def Chen_Bennett(m, x, D, rhol, rhog, mul, mug, kl, Cpl, Hvap, sigma,
dPsat, Te):
r'''Calculates heat transfer coefficient for film boiling of saturated
fluid in any orientation of flow. Correlation
is developed in [1]_ and [2]_, and reviewed in [3]_. This model is one of
the most often used, and replaces the `Chen_Edelstein` correlation. It uses
the Dittus-Boelter correlation for turbulent convection and the
Forster-Zuber correlation for pool boiling, and combines them with two
factors `F` and `S`.
.. math::
h_{tp} = S\cdot h_{nb} + F \cdot h_{sp,l}
.. math::
h_{sp,l} = 0.023 Re_l^{0.8} Pr_l^{0.4} k_l/D
.. math::
Re_l = \frac{DG(1-x)}{\mu_l}
.. math::
h_{nb} = 0.00122\left( \frac{\lambda_l^{0.79} c_{p,l}^{0.45}
\rho_l^{0.49}}{\sigma^{0.5} \mu^{0.29} H_{vap}^{0.24} \rho_g^{0.24}}
\right)\Delta T_{sat}^{0.24} \Delta p_{sat}^{0.75}
.. math::
F = \left(\frac{Pr_1+1}{2}\right)^{0.444}\cdot (1+X_{tt}^{-0.5})^{1.78}
.. math::
S = \frac{1-\exp(-F\cdot h_{conv} \cdot X_0/k_l)}
{F\cdot h_{conv}\cdot X_0/k_l}
.. math::
X_{tt} = \left( \frac{1-x}{x}\right)^{0.9} \left(\frac{\rho_g}{\rho_l}
\right)^{0.5}\left( \frac{\mu_l}{\mu_g}\right)^{0.1}
.. math::
X_0 = 0.041 \left(\frac{\sigma}{g \cdot (\rho_l-\rho_v)}\right)^{0.5}
Parameters
----------
m : float
Mass flow rate [kg/s]
x : float
Quality at the specific tube interval []
D : float
Diameter of the tube [m]
rhol : float
Density of the liquid [kg/m^3]
rhog : float
Density of the gas [kg/m^3]
mul : float
Viscosity of liquid [Pa*s]
mug : float
Viscosity of gas [Pa*s]
kl : float
Thermal conductivity of liquid [W/m/K]
Cpl : float
Heat capacity of liquid [J/kg/K]
Hvap : float
Heat of vaporization of liquid [J/kg]
sigma : float
Surface tension of liquid [N/m]
dPsat : float
Difference in Saturation pressure of fluid at Te and T, [Pa]
Te : float
Excess temperature of wall, [K]
Returns
-------
h : float
Heat transfer coefficient [W/m^2/K]
Notes
-----
[1]_ and [2]_ have been reviewed, but the model is only put together in
the review of [3]_. Many other forms of this equation exist with different
functions for `F` and `S`.
Examples
--------
>>> Chen_Bennett(m=0.106, x=0.2, D=0.0212, rhol=567, rhog=18.09,
... mul=156E-6, mug=7.11E-6, kl=0.086, Cpl=2730, Hvap=2E5, sigma=0.02,
... dPsat=1E5, Te=3)
4938.275351219369
See Also
--------
Chen_Edelstein
turbulent_Dittus_Boelter
Forster_Zuber
References
----------
.. [1] Bennett, Douglas L., and John C. Chen. "Forced Convective Boiling in
Vertical Tubes for Saturated Pure Components and Binary Mixtures."
AIChE Journal 26, no. 3 (May 1, 1980): 454-61. doi:10.1002/aic.690260317.
.. [2] Bennett, Douglas L., M.W. Davies and B.L. Hertzler, The Suppression
of Saturated Nucleate Boiling by Forced Convective Flow, American
Institute of Chemical Engineers Symposium Series, vol. 76, no. 199.
91-103, 1980.
.. [3] Bertsch, Stefan S., Eckhard A. Groll, and Suresh V. Garimella.
"Review and Comparative Analysis of Studies on Saturated Flow Boiling in
Small Channels." Nanoscale and Microscale Thermophysical Engineering 12,
no. 3 (September 4, 2008): 187-227. doi:10.1080/15567260802317357.
