cfx fsi 6dof

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


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


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


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


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)


Creating a Rigid Body in CFX-Pre

Insert a Rigid Body into the Flow Analysis


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


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


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


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


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


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


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



Hull wall boundary mesh motion defined by the Rigid Body Solution



Subdomain mesh motion also defined by the Rigid Body Solution Hull and subdomain rotate and translate together as a rigid body



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


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



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


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


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).



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



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


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


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


Rigid Body Solution


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

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