class Mass(Chainable):
def __init__(self, **kwargs):
super(Mass, self).__init__(**kwargs)
self.set_guard('mass', ureg.kg)
self.link_attr('mass', core.mul, density='density', volume='volume')
self.set_guard('density', ureg.kg / ureg.m**3)
self.link_attr('density', core.reciprocal, value='specific_volume')
self.link_attr('density',
density.from_specific_weight,
specific_weight='specific_weight')
self.set_guard('specific_volume', ureg.m**3 / ureg.kg)
self.link_attr('specific_volume', core.reciprocal, value='density')
self.set_guard('specific_weight', ureg.N / ureg.m**3)
mass = Guarded()
density = Guarded()
specific_volume = Guarded()
specific_weight = Guarded()
class Viscosity(Chainable):
def __init__(self, **kwargs):
super(Viscosity, self).__init__(**kwargs)
self.set_guard('viscosity_dynamic', ureg.Pa * ureg.s)
self.link_attr('viscosity_dynamic', core.mul, viscosity_kinematic='viscosity_kinematic', density='density')
self.set_guard('viscosity_kinematic', ureg.m ** 2 / ureg.s)
self.link_attr('viscosity_kinematic', core.div, viscosity_dynamic='viscosity_dynamic', density='density')
viscosity_dynamic = Guarded()
viscosity_kinematic = Guarded()
class Surface(Chainable):
def __init__(self, **kwargs):
super(Surface, self).__init__(**kwargs)
self.set_guard('cross_section', ureg.m**2)
cross_section = Guarded()
class Shearing(Chainable):
def __init__(self, **kwargs):
super(Shearing, self).__init__(**kwargs)
self.set_guard('shear_rate', ureg.s**-1)
shear_rate = Guarded()
class Vector(Chainable):
def __init__(self, **kwargs):
super(Vector, self).__init__(**kwargs)
self.set_guard('coordinate', ureg.m)
coordinate = Guarded()
class Segment(Chainable):
def __init__(self, **kwargs):
super(Segment, self).__init__(**kwargs)
self.set_guard('point_1', ureg.m)
self.set_guard('point_2', ureg.m)
self.set_guard('distance', ureg.m)
self.link_attr('distance',
geometry.distance,
point_1='point_1',
point_2='point_2')
point_1 = Guarded()
point_2 = Guarded()
distance = Guarded()
class Pressure(Chainable):
r"""
Pressure
"""
def __init__(self, **kwargs):
super(Pressure, self).__init__(**kwargs)
self.set_guard('pressure', ureg.Pa, [0., inf])
pressure = Guarded()
class ThermalConductivity(Chainable):
def __init__(self, **kwargs):
super(ThermalConductivity, self).__init__(**kwargs)
self.set_guard('thermal_conductivity', ureg.W / (ureg.m * ureg.K))
self.link_attr('thermal_conductivity', core.reciprocal, value='thermal_conductivity')
self.set_guard('thermal_resistivity', ureg.m * ureg.K / ureg.W)
self.link_attr('thermal_resistivity', core.reciprocal, value='thermal_conductivity')
self.set_guard('thermal_conductance', ureg.W / ureg.K)
self.link_attr('thermal_conductance', core.reciprocal, value='thermal_resistance')
self.set_guard('thermal_resistance', ureg.K / ureg.W)
self.link_attr('thermal_resistance', core.reciprocal, value='thermal_conductance')
self.set_guard('heat_transfer_coeff', ureg.W / (ureg.K * ureg.m ** -2))
self.link_attr('heat_transfer_coeff', core.reciprocal, value='thermal_insulance')
self.set_guard('thermal_insulance', ureg.K * ureg.m ** 2 / ureg.W)
