1、AgendavIntroductionvSingle moving reference frame(SRF)model vMultiple moving reference frame(MRF)modelvMixing plane modelvSliding mesh modelvQuestions?MotivationvFlows involving rotating domains occur frequently in engineeringvExamplescompressors and turbinesfans and pumpsrotating cavities,seals,and
2、 bearingsmixing equipmentfluid coupling devices and torque convertersair motorsmarine and aircraft propellersand many morevComputational Fluid Dynamics(CFD)today plays a central role in the design and analysis of rotating machineryExamples of Rotating Machinerygas turbine engineautomotive water pump
3、tube axial fansteam turbineHVAC blower unithydro turbineGoals of the TrainingvProvide an introduction to rotating machinery modelingvExamine the four major classes of rotating machinery problemsSingle rotating reference frame(SRF)Multiple rotating reference frame(MRF)Mixing planeSliding meshvPresent
4、 details on modeling rotating machinery problems using FluentModel setupSolution process(steady-state and unsteady)vAnswer your questions!Types of Rotating Machinery vIn this course,we will classify rotating machinery as follows:Turbomachinery-machines which add work to or extract work from a fluidv
5、compressors,fans,pumps-add work to achieve a pressure rise in the fluidvturbines,windmills-extract work from fluid to drive other machines Mixing equipment-machines which are designed to mix fluid(and possibly solid)materials for use in a chemical processing applicationvindustrial mixing tanks Rotat
6、ing tanks,seals,cavities,and other devicesvdisk cavities and labyrinth seals in gas turbine enginesvelectric motor cooling passagesvdisk drivesvrotating tires on automotive vehiclesvAll of these applications involve rotating surfaces and domains(and thus may use a rotating reference frame for modeli
7、ng)Classification of Turbomachinery vAxial machinesFlow through the machine is(in general)aligned with the axis of rotationExamples:propellers,axial fans/compressors/turbines,swirlers vCentrifugal machinesFlow through the machine is(in general)perpendicular to the axis of rotationExamples:liquid pum
8、ps,centrifugal fans/compressors,radial turbinesvMixed FlowFlow through the machine is somewhere between axial and centrifugalExample:mixed flow compressorBasic Problem StatementvWe wish to solve for the flow through a domain which contains rotating componentsvpropeller,compressor/turbine blade,radia
9、l impeller,etc.stationary and/or rotating surfacesvducts walls,bores and cavities,seal teeth surfaces,etc.vRotation(s)assumed to be steadyaccelerating reference frames can be modeled with source terms(not considered here)vWell-posed boundary conditionsflowrates,pressures,temperatures,other scalars a
10、t inlet/outlet boundarieswall motion,thermal,other BCs at wallsvOther considerationslaminar/turbulent flow,other physics(e.g.multiphase flow,heat transfer)level of interaction between moving/stationary componentsModeling ApproachesvSingle Rotating Frame(SRF)Entire computational domain is referred to
11、 rotating reference framevMultiple Rotating Frame(MRF)Selected regions of the domain are referred to rotating reference framesIgnore interaction effects steady-statevMixing Plane(MPM)Influence of neighboring regions accounted for through use of a mixing plane model at rotating/stationary domain inte
12、rfacesIgnore circumferential non-uniformities in the flow steady-statevSliding Mesh(SMM)Motion of specific regions accounted for by mesh motion algorithm Flow variables interpolated across a sliding interfaceUnsteady problem-can capture all interaction effects with complete fidelitySingle Reference
13、Frame(SRF)ModelingIntroduction to the SRF ModelvMany problems which involve rotating components can be modeled using a single rotating reference frame.vWhy use a rotating reference frame?Flowfield which is unsteady in the stationary frame becomes steady in the rotating frameSteady-state problems are
14、 easier to solve.vsimpler BCsvlow computational costveasier to post-process and analyzevWe will discuss issues related to SRF modeling in this section,but many concepts(e.g.solver settings,physical models,etc.)will also apply to MRF,mixing plane,and sliding mesh modeling.Illustration of SRF modelbla
15、dehubdomainrotatingreferenceframeaxisshroud/casingImplications of SRFvSingle fluid domainvDomain rotates with a constant rotational speed about a specified rotational axisEntire domain moves with the reference framevBoundaries which move with the fluid domain may assume any shapevBoundaries which ar
16、e stationary(with respect to the laboratory or fixed frame)must be surfaces of revolutionvCan employ rotationally-periodic boundaries for efficiency(reduced domain size)Stationary Walls in SRF Modelsstationary wallrotorbaffleCorrectWrong!Wall with baffles not a surfaceof revolution!N-S Equations:Rot
17、ating Reference FramevTwo different formulations are used in FluentRelative Velocity Formulation(RVF)vObtained by transforming the stationary frame N-S equations to a rotating reference framevUses the relative velocity as the dependent variable in the momentum equationsvUses the relative total inter
