A Diffusion Model for Rarefied Flows in Curved Channels

Aoki, Kazuo; Degond, Pierre; Mieussens, Luc; Takata, Shigeru; Yoshida, Hiroaki

doi:10.1137/070690328

Cited by 33 publications

(42 citation statements)

References 38 publications

(89 reference statements)

Supporting

Mentioning

Contrasting

Order By: Relevance

“…In contrast, a macroscopic system, consisting of a partial differential equation of convection-diffusion type and its connection condition, that describes rarefied gas flows in a two-dimensional ͑2D͒ curved channel was proposed recently. 15 With the help of this system, we can obtain the properties of gas flows through a twisty 2D channel at arbitrary Knudsen numbers with a small computational load. The system is derived from the Boltzmann equation and its boundary condition by a systematic asymptotic analysis under the assumption that the channel width is small compared with the length scale of variation of the temperature, the density, and the channel curvature along the channel.…”

Section: Introductionmentioning

confidence: 99%

“…We should mention that the Bhatnagar-Gross-Krook ͑BGK͒ model 16,17 is used in Ref. 15 in place of the original Boltzmann equation, but the analysis for the latter equation is essentially the same. It should be emphasized that the macroscopic system is valid for any Knudsen number. In the present study, we investigate the gas flows through curved channels of various shapes for a wide range of the Knudsen number by exploiting the macroscopic system derived in Ref.…”

Section: Introductionmentioning

confidence: 99%

“…It should be emphasized that the macroscopic system is valid for any Knudsen number. In the present study, we investigate the gas flows through curved channels of various shapes for a wide range of the Knudsen number by exploiting the macroscopic system derived in Ref. 15. At the same time, we extend the system, which was originally derived on the basis of the BGK model, to the case of the more sophisticated ellipsoidal-statistical ͑ES͒ model.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Rarefied gas flows through a curved channel: Application of a diffusion-type equation

Aoki¹,

Takata²,

Tatsumi³

et al. 2010

Physics of Fluids

View full text Add to dashboard Cite

Rarefied gas flows through a curved two-dimensional channel, caused by a pressure or a temperature gradient, are investigated numerically by using a macroscopic equation of convection-diffusion type. The equation, which was derived systematically from the Bhatnagar-Gross-Krook model of the Boltzmann equation and diffuse-reflection boundary condition in a previous paper ͓K. Aoki et al., "A diffusion model for rarefied flows in curved channels," Multiscale Model. Simul. 6, 1281 ͑2008͔͒, is valid irrespective of the degree of gas rarefaction when the channel width is much shorter than the scale of variations of physical quantities and curvature along the channel. Attention is also paid to a variant of the Knudsen compressor that can produce a pressure raise by the effect of the change of channel curvature and periodic temperature distributions without any help of moving parts. In the process of analysis, the macroscopic equation is ͑partially͒ extended to the case of the ellipsoidal-statistical model of the Boltzmann equation.

show abstract

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Rarefied gas flows through a curved channel: Application of a diffusion-type equation

Aoki¹,

Takata²,

Tatsumi³

et al. 2010

Physics of Fluids

View full text Add to dashboard Cite

show abstract

“…Based on this effect, small amounts of gas can be moved in Knudsen pumps. 13 The interplay between the thermal stress and the thermal transpiration, and their contribution to the slip velocity has been studied using the asymptotic theory. [14][15][16] A rarefied gas may be subjected to two different thermal forces: (a) a transpiration force due to a temperature gradient in the wall, (b) thermal stresses, due to temperature gradients in the bulk of the gas.…”

Section: Introductionmentioning

confidence: 99%

Thermal stress vs. thermal transpiration: A competition in thermally driven cavity flows

Rana

Struchtrup

2015

Physics of Fluids

View full text Add to dashboard Cite

The driven cavity flow over the whole range of the Knudsen number Phys. The velocity dependent Maxwell (VDM) model for the boundary condition of a rarefied gas, recently presented by Struchtrup ["Maxwell boundary condition and velocity dependent accommodation coefficient," Phys. Fluids 25, 112001 (2013)], provides the opportunity to control the strength of the thermal transpiration force at a wall with temperature gradient. Molecular simulations of a heated cavity with varying parameters show intricate flow patterns for weak, or inverted transpiration force. Microscopic and macroscopic transport equations for rarefied gases are solved to study the flow patterns and identify the main driving forces for the flow. It turns out that the patterns arise from a competition between thermal transpiration force at the boundary and thermal stresses in the bulk. C 2015 AIP Publishing LLC.

show abstract

“…A simpler geometry has been proposed by Aoki et al [29,30] consisting of a channel with alternating curved and straight sections with periodic temperature gradient as shown in Fig. 2.4.…”

Section: 1mentioning

confidence: 99%

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

Bond¹

View full text Add to dashboard Cite

Recent advances in micro-scale fabrication have uncovered the limitations of classical uid dynamics analysis techniques. The current status of numerical techniques for micro-ows is found to be highly varied with no accepted best-practice. This situation encourages investigation of new and improved methods in the eld. 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 ux 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 Uni ed Gas Kinetic schemes. The e ect 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 Uni ed 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 ow phenomena including rare ed e ects such as thermal creep. Pressure gradient inducing thermal creep driven ows in microchannels, commonly referred to as Knudsen pumps, are investigated across a range of rarefaction with particular focus on the e ects of realistic gas coe cients and geometric con guration 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 ow structure of each geometry is investigated for a range of channel aspect ratios and Knudsen numbers where the Knudsen numbers are nely spaced between 0.1 and 2.0 to allow approximate performance extrema to be identi ed. The in uence of Prandtl number is found to be signi cant with increased maximum mass ow rates for argon and nitrogen of 5.5-6% when compared to a gas with Maxwellian molecular model. The impact of speci c heat ratio is found to be comparatively minor with a di erence of 0.5% between the argon and nitrogen. The two new channel designs are found to lie between the classical and existing ...

show abstract

A Diffusion Model for Rarefied Flows in Curved Channels

Cited by 33 publications

References 38 publications

Rarefied gas flows through a curved channel: Application of a diffusion-type equation

Rarefied gas flows through a curved channel: Application of a diffusion-type equation

Thermal stress vs. thermal transpiration: A competition in thermally driven cavity flows

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

Contact Info

Product

Resources

About