Module pychnosz.models.iapws95
IAPWS-95 water model implementation.
This module implements the IAPWS-95 formulation for the thermodynamic properties of ordinary water substance for general and scientific use. This is the international standard for water properties.
This implementation exactly matches the R CHNOSZ package, with identical coefficients and derivative calculations. No shortcuts or approximations - full fidelity to Wagner & Pruss (2002).
References: - Wagner, W., & Pruß, A. (2002). The IAPWS formulation 1995 for the thermodynamic properties of ordinary water substance for general and scientific use. Journal of Physical and Chemical Reference Data, 31(2), 387-535. - Fernández, D. P., et al. (1997). A formulation for the static permittivity of water and steam at temperatures from 238 K to 873 K at pressures up to 1200 MPa. Journal of Physical and Chemical Reference Data, 26(4), 1125-1166. - R CHNOSZ package IAPWS95.R implementation
Functions
def rho_IAPWS95_accurate(T: float | numpy.ndarray,
P: float | numpy.ndarray,
state: str = '',
trace: int = 0) ‑> numpy.ndarray-
Expand source code
def rho_IAPWS95_accurate(T: Union[float, np.ndarray], P: Union[float, np.ndarray], state: str = "", trace: int = 0) -> np.ndarray: """ Return density in kg/m³ corresponding to given pressure (bar) and temperature (K). Exact implementation matching R CHNOSZ rho.IAPWS95 function with numerical root finding. """ T = np.atleast_1d(np.asarray(T, dtype=float)) P = np.atleast_1d(np.asarray(P, dtype=float)) # Ensure T and P have same length if len(P) < len(T): P = np.resize(P, len(T)) elif len(T) < len(P): T = np.resize(T, len(P)) rho = np.full_like(T, np.nan) # Critical point constants T_critical = 647.096 # K P_critical = 22.064 # MPa # Convert pressure from bar to MPa (matching R code line 60) P_MPa = P / 10.0 for i in range(len(T)): if np.isnan(T[i]) or np.isnan(P[i]) or T[i] <= 0 or P[i] <= 0: continue # Function to find zero: P_calculated - P_target = 0 def dP(rho_guess): if rho_guess <= 0: return float('inf') try: # Use the accurate IAPWS95 pressure calculation P_calc_MPa = accurate_iapws95.calculate_IAPWS95_property('P', T[i], rho_guess) return P_calc_MPa - P_MPa[i] except: return float('inf') # Phase identification and initial guess setup (matching R logic) try: Psat = _WP02_auxiliary_accurate("P.sigma", T[i])[0] # This is in MPa if T[i] > T_critical: # Above critical temperature - supercritical interval = [0.1, 1000.0] elif P_MPa[i] > P_critical: # Above critical pressure - supercritical rho_sat = _WP02_auxiliary_accurate("rho.liquid", T[i])[0] # For high pressures, we need much higher densities # Estimate upper bound based on pressure scaling rho_upper = rho_sat + (P_MPa[i] - P_critical) * 4.0 # Rough scaling interval = [rho_sat, min(rho_upper, 1500.0)] # Cap at reasonable max density elif P_MPa[i] <= 0.9999 * Psat: # Steam region rho_sat = _WP02_auxiliary_accurate("rho.vapor", T[i])[0] interval = [rho_sat * 0.1, rho_sat * 2.0] elif P_MPa[i] >= 1.00005 * Psat: # Liquid water region rho_sat = _WP02_auxiliary_accurate("rho.liquid", T[i])[0] interval = [rho_sat * 0.9, rho_sat * 1.1] else: # Close to saturation - use liquid estimate rho_sat = _WP02_auxiliary_accurate("rho.liquid", T[i])[0] interval = [rho_sat * 0.95, rho_sat * 1.05] # Numerical root finding using Brent's method try: rho[i] = brentq(dP, interval[0], interval[1], xtol=1e-10, rtol=1e-10) except Exception as e: if trace > 0: print(f"Warning: rho_IAPWS95_accurate problems finding density at {T[i]} K and {P[i]} bar: {e}") rho[i] = np.nan except Exception as e: if trace > 0: print(f"Warning: rho_IAPWS95_accurate problems with phase identification at {T[i]} K and {P[i]} bar: {e}") rho[i] = np.nan return rhoReturn density in kg/m³ corresponding to given pressure (bar) and temperature (K).
Exact implementation matching R CHNOSZ rho.IAPWS95 function with numerical root finding.
def water_IAPWS95(properties: str | List[str],
T: float | numpy.ndarray = 298.15,
P: float | numpy.ndarray = 100.0) ‑> float | numpy.ndarray | Dict[str, Any]-
Expand source code
def water_IAPWS95(properties: Union[str, List[str]], T: Union[float, np.ndarray] = 298.15, P: Union[float, np.ndarray] = 100.0) -> Union[float, np.ndarray, Dict[str, Any]]: """ Calculate water properties using IAPWS-95. This function provides the main interface to IAPWS-95 water properties, using the accurate implementation that matches R CHNOSZ exactly. Parameters ---------- properties : str or list of str Property or properties to calculate: - 'P': Pressure in MPa - 'S': Entropy in kJ/(kg·K) - 'U': Internal energy in kJ/kg - 'H': Enthalpy in kJ/kg - 'G': Gibbs free energy in kJ/kg - 'Cv': Isochoric heat capacity in kJ/(kg·K) - 'Cp': Isobaric heat capacity in kJ/(kg·K) - 'w': Speed of sound in m/s - 'rho': Density in kg/m³ T : float or array Temperature in Kelvin P : float or array Pressure in kPa (note: different from other modules that use bar) Returns ------- float, array, or dict Calculated water properties Examples -------- >>> import numpy as np >>> >>> # Single property at standard conditions >>> rho = water_IAPWS95('rho', T=298.15, P=100.0) # 100 kPa = 1 bar >>> print(f"Density: {rho:.3f} kg/m³") >>> >>> # Multiple properties >>> props = water_IAPWS95(['rho', 'Cp'], T=298.15, P=100.0) >>> print(f"Density: {props['rho']:.3f} kg/m³") >>> print(f"Heat capacity: {props['Cp']:.3f} kJ/(kg·K)") >>> >>> # Array calculations >>> T_array = np.array([273.15, 298.15, 373.15]) >>> densities = water_IAPWS95('rho', T=T_array, P=100.0) """ # Convert pressure from kPa to bar for the accurate implementation if isinstance(P, (int, float)): P_bar = P / 100.0 else: P_bar = np.asarray(P) / 100.0 # Use the accurate implementation return water_IAPWS95_accurate(properties, T=T, P=P_bar)Calculate water properties using IAPWS-95.
This function provides the main interface to IAPWS-95 water properties, using the accurate implementation that matches R CHNOSZ exactly.
