Arrhenius approximate shear stress law
DESCRIPTION
S = 2 * eta * D
where S is the extra-stress tensor, D is the rate of deformation tensor, and eta is the viscosity.
The temperature dependence
of the viscosity is denoted by a function H(T), where T is the temperature.
H(T) comes as a factor
in the viscosity law which is written as follows :
eta (g,T) = eta (g * H(T)) * H(T)
The approximate Arrhenius
shear stress law is obtained as the first order Taylor expansion of the
original Arrhenius law.
For the Arrhenius
approximate law, the function H(T) is written as follows :
H(T) = exp [ - alpha * ( T - Talpha ) ] .
where alpha is the first order coefficient of the Taylor expansion, Talpha is a reference temperature.
This law differs from
the original Arrhenius approximate law as follows : a time-temperature
equivalence has been
introduced by scaling
the shear rate g by the temperature dependence H(T). The same scaling factor
H(T) therefore
affects the shear
rate in the first equation above.
| -1 | Upper level menu |
| 1 | Modify alfa = 0.0000000E+00 |
| 2 | Modify talfa = 0.0000000E+00 |
A high value of the parameter alpha leads to strong non-linearities. A Picard iteration is recommended insteadSEE ALSO
of a full Newton iteration. In case the program diverges, an evolution scheme (on alpha) must be used.The units for alpha and Talpha are:
parameter mass length time temperature alfa - - - -1 talfa - - - 1
generalized Newtonian fluids (UM) continuum equations (UM) temperature dependence of viscosity (RM) Arrhenius approximate law (RM) evolution (UM) s-dependence (RM) create a new task (RM) system of units (RM)