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Research Papers: Fundamental Issues and Canonical Flows

Quantifying the Direct Influence of Diffusive Mass Transfer in Rarefied Gas Mixing Simulations

[+] Author and Article Information
Masoud Darbandi

Department of Aerospace Engineering,
Center of Excellence in Aerospace Systems,
Institute for Nanoscience and Nanotechnology,
Sharif University of Technology,
P.O. Box 11365-11155,
Tehran 14588-89694, Iran
e-mail: darbandi@sharif.edu

Moslem Sabouri

Department of Aerospace Engineering,
Center of Excellence in Aerospace Systems,
Sharif University of Technology,
Tehran 14588-89694, Iran
e-mail: sabouri@ae.sharif.edu

1Corresponding author.

Contributed by the Fluids Engineering Division of ASME for publication in the JOURNAL OF FLUIDS ENGINEERING. Manuscript received March 2, 2017; final manuscript received August 1, 2017; published online October 24, 2017. Assoc. Editor: Moran Wang.

J. Fluids Eng 140(3), 031207 (Oct 24, 2017) (9 pages) Paper No: FE-17-1127; doi: 10.1115/1.4038085 History: Received March 02, 2017; Revised August 01, 2017

This work utilizes the direct simulation Monte Carlo (DSMC) calculations and examines the influence of rarefication on the mixing length and effective diffusion coefficient in a two-species mixing problem. There have been efforts in past rarefied mixing flow studies to bridge between the mixing evolution rate and Knudsen number. A careful review of those efforts shows that the past derived relations did not determine the weights of Reynolds (or Peclet) number in the rarefaction influences. Although they indicated that an increase in Knudsen would decrease the mixing length, such reductions were primarily due to the Reynolds (or Peclet) reduction. Therefore, those studies could not explicitly appraise the contribution of rarefaction in the total mass diffusion magnitude. This work focuses specifically on the role of rarefaction in the total diffusive mass transfer magnitude in rarefied gas mixing problems. It excludes the contributions of momentum and heat to the mass diffusion via imposing suitable velocity, pressure, and temperature fields in the mixer domain. The results show that there will be some decreases in the diffusive mass fluxes and some increases in the mixing length as Knudsen increases. Using the Fick’s law, the effective diffusion coefficient is then calculated in the mixer zone. The results show that this coefficient may vary considerably throughout the mixer zone due to the local rarefaction level variation. The results of all investigated cases indicate that the trends of their effective diffusion coefficient variations approach to a limiting value as the rarefaction level decreases.

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Figures

Grahic Jump Location
Fig. 1

Schematic of the current parallel-stream mixer geometry

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Fig. 2

Dependency of diffusion mass flux on grid sizes and number of simulated particles

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Fig. 3

Variations in x-component mixture velocity and mixture temperature along two arbitrary horizontal lines for the micromixer with Kn = 0.057

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Fig. 4

Nitrogen gas mass fraction contour plots within the mixers with five different Kn values using molecular simulations ((a)–(e)) and continuum theory (f)

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Fig. 5

Variations in N2 mass fraction along the lower boundary of mixer including five molecular simulations and one continuum solution

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Fig. 6

Evolution of RDD along the mixer considering five molecular simulations and one continuum solution

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Fig. 7

Quantification of rarefaction effect on the mixing length and time to mix parameters

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Fig. 8

Diffusion mass fluxes along the mixer centerline considering five rarefied molecular simulations and comparison with continuum theory prediction

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Fig. 9

Diffusion mass fluxes at section crossing the end of splitter plate considering five rarefied molecular simulations and comparison with continuum theory solution

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Fig. 10

Variation in nondimensional effective diffusion coefficient along the mixer centerline imposing various rarefaction levels

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Fig. 11

Variation in nondimensional effective diffusion coefficient at section crossing the end of splitter plate imposing various rarefaction levels

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