Chapter 12Moving Zones Introduction to CFX Topics Domain Motion Mesh Defomation Appendix Rotating Fluid Domains
Single Frame of Reference Multiple Frames of Reference Frame Change Models Pitch Change Mesh Defomation Appendix Moving Solid Domains Translation Rotation Overview of Moving Zones
Many engineering problems involve flows through domains which contain moving components Rotational motion: Flow though propellers, axial turbine blades, radial pump impellers, etc. Translational motion: Train moving in a tunnel, longitudinal sloshing of fluid in a tank, etc. General rigid-body motion Boat hulls, etc. Boundary deformations Flap valves, flexible pipes, blood vessels, etc. Overview of Moving Zones
There are several modeling approaches for moving domains: For rotational motion the equations of fluid flow can be solved in a rotating reference frame Additional acceleration terms are added to the momentum equations Solutions become steady with respect to the rotating reference frame Can couple with stationary domains through interfaces Some limitations apply, as discussed below Translational motion can be solved by moving the mesh as a whole Interfaces can be used to allow domains to slide past each other More general rigid-body motion can be solved using a 6-DOF solver combined with mesh motion, or the immersed solid approach If the domain boundaries deform, we can solve the equations using mesh motion techniques Domain position and shape are functions of time Mesh deformed using smoothing, dynamic mesh loading or remeshing Rotating Reference Frames vs. Mesh Motion
y x Domain Moving Reference Frame flow solved in a rotating coordinate system This slide illustrates the two approaches.Notice that in the moving reference frame approach, the axes are attached to the moving domain and are rotate with it.Therefore the axes always remain in the same position with respect to the moving domain.Again, because the frame is accelerating, additional terms are added to the equations of motion of the fluid. In contrast, the moving/deforming domain approach permits a time-dependent deformation of the computational domain, which requires tracking the mesh with respect to a fixed frame of reference. Mesh Deformation Domain changes shape as a function of time Rotating Reference Frames
Why use a rotating reference frame? Flow field which is unsteady when 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 Can employ rotationally-periodic boundaries for efficiency (reduced domain size) Single Frame of Reference (SFR)
Single Frame of Reference assumes all domains rotate with a constant speed with respect to a single specified axis Wall boundaries must conform to the following requirements: Walls which are stationary in the local reference frame (i.e. rotating walls when viewed from a stationary reference frame) may assume any shape Walls which are counter-rotating in the local reference frame (i.e. stationary walls when viewed from a stationary reference frame) must be surfaces of revolution Correct baffle The wall with baffles is not a surface of revolution!This case requires a rotating domain placed around the rotor while the stationary wall and baffles remain in a stationary domain Wrong! rotor stationary wall Single Versus Multiple Frames of Reference
When domains rotate at different rates or when stationary walls do not form surfaces of revolution Multiple Frames of Reference (MFR) are needed (not available with the CFD-Flow product) Domain interface with change in reference frame Stationary Domain This slide illustrates the difference between a single blade passage case on the left, which can be solved using the SRF approach by assuming rotational periodic boundary conditions, versus a multiple domain model on the right, which consists of a blower wheel and casing.Note the interface which separates the two zones. The interface can be treated in a number of ways, each with its own inherent assumptions and limitations. Rotating domain Single Component (blower wheel blade passage) Multiple Component (blower wheel + casing) Multiple Frames of Reference (MFR)
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 multiple domains some domains will be rotating, others stationary The domains communicate across one or more interfaces and a change in reference frame occurs at the interface The way in whichthe interface is treated leads to one of the following approaches, known as Frame Change Models: Frozen Rotor Steady-state solution Rotational interaction between reference frames is not accounted for i.e. the stationary domain sees the rotating components at a fixed position Stage Steady-state solution Interaction between reference frames are approximated through circumferential averaging at domain interfaces Transient Rotor Stator (TRS) Transient solution Accurately models the relative motion between moving and stationary domains at the expense of more CPU time Frozen Rotor Frame Change Model
Frozen Rotor: Components have a fixed relative position, but the appropriate frame transformation and pitch change is made Steady-state solution Pitch change is accounted for rotation Frozen Rotor Frame Change Model
Frozen Rotor Usage: The quasi-steady approximation involved becomes small when the through flow speed is large relative to the machine speed at the interface This model requires the least amount of computational effort of the three frame change models Transient effects at the frame change interface are not modeled Pitch ratio should be close to one to minimize scaling of profiles A discussion on pitch change will follow Profile scaled down Pitch ratio is ~2 Stage Frame Change Model
Stage: Performs a circumferential averaging of the fluxes through bands on the interface Accounts for time-averaged interactions, but not transient interactions Steady-state solution upstream downstream Stage Frame Change Model
