资源描述
Click to edit Master text styles,Second Level,Third Level,Fourth Level,Fifth Level,title style,Fluent Inc.,9/20/2024,163,Fluent,Software,Training,UGM 2001,Introduction to Rotating Machinery Analysis Using Fluent,Frank Kelecy,Fluent Inc.,Agenda,Introduction,Single moving reference frame (SRF) model,Multiple moving reference frame (MRF) model,Mixing plane model,Sliding mesh model,Questions?,Motivation,Flows involving rotating domains occur frequently in engineering,Examples,compressors and turbines,fans and pumps,rotating cavities, seals, and bearings,mixing equipment,fluid coupling devices and torque converters,air motors,marine and aircraft propellers,and many more,Computational Fluid Dynamics (CFD) today plays a central role in the design and analysis of rotating machinery,Examples of Rotating Machinery,gas turbine engine,automotive water pump,tube axial fan,steam turbine,HVAC blower unit,hydro turbine,Goals of the Training,Provide an introduction to rotating machinery modeling,Examine the four major classes of rotating machinery problems,Single rotating reference frame (SRF),Multiple rotating reference frame (MRF),Mixing plane,Sliding mesh,Present details on modeling rotating machinery problems using Fluent,Model setup,Solution process (steady-state and unsteady),Answer your questions!,Types of Rotating Machinery,In this course, we will classify rotating machinery as follows:,Turbomachinery - machines which add work to or extract work from a fluid,compressors, fans, pumps - add work to achieve a pressure rise in the fluid,turbines, 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 application,industrial mixing tanks,Rotating tanks, seals, cavities, and other devices,disk cavities and labyrinth seals in gas turbine engines,electric motor cooling passages,disk drives,rotating tires on automotive vehicles,All of these applications involve rotating surfaces and domains (and thus may use a rotating reference frame for modeling),Classification of Turbomachinery,Axial machines,Flow through the machine is (in general) aligned with the axis of rotation,Examples: propellers, axial fans/compressors/turbines, swirlers,Centrifugal machines,Flow through the machine is (in general) perpendicular to the axis of rotation,Examples: liquid pumps, centrifugal fans/compressors, radial turbines,Mixed Flow,Flow through the machine is somewhere between axial and centrifugal,Example: mixed flow compressor,Basic Problem Statement,We wish to solve for the flow through a domain which contains,rotating components,propeller, compressor/turbine blade, radial impeller, etc.,stationary and/or rotating surfaces,ducts walls, bores and cavities, seal teeth surfaces, etc.,Rotation(s) assumed to be,steady,accelerating reference frames can be modeled with source terms (not considered here),Well-posed boundary conditions,flowrates, pressures, temperatures, other scalars at inlet/outlet boundaries,wall motion, thermal, other BCs at walls,Other considerations,laminar/turbulent flow, other physics (e.g. multiphase flow, heat transfer),level of interaction between moving/stationary components,Modeling Approaches,Single Rotating Frame (SRF),Entire computational domain is referred to rotating reference frame,Multiple Rotating Frame (MRF),Selected regions of the domain are referred to rotating reference frames,Ignore interaction effects steady-state,Mixing Plane (MPM),Influence of neighboring regions accounted for through use of a mixing plane model at rotating/stationary domain interfaces,Ignore circumferential non-uniformities in the flow steady-state,Sliding Mesh (SMM),Motion of specific regions accounted for by mesh motion algorithm,Flow variables interpolated across a sliding interface,Unsteady problem - can capture all interaction effects with complete fidelity,Single Reference Frame(SRF) Modeling,Introduction to the SRF Model,Many problems which involve rotating components can be modeled using a,single,rotating reference frame.,Why use a rotating reference frame?,Flowfield which is,unsteady,in the stationary frame becomes,steady,in the rotating frame,Steady-state problems are easier to solve.,simpler BCs,low computational cost,easier to post-process and analyze,We 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 model,blade,hub,domain,rotating,reference,frame,axis,shroud/casing,Implications of SRF,Single fluid domain,Domain rotates with a constant rotational speed about a specified rotational axis,Entire domain moves with the reference frame,Boundaries which,move with the fluid,domain may assume any shape,Boundaries which are,stationary,(with respect to the laboratory or fixed frame),must be surfaces of revolution,Can employ rotationally-periodic boundaries for efficiency (reduced domain size),Stationary Walls in SRF Models,stationary