atw 2018-04v6
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<strong>atw</strong> Vol. 63 (<strong>2018</strong>) | Issue 4 ı April<br />
| | Fig. 1.<br />
Schematic representation of horizontal flow and different morphologies.<br />
(Algebraic Interfacial Area Density<br />
Model) is developed for detection of<br />
the local morphology and corresponding<br />
switch between them [16]. The<br />
recently developed GENTOP- model<br />
combines both concepts. GENTOP<br />
(Generalized Two-Phase Flow) approach<br />
is able to simulate co-existing<br />
large-scaled (continuous) and smallscaled<br />
(polydispersed) structures [17].<br />
All these models are validated for adiabatic<br />
cases without any phase change.<br />
Therefore, the start point of the current<br />
work project is using the available<br />
models and integrating phase transition<br />
and con densation models into<br />
them. In the current work as initial<br />
stages the AIAD model has been used<br />
since in this model 2 continues phases<br />
should be considered and it is less complicated<br />
compare to GENTOP model<br />
which also considers a poly- dispersed<br />
phase. In the proceeding sections a<br />
more detail explanation of AIAD model<br />
will be given.<br />
2 CFD model formulation<br />
In the current work a multi-field twophase<br />
CFD approach is used with<br />
ANSYS CFX 17.2 in order to simulate<br />
the condensation inside horizontal<br />
pipe flows. The mass, momentum and<br />
energy equations can be defined,<br />
respectively, as follow:<br />
• Mass conservation equation:<br />
(1)<br />
where S Mi describes user specified<br />
mass source.<br />
χ iβ the mass flow rate per unit volume<br />
from phase β to phase i.<br />
• Momentum conservation equation:<br />
(2)<br />
where S mi is the momentum source<br />
caused by external body forces<br />
and user defined momentum<br />
sources.<br />
M i is the interfacial forces acting<br />
on phase i due to the presence<br />
of other phases.<br />
χ + iβ v β – χ + βi v i is the momentum<br />
transfer induced<br />
by mass transfer.<br />
• The total energy equation:<br />
(3)<br />
where: h tot is the total enthalpy<br />
related to static enthalpy by:<br />
(4)<br />
<br />
T i , λ i represents the temperature<br />
and the thermal conductivity<br />
of phase i.<br />
S Ei describes external heat sources.<br />
Q i is interphase heat transfer<br />
to phase i across interfaces<br />
with the other phase.<br />
χ + iβ h βs – χ + βi h is denotes the interphase<br />
mass transfer.<br />
In ANSYS CFX in order to describe the<br />
phase change which occurs due to the<br />
interphase heat transfer, the Thermal<br />
Phase Change Model has been introduced<br />
[30]. This model is particularly<br />
useful in simulation of the condensation<br />
of saturated vapor. The heat<br />
flux from the interface to phase i and<br />
phase β is:<br />
q i = h i (T sat – T i ) (5)<br />
q β = h β (T sat – T β ) (6)<br />
where h i , h β and T sat are heat transfer<br />
coefficients of the phase i and phase<br />
β and the saturation temperature,<br />
respectively. ṁ iβ is the mas flux from<br />
phase β to phase i. H is and H βs are the<br />
interfacial enthalpy values which<br />
come into and out of the phase due<br />
to phase change which occurs. By<br />
usage of the total heat balance<br />
equation the interphase mas flux can<br />
be determined as follow:<br />
<br />
| | Fig. 2.<br />
3D geometry of the pipe and mesh of the cross section.<br />
(7)<br />
ṁ iβ > 0 → H is = H i,sat , H βs = H β (8)<br />
ṁ iβ < 0 → H is = H i , H βs = H β,sat (9)<br />
In the current work, the steam<br />
con sidered to be in saturation temperature.<br />
Therefore, the heat flux<br />
from the steam to the interface equals<br />
zero since both are in saturation<br />
temperature. As a result, the interphase<br />
mass flux formula can be<br />
written as:<br />
<br />
(10)<br />
In this work in order to model the heat<br />
transfer coefficient the Hughes and<br />
Duffy model has been used which is<br />
based on the SRT model [9]. They<br />
used the Surface Renewal Theory<br />
(SRT) and the Kolmogorov turbulent<br />
length scale theory to find a correlation<br />
for heat transfer coefficient.<br />
Therefore, the heat transfer coefficient<br />
was derived as:<br />
<br />
(11)<br />
where ε is the turbulent dissipation, v l<br />
is the kinematic viscosity and λ is the<br />
thermal conductivity.<br />
3 Computational grid and<br />
boundary conditions<br />
In Figure 2 the pipe and the boundary<br />
conditions are shown. The pipe is<br />
horizontal and has 1 m length<br />
and 0.043 m diameter. In order to<br />
define a mesh for the pipe ANSYS<br />
ICEM software is used. Due to the<br />
higher importance of the wall region<br />
compare to the middle of the pipe,<br />
the mesh near the wall needs to be<br />
finer than the mesh in the pipe<br />
center. The number of nodes is<br />
1,250,000.<br />
Mass flow rate<br />
[Kg/s]<br />
Temperature<br />
(k)<br />
Inlet 0.5 537.1<br />
Wall - 312.18<br />
outlet outflow -<br />
ENVIRONMENT AND SAFETY 239<br />
CFD Modeling and Simulation of Heat and Mass Transfer in Passive Heat Removal Systems<br />
Environment and Safety<br />
ı Amirhosein Moonesi, Shabestary, Eckhard Krepper and Dirk Lucas