Moving Zones

Introduction • Many engineering problems involve flows through domains which contain translating or rotating components. • Examples – Translational motion: • Train moving in a tunnel, longitudinal sloshing of fluid in a tank, etc. • Examples – Rotational motion: • Flow though propellers, axial turbine blades, radial pump impellers, etc. • There are two basic modeling approaches for moving domains: • If the domain does not change shape as it moves (rigid motion), we can solve the equations of fluid flow in a moving reference frame. • Additional acceleration terms added to the momentum equations • Solutions become steady with respect to the moving reference frame • Can couple with stationary domains through interfaces • If the domain changes shape (deforms) as it moves, we can solve the equations using dynamic mesh (DM) techniques. • Domain position and shape are functions of time. • Solutions are inherently unsteady.

x Domain Moving Reference Frame vs. Dynamic Mesh y Moving Reference Frame – Domain moves with rotating coordinate system Dynamic Mesh – Domain changes shape as a function of time

Overview of Modeling Approaches • Single Reference Frame (SRF) • Entire computational domain is referred to a moving reference frame • Multiple Reference Frame (MRF) • Selected regions of the domain are referred to moving reference frames • Interaction effects are ignored  steady-state • Mixing Plane (MPM) • Influence of neighboring regions accounted for through use of a mixing plane model at rotating/stationary domain interfaces • Circumferential non-uniformities in the flow are ignored steady-state • Sliding Mesh (SMM) • Motion of specific regions accounted for by a mesh motion algorithm • Flow variables interpolated across a sliding interface • Unsteady problem - can capture all interaction effects with complete fidelity, but more computationally expensive than SRF, MRF, or MPM • Dynamic Mesh (DM) • Like sliding mesh, except that domains are allowed to move and deform with time • Mesh deformation accounted for using spring analogy, remeshing, and mesh extrusion techniques

Introduction to SRF Modeling • SRF assumes asingle fluid domain which rotates with a constant speed with respect to a specified axis. • Why use a rotating reference frame? • Flow field which is unsteadywhen viewed in a stationary frame can become steady when viewed in a rotating frame • Steady-state problems are easier to solve... • simpler BCs • low computational cost • easier to post-process and analyze • NOTE: You may still have unsteadiness in the rotating frame due to turbulence, circumferentially non-uniform variations in flow, separation, etc. • example: vortex shedding from fan blade trailing edge • Wall boundaries must conform to the following requirements: • Walls which move with the fluid domain may assume any shape • Walls which are stationary (with respect to the fixed frame) must be surfaces of revolution • Can employ rotationally-periodic boundaries for efficiency (reduced domain size)

Stationary Walls in SRF Models baffle stationary wall rotor Wrong! Correct Wall with baffles not a surface of revolution!

y y CFD domain x rotating frame z stationary frame x z axis of rotation N-S Equations: Rotating Reference Frames • Equations can be solved in absolute or rotating (relative) reference frame. • Relative Velocity Formulation (RVF) • Obtained by transforming the stationary frame N-S equations to a rotating reference frame • Uses the relative velocity and relative total internal energy as the dependent variables • Absolute Velocity Formulation (AVF) • Derived from the relative velocity formulation • Uses the absolute velocity and absolute total internal energy as the dependent variables • Rotational source terms appear in momentum equations. • Refer to Appendix for a detailed listing of equations

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

Comparison of Formulations • Relative Velocity Formulation: x-momentum equation Coriolis acceleration Centripetal acceleration • Absolute Velocity Formulation: x-momentum equation Coriolis + Centripetal accelerations

Solver Choice recommendations: Pressure Based – Incompressible, low-speed (subsonic) compressible flows Density Based – High-speed (transonic, supersonic) compressible flows Velocity Formulation recommendations: Use absolute velocity formulation (AVF) when inflow comes from a stationary domain Use relative velocity formulation (RVF) with closed domains (all surfaces are moving) or if inflow comes from a rotating domain NOTE: RVF is only available in the segregated solver Gradient Option Use Node-Based gradients for tet/hybrid meshes Use Least Squares gradients for polyhedral cells SRF Set-up: Solver

