modifying buoyantpimplefoam for the simulation of solid

Theory Solver Thermophysical Models Tutorial Case References

Modifying buoyantPimpleFoam for the Simulation ofSolid-Liquid Phase Change with

Temperature-dependent Thermophysical Properties

Daniel Hummel

Ostbayerische Technische Hochschule (OTH) Amberg-WeidenFriedrich-Alexander Universitat (FAU) Erlangen-Nurnberg

2017-11-22

Daniel Hummel 2017-11-22 1 / 81


In this tutorial

The theory behind the enthalpy method for solid-liquid phase changeis briefly introduced,

the implementation of a new solver for the transient simulation ofsolid-liquid phase change problems is described,

new thermophysical models for temperature-dependentthermophysical properties, read from tables, are implemented and

a tutorial case for the melting of a phase change material is set up

Daniel Hummel 2017-11-22 2 / 81


The Enthalpy Method for Solid-Liquid Phase Change

The enthalpy (or enthalpy-porosity) method is a widespread fixed gridmethod for solid-liquid phase change

Prominent contributions by Voller and co-authors, see Voller [7]for a good overview

Enthalpy of a pure substance with distinct melting temperature canbe approximated by

H =

{csT T < Tm

cl + (cs − cl)Tm + L T > Tm(1)

Daniel Hummel 2017-11-22 3 / 81



By defining the liquid volume fraction gl as step function

gl =

{0 TC < Tm

1 TC > Tm,(2)

the enthalpy can be expressed by

H = (1− gl)∫ T

T ref

ρcsdT + gl

∫ T

T ref

ρcldT + ρglL. (3)

The nonlinear term can be isolated into a source term (refer to Voller[7] for details)

ρc∂T

∂t= k∇2T − ∂ρ

∂tglL. (4)

Daniel Hummel 2017-11-22 4 / 81



In phase change problems that involve fluid flow, the conservation of mass,momentum and energy has to be considered – the set of equations to besolved then reads

∂ρ

∂t+∇~u = 0, (5)

ρ∂~u

∂t= µ∇2~u− ~u(∇~u)−∇P + ~Ξ, (6)

ρc∂T

∂t= k∇2T − ρc~u∇T − ∂ρglL

∂t. (7)

Daniel Hummel 2017-11-22 5 / 81



Buoyancy force term is incorporated in a source term ~Ξ in themomentum equation

For constant density but yet the consideration of natural convectiondue to temperature differences: Boussinesq approximation

Buoyancy is expressed by a linear function of the deviation oftemperature

~Γ = ρ~gb(T − Tref), (8)

Temperature-dependent density: no need for the Boussinesqapproximation

Buoyancy force due to density variations can be expressed by

~Γ = ~g(ρ− ρref). (9)

Daniel Hummel 2017-11-22 6 / 81



Besides the buoyancy source term ~Γ, the source term in the momentumequation comprises an additional function

~Ξ = ~Γ + Z~u. (10)

Multiplied by the velocity vector, the velocity treatment function Zbecomes large if the liquid volume fraction tends to zero and therebyforces the velocity in the solid to zero. For isothermal phase changeproblems, Brent et al. [1] suggest the simple function

Z = C(1− gl), (11)

where constant C has an arbitrary large value.

Daniel Hummel 2017-11-22 7 / 81


Thermophysical Properties

Example material for the project: n-octadecane (C18H38)

A parrafin that is frequently used as phase change material

According to experimental data, the thermophysical properties showstrong temperature dependence

Discontinuity at phase change temperature of roughly 300 K

Daniel Hummel 2017-11-22 8 / 81



260 280 300 320 340

2

3

4

·10−3

T (K)

µ(P

as)

Figure: Dynamic viscosity (values originally from Ducoulombier et al. [3],modified)

Daniel Hummel 2017-11-22 9 / 81



240 260 280 300 320 340 360

750

800

850

T (K)

ρ(kgm

−3)

Figure: Density (values originally from Seyer et al. [5] and Velez et al. [6],modified)

Daniel Hummel 2017-11-22 10 / 81



240 260 280 300 320 340 360

1500

2000

2500

T (K)

c(J

kg−1K

−1)

Figure: Specific heat capacity (values originally from Marano et al. [4],modified)

Daniel Hummel 2017-11-22 11 / 81



240 260 280 300 320 340 360

0.2

0.3

0.4

T (K)

k(W

m−1K

−1)

Figure: Thermal conductivity (values originally from Velez et al. [6], modified)

Daniel Hummel 2017-11-22 12 / 81


Introduction and Preparation

Based on buoyantPimpleFoam

Only few modifications are required

solidLiquidPhaseChangeFoam

A solver for the transient simulation of isothermal solid-liquid phasechange with temperature-dependent thermophysical properties

