Rarefied gas flow into a vacuum from a plane long channel closed at one end

The time-dependent problem of rarefied gas flow into a vacuum from a plane long channel closed at one end is solved on the basis of the kinetic S-model. The effect of diffuse molecular reflection from the channel walls on the flow velocity and the process of channel cavity vacuumization is studied as a function of the channel length and the extent of gas rarefaction under the condition that the wall temperature is maintained to be constant. The kinetic equation is solved numerically using a conservative finite-difference method of the second order of accuracy in spatial coordinates. The possibility of simplification of the problem for long times by means of reduction to the diffusion process is considered.     

Numerical investigation of rarefied diatomic gas flows through a plane channel into a vacuum

Rarefied flows through a plane microchannel into a vacuum are numerically investigated on the basis of the model kinetic equation for a diatonic gas (nitrogen). The dependence of the gas flow rate through the channel on the Knudsen number, the wall temperature, and the channel length is determined. The energy flux transferred to the cold diatomic gas from the hot channel walls is calculated. The results for diatomic and monatomic gases are compared.     

Two-dimensional nonstationary gas dissipation into a vacuum from a plane or axisymmetric channel

The nonstationary escape of an ideal polytropic gas from a plane or axisymmetric channel is investigated. It is hence assumed that the gas is initially at rest, and the diaphragm separating it from the vacuum can be at any section of the channel.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 1, pp. 76–83, January–February, 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.     

Rarefied hypersonic flow in a plane channel with a surface glow discharge

The gasdynamic structure of a hypersonic molecular nitrogen flow in a plane channel whose opposite surfaces are segmented electrodes for generating a continuous surface glow discharge is investigated using a two-dimensional computational model. The electrodynamic structure of the surface glow discharge in the hypersonic rarefied gas flow (distributions of the charged particle concentrations, current density, and electric potential) is studied. A two-dimensional conjugate electrical-gasdynamic model consisting of the continuity, Navier-Stokes, and energy conservation equations and the chargedparticle continuity equations in the ambipolar approximation is proposed. The real thermophysical and transport properties of molecular nitrogen are taken into account. It is shown that using a surface glow discharge in a hypersonic rarefied gas flow makes it possible effectively to modify the shock-wave flow structure and hence to consider this type of discharge as additional tool for controlling rarefied gas flows.     

Translational nonequilibrium of a gas flow into vacuum in a constant-section channel

A single-species gas flow into vacuum in a constant-section channel is computed by means of the Direct Simulation Monte Carlo method. It is shown that the longitudinal, transverse, and total kinetic temperatures are significantly different in the head part of the flow, which is a consequence of the arising translational nonequilibrium. The flow is almost self-similar in the entire region of flow expansion (except for distributions of the transverse and total kinetic temperatures in the head part of the gas flow), which allows one to predict flow parameters at times greater than those used in simulations. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 47, No. 4, pp. 54–59, July–August, 2006.     

A numerical study of riblet effects on laminar flow through a plane channel

Numerical computations are reported of fully-developed flow through plane channels with knife-edge riblets. The study has covered riblet height: spacing ratios from 0.5 to 3 and riblet heights ranging from 0.1%–4.0% of the distance between the channel walls. In no case did results indicate a reduction in drag compared with the case of a smooth channel, a result that is in contrast with earlier studies. It is suggested that apparent drag reductions reported earlier in laminar flow may have arisen from the use of an insufficiently fine grid.     

Evaporation of polydispersed droplets in a highly turbulent channel flow

A model experiment for the study of evaporating turbulent two-phase flows is presented here. The study focuses on a situation where pre-atomized and dispersed droplets vaporize and mix in a heated turbulent flow. The test bench consists in a channel flow with characteristics of homogeneous and isotropic turbulence where fluctuations levels reach very high values (25% in the established zone). An ultrasonic atomizer allows the injection of a mist of small droplets of acetone in the carrier flow. The large range diameters ensure that every kind of droplet behavior with regards to turbulence is possible. Instantaneous concentration fields of the vaporized phase are extracted from fluorescent images (PLIF) of the two phase flow. The evolution of the mixing of the acetone vapor is analyzed for two different liquid mass loadings. Despite the high turbulence levels, concentration fluctuations remain significant, indicating that air and acetone vapor are not fully mixed far from the injector.     

Developed turbulent flow in a plane channel with simultaneous injection through one porous wall and suction through the other

Results of a numerical-theoretical study of a developed turbulent flow of an incompressible fluid in a plane channel with simultaneous injection of mass through one porous wall and suction of the same mass through the other are presented. The system of equations of averaged motion is closed using a turbulent-stress model. The calculated data of the mean and fluctuational characteristics are in reasonable agreement with experimental results for two values of the Reynolds number of the main flow (Re=10,400 and34,000). Al-Farabi Kazakh National State University, Almaty 480121. Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 39, No. 1, pp. 61–68, January–February, 1998.     

