Air cooler sizing and rating (ht.air_cooler)

ht.air_cooler.Ft_aircooler(Thi, Tho, Tci, Tco, Ntp=1, rows=1)

Calculates log-mean temperature difference correction factor for a crossflow heat exchanger, as in an Air Cooler. Method presented in [1], fit to other’s nonexplicit work. Error is < 0.1%. Requires number of rows and tube passes as well as stream temperatures.

$$F_T = 1 - \sum_{i=1}^m \sum_{k=1}^n a_{i,k}(1-r_{1,m})^k\sin(2i\arctan R)$$

$$R = \frac{T_{hi} - T_{ho}}{T_{co}-T_{ci}}$$

$$r_{1,m} = \frac{\Delta T_{lm}}{T_{hi} - T_{ci}}$$

Parameters

Thifloat

Temperature of hot fluid in [K]

Thofloat

Temperature of hot fluid out [K]

Tcifloat

Temperature of cold fluid in [K]

Tcofloat

Temperature of cold fluid out [K]

Ntpint

Number of passes the tubeside fluid will flow through [-]

rowsint

Number of rows of tubes [-]

Returns

Ftfloat

Log-mean temperature difference correction factor [-]

Notes

This equation assumes that the hot fluid is tubeside, as in the case of air coolers. The model is not symmetric, so ensure to switch around the inputs if using this function for other purposes.

This equation appears in [1]. It has been verified. For some cases, approximations are made to match coefficients with the number of tube passes and rows provided. 16 coefficients are used for each case; 8 cases are considered:

• 1 row 1 pass

• 2 rows 1 pass

• 2 rows 2 passes

• 3 rows 1 pass

• 3 rows 3 passes

• 4 rows 1 pass

• 4 rows 2 passes

• 4 rows 4 passes

References

1(1,2)

Roetzel, W., and F. J. L. Nicole. “Mean Temperature Difference for Heat Exchanger Design-A General Approximate Explicit Equation.” Journal of Heat Transfer 97, no. 1 (February 1, 1975): 5-8. doi:10.1115/1.3450288

Examples

>>> Ft_aircooler(Thi=125., Tho=45., Tci=25., Tco=95., Ntp=1, rows=4)
0.550509360409

ht.air_cooler.air_cooler_noise_GPSA(tip_speed, power)

Calculates the noise generated by an air cooler bay with one fan according to the GPSA handbook [1].

$$\text{PWL[dB(A)]} = 56 + 30\log_{10}\left( \frac{\text{tip speed} [m/min]}{304.8 [m/min]}\right) + 10\log_{10}( \text{power}[hp])$$

Parameters

tip_speedfloat

Tip speed of the air cooler fan blades, [m/s]

powerfloat

Shaft power of single fan motor, [W]

Returns

noisefloat

Sound pressure level at 1 m from source, [dB(A)]

Notes

Internal units are in m/minute, and hp.

References

1(1,2)

GPSA. “Engineering Data Book, SI.” 13th edition. Gas Processors Suppliers Association (2012).

Examples

Example problem from GPSA [1].

>>> air_cooler_noise_GPSA(tip_speed=3177/minute, power=25.1*hp)
100.5368047795

ht.air_cooler.air_cooler_noise_Mukherjee(tip_speed, power, fan_diameter, induced=False)

Calculates the noise generated by an air cooler bay with one fan according to [1].

$$\text{SPL[dB(A)]} = 46 + 30\log_{10}\text{(tip speed)}[m/s] + 10\log_{10}( \text{power}[hp]) - 20 \log_{10}(D_{fan})$$

Parameters

tip_speedfloat

Tip speed of the air cooler fan blades, [m/s]

powerfloat

Shaft power of single fan motor, [W]

fan_diameterfloat

Diameter of air cooler fan, [m]

inducedbool

Whether the air cooler is forced air (False) or induced air (True), [-]

Returns

noisefloat

Sound pressure level at 1 m from source (p0=2E-5 Pa), [dB(A)]

Notes

Internal units are in m/minute, hp, and m.