Daniel Hummel 2017-11-22 13 / 81


Introduction and Preparation

The entire directory of buoyantPimpleFoam is copied to the user directoryand renamed to solidLiquidPhaseChangeFoam. After renaming the .C fileand the entry in Make/files accordingly, the path where the executable iscompiled is changed to the user directory.cd $WM_PROJECT_USER_DIR

mkdir --parents applications/solvers/heatTransfer

cp -r $FOAM_SOLVERS/heatTransfer/buoyantPimpleFoam $WM_PROJECT_USER_DIR/applications/solvers/heatTransfer/

cd $WM_PROJECT_USER_DIR/applications/solvers/heatTransfer/

mv buoyantPimpleFoam solidLiquidPhaseChangeFoam

cd solidLiquidPhaseChangeFoam

mv buoyantPimpleFoam.C solidLiquidPhaseChangeFoam.C

sed -i s/"buoyantPimpleFoam"/"solidLiquidPhaseChangeFoam"/g Make/files

sed -i s/"FOAM_APPBIN"/"FOAM_USER_APPBIN"/g Make/files

wclean

wmake

Daniel Hummel 2017-11-22 14 / 81


Modify Momentum Equation

The buoyancy force and velocity treatment source terms are added to theleft hand side of the momentum equation.

vi UEqn.H

Listing 1: UEqn.H

10+ g*(rho-rhoRef)

11+ fvm::Sp(C*(1-gl),U)

Daniel Hummel 2017-11-22 15 / 81


Modify Energy Equation

The enthalpy source term is added to the right hand side of the energyequation.

vi EEqn.H

Listing 2: EEqn.H

22- L*(fvc::ddt(rho, gl))

Daniel Hummel 2017-11-22 16 / 81


Modify Energy Equation

The liquid volume fraction update is added to the bottom of the energyequation. The Cp values from the thermophysical model are stored in anew variable.

Listing 3: EEqn.H

38volScalarField glNew = gl + glRelax*(thermo.T()-Tmelt)*thermo.Cp()/L;

39gl = max(scalar(0), min(glNew, scalar(1)));

40}

41Cp = thermo.Cp();

The energy equation is iterated ten times by adding a simple for-loop atthe top of the energy equation:

Listing 4: EEqn.H

1for (int i=0; i<10; i++ )

Daniel Hummel 2017-11-22 17 / 81


Modify createFields

Fields for the liquid volume fraction and the specific heat (only forpost-processing purposes) are created. All phase-change related constantsare read from the new dictionary phaseChangeProperties.

vi createFields.H

Listing 5: createFields.H

107volScalarField gl

108(

109IOobject

110(

111"gl",

112runTime.timeName(),

113mesh,

114IOobject::MUST_READ,

115IOobject::AUTO_WRITE

116),

117mesh

118);

119120IOdictionary phaseChangeProperties

Daniel Hummel 2017-11-22 18 / 81


Modify createFields


121(

122IOobject

123(

124"phaseChangeProperties",

125runTime.constant(),

126mesh,

127IOobject::MUST_READ_IF_MODIFIED,

128IOobject::NO_WRITE

129)

130);

131132dimensionedScalar rhoRef

133(

134phaseChangeProperties.lookup("rhoRef")

135);

136137dimensionedScalar Tmelt

138(

139phaseChangeProperties.lookup("Tmelt")

140);

141142dimensionedScalar L

143(

144phaseChangeProperties.lookup("L")

145);

Daniel Hummel 2017-11-22 19 / 81


Modify createFields


146147dimensionedScalar C

148(

149phaseChangeProperties.lookup("C")

150);

151152dimensionedScalar glRelax

153(

154phaseChangeProperties.lookup("glRelax")

155);

156157volScalarField Cp

158(

159IOobject

160(

161"Cp",

162runTime.timeName(),

163mesh,

164IOobject::NO_READ,

165IOobject::AUTO_WRITE

166),

167thermo.Cp()

168);

Daniel Hummel 2017-11-22 20 / 81


Compile the solver

The new solver is compiled.

wclean

wmake

Daniel Hummel 2017-11-22 21 / 81


General Procedure

The implementation is mainly adopted from Choquet [2]

Extended by the implementation of a temperature-dependent viscosityand a modified temperature calculation

The Newton-Raphson solver for the temperature calculation inOpenFOAM is replaced by a temperature interpolation from tablevalues

Daniel Hummel 2017-11-22 22 / 81


General Procedure

The implementation requires that the original basic and specie foldersare copied to the user directory

Three main changes are done in the specie folder, where thetransport, equationOfState and thermo models are located.

