Three-dimensional (3D) direct simulation Monte Carlo (DSMC) has been used to simulate flow in a straight microchannel using an in-house parallelized code. In the present work, a comparative study of seven boundary conditions is carried out with respect to time required for achieving steady-state, accuracy in predicting the specified pressure at the boundaries, and the total simulation time required for attaining a statistical error within one percent. The effect of changing the Knudsen number, pressure ratio (PR), and cross aspect ratio (CAR) on these parameters is also studied. The presence of a boundary is seen to affect the simulated pressure in a cell when compared to the specified pressure, the difference being highest for corner cells and least for cells away from walls. All boundary conditions tested work well at the inlet boundary; however, similar results are not obtained at the outlet boundary. For the same cell size, the schemes that employ first- and second-order corrections lead to a smaller pressure difference compared to schemes applying no corrections. The best predictions can be obtained by using first-order corrections with finer cell size close to the boundary. For most of the simulated cases, the boundary condition employing the characteristic scheme with nonequilibrium effect leads to the minimum simulation time. Considering the nonequilibrium effect, prediction of inlet and outlet pressures and the speed of simulation, the characteristic scheme with nonequilibrium effect performs better than all the other schemes, at least over the range of parameters investigated herein.

References

References
1.
Amon
,
C. H.
,
Murthy
,
J.
,
Yao
,
S. C.
,
Narumanchi
,
S.
,
Wu
,
C. F.
, and
Hsieh
,
C. C.
,
2001
, “
MEMS Enabled Thermal Management of High Heat Flux Devices EDIFICE: Embedded Droplet Impingement for Integrated Cooling of Electronics
,”
Exp. Therm. Fluid Sci.
,
25
(
5
), pp.
231
242
.
2.
Agrawal
,
A.
,
2011
, “
A Comprehensive Review on Gas Flow in Microchannels
,”
Int. J. Micro-Nano Scale Transp.
,
2
(
1
), pp.
1
40
.
3.
Bird
,
G. A.
,
1994
,
Molecular Gas Dynamics and the Direct Simulation of Gas Flows
,
Oxford University Press
,
New York
.
4.
Piekos
,
E. S.
, and
Breuer
,
K. S.
,
1996
, “
Numerical Modeling of Micromechanical Devices Using the Direct Simulation Monte Carlo Method
,”
ASME J. Fluids Eng.
,
118
(
3
), pp.
464
469
.
5.
Yan
,
F.
, and
Farouk
,
B.
,
2002
, “
Computations of Low Pressure Fluid Flow and Heat Transfer in Ducts Using the Direct Simulation Monte Carlo Method
,”
ASME J. Heat Transfer
,
124
(
4
), pp.
609
616
.
6.
Le
,
M.
,
Hassan
,
I.
, and
Esmail
,
N.
,
2006
, “
DSMC Simulation of Subsonic Flows in Parallel and Series Microchannels
,”
ASME J. Fluids Eng.
,
128
(
6
), pp.
1153
1163
.
7.
Wang
,
M.
, and
Li
,
Z.
,
2006
, “
Gases Mixing in Microchannels Using the Direct Simulation Monte Carlo Method
,”
Int. J. Heat Mass Transfer
,
49
(9–10), pp.
1696
1702
.
8.
Wang
,
Q. W.
,
Zhao
,
C. L.
,
Zeng
,
M.
, and
Wu
,
Y. N.
,
2008
, “
Numerical Investigation of Rarefied Diatomic Gas Flow and Heat Transfer in a Microchannel Using DSMC With Uniform Heat Flux Boundary Condition—Part II: Applications
,”
Numer. Heat Transfer, Part B
,
53
(2), pp.
174
187
.
9.
Zhen
,
C. E.
,
Hong
,
Z. C.
,
Lin
,
Y. J.
, and
Hong
,
N. T.
,
2007
, “
Comparison of 3-D and 2-D DSMC Heat Transfer Calculations of Low-Speed Short Microchannel Flows
,”
Numer. Heat Transfer, Part A
,
52
(
3
), pp.
239
250
.
10.
Gavasane
,
A.
,
Agrawal
,
A.
,
Pradeep
,
A. M.
, and
Bhandarkar
,
U.
,
2017
, “
Simulation of a Temperature Drop of the Flow of Rarefied Gases in Microchannels
,”
Numer. Heat Transfer Part A
,
71
(
10
), pp.
1066
1079
.
11.
Hong
,
Z.
,
Zhen
,
C.
, and
Yang
,
C.
,
2008
, “
Fluid Dynamics and Heat Transfer Analysis of Three-Dimensional Microchannel Flows With Microstructures
,”
Numer. Heat Transfer Part A
,
54
(3), pp.
293
314
.
12.
Hsieh
,
T.