18、nal energy as the dependent variable in the energy equationAbsolute Velocity Formulation(AVF)vDerived from the relative velocity formulationvUses the absolute velocity as the dependent variable in the momentum equationsvUses the absolute total internal energy as the dependent variable in the energy
19、equationReference Framesxyzzyxstationaryframerotatingframeaxis ofrotationrCFD domainorRvAssumptionsNo translation()Steady rotation(=constant)about specified axisvaxis passes through origin of rotating frameIgnore body forces due to gravity and other effectsIgnore energy sourcesvDefinitionsAbsolute v
20、elocity()-Fluid velocity with respect to the stationary(absolute)reference frameRelative velocity()-Fluid velocity with respect to the rotating reference framev3-D compressible,laminar forms of the equations presented in the following slidesAssumptions and DefinitionsVW0/=dtrdoThe Velocity Trianglev
21、The relationship between the absolute and relative velocities is given byvIn turbomachinery,this relationship can be illustrated using the laws of vector addition.This is known as the Velocity TrianglerUUWV=VWURelative Velocity FormulationqwwwpeWteBzpwWtwBypwWtwBxpwWtwWtzvrzyvryxvrxtrtrzvrzzzyvryyyx
22、vrxxx=0(continuity)(x momentum)(y momentum)(z momentum)(energy)Relative Velocity Formulation(2)=kWwzWjWwyWiWwxWTqRWeekwjwiwWzvrzyvryxvrxtrzyx32323221222(relative velocity vector)(relative total internal energy)(Fouriers Law)(viscous terms)Relative Velocity Formulation(3)vAcceleration terms due to ro
23、tating reference framerWkBjBiBBzyx=2CoriolisaccelerationcentripetalaccelerationAbsolute Velocity FormulationqvvvpeWteBzpvWtvBypvWtvBxpvWtvWtzvzyvyxvxttzvzzzyvyyyxvxxx=0(continuity)(x momentum)(y momentum)(z momentum)(energy)Absolute Velocity Formulation(2)=kVvzVjVvyViVvxVTqVeekvjvivVzvzyvyxvxtzyx323
24、232212(absolute velocity vector)(total internal energy)(Fouriers Law)(viscous terms)Absolute Velocity Formulation(3)vAcceleration term due to rotating reference frameVkBjBiBBzyx=Acceleration reduces to single term involvingrotational speed and absolute velocitySRF Geometries:2-Dv2-D Problems2-D plan
25、ar geometries rotate about axis normal to x-y plane with specified origin(periodic boundaries are permitted)2-D axisymmetric geometries rotate about the x-axisPlanarAxisymmetricxyxSRF Geometries:3-Dv3-D ProblemsUser defines both rotational axis origin and direction for the fluid domainPeriodic bound
26、aries permittedoriginrotational axisChoice of SolvervSame considerations for general flowfield modeling apply to SRF solver choiceuSegregated Solver:incompressible,low speed compressible flows lExamples:Fans,blowers,pumpsuCoupled Solvers:high speed compressible flows,above Mach 0.3lExamples:high pre
27、ssure axial compressors,turbines,turbochargersvVelocity Formulation recommendationsuUse AVF when inflow comes from a stationary domainuUse RVF with closed domains(all surfaces are moving)or if inflow comes froma rotating domainlNOTE:RVF only available in the segregated solveruIn many cases,either ca
28、n be used successfullyBoundary Conditions and Physical ModelsvBasic BCs used in SRF analysisFluid BCInflow BCsvPressure InletvVelocity InletvMass Flow InletOutflow BCsvPressure OutletWallsPeriodicsvPhysical modelsTurbulence modelsDPMMultiphase,real gas,heat transferFluid BCsvUse fluid BC panel to se
29、lect rotational axis origin and direction vector for rotating reference frameNote:all direction vectors should be unit vectors but Fluent will normalize them if they arentvSelect Moving Reference Frame as the Motion Type for SRFvEnter rotational speedTranslation velocity set to zero Velocity Inletsv
30、Used for incompressible,mildly compressible flows when inlet velocity is knownvCan specify absolute or relative velocity vector vCan specify vector components in Cartesian or cylindrical coordinatesvFor 2-D,axisymmetric with swirl and 3-D problems you can specify tangential velocity aslocityangular
31、veuser velocityntialuser tange,=inpinpinpinpVrVVPressure Inlets(1)vPressure inlets can be used with either incompressible or compressible flows.vDefinition of total pressure depends on velocity formulation and compressibility:12222112121=kktttMkppWppVppincompressible,AVFincompressible,RVFcompressibl
32、e,AVFPressure Inlets(2)vSpecify appropriate total pressure and total temperaturevIf inlet flow is supersonic,specify static pressure such that desired Mach number corresponds to pt/p vSpecify flow direction vectoruCan use Cartesian,cylindrical,or local cylindrical coordinate systemuFrame of flow dir
33、ection depends on velocity formulation!uYou cannot use a frame of reference for the direction which is different from the velocity formulationMass Flow InletsvPrescribe total mass flow rate or mass flux and total temperature for compressible flowsvTotal pressure“floats”since the mass flow rate is fi