'''
G = m/(pi/4*D**2)
Rel = D*G*(1-x)/mul
Prl = Prandtl(Cp=Cpl, mu=mul, k=kl)
hl = turbulent_Dittus_Boelter(Re=Rel, Pr=Prl)*kl/D
Xtt = Lockhart_Martinelli_Xtt(x=x, rhol=rhol, rhog=rhog, mul=mul, mug=mug)
F = ((Prl+1)/2.)**0.444*(1 + Xtt**-0.5)**1.78
X0 = 0.041*(sigma/(g*(rhol-rhog)))**0.5
S = (1 - exp(-F*hl*X0/kl))/(F*hl*X0/kl)
hnb = Forster_Zuber(Te=Te, dPsat=dPsat, Cpl=Cpl, kl=kl, mul=mul, sigma=sigma,
Hvap=Hvap, rhol=rhol, rhog=rhog)
return hnb*S + hl*F
def Chen_Edelstein(m, x, D, rhol, rhog, mul, mug, kl, Cpl, Hvap, sigma,
dPsat, Te):
r'''Calculates heat transfer coefficient for film boiling of saturated
fluid in any orientation of flow. Correlation
is developed in [1]_ and [2]_, and reviewed in [3]_. This model is one of
the most often used. It uses the Dittus-Boelter correlation for turbulent
convection and the Forster-Zuber correlation for pool boiling, and
combines them with two factors `F` and `S`.
.. math::
h_{tp} = S\cdot h_{nb} + F \cdot h_{sp,l}
.. math::
h_{sp,l} = 0.023 Re_l^{0.8} Pr_l^{0.4} k_l/D
.. math::
Re_l = \frac{DG(1-x)}{\mu_l}
.. math::
h_{nb} = 0.00122\left( \frac{\lambda_l^{0.79} c_{p,l}^{0.45}
\rho_l^{0.49}}{\sigma^{0.5} \mu^{0.29} H_{vap}^{0.24} \rho_g^{0.24}}
\right)\Delta T_{sat}^{0.24} \Delta p_{sat}^{0.75}
.. math::
F = (1 + X_{tt}^{-0.5})^{1.78}
.. math::
X_{tt} = \left( \frac{1-x}{x}\right)^{0.9} \left(\frac{\rho_g}{\rho_l}
\right)^{0.5}\left( \frac{\mu_l}{\mu_g}\right)^{0.1}
.. math::
S = 0.9622 - 0.5822\left(\tan^{-1}\left(\frac{Re_L\cdot F^{1.25}}
{6.18\cdot 10^4}\right)\right)
Parameters
----------
m : float
Mass flow rate [kg/s]
x : float
Quality at the specific tube interval []
D : float
Diameter of the tube [m]
rhol : float
Density of the liquid [kg/m^3]
rhog : float
Density of the gas [kg/m^3]
mul : float
Viscosity of liquid [Pa*s]
mug : float
Viscosity of gas [Pa*s]
kl : float
Thermal conductivity of liquid [W/m/K]
Cpl : float
Heat capacity of liquid [J/kg/K]
Hvap : float
Heat of vaporization of liquid [J/kg]
sigma : float
Surface tension of liquid [N/m]
dPsat : float
Difference in Saturation pressure of fluid at Te and T, [Pa]
Te : float
Excess temperature of wall, [K]
Returns
-------
h : float
Heat transfer coefficient [W/m^2/K]
Notes
-----
[1]_ and [2]_ have been reviewed, but the model is only put together in
the review of [3]_. Many other forms of this equation exist with different
functions for `F` and `S`.
Examples
--------
>>> Chen_Edelstein(m=0.106, x=0.2, D=0.0212, rhol=567, rhog=18.09,
... mul=156E-6, mug=7.11E-6, kl=0.086, Cpl=2730, Hvap=2E5, sigma=0.02,
... dPsat=1E5, Te=3)
3289.058731974052
See Also
--------
turbulent_Dittus_Boelter
Forster_Zuber
References
----------
.. [1] Chen, J. C. "Correlation for Boiling Heat Transfer to Saturated
Fluids in Convective Flow." Industrial & Engineering Chemistry Process
Design and Development 5, no. 3 (July 1, 1966): 322-29.
doi:10.1021/i260019a023.
.. [2] Edelstein, Sergio, A. J. Pérez, and J. C. Chen. "Analytic
Representation of Convective Boiling Functions." AIChE Journal 30, no.
5 (September 1, 1984): 840-41. doi:10.1002/aic.690300528.
.. [3] Bertsch, Stefan S., Eckhard A. Groll, and Suresh V. Garimella.
"Review and Comparative Analysis of Studies on Saturated Flow Boiling in
Small Channels." Nanoscale and Microscale Thermophysical Engineering 12,
no. 3 (September 4, 2008): 187-227. doi:10.1080/15567260802317357.
'''
G = m/(pi/4*D**2)
Rel = D*G*(1-x)/mul
Prl = Prandtl(Cp=Cpl, mu=mul, k=kl)
hl = turbulent_Dittus_Boelter(Re=Rel, Pr=Prl)*kl/D
Xtt = Lockhart_Martinelli_Xtt(x=x, rhol=rhol, rhog=rhog, mul=mul, mug=mug)
F = (1 + Xtt**-0.5)**1.78
Re = Rel*F**1.25
S = 0.9622 - 0.5822*atan(Re/6.18E4)
hnb = Forster_Zuber(Te=Te, dPsat=dPsat, Cpl=Cpl, kl=kl, mul=mul, sigma=sigma,
Hvap=Hvap, rhol=rhol, rhog=rhog)
return hnb*S + hl*F