Introduction Theory Algorithm Result Discussion and Improvements

InterDyMFoam coupled with forces and meshmotion in 6-DoF

Erik Ekedahl

Erik Ekedahl OpenFOAM 1/18

Introduction Theory Algorithm Result Discussion and Improvements

Outline

1 Introduction and motivation

2 Theory

3 AlgorithmUsagePossible Alterations

4 Result

5 Discussion and Improvements

Erik Ekedahl OpenFOAM 2/18

Introduction Theory Algorithm Result Discussion and Improvements

Motivation

Volume-of-Fluid method and dynamic mesh with 6-degreesof freedomMarine ApplicationsBase:interDyMFoam - Volume of Fluid.

Erik Ekedahl OpenFOAM 3/18

Introduction Theory Algorithm Result Discussion and Improvements

Motivation

Volume-of-Fluid method and dynamic mesh with 6-degreesof freedomMarine ApplicationsBase:interDyMFoam - Volume of Fluid.

Erik Ekedahl OpenFOAM 3/18

Introduction Theory Algorithm Result Discussion and Improvements

Motivation

Volume-of-Fluid method and dynamic mesh with 6-degreesof freedomMarine ApplicationsBase:interDyMFoam - Volume of Fluid.

Erik Ekedahl OpenFOAM 3/18

Introduction Theory Algorithm Result Discussion and Improvements

Theory

Two phases; gas and liquid in this case.Interface

γ =

1 if in the water0 < γ < 1 in the region around the surface0 if in the air

Under-relaxation

φnew = αφnew + (1− α)φold (1)

Erik Ekedahl OpenFOAM 4/18

Introduction Theory Algorithm Result Discussion and Improvements

Theory

Two phases; gas and liquid in this case.Interface

γ =

1 if in the water0 < γ < 1 in the region around the surface0 if in the air

Under-relaxation

φnew = αφnew + (1− α)φold (1)

Erik Ekedahl OpenFOAM 4/18

Introduction Theory Algorithm Result Discussion and Improvements

Theory

Two phases; gas and liquid in this case.Interface

γ =

1 if in the water0 < γ < 1 in the region around the surface0 if in the air

Under-relaxation

φnew = αφnew + (1− α)φold (1)

Erik Ekedahl OpenFOAM 4/18

Introduction Theory Algorithm Result Discussion and Improvements

Six Degrees of Freedom

ls

Figure: 6-DOF

Erik Ekedahl OpenFOAM 5/18

Introduction Theory Algorithm Result Discussion and Improvements

Forces and Moments

F =

∫S

F ext + F flow (2)

M =

∫S

Mext + Mflow (3)

Forces from gravity, pressure and viscous effects

Erik Ekedahl OpenFOAM 6/18

Introduction Theory Algorithm Result Discussion and Improvements

Forces and Moments

F =

∫S

F ext + F flow (2)

M =

∫S

Mext + Mflow (3)

Forces from gravity, pressure and viscous effects

Erik Ekedahl OpenFOAM 6/18

Introduction Theory Algorithm Result Discussion and Improvements

Rotation and Translation

Quaternion - Hamilton 1843Base: {1, i , j , k} as a1 + bi + cj + dkWhere a, b,c and d are real numbers andi2 = j2 = k2 = ijk = −1Composed of one vector and one scalar in OF.Euler angles→ quaternion and back.

Erik Ekedahl OpenFOAM 7/18

Introduction Theory Algorithm Result Discussion and Improvements

Rotation and Translation

Quaternion - Hamilton 1843Base: {1, i , j , k} as a1 + bi + cj + dkWhere a, b,c and d are real numbers andi2 = j2 = k2 = ijk = −1Composed of one vector and one scalar in OF.Euler angles→ quaternion and back.

