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A statistical method for simulation of boiling flow inside a Platinum microchannel
Journal Pre-proof A statistical method for simulation of boiling flow inside a Platinum microchannel Majid Zarringhalam, Hossein Ahmadi-Danesh-Ashtiani, Davood Toghraie, Reza Fazaeli
PII: DOI: Reference:
S0378-4371(19)32154-5 https://doi.org/10.1016/j.physa.2019.123879 PHYSA 123879
To appear in:
Physica A
Received date : 27 December 2018 Revised date : 14 February 2019 Please cite this article as: M. Zarringhalam, H. Ahmadi-Danesh-Ashtiani, D. Toghraie et al., A statistical method for simulation of boiling flow inside a Platinum microchannel, Physica A (2019), doi: https://doi.org/10.1016/j.physa.2019.123879. This is a PDF file of an article that has undergone enhancements after acceptance, such as the addition of a cover page and metadata, and formatting for readability, but it is not yet the definitive version of record. This version will undergo additional copyediting, typesetting and review before it is published in its final form, but we are providing this version to give early visibility of the article. Please note that, during the production process, errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.
© 2019 Published by Elsevier B.V.
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A statistical method for simulation of boiling flow inside a
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Platinum microchannel
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Majid Zarringhalam1, Hossein Ahmadi-Danesh-Ashtiani2, Davood Toghraie3*, Reza Fazaeli4
1
Department of Mechanical Engineering, South Tehran Branch, Islamic Azad University, Tehran, Iran 2
Department of Energy and Mechanical Engineering, Faculty of Engineering, South Tehran Branch, Islamic Azad University, Tehran, Iran 3
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*Department of Mechanical Engineering, Khomeinishahr Branch, Islamic Azad University, Khomeinishahr, Iran, [email protected] 4
Department of Chemistry, South Tehran Branch, Islamic Azad University, Tehran, Iran
Abstract
This paper presents molecular dynamics simulations to study on the effects of external driving force and boundary wall temperature on the density, velocity and temperature profiles of Argon fluid atoms, flowed in a platinum microchannel with square section. The Argon atoms are structured in three regions. Two thin liquid film of Argon sandwich central vapor zone. Applying wall temperatures in
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the range of 84K to 133K prepares boiling condition which causes liquid atoms move from lateral layers to central bins of microchannel. Afterward, density of central layers of microchannel increases which is highlighted by sampling data after equilibrium condition of system energy in 4 time steps. It
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is concluded that augmentation of external driving forces on the Argon atoms from 0.002 to 0.01 and 0.02 eV/Angstrom can increase flow temperature from 180K to 1920K and 7570K, respectively which is noticeable for practical application such as medical especially in Cryosurgery. Moreover, augmentation of external forces can increase velocity profiles of Argon fluid flow. Generally, density was independent from variation of external force and boundary wall temperature in the studied limits. Also, alteration of boundary wall temperature does not play very important role on the velocity and
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temperature of Argon fluid inside microchannel. Keywords: Microchannel, Boiling flow, Molecular dynamic simulation
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Nomenclature intermolecular force on molecule i by molecule j
Fext
external applied force molecule mass
rc
cutoff distance
rij
position between molecules i and j
t
time step
T
temperature
Vi
velocity of molecule i
Nbin,
number of bins
Natom, number of atom Greek symbols energy parameter in Lennard-Jones (LJ) potential length parameter of LJ potential
ρ
density
ϕ
interaction potential
δ,
delta deviation
Subscripts f,
liquid;
s,
solid;
1- Introduction
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σ
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ε
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Fij
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Nowadays, due to scientific advances in the field of manufacturing the equipments in micro and nanoscale, detail understanding in behavior of systems has become strong challenge among researchers. Because, manufacturing limitations in preparing laboratory requirement are serious obstacles to extend knowledge in very small sizes. Also, determination of flow
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parameters is essential for the proper design and optimal performance of different micro and nano channels for practical application. Moreover, high cost of simulating and checking the specifications of the micro scale systems is another reason to motivate researchers to use numerical method in their scientific investigations. Hence, molecular dynamic simulation 2
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(MDS) method is one of the ways to consider the interaction of molecules in molecular and atomic levels of micro and nanoscales. Molecular dynamics simulation is new statistical method which allows atoms to interact for a fixed period of time. Then physical
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movements of atoms are studied to receive a view of the dynamic evolution of the system. During past years, on the one side, molecular dynamics simulation method has emerged as a
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powerful tool for probing the microscopic behavior of fluids at interfaces. On the other side, investigation in modeling of fluid flow under phase change condition inside very small nanochannels has become active in academic societies. Researchers have done many researches with limited number of atoms, flowed in nanochannels to consider effects of
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surface roughness, explosive boiling phenomenon and so on. Also, despite of extensive researches on heat transfer in heat exchangers and microchannels in continuity domain [4551], lack of molecular dynamic study on the phase change phenomenon with large number of atoms in different ideal and roughened microchannels is seen. This is the reason behind the idea of presenting, molecular dynamic simulation of boiling flow by large number of Argon fluid atoms inside smooth microchannel with cubic section in present work.
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Liakopoulos et al. [1] studied the Darcy-Weisbach friction factor applicable to nanoscale liquid transport processes by Non-equilibrium molecular dynamics simulations to understand
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the atomic behavior of liquids moving in nanochannels. These researchers compared atomistic simulation results with continuum Navier-Stokes solutions, and extended the applicability of continuum theory to nanoscale liquid flows. They presented that predictions of classical continuum theory in power dissipation do not apply in the case of nanochannels
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and have to be modified accordingly with input from atomistic simulations such as slip velocity and profiles of variable viscosity. Liakopoulos et al. [2] employed Non-equilibrium molecular dynamic simulation to study the detailed atomic behavior of fluids moving in nanochannels with various degrees of wall 3
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hydrophobicity/hydrophilicity and roughness. They showed dependence of friction factor not only on geometric characteristics, but also on the nature of interactions between the fluid and the walls. Furthermore, they concluded that friction factor is enhanced when the channel
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walls become more hydrophobic. Finally, they presented the dimensional criteria of roughness which allows us to use expression for the Darcy–Weisbach friction factor, f, to
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estimates of f for nanochannel flows.
Toghraie Semiromi et al. [3] used Molecular dynamics simulation to perform annular flow boiling in a nanochannel. These researchers developed an annular flow model to predict the superheated flow boiling heat transfer characteristics in a nanochannel. They also employed
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an external driving force ranging from 1 to 12 pN (pN= pico newton) to characterize the forced annular boiling flow in a nanochannel, along the flow direction to inlet fluid particles during the simulation. They showed that saturation condition and superheat temperature degree have great influences on the liquid–vapor interface. Moreover, they reported that because of the relatively strong influence of the surface tension in small channels, the interface between the liquid film and the vapor core is fairly smooth, and the mean velocity
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along the stream-wise direction does not change anymore. Zhang et al. [4] carried out an investigation on the effects of nanochannels on the explosive
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phase transition of ultrathin liquid Argon film on the copper substrate in confined space using molecular dynamics simulation. They showed that nanochannels can facilitate the thermal energy transfer from solid copper surface to the liquid Argon which leads to stronger explosive boiling than the flat surface. Also, their result demonstrates that liquid Argon atoms
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adjacent to the copper surface are overheated and consequently a cluster of liquid Argon detaches from the surface which leads to appear immediate explosive boiling. Moreover, increasing nanochannel heights causes to enhance Argon temperature and reducing time to reach equilibrium state when it detaches from the solid surface increases.
