Effect of surface gas condensation on the velocity of a reflected shock wave

The time-dependent one-dimensional problem of the normal reflection of a shock wave propagating at constant velocity in a gas (vapor) at rest from the plane surface of its condensed phase under steady-state condensation-evaporation conditions on the interphase plane is considered within the framework of the kinetic equation for a monatomic gas with a model collision operator (S-model). The solution is obtained using a conservative second-order finite-difference method. Attention is concentrated on the steady-state regime of the condensation process. The effect of the condensation (evaporation) coefficient on the velocity of the reflected shock wave is studied.     

Water Evaporation Versus Condensation in a Hygroscopic Soil

The liquid/vapour phase change of water in soil is involved in many environmental geotechnical processes. In the case of hygroscopic soils, the liquid water is strongly adsorbed on the solid phase and this particular thermodynamic state can highly influence the phase change kinetics. Based on the linear Thermodynamic of Irreversible Processes ideas, the non-equilibrium phase change rate is written as a linear function of the water chemical potential difference between the liquid and vapour state. In this relation, the system is characterized by a phenomenological coefficient that depends on the state variables. Using an original experimental set-up able to analyze the response of a porous medium subjected to non-equilibrium conditions, the phase change coefficient is determined in various configurations. This paper focuses on the influence of the gas phase pressure and underlines that a low gas pressure decreases the phase change kinetics. Then, evaporation and condensation processes are compared showing an asymmetric behaviour. These experimental results are interpreted from a microscopic point of view by relying on recent works dealing with molecular dynamics numerical simulation of the liquid/gas interface.     

Strong evaporation of a filler from a porous body with a plane surface

The problem of strong evaporation of matter filling periodic rectangular semi-infinite channels in a porous two-dimensional body is solved by a method of direct statistical modeling. The depths of the channels, the outer surface elements of the body, and the distance from the outer to the evaporation surface are assumed equal in order of magnitude to the mean free path of the molecules. Boundary conditions are obtained for the gas dynamics equations in Euler form, making it possible to describe adequately the flow outside the Knudsen layer. The flow structure in this last is investigated as a function of the determining parameters.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 2, pp. 130–134, March–April, 1986.In conclusion I express my gratitude to V. S. Galkin and N. K. Makashev for their discussion of the results obtained.     

Stability of two-layer fluid flow

The problem of two-layer convective flow of viscous incompressible fluids in a horizontal channel with solid walls in the presence of evaporation is considered in the Oberbeck–Boussinesq approximation assuming that the interface is an undeformable thermocapillary surface and taking into account the Dufour effect in the upper layer which is a mixture of gas and liquid vapor. The effects of longitudinal temperature gradients at the boundaries of the channel and the thicknesses of the layer on the flow pattern and the evaporation rate are studied under conditions of specified gas flow and the absence of vapor flow on the upper boundary of the channel. It is shown that the long-wavelength asymptotics for the decrement is determined from the flow characteristics, the longwavelength perturbations occurring in the system decay monotonically, and the thermal instability mechanism is not potentially the most dangerous.     

Stability of two-layer fluid flows with evaporation at the interface

The problem of stability of two-layer (fluid-gas) flows with account of evaporation at the thermocapillary interface is studied under the condition of a fixed gas flow rate. In the upper gas-vapor layer, the Dufour effect is taken into account. A novel exact solution of the Navier–Stokes equations in the Boussinesq approximation is constructed. The effects of longitudinal temperature gradients, gravity, thicknesses of the gas and fluid layers, and the gas flow rate on the flow structure, the onset of recirculated flows near the interface, the evaporation rate, and the properties of characteristic disturbances are investigated.     

Spherical flow of a diatomic gas from an evaporating drop

The spherical expansion of gas from an evaporating drop is investigated on the basis of the numerical solution to a model kinetic equation for a gas with rotational degrees of freedom. Examples considered are the stationary evaporation of a drop with given temperature into the vacuum and evaporation of a drop into a gas-filled space under the condition of an energy balance on the drop surface.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 4, pp. 184–187, July–August, 1980.     

