OpenFOAMDEM

2

44OpenCAE@ 2015/12/13

OpenFOAMDEM

OpenFOAM-2.0.0DEM

2011/6/16 OpenFOAM-2.0.0DEM(Discrete Element Method) (Lagrangian)

2014/2/17 OpenFOAM-2.3.0DPM(Discrete ParHcle Modeling) MP-PIC(MulHphase ParHcle-in-Cell)

Release History

OpenFOAMDEMdocument

Ver. 2.3.x

13 ( ErgunWenYuDrag PlessisMasliyahDrag SRF SaffmanMeiLiSForce TomiyamaLiS WenYuDrag gravity nonInerHalFrame nonSphereDrag paramagneHc pressureGradient sphereDrag virtualMass )

constant/kinemaHcCloudProperHeserror

13

?

$FOAM_SRC/lagrangian/intermediate/submodels/KinemaHc/ParHcleForces

. Drag Gravity LiS NonInerHalFrame ParamagneHc ParHcleForce PressureGradient SRF VirtualMass forceSuSp

$tree -L 1Drag/ ErgunWenYuDrag NonSphereDrag PlessisMasliyahDrag SphereDrag WenYuDrag

LiS LiSForce SaffmanMeiLiS TomiyamaLiS

tree

(5) ErgunWenYuDrag NonSphereDrag PlessisMasliyahDrag SphereDrag WenYuDrag

Re: u: d: :

Re = f u f us ds

f

(Sphere)

Sphere

Re

(Sphere)

F = 34msCd Re

fsds

2 u

value.Sp() = mass*0.75*muc*CdRe(Re)/(p.rho()*sqr(p.d()));

SphereDragForce.C

OpenFOAMSp

if (Re > 1000.0) { return 0.424*Re; } else { return 24.0*(1.0 + 1.0/6.0*pow(Re, 2.0/3.0)); }

Re

(NonSphere)

Cd =24Re

1+ a Reb( )+ c ReRe+ d

NonSphere

A. Haier and O. Levenspiel, Powder Technol., 58, 63-70 (1989)

a ( ) = exp 2.3288 6.4581 + 2.4486 2( )b ( ) = 0.0964+ 0.5565

c ( ) = exp 4.905013.8944 +18.4222 2 10.2599 3( )d ( ) = exp 1.4681+12.2584 20.7322 2 +15.8855 3( )

F = 34msCd Re

fsds

2 u f us

(NonSphere)

Cd CdRe return 24.0*(1.0 + a_*pow(Re, b_)) + Re*c_/(1 + d_/(Re + ROOTVSMALL));

Cd =24Re

1+ a Reb( )+ c1+ d / Re+ small( )

value.Sp() = mass*0.75*muc*CdRe(Re)/(p.rho()*sqr(p.d()));

F = 34msCd Re

fsds

2 u

a, b, c, dNonSphereDragForce.C

NonSphereDragForce.C

NonSphereDragForce.C

(WenYu)

nRe

(WenYu)

=34Cd

1 n( )ds

f u f us n2.65

f: s:

: Cd: n: d: : u: V:

Ff =1 n

u f us( )Vs

C. Y. Wen and Y. H. Yu, Chem. Eng. Prog. S. Ser., 62, 100-113 (1966).

Ff =Vs1 n

34Cd

1 n( )ds

f n2.65 u f us

2

Ff =mss

34CdRes f

nds2 n

2.65 u f us

Vs =mss, f =

Res fn u f us ds

(WenYu)

return forceSuSp ( vector::zero, (mass/p.rho()) *0.75*CdRe(alphac*Re)*muc*pow(alphac, -2.65)/(alphac*sqr(p.d())) );

Su

mss

34CdRecc

2.65

cds2

Ff =mss

34CdRes f

nds2 n

2.65 u f usWenYuDragForce.C

(ErgunWenYu)

f: s:

: Cd: n: d: : u: :

Wen-Yu (n > 0.8)

Ergun (n < 0.8)

=1501 n( )2

n2 fds2 +1.75

1 n( )n

fdsu f us

S. Ergun, Chem. Eng. Prog., 48, 89-94 (1952).

nRe

(ErgunWenYu)

f: s:

: Cd: n: d: : u: V:

Ff =1 n

u f us( )Vs

C. Y. Wen and Y. H. Yu, Chem. Eng. Prog. S. Ser., 62, 100-113 (1966).

Ff =mss

fnd 2s

1501 n( )n

+1.75Re!"#

$%&u f us

Vs =mss

f =Re fu f us ds

Ff =mss

1 n

u f us( )

=1501 n( )2

n2 fds2 +1.75

1 n( )n

Re fds2

=1501 n( )2

n2 fds2 +1.75

1 n( )n

fdsu f us

(ErgunWenYu)

if (alphac < 0.8) { return forceSuSp ( vector::zero, (mass/p.rho()) *(150.0*(1.0 - alphac)/alphac + 1.75*Re)*muc/(alphac*sqr(p.d())) ); }

mss

1501c( )c

+1.75Re!"#

$%&

fcd

2s

Ff =mss

fnd 2s

1501 n( )n

+1.75Re!"#

$%&u f us

ErgunWenYuDragForce.C

(PlessisMasliyah)

Plessis-Masliyah (RUC)

A = 26.8n3

1 n( )23 1 1 n( )

13

!

