Index

Power law

Ver: 1   DESCRIPTION For a Generalized Newtonian fluid, the constitutive equation has the form
S = 2 eta D
where S is the extra-stress tensor, D is the rate of deformation tensor, and eta is the viscosity.

The shear-rate dependence of the viscosity is denoted by a function F(g), where g is the shear-rate.

For the power law viscosity, the function F(g) is written as follows :
F(g) = fac * (tnat*g)**(expo-1)
where fac is the viscosity corresponding to a shear rate g = 1/tnat,
and expo is the power law index.

Default values : fac = 1, tnat = 1, expo = 1

Selecting an option allows the user to modify the corresponding material parameter.

 
OPTIONS  
 -1   Upper level menu
  1   Modify  fac  = 1.0000000E+00
  2   Modify  tnat = 1.0000000E+00
  3   Modify  expo = 1.0000000E+00
NOTES  
A low value for the power law index expo leads to strong non-linearities.

A Picard iteration is recommended instead of a full Newton iteration for cases where expo < 0.7.
An evolution scheme can also be used, starting from expo=1 (Newtonian fluid) and ending at the desired value.

The units for g and the parameters fac, tnat and expo are :
 
 
parameter
mass
length
time
temperature
g
-
-
-1
 -
tnat
-
-
 1
 -
fac
1
-1
-1
 -
expo
-
-
-
 -

SEE ALSO