Parameters
properties:strorlistofstr- Property or properties to calculate: - 'P': Pressure in MPa - 'S': Entropy in kJ/(kg·K) - 'U': Internal energy in kJ/kg - 'H': Enthalpy in kJ/kg - 'G': Gibbs free energy in kJ/kg - 'Cv': Isochoric heat capacity in kJ/(kg·K) - 'Cp': Isobaric heat capacity in kJ/(kg·K) - 'w': Speed of sound in m/s - 'rho': Density in kg/m³
T:floatorarray- Temperature in Kelvin
P:floatorarray- Pressure in kPa (note: different from other modules that use bar)
Returns
float, array,ordict- Calculated water properties
Examples
>>> import numpy as np >>> >>> # Single property at standard conditions >>> rho = water_IAPWS95('rho', T=298.15, P=100.0) # 100 kPa = 1 bar >>> print(f"Density: {rho:.3f} kg/m³") >>> >>> # Multiple properties >>> props = water_IAPWS95(['rho', 'Cp'], T=298.15, P=100.0) >>> print(f"Density: {props['rho']:.3f} kg/m³") >>> print(f"Heat capacity: {props['Cp']:.3f} kJ/(kg·K)") >>> >>> # Array calculations >>> T_array = np.array([273.15, 298.15, 373.15]) >>> densities = water_IAPWS95('rho', T=T_array, P=100.0) def water_IAPWS95_accurate(properties: str | List[str],
T: float | numpy.ndarray = 298.15,
P: float | numpy.ndarray = 1.0,
rho: float | numpy.ndarray | None = None) ‑> float | numpy.ndarray | Dict[str, Any]-
Expand source code
def water_IAPWS95_accurate(properties: Union[str, List[str]], T: Union[float, np.ndarray] = 298.15, P: Union[float, np.ndarray] = 1.0, rho: Optional[Union[float, np.ndarray]] = None) -> Union[float, np.ndarray, Dict[str, Any]]: """ Calculate water properties using accurate IAPWS-95 implementation. This function provides an accurate implementation of IAPWS-95 that matches the R CHNOSZ package exactly, with no shortcuts or approximations. Parameters ---------- properties : str or list of str Property or properties to calculate ('P', 'S', 'U', 'H', 'G', 'Cv', 'Cp', 'w', 'rho') T : float or array Temperature in Kelvin P : float or array Pressure in bar (used to calculate density if rho not provided) rho : float or array, optional Density in kg/m³. If provided, used directly; if not, calculated from T,P Returns ------- float, array, or dict Calculated water properties Examples -------- >>> # Single property with T,P >>> p = water_IAPWS95_accurate('P', T=298.15, P=1.0) >>> >>> # Single property with T,rho >>> p = water_IAPWS95_accurate('P', T=298.15, rho=997.0) >>> >>> # Multiple properties >>> props = water_IAPWS95_accurate(['rho', 'Cp'], T=298.15, P=1.0) """ # Handle input types if isinstance(properties, str): properties = [properties] single_prop = True else: single_prop = False # Convert inputs T = np.atleast_1d(np.asarray(T, dtype=float)) if rho is None: # Calculate density from T,P P = np.atleast_1d(np.asarray(P, dtype=float)) rho_calc = rho_IAPWS95_accurate(T, P) else: # Use provided density rho_calc = np.atleast_1d(np.asarray(rho, dtype=float)) P = np.atleast_1d(np.asarray(P, dtype=float)) # Ensure same length max_len = max(len(T), len(rho_calc)) if len(T) < max_len: T = np.resize(T, max_len) if len(rho_calc) < max_len: rho_calc = np.resize(rho_calc, max_len) # Calculate properties results = {} # Reference state correction constants (from R water.R lines 187-194) # Convert to SUPCRT reference state at the triple point # difference = SUPCRT - IAPWS ( + entropy in G ) M = 18.015268 # g/mol, molar mass of water Tr = 298.15 # Reference temperature cal_to_J = 4.184 # Conversion factor from cal to J # Pre-calculate reference corrections (from R) dH = (-68316.76 - 451.75437) * cal_to_J # J/mol dS = (16.7123 - 1.581072) * cal_to_J # J/mol/K dU = (-67434.5 - 451.3229) * cal_to_J # J/mol dA_base = (-55814.06 + 20.07376) * cal_to_J # J/mol for prop in properties: if prop.lower() == 'rho': # Return density results[prop] = rho_calc if len(rho_calc) > 1 else rho_calc[0] else: # Calculate other properties prop_values = np.full(max_len, np.nan) for i in range(max_len): if not (np.isnan(T[i]) or np.isnan(rho_calc[i]) or T[i] <= 0 or rho_calc[i] <= 0): try: # Get raw IAPWS95 value in kJ/kg (specific units) raw_value = accurate_iapws95.calculate_IAPWS95_property(prop, T[i], rho_calc[i]) # Convert to J/mol (molar units) and apply reference state corrections if prop.lower() == 'g': # Gibbs energy: IAPWS95("g")*M + dG dG = (-56687.71 + 19.64228 - dS * (T[i] - Tr)) * cal_to_J prop_values[i] = raw_value * M + dG elif prop.lower() == 'h': # Enthalpy: IAPWS95("h")*M + dH prop_values[i] = raw_value * M + dH elif prop.lower() == 'u': # Internal energy: IAPWS95("u")*M + dU prop_values[i] = raw_value * M + dU elif prop.lower() == 'a': # Helmholtz energy: IAPWS95("a")*M + dA dA = dA_base - dS * (T[i] - Tr) prop_values[i] = raw_value * M + dA elif prop.lower() == 's': # Entropy: IAPWS95("s")*M + dS prop_values[i] = raw_value * M + dS elif prop.lower() in ['cv', 'cp']: # Heat capacities: just convert to molar units (no reference correction) prop_values[i] = raw_value * M else: # Other properties (P, w, etc.): use as-is or convert units as needed if prop.lower() == 'w': # Speed of sound: convert m/s to cm/s (factor of 100) prop_values[i] = raw_value * 100 elif prop.lower() == 'p': # Pressure: convert from MPa to bar (factor of 10) prop_values[i] = raw_value * 10 else: # Other properties: return as-is prop_values[i] = raw_value except Exception: prop_values[i] = np.nan results[prop] = prop_values if len(prop_values) > 1 else prop_values[0] # Return results if single_prop: return results[properties[0]] else: return resultsCalculate water properties using accurate IAPWS-95 implementation.
This function provides an accurate implementation of IAPWS-95 that matches the R CHNOSZ package exactly, with no shortcuts or approximations.
