Viscous Flow Around Metal Spheres在金属球上的粘性流.ppt

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1、ViscousFlowAroundMetalSpheresTerminalVelocityandAccelerationProfileasaFunctionofRadiusIntroductionCharacterizeviscousflowaroundasphereFinddependenceofterminalvelocityonradiusFinddependenceofaccelerationprofileonradiusIntroductionClassicalprobleminfluiddynamics

2、SpecialflowregimecalledStoke’sFlowViscousforcesdominatetheflowOftenusedtodeterminefluidviscosityOurExperimentalSetupGraduatedcylinderfilledwithglycerinDifferentsizesofmetalballsDigitalCamcorderExperimentalSetup6differentsizedsteelballsExperimentalSetupExperime

3、ntalSetupAvideodatafileofthe6.35mmballsTheoreticalModelsTerminalVelocityAnticipatedterminalvelocityv.radius.TheoreticalModelsAccelerationProfileTheoreticalModelsTheoreticalModelsTheoreticalModelsTheoreticalModelsTheoreticalModelsNavierStokesAnalysisNon-dimen

4、sionalizingtheEqnsTheoreticalModelsForStokesFlowRe<<1SotheEquationssimplifytoTheoreticalModelsNavierStokesAnalysisTheoreticalModelsAnalyticalSolnfortheSphereTheoreticalModelsTheAnalyticalExpressionforDragForceFmatchesDimensionalAnalysisStoke’sLawResults&A

5、nalysisUsedvideofromcamcordertofindexperimentalspeedsCalculatedtheoreticalspeedsusingmodelCompared:ExperimentalTheoreticalPredictedScalingRatefromDimensionalAnalysis(V~r^2)Results&AnalysisResults&AnalysisErrorsourcesViscosityisafunctionoftemperature!Results&An

6、alysisErrorSources(cont.)Bubbleseffectivelyreduceviscositywhenthey’reinaball’spathBubbleseffectivelyincreasebuoyancywhenthey’repiggybackingonaballSidewalleffects(disruptionofflowlines)Instrumentresolution(timeanddistance)Results&AnalysisVelocityProfileAnalysis

7、Terminalvelocityreachedforsmallestballin0.007seconds,fasterthancamera.Reachedforlargestballin0.303second,buttimesanddistancesinvolvedwerestilltoofast:Results&AnalysisResults&AnalysisConclusionExperimentalterminalvelocitymatcheswithdimensionalanalysisandtheoret

8、icalmodelsignificanterrorsduetotemperatureandothereffectsAccelerationprofilecannotbemeasuredwithcurrentequipmentresolutionistoolowrelativetophenomenatobeobserved