Artículo Académico / Academic Paper
Recibido: 05-09-2022, Aprobado tras revisión: 11-01-2023
Forma sugerida de citación: Toapanta, F; Tamay, C.; Quitiaquez, W. (2023). “Análisis numérico mediante CFD para el proceso
de ebullición forzada con isobutano que circula por tubos cuadrados”. Revista Técnica “energía”. No. 19, Issue II, Pp. 110-118
ISSN On-line: 2602-8492 - ISSN Impreso: 1390-5074
Doi: https://doi.org/10.37116/revistaenergia.v19.n2.2023.534
© 2023 Operador Nacional de Electricidad, CENACE
Numerical analysis by CFD for the forced boiling process with isobutane
circulating through square tubes
Análisis numérico mediante CFD para el proceso de ebullición forzada con
isobutano que circula por tubos cuadrados
F. Toapanta1 C. Tamay1 W. Quitiaquez1
1Ingeniería Mecánica, Universidad Politécnica Salesiana, Quito, Ecuador
E-mail: ltoapanta@ups.edu.ec; ctamay@ups.edu.ec; wquitiaquez@ups.edu.ec
Abstract
The purpose of this investigation is to compare the
development of the boiling phenomenon in an
analytical and numerical way, by means of the heat
transfer coefficient for two phases and the steam
quality with the R600a refrigerant, inside a square
steel tube up to 3 cm side, the simulation is carried
out using a software for computational fluid
dynamics (fluid ANSYS). Finding an increase in
steam quality for high calorie flow and low
thickness. Finally, it finds the maximum phase
change by boiling for flow of 400 kg/m²·s, heat of
20,000 W/m², with 88% steam for the central point
in the exit edge condition.
Resumen
El propósito de esta investigación es analizar el
desarrollo del fenómeno de ebullición de forma
numérica, mediante el coeficiente de transferencia de
calor para dos fases y la calidad del vapor con el
refrigerante R600a, en el interior de un tubo
cuadrado de acero de hasta 3 cm de lado, la
simulación se realiza mediante un software de
dinámica de fluidos computacional (Fluid ANSYS).
Encontrar un aumento en la calidad del vapor para
un flujo alto de calor y un espesor bajo. Finalmente,
encuentra el máximo cambio de fase por ebullición
para caudal de 400 kg/m²·s, calor de 20.000 W/m²,
con 88% de vapor para el punto central en condición
de borde de salida.
Index terms Boiling, Isobutane, CFD, Simulation,
ANSYS
Palabras clave Ebullición, Isobutano, CFD,
Simulación, ANSYS
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Edición No. 19, Issue II, Enero 2023
1. INTRODUCCIÓN
Two-phase flow and boiling phenomena are used in
a variety of processes and applications, such as
refrigeration systems, air conditioning and heat
pumping, energy conversion and heat exchange
systems, thermal chemical processes, cooling of
electronic components of high power, among others [1].
The study of the boiling process in domestic,
commercial, and industrial refrigeration applications has
increased in recent years, however, most of these studies
have emphasized round pipes and research on other
types of geometry is almost nil. Square pipes in the
transport of fluids are important in installations with few
irregularities and for long lengths.
Compliance with environmental regulations requires
the use of environmentally friendly refrigerants.
Refrigerant manufacturers are currently pushing their
efforts in the development of new low-GWP
refrigerants, which can replace common HFCs [2]. A
natural refrigerant (R600a) not only has a value of zero
in ODP and very low GWP, but it also has other
thermodynamic advantages over other refrigerants, such
as a low liquid density than most HFC's [3], [4].
With the phasing out of conventional refrigerants,
isobutane (R600a) emerged as the main alternative in
the refrigeration industry. Hydrocarbons, the class of
refrigerant to which R600a belongs, are viable
substitutes as they possess favorable cooling thermal
properties. However, the investigation of this refrigerant
goes beyond its use alone; its compatibility and
performance with compressor oils are currently being
investigated [5].