Parameters
properties:strorlistofstr- Property or properties to calculate ('P', 'S', 'U', 'H', 'G', 'Cv', 'Cp', 'w', 'rho')
T:floatorarray- Temperature in Kelvin
P:floatorarray- Pressure in bar (used to calculate density if rho not provided)
rho:floatorarray, optional- Density in kg/m³. If provided, used directly; if not, calculated from T,P
Returns
float, array,ordict- Calculated water properties
Examples
>>> # Single property with T,P >>> p = water_IAPWS95_accurate('P', T=298.15, P=1.0) >>> >>> # Single property with T,rho >>> p = water_IAPWS95_accurate('P', T=298.15, rho=997.0) >>> >>> # Multiple properties >>> props = water_IAPWS95_accurate(['rho', 'Cp'], T=298.15, P=1.0) def water_iapws95(properties: str | List[str],
T: float | numpy.ndarray = 298.15,
P: float | numpy.ndarray = 100.0) ‑> float | numpy.ndarray | Dict[str, Any]-
Expand source code
def water_IAPWS95(properties: Union[str, List[str]], T: Union[float, np.ndarray] = 298.15, P: Union[float, np.ndarray] = 100.0) -> Union[float, np.ndarray, Dict[str, Any]]: """ Calculate water properties using IAPWS-95. This function provides the main interface to IAPWS-95 water properties, using the accurate implementation that matches R CHNOSZ exactly. Parameters ---------- properties : str or list of str Property or properties to calculate: - 'P': Pressure in MPa - 'S': Entropy in kJ/(kg·K) - 'U': Internal energy in kJ/kg - 'H': Enthalpy in kJ/kg - 'G': Gibbs free energy in kJ/kg - 'Cv': Isochoric heat capacity in kJ/(kg·K) - 'Cp': Isobaric heat capacity in kJ/(kg·K) - 'w': Speed of sound in m/s - 'rho': Density in kg/m³ T : float or array Temperature in Kelvin P : float or array Pressure in kPa (note: different from other modules that use bar) Returns ------- float, array, or dict Calculated water properties Examples -------- >>> import numpy as np >>> >>> # Single property at standard conditions >>> rho = water_IAPWS95('rho', T=298.15, P=100.0) # 100 kPa = 1 bar >>> print(f"Density: {rho:.3f} kg/m³") >>> >>> # Multiple properties >>> props = water_IAPWS95(['rho', 'Cp'], T=298.15, P=100.0) >>> print(f"Density: {props['rho']:.3f} kg/m³") >>> print(f"Heat capacity: {props['Cp']:.3f} kJ/(kg·K)") >>> >>> # Array calculations >>> T_array = np.array([273.15, 298.15, 373.15]) >>> densities = water_IAPWS95('rho', T=T_array, P=100.0) """ # Convert pressure from kPa to bar for the accurate implementation if isinstance(P, (int, float)): P_bar = P / 100.0 else: P_bar = np.asarray(P) / 100.0 # Use the accurate implementation return water_IAPWS95_accurate(properties, T=T, P=P_bar)Calculate water properties using IAPWS-95.
This function provides the main interface to IAPWS-95 water properties, using the accurate implementation that matches R CHNOSZ exactly.
Parameters
properties:strorlistofstr- Property or properties to calculate: - 'P': Pressure in MPa - 'S': Entropy in kJ/(kg·K) - 'U': Internal energy in kJ/kg - 'H': Enthalpy in kJ/kg - 'G': Gibbs free energy in kJ/kg - 'Cv': Isochoric heat capacity in kJ/(kg·K) - 'Cp': Isobaric heat capacity in kJ/(kg·K) - 'w': Speed of sound in m/s - 'rho': Density in kg/m³
T:floatorarray- Temperature in Kelvin
P:floatorarray- Pressure in kPa (note: different from other modules that use bar)
Returns
float, array,ordict- Calculated water properties
Examples
>>> import numpy as np >>> >>> # Single property at standard conditions >>> rho = water_IAPWS95('rho', T=298.15, P=100.0) # 100 kPa = 1 bar >>> print(f"Density: {rho:.3f} kg/m³") >>> >>> # Multiple properties >>> props = water_IAPWS95(['rho', 'Cp'], T=298.15, P=100.0) >>> print(f"Density: {props['rho']:.3f} kg/m³") >>> print(f"Heat capacity: {props['Cp']:.3f} kJ/(kg·K)") >>> >>> # Array calculations >>> T_array = np.array([273.15, 298.15, 373.15]) >>> densities = water_IAPWS95('rho', T=T_array, P=100.0)
Classes
class AccurateIAPWS95Water-
Expand source code
class AccurateIAPWS95Water: """ Accurate IAPWS-95 water model implementation matching R CHNOSZ exactly. This class provides thermodynamic properties of water using the IAPWS-95 formulation with exact coefficients and derivative calculations from the Wagner & Pruss (2002) specification as implemented in R CHNOSZ. """ def __init__(self): """Initialize IAPWS95 water model with exact constants.""" # Physical constants (exactly matching R CHNOSZ) self.R = 0.46151805 # kJ/(kg·K) - Specific gas constant for water self.MW = 18.015268 # g/mol - Molecular weight # Critical constants (exactly matching R CHNOSZ) self.Tc = 647.096 # K - Critical temperature self.rhoc = 322.0 # kg/m³ - Critical density # Triple point constants self.Tt = 273.16 # K - Triple point temperature # Initialize coefficients exactly as in R CHNOSZ self._init_coefficients() def _init_coefficients(self): """Initialize coefficients for IAPWS-95 fundamental equation (exact R match).""" # Ideal gas coefficients (Table 6.1 Wagner & Pruss 2002, R CHNOSZ lines 114-117) self.n_ideal = np.array([ -8.32044648201, 6.6832105268, 3.00632, 0.012436, 0.97315, 1.27950, 0.96956, 0.24873 ]) self.gamma_ideal = np.array([ np.nan, np.nan, np.nan, 1.28728967, 3.53734222, 7.74073708, 9.24437796, 27.5075105 ]) # Residual part coefficients (Table 6.2 Wagner & Pruss 2002, R CHNOSZ lines 134-171) # c coefficients c_list = [np.nan]*7 + [1]*15 + [2]*20 + [3]*4 + [4] + [6]*4 + [np.nan]*5 self.c_res = np.array(c_list) # d coefficients self.d_res = np.array([ 1,1,1,2,2,3,4,1,1,1,2,2,3,4, 4,5,7,9,10,11,13,15,1,2,2,2,3,4, 4,4,5,6,6,7,9,9,9,9,9,10,10,12, 3,4,4,5,14,3,6,6,6,3,3,3,np.nan,np.nan ]) # t coefficients self.t_res = np.array([ -0.5,0.875,1,0.5,0.75,0.375,1,4,6,12,1,5,4,2, 13,9,3,4,11,4,13,1,7,1,9,10,10,3, 7,10,10,6,10,10,1,2,3,4,8,6,9,8, 16,22,23,23,10,50,44,46,50,0,1,4,np.nan,np.nan ]) # n coefficients (exact values from R CHNOSZ) self.n_res = np.array([ 0.12533547935523E-1, 0.78957634722828E1 ,-0.87803203303561E1 , 0.31802509345418 ,-0.26145533859358 ,-0.78199751687981E-2, 0.88089493102134E-2,-0.66856572307965 , 0.20433810950965 , -0.66212605039687E-4,-0.19232721156002 ,-0.25709043003438 , 0.16074868486251 ,-0.40092828925807E-1, 0.39343422603254E-6, -0.75941377088144E-5, 0.56250979351888E-3,-0.15608652257135E-4, 0.11537996422951E-8, 0.36582165144204E-6,-0.13251180074668E-11, -0.62639586912454E-9,-0.10793600908932 , 0.17611491008752E-1, 0.22132295167546 ,-0.40247669763528 , 0.58083399985759 , 0.49969146990806E-2,-0.31358700712549E-1,-0.74315929710341 , 0.47807329915480 , 0.20527940895948E-1,-0.13636435110343 , 0.14180634400617E-1, 0.83326504880713E-2,-0.29052336009585E-1, 0.38615085574206E-1,-0.20393486513704E-1,-0.16554050063734E-2, 0.19955571979541E-2, 0.15870308324157E-3,-0.16388568342530E-4, 0.43613615723811E-1, 0.34994005463765E-1,-0.76788197844621E-1, 0.22446277332006E-1,-0.62689710414685E-4,-0.55711118565645E-9, -0.19905718354408 , 0.31777497330738 ,-0.11841182425981 , -0.31306260323435E2 , 0.31546140237781E2 ,-0.25213154341695E4 , -0.14874640856724 , 0.31806110878444 ]) # Additional coefficients for complex terms (R CHNOSZ lines 162-171) alpha_list = [np.nan]*51 + [20,20,20,np.nan,np.nan] self.alpha_res = np.array(alpha_list) beta_list = [np.nan]*51 + [150,150,250,0.3,0.3] self.beta_res = np.array(beta_list) gamma_list = [np.nan]*51 + [1.21,1.21,1.25,np.nan,np.nan] self.gamma_res = np.array(gamma_list) epsilon_list = [np.nan]*51 + [1,1,1,np.nan,np.nan] self.epsilon_res = np.array(epsilon_list) a_list = [np.nan]*54 + [3.5,3.5] self.a_res = np.array(a_list) b_list = [np.nan]*54 + [0.85,0.95] self.b_res = np.array(b_list) B_list = [np.nan]*54 + [0.2,0.2] self.B_res = np.array(B_list) C_list = [np.nan]*54 + [28,32] self.C_res = np.array(C_list) D_list = [np.nan]*54 + [700,800] self.D_res = np.array(D_list) A_list = [np.nan]*54 + [0.32,0.32] self.A_res = np.array(A_list) # Index ranges (from R CHNOSZ Table 6.5) self.i1 = np.arange(0, 7) # 1:7 in R (0-based in Python) self.i2 = np.arange(7, 51) # 8:51 in R self.i3 = np.arange(51, 54) # 52:54 in R self.i4 = np.arange(54, 56) # 55:56 in R def _phi_ideal(self, delta: float, tau: float, derivative: str = 'phi') -> float: """ Calculate ideal gas part of dimensionless Helmholtz energy and derivatives. Exact implementation matching R CHNOSZ IAPWS95.idealgas function. """ if derivative == 'phi': # Equation 6.5 from Wagner & Pruss 2002 result = (np.log(delta) + self.n_ideal[0] + self.n_ideal[1]*tau + self.n_ideal[2]*np.log(tau)) # Sum term with exponentials for i in range(3, 8): # n[4:8] in R (indices 3:7 in Python) gamma_val = self.gamma_ideal[i] if not np.isnan(gamma_val): result += self.n_ideal[i] * np.log(1 - np.exp(-gamma_val*tau)) return result elif derivative == 'phi.delta': return 1.0/delta elif derivative == 'phi.delta.delta': return -1.0/(delta**2) elif derivative == 'phi.tau': result = self.n_ideal[1] + self.n_ideal[2]/tau # Sum term with exponentials and gamma for i in range(3, 8): gamma_val = self.gamma_ideal[i] if not np.isnan(gamma_val): exp_term = np.exp(-gamma_val*tau) result += self.n_ideal[i] * gamma_val * ((1-exp_term)**(-1) - 1) return result elif derivative == 'phi.tau.tau': result = -self.n_ideal[2]/(tau**2) # Sum term with exponentials for i in range(3, 8): gamma_val = self.gamma_ideal[i] if not np.isnan(gamma_val): exp_term = np.exp(-gamma_val*tau) result -= (self.n_ideal[i] * gamma_val**2 * exp_term * (1-exp_term)**(-2)) return result elif derivative == 'phi.delta.tau': return 0.0 elif derivative == 'phi.tau.tau.tau': # Third derivative with respect to tau result = 2*self.n_ideal[2]/(tau**3) # Sum term with exponentials for i in range(3, 8): gamma_val = self.gamma_ideal[i] if not np.isnan(gamma_val): exp_term = np.exp(-gamma_val*tau) result += (self.n_ideal[i] * gamma_val**3 * exp_term * (1-exp_term)**(-3) * (2*exp_term - 1)) return result elif derivative == 'phi.delta.delta.delta': # Third derivative with respect to delta return 2.0/(delta**3) elif derivative == 'phi.delta.tau.tau': # Mixed derivative: d³φ⁰/dδdτ² return 0.0 elif derivative == 'phi.delta.delta.tau': # Mixed derivative: d³φ⁰/dδ²dτ return 0.0 else: raise ValueError(f"Unknown derivative: {derivative}") def _delta_function(self, i: int, delta: float, tau: float) -> float: """Delta function for complex terms (R CHNOSZ Delta function).""" theta = self._theta_function(i, delta, tau) B_val = self.B_res[i] a_val = self.a_res[i] return theta**2 + B_val * ((delta-1)**2)**a_val def _theta_function(self, i: int, delta: float, tau: float) -> float: """Theta function for complex terms (R CHNOSZ Theta function).""" A_val = self.A_res[i] beta_val = self.beta_res[i] return (1-tau) + A_val * ((delta-1)**2)**(1/(2*beta_val)) def _psi_function(self, i: int, delta: float, tau: float) -> float: """Psi function for complex terms (R CHNOSZ Psi function).""" C_val = self.C_res[i] D_val = self.D_res[i] return np.exp(-C_val*(delta-1)**2 - D_val*(tau-1)**2) def _delta_derivatives(self, i: int, delta: float, tau: float) -> Dict[str, float]: """Calculate Delta function derivatives (matching R CHNOSZ exactly).""" theta = self._theta_function(i, delta, tau) A_val = self.A_res[i] B_val = self.B_res[i] a_val = self.a_res[i] b_val = self.b_res[i] beta_val = self.beta_res[i] # dDelta/ddelta dDelta_ddelta = ((delta-1) * (A_val*theta*2/beta_val*((delta-1)**2)**(1/(2*beta_val)-1) + 2*B_val*a_val*((delta-1)**2)**(a_val-1))) # d²Delta/ddelta² (handle division by zero when delta ≈ 1) if abs(delta - 1) < 1e-15: # Use L'Hôpital's rule or limit behavior