self.link_attr('thermal_insulance', core.reciprocal, value='heat_transfer_coeff')
self.set_guard('thermal_diffusivity', ureg.m ** 2 / ureg.s)
self.link_attr('thermal_diffusivity', thermal.thermal_diffusivity, thermal_conductivity='thermal_conductivity',
density='density', specific_heat_capacity='specific_heat_capacity')
self.set_guard('thermal_transmittance_convection', ureg.K * ureg.m ** 2 / ureg.W)
self.set_guard('thermal_transmittance_radiation', ureg.K * ureg.m ** 2 / ureg.W)
thermal_conductivity = Guarded()
thermal_resistivity = Guarded()
thermal_conductance = Guarded()
thermal_resistance = Guarded()
heat_transfer_coeff = Guarded()
thermal_insulance = Guarded()
thermal_diffusivity = Guarded()
thermal_transmittance_convection = Guarded()
thermal_transmittance_radiation = Guarded()
class VolumeFlow(Surface, Segment):
def __init__(self, **kwargs):
super(VolumeFlow, self).__init__(**kwargs)
self.set_guard('volumeflow', ureg.m**3 / ureg.s)
self.link_attr('volumeflow',
core.mul,
segment='distance',
surface='cross_section',
dt=1. * ureg.s)
volumeflow = Guarded()
class ThermalPolymer(Chainable):
def __init__(self, **kwargs):
super(ThermalPolymer, self).__init__(**kwargs)
self.set_guard('temperature_glass', ureg.degC, [-273.15, inf])
self.link_attr('temperature_glass',
thermal_polymer.temperature_glass,
temperature_melt='temperature_melt')
self.link_attr('temperature_melt',
thermal_polymer.temperature_melt,
temperature_glass='temperature_glass')
temperature_glass = Guarded()
class Thermal(Chainable):
def __init__(self, **kwargs):
super(Thermal, self).__init__(**kwargs)
self.set_guard('temperature', ureg.degC, [-273.15, inf],
'Temperature of the material')
self.set_guard('temperature_melt', ureg.degC, [-273.15, inf],
'Melting temperature of the material')
self.set_guard('temperature_vapor', ureg.degC, [-273.15, inf])
self.set_guard('specific_heat_capacity', ureg.J / (ureg.kg * ureg.K))
self.link_attr('specific_heat_capacity',
thermal.specific_heat_capacity,
thermal_conductivity='thermal_conductivity',
density='density',
thermal_diffusivity='thermal_diffusivity')
self.set_guard('thermal_diffusivity', ureg.m**2 / ureg.s)
self.link_attr('thermal_diffusivity',
thermal.thermal_diffusivity,
thermal_conductivity='thermal_conductivity',
specific_heat_capacity='specific_heat_capacity',
density='density')
self.set_guard('thermal_conductivity', ureg.W / (ureg.m * ureg.K))
self.link_attr('thermal_conductivity',
thermal.thermal_conductivity,
thermal_diffusivity='thermal_diffusivity',
specific_heat_capacity='specific_heat_capacity',
density='density')
self.set_guard('thermal_expansion_coeff', ureg.um / (ureg.m * ureg.K))
temperature = Guarded()
r"""Temperature of a material """
temperature_melt = Guarded()
temperature_vapor = Guarded()
specific_heat_capacity = Guarded()
thermal_diffusivity = Guarded()
thermal_conductivity = Guarded()
thermal_expansion_coeff = Guarded()
class TwoDomainTaitpvT(Chainable):
r"""
The modified 2-domain Tait pvT model is used to determine the density of the material as a function of the temperature and pressure. This variation impacts on many aspects of the flow simulation.
