Numerical investigation of gaseous heat and mass transfer: the effect of rarefaction

Bond, Daryl (2015). Numerical investigation of gaseous heat and mass transfer: the effect of rarefaction PhD Thesis, School of Mechanical and Mining Engineering, The University of Queensland. doi:10.14264/uql.2015.511

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Author Bond, Daryl
Thesis Title Numerical investigation of gaseous heat and mass transfer: the effect of rarefaction
School, Centre or Institute School of Mechanical and Mining Engineering
Institution The University of Queensland
DOI 10.14264/uql.2015.511
Publication date 2015-04-24
Thesis type PhD Thesis
Open Access Status Other
Supervisor Vincent Wheatley
Mark Goldsworthy
Michael Macrossan
Total pages 245
Language eng
Subjects 0913 Mechanical Engineering
Formatted abstract
Recent advances in micro-scale fabrication have uncovered the limitations of classical fluid dynamics analysis techniques. The current status of numerical techniques for micro-flows is found to be highly varied with no accepted best-practice. This situation encourages investigation of new and improved methods in the field. In this work a new numerical method based upon the solution of the model Boltzmann equation using arbitrary order polynomials is presented. The S-model is solved by a discrete ordinate method with velocity space discretized with a truncated Hermite polynomial expansion. Physical space is discretized according to the Conservative Flux Approximation scheme with extension to allow non-uniform grid spacing. This approach, which utilizes Legendre polynomials, allows the spatial representation and flux calculation to be of arbitrary order. High order boundary conditions are implemented. Various results are shown to demonstrate the utility and limitations of the method with comparison to solutions of the Euler and Navier-Stokes equations and from the Direct Simulation Monte Carlo and Unified Gas Kinetic schemes. The effect of both the velocity space discretization and Knudsen number on the convergence properties of the scheme are also investigated. Due to limitations in the geometric adaptability of the new method an implementation of the Unified Gas Kinetic Scheme with a variety of enhancements is also presented. These enhancements include internal degree of freedom handling and advanced gas-surface interaction mechanisms including a model of the adsorption and desorption of gas molecules by a surface. 

The numerical methods developed are used to investigate physical flow phenomena including rarefied effects such as thermal creep. Pressure gradient inducing thermal creep driven flows in micro-channels, commonly referred to as Knudsen pumps, are investigated across a range of rarefaction with particular focus on the effects of realistic gas coefficients and geometric configuration on performance. A range of geometries are investigated consisting of a previously proposed curved-straight channel and three newly developed channels including a novel two dimensional matrix pump arrangement and classical linear designs. Use of the S-model kinetic equations enables investigation with realistic values of the Prandtl number and viscosity index for argon and nitrogen as well as for Maxwell molecules. The pumping performance and flow structure of each geometry is investigated for a range of channel aspect ratios and Knudsen numbers where the Knudsen numbers are finely spaced between 0.1 and 2.0 to allow approximate performance extrema to be identified. The influence of Prandtl number is found to be significant with increased maximum mass flow rates for argon and nitrogen of 5.5-6% when compared to a gas with Maxwellian molecular model. The impact of specific heat ratio is found to be comparatively minor with a difference of 0.5% between the argon and nitrogen. The two new channel designs are found to lie between the classical and existing curved geometry in terms of mass flow rate and pumping performance. The matrix pump design is found to perform significantly better than all other designs with peak mass flow rates a factor of 1.5 greater than the closest comparable competitor that was investigated. The matrix pump design also has the ability to configure the flow allowing preferential vectoring of flow paths. Investigation into surface accommodation using the Cercignani-Lampis boundary condition is also carried out with results indicating that tailored surface accommodation is able to drastically improve pump performance.

Further investigation is performed using the adsorbing gas-surface interaction model with focus on an apparent breakdown in the relationship between heat and mass transfer as the Knudsen number of the flow increases. Argon gas flows are simulated through channels, cavities and an external surface whilst tracking this relationship. For the test cases performed there is shown to be a distinct change in the ratio of heat transfer to mass transfer as the flow transitions from continuum to rarefied flow. The mechanism by which this effect takes place is examined and explained in the context of rarefied flows.
Keyword Rarefied
Micro-channel
High-order
Knudsen pump
Heat and mass transfer
Polynomial
Shakhov
BGK

Document type: Thesis
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Created: Wed, 22 Apr 2015, 14:44:10 EST by Daryl Bond on behalf of Scholarly Communication and Digitisation Service