wall,rotor,baffle,Correct,Wrong!,Wall with baffles,not,a surface,of revolution!,N-S Equations: Rotating Reference Frame,Two different formulations are used in Fluent,Relative Velocity Formulation (RVF),Obtained by transforming the stationary frame N-S equations to a rotating reference frame,Uses the,relative velocity,as the dependent variable in the momentum equations,Uses the,relative total internal energy,as the dependent variable in the energy equation,Absolute Velocity Formulation (AVF),Derived from the relative velocity formulation,Uses the,absolute velocity,as the dependent variable in the momentum equations,Uses the,absolute total internal energy,as the dependent variable in the energy equation,Reference Frames,x,y,z,z,y,x,stationary,frame,rotating,frame,axis of,rotation,CFD domain,Assumptions,No translation ( ),Steady rotation (,w =,constant) about specified axis,axis passes through origin of rotating frame,Ignore body forces due to gravity and other effects,Ignore energy sources,Definitions,Absolute velocity ( ) - Fluid velocity with respect to the stationary (absolute) reference frame,Relative velocity ( ) - Fluid velocity with respect to the rotating reference frame,3-D compressible, laminar forms of the equations presented in the following slides,Assumptions and Definitions,The Velocity Triangle,The relationship between the absolute and relative velocities is given by,In turbomachinery, this relationship can be illustrated using the laws of vector addition. This is known as the Velocity Triangle,Relative Velocity Formulation,(continuity),(x momentum),(y momentum),(z momentum),(energy),Relative Velocity Formulation (2),(relative velocity vector),(relative total internal energy),(Fouriers Law),(viscous terms),Relative Velocity Formulation (3),Acceleration terms due to rotating reference frame,Coriolis,acceleration,centripetal,acceleration,Absolute Velocity Formulation,(continuity),(x momentum),(y momentum),(z momentum),(energy),Absolute Velocity Formulation (2),(absolute velocity vector),(total internal energy),(Fouriers Law),(viscous terms),Absolute Velocity Formulation (3),Acceleration term due to rotating reference frame,Acceleration reduces to single term involving,rotational speed and,absolute velocity,SRF Geometries: 2-D,2-D Problems,2-D planar geometries rotate about axis normal to x-y plane with specified origin (periodic boundaries are permitted),2-D axisymmetric geometries rotate about the x-axis,Planar,Axisymmetric,x,y,x,SRF Geometries: 3-D,3-D Problems,User defines both rotational axis origin and direction for the fluid domain,Periodic boundaries permitted,origin,rotational axis,Choice of Solver,Same considerations for general flowfield modeling apply to SRF solver choice,Segregated Solver,: incompressible, low speed compressible flows,Examples: Fans, blowers, pumps,Coupled Solvers,: high speed compressible flows, above Mach 0.3,Examples: high pressure axial compressors, turbines, turbochargers,Velocity Formulation recommendations,Use AVF when inflow comes from a stationary domain,Use RVF with closed domains (all surfaces are moving) or if inflow comes froma rotating domain,NOTE: RVF only available in the segregated solver,In many cases, either can be used successfully,Boundary Conditions and Physical Models,Basic BCs used in SRF analysis,Fluid BC,Inflow BCs,Pressure Inlet,Velocity Inlet,Mass Flow Inlet,Outflow BCs,Pressure Outlet,Walls,Periodics,Physical models,Turbulence models,DPM,Multiphase, real gas, heat transfer,Fluid BCs,Use fluid BC panel to select rotational axis origin and direction vector for rotating reference frame,Note: all direction vectors should be unit vectors but Fluent will normalize them if they arent,Select,Moving Reference Frame,as the,Motion Type,for SRF,Enter rotational speed,Translation velocity set to zero,Velocity Inlets,Used for incompressible, mildly compressible flows when inlet velocity is known,Can specify absolute or relative velocity vector,Can specify vector components in Cartesian or cylindrical coordinates,For 2-D, axisymmetric with swirl and 3-D problems you can specify tangential velocity as,Pressure Inlets (1),Pressure inlets can be used with either incompressible or compressible flows.,Definition of total pressure depends on velocity formulation and compressibility:,incompressible, AVF,incompressible, RVF,compressible, AVF,Pressure Inlets (2),Specify appropriate total pressure and total temperature,If inlet flow is supersonic, specify static pressure such that desired Mach number corresponds to p,t,/p,Specify flow direction vector,Can use Cartesian, cylindrical, or local cylindrical coordinate system,Frame of flow direction depends on velocity formulation!,You cannot use a frame of reference for the direction which is different from the velocity formulation,Mass Flow