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.

简介：A3-DnumericalformulationisproposedonthehorizontalCartesian,verticalsigma-coordinategridformodelingnon-hydrostaticpressurefree-surfaceflows.Thepressuredecompositiontechniqueandθsemi-implicitmethodareused,withthesolutionprocedurebeingsplitintotwosteps.First,withtheimplicitpartsofnon-hydrostaticpressuresexcluded,theprovisionalvelocityfieldandfreesurfaceareobtainedbysolvinga2-DPoissonequation.Second,thetheoryofthedifferentialoperatorisemployedtoderivethe3-DPoissonequationfornon-hydrostaticpressures,whichissolvedtoobtainthenon-hydrostaticpressuresandtoupdatetheprovisionalvelocityfield.Whenthenon-orthogonalsigma-coordinatetransformationisintroduced,additionaltermscomeintobeing,resultingina15-diagonal,diagonallydominantbutunsymmetriclinearsysteminthe3-DPoissonequationfornon-hydrostaticpressures.TheBiconjugateGradientStabilized(BiCGstab)methodisusedtosolvetheresulting3-Dunsymmetriclinearsysteminsteadoftheconjugategradientmethod,whichcanonlybeusedforsymmetric,positive-definitelinearsystems.Threetestcasesareusedforvalidations.Thesuccessfulsimulationsofthesmall-amplitudewave,asupercriticalflowoverarampandaturbulentflowintheopenchannelindicatethatthenewmodelcansimulatewellnon-hydrostaticflows,supercriticalflowsandturbulentflows.