Manufacturing Solutions

Carreau Yasuda Model

Carreau Yasuda Model

Previous topic Next topic No expanding text in this topic  

Carreau Yasuda Model

Previous topic Next topic JavaScript is required for expanding text JavaScript is required for the print function  

Carreau Yasuda model is expressed by the following equation. This model has five parameters, zero shear viscosity, infinite shear viscosity, time constant, transition parameter, and power law exponent.

cy

This model has a well defined upper (zero shear viscosity) and lower (infinite shear viscosity) limits for the polymer viscosity. Typically, the value of transition parameter is 2. Time constant lambda alters the nonlinear behavior of the fluid and its dependence on the shear rate. If the time constant is 0, then the fluid becomes Newtonian, with a high value for the time constant, eta becomes a strong function of shear rate. By suitable choice of parameters, many other models can be mimicked by this model.

 

Syntax

Syntax of the data packet Polymer is as follows:

Polymer  

PolymerName

{

 

ConstitutuveModel =

"Carreau"

 

Density =

ρ

 

SpecificHeat =

Cp(T)

 

Conductivity =

K(T)

 

CoeffOfThermalExpansion =

βT

 

VolumetricHeatSource =

Qvol

 

TimeConstant =

λ

 

Exponent =

n

 

ZeroShearViscosity =

η0

 

InfiniteShearViscosity =

ηinf

 

TransitionParameter =

a

 

TemperatureDependence =

"None" }

 

Explanation of Parameters

Parameter

Description

Units

Data Type

Condition

Typical Value

ConstitutiveModel

Describes the model used

None

String

Required

"Carreau"

Density

Density of the polymer

kg/m^3

Constant

Required

995.0

SpecificHeat

Specific heat at constant pressure

J/kg/K

Constant / F(T)

Required

2000.0

Conductivity

Thermal conductivity

W/m/K

Constant / F(T)

Required

0.167

CoeffOfThermalExpansion

Indicates the change in volume with change in temperature

1/K

Constant

Required

1.0e-05

VolumetricHeatSource

Heat generated/ removed in the volume by methods like electrical heating

W/m^3

Constant

Required

0.0

Exponent

Power law index, defines the dependency of viscosity on shear rate.

None

Constant

Required

0.66

ZeroShearViscosity

Value of viscosity as shear rate tends to 0

Pa-s

Constant

Required

100.00

InfiniteShearViscosity

Value of viscosity as shear rate tends to infinity

Pa-s

Constant

Required

0.1

TransitionParameter

A parameter of Carreau Yasuda model

None

Constant

Required

2

TimeConstant

A parameter of Carreau Yasuda model

s

Constant

Required

1

TemperatureDependence

See Temperature Dependence

None

String

Required

"WLF"

ReferenceTemperature

Temperature at which data is calculated for the initialization step.

K

Constant

Required only if TD is not "None"

533

FreezeTemperature

This is the no flow temperature. Below this temperature, material ceases to flow.

K

Constant

Required only if TD is not "None"

350

ActivationEnergy

A parameter required by Arrhenius model.

J/mol

Constant

Required only if TD is Exp(Q/RT)

16628

UniversalGasConstant

A parameter from state equation PV = nRT, R is universal Gas constant.

J/mol/K

Constant

Required only if TD is Exp(Q/RT)

8.314

TemperatureSensitivity

A derived parameter which has the same physical meaning as Q/R.

K

Constant

Required only if TD is Exp(Tb/T)

2000 K

WLFConstant1

Constant C1 of WLF model

None

Constant

Required only if TD is WLF

17.44

WLFConstant2

Constant C2 of WLF model. This is like DeltaT, hence the value is same in K and Celsius.

K

Constant

Required only if TD is WLF

51.6

GlassTransitionTemperature

Temperature below with polymer molecules ceases to move (frozen). There are few definitions of this term.

K

Constant

Required only if TD is WLF

320

Beta

Parameter in the relationship Exp(-Beta(DeltaT))

None

Constant

Required only if TD is Exp(-Beta(DeltaT))

0.005

F(T) - Function of Temperature. Can be specified as a TABLE1 or Tcl function.

TD - TemperatureDependence

 

See Also:

Polymer Material Properties