Lenz's Law: Magnet Through a Copper Tube
Here, we reproduce an experiment from high school physics: a permanent magnet falls through
a copper pipe. The temporal change of the magnetic field in the copper induces currents which
themselves create an opposing magnetic field that brakes the fall. As a result, an equilibrium for the magnet's velocity can be reached. This phenomena is also known as Len'z law.
References :
"Levin
Yan, Silveira Fernando, Rizzato Felipe, ‚Electromagnetic braking : A
simple quantitative model‘, American Journal of Physics, Vol. 74, No. 9,
September 2006"
*CONTROL_TERMINATION *CONTROL_TIMESTEP *DATABASE_BINARY_D3PLOT *DEFINE_CURVE_TITLE *EM_CIRCUIT *EM_CONTROL
*EM_CONTROL_COUPLING *EM_CONTROL_TIMESTEP *EM_MAT_001
*EM_MAT_002
*EM_OUTPUT
*EM_PERMANENT_MAGNET
*EM_SOLVER_BEM
*EM_SOLVER_BEMMAT
*EM_SOLVER_FEM
*EM_SOLVER_FEMBEM_MONOLITHIC *END *KEYWORD *MAT_RIGID *PARAMETER *PART *SECTION_SOLID *TITLE
$ ******************************************************************************
$
$ P R E A M B L E
$
$ ******************************************************************************
*KEYWORD
$ system of units:
$ m, s, kg, N, A
*TITLE
TAILSIT: LENZ EXPERIMENT
$X Requires LS-DYNA MPP R13.0.0 or Post April 2021 Dev with double precision
$
$ ******************************************************************************
$
$ P A R A M E T E R D E F I N I T I O N S
$
$ ******************************************************************************
*PARAMETER
$--------1---------2---------3---------4---------5---------6---------7---------8
R murel 1e0
R dt 1e-3
R endt 0.250
R sigma 5.7143e7
R sigmaEps 1e5
R roMagnet 3729.5
R roCopper 449.71
R young 200e9
R pr 0.3
R v0 0.0
R magnetis 3.12739e5
I magnetId 2
I refId 3
I tubeId 1
ImagnetMat 1
I tubeMat 2
I refMat 3
I north 3
I south 4
I cyclBEM 2
I cyclFEM 1000
*SET_NODE_GENERAL
$--------1---------2---------3---------4---------5---------6---------7---------8
$ sid da1 da2 da3 da4 solver
1 0.0 0.0 0.0 0.0MECH
$--------1---------2---------3---------4---------5---------6---------7---------8
$ option e1 e2 e3 e4 e5 e6 e7
ALL
$
$ ******************************************************************************
$
$ C O N T R O L
$
$ ******************************************************************************
*CONTROL_TERMINATION
$--------1---------2---------3---------4---------5---------6---------7---------8
$ endtim endcyc dtmin endeng endmas nosol
&endt
*CONTROL_TIMESTEP
$--------1---------2---------3---------4---------5---------6---------7---------8
$ dtinit tssfac isdo tslimt dt2ms lctm erode ms1st
1.e-5
*DATABASE_BINARY_D3PLOT
$--------1---------2---------3---------4---------5---------6---------7---------8
$ dt
&dt
$
$ ******************************************************************************
$
$ P A R T S
$
$ ******************************************************************************
*PART
$--------1---------2---------3---------4---------5---------6---------7---------8
magnet
$ pid secid mid eosid hgid grav adpopt tmid
&magnetId 1&magnetMat
*PART
tube
$ pid secid mid eosid hgid grav adpopt tmid
&tubeId 1 &tubeMat
*PART
reference object
$ pid secid mid eosid hgid grav adpopt tmid
&refId 1 &refMat
*SECTION_SOLID
$--------1---------2---------3---------4---------5---------6---------7---------8
$ secid elform aet
1 1
$
$ ******************************************************************************
$
$ M A T E R I A L
$
$ ******************************************************************************
*MAT_RIGID
$--------1---------2---------3---------4---------5---------6---------7---------8
$ mid ro E PR N couple M alias
&tubeMat &roCopper &young &pr
$ cmo con1 con2
1.0 7 7
$ lco a2 a3 v1 v2 v3
0.0 0.0 0.0 0.0 0.0 0.0
*MAT_RIGID
$--------1---------2---------3---------4---------5---------6---------7---------8
