def test_cbrt_values():
m = pyo.ConcreteModel()
flib = functions_lib()
m.cbrt = pyo.ExternalFunction(library=flib, function="cbrt")
assert (abs(pyo.value(m.cbrt(-27.0)) + 3.0) < 0.00001)
assert (abs(pyo.value(m.cbrt(0.0))) < 0.00001)
assert (abs(pyo.value(m.cbrt(27.0)) - 3.0) < 0.00001)
def test_cbrt_hes():
m = pyo.ConcreteModel()
flib = functions_lib()
m.cbrt = pyo.ExternalFunction(library=flib, function="cbrt")
h = 1e-6
tol = 1e-5
for v in [-27.0, -0.5, 0.5, 27]:
f1, g1, h1 = m.cbrt.evaluate_fgh(args=(v, ))
f2, g2, h2 = m.cbrt.evaluate_fgh(args=(v + h, ))
hfd = (g2[0] - g1[0]) / h
assert (abs(h1[0] - hfd) < tol)
def delta_temperature_underwood_callback(b):
"""
This is a callback for a temperaure difference expression to calculate
:math:`\Delta T` in the heat exchanger model using log-mean temperature
difference (LMTD) approximation given by Underwood (1970). It can be
supplied to "delta_temperature_callback" HeatExchanger configuration option.
This uses a cube root function that works with negative numbers returning
the real negative root. This should always evaluate successfully.
"""
# external function that ruturns the real root, for the cuberoot of negitive
# numbers, so it will return without error for positive and negitive dT.
b.cbrt = ExternalFunction(library=functions_lib(), function="cbrt")
dT1 = b.delta_temperature_in
dT2 = b.delta_temperature_out
@b.Expression(b.flowsheet().config.time)
def delta_temperature(b, t):
return ((b.cbrt(dT1[t]) + b.cbrt(dT2[t]))/2.0)**3
def build(self):
"""
Building model
Args:
None
Returns:
None
"""
# Call UnitModel.build to setup dynamics
super().build()
config = self.config
# Add variables
self.overall_heat_transfer_coefficient = Var(
self.flowsheet().config.time,
domain=PositiveReals,
initialize=100,
doc="Overall heat transfer coefficient")
self.overall_heat_transfer_coefficient.latex_symbol = "U"
self.area = Var(domain=PositiveReals,
initialize=1000,
doc="Heat exchange area")
self.area.latex_symbol = "A"
if config.flow_pattern == HeatExchangerFlowPattern.crossflow:
self.crossflow_factor = Var(
self.flowsheet().config.time,
initialize=1,
doc="Factor to adjust coutercurrent flow heat transfer "
"calculation for cross flow.")
if config.delta_temperature_rule == delta_temperature_underwood2_rule:
# Define a cube root function that return the real negative root
# for the cube root of a negative number.
self.cbrt = ExternalFunction(library=functions_lib(),
function="cbrt")
# Add Control Volumes
_make_heater_control_volume(self,
"side_1",
config.side_1,
dynamic=config.dynamic,
has_holdup=config.has_holdup)
_make_heater_control_volume(self,
"side_2",
config.side_2,
dynamic=config.dynamic,
has_holdup=config.has_holdup)
# Add Ports
self.add_inlet_port(name="inlet_1", block=self.side_1)
self.add_inlet_port(name="inlet_2", block=self.side_2)
self.add_outlet_port(name="outlet_1", block=self.side_1)
self.add_outlet_port(name="outlet_2", block=self.side_2)
# Add convienient references to heat duty.
add_object_reference(self, "heat_duty", self.side_2.heat)
self.side_1.heat.latex_symbol = "Q_1"
self.side_2.heat.latex_symbol = "Q_2"
@self.Expression(self.flowsheet().config.time,
doc="Temperature difference at the side 1 inlet end")
def delta_temperature_in(b, t):
if b.config.flow_pattern == \
HeatExchangerFlowPattern.countercurrent:
return b.side_1.properties_in[t].temperature -\
b.side_2.properties_out[t].temperature
elif b.config.flow_pattern == HeatExchangerFlowPattern.cocurrent:
return b.side_1.properties_in[t].temperature -\
b.side_2.properties_in[t].temperature
elif b.config.flow_pattern == HeatExchangerFlowPattern.crossflow:
return b.side_1.properties_in[t].temperature -\
b.side_2.properties_out[t].temperature
else:
raise ConfigurationError(
"Flow pattern {} not supported".format(
b.config.flow_pattern))
@self.Expression(self.flowsheet().config.time,
doc="Temperature difference at the side 1 outlet end")
def delta_temperature_out(b, t):
if b.config.flow_pattern == \
HeatExchangerFlowPattern.countercurrent:
return b.side_1.properties_out[t].temperature -\
b.side_2.properties_in[t].temperature
elif b.config.flow_pattern == HeatExchangerFlowPattern.cocurrent:
return b.side_1.properties_out[t].temperature -\
b.side_2.properties_out[t].temperature
elif b.config.flow_pattern == HeatExchangerFlowPattern.crossflow:
return b.side_1.properties_out[t].temperature -\
b.side_2.properties_in[t].temperature
# Add a unit level energy balance
def unit_heat_balance_rule(b, t):
return 0 == self.side_1.heat[t] + self.side_2.heat[t]
self.unit_heat_balance = Constraint(self.flowsheet().config.time,
rule=unit_heat_balance_rule)
# Add heat transfer equation
self.delta_temperature = Expression(
self.flowsheet().config.time,
rule=config.delta_temperature_rule,
doc="Temperature difference driving force for heat transfer")
self.delta_temperature.latex_symbol = "\\Delta T"
if config.flow_pattern == HeatExchangerFlowPattern.crossflow:
self.heat_transfer_equation = Constraint(
self.flowsheet().config.time,
rule=_cross_flow_heat_transfer_rule)
else:
self.heat_transfer_equation = Constraint(
self.flowsheet().config.time, rule=_heat_transfer_rule)