If the air cooler is induced, the sound pressure level is reduced by 3 dB.

References

1

Mukherjee, R., and Geoffrey Hewitt. Practical Thermal Design of Air-Cooled Heat Exchangers. New York: Begell House Publishers Inc.,U.S., 2007.

Examples

>>> air_cooler_noise_Mukherjee(tip_speed=3177/minute, power=25.1*hp, fan_diameter=4.267)
99.1102632909

ht.air_cooler.dP_ESDU_high_fin(m, A_min, A_increase, flow_area_contraction_ratio, tube_diameter, pitch_parallel, pitch_normal, tube_rows, rho, mu)

Calculates the air-side pressure drop for a high-finned tube bank according to the ESDU [1] method, as described in [2]. This includes the effects of friction of the fin, and acceleration.

$$\Delta P = (K_{acc} + n_{rows} K_{f}) \frac{1}{2}\rho v_{max}^2$$

$$K_{f} = 4.567 Re_D^{-0.242} \left(\frac{A}{A_{tube,only}} \right)^{0.504} \left(\frac{p_1}{D_o}\right)^{-0.376} \left(\frac{p_2}{D_{o}}\right)^{-0.546}$$

$$K_{acc} = 1 + \text{(flow area contraction ratio)}^2$$

Parameters

mfloat

Mass flow rate of air across the tube bank, [kg/s]

A_minfloat

Minimum air flow area, [m^2]

A_increasefloat

Ratio of actual surface area to bare tube surface area $A_{increase} = \frac{A_{tube}}{A_{bare, total/tube}}$, [-]

flow_area_contraction_ratiofloat

Ratio of A_min to A_face, [-]

tube_diameterfloat

Diameter of the bare tube, [m]

pitch_parallelfloat

Distance between tube center along a line parallel to the flow; has been called longitudinal pitch, pp, s2, SL, and p2, [m]

pitch_normalfloat

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_rowsint

Number of tube rows per bundle, [-]

rhofloat

Average (bulk) density of air across the tube bank, [kg/m^3]

mufloat

Average (bulk) viscosity of air across the tube bank, [Pa*s]

Returns

dPfloat

Overall pressure drop across the finned tube bank, [Pa]

Notes

The data used by the ESDU covered:

• fin density 4 to 11/inch

• tube outer diameters 3/8 to 2 inches

• fin heights 1/3 to 5/8 inches

• fin tip to fin root diameters 1.2 to 2.4

• Reynolds numbers 5000 to 50000

[1] claims 72% of experimental points were within 10% of the results of the correlation.

The Reynolds number used in this equation is that based on V_max, calculated using the minimum flow area.

References

1(1,2)

“High-Fin Staggered Tube Banks: Heat Transfer and Pressure Drop for Turbulent Single Phase Gas Flow.” ESDU (October 1, 1986).

2

Hewitt, G. L. Shires T. Reg Bott G. F., George L. Shires, and T. R. Bott. Process Heat Transfer. 1E. Boca Raton: CRC Press, 1994.

Examples

>>> from fluids.geometry import AirCooledExchanger
>>> 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)

>>> dP_ESDU_high_fin(m=0.914, A_min=AC.A_min, A_increase=AC.A_increase, flow_area_contraction_ratio=AC.flow_area_contraction_ratio, tube_diameter=AC.tube_diameter, pitch_parallel=AC.pitch_parallel, pitch_normal=AC.pitch_normal, tube_rows=AC.tube_rows, rho=1.217,  mu=0.000018)
485.630768779

ht.air_cooler.dP_ESDU_low_fin(m, A_min, A_increase, flow_area_contraction_ratio, tube_diameter, fin_height, bare_length, pitch_parallel, pitch_normal, tube_rows, rho, mu)

