7.6.20.12.2. Arrhenius_Carreau

Syntax

Viscosity [{of} SpeciesName] = Arrhenius_Carreau [Mu_Zero = mu_zero | Mu_Inf = mu_inf | N = n | A = a | Lambda = lambda | K = k | T_Ref = t_ref | Skip_Sensitivities = skip_sensitivities | Sensitivity_Scaling = sensitivity_scaling | Ramp_Sensitivities_Over_Time = ramp_sensitivities_over_time]

Scope

Aria Material

Summary

This viscosity model is a function of the shear rate (Carreau model) and temperature (Arrhenius model). The two contributions are combined multiplicatively.

$\mu\left(\dot{\gamma},T\right) = \left[\mu_{\infty} + \left(\mu_{\circ} - \mu_{\infty}\right) \left(1 + \left(\lambda\dot{\gamma}\right)^a\right)^{\frac{n-1}{a}} \right] e^{\frac{K}{T}-\frac{K}{T_{ref}}},$

where $\mu_\infty$ is the infinite shear viscosity (defaults to zero), $\mu_\circ$ is the zero shear viscosity, $n$ and $a$ (defaults to 2) are model parameters, $\dot{\gamma}$ is the shear rate, $\lambda$ is a time constant (defaults to 1), $T_{ref}$ is a reference temperature and $K$ is an Arrhenius constant.

Parameter	Value	Default
{of}	{of \| species \| subindex}	–
SpeciesName	string	–
mu_zero	real	–
mu_inf	real	0
n	real	–
a	real	2
lambda	real	1
k	real	–
t_ref	real	–
skip_sensitivities	integer	–
sensitivity_scaling	real	1
ramp_sensitivities_over_time	real	-1