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Pengfei et al. [5] simulated a cuboid system with hot and cold walls in the bottom and top ends containing working fluid between the two walls by molecular dynamics simulation. They studied nanoscale vaporization and condensation. They set two different high
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temperatures for the hot wall to show the normal and explosive vaporizations. Their results showed that nanostructure facilitates phase change, because of distances between surfaces of
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the nanostructures. Also it increased surface area which enhanced heat transfer. Moreover, they reported higher temperature of the hot wall make faster transport of the working fluid as a cluster moving from the hot wall to the cold wall.
Ji and Yan [6] carried out a numerical investigation on the triple-phase system of Argon in a
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platinum microchannel heat sink by Molecular dynamics (MD) method to get a microscopic viewpoint into the complex liquid–vapor–solid system. Their results showed that for a completely wetting system of mono-atomic fluid and substrates. Also, there was a nonevaporating liquid film with thickness in nanometers existing on the heating solid surface. They reported that liquid film thickness liquid film varies only slightly with the number of Argon molecules but reduce with the increase of heating substrate temperature.
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Furthermore, strong interactions of solid and liquid molecules reduce potential energy in the thin liquid film toward the heating wall.
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Toghraie and Azimian [7] studied heat transfer characteristics of superheated flow boiling in a nanochannel with 70000 particles by Molecular dynamics simulation. They enforced an external driving force ranging from 1 to12 pN along the flow direction to inlet fluid particles during the simulation. It was concluded that saturation condition
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and degree of superheat have great influences on the liquid-vapor interface. Their results showed that viscosity profile is independent from external force. Moreover, they observed viscosity does not change by temperature variation of lower surface in superheat condition. Finally, they reported that due to the strong influence of surface 5
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tension in small channel, the interface between the liquid film and vapor core is fairly smooth. Also, the mean velocity along the stream-wise direction does not change anymore.
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Fu [8] employed Molecular dynamic simulations to investigate the effects of nanostructure on rapid boiling of water which was heated on a hot copper plate. Their
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results showed that nanostructure intense boiling process and heat transfer from water. So, cluster of liquid water moves upward during phase change. They also reported effect of nanostructure size on phase change and concluded that increasing nanostructure size leads to higher temperature of water. Moreover, they observed a non-vaporized
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molecular layer on the surface of the copper plate even with continuous heat flux is passing into water through the plate.
Cao et al. [9] studied the fluid wetting flow in nanochannels with nanostructured triangular surface to investigate its effect on the boundary slip and friction of the liquid nanoflow. They reported nanostructures can increase the surface hydrophilicity for a hydrophilic liquid-solid interaction. In fact, it can produce higher hydrophobicity for a
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hydrophobic interaction which leads to the large velocity slip of the liquid flow. Sofos et al. [10] studied Density, velocity, temperature and strain rate profiles of planar
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Poiseuille flow of liquid Argon using non-equilibrium molecular dynamics simulations. In this research, channel width was in the range 0.9-17.1nm. They reported that fluid velocity can be successfully fitted by parabolas as system temperature, the magnitude of the external force and enhancement of channel width. They also showed that the
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temperature distribution across the channel is uniform for fluid strain rates below a critical value.
Chao and Binwu [11] studied Argon flow inside micro channel using molecular dynamic simulation method enforcing periodical external force. In this research, two kinds of wall 6
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(hydrophilic and hydrophobic) were simulated on the flow. They reported that due to lower density and smaller number of fluid particles near the walls, the solid-liquid interfacial interaction is weak. Furthermore, the velocity and the temperature of fluid are higher than
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that of hydrophilic walls at the center of channel. Because of the strong solid-liquid interfacial interaction for hydrophilic walls, Argon particles are firmly adsorbed on the walls
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and it is not easy to present the velocity slip and temperature jump near the wall.
Also, the published papers in references [12–20] present the effect of surface roughness on the fluid flow characteristics with limited number of atoms into different nanochannels under single phase flow condition.
in references [21–41].
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Moreover, studies on the effect of adding nanoparticles on the flow parameters were studied
Above review shows researches have focused in nanoscale channels with limited number of atoms. Furthermore, MD simulation phase change is limited mostly to mentioned literature. Therefore, presenting study of boiling flow under phase change condition with large number of atoms in microchannel can make a good understanding of such fluid flow behavior for
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practical application. Also, this subject can be as a gate for researchers to develop it with more investigation inside different shape channel even with larger size under multi phases
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flow affected by surface phenomenon and so on.
2- Simulation method
In present work, molecular dynamics simulation method is employed to simulate the Argon
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fluid flow inside platinum microchannel with cubic section under boiling condition. Boiling process is supported by applied temperatures of 84K, 96K, 108K, 114K and 133 K on the Platinum microchannel wall surfaces and Argon flow is supported by external driving forces
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of 0.002, 0.01 & 0.02 eV/Angstrom which are enforced on the Argon fluid atoms at the inlet section of microchannel respectively. The simulation tool is the large-scale atomic/molecular massively parallel simulation
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(LAMMPS) as available open-source software for molecular dynamics simulation which has been written in C++ and is developed at Sandia National Labs. This software is used due to
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simplicity and ease of operation. Calculations and Sampling data are reported in accordance with the metal units of LAMMPS manual as following table:
Table 1: Quantities units
Mass Distance Time Energy Velocity Force
Units
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Quantity
grams/mole Angstroms
picoseconds eV
Angstroms/picoseconds eV/Angstroms K
Density
gram/cm3
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Temperature
The microchannel is schematically shown in Fig. 1. In this figure, the Argon atoms are segregated in 3 segments: the vapor phases are moving along the middle section of the micro channel, and the two liquid segment cover vapor zone in thin films along the channel walls.
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Generally, sum number of 10000000 Argon atoms is put in prementioned 3 segments. Dimensions of microchannel are 10000*5000*5000 A3. Atomic structure of Platinum layers of microchannel walls are faced center cubic (FCC) lattice which are in contact with the
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liquid Argon atoms internally. Argon atoms in simulation are arranged in FCC structure by 5.26 a lattice constant. The microchannel height is divided into equitable distribution of Nbin,z =2200 bins.
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Calculations of fluid parameters are exported with respect to number of atoms and data are reported for each bin to be graphed regularly. Moreover, calculation of velocity and
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temperature are done for each layer separately and results are reported orderly.