d2Delta_ddelta2 = (4*B_val*a_val*(a_val-1) + 2*A_val**2*(1/beta_val)**2 + A_val*theta*4/beta_val*(1/(2*beta_val)-1)) else: d2Delta_ddelta2 = (1/(delta-1)*dDelta_ddelta + (delta-1)**2 * ( 4*B_val*a_val*(a_val-1)*((delta-1)**2)**(a_val-2) + 2*A_val**2*(1/beta_val)**2 * (((delta-1)**2)**(1/(2*beta_val)-1))**2 + A_val*theta*4/beta_val*(1/(2*beta_val)-1) * ((delta-1)**2)**(1/(2*beta_val)-2))) # Delta^b derivatives delta_func = self._delta_function(i, delta, tau) dDelta_bi_ddelta = b_val * delta_func**(b_val-1) * dDelta_ddelta d2Delta_bi_ddelta2 = (b_val * (delta_func**(b_val-1) * d2Delta_ddelta2 + (b_val-1) * delta_func**(b_val-2) * dDelta_ddelta**2)) # Tau derivatives dDelta_bi_dtau = -2*theta*b_val*delta_func**(b_val-1) d2Delta_bi_dtau2 = (2*b_val*delta_func**(b_val-1) + 4*theta**2*b_val*(b_val-1)*delta_func**(b_val-2)) # Mixed derivative d2Delta_bi_ddelta_dtau = (-A_val*b_val*2/beta_val*delta_func**(b_val-1)*(delta-1) * ((delta-1)**2)**(1/(2*beta_val)-1) - 2*theta*b_val*(b_val-1)*delta_func**(b_val-2)*dDelta_ddelta) return { 'dDelta_ddelta': dDelta_ddelta, 'd2Delta_ddelta2': d2Delta_ddelta2, 'dDelta_bi_ddelta': dDelta_bi_ddelta, 'd2Delta_bi_ddelta2': d2Delta_bi_ddelta2, 'dDelta_bi_dtau': dDelta_bi_dtau, 'd2Delta_bi_dtau2': d2Delta_bi_dtau2, 'd2Delta_bi_ddelta_dtau': d2Delta_bi_ddelta_dtau } def _psi_derivatives(self, i: int, delta: float, tau: float) -> Dict[str, float]: """Calculate Psi function derivatives (matching R CHNOSZ exactly).""" C_val = self.C_res[i] D_val = self.D_res[i] psi = self._psi_function(i, delta, tau) return { 'dPsi_ddelta': -2*C_val*(delta-1)*psi, 'd2Psi_ddelta2': (2*C_val*(delta-1)**2 - 1) * 2*C_val*psi, 'dPsi_dtau': -2*D_val*(tau-1)*psi, 'd2Psi_dtau2': (2*D_val*(tau-1)**2 - 1) * 2*D_val*psi, 'd2Psi_ddelta_dtau': 4*C_val*D_val*(delta-1)*(tau-1)*psi } def _phi_residual(self, delta: float, tau: float, derivative: str = 'phi') -> float: """ Calculate residual part of dimensionless Helmholtz energy and derivatives. Exact implementation matching R CHNOSZ IAPWS95.residual function. """ if derivative == 'phi': # Four terms as in R CHNOSZ phi function (lines 201-206) term1 = np.sum(self.n_res[self.i1] * delta**self.d_res[self.i1] * tau**self.t_res[self.i1]) term2 = np.sum(self.n_res[self.i2] * delta**self.d_res[self.i2] * tau**self.t_res[self.i2] * np.exp(-delta**self.c_res[self.i2])) term3 = 0.0 for i in self.i3: alpha_val = self.alpha_res[i] beta_val = self.beta_res[i] epsilon_val = self.epsilon_res[i] gamma_val = self.gamma_res[i] if not (np.isnan(alpha_val) or np.isnan(beta_val)): term3 += (self.n_res[i] * delta**self.d_res[i] * tau**self.t_res[i] * np.exp(-alpha_val*(delta-epsilon_val)**2 - beta_val*(tau-gamma_val)**2)) term4 = 0.0 for i in self.i4: if not np.isnan(self.b_res[i]): delta_func = self._delta_function(i, delta, tau) psi_val = self._psi_function(i, delta, tau) term4 += self.n_res[i] * delta_func**self.b_res[i] * delta * psi_val return term1 + term2 + term3 + term4 elif derivative == 'phi.delta': # phi.delta implementation (R CHNOSZ lines 208-214) term1 = np.sum(self.n_res[self.i1] * self.d_res[self.i1] * delta**(self.d_res[self.i1]-1) * tau**self.t_res[self.i1]) term2 = np.sum(self.n_res[self.i2] * np.exp(-delta**self.c_res[self.i2]) * (delta**(self.d_res[self.i2]-1) * tau**self.t_res[self.i2] * (self.d_res[self.i2] - self.c_res[self.i2] * delta**self.c_res[self.i2]))) term3 = 0.0 for i in self.i3: alpha_val = self.alpha_res[i] beta_val = self.beta_res[i] epsilon_val = self.epsilon_res[i] gamma_val = self.gamma_res[i] if not (np.isnan(alpha_val) or np.isnan(beta_val)): exp_term = np.exp(-alpha_val*(delta-epsilon_val)**2 - beta_val*(tau-gamma_val)**2) term3 += (self.n_res[i] * delta**self.d_res[i] * tau**self.t_res[i] * exp_term * (self.d_res[i]/delta - 2*alpha_val*(delta-epsilon_val))) term4 = 0.0 for i in self.i4: if not np.isnan(self.b_res[i]): delta_func = self._delta_function(i, delta, tau) psi_val = self._psi_function(i, delta, tau) psi_derivs = self._psi_derivatives(i, delta, tau) delta_derivs = self._delta_derivatives(i, delta, tau) term4 += (self.n_res[i] * (delta_func**self.b_res[i] * (psi_val + delta*psi_derivs['dPsi_ddelta']) + delta_derivs['dDelta_bi_ddelta'] * delta * psi_val)) return term1 + term2 + term3 + term4 elif derivative == 'phi.delta.delta': # phi.delta.delta implementation (R CHNOSZ lines 216-224) term1 = np.sum(self.n_res[self.i1] * self.d_res[self.i1] * (self.d_res[self.i1]-1) * delta**(self.d_res[self.i1]-2) * tau**self.t_res[self.i1]) term2 = 0.0 for i in self.i2: d_val = self.d_res[i] c_val = self.c_res[i] exp_term = np.exp(-delta**c_val) factor = ((d_val - c_val*delta**c_val) * (d_val - 1 - c_val*delta**c_val) - c_val**2 * delta**c_val) term2 += (self.n_res[i] * exp_term * delta**(d_val-2) * tau**self.t_res[i] * factor) term3 = 0.0 for i in self.i3: alpha_val = self.alpha_res[i] beta_val = self.beta_res[i] epsilon_val = self.epsilon_res[i] gamma_val = self.gamma_res[i] if not (np.isnan(alpha_val) or np.isnan(beta_val)): d_val = self.d_res[i] exp_term = np.exp(-alpha_val*(delta-epsilon_val)**2 - beta_val*(tau-gamma_val)**2) factor = (-2*alpha_val*delta**d_val + 4*alpha_val**2*delta**d_val*(delta-epsilon_val)**2 - 4*d_val*alpha_val*delta**(d_val-1)*(delta-epsilon_val) + d_val*(d_val-1)*delta**(d_val-2)) term3 += self.n_res[i] * tau**self.t_res[i] * exp_term * factor term4 = 0.0 for i in self.i4: if not np.isnan(self.b_res[i]): delta_func = self._delta_function(i, delta, tau) psi_val = self._psi_function(i, delta, tau) psi_derivs = self._psi_derivatives(i, delta, tau) delta_derivs = self._delta_derivatives(i, delta, tau) term4 += (self.n_res[i] * (delta_func**self.b_res[i] * (2*psi_derivs['dPsi_ddelta'] + delta*psi_derivs['d2Psi_ddelta2']) + 