Stage Usage: allows steady state predictions to be obtained for multi-stage machines incurs a one-time mixing loss equivalent to assuming that the physical mixing supplied by the relative motion between components is sufficiently large to cause any upstream velocity profile to mix out prior to entering the downstream machine component The Stage model requires more computational effort than the Frozen Rotor model to solve, but not as much as the Transient Rotor-Stator model You should obtain an approximate solution using a Frozen Rotor interface and then restart with a Stage interface to obtain the best results Transient Rotor Stator Frame Change Model
predicts the true transient interaction of the flow between a stator and rotor passage the transient relative motion between the components on each side of the interface is simulated The principle disadvantage of this method is that the computer resources required may be large Pitch Change When the full 360o of rotating and stationary components are modeled the two sides of the interface completely overlap However, often rotational periodicity is used to reduce the problem size Example: A rotating component has 113 blades and is connected to a downstream stator containing 60 vanes Using rotationally periodicity, a single rotor and stator blade could be modeled This would lead to pitch change at the interface of (360/113): (360/60) = 0.53:1 Alternatively two rotor blades could be modeled with a single stator vane, as shown to the right, giving a pitch ratio of 2*(360/113):(360/60) = 1.06:1 Pitch Change When using the Frozen Rotor model the pitch change should be close to 1 for best accuracy Pitch change is accounted for by taking the side 1 profile and stretching or compressing it to fit onto side 2 Some stretching / compressing is acceptable, although not ideal For the Stage model the pitch ratio does not need to be close to 1 since the profile is averaged in the circumferential direction Very large pitch changes, e.g. 10, can cause problems For the Transient Rotor Stator model the pitch change should be exactly 1, which may mean rotational periodicity cannot be used If the pitch change is not 1, the profile is stretched as with Frozen Rotor, but this is not an accurate approach Pitch Change The Pitch Change can be specified in several ways
None Automatic (ratio of the two areas) Value (explicitly provide pitch ratio) Specified Pitch Angles (specify Pitch angle on both sides) Select this method when possible When a pitch change occurs the two sides do not need to line up physically, they just need to sweep out the same surface of revolution Flow passes through the overlapping portion as expected.Flow entering the interface at point 1 is transformed and appears on the other side at point 2. Pitch Change An intersection algorithm is used to find the overlapping parts of each mesh face at the interface The intersection can be performed in physical space, in the radial direction or in the axial direction Physical Space:used when Pitch Change = None No correction is made for rotational offset or pitch change Radial Direction:used when the radial variation is > axial variation E.g. the surface of constant z below Axial Direction:used when the axial variation is > radial variation E.g. the surface of constant r Interfaces that contain surfaces of both constant r and z should be split, otherwise the intersection will fail Split interfaces when they have both regions of constantz and regions of constantr Setup Guidelines When Setting Boundary Conditions, consider whether the input quantities are relative to the Stationary frame, or the Rotating frame Walls which are tangential to the direction of rotation in a rotating frame of reference can be set to be stationary in the absolute frame of reference by assigning a Wall Velocity which is counter-rotating Use the Alternate Rotation Model if the bulk of the flow is axial (in the stationary frame) and would therefore have a high relative velocity when considered in the rotating frame E.g. the flow approaching a fan will be generally axial, with little swirl Used to avoid false swirl Navier-Stokes Equations: Rotating Reference Frames
Equations can be solved in absolute or rotating (relative) reference frame Relative Velocity Formulation Obtained by transforming the stationary frame N-S equations to a rotating reference frame Uses the relative velocity as the dependent variable Default solution method when Domain Motion is Rotating Absolute Velocity Formulation Derived from the relativevelocity formulation Uses the absolute velocityas the dependent variable Can be used by enablingAlternate Rotation Modelin CFX-Pre setup Rotational source terms appearin momentum equations x y z stationary frame rotating axis of rotation CFD domain Let us now briefly examine the forms of the Navier-Stokes equations appropriate for moving reference frames.Basically, the transformation from the stationary frame to the moving frame can be done mathematically in two different ways. In the first form, the momentum equations are expressed in terms of the velocity relative to the moving frame.This form is known as the Relative Velocity Formulation.The second form utilizes the velocities referred to the absolute frame of reference in the momentum equations, and is known as the Absolute Velocity Formulation.In both cases, additional acceleration terms result from the transformations. 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 It is important to understand the relationship between the velocity viewed from the stationary and relative frames. This relationship is often called the velocity triangle, and can be expressed by the simple vector equation: Here, V is the velocity in the stationary or absolute frame ,W is the velocity viewed from the moving frame, and U is the frame velocity.For a rotating reference frame, U is simply Notice from the picture of the moving turbine blade that a flow approaching the blade in the x direction appears to be moving with a positive angle due to the downward motion of the blade. Comparison of Formulations