Fig. 1: Schematic of microchannel
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External driving forces are enforced parallel with X axe and wall temperatures are applied in Z axe. The interatomic force between Argon-Argon atoms are described as following LJ potential:
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( rij ) 4 rij
12
rij
6
ri j rc
(1)
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Where the distance between molecules i and j is shown with rij, Ԑ is Energy parameter which introduce the depth of the potential well, and cut-off radius is shown by rc is supposed to be 8.5125 angstrom. The atomic mass, diameter, and potential depth of Argon atoms of present
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research were indicated as much as m=mf=mAr=39.95 grams/mole, σ=σf=σAr=3.405 A° and Ԑ=Ԑf=ԐAr=1.67*10-21J respectively. Also, for the platinum atoms, parameters are as following: atomic mass ms=mpt=195.08 grams/mole, diameter σs=σpt= 2.475 A°, and potential depth Ԑs=Ԑpt=1.67*1021 J. For interaction of Argon-platinum atoms, the modified Lennard-Jones
respectively [42, 43]: w ( rij ) 4 sf sf rij sf
s
f
12
sf rij
sf
6
s
2
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potential coupled with combining rule of Lorentz–Berthelot as equations number 2 and 3
ri j rc f
(2)
(3)
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The velocity Verlet method [44] is employed to integrate the Newton equation as following formula,
v (t t ) v (t ) a (t ) t
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(5)
r (t t ) r (t ) v (t ) t
(6)
According to Fig. 2, After 200000 time step, the energy of system reaches to steady state and no energy fluctuation is seen. But, computation running is continued by more than 1000000
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time step. Sampling data for density is sorted out in 4 sequences of 250000, 500000, 750000 and 1000000 respectively. Also, velocity and temperature results are presented at time step 1000000.
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-4 8 5 6 0
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Energy
-4 8 5 6 5
-4 8 5 7 0
-4 8 5 7 5
0
100000
200000
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-4 8 5 8 0 300000
400000
500000
600000
700000
800000
900000
1E+06
T im e S te p
Fig. 2: Energy stability per time step.
Fig. 3 and Fig. 4 show the radial distribution function (RDF) before and after phase change orderly. Function g(r) defines the probability of finding a particle at a distance r from another
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tagged particle which is varied greatly for liquid and gas phase under boiling process.
Fig. 3. radial distribution function (RDF) before phase change
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3- Results and discussion
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Fig. 4 radial distribution function (RDF) after phase change
In the present study, annular boiling flow of Argon fluid is simulated by molecular dynamic
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simulation inside platinum microchannel. Different temperatures were applied on the walls of microchannel. Also, different external driving forces were enforced on the Argon atoms at the entrance of microchannel. Results of velocity, temperature and density of Argon atoms
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are presented per Nbin,z=2200 bins.
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T=84 K T=96 K T=108 K T=114 K T=133 K
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0.02
0.01
0
500
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Density of argon fluid (gram/cm^dim)
0.03
1000
1500
2000
Number of bin
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Fig. 5: Density profile versus temperature at time step 250000
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F=0.002 ev/angstrom F=0.01 ev/angstrom F=0.02 ev/angstrom
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0.02
0.01
0
500
Pr e-
Density of argon fluid (gram/cm^dim)
0.03
1000
1500
2000
Number of bin
Fig. 6: Density profile versus external force at time step 250000
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Fig.5 and Fig.6 show density of Argon fluid inside microchannel after 250000 time steps. Fig.6 present density profiles affected by external driving forces of 0.002, 0.01 and 0.02 eV/Angstrom (enforced on the Argon atoms at the inlet section of microchannel) and under
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wall temperature of 108 K and Fig.6 exhibits effect of different boundary wall temperatures in the range of 84K to 133K on the density profile, under external force of 0.002 ev/Angstrom. As can be seen from the Fig.5, Density of Argon in 2 thin annular regions is averagely fluctuated between 0.011 and 0.015 gram/cm3, whereas; it reaches to absolute zero
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in middle section of microchannel. It is clear that maximum density is belonged to 2 peripheral regions symmetrically which is in accordance with previous research results, reported by Toghraie [4 and 7]. Because Argon atoms are located in 1000 lateral layers which are near the microchannel walls. Hence, there is no Argon atom into 200 central layers of 14
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microchannel in time step 250000. Therefore, it can be concluded that in this time step, evaporation process of Argon atoms does not move liquid atoms from lateral region to central region. Since density profiles of all temperatures are approximately match together, it is clear
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that increasing and decreasing of temperature in the mentioned range has no significant effect on the density profile. Also, in accordance with Fig.6, amplitude of density under different
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external driving force is varied between 0.011 and 0.016 in symmetric lateral bins. Furthermore, central bins have zero amount of density which is according to the effect of different wall temperatures drawn in Fig.5. These results are also validated by previous researches of Togharai and Azimian [4,7] in nanoscale with the similar atomic structure of
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70000 argon atoms inside nanochannel under the same boundary condition. It is indicated from Fig.6, that variation of density profiles under external driving forces (from 0.002 to and 0.02 ev/Angstrom) are mostly similar which demonstrates independency of these parameters at time step 2500000. In fact, it can be deduced from all above evidences that in the lowest time steps, argon atoms are not energized yet from boundary wall temperatures. Therefore, atoms can be just irritated not derived. Hence, their kinetic energy are not so powerful to
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move them in Z direction in contradict with external driving force in X direction.
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T=84 K T=96 K T=108 K T=114 K T=133 K
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0.02
0.01
500
Pr e-
Density of argon fluid (gram/cm^dim)
0.03
1000
1500
2000
Number of bin
Fig. 7: Density profile versus temperature at time step 500000
0.02
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F=0.002 ev/angstrom F=0.01 ev/angstrom F=0.02 ev/angstrom
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Density of argon fluid (gram/cm^dim)
0.03
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0.01
0
500
1000
1500
Number of bin
16
2000
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Fig. 8: Density profile versus external force at time step 500000
Fig.7 and Fig.8 present density profiles of Argon fluid flow after 500000 time steps. These
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graphs are prepared by calculation of density with respect to number of Argon atoms appropriated for each bins. Fig.8 shows the effects of driving forces of 0.002, 0.01 and 0.02
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eV/Angstrom and Fig.7 is related to the effects of applied wall temperatures of 84K, 96K, 108K, 116K and 133K on the density profile. As can be seen from the graphs, in contrast to the results of density in time step 2500000, no zero value of density is seen except few points related to bin numbers between 1160 and 1190. In the other words, increasing time step under
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steady condition, prepares Argon atoms to move from lateral layers to the middle section of microchannel due to completion of evaporation process, progressed by more time steps. It means argon atoms are moving from lateral layers to central region of microchannel by thermal driving force which is produced by boiling process. Also, increasing boundary wall temperatures from 84K to 133 degree of Kelvin accelerate this phenomenon, but it needs more time steps to be visible in graphs. In addition, it is clear from previous figures of density
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that increasing time step from 250000 to 500000, brings higher oscillation in density profiles of two lateral regions. Because, at low time steps thermal energy of microchannel walls is
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transferred to fluid flow in terms of latent heat of evaporation and increasing time steps result in completion of boiling and kinetic energy enhancement by more number of argon atoms in
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gas phase.
