简介:Thedirect-forcingfictitiousdomainmethodisextendedtosimulatethelocomotionofapassivelypitchingfoil.Ourstudyfocusesonthehysteresisphenomenonthatthecriticalfrequencyforthereverseofthelocomotiondirectionofthewingincaseofdecreasingfrequencyissmallerthanthatincaseofincreasingfrequency.Inoursimulations,thehysteresisphenomenonisproducedbyimposingdifferentinitialconditionsatasamefrequency.Ourresultsindicatethattheratiooftheheavingamplitudesoftwofoiledgesiscrucialtothedirectionofthefoil'shorizontalmotion,andtheamplitudeoftheleadingedgeisgenerallysmaller.Thecriticalfrequenciesforthereverseofthelocomotiondirectionareincreased,whenthefoil-fluiddensityratioisdecreasedorthespringconstantisincreased.Thecriticalfrequenciesinthebi-stabilityregimealsodependontheinitialvelocityimposed,andthehysteresisloopgenerallybecomeslargeriftheinitialvelocitiesareclosertotheterminallocomotionvelocitiesofthefoil.