2*delta_derivs['dDelta_bi_ddelta'] * (psi_val + delta*psi_derivs['dPsi_ddelta']) + delta_derivs['d2Delta_bi_ddelta2'] * delta * psi_val)) return term1 + term2 + term3 + term4 elif derivative == 'phi.tau': # phi.tau implementation (R CHNOSZ lines 226-231) term1 = np.sum(self.n_res[self.i1] * self.t_res[self.i1] * delta**self.d_res[self.i1] * tau**(self.t_res[self.i1]-1)) term2 = np.sum(self.n_res[self.i2] * self.t_res[self.i2] * delta**self.d_res[self.i2] * tau**(self.t_res[self.i2]-1) * np.exp(-delta**self.c_res[self.i2])) term3 = 0.0 for i in self.i3: alpha_val = self.alpha_res[i] beta_val = self.beta_res[i] epsilon_val = self.epsilon_res[i] gamma_val = self.gamma_res[i] if not (np.isnan(alpha_val) or np.isnan(beta_val)): exp_term = np.exp(-alpha_val*(delta-epsilon_val)**2 - beta_val*(tau-gamma_val)**2) term3 += (self.n_res[i] * delta**self.d_res[i] * tau**self.t_res[i] * exp_term * (self.t_res[i]/tau - 2*beta_val*(tau-gamma_val))) term4 = 0.0 for i in self.i4: if not np.isnan(self.b_res[i]): psi_val = self._psi_function(i, delta, tau) psi_derivs = self._psi_derivatives(i, delta, tau) delta_derivs = self._delta_derivatives(i, delta, tau) term4 += (self.n_res[i] * delta * (delta_derivs['dDelta_bi_dtau'] * psi_val + self._delta_function(i, delta, tau)**self.b_res[i] * psi_derivs['dPsi_dtau'])) return term1 + term2 + term3 + term4 elif derivative == 'phi.tau.tau': # phi.tau.tau implementation (R CHNOSZ lines 233-239) term1 = np.sum(self.n_res[self.i1] * self.t_res[self.i1] * (self.t_res[self.i1]-1) * delta**self.d_res[self.i1] * tau**(self.t_res[self.i1]-2)) term2 = np.sum(self.n_res[self.i2] * self.t_res[self.i2] * (self.t_res[self.i2]-1) * delta**self.d_res[self.i2] * tau**(self.t_res[self.i2]-2) * np.exp(-delta**self.c_res[self.i2])) term3 = 0.0 for i in self.i3: alpha_val = self.alpha_res[i] beta_val = self.beta_res[i] epsilon_val = self.epsilon_res[i] gamma_val = self.gamma_res[i] if not (np.isnan(alpha_val) or np.isnan(beta_val)): exp_term = np.exp(-alpha_val*(delta-epsilon_val)**2 - beta_val*(tau-gamma_val)**2) tau_factor = (self.t_res[i]/tau - 2*beta_val*(tau-gamma_val)) term3 += (self.n_res[i] * delta**self.d_res[i] * tau**self.t_res[i] * exp_term * (tau_factor**2 - self.t_res[i]/tau**2 - 2*beta_val)) term4 = 0.0 for i in self.i4: if not np.isnan(self.b_res[i]): delta_func = self._delta_function(i, delta, tau) psi_val = self._psi_function(i, delta, tau) psi_derivs = self._psi_derivatives(i, delta, tau) delta_derivs = self._delta_derivatives(i, delta, tau) term4 += (self.n_res[i] * delta * (delta_derivs['d2Delta_bi_dtau2'] * psi_val + 2*delta_derivs['dDelta_bi_dtau'] * psi_derivs['dPsi_dtau'] + delta_func**self.b_res[i] * psi_derivs['d2Psi_dtau2'])) return term1 + term2 + term3 + term4 elif derivative == 'phi.delta.tau': # phi.delta.tau implementation (R CHNOSZ lines 241-248) term1 = np.sum(self.n_res[self.i1] * self.d_res[self.i1] * self.t_res[self.i1] * delta**(self.d_res[self.i1]-1) * tau**(self.t_res[self.i1]-1)) term2 = np.sum(self.n_res[self.i2] * self.t_res[self.i2] * delta**(self.d_res[self.i2]-1) * tau**(self.t_res[self.i2]-1) * (self.d_res[self.i2] - self.c_res[self.i2]*delta**self.c_res[self.i2]) * np.exp(-delta**self.c_res[self.i2])) term3 = 0.0 for i in self.i3: alpha_val = self.alpha_res[i] beta_val = self.beta_res[i] epsilon_val = self.epsilon_res[i] gamma_val = self.gamma_res[i] if not (np.isnan(alpha_val) or np.isnan(beta_val)): exp_term = np.exp(-alpha_val*(delta-epsilon_val)**2 - beta_val*(tau-gamma_val)**2) delta_factor = (self.d_res[i]/delta - 2*alpha_val*(delta-epsilon_val)) tau_factor = (self.t_res[i]/tau - 2*beta_val*(tau-gamma_val)) term3 += (self.n_res[i] * delta**self.d_res[i] * tau**self.t_res[i] * exp_term * delta_factor * tau_factor) term4 = 0.0 for i in self.i4: if not np.isnan(self.b_res[i]): delta_func = self._delta_function(i, delta, tau) psi_val = self._psi_function(i, delta, tau) psi_derivs = self._psi_derivatives(i, delta, tau) delta_derivs = self._delta_derivatives(i, delta, tau) term4 += (self.n_res[i] * (delta_func**self.b_res[i] * (psi_derivs['dPsi_dtau'] + delta*psi_derivs['d2Psi_ddelta_dtau']) + delta*delta_derivs['dDelta_bi_ddelta']*psi_derivs['dPsi_dtau'] + delta_derivs['dDelta_bi_dtau'] * (psi_val + delta*psi_derivs['dPsi_ddelta']) + delta_derivs['d2Delta_bi_ddelta_dtau']*delta*psi_val)) return term1 + term2 + term3 + term4 else: raise ValueError(f"Unknown derivative: {derivative}") def calculate_IAPWS95_property(self, property_name: str, T: float, rho: float) -> float: """ Calculate individual IAPWS95 property (matching R CHNOSZ IAPWS95 function). Parameters ---------- property_name : str Property name (matching R CHNOSZ property names) T : float Temperature in K rho : float Density in kg/m³ Returns ------- float Property value """ # Calculate dimensionless variables (Equation 6.4) delta = rho / self.rhoc tau = self.Tc / T # Property calculations matching R CHNOSZ (lines 32-81) if property_name.lower() == 'p': # Pressure in MPa (R line 34: x*rho*R*T/1000) x = 1 + delta * self._phi_residual(delta, tau, 'phi.delta') return x * rho * self.R * T / 1000.0 elif property_name.lower() == 's': # Entropy in kJ/(kg·K) (R lines 36-38) phi_ideal = self._phi_ideal(delta, tau, 'phi') phi_residual = self._phi_residual(delta, tau, 'phi') phi_tau_ideal = self._phi_ideal(delta, tau, 'phi.tau') phi_tau_residual = self._phi_residual(delta, tau, 'phi.tau') x = tau * (phi_tau_ideal + phi_tau_residual) - phi_ideal - phi_residual return x * self.R elif property_name.lower() == 'u': # Internal energy in kJ/kg (R lines 40-42) phi_tau_ideal = self._phi_ideal(delta, tau, 'phi.tau') phi_tau_residual = self._phi_residual(delta, tau, 'phi.tau') x = tau * (phi_tau_ideal + phi_tau_residual) return x * self.R * T elif property_name.lower() == 'h': # Enthalpy in kJ/kg (R lines 44-46) phi_tau_ideal = self._phi_ideal(delta, tau, 'phi.tau') phi_tau_residual = self._phi_residual(delta, tau, 'phi.tau') phi_delta_residual = self._phi_residual(delta, tau, 'phi.delta') x = 1 + tau * (phi_tau_ideal + phi_tau_residual) + delta * phi_delta_residual return x * self.R * T elif property_name.lower() == 'g': # Gibbs energy in kJ/kg (R lines 48-50) phi_ideal = self._phi_ideal(delta, tau, 'phi') phi_residual = self._phi_residual(delta, tau, 'phi') phi_delta_residual = self._phi_residual(delta, tau, 'phi.delta') x = 1 + phi_ideal + phi_residual + delta * phi_delta_residual return x * self.R * T elif property_name.lower() == 'cv': # Isochoric heat capacity in kJ/(kg·K) (R lines 52-54) phi_tau_tau_ideal = self._phi_ideal(delta, tau, 'phi.tau.tau') phi_tau_tau_residual = self._phi_residual(delta, tau, 'phi.tau.tau') x = -tau**2 * (phi_tau_tau_ideal + phi_tau_tau_residual) return x * self.R elif property_name.lower() == 'cp': # Isobaric heat capacity in kJ/(kg·K) (R lines 56-60) phi_tau_tau_ideal = self._phi_ideal(delta, tau, 'phi.tau.tau') phi_tau_tau_residual = self._phi_residual(delta, tau, 'phi.tau.tau') phi_delta_residual = self._phi_residual(delta, tau, 'phi.delta') phi_delta_tau_residual = self._phi_residual(delta, tau, 'phi.delta.tau') phi_delta_delta_residual = self._phi_residual(delta, tau, 'phi.delta.delta') term1 = -tau**2 * (phi_tau_tau_ideal + phi_tau_tau_residual) term2 = ((1 + delta*phi_delta_residual - delta*tau*phi_delta_tau_residual)**2 / (1 + 2*delta*phi_delta_residual + delta**2*phi_delta_delta_residual)) x = term1 + term2 return x * self.R elif property_name.lower() == 'w': # Speed of sound in m/s (R lines 71-75) phi_tau_tau_ideal = self._phi_ideal(delta, tau, 'phi.tau.tau') phi_tau_tau_residual = self._phi_residual(delta, tau, 'phi.tau.tau') phi_delta_residual = self._phi_residual(delta, tau, 'phi.delta') phi_delta_tau_residual = self._phi_residual(delta, tau, 'phi.delta.tau') phi_delta_delta_residual = self._phi_residual(delta, tau, 'phi.delta.delta') x = (1 + 2*delta*phi_delta_residual + delta**2*phi_delta_delta_residual - ((1 + delta*phi_delta_residual - delta*tau*phi_delta_tau_residual)**2 / (tau**2 * (phi_tau_tau_ideal + phi_tau_tau_residual)))) return np.sqrt(x * self.R * T) else: raise ValueError(f"Unknown property: {property_name}") def calculate(self, properties: Union[str, List[str]], T: Union[float, np.ndarray] = 298.15, rho: Union[float, np.ndarray] = 1000.0) -> Union[float, np.ndarray, Dict[str, Any]]: """ Calculate water properties using accurate IAPWS-95. Parameters ---------- properties : str or list of str Property or list of properties to calculate T : float or array Temperature in Kelvin rho : float or array Density in kg/m³ Returns ------- float, array, or dict Calculated properties """ # Handle input types if isinstance(properties, str): properties = [properties] single_prop = True else: single_prop = False # Convert inputs to arrays T = np.atleast_1d(np.asarray(T, dtype=float)) rho = np.atleast_1d(np.asarray(rho, dtype=float)) # Ensure same length max_len = max(len(T), len(rho)) if len(T) < max_len: T = np.resize(T, max_len) if len(rho) < max_len: rho = np.resize(rho, max_len) # Calculate properties results = {} for prop in properties: prop_values = np.full(max_len, np.nan) for i in range(max_len): if not (np.isnan(T[i]) or np.isnan(rho[i]) or T[i] <= 0 or rho[i] <= 0): try: prop_values[i] = self.calculate_IAPWS95_property(prop, T[i], rho[i]) except Exception: prop_values[i] = np.nan results[prop] = prop_values if len(prop_values) > 1 else prop_values[0] # Return results if single_prop: return results[properties[0]] else: return resultsAccurate IAPWS-95 water model implementation matching R CHNOSZ exactly.
This class provides thermodynamic properties of water using the IAPWS-95 formulation with exact coefficients and derivative calculations from the Wagner & Pruss (2002) specification as implemented in R CHNOSZ.
Initialize IAPWS95 water model with exact constants.
Methods
def calculate(self,
properties: str | List[str],
T: float | numpy.ndarray = 298.15,
rho: float | numpy.ndarray = 1000.0) ‑> float | numpy.ndarray | Dict[str, Any]-
Expand source code
def calculate(self, properties: Union[str, List[str]], T: Union[float, np.ndarray] = 298.15, rho: Union[float, np.ndarray] = 1000.0) -> Union[float, np.ndarray, Dict[str, Any]]: """ Calculate water properties using accurate IAPWS-95. Parameters ---------- properties : str or list of str Property or list of properties to calculate T : float or array Temperature in Kelvin rho : float or array Density in kg/m³ Returns ------- float, array, or dict Calculated properties """ # Handle input types if isinstance(properties, str): properties = [properties] single_prop = True else: single_prop = False # Convert inputs to arrays T = np.atleast_1d(np.asarray(T, dtype=float)) rho = np.atleast_1d(np.asarray(rho, dtype=float)) # Ensure same length max_len = max(len(T), len(rho)) if len(T) < max_len: T = np.resize(T, max_len) if len(rho) < max_len: rho = np.resize(rho, max_len) # Calculate properties results = {} for prop in properties: prop_values = np.full(max_len, np.nan) for i in range(max_len): if not (np.isnan(T[i]) or np.isnan(rho[i]) or T[i] <= 0 or rho[i] <= 0): try: prop_values[i] = self.calculate_IAPWS95_property(prop, T[i], rho[i]) except Exception: prop_values[i] = np.nan results[prop] = prop_values if len(prop_values) > 1 else prop_values[0] # Return results if single_prop: return results[properties[0]] else: return resultsCalculate water properties using accurate IAPWS-95.
