Plane Couette flow of binary gaseous mixture in the whole range of the Knudsen number

Sharipov, Felix; Cumin, Liliana M. Gramani; Kalempa, Denize

doi:10.1016/j.euromechflu.2004.03.002

Cited by 46 publications

(33 citation statements)

References 20 publications

Supporting

Mentioning

Contrasting

Unclassified

Order By: Relevance

“…This makes current DSMC methods unsuitable for low speed, low Knudsen number flows [7]. Similar problems occur in hybrid DSMC/Navier-Stokes solvers for mixed-density flows [8] and direct solutions of the Boltzmann equation [9]. Significant effort has been made to extend the validity of continuumbased equations and develop higher-order equation sets, such as Grad's 13 moment method and the Burnett equations.…”

Section: Introductionmentioning

confidence: 99%

Capturing Knudsen layer phenomena using a lattice Boltzmann model

et al. 2006

View full text Add to dashboard Cite

In recent years, lattice Boltzmann methods have been increasingly used to simulate rarefied gas flows in micro-and nano-scale devices. This is partly due to the fact that the method is computationally efficient, particularly when compared to solution techniques like the direct simulation Monte Carlo approach. However, lattice Boltzmann models developed for rarefied gas flows have difficulty in capturing the nonlinear relationship between the shear stress and strain rate within the Knudsen layer. As a consequence, these models are equivalent to slip-flow solutions of the Navier-Stokes equations.In this paper, we propose an effective mean free path to address the Knudsen layer effect, so that the capabilities of lattice Boltzmann methods can be extended beyond the slip-flow regime. The model has been applied to rarefied shear-driven and pressure-driven flows between parallel plates at Knudsen numbers between 0.01 and 1. Our results show that the proposed approach significantly improves the near-wall accuracy of the lattice Boltzmann method and provides a computationally economic solution technique over a wide range of Knudsen numbers.

show abstract

Section: Introductionmentioning

confidence: 99%

Capturing Knudsen layer phenomena using a lattice Boltzmann model

et al. 2006

View full text Add to dashboard Cite

show abstract

“…Highly accurate methods have been developed for these flows, including directly solving the Boltzmann equation and using the direct simulation Monte Carlo (DSMC) method. However, for low-speed gas flows, accurate solutions from these kinetic methods are often beyond current computer capabilities, certainly for practical device design purposes in 3D; DSMC suffers large statistical scatter, while direct solution of the Boltzmann equation is very computationallydemanding 7,8 . While DSMC, molecular dynamics, and direct kinetic methods are beyond the scope of this review paper -and really require a separate article of their own 9 -in the absence of experimental micro-or nano-flow data they are often relied on to provide independent benchmark data; many of the models outlined below are explicitly validated against DSMC or other numerical/molecular data.…”

Section: Introductionmentioning

confidence: 99%

Simulating Fluid Flows in Micro and Nano Devices: The Challenge of Non-Equilibrium Behaviour

Reese¹,

Zhang²

2009

Jnl of Comp & Theo Nano

View full text Add to dashboard Cite

We review some recent developments in the modelling of non-equilibrium (rarefied) gas flows at the micro-and nano-scale, concentrating on two different but promising approaches: extended hydrodynamic models, and lattice Boltzmann methods.Following a brief exposition of the challenges that non-equilibrium poses in micro-and nano-scale gas flows, we turn first to extended hydrodynamics, outlining the effective abandonment of Burnett-type models in favour of high-order regularised moment equations. We show that the latter models, with properly-constituted boundary conditions, can capture critical non-equilibrium flow phenomena quite well. We then review the boundary conditions required if the conventional Navier-Stokes-Fourier (NSF) fluid dynamic model is applied at the micro scale, describing how 2 nd -order Maxwell-type conditions can be used to compensate for some of the non-equilibrium flow behaviour near solid surfaces. While extended hydrodynamics is not yet widely-used for real flow problems because of its inherent complexity, we finish this section with an outline of recent 'phenomenological extended hydrodynamics' (PEH) techniques -essentially the NSF equations scaled to incorporate nonequilibrium behaviour close to solid surfaces -which offer promise as engineering models.Understanding non-equilibrium within the lattice Boltzmann (LB) framework is not as advanced as in the hydrodynamic framework, although LB can borrow some of the techniques which are being developed in the latter -in particular, the near-wall scaling of certain fluid properties that has proven effective in PEH. We describe how, with this modification, the standard 2 nd -order LB method is showing promise in predicting some rarefaction phenomena, indicating that instead of developing higher-order off-lattice LB methods with a large number of discrete velocities, a simplified high-order LB method with near-wall scaling may prove to be just as effective as a simulation tool.

show abstract

“…As was shown in Sharipov and Seleznev (1998), isothermal rarefied gas flows are well described by the model proposed by (BGK) Bhatnagar et al (1954). To confirm this claim a comparison of the shear stress P m for the stationary Couette flow (h = ¥) obtained from the Boltzmann equation (Sone et al 1990) with that calculated from the BGK model using the technique described in Sharipov et al (2004) is performed in Table 1. The results of Sone et al (1990) were recalculated in our notations.…”

Section: Hydrodynamic Regimementioning

confidence: 83%

“…Cercignani and Pagani 1966;Gross and Ziering 1958;Loyalka et al 1979;Marques et al 2000;Sharipov et al 2004;Siewert 2002;Sone et al 1990;Willis 1962). As will be shown below such a solution can be applied at any gas rarefaction, but only to slowly oscillating surfaces.…”

Section: Introductionmentioning

confidence: 95%

Oscillatory Couette flow at arbitrary oscillation frequency over the whole range of the Knudsen number

Sharipov

Kalempa

2007

Microfluid Nanofluid

Self Cite

View full text Add to dashboard Cite

The oscillatory Couette flow is important for further advancement of microengineering. In practice the size of the microfluidics can be so small that it can be compared with the molecular mean free path. Moreover, the oscillation frequency can be close to that of the intermolecular collisions. Under such conditions the problem must be solved on the kinetic level. In the present work, the oscillatory Couette flow is considered on the basis of the non-stationary kinetic equation. The solution to the problem is determined by two parameters: the Knudsen number and the ratio of collision frequency to oscillation frequency. The kinetic equation is solved by the discrete velocity method over the wide range of both parameters.

show abstract

Plane Couette flow of binary gaseous mixture in the whole range of the Knudsen number

Cited by 46 publications

References 20 publications

Capturing Knudsen layer phenomena using a lattice Boltzmann model

Capturing Knudsen layer phenomena using a lattice Boltzmann model

Simulating Fluid Flows in Micro and Nano Devices: The Challenge of Non-Equilibrium Behaviour

Oscillatory Couette flow at arbitrary oscillation frequency over the whole range of the Knudsen number

Contact Info

Product

Resources

About