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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
transportModel Newtonian;
nu [ 0 2 -1 0 0 0 0 ] 1.5e-05;

7.3.2 Bird-Carreau model
The Bird-Carreau model is: ![]() | (7.21) |

transportModel BirdCarreau;
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
The Cross Power Law model is: ![]() | (7.22) |
transportModel CrossPowerLaw;
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,

![]() | (7.23) |
transportModel powerLaw;
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

![]() | (7.24) |
transportModel HerschelBulkley;
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,


![]() | (7.25) |
transportModel Casson;
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:transportModel strainRateFunction;
strainRateFunctionCoeffs
{
function polynomial ((0 0.1) (1 1.3));
}
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OpenFOAM v9 User Guide: 7.3 Transport/rheology models