,
Hong
,
C.
, and
Pan
,
Y.
,
2010
, “
Flow Characteristics of Three-Dimensional Microscale Backward Facing Step Flows
,”
Numer. Heat Transfer Part A
,
57
(
5
), pp.
331
345
.
13.
Liou
,
T.
, and
Lin
,
C.
,
2015
, “
Three-Dimensional Rarefied Gas Flows in Constricted Microchannels With Different Aspect Ratios: Asymmetry Bifurcations and Secondary Flows
,”
Microfluid. Nanofluid.
,
18
(
2
), pp.
279
292
.
14.
Gavasane
,
A.
,
Agrawal
,
A.
,
Pradeep
,
A.
, and
Bhandarkar
,
U.
,
2015
, “
Study of Temperature Drop in Microchannel Using Direct Simulation Monte Carlo Method
,”
AIP Conf. Proc.
,
1628
(
1
), pp.
785
791
.
15.
Le
,
M.
, and
Hassan
,
I.
,
2006
, “
Simulation of Heat Transfer in High Speed Microflows
,”
Appl. Therm. Eng.
,
26
(
16
), pp.
2035
2044
.
16.
Le
,
M.
, and
Hassan
,
I.
,
2007
, “
The Effects of Outlet Boundary Conditions on Simulating Supersonic Microchannel Flows Using DSMC
,”
Appl. Therm. Eng.
,
27
(
1
), pp.
21
30
.
17.
Titov
,
E.
, and
Levin
,
D.
,
2007
, “
Extension of the DSMC Method to High Pressure Flows
,”
Int. J. Comput. Fluid Dyn.
,
21
(
9–10
), pp.
351
368
.
18.
Gatsonis
,
N. A.
,
Al-Kouz
,
W. G.
, and
Chamberlin
,
R. E.
,
2010
, “
Investigation of Rarefied Supersonic Flows Into Rectangular Nanochannels Using a Three-Dimensional Direct Simulation Monte Carlo Method
,”
Phys. Fluids
,
22
(
3
), p.
032001
.
19.
Watvisave
,
D. S.
,
Bhandarkar
,
U. V.
, and
Puranik
,
B. P.
,
2011
,“
An Investigation of Pressure Boundary Conditions for the Simulation of a Micro-Nozzle Using DSMC Method
,”
28th International Symposium on Shock Waves
, Manchester, UK, July 17–22, Paper No. 2481.
20.
Liu
,
H. F.
,
2005
, “
Hypersonic Rarefied Flow Simulation Using 2D Unstructured DSMC With Free Stream Condition
,”
24th International Symposium on Rarefied Gas Dynamics
, Bari, Italy, July 10–16, pp.
1223
1228
.
21.
Lilley
,
C. R.
, and
Macrossan
,
M. N.
,
2003
, “
Methods for Implementing the Stream Boundary Condition in DSMC Computations
,”
Int. J. Numer. Methods Fluids
,
42
(
12
), pp.
1363
1371
.
22.
Ikegawa
,
M.
, and
Kobayashi
,
J.
,
1990
, “
Development of a Rarefied Gas Flow Simulator Using the Direct Simulation Monte Carlo Method: 2-D Flow Analysis with the Pressure Conditions Given at the Upstream and Downstream Boundaries
,”
JSME Int. J. Ser. II
,
33
(
3
), pp.
463
467
.
23.
Wu
,
J.
,
Lee
,
W.
, and
Wong
,
S.
,
2001
, “
Pressure Boundary Treatment in Micromechanical Devices Using The Direct Simulation Monte Carlo Method
,”
JSME Int. J. Ser. B
,
44
(
3
), pp.
439
450
.
24.
Nance
,
R.
,
Hash
,
D.
, and
Hassan
,
H.
,
1997
, “
Role of Boundary Conditions in Monte Carlo Simulation of MEMS Devices
,”
35th Aerospace Sciences Meeting and Exhibit
, Reno, NV, Jan. 6–9, pp.
6
9
.
25.
Wang
,
M.
, and
Li
,
Z.
,
2004
, “
Simulation of Gas Flows in Micro Geometries Using the Direct Simulation Monte Carlo Method
,”
Int. J. Heat Fluid Flow
,
25
(
6
), pp.
975
985
.
26.
Liou
,
W. W.
, and
Fang
,
Y. C.
,
2000
, “
Implicit Boundary Conditions for Direct Simulation Monte Carlo Method in MEMS Flow Predictions
,”
Comput. Model. Eng. Sci.
,
1
(4), pp.
119
128
.
27.
White
,
C.
,
Borg
,
M.
,
Scanlon
,
T.
, and
Reese
,
J.
