Revista de Ciencias Tecnológicas (RECIT). Volumen 3 (1): 10-22
Revista de Ciencias Tecnológicas (RECIT). Universidad Autónoma de Baja California ISSN 2594-1925
Volumen 6 (2): e250. Abril-Junio, 2023. https://doi.org/10.37636/recit.v6n2e250.
1 ISSN: 2594-1925
Research article
Simulation of a micro-evaporator for a single horizontal 1-
mm circular micro-tube
Simulación de un micro-evaporador para un micro-tubo horizontal
circular de 1-mm
César Manuel Valencia-Castillo1 , Giuseppe Zummo2 , Luca Saraceno2, Felipe Noh-Pat3,
Pedro Cruz-Alcántar4
1CARHS, Universidad Autónoma de San Luis Potosí, Carr. Tamazunchale - San Martín Km. 5, 79960
Tamazunchale, San Luis Potosí, México
2Energy Technologies Department, ENEA, Via Anguillarese 301, 00123, Roma, Italia
3Facultad de Ingeniería, Universidad Autónoma de Campeche, Predio s/n Col. ExHacienda Kalá, 24085
Campeche, Campeche, México
4COARA, Universidad Autónoma de San Luis Potosí, Carr. Cedral Km 5+600, 78700 Matehuala, San Luis Potosí,
México
Corresponding author: César Manuel Valencia-Castillo, CARHS, Universidad Autónoma de San Luis Potosí, Carr. Tamazunchale - San
Martín Km. 5, 79960 Tamazunchale, San Luis Potosí, México. E-mail: cesar.valencia@uaslp.mx. ORCID: 0000-0003-3831-8121.
Received: March 31, 2023 Accepted: May 22, 2023 Published: June 6, 2023
Abstract. - Flow boiling into micro-channels is a good option of cooling solutions for electronic devices. Numerical
simulations allow designing correctly before manufacturing. In this paper, the results of a steady-state one-
dimensional simulation are presented for a single horizontal circular 1-mm tube. Through the refrigerant flows,
two regions are distinguished: subcooled liquid flow and two-phase flow. Typical equations and correlations have
been used for subcooled liquid flow; while one theoretical model has been used for two-phase flow. The results
presented here are those by using perfluorohexane, which is used in the formulation of FC-72, a refrigerant for
cooling electronic devices. For the range of tested parameters, the next conclusions come: i) from the point of view
of choosing the pump, the highest subcooled level, and inlet pressure should be preferred; ii) in order to avoid the
critical heat flux condition, the lowest inlet pressure should be preferred; iii) there is a contradiction for choosing
the right inlet pressure because is opposite for the point of view of pump selection and critical heat flux condition.
Keywords: Micro-evaporator; Flow boiling; Numerical simulation; Subcooled liquid flow; Two-phase flow.
Resumen. - El flujo en ebullición dentro de micro-canales es una buena opción para el enfriamiento de dispositivos
electrónicos. Las simulaciones numéricas permiten diseñar correctamente antes de la manufactura. En este
artículo, los resultados de una simulación uni-dimensional, en estado estacionario, son presentados para un tubo
horizontal circular de 1 mm. Mientras el fluido fluye, se distinguen dos regiones: flujo de líquido sub-enfriado y
flujo bifásico. Ecuaciones y correlaciones típicas han sido utilizadas para el flujo de líquido sub-enfriado; mientras
que un modelo teórico ha sido utilizado para el flujo bifásico. Los resultados aquí presentados son aquellos
utilizando perfluorohexano, el cual es utilizado en la formulación del FC-72, un refrigerante para el enfriamiento
de dispositivos electrónicos. Para el rango de los parámetros aquí probados, se obtienen las siguientes
conclusiones: i) desde el punto de vista de la selección de la bomba, el nivel más alto de sub-enfriamiento y de
presión de ingreso serían preferidos; ii) para evitar la condición de flujo de calor crítico, la más baja presión de
ingreso sería preferida; iii) hay una contradicción en la selección de la presión de ingreso correcta porque es
opuesta desde el punto de vista de la selección de la bomba y de la condición de flujo de calor crítico.
