Ansys 12.0 CFX 官方教程9A

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1、Turbulence9-1ANSYS,Inc.Proprietary 2009 ANSYS,Inc.All rights reserved.April 28,2009Inventory#002598Training Manual9-1ANSYS,Inc.Proprietary 2009 ANSYS,Inc.All rights reserved.April 28,2009Inventory#002598Chapter 9TurbulenceIntroduction to CFX Turbulence9-2ANSYS,Inc.Proprietary 2009 ANSYS,Inc.All righ

2、ts reserved.April 28,2009Inventory#002598Training ManualWhat is Turbulence?Unsteady,irregular(non-periodic)motion in which transported quantities(mass,momentum,scalar species)fluctuate in time and space Identifiable swirling patterns characterize turbulent eddies Enhanced mixing(matter,momentum,ener

3、gy,etc.)results Fluid properties and velocity exhibit random variations Statistical averaging results in accountable,turbulence related transport mechanisms This characteristic allows for turbulence modeling Contains a wide range of turbulent eddy sizes(scales spectrum)The size/velocity of large edd

4、ies is on the order of the mean flow Large eddies derive energy from the mean flow Energy is transferred from larger eddies to smaller eddies In the smallest eddies,turbulent energy is converted to internal energy by viscous dissipationTurbulence9-3ANSYS,Inc.Proprietary 2009 ANSYS,Inc.All rights res

5、erved.April 28,2009Inventory#002598Training ManualIs the Flow Turbulent?External FlowsInternal FlowsNatural Convection000,500Re xalong a surfacearound an obstaclewherewhereOther factors such as free-stream turbulence,surface conditions,and disturbances may cause transition to turbulence at lower Rey

6、nolds numbers,3002 Rehd000,20Re dis the Rayleigh numberLULReetc.,hddxL kTLgCTLgp323Ra910PrRakCpPris the Prandtl number Flows can be characterized by the Reynolds Number,ReTurbulence9-4ANSYS,Inc.Proprietary 2009 ANSYS,Inc.All rights reserved.April 28,2009Inventory#002598Training ManualObservation by

7、O.ReynoldsLaminar(Low Reynolds Number)Transition(Increasing Reynolds Number)Turbulent(Higher Reynolds Number)Turbulence9-5ANSYS,Inc.Proprietary 2009 ANSYS,Inc.All rights reserved.April 28,2009Inventory#002598Training ManualTurbulent Flow StructuresEnergy Cascade Richardson(1922)SmallstructuresLarges

8、tructuresTurbulence9-6ANSYS,Inc.Proprietary 2009 ANSYS,Inc.All rights reserved.April 28,2009Inventory#002598Training ManualGoverning EquationsConservation EquationsContinuityMomentumEnergywhereNote that there is no turbulence equation in the governing Navier-Stokes equations!0)(iiuxtjijijijixxPuuxut

9、)()(jiijijjiijxuxuxu32221itotuhh)()()(jijijjtotjtotxTuxtPuhxhtTurbulence9-7ANSYS,Inc.Proprietary 2009 ANSYS,Inc.All rights reserved.April 28,2009Inventory#002598Training ManualOverview of Computational Approaches Direct Numerical Simulation(DNS)Theoretically,all turbulent(and laminar/transition)flow

10、s can be simulated by numerically solving the full Navier-Stokes equations Resolves the whole spectrum of scales.No modeling is required But the cost is too prohibitive!Not practical for industrial flows Large Eddy Simulation(LES)type models Solves the spatially averaged N-S equations Large eddies a

11、re directly resolved,but eddies smaller than the mesh are modeled Less expensive than DNS,but the amount of computational resources and efforts are still too large for most practical applications Reynolds-Averaged Navier-Stokes(RANS)models Solve time-averaged Navier-Stokes equations All turbulent le

12、ngth scales are modeled in RANS Various different models are available This is the most widely used approach for calculating industrial flows There is not yet a single,practical turbulence model that can reliably predict all turbulent flows with sufficient accuracyTurbulence9-8ANSYS,Inc.Proprietary

13、2009 ANSYS,Inc.All rights reserved.April 28,2009Inventory#002598Training ManualRANS Modeling Time Averaging Ensemble(time)averaging may be used to extract the mean flow properties from the instantaneous ones The instantaneous velocity,ui,is split into average and fluctuating components The Reynolds-