SRF Set-up: Fluid BCs • Use fluid BC panel to define rotational axis origin and direction vector for rotating reference frame • Direction vectors should be unit vectors but Fluent will normalize them if they aren’t • Select Moving ReferenceFrame as the Motion Typefor SRF • Enter Rotational Velocity • Rotation direction defined by right-hand rule • Negative speed implies rotation in opposite direction

SRF Set-up: Inlet/Outlet Boundaries • Velocity Inlets: • Absolute or relative velocities may be defined regardless of formulation. • Pressure Inlet: • Definition of total pressure depends on velocity formulation: • Pressure Outlet: • For axial flow problems with swirl at outlet, radial equilibrium assumption option can be applied such that: • Specified pressure is hub pressure • Other BCs for SRF problems • Non-reflecting BCs • Target mass flow outlet incompressible, AVF incompressible, RVF

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… Activate “Moving Wall” option Set Rotation-Axis Origin and Direction same as fluid zone For stationary surfaces(in the absolute frame) use zero Rotational speed, Absolute For moving surfaces, use zero Rotational speed, Relative to Adjacent Cell Zone Wall BCs

Solution Strategies for SRF Problems • SRF problems may be more difficult to solve because of large flow gradients resulting from the rotation of the fluid domain. • May require a finer mesh to resolve steep gradients due to rotational effects. • Some things to consider for troublesome cases: • Make sure the mesh quality is good (max cell skewness < 0.9 – 0.95). • Start problems using first order discretizations. • Reduce underrelaxation factors / Courant numbers to enhance stability. • Use FMG initialization for hard-to-start problems. • Especially desirable for compressors, pumps, and similar applications . • Consider running the problem as a transient calculation. • Can provide more robust convergence versus the standard steady-state approach. • Use first order discretization in time and about 2-3 time steps per iteration. • Run until steady-state is achieved.

Multiple Zone Modeling • Many rotating machinery problems involve stationary components which cannot be described by surfaces of revolution (SRF not valid). • Systems like these can be solved by dividing the domain into multiplefluid zones – some zones will be rotating, others stationary. • The multiple zones communicate across one or more interfaces. • The way in which the interface is treated leads to one of following approaches for mutiple zones models: • Multiple reference frame model (MRF)  Steady-state solution • Simplified interface treatment - rotational interaction between reference frames is not accounted for. • Mixing plane model (MPM)  Steady-state solution • Interaction between reference frames are approximated through circumferential averaging at fluid zone interfaces (mixing planes). • Sliding mesh model (SMM)  Unsteady solution • Accurately models the relative motion between moving and stationary zones at the expense of more CPU time (inherently unsteady).

Single Versus Multiple Component Modeling interface Single Component (blower wheel blade passage) Multiple Component (blower wheel + casing)

Introduction to the MRF Model • The computational domain is divided into stationary and rotating fluid zones. • Interfaces separate zones from each other. • Interfaces can be Conformal or Non-Conformal. • Flow equations are solved in each fluid zone. • Flow is assumed to be steady in each zone (clearly an approximation). • SRF equations used in rotating zones. • At the interfaces between the rotating and stationary zones, appropriate transformations of the velocity vector and velocity gradients are performed to compute fluxes of mass, momentum, energy, and other scalars. • MRF ignores the relative motions of the zones with respect to each other. • Does not account for fluid dynamic interaction between stationary and rotating components. • For this reason MRF is often referred to as the “frozen rotor” approach. • Ideally, the flow at the MRF interfaces should be relatively uniform or “mixed out.”

