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Water Boiling Heat
Transfer in Vertical
Jacketed Pipe: A
CFD Model
Mohammad Amin Abdollahi
June 2015
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Boiling Heat Transfer Heat transfer of boiling is an important
phenomenon which is widely used as a
key solution for critical applications, such
as:
BWR type light-water nuclear reactors
fixed-bed catalyst reactors coolant
Column Reboilers
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Boiling Heat Transfer Many correlations have been developed
to predict and formulize the convective
heat transfer coefficient and so the heat
flux in vertical tube-side and shell-side
thermosyphon reboilers.
The correlation developed by Chen is one
of the most widely used methods for
calculating heat-transfer coefficients in
convective boiling.
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Boiling Heat Transfer Assumption of Chens Correlation:
the convective and nucleate boiling
sections of heat transfer can be added to
each other, considering parameters which
import suppression effect of convection on
nucleate boiling.
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Boiling Heat Transfer Chen used the DittusBoelter equation, a
predecessor of the SeiderTate equation for turbulent flow, as follows:
= 0.023(
)
0.80.4
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Boiling Heat Transfer Chen used the ForsterZuber correlation
for the nucleate boiling heat-transfer
coefficient which is usually stated by:
= 0.00122
0.79,0.45
0.490.25
0.240.75
0.50.290.240.24
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Vertical jacketed pipe model
A vertical jacketed pipe which uses
saturated water as coolant in annulus side
has been modeled.
The saturated water boils in constant
temperature by absorbing the heat from
the tube side while flowing through the
annulus around the tube.
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Vertical jacketed pipe model
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Vertical jacketed pipe model
Saturated Water/Steam Properties At 563 K
Liquid Phase Vapor Phase
Pressure (MPa) 7.455
Density (kg/m3) 732.19 39.05
Enthalpy (KJ/kg) 1289.2 2766.9
Cp (J/kg.K) 5.4897 5.5736
Viscosity (cP) 0.08971 0.019147
Thermal Conductivity (W/m2.K)
0.56521 0.064641
Surface tension (N/m)
0.01669 -
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Vertical jacketed pipe model
A 3D full CFD model developed using
ANSYS-FLUENT and it was meshed with
4160 quadrilateral concurrent cells.
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Calculation and Simulation Considering different values for vapor fraction
and by using Chens relevant heat transfer coefficient, the void fraction and equivalent
length of jacketed pipe were calculated.
By curve fitting for scatters of jacketed pipe
length against vapor fraction, an implicit
correlation is derived with a 5th degree
polynomial curve.
y = 37500x5 - 29394x4 + 6854.2x3 - 420.58x2 +
48.771x + 0.0217, (R2=1)
by this correlation, the relevant vapor quality
at the end of the pipe is observed as 6.36%.
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Calculation and Simulation By curve fitting for scatters of heat transfer
coefficient against jacketed pipe length,
an implicit correlation was derived with a
3rd degree polynomial curve.
y = 643.75x3 - 3599.8x2 - 9575.9x + 93047,
(R2=1)
Below table indicates the new data
obtained by this correlation.
Jacketed pipe length
(m)
Heat transfer coefficient(W/m2
.0k)
Heat flux (W/m2)
Void fraction
0.1-2.7 92054-53620 920540-536200
0.0278-0.5558
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Calculation and Simulation Modified data for Heat Flux by curve
fitting:
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Calculation and Simulation Modified data for void fraction by curve
fitting:
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Calculation and Simulation It is also necessary to calculate the critical
heat flux Using Mostinski correlation.
Assuming the critical pressure of 22.064 MPa,
the critical heat flux will be 3820000 W/m2.
It is obvious that the calculated heat flux is
less than 70% of critical heat flux in order to
keep the flow regime in bubbly flow.
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CFD Simulation Results By comparing the results of the CFD
method with the ones of theoretical
correlations, it could be seen that there is a
good consistency between the results of
CFD and theoretical correlations
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CFD Simulation Results Results of Heat Flux against pipe length:
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CFD Simulation Results Results of Void Fraction against pipe length:
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CFD Simulation Results While there is a good adaption between the
results of theoretical correlations and CFD
simulation, it could be referred also to other
data acquired from the CFD model, which
are not extractable from theoretical
correlations easily.
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CFD Simulation Results Results of mass transfer rate against pipe length:
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CFD Simulation Results Contour and Vectors of Velocity at Outlet of
jacketed pipe:
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Conclusion The CFD model developed in this article,
presents reasonable results regarding
compatibility of general trends of heat flux and
void fraction with predictions of theoretical
correlations.
It is notable that theoretical correlations just
produce average figures irrespective of the
radial distance in annulus and flow velocity
curve generated from hydraulic effects.
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Conclusion The capability of predicting hydraulic and
heat transfer behavior of the fluid in all
directions and in all sections of the geometry
of the problem makes this CFD method a
powerful tool for design and simulation.
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Thanks for your kind attention!