Lattice Boltzmann simulation of nonequilibrium effects in oscillatory gas flow

Tang, G.H.; Gu, Xinjian; Rw, Barber; Emerson, David R.; Zhang, Yonghao

doi:10.1103/physreve.78.026706

Cited by 30 publications

(27 citation statements)

References 44 publications

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“…The phase lag and amplitude reduction are a result of the increase in slip. Tang et al [29] also observed similar phase lag of fluid velocity for different Stokes numbers and TMAC in their Lattice Boltzmann simulation of oscillatory gas flows.…”

Section: Phase Lag Of Fluid Velocity Due To Wall Hydrophobicitymentioning

confidence: 59%

See 1 more Smart Citation

Analysis of boundary slip in a flow with an oscillating wall

Thalakkottor

Mohseni

2013

Phys. Rev. E

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Molecular dynamic (MD) simulation is used to study slip at the fluid-solid boundary in an unsteady flow based on the Stokes second problem. An increase in slip is observed in comparison to the steady flow for shear rates below the critical shear rate of the corresponding steady flow. This increased slip is attributed to fluid inertial forces not represented in a steady flow. An unsteady mathematical model for slip is established, which estimates the increment in slip at the boundary. The model shows that slip is also dependent on acceleration in addition to the shear rate of fluid at the wall. By writing acceleration in terms of shear rate, it is shown that slip at the wall in unsteady flows is governed by the gradient of shear rate and shear rate of the fluid. Non-dimensionalizing the model gives a universal curve which can be used to find the slip boundary condition at the fluid-solid interface based on the information of shear rate and gradient of shear rate of the fluid. A governing non-dimensional number, defined as the ratio of phase speed to speed of sound, is identified to help in explaining the mechanism responsible for the transition of slip boundary condition from finite to a perfect slip and determining when this would occur. Phase lag in fluid velocity relative to wall is observed. The lag increases with decreasing time period of wall oscillation and increasing wall hydrophobicity. The phenomenon of hysteresis is seen when looking into the variation of slip velocity as a function of wall velocity and slip velocity as a function of fluid shear rate. The cause for hysteresis is attributed to the unsteady inertial forces of the fluid.

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Section: Phase Lag Of Fluid Velocity Due To Wall Hydrophobicitymentioning

confidence: 59%

“…Boundary slip has been the subject of less investigation in unsteady flows. A few exceptions are in unsteady gas flows [26,27] and analytic solutions for continuum scale problems [28][29][30][31]. However, to the authors knowledge, for liquids at micro-scales the research has been limited to steady flows.…”

Section: Introductionmentioning

confidence: 99%

Analysis of boundary slip in a flow with an oscillating wall

Thalakkottor

Mohseni

2013

Phys. Rev. E

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“…While several canonical shear-driven gas flows, e.g, oscillatory Couette flow, have been examined using a variety of numerical and analytical methods, these flows are isothermal in the linear limit (Park, Bahukudumbi & Beskok 2004;Hadjiconstantinou 2005a;Sharipov & Kalempa 2007Tang et al 2008). The leading-order effect of unsteadiness in these flows occurs via a modification to the classical Navier-Stokes description at second order in the Knudsen number, i.e.…”

Section: J Nassios and J E Sadermentioning

confidence: 99%

Asymptotic analysis of the Boltzmann–BGK equation for oscillatory flows

Nassios

Sader

2012

J. Fluid Mech.

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Kinetic theory provides a rigorous foundation for calculating the dynamics of gas flow at arbitrary degrees of rarefaction, with solutions of the Boltzmann equation requiring numerical methods in many cases of practical interest. Importantly, the near-continuum regime can be examined analytically using asymptotic techniques. These asymptotic analyses often assume steady flow, for which analytical slip models have been derived. Recently, developments in nanoscale fabrication have stimulated research into the study of oscillatory non-equilibrium flows, drawing into question the applicability of the steady flow assumption. In this article, we present a formal asymptotic analysis of the unsteady linearized Boltzmann-BGK equation, generalizing existing theory to the oscillatory (time-varying) case. We consider the near-continuum limit where the mean free path and oscillation frequency are small. The complete set of hydrodynamic equations and associated boundary conditions are derived for arbitrary Stokes number and to second order in the Knudsen number. The first-order steady boundary conditions for the velocity and temperature are found to be unaffected by oscillatory flow. In contrast, the second-order boundary conditions are modified relative to the steady case, except for the velocity component tangential to the solid wall. Application of this general asymptotic theory is explored for the oscillatory thermal creep problem, for which unsteady effects manifest themselves at leading order.

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“…In the pressure-driven flow, this "wall-scaling" approach provides a significant improvement for Knudsen numbers up to 0.5. Later, this scheme has also been applied to study the rarefied thermal [31] and oscillatory Couette flow [32] in the early transition flow regime with great success.…”

Section: Introductionmentioning

confidence: 99%

Comparative study of the discrete velocity and lattice Boltzmann methods for rarefied gas flows through irregular channels

Lindsay

Liu

et al. 2017

Phys. Rev. E

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Rooted from the gas kinetics, the lattice Boltzmann method is a powerful tool in modeling hydrodynamics. In the past decade, it has been extended to simulate the rarefied gas flow beyond the Navier-Stokes level, either by using the high-order Gauss-Hermite quadrature, or by introducing the relaxation time that is a function of the gas-wall distance. While the former method, with a limited number of discrete velocities (i.e. D2Q36), is accurate up to the early transition flow regime, the latter method, with the same discrete velocities as that used in simulating hydrodynamics (i.e. D2Q9), is accurate up to the free-molecular flow regime in the Poiseuille flow between two parallel plates. This is quite astonishing in the sense that more discrete velocities are less accurate. In this paper, by solving the Bhatnagar-Gross-Krook kinetic equation accurately via the discrete velocity method, we find that the accuracy of the lattice Boltzmann method is reduced significantly in the simulation of rarefied gas flows through the rough surface and porous media. Our simulation results could serve as benchmarking cases for future development of the lattice Boltzmann method for modeling and simulation of rarefied gas flows in complex geometries.

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Lattice Boltzmann simulation of nonequilibrium effects in oscillatory gas flow

Cited by 30 publications

References 44 publications

Analysis of boundary slip in a flow with an oscillating wall

Analysis of boundary slip in a flow with an oscillating wall

Asymptotic analysis of the Boltzmann–BGK equation for oscillatory flows

Comparative study of the discrete velocity and lattice Boltzmann methods for rarefied gas flows through irregular channels

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