CFX-FSI_13.0_lect-06_6DOF

Customer Training Material

L t Lecture 6 6-DOF Rigid g Body y Solver

Solving FSI Applications Using ANSYS Mechanical and CFX ANSYS, Inc. Proprietary © 2010 ANSYS, Inc. All rights reserved.

L6-1

Release 13.0 December 2010

FSI with ANSYS Mechanical and CFX

Rigid Body FSI

Customer Training Material

• CFX includes a 6-DOF rigid body solver • Fluid forces/torques on a body auto-calculated • Body B d response iincluded l d d in i flow fl solution l ti – 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

ANSYS, Inc. Proprietary © 2010 ANSYS, Inc. All rights reserved.

L6-2

Release 13.0 December 2010

FSI with ANSYS Mechanical and CFX

Rigid Body Dynamics

Customer Training Material

• 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 p translation and rotation

ANSYS, Inc. Proprietary © 2010 ANSYS, Inc. All rights reserved.

L6-3

Release 13.0 December 2010

FSI with ANSYS Mechanical and CFX

Rigid Translation

Customer Training Material

• Translational equation of motion, applied to Centre of Mass P = mx& = Linear Momentum

dP = m&x&G = ΣF dt

&x&G = Acceleration about centre of mass

ΣF = FAero + mg − Σ[kSpring ( x − x so )] + ΣFExt • 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 ANSYS, Inc. Proprietary © 2010 ANSYS, Inc. All rights reserved.

L6-4

Release 13.0 December 2010

FSI with ANSYS Mechanical and CFX

Rigid Rotation

Customer Training Material

• Rotational equation of motion about Centre of Mass

dΠ d ( I ω B ) = = ΣM dt dt

Π

= Angular Momentum

I

= Moment of Inertia tensor

d ( IωB ) = ω B × I ω B + I ω& B dt

ω& B = I −1 ( M B − ω B × I ω B )

M B = M Aero − Σ[kSpring p g (θ − θ so )] + ΣM Ext

• Two methods of discretization available – Simo-Wong [1] (Default. Second order, iteratively conservative) – First Fi t Order O d Backward B k d Euler E l

• Can add influence of external torsion spring or external q to ΣMExt torque [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) ANSYS, Inc. Proprietary © 2010 ANSYS, Inc. All rights reserved.

L6-5

Release 13.0 December 2010

FSI with ANSYS Mechanical and CFX

Creating a Rigid Body in CFX-Pre

Customer Training Material

• Insert a Rigid Body into the Flow Analysis

ANSYS, Inc. Proprietary © 2010 ANSYS, Inc. All rights reserved.

L6-6

Release 13.0 December 2010

FSI with ANSYS Mechanical and CFX

Rigid Body Basic Settings

Customer Training Material

• 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 a point

• Mass Moment of Inertia – E Enter t components t for f the th Mass M Moment M t of Inertia tensor • See next slides

– As calculated with respect to the rigid body coordinate frame ANSYS, Inc. Proprietary © 2010 ANSYS, Inc. All rights reserved.

L6-7

Release 13.0 December 2010

FSI with ANSYS Mechanical and CFX

Mass Moment of Inertia Tensor

Customer Training Material

• This tensor describes an objects resistance to changes in its rotation rate ⎡I I I ⎤ xx

⎢ I = ⎢ I yx ⎢ ⎣ I zx

xy

I yy I zy

xz

⎥ I yz ⎥ I zz ⎥⎦

• It’s 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 Non zero when you have rotation about the xx-axis axis

• Ixy describes the moment of inertia around the y-axis when the objects are rotated around the x-axis x-axis, etc – Non-zero when you have rotation about the x and y axis ANSYS, Inc. Proprietary © 2010 ANSYS, Inc. All rights reserved.

L6-8

Release 13.0 December 2010

FSI with ANSYS Mechanical and CFX

Mass Moment of Inertia Tensor

Customer Training Material

• For rotation about only the y-axis, the tensor simplifies to: ⎡0 0 I = ⎢⎢0 I yy ⎣⎢0 0

0⎤ 0⎥⎥ 0⎥⎦

• For rotation about the x and y axes we have: ⎡ I xx I = ⎢⎢ I yx ⎢⎣ 0

I xy I yy 0

0⎤ 0⎥⎥ 0⎥⎦

• See http://en.wikipedia.org/wiki/Moment_of_inertia for detailed background on mass moment of inertia

ANSYS, Inc. Proprietary © 2010 ANSYS, Inc. All rights reserved.

L6-9

Release 13.0 December 2010

FSI with ANSYS Mechanical and CFX

Rigid Body Dynamics

Customer Training Material

• 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 DOF

• Enter Gravity Vector – Acts at the centre of mass as set by y Coord Frame – Should be consistent with Domain gravity (if specified in the Domain)

• Everything specified in Rigid Body Coord Frame ANSYS, Inc. Proprietary © 2010 ANSYS, Inc. All rights reserved.

L6-10

Release 13.0 December 2010

FSI with ANSYS Mechanical and CFX

Rigid Body Initialization

Customer Training Material

• All state variables defining rigid body can be initialized in terms of the rigid body coordinate frame • Default behaviour is to use Automatic – Assumes quiescent conditions unless a previous solution is provided to restart from

ANSYS, Inc. Proprietary © 2010 ANSYS, Inc. All rights reserved.

