OpenFOAM_transportProperties
https://cfd.direct/openfoam/user-guide/transport-rheology/
7.3 Transport/rheology models
In OpenFOAM, solvers that do not include energy/heat, include a library of models for viscosity 
. The models typically relate viscosity to strain rate 
and are specified by the user in the transportProperties dictionary. The available models are listed in the following sections.
7.3.1 Newtonian model
The Newtonian model assumes 
is constant. Viscosity is specified by a dimensionedScalar nu in transportProperties, e.g.
nu [ 0 2 -1 0 0 0 0 ] 1.5e-05;
Note the units for kinematic viscosity are 
.
7.3.2 Bird-Carreau model
![a (n− 1)∕a ν = ν∞ + (ν0 − ν∞ )[1 + (k˙γ) ]](https://cdn.cfd.direct/docs/user-guide-v5/img/user537x.png) |
(7.16) |
where the coefficient 
has a default value of 2. An example specification of the model in transportProperties is:
BirdCarreauCoeffs
{
nu0 [ 0 2 -1 0 0 0 0 ] 1e-03;
nuInf [ 0 2 -1 0 0 0 0 ] 1e-05;
k [ 0 0 1 0 0 0 0 ] 1;
n [ 0 0 0 0 0 0 0 ] 0.5;
}
7.3.3 Cross Power Law model
 |
(7.17) |
An example specification of the model in transportProperties is:
CrossPowerLawCoeffs
{
nu0 [ 0 2 -1 0 0 0 0 ] 1e-03;
nuInf [ 0 2 -1 0 0 0 0 ] 1e-05;
m [ 0 0 1 0 0 0 0 ] 1;
n [ 0 0 0 0 0 0 0 ] 0.5;
}
7.3.4 Power Law model
The Power Law model provides a function for viscosity, limited by minimum and maximum values, 
and 
respectively. The function is:
 |
(7.18) |
An example specification of the model in transportProperties is:
powerLawCoeffs
{
nuMax [ 0 2 -1 0 0 0 0 ] 1e-03;
nuMin [ 0 2 -1 0 0 0 0 ] 1e-05;
k [ 0 2 -1 0 0 0 0 ] 1e-05;
n [ 0 0 0 0 0 0 0 ] 1;
}
7.3.5 Herschel-Bulkley model
The Herschel-Bulkley model combines the effects of Bingham plastic and power-law behavior in a fluid. For low strain rates, the material is modelled as a very viscous fluid with viscosity 
. Beyond a threshold in strain-rate corresponding to threshold stress 
, the viscosity is described by a power law. The model is:
 |
(7.19) |
An example specification of the model in transportProperties is:
HerschelBulkleyCoeffs
{
nu0 [ 0 2 -1 0 0 0 0 ] 1e-03;
tau0 [ 0 2 -2 0 0 0 0 ] 1;
k [ 0 2 -1 0 0 0 0 ] 1e-05;
n [ 0 0 0 0 0 0 0 ] 1;
}
7.3.6 Casson model
The Casson model is a basic model used in blood rheology that specifies minimum and maximum viscosities, 
and 
respectively. Beyond a threshold in strain-rate corresponding to threshold stress 
, the viscosity is described by a “square-root” relationship. The model is:
 |
(7.20) |
An example specification of model parameters for blood is:
CassonCoeffs
{
m [ 0 2 -1 0 0 0 0 ] 3.934986e-6;
tau0 [ 0 2 -2 0 0 0 0 ] 2.9032e-6;
nuMax [ 0 2 -1 0 0 0 0 ] 13.3333e-6;
nuMin [ 0 2 -1 0 0 0 0 ] 3.9047e-6;
}
7.3.7 General strain-rate function
A strainRateFunction model exists that allows a user to specify viscosity as a function of strain rate at run-time. It uses the same Function1 functionality to specify the function of strain-rate, used by time varying properties in boundary conditions described in section 5.2.3.4. An example specification of the model in transportProperties is shown below using the polynomial function:
strainRateFunctionCoeffs
{
function polynomial ((0 0.1) (1 1.3));
}
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