Embed Size (px)
Citation preview
Non-Newtonian Models in OpenFOAM,
Implementation a non-Newtonian model
Naser Hamedi
Energy Sciences Department, Fluid Mechanics Division, Lund University
Contents
• Non-Newtonian fluids
• Non-Newtonian models in OpenFOAM
• TransportModels in OpenFOAM
• Casson model
• Shear rate
• Non-Newtonian solvers
• Adding Casson model to OpenFOAM
• Run the channel flow case
Non-Newtonian fluid
• . In Newtonian fluids, the strain shear rate is linearly
dependent to shear stress with a constant coefficient
which is called viscosity.
𝜏 = 𝜇 𝛾
• Fluids in which shear stress is not directly
proportional to deformation rate are non-Newtonian
flow.
• Examples: Toothpaste and paint.
Non-newtonian curves
Chhabra, R. P. and Richardson, J. F., Non-Newtonian flow in the process industries: Fundamentals
and engineering Applications. Butterworth-Heinemann, Oxford, (1999).
Non-Newtonian models in OpenFOAM
Non-Newtonian Model Mathematical Eq. Coefficient
powerLaw 𝜂 = 𝐾 𝛾𝑛−1K: Consistency index
𝛾: Shear rate
n: power law index
CrossPwerLaw 𝜂 =𝜂0−𝜂𝑖𝑛𝑓
1+ 𝑚 𝛾 𝑛+𝜂𝑖𝑛𝑓
m: time constant
𝜂0: lower bound viscosity
𝜂𝑖𝑛𝑓: upper bound viscosity
𝛾: Shear rate
HerschelBulckley 𝜂 = 𝜏𝑦 + 𝑘 𝛾 𝑛−1
𝜏𝑦: yield stress
𝑘: time constant
𝛾: Shear strain rate
BirdCarrea 𝜂 = 𝜂𝑖𝑛𝑓 + 𝜂0 − 𝜂𝑖𝑛𝑓 1 + 𝑘 𝛾 𝑛−1
k: time constant
𝜂0: lower bound viscosity
𝜂𝑖𝑛𝑓: upper bound viscosity
𝛾: Shear rate
viscosityModel in OpenFOAM is a defined as an abstract class (powerLaw, HerschelBuckley, etc).
TransportModels in OpenFOAM
• The transport model library in OpenFOAM is classified into two
base classes, transport models and viscosity models.
• The role of the transport models is not transporting the
properties. On the other words, the viscosity is made accessible
by transport models.
• There are two implementations of transport model classes,singlePhaseTransportModel and
incompressibleTwoPhaseMixer.
• All of the single phase solvers in OpenFOAM uses singlePhaseTransportModel to calculate the viscosity
nu().
• additional data stored by incompressibleTwoPhaseMixer
Casson model
• Many models have been developed to describe the blood
viscosity. The Casson model is the most widely used
model to model the human blood:
• 𝜂 =𝜏𝑦
𝛾+ 𝑚
• η is the viscosity, τy is yield stress, 𝛾 is shear strain rate
(1/s) and m is consistency index.
Strain rate
• The shear strain rate (strainRate()) is a member
function in viscosityModel class which is defined in viscosityModel.C:
Foam::tmp<Foam::volScalarField>
Foam::viscosityModel::strainRate() const
{
return sqrt(2.0)*mag(symm(fvc::grad(U_)));
}
Non-Newtonian solvers in OpenFOAM
SimpleFoamSteady state solver for incompressible, turbulent flow of non-
Newtonian fluid
nonNewtonianIcoFoamTransient solver for incompressible, laminar flow of non-Newtonian
fluid
PISOFoamTransient solver for incompressible, turbulent flow of non-Newtonian
fluid
nonNewtonianicoFoam
• The only difference between icoFoam and nonNewtonianIcoFoam
is the fluid (an object) which is defined in nonNewtonianIcoFoam to
access to all member functions and member data of singlephaseTransportModel.