Palabras clave: Micro-evaporador; Flujo en ebullición; Simulación numérica; Flujo de líquido sub-enfriado; Flujo
bifásico.
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1. Introduction
In micro devices, flow boiling into micro-
channels seems to be one of the most efficient
cooling solutions for high-power density
electronic devices, being the main challenge the
space limitation.
Research on this topic has been treated
theoretically, numerically, and experimentally;
Szczukiewicz et al. [1] have published a
complete review. Despite the important research
accomplishments that have been obtained over
the last years, some aspects, including local
physical mechanisms related to heat transfer,
remain unclear [2].
Generally, numerical simulations provide an
efficient tool to estimate the thermodynamic
behavior dependent on geometry and operation
conditions.
Numerical simulations of flow boiling have been
performed in the past years [3-8]. Guo et al. [9]
have published a complete review. Despite
simulations needing to be compared with
experimental results, they serve as a guide to
design loops for cooling systems.
The work here presented is the beginning of a
project that pretends to simulate for designing of
micro-scale cooling systems. Part of the research
team is working on the experimental activity.
The project’s aim is to have a tool to design these
systems before manufacturing.
In the present paper, the results of simulations for
an evaporator are showed. The evaporator
consists of a single 1-mm horizontal circular tube
that receives constant heat flux. Inside the tube,
fluid is forced to flow. By input physical
geometry parameters and fluid properties, among
them the outlet quality, the simulation computes
the mass flux and the critical heat flux among
others outputs.
1.1. Background (Theoretical framework,
state of the art)
Cheng & Thome [10] have performed some
simulations for flow boiling heat transfer and
two-phase pressure drops in microscale channels
using R236fa and as working fluids. Imke
[11] developed a numerical tool to simulate
micro-channel flow and heat transfer in compact
heat exchangers. Ghajar & Darabi [12] have
performed numerical simulations for a micro-
loop heat pipe under steady-state conditions,
obtaining the optimized geometry dimensions.
Magnini & Matar [13] have optimized the design
of micro-evaporators via numerical simulations.
Cheng et al. [14] have reviewed flow boiling
heat transfer, flow patterns and two-phase
pressure drops in macro- and micro-channel
evaporators. Marcinichen & Thome [15] have
simulated a two-phase cooling cycle, integrated
by a multi micro-channels evaporator. Yildiz
[16] has modeled a vapor compression
refrigeration cycle for a micro-scale refrigerator.
Karayiannis & Mahmoud [17] have compared
the different integrated systems using micro-
channels. Oudah et al. [18] have numerically
simulated flow boiling R134a refrigerant’s heat
transfer in a tube having 4.35 mm internal
diameter; they claimed an enhancement in the
local heat transfer coefficient when the
temperature of saturation increased from to
. Lorenzini & Joshi [19] have validated a
proposed CFD and heat transfer model for the
dielectric refrigerant HFE-7200 under flow
boiling conditions, providing evidence that such
modeling technique is capable to predict the non-
trivial features of two-phase flow in complex
cooling layers. Keepaiboon et al. [20] have
established the functional relationship of two-
phase flow boiling heat transfer correlation of the
refrigerant R134a during flow boiling in a
rectangular microchannel (at high mass flux)
with the Reynolds number, the boiling number,
Revista de Ciencias Tecnológicas (RECIT). Volumen 6 (2): e250
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and the Weber number. Jain et al. [21] have
proposed a one-dimensional semi-mechanistic
model, combining pressure and heat transfer
coefficient, for flow boiling in a rectangular
mini/micro-channel, evaluating the transient
local heat transfer coefficient in conjunction with
the local transient pressure.
Yuan et al. [22] have performed a steady
simulation model based on one-dimensional flow
direction of flow boiling in micro-channel for
refrigerants R134a and R1234ze(E), being to
highlight that the local heat transfer coefficient:
i) of R1234ze(E) is lower than that of R134a, and
ii) decreases (in the two-phase region) along the
flow direction, which indicates that the nuclear
boiling is dominant. Majumdar et al. [23] have
simulated, by solving mass, momentum and
energy conservation equations, a configuration
of fluid flowing in a vertical heated tube for water
and for liquid nitrogen, comparing the
experimental data with numerical predictions
based on four different correlations, finding that,
for the case of boiling water, the predictions
using the correlations agreed with the
experimental results, while there are large
discrepancies for the case of boiling hydrogen.