Calculates the air-side pressure drop for a low-finned tube bank according to the ESDU [1] method, as described in [2]. This includes the effects of friction of the fin, and acceleration.

$$\Delta P = (K_{acc} + n_{rows} K_{f}) \frac{1}{2}\rho v_{max}^2$$

$$K_{f} = 4.71 Re_D^{-0.286} \left(\frac{\text{fin height}} {\text{bare length}}\right)^{0.51} \left(\frac{p_1 - D_o}{p_2 - D_o}\right)^{0.536} \left(\frac{D_o}{p_1 - D_o}\right)^{0.36}$$

$$K_{acc} = 1 + \text{(flow area contraction ratio)}^2$$

Parameters

mfloat

Mass flow rate of air across the tube bank, [kg/s]

A_minfloat

Minimum air flow area, [m^2]

A_increasefloat

Ratio of actual surface area to bare tube surface area $A_{increase} = \frac{A_{tube}}{A_{bare, total/tube}}$, [-]

flow_area_contraction_ratiofloat

Ratio of A_min to A_face, [-]

tube_diameterfloat

Diameter of the bare tube, [m]

fin_heightfloat

Height above bare tube of the tube fins, [m]

bare_lengthfloat

Length of bare tube between two fins $\text{bare length} = \text{fin interval} - t_{fin}$, [m]

pitch_parallelfloat

Distance between tube center along a line parallel to the flow; has been called longitudinal pitch, pp, s2, SL, and p2, [m]

pitch_normalfloat

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_rowsint

Number of tube rows per bundle, [-]

rhofloat

Average (bulk) density of air across the tube bank, [kg/m^3]

mufloat

Average (bulk) viscosity of air across the tube bank, [Pa*s]

Returns

dPfloat

Overall pressure drop across the finned tube bank, [Pa]

Notes

Low fins are fins which were formed on the tube outside wall, normally by the cold rolling process. The data used by the ESDU covered:

• fin density 11 to 32/inch

• tube outer diameters 0.5 to 1.25 inches

• fin heights 0.03 to 0.1 inches

• Reynolds numbers 1000 to 80000

[1] compared this correlation with 81 results and obtained a standard deviation of 7.7%.

The Reynolds number used in this equation is that based on V_max, calculated using the minimum flow area.

References

1(1,2)

“High-Fin Staggered Tube Banks: Heat Transfer and Pressure Drop for Turbulent Single Phase Gas Flow.” ESDU (October 1, 1986).

2

Hewitt, G. L. Shires T. Reg Bott G. F., George L. Shires, and T. R. Bott. Process Heat Transfer. 1E. Boca Raton: CRC Press, 1994.

Examples

>>> from fluids.geometry import AirCooledExchanger
>>> 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)

>>> dP_ESDU_low_fin(m=0.914, A_min=AC.A_min, A_increase=AC.A_increase,
... flow_area_contraction_ratio=AC.flow_area_contraction_ratio,
... tube_diameter=AC.tube_diameter, fin_height=AC.fin_height,
... bare_length=AC.bare_length, pitch_parallel=AC.pitch_parallel,
... pitch_normal=AC.pitch_normal, tube_rows=AC.tube_rows, rho=1.217,
... mu=0.000018)
464.5433141865

ht.air_cooler.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)

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].

$$Nu = 0.134Re^{0.681} Pr^{0.33}\left(\frac{S}{h}\right)^{0.2} \left(\frac{S}{b}\right)^{0.1134}$$

Parameters

mfloat

Mass flow rate of air across the tube bank, [kg/s]

Afloat

Surface area of combined finned and non-finned area exposed for heat transfer, [m^2]

A_minfloat

Minimum air flow area, [m^2]

A_increasefloat

Ratio of actual surface area to bare tube surface area $A_{increase} = \frac{A_{tube}}{A_{bare, total/tube}}$, [-]

A_finfloat

Surface area of all fins in the bundle, [m^2]

