def Knott(m,
x,
D,
rhol,
rhog,
Cpl=None,
kl=None,
mu_b=None,
mu_w=None,
L=None,
hl=None):
r'''Calculates the two-phase non-boiling heat transfer coefficient of a
liquid and gas flowing inside a tube of any inclination, as in [1]_ and
reviewed in [2]_.
Either a specified `hl` is required, or `Cpl`, `kl`, `mu_b`, `mu_w` and
`L` are required to calculate `hl`.
.. math::
\frac{h_{TP}}{h_l} = \left(1 + \frac{V_{gs}}{V_{ls}}\right)^{1/3}
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]
Cpl : float, optional
Constant-pressure heat capacity of liquid [J/kg/K]
kl : float, optional
Thermal conductivity of liquid [W/m/K]
mu_b : float, optional
Viscosity of liquid at bulk conditions (average of inlet/outlet
temperature) [Pa*s]
mu_w : float, optional
Viscosity of liquid at wall temperature [Pa*s]
L : float, optional
Length of the tube [m]
hl : float, optional
Liquid-phase heat transfer coefficient as described below, [W/m^2/K]
Returns
-------
h : float
Heat transfer coefficient [W/m^2/K]
Notes
-----
The liquid-only heat transfer coefficient will be calculated with the
`laminar_entry_Seider_Tate` correlation, should it not be provided as an
input. Many of the arguments to this function are optional and are only
used if `hl` is not provided.
`hl` should be calculated with a velocity equal to that determined with
a combined volumetric flow of both the liquid and the gas. All other
parameters used in calculating the heat transfer coefficient are those
of the liquid. If the viscosity at the wall temperature is not given, the
liquid viscosity correction in `laminar_entry_Seider_Tate` is not applied.
Examples
--------
>>> Knott(m=1, x=.9, D=.3, rhol=1000, rhog=2.5, Cpl=2300, kl=.6, mu_b=1E-3,
... mu_w=1.2E-3, L=4)
4225.536758045839
References
----------
.. [1] Knott, R. F., R. N. Anderson, Andreas. Acrivos, and E. E. Petersen.
"An Experimental Study of Heat Transfer to Nitrogen-Oil Mixtures."
Industrial & Engineering Chemistry 51, no. 11 (November 1, 1959):
1369-72. doi:10.1021/ie50599a032.
.. [2] Dongwoo Kim, Venkata K. Ryali, Afshin J. Ghajar, Ronald L.
Dougherty. "Comparison of 20 Two-Phase Heat Transfer Correlations with
Seven Sets of Experimental Data, Including Flow Pattern and Tube
Inclination Effects." Heat Transfer Engineering 20, no. 1 (February 1,
1999): 15-40. doi:10.1080/014576399271691.
'''
Vgs = m * x / (rhog * pi / 4 * D**2)
Vls = m * (1 - x) / (rhol * pi / 4 * D**2)
if not hl:
V = Vgs + Vls # Net velocity
Re = Reynolds(V=V, D=D, rho=rhol, mu=mu_b)
Pr = Prandtl(Cp=Cpl, k=kl, mu=mu_b)
Nul = laminar_entry_Seider_Tate(Re=Re,
Pr=Pr,
L=L,
Di=D,
mu=mu_b,
mu_w=mu_w)
hl = Nul * kl / D
return hl * (1 + Vgs / Vls)**(1 / 3.)
def Aggour(m,
x,
alpha,
D,
rhol,
Cpl,
kl,
mu_b,
mu_w=None,
L=None,
turbulent=None):
r'''Calculates the two-phase non-boiling laminar heat transfer coefficient
of a liquid and gas flowing inside a tube of any inclination, as in [1]_
and reviewed in [2]_.
Laminar for Rel <= 2000:
.. math::
h_{TP} = 1.615\frac{k_l}{D}\left(\frac{Re_l Pr_l D}{L}\right)^{1/3}
\left(\frac{\mu_b}{\mu_w}\right)^{0.14}
Turbulent for Rel > 2000:
.. math::
h_{TP} = 0.0155\frac{k_l}{D} Pr_l^{0.5} Re_l^{0.83}
.. math::
Re_l = \frac{\rho_l v_l D}{\mu_l}
.. math::
V_l = \frac{V_{ls}}{1-\alpha}
Parameters
----------
m : float
Mass flow rate [kg/s]
x : float
Quality at the specific tube interval [-]
alpha : float
Void fraction in the tube, [-]
D : float
Diameter of the tube [m]
rhol : float
Density of the liquid [kg/m^3]
Cpl : float
Constant-pressure heat capacity of liquid [J/kg/K]
kl : float
Thermal conductivity of liquid [W/m/K]
mu_b : float
Viscosity of liquid at bulk conditions (average of inlet/outlet
temperature) [Pa*s]
mu_w : float, optional
Viscosity of liquid at wall temperature [Pa*s]
L : float, optional
Length of the tube, [m]
turbulent : bool or None, optional
Whether or not to force the correlation to return the turbulent
result; will return the laminar regime if False
Returns
-------
h : float
Heat transfer coefficient [W/m^2/K]
Notes
-----
Developed with mixtures of air-water, helium-water, and freon-12-water and
vertical tests. Studied flow patterns were bubbly, slug, annular,
bubbly-slug, and slug-annular regimes. Superficial velocity ratios ranged
from 0.02 to 470.