Erik Ekedahl OpenFOAM 7/18

Introduction Theory Algorithm Result Discussion and Improvements

Rotation and Translation

Quaternion - Hamilton 1843Base: {1, i , j , k} as a1 + bi + cj + dkWhere a, b,c and d are real numbers andi2 = j2 = k2 = ijk = −1Composed of one vector and one scalar in OF.Euler angles→ quaternion and back.

Erik Ekedahl OpenFOAM 7/18

Introduction Theory Algorithm Result Discussion and Improvements

Rotation and Translation

Quaternion - Hamilton 1843Base: {1, i , j , k} as a1 + bi + cj + dkWhere a, b,c and d are real numbers andi2 = j2 = k2 = ijk = −1Composed of one vector and one scalar in OF.Euler angles→ quaternion and back.

Erik Ekedahl OpenFOAM 7/18

Introduction Theory Algorithm Result Discussion and Improvements

Rotation and Translation

Quaternion - Hamilton 1843Base: {1, i , j , k} as a1 + bi + cj + dkWhere a, b,c and d are real numbers andi2 = j2 = k2 = ijk = −1Composed of one vector and one scalar in OF.Euler angles→ quaternion and back.

Erik Ekedahl OpenFOAM 7/18

Introduction Theory Algorithm Result Discussion and Improvements

mesh Deformation

Figure: the xy -plane at time 0seconds

Figure: the xy -plane at time 16seconds

Erik Ekedahl OpenFOAM 8/18

Introduction Theory Algorithm Result Discussion and Improvements

Algorithm

while Time is running doExtract forces and moments from pressure, buoyancy.Extract forces and moments from viscous effects.Divide by mass for forces and inertia for momentum.Extract the acceleration by multiplication of the real timeinterval.Reset and move center of gravity.Translate patch to origo.Rotate in accordance to momentum.Translate back to origo.Translate according to forces.

end while

Erik Ekedahl OpenFOAM 9/18

Introduction Theory Algorithm Result Discussion and Improvements

Algorithm

while Time is running doExtract forces and moments from pressure, buoyancy.Extract forces and moments from viscous effects.Divide by mass for forces and inertia for momentum.Extract the acceleration by multiplication of the real timeinterval.Reset and move center of gravity.Translate patch to origo.Rotate in accordance to momentum.Translate back to origo.Translate according to forces.

end while

Erik Ekedahl OpenFOAM 9/18

Introduction Theory Algorithm Result Discussion and Improvements

Algorithm

while Time is running doExtract forces and moments from pressure, buoyancy.Extract forces and moments from viscous effects.Divide by mass for forces and inertia for momentum.Extract the acceleration by multiplication of the real timeinterval.Reset and move center of gravity.Translate patch to origo.Rotate in accordance to momentum.Translate back to origo.Translate according to forces.

end while

Erik Ekedahl OpenFOAM 9/18

Introduction Theory Algorithm Result Discussion and Improvements

Algorithm

while Time is running doExtract forces and moments from pressure, buoyancy.Extract forces and moments from viscous effects.Divide by mass for forces and inertia for momentum.Extract the acceleration by multiplication of the real timeinterval.Reset and move center of gravity.Translate patch to origo.Rotate in accordance to momentum.Translate back to origo.Translate according to forces.

end while

Erik Ekedahl OpenFOAM 9/18

Introduction Theory Algorithm Result Discussion and Improvements

Algorithm

while Time is running doExtract forces and moments from pressure, buoyancy.Extract forces and moments from viscous effects.Divide by mass for forces and inertia for momentum.Extract the acceleration by multiplication of the real timeinterval.Reset and move center of gravity.Translate patch to origo.Rotate in accordance to momentum.Translate back to origo.Translate according to forces.

end while

Erik Ekedahl OpenFOAM 9/18

Introduction Theory Algorithm Result Discussion and Improvements

Algorithm

while Time is running doExtract forces and moments from pressure, buoyancy.Extract forces and moments from viscous effects.Divide by mass for forces and inertia for momentum.Extract the acceleration by multiplication of the real timeinterval.Reset and move center of gravity.Translate patch to origo.Rotate in accordance to momentum.Translate back to origo.Translate according to forces.

