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Research Papers

DSMC Simulation of Low Knudsen Micro/Nanoflows Using Small Number of Particles per Cells

[+] Author and Article Information
Ehsan Roohi

e-mail: e.roohi@ferdowsi.um.ac.ir

Hamid Niazmand

Department of Mechanical Engineering,
Faculty of Engineering,
Ferdowsi University of Mashhad,
P.O. Box 91775-1111,
Mashhad, Iran

Stefan Stefanov

Institute of Mechanics,
Bulgarian Academy of Science,
Acad. G. Bontchev Street,
Sofia 1113, Bulgaria

1Corresponding author.

Contributed by the Heat Transfer Division of ASME for publication in the Journal of Heat Transfer. Manuscript received July 13, 2012; final manuscript received February 1, 2013; published online September 11, 2013. Assoc. Editor: Sushanta K. Mitra.

J. Heat Transfer 135(10), 101008 (Sep 11, 2013) (8 pages) Paper No: HT-12-1367; doi: 10.1115/1.4024505 History: Received July 13, 2012; Revised February 01, 2013

Direct simulation Monte Carlo (DSMC) method in low Knudsen rarefied flows at micro/nanoscales remains a big challenge for researchers due to large computational requirements. In this article, the application of the simplified Bernoulli-trials (SBT)/dual grid collision scheme is extended for solving low Knudsen/low speed and low Knudsen/high gradient rarefied micro/nanoflows. The main advantage of the SBT algorithm is to provide accurate calculations using much smaller number of particles per cell, i.e., 〈N〉 ≈ 2, which is quite beneficial for near continuum DSMC simulations where the requirement of fine meshes faces the simulation with serious memory restrictions. Comparing the results of the SBT/dual grid scheme with the no time counter (NTC) scheme and majorant frequency scheme (MFS), it is shown that the SBT/dual grid scheme could successfully predict the thermal pattern and hydrodynamics field as well as surface parameters such as velocity slip, temperature jump and wall heat fluxes. Therefore, we present SBT/dual grid algorithm as a suitable alternative of the standard collision schemes in the DSMC method for typical micro/nanoflows solution. Nonlinear flux-corrected transport (FCT) algorithm is also employed as a filter to extract the smooth solution from the noisy DSMC calculation for low speed/low Knudsen number DSMC calculations.

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Figures

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Fig. 1

The simplified Bernoulli-trials collision procedure

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Fig. 2

DSMC flowchart for staggered grid

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Fig. 3

The majorant frequency scheme collision procedure

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Fig. 4

Geometrical configuration of microcavity

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Fig. 5

Grid independency test

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Fig. 6

Effect of number of particle per cell in accuracy of the NTC collision scheme

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Fig. 7

Effect of applying two sampling in each iteration

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Fig. 8

Comparison of the SBT and NTC schemes in prediction of flow field

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Fig. 9

Comparison of the SBT and NTC schemes in prediction of thermal pattern

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Fig. 10

Comparison of SBT and NTC schemes in prediction of centerline velocity in low speed cavity flows (case 2)

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Fig. 11

Velocity slip and Temperature jump along the driven lid computed by SBT and NTC schemes: (a) Case 1 and (b) case 2

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Fig. 12

Accuracy of SBT scheme in prediction of wall heat flux (case 1)

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Fig. 13

Accuracy of SBT scheme in prediction of wall shear stress (case 1)

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Fig. 14

The geometry and flow configuration of nanoflat plate

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Fig. 15

Effect of number of simulators on the accuracy of the results. The profiles are shifted to right for MFS and SBT schemes for more clarity.

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Fig. 16

Accuracy of three schemes in evaluation of temperature profile with small number of particle per cell

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Fig. 17

Comparison of SBT and NTC scheme in evaluation of thermal pattern

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