For the transport model, the model const is copied an modified

The new equationOfState model is based on perfectGas

The new thermo model is derived from hConst

Daniel Hummel 2017-11-22 23 / 81


General Procedure

After some preparatory steps, the modification of const, perfectGas andhConst is similar:

1 Copy existing model and rename folders and files

2 In the .C, .H and I.H files, replace all instances of const with table

or perfectGas with rhoTable or hConst with hTable, respectively(for thermo and transport models, also replace the instantiated typenames in the .H files)

3 The member functions in the I.H files are modified

4 The interpolation files that are included in the I.H files are created

Daniel Hummel 2017-11-22 24 / 81


General Procedure

The temperature is calculated from enthalpy inspecie/thermo/thermo/thermoI.H

For the implementation of the temperature interpolation from tables,steps 4 and 5 also apply

After declaring the new thermophysical model inspecie/include/thermoPhysicsTypes.H andbasic/rhoThermo/rhoThermos.C, the table value files are inserted

Finally, the implementation is completed by compiling both specieand basic libraries

Daniel Hummel 2017-11-22 25 / 81


General Procedure

Interpolations as suggested by Choquet [2]

i = int floor

(fabs

(T − T0dT

))(12)

with T : current temperature, T0: temperature that refers to the firsttable value, dT : temperature difference between table valuesThe temperature at the calculated index is computed by

Ttabulated = T0 + i · dT (13)

Interpolation:

µ = µtabulated(i) + µtabulated(i+ 1)− µtabulated(i) ·(T − Ttabulated

dT

)(14)

µtabulated(i): ith value in the viscosity tableDaniel Hummel 2017-11-22 26 / 81


General Procedure

First, the basic and specie folders are copied into the user directory.

cd $WM_PROJECT_USER_DIR

rm -r src/thermophysicalModels

mkdir --parents src/thermophysicalModels

cp -r $WM_PROJECT_DIR/src/thermophysicalModels/specie $WM_PROJECT_USER_DIR/src/thermophysicalModels/specie

cp -r $WM_PROJECT_DIR/src/thermophysicalModels/basic $WM_PROJECT_USER_DIR/src/thermophysicalModels/basic

cd $WM_PROJECT_USER_DIR/src/thermophysicalModels

Daniel Hummel 2017-11-22 27 / 81


General Procedure

Analogous to the steps executed for the adaption of solver described inSection 1, the Make/files are adopted

sed -i s/"FOAM_LIBBIN"/"FOAM_USER_LIBBIN"/g basic/Make/files

sed -i s/"FOAM_LIBBIN"/"FOAM_USER_LIBBIN"/g specie/Make/files

Daniel Hummel 2017-11-22 28 / 81


General Procedure

vi basic/Make/options

Delete the original path to the specie lnInclude3-I$(LIB_SRC)/thermophysicalModels/specie/lnInclude \

and add one that directs to the new specie model that will be created inthe user project directory.

Listing 8: basic/Make/options

2-I$(LIB_SRC)/transportModels/compressible/lnInclude \

3-I$(WM_PROJECT_USER_DIR)/src/thermophysicalModels/specie/lnInclude \

4-I$(LIB_SRC)/thermophysicalModels/thermophysicalProperties/lnInclude \

In order to direct the compiler to the libraries in the user directory first,add the lines

Listing 9: basic/Make/options

9LIB_LIBS = \

10-L$(FOAM_USER_LIBBIN) \

Daniel Hummel 2017-11-22 29 / 81


Transport

cp -r specie/transport/const/ specie/transport/table

mv specie/transport/table/constTransport.C specie/transport/table/tableTransport.C

mv specie/transport/table/constTransport.H specie/transport/table/tableTransport.H

mv specie/transport/table/constTransportI.H specie/transport/table/tableTransportI.H

sed -i s/"constTransport"/"tableTransport"/g specie/transport/table/*

sed -i s/"const<"/"table<"/g specie/transport/table/tableTransport.H

Daniel Hummel 2017-11-22 30 / 81


Transport

vi specie/transport/table/tableTransportI.H

Daniel Hummel 2017-11-22 31 / 81


Transport

Listing 10: specie/transport/table/tableTransportI.H

82template<class Thermo>

83inline Foam::scalar Foam::tableTransport<Thermo>::mu

84(

85const scalar p,

86const scalar T

87) const

88{

89//return mu_;

90#include "muInterpolation.H"

91}

Daniel Hummel 2017-11-22 32 / 81


Transport



95inline Foam::scalar Foam::tableTransport<Thermo>::kappa

96(

97const scalar p,

98const scalar T

99) const

100{

101//return this->Cp(p, T)*mu(p, T)*rPr_;

102#include "kappaInterpolation.H"

103}

Daniel Hummel 2017-11-22 33 / 81


Transport



107inline Foam::scalar Foam::tableTransport<Thermo>::alphah

108(

109const scalar p,

110const scalar T

111) const

112{

113//return mu(p, T)*rPr_;