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T=84 K T=96 K T=108 K T=114 K T=133 K
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0.02
0.01
0
500
Pr e-
Density of argon fluid (gram/cm^dim)
0.03
1000
1500
2000
Number of bin
Fig. 9: Density profile versus temperature at time step 750000
0.02
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F=0.002 ev/angstrom F=0.01 ev/angstrom F=0.02 ev/angstrom
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Density of argon fluid (gram/cm^dim)
0.03
0.01
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0
500
1000
1500
2000
Number of bin
Fig. 10: Density profile versus external force at time step 750000
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Fig.9 and Fig.10 exhibit results of density after 750000 time step. As can be seen from these graphs, all density profiles (affected by different wall temperatures and external driving force), have the same trend which presents independency of density from boundary wall
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temperatures and external force in the range of discussed. On the other side, increasing time step leads to reach higher density in the central region of microchannal which shows more
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Argon atoms are moved from annular sections near the microchannel walls to the central bins of middle segment. Therefore, increasing time step causes stronger phase change while; total energy of system is unchanged. That is the reason behind movement of Argon atoms by support of boiling process. In addition, as can be seen from the Fig. 9, and Fig. 10, there is
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not any empty layer and the range of density fluctuation of central layers is limited in domain between 0.004 to 0.008 gram/cm3. It indicates that more space of microchannel is in vapor phase. Furthermore, increasing time steps brings visible difference between graphs of each figure which means difference in wall temperatures and external forces can have ignorable effects on the distribution of argon atoms inside microchannel. Generally, the average value of density between maximum and minimum is significantly lower than that at time steps
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250000 and 500000.
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T=84 K T=96 K T=108 K T=114 K T=133 K
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0.02
0.01
0
500
Pr e-
Density of argon fluid (gram/cm^dim)
0.03
1000
1500
2000
Number of bin
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Fig. 11: Density profile versus temperature at time step 1000000
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F=0.002 ev/angstrom F=0.01 ev/angstrom F=0.02 ev/angstrom
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0.02
0.01
0
500
Pr e-
Density of argon fluid (gram/cm^dim)
0.03
1000
1500
2000
Number of bin
Fig. 12: Density profile versus external force at time step 1000000
Fig.11 and Fig.12 present density profiles of Argon after 1000000 time step versus external
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driving forces and wall temperatures. As is clear from these 2 graphs, atoms have moved from lateral thin segments to central region of microchannel while; total energy of system is
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unchanged. So, empty bins have steadily filled with fluid atoms. Therefore, all layers are included similar number of Argon atoms and of density value. Moreover, densities of layers are approximately in the same fluctuation limits. Meanwhile, all 3 classified segments have similar limits of minimum and maximum of density values. Profiles are nearly the same and
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completely independent from fluid phases and regions classification. On the other side; fluctuation of layers density is higher than that at the previous time steps which infers to completion of evaporation process and increasing kinetic energy and motion of atoms parallel with thermal driving force of boiling in Z direction. 21
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T=84 K T=96 K T=108 K T=114 K T=133 K
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3.5 3
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2.5 2 1.5 1 0.5 0
500
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Velocity of argon fluid (angstroms/picoseconds)
4
1000
1500
2000
Number of bin
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Fig. 13: Velocity profile versus temperature at time step 1000000
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F=0.002 ev/angstrom F=0.01 ev/angstrom F=0.02 ev/angstrom
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25
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20
15
10
5
0
500
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Velocity of argon fluid (angstroms/picoseconds)
30
1000
1500
2000
Number of bin
Fig. 14: Velocity profile versus external force at time step 1000000
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Fig.13 and Fig.14 show the velocity profiles of Argon atoms after completion of boiling process. Vertical axe shows velocity values of Argon atoms versus bin numbers as shown in horizontal vector. Sampling data of all velocities was done at time step 10000000. Fig.13,
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exhibits the relation of velocity profiles with boundary wall temperatures of 84K, 96K, 108K, 114D and 133 degree of Kelvin. It is seen from these graphs that the velocity values are approximately match together which indicated that variation of wall temperatures in the mentioned ranges does not influence on the velocity profile. Because, energy of hot boundary
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surface of microchannel walls is applied parallel with Z direction not in the flow direction. Hence, velocity and boundary wall temperature are independent. As can be seen from Fig.14, enforcing external driving forces of 0.002, 0.01 and 0.02 eV/Angstrom are concluded in velocities of 2, 10.6 and 21.5 angstroms/picoseconds orderly. It means that increasing 23
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external force causes strong enhancement in velocity profile. It also can be convinced academically by Newton’s second law in MD simulations as equation 7,
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d 2 ri d vi Fi Fij Fext mi ai mi 2 mi dt dt i j
(7)
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In other words, applying external driving forces on the Argon atoms is expressed directly as fluid flow and noticeable velocity augmentation in X direction whereas, increasing boundary wall temperature of microchannel increases thermal driving force in Z direction which is not
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significant.
T=84 K T=96 K T=108 K T=114 K T=133 K
300
200
150
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250
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Temprature of argon fluid (K)
350
100
500
1000
1500
Number of bin
2000
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Fig. 15: temperature profile under different wall temperature at time step 1000000
24
6000
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F=0.002 ev/angstrom F=0.01 ev/angstrom F=0.02 ev/angstrom
4000
2000
0 500
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Temprature of argon fluid (K)
8000
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1000
1500
2000
Number of bin
Fig. 16: temperature profile under external force at time step 1000000
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Fig.15 and Fig.16 show temperature profiles of Argon fluid which is shown in vertical axe versus number of bins as horizontal axe. Results are presented after 1000000 time steps under
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steady state of total energy graph.
Fig. 15 shows fitted curve of temperature profiles which are affected by different boundary wall temperatures of 84, 96, 108, 114 and 133K. It is seen from this figure that temperature of Argon fluid is varied from 85K to 140K at near the wall surfaces, whereas; maximum is around 300 K in the center of microchannel. It is clear that increasing microchannel wall
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temperature can bring noticeable augmentation in temperature profile of Argon fluid. Moreover, range of temperature enhancement is also increased from lateral layers near walls to central layers in the middle of channel. Because, fluid atoms are in gas phase in the middle
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of channel under boiling process which is driven by the highest applied temperature of present study. Furthermore, effect of altering boundary temperature on microchannel walls from 84K to 114K is not as strong as that from 114K to 133K, because Argon atoms are
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completely in gas phase at higher temperature. It is interpreted that the applied energy by temperature 114K to 133K is converted to high temperature of Argon in single gas phase,
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instead of converting to latent heat of phase change.
As is shown in Fig.16, Argon temperature values are linearly, and approximately constant. But, changing external driving force from 0.002 to 0.01 and 0.02 eV/Angstrom can leads Argon fluid temperature profiles to augmentate from 180K to 1920K and 7570K respectively.
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To convince such high temperature caused by external force and its influence on velocity, it can be referred to Gaussian distribution based on the specified temperature as following formula:
1 N atm
N atm
1
2m v i 1
i
2
3 kBT 2
(8)
Therefore, external forces increase velocity which causes augmentation of Argon fluid
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temperature consequently. So, outcome of enforcing external forces of 0.01 and 0.02
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eV/Angstrom on the fluid temperature shall be very important for practical application.
5- Conclusion
In this study, we carried out simulation of boiling flow of Argon fluid inside cubic microchannel under different external driving forces and different boundary wall temperatures to investigate their effects on the improvement of phase change process from
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liquid to gas phase. Microchannel was divided into 3 regions which 2 lateral liquid regions covered central vapor region which was empty at the first. Central region was filled with Argon vapor atoms during evaporation process. The system reaches to equilibrium state
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before 200000 time steps. Sampling data of density were at 4 time steps of 250000, 500000, 750000 and 1000000 regularly. Finally, temperature and velocity profiles of Argon atoms in 2200 bins were reported after 1000000 time steps. The key findings and conclusions from the
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present investigation were as follows:
microchannel does not alter density profile.
