Troubleshooting a Flow-InducedVibration Problem on a Syngas

Compressor

Retrofitting the centrifugal reinjection compressor with a two-bed intercooled radialflow design increased its efficiency from historical levels of 64.4% to 71.75% resulting

in a substantial power savings.

Wüliam J. Leingang and Kevan A. VickFarmland Industries, Inc., Lawrence, KS 66044

Farmland Industries owns and operates a 907MTPD (1000 STPD) aromonia plant at itsLawrence, Kansas Facility. The plant wasconstructed by M.W. Kellogg in 1971. Thesynthesis gas compressor train consists ofone condensing turbine, one back-pressureturbine, one low pressure case (Ist body)compressor and one high pressure case (2ndbody) compressor. The high pressure case isa Clark model 2B9-8 vertically splitcentrifugal compressor. The high pressure casecompressor is an 8 itnpeller machine whichpresently compresses an 8.6 molecular weight(MW) gas at 6.48 MPa, 9 degree Celsius anddischarges a 11.6 MW gas at 14.48 MPa, 69degree C. The high pressure case compressorfeatures a re-injection point between the 7thand 8th impellers which recycles a 12.1molecular weight gas from the process loop at13.45 MPa 48 degrees C. The recycle massflowrate is approximately 253,600 kg/hcompared to the makeup section flowrate of44,200 kg/h. See figure 1.

the process synthesis loop. Due to theadditional conversion of ammonia in theprocess loop, the high pressure casecompressor realized a decrease in recycledgas from 276,240 kg/h to 253,600 kg/h atequivalent NH3 production rates. Themolecular weight of the recycled gasincreased from 11.6 to 12.1.

As part of the retrofit, the OEMmodified the recycle impeller, guide vanes,and balance piston. The recycle impeller wasreplaced with a smaller impeller. The oldimpeller had 18 vanes and a 45.72 centimeter(18 inch) outer diameter. The new impellernow has 19 vanes and a 40.64 centimeter (16inch) outer diameter. The discharge head wasmachined to accommodate a new balance pistonlabyrinth seal. The recycle inlet ring,recycle inlet guide, bridgeover and balancepiston were replaced. The recycle inlet vanewas reused after machining 0.3175 cm (0.125inch) off its base.

BACKGROUND:

After 18 years of operation, the FarmlandLawrence Ammonia Plant underwent a December1989 converter retrofit in order to boostammonia plant efficiency and production. Theconverter was retrofitted from a four bedguenched axial flow design to a two bedintercooled radial flow design. Ammoniaproduction increased from 907 MTPD (1000 STPD)to 1132 MTPD (1250 STPD). As part of theammonia converter retrofit, the synthesis gascompressor was modified by the OriginalEquipment Manufacturer (OEM) primarily toaccommodate the lower pressure drop through

Upon reaching higher production rates onDecember 27th, 1989 an unusual vibration wasnoted on the low pressure case and highpressure case compressors, piping, foundationand several remote heat exchangers. Thevibration appeared to be transmitted bothstructurally and acoustically. After a dayof operation the unit was removed fromservice on December 29th, 1989, disassembledand inspected. Upon inspection thecompressor showed a wiped suction end oilseal ring, minor indentations on severalimpellers and the thrust bearing assemblyshowed evidence of high frequency frettingafter two days of service. Although none of

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these items appeared to be the source of theproblem, both the rotor and oil seal werereplaced. After reassembly, the vibrationproblem resurfaced with the January Ist, 1990start-up. No readily identifiable change wasnoted in the vibration amplitude or frequency.

After some study Farmland concluded thatthe vibration was some type of a flow relatedphenomena, but the vibration problem could notbe isolated to any partioular mechanism orlocation. The following section describes someof the attempts to troubleshoot and resolve thevibration problem.