114return kappa(p,T)/this->Cpv(p,T);

115}

Daniel Hummel 2017-11-22 34 / 81


Transport

vi specie/transport/table/muInterpolation.H

Listing 13: specie/transport/table/muInterpolation.H

1int i_index;

2scalar dT=1;

3scalar T0=250;

4scalar Temp_tabulated;

5scalar mu_T_tabulated;

67// Dynamic viscosity mus (Pa s):

89scalar mu_tabulated[101]=

10{

11#include "mu.H"

12};

1314// linear interpolation to calculate mu(T) (Pa s)

15i_index = int(floor(fabs((T-T0)/dT)));

16Temp_tabulated = T0+i_index*dT;

17mu_T_tabulated = mu_tabulated[i_index]

18+ (mu_tabulated[i_index+1]-mu_tabulated[i_index])*(T-Temp_tabulated)/dT;

1920return mu_T_tabulated;

Daniel Hummel 2017-11-22 35 / 81


Transport

vi specie/transport/table/kappaInterpolation.H

Listing 14: specie/transport/table/kappaInterpolation.H

1int i_index;

2scalar dT=1;

3scalar T0=250;


5scalar kappa_T_tabulated;

67// Thermal conductivity kappa (W/(m.K)), tabulated :

89scalar kappa_tabulated[101]=

10{

11#include "kappa.H"

12};

1314// linear interpolation to calculate kappa(T) W/(m.K)



17kappa_T_tabulated = kappa_tabulated[i_index]

18+ (kappa_tabulated[i_index+1]-kappa_tabulated[i_index])*(T-Temp_tabulated)/dT;

1920return kappa_T_tabulated;

Daniel Hummel 2017-11-22 36 / 81


Equation of State

cp -r specie/equationOfState/perfectGas/ specie/equationOfState/rhoTable

mv specie/equationOfState/rhoTable/perfectGas.C specie/equationOfState/rhoTable/rhoTable.C

mv specie/equationOfState/rhoTable/perfectGas.H specie/equationOfState/rhoTable/rhoTable.H

mv specie/equationOfState/rhoTable/perfectGasI.H specie/equationOfState/rhoTable/rhoTableI.H

sed -i s/"perfectGas"/"rhoTable"/g specie/equationOfState/rhoTable/*

Daniel Hummel 2017-11-22 37 / 81


Equation of State

vi specie/equationOfState/rhoTable/rhoTableI.H

Listing 15: specie/equationOfState/rhoTable/rhoTableI.H

73template<class Specie>

74inline Foam::scalar Foam::rhoTable<Specie>::rho(scalar p, scalar T) const

75{

76//return p/(this->R()*T);

77#include "rhoInterpolation.H"

78}

Daniel Hummel 2017-11-22 38 / 81


Equation of State



103inline Foam::scalar Foam::rhoTable<Specie>::psi(scalar p, scalar T) const

104{

105//return 1.0/(this->R()*T);

106return 0;

107}

Daniel Hummel 2017-11-22 39 / 81


Equation of State



111inline Foam::scalar Foam::rhoTable<Specie>::Z(scalar p, scalar T) const

112{

113//return 1;

114return 0;

115}

Daniel Hummel 2017-11-22 40 / 81


Equation of State



119inline Foam::scalar Foam::rhoTable<Specie>::CpMCv(scalar p, scalar T) const

120{

121//return this->R();

122return 0;

123}

Daniel Hummel 2017-11-22 41 / 81


Equation of State

vi specie/equationOfState/rhoTable/rhoInterpolation.H

Listing 19: specie/equationOfState/rhoTable/rhoInterpolation.H

1int i_index;

2scalar dT=1;

3scalar T0=250;


5scalar rho_T_tabulated;

67// Density (kg/m^3), tabulated :

8910scalar rho_tabulated[101]=

11{

12#include "rho.H"

13};

1415// linear interpolation to calculate rho(T) in kg/m^3

16i_index = int(fabs(floor((T-T0)/dT)));


18rho_T_tabulated = rho_tabulated[i_index]

19+ (rho_tabulated[i_index+1]-rho_tabulated[i_index])*(T-Temp_tabulated)/dT;

2021return rho_T_tabulated;

Daniel Hummel 2017-11-22 42 / 81


Thermo

cp -r specie/thermo/hConst/ specie/thermo/hTable

mv specie/thermo/hTable/hConstThermo.C specie/thermo/hTable/hTableThermo.C

mv specie/thermo/hTable/hConstThermo.H specie/thermo/hTable/hTableThermo.H

mv specie/thermo/hTable/hConstThermoI.H specie/thermo/hTable/hTableThermoI.H

sed -i s/"hConstThermo"/"hTableThermo"/g specie/thermo/hTable/*

sed -i s/"hConst<"/"hTable<"/g specie/thermo/hTable/hTableThermo.H

Daniel Hummel 2017-11-22 43 / 81


Thermo

vi specie/thermo/hTable/hTableThermoI.H

Listing 20: specie/thermo/hTable/hTableThermoI.H

91template<class EquationOfState>

92inline Foam::scalar Foam::hTableThermo<EquationOfState>::Cp

93(

94const scalar p,

95const scalar T

96) const

97{

98//return Cp_ + EquationOfState::Cp(p, T);

