Advanced models of fuel droplet heating and evaporation

Although the Hertz-Knudsen (HK) relation is often used to correlate evaporation data, the relation contains two empirical parameters (the evaporation and condensation coefficients) that have inexplicably been found to span 3 orders of magnitude. Explicit expressions for these coefficients have yet to be determined. This review will examine sources of error in the HK relation that have led to the coefficients’ scatter. Through an examination of theoretical, experimental, and molecular dynamics simulation studies of evaporation, this review will show that the HK relation is incomplete, since it is missing an important physical concept: the coupling between the vapor and liquid phases during evaporation. The review also examines a modified HK relation, obtained from the quantum-mechanically based statistical rate theory (SRT) expression for the evaporation flux and applying a limit to it in which the thermal energy is dominant. Explicit expressions for the evaporation and condensation coefficients are define...

Expressions for the Evaporation and Condensation Coefficients in the Hertz-Knudsen Relation.

Shear flow and thermal creep flow (flow induced by the temperature gradient along the boundary wall) of a rarefied gas over a plane wall are considered on the basis of the linearized Boltzmann equation for hard‐sphere molecules and diffuse reflection boundary condition. These fundamental rarefied gas dynamic problems, typical half‐space boundary‐value problems of the linearized Boltzmann equation, are analyzed numerically by the finite‐difference method developed recently by the authors, and the velocity distribution functions, as well as the macroscopic variables, are obtained with good accuracy. From the results, the shear and thermal creep slip coefficients and their associated Knudsen layers of a slightly rarefied gas flow past a body are derived. The results for the slip coefficients and Knudsen layers are compared with experimental data and various results by the Boltzmann–Krook–Welander (BKW) equation, the modified BKW equation, and a direct simulation method.

Numerical analysis of the shear and thermal creep flows of a rarefied gas over a plane wall on the basis of the linearized Boltzmann equation for hard-sphere molecules

Cercignani’s second-order slip model has been neglected over the years, perhaps due to Sreekanth’s claim that it cannot fit his experimental data. In this paper we show that Sreekanth’s claim was based on an incorrect interpretation of this model. We also show that Cercignani’s second-order slip model, when modified and used appropriately, is in good agreement with solutions of the Boltzmann equation for a hard-sphere gas for a wide range of rarefaction. Given its simplicity, we expect this model to be a valuable tool for describing isothermal micro- and nanoscale flows to the extent that the hard-sphere approximation is appropriate.

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Comment on Cercignani's second-order slip coefficient

Analysis of intensive evaporation and condensation

The steady behavior of a gas in contact with its condensed phase of arbitrary shape is investigated on the basis of kinetic theory. The Knudsen number of the system (the mean free path of the gas molecules divided by the characteristic length of the system) being assumed to be fairly small, the hydrodynamic equations for the macroscopic quantities, the velocity, temperature, and pressure, of the gas and their boundary conditions on the interface of the gas and its condensed phase are derived, and two simple examples (evaporation from a sphere, two-surface problem of evaporation and condensation) are worked out.

Kinetic Theory of Evaporation and Condensation : Hydrodynamic Equation and Slip Boundary Condition

The behavior of a gas in contact with its condensed phase is considered on the basis of a relaxation model of the linearized Boltzmann equation. The temperature and density distributions of the gas in the Knudsen layer as well as so called slip boundary condition on the interface of the gas and its condensed phase are obtained.

Kinetic Theory of Evaporation and Condensation

The asymptotic behavior for small mean free path of steady flow of a gas in contact with its condensed phase of arbitrary shape is investigated on the basis of kinetic theory. The hydrodynamic equations for the macroscopic quantities, the velocity, temperature, and pressure, of the gas and their boundary conditions on the interface between the gas and its condensed phase are derived up to the order of the Knudsen number squared, together with the Knudsen-layer correction near the interface. In the analysis, the perturbations from a uniform equilibrium state are assumed to be small, but their nonlinear effects are taken into account correctly so that the results obtained can be applied when the Reynolds number of the system is finite. This is an extension of the corresponding linearized theory by the same authors, which is valid only for very small Reynolds number.

Kinetic Theory of Slightly Strong Evaporation and Condensation–Hydrodynamic Equation and Slip Boundary Condition for Finite Reynolds Number–

Experimental investigations on the stability characteristics of a natural convection plume in air above a horizontal line source of heat were performed. The results obtained experimentally confirm the predictions of the linear stability theory over an appreciably wide range of Grashof number. A slow fluctuation of a laminar plume, which is called swaying motion, was observed. Turbulent bursts in the transitional processes to turbulence were not detected but gradual and smooth breakdown of the initially regular disturbance waves were observed as the Grashof number increased.

Experimental Study on Instability of Natural Convection Flow above a Horizontal Line Heat Source

Temperature and number density fields of a binary gas mixture over a plane solid wall kept at a constant temperature have been studied analytically on the basis of the linearized version of the Boltzmann equation of BGK type subject to the boundary condition of Maxwell’s type (specular‐diffusive reflection). An analysis within the Knudsen layer in the vicinity of the wall has been carried out by solving the set of equations accurately, which has enabled us to obtain the distributions of the temperature and number density explicitly over the entire flow field. Fictitious gas mixtures have been taken up, in addition to the mixtures of real gases such as helium–neon, helium–argon, neon–argon and so on, in order to see the effects of the molecular mass ratio, the concentration ratio and the accommodation coefficients of the component gases on the temperature and number density fields by suppressing the effects associated with the transport coefficients. The macroscopic jump coefficients in temperature at the wall have also been given for making a comparison with the other results available. The comparison with the theoretical results by other authors for a helium–argon mixture case shows a reasonably good agreement. The experimental data, however, seem to be too large compared with the present results, which may partly be attributable to some ambiguities in the definitions of some quantities involved in the experiment.

Yoshimoto Onishi

Papers

Kinetic Theory of Evaporation and Condensation : Hydrodynamic Equation and Slip Boundary Condition

Kinetic Theory of Evaporation and Condensation

Kinetic Theory of Slightly Strong Evaporation and Condensation–Hydrodynamic Equation and Slip Boundary Condition for Finite Reynolds Number–

Experimental Study on Instability of Natural Convection Flow above a Horizontal Line Heat Source

Kinetic theory analysis for temperature and density fields of a slightly rarefied binary gas mixture over a solid wall