"#

$

%& 1 1 n( )

23

!

"#

$

%&2

B = n2

1 1 n( )23

!

"#

$

%&2

= A1 n( )2

n2 fds2 +B

1 n( )n

fdsu f us

Ergun

J. P. Du Plessis and J. H. Masliyah, Trans. Porous Media, 3, 145-161 (1988).

(PlessisMasliyah)

f: s:

: Cd: n: d: : u: V:

Ff =1 n

u f us( )Vs

Ff =mss

fnd 2s

A1 n( )n

+BRe!"#

$%&u f us

Vs =mss

f =Re fu f us ds

Ff =mss

1 n

u f us( )

= A1 n( )2

n2 fds2 +B

1 n( )n

Re fds2

= A1 n( )2

n2 fds2 +B

1 n( )n

fdsu f us

(PlessisMasliyah)

scalar A = 26.8*pow3(alphac) /( sqr(cbrtAlphap) *(1.0 - cbrtAlphap) *sqr(1.0 - sqr(cbrtAlphap)) + SMALL );

scalar B = sqr(alphac) /sqr(1.0 - sqr(cbrtAlphap));

vector::zero, (mass/p.rho()) *(A*(1.0 - alphac)/alphac + B*Re)*muc/(alphac*sqr(p.d()))

mss

A1c( )c

+BRe!"#

$%&

fcd

2s

A = 26.8n3

1 n( )23 1 1 n( )

13

!

"#

$

%& 1 1 n( )

23

!

"#

$

%&2

B = n2

1 1 n( )23

!

"#

$

%&2

Ff =mss

fnd 2s

A1 n( )n

+BRe!"#

$%&u f us

PlessisMasliyahDragForce.C

(2) SaffmanMeiLiS TomiyamaLiS

Re = f u f us ds

f

Re: u: d: :

scalar Cl = this->Cl(p, curlUc, Re, muc); value.Su() = mass/p.rho()*p.rhoc()*Cl*((p.Uc() - p.U())^curlUc);

LiSForce.C

F = mss

cCl uc us( ) uc( )( )

(SaffmanMei)

Fl =ClAp f u f us

2

2

(Saffman)

Fl,Sa = 6.46 fud2

!

"#

$

%&2 G

!

"#

$

%&

12

(Saffman-Mei)FlFl,Sa

= 1 0.331412

!

"#

$

%&exp Res

10!

"#

$

%&+ 0.3314

12

= 0.0524 Res( )12

Res 40

Res > 40

R. Mei, Int. J. MulHphase Flow, 18, 145-147 (1992)

Res =uds

=12Res

2

=12ReGRes

=ReG

12

Res

ReG =Gds

2

G = duldy u = u f us

(SaffmanMei)

Fl,Sa = 6.46 f u f usds2

!

"#

$

%&2

u

!

"#

$

%&

12

= 6.46 fds4

ReG u f us

= 6.46 3mss

1ReG

f u f us u2

Res =uds

=12Res

2

=12ReGRes

=ReG

12

Res

ReG =Gds

2

G = duldy

= u

u = u f us

(Saffman)

FlFl,Sa

=mei

Fl = 6.46mei3mss

1ReG

f u f us u2

=32

1ReG

6.46mei mss

f u f us u

Cl (OpenFOAM)

(SaffmanMei)

scalar Rew = p.rhoc()*mag(curlUc)*sqr(p.d())/(muc + ROOTVSMALL); scalar beta = 0.5*(Rew/(Re + ROOTVSMALL)); scalar alpha = 0.3314*sqrt(beta); scalar f = (1.0 - alpha)*exp(-0.1*Re) + alpha; ... if (Re < 40) { Cld = 6.46*f; } else { Cld = 6.46*0.0524*sqrt(beta*Re); } return 3.0/(mathemaHcal::twoPi*sqrt(Rew))*Cld;

SaffmanMeiLiSForce.C

Rew =l u ds

2

l

= 0.3314

= 0.3314 Rew2Re

=Rew2Re

Cld = 6.460.0524 Re

= 6.460.0524 Rew2

Cld = 6.46 f f = 1( ) exp 0.1Re( )+

= 1 0.3314 Rew2Re

#

$%

&

'( exp Re

10#

$%

&

'(+ 0.3314

Rew2Re

()OpenFOAM, OpenFOAMCldFL/FLSax6.46

Cl =32

1ReG

6.46mei

Cld (OpenFOAM)