99#include "cpInterpolation.H"

100}

Daniel Hummel 2017-11-22 44 / 81


Thermo



104inline Foam::scalar Foam::hTableThermo<EquationOfState>::Ha

105(

106const scalar p, const scalar T

107) const

108{

109//return Cp_*T + Hf_ + EquationOfState::H(p, T);

110#include "haInterpolation.H"

111}

Daniel Hummel 2017-11-22 45 / 81


Thermo



115inline Foam::scalar Foam::hTableThermo<EquationOfState>::Hs

116(

117const scalar p, const scalar T

118) const

119{

120//return Cp_*T + EquationOfState::H(p, T);

121return Ha(p,T)-Hc();

122}

Daniel Hummel 2017-11-22 46 / 81


Thermo



126inline Foam::scalar Foam::hTableThermo<EquationOfState>::Hc() const

127{

128//return Hf_;

129return 0;

130}

Daniel Hummel 2017-11-22 47 / 81


Thermo

vi specie/thermo/hTable/cpInterpolation.H

Listing 24: specie/thermo/hTable/cpInterpolation.H

1int i_index;

2scalar dT=1;

3scalar T0=250;


5scalar Cp_T_tabulated;

67// Specific heat at constant pressure (J/(kg K)), tabulated :

8scalar Cp_tabulated[101]=

9{

10#include "cp.H"

11};

1213// linear interpolation to calculate Cp(T) in J/(kg.K)



16Cp_T_tabulated = Cp_tabulated[i_index]

17+ (Cp_tabulated[i_index+1]-Cp_tabulated[i_index])*(T-Temp_tabulated)/dT;

1819// return cp(T) in J/(kmol.K)

20return Cp_T_tabulated*this->W();

Daniel Hummel 2017-11-22 48 / 81


Thermo

vi specie/thermo/hTable/haInterpolation.H

Listing 25: specie/thermo/hTable/haInterpolation.H

1int i_index;

2scalar dT=1;

3scalar T0=250;


5scalar h_T_tabulated;

67// enthalpy (J/kg), tabulated:

89scalar h_tabulated[101] =

10{

11#include "ha.H"

12};

1314// linear interpolation to calculate h(T) in J/kg



17h_T_tabulated = h_tabulated[i_index]

18+ (h_tabulated[i_index+1]-h_tabulated[i_index])*(T-Temp_tabulated)/dT;

1920// return h(T) in J/kmol

21return h_T_tabulated*this->W();

Daniel Hummel 2017-11-22 49 / 81


Modify Temperature Calculation

vi specie/thermo/thermo/thermoI.H

Listing 26: specie/thermo/thermo/thermoI.H

30/*template<class Thermo, template<class> class Type>

31//inline Foam::species::thermo<Thermo, Type>::thermo

32//(

33// const Thermo& sp

34//)

35//:

36// Thermo(sp)

37//{}

38//

39//

40//template<class Thermo, template<class> class Type>

41//inline Foam::scalar Foam::species::thermo<Thermo, Type>::T

42//(

43// scalar f,

44// scalar p,

45// scalar T0,

46// scalar (thermo<Thermo, Type>::*F)(const scalar, const scalar) const,

47// scalar (thermo<Thermo, Type>::*dFdT)(const scalar, const scalar)

48// const,

49// scalar (thermo<Thermo, Type>::*limit)(const scalar) const

50//) const

Daniel Hummel 2017-11-22 50 / 81




51//{

52// if (T0 < 0)

53// {

54// FatalErrorInFunction

55// << "Negative initial temperature T0: " << T0

56// << abort(FatalError);

57// }

58//

59// scalar Test = T0;

60// scalar Tnew = T0;

61// scalar Ttol = T0*tol_;

62// int iter = 0;

63//

64// do

65// {

66// Test = Tnew;

67// Tnew =

68// (this->*limit)

69// (Test - ((this->*F)(p, Test) - f)/(this->*dFdT)(p, Test));

70//

71// if (iter++ > maxIter_)

Daniel Hummel 2017-11-22 51 / 81




72// {

73// FatalErrorInFunction

74// << "Maximum number of iterations exceeded: " << maxIter_

75// << abort(FatalError);

76// }

77//

78// } while (mag(Tnew - Test) > Ttol);

