425 lines
15 KiB
Python
425 lines
15 KiB
Python
from __future__ import annotations
|
|
|
|
from app.simulation.core.errors import RecoverableTrialStateError
|
|
|
|
from dataclasses import dataclass
|
|
from math import acos, cos, isfinite, log, pi, sqrt
|
|
|
|
from app.simulation.performance import profile_property
|
|
|
|
UNIVERSAL_GAS_CONSTANT = 8.31446261815324
|
|
# Simcenter Amesim 2404 ``sag_reinit_eos_`` keeps more digits than the
|
|
# commonly printed Peng-Robinson constants 0.45724 and 0.07780.
|
|
PENG_ROBINSON_A_COEFFICIENT = 0.457235583
|
|
PENG_ROBINSON_B_COEFFICIENT = 0.07779607
|
|
|
|
|
|
@dataclass(frozen=True)
|
|
class PengRobinsonFluid:
|
|
"""Pure-fluid Peng-Robinson equation-of-state helper.
|
|
|
|
The class covers the equation-of-state layer plus the enthalpy departure
|
|
needed to compare AMESim pneumatic ``pn2hpti`` reference enthalpy flows.
|
|
"""
|
|
|
|
name: str
|
|
molar_mass: float
|
|
critical_temperature: float
|
|
critical_pressure: float
|
|
acentric_factor: float
|
|
|
|
@property
|
|
def specific_gas_constant(self) -> float:
|
|
return UNIVERSAL_GAS_CONSTANT / self.molar_mass
|
|
|
|
@property
|
|
def a_parameter(self) -> float:
|
|
return (
|
|
PENG_ROBINSON_A_COEFFICIENT
|
|
* UNIVERSAL_GAS_CONSTANT
|
|
* UNIVERSAL_GAS_CONSTANT
|
|
* self.critical_temperature
|
|
* self.critical_temperature
|
|
/ self.critical_pressure
|
|
)
|
|
|
|
@property
|
|
def b_parameter(self) -> float:
|
|
return (
|
|
PENG_ROBINSON_B_COEFFICIENT
|
|
* UNIVERSAL_GAS_CONSTANT
|
|
* self.critical_temperature
|
|
/ self.critical_pressure
|
|
)
|
|
|
|
@property
|
|
def kappa(self) -> float:
|
|
omega = self.acentric_factor
|
|
return 0.37464 + 1.54226 * omega - 0.26992 * omega * omega
|
|
|
|
def alpha(self, temperature: float) -> float:
|
|
self._validate_temperature(temperature)
|
|
reduced_temperature = temperature / self.critical_temperature
|
|
return (1.0 + self.kappa * (1.0 - sqrt(reduced_temperature))) ** 2.0
|
|
|
|
def alpha_temperature_derivative(self, temperature: float) -> float:
|
|
self._validate_temperature(temperature)
|
|
reduced_temperature = temperature / self.critical_temperature
|
|
sqrt_reduced_temperature = sqrt(reduced_temperature)
|
|
alpha_base = 1.0 + self.kappa * (1.0 - sqrt_reduced_temperature)
|
|
return -(
|
|
alpha_base
|
|
* self.kappa
|
|
/ (self.critical_temperature * sqrt_reduced_temperature)
|
|
)
|
|
|
|
def alpha_temperature_second_derivative(self, temperature: float) -> float:
|
|
self._validate_temperature(temperature)
|
|
reduced_temperature = temperature / self.critical_temperature
|
|
sqrt_reduced_temperature = sqrt(reduced_temperature)
|
|
alpha_base = 1.0 + self.kappa * (1.0 - sqrt_reduced_temperature)
|
|
return (
|
|
self.kappa
|
|
/ (2.0 * self.critical_temperature * self.critical_temperature)
|
|
* (
|
|
self.kappa / reduced_temperature
|
|
+ alpha_base / (reduced_temperature * sqrt_reduced_temperature)
|
|
)
|
|
)
|
|
|
|
def attractive_parameter(self, temperature: float) -> float:
|
|
return self.a_parameter * self.alpha(temperature)
|
|
|
|
def attractive_parameter_temperature_derivative(self, temperature: float) -> float:
|
|
return self.a_parameter * self.alpha_temperature_derivative(temperature)
|
|
|
|
def attractive_parameter_temperature_second_derivative(
|
|
self,
|
|
temperature: float,
|
|
) -> float:
|
|
return self.a_parameter * self.alpha_temperature_second_derivative(temperature)
|
|
|
|
@profile_property(
|
|
"pressure_from_molar_volume",
|
|
layer="kernel",
|
|
minimum_mode="audit",
|
|
)
|
|
def pressure_from_molar_volume(self, temperature: float, molar_volume: float) -> float:
|
|
self._validate_temperature(temperature)
|
|
if molar_volume <= self.b_parameter:
|
|
raise RecoverableTrialStateError("Molar volume must be larger than Peng-Robinson b parameter.")