Slow two-phase flow through a sinusoidal channel

The two-phase flow through a symmetric sinusoidal channel is studied by means of a regular perturbation analysis, where the small parameter is defined as the ratio between the amplitude of variation of the channel wall and the average thickness of the non-wetting phase. Results are valid for Reynolds numbers of the same order of magnitude as that of the expansion parameter. It is thus found that the fluid-fluid interface presents a wavy shape characterized by an amplitude and a phase-shift with respect to the fixed solid-fluid interface. Instabilities of the two-phase flow can arise for large values of the viscosity, flow rate and phase thickness ratios. Results are expected to be a first step towards the understanding of the hydrodynamics of trickle bed reactors, where several flow regimes are possible.     

Nonsteady-state nonisothermal flow of a magnetic liquid in a plane channel

Magnetic liquids are finding wider and wider use in various fields of technology [1]. Such liquids can be used as heat exchange fluids in equipment which generates a magnetic field under conditions of weightlessness [2] and in a number of other applications. The efficiency of heat exchange equipment is determined to a significant degree by the temperature of the magnetic liquid. In connection with this fact, it is of interest to examine nonisothermal flows at a temperature near the Curie point, where the dependence of volume magnetization M on temperature is expressed most clearly. In this case the character of the liquid flow will be affected not only by the dependence of saturation volume magnetization on temperature, but also by temperature inhomogeneity caused by development of external heat sources and sinks produced by the magnetocaloric effect. We note that although this is a weak effect [3], the temperature redistribution over channel section which it produces may be significant. With a high gradient in the external magnetic field H even a small change in temperature can significantly change the force acting on a magnetic liquid element. The unique features of magnetic liquid flow at a temperature close to the Curie point can be investigated by simultaneously solving the equations of motion and thermal conductivity.Translated from Zhurnal Prikladnoi Mekhaniki i Technicheskoi Fiziki, No. 1, pp. 93–96, January–February, 1984.The author expresses his gratitude to the participants in K. B. Pavlov's scientific seminar for their evaluation of the study.     

Steady two-dimensional merging flow from two channels into a single channel

Two-dimensional steady symmetric merging flow from two channels into a single one is investigated. The geometry of the configuration has been chosen such that it can be mapped conformally onto a rectangular geometry, thus facilitating the numerical solution procedure for the governing Navier-Stokes equations. Computed velocity profiles and streamline patterns are presented in graphical form. Furthermore, results concerning the inlet length are given.     

Heat and mass transfer associated with low-velocity vapor flow in the plane channel of a thermal protection system of the radiative-evaporative type

A self-similar solution describing the heat and mass transfer processes associated with radiative-conductive heat exchange between the walls of a plane channel and evaporation from one of the walls is obtained. It is assumed that the medium is optically transparent and that the geometric parameters of the channel and the values of the heat flux and vapor pressure are such that the characteristic Mach number of the flow M₀ satisfies the condition M ₀ ² 1.Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No.6, pp. 22–28, November–December, 1992.     

Lateral migration of a capsule in a plane Poiseuille flow in a channel

Three-dimensional numerical simulation is presented on the motion of a deformable capsule undergoing large deformation in a plane Poiseuille flow in a channel at small inertia. The capsule is modeled as a liquid drop surrounded by an elastic membrane which follows neo-Hookean law. The numerical methodology is based on a mixed finite-difference/Fourier transform method for the flow solver and a front-tracking method for the deformable interface. The methodology can address large deformation of a capsule over a wide range of capsule-to-medium viscosity ratio. An extensive validation of the methodology is presented on capsule deformation in linear shear flow and compared with the boundary-element/integral simulations. Motion of a capsule in wall-bounded parabolic flow is simulated over an extended period of time to consider both transient and steady-state motion. Lateral migration of the capsule towards the centerline of the channel is observed. Results are presented over a range of capillary number, viscosity ratio, capsule-to-channel size ratio, and lateral location. After an initial transient phase during which the capsule deforms very quickly, the flow of the capsule is observed to be a quasi-steady process irrespective of capillary number (Ca)$(\mathit{Ca})$, capsule-to-channel size ratio (a/H)$(a/H)$, and viscosity ratio (λ)$(\lambda )$. Migration velocity and capsule deformation are observed to increase with increasing Ca$\mathit{Ca}$ and a/H$a/H$, but decrease with increasing λ$\lambda$, and increasing distance from the wall. Numerical results on the capsule migration are compared with the analytical results for liquid drops, and capsules with Hookean membrane which are valid in the limit of small deformation. Unlike the prediction for liquid drops, capsules are observed to migrate toward the centerline for 0.2?λ?5$0.2?\lambda ?5$ range considered here. The migration velocity is observed to depend linearly on (a/H)³$(a/H{)}^3$, in agreement with the small-deformation theory, but non-linearly on Ca$\mathit{Ca}$ and the distance from the wall, in violation of the theory. Using the present numerical results and the analytical results, we present a correlation that can reasonably predict migration velocity of a capsule for moderate values of a/H$a/H$ and Ca$\mathit{Ca}$.