L6-11

Release 13.0 December 2010

FSI with ANSYS Mechanical and CFX

Rigid Body Mesh Motion

Customer Training Material

• 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 •T To maintain i t i mesh h quality, lit you may wantt other th boundaries/interfaces b d i /i t f to move using only the translations/rotations from the RB solution ANSYS, Inc. Proprietary © 2010 ANSYS, Inc. All rights reserved.

L6-12

Release 13.0 December 2010

FSI with ANSYS Mechanical and CFX

Rigid Body Mesh Motion Example

Customer Training Material

• Ship hull example • 2-DOF 2 DOF – Rotation about y-axis – Translation along the zaxis

• A subdomain moves with the rigid body so that near-wall mesh quality can be maintained • See EX4 in the examples folder

ANSYS, Inc. Proprietary © 2010 ANSYS, Inc. All rights reserved.

L6-13

Release 13.0 December 2010

FSI with ANSYS Mechanical and CFX

Rigid Body Mesh Motion Example

Customer Training Material

• Hull wall boundary mesh motion defined by the Rigid Body Solution

ANSYS, Inc. Proprietary © 2010 ANSYS, Inc. All rights reserved.

L6-14

Release 13.0 December 2010

FSI with ANSYS Mechanical and CFX

Rigid Body Mesh Motion Example

Customer Training Material

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

ANSYS, Inc. Proprietary © 2010 ANSYS, Inc. All rights reserved.

L6-15

Release 13.0 December 2010

FSI with ANSYS Mechanical and CFX

Rigid Body Mesh Motion Example

Customer Training Material

• 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

ANSYS, Inc. Proprietary © 2010 ANSYS, Inc. All rights reserved.

L6-16

Release 13.0 December 2010

FSI with ANSYS Mechanical and CFX

Rigid Body Mesh Motion Example

Customer Training Material

• 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 ANSYS, Inc. Proprietary © 2010 ANSYS, Inc. All rights reserved.

L6-17

Release 13.0 December 2010

FSI with ANSYS Mechanical and CFX

Rigid Body Mesh Motion Example

Customer Training Material

• 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

ANSYS, Inc. Proprietary © 2010 ANSYS, Inc. All rights reserved.

L6-18

Release 13.0 December 2010

FSI with ANSYS Mechanical and CFX

CEL Access of Rigid Body Variables

Customer Training Material

• 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 /ANSYS I Inc/v130/CFX/etc / 130/CFX/ t to find the short form names ANSYS, Inc. Proprietary © 2010 ANSYS, Inc. All rights reserved.

L6-19

Release 13.0 December 2010

FSI with ANSYS Mechanical and CFX

Rigid Body Solver Control

Customer Training Material

• Solver Control > Rigid Body Control • Update Frequency – Every Time Step • Explicit coupling between the rigid body solution and the flow field field. Lowest computational cost, but weakest coupling. Suitable for loosely coupled cases; will be unstable for more tightly coupled l d 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 (bodymass 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 underrelaxation (see later). later)

ANSYS, Inc. Proprietary © 2010 ANSYS, Inc. All rights reserved.

L6-20

Release 13.0 December 2010

FSI with ANSYS Mechanical and CFX

Rigid Body Solver Control

Customer Training Material

• 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. timestep After each RB update within a timestep, the flow solver will perform the number of p set under Basic coefficient loops Settings.

• Under Internal Coupling Data Transfer Control can set Under Relaxation Factors and Convergence Control – Available for Update Frequency other than Every Timestep ANSYS, Inc. Proprietary © 2010 ANSYS, Inc. All rights reserved.

L6-21

Release 13.0 December 2010

FSI with ANSYS Mechanical and CFX

Rigid Body Solver Control

Customer Training Material

– Can adjust under relaxation for forces & torques sent to the RB solver and for mesh motion received from f the RB solver • External Force set via a Linear Spring is not under-relaxed

–U Under d relaxation l ti is i usually ll the th first fi t choice to improve robustness and is easy to use – Default D f lt under d relaxation l ti is i 0.75 0 75

• The default Simo Wong g Integration g Method for Angular Momentum is recommended

ANSYS, Inc. Proprietary © 2010 ANSYS, Inc. All rights reserved.

L6-22

Release 13.0 December 2010

FSI with ANSYS Mechanical and CFX

Rigid Body Monitor Plots

Customer Training Material

• 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 ANSYS, Inc. Proprietary © 2010 ANSYS, Inc. All rights reserved.

L6-23

Release 13.0 December 2010

FSI with ANSYS Mechanical and CFX

Rigid Body Monitor Plots

Customer Training Material

• Can also access additional plots; create a new monitor or right-click to access Monitor Properties p – Angular/Linear Acceleration and Angular/Linear Velocity are available in addition to the default Position, Euler Angle and Force/Motion Convergence plots

ANSYS, Inc. Proprietary © 2010 ANSYS, Inc. All rights reserved.

L6-24

Release 13.0 December 2010

FSI with ANSYS Mechanical and CFX

Rigid Body Solution

ANSYS, Inc. Proprietary © 2010 ANSYS, Inc. All rights reserved.

Customer Training Material

L6-25

Release 13.0 December 2010

FSI with ANSYS Mechanical and CFX

Limitations

Customer Training Material

• 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 Can t make a rigid body rotate about a point point, other than its center of mass

ANSYS, Inc. Proprietary © 2010 ANSYS, Inc. All rights reserved.

L6-26

Release 13.0 December 2010