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Research Papers: Fundamental Issues and Canonical Flows

Comparison of Various Pressure Based Boundary Conditions for Three-Dimensional Subsonic DSMC Simulation

[+] Author and Article Information
Niraj Shah

Mechanical Engineering Department,
Institute of Technology,
Nirma University,
Ahmedabad 382481, Gujarat, India
e-mail: niraj.shah@nirmauni.ac.in

Abhimanyu Gavasane

Centre for Research in Nanotechnology
in Science,
Indian Institute of Technology Bombay,
Mumbai 400076, Maharashtra, India
e-mail: abhimanyug@iitb.ac.in

Amit Agrawal

Department of Mechanical Engineering,
Indian Institute of Technology Bombay,
Mumbai 400076, Maharashtra, India
e-mail: amit.agrawal@iitb.ac.in

Upendra Bhandarkar

Department of Mechanical Engineering,
Indian Institute of Technology Bombay,
Mumbai 400076, Maharashtra, India
e-mail: bhandarkar@iitb.ac.in

1Corresponding author.

Contributed by the Fluids Engineering Division of ASME for publication in the JOURNAL OF FLUIDS ENGINEERING. Manuscript received April 22, 2017; final manuscript received August 3, 2017; published online October 19, 2017. Assoc. Editor: Riccardo Mereu.

J. Fluids Eng 140(3), 031205 (Oct 19, 2017) (12 pages) Paper No: FE-17-1242; doi: 10.1115/1.4037679 History: Received April 22, 2017; Revised August 03, 2017

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.

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Figures

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Fig. 1

Flowchart of DSMC processes

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Fig. 2

(a) Microchannel geometry (computational domain) along with one representative cell and its enlarged view showing subcells and (b) implementation details of MPI based parallel code

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Fig. 3

(a) Comparison of simulated normalized pressure distribution at the centerline of channel with analytical solution [42] and (b) comparison of simulated and analytical [41] cross section average velocity distribution along the channel length

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Fig. 4

(a) Comparison of simulated normalized velocity distribution along normalized channel height with analytical solution [41] and (b) comparison of simulated normalized velocity distribution along normalized channel width with analytical solution [41]

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Fig. 5

Net number of molecules crossing inlet and outlet boundaries with time steps

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Fig. 6

(a) Centerline pressure variation along length of microchannel for different boundary conditions [2328,40] and (b) variation of nondimensional pressure along length of microchannel for different boundary conditions [2328,40]

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Fig. 7

(a) Centerline translational temperature variation along length of microchannel for different boundary conditions [2328,40] and (b) centerline stream velocity variation along length of microchannel for different boundary conditions [2328,40]

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Fig. 8

Percentage difference between simulated pressure in a cell and the specified pressure at the outlet boundary for White et al. [27] boundary type

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Fig. 9

Comparison of maximum percentage difference between cell center pressure adjacent to boundary and specified pressure for different boundary conditions at inlet and outlet for ((a), (b)) inlet Knudsen number, ((c), (d)) PR and ((e) (f)) CAR

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Fig. 10

Comparison of normalized time for different boundary conditions for (a) inlet Knudsen number, (b) PR, and (c) CAR

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