Effect of heat-flux boundary conditions on the Rayleigh-Bénard instability in a rarefied gas

Ben-Ami, Y.; Manela, A.

doi:10.1103/physrevfluids.4.033402

Cited by 9 publications

(4 citation statements)

References 25 publications

(60 reference statements)

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“…To apply the latter, the boundary temperature is treated as unknown, and a modification of the conventional computational scheme is required. This is carried out using recent contributions by the authors [40,41,43,44],…”

Section: Numerical Scheme: Dsmc Methodsmentioning

confidence: 99%

Acoustic wave propagation at nonadiabatic conditions: The continuum limit of a thin acoustic layer

Ben-Ami

Manela

2020

Phys. Rev. Fluids

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Existing works on sound propagation in rarefied gases have focused on wave transmission at adiabatic conditions, where a reference uniform equilibrium state prevails. To extend these studies, we analyze the propagation of acoustic waves in a slightly rarefied gas at nonadiabatic conditions, where arbitrarily large reference temperature and density gradients are imposed. Considering a planar slab configuration, constant wall heating is applied at the confining walls to maintain the non-uniform reference thermodynamic distributions. Acoustic excitation is then enforced via small-amplitude harmonic wall oscillations and normal heatflux perturbations. Focusing on continuum-limit conditions of small Knudsen numbers and high actuation frequencies (yet small compared with the mean collision frequency), the gas domain affected by wall excitation is confined to a thin layer (termed "acoustic layer") in the vicinity of the excited boundary, and an approximate solution is derived based on asymptotic expansion of the acoustic fields. The application of thermoacoustic wall excitation necessitates the formation of an ever thinner "thermal layer" that governs the transmission of wall unsteady heat flux into sound waves. The results of the approximate analysis, supported by continuummodel finite-differences and direct simulation Monte Carlo calculations, clarify the impacts of system non-adiabaticity and gas kinetic model of interaction on sound propagation. Primarily, reference wall heating results in an extension of the acoustic layer and consequent sound wave radiation over larger distances from the wall source. Considering the entire range of inverse power law (repulsion point center) interactions, it is also found that wave attenuation is affected by the kinetic model of gas collisions, yielding stronger decay rates in gases with softer molecular interactions. The results are used to generalize the counterpart adiabatic-system findings for the amount of boundary heat-flux required for the silencing of vibroacoustic sound at nonadiabatic reference conditions.

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Section: Numerical Scheme: Dsmc Methodsmentioning

confidence: 99%

Acoustic wave propagation at nonadiabatic conditions: The continuum limit of a thin acoustic layer

Ben-Ami

Manela

2020

Phys. Rev. Fluids

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“…To apply the latter, the boundary temperature is treated as unknown, and a modification of the conventional numerical scheme is required. This is carried out based on recent contributions by the authors [36,[38][39][40][41], where a non-iterative algorithm for the imposition of a heat-flux condition has been suggested and tested. For completeness, the algorithm is repeated here.…”

Section: Numerical Scheme: Dsmc Methodsmentioning

confidence: 99%

“…At Kn ≪ 1, these modes should approximate the initial Knudsen-layer behaviour of the gas, inevitably missing in the NSF description. As in the NSF approximation, once the transformed G(λ, t) fields are determined, the solution is transformed back to the (x, t) plane using Eq (40).…”

Section: Specular Wallmentioning

confidence: 99%

The effect of a solid boundary on the propagation of thermodynamic disturbances in a rarefied gas

Ben-Ami

Manela

2020

Physics of Fluids

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We study the effect of a rigid boundary on the propagation of thermodynamic disturbances in a gas at non-continuum conditions. We consider a semi-infinite setup confined by an infinite planar wall and introduce initial gas disturbances in the form of density and temperature inhomogeneities. The problem is formulated for arbitrary small-amplitude perturbations, and analyzed in the entire range of gas rarefaction rates, governed by the Knudsen (Kn) number. Our results describe the system relaxation to equilibrium, with specific emphasis on the effect of the solid surface. Analytical solutions are obtained in the free-molecular and nearcontinuum (based on the Navier-Stokes-Fourier and regularized thirteen moment equations) regimes and compared with direct simulation Monte Carlo results. The impact of the solid wall is highlighted by comparing between diffuse (adiabatic or isothermal) and specular boundary reflections. Focusing on a case of an initial temperature disturbance, the results indicate that the system relaxation time shortens with increasing Kn. The isothermal boundary consistently reverberates the weakest acoustic disturbance, as the energy carried by the impinging wave is partially absorbed by the surface. The specular and adiabatic wall systems exhibit identical responses in the continuum limit, while departing with increasing Kn due to higher-order moment effects. The unsteady normal force exerted by the gas on the surface is quantified and analyzed.

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“…They considered a modified Ra, defined by Golshtein and Elperin [34] for a hard-sphere gas, and showed that the derived neutral curves are asymptotically equivalent with a line of constant Rayleigh (Ra ≈ 1773) at r = 0.1 and Kn < 0.01 in the (Fr, Kn) plane. Recently, Ben-Ami and Manela [54] replaced the isothermal wall conditions by the heat-flux boundary conditions and applied the linear temporal stability to the problem. They demonstrated that the heat-flux boundary causes destabilizing effects, extending the convection zone limits to a lower critical Rayleigh (at the onset of convection) and higher rarefaction limits.…”

Section: Introductionmentioning

confidence: 99%

Numerical study of heat transfer in Rayleigh-Bénard convection under rarefied gas conditions

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Effect of heat-flux boundary conditions on the Rayleigh-Bénard instability in a rarefied gas

Cited by 9 publications

References 25 publications

Acoustic wave propagation at nonadiabatic conditions: The continuum limit of a thin acoustic layer

Acoustic wave propagation at nonadiabatic conditions: The continuum limit of a thin acoustic layer

The effect of a solid boundary on the propagation of thermodynamic disturbances in a rarefied gas

Numerical study of heat transfer in Rayleigh-Bénard convection under rarefied gas conditions

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