def h_ESDU_low_fin(m,
A,
A_min,
A_increase,
A_fin,
A_tube_showing,
tube_diameter,
fin_diameter,
fin_thickness,
bare_length,
pitch_parallel,
pitch_normal,
tube_rows,
rho,
Cp,
mu,
k,
k_fin,
Pr_wall=None):
r'''Calculates the air side heat transfer coefficient for an air cooler
or other finned tube bundle with low fins using the formulas of [1]_ as
presented in [2]_ (and also [3]_).
.. math::
Nu = 0.183Re^{0.7} \left(\frac{\text{bare length}}{\text{fin height}}
\right)^{0.36}\left(\frac{p_1}{D_{o}}\right)^{0.06}
\left(\frac{\text{fin height}}{D_o}\right)^{0.11}
Pr^{0.36} \cdot F_1\cdot F_2
.. math::
h_{A,total} = \frac{\eta A_{fin} + A_{bare, showing}}{A_{total}} h
.. math::
h_{bare,total} = A_{increase} h_{A,total}
Parameters
----------
m : float
Mass flow rate of air across the tube bank, [kg/s]
A : float
Surface area of combined finned and non-finned area exposed for heat
transfer, [m^2]
A_min : float
Minimum air flow area, [m^2]
A_increase : float
Ratio of actual surface area to bare tube surface area
:math:`A_{increase} = \frac{A_{tube}}{A_{bare, total/tube}}`, [-]
A_fin : float
Surface area of all fins in the bundle, [m^2]
A_tube_showing : float
Area of the bare tube which is exposed in the bundle, [m^2]
tube_diameter : float
Diameter of the bare tube, [m]
fin_diameter : float
Outer diameter of each tube after including the fin on both sides,
[m]
fin_thickness : float
Thickness of the fins, [m]
bare_length : float
Length of bare tube between two fins
:math:`\text{bare length} = \text{fin interval} - t_{fin}`, [m]
pitch_parallel : float
Distance between tube center along a line parallel to the flow;
has been called `longitudinal` pitch, `pp`, `s2`, `SL`, and `p2`, [m]
pitch_normal : float
Distance between tube centers in a line 90° to the line of flow;
has been called the `transverse` pitch, `pn`, `s1`, `ST`, and `p1`, [m]
tube_rows : int
Number of tube rows per bundle, [-]
rho : float
Average (bulk) density of air across the tube bank, [kg/m^3]
Cp : float
Average (bulk) heat capacity of air across the tube bank, [J/kg/K]
mu : float
Average (bulk) viscosity of air across the tube bank, [Pa*s]
k : float
Average (bulk) thermal conductivity of air across the tube bank,
[W/m/K]
k_fin : float
Thermal conductivity of the fin, [W/m/K]
Pr_wall : float, optional
Prandtl number at the wall temperature; provide if a correction with
the defaults parameters is desired; otherwise apply the correction
elsewhere, [-]
Returns
-------
h_bare_tube_basis : float
Air side heat transfer coefficient on a bare-tube surface area as if
there were no fins present basis, [W/K/m^2]
Notes
-----
The tube-row count correction factor `F2` can be disabled by setting `tube_rows`
to 10. The property correction factor `F1` can be disabled by not specifying
`Pr_wall`. A Prandtl number exponent of 0.26 is recommended in [1]_ for
heating and cooling for both liquids and gases.
There is a third correction factor in [1]_ for tube angles not 30, 45, or
60 degrees, but it is not fully explained and it is not shown in [2]_.
Another correction factor is in [2]_ for flow at an angle; however it would
not make sense to apply it to finned tube banks due to the blockage by the
fins.
Examples
--------
>>> AC = AirCooledExchanger(tube_rows=4, tube_passes=4, tubes_per_row=8, tube_length=0.5,
... tube_diameter=0.0164, fin_thickness=0.001, fin_density=1/0.003,
... pitch_normal=0.0313, pitch_parallel=0.0271, fin_height=0.0041, corbels=True)
>>> h_ESDU_low_fin(m=0.914, A=AC.A, A_min=AC.A_min, A_increase=AC.A_increase, A_fin=AC.A_fin,
... A_tube_showing=AC.A_tube_showing, tube_diameter=AC.tube_diameter,
... fin_diameter=AC.fin_diameter, bare_length=AC.bare_length,
... fin_thickness=AC.fin_thickness, tube_rows=AC.tube_rows,
... pitch_normal=AC.pitch_normal, pitch_parallel=AC.pitch_parallel,
... rho=1.217, Cp=1007., mu=1.8E-5, k=0.0253, k_fin=15)
553.853836470948
References
----------
.. [1] Hewitt, G. L. Shires, T. Reg Bott G. F., George L. Shires, and T.