A_tube_showingfloat

Area of the bare tube which is exposed in the bundle, [m^2]

tube_diameterfloat

Diameter of the bare tube, [m]

fin_diameterfloat

Outer diameter of each tube after including the fin on both sides, [m]

fin_thicknessfloat

Thickness of the fins, [m]

bare_lengthfloat

Length of bare tube between two fins $\text{bare length} = \text{fin interval} - t_{fin}$, [m]

rhofloat

Average (bulk) density of air across the tube bank, [kg/m^3]

Cpfloat

Average (bulk) heat capacity of air across the tube bank, [J/kg/K]

mufloat

Average (bulk) viscosity of air across the tube bank, [Pa*s]

kfloat

Average (bulk) thermal conductivity of air across the tube bank, [W/m/K]

k_finfloat

Thermal conductivity of the fin, [W/m/K]

Returns

h_bare_tube_basisfloat

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 1000 < Re < 8000 , 11.13 mm < 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.

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.

Examples

>>> from fluids.geometry import AirCooledExchanger
>>> from scipy.constants import inch
>>> 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)
1422.872240323

ht.air_cooler.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)

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].

$$Nu = 0.242 Re^{0.658} \left(\frac{\text{bare length}} {\text{fin height}}\right)^{0.297} \left(\frac{P_1}{P_2}\right)^{-0.091} P_r^{1/3}\cdot F_1\cdot F_2$$

$$h_{A,total} = \frac{\eta A_{fin} + A_{bare, showing}}{A_{total}} h$$

$$h_{bare,total} = A_{increase} h_{A,total}$$

Parameters

mfloat

Mass flow rate of air across the tube bank, [kg/s]

Afloat

Surface area of combined finned and non-finned area exposed for heat transfer, [m^2]

A_minfloat

Minimum air flow area, [m^2]

A_increasefloat

Ratio of actual surface area to bare tube surface area $A_{increase} = \frac{A_{tube}}{A_{bare, total/tube}}$, [-]

A_finfloat

Surface area of all fins in the bundle, [m^2]

A_tube_showingfloat

Area of the bare tube which is exposed in the bundle, [m^2]

tube_diameterfloat

Diameter of the bare tube, [m]

fin_diameterfloat

Outer diameter of each tube after including the fin on both sides, [m]

fin_thicknessfloat

Thickness of the fins, [m]

bare_lengthfloat

Length of bare tube between two fins $\text{bare length} = \text{fin interval} - t_{fin}$, [m]

pitch_parallelfloat

Distance between tube center along a line parallel to the flow; has been called longitudinal pitch, pp, s2, SL, and p2, [m]

pitch_normalfloat

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_rowsint

Number of tube rows per bundle, [-]

rhofloat

Average (bulk) density of air across the tube bank, [kg/m^3]

Cpfloat

Average (bulk) heat capacity of air across the tube bank, [J/kg/K]

mufloat

Average (bulk) viscosity of air across the tube bank, [Pa*s]

kfloat

Average (bulk) thermal conductivity of air across the tube bank, [W/m/K]

k_finfloat

Thermal conductivity of the fin, [W/m/K]

Pr_wallfloat, 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_basisfloat

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.

References

1(1,2,3)

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.

Examples

>>> from fluids.geometry import AirCooledExchanger
>>> from scipy.constants import inch
>>> 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)
1390.88891804

ht.air_cooler.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)

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]).

$$Nu = 0.183Re^{0.7} \left(\frac{\text{bare length}}{\text{fin height}} \right)^{0.36}\left(\frac{p_1}{D_{o}}\right)^{0.06} \left(\frac{\text{fin height}}{D_o}\right)^{0.11} Pr^{0.36} \cdot F_1\cdot F_2$$

$$h_{A,total} = \frac{\eta A_{fin} + A_{bare, showing}}{A_{total}} h$$

$$h_{bare,total} = A_{increase} h_{A,total}$$

Parameters

mfloat

Mass flow rate of air across the tube bank, [kg/s]