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1) Enforcing different external forces on the Argon fluid atoms at the inlet section of
2) Generally, applying different temperatures in the limitation of 84K to 133K on the microchannel boundary wall have not strong effect on the density, velocity of Argon fluid whereas; they increases temperature profiles of Argon fluid.
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3) Extending evaporation process in equilibrium state condition causes higher translocation of Argon atoms from lateral region to central segment which brings density enhancement in central layers of microchannel.
4) Enforcing external driving forces of 0.002, 0.01 and 0.02 eV/Angstrom on the argon atoms at entrance region of microchannel result in velocities of 2, 10.6 and 21.5 angstroms/picoseconds orderly. Hence, increasing external force can brings
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proportional increase in velocity and consequently, temperature of Argon fluid inside microchannel shall be increased with respect to relation of velocity and temperature.
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5) Applying external driving forces of 0.01 and 0.02 eV/Angstrom can augmentate fluid temperature as much as 1920K and 7570K respectively which needs to be controlled in some of practical application, such as medical surgeries especially for the time Argon fluid is used as very cold fluid to destroy abnormal tissues and tumors.
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The extension of this paper can be completed by investigation of microchannel surface roughness effects in the same boiling flow condition.
6- References
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Using of a statistical method Investigation of boiling flow by large number of Argon atoms inside a cubic microchannel Implementation of Molecular dynamic simulation Augmentation of external driving forces on the Argon atoms can increase flow temperature
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• • •
PII: DOI: Reference:
S0378-4371(19)32154-5 https://doi.org/10.1016/j.physa.2019.123879 PHYSA 123879
To appear in:
Physica A
Received date : 27 December 2018 Revised date : 14 February 2019 Please cite this article as: M. Zarringhalam, H. Ahmadi-Danesh-Ashtiani, D. Toghraie et al., A statistical method for simulation of boiling flow inside a Platinum microchannel, Physica A (2019), doi: https://doi.org/10.1016/j.physa.2019.123879. This is a PDF file of an article that has undergone enhancements after acceptance, such as the addition of a cover page and metadata, and formatting for readability, but it is not yet the definitive version of record. This version will undergo additional copyediting, typesetting and review before it is published in its final form, but we are providing this version to give early visibility of the article. Please note that, during the production process, errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.
© 2019 Published by Elsevier B.V.
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A statistical method for simulation of boiling flow inside a
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Platinum microchannel
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Majid Zarringhalam1, Hossein Ahmadi-Danesh-Ashtiani2, Davood Toghraie3*, Reza Fazaeli4
1
Department of Mechanical Engineering, South Tehran Branch, Islamic Azad University, Tehran, Iran 2
Department of Energy and Mechanical Engineering, Faculty of Engineering, South Tehran Branch, Islamic Azad University, Tehran, Iran 3
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*Department of Mechanical Engineering, Khomeinishahr Branch, Islamic Azad University, Khomeinishahr, Iran, [email protected] 4
Department of Chemistry, South Tehran Branch, Islamic Azad University, Tehran, Iran
Abstract
This paper presents molecular dynamics simulations to study on the effects of external driving force and boundary wall temperature on the density, velocity and temperature profiles of Argon fluid atoms, flowed in a platinum microchannel with square section. The Argon atoms are structured in three regions. Two thin liquid film of Argon sandwich central vapor zone. Applying wall temperatures in
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the range of 84K to 133K prepares boiling condition which causes liquid atoms move from lateral layers to central bins of microchannel. Afterward, density of central layers of microchannel increases which is highlighted by sampling data after equilibrium condition of system energy in 4 time steps. It
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is concluded that augmentation of external driving forces on the Argon atoms from 0.002 to 0.01 and 0.02 eV/Angstrom can increase flow temperature from 180K to 1920K and 7570K, respectively which is noticeable for practical application such as medical especially in Cryosurgery. Moreover, augmentation of external forces can increase velocity profiles of Argon fluid flow. Generally, density was independent from variation of external force and boundary wall temperature in the studied limits. Also, alteration of boundary wall temperature does not play very important role on the velocity and
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temperature of Argon fluid inside microchannel. Keywords: Microchannel, Boiling flow, Molecular dynamic simulation
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Nomenclature intermolecular force on molecule i by molecule j
Fext
external applied force molecule mass
rc
cutoff distance
rij
position between molecules i and j
t
time step
T
temperature
Vi
velocity of molecule i
Nbin,
number of bins
Natom, number of atom Greek symbols energy parameter in Lennard-Jones (LJ) potential length parameter of LJ potential
ρ
density
ϕ
interaction potential
δ,
delta deviation
Subscripts f,
liquid;
s,
solid;
1- Introduction
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σ
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ε
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Fij
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Nowadays, due to scientific advances in the field of manufacturing the equipments in micro and nanoscale, detail understanding in behavior of systems has become strong challenge among researchers. Because, manufacturing limitations in preparing laboratory requirement are serious obstacles to extend knowledge in very small sizes. Also, determination of flow
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parameters is essential for the proper design and optimal performance of different micro and nano channels for practical application. Moreover, high cost of simulating and checking the specifications of the micro scale systems is another reason to motivate researchers to use numerical method in their scientific investigations. Hence, molecular dynamic simulation 2
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(MDS) method is one of the ways to consider the interaction of molecules in molecular and atomic levels of micro and nanoscales. Molecular dynamics simulation is new statistical method which allows atoms to interact for a fixed period of time. Then physical
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movements of atoms are studied to receive a view of the dynamic evolution of the system. During past years, on the one side, molecular dynamics simulation method has emerged as a
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powerful tool for probing the microscopic behavior of fluids at interfaces. On the other side, investigation in modeling of fluid flow under phase change condition inside very small nanochannels has become active in academic societies. Researchers have done many researches with limited number of atoms, flowed in nanochannels to consider effects of
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surface roughness, explosive boiling phenomenon and so on. Also, despite of extensive researches on heat transfer in heat exchangers and microchannels in continuity domain [4551], lack of molecular dynamic study on the phase change phenomenon with large number of atoms in different ideal and roughened microchannels is seen. This is the reason behind the idea of presenting, molecular dynamic simulation of boiling flow by large number of Argon fluid atoms inside smooth microchannel with cubic section in present work.
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Liakopoulos et al. [1] studied the Darcy-Weisbach friction factor applicable to nanoscale liquid transport processes by Non-equilibrium molecular dynamics simulations to understand
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the atomic behavior of liquids moving in nanochannels. These researchers compared atomistic simulation results with continuum Navier-Stokes solutions, and extended the applicability of continuum theory to nanoscale liquid flows. They presented that predictions of classical continuum theory in power dissipation do not apply in the case of nanochannels
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and have to be modified accordingly with input from atomistic simulations such as slip velocity and profiles of variable viscosity. Liakopoulos et al. [2] employed Non-equilibrium molecular dynamic simulation to study the detailed atomic behavior of fluids moving in nanochannels with various degrees of wall 3
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hydrophobicity/hydrophilicity and roughness. They showed dependence of friction factor not only on geometric characteristics, but also on the nature of interactions between the fluid and the walls. Furthermore, they concluded that friction factor is enhanced when the channel
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walls become more hydrophobic. Finally, they presented the dimensional criteria of roughness which allows us to use expression for the Darcy–Weisbach friction factor, f, to
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estimates of f for nanochannel flows.