14、averaged momentum equations are as follows The Reynolds stresses are additional unknowns introduced by the averaging procedure,hence they must be modeled(related to the averaged flow quantities)in order to close the system of governing equationsFluctuatingcomponentTime-averagecomponentExample:Fully-

15、DevelopedTurbulent Pipe FlowVelocity ProfileInstantaneouscomponentjiijuuRjijjijikikixRxuxxpxuutu(Reynolds stress tensor)NnniNituNtu1,1lim,xxtututuiii,xxxtui,xtui,xtui,xTurbulence9-9ANSYS,Inc.Proprietary 2009 ANSYS,Inc.All rights reserved.April 28,2009Inventory#002598Training ManualRANS Modeling The

16、Closure Problem Closure problem:Relate the unknown Reynolds Stresses to the known mean flow variables through new equations The new equations are the turbulence model Equations can be:Algebraic Transport equations All turbulence models contain empiricism Equations cannot be derived from fundamental

17、principles Some calibrating to observed solutions and“intelligent guessing”is contained in the modelsTurbulence9-10ANSYS,Inc.Proprietary 2009 ANSYS,Inc.All rights reserved.April 28,2009Inventory#002598Training ManualRANS Modeling The Closure Problem The RANS models can be closed in one of the follow

18、ing ways(1)Eddy Viscosity Models(via the Boussinesq hypothesis)Boussinesq hypothesis Reynolds stresses are modeled using an eddy(or turbulent)viscosity,T.The hypothesis is reasonable for simple turbulent shear flows:boundary layers,round jets,mixing layers,channel flows,etc.(2)Reynolds-Stress Models

19、(via transport equations for Reynolds stresses)Modeling is still required for many terms in the transport equations RSM is more advantageous in complex 3D turbulent flows with large streamline curvature and swirl,but the model is more complex,computationally intensive,more difficult to converge than

20、 eddy viscosity modelsijijkkijjijiijkxuxuxuuuR3232TTTurbulence9-11ANSYS,Inc.Proprietary 2009 ANSYS,Inc.All rights reserved.April 28,2009Inventory#002598Training Manual A large number of turbulence models are available in CFX,some have very specific applications while others can be applied to a wider

21、 class of flows with a reasonable degree of confidenceRANS Eddy-viscosity Models:1)Zero Equation model.2)Standard k-model.3)RNG k-model.4)Standard k-model.5)Baseline(BSL)zonal k-based model.6)SST zonal k-based model.7)(k-)1E model.RANS Reynolds-Stress Models:1)LRR Reynolds Stress2)QI Reynolds Stress

22、3)Speziale,Sarkar and Gatski Reynolds Stress4)SMC-model5)Baseline(BSL)Reynolds Stress modelEddy Simulation Models:1)Large Eddy Simulation(LES)transient2)Detached Eddy Simulation(DES)*transient 3)Scale Adaptive Simulation SST(SAS)*transient*Not available in the ANSYS CFD-Flo productAvailable Turbulen

23、ce ModelsTurbulence9-12ANSYS,Inc.Proprietary 2009 ANSYS,Inc.All rights reserved.April 28,2009Inventory#002598Training Manual The velocity profile near the wall is important:Pressure Drop Separation Shear Effects Recirculation Turbulence models are generally suited to model the flow outside the bound

24、ary layer Examination of experimental data yields a wide variety of results in the boundary layerThe above graph shows non-dimensional velocity versus non-dimensional distance from the wall.Different flows show different boundary layer profiles.Turbulence Near the WallTurbulence9-13ANSYS,Inc.Proprie

25、tary 2009 ANSYS,Inc.All rights reserved.April 28,2009Inventory#002598Training Manual By scaling the variables near the wall the velocity profile data takes on a predictable form(transitioning from linear to logarithmic behavior)Since near wall conditions are often predictable,functions can be used t

26、o determine the near wall profiles rather than using a fine mesh to actually resolve the profile These functions are called wall functionsLinearLogarithmicScaling the non-dimensional velocity and non-dimensional distance from the wall results in a predictable boundary layer profile for a wide range