end while

Erik Ekedahl OpenFOAM 9/18

Introduction Theory Algorithm Result Discussion and Improvements

Algorithm

while Time is running doExtract forces and moments from pressure, buoyancy.Extract forces and moments from viscous effects.Divide by mass for forces and inertia for momentum.Extract the acceleration by multiplication of the real timeinterval.Reset and move center of gravity.Translate patch to origo.Rotate in accordance to momentum.Translate back to origo.Translate according to forces.

end while

Erik Ekedahl OpenFOAM 9/18

Introduction Theory Algorithm Result Discussion and Improvements

Algorithm

while Time is running doExtract forces and moments from pressure, buoyancy.Extract forces and moments from viscous effects.Divide by mass for forces and inertia for momentum.Extract the acceleration by multiplication of the real timeinterval.Reset and move center of gravity.Translate patch to origo.Rotate in accordance to momentum.Translate back to origo.Translate according to forces.

end while

Erik Ekedahl OpenFOAM 9/18

Introduction Theory Algorithm Result Discussion and Improvements

Algorithm

while Time is running doExtract forces and moments from pressure, buoyancy.Extract forces and moments from viscous effects.Divide by mass for forces and inertia for momentum.Extract the acceleration by multiplication of the real timeinterval.Reset and move center of gravity.Translate patch to origo.Rotate in accordance to momentum.Translate back to origo.Translate according to forces.

end while

Erik Ekedahl OpenFOAM 9/18

Introduction Theory Algorithm Result Discussion and Improvements

Algorithm

while Time is running doExtract forces and moments from pressure, buoyancy.Extract forces and moments from viscous effects.Divide by mass for forces and inertia for momentum.Extract the acceleration by multiplication of the real timeinterval.Reset and move center of gravity.Translate patch to origo.Rotate in accordance to momentum.Translate back to origo.Translate according to forces.

end while

Erik Ekedahl OpenFOAM 9/18

Introduction Theory Algorithm Result Discussion and Improvements

Algorithm

while Time is running doExtract forces and moments from pressure, buoyancy.Extract forces and moments from viscous effects.Divide by mass for forces and inertia for momentum.Extract the acceleration by multiplication of the real timeinterval.Reset and move center of gravity.Translate patch to origo.Rotate in accordance to momentum.Translate back to origo.Translate according to forces.

end while

Erik Ekedahl OpenFOAM 9/18

Introduction Theory Algorithm Result Discussion and Improvements

ForceFoamDict

forceBalance forceBalanceEnabled yes;/* ———————————————————————– */// Mass of the moving part //M M [1 0 0 0 0 0 0] 136.51; M M [10 0 0 0 0 0] 108000;// Mass of the moving part inertia inertia [1 2 0 0 0 0 0] 648000;// Limit the maximum acceleration on the system (Bandwidthlimitation) accelLim accelLim [0 1 -2 0 0 0 0] 1.0e-2;// Acceleration due to gravity g g [0 1 -2 0 0 0 0] 9.81;// Direction vector of the acceleration due to gravity gVector (0 0-1);// Direction vector of the acceleration due to gravity CgCenter (00 0);/* ———————————————————————– */motionPatches ( cuber egion0);

Erik Ekedahl OpenFOAM 10/18

Introduction Theory Algorithm Result Discussion and Improvements

Usage

Alterations

Extract the archives.my6DOFFoam: run wclean then wmakekubtest: run application with ’my6DOFFoam’

Erik Ekedahl OpenFOAM 11/18

Introduction Theory Algorithm Result Discussion and Improvements

Usage

Alterations

Extract the archives.my6DOFFoam: run wclean then wmakekubtest: run application with ’my6DOFFoam’