ANALYSIS

The vibration was most pronounced on thehigh pressure case compressor and recyclesuction piping. The predominate vibrationfrequency was a very narrow band atapproximately 195 Hertz with multiple harmonies(2nd, 3rd, 4th.... etc.) also visible in thespectra. Vibration levels on the compressorcase were consistently measured as high as33.0 millimeters per second peak (1.3 ips)which is sufficient to cause damage. Vibrationwas also highest in the plane perpendicular tothe recycle suction flow. Vibration amplitudesperpendicular to the recycle suction flow wereroughly 5 to 10 times higher than amplitudesparallel to the recycle flow. Vibration andpressure frequency spectra were captured usinga CSI Model 2110 portable data collector. Thevibration transducer used was a CSI Model 360accelerometer.

The more typical vibration mechanisme suchas rubs, soft foundation, imbalance, oil whip,and misalignment were quickly ruled out as apotential vibration sources. These vibrationproblems are a function of the rotor dynamicsof the machine and are manifested as multiplesof the rotor whirl frequencies and rotorcriticals. Running speed during f uil rateoperation is roughly 10,500 rpm or 175 Hertz.Two frequency spectra (Fig. 2 S 3) are attachedin the appendix. Due to the sharpness of the195 Hertz response (the vibration peak), aresonance was suspected.

Pressure pulsation frequency spectra wereobtained from a PCB Model 3A01 piezoelectricpressure transducer inserted into the makeupsection suction, recycle suction and dischargelines. The transducer locations wereapproximately one meter from the compressorbody in the respective lines. Pressurepulsation amplitudes of 1.38, 34.5, and 3.45kPa peak to peak at 195 Hertz were obtained inthe makeup section suction, the recycle suctionand the discharge lines respectively. Thepressure pulsation amplitude (Fig. 4) of 34.5kPa peak to peak in the recycle suction linewas alarming due to the cyclic forces that werebeing generated on the compressor bundie and

The high pressure compressor wasoperating with an efficiency of 64.04% whichwas similar to historical levels. Thesecond body efficiency is calculated over theentire high pressure case and includes therecycle stage. In proximity to thecompressor, sound levels were judged to be inexcess of 100 dB.

Conversations with the OEM suggestedthat the vibration problem might be relatedto the new recycle suction strainer. The olddamaged strainer had been replaced duringthe retrofit and replaced with a nearlyidentical strainer. Based on this advice,Farmland removed the compressor train fromservice, depressurized the ammonia synthesisloop and removed the recycle suctionstrainer on January 13th, 1990. After threeweeks of service the recycle suctionstrainer had a 10 cm (3.9 inch) vibrationinduced crack down the center of thestrainer. The compressor returned to serviceand continued to vibrate at the unusualfrequency of 195 Hertz.

Another theory suggested that aninherent flow related vibration was excitinga structural piping resonance in the recyclesuction line. In such a situation the pipinghas a resonant frequency which matches thecyclic forcing frequency. The stiffness,mass and damping characteristics of the pipedetermine the resonant frequencies and modalgeometry of the pipes. This theory wasquickly ruled out by stiffening the recyclesuction piping. The recycle suction line wasstiffened by the addition of severalsupports. The vibration frequency andamplitudes remained unchanged throughout thisexperiment.

Other avenues such as acoustical pipingresonance as discussed by Baldwin K Simmons[i] were investigated. One theory suggestedthat a standing wave (an acousticalresonance) was generated in a dead lineconnected to the recycle suction line byvortex produced pressure pulses (Fig. 5).This same phenomena produces the sound heardfrom a Coke bottle when air blows over theopening. From basic wave theory thewavelength equals the speed of sound dividedby the frequency. If a standing wave wasactually occurring in a pipe, the pipelength would have to equal 1/4 wavelength oran odd numbered multiple of 1/4 to producea pressure node at the pipe inlet. Theclosed end of the pipe reflects the wave andbecomes a pressure antinode (that is thepoint of maximum pressure variation). Pipelength in this case would have to be 0.725meters (565.7 meters/ second divided by 195Hertz times 1/4 wavelength) or a multiplethereof. There were several dead lines

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connected to the recycle suction pipe whichapproximately matched this length. Farmlandtested this theory by opening valves andchanging acoustical lengths. Unfortunately,none of these lines were the source of thevibration.