The high latent heat of the R600a requires a smaller
compressor size to provide the same capacity [6]. Due
to its good cooling performance and environmentally
friendly characteristics, R600a has been used as an
alternative refrigerant in heat transfer applications such
as refrigerators, freezers, and heat pumps, although it is
flammable [7].
Flow boiling in refrigerants within the tube in
macroscale or conventional channels can be classified
according to nucleate boiling (related to the formation
of vapor bubbles on the surface of the tube wall) and
convective boiling (related to conduction and
convection) [8], [9].
Copetti et al. [10] carried out an experiment to
investigate the heat transfer of the boiling flow for
R600a in a tube with an internal diameter of 2.6mm.
They found that the heat transfer coefficient increased
with heat flow at low steam qualities.
Unlike experimental studies, Computational Fluid
Dynamics (CFD) simulations are better able to provide
detailed information on local hydrodynamics and two-
phase boiling flow heat transfer, therefore it can be used
as a tool. of additional research [11]. The difficulty of
flow boiling simulation is mainly due to two challenges:
the interface tracking algorithm and the phase change
model. The domain flux of surface tension makes
monitoring difficult because the interfacial curvature is
inversely proportional to the dimension [12].
Ferrari et al. [13] conclude that, the velocity of the
bubble in a square channel is always larger than that in a
circular channel. This happens because the cross-
sectional area occupied by the liquid film in a square
channel is larger.
Over the years, various methods have been
developed for the study of phase change [14], [15]. The
Lagrangian or Eulerian method is used to evaluate the
interface. In Lagrangian methods, the interface is
represented by mesh faces, which allows an accurate
evaluation of the normal gradient of the interface [16],
[17]. However, it is expensive to trace complex
interfacial deformation in transient problems using a
moving mesh with Lagrangian methods. In Eulerian
methods, the interface geometry is reconstructed from a
color function that is used to track phases, such as the
volume fraction in fluid volume (VOF) methods. This
allows convenient monitoring of complex interface
deformations [18], [19].
The objective of this research is to determine
numerically by ANSYS Fluent, the boiling process of
the natural refrigerant R600a that circulates inside large
square pipes.
2. METODOS Y MATERIALES
For this study, a square pipe section is considered,
1.5 m long with a variable side distance starting from 20
mm to 30 mm, these dimensions are found in the
Ecuadorian industry. In Fig. 1, the dimensions of the
pipe to be simulated can be seen. On the other hand, it is
essential to clarify the material of the pipe, it is
commercial steel distributed in the Ecuadorian industry.
Figure 1: Diagram and dimensions of the analysis pipe
The analysis is carried out for various types of
square tubes, with different side lengths. However, the
mass flow for R600a is modified with values of 300 and
400 kg/m²·s, in addition, the heat flow is also a variant
in this study, it is analyzed for values of 10, 15 and 20
kW/m².
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It has already been mentioned, the fluid to be used is
R600a (Isobutane) refrigerant, which is a natural
refrigerant and very friendly to the environment and
completely safe. The boiling process is carried out at a
temperature of 8 °C, where the fluid enters in a state of
saturated liquid and the output is a mixture of liquid
with steam at the same entering temperature.
Table 1 shows the thermophysical properties of
R600a at saturation temperature, for the liquid phase as
well as for the vapor phase.
Tabla 1: Thermophysical properties of R600a refrigerant [20],
[21]
Property
Liquid phase
Vapor
phase
T=5°C
T=8°C
T=8°C
Density,
[kg/m3]
574.6
571
5.507
Specific heat,
[J/kgK]
2327
2345
1690
Thermal
conductivity,
[W/m·K]
0.09652
0.09535
0.01516
Viscosity,
[Pa·s]
0.0001879
0.0001815
7.205e-6
Molecular
weight,
[kg/kmol]
58.12
58.12
58.12
Surface
tension, [N/m]
0.01218
0.01182
0.01182
Enthalpy of
vaporization,
[J/kg]
350100
347100
347100
Saturation
pressure,
[kPa]
186.4
206.3
206.3
2.1. Numerical models
The term boiling is used to describe the situation
where the temperature is higher than the temperature at
the boiling point. The energy is transferred directly from
the wall to the liquid, this heat will cause the
temperature of the liquid to increase and generate steam.