R. Bott. Process Heat Transfer. 1st edition. Boca Raton: CRC Press,
1994.
.. [2] "High-Fin Staggered Tube Banks: Heat Transfer and Pressure Drop for
Turbulent Single Phase Gas Flow." ESDU 86022 (October 1, 1986).
.. [3] Rabas, T. J., and J. Taborek. "Survey of Turbulent Forced-Convection
Heat Transfer and Pressure Drop Characteristics of Low-Finned Tube Banks
in Cross Flow." Heat Transfer Engineering 8, no. 2 (January 1987):
49-62.
'''
fin_height = 0.5 * (fin_diameter - tube_diameter)
V_max = m / (A_min * rho)
Re = Reynolds(V=V_max, D=tube_diameter, rho=rho, mu=mu)
Pr = Prandtl(Cp=Cp, mu=mu, k=k)
Nu = (0.183 * Re**0.7 * (bare_length / fin_height)**0.36 *
(pitch_normal / fin_diameter)**0.06 *
(fin_height / fin_diameter)**0.11 * Pr**0.36)
staggered = abs(1 - pitch_normal / pitch_parallel) > 0.05
F2 = ESDU_tube_row_correction(tube_rows=tube_rows, staggered=staggered)
Nu *= F2
if Pr_wall is not None:
F1 = wall_factor(Pr=Pr,
Pr_wall=Pr_wall,
Pr_heating_coeff=0.26,
Pr_cooling_coeff=0.26,
property_option=WALL_FACTOR_PRANDTL)
Nu *= F1
h = k / tube_diameter * Nu
efficiency = fin_efficiency_Kern_Kraus(Do=tube_diameter,
D_fin=fin_diameter,
t_fin=fin_thickness,
k_fin=k_fin,
h=h)
h_total_area_basis = (efficiency * A_fin + A_tube_showing) / A * h
h_bare_tube_basis = h_total_area_basis * A_increase
return h_bare_tube_basis
def h_ESDU_high_fin(m,
A,
A_min,
A_increase,
A_fin,
A_tube_showing,
tube_diameter,
fin_diameter,
fin_thickness,
bare_length,
pitch_parallel,
pitch_normal,
tube_rows,
rho,
Cp,
mu,
k,
k_fin,
Pr_wall=None):
r'''Calculates the air side heat transfer coefficient for an air cooler
or other finned tube bundle with the formulas of [2]_ as presented in [1]_.
.. math::
Nu = 0.242 Re^{0.658} \left(\frac{\text{bare length}}
{\text{fin height}}\right)^{0.297}
\left(\frac{P_1}{P_2}\right)^{-0.091} P_r^{1/3}\cdot F_1\cdot F_2
.. math::
h_{A,total} = \frac{\eta A_{fin} + A_{bare, showing}}{A_{total}} h
.. math::
h_{bare,total} = A_{increase} h_{A,total}
Parameters
----------
m : float
Mass flow rate of air across the tube bank, [kg/s]
A : float
Surface area of combined finned and non-finned area exposed for heat
transfer, [m^2]
A_min : float
Minimum air flow area, [m^2]
A_increase : float
Ratio of actual surface area to bare tube surface area
:math:`A_{increase} = \frac{A_{tube}}{A_{bare, total/tube}}`, [-]
A_fin : float
Surface area of all fins in the bundle, [m^2]
A_tube_showing : float
Area of the bare tube which is exposed in the bundle, [m^2]
tube_diameter : float
Diameter of the bare tube, [m]
fin_diameter : float
Outer diameter of each tube after including the fin on both sides,
[m]
fin_thickness : float
Thickness of the fins, [m]
bare_length : float
Length of bare tube between two fins
:math:`\text{bare length} = \text{fin interval} - t_{fin}`, [m]
pitch_parallel : float
Distance between tube center along a line parallel to the flow;
has been called `longitudinal` pitch, `pp`, `s2`, `SL`, and `p2`, [m]
pitch_normal : float
Distance between tube centers in a line 90° to the line of flow;
has been called the `transverse` pitch, `pn`, `s1`, `ST`, and `p1`, [m]
tube_rows : int
Number of tube rows per bundle, [-]
rho : float
Average (bulk) density of air across the tube bank, [kg/m^3]
Cp : float
Average (bulk) heat capacity of air across the tube bank, [J/kg/K]
mu : float
Average (bulk) viscosity of air across the tube bank, [Pa*s]
k : float
Average (bulk) thermal conductivity of air across the tube bank,
[W/m/K]
k_fin : float
Thermal conductivity of the fin, [W/m/K]
Pr_wall : float, optional
Prandtl number at the wall temperature; provide if a correction with
the defaults parameters is desired; otherwise apply the correction
elsewhere, [-]
Returns
-------
h_bare_tube_basis : float
Air side heat transfer coefficient on a bare-tube surface area as if
there were no fins present basis, [W/K/m^2]
Notes
-----
The tube-row count correction factor is 1 for four or more rows, 0.92 for
three rows, 0.84 for two rows, and 0.76 for one row according to [1]_.