(Tomiyama)

A. Tomiyama et al., Chem. Eng. Sci., 57, 1849-1858 (2002)

Cl =min 0.288tanh 0.121Res( ), f( )= f

Fl =Cl f mss

u u f( )

Eod < 44 Eod 10.7

f = 0.00105Eod3 0.0159Eod

2 0.0204Eod + 0.474

Eod =g f s( )dH2

Eo: Etvs dH: dv: E: ds:

E = dVdH

=1

1+ 0.163Eo0.757

dH = 1+ 0.163Eo0.757( )dV

dH = 1+ 0.163Eo0.757( )

13 ds

(Tomiyama)

scalar Eo = p.Eo(g, p.d(), sigma_); scalar dH = p.d()*cbrt(1.0 + 0.163*pow(Eo, 0.757)); scalar Eod = p.Eo(g, dH, sigma_); scalar f = 0.00105*pow3(Eod) - 0.0159*sqr(Eod) - 0.0204*Eod + 0.474; if (Eod 4) && (Eod

(6) SRF gravity nonInerHalFrame paramagneHc pressureGradient virtualMass

SRF

f: s:

F: m: g: : V:

value.Su() = mass*(1.0 - p.rhoc()/p.rho()) *(2.0*(p.U() ^ omega) + (omega ^ (r ^ omega)));

SRF (Single RotaTng Frame)()

FSRF =ms 2v + r ( )

()

FSRF =ms 1 fs

"

#$

%

&' 2v + r ( )

SRFForce.C

v = drdt

(gravity)

Fg =msg lgVs

f: s:

F: m: g: : V: Vs =

mss

Fg =msg 1ls

"

#$

%

&'

OpenFOAM

value.Su() = mass*g_*(1.0 - p.rhoc()/p.rho());GravityForce.C

(nonInerTalFrame)

FnIF =ms w+ 2v + r ( )

Lagragian

v = drdt

value.Su() = mass *( -W_ + (r ^ omegaDot_) + 2.0*(p.U() ^ omega_) + (omega_ ^ (r ^ omega_)) );

NonInerHalFrameForce.C

(paramagneTc)

Fmg =ms 30

+3

H H#

$%

&

'(

?

value.Su()= mass*3.0*constant::electromagneHc::mu0.value()/p.rho() *magneHcSuscepHbility_/(magneHcSuscepHbility_ + 3) *HdotGradHInterp.interpolate(p.posiHon(), p.currentTetIndices());

ParamagneHcForce.C

(pressureGradient)

Fp =ms fs

u ft

+u f u f!

"#

$

%&

=ms fs

Du fDt

OpenFOAMBug (Bug #0001302)

value.Su() = mass*p.rhoc()/p.rho()*DUcDt;

PressureGradientForce.C

(virtualMass)

Fvm = cvmFp

= cvmms fs

Du fDt

Cvm: (0.5)

forceSuSp value = PressureGradientForce::calcCoupled(p, dt, mass, Re, muc); value.Su() *= Cvm_;

VirtualMassForce.C

OpenFOAMDEM

Ver.2.3.x13

force

template class SphereDragForce : public ParHcleForce

SphereDrag/SphereDragForce.H

forceParHcleForce

class derive : public base

basederive

C++()

$FOAM_SRC/lagrangian/intermediate/submodels/KinemaHc/ParHcleForces/ParHcleForce/

ParHcleForce

force

ParHcleForce

Owner Mesh Coeffs

cacheFields calcCoupled

calcNonCoupled massAdd

ParHcleForce.H

virtual forceSuSp calcCoupled ( const typename CloudType::parcelType& p, const scalar dt, const scalar mass, const scalar Re, const scalar muc ) const;

virtual: ()

C++()ParHcleForcecalcCoupled, calcNonCoupled, massAdd (0)

DragForce

ParHcleForce

Owner Mesh Coeffs

cacheFields calcCoupled

calcNonCoupled massAdd

Owner Mesh Coeffs

cacheFields calcCoupled

calcNonCoupled massAdd

SphereDragForce

SpereDragForcecalcCoupled calcCoupled (Drag(ErgunWenYuDrag, NonSphereDrag, PlessisMasliyahDrag, WenYuDrag))

