Takeo Soga

Kinetic analysis of evaporation and condensation in a vapor‐gas mixture

Evaporation and condensation of vapor‐gas mixture is studied on the basis of the kinetic BGK–Morse model equation. The linearized kinetic model equation is solved using the half‐range Hermite polynomials and various slip coefficients are obtained. The obtained slip coefficient of vapor pressure is insensitive to the variation in concentration of a noncondensable gas. When the mean concentration of noncondensable gas is very small, an exponential distribution of noncondensable gas is obtained and a set of nonlinear equations is transformed to that of linear equations for pure vapor. It is found from the linear and nonlinear solutions that the impedance of mass flux in the two‐surface problem is composed of surface and induced resistances and that the latter is proportional to the total amount of the noncondensable gas rather than the mean concentration of it.

A kinetic theory analysis of evaporation and condensation of a diatomic gas

The evaporation and condensation problem of diatomic gas was studied based on the BGK–Morse kinetic model equation. The results showed that (1) the macroscopic jump coefficients were insensitive to the variation in the relaxation time of internal energy, (2) the pressure jump caused by evaporation (condensation) or by heat transfer was almost the same as the value of a monatomic gas, and (3) the temperature jumps of a diatomic gas were smaller than those of a monatomic gas in accordance with the quantities of specific heats. Approximate expressions of macroscopic jump coefficients of a diatomic gas for arbitrary values of the internal degrees of freedom and those of accommodation coefficients of mass, translational energy, and internal energy are obtained using the jump coefficients of a monatomic gas.

A kinetic analysis of thermal force on a spherical particle of high thermal conductivity in a monatomic gas

A linearized version of the hierarchy kinetic model equation was solved by applying a singular perturbation method and the half‐range Hermite polynomials. The solution retains correct results up to O(Kn2) and suggests that, if the thermal conductivity of the spherical particle is infinite and the impinging molecules suffer complete energy accomodation at the surface, the thermal force of O(Kn2) disappears (or thermal force is very small) in the near continuum regime. The present results also indicate that the thermal force is sensitive to the variation in the energy accomodation coefficient for the accommodation coefficient of tangential momentum nearly equal to unity. With the effect of such accommodation coefficients, the present results are used to explain the existing experimental results from the viewpoint of kinetic theory as long as the Knudsen number is small.

On the Numerical Simulation of Rotating Rarefied Flow in the Cylinder with Smooth Surface

Numerical simulation of impulsively started rotational flow in the cylinder with smooth surface was carried out using the DSMC method. Results of present simulation affirmed that an isothermal solid rotation of the fluid was the thermally and mechanically equilibrium state of the rotating fluid. Integrating mass, angular momentum, and energy conservation equations, we obtained area‐angular velocity relation of the rotating fluid (vortex filament) under compression or under expansion. We found that speed ratio (Mach number) of the peripheral velocity on the surface of the cylinder changed very slightly as the fluid was compressed or expanded so long as the peripheral Mach number was low or moderate subsonic. Thus, theoretical results suggested that most part of the work done by the compression of the vortex filament reduced to the internal energy of the fluid and the ratio of the energy of rotating fluid to the internal energy, Erot/cvT = s2 /3 ≈ constant. These theoretical predictions were affirmed by the...

On the Application of the Moment equations to the Thermally Induced Flows

Moment equations derived from the Boltzmann equation for the two‐dimensional flows were formulated and generalized slip boundary conditions for the moments were derived. Fifty one moments relevant to the eigenfunctions included in the Chapman‐Enskog solutions of the second order approximation were taking into account. These moment equations were applied to thermally induced flows in a two‐dimensional vessel. The moment equations were solved using the MacCormack’s difference scheme. Present results showed that the moment equations and the slip boundary conditions were applicable for the two‐dimensional flows in the transition regime. Thermally induced slip flow adjacent to the solid wall decreased linearly in accordance with the decrease of the Knudsen number relevant to the size of the vessel. The values of obtained slip coefficient, velocity/(gradient of temperature along the solid wall), increased as the number of moment equations increased. Present results suggested that moments should be selected so a...

Application of the moment equations to the shock-tube problem

Moment equations derived from the Boltzmann equation were applyed to the Riemann problem. A new closure method of the moment equations were proposed. It was demonstrated that supplemented moment equations were applicable to the analysis of moderately strong shock waves. Various higher order moments of the distribution function in the shock wave were obtained. Present result suggested that these higher order moments would not be simply expressed in terms of higher order derivatives of velocity, temperature, and pressure. If we include more higher moment equations present results may be considerablly improved. Present method is expected for the analysis of nonequilibrium rarefied flow connecting with higher order moments demonstrated in this paper.

A kinetic analysis of unsteady evaporation and condensation with an Oseen‐like approximation

A linearized kinetic model equation with an Oseen‐like approximation was applied to study the moderately strong unsteady evaporation and condensation problems. Asymptotic solutions were obtained for the weak (linearized) evaporation and condensation problems, disjoining the fluid dynamic equation with the Oseen approximation from the Knudsen layer equation. The asymptotic solution yielded correct features of the flow due to evaporation or condensation. The kinetic model equation was further applied to study the moderately strong evaporation and condensation problems. The results showed good agreement with the previous results derived from the nonlinear treatments and confirmed that the conventional slip flow theory is applicable for studying the moderately strong evaporation and condensation problems.