Since the recycle (the 8th stage) impellerhad been replaced during the outage, it wastheorized that the impeller was improperlysized. The OEM recalculated the optimumgeometry and performance for the 8th stageimpeller. An investigation revealed nopotential vibration sources of the magnitudeseen on this machine.

Another theory suggested that one or moreimpeller stages were in surge. Surge is anunstable operating condition in which theonset of flow reversal occurs. Surge isespecially dangerous to compressors due to thecyclic axial loading it applies. Farmlandtested the compressor by manually opening theanti-surge bypass valves. Since vibrationlevels and freguencies remained constant, itwas surmised that the unit was not operatingin surge.

Af ter exhausting most avenues, the OEMrecalled two experiences where high vibrationand noise were generated by cavity openings inthe interstage diaphragms of similar machines.Apparently, in the manufacturing of theseinterstage diaphragms these openings wereinstalled to remove sand from the sand casting.These openings are frequently referred to as"cored casting openings". The OEM had littleinformation on the other two vibration problemsassociated with these cavities. The cavityruns the circumference of the diaphragm. Thecavity ports to the outerside of diaphragm andat the bundie splitline. (See figure 7 and 8.)Apparently, high pressure recycle gas leaked tothe lower pressure makeup section of themachine through these "cored" openings (hencereeirculation). Later diaphragm designsincorporate a better casting design. Thenewer diaphragm castings feature a removableplug so that the diaphragm could be sealedafter removing the sand.

Farmland removed the syn gas compressorfrom service on February Ist, 1990. Thecompressor was disassembled and inspected onFebruary 2nd, 1990. It was noted that theinterstage diaphragms did indeed feature the(older design) cored casting openings.Evidence of internal gas recirculation throughthe cored castings openings toward the lowpressure suction end of the compressor waseasily seen. It was also noted that thediaphragms rail fits were severely worn,further suggesting that recycle gas and highpressure makeup gas had been bypassing therecycle impeller for many years.

The makeup section of the bundie wasrebuilt using plugged diaphragms. Nochanges were made to the recycle section ofthe compressor during this latest repairoutage. A spare rotor was cleaned, balancedand reinstalled in the Lawrence high pressurecase compressor. Final assembly wascompleted by February 4th, 1990 and anuneventful start-up of the high pressuresynthesis gas compressor followed. Theunusual vibration did not return.

THEORY

It appears certain that the vibrationproblem was generated by a vortex-inducedacoustic resonance within the compressorbundie. Two different theories exist toexplain why the high pressure compressorsuffered this vibration problem. Thetheories differ in regards to where theacoustic resonance resided and what mechanismgenerated the vortices.

An acoustic resonance is a phenomenonwhere a standing wave is produced in anelastic fluid. For a long narrow cavitywith openings at both ends, the cavity'sresonant length would have to egual 1/2 thewavelength of the standing wave (or amultiple of 1/2) to produce a pressure nodeat both cavity openings. Pressurevariations are zero at the cavity openings,because the openings are exposed to constantpressure. Maximum pressure variation (apressure antinode) would be located at thecenter of the cavity. The sound createdfrom an organ pipe is a perfect example ofthis type of resonance. In both of thefollowing theories, vortices were beingamplified in a resonant cavity, either therecycle inlet ring or the diaphragm cavities.The standing wave frequency is determined bythe equation:

f —X

where c is the speed of sound andX is the resonant wavelength.

Since the operating characteristics ofthe syn gas compressor are typically dictatedby the proces s and operate within a fixedrange, the problem did not originally occur.As a result of the converter retrofit, thechanges in molecular weight and maas flowrateof the recycle gas are suspected to havetriggered the acoustic resonance. As aresult of these changes, the recycle gasinlet velocity and the speed of sounddecreased. Coincidentally, these operatingconditions feil within a range conducive toan acoustical resonance.

