简介:Inordertoinvestigatethescaleefectofturbulentflowaroundacircularcylinder,twosimilaritynumbers(criteria)basedonturbulentkineticanddissipationratesassociatedwiththefluctuationcharacteristicsofturbulencewakearededucedbyanalyzingtheReynoldsaveragedNavier–Stokesequations(RANS).TheRNGk–εmodelsandfinitevolumemethodareusedtosolvethegoverningequationsandthesecond-orderimplicittimeandupwindspacediscretizationalgorithmsareusedtodiscretethegoverningequations.Anumericalcomputationofflowparametersaroundatwo-dimensionalcircularcylinderwithReynoldsnumbersrangingfrom102to107isaccomplishedandtheresultindicatesthatthefluctuationofturbulenceflowalongthecenterlineinthewakeofcircularcylindercanneverbechangedwithincreasingReynoldsnumberswhenRe3×106.Thisconclusionisusefulforcontrollingthescaleofnumericalcalculationsandforapplyingmodeltestdatatoengineeringpractice.
简介:WestudyamodifiedversionoftheLane-Emdenequationofthesecondkindmodellingathermalexplosioninaninfinitecylinderandasphere.Wefirstshowthatthesolutiontotherelevantboundaryvalueproblemisboundedandthatthesolutionsaremonotonedecreasing.Theupperbound,thevalueofthesolutionatzero,canbeapproximatedanalyticallyintermsofthephysicalparameters.Weobtainsolutionstotheboundaryvalueproblem,usingboththeTaylorseries(whichworkwellforweaknonlinearity)andthe(5-expansionmethod(validforstrongnonlinearity).Fromhere,weareabletodeducethequalitativebehaviorofthesolutionprofileswithachangeinanyoneofthephysicalparameters.
简介:Ananalysisisperformedtostudytransientfreeconvectiveboundarylayerflowofacouplestressfluidoveraverticalcylinder,intheabsenceofbodycouples.Thesolutionofthetime-dependentnon-linearandcoupledgoverningequationsiscarriedoutwiththeaidofanunconditionallystableCrank–Nicolsontypeofnumericalscheme.Numericalresultsforthesteady-statevelocity,temperatureaswellasthetimehistoriesoftheskin-frictioncoefcientandNusseltnumberarepresentedgraphicallyanddiscussed.Itisseenthatforallflowvariablesasthecouplestresscontrolparameter,Co,isamplified,thetimerequiredforreachingthetemporalmaximumincreasesbutthesteady-statedecreases.
简介:Adimpleappearsonafreesurfacewhilerotatingacylindertankfilledwithliquid.Thedimplestartstoconcentricallydeepertoadrainportatthebottomcenterofthetank.Overtime,thedimplepenetratesthedrainport,afreesurfaceformsalongandslenderstringshapeinthetank,andaso-calledvortexing(aircore)phenomenonoccurs.Thegenerationofavortexcoredependsonthesizeofthetankanddrainport,andonthepropertiesoftheliquidinthetank.Inthisstudy,theliquidlevelandthetimeatwhichthevortexcoreisinitiallygeneratedarenumericallyinvestigatedusingdifferentvaluesoftankdiameter,drainportdiameter,andinitialtankrotationalspeeds.Insteadofafullthree-dimensionalanalysis,atwo-dimensionalaxisymmetricsimulationisconducted.Themomentumconservationequationinthecircumferentialdirectionisadditionallysolvedinthetwo-dimensionalmeshsystem.Severalnon-dimensionalvariablesarecreated:theratiooftheaircoregenerationdistanceandtankdiameter,thediameterratioofthetankanddrainport,therotationalReynoldsnumber,therotationalFroudenumber,andtherotationalWebernumber.Finally,thenon-dimensionalaircoregenerationdistanceiscorrelatedwiththeothernon-dimensionalparameters.