Shingo Kosuge

Vapor flows caused by evaporation and condensation on two parallel plane surfaces: Effect of the presence of a noncondensable gas

A vapor in a gap between two parallel plane surfaces of its condensed phase, on which evaporation or condensation may take place, is considered in the case where another gas that neither evaporates nor condenses on the surfaces (say, a noncondensable gas) is also contained in the gap. The steady flow of the vapor caused by evaporation on one surface and condensation on the other and the behavior of the noncondensable gas are investigated on the basis of kinetic theory. First, fundamental features of the flow field are clarified for small values of the Knudsen number (associated with vapor–vapor collisions) by a systematic asymptotic analysis of the Boltzmann equation. Then, the problem is analyzed numerically by means of the direct simulation Monte Carlo method, and the steady behavior of the vapor and of the noncondensable gas (e.g., the spatial distributions of the macroscopic quantities) is clarified for a wide range of the Knudsen number. In particular, it is shown that, in the limit as the Knudsen number tends to zero (the continuum limit with respect to the vapor), there are two different types of the limiting behavior depending on the amount of the noncondensable gas, and evaporation and condensation can take place only when the average density of the noncondensable gas is vanishingly small in comparison with that of the vapor.

Shock-wave structure for a binary gas mixture: finite-difference analysis of the Boltzmann equation for hard-sphere molecules

Abstract The structure of a normal shock wave for a binary mixture of hard-sphere gases is analyzed numerically on the basis of the Boltzmann equation by a finite-difference method. In the analysis, the complicated collision integrals are computed efficiently as well as accurately by means of the numerical kernel method, which is the generalization to the case of a binary mixture of the method devised by Ohwada in 1993 in the shock-structure analysis for a single-component gas. The transition from the upstream to the downstream uniform state is clarified not only for the macroscopic quantities but also for the velocity distribution functions.

Numerical analysis of thermal-slip and diffusion-slip flows of a binary mixture of hard-sphere molecular gases

The thermal-slip (thermal-creep) and the diffusion-slip problems for a binary mixture of gases are investigated on the basis of the linearized Boltzmann equation for hard-sphere molecules with the diffuse reflection boundary condition. The problems are analyzed numerically by the finite-difference method incorporated with the numerical kernel method, which was first proposed by Sone, Ohwada, and Aoki [Phys. Fluids A 1, 363 (1989)] for a single-component gas. As a result, the behavior of the mixture is clarified accurately not only at the level of the macroscopic variables but also at the level of the velocity distribution function. In addition, accurate formulas of the thermal-slip and the diffusion-slip coefficients for arbitrary values of the concentration of a component gas are constructed by the use of the Chebyshev polynomial approximation.

Heat transfer in a gas mixture between two parallel plates: Finite-difference analysis of the Boltzmann equation

The problem of heat transfer and temperature distribution in a binary mixture of rarefied gases between two parallel plates with different temperatures is investigated on the basis of kinetic theory. Under the assumption that the gas molecules are hard spheres and undergo diffuse reflection on the plates, the Boltzmann equation is analyzed numerically by means of an accurate finite-difference method, in which the complicated nonlinear collision integrals are computed efficiently by the deterministic numerical kernel method. As a result, the overall quantities (the heat flow in the mixture, etc.) as well as the profiles of the macroscopic quantities (the molecular number densities of the individual components, the temperature of the total mixture, etc.) are obtained accurately for a wide range of the Knudsen number. At the same time, the behavior of the velocity distribution function is clarified with high accuracy.