In the Fluent ANSYS the boiling models are
developed in the context of the Eulerian multiphase
model. Multiphase flows are governed by conservation
equations for the continuity of the phase, momentum
and energy, these equations are shown below,
respectively.
Where, V _q is the velocity of phase q. And m_pq
characterizes the mass transfer from phase p to q, m_qp
is the transfer of mass from phase q to p, and you can
specify these separately. τ_q is the stress tensor for
phase q, u_q and λ_q is the shear and apparent viscosity
of phase q, F _q is a force external to the body, F
_(lift,q) bearing force, F _(wl,q) a wall lubrication
force, F _(vm,q) is a virtual mass force, F _(td,q) is a
turbulent dispersion force and R _pq is the interaction
force between the phases. V _pq is the speed between
the phases [22].
These fundamental formulas are the basis of the
Rensselaer Polytechnic Institute (RPI) models, the
phenomenon is modeled by the nucleate boiling of RPI
exposed by Kurual and Podowski [23].
The total heat flux from the wall to the liquid is
divided into two components, called convective heat
flux and evaporative heat flux.
(1)
(2)
(3)
(4)
(5)
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Edición No. 19, Issue II, Enero 2023
The heated surface of the wall is subdivided into,
area A_b which is covered by nucleation bubbles and a
portion (1-Ab), which is covered by fluid.
The convective heat flux qC is expressed as:
(6)
The evaporative flow qE is given by equation 7:
(7)
Where, h_c is the heat transfer coefficient for a
single phase, T_w and T_l are the wall and liquid
temperatures, respectively. V_d is the volume of the
bubble based on the exit diameter of the bubbles, N_w
is the density of the active nucleated site, ρ_v is the
density of the vapor, h_fv is the latent heat of
vaporization and f is the exit frequency of the bubble.
The κ-ε (kappa-epsilon) turbulence model is one of
the most widely used in the field of CFD simulation, the
two-equation model has presented robust results in the
turbulence field for both kinetic energy and energy
dissipation, kappa, and epsilon, respectively.
Within this two-equation model are other
submodels, such as standard, RNG and realizable. All
three could be used for the simulation of the boiling
process, however, the RNG model was chosen for its
great adaptability to the fluid and working geometry. On
the other hand, this model was derived using a certain
statistical technique normalization group theory, it is
like the standard basic model, although, it includes
certain improvements.
For the transport equations involving the κ-ε RNG
model are described below. Equation 8 represents the
turbulent kinetic energy and equation 9 is the turbulent
dissipation energy.
In the equations, G_k represents the turbulence kinetic
energy production due to the average velocity gradients.
G_b is the generation of turbulence kinetic energy due
to buoyancy. The quantity Y_M symbolizes the
contribution of the fluctuation dilation to incompressible
turbulence to the overall dissipation rate. C_1ε, C_2ε
and C_(3ε )are constants. σ_k and σ_ε are the turbulent
Prandtl number for k and ε, respectively. S_k and S_ε
are user-defined source terms [22].
3. RESULTS AND DISCUSSION
In the simulation process, meshing the convergence
of the solution is extremely important, since, with a
good mesh size, the transport equations for energy,
continuity, boiling, momentum and turbulence will be
obtained, they can be appropriately discretized inside
the analysis geometry.
In Fig. 2, the mesh made to the square steel tube can
be seen, as well as the size of the mesh, which for this
investigation is ideal.