Calculation of coupled problem between temperature and phase transformation during gas quenching in high pressure

The gas quenching is a modern, effective processing technology. On the basis of nonlinear surface heat-transfer coefficient obtained by Cheng during the gas quenching, the coupled problem between temperature and phase transformation during gas quenching in high pressure was simulated by means of finite element method. In the numerical calculation, the thermal physical properties were treated as the functions of temperature and the volume fraction of phase constituents. In order to avoid effectual "oscillation" of the numerical solutions under smaller time step, the Norsette rational approximate method was used.     

Investigation of a hypersonic viscous shock layer on rotating axisymmetric bodies in the presence of blowing

The hypersonic flow of a laminar stream of viscous compressible gas past blunt axisyrametric bodies rotating about the longitudinal axis is considered. It is assumed that gas blows from the surface of the body. The solution of the problem is obtained by a finite-difference method in a wide range of Reynolds numbers and blowing and rotation parameters. Some results of the calculations characterizing the effect of the rotation on the velocity and temperature profiles across the shock layer, on the friction and heat transfer coefficients, and the shock wave separation are given for the neighborhood of the stagnation point. For large Reynolds numbers and strong blowing an analytic solution of the problem is found in an approximation of two inviscid layers separated by a contact surface. The calculations are made for the flow past a sphere and a paraboloid and it is shown that in the presence of rotation the maximum of the heat flux is shifted from the stagnation point onto the side surface of the body. The dependence of the pressure distribution, the heat flux, and the friction coefficient is investigated for cases of constant and variable blowing over the contour of the body.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 1, pp. 106–114, January–February, 1986.     

The Stefan problem of evaporation of a volatile component from a binary liquid mixture

The study is concerned with the Stefan problem of evaporation of a volatile component from its solution with a virtually non-volatile material. The analysis provides an analytical solution to the problem based on mass-transfer fundamentals. Results yield the evaporation rate, interfacial mole fractions, concentration profiles in the gas and liquid phases, and the location of the evaporation front. The analysis can be used to provide the binary liquid diffusion coefficient of the volatile component based on experimental data for the liquid–gas interface position as a function of time. The requirements for such a measurement are discussed in terms of the volatility of the evaporating component and its initial concentration in the liquid mixture. Fig. 1 Gas–liquid interface movement in a partially filled tube

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The influence of thermal expansion flow on droplet evaporation

It has been demonstrated recently that it follows from conservation of mass that unsteady temperature fields create flow in an incompressible fluid with a temperature-dependent density even in the absence of gravity. The paper studies the influence of thermal expansion flow on spherically symmetric evaporation of an isolated droplet. A model problem of a droplet evaporating at a constant rate is first considered. In this idealized situation one can use the assumption of a thin thermal boundary layer to solve analytically the unsteady moving-boundary heat conduction problem to find the temperature field inside the droplet both with and without the thermal expansion flow. Next evaporation of a fuel droplet in a diesel engine is studied numerically. The heat diffusion equation is solved in the liquid phase while the standard quasi-steady model is used for the gas phase. The results of the calculation show that for high ambient temperatures the influence of the thermal expansion flow on the droplet lifetime can be considerable.     

Evaporation from a surface and vapor flow through a plane channel into a vacuum

Two-dimensional steady rarefied-gas channel flow between two parallel walls, from an evaporating face to a perfectly absorbing plane end face, is studied. The vapor is considered to be a monatomic gas. The corresponding problem for the kinetic equation with collision integral in BGK form is formulated and solved numerically by two different finite-difference methods. Attention is focused on the calculation of the total gas flow rate through the channel cross-section. The structure of the gas channel flow as a function of the flow rarefaction, the channel length, and the ratio of the evaporation temperature to the wall temperature is studied.Moscow. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 1, pp. 150–158, January–February, 1996.     

Pore Network Simulation of Evaporation of a Binary Liquid from a Capillary Porous Medium

A pore-network model of evaporation of a binary liquid mixture into a ternary gas phase is developed. The model is applied to study the influence of surface tension gradients induced by composition variations of the liquid on the phase distribution within a capillary porous medium. Numerical simulations based on the proposed model show that the surface tension gradients lead to the accumulation of liquid near the open edge of the network. This surface tension gradient effect is only significant for weakly disordered porous media.     

Reflection of a sound wave by an evaporating surface

The reflection of a sound wave traveling through saturated vapor by the flat surface of the condensed phase is considered. It is shown that the intensity of the reflected wave is less than in the absence of evaporation and depends nonmonotonically on the angle of incidence, the position of the minimum being determined by the coefficient of condensation and independent of the viscous and heat conducting properties of the gas. The effect can be used to measure the condensation coefficient. The structure of the layers that arise near the surface is considered. A new type of acoustic flow with a velocity of the order of the amplitude of the speed of sound is found.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. A, 149–156, July–August, 1988.     