A viscosity correction is only suggested for the laminar regime.
If the viscosity at the wall temperature is not given, the liquid viscosity
correction is not applied.
Examples
--------
>>> Aggour(m=1, x=.9, D=.3, alpha=.9, rhol=1000, Cpl=2300, kl=.6, mu_b=1E-3)
420.9347146885667
References
----------
.. [1] Aggour, Mohamed A. Hydrodynamics and Heat Transfer in Two-Phase
Two-Component Flows, Ph.D. Thesis, University of Manutoba, Canada
(1978). http://mspace.lib.umanitoba.ca/xmlui/handle/1993/14171.
.. [2] Dongwoo Kim, Venkata K. Ryali, Afshin J. Ghajar, Ronald L.
Dougherty. "Comparison of 20 Two-Phase Heat Transfer Correlations with
Seven Sets of Experimental Data, Including Flow Pattern and Tube
Inclination Effects." Heat Transfer Engineering 20, no. 1 (February 1,
1999): 15-40. doi:10.1080/014576399271691.
'''
Vls = m * (1 - x) / (rhol * pi / 4 * D**2)
Vl = Vls / (1. - alpha)
Prl = Prandtl(Cp=Cpl, k=kl, mu=mu_b)
Rel = Reynolds(V=Vl, D=D, rho=rhol, mu=mu_b)
if turbulent or (Rel > 2000.0 and turbulent is None):
hl = 0.0155 * (kl / D) * Rel**0.83 * Prl**0.5
return hl * (1 - alpha)**-0.83
else:
hl = 1.615 * (kl / D) * (Rel * Prl * D / L)**(1 / 3.)
if mu_w:
hl *= (mu_b / mu_w)**0.14
return hl * (1.0 - alpha)**(-1 / 3.)
def Martin_Sims(m,
x,
D,
rhol,
rhog,
hl=None,
Cpl=None,
kl=None,
mu_b=None,
mu_w=None,
L=None):
r'''Calculates the two-phase non-boiling heat transfer coefficient of a
liquid and gas flowing inside a tube of any inclination, as in [1]_ and
reviewed in [2]_.
.. math::
\frac{h_{TP}}{h_l} = 1 + 0.64\sqrt{\frac{V_{gs}}{V_{ls}}}
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]
hl : float, optional
Liquid-phase heat transfer coefficient as described below, [W/m^2/K]
Cpl : float, optional
Constant-pressure heat capacity of liquid [J/kg/K]
kl : float, optional
Thermal conductivity of liquid [W/m/K]
mu_b : float, optional
Viscosity of liquid at bulk conditions (average of inlet/outlet
temperature) [Pa*s]
mu_w : float, optional
Viscosity of liquid at wall temperature [Pa*s]
L : float, optional
Length of the tube [m]
Returns
-------
h : float
Heat transfer coefficient [W/m^2/K]
Notes
-----
No specific suggestion for how to calculate the liquid-phase heat transfer
coefficient is given in [1]_; [2]_ suggests to use the same procedure as
in `Knott`.
Examples
--------
>>> Martin_Sims(m=1, x=.9, D=.3, rhol=1000, rhog=2.5, hl=141.2)
5563.280000000001
>>> Martin_Sims(m=1, x=.9, D=.3, rhol=1000, rhog=2.5, Cpl=2300, kl=.6,
... mu_b=1E-3, mu_w=1.2E-3, L=24)
5977.505465781747
References
----------
.. [1] Martin, B. W, and G. E Sims. "Forced Convection Heat Transfer to
Water with Air Injection in a Rectangular Duct." International Journal
of Heat and Mass Transfer 14, no. 8 (August 1, 1971): 1115-34.
doi:10.1016/0017-9310(71)90208-0.
.. [2] Dongwoo Kim, Venkata K. Ryali, Afshin J. Ghajar, Ronald L.
Dougherty. "Comparison of 20 Two-Phase Heat Transfer Correlations with
Seven Sets of Experimental Data, Including Flow Pattern and Tube
Inclination Effects." Heat Transfer Engineering 20, no. 1 (February 1,
1999): 15-40. doi:10.1080/014576399271691.