Figure 2: Geometry meshing
Although the mesh looks perfect and does not show
irregularities, it is essential to carry out a meshing
convergence study, for this, the computational tool,
skewness, is used, which details how much is the
minimum value required for the mesh to work and
converge to any type of CFD simulation. Where a value
of 0 represents that all the elements are equilateral,
while, for an interval between 0-0.25 the mesh is
excellent and for values that are in 0.25-0.5 the mesh is
good.
(8)
(9)
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Fig. 3 shows the mesh convergence for the analysis
geometry after performing a meshing technique, under
the size regulation procedure. Likewise, it is appreciated
that the greatest number of elements are between 0-1,
therefore, the meshing is excellent for any simulation
process with Fluent.
Figure 3: Mesh convergence with the Skewness tool
Fig. 4a indicates that, the boiling process inside a
square tube occurs from the wall to the inside of the
tube, however, it is visualized in a plane in the central
part of the pipe, the red part represents the refrigerant
vapor, while the blue part is the liquid phase. The steam
is only located in the upper part, this is because the
liquid has a higher density than the steam and for this
reason only steam is seen in the upper part. On the other
hand, Figure 4b represents the progression of the boiling
process inside the square tube, this time in a 3D graph,
with 150 mm divisions in the length.
Figure 4: Boiling for case A, 0.030 m, thickness 1.5 mm, mass flow
of 300 kg/m2·s and heat flow of 10 kW/m2, a) 2D and b) 3D
Although the simulation for case A solved the
boiling problem inside a square tube, it is important to
compare these results with other simulations, where one
of the process variables is modified.
The boiling process is given by the application of
heat flow that enters through the walls of the tube, this
begins with 10 kW/m² and is modified twice, both for
15 and 20 kW/m², these values were chosen, since
which are very close to the theoretical value calculated
for the boiling phenomenon. However, the rate of entry
of refrigerant into the tube remains fixed.
In Fig. 5, the boiling in the central part of the square
tube is shown, for the three variations of heat flow. It is
visualized that, in the central axis of the tube, for heat
flow 10 kW/m2 the phenomenon is not present yet,
however, for 15 kW/m2 the boiling occurs in the last
third of the pipe. Finally, for the highest flux of 20
kW/m2 the process is exhibited upon reaching the center
of the full length of the tube.
Figure 5: Comparison of the boiling process with change of heat
flux of 10, 15, 20 kW/m2
Fig. 6 compares not only the change in heat flow,
but also the variation in the input mass flow. This figure
shows the behavior of the boiling phenomenon under
two changes, the mass flow, and the heat flow.
For higher mass flows the boiling does not stand out,
as for the lower mass flow, however, there is a phase
change of 35 % for the maximum heat flow of 20
kW/m2, almost half of that achieved with the mass flow
300 kg/s·m², so low flow rates are recommended to
support the boiling process. Furthermore, it must be
considered that the speed set guarantees a turbulent flow
regime.
The results shown in the previous figures indicate
how the boiling phenomenon occurs, however, these
have only been simulated for half of case A, the other
half corresponds to the change in the thickness of the
square tube. In Fig. 7 the boiling for this thickness of
pipe can be seen.
(a)
(b)
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Edición No. 19, Issue II, Enero 2023
Figure 6: Comparison of the boiling process with change in heat
flow and mass
Fig. 8 represents the boiling phenomenon for a 25
mm square tube with thicknesses of 1.5 and 2 mm, with
a constant mass flow of 300 kg/s·m², and heat flows that
vary from 10 to 20 kW/m2. The lines between cuts
symbolize the simulations for the 1.5 mm thickness and
the solid lines for the 2 mm thickness.
Figure 7: Boiling with modification of pipe thickness
It can be seen in the same figure that for higher
heat fluxes the steam quality is higher than for low
fluxes. Likewise, for heat flux of 10 kW/m2, the boiling
is similar and has no variation. It should be considered
that for higher heat fluxes a characteristic variation of
the phase change is shown.
Figure 8. Boiling for a 25 mm side square tube with different
thicknesses and mass flow 300 kg/s·m².
