Slip Boundary Conditions for the Compressible Navier–Stokes Equations

Aoki, Kazuo; Baranger, Céline; Hattori, Masanari; Kosuge, Shingo; Martalò, Giorgio; Mathiaud, Julien; Mieussens, Luc

doi:10.1007/s10955-017-1886-8

Cited by 30 publications

(15 citation statements)

References 58 publications

(156 reference statements)

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“…(25)- (27), ζ = 1.254 √ π Kn/2 and ϑ T = 2.399 √ π Kn/2 are the commonly used first-order nondimensional slip and jump coefficients for a hard-sphere gas, respectively [32]. The ϑ v (∂v/∂y) terms with ϑ v = 0.460 √ π Kn/2 mark an additional jump correction, recently derived by Aoki et al [33], to accompany the compressible Navier-Stokes equations.…”

Section: Continuum Limitmentioning

confidence: 99%

Nonlinear thermal effects in unsteady shear flows of a rarefied gas

Ben-Ami

Manela

2018

Phys. Rev. E

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We study the response of a rarefied gas in a slab to the motion of its boundaries in the tangential direction. Different from previous investigations, we consider boundaries displacements at nonsmall Mach (Ma) numbers, coupling the dynamic and thermodynamic gas states, and deviating the system from its low-velocity isothermal condition. The problem is studied in the entire range of gas rarefaction rates, combining limited case ballistic-and continuum-flow analyses with direct simulation Monte Carlo computations. A nonlinear solution is derived in the ballistic regime for arbitrary velocity profiles and amplitudes. At near-continuum conditions, a slip-flow timeperiodic solution is obtained for the case of oscillatory boundary motion, by expanding the flow field in an asymptotic Mach power series. The effect of replacing between isothermal and adiabatic surfaces is examined. The results indicate that, at all Knudsen (Kn) numbers, the thermodynamic fields and normal velocity component are dominated by double-frequency (and descending higher-order even-frequency harmonic) time dependence, different from the fundamental-frequency time dependence dominating the tangential gas velocity. At continuumlimit conditions, this stems from the quadratic viscous dissipation term (negligible at low-Mach conditions), coupling the square of the tangential velocity gradient as a forcing term. System nonlinearity also results in an unsteady normal force acting on the boundaries, overcoming the tangential force with increasing Ma. A marked difference from the latter is that the normal force either decreases with Kn or, at sufficiently small actuation frequencies, varies nonmonotonically with Kn, reaching a maximum at some intermediate rarefaction conditions.

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Section: Continuum Limitmentioning

confidence: 99%

Nonlinear thermal effects in unsteady shear flows of a rarefied gas

Ben-Ami

Manela

2018

Phys. Rev. E

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“…The presence of these profiles in other asymptotic regimes is worth investigating in the future, even starting from different kinetic models for polyatomic gases. Another interesting work, already in progress, concerns the derivation of suitable slip boundary conditions for the present macroscopic equations, following the procedure outlined in [24,50] for different Navier-Stokes systems. Moreover, this kind of analytical and numerical analysis could be repeated for other kinetic models.…”

Section: Discussionmentioning

confidence: 99%

A Note on the Steady Navier–Stokes Equations Derived from an ES–BGK Model for a Polyatomic Gas

Aoki

Bisi

Groppi

et al. 2021

Fluids

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The two-temperature Navier–Stokes equations derived from an ellipsoidal Bhatnagar-Gross-Krook (ES-BGK) model for a polyatomic gas (Phys. Rev. E102, 023104 (2020)) are considered in regimes where bulk viscosity is much greater than the shear viscosity. Possible existence of a shock-wave solution for the steady version of these hydrodynamic equations is investigated resorting to the qualitative theory of dynamical systems. Stability properties of upstream and downstream equilibria are discussed for varying parameters.

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“…(9) was derived for a "slightly compressible" gas, and not for the full compressible Navier Stokes equations studied hereafter. Investigation of the latter was carried out in a recent contribution by Aoki et al [17], where the slip and jump conditions were obtained for a temperature-fixed surface, taking into account the effect of density variations near the surface on the local mean free path. As these conditions, as in Eq.…”

Section: Problem Statement and Analysismentioning

confidence: 99%

“…Toward this end, we set ω = 0 in Eqs. (14)- (17), and introduce the scaling k = lδ −1 and Kn = aδ 5/2 ,…”

Section: The Limit Of Dominant Compressibilitymentioning

confidence: 99%

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

Ben-Ami

Manela

2019

Phys. Rev. Fluids

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We consider the effect of heat-flux boundary conditions, replacing the previously studied isothermal wall conditions, on the Rayleigh-Bénard instability in a rarefied gas. The problem is investigated in the limit of small Knudsen numbers, by means of a linear stability analysis of a slip flow model, and the direct simulation Monte Carlo method. In the latter, a noniterative algorithm is applied to implement the heat-flux conditions. The results delineate the instability domain in the parameters plane of the Knudsen number (Kn), Froude number (Fr), and walls reference temperature ratio. The heat-flux conditions result in a significant destabilizing effect, extending instability to larger Knudsen numbers. At large Fr, the Boussinesq limit is recovered, and transition to instability is governed by a critical value of the Rayleigh number. With decreasing Fr, gas compressibility becomes dominant, confining the convection layer to the vicinity of the upper cold wall. Asymptotic analysis of the low-Fr limit is carried out, to highlight the impact of difference in thermal conditions. The Monte Carlo scheme is applied to investigate system instability at supercritical states, where walls heat-flux conditions lead to elevated shear stresses. Nonmonotonic variations in the walls shear stress with Kn are observed and discussed.

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Slip Boundary Conditions for the Compressible Navier–Stokes Equations

Cited by 30 publications

References 58 publications

Nonlinear thermal effects in unsteady shear flows of a rarefied gas

Nonlinear thermal effects in unsteady shear flows of a rarefied gas

A Note on the Steady Navier–Stokes Equations Derived from an ES–BGK Model for a Polyatomic Gas

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

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