Gas pressure reducing valve noise

Jounlal of Sound and Vibration (1975) 41(4), 506-509

GAS PRESSURE REDUCING VALVE NOISE The application of Lighthill's eighth power of velocity relationship, for the noise generated by turbulent jets, to the special case of noise generated by gas pressure reducing valves, is discussed. An equivalent relationship expressed in convenient valve parameters is developed. Some experimental results are presented which indicate a reduced acoustic efficiency for small enclosed jets. The most directly applicable relationship to come from a large body of work on the noise due to turbulent jets is Lighthill's dimensional and empirical relationship [I] (a list of symbols is given in the Appendix) W " 10-4p: U 8 Afl2aSo.

(1)

A slightly modified form of expression (1), discussed in reference [1], is W ~_ 10-'* p~ U s Afl2po a~.

(2)

These relationships are not expressed in the most convenient form for valve noise considerations. The isentropically expanded jet velocity, for a negligible upstream velocity, can be expresse~t in terms of the upstream and downstream pressures as U = ax[{2/(~, - 1)} (1 - (P2/Px)'-Xl~}] '/2.

(3)

F o r air ~ = 1"4 and, given that ax = ao = 344"4 m s -x, substitution of equation (3) into expression (l) yields W - 1657.64G(1 - (P2/P,)~ 3"5, (4) where G represents mass flow. A useful approximation to equation (3) which is accurate to within five percent, for 0~
U "~ ax .,]I'43AP/Px.1/2 P21/29

(5)

Substitution of expression (5) into expression (2) yields W = (1-46 x 10-4 a6/po a~) (G2/Aj) (Ap2]px p2)3/2._

(6)

T o test expression (6), the noise due to air flow through an orifice plate, placed in a 0.05 m diameter pipe, exhausting to atmosphere, was measured in a reverberant chamber. Three different orifice plates (of diameters 0.0127, 0.00657 and 0.00319 m) each were tested with 0.965 m of 0.05 m pipe downstream. The sound power level of the noise produced, and the 1/3 octave band frequency spectrum, were measured over a wide range of measured mass flows and pressure ratios (PI[P2 ranged from 1.14:1 to 6.78:1). The experimental results for sound power level, plotted against the parameter (G2]A) x (Ap2]PxP2) 3/2, are shown in Figure 1, where AP is the total pressure drop, Px is the upstream pressure, Pa is atmospheric pressure, P2 is equal to Pa for Pa[PI > 0.528 and to 0.528 PI for PA[PI <~0.528, and A is the orifice cross-sectional area. Shown as a broken line in Figure 1 is the sound power level predicted by equation (4) (P2 = Pa for all values of Px). - Tile results for the two smaller orifice nlates show a linear relationship against the plotted 5o6

LE'Fi'ERS TO THE EDITOR i0-5

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Figure 1. W.P.L. (re 10 -12 Watts) vs. (G2/A)(zIP2]P~P2)312 (kg2/m 2 s2). Experimental: 0.0127 m orifice plate, v ; 0.00657 m orifice plate, o; 0.00319 m orifice plate, El. Solid lines are drawn at 10 dB per decade: i.e., linear. The arrow indicates the point at which the critical pressure ratio is reached. The broken line represents the noise level predicted by equation (4). The ratio in parentheses is the maximum pressure ratio applied across each orifice plate. Extensions of the level predicted by equation (4) and the data for the 0'00657 m orifice plate are shown in the right hand bottom corner.

parameter. An unexpected result was the range of pressure ratios, up to 6.78 : l, for which the relationship held. This would appear to indicate that shock associated noise [2] was not a significant factor. These two orifice plates did have divergent sections, 0.005 m long, in the form of a 90 ~ included angle cone. It is not thought however, that this would provide a correctly expanded jet. Figure 2 shows a typical 1/3 octave band spectrum, which was observed for all three orifice plates (with one single exception) at high subsonic and supersonic expanded jet velocities. A small number of constant bandwidth (40 Hz) spectra were taken and these indicate identifiable resonant peaks at multiples of 176 Hz (approx.) up to and above 5000 Hz. Equating half the wave length to the pipe length yields a frequency of 178"5 Hz. ' The sound power level variation and the 1/3 octave band spectral characteristics of the larger orifice plate were in general similar to those of the smaller orifice plates. The one exception was the result for the highest pressure ratio tested, with this orifice plate, of 3.0:1. The sound power level was some 4.0 dB higher than extrapolation of lower pressure ratio '

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5 0 8 ."

LETTERS TO THE EDITOR

results would indicate. Also there was a marked peak i.n the 6300 Hz 1/3 octave filter band. Both these results are consistent with the presence of shock associated noise. Expressions equivalent to equation (6) may be derived as follows. For subsonic flow G2 -'I'43a2Ap"2A2tpl12P tl2, and substitution into equation (6) yields -1 VJ JI 1 2 IV ~ 2.09 • I O-4(p~ aS/po aS) (A e 2/e I P2) 2 Aj,

(7)

"~ 2.09 • 10-4(y 2 a~/a~ at) (AP/PI)2 AP 2 Aj.