|
|
a_alpha = self.attractive_parameter(temperature)
|
|
b = self.b_parameter
|
|
repulsive = UNIVERSAL_GAS_CONSTANT * temperature / (molar_volume - b)
|
|
attractive = a_alpha / (molar_volume * (molar_volume + b) + b * (molar_volume - b))
|
|
return repulsive - attractive
|
|
|
|
@profile_property(
|
|
"pressure_from_density",
|
|
layer="kernel",
|
|
minimum_mode="audit",
|
|
)
|
|
def pressure_from_density(self, temperature: float, density: float) -> float:
|
|
if density <= 0.0:
|
|
raise ValueError("Density must be positive.")
|
|
return self.pressure_from_molar_volume(temperature, self.molar_mass / density)
|
|
|
|
@profile_property(
|
|
"pressure_temperature_derivative_at_density",
|
|
layer="kernel",
|
|
minimum_mode="audit",
|
|
)
|
|
def pressure_temperature_derivative_at_density(
|
|
self,
|
|
temperature: float,
|
|
density: float,
|
|
) -> float:
|
|
self._validate_temperature(temperature)
|
|
if density <= 0.0:
|
|
raise ValueError("Density must be positive.")
|
|
molar_volume = self.molar_mass / density
|
|
if molar_volume <= self.b_parameter:
|
|
raise RecoverableTrialStateError(
|
|
"Molar volume must be larger than Peng-Robinson b parameter."
|
|
)
|
|
b = self.b_parameter
|
|
denominator = molar_volume * (molar_volume + b) + b * (molar_volume - b)
|
|
return (
|
|
UNIVERSAL_GAS_CONSTANT / (molar_volume - b)
|
|
- self.attractive_parameter_temperature_derivative(temperature) / denominator
|
|
)
|
|
|
|
@profile_property(
|
|
"pressure_density_derivative_at_temperature",
|
|
layer="kernel",
|
|
minimum_mode="audit",
|
|
)
|
|
def pressure_density_derivative_at_temperature(
|
|
self,
|
|
temperature: float,
|
|
density: float,
|
|
) -> float:
|
|
self._validate_temperature(temperature)
|
|
if density <= 0.0:
|
|
raise ValueError("Density must be positive.")
|
|
molar_volume = self.molar_mass / density
|
|
if molar_volume <= self.b_parameter:
|
|
raise RecoverableTrialStateError(
|
|
"Molar volume must be larger than Peng-Robinson b parameter."
|
|
)
|
|
b = self.b_parameter
|
|
denominator = molar_volume * (molar_volume + b) + b * (molar_volume - b)
|
|
pressure_molar_volume_derivative = (
|
|
-UNIVERSAL_GAS_CONSTANT * temperature / (molar_volume - b) ** 2
|
|
+ self.attractive_parameter(temperature)
|
|
* 2.0
|
|
* (molar_volume + b)
|
|
/ denominator**2
|
|
)
|
|
molar_volume_density_derivative = -self.molar_mass / (density * density)
|
|
return pressure_molar_volume_derivative * molar_volume_density_derivative
|
|
|
|
def reduced_parameters(self, pressure: float, temperature: float) -> tuple[float, float]:
|
|
self._validate_pressure_temperature(pressure, temperature)
|
|
a_alpha = self.attractive_parameter(temperature)
|
|
b = self.b_parameter
|
|
A = a_alpha * pressure / (UNIVERSAL_GAS_CONSTANT * UNIVERSAL_GAS_CONSTANT * temperature * temperature)
|
|
B = b * pressure / (UNIVERSAL_GAS_CONSTANT * temperature)
|
|
return A, B
|
|
|
|
@profile_property(
|
|
"compressibility_roots",
|
|
layer="kernel",
|
|
minimum_mode="audit",
|
|
)
|
|
def compressibility_roots(self, pressure: float, temperature: float) -> tuple[float, ...]:
|
|
A, B = self.reduced_parameters(pressure, temperature)
|
|
coefficients = (
|
|
-(1.0 - B),
|
|
A - 3.0 * B * B - 2.0 * B,
|
|
-(A * B - B * B - B * B * B),
|
|
)
|
|
roots = _real_cubic_roots(*coefficients)
|
|
physical_roots = tuple(sorted(root for root in roots if root > B and isfinite(root)))
|
|
if not physical_roots:
|
|
raise ValueError("Peng-Robinson cubic produced no physical compressibility root.")
