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Proceedings of the 5TH International Symposium on FSI, AE & FIV+N At the 2002 ASME Int’l Mechanical Engineering Congress & Exposition 17-22 November 2002, New Orleans, Louisiana NCA-33378 ACOUSTIC VIBRATION IN A STACK INDUCED BY PIPE BENDS Eisinger, F.L. and Sullivan, R.E., Foster Wheeler Power Group Inc., Clinton New Jersey 08809-4000 and Feenstra, P. and Weaver, D.S., McMaster University Hamilton, Ontario, Canada Phone: 908-713-2394 Fax: 908-713-2380 E-Mail: frank_eisinger@fwc.com
p,q ABSTRACT

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Proceedings of the 5
TH
International Symposium on FSI, AE & FIV+NAt the 2002 ASME Int’l Mechanical Engineering Congress & Exposition17-22 November 2002, New Orleans, LouisianaNCA-33378ACOUSTIC VIBRATION IN ASTACK INDUCED BY PIPE BENDSEisinger, F.L. and Sullivan, R.E.,Foster Wheeler Power Group Inc., Clinton New Jersey 08809-4000andFeenstra, P. and Weaver, D.S.,McMaster UniversityHamilton, Ontario, CanadaPhone: 908-713-2394Fax: 908-713-2380E-Mail:frank_eisinger@fwc.com
ABSTRACTAcoustic vibration in two stack liners located insidea stack downstream of two induced draft fansoccurred at high loads. Measurements confirmedthat an acoustic wave developed in the fundamentaldiametral mode of the cylindrical stack liners. Itmanifested itself as a pure tone traveling through thestack to surrounding residential areas. It wassuspected that turbulent flow in the pipe bendsupstream of the stack and downstream of the fanswas the source of the excitation. Laboratory scalemodel tests confirmed that the bends indeed acted asthe source. Two guide vane configurations placedinside the bends were tested experimentally. Thetests showed that properly placed guide vanes wouldreduce the acoustic levels in the stack. The paper gives a description and evaluation of the problem.NOMENCLATUREc = speed of sound, m/sD = pipe diameter, mk = pressure drop coefficient, dimensionlessM = v/c = Mach number, dimensionless
∆
p = pressure drop, PaP = acoustic pressure, Pap,q = acoustic mode orders for cylindricalpipe, diametral andradial, respectively, dimensionlessv = flow velocity, m/s(
πα
)
p,q
= acoustic frequency parameter for cylindrical pipe,dimensionless
ρ
= mass density of gas, kg/m
3
Subscripts:a = absolutei = inside or inleto = outletac = acousticINTRODUCTIONNoise measurements in the residential areas inthe vicinity of a power plant revealed the existence of a persistent 50dB strong single tone noise generatedby an acoustic resonance condition which developedinside the 1.45m diameter 88m long vertical stackliners. As the upstream sections of the liners at their inlet consist of two 90 degree bends, it wassuspected that the likely driving source of theacoustic resonance is the flow turbulence generatedinside the bends.One fifth scale laboratory air flow model tests [1]confirmed the development of the acoustic waves.
