def __init__(self, identifier: str = 'gas',
latex: Optional[str] = None,
comment: Optional[str] = None) -> None:
"""
Args:
identifier:
Identifier of matter
latex:
Latex-version of identifier. If None, identical with identifier
comment:
Comment on matter
Note:
Do NOT define a self.__call__() method in this class
"""
super().__init__(identifier=identifier, latex=latex, comment=comment)
# self.a.calc = self._a
self.D_in_air = Property('D_in_air', 'm2/s',
calc=lambda T, p=atm(), x=0.: None)
self.T.ref = C2K(15.)
def _rho_el(self,
T: float = C2K(20),
p: float = atm(),
x: float = 0.) -> float:
"""
Reference:
Rykalin, in Radaj: Heat Effects of Welding, Springer 1992, p.68
T[deg C] rho [Ohm*mm]
0 1.26e-4
400 4e-4
800 10.2e-4
1200 12e-4
1600 12.6e-4
"""
T_Celsius = max(K2C(T), 20.)
# specific resistance in [Ohm m]
if T_Celsius < 800:
rho_el = (
(1.081e-8 * T_Celsius + 2.53e-6) * T_Celsius + 1.26e-3) * 1e-4
elif T < self.T_sol:
rho_el = (
(-3.75e-9 * T_Celsius + 1.2e-5) * T_Celsius + 3e-3) * 1e-4
else:
rho_el = 2 * 1.2e-6
return rho_el
def __init__(self, identifier: str = 'matter',
latex: Optional[str] = None,
comment: Optional[str] = None) -> None:
"""
Args:
identifier:
Identifier of matter
latex:
Latex-version of identifier.
If None, latex is identical with identifier
comment:
Comment on matter
Note:
Do NOT define a self.__call__() method in this class
"""
super().__init__(identifier=identifier, latex=latex, comment=comment)
self.a = Property('a', 'm$^2$/s', comment='thermal diffusity',
calc = self._a)
self.beta = Property('beta', '1/K', latex=r'$\beta_{th}$',
comment='volumetric thermal expansion')
self.c_p = Property('c_p', 'J/kg/K',
comment='specific heat capacity')
self.c_sound = Property('c_sound', 'm/s', latex='$c_{sound}$')
self.c_sound.calc = lambda T, p, x: None
self.composition: Dict[str, float] = OrderedDict()
self.compressible: bool = False
self.E = Property('E', 'Pa', comment="Young's (elastic) modulus")
self.h_melt: float = None
self.h_vap: float = None
self.k = Property('k', 'W/m/K', latex='$k$',
comment='thermal conductivity')
self.M = Property('M', 'kmol/kg', comment='molar mass')
self.M.calc = lambda T=0, p=0, x=0: None
self.nu_mech: float = None
self.rho = Property('rho', 'kg/m$^3$', latex=r'$\varrho$', ref=1.,
comment='density')
self.rho.T.ref = C2K(20.)
self.rho.p.ref = atm()
self.rho_el = Property('rho_el', r'$\Omega$', latex=r'$\varrho_{el}$',
comment='electric resistance')
self.T_boil: float = 0.
self.T_flash_point: float = 0.
self.T_liq: float = 0.
self.T_melt: float = 0.
self.T_sol: float = 0.
if self.E() is None or np.abs(self.E()) < 1e-20:
self.rho.calc = lambda T, p, x: self.rho.ref \
/ (1. + (T - self.rho.T.ref) * self.beta())
else:
self.rho.calc = lambda T, p, x: self.rho.ref \
/ (1. + (T - self.rho.T.ref) * self.beta()) \
/ (1. - (p - self.rho.p.ref) / self.E())
def _nu(self, T: float, p: float = atm(),
x: float = 0.) -> Optional[float]:
try:
rho = self.rho(T, p, x)
if rho is None or np.abs(rho) < 1e-10:
return None
return self.mu(T, p, x) / rho
except:
return None
def _mu(self,
T: float = C2K(20),
p: float = atm(),
x: float = 0.) -> float:
"""
[JONE96]: eta = eta0 * exp(E / (R*T)), eta0 = 0.3699e-3 kg/(m s),
E = 41.4e3 J/mol, and R = 8.3144 J/(K mol)
"""
return 0.3699e-3 * np.exp(41.4e3 / (8.3144*T)) \
if T > self.T_deform else 1e20
def set_all_ref(self, T: float, p: float = atm(), x: float = 0.) -> bool:
none_set = True
for attr in dir(self):
if not attr.startswith('_'):
val = getattr(self, attr)
if isinstance(val, Property):
print(f'{attr=}, {val=}')
none_set = False
val.T.ref = T
val.p.ref = p
val.x.ref = x
return not none_set
def _a(self, T: float, p: float = atm(), x: float = 0.) -> Optional[float]:
try:
k = self.k(T, p, x)
c_p = self.c_p(T, p, x)
rho = self.rho(T, p, x)
if k is None or c_p is None or rho is None:
return None
c_p__rho = c_p * rho
if np.abs(c_p__rho) < 1e-10:
return None
return k / c_p__rho
except:
return None
def _c_p(self,
T: float = C2K(20),
p: float = atm(),
x: float = 0.) -> float:
Tp = [
300, 600, 900, 1033, 1040, 1184, 1184.1, 1400, 1673, 1673.1, 1809,
1809.1, 2000, 3000
]
Up = [
430, 580, 760, 1260, 1160, 720, 610, 640, 680, 730, 760, 790, 790,
790
]
return np.interp(T, Tp, Up)
def _mu(self, T: float, p: float = atm(), x: float = 0.) -> float:
y_all, M_all, mu_all = [], [], []
for gas, mole_frac in self.components.items():
if mole_frac < 1e-8:
continue
p_partial = mole_frac * p
y_all.append(mole_frac)
M_all.append(gas.M(T, p, x))
mu_all.append(gas.mu(T, p_partial, x))
return mix_mole(y=y_all, M=M_all, property_=mu_all)
def _rho(self, T: float, p: float = atm(), x: float = 0.) -> float:
rho = 0.