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Theorv l determination of the speed of sound.

Upon viewing the compressor internals, itwas theorized that the recycle inlet flowsputter plate was the vortex sheddingmechanism. Flow across a bluff bodyobstruction produces vortices. Wellestablished test data from Leinhard [4_]indicates that a steady vortex street ispossible between Reynolds number of 300 and3xlOE5. The calculated Reynolds number at therecycle inlet is approximately 73,000 which iswell within the range of Reynolds numbersconducive for a steady vortex sheddingmechanism. The vortex shedding frequency (f)in Hertz is determined by the equation:

f = S * ü / d

where S is the Strouhal NumberU is average Flow Velocity, andd is the diameter of the obstruction

For this case after the retrofit 195 Hz= 0.2 * 27 m/s / d. Solving the eguationfor d, the flow obstruction diameter isroughly 2.77 centimeters which does not guitematch the thickness of the sputter plate at2.54 centimeters. The Strouhal number variesslightly with Reynolds number and geometry. Ifthe recycle inlet flow sputter (Fig. 7) wasthe vortex shedding mechanism, then the recycleinlet ring has to be the resonant cavity.Blevins [5.] has shown from a potential flowwake oscillator model that the force generatedis in the transverse direction to flow. Thisvortex shedding mechanism produces the cyclicforces in the proper direction reguired forresonance in the recycle inlet ring.

Theorv 2

There are two sets of potential cavitieswhich could produce the undesirable 195 Hertzvibration. The sandcasting cored cavities andthe diffuser ring both have cavity lengthswhich match within 10% of the observed 195Hertz acoustic length. Several factors hinderan exact determination of which diaphragmcavities are responsible for the acousticalresonance. For example the speed of sound inthe makeup section increases as work is done tothe compressed gas. The speed of sound withina gas is calculated by the equation:

c = z*k*(R/MW)*T

where z is the compressibility factork is the ratio of specific heatsR is the universal gas constantMW is the molecular weight, andT is the gas temperature.

In addition the makeup section gas has alower molecular weight than the recycle gas(Fig.l). As the recycle gas mixes with themakeup gas, the composition and temperature ofthe gas become unknown preventing an exact

The vortex shedding mechanism is alsodifficult to pinpoint to a specific diaphragmcavity without a comprehensive threedimensional mass flow profile. Researchhas found that flow across a cavityproduces an unstable shear layer. Vorticesimpinge on the downstream edge of the cavityopening (Fig. 11), generating alternatinginward and outward flow. This alternatingflow produces pressure pulsations with afrequency given by the equations:

f = 0.33{n-l/4)U/l

and

for turbulent boundary layers;Franke and Carr [<a]

f = 0.52 ü/1

for laminar boundary layersEthembabaoglu [7.]

where n is a positive integer,U is the free stream velocity andl is the length of the cavityopening (from leading edge to theimpingement edge)

Although, there is no easy way of determiningthe velocity of the gas bypassing at thebundie splitline, this equation demonstrateshow a resonant condition could occur. Asthe frequency of the generated vorticesmatches the resonant frequency of thecavity, the vortex-induced pressureoscillations in the cavity increase inmagnitude and synchronize resulting in fullresonance. This situation would be similarto the pipe acoustical resonance described byBaldwin & Simmons [JL].

RESULTS

At the time of this report the unusualvibration has not returned. Vibration levelsat 195 Hertz are virtually nonexistent (Fig.3) with 4 orders of magnitude decrease invibration amplitude. The calculatedefficiency over the entire high casecompressor increased from historical levelsof 64.4% to 71.75% resulting in a substantialpower savings. Pressure pulsation readingson the recycle suction inlet still show a 195Hertz pulse (Fig. 4), but the amplitudes areroughly one-tenth the levels of earlierreadings. Furthermore, the spectra show amild response (a rounded peak) at 195 Hertzand lacks the sharp definition (sharp peak)of a resonance as seen in earlier plots.

CONCLÜSION

The increase in compressor efficiency

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over historical averages indicates that gasrecirculation occurred freguently (if notcontinuously) prior to the retrofit. Farmlandhas three other operating compressors whichhave similar bundies that have neverexperienced the vibration problem. But basedon the efficiency increase of the Lawrenceunit, Farmland is planning bundie modificationsfor the other three units as well.

Without any practical way of calculatinga three dimensional mass flow profile leakingat the bundie splitline, the location of thevortex shedding mechanism and resonant cavitycan not be determined. In all likelihood, thevortex shedding mechanism has always beenpresent but without a resonant cavity thepressure pulsations are sufficiently damped.Since the operating characteristics of the unitare typically dictated by the process and varywithin a fixed range, the problem did notoriginally occur and the original designweakness went undetected. After thetechnology was available, the OEM laterimproved the diaphragm design using a superiorcasting design. With the cored castingopenings now plugged the opportunity for gasrecirculation is greatly reduced.

LITERATURE CITED

l Baldwin, R.M. and Simmons, H.R.; "Flow-Induced Vibration in Safety Relief Valves"ASME Journal of Pressure Vessel Technology,Vol 108, August 1986.

Ethembabaoglu, S.; "On the FluctuatingFlow Characteristics in the Vicinity ofGate Slots," Division of HydraulicEngineering, University of Trondheim,Norwegian Institute of Technology, 1973.

William J. Leingang

Kevan A. Vick

2 Toyama, K., Dean, R.C. and Runstadler, P.W.;"An Experimental Study Of Surge InCentrifugal Compressors"; CentrifugalCompressor and Pump Stability, Stall andSurge; Joint Gas Turbine and FluidsEngineering Conference, ASME 1976.

3 Dean, R.C. and Young L.R., "The TimeDomain Of Centrifugal Compressor And PumpStability And Surge"; Joint Gas Turbine andFluids Engineering Conference, ASME 1976.

4 Lienhard, J.H.; "Synopsis of Lift, Dragand Vortex Frequency Data for Rigid CircularCylinders" Washington State Üniversity,College of Engineering, Research DivisionBulletin 300; 1966.

5 Blevins, R.D.; Flow-Induced Vibration; VanNostrand Reinhold Co. 1990. ISBN:0-442-20828-6 Chapter 3, Pages 43-94,375-380

6 Franke, M.E. and Carr, D.L.; "Effect ofGeometry on Cavity Flow-Induced PressureOscillations," AIAA Paper 75-492, AIAA, NewYork, 1975.

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Low PressureSyn Gas Compressor

PRIOR TO RETROFIT

RECYCLE: 276,240 kg/hDISCHARGE:

AFTER RETROFIT

RECYCLE: 253,600 kg/hDISCHARGE:

Syn Gas Make-Up44,200 kg/h 8.6 MW6.48 MPA 9°C

RECYCLE GAS(Re-injection Between

7th & 8th Stage Impeller)

DISCHARGE_14.48 MPa

69°C

High Pressure CaseSyn Gas Compressor

11.6 MW, 13.1 MPa, 45°C11.1 MW, 14.48 MPa, 69°C

12.1 MW, 13.45 MPa, 47°C11.6 MW, 14.48 MPa, 69°C

Figure 1. Simplifïed process flow before and after revamp.

0.635 mm/s 170 Hertz (Running Speed)

— 26.8 mm/s 195 Hertz

400 600 800

FREQUENCY IN Hertz

Figure 2. Vibration frequency spectrum of thehigh pressure case syn gas compressor beforediaphragm replacement.

0.147 urn/o 172 Hertz (Running Speed)

0.006 nm/o 195 Hertz

i 200 400 600 800 1000

FREQUENCY IN Hert z

Figure 3. Vibration frequency spectrum of thehigh pressure case syn gas compressor afterdiaphragm replacement.