79//

80// return Tnew;

81//}*/

8283template<class Thermo, template<class> class Type>

84inline Foam::species::thermo<Thermo, Type>::thermo

85(

86const Thermo& sp

87)

88:

89Thermo(sp)

90{}

Daniel Hummel 2017-11-22 52 / 81




93template<class Thermo, template<class> class Type>

94inline Foam::scalar Foam::species::thermo<Thermo, Type>::T

95(

96scalar f,

97scalar p,

98scalar T0,

99scalar (thermo<Thermo, Type>::*F)(const scalar, const scalar) const,

100scalar (thermo<Thermo, Type>::*dFdT)(const scalar, const scalar) const,

101scalar (thermo<Thermo, Type>::*limit)(const scalar) const

102) const

103{

104#include "TInterpolation.H"

105}

Daniel Hummel 2017-11-22 53 / 81



vi specie/thermo/thermo/TInterpolation.H

Listing 30: specie/thermo/thermo/TInterpolation.H

1int i_index;

2scalar dH=5916.4;

3scalar h0=3.1558e+05;

4scalar enth_tabulated;

5scalar Tnew;

6scalar h = f;

78// Temperature (K), tabulated :

910scalar T_tabulated[101]=

11{

12#include "Th.H"

13};

1415// linear interpolation to calculate T(h) (K)

16i_index = int(floor(fabs((h-h0)/dH)));

17enth_tabulated = h0+i_index*dH;

18Tnew = T_tabulated[i_index] + (T_tabulated[i_index+1]-T_tabulated[i_index])*(h-enth_tabulated)/dH;

1920return Tnew;

Daniel Hummel 2017-11-22 54 / 81


Declaration, Table Insertion and Compilation

Include hTableThermo.H and rhoTable.H in thermoPhysicsTypes.H

vi specie/include/thermoPhysicsTypes.H

Listing 31: specie/include/thermoPhysicsTypes.H

51#include "tableTransport.H"

52#include "rhoTable.H"

53#include "hTableThermo.H"

Daniel Hummel 2017-11-22 55 / 81



Listing 32: specie/include/thermoPhysicsTypes.H

59typedef

60tableTransport

61<

62species::thermo

63<

64hTableThermo

65<

66rhoTable<specie>

67>,

68sensibleEnthalpy

69>

70> tableGasHThermoPhysics;

Daniel Hummel 2017-11-22 56 / 81



vi basic/rhoThermo/rhoThermos.C

Listing 33: basic/rhoThermo/rhoThermos.C

54#include "tableTransport.H"

55#include "hTableThermo.H"

56#include "rhoTable.H"

Listing 34: basic/rhoThermo/rhoThermos.C

64makeThermo

65(

66rhoThermo,

67heRhoThermo,

68pureMixture,

69tableTransport,

70sensibleEnthalpy,

71hTableThermo,

72rhoTable,

73specie

74);

Daniel Hummel 2017-11-22 57 / 81



cp ~/Downloads/hummelTables/rho ./specie/equationOfState/rhoTable/rho.H

cp ~/Downloads/hummelTables/ha ./specie/thermo/hTable/ha.H

cp ~/Downloads/hummelTables/cp ./specie/thermo/hTable/cp.H

cp ~/Downloads/hummelTables/mu ./specie/transport/table/mu.H

cp ~/Downloads/hummelTables/kappa ./specie/transport/table/kappa.H

cp ~/Downloads/hummelTables/Th ./specie/thermo/thermo/Th.H

Daniel Hummel 2017-11-22 58 / 81



cd specie

wclean libso

wmake libso

cd ..

cd basic

wclean libso

wmake libso

Daniel Hummel 2017-11-22 59 / 81


Description and Preparation

hot

T = 333.15 K

top (adiabatic)

bottom (adiabatic)

cold

T = 293.15 KT0 = 293.15 K

88.9 mm

63.5 mm

Figure: Domain with temperature boundaries and dimensions

Daniel Hummel 2017-11-22 60 / 81


Description and Preparation

cd $WM_PROJECT_USER_DIR/run

cp -r $FOAM_TUTORIALS/heatTransfer/buoyantSimpleFoam/buoyantCavity/ ./phaseChangeCavity/

cd phaseChangeCavity

cp $FOAM_TUTORIALS/heatTransfer/buoyantPimpleFoam/hotRoom/system/controlDict ./system/

cp $FOAM_TUTORIALS/heatTransfer/buoyantPimpleFoam/hotRoom/system/fvSolution ./system/

cp $FOAM_TUTORIALS/heatTransfer/buoyantPimpleFoam/hotRoom/system/fvSchemes ./system/

Daniel Hummel 2017-11-22 61 / 81


0 folder

The boundary conditions of patch frontAndBack are changed to empty

for p, p rgh, T and U.