27、of flowsTurbulence Near the WallTurbulence9-14ANSYS,Inc.Proprietary 2009 ANSYS,Inc.All rights reserved.April 28,2009Inventory#002598Training Manual Fewer nodes are needed normal to the wall when wall functions are useduyuyBoundary layerWall functions used to resolve boundary layerWall functions not

28、used to resolve boundary layerTurbulence Near the WallTurbulence9-15ANSYS,Inc.Proprietary 2009 ANSYS,Inc.All rights reserved.April 28,2009Inventory#002598Training ManualTurbulence Near The Wall y+is the non-dimensional distance from the wall It is used to measure the distance of the first node away

29、from the walluyBoundary layery+Wall functions are only valid within specific y+values If y+is too high the first node is outside the boundary layer and wall functions will be imposed too far into the domain If y+is too low the first node will lie in the laminar(viscous)part of the boundary layer whe

30、re wall functions are not validTurbulence9-16ANSYS,Inc.Proprietary 2009 ANSYS,Inc.All rights reserved.April 28,2009Inventory#002598Training Manual In some situations,such as boundary layer separation,wall functions do not correctly predict the boundary layer profile In these cases wall functions sho

31、uld not be used Instead,directly resolving the boundary layer can provide accurate results Not all turbulence models allow the wall functions to be turned offWall functions applicableWall functions not applicableTurbulence Near the WallTurbulence9-17ANSYS,Inc.Proprietary 2009 ANSYS,Inc.All rights re

32、served.April 28,2009Inventory#002598Training Manual Standard k-Model The“industrial CFD”standard since it offer a good compromise between numerical effort and computational accuracy Wall functions are always used y+should typically be 300 for the wall functions to be valid There is no lower limit on

33、 y+CFX uses Scalable wall functions If your mesh results in y+values below the valid range of the wall functions,the nodes nearest the wall are effectively ignored This ensures valid results,within the model limitations,but is a waste of mesh Known limitations:Separation generally under predicted si

34、nce wall functions are used Inaccuracies with swirling flows and flows with strong streamline curvaturek-epsilon ModelTurbulence9-18ANSYS,Inc.Proprietary 2009 ANSYS,Inc.All rights reserved.April 28,2009Inventory#002598Training Manual k-Model One of the advantages of the k-formulation is the near wal

35、l treatment for low-Reynolds number computations Here“low-Reynolds”refers to the turbulent Reynolds number,which is low in the viscous sub-layer,not the device Reynolds number In other words“low-Reynolds number computations”means the near wall mesh is fine enough to resolve the laminar(viscous)part

36、of the boundary layer which is very close to the wall A low-Reynolds number k-model only requires y+=2 If a low-Re k-model were available,it would require a much small y+In industrial flows,even y+2.A finer near wall mesh is required to achieve y+2.Turbulence9-20ANSYS,Inc.Proprietary 2009 ANSYS,Inc.

37、All rights reserved.April 28,2009Inventory#002598Training Manual Shear Stress Transport(SST)Model The SST model is based on the k-model and has the same automatic wall treatment It accounts for the transport of the turbulent shear stress and gives highly accurate predictions of the onset and the amo

38、unt of flow separation This is a good default choiceSST result and experimentk-fails to predict separationExperiment Gersten et al.SST ModelTurbulence9-21ANSYS,Inc.Proprietary 2009 ANSYS,Inc.All rights reserved.April 28,2009Inventory#002598Training Manualy+for the SST and k-omega Models When using t

39、he SST or k-models y+should be 300 so that the wall function approach is valid This will not take advantage of the low-Reynolds formulation,which is necessary for accurate separation prediction However,the model can still be used on these coarser near-wall mesh and produce valid results,within the l

40、imitations of the wall functions To take full advantage of the low-Reynolds formulation y+should be Turbulence and Near-Wall Modeling Modeling Flow Near the Wall Guidelines for Mesh Generation14/13Re 74 LyLyTurbulence9-23ANSYS,Inc.Proprietary 2009 ANSYS,Inc.All rights reserved.April 28,2009Inventory