|
|
return physical_roots
|
|
|
|
@profile_property(
|
|
"compressibility_factor",
|
|
layer="kernel",
|
|
minimum_mode="audit",
|
|
)
|
|
def compressibility_factor(
|
|
self,
|
|
pressure: float,
|
|
temperature: float,
|
|
phase: str = "vapor",
|
|
) -> float:
|
|
roots = self.compressibility_roots(pressure, temperature)
|
|
if phase == "vapor":
|
|
return roots[-1]
|
|
if phase == "liquid":
|
|
return roots[0]
|
|
if phase == "stable-single-root":
|
|
return roots[-1]
|
|
raise ValueError(f"Unsupported phase selector: {phase!r}")
|
|
|
|
@profile_property(
|
|
"molar_volume",
|
|
layer="kernel",
|
|
minimum_mode="audit",
|
|
)
|
|
def molar_volume(
|
|
self,
|
|
pressure: float,
|
|
temperature: float,
|
|
phase: str = "vapor",
|
|
) -> float:
|
|
z = self.compressibility_factor(pressure, temperature, phase=phase)
|
|
return z * UNIVERSAL_GAS_CONSTANT * temperature / pressure
|
|
|
|
@profile_property("density", layer="kernel", minimum_mode="audit")
|
|
def density(
|
|
self,
|
|
pressure: float,
|
|
temperature: float,
|
|
phase: str = "vapor",
|
|
) -> float:
|
|
return self.molar_mass / self.molar_volume(pressure, temperature, phase=phase)
|
|
|
|
@profile_property(
|
|
"residual_specific_enthalpy",
|
|
layer="kernel",
|
|
minimum_mode="audit",
|
|
)
|
|
def residual_specific_enthalpy(
|
|
self,
|
|
pressure: float,
|
|
temperature: float,
|
|
phase: str = "vapor",
|
|
) -> float:
|
|
"""Return Peng-Robinson enthalpy departure from ideal gas, J/kg."""
|
|
self._validate_pressure_temperature(pressure, temperature)
|
|
z = self.compressibility_factor(pressure, temperature, phase=phase)
|
|
_, B = self.reduced_parameters(pressure, temperature)
|
|
b = self.b_parameter
|
|
attractive = self.attractive_parameter(temperature)
|
|
d_attractive_d_temperature = (
|
|
self.attractive_parameter_temperature_derivative(temperature)
|
|
)
|
|
log_argument = (z + (1.0 + sqrt(2.0)) * B) / (
|
|
z + (1.0 - sqrt(2.0)) * B
|
|
)
|
|
residual_molar_enthalpy = (
|
|
UNIVERSAL_GAS_CONSTANT * temperature * (z - 1.0)
|
|
+ (
|
|
temperature * d_attractive_d_temperature
|
|
- attractive
|
|
)
|
|
* log(log_argument)
|
|
/ (2.0 * sqrt(2.0) * b)
|
|
)
|
|
return residual_molar_enthalpy / self.molar_mass
|
|
|
|
@profile_property(
|
|
"residual_specific_internal_energy_at_density",
|
|
layer="kernel",
|
|
minimum_mode="audit",
|
|
)
|
|
def residual_specific_internal_energy_at_density(
|
|
self,
|
|
temperature: float,
|
|
density: float,
|
|
) -> float:
|
|
"""Return Peng-Robinson internal-energy departure, J/kg."""
|
|
self._validate_temperature(temperature)
|
|
if density <= 0.0:
|
|
raise ValueError("Density must be positive.")
|
|
molar_volume = self.molar_mass / density
|
|
b = self.b_parameter
|
|
if molar_volume <= b:
|
|
raise RecoverableTrialStateError(
|
|
"Molar volume must be larger than Peng-Robinson b parameter."
|
|
)
|
|
attractive = self.attractive_parameter(temperature)
|
|
d_attractive_d_temperature = (
|
|
self.attractive_parameter_temperature_derivative(temperature)
|
|
)
|
|
log_argument = (
|
|
molar_volume + (1.0 + sqrt(2.0)) * b
|
|
) / (
|
|
molar_volume + (1.0 - sqrt(2.0)) * b
|
|
)
|
|
residual_molar_internal_energy = (
|
|
temperature * d_attractive_d_temperature - attractive
|
|
) * log(log_argument) / (2.0 * sqrt(2.0) * b)
|
|
return residual_molar_internal_energy / self.molar_mass
|
|
|
|
@profile_property(
|
|
"residual_isochoric_heat_capacity_at_density",
|
|
layer="kernel",
|
|
minimum_mode="audit",
|
|
)
|
|
def residual_isochoric_heat_capacity_at_density(
|
|
self,
|
|
temperature: float,
|
|
density: float,
|
|
) -> float:
|
|
"""Return the constant-volume heat-capacity departure, J/kg/K."""