Spherical expansion of vapor during evaporation of a droplet

The problem of the evaporation of a spherical particle is solved by a numerical finnite-difference method for the stationary and nonstationary cases on the basis of the generalized Krook kinetic equation [1]. Evaporation into a vacuum and into a flooded space are considered taking into account the reduction in size and cooling of the droplet. The minimum mass outflow is determined for stationary evaporation into a vacuum at small Knudsen numbers. The results are compared with those of other authors for both the spherical and plane problems. Most previous studies have used different approximations which reduce either to linearizing the problem [2, 3] or to use of the Hertz-Knudsen equation [4]. The inaccurate procedure of matching free molecular and diffusive flows at some distance from the surface of the droplet [5] is completely unsuitable in the absence of a neutral gas. Equations for the rate of growth of a droplet in a slightly supercooled vapor were obtained in [6] from a solution of the ellipsoidal kinetic model by the method of (expansion of) moments.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 2, pp. 97–102, March–April, 1976.     

Evaporation of a solid into a vacuum

In this article the boundary conditions relating the values of the hydrodynamic variables in a rarefaction wave to the surface temperature are derived. The gas-kinetic problem of the motion of vapor in a thin layer directly adjacent to a phase boundary is solved approximately for this case. If the temperature of the surface is held constant by external radiation, the resulting solution makes it possible to compute the surface temperature, the velocity of the evaporation front, and the recoil momentum.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 3, pp. 163–165, May–June, 1976.In conclusion, the author thanks S. I. Anisimov for useful discussions.     

Asymptotic theory of the Boltzmann system,for a steady flow of a slightly rarefied gas with a finite Mach number: General theory

A steady rarefied gas flow with Mach number of the order of unity around a body or bodies is considered. The general behaviour of the gas for small Knudsen numbers is studied by asymptotic analysis of the boundary-value problem of the Boltzmann equation for a general domain. The effect of gas rarefaction (or Knudsen number) is expressed as a power series of the square root of the Knudsen number of the system. A series of fluid-dynamic type equations and their associated boundary conditions that determine the component functions of the expansion of the density, flow velocity, and temperature of the gas is obtained by the analysis. The equations up to the order of the square root of the Knudsen number do not contain non-Navier–Stokes stress and heat flow, which differs from the claim by Darrozes (in Rarefied Gas Dynamics, Academic Press, New York, 1969). The contributions up to this order, except in the Knudsen layer, are included in the system of the Navier–Stokes equations and the slip boundary conditions consisting of tangential velocity slip due to the shear of flow and temperature jump due to the temperature gradient normal to the boundary.     

Warm up of an automotive catalyst substrate by pulsating flow: a single channel modelling approach

Rapid warm up of an automotive catalyst substrate is important for early light off. This work considers the results from a model of warm up in a single channel. The mass flow is pulsating with high amplitude, about 75% of mean flow, but without flow reversal. The flow regime is laminar within the channel. Pulsations occur with frequency in the range 16–100 Hz, and are important in close-coupled systems where the catalyst is located near to the engine and where the rate of rise of gas inlet temperature with time is rapid, about 15 K/s. The use of a single channel model with conjugate heat transfer enables the heat transfer coefficient to be evaluated and compared with results from steady flow simulations. The value of the augmentation factor based on heat flux is found to be less than unity. The value of the augmentation factor based on heat transfer coefficient depends on the method for calculating the mean heat transfer coefficient, but is generally less than unity. The changes caused by pulsations will be small in practical systems. Changes in wall temperature found in the simulations are the result of the cumulative effect of changes in the mass flow rate.     