The effect of two and three guide vanes installed inboth upstream bends was tested successfully. Thetests showed that the installation of guide vanesreduced the pressure drop through the bendssubstantially and also commensurably reduced theacoustic resonance peaks developed in the liners.This paper will provide the results of theexperimental full scale and laboratory scale tests andtheir interpretations. A theoretical analysis of thenoise reduction in the system due to the installation of guide vanes in the bends will also be given.BRIEF REVIEW OF PUBLICATIONSPredictions of acoustic pressures in a pipe basedon heat-generated one-dimensional wave theory waspublished by Chu [2,3] and its analogy to a flowvelocity and pressure drop-generated wave wasshown and discussed by Eisinger et al. [4]. Thetheory of Mach number and pressure drop-generatedacoustic waves was extensively utilized by Eisinger etal. [4] and Eisinger and Sullivan [5] in the prediction of acoustic vibration and its suppression in steamgenerator and heat exchange tube banks. Blevinsand Bressler [6] published experimental data fromcold air laboratory scale model tests relating theproduct of Mach number and pressure drop to theacoustic pressure levels in heat exchanger tubebanks.Turbulence-induced acoustic waves generated inpiping systems were extensively studied by Bull andNorton [7], Norton [8] and Fahy [9]. Carucci andMueller [10] presented experimental evidence for alarge number of full scale piping systems exposed toflow velocity and pressure drop related internalacoustic loading. Eisinger [11] and Eisinger andFrancis [12] developed design guidelines againstacoustic fatigue in piping systems utilizing the theoryof the strength of the acoustic waves inside a pipingsystem related to the flow Mach number and pressuredrop through the system.DESCRIPTION OF PROBLEM AND EVALUATIONStack Liner Geometry and Flow ConditionsThe 96m high concrete stack contains two side-by-side 1.45m in diameter 88m long cylindrical linersthrough which the final boiler exhaust gases arereleased to the atmosphere. Two 90 degree bendsplaced in series are located at the upstream end of each liner. Figure 1 shows schematically the liner configuration and Figure 2 shows the geometry of thebends.Gas flow discharged from induced draft fansthrough silencers (one fan for each liner) enters thebend portions of the liners, continues through thecylindrical portions and exits to the surroundingatmosphere at the top. Table 1 gives therepresentative gas flow parameters at the inlet andoutlet at full load. It can be seen that the gasundergoes temperature, pressure and densitychanges over the length of the flow path.Full Scale Sound and Vibration MeasurementsSound measurements conducted in thesurrounding areas of the power plant have revealedthe existence of a single tone 50dB (re: 2 x 10
-5
Pa)noise at a frequency of 144Hz. Figure 3 shows atypical sound spectrum taken in the vicinity of theplant.Structural vibration (acceleration) measurementswere taken on the pipe bends at the accessible lower end of the stack liners. A single frequency responseat a frequency of 172 Hz was measured in the bendarea. Figure 4 shows a typical accelerationspectrum.Interpretation of Measurements. The frequency of acoustic waves (higher order acoustic modes) in acylinder is given by [8]
( )
iiq p,q p,
π
Dcf
πα=
(1)where c
i
is the speed of sound in the medium insidethe cylinder, D
i
is the inside diameter of the cylinder and (
πα
)p,q is a parameter representing the acousticmode. Here p,q are the mode orders giving thenumber of diametral and cylindrical nodal lines,respectively.Using equation (1) and flow data in Table 1 for p =1, q = 0, i.e. for the first diametral acoustic mode with(
πα
)
1,0
= 1.8412 [8], we obtain for the acousticfrequencies the following values: f
i
= 172Hz at thestack inlet, and f
o
= 144Hz at the stack outlet (Table1). These frequencies match those measured at thebends and in the plant surrounding areas,respectively, confirming the existence of the diametralacoustic mode inside the entire length of the stackliners. A gradual change of the acoustic frequencyoccurs, consistent with the variation of thetemperature and pressure of the gas inside the stackliners.Scale Model Laboratory Tests with Cold Air Laboratory model testing of one simulated stackliner (one fifth scale) exposed to air flow at ambientatmospheric conditions was performed [1]. The mainpurpose of the test was to determine whether acoustic waves would be generated and if generatedwhether their strength could be reduced by insertingguide vanes in the bends. The motivation of utilizing