Son & Park [24], by introducing a new numerical
phase–change model that reflects the thermal-
fluidic discontinuities through the phase interface
more faithfully, claimed that heir model exhibits
superior consistency with the empirical
correlation than the Lee model.
Wang & Wu [25] have proposed a novel battery
thermal management system (BTMS) using the
dielectric, non-flammable HFE-7000 refrigerant,
improving the thermal performance of the battery
module, showing good agreement between the
numerical results and experimental data. Zhou et
al. [26] have conducted a one-dimensional
numerical study for the heat leak simulation,
validating by the experimental data of the loop
heat pipe, and showing that their model improves
the prediction accuracy for radial heat leak. Bard
et al. [27], by using a number of data science
methods and techniques to accurately predict
the heat transfer coefficient during flow boiling
in mini/micro-channels, have proved that
machine learning is an extremely useful tool
when predicting the heat transfer coefficient
across a variety of different fluids. Moradkhani
et al. [28] developed a general explicit model for
estimating the saturated flow boiling frictional
pressure drop in macro and mini/micro channels
heat exchangers, predicting the database with a
reasonable value of average absolute relative
deviation of 21.34%. Dai et al. [29] have
numerically simulated, by the volume of flow
(VOF) multiphase model, the flow boiling heat
transfer process in a horizontal smooth copper
tube, showing that the heat transfer coefficients
of simulation have great accuracy with a
numerical deviation of ± 20%.
For modelling of boiling in small channels there
are a considerable number of heat transfer
correlations. According to Sardeshpande &
Ranade [30], one of the major difficulties in
modelling two-phase flow is the determination of
the geometry of the flow pattern. Kattan et al.
[31] argue that the models based on distinguish
between flow regimes should be seriously
considered for general use. So, it seems that the
flow pattern has a crucial role on heat transfer
coefficient.
2. Methodology
The simulations have been performed for a
smooth horizontal circular tube of inner diameter
and heated length . A boundary condition of
the second kind (Neumann condition), i.e.,
constant heat flux, has been imposed on the inner
surface of the tube. The simulations are
performed for steady state, one-dimensional
(axial) conditions, using the differential axial
distance . The working fluid is
perfluorohexane (), a fluorocarbon that,
due to its , is used in
Revista de Ciencias Tecnológicas (RECIT). Volumen 6 (2): e250
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formulation of the FC72, a refrigerant for
electronics cooling. Other properties of the
perfluorohexane are, at :
,
, ,
. The fluid enters to the
tube at the pressure and the subcooled level
of (temperature difference below the
saturation temperature as function of ). The
outlet quality is an algorithm input as well.
The output of the algorithm is the mass flux
required for the input parameters, and the critical
heat flux .
Figure 1 outlines the system under analysis.
Figure 1. Schematic of the system.
The fixed input parameters are:
, , ,
, .
While the input parameters that have been tested
according to the matrix showed in table 1.
Table 1. Matrix of tested parameters.
0
5
10
15
20
0.5
1.0
1.4
Figure 2 shows the flow chart of the used
algorithm to simulate both, subcooled liquid flow
and two-phase flow. During design of an
evaporator, it is important to establish the desired
flow pattern during two-phase flow, which is
related to the quality. It is the reason to consider
the outlet quality () as an input parameter.
In this paper, a value of has been used as
fixed outlet quality, which could resemble,
depending on many variables, an up limit of slug
to annular flow. Others quantities for this
variable should be analyzed for different
applications. The mass flux, needed to maintain
the input parameters, is the output of the
algorithm. The algorithm has been written in
Python. The fluid properties have been obtained
using Refprop (version 9.1). All the properties
are obtained as function of pressure and
temperature.
The classification of the tube scale has been done
in the next basis. For the subcooled liquid region,
according to Kandlikar et al. [32] a minichannel
is a channel whose hydraulic diameter is ranged
. So, according with this
classification, the here analyzed tube is a mini-
tube.