In Fig. 9, the boiling for heat flow of 10 kW/m2,
mass flow of 300 kg/s·m² and side modification of 30,
25 and 20 mm is visualized, Figures 9 a, b and c,
respectively.
For case A, the boiling process has reached 8.5 % as
steam at the outlet, in case B the vapor phase reached
21.82 % and in case C it is 70.89 %. This shows that if
the side decreases the boiling effect increases.
(a)
(b)
(d)
(c)
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Figure 9: Boiling for heat flow of 10 kW/m2, mass flow of 300
kg/s·m² and side modification of 30, 25 and 20 mm
4. CONCLUSIONS AND RECOMMENDATIONS
At the end of the numerical-thermal study of the
boiling process in cured tubes, the following
conclusions were reached:
The heat flow that is needed to carry out the
boiling phenomenon inside a square tube is only
3.25 % of what is required for total evaporation,
which is why it was chosen to simulate with heat
flows that exceed this percentage up to 7 %
which is a flow of 20 kW/m².
The mass flow was placed according to the
turbulent flow study for both the analytical and
numerical part, a flow of 300 kg/s·m² was
designated, because, with this, the flow and the
Reynolds number are always in regime turbulent.
In addition, 33 % was added in the rate of entry
and observe how the boiling effect is modified
inside the tube.
For the simulation carried out on two tubes with
a side 25 mm, thickness 1.5 mm, heat flow 15
kW/m². with modification of the mass flow of
300 kg/s·m² and after 400 kg/s·m², qualities of
steam at the outlet of 72.75 and 51.15 %,
respectively, which indicates a reduction of 29.7
% in the vapor phase due to the increase in
velocity. However, by increasing 0.5 mm in
thickness, the decrease of 2.15 % in the vapor
phase is determined for the mass flow of 300
kg/s·m² and 3.65 % in the simulation with the
increase in flow to
400 kg/s·m².
Square pipes are frequently used in the
refrigeration industry; however, the length of
these pipes corresponds to very large air
conditioning processes. therefore, it is
recommended to use this study for very large
cases.
ACKNOWLEDGEMENTS
The authors of this research thank the mechanical
engineering career of the Salesian Polytechnic
University, the Research Group in Engineering,
Productivity and Industrial Simulation (GIIPSI) and the
Branch ASHRAE UPS-QUITO.
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Fernando Toapanta-Ramos.-
Nació en Quito, Ecuador en 1986.
Recibió su título de Ingeniero
Mecánico de la Universidad
Politécnica Salesiana en 2012; de
Master en Gestión de Energías de
la Universidad de Técnica de
Cotopaxi, Latacunga en 2016; y su
título de Doctor en la Universidad Pontificia
Bolivariana, en la escuela de ingeniería, de Colombia.
Sus campos de investigación están relacionados con el
Desarrollo fluidos con nanopartículas, nanorefrigerantes
y simulaciones de CFD con fenómenos relacionados a la
transferencia de calor, termodinámica y mecánica de
fluidos.
Cristina Tamay Clavón.- Nació
en Quito el 2 de enero 1990.
Recibió su título de Ingeniera
Mecánica de la Universidad
Politécnica Salesiana en 2020.
Actualmente, está estudiando
fenómenos relacionados al
comercio e intercambio monetario.
William Quitiaquez.- Nació en
Quito, Ecuador en 1988. Recibió
su título de Ingeniero Mecánico de
la Universidad Politécnica
Salesiana en 2011; de Master en
Gestión de Energías de la
Universidad de Técnica de
Cotopaxi, Latacunga en 2015; y su
título de Doctor en la Universidad Pontificia
Bolivariana, en la escuela de ingeniería, de Colombia.
Sus campos de investigación están relacionados con el
Desarrollo fluidos con nanopartículas, nanorefrigerantes
y simulaciones de CFD con fenómenos relacionados a la
transferencia de calor, termodinámica y mecánica de
fluidos.
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