$ mid ro E PR N couple M alias
&magnetMat &roMagnet &young &pr
$ cmo con1 con2
1.0 4 7
$ lco a2 a3 v1 v2 v3
0.0 0.0 0.0 0.0 0.0 0.0
*MAT_RIGID
$--------1---------2---------3---------4---------5---------6---------7---------8
$ mid ro E PR N couple M alias
&refMat &roMagnet &young &pr
$ cmo con1 con2
1.0 4 7
$ lco a2 a3 v1 v2 v3
0.0 0.0 0.0 0.0 0.0 0.0
$
$ ******************************************************************************
$
$ S T R U C T U R A L L O A D S [ F R E E F A L L ]
$
$ ******************************************************************************
*DEFINE_CURVE_TITLE
$--------1---------2---------3---------4---------5---------6---------7---------8
constant gravity
1 0 0.0 0.0 0.0 0.0 0
0E+00,9.81
5E+02,9.81
*INITIAL_VELOCITY_GENERATION
$--------1---------2---------3---------4---------5---------6---------7---------8
&magnetId 2 0.0 0.0 0.0 &v0 0 0
0.0 0.0 0.0 0.0 0.0 0.0 0 0
*LOAD_BODY_Z
$--------1---------2---------3---------4---------5---------6---------7---------8
1 1.0 0
$
$ ******************************************************************************
$
$ E L E C T R O M A G N E T I C M A T E R I A L
$
$ ******************************************************************************
*EM_MAT_001
$--------1---------2---------3---------4---------5---------6---------7---------8
$ mid mtype sigma eosid deatht rdltype
&magnetMat 4 &sigmaEps 0
*EM_MAT_001
$--------1---------2---------3---------4---------5---------6---------7---------8
$ mid mtype sigma eosid deatht rdltype
&tubeMat 4 &sigma 0
*EM_MAT_001
$--------1---------2---------3---------4---------5---------6---------7---------8
$ mid mtype sigma eosid deatht rdltype
&refMat 1
$
$ ******************************************************************************
$
$ E L E C T R O M A G N E T I C C O N T R O L
$
$ ******************************************************************************
*EM_CONTROL
$--------1---------2---------3---------4---------5---------6---------7---------8
$ emsol numls dt
1 &dt
*EM_CONTROL_COUPLING
2
*EM_SOLVER_FEM
$--------1---------2---------3---------4---------5---------6---------7---------8
$ reltol maxiter stype precon uselast ncyclfem
1.e-6 10000 1 1 1 &cyclFEM
*EM_SOLVER_BEM
$--------1---------2---------3---------4---------5---------6---------7---------8
$ reltol maxiter solvetype precon uselast ncyclbem
1.e-6 10000 2 2 1 &cyclBEM
*EM_SOLVER_FEMBEM
$--------1---------2---------3---------4---------5---------6---------7---------8
$ reltol maxiter forcon
1.e-4 50 3
*EM_SOLVER_BEMMAT
$--------1---------2---------3---------4---------5---------6---------7---------8
$ matId relTol
1 1.e-14
*EM_SOLVER_BEMMAT
$--------1---------2---------3---------4---------5---------6---------7---------8
$ matId relTol
2 1.e-14
*EM_SOLVER_BEMMAT
$--------1---------2---------3---------4---------5---------6---------7---------8
$ matId relTol
3 1.e-14
*EM_OUTPUT
$--------1---------2---------3---------4---------5---------6---------7---------8
$ matS matF solS solF mesh memory timing d3plotAsc
4 4 4 4 0 0 0 0
$ mf2 gmv d3plotFor timeHist
0 0 0
*EM_PERMANENT_MAGNET
$--------1---------2---------3---------4---------5---------6---------7---------8
$ ID Part ID - North South M
1 &magnetId &north &south &magnetis
*EM_SOLVER_FEMBEM_MONOLITHIC
$--------1---------2---------3---------4---------5---------6---------7---------8
$ COUPLING KSP_TYPE KSP_ATOL KSP_RTOL KSP_MAXIT GMRES_RST DEBUG
0 1.e-8 1.e-5 10000
$--------1---------2---------3---------4---------5---------6---------7---------8
$NEWT_STOL NEWT_ATOL NEWT_RTOL NEWT_MAXI
$--------1---------2---------3---------4---------5---------6---------7---------8
$ LS_ON LS_FTOL LS_GTOL LS_RTOL LS_SAMPL LS_NUM_SP LS_MAXFUN
2
$--------1---------2---------3---------4---------5---------6---------7---------8
$USE_ENERG STOP_ERR WIDTH_ERR XTRAPF
*END
