补充氦气Peng-Robinson物性库

PythonModels/core/peng_robinson.py

@@ -0,0 +1,195 @@
+from __future__ import annotations
+
+from dataclasses import dataclass
+from math import acos, cos, isfinite, pi, sqrt
+
+UNIVERSAL_GAS_CONSTANT = 8.31446261815324
+
+
+@dataclass(frozen=True)
+class PengRobinsonFluid:
+    """Pure-fluid Peng-Robinson equation-of-state helper.
+
+    The class intentionally covers the equation-of-state layer first: pressure,
+    compressibility factor, molar volume, and density. Caloric departure
+    properties are left out until the test_mql energy equations need them.
+    """
+
+    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 (
+            0.45724
+            * UNIVERSAL_GAS_CONSTANT
+            * UNIVERSAL_GAS_CONSTANT
+            * self.critical_temperature
+            * self.critical_temperature
+            / self.critical_pressure
+        )
+
+    @property
+    def b_parameter(self) -> float:
+        return 0.07780 * 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 attractive_parameter(self, temperature: float) -> float:
+        return self.a_parameter * self.alpha(temperature)
+
+    def pressure_from_molar_volume(self, temperature: float, molar_volume: float) -> float:
+        self._validate_temperature(temperature)
+        if molar_volume <= self.b_parameter:
+            raise ValueError("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
+
+    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)
+
+    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
+
+    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
+
+    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}")
+
+    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
+
+    def density(
+        self,
+        pressure: float,
+        temperature: float,
+        phase: str = "vapor",
+    ) -> float:
+        return self.molar_mass / self.molar_volume(pressure, temperature, phase=phase)
+
+    @staticmethod
+    def _validate_temperature(temperature: float) -> None:
+        if temperature <= 0.0:
+            raise ValueError("Temperature must be positive.")
+
+    @classmethod
+    def _validate_pressure_temperature(cls, pressure: float, temperature: float) -> None:
+        if pressure <= 0.0:
+            raise ValueError("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,
+    acentric_factor=-0.385,
+)
+
+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)

PythonModels/systems/test_mql_config.py

@@ -6,6 +6,7 @@ from dataclasses import dataclass
 from math import isfinite
 from typing import Any
 
+from PythonModels.core.peng_robinson import HELIUM_PR, PengRobinsonFluid
 from PythonModels.systems.test_mql import COMPONENT_SPECS, GLOBAL_PARAMETERS
 
 
@@ -58,6 +59,7 @@ class TestMqlResolvedComponent:
 class TestMqlConfig:
     raw_global_parameters: dict[str, str]
     global_parameters: dict[str, float]
+    fluid: PengRobinsonFluid
     components: tuple[TestMqlResolvedComponent, ...]
 
     @classmethod
@@ -75,6 +77,7 @@ class TestMqlConfig:
         return cls(
             raw_global_parameters=raw_globals,
             global_parameters=numeric_globals,
+            fluid=HELIUM_PR,
             components=components,
         )