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3.45 kPa peak to peak 195 Hertz

AFTER DIAPHRAGM REPLACEMENT

34.5 kPa peak to peak 195 Hertz

BEFORE DIAPHRAGM

REPLACEMENT

"U.

200 400 600

Frequency in Hertz

800 1000

Figure 4. Pressure pulsation spectrum from therecycle gas inlet line before and afterdiaphragm replacement.

ALTERNATINGSTREAMLIHES

•ALTERNATINGIMPINGEMENT

ANGLES

Figure 5. Vortex produced pressure pulses.

R« < 5 HEGIME Of UHSEPAHATEO FLOW

VOR7ICES IN WAKE

4fl < Hi < 30 ANQ SO < fli < Ï5BTlia REGIMES INÏIHICH ÏORTEXSTREET IS LAMIHAR

3oa < R» :̂ 3 x ia5 VGRTEX STREET is FULLYTURBULENT

3 X IQ5 g Kt < 3JS X 1B8

LAMINAR BQUNQARY LAYER HAS UNDERGQNETURBULENT TRANSITION AND WAKE ISNARRGWER Arjo DISORGANIZED

3Ji_XtpB «ÏJh

RÏ-ESTABL1SHMEHT OF TURBU-LENT VOBTEX STREET

Regimes of Huid flow acrou smoolh circular cylindcn (Uenhard. 1

Figure 6. Regimes of fluid flow across smoothcircular cylinders.

Cored Casting Openings

RECÏCLE ' 7th Stage(8th Stage) DIAPHKAGM

Figure 7. Side view of bundie showingbypassing of recycle gas along outer surface ofbundie.

!\

Figure 8. Splitline view of the makeup sectiondiaphragms and guide vanes.

Vibration at 195 Hz33.0 mm/s peak (1.3 ips)

Length, L

Bundie Splitline

Figure 9. Axial view of recycle inlet ringrepresenting theory 1.

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33.0 mm/s peakNaxirsumPressureVariation

3.3 mra/s peak

Cavity Length, L

(Dashed Line)

Opening Length, l

Pressure Noties

mdle Splitline

Figure 10* Axial view of diaphragm cavitiesrepresenting theory 2*

Opening Length

Diaphragm Splitline

Impingement Edge

C/ S = Boundary Layer Thickne

VelocityProfile

\

Figure 11. Enlarged view of flow overdiaphragm cavities represeiitieg theory 2:altereating shear waves.

Figure 13. Photograpfa showing splitline view oftwo oïder style diaphragms with cored castingopenings. Cored casting openings on top rightside of both diaphragms.

Figure 12. Photograph showing assembleddiaphragms, guide vanes and compressor rotor. Figure 14. Second body syn gas compressor.

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DISCUSSION

Zulkarnain Tje'Mat, Kujang Fertilizer Co. Ltd.,Cikampek, Indonesia: Did your compressor use vibrationmonitor or probe from Bentley Nevada? Is there anyinformation from the OEM about this unusual case?Leingang: Yes, our compressor was outfitted with two non-contacting probes per hearing. The probes are mounted in the

hearing housing at approximately 90 ° from each other. Thevibration spectra from the noncontacting probes confirmed thedata taken with the portable CSI 2110 accelerometer. Spectrataken on the majority of sensor locations showed the 195 Hzfrequency throughout the duration of the vibration problem.Tje'Mat: Is there any information from Dresser Rand aboutthis case? This case happened after revamp for the syngascompressor, so it should be any relation with revamp.Leingang: The OEM did help out quite a bit. This problemhappened after the high pressure (second body) compressor wasmodified by the OEM. When the problem occurred the OEMreally didn't have a good feel for the problem themselves. Theyhad experienced similar problems twice before. In bothcircumstances diaphragm replacement significantly reduced oreliminated the vibration problem. Both experiences were anumber of years ago and one experience was overseas. In alllikelihood the vibration and acoustical data gatheringtechnology was not available at the time of the problem. S othe OEM really didn't have a good feel for what the mechanismmight have been.