• Fluid is defined in createField.H.
fvVectorMatrix UEqn
(
fvm::ddt(U)
+ fvm::div(phi, U)
- fvm::laplacian(fluid.nu(), U)
);
solve(UEqn == -fvc::grad(p))
Adding Casson model-1
• The viscosity models are located in:
$FOAM_SRC/transportModels/incompressible/viscosityModels
• To make a new viscosity model, first we make copy a viscosity model e.g. BirdCarrea model in a directory that we create
in the OpenFOAM installation:
cd $WM_PROJECT_DIR
cp -r --parents \ src/transportModels/incompressible/viscosityModels/BirdCarreau/ \
$WM_PROJECT_USER_DIR/
cd $WM_PROJECT_USER_DIR/src/transportModels/incompressible/viscosityModels
mv BirdCarreau Casson
cd Casson
mv BirdCarreau.C Casson.C
mv BirdCarreau.H Casson.H
sed -i s/BirdCarreau/Casson/g Casson.C
sed –i s/BirdCarreau/Casson/g Casson.H
Adding Casson model-2
• We also need Make/files and Make/options:
mkdir Make
• Create Make/files and add Casson model to it:
Casson.C
LIB = $(FOAM_USER_LIBBIN)/libCasson
• Create Make/options:
EXE_INC = \
-I$(LIB_SRC)/transportModels/incompressible/lnInclude \
-I$(LIB_SRC)/finiteVolume/lnInclude
LIB_LIBS = \
-lfiniteVolume
Adding Casson model-2
• In Casson.C to define the viscosity function:
return max
(
nuMin_,
min
(
nuMax_,
pow
(
pow(
tau0_/max
(
strainRate(),
dimensionedScalar("VSMALL", dimless/dimTime, VSMALL)
),0.5
)
+pow(m_,0.5)
,
scalar(2.0)
)
)
);
𝜂 =𝜏𝑦
𝛾+ 𝑚
• The key note to define the Casson non-Newtonian model is defining the values in which the model
function shows singularity.
• We have to define some values for the viscosity in very high value (as nuMax) and very low value (as
nuMin).
Adding Casson model-3
• In Casson.C to define the constructors:
m_(CassonCoeffs_.lookup("m")),
tau0_(CassonCoeffs_.lookup("tau0")),
nuMin_(CassonCoeffs_.lookup("nuMin")),
nuMax_(CassonCoeffs_.lookup("nuMax")),
CassonCoeffs_.lookup("m") >> m_;
CassonCoeffs_.lookup("tau0") >> tau0_;
CassonCoeffs_.lookup("nuMin") >> nuMin_;
CassonCoeffs_.lookup("nuMax") >> nuMax_;
• In Casson.C to define the member functions:
• In Casson.H in class Casson decleration:
dimensionedScalar m_;
dimensionedScalar tau0_;
dimensionedScalar nuMin_;
dimensionedScalar nuMax_;
• To compile: wmake libso
Run the 2D-channel flow case
• Channel 50×1×0.1 (m3)
• Long enough channel length to have fully-developed velocity profile
• The discretized domain was created in ANSYS ICEM and exported with .msh extension.
• To export in OpenFOAM:
fluentMeshtoFoam fluent.msh
Name of the file
0/pFoamFile
{
version 2.0;
format ascii;
class volScalarField;
object p;
}
// * * * * * * * * * * * * * * * * * * * * * *
* * * * * * * * * * * * * * * //
dimensions [0 2 -2 0 0 0 0];
internalField uniform 0;
boundaryField
{
INLET
{
type zeroGradient;
}
OUTLET
{
type fixedValue;
value uniform 0;
}
FIXED_WALLS
{
type zeroGradient;
}
FRONT_AND_BACK
{
type empty;
}
}
//
****************************************
********************************* //
0/Udimensions [0 1 -1 0 0 0 0];
internalField uniform (0 0 0);
boundaryField
{
INLET
{
type fixedValue;
value uniform (1 0 0);
}
OUTLET
{
type zeroGradient;
}
FIXED_WALLS
{
type fixedValue;
value uniform (0 0 0);
}
FRONT_AND_BACK
{
type empty;
}
}
Run the 2D-channel flow case
• In constant/transportProperties we add:
transportModel Casson;
.
.
.
.
CassonCoeffs
{
m m [ 0 2 -1 0 0 0 0 ] 0.00414;
tau0 tau0 [0 2 -2 0 0 0 0] 0.0038;
nuMin nuMin [0 2 -1 0 0 0 0] 0.0001;
nuMax nuMax [0 2 -1 0 0 0 0] 100;
}
Run the 2D-channel flow case
• In system/controlDict:
application nonNewtonianIcoFoam;.
.
.
.
libs
(
"libCasson.so"
);
• And finally:
nonNewtonianIcoFoam
Results
INLET
Naser HamediEmail: [email protected]