Inlets,Prescribe total mass flow rate or mass flux and total temperature for compressible flows,Total pressure “floats” since the mass flow rate is fixed,Permits flow direction specification in,absolute frame,only,Fluent 6 permits direction specification in Cartesian and cylindrical coordinates,Pressure Outlets,Specify static pressure at the outlet,Can employ a radial equilibrium assumption which computes a radial pressure variation from,The specified pressure is then assumed to be the,hub static pressure,Backflow,Backflow occurs when the static pressure in a cell adjacent to a pressure boundary falls,below,the prescribed boundary pressure,For SRF problems, the direction of the backflow is,normal to the boundary in the absolute frame if AVF is used,normal to the boundary in the relative frame if RVF is used,Recommendation,As some backflow may occur during the solution process, prescribe reasonable values for all backflow quantities,Try to minimize (or eliminate) backflow by extending your outlet boundary further downstream,Wall BCs,Wall BCs enforce zero normal velocity at all wall surfaces,no slip (zero velocity) for viscous flows,For moving reference frames, you can specify the wall motion in either the absolute or relative frames,Recommended specification of wall BCs for all moving reference frame problems,For,stationary surfaces,(in the lab,frame) use,zero Rotational speed, Absolute,For,moving surfaces, use,zero Rotational speed, Relative to Adjacent Cell Zone,Periodic BCs,Rotational periodic BCs rely on the rotational axis specification to transfer information correctly,Rotationally periodic boundaries can be used in SRF problems to reduce mesh size provided both the geometry and flow are periodic,Notes:,If 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 periodics,Once the periodic BCs have been set, perform a,grid check,to see if the reported periodic angles are correct,Turbulence Models for Rotating Machinery,DPM Modeling,You can use DPM and pathline models for SRF problems,Particle paths are computed in the,relative frame,If you want to see particle paths in the absolute frame, you can access the following switch in the TUI:,define/models/dpm/tracking/,track-in-absolute-frame,Note that particles moving in absolute frame may hit wall surfaces, since the rotation of the frame is not accounted for,particle injection at blade tips,Other Models,Multiphase Models,VOF, ASMM, Eulerian (Fluent 6) multiphase models are all compatible with SRF modeling in Fluent,Examples: mixing tanks, multiphase pumps flows,Real Gas Model,Can model specific fluids using non-ideal gas equation of state,Employs the REFPROP library from NIST,For use with the coupled-solvers only!,Available fluids include: carbon dioxide, ammonia, butane, ethane, propane, propylene, wide range of refrigerants (e.g. R11, R12, R134a, etc.),Heat Transfer,Conduction and radiation models can be enabled with SRF models,Note: For conducting solids which are contained in a moving reference frame, you dont need to activate the Moving Reference Frame option!,Solver Settings (1),Segregated solver,Pressure-Velocity Coupling Method,SIMPLE,is sufficient for most problems,Use,PISO,for unsteady problems (e.g.sliding mesh),Pressure Interpolation,Standard,scheme is acceptable for low speed flows, but for highly swirling flows.,use,PRESTO!,if you have a quad or hex mesh,use,Body Force Weighted,scheme for mixed meshes,Other equations - use second order discretizations,Can start with first order for stability, especially for problems with high rotational speeds,Solver Settings (2),Coupled solvers,Use first order discretizations to begin your calculation - then switch to second order when the solution is close to convergence,Use default Courant numbers as a start (1 for explicit solver, 5 for implicit solver),For coupled-explicit solver,Use 4 levels of FAS multigrid for most problems,helps propagate solution more rapidly through the domain,Use more levels of you have a very large mesh,Example SRF Calculations,Two examples will now be presented to illustrate typical SRF modeling procedures:,2-D swirling flow through a disk cavity,3-D flow through a propeller fan,Disk Cavity,Disk cavity air flow study based on the experiments of Pincombe, 1981,Disk geometry: radius (b) = 443 mm, width = 59 mm, bore = 44.3 mm,Solutions obtained for following conditions : Cw = Q/,n,b=1092, Re,f=w,b,2,/n=10,5,Three different numerical configurations were examined:,Case 1 - Stationary frame, moving walls,Case 2 - SRF, RVF,Case 3 - SRF, AVF,All cases used the same mesh (20576 quad cells) , 2D segregated solver (axisymmetric with swirl), incompressible flow, RKE turbulence model, second order discretizations,Disk Cavity - Mesh,both walls rotate,inlet,outlet,axis,inlet tube,Disk Cavity - Stream Function,Case 