Parameters
properties:strorlistofstr- Property or list of properties to calculate
T:floatorarray- Temperature in Kelvin
rho:floatorarray- Density in kg/m³
Returns
float, array,ordict- Calculated properties
def calculate_IAPWS95_property(self, property_name: str, T: float, rho: float) ‑> float-
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def calculate_IAPWS95_property(self, property_name: str, T: float, rho: float) -> float: """ Calculate individual IAPWS95 property (matching R CHNOSZ IAPWS95 function). Parameters ---------- property_name : str Property name (matching R CHNOSZ property names) T : float Temperature in K rho : float Density in kg/m³ Returns ------- float Property value """ # Calculate dimensionless variables (Equation 6.4) delta = rho / self.rhoc tau = self.Tc / T # Property calculations matching R CHNOSZ (lines 32-81) if property_name.lower() == 'p': # Pressure in MPa (R line 34: x*rho*R*T/1000) x = 1 + delta * self._phi_residual(delta, tau, 'phi.delta') return x * rho * self.R * T / 1000.0 elif property_name.lower() == 's': # Entropy in kJ/(kg·K) (R lines 36-38) phi_ideal = self._phi_ideal(delta, tau, 'phi') phi_residual = self._phi_residual(delta, tau, 'phi') phi_tau_ideal = self._phi_ideal(delta, tau, 'phi.tau') phi_tau_residual = self._phi_residual(delta, tau, 'phi.tau') x = tau * (phi_tau_ideal + phi_tau_residual) - phi_ideal - phi_residual return x * self.R elif property_name.lower() == 'u': # Internal energy in kJ/kg (R lines 40-42) phi_tau_ideal = self._phi_ideal(delta, tau, 'phi.tau') phi_tau_residual = self._phi_residual(delta, tau, 'phi.tau') x = tau * (phi_tau_ideal + phi_tau_residual) return x * self.R * T elif property_name.lower() == 'h': # Enthalpy in kJ/kg (R lines 44-46) phi_tau_ideal = self._phi_ideal(delta, tau, 'phi.tau') phi_tau_residual = self._phi_residual(delta, tau, 'phi.tau') phi_delta_residual = self._phi_residual(delta, tau, 'phi.delta') x = 1 + tau * (phi_tau_ideal + phi_tau_residual) + delta * phi_delta_residual return x * self.R * T elif property_name.lower() == 'g': # Gibbs energy in kJ/kg (R lines 48-50) phi_ideal = self._phi_ideal(delta, tau, 'phi') phi_residual = self._phi_residual(delta, tau, 'phi') phi_delta_residual = self._phi_residual(delta, tau, 'phi.delta') x = 1 + phi_ideal + phi_residual + delta * phi_delta_residual return x * self.R * T elif property_name.lower() == 'cv': # Isochoric heat capacity in kJ/(kg·K) (R lines 52-54) phi_tau_tau_ideal = self._phi_ideal(delta, tau, 'phi.tau.tau') phi_tau_tau_residual = self._phi_residual(delta, tau, 'phi.tau.tau') x = -tau**2 * (phi_tau_tau_ideal + phi_tau_tau_residual) return x * self.R elif property_name.lower() == 'cp': # Isobaric heat capacity in kJ/(kg·K) (R lines 56-60) phi_tau_tau_ideal = self._phi_ideal(delta, tau, 'phi.tau.tau') phi_tau_tau_residual = self._phi_residual(delta, tau, 'phi.tau.tau') phi_delta_residual = self._phi_residual(delta, tau, 'phi.delta') phi_delta_tau_residual = self._phi_residual(delta, tau, 'phi.delta.tau') phi_delta_delta_residual = self._phi_residual(delta, tau, 'phi.delta.delta') term1 = -tau**2 * (phi_tau_tau_ideal + phi_tau_tau_residual) term2 = ((1 + delta*phi_delta_residual - delta*tau*phi_delta_tau_residual)**2 / (1 + 2*delta*phi_delta_residual + delta**2*phi_delta_delta_residual)) x = term1 + term2 return x * self.R elif property_name.lower() == 'w': # Speed of sound in m/s (R lines 71-75) phi_tau_tau_ideal = self._phi_ideal(delta, tau, 'phi.tau.tau') phi_tau_tau_residual = self._phi_residual(delta, tau, 'phi.tau.tau') phi_delta_residual = self._phi_residual(delta, tau, 'phi.delta') phi_delta_tau_residual = self._phi_residual(delta, tau, 'phi.delta.tau') phi_delta_delta_residual = self._phi_residual(delta, tau, 'phi.delta.delta') x = (1 + 2*delta*phi_delta_residual + delta**2*phi_delta_delta_residual - ((1 + delta*phi_delta_residual - delta*tau*phi_delta_tau_residual)**2 / (tau**2 * (phi_tau_tau_ideal + phi_tau_tau_residual)))) return np.sqrt(x * self.R * T) else: raise ValueError(f"Unknown property: {property_name}")Calculate individual IAPWS95 property (matching R CHNOSZ IAPWS95 function).
Parameters
property_name:str- Property name (matching R CHNOSZ property names)
T:float- Temperature in K
rho:float- Density in kg/m³
Returns
float- Property value
class IAPWS95Water-
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class IAPWS95Water: """ IAPWS-95 water model interface class. This class provides thermodynamic properties of water using the IAPWS-95 formulation based on a fundamental equation for the Helmholtz free energy. This interface handles unit conversions and provides a standardized API that matches other water models in the package. """ def __init__(self): """Initialize IAPWS95 water model.""" pass def available_properties(self) -> List[str]: """ Get list of available properties. Returns ------- List[str] List of available property names """ return ['P', 'S', 'U', 'H', 'G', 'Cv', 'Cp', 'w', 'rho'] def calculate(self, properties: Union[str, List[str]], T: Union[float, np.ndarray] = 298.15, P: Union[float, np.ndarray] = 100.0) -> Union[float, np.ndarray, Dict[str, Any]]: """ Calculate water properties using IAPWS-95. Parameters ---------- properties : str or list of str Property or list of properties to calculate T : float or array Temperature in Kelvin P : float or array Pressure in kPa Returns ------- float, array, or dict Calculated properties """ # Convert pressure from kPa to bar for the accurate implementation if isinstance(P, (int, float)): P_bar = P / 100.0 else: P_bar = np.asarray(P) / 100.0 # Use the accurate implementation (defined above in this file) return water_IAPWS95_accurate(properties, T=T, P=P_bar)IAPWS-95 water model interface class.
This class provides thermodynamic properties of water using the IAPWS-95 formulation based on a fundamental equation for the Helmholtz free energy.
This interface handles unit conversions and provides a standardized API that matches other water models in the package.
Initialize IAPWS95 water model.
Methods
def available_properties(self) ‑> List[str]-
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def available_properties(self) -> List[str]: """ Get list of available properties. Returns ------- List[str] List of available property names """ return ['P', 'S', 'U', 'H', 'G', 'Cv', 'Cp', 'w', 'rho']Get list of available properties.
Returns
List[str]- List of available property names
def calculate(self,
properties: str | List[str],
T: float | numpy.ndarray = 298.15,
P: float | numpy.ndarray = 100.0) ‑> float | numpy.ndarray | Dict[str, Any]-
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def calculate(self, properties: Union[str, List[str]], T: Union[float, np.ndarray] = 298.15, P: Union[float, np.ndarray] = 100.0) -> Union[float, np.ndarray, Dict[str, Any]]: """ Calculate water properties using IAPWS-95. Parameters ---------- properties : str or list of str Property or list of properties to calculate T : float or array Temperature in Kelvin P : float or array Pressure in kPa Returns ------- float, array, or dict Calculated properties """ # Convert pressure from kPa to bar for the accurate implementation if isinstance(P, (int, float)): P_bar = P / 100.0 else: P_bar = np.asarray(P) / 100.0 # Use the accurate implementation (defined above in this file) return water_IAPWS95_accurate(properties, T=T, P=P_bar)Calculate water properties using IAPWS-95.
Parameters
properties:strorlistofstr- Property or list of properties to calculate
T:floatorarray- Temperature in Kelvin
P:floatorarray- Pressure in kPa
Returns
float, array,ordict- Calculated properties