guide vanes to reduce pressure drop and therebyreduce the generated acoustic pressure levels wasbased on the past studies of piping systems [11], [12],where a relationship between acoustic pressure Pand the product of Mach number M and pressuredrop
∆
p has clearly been established.The tests were designed to first obtain baselinedata for the unmodified scale model and then datawith two and three guide vanes inserted into both of the 90 degree bends.The recommended “optimum” arrangement of guide vanes [13] has been chosen for the tests.Figure 5 shows the arrangement of the guide vanesinserted into the larger 2.45m radius bend and thesmaller 1.53m radius bend, respectively. The“optimum” vane arrangement based on the equalradius ratio concept is shown in Figure 6 for two andthree guide vanes in the smaller 1.52m radius bend.A similar arrangement was devised for the larger radius bend.The scale model pipe system made of acrylicmaterial was exposed to air flow generated by acentrifugal fan within a range of flow velocities. Ateach flow condition, average flow velocities, pressuredrop through the bends, and acoustic resonantpressures generated in the straight pipe downstreamof the bends, was measured. Table 2 gives theresults for two sets of tests for three flow conditionsfor the unmodified and for the modified structure withtwo and three guide vanes installed.At each flow velocity v, the maximum acousticpressure P, the pressure drop through the bends
∆
p,and the product of Mach number M = v/c andpressure drop, M
∆
p, are given in Table 2 for a speedof sound of c = 346.9 m/s at 25
o
C.The results show that the pressure drop throughthe bends is reduced by an average of 32.5% withtwo guide vanes and practically is not further reducedby the three guide vanes.It can also be seen that the installed guide vanesreduce the generated maximum acoustic pressuressignificantly (here again, the three guide vanes didnot improve the results over those of the two guidevanes).From the experimental data the numerical values of the pressure drop coefficients through the bends(excluding explicit friction effects)
2
ρ
v2
1∆
pk
=
(2)can be evaluated at k = 0.728 for the two bends withno guide vanes, and k = 0.491 for the bends with twoor three guide vanes, respectively.In order to visualize the relationship between theacoustic pressures and the parameter (M
∆
p), thevalues in Table 2 for both the bends with no guidevanes and with two guide vanes have beennormalized to atmospheric pressure p
o
= 1.0135 x10
5
Pa and plotted in Figure 7. It can be seen that aclear relationship between P and M
∆
p for bothconditions emerges in the form of
( ) ( )
2.
1
oo
p/p
∆
M72
1
pP
=
(3)indicating a strong exponential relationship betweenthe flow parameter M
∆
p in the bends and thegenerated maximum acoustic pressure P in thecylindrical pipe downstream.Prediction of Acoustic Pressures in Full ScaleSystemTable 3 summarizes the flow parameters in thebend area in the full scale arrangement at full load.Two conditions are shown: 1) The srcinal conditionwith no guide vanes and 2) The modifiedarrangement with two guide vanes installed in each of the upstream bends. Here the pressure drop datawere calculated using the experimentally-determinedpressure drop coefficients of k = 0.728 and 0.491 for the bends with no vanes and two guide vanes,respectively.Table 4 gives the acoustic parameters, again, for the two conditions of the bends without and with twoguide vanes installed.The parameter M
∆
p represents a common linkbetween the scale model tests with cold air and thefull scale hot conditions. On this basis, the predictionof the reduction of acoustic pressures in the full scalesystem can be predicted. Based on Figure 7 andequation (3) the reduction in the predicted acousticpressures in the full scale hot stack liners due to theinstalled guide vanes will be from 21.0 x 10
-3
Pa or 60.4dB (re: 2 x 10
-5
Pa) to 9.17 x 10
-3
Pa (53.2dB), or a total of 7.2dB. Considering that no additionallosses will occur to the acoustic waves travelingthrough the stack liners, the stack noise emissionsare thus predicted to be reduced by a minimum of 7.2dB (Fig. 7).DISCUSSION AND SUMMARYBased on experimental data corroborated withtheoretical analysis, the full scale facility has providedclear evidence of the existence of an acousticresonance condition in the upstream bends and of anacoustic wave traveling through the stack liners intothe surrounding areas of the plant.