Afloat

Surface area of combined finned and non-finned area exposed for heat transfer, [m^2]

A_minfloat

Minimum air flow area, [m^2]

A_increasefloat

Ratio of actual surface area to bare tube surface area $A_{increase} = \frac{A_{tube}}{A_{bare, total/tube}}$, [-]

A_finfloat

Surface area of all fins in the bundle, [m^2]

A_tube_showingfloat

Area of the bare tube which is exposed in the bundle, [m^2]

tube_diameterfloat

Diameter of the bare tube, [m]

fin_diameterfloat

Outer diameter of each tube after including the fin on both sides, [m]

fin_thicknessfloat

Thickness of the fins, [m]

bare_lengthfloat

Length of bare tube between two fins $\text{bare length} = \text{fin interval} - t_{fin}$, [m]

pitch_parallelfloat

Distance between tube center along a line parallel to the flow; has been called longitudinal pitch, pp, s2, SL, and p2, [m]

pitch_normalfloat

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_rowsint

Number of tube rows per bundle, [-]

rhofloat

Average (bulk) density of air across the tube bank, [kg/m^3]

Cpfloat

Average (bulk) heat capacity of air across the tube bank, [J/kg/K]

mufloat

Average (bulk) viscosity of air across the tube bank, [Pa*s]

kfloat

Average (bulk) thermal conductivity of air across the tube bank, [W/m/K]

k_finfloat

Thermal conductivity of the fin, [W/m/K]

Pr_wallfloat, 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_basisfloat

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.

References

1(1,2,3)

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(1,2,3)

“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.

Examples

>>> from fluids.geometry import AirCooledExchanger
>>> 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)
553.85383647

ht.air_cooler.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)

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:

$$Nu_d = 0.22Re_d^{0.6}\left(\frac{A}{A_{tube,only}}\right)^{-0.15}Pr^{1/3}$$

Staggered:

$$Nu_d = 0.38 Re_d^{0.6}\left(\frac{A}{A_{tube,only}}\right)^{-0.15}Pr^{1/3}$$

Parameters

mfloat

Mass flow rate of air across the tube bank, [kg/s]

Afloat

Surface area of combined finned and non-finned area exposed for heat transfer, [m^2]

A_minfloat

Minimum air flow area, [m^2]

A_increasefloat

Ratio of actual surface area to bare tube surface area $A_{increase} = \frac{A_{tube}}{A_{bare, total/tube}}$, [-]

A_finfloat

Surface area of all fins in the bundle, [m^2]

A_tube_showingfloat

Area of the bare tube which is exposed in the bundle, [m^2]

tube_diameterfloat

Diameter of the bare tube, [m]

fin_diameterfloat

Outer diameter of each tube after including the fin on both sides, [m]

fin_thicknessfloat

Thickness of the fins, [m]

bare_lengthfloat

Length of bare tube between two fins $\text{bare length} = \text{fin interval} - t_{fin}$, [m]

pitch_parallelfloat

Distance between tube center along a line parallel to the flow; has been called longitudinal pitch, pp, s2, SL, and p2, [m]

pitch_normalfloat

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_rowsint

Number of tube rows per bundle, [-]

rhofloat

Average (bulk) density of air across the tube bank, [kg/m^3]

Cpfloat

Average (bulk) heat capacity of air across the tube bank, [J/kg/K]

mufloat

Average (bulk) viscosity of air across the tube bank, [Pa*s]

kfloat

Average (bulk) thermal conductivity of air across the tube bank, [W/m/K]

k_finfloat

Thermal conductivity of the fin, [W/m/K]

Returns

h_bare_tube_basisfloat

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].

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(1,2,3)

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.

Examples

Example 12.1 in [3]:

>>> from fluids.geometry import AirCooledExchanger
>>> from scipy.constants import foot, inch
>>> 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)
969.285081857