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Abstract
In order to capture critical near-wall phenomena in gas micro- and nanoflows
within conventional CFD codes, we present scaled Navier-Stokes-Fourier (NSF) constitutive relations. Our scaling is mathematically equivalent to applying an 'effective' viscosity to the original constitutive relations. An expression for this 'effective' transport coefficient is obtained from the half-space Kramer's flow problem. The advantage of our model over the traditional NSF equations is that the non-equilibrium flow near to the wall (the momentum Knudsen layer) can be described. Its advantage over higher-order hydrodynamic models for gas micro- and nanoflows is that the boundary conditions remain the same as required for the traditional NSF equations, so modifications to current CFD codes (provided they are already capable of modelling slip at solid surfaces) would be minimal. As an application example, we apply our model to the isothermal problem of a microsphere moving through a gas: we show that our model gives excellent results in the Knudsen number range Kn . 0:1 and acceptable results up to Kn ¼ 0:25. This is much better than the traditional NSF model with non-scaled constitutive relations.
within conventional CFD codes, we present scaled Navier-Stokes-Fourier (NSF) constitutive relations. Our scaling is mathematically equivalent to applying an 'effective' viscosity to the original constitutive relations. An expression for this 'effective' transport coefficient is obtained from the half-space Kramer's flow problem. The advantage of our model over the traditional NSF equations is that the non-equilibrium flow near to the wall (the momentum Knudsen layer) can be described. Its advantage over higher-order hydrodynamic models for gas micro- and nanoflows is that the boundary conditions remain the same as required for the traditional NSF equations, so modifications to current CFD codes (provided they are already capable of modelling slip at solid surfaces) would be minimal. As an application example, we apply our model to the isothermal problem of a microsphere moving through a gas: we show that our model gives excellent results in the Knudsen number range Kn . 0:1 and acceptable results up to Kn ¼ 0:25. This is much better than the traditional NSF model with non-scaled constitutive relations.
Original language | English |
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Publication status | Published - 5 Sep 2006 |
Event | European Conference on Computational Fluid Dynamics - Egmond aan Zee, Netherlands Duration: 5 Sep 2006 → 8 Sep 2006 |
Conference
Conference | European Conference on Computational Fluid Dynamics |
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Country | Netherlands |
City | Egmond aan Zee |
Period | 5/09/06 → 8/09/06 |
Keywords
- fluid dynamics
- nanofluidics
- gas
Fingerprint Dive into the research topics of 'Computing the near-wall region in gas micro- and nanofluidics: critical Knudsen layer phenomena'. Together they form a unique fingerprint.
Projects
- 1 Finished
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Fluid Flow and Heat Transfer in Gas Microsystems
Reese, J.
EPSRC (Engineering and Physical Sciences Research Council)
1/01/04 → 30/09/07
Project: Research
Research output
- 1 Article
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Computing the near-wall region in gas micro- and nanofluidics: critical Knudsen layer phenomena
Reese, J. M., Zheng, Y. & Lockerby, D. A., Jun 2007, In: Journal of Computational and Theoretical Nanoscience. 4, 4, p. 807-813 7 p.Research output: Contribution to journal › Article › peer-review
Open AccessFile18 Citations (Scopus)151 Downloads (Pure)