The property correction factor can be disabled by not specifying
`Pr_wall`. A Prandtl number exponent of 0.26 is recommended in [1]_ for
heating and cooling for both liquids and gases.
Examples
--------
>>> AC = AirCooledExchanger(tube_rows=4, tube_passes=4, tubes_per_row=20, tube_length=3,
... tube_diameter=1*inch, fin_thickness=0.000406, fin_density=1/0.002309,
... pitch_normal=.06033, pitch_parallel=.05207,
... fin_height=0.0159, tube_thickness=(.0254-.0186)/2,
... bundles_per_bay=1, parallel_bays=1, corbels=True)
>>> h_ESDU_high_fin(m=21.56, A=AC.A, A_min=AC.A_min, A_increase=AC.A_increase, A_fin=AC.A_fin,
... A_tube_showing=AC.A_tube_showing, tube_diameter=AC.tube_diameter,
... fin_diameter=AC.fin_diameter, bare_length=AC.bare_length,
... fin_thickness=AC.fin_thickness, tube_rows=AC.tube_rows,
... pitch_normal=AC.pitch_normal, pitch_parallel=AC.pitch_parallel,
... rho=1.161, Cp=1007., mu=1.85E-5, k=0.0263, k_fin=205)
1390.888918049757
References
----------
.. [1] Hewitt, G. L. Shires, T. Reg Bott G. F., George L. Shires, and T.
R. Bott. Process Heat Transfer. 1st edition. Boca Raton: CRC Press,
1994.
.. [2] "High-Fin Staggered Tube Banks: Heat Transfer and Pressure Drop for
Turbulent Single Phase Gas Flow." ESDU 86022 (October 1, 1986).
.. [3] Rabas, T. J., and J. Taborek. "Survey of Turbulent Forced-Convection
Heat Transfer and Pressure Drop Characteristics of Low-Finned Tube Banks
in Cross Flow." Heat Transfer Engineering 8, no. 2 (January 1987):
49-62.
'''
fin_height = 0.5 * (fin_diameter - tube_diameter)
V_max = m / (A_min * rho)
Re = Reynolds(V=V_max, D=tube_diameter, rho=rho, mu=mu)
Pr = Prandtl(Cp=Cp, mu=mu, k=k)
Nu = 0.242 * Re**0.658 * (bare_length / fin_height)**0.297 * (
pitch_normal / pitch_parallel)**-0.091 * Pr**(1 / 3.)
if tube_rows < 2:
F2 = 0.76
elif tube_rows < 3:
F2 = 0.84
elif tube_rows < 4:
F2 = 0.92
else:
F2 = 1.0
Nu *= F2
if Pr_wall is not None:
F1 = wall_factor(Pr=Pr,
Pr_wall=Pr_wall,
Pr_heating_coeff=0.26,
Pr_cooling_coeff=0.26,
property_option=WALL_FACTOR_PRANDTL)
Nu *= F1
h = k / tube_diameter * Nu
efficiency = fin_efficiency_Kern_Kraus(Do=tube_diameter,
D_fin=fin_diameter,
t_fin=fin_thickness,
k_fin=k_fin,
h=h)
h_total_area_basis = (efficiency * A_fin + A_tube_showing) / A * h
h_bare_tube_basis = h_total_area_basis * A_increase
return h_bare_tube_basis