Conformal interfaces An interior mesh surface separates cells from adjacent fluid zones. Face mesh must be identical on either side of the interface. Non-conformal interfaces Cells zones are physically disconnected from each other. Interface consists of two overlapping surfaces (type = interface) Fluent NCI algorithm passes fluxes from on surface to the other in a conservative fashion (i.e. mass, momentum, energy fluxes are conserved). User creates interfaces using DefineGrid Interfaces… Interfaces may be periodic Require identical translational or rotational offset. Interfaces in MRF Models Conformal interface Non-conformal interface

stationary zone rotating zone Interface Shapes • Walls which are contained within the rotating fluid zone interfaces are assumed to be moving with the fluid zones and may assume any shape. • Stationary walls are permitted if they are surfaces of revolution. • The interface between a the two zones must be a surface of revolution with respect to the axis of rotation of the rotating zone. • Periodic interfaces are permitted but the periodic angles (or offsets) must be identical for all zones. Consider a mixing impeller inside a rectangular vessel: - Problem can be described with two reference frames or zones. Interface is not a surface or revolution Wrong! Correct

Example of Rotationally Periodic Interface Each zone has same periodic angle (40 deg) periodic non-conformal interface Centrifugal compressor stage

MRF Set-Up • Generate mesh with appropriate stationary and rotating fluid zones • Can choose conformal or non-conformal interfaces between cell zones • For each rotating fluid zone (Fluid BC), select Moving Reference Frame as the Motion Typeand enter the rotational speed. • Identical to SRF except multiple zones • Stationary zones remain withStationary option enabled • Set up for other BCs and Solver settings same as SRF model.

Solution Strategies for MRF Problems • Like SRF problems, MRF problems may be difficult to solve because of large flow gradients resulting from the rotation of one or more fluid zones. • Interactions between adjacent cell zones may need to use lower under-relaxations than default. • Some things to consider for troublesome cases: • Make sure the mesh quality is good (max cell skewness < 0.9 – 0.95), particularly in the vicinity of grid interfaces. • Use FMG initialization. • Can employ unsteady time-marching as a means of achieving a stable steady-state solution. • NOTE: MRF is a steady-state method - transient solutions are not meaningful! • If MRF is producing unstable or unrealistic results, you may want to run the case using the unsteady, sliding mesh model.

Introduction to Mixing Plane Model (MPM) • The MPM was originally implemented to accommodate rotor/stator and impeller/vane flows in axial and centrifugal turbomachines. • Can also be applied to a more general class of problems. • Domain is comprised of multiple, single-passage, rotating and stationary fluid zones • Each zone is “self contained” with a inlet, outlet, wall, periodic BCs (i.e. each zone is an SRF model). • Steady-state SRF solutions are obtained in each domain, with the domains linked by passing boundary conditions from one zone to another. • The BC “links” between the domains are called the mixing planes. • BCs are passed as circumferentially averaged profiles of flow variables, which are updated at each iteration. • Profiles can be radial or axial. • As the solution converges, the mixing plane boundary conditions will adjust to the prevailing flow conditions.

MRF vs MPM • MRF can be used only if we have equal periodic angles for each row. • Flow properties are passed locally along the interface, which may lead to some unphysical behavior. • Odd blade numbers may require modeling the entire (360 deg.) geometry in order to have equal periodic angles for each blade row. • The MPM requires only asingle blade passage per bladerow regardless of the number of blades. • This is accomplished by mixing out (averaging) the circumferential non-uniformities in the flow at the mixing plane interface. MRF MPM

radial machines axial machines Mixing Plane Configurations • A mixing plane is an interface that consists of the outlet of an upstream domain and the inlet to the adjacent downstream domain. • The inlet/outlet boundaries must be assigned BC types in one of the following combinations: • Pressure-Outlet / Pressure-Inlet • Pressure-Outlet / Velocity-Inlet • Pressure-Outlet / Mass-Flow-Inlet • The MPM has been implemented for both axial and radial turbomachinery blade rows. • For axial machines, radial profiles are used. • For radial (centrifugal) machines, axial profiles are used.