The 2-domain Tait pvT model is given by the following equations:
.. math::
v(T, p)=v_{0}(T)\left[1-C \ln \left(1+\frac{p}{B(T)}\right)\right]+v_{t}(T, p)
where:
* :math:`v(T, p)` is the specific geometry at temperature and pressure
* :math:`v_0` is the specific geometry at zero gauge pressure
* :math:`T` is the temperature
* :math:`p` is the pressure
* :math:`C` is a constant
* :math:`B` accounts for the pressure sensitivity of the material
The input for fully specified state:
* b_1s
* b_1m
* b_2s
* b_2m
* b_3s
* b_3m
* b_4s
* b_4m
* b_5
* b_6
* b_7
* b_8
* b_9
* temperature
* pressure
"""
@cite('osswald_polymer_2006')
def __init__(self, **kwargs):
super(TwoDomainTaitpvT, self).__init__(**kwargs)
self.temperature_transition = self.temperature_transition # need for initialization of material state
self.set_guard('_B', ureg.Pa)
self.link_attr('_B',
twodomaintaitpvt.get_B,
T='temperature',
b_3='_b_3',
b_4='_b_4',
b_5='b_5')
self.set_guard('b_1s', ureg.m**3 / ureg.kg)
self.set_guard('b_1m', ureg.m**3 / ureg.kg)
self.set_guard('_b_1', ureg.m**3 / ureg.kg)
self.link_attr('_b_1',
twodomaintaitpvt.switch_m_s,
T='temperature',
T_t='temperature_transition',
s='b_1s',
m='b_1m')
self.set_guard('b_2s', ureg.m**3 / (ureg.kg * ureg.K))
self.set_guard('b_2m', ureg.m**3 / (ureg.kg * ureg.K))
self.set_guard('_b_2', ureg.m**3 / (ureg.kg * ureg.K))
self.link_attr('_b_2',
twodomaintaitpvt.switch_m_s,
T='temperature',
T_t='temperature_transition',
s='b_2s',
m='b_2m')
self.set_guard('b_3s', ureg.Pa)
self.set_guard('b_3m', ureg.Pa)
self.set_guard('_b_3', ureg.Pa)
self.link_attr('_b_3',
twodomaintaitpvt.switch_m_s,
T='temperature',
T_t='temperature_transition',
s='b_3s',
m='b_3m')
self.set_guard('b_4s', ureg.K**-1)
self.set_guard('b_4m', ureg.K**-1)
self.set_guard('_b_4', ureg.K**-1)
self.link_attr('_b_4',
twodomaintaitpvt.switch_m_s,
T='temperature',
T_t='temperature_transition',
s='b_4s',
m='b_4m')
self.set_guard('b_5', ureg.K)
self.set_guard('b_6', ureg.K / ureg.Pa)
self.set_guard('b_7', ureg.m**3 / ureg.kg)
self.set_guard('b_8', ureg.K**-1)
self.set_guard('b_9', ureg.Pa**-1)
self.set_guard('specific_volume_zero_gauge_pressure',
ureg.m**3 / ureg.kg)
self.link_attr('specific_volume_zero_gauge_pressure',
twodomaintaitpvt.get_v_0,
T='temperature',
b_1='_b_1',
b_2='_b_2',
b_5='b_5')
self.set_guard('specific_volume_transition_temperature',
ureg.m**3 / ureg.kg)
self.link_attr('specific_volume_transition_temperature',
twodomaintaitpvt.get_v_t,
p='pressure',
T='temperature',
T_t='temperature_transition',
b_5='b_5',
b_7='b_7',
b_8='b_8',
b_9='b_9')
self.link_attr('specific_volume',
twodomaintaitpvt.get_specific_volume,
p='pressure',
v_0='specific_volume_zero_gauge_pressure',
v_t='specific_volume_transition_temperature',
B='_B')
self.set_guard('temperature_transition', ureg.degC)
self.link_attr('temperature_transition',
twodomaintaitpvt.get_T_t,
p='pressure',
b_5='b_5',
b_6='b_6')
_B = Guarded()
b_1s = Guarded()
b_1m = Guarded()
_b_1 = Guarded()
b_2s = Guarded()
b_2m = Guarded()
_b_2 = Guarded()
b_3m = Guarded()
b_3s = Guarded()
_b_3 = Guarded()
b_4m = Guarded()
b_4s = Guarded()
_b_4 = Guarded()
b_5 = Guarded()
b_6 = Guarded()
b_7 = Guarded()
b_8 = Guarded()
b_9 = Guarded()
specific_volume_zero_gauge_pressure = Guarded()
specific_volume_transition_temperature = Guarded()
temperature_transition = Guarded()
class CrossWLF(Chainable):
r"""
This 6-parameter model considers the effects of shear rate and temperature on the viscosity. Similar to the Bird-Carreau model,
this model describes both Newtonian and shear thinning behavior. The shear thinning part is modeled by the general Cross equation,\
