def h_Ganguli_VDI(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):
r'''Calculates the air side heat transfer coefficient for an air cooler
or other finned tube bundle with the formulas of [1]_ as modified in [2]_.
Inline:
.. math::
Nu_d = 0.22Re_d^{0.6}\left(\frac{A}{A_{tube,only}}\right)^{-0.15}Pr^{1/3}
Staggered:
.. math::
Nu_d = 0.38 Re_d^{0.6}\left(\frac{A}{A_{tube,only}}\right)^{-0.15}Pr^{1/3}
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]
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 VDI modifications were developed in comparison with HTFS and HTRI data
according to [2]_.
For cases where the tube row count is less than four, the coefficients are
modified in [2]_. For the inline case, 0.2 replaces 0.22. For the stagered
cases, the coefficient is 0.2, 0.33, 0.36 for 1, 2, or 3 tube rows
respectively.
The model is also showin in [4]_.
Examples
--------
Example 12.1 in [3]_:
>>> AC = AirCooledExchanger(tube_rows=4, tube_passes=4, tubes_per_row=56, tube_length=36*foot,
... tube_diameter=1*inch, fin_thickness=0.013*inch, fin_density=10/inch,
... angle=30, pitch_normal=2.5*inch, fin_height=0.625*inch, corbels=True)
>>> h_Ganguli_VDI(m=130.70315, 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_parallel=AC.pitch_parallel, pitch_normal=AC.pitch_normal,
... rho=1.2013848, Cp=1009.0188, mu=1.9304793e-05, k=0.027864828, k_fin=238)
969.2850818578595
References
----------
.. [1] Ganguli, A., S. S. Tung, and J. Taborek. "Parametric Study of
Air-Cooled Heat Exchanger Finned Tube Geometry." In AIChE Symposium
Series, 81:122-28, 1985.
.. [2] Gesellschaft, V. D. I., ed. VDI Heat Atlas. 2nd edition.
Berlin; New York:: Springer, 2010.
.. [3] Serth, Robert W., and Thomas Lestina. Process Heat Transfer:
Principles, Applications and Rules of Thumb. Academic Press, 2014.
.. [4] Kroger, Detlev. Air-Cooled Heat Exchangers and Cooling Towers:
Thermal-Flow Performance Evaluation and Design, Vol. 1. Tulsa, Okl:
PennWell Corp., 2004.
'''
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)
if abs(1 - pitch_normal / pitch_parallel
) < 0.05: # in-line, with a tolerance of 0.05 proximity
if tube_rows < 4:
coeff = 0.2
else:
coeff = 0.22
else: # staggered
if tube_rows == 1:
coeff = 0.2
elif tube_rows == 2:
coeff = 0.33
elif tube_rows == 3:
coeff = 0.36
else:
coeff = 0.38
# VDI example shows the ratio is of the total area, to the original bare tube area
# Serth example would match Nu = 47.22 except for lazy rounding
Nu = coeff * Re**0.6 * Pr**(1 / 3.) * (A_increase)**-0.15
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
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_Briggs_Young(m, A, A_min, A_increase, A_fin, A_tube_showing,
tube_diameter, fin_diameter, fin_thickness, bare_length,
rho, Cp, mu, k, k_fin):
r'''Calculates the air side heat transfer coefficient for an air cooler
or other finned tube bundle with the formulas of Briggs and Young [1], [2]_
[3]_.
.. math::
Nu = 0.134Re^{0.681} Pr^{0.33}\left(\frac{S}{h}\right)^{0.2}
\left(\frac{S}{b}\right)^{0.1134}
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]
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]
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 limits on this equation are :math:`1000 < Re < `8000`,
11.13 mm :math:`< D_o < ` 40.89 mm, 1.42 mm < fin height < 16.57 mm,
0.33 mm < fin thickness < 2.02 mm, 1.30 mm < fin pitch < 4.06 mm, and
24.49 mm < normal pitch < 111 mm.
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_Briggs_Young(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,
... rho=1.161, Cp=1007., mu=1.85E-5, k=0.0263, k_fin=205)
1422.8722403237716
References
----------
.. [1] Briggs, D.E., and Young, E.H., 1963, "Convection Heat Transfer and
Pressure Drop of Air Flowing across Triangular Banks of Finned Tubes",
Chemical Engineering Progress Symp., Series 41, No. 59. Chem. Eng. Prog.
Symp. Series No. 41, "Heat Transfer - Houston".
.. [2] Mukherjee, R., and Geoffrey Hewitt. Practical Thermal Design of
Air-Cooled Heat Exchangers. New York: Begell House Publishers Inc.,U.S.,
2007.
.. [3] Kroger, Detlev. Air-Cooled Heat Exchangers and Cooling Towers:
Thermal-Flow Performance Evaluation and Design, Vol. 1. Tulsa, Okl:
PennWell Corp., 2004.
'''
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 = 0.134 * Re**0.681 * Pr**(1 / 3.) * (bare_length / fin_height)**0.2 * (
bare_length / fin_thickness)**0.1134
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