The laboratory scale model tests confirmed thatthe source of the acoustic wave propagating in thecylindrical portions of the stack liners was in theupstream bends. Here the turbulent flow conditionsas measured by the input parameter M
∆
p give rise tothe development of the acoustic wave in thedownstream pipe with an acoustic pressure P whichis exponentially proportional to this parameter.The guide vanes installed inside the bends havereduced the pressure drop through the bends byabout one third and strongly (disproportionately)reduced the generated acoustic pressures andtherefore the noise produced by the resonantcondition at the same flows. Utilizing theexperimentally derived relationship between acousticpressure P and M
∆
p, given by equation (3) the noiseproduced in the full scale facility by the acousticresonant condition can be reduced by 7.2dB byinstalling 2 guide vanes in each of the upstreambends. This significant reduction would eliminate theconcern with the single tone noise emitted from thestack prior to the modification.CONCLUSIONSThe results show that the upstream bends in thestack liners were the primary source of the singletone noise generated in the straight cylindrical linerswhich propagated into the surrounding areas of theplant. It has been shown that guide vanes installedinside each of the bends (two optimally placed vanesper bend) will reduce the pressure drop through thesystem by one third and substantially reduce thegenerated noise level by over 7dB. Thus, theinstallation of guide vanes in the upstream bends is adesirable feature as it makes the system more energyefficient and also much less noisy. It is thereforerecommended that in systems of similar size theinstallation of guide vanes in the bends becomes astandard design feature.ACKNOWLEDGEMENTThe authors gratefully acknowledge thepermission of Foster Wheeler Power Group, Inc. topublish the results contained in this paper.REFERENCES[1] Weaver, D.S., Feenstra, P., Ewing, D., 1997,“Scale Model Testing of Pipe Elbow Turbulence-Induced Acoustic Resonance in a StraightCircular Pipe”, Project Report, Department of Mechanical Engineering, McMaster University,Hamilton, Ontario, Canada, November, 34pages.[2] Chu, B.T., 1955 “Pressure Waves Generated byAddition of Heat in a Gaseous Medium”,National Advisory Committee for Aeronautics.Technical Note 3411, pp. 1-47.[3] Chu, B.T., 1956, “Stability of SystemsContaining a Heat Source – the RayleighCriterion”. National Advisory Committee for Aeronautics Research Memorandum 56D27.[4] Eisinger, F.L., Francis, J.T., and Sullivan, R.E.,1996, “Prediction of Acoustic Vibration in SteamGenerator and Heat Exchanger Tube Banks”,ASME Journal of Pressure Vessel Technology,Vol. 118, pp. 221-236.[5] Eisinger, F.L., and Sullivan, R.E., 1996“Experience with Unusual Acoustic Vibration inHeat Exchangers and Steam Generator TubeBanks, Journal of Fluids and Structures, Vol. 10,pp. 99-107.[6] Blevins, R.D., and Bressler, M.M., 1992“Experiments on Acoustic Resonance in HeatExchanger Tube Bundles”, ASME PVP-Vol. 243,Symposium on Flow-Induced Vibration andNoise, Vol. 4, pp. 59-79, also, 1993, Journal of sound and Vibration, Vol. 164 (3), pp. 503-533.[7] Bull, M.K., and Norton, M.P., 1982, “OnCoincidence in Relation to Prediction of PipeWall Vibration and Noise Radiation Due toTurbulent Pipe Flow Disturbed by Pipe Fittings”,International Conference on Flow InducedVibration in Fluid Engineering, Reading, EnglandBHRA fluid Engineering, pp. 347-368.[8] Norton, M.P., 1989, “Fundamentals of Noise andVibration Analysis for Engineers”, CambridgeUniversity Press, Cambridge, U.K.[9] Fahy, F.J., 1998, “Sound and StructuralVibration,” Academic Press, London, New York.[10] Carucci, V.A., and Mueller, R.T., 1982,“Acoustically Induced Piping Vibration in HighCapacity Pressure Reducing Systems”, ASMEPaper No. 82-WA/PVP-8.[11] Eisinger, F.L., 1997, “Designing Piping SystemsAgainst Acoustically Induced Structural Fatigue”,ASME Journal of Pressure Vessel Technology,Vol. 119, pp. 379-383.[12] Eisinger, F.L., and Francis, J.T., 1999,“Acoustically Induced Structural Fatigue of Piping Systems “, ASME Journal of PressureVessel Technology, Vol. 121, pp. 438-443.[13] Blevins, R.D., 1984, “Applied Fluid DynamicsHandbook, Van Nostrand Reinhold Company,New York, N.Y.

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