Toghraie Semiromi et al. [3] used Molecular dynamics simulation to perform annular flow boiling in a nanochannel. These researchers developed an annular flow model to predict the superheated flow boiling heat transfer characteristics in a nanochannel. They also employed
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an external driving force ranging from 1 to 12 pN (pN= pico newton) to characterize the forced annular boiling flow in a nanochannel, along the flow direction to inlet fluid particles during the simulation. They showed that saturation condition and superheat temperature degree have great influences on the liquid–vapor interface. Moreover, they reported that because of the relatively strong influence of the surface tension in small channels, the interface between the liquid film and the vapor core is fairly smooth, and the mean velocity
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along the stream-wise direction does not change anymore. Zhang et al. [4] carried out an investigation on the effects of nanochannels on the explosive
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phase transition of ultrathin liquid Argon film on the copper substrate in confined space using molecular dynamics simulation. They showed that nanochannels can facilitate the thermal energy transfer from solid copper surface to the liquid Argon which leads to stronger explosive boiling than the flat surface. Also, their result demonstrates that liquid Argon atoms
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adjacent to the copper surface are overheated and consequently a cluster of liquid Argon detaches from the surface which leads to appear immediate explosive boiling. Moreover, increasing nanochannel heights causes to enhance Argon temperature and reducing time to reach equilibrium state when it detaches from the solid surface increases.
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Pengfei et al. [5] simulated a cuboid system with hot and cold walls in the bottom and top ends containing working fluid between the two walls by molecular dynamics simulation. They studied nanoscale vaporization and condensation. They set two different high
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temperatures for the hot wall to show the normal and explosive vaporizations. Their results showed that nanostructure facilitates phase change, because of distances between surfaces of
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the nanostructures. Also it increased surface area which enhanced heat transfer. Moreover, they reported higher temperature of the hot wall make faster transport of the working fluid as a cluster moving from the hot wall to the cold wall.
Ji and Yan [6] carried out a numerical investigation on the triple-phase system of Argon in a
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platinum microchannel heat sink by Molecular dynamics (MD) method to get a microscopic viewpoint into the complex liquid–vapor–solid system. Their results showed that for a completely wetting system of mono-atomic fluid and substrates. Also, there was a nonevaporating liquid film with thickness in nanometers existing on the heating solid surface. They reported that liquid film thickness liquid film varies only slightly with the number of Argon molecules but reduce with the increase of heating substrate temperature.
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Furthermore, strong interactions of solid and liquid molecules reduce potential energy in the thin liquid film toward the heating wall.
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Toghraie and Azimian [7] studied heat transfer characteristics of superheated flow boiling in a nanochannel with 70000 particles by Molecular dynamics simulation. They enforced an external driving force ranging from 1 to12 pN along the flow direction to inlet fluid particles during the simulation. It was concluded that saturation condition
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and degree of superheat have great influences on the liquid-vapor interface. Their results showed that viscosity profile is independent from external force. Moreover, they observed viscosity does not change by temperature variation of lower surface in superheat condition. Finally, they reported that due to the strong influence of surface 5
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tension in small channel, the interface between the liquid film and vapor core is fairly smooth. Also, the mean velocity along the stream-wise direction does not change anymore.
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Fu [8] employed Molecular dynamic simulations to investigate the effects of nanostructure on rapid boiling of water which was heated on a hot copper plate. Their
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results showed that nanostructure intense boiling process and heat transfer from water. So, cluster of liquid water moves upward during phase change. They also reported effect of nanostructure size on phase change and concluded that increasing nanostructure size leads to higher temperature of water. Moreover, they observed a non-vaporized
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molecular layer on the surface of the copper plate even with continuous heat flux is passing into water through the plate.
Cao et al. [9] studied the fluid wetting flow in nanochannels with nanostructured triangular surface to investigate its effect on the boundary slip and friction of the liquid nanoflow. They reported nanostructures can increase the surface hydrophilicity for a hydrophilic liquid-solid interaction. In fact, it can produce higher hydrophobicity for a
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hydrophobic interaction which leads to the large velocity slip of the liquid flow. Sofos et al. [10] studied Density, velocity, temperature and strain rate profiles of planar
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Poiseuille flow of liquid Argon using non-equilibrium molecular dynamics simulations. In this research, channel width was in the range 0.9-17.1nm. They reported that fluid velocity can be successfully fitted by parabolas as system temperature, the magnitude of the external force and enhancement of channel width. They also showed that the
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temperature distribution across the channel is uniform for fluid strain rates below a critical value.
Chao and Binwu [11] studied Argon flow inside micro channel using molecular dynamic simulation method enforcing periodical external force. In this research, two kinds of wall 6
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(hydrophilic and hydrophobic) were simulated on the flow. They reported that due to lower density and smaller number of fluid particles near the walls, the solid-liquid interfacial interaction is weak. Furthermore, the velocity and the temperature of fluid are higher than
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that of hydrophilic walls at the center of channel. Because of the strong solid-liquid interfacial interaction for hydrophilic walls, Argon particles are firmly adsorbed on the walls
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and it is not easy to present the velocity slip and temperature jump near the wall.
Also, the published papers in references [12–20] present the effect of surface roughness on the fluid flow characteristics with limited number of atoms into different nanochannels under single phase flow condition.
in references [21–41].
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Moreover, studies on the effect of adding nanoparticles on the flow parameters were studied
Above review shows researches have focused in nanoscale channels with limited number of atoms. Furthermore, MD simulation phase change is limited mostly to mentioned literature. Therefore, presenting study of boiling flow under phase change condition with large number of atoms in microchannel can make a good understanding of such fluid flow behavior for
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practical application. Also, this subject can be as a gate for researchers to develop it with more investigation inside different shape channel even with larger size under multi phases
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flow affected by surface phenomenon and so on.
2- Simulation method
In present work, molecular dynamics simulation method is employed to simulate the Argon
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fluid flow inside platinum microchannel with cubic section under boiling condition. Boiling process is supported by applied temperatures of 84K, 96K, 108K, 114K and 133 K on the Platinum microchannel wall surfaces and Argon flow is supported by external driving forces
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of 0.002, 0.01 & 0.02 eV/Angstrom which are enforced on the Argon fluid atoms at the inlet section of microchannel respectively. The simulation tool is the large-scale atomic/molecular massively parallel simulation
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(LAMMPS) as available open-source software for molecular dynamics simulation which has been written in C++ and is developed at Sandia National Labs. This software is used due to
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simplicity and ease of operation. Calculations and Sampling data are reported in accordance with the metal units of LAMMPS manual as following table:
Table 1: Quantities units
Mass Distance Time Energy Velocity Force
Units
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Quantity
grams/mole Angstroms
picoseconds eV
Angstroms/picoseconds eV/Angstroms K
Density
gram/cm3
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Temperature
The microchannel is schematically shown in Fig. 1. In this figure, the Argon atoms are segregated in 3 segments: the vapor phases are moving along the middle section of the micro channel, and the two liquid segment cover vapor zone in thin films along the channel walls.
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Generally, sum number of 10000000 Argon atoms is put in prementioned 3 segments. Dimensions of microchannel are 10000*5000*5000 A3. Atomic structure of Platinum layers of microchannel walls are faced center cubic (FCC) lattice which are in contact with the
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liquid Argon atoms internally. Argon atoms in simulation are arranged in FCC structure by 5.26 a lattice constant. The microchannel height is divided into equitable distribution of Nbin,z =2200 bins.