Set fluid zones as Moving ReferenceFrames and define zone velocities. Assign appropriate BC types to inlet-outlet boundary pairs. Select upstream and downstream zones which will comprise mixing plane pair. Set the number of points for profile interpolation. Should be about the same axial/radial resolution as the mesh. Mixing Plane Geometry determinesmethod of circumferential averaging. Choose Radial for axial flow machines. Choose Axial for radial flow machines. Mixing plane controls Under-Relaxation - Profile changes are underrelaxed using factor between 0 and 1 MPM Setup

Solution Strategies for Mixing Plane Models • Because the mixing plane model involves modifying boundary conditions at the mixing plane interface, rapid changes in flow conditions at the mixing plane may cause convergence difficulties. • Try reducing the mixing plane under-relaxation factor to 0.1 - 0.5 to help stabilize the solution. • Some other things to consider for troublesome cases • Make sure the mesh quality is good (max cell skewness < 0.9 – 0.95). • Use FMG initialization for hard-to-start problems. • FMG initialization is compatible with the mixing plane model. • Reduce under-relaxation factors and/or Courant numbers. • Run you case with fixed BCs for some interations, then enable the mixing planes.

Shock interaction potential interaction stator rotor wake interaction Introduction to Sliding Mesh Model (SMM) • The relative motion of stationary and rotating components in a turbo-machine will give rise to unsteady interactions. These interactions are generally classified as follows: • Potential interactions(pressure wave interactions) • Wake interactions • Shock interactions • Both MRF and MPM neglect unsteady interaction entirely and thus are limited to flows where these effects are weak. • If unsteady interaction can not be neglected, we can employ the SlidingMesh Model to account for the relative motions of the stationary and rotating components.

moving mesh zone cells at time t cells at time t+Dt How the Sliding Mesh Model Works • Like the MRF model, the domain is divided into moving and stationary zones, separated by non-conformal interfaces. • Unlike the MRF model, each moving zone’s mesh will be updated as a function of time, thus making the mathematical problem inherently unsteady. • Another difference with MRF is that the governing equations have a new moving mesh form, and are solved in the stationary reference frame for absolute quantities (see Appendix for more details). • Moving reference frame formulation is NOT used here (i.e. no Coriolis, centripetal accelerations). • Equations are a special case of the general moving/deforming mesh formulation. • Assumes rigid mesh motion and sliding, non-conformal interfaces.

time t = 0 t + Dt Sliding Interfaces • Sliding interfaces must follow the same rules as MRF problems: • Any translation of the interface cannot be normal to itself. • The interface between a rotating zone and an adjacent stationary/rotating zone must be a surface of revolution with respect to the axis of rotation of the rotating subdomain. • Many failures of sliding mesh models can be traced to interface geometries which become disconnected as the mesh is moved! • Sliding interfaces can be partially-overlapping. • Can either be: • Periodic • Walls • If periodic, boundaryzones must also beperiodic and have identical offsets. Elliptic interface is not a surface of revolution.

Sliding Mesh Setup • Enable unsteady solver. • Define sliding zones as Interface BC types. • For moving zones, select Moving Mesh as Motion Type in Fluid BC panel. • For each interface zone pair, create a non-conformal interface • Enable Periodic option if sliding/rotating motion is periodic. • Enable Coupled for conjugate heat transfer. • Other BCs are same as SRF, MRF models.

Choose appropriate Time Step Size and Max Iterations Per Time step to ensure good convergence with each time step. Time Step Size should be no larger than the time it takes for a moving cell to advance past a stationary point: Advance the solution until the flow becomes time-periodic (pressures, velocities, etc., oscillate with a repeating time variation). Usually requires several revolutions of the grid. Good initial conditions can reduce the time needed to achieve time-periodicity. Solution Strategies for SMM Problems Ds = average cell size wR= characteristic velocity of the moving zone (R = mean radius of interface surface)

What is the Dynamic Mesh (DM) Model? • A method by which the solver (FLUENT) can be instructed to moveboundaries and/or objects, and to adjust the mesh accordingly. • Examples: • Automotive piston moving inside a cylinder • A flap moving on an airplane wing • A valve opening and closing • An artery expanding and contracting Volumetric fuel pump

Dynamic Mesh (DM) Model: Features • Internal node positions are automatically calculated based on user specified boundary/object motion, cell type, and meshing schemes • Spring analogy (smoothing) • Local remeshing • Layering • 2.5 D • User defined mesh motion • Boundaries/Objects motion can be moved based on: • In-cylinder motion (RPM, stroke length, crank angle, …) • Prescribed motion via profiles or UDF • Coupled motion based on hydrodynamic forces from the flow solution, via FLUENT’s 6 DOF model. • Different mesh motion schemes may be used for different zones. Connectivity between adjacent zones may be non-conformal.