gedit 0/p 0/p_rgh 0/T 0/U

The temperature values are changed to fit the test case:

sed -i s/"293"/"293.15"/g 0/T

sed -i s/"288.15"/"293.15"/g 0/T

sed -i s/"307.75"/"333.15"/g 0/T

Daniel Hummel 2017-11-22 62 / 81


0 folder

Boundary and initial conditions for the liquid volume fraction field gl aregenerated:

vi 0/gl

Listing 35: 0/gl

1FoamFile

2{

3version 2.0;

4format ascii;

5class volScalarField;

6object gl;

7}

8dimensions [0 0 0 0 0 0 0];

9internalField uniform 0;

10boundaryField

11{

12frontAndBack {type empty;}

13topAndBottom {type zeroGradient;}

14hot {type zeroGradient;}

15cold {type zeroGradient;}

16}

Daniel Hummel 2017-11-22 63 / 81


Constant folder

As laminar flow is assumed, the turbulence model is disabled.

sed -i s/"simulationType RAS;"/"simulationType laminar;"/g constant/turbulenceProperties

The entries in thermophysicalProperties are replaced by the table values atthe initial temperature. The acceleration due to gravity is set in thenegative z coordinate.

sed -i s/"28.96"/"254.5"/g constant/thermophysicalProperties

sed -i s/"1004.4"/"1700"/g constant/thermophysicalProperties

sed -i s/"1.831e-05"/"0.0041058"/g constant/thermophysicalProperties

sed -i s/"0.705"/"23.794"/g constant/thermophysicalProperties

sed -i s/"(0 -9.81 0)"/"(0 0 -9.81)"/g constant/g

Daniel Hummel 2017-11-22 64 / 81


Constant folder

The new thermophysical model is used by changing the keywords fortransport, equationOfState and thermo models.

sed -i s/"const"/"table"/g constant/thermophysicalProperties

sed -i s/"hConst"/"hTable"/g constant/thermophysicalProperties

sed -i s/"perfectGas"/"rhoTable"/g constant/thermophysicalProperties

Daniel Hummel 2017-11-22 65 / 81


Constant folder

The values for latent heat of fusion, melting temperature, referencedensity, velocity treatment function constant and liquid volume updaterelaxation factor are set.

vi constant/phaseChangeProperties

Listing 36: constant/phaseChangeProperties

1FoamFile

2{

3version 2.0;

4format ascii;

5class dictionary;

6object transportProperties;

7}

8L L [0 2 -2 0 0 0 0] 212490;

9Tmelt Tmelt [0 0 0 1 0 0 0] 300;

10rhoRef rhoRef [1 -3 0 0 0 0 0] 755.05;

11C C [1 -3 -1 0 0 0 0] 5e4;

12glRelax glRelax [0 0 0 0 0 0 0] 0.9;

Daniel Hummel 2017-11-22 66 / 81


System folder

sed -i s/"76"/"88.9"/g system/blockMeshDict

sed -i s/"260"/"31.75"/g system/blockMeshDict

sed -i s/"(35 150 15)"/"(40 1 30)"/g system/blockMeshDict

In blockMeshDict, the patch type of frontAndBack is changed to empty

and the mesh is created.

vi system/blockMeshDict

blockMesh

Daniel Hummel 2017-11-22 67 / 81


System folder

The simulation is run for 1200 s. The first time step is set to 0.0001 andthen controlled by a Courant Number of 1. Solution directories are writtenfor every 60 seconds.

sed -i s/"2000;"/"1200;"/g system/controlDict

sed -i s/"2;"/"1e-4;"/g system/controlDict

sed -i s/"timeStep;"/"adjustableRunTime;"/g system/controlDict

sed -i s/"100;"/"60;"/g system/controlDict

sed -i s/"no;"/"yes;"/g system/controlDict

sed -i s/"0.5;"/"1;"/g system/controlDict

Daniel Hummel 2017-11-22 68 / 81


System folder

Fields for density, thermal diffusivity, dynamic viscosity and compressibilityare written every 60 seconds.

vi system/controlDict

Listing 37: system/controlDict

52functions

53{

54writeThermophysicalProperties

55{

56type writeObjects;

57libs ("libutilityFunctionObjects.so");

58objects (thermo:alpha thermo:mu thermo:psi thermo:rho thermo:Cp);

59writeControl adjustableRunTime;

60writeInterval 60;

