and lately found that the slopes and magnitudes of the plotted data of cavitation seemed to be all identical for a given Xfz (coefficient of incipient cavitation) value1. This happens irrespective of the underlying turbulence input such as flow rate, inlet pressure and so on. This points to the conclusion, that cavitation is not a hydraulic phenomena, rather an aerodynamic one caused by rapid pressure fluctuations in the fluid.
Cavitation is an aerodynamic phenomenon On closer examination of the seemingly constant slopes of cavitation produced sound levels led me to investigate the possible causes of these results. Laboratory tests conducted already several years ago[1] showed that the predominant sound produced by cavitation (imploding vapor bubbles) agreed with results calculated with aerodynamic noise equations rather than those applied for liquid turbulence. This led to the following conclusions: First, one has to realize, that vapor bubbles within the liquid implode where the entrained vapor compresses at or near sonic velocity. Sounds produced by gas jets at or near sonic velocity, follow a mixed bipolar- quadruple pattern, which is proportional to U4, where U is the jet velocity[4].
It is also known, that the mechanical power of a gas jet follows the U2 relationship. Adding all exponents together, one finds the cavitation sound is a function of U6 and, since at choked flow (sonic velocity) U is a function of inlet pressure2 and not of pressure drop such as (P1-P2)0.5. Thus one can write LAcav (the sound level of beginning cavitation) is proportional to P6. Or, even better: LAcav1= 60 log(X / Xfz), where X = (P1 – P2) / (P1 – Pv) and Xfz = the pressure ratio where there is a first discernible flow change due to cavitation. For example, at a pressure condition with X = 0.4 and an Xfz of 0.25, the sound level for cavitation only will be 60 log(0.4/0.25) = 12.25 dB. This has to be added to the turbulent sound level at the given pressure ratio. It may be prudent to add about 3 dB to account for the A-weighted correction of the higher cavitation peak frequencies above 1000 Hz. Offhand, this looks much too simple, yet observations from the test data demonstrate very good correlation. An old adage states that what goes up has to go down. This is true as well for the cavitation curve. It happens approximately
half-way between Xfz and the vapor pressure or X = 1. The reason is, that the downstream pressure P2 corresponding to Xfz is very high and, as a result, there is a large pressure drop between this P2 and the vapor pressure, causing the vapor bubbles to violently implode. However, at the above described mid-point (defined as Xy) the P2 pressure is only one half of what it was at the Xfz level. From valve sizing for gases we know, when the pressure drop in an orifice is less that 50% of the inlet pressure, then there is no longer choked flow, or consequently sonic velocity. This phenomenon happens with liquids too and as a result, the caviation curve decreases rapidly till the cavitation sound level is zero, once X = 1 or the vapor pressure is reached and vapor bubble collapse no longer occurs. This secondary cavitation process can (somewhat simplified) be described as: LAcav2 = 140 log (X / Xy). The total valve noise is now: LAext. = Turbulent sound level + LAcav1 – LAcav2. in dB(A).
Benefits of the method The illustration in Figure 1 shows the standard cavitation curves using the above equations. These curves fit every valve and service conditions (subject to some limitations described below). The only variable is Xfz. Of interest is the fact that the magnitude of cavitation noise increases drastically with lowering of Xfz. The lesson here is to select valves having a higher Xfz to reduce noise and also cavitation damage. Test data have shown this schema is applicable for Xfz values as low as 0.1 and as high as Xfz = 0.7 (see Table 1 below).
Table 1 Tabulation of cavitation parameters: Xfz x 10
1
2
3
4
5
6
7
Xy
0.55
0.60
0.65
0.70
0.75
0.80
0.85
29
20
15
10.6
7.5
4.4
Max. Magnitude* 44
* in dB , add 3 dB for A weighted scale
1 See VALVEWORLD, November 2014 issue, pp. 173-177. 2 In this case the downstream pressure at the point where X = Xfz. 80
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C O N T R O L & S M A RT V A LV E S erratic test data, it confirms again the 25FL log(X) turbulent sound trend line. Finally, it indicates an about 18 dB maximum cavitation amplitude as would be expected from figure 1, confirming, that the cavitation slopes and magnitudes are independent of valve size and flow conditions. It is expected, that this proposed method will not only greatly simplify noise calculations but also will improve the accuracy of such estimates.
