Vapor flows with evaporation and condensation in the continuum limit: effect of a trace of noncondensable gas

Aoki, Kazuo; Takata, Shigeru; Taguchi, Satoshi

doi:10.1016/s0997-7546(02)00008-0

Cited by 30 publications

(60 citation statements)

References 35 publications

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“…For an evaporating flow we obtain one extra condition in case (i) compared with the case of a pure vapor. Evaporating flows are not studied in case (ii), since then the non-condensable gas is blown away by the evaporating vapor flow and can not stay in the Knudsen layer [14,17]. For a condensing flow we obtain, both in case (i) and (ii), the same number of conditions as in the case of a pure vapor.…”

Section: Discussionmentioning

confidence: 92%

Boundary layers for the nonlinear discrete Boltzmann equation: Condensing vapor flow in the presence of a non-condensable gas

Bernhoff¹

2012

AIP Conference Proceedings

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Abstract. Half-space problems for the Boltzmann equation are of great importance in the study of the asymptotic behavior of the solutions of boundary value problems of the Boltzmann equation for small Knudsen numbers. Half-space problems provide the boundary conditions for the fluid-dynamic-type equations and Knudsen-layer corrections to the solution of the fluid-dynamic-type equations in a neighborhood of the boundary. Here we consider a half-space problem of condensation for a pure vapor in the presence of a non-condensable gas by using discrete velocity models (DVMs) of the Boltzmann equation. The Boltzmann equation can be approximated by DVMs up to any order, and these DVMs can be applied for numerical methods, but also for mathematical studies to bring deeper understanding and new ideas. For one-dimensional half-space problems, the discrete Boltzmann equation (the general DVM) reduces to a system of ODEs. We obtain that the number of parameters to be specified in the boundary conditions depends on whether the condensing vapor flow is subsonic or supersonic. This behavior has earlier been found numerically. We want to stress that our results are valid for any finite number of velocities. This is an extension of known results for single-component gases (and for binary mixtures of two vapors) to the case when a non-condensable gas is present. The vapor is assumed to tend to an assigned Maxwellian, with a flow velocity towards the condensed phase, at infinity, while the non-condensable gas tends to zero at infinity. Steady condensation of the vapor takes place at the condensed phase, which is held at a constant temperature. We assume that the vapor is completely absorbed, that the non-condensable gas is diffusively reflected at the condensed phase, and that vapor molecules leaving the condensed phase are distributed according to a given distribution. The conditions, on the given distribution at the condensed phase, needed for the existence of a unique solution of the problem are investigated, assuming that the given distribution at the condensed phase is sufficiently close to the Maxwellian at infinity and that the total mass of the non-condensable gas is sufficiently small. Exact solutions and solvability conditions are found for a specific simplified discrete velocity model (with few velocities).

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Section: Discussionmentioning

confidence: 92%

Boundary layers for the nonlinear discrete Boltzmann equation: Condensing vapor flow in the presence of a non-condensable gas

Bernhoff¹

2012

AIP Conference Proceedings

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“…Introducing a pressure difference between the walls induces a flow of A from one wall to the other. Classical asymptotic analysis produces an anomaly ("ghost effect") in the form of infinitesimally thin boundary layers of species B completely stopping the flow of A [7,8]. Instead, the above scaling procedure leads to a boundary layer of finite thickness slowing down the flow of A depending on the concentration of B.…”

Section: Diffusive Scaling and Closure Relationsmentioning

confidence: 99%

“…In combination with a meaningful scaling this produces explicit formulas for the transport coefficients and closure relations depending on details of the model collision operator. The theory is applicable even in cases when the classical asymptotic analysis approach fails or leads to physically irrelevant results [7,8]. …”

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confidence: 99%

Discrete Velocity Models: A Study of the Hydrodynamic Limit

Babovsky¹

2016

Proceedings of the VII European Congress on Computational Methods in Applied Sciences and Engineering (ECCOMAS Congress 2016)

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Abstract. We investigate Discrete Velocity Models as a numerical tool for the simulation of rarefied flows in the hydrodynamic limit. The study is based on the analysis of the bifurcation structure of a related linearized transport operator. In combination with a meaningful scaling this produces explicit formulas for the transport coefficients and closure relations depending on details of the model collision operator. The theory is applicable even in cases when the classical asymptotic analysis approach fails or leads to physically irrelevant results [7,8].

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“…Equations (4a) and (4b) form a closed set of equations forp (0) , (1) . Equations (5a) -(5c) form a closed set of linear equations forp (1) , X A (1) ,T (1) , andŵ (2) . Next we consider the boundary condition at the interface for Eqs.…”

Section: Asymptotic Analysis -Slowly Varying Solutionmentioning

confidence: 99%

“…Half-space problem of evaporation and condensation is one of the most fundamental boundary-value problems in kinetic theory and has been intensively studied (see, for example, [1,2] and the references therein). One of the important aspects of the problem is that the information about the conditions for the steady evaporation and condensation flows provides the fluid-dynamic equations with the appropriate boundary conditions; that is, it allows us to complete the macroscopic description of vapor flows with the phase change at ordinary pressure.…”

Section: Introductionmentioning

confidence: 99%

Half-space problem of weak evaporation and condensation of a binary mixture of vapors

Takata¹

2005

AIP Conference Proceedings

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Abstract. Half-space problem of weak evaporation and condensation of a binary mixture of vapors is investigated on the basis of the BGK-type Boltzmann model. By a systematic asymptotic analysis, it is shown that the steady evaporation and condensation takes place only if the parameters that characterize the state of the condensed phase and that of the vapors at a far distance satisfy one relation for the condensation case and three relations for the evaporation case. As an application, the resulting relations are used as the boundary conditions of the Euler system in the study of the two-surface problem of a vapor mixture for small Knudsen numbers. This system has two branches of solutions, which causes two different solutions for the same physical situation in the continuum limit. This result is discussed in connection with the ghost effect.

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Vapor flows with evaporation and condensation in the continuum limit: effect of a trace of noncondensable gas

Cited by 30 publications

References 35 publications

Boundary layers for the nonlinear discrete Boltzmann equation: Condensing vapor flow in the presence of a non-condensable gas

Boundary layers for the nonlinear discrete Boltzmann equation: Condensing vapor flow in the presence of a non-condensable gas

Discrete Velocity Models: A Study of the Hydrodynamic Limit

Half-space problem of weak evaporation and condensation of a binary mixture of vapors

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