Relative Velocity Formulation: x-momentum equation Absolute Velocity Formulation: x-momentum equation Coriolis acceleration Centripetal acceleration Coriolis + Centripetal accelerations Lets now compare the two formulations.To do this we will simply consider the x momentum equation. For the relative velocity formulation, we observe that the x component of the relative velocity is being solver for, and that the convecting velocity is the relative velocity. It should be noted here that in a moving frame, scalars are convected along relative streamlines and we will employ a similar kind of convection term for such scalar equations as turbulence kinetic energy and dissipation rate, and species transport.Also note the presence of additional acceleration terms, which have been placed on the right hand side.The first acceleration is called the Coriolis acceleration (2w x W), and has the property of acting perpendicular to the direction of motion of the fluid and to the axis of rotation.The second term is called the Centripetal acceleration, which acts in the radial direction.Both of these accelerations act as momentum source terms in the momentum equations, and can lead to difficulties if the rotational speed is very large. For the absolute velocity formulation, we now solve for the x component of the absolute velocity.Note that the relative velocity is still the convecting velocity, and that the accerlation terms can be collapsed into a single term (w x V), due to the fact that the Corilolis acceleration becomes (w x W). It should be stressed that these equations are equivalent representations of the flow in the moving frame, and that either form can be used for CFD.However, since the numerical errors are different for each form, on a finite grid there may be an advantage in using one form over another.We will return to this point shortly. Mesh Deformation Mesh Deformation can be applied in simulations where boundaries or objects are moved The solver calculates nodal displacements of these regions and adjusts the surrounding mesh to accommodate them Examples of deforming meshes include Automotive piston moving inside a cylinder A flap moving on an airplane wing A valve opening and closing An artery expanding and contracting Mesh Deformation Internal node positions can be automatically calculated based on user specified boundary / object motion Automatic Smoothing Boundary / object motion can be moved based on: Specified Displacement Expressions and User Functions can be used Sequential loading of pre-defined meshes Requires User Subroutines Coupled motion For example, two-way Fluid Structure Interaction using coupling of CFX with ANSYS Mesh Deformation Setup guidelines when using Expressions / Functions to describe Mesh Motion Under Basic Settings for the Domain, set Mesh Deformation to Regions of Motion Specified Create expressions to describe either nodal displacements or physical nodal locations Apply Mesh Motion equations at boundaries that are moving Mesh Deformation See the following tutorials for information on other mesh motion types: Fluid Structure Interaction and Mesh Deformation Oscillating Plate with Two-Way Fluid-Structure Interaction Dynamic remeshing is also available Advanced topic Used for significant mesh deformation, where addition/subtraction of elements is required to maintain element quality, e.g. Internal Combustion Engine Uses Multi-configuration setup Dynamic remeshing occurs in ICEM CFD using a range of meshing algorithms Chapter 12 AppendixMoving Solid Zones
Introduction to CFX Motion in Solid Domains
In most simulations it is not necessary to specify any motion in solid domains Consider a rotating blade simulation in which the blade is included as a solid domain, and heat transfer is solved through the blade Even though the fluid domain is solved in a rotating frame of reference, the mesh is never actually rotated in the solver, therefore it will always line up with the solid The solid domain does not need to be placed in a rotating frame of reference since the heat transfer solution has no Coriolis or Centripetal terms Solid domain motion should be used when the advection of energy needs to be considered For example, a hot jet impinging on a rotating disk.To prevent a hot spot from forming the advection of energy in the solid needs to be included Motion in Solid Domains
Solid Domain Motion can be classified into two areas: Translational Motion For example, a process where a solid moves continuously in a linear direction while cooling Rotational Motion For example, a brake rotor which is heated by brake pads q q=0 Tin = Tspec Motion in Solid Domains
In Solid Domains, the conservation of the energy equation can account for heat transport due to motion of the solid, conduction andvolumetric heat sources Note that the solid is never physically moved when using this approach, there is only an additional advection term added to the energy equation Solid Velocity Translating Solid Domains
Enable Solid Motion Specify Solid Motion in terms of Cartesian Velocity Components The solid should extend completely through the domain for this approach to be valid Rotating Solid Domains
Rotating Solid Domains can be set up in one of two ways: Solid Motion Method Set the Domain Motion to Stationary On the Solid Models tab, set Solid Motion to Rotating The solid mesh does not physically rotate, but the model accounts for the rotational motion of the solid energy The solid should be defined by a surface of revolution for this approach to be valid.For example a solid brake disk is OK, a vented brake disk is not. Rotating Solid Domains
Rotating Domain Method Set the Domain Motion to Rotating Do not set any Solid Motion Without using Transient Rotor Stator interfaces, this method puts the mesh coordinates in the relative frame, but does not account for rotational motion of the solid energy Useful only for visualization of rotating components which are solved in the stationary frame of reference To account for rotational motion of solid energy or a heat source which rotates with the solid, a Transient simulation is required and a Transient Rotor Stator interface must be used Note: Solid Motion as applied on the Solid Models tab is calculated relative to the Domain Motion, so is not normally used if Domain Motion is Rotating This is the most general approach and could be used to model a vented brake disk.