AbstractPressurewavevelocityinahydraulicsystemwasdeterminedusingpiezopressuresensorswithoutremovingfluidfromthesystem.Themeasurementswerecarriedoutinalowpressurerange(0.26bar)andtheresultswerecomparedwiththeresultsofotherstudies.Thismethodisnotasaccurateasmeasurementwithseparatemeasurementequipment,butthefluidisintheactualmachinethewholetimeandtheeffectofairistakenintoconsiderationifairispresentinthesystem.Theamountofairisestimatedbycalculationsandcomparisonsbetweenotherstudies.Thismeasurementequipmentcanalsobeinstalledinanexistingmachineanditcanbeprogrammedsothatitmeasuresinrealtime.Thus,itcouldbeusede.g.tocontroldampers.KeywordsBulkmodulus,pressurewave,soundvelocity.I.INTRODUCTIONRESSUREwavevelocity(soundvelocity)isanimportantfactorwhenhydraulicsystemsareanalyzedanddevised.Itisaparameterinmanyequationsthatmodelthedynamicsofhydraulicsystemsanditisalsoanimportantparameterwhendampersofhydraulicsystemsaredimensioned.Withthehelpofpressurewavevelocitythebulkmodulusofahydraulicsystemcanbedefined,orviceversa.Differentmeansformeasuringpressurewavevelocityarepresentedinmanystudies.Normallythesemeasurementsarecarriedoutinseparatemeasurementequipment,sothatthemeasuredfluidisremovedfromtheoriginalmachine.Thisaffectscertaincharacteristicsofthefluid,suchastheamountofairormoistureconcentration,andtheresultsofpressurewavevelocitymeasurementsmaydifferfromtheoriginalsituation.Separatewavevelocitymeasurementinstrumentationisveryoftendesignedinsuchawaythatatleastentrainedaircanberemovedfromthemeasuredfluid.Thus,theresultsofmeasurementdonottaketheeffectofairintoconsideration,oronlydissolvedairisnoticed.Thisdoesnotcorrespondtorealsystems,becauseairispresentinfluids,especiallyatlowpressures.Separatepressurewavemeasurementequipmentusuallycannotbeconnectedtothemachine,soreal-timemeasurementofwavevelocityisimpossible.Inmanyearlierstudiespressurewavevelocityhasbeenmeasuredwithultrasonictransducers.Theultrasoundtechniquemaybebasedon,e.g.time-of-flightorpulse-echoprinciples.Thismethodisveryaccurate；anaccuracyofeven0.005m/scanbeachieved,1althoughlargererrorshavealsobeenpresentedintheliterature2-4.Benefitsoftheultrasoundtechniqueare,e.g.long-termstability,precision,sensitivity,capabilityofapplyingtoopticallyopaque,concentratedandelectricallynon-conductingsystemsandthepossibilitytoautomatethemeasurement.However,instrumentationdesignandthesamplestudiedmayaffecttheaccuracyofthemethod.5.Anothermethodfordefiningpressurewavevelocityistomeasurethebulkmodulusofafluidusingamethodbasedondeterminationofthevolumechangeofthesampleundercompressionorexpansion.6-9.Useofthistechniquepreventsunwantedpressuregradientsbetweenthesampleandthesurroundingsystem.Theusefulpressurerangeofthemethodiswide(0.1-350MPa).Theamountofentrainedaircanalsobetakenintoconsideration.Drawbacksofthemethodaretheneedtofirstdeterminethespecificvolumeofthesampleunderatmosphericpressureandtheobviousrequirementofmeasuringthedensityofthesampleunderallthepressuresused.Thus,thismethodcannotbeusedforcontinuousreal-timemeasurements.Calculationofthebulkmodulusandfurthermorethepressurewavevelocity(soundvelocity)isshownin(1)and(2)inchapterII.Someresearchershaveusedpressuretransducerstodetectpressurewavevelocitiesinoils.HarmsandPrinke10presentedamethodbasedonphasedifference.Inthismethodexcitationshouldbeconstant,e.g.pumprippling,becausethesignaliscomparedattwopointsandthevalueofthewavevelocityiscalculatedfromthetimedifferenceofthesesignals10.Choetal.11andYuetal.12measuredthewavepropagationtimeandcalculatedacross-correlationfunctionofthepressuresignals.Methodsbasedonpressuremeasurementsmakereal-timemeasurementspossibleandtheinfluenceofaircanbetakenintoconsideration.YetanothermethodfordeterminingpressurewavevelocitywaspresentedbyApfel13.Thismethodisatechniquethatmeasurestheadiabaticcompressibilityanddensityofafluidwhenthesampleamountsareextremelysmall,4nl-4l.Pressurewavevelocitiescanbecalculatedfromthesedata.Thismethodisapplicable,e.g.forsupercooledorsuperheatedsamples,biologicalorhazardoussamplesorineverycasewhenthebulkpropertiesoffluidshavetobedeterminedfromsmallsampleamounts.Thefluidstudiedisacousticallylevitatedonanimmisciblehostliquidatacertainspotofthetestequipment.Areferencemeasurementofafluidwhosepropertiesarewell-knownismadeattheexactsamespot.Theresultsarerelativelyaccurate(withina2%margincomparedwiththesamevaluesdeterminedbytraditionalmethods).Inordertocalculatepressurewavevelocities,thedensityoftheMeasuringPressureWaveVelocityinaHydraulicSystemLariKela,andPekkaVhojaPWorldAcademyofScience,EngineeringandTechnology492009610samplehastobemeasuredusingdifferentequipment.Obviously,thismethodissuitableforlaboratoryexperimentsonly.13-14.Pressurewavevelocity(soundvelocity)canbeusedtoevaluatevariousimportantcharacteristicpropertiesoffluids.Forinstance,ithasbeenusedtodeterminetheconcentrationofsolventsinoils4,tocalculatethephysicalpropertiesofhydraulicandotherlubricatingfluids,aswellasfueloils7,15-17,toestimatethestructuralandmechanicalpropertiesoffats18andthephysicalpropertiesofpetroleumfractionsandpetroleumreservoirfluids3,5andtodeterminethecompositionofoil-watermixturesandemulsions2ortomeasurethepropertiesofmagnetorheological(MR)fluids19.Themostimportantaimofthisstudywastodevelopamethodformeasuringpressurewavevelocitythatenablesreal-timemeasurements,whicharenecessaryif,e.g.real-timecontrolsystemsforhydraulicsareconstructed.AnotheraimwastocollectdataforfutureresearchwithaHelmholtzresonatorattachedtothissystem.II.THEORETICALASPECTSOFPRESSUREWAVEVELOCITYDETERMINATIONSThebulkmodulusofelasticmaterialBisdefinedasthequotientofpressurevariationandrelativevolumevariationaffectedbypressurevariationB=VdVdP(1)wherePispressureandVisvolume20.Pressurewavesconsideredinthispaperaresimilartowavesthatproduceaudiblesound.Thus,pressurewavesarehandledaslongitudinalvibrationmoleculesmovingbackandforthinthedirectionofpropagationofthewave,producingsuccessivecondensationsandexpansionsinthemedium.Thesealterationsofdensitiesaresimilartothoseproducedbylongitudinalwavesinabar.Asseeninmanystudies,mentionedalsointhispaper,thedifficultyofthemathematicsissidesteppedbyrestrictingthewavesunderconsiderationtoonedimension.21.Itisworthnotingthatatravellingwavedoesnotcarrymaterial,justthewaveanditsenergymove.Choetal.11havepresentedthreedefinitionsforbulkmodulus,whicharewidelyusedinmanytextbooks.Thesedefinitionsareonlyapplicabletotheirownspecificconditions,andinthispaperthesonicbulkmodulus(2)isused,whichhasthesamevalueastheadiabaticbulkmodulus.ThesonicbulkmodulusBisderivedfromthesonicvelocityinthefluidandfluiddensity11,20B=a2(2)whereisdensityandaiswavevelocity(soundvelocity).Equation(2)canbesolvedforthebulkmodulusorwavevelocity,dependingonwhichoneistheknownfactor.Inthispaperdensityisknownandwavevelocityismeasured,sothebulkmoduluscanbecalculated.Butas(2)presents,thesameparametersthataffectthevalueofwavevelocityalsoaffectthebulkmodulusandthisistakenintoconsiderationinthetheoryreview.Themainfactorsthataffectthevalueoftheeffectivebulkmodulusofahydraulicsystemarefluidpressureandtemperature.TheireffectsarepresentedinFig.1.Otherfactorsthataffectthevalueoftheeffectivebulkmodulusare,e.g.theaircontentofthefluid,piperigidityandinterfaceconditionsbetweenthefluidandtheair12.Fig.1Effectoftemperatureandpressureonwavevelocityinanoilsample:335.1K,370.7K,402.1K5Partoftheaircontentdissolvesinamolecularformandtherestofit,entrainedair,existsintheformofsmallbubbles.Dissolvedairhasonlyalittleeffectonthebulkmodulus11,butthevolumetricpercentofentrainedairwithinafluidisoneofthemostinfluentialvariableswhenthebulkmodulusisevaluated.Ithasbeenprovedthatonepercententrainedaircanreducetheeffectivebulkmodulusofafluidbyasmuchas1085MPa,whichcorrespondstoa75percentdecreaseinthefluidmanufacturersvalue22.Itshouldbenotedthatalsoothergases,notonlyair,affectthebulkmodulusandsonicwavevelocity,andthetypeofgashasagreatereffectthandoesthequantityofthegas23.Thelowerthemolecularweightofthegas,thegreatertheeffectonthesonicwavevelocity23.Fluidpressurehasaneffectonthevalueofthebulkmodulus,particularlyinthelowerrangeofpressure.Onereasonfortheeffectofpressureonthebulkmodulusistherelationshipbetweenentrainedaircontentanddissolvedaircontentinafluid.Someentrainedairbecomesdissolvedairwhenpressureincreases.12.Theinfluenceofpressurecanbediscussedatthemolecularlevel,also.Ifthepressureofthefluidunderstudyislow,thefluidmoleculesfitamongeachothereasilyandasignificantamountoffreespaceisstillavailable.Whenthefluidiscompressed,thefreespacedecreasesquicklyatlowerpressures.Whenthepressureofthesystemishigh,thefreespaceisalmostnegligible.Atthispointafurtherdecreaseinvolumeisconnectedwithinteractionsbetweenfluidmoleculesandtheirneighbouringmolecules.24.IfahydraulicsystemspressureismorethanWorldAcademyofScience,EngineeringandTechnology49200961150bar,theeffectoffreeairisonlyminor9.Fluidtemperatureaffectsthedensityoftheaircontent,thesizeofairbubblesinthefluidandthereforetheequivalentcompressibilityofthefluid.Anincrementoftemperaturealsocauseschangesinthemolecularlevelofthefluid.Morevigorouscollisionsbetweenmoleculesareobserved,whichmayeventuallycausechangesinmolecularstructures,andadecreaseintheireffectivevolumeisprobable.24.Therebytemperaturehasanimportantinfluenceonthebulkmodulusandsonicwavevelocity,especiallyindynamicsituations.Theinfluenceoftemperaturehasbeenstudied,e.g.by23.Theirstudiesincludedatemperaturerangebetween-30Cand130C,andtheeffectoftemperatureonsonicwavevelocityseemedtobesignificant23.However,theeffectoffluidtemperaturecanbeignoredifthefluidtemperatureisapproximatelyconstant12,andinmanystudiesthishasbeendone.Inaddition,thebulkmodulusoflubricatingoilsatlowpressurescanbealmostindependentofthetemperature25.Thedensityandbulkmodulusofsolidparts(e.g.pipes)willnotvaryasmuchasthedensityofafluidwhentemperatureandpressurevary10.Thus,theeffectofpiperigidityonthebulkmoduluscanbeignoredifrigidpipesareassumedinahydraulicsystem12.Themoisturecontentofthefluidmayalsoplayaroleifpressurewavevelocitiesaredetermined；itslightlyreducesthevalueofthepressurewavevelocity23.Theviscosityofthefluidalsoaffectsthepressurewavevelocity26,butofcoursetheviscosityofafluiddependsonitsmolecularstructureinthefirstplace,hencetheeffectofviscosityonthepressurewavevelocityvarieswithdifferentfluids.III.TESTEQUIPMENTThetestequipmentandtheprincipleofmeasurementaredepictedinFigs.2and3,respectively.Themeasurementswerecarriedoutbyidentifyingapressurepulseattwopoints,P1andP2,usingpiezosensors.ThedistancebetweenpointsP