which is a popular and earlier alternative to the Bird-Carreau-Yasuda model:
"""
@cite('osswald_polymer_2015')
def __init__(self, **kwargs):
super(CrossWLF, self).__init__(**kwargs)
self.set_guard('A_1', ureg.dimensionless)
self.set_guard('A_2', ureg.K, [0., inf])
self.set_guard('D_1', ureg.Pa * ureg.s)
self.set_guard('D_2', ureg.K)
self.set_guard('D_3', ureg.K / ureg.Pa)
self.set_guard('n', ureg.dimensionless)
self.set_guard('tau_star', ureg.Pa)
self.link_attr('tau_star', crosswlf.critical_shear_stress, n='n')
self.link_attr('temperature_glass',
crosswlf.glass_transition_temperature,
D_2='D_2',
D_3='D_3',
p='pressure')
self.link_attr('viscosity_zero_shear_rate',
crosswlf.zero_shear_viscosity,
temperature='temperature',
D_1='D_1',
temperature_glass_transition='temperature_glass',
A_1='A_1',
A_2='A_2')
self.link_attr('viscosity_dynamic',
crosswlf.viscosity_dynamic,
shear_rate='shear_rate',
tau_star='tau_star',
zero_shear_viscosity='viscosity_zero_shear_rate',
n='n')
A_1 = Guarded()
A_2 = Guarded()
D_1 = Guarded()
D_2 = Guarded()
D_3 = Guarded()
n = Guarded()
tau_star = Guarded()
viscosity_zero_shear_rate = Guarded()
class Volume(Chainable):
def __init__(self, **kwargs):
super(Volume, self).__init__(**kwargs)
self.set_guard('volume', ureg.m**3)
volume = Guarded()
class CrossArrhenius(Chainable):
r"""
The model is based on the assumption that the fluid flow obeys the Arrhenius equation for molecular kinetics.
.. math::
\eta(T, \dot{\gamma})=\frac{\eta_{0}(T)}{1+(\lambda(T) \dot{\gamma})^{a}}
where:
* :math:`\eta_{0}\left(T_{\mathrm{ref}}\right)` zero shear rate viscosity at reference temperature
* :math:`\lambda\left(T_{\text { ref }}\right)` “relaxation time” at reference temperature
* :math:`a` “shear-thinning”constant
* :math:`E_{\mathrm{a}}` Arrhenius activation energy
* :math:`R` gas constant
* :math:`T` temperature
* :math:`T_{ref}` reference temperature
The input for fully specified state:
* temperature
* temperature_cross_arrhenius_ref
* arrhenius_activation_energy
* relaxation_time_ref
* shear_rate
* shear_thinning_const
* viscosity_zero_shear_rate_ref
"""
@cite('osswald_polymer_2006')
def __init__(self, **kwargs):
super(CrossArrhenius, self).__init__(**kwargs)
self.set_guard('arrhenius_activation_energy', ureg.J / ureg.mol)
self.set_guard('_arrhenius', ureg.dimensionless)
self.link_attr(
'_arrhenius',
crossarrhenius.arrhenius_shift,
temperature='temperature',
arrhenius_activation_energy='arrhenius_activation_energy',
temperature_ref='temperature_cross_arrhenius_ref')
self.set_guard('relaxation_time', ureg.s)
self.link_attr(
'relaxation_time',
crossarrhenius.relaxation_time,
relaxation_time_ref='relaxation_time_ref',
zero_shear_viscosity_ref='viscosity_zero_shear_rate_ref')
self.set_guard('relaxation_time_ref', ureg.s)
self.link_attr('viscosity_dynamic',
crossarrhenius.viscosity_dynamic,
shear_rate='shear_rate',
zero_shear_viscosity='viscosity_zero_shear_rate',
relaxation_time='relaxation_time',
shear_thinning_const='shear_thinning_const')
self.set_guard('viscosity_zero_shear_rate', ureg.Pa * ureg.s)
self.link_attr(
'viscosity_zero_shear_rate',
crossarrhenius.zero_shear_viscosity,
arrhenius='_arrhenius',
zero_shear_viscosity_ref='viscosity_zero_shear_rate_ref')
self.set_guard('viscosity_zero_shear_rate_ref', ureg.Pa * ureg.s)
self.set_guard('shear_thinning_const', ureg.dimensionless)
self.set_guard('temperature_cross_arrhenius_ref', ureg.degC)
arrhenius_activation_energy = Guarded()
_arrhenius = Guarded()
relaxation_time = Guarded()
relaxation_time_ref = Guarded()
viscosity_zero_shear_rate = Guarded()
viscosity_zero_shear_rate_ref = Guarded()
shear_thinning_const = Guarded()
temperature_cross_arrhenius_ref = Guarded()