def Rac_Nusselt_Rayleigh(H, L, W, insulated=True):
r'''Calculates the critical Rayleigh number for free convection to begin
in the Nusselt-Rayleigh parallel horizontal plate scenario. There are
actually two cases - one for the top plate to be insulated (adiabatic) and
the other where it has infinite thermal conductivity/is infinitely thin or
not present (perfectly conducting). All real cases will lie between the
two.
Parameters
----------
H : float
Distance between the two plates, [m]
L : float
Length of the plates, [m]
W : float
Width of the plates, [m]
insulated : bool, optional
Whether the top plate is insulated or uninsulated, [-]
Returns
-------
Rac : float
Critical Rayleigh number, [-]
Examples
--------
>>> Rac_Nusselt_Rayleigh(1, .5, 2, False)
2530.500000000005
>>> Rac_Nusselt_Rayleigh(1, .5, 2, True)
2071.0089443385655
Notes
-----
Splines have been fit to data in [1]_ for the uninsulated case and [2]_
for the insulated case. The data is presented in the original papers and
in [3]_.
References
----------
.. [1] Catton, Ivan. "Effect of Wall Conduction on the Stability of a Fluid
in a Rectangular Region Heated from Below." Journal of Heat Transfer 94,
no. 4 (November 1, 1972): 446-52. https://doi.org/10.1115/1.3449966.
.. [2] Catton, Ivan. "Convection in a Closed Rectangular Region: The Onset
of Motion." Journal of Heat Transfer 92, no. 1 (February 1, 1970):
186-88. https://doi.org/10.1115/1.3449626.
.. [3] Rohsenow, Warren and James Hartnett and Young Cho. Handbook of Heat
Transfer, 3E. New York: McGraw-Hill, 1998.
'''
H_L_ratio = min(max(H / L, 0.125), 12.0)
W_L_ratio = min(max(W / L, 0.125), 12.0)
if insulated:
Rac = exp(bisplev(W_L_ratio, H_L_ratio, tck_insulated_Catton))
else:
Rac = exp(bisplev(W_L_ratio, H_L_ratio, tck_uninstulated_Catton))
return Rac
def API520_SH(T1, P1):
r'''Calculates correction due to steam superheat for steam flow for use in
API 520 relief valve sizing. 2D interpolation among a table with 28
pressures and 10 temperatures is performed.
Parameters
----------
T1 : float
Temperature of the fluid entering the valve [K]
P1 : float
Upstream relieving pressure; the set pressure plus the allowable
overpressure, plus atmospheric pressure, [Pa]
Returns
-------
KSH : float
Correction due to steam superheat [-]
Notes
-----
For P above 20679 kPag, use the critical flow model.
Superheat cannot be above 649 degrees Celsius.
If T1 is above 149 degrees Celsius, returns 1.
Examples
--------
Custom example from table 9:
>>> API520_SH(593+273.15, 1066.325E3)
0.7201800000000002
References
----------
.. [1] API Standard 520, Part 1 - Sizing and Selection.
'''
if P1 > 20780325.0: # 20679E3+atm
raise Exception('For P above 20679 kPag, use the critical flow model')
if T1 > 922.15:
raise Exception('Superheat cannot be above 649 degrees Celcius')
if T1 < 422.15:
return 1. # No superheat under 15 psig
return float(bisplev(T1, P1, API520_KSH_tck))
def API520_SH(T1, P1):
r'''Calculates correction due to steam superheat for steam flow for use in
API 520 relief valve sizing. 2D interpolation among a table with 28
pressures and 10 temperatures is performed.
Parameters
----------
T1 : float
Temperature of the fluid entering the valve [K]
P1 : float
Upstream relieving pressure; the set pressure plus the allowable
overpressure, plus atmospheric pressure, [Pa]
Returns
-------
KSH : float
Correction due to steam superheat [-]
Notes
-----
For P above 20679 kPag, use the critical flow model.
Superheat cannot be above 649 degrees Celsius.
If T1 is above 149 degrees Celsius, returns 1.
Examples
--------
Custom example from table 9:
>>> API520_SH(593+273.15, 1066.325E3)
0.7201800000000002
References
----------
.. [1] API Standard 520, Part 1 - Sizing and Selection.
'''
if P1 > 20780325.0: # 20679E3+atm
raise Exception('For P above 20679 kPag, use the critical flow model')
if T1 > 922.15:
raise Exception('Superheat cannot be above 649 degrees Celcius')
if T1 < 422.15:
return 1. # No superheat under 15 psig
return float(bisplev(T1, P1, API520_KSH_tck))