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Calculations of fluid parameters are exported with respect to number of atoms and data are reported for each bin to be graphed regularly. Moreover, calculation of velocity and
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temperature are done for each layer separately and results are reported orderly.
Fig. 1: Schematic of microchannel
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External driving forces are enforced parallel with X axe and wall temperatures are applied in Z axe. The interatomic force between Argon-Argon atoms are described as following LJ potential:
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( rij ) 4 rij
12
rij
6
ri j rc
(1)
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Where the distance between molecules i and j is shown with rij, Ԑ is Energy parameter which introduce the depth of the potential well, and cut-off radius is shown by rc is supposed to be 8.5125 angstrom. The atomic mass, diameter, and potential depth of Argon atoms of present
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research were indicated as much as m=mf=mAr=39.95 grams/mole, σ=σf=σAr=3.405 A° and Ԑ=Ԑf=ԐAr=1.67*10-21J respectively. Also, for the platinum atoms, parameters are as following: atomic mass ms=mpt=195.08 grams/mole, diameter σs=σpt= 2.475 A°, and potential depth Ԑs=Ԑpt=1.67*1021 J. For interaction of Argon-platinum atoms, the modified Lennard-Jones
respectively [42, 43]: w ( rij ) 4 sf sf rij sf
s
f
12
sf rij
sf
6
s
2
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potential coupled with combining rule of Lorentz–Berthelot as equations number 2 and 3
ri j rc f
(2)
(3)
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The velocity Verlet method [44] is employed to integrate the Newton equation as following formula,
v (t t ) v (t ) a (t ) t
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(5)
r (t t ) r (t ) v (t ) t
(6)
According to Fig. 2, After 200000 time step, the energy of system reaches to steady state and no energy fluctuation is seen. But, computation running is continued by more than 1000000
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time step. Sampling data for density is sorted out in 4 sequences of 250000, 500000, 750000 and 1000000 respectively. Also, velocity and temperature results are presented at time step 1000000.
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-4 8 5 6 0
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Energy
-4 8 5 6 5
-4 8 5 7 0
-4 8 5 7 5
0
100000
200000
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-4 8 5 8 0 300000
400000
500000
600000
700000
800000
900000
1E+06
T im e S te p
Fig. 2: Energy stability per time step.
Fig. 3 and Fig. 4 show the radial distribution function (RDF) before and after phase change orderly. Function g(r) defines the probability of finding a particle at a distance r from another
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tagged particle which is varied greatly for liquid and gas phase under boiling process.
Fig. 3. radial distribution function (RDF) before phase change
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3- Results and discussion
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Fig. 4 radial distribution function (RDF) after phase change
In the present study, annular boiling flow of Argon fluid is simulated by molecular dynamic
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simulation inside platinum microchannel. Different temperatures were applied on the walls of microchannel. Also, different external driving forces were enforced on the Argon atoms at the entrance of microchannel. Results of velocity, temperature and density of Argon atoms
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are presented per Nbin,z=2200 bins.
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Fig. 5: Density profile versus temperature at time step 250000
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Fig. 6: Density profile versus external force at time step 250000
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Fig.5 and Fig.6 show density of Argon fluid inside microchannel after 250000 time steps. Fig.6 present density profiles affected by external driving forces of 0.002, 0.01 and 0.02 eV/Angstrom (enforced on the Argon atoms at the inlet section of microchannel) and under
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wall temperature of 108 K and Fig.6 exhibits effect of different boundary wall temperatures in the range of 84K to 133K on the density profile, under external force of 0.002 ev/Angstrom. As can be seen from the Fig.5, Density of Argon in 2 thin annular regions is averagely fluctuated between 0.011 and 0.015 gram/cm3, whereas; it reaches to absolute zero
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in middle section of microchannel. It is clear that maximum density is belonged to 2 peripheral regions symmetrically which is in accordance with previous research results, reported by Toghraie [4 and 7]. Because Argon atoms are located in 1000 lateral layers which are near the microchannel walls. Hence, there is no Argon atom into 200 central layers of 14
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microchannel in time step 250000. Therefore, it can be concluded that in this time step, evaporation process of Argon atoms does not move liquid atoms from lateral region to central region. Since density profiles of all temperatures are approximately match together, it is clear
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that increasing and decreasing of temperature in the mentioned range has no significant effect on the density profile. Also, in accordance with Fig.6, amplitude of density under different
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external driving force is varied between 0.011 and 0.016 in symmetric lateral bins. Furthermore, central bins have zero amount of density which is according to the effect of different wall temperatures drawn in Fig.5. These results are also validated by previous researches of Togharai and Azimian [4,7] in nanoscale with the similar atomic structure of
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70000 argon atoms inside nanochannel under the same boundary condition. It is indicated from Fig.6, that variation of density profiles under external driving forces (from 0.002 to and 0.02 ev/Angstrom) are mostly similar which demonstrates independency of these parameters at time step 2500000. In fact, it can be deduced from all above evidences that in the lowest time steps, argon atoms are not energized yet from boundary wall temperatures. Therefore, atoms can be just irritated not derived. Hence, their kinetic energy are not so powerful to
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move them in Z direction in contradict with external driving force in X direction.
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Fig. 7: Density profile versus temperature at time step 500000
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Fig. 8: Density profile versus external force at time step 500000
Fig.7 and Fig.8 present density profiles of Argon fluid flow after 500000 time steps. These
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graphs are prepared by calculation of density with respect to number of Argon atoms appropriated for each bins. Fig.8 shows the effects of driving forces of 0.002, 0.01 and 0.02
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eV/Angstrom and Fig.7 is related to the effects of applied wall temperatures of 84K, 96K, 108K, 116K and 133K on the density profile. As can be seen from the graphs, in contrast to the results of density in time step 2500000, no zero value of density is seen except few points related to bin numbers between 1160 and 1190. In the other words, increasing time step under
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steady condition, prepares Argon atoms to move from lateral layers to the middle section of microchannel due to completion of evaporation process, progressed by more time steps. It means argon atoms are moving from lateral layers to central region of microchannel by thermal driving force which is produced by boiling process. Also, increasing boundary wall temperatures from 84K to 133 degree of Kelvin accelerate this phenomenon, but it needs more time steps to be visible in graphs. In addition, it is clear from previous figures of density
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that increasing time step from 250000 to 500000, brings higher oscillation in density profiles of two lateral regions. Because, at low time steps thermal energy of microchannel walls is
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transferred to fluid flow in terms of latent heat of evaporation and increasing time steps result in completion of boiling and kinetic energy enhancement by more number of argon atoms in
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gas phase.
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Fig. 9: Density profile versus temperature at time step 750000
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Fig. 10: Density profile versus external force at time step 750000
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Fig.9 and Fig.10 exhibit results of density after 750000 time step. As can be seen from these graphs, all density profiles (affected by different wall temperatures and external driving force), have the same trend which presents independency of density from boundary wall
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temperatures and external force in the range of discussed. On the other side, increasing time step leads to reach higher density in the central region of microchannal which shows more
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Argon atoms are moved from annular sections near the microchannel walls to the central bins of middle segment. Therefore, increasing time step causes stronger phase change while; total energy of system is unchanged. That is the reason behind movement of Argon atoms by support of boiling process. In addition, as can be seen from the Fig. 9, and Fig. 10, there is
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not any empty layer and the range of density fluctuation of central layers is limited in domain between 0.004 to 0.008 gram/cm3. It indicates that more space of microchannel is in vapor phase. Furthermore, increasing time steps brings visible difference between graphs of each figure which means difference in wall temperatures and external forces can have ignorable effects on the distribution of argon atoms inside microchannel. Generally, the average value of density between maximum and minimum is significantly lower than that at time steps
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250000 and 500000.
