Thesis
Micro gas flows : modelling the dynamics of Knudsen layers
- Creator
- Awarding institution
- University of Strathclyde
- Date of award
- 2012
- Thesis identifier
- T13489
- Qualification Level
- Qualification Name
- Department, School or Faculty
- Abstract
- The behaviour of gas flows in microscale systems cannot be accurately described by the Navier-Stokes-Fourier (N-S-F) equations of macroscale fluid dynamics. Micro and nano-scale gas flows often display non-standard fluid behaviour, and near a solid bounding surface they are dominated by the effect of gas molecule-surface interactions. This leads to the formation of a Knudsen layer (KL): a local thermodynamically non-equilibrium region of thickness of a few mean free paths (MFP) from the surface. Linear constitutive relations for shear stress and heat flux are no longer necessarily valid in the KL. To account for this, we investigate a power-law (PL) form of the probability distribution function for free paths of rarefied gas molecules in arbitrary wall confinements. PL based geometry dependent MFP models are derived for planar and non-planar geometry systems by taking into account the boundary limiting effects on the molecular free paths. Molecular dynamics (MD) numerical experiments are carried out to rigorously validate the PL model, under a wide range of rarefaction conditions. MD is the most appropriate simulation tool as it is deterministic, allowing for realistic molecular behaviour, i.e. molecular attractions, repulsions, movements and scatterings. The free path measurements of individual molecules convey that conventional form of exponential distribution function is not valid under rarefied conditions and follow Lévy type of flights, irrespective of the presence of the wall. MFP profiles of MD measurements and PL model for confined surfaces in the transition flow regime show sharp gradients close to the wall, while exponential model predicts shallower gradients. As gas transport properties can be related to the MFP through kinetic theory, the N-S-F constitutive relations, and the velocity slip and the temperature jump boundary conditions are then modified in order to better capture the flow behaviour in the Knudsen layers close to surfaces. The new modelling technique is tested for isothermal and non-isothermal gas flows in both planar and non-planar confinements. The results show that our approach greatly improves the near-wall accuracy of the N-S-F equations, well beyond the slip-flow regime. In general, the current method exhibits good agreement for velocity and temperature profiles up to Kn ~ 1, and for integral flow parameters up to Kn ~ 5, without tuning any slip and jump coefficients. The PL scaling can be readily extended to complex geometries, and straightforwardly incorporated into existing computational fluid dynamics (CFD) codes. The current work is significant from the numerical simulation point of view because simulation tools are better developed for N-S-F equations, when compared to other higher order equations such as Burnett, R26 etc.
- Resource Type
- DOI
- Date Created
- 2012
- Former identifier
- 991514
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