chapter 12 moving zones introduction to cfx
DESCRIPTION
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 RotationTRANSCRIPT
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.