for gas, mole_frac in self.components.items():
if mole_frac < 1e-8:
continue
p_partial = mole_frac * p
rho_i = gas.rho(T, p_partial, x)
if rho_i is None:
return None
rho += mole_frac * rho_i
return rho
def _rho(self,
T: float = C2K(20),
p: float = atm(),
x: float = 0.) -> float:
"""
Reference for liquid iron:
Steinberg, D. J.: Met. Trans. 5 (1974), 1341, in [Iida93]
"""
T_Celsius = min(K2C(T), 1600)
if T_Celsius > 1536:
rho = 7030 + (-8.8e-1) * (T_Celsius - 1536)
elif T_Celsius > 723:
rho = (-1e-4 * T_Celsius - 0.2) * T_Celsius + 7852.3
else:
rho = (-1e-4 * T_Celsius - 0.3) * T_Celsius + 7849.1
return rho
def __init__(self,
identifier: str = 'Property',
unit: str = '/',
absolute: bool = True,
latex: Optional[str] = None,
val: Optional[Union[float, Iterable[float]]] = None,
ref: Optional[Union[float, Iterable[float]]] = None,
comment: Optional[str] = None,
calc: Optional[Callable[..., float]] = None) -> None:
super().__init__(identifier=identifier,
unit=unit,
absolute=absolute,
latex=latex,
val=val,
ref=ref,
comment=comment)
# reference temperature gases: 15C, solids: 20C or 25C, liquids: 20C
T_Celsius = 20.
self.T = Parameter(identifier='T', unit='K', absolute=True)
self.T.ref = C2K(T_Celsius)
self.T['operational'] = Range(C2K(-40.), C2K(200.))
self.T.accuracy = Range('-1', '+1')
self.p = Parameter(identifier='p', unit='Pa', absolute=True)
self.p.ref = atm()
self.p['operational'] = Range(0. + self.p.ref, 100e5 + self.p.ref)
self.p.accuracy = Range('-1%FS', '+1%FS')
self.x = Parameter(identifier='x', unit='/', absolute=True)
self.x['operational'] = Range(0., 1.)
self.x.ref = 0.
self.accuracy = Range('-1%', '1%')
self.repeatability = Range('-0.1', '+0.1', '95%')
if calc is None:
calc = lambda T, p, x: 1.
self.calc = calc
self.regression_coefficients: Optional[Iterable[float]] = None
def _k(self, T: float, p: float = atm(), x: float = 0.) -> float:
y_all, M_all, k_all, mu_all = [], [], [], []
for gas, mole_frac in self.components.items():
if mole_frac < 1e-8:
continue
p_partial = mole_frac * p
y_all.append(mole_frac)
M_all.append(gas.M(T, p, x))
k_all.append(gas.k(T, p_partial, x))
mu_all.append(gas.mu(T, p_partial, x))
if self._k_mix_formula.startswith('mas'):
k = mix_mason(y=y_all, M=M_all, k=k_all, mu=mu_all)
else:
k = mix_mole(y=y_all, M=M_all, property_=k_all)
return k
def _mu(self, T: float, p: float = atm(),
x: float = 0.) -> Optional[float]:
try:
return self.nu(T, p, x) * self.rho(T, p, x)
except:
return None
def _k(self, T: float = C2K(20), p: float = atm(), x: float = 0.) -> float:
Tp = [
300, 600, 900, 1184, 1400, 1673, 1673.1, 1809, 1809.1, 2000, 3000
]
Up = [59.6, 54.6, 37.4, 28.2, 30.6, 33.7, 33.4, 34.6, 40.3, 42.6, 48]
return np.interp(T, Tp, Up)