'''
Vgs = m * x / (rhog * pi / 4 * D**2)
Vls = m * (1 - x) / (rhol * pi / 4 * D**2)
if hl is None:
V = Vgs + Vls # Net velocity
Re = Reynolds(V=V, D=D, rho=rhol, mu=mu_b)
Pr = Prandtl(Cp=Cpl, k=kl, mu=mu_b)
Nul = laminar_entry_Seider_Tate(Re=Re,
Pr=Pr,
L=L,
Di=D,
mu=mu_b,
mu_w=mu_w)
hl = Nul * kl / D
return hl * (1.0 + 0.64 * (Vgs / Vls)**0.5)
def accept(self):
Dp=Ltot=nc=0
elements=list()
Q=float(self.form.editFlow.text())/3600
if not self.isLiquid:
Q=Q/self.Rho
if self.form.comboWhat.currentText()=='<on selection>':
elements = FreeCADGui.Selection.getSelection()
else:
o=FreeCAD.ActiveDocument.getObjectsByLabel(self.form.comboWhat.currentText())[0]
if hasattr(o,'PType') and o.PType=='PypeBranch':
elements=[FreeCAD.ActiveDocument.getObject(name) for name in o.Tubes+o.Curves]
elif hasattr(o,'PType') and o.PType=='PypeLine':
group=FreeCAD.ActiveDocument.getObjectsByLabel(o.Label+'_pieces')[0]
elements=group.OutList
self.form.editResults.clear()
for o in elements:
loss=0
if hasattr(o,'PType') and o.PType in ['Pipe','Elbow']:
ID=float(o.ID)/1000
e=float(self.form.editRough.text())*1e-6/ID
v=Q/((ID)**2*pi/4)
Re=Reynolds(V=v,D=ID,rho=self.Rho, mu=self.Mu)
f=friction.friction_factor(Re, eD=e) # Darcy, =4xFanning
if o.PType=='Pipe':
L=float(o.Height)/1000
Ltot+=L
K=K_from_f(fd=f, L=L, D=ID)
loss=dP_from_K(K,rho=self.Rho,V=v)
FreeCAD.Console.PrintMessage('%s: %s\nID=%.2f\nV=%.2f\ne=%f\nf=%f\nK=%f\nL=%.3f\nDp = %.5f bar\n***'%(o.PType,o.Label,ID,v,e,f,K,L,loss/1e5))
self.form.editResults.append('%s\t%.1f mm\t%.1f m/s\t%.5f bar'%(o.Label,ID*1000,v,loss/1e5))
elif o.PType=='Elbow':
ang=float(o.BendAngle)
R=float(o.BendRadius)/1000
nc+=1
K=fittings.bend_rounded(ID,ang,f,R)
loss=dP_from_K(K,rho=self.Rho,V=v)
FreeCAD.Console.PrintMessage('%s: %s\nID=%.2f\nV=%.2f\ne=%f\nf=%f\nK=%f\nang=%.3f\nR=%f\nDp = %.5f bar\n***'%(o.PType,o.Label,ID,v,e,f,K,ang,R,loss/1e5))
self.form.editResults.append('%s\t%.1f mm\t%.1f m/s\t%.5f bar'%(o.Label,ID*1000,v,loss/1e5))
elif o.PType=='Reduct':
pass
elif hasattr(o,'Kv') and o.Kv>0:
if self.isLiquid:
loss=(Q*3600/o.Kv)**2*100000
elif self.form.comboFluid.currentText()=='water' and not self.isLiquid:
pass # TODO formula for steam
else:
pass # TODO formula for gases
if hasattr(o,'ID'):
ID = float(o.ID)/1000
v=Q/(ID**2*pi/4)
else:
v = 0
ID = 0
self.form.editResults.append('%s\t%.1f mm\t%.1f m/s\t%.5f bar'%(o.Label,ID*1000,v,loss/1e5))
Dp+=loss
if Dp>200: result=' = %.3f bar'%(Dp/100000)
else: result=' = %.2e bar'%(Dp/100000)
self.form.labResult.setText(result)
self.form.labLength.setText('Total length = %.3f m' %Ltot)
self.form.labCurves.setText('Nr. of curves = %i' %nc)
def Shah(m, x, D, rhol, mul, kl, Cpl, P, Pc):
r'''Calculates heat transfer coefficient for condensation
of a fluid inside a tube, as presented in [1]_ and again by the same
author in [2]_; also given in [3]_. Requires no properties of the gas.
Uses the Dittus-Boelter correlation for single phase heat transfer
coefficient, with a Reynolds number assuming all the flow is liquid.