|
|
self._validate_temperature(temperature)
|
|
if density <= 0.0:
|
|
raise ValueError("Density must be positive.")
|
|
molar_volume = self.molar_mass / density
|
|
b = self.b_parameter
|
|
if molar_volume <= b:
|
|
raise RecoverableTrialStateError(
|
|
"Molar volume must be larger than Peng-Robinson b parameter."
|
|
)
|
|
log_argument = (
|
|
molar_volume + (1.0 + sqrt(2.0)) * b
|
|
) / (
|
|
molar_volume + (1.0 - sqrt(2.0)) * b
|
|
)
|
|
residual_molar_cv = (
|
|
temperature
|
|
* self.attractive_parameter_temperature_second_derivative(temperature)
|
|
* log(log_argument)
|
|
/ (2.0 * sqrt(2.0) * b)
|
|
)
|
|
return residual_molar_cv / self.molar_mass
|
|
|
|
@staticmethod
|
|
def _validate_temperature(temperature: float) -> None:
|
|
if temperature <= 0.0:
|
|
raise RecoverableTrialStateError("Temperature must be positive.")
|
|
|
|
@classmethod
|
|
def _validate_pressure_temperature(cls, pressure: float, temperature: float) -> None:
|
|
if pressure <= 0.0:
|
|
raise RecoverableTrialStateError("Pressure must be positive.")
|
|
cls._validate_temperature(temperature)
|
|
|
|
HELIUM_PR = PengRobinsonFluid(
|
|
name="helium",
|
|
molar_mass=0.004002602,
|
|
critical_temperature=5.1953,
|
|
critical_pressure=227_460.0,
|
|
# Simcenter Amesim 2404 helium_eos.data.
|
|
acentric_factor=-0.382,
|
|
)
|
|
|
|
NITROGEN_PR = PengRobinsonFluid(
|
|
name="nitrogen",
|
|
molar_mass=0.0280134,
|
|
critical_temperature=126.192,
|
|
critical_pressure=3.3958e6,
|
|
acentric_factor=0.0372,
|
|
)
|
|
|
|
AIR_PR = PengRobinsonFluid(
|
|
name="air",
|
|
molar_mass=0.02896513,
|
|
critical_temperature=132.5306,
|
|
critical_pressure=3.786e6,
|
|
acentric_factor=0.0335,
|
|
)
|
|
|
|
|
|
def _real_cubic_roots(a: float, b: float, c: float) -> tuple[float, ...]:
|
|
"""Return real roots for x**3 + a*x**2 + b*x + c = 0."""
|
|
|
|
depressed_p = b - a * a / 3.0
|
|
depressed_q = 2.0 * a * a * a / 27.0 - a * b / 3.0 + c
|
|
discriminant = (depressed_q / 2.0) ** 2.0 + (depressed_p / 3.0) ** 3.0
|
|
offset = -a / 3.0
|
|
tolerance = 1e-14
|
|
|
|
if discriminant > tolerance:
|
|
sqrt_discriminant = sqrt(discriminant)
|
|
u = _real_cube_root(-depressed_q / 2.0 + sqrt_discriminant)
|
|
v = _real_cube_root(-depressed_q / 2.0 - sqrt_discriminant)
|
|
return (u + v + offset,)
|
|
|
|
if abs(discriminant) <= tolerance:
|
|
u = _real_cube_root(-depressed_q / 2.0)
|
|
return tuple(sorted({2.0 * u + offset, -u + offset}))
|
|
|
|
if depressed_p >= 0.0:
|
|
raise ValueError("Unexpected cubic state with three real roots and non-negative p.")
|
|
radius = 2.0 * sqrt(-depressed_p / 3.0)
|
|
argument = (3.0 * depressed_q / (2.0 * depressed_p)) * sqrt(-3.0 / depressed_p)
|
|
argument = max(-1.0, min(1.0, argument))
|
|
theta = acos(argument) / 3.0
|
|
roots = [
|
|
radius * cos(theta - 2.0 * pi * index / 3.0) + offset
|
|
for index in range(3)
|
|
]
|
|
return tuple(sorted(roots))
|
|
|
|
|
|
def _real_cube_root(value: float) -> float:
|
|
if value == 0.0:
|
|
return 0.0
|
|
return (1.0 if value > 0.0 else -1.0) * abs(value) ** (1.0 / 3.0)
|