For the two-phase region, according to Kew &
Cornwell [33], confinement effects are
significant for channels having hydraulic
diameters such that the confinement number is
higher than , being the confinement number
defined as
. For the
conditions at the tube outlet, the confinement
number of the 15 sets of parameters here
analyzed results as minimum and
as maximum. So, according to this argument, the
here analyzed tube is a micro-tube.
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Figure 2. Flow chart of the present algorithm.
2.1.Subcooled liquid region
For the present analysis, the subcooling level
must be .
For , the conditions in the inlet are
those of saturated liquid, so there is not
subcooled liquid region ( ).
For , the conditions in the inlet are
those of subcooled liquid. In this case, as shown
in the flow chart (see figure 2), the convergence
is reached when , where
is the saturation temperature as function of the
local pressure and is the local liquid
temperature.
The aforementioned convergence means that the
fluid just got the state of saturated liquid at the
axial position . This position represents the axial
length from the tube inlet , i.e., the region
where the fluid is as subcooled liquid.
Frictional pressure drop has been estimated, for
developing laminar region, according to the
equation 2 described by Shah & London [34]
(based in the work of Hornbeck [35]).
(1)
Where
. The length of the
hydrodynamic developing region has been
estimated by .
For fully-developed laminar region and turbulent
region, frictional pressure drop has been
estimated according to:
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(2)
Where is the Fanning friction factor, being
for fully-developed laminar region, and
for turbulent region,
according to the Blasius equation.
So, for the present analysis, if all the
subcooled liquid region would be hydrodynamic
developing, and if part the subcooled
liquid region would be hydrodynamic developing
and the rest would be fully-developed.
Just to point out, gravitational effect has not been
taken in account due to the fact that the tube is
horizontally oriented.
From an energy balance, temperature has been
computed according to:
(3)
2.2. Two-phase region
The routine for two-phase has been performed by
using the theoretical model developed by
Revellin & Thome [36]. There, a system of five
ordinary differential equations is solved for five
dependent variables: liquid and vapor velocities
and pressures, , , , and , respectively,
and radius of the vapor core , being the
independent variable the axial distance . The
five equations are:
(4a)
(4b)
(4c)
(4d)
(4e)
Equations 4a and 4b have been derived by the
conservation of mass. Equations 4c and 4d come
from conservation of momentum. Finally,
equation 4e is the Laplace-Young equation.
The system has been numerically solved using
the 4th-order Runge-Kutta method imposing five
boundary conditions for (saturated liquid),
i.e. where two-phase region begins. When the
tube outlet is reached (), an outlet quality is
computed.
As shown in the flow chart (see figure 2), the
convergence is reached when
. The output of the algorithm is the required
mass flux for the input parameters.
Once the mass flux has been computed, the entire
algorithm runs again to get the critical heat flux.
The convergence is reached when a minimal
liquid film thickness occurs in the tube outlet, i.e.
dry-out condition, according to:
(5)
Where ,
, and
,
according to Revellin & Thome [36].
3. Results and discussions
The figures in this section show results as
function of the subcooled level. The results here
presented are the contribution in the study of flow
boiling inside micro-tube, according with the
parametric analysis of table 1.
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Verification of the present algorithm has been
performed by solving the case presented by
Revellin & Thome [36].
Figure 3. Verification with the results from Revellin &
Thome [36].
Figure 3 shows the comparison between the
results of Revellin & Thome [36] and the results
from the present algorithm. The maximum
deviation has been , for . This
small difference could be attributed to the used
properties, the used equations in the subcooled
liquid, among others. Due to the very small
difference, it is having been verified.
Once it has been verified, some simulations have
been run. Three inlet pressures are shown in the
figures. Note that the value of
corresponds to the case when saturated liquid
enters to the tube; while to the case
when subcooled liquid enters to the tube (the
higher , the lower the inlet temperature).
The mass flux, together with the pressure drop,
are important parameters to select the right pump
of the loop.
The is an important parameter to design
because this condition is always avoided.
Figure 4. Mass flux as function of subcooled level.
Figure 4 shows the required mass flux according
to the subcooled level and the inlet pressure.