Steady flows of a highly rarefied gas induced by nonuniform wall temperature

Steady behavior of a rarefied gas between parallel plates with sinusoidal temperature distribution is investigated on the basis of the Boltzmann equation. The Cercignani–Lampis (CL) model or the Lord model for diffuse scattering with incomplete energy accommodation is adopted as the boundary condition on the plates. Most of the analysis is carried out numerically with special interest in the free-molecular limit. In the case of the CL model, the nonuniform temperature distribution of the plates may induce a steady free-molecular flow, which is in contrast with the earlier results for the Maxwell-type model [Y. Sone, J. Mec. Theor. Appl. 3, 315 (1984); J. Mec. Theor. Appl. 4, 1 (1985)]. This fact is confirmed through an accurate deterministic computation based on an integral equation. In addition, computations for a wide range of parameters by means of the direct simulation Monte Carlo method reveal that the flow field changes according to the accommodation coefficients and is classified into four types. T...

Shock wave structure in polyatomic gases: Numerical analysis using a model Boltzmann equation

The structure of a standing plane shock wave in a polyatomic gas is investigated on the basis of kinetic theory, with special interest in the CO2 gas. The polyatomic version of the ellipsoidal statistical model is employed, and the shock structure is obtained numerically for several Mach numbers for a pseudo-CO2 gas, which is an artificial CO2 gas with smaller ratio of the bulk viscosity to the viscosity. The double-layer structure consisting of a thin upstream layer with a steep change and a much thicker downstream layer with a mild change, which has been known for a long time and was confirmed recently by the extended thermodynamics [S. Taniguchi et al., Int. J. Non-Linear Mech. 79, 66 (2016)], is reproduced.

Slow evaporation and condensation on a spherical droplet in the presence of a noncondensable gas

A spherical droplet is placed in a binary mixture composed of the vapor of the droplet and another gas which neither evaporates nor condenses (a noncondensable gas). The mixture is in an equilibrium state at rest at infinity. A slow steady flow of the vapor caused by weak evaporation or condensation, under the influence of the noncondensable gas, is investigated on the basis of a linearized model Boltzmann equation. Numerical analyses by means of a finite-difference method are carried out for a wide range of the Knudsen number (i.e., from a large to small droplet compared to the molecular mean free path). The numerical results, together with analytical solutions for small and large Knudsen numbers, clarify the behavior the mixture, i.e., the mass- and heat-flow rates from or onto the droplet as well as spatial distributions of the macroscopic quantities, in the entire range of gas rarefaction. The solution for the steady heat transfer problem between a solid sphere and a binary gas mixture is also obtaine...

Flows of a Binary Mixture of Rarefied Gases between Two Parallel Plates

A binary mixture of rarefied gases between two parallel plates is considered. The Poiseuille flow, the thermal transpiration, and a flow caused by a concentration gradient of a component gas along the plates are investigated on the basis of the linearized Boltzmann equation for hard‐sphere gases with the diffuse reflection boundary condition. Accurate numerical analyses are performed by means of a finite‐difference method, in which the complicated collision integrals are computed efficiently by the numerical kernel method. As a result, the behavior of the mixture is clarified at the level of the velocity distribution functions as well as the macroscopic quantities for a wide range of the Knudsen number.

Numerical analysis of the Taylor-Vortex flow of a slightly rarefied gas

The axisymmetric Taylor-vortex flow of a rarefied gas between two coaxial circular cylinders, a rotating inner cylinder and a resting outer one, is investigated numerically for small Knudsen numbers on the basis of the compressible Navier-Stokes (CNS) equations and their appropriate slip boundary conditions. The accuracy of the result as an approximate solution to the Boltzmann equation is confirmed by comparing it with the result obtained by the direct simulation Monte Carlo (DSMC) method for Knudsen numbers of the order of 10−2. The flow field for smaller Knudsen numbers (of the order of 10−3) exhibits a boundary-layer like structure near the cylinders. It is shown that, compared with the cylindrical Couette flow, the velocity slip in the circumferential direction is enhanced in the Taylor-vortex flow.

Finite-difference methods for the Boltzmann equation for binary gas mixtures

A finite-difference method for the Boltzmann equation for a binary mixture of hard-sphere gases that has been developed in the authors’ group is explained. Then, its applications to some fundamental problems of rarefied gas dynamics are presented.