Strong recondensation in a one-component and a two-component rarefied gas for an arbitrary value of Knudsen number

As is known, surface phenomena such as evaporation, absorption, and reflection of molecules from the surface of a body depend strongly on its temperature [1–5]. This leads to the establishment of a flow of a substance between two surfaces maintained at different temperatures (recondensation). The phenomenon of recondensation was studied in kinetic theory comparatively long ago. However, up to the present, only the case of small mass flows in a onecomponent gas has been investigated completely [3,4]. Meanwhile it is clear that by the creation of appropriate conditions we can obtain considerable flows of the recondensing substance, so that the mass-transfer rate will be of the order of the molecular thermal velocity. Such a numerical solution of the problem with strong mass flows along the normal to the surface for small Knudsen numbers for a model Boltzmann kinetic equation was obtained in [7]. In this study we numerically solve the problem of strong recondensation between two infinite parallel plates over a wide range of Knudsen numbers for a one-component and a two-component gas, on the basis of the model Boltzmann kinetic equation [6] for a one-component gas and the model Boltzmann kinetic equation for a binary mixture in the form assumed by Hamel [8], for a ratio of the plate temperatures equal to ten. We also investigate the effect of the relative plate motion on the recondensation flow.Moscow. Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 5, pp. 130–138, September–October, 1972.     

Effect of a magnetic field on the flow in the vicinity of the stagnation point of a blunt body with ablation of a protective layer

During hypersonic flow around a blunt-nosed body, the gas which passes through the bow shock is heated to high temperatures, where dissociation, ionization, and inverse phenomena (recombination) take place in the gas. If an ionized gas moves in a magnetic field, the ponderomotive force which is set up changes the nature of its motion close to the stagnation point, decreasing the frictional stress and heat transfer at the wall (at the contact surface of the gas and the body about which the gas flows). In this case, the intense heat fluxes from the strongly heated gas to the body about which the gas flows cause phase changes in the surface of the body (melting, sublimation, etc.). These processes, in turn, affect the flow in the vicinity of the stagnation point due to realization of the heat of phase transition, the conduction of heat from the entrained mass, and the diffusion of evaporating material into the boundary layer. References [1, 2] are devoted to a study of the joint influence of the magneto-gasdynamic and ablation effects. The magnetogasdynamic layers and the wall profile of the external velocity (flow around wedges) are discussed in [1], and special cases of such boundary layers-flow close to the stagnation line (the two-dimensional case) and close to the stagnation point (the axisymmetric case) of a blunt body are considered in [2]. Melting and evaporation are taken into account by setting the longitudinal and the transverse velocity components at the wall not equal to zero-the first taking into account the flow of the molten material and the second pyrolysis of the vapor of the surface material into the gaseous boundary layer. However, the values of these components, also the enthalpy on the wall h_w(in[1, 2] h_W 0), are not known beforehand and must be determined from the boundary conditions at the wall which express the mass and heat balances. The general formulation of the problem given in the gasdynamics case by G. A. Triskii in [3, 4], and elsewhere includes a consideration of the boundary-layer equations in the gas, the boundary-layer equations in the melted zone, and the heat conductivity equations in the solid with boundary conditions at the outer edge of the boundary layer, on the gas-molten zone interface, on the molten zone-solid interface, and inside the solid. This approach to the problem can also be utilized in the magnetogasdynamic case, as it is in this article with certain simplifying assumptions as compared with [3, 4]. In this sense, the present article is an extension of the results of [3, 4] to the field of magnetogasdynamics.In conclusion, the author thanks K. A. Lur'e for proposing the subject and useful discussions.     

Numerical analysis of the effects of temperature and concentration jumps on transient evaporation of moderately large (0.01 ≲ Kn ≲ 0.3) droplets in non-isothermal multicomponent gaseous mixtures

In this study transient evaporation of a single moderately large (0.01 | Kn | 0.3) droplet in non-isothermal multicomponent gaseous mixture taking into account the effects of temperature and concentration jumps is investigated numerically. System of nonstationary nonlinear energy and mass conservation equations is solved using anelastic approximation. The performed analysis is pertinent to slow droplet evaporation when Mach number is much less then unity (Mԁ). Transport coefficients are calculated as functions of temperature and concentrations of the gaseous species. The dependence of the droplet surface temperature on time is taken into account. Comparison of numerical results obtained using models with different types of boundary conditions at the gas-liquid interface is performed. It is found that the effect of temperature and concentration jumps on the evaporation of moderately large droplet during warming-up period is significant when the temperature and vapor concentration at the droplet surface is relatively low. It is shown that in case of large concentrations at the droplet surface boundary conditions for concentration jump obtained from kinetic theory and those obtained from the Fick's law yield the same results. It is shown also that taking into account the kinetic effects results in a significant deviation from the D²-law.