9.Hydraulic forces

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1、9HydraulicforcesThepressureriseintheimpellergenerateshydraulicforcesandmomentswhichactontherotor.Inparticularforcesinaxialandradialdirectionaresignificantforappropriatesizingofshaftandbearings.Whiletheradialforceisdeterminedbythepressuredistributionaroundtheimpellercircumference,theaxialforceisg

2、overnedbytheflowthroughtheimpellersidewallgapsandtheresultingpres-suredistributionsontheshrouds.Becauseofitshighrelevanceinthedeterminationoftheaxialforcesactingonturbomachinerotorsthereisawealthofpublicationsdealingwiththesubjectofflowthroughtheimpellersidewallgaps.Acomprehensivecollectionofrel

3、evantquotationscanbefoundin[3.29].9.1FlowphenomenaintheimpellersidewallgapsForreasonsofmechanicaldesign,axialclearancesarerequiredbetweentheshroudsofaclosedimpellerandthecasing(called“impellersidewallgaps”).Widthandshapeoftheresultingliquid-filledspacesbetweenimpellerandcasingareessentiallydeter

4、minedbyaspectsofthemechanicaldesign.Thefluidcontainedintheimpellersidewallgapscannotbeatrestwhentheimpellerrotates:immediatelyattheshroudthefluidadherestothesolidwallandhasthusthevelocitycu=ω×r.Aboundarylayerisformedinwhichthetangentialvelocitydropswithincreasingdistancefromtheshroud.Thefluidals

5、oadherestothecasingwallwherethevelocityiszerocu=0.Thevelocityincreasesinthecas-ingwallboundarylayer,Fig.9.1.WithtightsidewallgapsorlowReynoldsnumbersbothboundarylayersaremerged;withwidegapstheyareseparatedandacoreflowisformed.Theflowintheimpellersidewallgapcanbelaminarorturbulent.Inmostapplicati

6、onswithwaterpumpingtheflowisturbulentandtheboundarylayersareseparatedasde-pictedinFig.9.1;onlythiscaseistreatedinthefollowing.Thecentrifugalforcesintherotatingboundarylayergenerateafluidtransportradiallyoutwards.Thustheshroudactsinasimilarwayasafrictionpump(Chap.3.10.3).Forreasonsofcontinuity,fl

7、uidflowsbackradiallyinwardsalongthecasingwall.Inthemeridionalsectionacirculatingflowisthusestablishedintheimpellersidewallgaps.Figure9.1showsthecorrespondingvelocitydistribu-tionsinradialandcircumferentialdirection.Usuallyth