1,Case 2,Case 3,separated flow,Nearly identical flow patterns observed for all three cases.,Radial Velocity Profile (r/b = 0.633),Radial Velocity Profile (r/b = 0.833),Disk Cavity - Results,Force results,Conclusions,All three numerical approaches yield essentially the same results,Demonstrate the equivalence of stationary, AVF, RVF approaches,Propeller Fan,3-D model of a four blade propeller fan,Results compared with data from open literature:,Oh,K-J and Kang, S-H,“A numerical investigation of the dual performance characteristics of a small propeller fan using viscous flow calculations”,Computers and Fluids,28 (1999) pp. 815-823,Solutions obtained for a range of flowrates at 2000 rpm,Numerical model,Mesh size = 269265 cells (tets + wedges),Segregated Solver with moving reference frame,Incompressible flow (air),Realizable k-e model with non-equilibrium wall functions,Propeller Fan - Mesh,Comparison to Data: Head Coefficient,Comparison to Data: Power Coefficient,Fan Flowfield: Flow Coefficient = 0.1,Significant flow reversal,upstream of fan face,Static pressure contours,displayed on fan surfaces,Fan Flowfield: Flow Coefficient = 0.35,Strong radial outflow,Fan Flowfield: Flow Coefficient = 0.5,Strong axial outflow,SRF Appendix,Additional Examples,2-D axisymmetric flow in a labyrinth seal,3-D flow in a transonic axial compressor blade row,Labyrinth Seal,2D axisymmetric model of five tooth labyrinth seal,Results compared with experimental data of Milward and Edwards (ASME 94-GT-56),Numerical model,steady-state, incompressible flow,2D axisymmetric, with swirl and viscous dissipation,segregated solver,RNG KE turbulence model,mesh adaption used to resolve temperature gradients,solutions calculated over range of rotational speeds (2500 - 13000 rpm),Labyrinth Seal - Mesh,adapted cells,Labyrinth Seal - Total Temperature,Total Temperature (2),windage heating due,to viscous dissipation,Comparison with Data,Transonic Axial Compressor,Transonic compressor rotor (NASA Rotor 37),36 blades,Design conditions,17188 rpm, PR = 2.1, mass flow = 20.2 kg/s,Numerical model,steady-state, compressible flow,coupled implicit solver,mesh: 90,000 hex cells,standard KE turbulence model (inlet TU=3.5%),inlet profiles from test data,back pressure varied to obtain speed line,Rotor 37 - Mesh,Comparison with Data - Pressure Ratio,Choked mass flow,predicted: 20.80 kg/s,data: 20.93 kg/s,Pressure Ratio - Choked Flow,Relative Mach No. - Choked Flow,Pressure Ratio - 94.3% Relative Massflow,Relative Mach No. - 94.3% Relative Massflow,Multiple Reference Frame(MRF) Modeling,Introduction,Many rotating machinery problems involve stationary components which cannot be described by surfaces of revolution (SRF not valid),Systems like these which involve both stationary and rotating components can be addressed with Fluent using three different approaches,Multiple reference frame model (MRF),Mixing plane model (MPM),Sliding mesh model (SMM),The MRF approach is the simplest and perhaps the most approximate of the three approaches,What is the MRF Model?,The domain is divided into stationary and rotating subdomains.,More than one rotating subdomain is permitted, and the sudomains can rotate at different speeds.,At the interfaces between the rotating and stationary domains, appropriate transformations of the velocity vector and velocity gradients are performed to compute fluxes of mass, momentum, energy, and other scalars,No account is taken for the (assumed) relative motion of one domain with respect to the other,For this reason MRF is often referred to as the “frozen rotor” approach,Implications of the MRF Model,Multiple fluid domains,Rotating subdomains move with prescribed rotational speeds,assume steady rotation,Walls which are contained,within the rotating subdomain interfaces,are assumed to be moving with the fluid and may assume any shape,The interface between a rotating subdomain and the adjacent stationary subdomain,must be a surface of revolution,with respect to the axis of rotation of the rotating subdomain,Can employ rotationally periodic boundaries, but the,periodic angles of all subdomains must be equal,Illustration of Interface Rules for MRF,Correct,Wrong!,Interface is not a surface,or revolution,stationary subdomain,rotating subdomain,Limitations of the MRF Model,MRF models ignore the relative motions of the subdomains with each other, and thus do not account for fluid dynamic interaction between stationary and rotating components,Ideally, the flow at the MRF interfaces should be relatively uniform or “mixed out”,MRF can produce misleading results in cases where the flow passes across the rotating domain (flow enters and leaves the outer boundary of the rotating domain),Example: crossflow fans,For these cases, you should use the sliding mesh model,Setting
展开阅读全文