34、xedvPermits flow direction specification in absolute frame onlyuFluent 6 permits direction specification in Cartesian and cylindrical coordinatesPressure OutletsvSpecify static pressure at the outletvCan employ a radial equilibrium assumption which computes a radial pressure variation fromThe specif
35、ied pressure is then assumed to be the hub static pressureRVRp2=BackflowvBackflow occurs when the static pressure in a cell adjacent to a pressure boundary falls below the prescribed boundary pressurevFor SRF problems,the direction of the backflow isnormal to the boundary in the absolute frame if AV
36、F is usednormal to the boundary in the relative frame if RVF is usedvRecommendationAs some backflow may occur during the solution process,prescribe reasonable values for all backflow quantitiesTry to minimize(or eliminate)backflow by extending your outlet boundary further downstreamWall BCsvWall BCs
37、 enforce zero normal velocity at all wall surfacesuno slip(zero velocity)for viscous flowsvFor moving reference frames,you can specify the wall motion in either the absolute or relative framesvRecommended specification of wall BCs for all moving reference frame problemsuFor stationary surfaces(in th
38、e lab frame)use zero Rotational speed,AbsoluteuFor moving surfaces,use zero Rotational speed,Relative to Adjacent Cell Zone Periodic BCsvRotational periodic BCs rely on the rotational axis specification to transfer information correctlyvRotationally periodic boundaries can be used in SRF problems to
39、 reduce mesh size provided both the geometry and flow are periodicvNotes:uIf you are using the make-periodic command in the TUI,make sure you set the rotational axis in the Fluid BC panel first before creating the periodicsuOnce the periodic BCs have been set,perform a grid check to see if the repor
40、ted periodic angles are correctTurbulence Models for Rotating MachineryModelStrengthsWeaknessesSpalart-AllmarasEconomical(1-eq.);good track recordfor mildly complex B.L.type of flowsNot very widely tested yet;lack ofsubmodels(bustion,buoyancy)STD k-Robust,economical,reasonablyaccurate;long accumulat
41、edperformance dataMediocre results for complex flowsinvolving severe pressuregradients,strong streamlinecurvature,swirl and rotationRNG k-Good for moderately complexbehavior like jet impingement,separating flows,swirling flows,andsecondary flowsSubjected to limitations due toisotropic eddy viscosity
42、assumptionRealizablek-Offers largely the same benefits asRNG;resolves round-jet anomalyRecommended k-model forturbomachinerySubjected to limitations due toisotropic eddy viscosityassumptionReynoldsStressModelPhysically most complete model(history,transport,and anisotropy ofturbulent stresses are all
43、 accountedfor)Requires more cpu effort(2-3x);tightly coupled momentum andturbulence equationsDPM ModelingvYou can use DPM and pathline models for SRF problemsvParticle paths are computed in the relative framevIf you want to see particle paths in the absolute frame,you can access the following switch
44、 in the TUI:define/models/dpm/tracking/track-in-absolute-framevNote that particles moving in absolute frame may hit wall surfaces,since the rotation of the frame is not accounted forparticle injection at blade tipsOther ModelsvMultiphase ModelsVOF,ASMM,Eulerian(Fluent 6)multiphase models are all com
45、patible with SRF modeling in FluentExamples:mixing tanks,multiphase pumps flowsvReal Gas ModelCan model specific fluids using non-ideal gas equation of stateEmploys the REFPROP library from NISTFor use with the coupled-solvers only!Available fluids include:carbon dioxide,ammonia,butane,ethane,propan
46、e,propylene,wide range of refrigerants(e.g.R11,R12,R134a,etc.)vHeat TransferConduction and radiation models can be enabled with SRF modelsNote:For conducting solids which are contained in a moving reference frame,you dont need to activate the Moving Reference Frame option!Solver Settings(1)vSegregat
47、ed solverPressure-Velocity Coupling MethodvSIMPLE is sufficient for most problemsvUse PISO for unsteady problems(e.g.sliding mesh)Pressure InterpolationvStandard scheme is acceptable for low speed flows,but for highly swirling flows.vuse PRESTO!if you have a quad or hex meshvuse Body Force Weighted
48、scheme for mixed meshesOther equations-use second order discretizationsvCan start with first order for stability,especially for problems with high rotational speedsSolver Settings(2)vCoupled solversUse first order discretizations to begin your calculation-then switch to second order when the solutio
49、n is close to convergenceUse default Courant numbers as a start(1 for explicit solver,5 for implicit solver)For coupled-explicit solvervUse 4 levels of FAS multigrid for most problemshelps propagate solution more rapidly through the domainvUse more levels of you have a very large meshExample SRF Cal
50、culationsvTwo examples will now be presented to illustrate typical SRF modeling procedures:2-D swirling flow through a disk cavity3-D flow through a propeller fanDisk CavityvDisk cavity air flow study based on the experiments of Pincombe,1981vDisk geometry:radius (b)=443 mm,width=59 mm,bore=44.3 mmv