CdRe

ParHcleForce

DragForce

Li[Force

ParHcleForce

Owner Mesh Coeffs

cacheFields calcCoupled

calcNonCoupled massAdd

Owner Mesh Coeffs

cacheFields calcCoupled

calcNonCoupled massAdd

LiSForce

Li[ForcecalcCoupled, cacheFieldsCl

curlUc, Su Uc,Su

Cl

Owner Mesh Coeffs

cacheFields calcCoupled

calcNonCoupled massAdd

LiSForce

Cl

TomiyamaLiSForce

Owner Mesh Coeffs

cacheFields calcCoupled

calcNonCoupled massAdd

Cl

TomiyamaLi[ForceCl Cl (LiSForce(TomiyamaLiSForce, SaffmanMeiLiSForce))

ParHcleForce LiSForce LiSForce

Li[Force

GravityForce

ParHcleForce

Owner Mesh Coeffs

cacheFields calcCoupled

calcNonCoupled massAdd

Owner Mesh Coeffs

cacheFields calcCoupled

calcNonCoupled massAdd

GravityForce

GravityForcecalcNonCoupled, g

g

ParHcleForce

GravityForce

NonInerTalForce

ParHcleForce

Owner Mesh Coeffs

cacheFields calcCoupled

calcNonCoupled massAdd

Owner Mesh Coeffs

cacheFields calcCoupled

calcNonCoupled massAdd

NonInerHalForce

NonInerTalForcecalcNonCoupled, cacheFields, W, omega, omegaDot, CentreOfRotaTon

W

ParHcleForce

NonInerHalForce

omega omegaDot

centreOfRotaHon

ParamagneTcForce

ParHcleForce

Owner Mesh Coeffs

cacheFields calcCoupled

calcNonCoupled massAdd

Owner Mesh Coeffs

cacheFields calcCoupled

calcNonCoupled massAdd

ParamagneHcForce

NonInerTalForcecalcNonCoupled, cacheFields, HdotGradHName, magneTcSuscepTbility

HdotGradHName

ParHcleForce

ParamegneHcForce

magneHcSuscepHbility

PressureGradientForce

ParHcleForce

Owner Mesh Coeffs

cacheFields calcCoupled

calcNonCoupled massAdd

Owner Mesh Coeffs

cacheFields calcCoupled

calcNonCoupled massAdd

PressureGradientForce

PressureGradientForcecalcCoupled, massAdd, cacheFields, DUcDtInterp

DUcDtInterp

ParHcleForce

PressureGradientForce

VirtualMassForce

Owner Mesh Coeffs

cacheFields calcCoupled

calcNonCoupled massAdd

VirtualMassForce

Vi_ualMassForcecalcCoupled, massAdd, cacheFields

ParHcleForce

PressureGradientForce

Owner Mesh Coeffs

cacheFields calcCoupled

calcNonCoupled massAdd

PressureGradientForce

DUcDtInterp

VirtualMassForce

DUcDtInterp

SRFForce

ParHcleForce

Owner Mesh Coeffs

cacheFields calcCoupled

calcNonCoupled massAdd

Owner Mesh Coeffs

cacheFields calcCoupled

calcNonCoupled massAdd

SRFForce

SRFForcecalcNonCoupled, cacheFields

ParHcleForce

SRFForce

coupled or nonCoupled

Coupled nonCoupled

LiSForce (TomiyamaLiSForce, SaffmanMeiLiSForce)

DragForce (SphereDrag, ErgunWenYuDrag, NonSphereDrag, PlessisMasliyahDrag, WenYuDra)

GravityForce

NonInerHalForce

ParamegneHcForce

PressureGradientForce

VirtualMassForceSRFForce

couplednonCoupled?

$FOAM_SRC/lagrangian/intermediate/submodels/KinemaHc/ParHcleForces/forceSuSp

forceSuSp.H F = Sp U Up( )+ Su

F: Su: () Sp: (/)

coupled (Sp) nonCoupled (Su)

forceSuSp

class forceSuSp : public Tuple2

forceSuSp.H

class derive : public base

basederive

C++()

forceSuSpTuple2

Tuple2

first second reverseTuple2

forceSuSp

first second reverseTuple2

Su Sp

forceSuSpforceSuSpI.H

inline Foam::vector& Foam::forceSuSp::Su() { return first(); } inline Foam::scalar& Foam::forceSuSp::Sp() { return second(); }

Su()Tuple2first()Sp()second()

Su Sp

References

A. Haier and O. Levenspiel, Powder Technol., 58, 63-70 (1989).

C. Y. Wen and Y. H. Yu, Chem. Eng. Prog. S. Ser., 62, 100-113 (1966).

S. Ergun, Chem. Eng. Prog., 48, 89-94 (1952). J. P. Du Plessis and J. H. Masliyah, Trans. Porous Media, 3, 145-161 (1988).

R. Mei, Int. J. Multiphase Flow, 18, 145-147 (1992). A. Tomiyama et al., Chem. Eng. Sci., 57, 1849-1858 (2002). C++()