We feel confident that the problem was an acousticalresonance residing in one of the bundie cavities. It was notrelated to the new recycle wheel or any of the physical changesto the compressor that the OEM had completed as part of theretrofit. The changes in the recycle suction gas triggered theproblem. Had the cored casting openings been plugged, thevibration problem never would have existed. The efficiencyloss due to the leakage was present prior to and immediatelyafter the converter retrofit. The OEM had made no changes inthe makeup suction diagrams, so we feel confident in sayingthat the problems stem from the gas bypassing (that isrecirculating through the unit and not the recycle impeller).R. Frey, M. W. Kellogg Company, Houston, TX: I wouldlike to compliment you on an interesting study showing theeffect of a small detail on a plant operation and I find flowinduced vibration a fascinating subject. We had a similarincident on an air compressor in an ammonia plant on a failureof a wheel, which also was a resonant condition. However, wesolved this with a wave trap on our piping, which is a slightlydifferent situation. One of the elements of your changeout wasthe fact that you put a 19 vane impeller in, where you had an18 vane before. Was this investigated on the Campbelldiagrams to see what harmonies this would result in? By either

you or your OEM in the course of this investigation?Leingang: Yes, we did look at that area and the OEM alsocovered that.Frey: I would like to say that we also had a flow inducedvibration failure on a vent off of a distillation column aboutfour months ago in Belgium, which was a 2 in. heavy dutypipe, which failed by the same mechanism. Your theorynumber 2 in the paper is that acoustic isolation has been fairlywell studied in the aeronautical industry, but we don't pay toomuch attention to it in our industry. This resulted in a fairlyserious depressurization situation.S.R. Ghosh, Kribhco, Surat, India: You have mentionedthe flow induced vibration. In that case, the flow inducedvibration you have got signature in multiple frequency. Didthe absolute vibration level increase?Leingang: Yes, it increased several mils peak to peakdisplacement on our compressor.Ghosh: What I mean to say is that a noncontact probe willonly show the absolute level of vibration. But, from the samejack, you can use a real-time analyzer and also see. That is,when your flow induced vibration is there, you can get into themultiple frequency of the number of impeller vanes. Was itanalyzed?Leingang: To answer your question, vane passing frequenciesand beat frequencies theories were investigated, but werequickly disproved. This vibration problem was a totallydifferent mechanism. Vortices generaled over a cavity canproduce a standing wave. A standing wave is very differentfrom a vane passing pressure wakes. Pressure wakes aregeneraled off of each vane as it passes through Ihe gas.Thevane passing frequency is calculated as Ihe number of vanesmulliplied by Ihe rolor operaling speed. In Ihe case of Iherecycle wheel Ihe vane passing frequency would be 3,268 Herlz(19 vanes mulliplied by 172 Herlz) which is far above thetroublesome 195 Hertz. The vane passing frequencies werepresent in the vibration speclra, bul at low amplitudes which islypical for this machine. In addilion the 195 Hz vibrationshowed no dependence on operating speed.Vane passing wakescan be an excilation source for resonances, if the vane passingfrequencies are close to resonant frequencies. These resonantfrequencies can be eilher structural or acoustical.

Our 195 Herlz vibration was nol exciled by a vane passingfrequency, bul it was a standing wave (an acoustical resonance)which works on a similar mechanism as to an organ pipe, or aCoke bottle. You take a Coke bottle, blow over the opening,and you generale vorlices as the boundary layer impacts on thetrailing edge of Ihe botlle. If these vortices form an alternatingshear wave across the top of bottle such that the shear wavefrequency match the resonant frequency of the cavity, a

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standing wave (an acoustic resonance) forms. The resonantfrequency of the cavity is primarily a function of the cavitygeometry and speed of sound. The tone (frequency) heard froman organ pipe is dependent on the pipe length. Vary the lengthof the organ pipe and the pitch (frequency) varies accordingly.

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