Erik Ekedahl OpenFOAM 11/18

Introduction Theory Algorithm Result Discussion and Improvements

Usage

Alterations

Extract the archives.my6DOFFoam: run wclean then wmakekubtest: run application with ’my6DOFFoam’

Erik Ekedahl OpenFOAM 11/18

Introduction Theory Algorithm Result Discussion and Improvements

Possible Alterations

Alterations

Initial ValuesaccelLim - Limits the motion due to the Forces andMoments.Under-relaxation inMesh - blockMesh and snappyHexMesh

Erik Ekedahl OpenFOAM 12/18

Introduction Theory Algorithm Result Discussion and Improvements

Possible Alterations

Alterations

Initial ValuesaccelLim - Limits the motion due to the Forces andMoments.Under-relaxation inMesh - blockMesh and snappyHexMesh

Erik Ekedahl OpenFOAM 12/18

Introduction Theory Algorithm Result Discussion and Improvements

Possible Alterations

Alterations

Initial ValuesaccelLim - Limits the motion due to the Forces andMoments.Under-relaxation inMesh - blockMesh and snappyHexMesh

Erik Ekedahl OpenFOAM 12/18

Introduction Theory Algorithm Result Discussion and Improvements

Possible Alterations

Alterations

Initial ValuesaccelLim - Limits the motion due to the Forces andMoments.Under-relaxation inMesh - blockMesh and snappyHexMesh

Erik Ekedahl OpenFOAM 12/18

Introduction Theory Algorithm Result Discussion and Improvements

Set up

Domain - 40 meter kub with 6 meter cube in the origoBC’s - slip and reflecting walls, movingWallVelocity for thecubeInitial values

Erik Ekedahl OpenFOAM 13/18

Introduction Theory Algorithm Result Discussion and Improvements

Set up

Domain - 40 meter kub with 6 meter cube in the origoBC’s - slip and reflecting walls, movingWallVelocity for thecubeInitial values

Erik Ekedahl OpenFOAM 13/18

Introduction Theory Algorithm Result Discussion and Improvements

Set up

Domain - 40 meter kub with 6 meter cube in the origoBC’s - slip and reflecting walls, movingWallVelocity for thecubeInitial values

Erik Ekedahl OpenFOAM 13/18

Introduction Theory Algorithm Result Discussion and Improvements

Result: cube at initial timestep

Figure: Time 0

Erik Ekedahl OpenFOAM 14/18

Introduction Theory Algorithm Result Discussion and Improvements

Result: cube is tilted and begining to turn

Figure: Time 6 seconds

Erik Ekedahl OpenFOAM 15/18

Introduction Theory Algorithm Result Discussion and Improvements

Result: cube just before divergence

Figure: Time 10 seconds

Erik Ekedahl OpenFOAM 16/18

Introduction Theory Algorithm Result Discussion and Improvements

Discussion

This is a first draftUnstable without proper dampingSkewed cells

Erik Ekedahl OpenFOAM 17/18

Introduction Theory Algorithm Result Discussion and Improvements

Discussion

This is a first draftUnstable without proper dampingSkewed cells

Erik Ekedahl OpenFOAM 17/18

Introduction Theory Algorithm Result Discussion and Improvements

Discussion

This is a first draftUnstable without proper dampingSkewed cells

Erik Ekedahl OpenFOAM 17/18

Introduction Theory Algorithm Result Discussion and Improvements

Improvements

Spring-dampingOptimize under-relaxationAutomate calculation of inertia and center of gravity

Erik Ekedahl OpenFOAM 18/18

Introduction Theory Algorithm Result Discussion and Improvements

Improvements

Spring-dampingOptimize under-relaxationAutomate calculation of inertia and center of gravity

Erik Ekedahl OpenFOAM 18/18

Introduction Theory Algorithm Result Discussion and Improvements

Improvements

Spring-dampingOptimize under-relaxationAutomate calculation of inertia and center of gravity

Erik Ekedahl OpenFOAM 18/18