(8)

For choked flow G2 = a~p~{2/('/+ l)}t+~m-t)A~ and PtP2 = P~{2/(~'+ 1)}~a~-'>. Substitution into equation (6) yields I V " 1-46 X 10-'{2/(~ + I)} 2-~/2''-'' (p2 a~/po a~) (AP/P,) 3 A j,

(9)

~_ 1-46 x 10-4r2{2/(y at- 1)}2-'/2(~-1) (a~/po a~) (AP/Pa) AP z Aj.

(10)

Equations (7) and (9) show the Lighthill expression, in terms of upstream sonic velocity, modified by pressure ratios. Equations (8) and (10) give equivalent expressions which do not contain P 2 . '; Examination of Figure I shows that only the sound power levels measured for the 0.0127 m diameter orifice plate are in even approximate agreement with the levels predicted by equation (4). The sound power levels for the 0.00657 m diameter orifice plate are generally 7.0 dB below those of the larger orifice plate. Similarly the sound power levels for the 0"00319 m diameter orifice plate, are 8.0 dB below those of the 0.00657 m diameter orifice plate. The reasons for this occurrence are not clearly understood. The inflow turbulence, for the smaller orifice plates, would be expected to be of lower intensity, due to the lower Reynolds number and the higher contraction ratio. However, it seems unlikely that this could account for the 15.0 dB difference between the largest and the smallest orifice plate. The only other explanation offered here is that, due to the presence of solid boundaries downstream of the throat, there exists a pressure back reaction on the flow, which is sufficient to reduce the noisegenerated by the smaller jets. Returning to equation (6), the results for the three orifice plates will collapse when plotted against a modified parameter of the form

IV oc (GZ/Ap) (Apz/pt pz) 3'z (A/Ap) o4,

(11)

where Ap is the cross-sectional area of the downstream pipe. (Ap is used as a reference only to maintain dimensional correctness.) With the dummy variable As, neglected, similar modification of equations (8) and (10) yields, for subsonic flow,

IV oc (Ap/pt) 2 Ap 2 A~'4,

(12)

IV o~ (AP/P 0 AP ~ A~'4.

(13)

and, for choked flow,

The above relationships have some agreement with a relationship inferred from the work of Schuder [3]. Schuder performed a dimensional analysis of ~/alve noise and carried out extensive tests on a large range of valves. The relationship inferred from Schuder's curves for a double ported globe valve at high pressure ratios is IV o:

(Ap/p,) t65 A P t S A ~ . 2 . .

(14)

While the apparent attenuation of the noise from small enclosed jets is insufficiently - e~lblained, it would seem to have application in the design of quiet valves. Also, for a given

LETTERSTO THE EDITOR

509

valve pressure ratio, a correctly expanded supersonic exhaust jet is preferable to an underexpanded jet with its associated shock ceils. Equation (6) provides a useful alternative form of Lighthill's eighth power of velocity relationship. These rqsults arose from work primarily intended to investigate the dipole noise generating mechanism o f " q u i e t " gas pressure reducing valves. Only the small amount o f data presented here is available at this time. It is intended, in the near future, to submit a paper for publication ~vhich deals with both aspects of valve noise. ACKNOWLEDGMENTS The author wishes to gratefully acknowledge Associate Professor A. Williams of Monash University and the State Electricity Commission of Victoria. The former for useful and encouraging discussions, and the latter for sponsoring him during this project. Department of Alechanical Engineering, Monash University, Clayton, Victoria 3168, Australia (Received 22 April 1975)

P . L . JENVEY

REFERENCES I. M. J. LIGHTHILL1963 American Institute of Aeronautics attd Astronautics Journal 1, 1507-1517. Jet noise. 2. M. J. FISHER,P. A. LUSHAND M. HARPERBOURNE1973 Journal of Sound and Vibration 28, 563585. Jet noise. 3. C. B. Sr 1970 Chemical Processing November, 10-15. New technique for valve noise prediction. APPENDIX: LISTOF SYMBOLS A Aj Ap a, ao a~ 6: z/P PI Pz U W 9pj I ~'

cross-sectional area of the orifice (mz) cross-sectional area of the jet (m z) cross-sectional area of the downstream pipe (m z) upstream sonic velocity (ms -~) ambient sonic velocity (m s -~) local jet sonic velocity (m s-~) mass flow rate (kg s-~) totalprcssuredrop(Pa) upstream pressure (Pa) downstream pressure (Pa) jet expanded velocity (ms -~) acoustic power (Watts) jet density (kg m -a) ratio of specific heats