1andP2(variableLinFig.3)isknownandtwodifferentdistanceswereusedinthetests.Theshorterdistancewas2.75mandthelongerwas4.26m.DistancesL1andL2werealways1.03mand0.11m,respectively.Apressurewavewasexcitedbymeansofapistoninsideapipe.Thisexcitationsystemenablesexcitationofapurepressurewave,becauseunnecessaryelbowsandinterfacesareavoided,sothatreflectionsandtransmissionsofthewaveareminimized.Thepistonwasmovedlightlybutrapidlywithahammer.Asphericalplugvalveandanadjustablevalvewereinstalledinthetestequipmentsothatflowandpressurecouldbecontrolledduringthemeasurements.Thispropertywasusedinthemeasurementssothattwomeasurementserieswerecarriedout.Thefirstonewasdoneunderconstantpressurewithoutflowwiththebothvalvesclosed.Thesecondonewasdonewithflow,sothatflow(andpressure)wascontrolledwiththeadjustablevalve.Theeffectofflowonwavevelocityisinsignificant,asseenlaterinthetext.Themeasurementswerecarriedoutovertwodayssothattemperaturecouldbeassumedtobeconstant.Thetestequipmentdidnotincludeatemperaturesensor,butthetestequipmentwasinsidealaboratorysothatthefluidtemperaturecouldbeassumedtobethesameasthesurroundingtemperature.Thelowestpressureusedwas0.2barandthehighestwas6.1bar,and545measurementswereexecutedbetweentheselimits.ExamplesofthemeasurementresultsaredepictedinFigs.4and5.ThemeasurementsystemincludedoneKyowaPG-20KUpressuresensor(forreferencepressure),twoKuliteHKM-375M-7barVGpressuresensors(forrecognizingapressurewaveattwopoints),aKyowaStrainAmplifierDPM-6H(fortheKyowapressuresensor),aThandar30V-2Aprecisionpowersupply(fortheKulitepressuresensors),aNationalInstrumentsUSB-621116-input(16bit250kS/s)DAQcard,aHPCompaqnx9010laptopcomputerwithMicrosoftWindowsXP,DasyLabv.8.00.004measurementsoftwareandMeasurement&AutomationExplorerv.001.Themeasurementfrequencywas25kHz(0.04ms)andtheblocksizewas1024bit.Fig.2TestequipmentFig.3PrincipleofthemeasurementsFig.4Responseofthepressurewaveatdetectionpointone(upper,dottedline)andtwo(lower,dashedline).NotethepressuredifferencebetweenthedetectionpointsbecauseofflowWorldAcademyofScience,EngineeringandTechnology492009612Fig.5Samecaseasabove.Thetimedifferencebetweenthedetectionpointscanbereadfromthesurveybox.NotethatthelinesaremodifiedforpublishingbydecreasingtheirresolutionsnotablyfromtheoriginalThevolumeflowofthetestequipmentQcanbeestimatedwiththeHagen-Poiseulleequation(3)27Q=)(128214ppld(3)wheredispipediameter,isdynamicviscosity,lispipelength,p1ispressureatpoint1andp2ispressureatpoint2.Duringthemeasurementspressurewillvaryfromzeroto0.5bar(pipelength2.75m)ortoalmostonebar(pipelength4.26m).Thismeansthattheabsolutemaximumflow,whichisevenoverestimatedhereonpurpose,isconstantlylessthan1.2l/min(0.4m/s)atatemperatureof18Canditseffectontheresultsisimpossibletonoticeinthisarrangement.FluidviscositywasmeasuredwithaBrookfieldDV-II+rotationviscometeranddensitybyusingthespecificweightmethod(weighinganaccuratevolumeofthefluidatthedesiredtemperature).Fluiddensitywas874kg/m3atatemperatureof18Cand864kg/m3atatemperatureof40C.Thedynamicfluidviscositiesatthecorrespondingtemperatureswere121cPand42cP.Thefluidwasacommercialmineraloil-basedhydraulicoil.IV.RESULTSOFMEASUREMENTSAltogether545measurementswereanalyzed.Theaveragepressureofthemeasurementswas2.9barandthemeasuredaveragepressurewavevelocity(soundvelocity),1377m/s.TheresultsofallthemeasurementsarepresentedinFig.6,whichindicatesthemagnitudeofthewavevelocityinthepressurerangebetween0.2barand6bar.InFig.6themeasuredresultsoftheflowsituationandnon-flowsituationaresep