Cfx Fsi 6dof

Lecture 8 6-DOF Rigid Body Solver in CFX 14. 5 Release

Solving FSI Applications Using ANSYS Mechanical and ANSYS CFX 1

© 2011 ANSYS, Inc.

July 26, 2013

Release 14.5

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 2way FSI instead

2

© 2011 ANSYS, Inc.

July 26, 2013

Release 14.5

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

3

© 2011 ANSYS, Inc.

July 26, 2013

Release 14.5

Rigid Translation Translational equation of motion, applied to Centre of Mass

dP  mxG  F dt

P  mx = Linear Momentum

xG = Acceleration about centre of mass

F  FAero  mg  [kSpring ( x  xso )]  FExt 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 ΣF 4

© 2011 ANSYS, Inc.

July 26, 2013

Release 14.5

Rigid Rotation Rotational equation of motion about Centre of Mass

dΠ d ( I B )   M dt dt

Π

= Angular Momentum

I

= Moment of Inertia tensor

d ( I B )  B  I B  I  B dt

 B  I 1 ( M B  B  I B )

M B  M Aero  [kSpring (  so )]  M Ext

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 ΣMExt [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) 5

© 2011 ANSYS, Inc.

July 26, 2013

Release 14.5

Creating a Rigid Body in CFX-Pre Insert a Rigid Body into the Flow Analysis

6

© 2011 ANSYS, Inc.

July 26, 2013

Release 14.5

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 • 7

Inertia tensor – see next slides As calculated with respect to the rigid body coordinate frame © 2011 ANSYS, Inc.

July 26, 2013

Release 14.5

Mass Moment of Inertia Tensor This tensor describes an objects resistance to changes in its rotation rate

 I xx  I   I yx  I zx 

I xy I yy I zy

It’s a symmetric tensor, so Ixy = Iyx • Hence only 6 components are entered on the Basic Settings panel

I xz   I yz  I zz 

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 8

© 2011 ANSYS, Inc.

July 26, 2013

Release 14.5

Mass Moment of Inertia Tensor For rotation about only the y-axis, the tensor simplifies to:

0 0 I  0 I yy 0 0

For rotation about the x and y axes we have:

 I xx I   I yx  0

•

9

© 2011 ANSYS, Inc.

I xy I yy 0

0 0 0 0 0 0

See http://en.wikipedia.org/wiki/Moment_of_inertia for detailed background on mass moment of inertia July 26, 2013

Release 14.5

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 10

© 2011 ANSYS, Inc.

July 26, 2013

Release 14.5

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

11

© 2011 ANSYS, Inc.

July 26, 2013

Release 14.5

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 12

© 2011 ANSYS, Inc.

July 26, 2013

Release 14.5

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

13

© 2011 ANSYS, Inc.

July 26, 2013

Release 14.5

Rigid Body Mesh Motion Example Hull wall boundary mesh motion defined by the Rigid Body Solution

14

© 2011 ANSYS, Inc.

July 26, 2013

Release 14.5

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

15

© 2011 ANSYS, Inc.

July 26, 2013

Release 14.5

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

16

© 2011 ANSYS, Inc.

July 26, 2013

Release 14.5

Rigid Body Mesh Motion Example The 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 17

© 2011 ANSYS, Inc.

July 26, 2013

Release 14.5

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

18

© 2011 ANSYS, Inc.

July 26, 2013

Release 14.5

CEL Access of Rigid Body Variables Use 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 19

© 2011 ANSYS, Inc.

July 26, 2013

Release 14.5

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 don’t get a chance to stabilize after receiving the new rigid body position. Can use under-relaxation (see later).

20

© 2011 ANSYS, Inc.

July 26, 2013

Release 14.5

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 21

© 2011 ANSYS, Inc.

July 26, 2013

Release 14.5

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 22

© 2011 ANSYS, Inc.

July 26, 2013

Release 14.5

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

23

© 2011 ANSYS, Inc.

July 26, 2013

Release 14.5

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 Convergence plots

24

© 2011 ANSYS, Inc.

July 26, 2013

Release 14.5

Rigid Body Solution

25

© 2011 ANSYS, Inc.

July 26, 2013

Release 14.5

Limitations Can’t 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

Can’t be used in rotating domains General constraints can’t be applied • Can’t make a translatable rigid body rotate about a point, other than its center of mass

26

© 2011 ANSYS, Inc.

July 26, 2013

Release 14.5