As expected, for higher subcooled level, less
mass flux is required. For subcooled liquid
entering to the tube, less mass flux is required for
lower liquid temperature due to it can carry more
energy (heat flux) along the tube.
There is not a regular tendency by inlet pressure
comparison. For the case when saturated liquid
enters to the tube ( ), the highest inlet
pressure () requires more mass flux than
the lowest inlet pressure (); while for the
highest subcooled level ( ), it is
totally opposite.
From the point of view of the mass flux, in order
to reduce the pump power, higher subcooled
level should be chosen.
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Figure 5. Ratio of length of two-phase and total length as
function of subcooled level.
Figure 5 shows the ratio of length of two-phase
and the total heated length according to the
subcooled level and the inlet pressure.
For the case when saturated liquid enters to the
tube ( ), the entire tube is in two-
phase flow (
). As subcooled
level increases, the length of two-phase decreases
because the fluid needs more length of subcooled
liquid in order to reach the state of saturated
liquid.
For higher inlet pressure, less length of two-
phase exists. It seems that fluid properties for
higher inlet pressure leads to need longer length
of subcooled liquid in order to get the state of
saturated liquid.
Figure 6. Pressure drop as function of subcooled level.
Figure 6 shows the pressure drop along the tube
according to the subcooled level and the inlet
pressure. It is possible to see a slight tendency to
reduce the pressure drop for higher subcooled
levels.
As high the inlet pressure as less pressure drop.
It is because the fluid has more enthalpy for
higher pressure. From the point of view of the
pressure drop, in order to reduce the pump power,
higher inlet pressure should be chosen. Note that
this pressure drop is only of the evaporator. In
order to choose a pump, it is necessary to analyze
all the loop components.
Figure 7. Ratio of heat flux and as function of
subcooled level.
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Figure 7 shows the ratio of the actual heat flux
and the critical heat flux according to the
subcooled level and the inlet pressure. It is a very
slight reduction of this ratio for higher subcooled
levels, for higher inlet pressure, the actual heat
flux is closer to the ; for example, for
the actual heat flux represents around
of the , while for
represents around .
From the point of view of the , it would be
preferred the lowest inlet pressure in order to be
farther of this condition. Finally, note that the
decision of the inlet pressure is a quandary
because it should be the highest thinking in the
pump selection but the lowest thinking in the
critical heat flux.
5. Conclusions
From the simulations for an evaporator showed
in this paper, the next conclusions are found.
To choose the right pump, the highest
subcooled level and inlet pressures should be
preferred.
To avoid the critical heat flux condition,
the lowest inlet pressure should be preferred.
The right inlet pressure is difficult to
decide because is opposite for the point of view
of pump selection and critical heat flux
condition.
The results here presented are for a circular
tube. The next step will be to simulate for a
rectangular channel.
6. Acknowledgment
The authors thank to the PRODEP, granted by
the Ministry of Education of Mexico.
7. Authorship acknowledgment
César Manuel Valencia-Castillo: Methodology;
Analysis; Resources; Documentary research; Original
draft; Script. Giuseppe Zummo: Ideas; Analysis;
Resources. Luca Saraceno: Ideas; Analysis. Felipe Noh-
Pat: Methodology; Analysis; Documentary research;
Script. Pedro Cruz-Alcántar: Script; Edition.
Nomenclature
Symbol
Description
SI unit
Roman
Cross sectional area
Specific heat capacity
Critical heat flux
Differential axial length
Inner tube diameter
Fanning friction factor
Gravitational acceleration
Mass flux
Specific enthalpy
Axial heated length
Mass flow rate
Pressure
Inner tube perimeter
Heat flux
Radius of the vapor core
Reynolds number
Temperature
Velocity
Mass quality
Dimensionless length
Axial distance from the inlet
Greek
Liquid film thickness
Pressure drops
Temperature difference
Dynamic viscosity
Density
Surface tension
Shear stress
Subscripts
Frictional
Liquid-Vapor interfacial
Tube inlet
Liquid phase
Change of phase (when ) or Liquid-Vapor (when )
Liquid-Wall
Tube outlet
Saturated
Subcooled liquid
Subcooling
Two-phase
Vapor phase
Axial local position
Indicative for saturated liquid
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