61}

62}

Daniel Hummel 2017-11-22 69 / 81


Run Tutorial and View Results

solidLiquidPhaseChangeFoam >log&

paraFoam -builtin

Daniel Hummel 2017-11-22 70 / 81



Figure: Temperature Field after 1200 s

Daniel Hummel 2017-11-22 71 / 81



Figure: Liquid Volume Fraction Field after 1200 s

Daniel Hummel 2017-11-22 72 / 81



Figure: Density Field After 1200 s

Daniel Hummel 2017-11-22 73 / 81



Figure: Specific Heat Capacity field after 1200 s

Daniel Hummel 2017-11-22 74 / 81



Figure: Dynamic Viscosity Field after 1200 s

Daniel Hummel 2017-11-22 75 / 81



Figure: Thermal Diffusivity Field after 1200 s

Daniel Hummel 2017-11-22 76 / 81


Brent, A. D. et al. “Enthalpy-Porosity Technique for ModelingConvection-Diffusion Phase Change”. In: Numerical Heat Transfer13.3 (1988), 297–318.

Choquet, I. ThermophysicalModels library in OpenFOAM-2.3.x –How to implement a new thermophysical model. 2014. url:www.tfd.chalmers.se/~hani/kurser/OS_CFD_2014/

isabelleChoquet/thermophysicalModels-OF-2.3-

updated_HN141009.pdf.

Ducoulombier, D. et al. “Pressure (1-1000 bars) and Temperature(20-100 ◦C) Dependence of the Viscosity of Liquid Hydrocarbons”.In: The Journal of Physical Chemistry 90.8 (1986), 1692–1700.

Marano, J. J. and Holder, G. D. “A General Equation forCorrelating the Thermophysical Properties of n-Paraffins, n-Olefins,and other Homologous Series. 3. Asymptotic Behavior Correlations

Daniel Hummel 2017-11-22 76 / 81

www.tfd.chalmers.se/~hani/kurser/OS_CFD_2014/isabelleChoquet/thermophysicalModels-OF-2.3-updated_HN141009.pdf




for Thermal and Transport Properties”. In: Industrial & EngineeringChemistry Research 36.6 (1997), 2399–2408.

Seyer, W. F. et al. “The Density and Transition Points of then-Paraffin Hydrocarbons”. In: Journal of the American ChemicalSociety 66.2 (1944), 179–182.

Velez, C. et al. “Temperature-Dependent Thermal Properties ofSolid/Liquid Phase Change Even-Numbered n-Alkanes:n-Hexadecane, n-Octadecane and n-Eicosane”. In: Applied Energy143 (2015), 383–394.

Voller, V. “An Overview of Numerical Methods for Solving PhaseChange Problems”. In: Advances in Numerical Heat Transfer. 1996.

Daniel Hummel 2017-11-22 77 / 81


Solver

cp -r ~/Downloads/solidLiquidPhaseChangeFoam $WM_PROJECT_USER_DIR/applications/solvers/heatTransfer/

Daniel Hummel 2017-11-22 77 / 81


Interpolation Files

cp -r ~/Downloads/hummelInterpolationFiles/rhoInterpolation.H /specie/equationOfState/rhoTable/

rhoInterpolation.H

cp -r ~/Downloads/hummelInterpolationFiles/cpInterpolation.H specie/thermo/hTable/cpInterpolation.H

cp -r ~/Downloads/hummelInterpolationFiles/haInterpolation.H specie/thermo/hTable/haInterpolation.H

cp -r ~/Downloads/hummelInterpolationFiles/TInterpolation.H specie/thermo/thermo/TInterpolation.H

cp -r ~/Downloads/hummelInterpolationFiles/kappaInterpolation.H specie/transport/table/kappaInterpolation.H

cp -r ~/Downloads/hummelInterpolationFiles/muInterpolation.H specie/transport/table/muInterpolation.H

Daniel Hummel 2017-11-22 78 / 81


Tables

cp ~/Downloads/hummelTables/rho ./specie/equationOfState/rhoTable/rho.H

cp ~/Downloads/hummelTables/ha ./specie/thermo/hTable/ha.H

cp ~/Downloads/hummelTables/cp ./specie/thermo/hTable/cp.H

cp ~/Downloads/hummelTables/mu ./specie/transport/table/mu.H

cp ~/Downloads/hummelTables/kappa ./specie/transport/table/kappa.H

cp ~/Downloads/hummelTables/Th ./specie/thermo/thermo/Th.H

Daniel Hummel 2017-11-22 79 / 81


Thermophysical Models

cp -r ~/Downloads/hummelThermophysicalModels/specie $WM_PROJECT_USER_DIR/src/thermophysicalModels/cp -r ~/Downloads/hummelThermophysicalModels/basic $WM_PROJECT_USER_DIR/src/thermophysicalModels/

Daniel Hummel 2017-11-22 80 / 81


Tutorial

cp -r ~/Downloads/phaseChangeCavity $WM_PROJECT_USER_DIR/run/

Daniel Hummel 2017-11-22 81 / 81

modifying buoyantpimplefoam for the simulation of solid

Documents