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Fig. 11: Density profile versus temperature at time step 1000000
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Fig. 12: Density profile versus external force at time step 1000000
Fig.11 and Fig.12 present density profiles of Argon after 1000000 time step versus external
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driving forces and wall temperatures. As is clear from these 2 graphs, atoms have moved from lateral thin segments to central region of microchannel while; total energy of system is
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unchanged. So, empty bins have steadily filled with fluid atoms. Therefore, all layers are included similar number of Argon atoms and of density value. Moreover, densities of layers are approximately in the same fluctuation limits. Meanwhile, all 3 classified segments have similar limits of minimum and maximum of density values. Profiles are nearly the same and
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completely independent from fluid phases and regions classification. On the other side; fluctuation of layers density is higher than that at the previous time steps which infers to completion of evaporation process and increasing kinetic energy and motion of atoms parallel with thermal driving force of boiling in Z direction. 21
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T=84 K T=96 K T=108 K T=114 K T=133 K
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Velocity of argon fluid (angstroms/picoseconds)
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Fig. 13: Velocity profile versus temperature at time step 1000000
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F=0.002 ev/angstrom F=0.01 ev/angstrom F=0.02 ev/angstrom
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Fig. 14: Velocity profile versus external force at time step 1000000
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Fig.13 and Fig.14 show the velocity profiles of Argon atoms after completion of boiling process. Vertical axe shows velocity values of Argon atoms versus bin numbers as shown in horizontal vector. Sampling data of all velocities was done at time step 10000000. Fig.13,
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exhibits the relation of velocity profiles with boundary wall temperatures of 84K, 96K, 108K, 114D and 133 degree of Kelvin. It is seen from these graphs that the velocity values are approximately match together which indicated that variation of wall temperatures in the mentioned ranges does not influence on the velocity profile. Because, energy of hot boundary
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surface of microchannel walls is applied parallel with Z direction not in the flow direction. Hence, velocity and boundary wall temperature are independent. As can be seen from Fig.14, enforcing external driving forces of 0.002, 0.01 and 0.02 eV/Angstrom are concluded in velocities of 2, 10.6 and 21.5 angstroms/picoseconds orderly. It means that increasing 23
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external force causes strong enhancement in velocity profile. It also can be convinced academically by Newton’s second law in MD simulations as equation 7,
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d 2 ri d vi Fi Fij Fext mi ai mi 2 mi dt dt i j
(7)
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In other words, applying external driving forces on the Argon atoms is expressed directly as fluid flow and noticeable velocity augmentation in X direction whereas, increasing boundary wall temperature of microchannel increases thermal driving force in Z direction which is not
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significant.
T=84 K T=96 K T=108 K T=114 K T=133 K
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Fig. 15: temperature profile under different wall temperature at time step 1000000
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Fig. 16: temperature profile under external force at time step 1000000
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Fig.15 and Fig.16 show temperature profiles of Argon fluid which is shown in vertical axe versus number of bins as horizontal axe. Results are presented after 1000000 time steps under
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steady state of total energy graph.
Fig. 15 shows fitted curve of temperature profiles which are affected by different boundary wall temperatures of 84, 96, 108, 114 and 133K. It is seen from this figure that temperature of Argon fluid is varied from 85K to 140K at near the wall surfaces, whereas; maximum is around 300 K in the center of microchannel. It is clear that increasing microchannel wall
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temperature can bring noticeable augmentation in temperature profile of Argon fluid. Moreover, range of temperature enhancement is also increased from lateral layers near walls to central layers in the middle of channel. Because, fluid atoms are in gas phase in the middle
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of channel under boiling process which is driven by the highest applied temperature of present study. Furthermore, effect of altering boundary temperature on microchannel walls from 84K to 114K is not as strong as that from 114K to 133K, because Argon atoms are
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completely in gas phase at higher temperature. It is interpreted that the applied energy by temperature 114K to 133K is converted to high temperature of Argon in single gas phase,
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instead of converting to latent heat of phase change.
As is shown in Fig.16, Argon temperature values are linearly, and approximately constant. But, changing external driving force from 0.002 to 0.01 and 0.02 eV/Angstrom can leads Argon fluid temperature profiles to augmentate from 180K to 1920K and 7570K respectively.
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To convince such high temperature caused by external force and its influence on velocity, it can be referred to Gaussian distribution based on the specified temperature as following formula:
1 N atm
N atm
1
2m v i 1
i
2
3 kBT 2
(8)
Therefore, external forces increase velocity which causes augmentation of Argon fluid
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temperature consequently. So, outcome of enforcing external forces of 0.01 and 0.02
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eV/Angstrom on the fluid temperature shall be very important for practical application.
5- Conclusion
In this study, we carried out simulation of boiling flow of Argon fluid inside cubic microchannel under different external driving forces and different boundary wall temperatures to investigate their effects on the improvement of phase change process from
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liquid to gas phase. Microchannel was divided into 3 regions which 2 lateral liquid regions covered central vapor region which was empty at the first. Central region was filled with Argon vapor atoms during evaporation process. The system reaches to equilibrium state
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before 200000 time steps. Sampling data of density were at 4 time steps of 250000, 500000, 750000 and 1000000 regularly. Finally, temperature and velocity profiles of Argon atoms in 2200 bins were reported after 1000000 time steps. The key findings and conclusions from the
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present investigation were as follows:
microchannel does not alter density profile.
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1) Enforcing different external forces on the Argon fluid atoms at the inlet section of
2) Generally, applying different temperatures in the limitation of 84K to 133K on the microchannel boundary wall have not strong effect on the density, velocity of Argon fluid whereas; they increases temperature profiles of Argon fluid.
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3) Extending evaporation process in equilibrium state condition causes higher translocation of Argon atoms from lateral region to central segment which brings density enhancement in central layers of microchannel.
4) Enforcing external driving forces of 0.002, 0.01 and 0.02 eV/Angstrom on the argon atoms at entrance region of microchannel result in velocities of 2, 10.6 and 21.5 angstroms/picoseconds orderly. Hence, increasing external force can brings
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proportional increase in velocity and consequently, temperature of Argon fluid inside microchannel shall be increased with respect to relation of velocity and temperature.
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5) Applying external driving forces of 0.01 and 0.02 eV/Angstrom can augmentate fluid temperature as much as 1920K and 7570K respectively which needs to be controlled in some of practical application, such as medical surgeries especially for the time Argon fluid is used as very cold fluid to destroy abnormal tissues and tumors.
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The extension of this paper can be completed by investigation of microchannel surface roughness effects in the same boiling flow condition.
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Using of a statistical method Investigation of boiling flow by large number of Argon atoms inside a cubic microchannel Implementation of Molecular dynamic simulation Augmentation of external driving forces on the Argon atoms can increase flow temperature
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• • •