.. math::
h_{TP} = h_L\left[(1-x)^{0.8} +\frac{3.8x^{0.76}(1-x)^{0.04}}
{P_r^{0.38}}\right]
Parameters
----------
m : float
Mass flow rate [kg/s]
x : float
Quality at the specific interval [-]
D : float
Diameter of the channel [m]
rhol : float
Density of the liquid [kg/m^3]
mul : float
Viscosity of liquid [Pa*s]
kl : float
Thermal conductivity of liquid [W/m/K]
Cpl : float
Constant-pressure heat capacity of liquid [J/kg/K]
P : float
Pressure of the fluid, [Pa]
Pc : float
Critical pressure of the fluid, [Pa]
Returns
-------
h : float
Heat transfer coefficient [W/m^2/K]
Notes
-----
[1]_ is well written an unambiguous as to how to apply this equation.
Examples
--------
>>> Shah(m=1, x=0.4, D=.3, rhol=800, mul=1E-5, kl=0.6, Cpl=2300, P=1E6, Pc=2E7)
2561.2593415479214
References
----------
.. [1] Shah, M. M. "A General Correlation for Heat Transfer during Film
Condensation inside Pipes." International Journal of Heat and Mass
Transfer 22, no. 4 (April 1, 1979): 547-56.
doi:10.1016/0017-9310(79)90058-9.
.. [2] Shah, M. M., Heat Transfer During Film Condensation in Tubes and
Annuli: A Review of the Literature, ASHRAE Transactions, vol. 87, no.
3, pp. 1086-1100, 1981.
.. [3] Kakaç, Sadik, ed. Boilers, Evaporators, and Condensers. 1st.
Wiley-Interscience, 1991.
'''
VL = m / (rhol * pi / 4 * D**2)
ReL = Reynolds(V=VL, D=D, rho=rhol, mu=mul)
Prl = Prandtl(Cp=Cpl, k=kl, mu=mul)
hL = turbulent_Dittus_Boelter(ReL, Prl) * kl / D
Pr = P / Pc
return hL * ((1 - x)**0.8 + 3.8 * x**0.76 * (1 - x)**0.04 / Pr**0.38)
def Cavallini_Smith_Zecchin(m, x, D, rhol, rhog, mul, mug, kl, Cpl):
r'''Calculates heat transfer coefficient for condensation
of a fluid inside a tube, as presented in
[1]_, also given in [2]_ and [3]_.
.. math::
Nu = \frac{hD_i}{k_l} = 0.05 Re_e^{0.8} Pr_l^{0.33}
Re_{eq} = Re_g(\mu_g/\mu_l)(\rho_l/\rho_g)^{0.5} + Re_l
v_{gs} = \frac{mx}{\rho_g \frac{\pi}{4}D^2}
v_{ls} = \frac{m(1-x)}{\rho_l \frac{\pi}{4}D^2}
Parameters
----------
m : float
Mass flow rate [kg/s]
x : float
Quality at the specific interval [-]
D : float
Diameter of the channel [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
Constant-pressure heat capacity of liquid [J/kg/K]
Returns
-------
h : float
Heat transfer coefficient [W/m^2/K]
Notes
-----
Examples
--------
>>> Cavallini_Smith_Zecchin(m=1, x=0.4, D=.3, rhol=800, rhog=2.5, mul=1E-5, mug=1E-3, kl=0.6, Cpl=2300)
5578.218369177804
References
----------
.. [1] A. Cavallini, J. R. Smith and R. Zecchin, A dimensionless correlation
for heat transfer in forced convection condensation, 6th International
Heat Transfer Conference., Tokyo, Japan (1974) 309-313.
.. [2] Kakaç, Sadik, ed. Boilers, Evaporators, and Condensers. 1st.
Wiley-Interscience, 1991.
.. [3] Balcılar, Muhammet, Ahmet Selim Dalkılıç, Berna Bolat, and Somchai
Wongwises. "Investigation of Empirical Correlations on the Determination
of Condensation Heat Transfer Characteristics during Downward Annular
Flow of R134a inside a Vertical Smooth Tube Using Artificial
Intelligence Algorithms." Journal of Mechanical Science and Technology
25, no. 10 (October 12, 2011): 2683-2701. doi:10.1007/s12206-011-0618-2.
'''
Prl = Prandtl(Cp=Cpl, mu=mul, k=kl)
Vl = m * (1 - x) / (rhol * pi / 4 * D**2)
Vg = m * x / (rhog * pi / 4 * D**2)
Rel = Reynolds(V=Vl, D=D, rho=rhol, mu=mul)
Reg = Reynolds(V=Vg, D=D, rho=rhog, mu=mug)
'''The following was coded, and may be used instead of the above lines,
to check that the definitions of parameters here provide the same results
as those defined in [1]_.
G = m/(pi/4*D**2)
Re = G*D/mul
Rel = Re*(1-x)
Reg = Re*x/(mug/mul)'''
Reeq = Reg * (mug / mul) * (rhol / rhog)**0.5 + Rel
Nul = 0.05 * Reeq**0.8 * Prl**0.33
return Nul * kl / D # confirmed to be with respect to the liquid