,
2012
, “
Accounting for Rotational Non-Equilibrium Effects in Subsonic DSMC Boundary Conditions
,”
J. Phys. Conf. Ser.
,
362
, p.
012016
.
28.
Farbar
,
E.
, and
Boyd
,
I.
,
2014
, “
Subsonic Flow Boundary Conditions for the Direct Simulation Monte Carlo Method
,”
Comput. Fluids
,
102
, pp.
99
110
.
29.
Sengil
,
N.
, and
Edis
,
F. O.
,
2009
, “
Highly Efficient Volume Generation Reservoirs in Molecular Simulations of Gas Flows
,”
J. Comput. Phys.
,
228
(
12
), pp.
4303
4308
.
30.
Ewart
,
T.
,
Firpo
,
J. L.
,
Graur
,
I.
,
Perrier
,
P.
, and
Meolans
,
J. G.
,
2009
, “
DSMC Simulation: Validation and Application to Low Speed Gas Flows in Microchannels
,”
ASME J. Fluids Eng.
,
131
(
1
), p.
014501
.
31.
Guo
,
K. L.
,
Liaw
,
G. S.
, and
Chou
,
L. C.
,
1996
, “
Shock Structure Prediction for Gas Mixtures by a Modified Direct Simulation Monte Carlo Method
,”
AIAA
Paper No. 96-1818.
32.
Watvisave
,
D. S.
,
2014
, “
A Numerical Investigation of Wall Effects in High Knudsen Number, High Speed, Internal Flows
,” Ph.D. thesis, Indian Institute of Technology Bombay, Mumbai, India.
33.
Aktas
,
O.
,
Aluru
,
M.
, and
Ravaioli
,
U.
,
2001
, “
Application of a Parallel DSMC Technique to Predict Flow Characteristics in Microfluidic Filters
,”
J. Micro Electro Mech. Syst.
,
10
(
4
), pp.
538
549
.
34.
Darbdi
,
M.
,
Akhlaghi
,
H.
,
Karchani
,
A.
, and
Vakili
,
S.
,
2010
, “
Various Boundary Condition Implementation to Study Microfilters Using DSMC Simulation
,”
ASME
Paper No. IMECE2010-40379.
35.
Cave
,
H. M.
,
Tseng
,
K. C.
,
Wu
,
J. S.
,
Jermy
,
M. C.
,
Huang
,
J. C.
, and
Krumdieck
,
S. P.
,
2008
, “
Implementation of Unsteady Sampling Procedures for the Parallel Direct Simulation Monte Carlo Method
,”
J. Comput. Phys.
,
227
(
12
), pp.
6249
6271
.
36.
Agrawal
,
A.
, and
Prabhu
,
S. V.
,
2008
, “
Survey on Measurement of Tangential Momentum Accommodation Coefficient
,”
J. Vacuum Sci. Technol. A
,
26
(
4
), pp.
634
645
.
37.
Prashanth
,
P. S.
, and
Kakkassery
,
J. K.
,
2006
, “
Direct Simulation Monte Carlo (DSMC): A Numerical Method for Transition Regime Flows—A Review
,”
J. Indian Inst. Sci.
,
86
, pp.
169
192
.http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.101.2248&rep=rep1&type=pdf
38.
Hadjiconstantinou
,
N. G.
,
Garcia
,
A. L.
,
Bazant
,
M. Z.
, and
He
,
G.
,
2003
, “
Statistical Error in Particle Simulations of Hydrodynamic Phenomena
,”
J. Comput. Phys.
,
187
(
1
), pp.
274
297
.
39.
Whitfield
,
D. L.
, and
Janus
,
J. M.
, 1984, “Three-Dimensional Unsteady Euler Equation Solutions Using Flux Vector Splitting,”
AIAA
Paper No. AIAA-84-1552.
40.
Yang
,
J.
,
Ye
,
J. J.
,
Zheng
,
J. Y.
,
Wong
,
I.
,
Lam
,
C. K.
,
Xu
,
P.
,
Chen
,
R. X.
, and
Zhu
,
Z. H.
,
2010
, “
Using Direct Simulation Monte Carlo With Improved Boundary Conditions for Heat and Mass Transfer in Microchannels
,”
ASME J. Heat Transfer
,
132
(
4
), p.
410081
.
41.
Ebert
,
W. A.
, and
Sparrow
,
E. M.
,
1965
, “
Slip Flow in Rectangular and Annular Ducts
,”
ASME J. Basic Eng.
,
87
(
4
), pp.
1018
1024
.
42.
Jang
,
J.
, and
Wereley
,
S. T.
,
2004
, “
Pressure Distribution of Gaseous Slip Flow in Straight and Uniform Rectangular Microchannels
,”
Microfluid. Nanofluid.
,
1
(
1
), pp.
41
51
.
You do not currently have access to this content.