When flashing is cavitation The experimental data shown in Figure 5 indicates pressure ratios extending beyond the vapor pressure, where the vapor stays in solution and the bubbles no longer implode, at least in theory. However, as the data clearly shows, there is a significant increase in the sound level beyond X = Pv, an increase that should not occur, when a homogeneous liquid / vapor mass travels through a pipe. In this case, the vapor pressure was 2 bar and a vacuum was produced beyond X =1 in order to achieve higher pressure ratios. Here is a suggested explanation: Further decrease in pressure beyond the vapor Incidentally, the trend line of turbulent sound between X=0.1 and 1 is proportional to 25FL log(X), see blue line, unless small orifice sizes are involved (to be discussed in subsequent paragraphs). Figure 2 is another way to show the accuracy of this method. Here we see the pipe internal sound levels which, except for the beginning turbulent portion, has a slope of (X/Xfz)6, see light blue line. This agrees with the P6 power discussed ealier. Figure 3 shows test data of a 0.150 m butterfly valve with a Cv of 592. Typical for large valves, this Xfz number is only 0.14 (note double X scale). Even though the test data is incomplete, it shows the accuracy of the turbulence and cavitation slopes. Note, even with only a pressure ratio of 0.4, the cavitation noise already exceeded the turbulence noise by 38 dB, as predicted. Another example is a 0.100m Eccentric Rotary Plug valve with an Fd of 0.25 and Xfz of 0.3 as given in Figure 4. It again shows good agreement with both turbulent and cavitation slopes. Note that here the additional cavitation noise peaks at 17 dB in contrast with the previous data due to the higher Xfz number. Fd is the ratio between a valve orifice and the sound producing jet diameter. Fig 4a shows test data of a 0.025 m (1 inch) Globe Valve. Despite the rather
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C O N T R O L & S M A RT V A LV E S Limitations of the method
pressure Pv causes the entrapped gas to expand at the rate of Pv / P2 following gas laws (temperature changes can be ignored due to the short time spans involved). Using the data from Figure 5 at the pressure ratio X of 1.2, the vapor volume now increases, five times (2 / 0.4) from the 2 bar vapor pressure . This makes the total volume in the pipe, including the water, increase substantially. This results in a velocity-head pressure of nearly 1.6 bar inside the pipe. This in turn requires a static back pressure of about 2 bar, in order to push the high volume through the downstream pipe (in thermo-dynamic terms, the volume of the entrapped gas expands from 14.2 m3/kg to 63 m3/kg, a ratio of 4.43/1 (close to the assumed pressure ratio). There now exists a pressure differential of 2 bar minus 0.4 bar ( the static valve outlet pressure and new vapor pressure in the pipe) equals 1.6 bar that could , using the slope relationship of 60 log(1.2 / 1), cause a sound level increase of 4.8 dB, which is close to the measured data. This backpressure- created cavitation causing the often cited destruction of valve parts, is erroneously attributed to a process of flashing. Such an occurrence is confirmed by the upward slope of the sound level above X = Pv in figure 5 It clearly shows that instead of flashing, 84
we have cavitation reoccurring, following at the same rate of increase (60 dB per decade of X / Xfz), except this time, the vapor pressure now is the new Xfz. One can argue that, whenever there is a closed pipe downstream of a valve, one will experience cavitation and associated valve damage.
As far as limitations are concerned, this method is not applicable for multi-stage valves, nor pipe sizes where the first coincidence frequency is below 5,000 Hertz (typically pipes larger than 0.2 m). This also applies to small valves or orifice sizes. A typical example is shown in Fig. 6. Due to the small jet diameter (0.004 m) the cavitation peak frequency is high, about 50% of fo. Due to the unsteadiness of the pipe resonance modes,[7] the transmission loss in this area vacillates between (fo / fp)2 and (fo /fp)3 where fo is the pipe’s first coincidence frequency and fp is the pipe’s internal peak noise frequency. As shown in Fig. 6 this seems to happen at Xfz pressure ratio when, due to the onset of cavitation, the noise peak frequency fp, suddenly changes. The graph shows both slopes in order to indicate the difference. Here the lower rate matches the turbulence while the higher rate does fit the predicted cavitation profile. This poses a great area of uncertainty and creates difficulties in correct sound calculations. Luckily, it seems to affect only small orifices having relatively high frequencies. A note of caution: All shown test data was measured using schedule 40 pipes. While heavier pipe walls will reduce the overall sound level, it is not expected to affect the slope and magnitude of the cavitation sound itself. However, more research is needed in this area.
