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2011 ANSYS, Inc. July 26, 20131 Release 14.5
14. 5 Release
Solving FSI Applications Using ANSYS Mechanical and ANSYS CFX
Lecture 86-DOF Rigid Body Solver in CFX
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Rigid Body FSI
CFX includes a 6-DOF rigid body solver
Fluid forces/torques on a body auto-calculated
Body response included in flow solution Either via mesh motion or via immersed solid
Simplified FSI case where body does not change shape under fluid load Can make assumptions about its behaviour Does not need the expense of a full structural simulation If stresses are of interest then 6DOF is not suitable; perform a 2-
way FSI instead
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Rigid Body Dynamics
Forces and torques acting on a rigid body can be summed and assumed to act on/about the centre of mass
Chasles Theorem: The general displacement of a rigid body is a linear motion of a origin point plus a rotation around the origin point
Can separate translation and rotation
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Rigid Translation
Translational equation of motion, applied to Centre of Mass
Discretized using implicit Newmark integration scheme Default integration parameters give 2nd order accuracy Advantage over previous explicit CEL implementation
Can add influence of external spring or external force to F
FxP
Gmdt
d
Gx = Acceleration about centre of mass
ExtSpringAero )]([ FxxFF sokmg
= Linear MomentumxP m
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Rigid Rotation
Rotational equation of motion about Centre of Mass
Two methods of discretization available Simo-Wong [1] (Default. Second order, iteratively conservative) First Order Backward Euler
Can add influence of external torsion spring or external torque to MExt
MI
dt
d
dt
d B )(
BBBB
dt
d
II
I
)()(1 BBBB IMI
= Angular Momentum
ExtsoSpringAero )]([ MMM kB
= Moment of Inertia tensorI
[1] Simo, J.C., Wong, K.K., Unconditionally Stable Algorithms for Rigid Body Dynamics that exactly Preserves Energy and Momentum, Int. J. Num. Methods in Eng., vol. 31, 19-52 (1991)
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Creating a Rigid Body in CFX-Pre
Insert a Rigid Body into the Flow Analysis
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Rigid Body Basic Settings
Mass
Rigid body mass
Location
The 2D boundary region of the rigid body
Coord Frame
Must create a Coord Frame at the centre of mass (based on the initial rigid body position) and select here
Cannot constrain a body to rotate about an arbitrary point, unless translations of turned off
Mass Moment of Inertia
Enter components for the Mass Moment of Inertia tensor see next slides
As calculated with respect to the rigid body coordinate frame
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Mass Moment of Inertia Tensor
This tensor describes an objects resistanceto changes in its rotation rate
Its a symmetric tensor, so Ixy = Iyx Hence only 6 components are entered on the Basic Settings panel
Ixx describes the moment of inertia around the x-axis when the objects are rotated around the x-axis Non-zero when you have rotation about the x-axis
Ixy describes the moment of inertia around the y-axis when the objects are rotated around the x-axis, etc Non-zero when you have rotation about the x and y axis
zzzyzx
yzyyyx
xzxyxx
III
III
III
I
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Mass Moment of Inertia Tensor
For rotation about only they-axis, the tensor simplifies to:
For rotation about the x and yaxes we have:
See http://en.wikipedia.org/wiki/Moment_of_inertia for detailed background on mass moment of inertia
000
00
000
yyII
000
0
0
yyyx
xyxx
II
II
I
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Rigid Body Dynamics
External Forces / Torques Use Spring or Value option
- Spring: Set Origin coords and Spring Constant
- Value: Enter Cartesian components (can use CEL expressions)
Degrees of Freedom Select Translational / Rotational DOF Default is None need to set at least one
Enter Gravity Vector Acts at the centre of mass as set by Coord
Frame
Should be consistent with Domain gravity (if specified in the Domain)
Everything specified in Rigid Body Coord Frame
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Rigid Body Initialization
All state variables defining rigid body can be initialized in terms of the rigid body coordinate frame
Default behavior is to use Automatic Assumes quiescent conditions unless a
previous solution is provided to restart from
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Rigid Body Mesh Motion
After creating the rigid body, set mesh motion parameters on boundaries, subdomains and/or interfaces
Option = Rigid Body Solution
Rigid Body =
Motion Constraints Can ignore Translations or Rotations
The boundary that corresponds to the rigid body should clearly move with the rigid body, without ignoring any motion
To maintain mesh quality, you may want other boundaries/interfaces to move using only the translations/rotations from the RB solution
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Rigid Body Mesh Motion Example
Ship hull example
2-DOF Rotation about y-axis Translation along the z-axis
