Capturing the Knudsen Layer in Continuum-Fluid Models of Nonequilibrium Gas Flows

Lockerby, Duncan A.; Reese, Jason M.; Gallis, Michail A.

doi:10.2514/1.13530

Cited by 99 publications

(82 citation statements)

References 8 publications

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“…This concept is similar to the 'wall-function' proposed in Lockerby et al (2005b). However, there are some marked differences in the model we propose below, most notably the presence of a second-order contribution to the near-wall scaling (secondorder, in that it is dependent on a local Knudsen number) and a more accurate functional form (we also do not continue to use the phrase 'wall-function' in the present paper, to avoid confusion with those wall-functions associated with turbulence modelling).…”

Section: Near-wall Scaling Of the Constitutive Relationsmentioning

confidence: 92%

“…The functional form given in (24) is qualitatively different to that proposed by Lockerby et al (2005b) and Guo et al (2007), and has been chosen to reproduce the Knudsen layer's actual structure more accurately; it allows for an indefinitely steep profile in the inner most regions of the Knudsen layer, and a more gradual decay in the outer regions. It also allows for a second-order contribution to the Knudsen layer.…”

Section: Near-wall Scaling Of the Constitutive Relationsmentioning

confidence: 99%

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On the modelling of isothermal gas flows at the microscale

Lockerby

Reese

2008

J. Fluid Mech.

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This paper makes two new propositions regarding the modelling of rarefied (nonequilibrium) isothermal gas flows at the microscale. The first is a new test case for benchmarking high-order, or extended, hydrodynamic models for these flows. This standing time-varying shear-wave problem does not require boundary conditions to be specified at a solid surface, so is useful for assessing whether fluid models can capture rarefaction effects in the bulk flow. We assess a number of different proposed extended hydrodynamic models, and we find the R13 equations perform the best in this case.Our second proposition is a simple technique for introducing non-equilibrium effects caused by the presence of solid surfaces into the computational fluid dynamics framework. By combining a new model for slip boundary conditions with a near-wall scaling of the Navier-Stokes constitutive relations, we obtain a model that is much more accurate at higher Knudsen numbers than the conventional second-order slip model. We show that this provides good results for combined Couette/Poiseuille flow, and that the model can predict the stress/strain-rate inversion that is evident from molecular simulations. The model's generality to non-planar geometries is demonstrated by examining low-speed flow around a micro-sphere. It shows a marked improvement over conventional predictions of the drag on the sphere, although there are some questions regarding its stability at the highest Knudsen numbers.

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Section: Near-wall Scaling Of the Constitutive Relationsmentioning

confidence: 92%

Section: Near-wall Scaling Of the Constitutive Relationsmentioning

confidence: 99%

On the modelling of isothermal gas flows at the microscale

Lockerby

Reese

2008

J. Fluid Mech.

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“…(1.1), a low-speed micro gas flow will have a uniformly negligible local Knudsen number because the gradients of the flow variables are negligibly small. Nevertheless, non-equilibrium effects are far from negligible in these cases (Lockerby et al 2005a). For hypersonic aerodynamic flows it has been suggested (Macrossan 2006) that Ma · Kn L , where Ma is the local Mach number, is a more appropriate breakdown parameter; however, this parameter would be inappropriate for low-speed gas flows, which have a very small Mach number but can still be quite rarefied.…”

Section: Introductionmentioning

confidence: 99%

Switching Criteria for Hybrid Rarefied Gas Flow Solvers

Lockerby¹,

Struchtrup²,

Reese³

2008

AIP Conference Proceedings

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Switching criteria for hybrid hydrodynamic/molecular gas flow solvers are developed, and are demonstrated to be more appropriate than conventional criteria for identifying thermodynamic non-equilibrium. For switching from a molecular/kinetic solver to a hydrodynamic (continuum-fluid) solver, the criterion is based on the difference between the hydrodynamic non-equilibrium fluxes (i.e. the Navier-Stokes stress and Fourier heat flux) and the actual values of stress and heat flux as computed from the molecular solver. For switching from hydrodynamics to molecular/kinetic, a similar criterion is used but the values of stress and heat flux are approximated through higher-order constitutive relations; in this case, we use the R13 equations [Struchtrup & Torrilhon, Phys. Fluids 15(9), 2668-2680]. The efficacy of our proposed switching criteria is tested within an illustrative hybrid BGK/Navier-Stokes solver. For the test cases investigated, the results from the hybrid procedure compare very well with the full kinetic solution, and are obtained at a fraction of the computational cost.

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“…Instead, the technique we investigate in this paper is the method of constitutiverelation scaling developed by Lockerby et al [2]. This technique uses linearised kinetic theory results to determine a phenomenological function f (n/λ) with which to scale the constitutive relationship for shear stress in planar flows, i.e.…”

Section: Constitutive-relation Scalingmentioning

confidence: 99%

“…The slip coefficient ζ slip , equal to 1 in Maxwell's original derivation, is taken to be ≈ 0.8 when constitutive-relation scaling methods are used (as described below) because this value better approximates the true slip magnitude for gas flow over planar surfaces [2]. For temperature jump at solid boundaries, Smoluchowski's description is used [3]:…”

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confidence: 99%

Evaluating constitutive scaling models for application to compressible microflows

O’Hare

Scanlon

Emerson

et al. 2008

International Journal of Heat and Mass Transfer

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We demonstrate here, for the first time, the constitutive scaling approach applied to simulate a fully compressible, non-isothermal micro gas flow within a mainstream computational physics framework. First, the physics underlying these new constitutive-relation scaling models for rarefied gas flows at the microscale, in particular, the Knudsen layer, is discussed. Results for Couette-type flows in microchannels, including heat transfer effects due to rarefaction, are then reported and we show comparisons with both traditional Navier-Stokes-Fourier solutions and independent numerical studies. We discuss the limitations of the constitutive scaling process, such as the breakdown of the model as the Knudsen number increases and the influence of the wall interaction model on the numerical results. Advantages of the constitutive scaling technique are described, with particular reference to the practicality of using it for microscale engineering design.

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Capturing the Knudsen Layer in Continuum-Fluid Models of Nonequilibrium Gas Flows

Cited by 99 publications

References 8 publications

On the modelling of isothermal gas flows at the microscale

On the modelling of isothermal gas flows at the microscale

Switching Criteria for Hybrid Rarefied Gas Flow Solvers

Evaluating constitutive scaling models for application to compressible microflows

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