The nodes move as if connected via springs, or as if they were part of a sponge. Connectivity remains unchanged; Limited to relatively small deformations when used as a stand-alone meshing scheme. Available for tri and tet meshes; May be used with quad, hex and wedge mesh element types, but that requires a special command. Spring Analogy (Spring Smoothing)

As user-specified skewness and size limits are exceeded, local nodes and cells are added or deleted. As cells are added or deleted, connectivity changes. Available only for tri and tet mesh elements. The animation also shows smoothing (which one typically uses together with remeshing). Local Remeshing

Cells are added or deleted as the zone grows and shrinks. As cells are added or deleted, connectivity changes. Available for quad, hex and wedge mesh elements. Layering

Initial mesh needs proper decomposition; Layering: Valve travel region; Lower cylinder region. Remeshing: Upper cylinder region. Non-conformal interface between zones. Combination of Approaches

Dynamic Mesh Setup • Enable unsteady solver. • Enable Dynamic Mesh model in DefineDynamic Mesh. • Activate desired Mesh Methods and set parameters as appropriate. • Define boundary motion in the Dynamic Mesh Zones GUI. • UDF may be required. • Other models, BCs, and solver settings are same as SRF, MRF models. • Mesh motion can be previewed using SolveMesh Motion utility. • Fluent will identify mesh quality problems if they occur during the preview.

Other Dynamic Mesh Options • 2.5 D Mesh Motion • Special remeshing approach for extruded geometries. • Permits tri mesh to be extruded as wedge elements through volume. • Advantage – can handle small gaps better than tet elements. • User-Defined Mesh Motion • Mesh motion controlled through a UDF. • No change in mesh topology can occur. • Advantage – can provide for general mesh motions not possible with spring analogy, remeshing, or layer approaches. • 6 DOF Model • Permits moving mesh surfaces to represent moving objects with defined mass, moments of inertia. • Motions of surfaces respond to pressures ans stresses computed by the CFD solution. • Gravitational and other forces can be added to force balance. • Additional information on these options are provided in the Appendix and the User’s Guide.

Outline • Introduction and Overview of Modeling Approaches • Single-Reference Frame (SRF) Model • Multiple Zones and Multiple-Reference Frame (MRF) Model • Mixing Plane Model (MPM) • Sliding Mesh Model (SMM) • Dynamic (Moving and Deforming) Mesh Model • Summary • Appendix

Summary • Five different approaches may be used to model flows over moving parts. • Single (Rotating) Reference Frame Model • Multiple Reference Frame Model • Mixing Plane Model • Sliding Mesh Model • Dynamic Mesh Model • First three methods are primarily steady-state approaches while sliding mesh and dynamic mesh are inherently unsteady. • Enabling these models, involves in part, changing the stationary fluid zones to either Moving Reference Frame or Moving Mesh. • Most physical models are compatible with moving reference frames or moving meshes (e.g. multiphase, combustion, heat transfer, etc.) • Follow best practice guidelines provided in the previous slides.

Appendix • Navier-Stokes equations for moving reference frames • Relative Velocity Formulation • Absolution Velocity Formulation • Navier-Stokes equations for moving mesh problems

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 • NOTE: RVF and AVF are equivalent forms of the N-S equations! • Identical solutions should be obtained from either formulation with equivalent boundary conditions

Moving Zones

Moving Zones

Presentation Transcript

Management Zones

Ocean Zones

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Zones of Peace, Zones of Chaos

Trading zones

DRAFT ZONES

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Innovation Zones

Zones -:

Riparian Zones

Shear zones

Time Zones

Time Zones

Time Zones

Thermal Zones

TIME ZONES

Climate Zones

Time Zones

Climate Zones

OCEAN ZONES

SECURITY ZONES