41、#002598Training ManualOther Turbulence Models When RANS models are not adequate,Eddy Simulation models can be used As already mentioned,these are more computationally expensive Large Eddy Simulation(LES)Resolves the large eddies,models the small eddies Problem:Requires a very fine boundary layer mes

42、h,making it impractical for most flows Detached Eddy Simulation(DES)Uses a RANS model in the boundary layer,switches over to LES in the bulk flow A“standard”boundary layer mesh can be used Problem:the RANS to LES switch depends on the mesh,which can give unphysical results on the“wrong”mesh Scale-Ad

43、aptive Simulation(SAS)Like DES,but without the mesh dependency problemsTurbulence9-24ANSYS,Inc.Proprietary 2009 ANSYS,Inc.All rights reserved.April 28,2009Inventory#002598Training ManualInlet Turbulence Conditions Unless turbulence is being directly simulated,it is accounted for by modeling the tran

44、sport of turbulence properties,for example k and Similar to mass and momentum,turbulence variables require boundary condition specifications Several options exist for the specification of turbulence quantities at inlets(details on next slide)Unless you have absolutely no idea of the turbulence level

45、s in your simulation(in which case,you can use the Medium(Intensity=5%)option),you should use well chosen values of turbulence intensities and length scales Nominal turbulence intensities range from 1%to 5%but will depend on your specific application The default turbulence intensity value of 0.037(t

46、hat is,3.7%)is sufficient for nominal turbulence through a circular inlet,and is a good estimate in the absence of experimental dataTurbulence9-25ANSYS,Inc.Proprietary 2009 ANSYS,Inc.All rights reserved.April 28,2009Inventory#002598Training ManualInlet Turbulence Conditions Default Intensity and Aut

47、ocompute Length Scale The default turbulence intensity of 0.037(3.7%)is used together with a computed length scale to approximate inlet values of k and .The length scale is calculated to take into account varying levels of turbulence.In general,the autocomputed length scale is not suitable for exter

48、nal flows Intensity and Autocompute Length Scale This option allows you to specify a value of turbulence intensity but the length scale is still automatically computed.The allowable range of turbulence intensities is restricted to 0.1%-10.0%to correspond to very low and very high levels of turbulenc

49、e accordingly.In general,the autocomputed length scale is not suitable for external flows Intensity and Length Scale You can specify the turbulence intensity and length scale directly,from which values of k and are calculated Low(Intensity=1%)This defines a 1%intensity and a viscosity ratio equal to

50、 1 Medium(Intensity=5%)This defines a 5%intensity and a viscosity ratio equal to 10This is the recommended option if you do not have any information about the inlet turbulence High(Intensity=10%)This defines a 10%intensity and a viscosity ratio equal to 100 Specified Intensity and Eddy Viscosity Rat

51、io Use this feature if you wish to enter your own values for intensity and viscosity ratio k and Epsilon Specify the values of k and directly Zero Gradient Use this setting for fully developed turbulence conditionsTurbulence9-26ANSYS,Inc.Proprietary 2009 ANSYS,Inc.All rights reserved.April 28,2009In

52、ventory#002598Training ManualExample:Pipe Expansion with Heat Transfer q=const.OutletaxisHH40 x HInletq=0.dD Reynolds Number ReD=40750 Fully Developed Turbulent Flow at Inlet Experiments by Baughn et al.(1984)Turbulence9-27ANSYS,Inc.Proprietary 2009 ANSYS,Inc.All rights reserved.April 28,2009Invento

53、ry#002598Training Manual Plot shows dimensionless distance versus Nusselt Number Best agreement is with SST and k-omega models which do a better job of capturing flow recirculation zones accuratelyExample:Pipe Expansion with Heat TransferTurbulence9-28ANSYS,Inc.Proprietary 2009 ANSYS,Inc.All rights

54、reserved.April 28,2009Inventory#002598Training ManualSummary:Turbulence Modeling Guidelines Successful turbulence modeling requires engineering judgment of:Flow physics Computer resources available Project requirements Accuracy Turnaround time Near-wall treatments Modeling procedure Calculate characteristic Re and determine whether the flow is turbulent Estimate y+before generating the mesh The SST model is good choice for most flows Use the Reynolds Stress Model or the SST model with Curvature Correction(see documentation)for highly swirling,3-D,rotating flows