A subdomain moves with the rigid body so that near-wall mesh quality can be maintained
See EX1 in the examples folder
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Rigid Body Mesh Motion Example
Hull wall boundary mesh motion defined by the Rigid Body Solution
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Rigid Body Mesh Motion Example
Subdomain mesh motion also defined by the Rigid Body Solution Hull and subdomain rotate and translate together as a rigid body
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Rigid Body Mesh Motion Example
A Domain Interface is used between the subdomain and the rest of the domain
The subdomain side of the interface uses the same mesh motion setting as the subdomain and hull
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Rigid Body Mesh Motion ExampleThe other side of the interface uses the Rigid Body Solution to set the mesh motion, but Ignore Rotations is selected
The mesh slides at the domain interface so rotational motion is not transmitted to the outer domain
Translational motion is passed and absorbed by the outer domain
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Rigid Body Mesh Motion Example
This example demonstrates the preferred topology when rotation about a single axis is included
For rotation about multiple axes surround the rigid body with a sphere when significant rotation occurs
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CEL Access of Rigid Body VariablesUse the rbstate() CEL function to access rigid body variables E.g. rbstate(Linear Velocity X)@RigidBodyObject
The returned values are with respect to the Global Coord Frame
Variables that can be accessed are: Position X/Y/Z, Linear Velocity X/Y/Z, Linear Acceleration X/Y/Z, Euler
Angle X/Y/Z, Angular Velocity X/Y/Z,Angular Acceleration X/Y/Z
If a component (X/Y/Z) is not provided the magnitude is returned, except for Euler Angle which requires a component
A beta feature allows values to be returned in the rigid body coordinate frame E.g. rbstate(linacc x_Coord Name)@RigidBodyObject
where linacc x is the short form variable name. See the VARIABLES file in .../ANSYS Inc/v130/CFX/etc to find the short form names
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Rigid Body Solver Control
Solver Control > Rigid Body Control
Update Frequency Every Time Step
Explicit coupling between the rigid body solution and the flow field. Lowest computational cost, but weakest coupling. Suitable for loosely coupled cases; will be unstable for more tightly coupled cases
Every Coefficient Loop / Iteration
Tighter coupling that is iteratively-implicit. Higher computational cost, but more stable for large timestep use and cases with high virtual-mass (body-mass ratio). May still fail the forces from the flow field dont get a chance to stabilize after receiving the new rigid body position. Can use under-relaxation (see later).
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Rigid Body Solver Control
Update Frequency (cont.) General Coupling Control
The most robust approach; same approach as stagger/coupling iterations in 2-way FSI. Set the number of Rigid Body updates to perform per timestep. After each RB update within a timestep, the flow solver will perform the number of coefficient loops set under Basic Settings.
Under Internal Coupling Data Transfer Control can set Under Relaxation Factors and Convergence Control Available for Update Frequency other
than Every Timestep
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Rigid Body Solver Control
Can adjust under relaxation for forces & torques sent to the RB solver and for mesh motion received from the RB solver
External Force set via a Linear Spring is not under-relaxed
Under relaxation is usually the first choice to improve robustness and is easy to use
Default under relaxation is 0.75
The default Simo Wong Integration Method for Angular Momentum is recommended
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Rigid Body Monitor Plots
Default monitor plots are created Rigid Body Convergence, Euler Angles
& Position
Select under Monitors > Rigid Body Motion convergence is based on the
distance moved compared to the last time the RB solver was called
Force/Torque convergence is based on the change in force/torque divided by the force/torque magnitude
See CFX-Pre Solver Control doc for further details
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Rigid Body Monitor Plots
Can also access additional plots; create a new monitor or right-click to access Monitor Properties Angular/Linear Acceleration and
Angular/Linear Velocity are available in addition to the default Position, Euler Angle and Force/Motion Convergenceplots
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Rigid Body Solution
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Limitations
Cant be combined with MFX 2-way FSI
No contact/collision modelling with walls or other rigid bodies Practically, this only matters for the Immersed Solid approach since the
mesh would fold prior to a collision
An immersed solid driven by 6-DOF has no problems moving through a wall and outside the flow domain
Cant be used in rotating domains
General constraints cant be applied Cant make a translatable rigid body rotate about a point, other than its
center of mass