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C O N T R O L & S M A RT V A LV E S Conclusions 1. Cavitation is an aerodynamic phenomenon caused by pressure changes in the liquid. 2. The slope and magnitude of the cavitation sound level is determined by the coefficient of incipient cavitation Xfz. 3. The max. cavitation sound level occurs midway between Xfz and the vapor pressure. 4. Typically, all turbulence created sound between pressure ration of 0.1 and the vapor pressure follows a 25FL log (X) relationship. 5. Flashing in a downstream pipe can cause cavitation in the valve. Mass Flow, W = 7.7 x 10-4 x Cv x ΔP0.5 kg/s Jet velocity, Uvc = ( 2 x ΔP / FL2 x ρi)0.5 m/s Acoustical efficiency factor η = 10-4 x Uvc / Ci dimensionless Wmo, the mechanical power converted, Wmo = W x Uvc2 x FL2/ 2 Watts Note, Wmo is proportional to P1.5 Acoustic power, Wa = η x Wmo / 4 Watts Jet diameter, Dj = 0.0045 x Fd x (Cv x FL )0.5 m Peak frequency of jet noise, fp = Nstr x Uvc /Dj Hertz. Nstr = 0.08. Internal sound pressure, Lpi = 10 log(3.2 x 109 x Wa x ρi x Ci / Di2) dB
References 1.
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4.
5.
6. 7.
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Baumann H., Page G. A method to predict sound levels from hydrodynamic sources, associated with flow through throttling valves. NOISE CONTROL ENGINEERING JOURNAL, 43(5). September-October, 1995, pp. 145-158. Industrial –process control valves- part 8-4 Prediction of Noise created by Hydraulic Fluids., International Standard IEC 60534-8-4, (International Electrotechncal Commission, Geneva, Switzerland. Kiesbauer J., Baumann H. D. A method to estimate hydrodynamic noise produced in valves by submerged turbulent and cavitating water jets. NOISE CONTROL ENGINEERING JOURNAL, 52 (2), March-April, 2004. Beranek, L.L, Ver, I.L. NOISE AND VIBRATION CONTROL ENGINEERING, Second edition, John Wiley and Sons, Inc. 2001, p.614 Baumann H. D. determination of peak internal sound frequency generated by throttling valves for the calculation of transmission losses. NOISE CONTROL ENGINEERING JOURNAL, 36 (2) 1991, pp75-82. This authors own test data. Blake, W.K. Mechanics of Flow-Induced Sound and Vibration V2: Complex flow…, Volume 2, AKADEMIA PRESS, June 1986p. 685, figure 0.4.
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C O N T R O L & S M A RT V A LV E S LAext. = Cav1- Cav2 dB(A) NOTE: LAext. must not be less than Lat.
Thank you I would like to thank both Edward W. Singleton of KKI Corp. UK and Prof. Dr. Michael Johnson of Utah State University for their helpful comments and advice.
About the author
Pipe’s first co-incidence frequency fo; fo = 0.586 x Ci / Di Hertz ΔTLfp , frequency dependent transmission loss, ΔTLfp = 20 log( fp / fo) Transmission loss TL = 10 log(Cp x ρP x tp / Co x ρo x Di) + ΔTLfp dB Turbulent Sound Level: Lat = Lpi + TL – (Di +2 / Di), dB Primary CAVITATION SOUND LEVEL Cav1 , if X is larger than Xfz but equal or less than Xy where
Xy = [Xfz + ( P1 –Pv / P1)] / 2 Cav1 = Lat + 60 log(X / Xfz) +NA. dB(A), where NA is a constant accounting for the contributions by the A-weighted sound additions, NA = 3 dB (high frequency cavitation noise (above 1000 Hz) only). If X is larger than Xy; Z= 60 [(X – Xy / Xy – Xfz) +1] Secondary CAVITATION SOUND LEVEL: Cav2 = [Z log(X/Xy) + NA + 25 FL log(1/ Xy)]. dB(A)
Dr. Hans D. Baumann P.E. is a world renowned expert on control valve and acoustic technologies besides being an author of over 130 technical papers and seven books on control technology and acoustics, including “CONTROL VALVE PRIMER – A user guide”, published by ISA and now in the fourth edition. For 36 years, he represented the USA as Technical Expert on WG 9 of IEC committee TC 65. He is the holder of over 100 US patents and he developed the first scientific method to predict aerodynamic sound levels of valves.
