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The problem of ice formation in unsaturated soil in the presence of pressure gradient and capillary forces is formulated. The complete system of conditions on the crystallization surface is derived. The one-dimensional problem is investigated in the self-similar formulation. The dependence of the amount of the ice formed on the problem parameters is also investigated. It is found that the ice saturation increases as the pressure on the cooling wall that initiates water inflow to the front decreases and also in the regime of more intense cooling. Increase in the pressure leads to water outflow from the front and decrease in the ice saturation.

The steady laminar flow of an incompressible power-law fluid in a plane T-shaped channel is studied at given pressure differences between the inflow and outflow sections. A non-Newtonian fluid, whose rheological behavior is governed by the Ostwald—de Waele law is called the power-law fluid. The mathematical formulation of the problem includes the equations of motion and continuity. The no-slip condition is imposed on solid walls. The problem solution is obtained using a finite-difference method invoking the SIMPLE procedure. A parametric investigation of the kinematic and dynamic flow parameters is carried out for different values of the relevant parameters of the problem. The flow regime map is constructed for different pressure differences between the inflow and outflow boundaries and different nonlinearity exponents of the rheological model.

The unsteady two-dimensional problem of the reflection of a uniform supersonic rarefied-gas flow incident normal on a wall with an orifice and the gas outflow through the orifice (slot or channel) is solved on the basis of the kinetic S-model. The slot influence on the reflection nature, the velocity of the shock wave reflected from the wall, and the formation of a gas jet flowing out into a vacuum is studied as a function of the incident flow velocity, the gas rarefaction degree, and the conditions imposed on the wall. The effect of the wall thickness, that is, the length of the channel, through which the gas flows out, is also investigated. The gas flow rate through the orifice is calculated as the main integral characteristic. The attainment of steady reflection regime in the outflow process is traced. The kinetic equation is solved numerically using the conservative difference method of the second order with respect to all variables.

The problem of the generation of cavitation self-oscillations in a liquid flow in a pipe with two resistances is considered. The first resistance is a cavitator, behind which there is an artificial ventilated cavity, where the mean pressure is greater than the atmospheric pressure, while the liquid and gas outflow into the atmosphere takes place through the second resistance. Investigations show that the self-oscillation frequencies are chiefly determined by the cavity properties and the conditions of the outflow into the atmosphere. The generation of different self-oscillation modes is directly associated with the number of waves formed along the cavity length. It is shown that the pressure pipeline properties and the cavity volume have an effect on the cavitation self-oscillation mode (up to four frequency modes can be observable at the same geometry and hydraulic flow parameters). The question arises of whether the self-oscillations can be used for generating pulsed jets at the outlet. It seems that it is the first mode regime that is most suitable for producing the pulsed jets, since in this case the pressure fluctuations in the cavity are maximum. Using the exponential Voitsekhovskii nozzle the regimes, in which an intermittent jet flow of the liquid is realized at the outlet, are experimentally obtained.

Asymptotic methods are applied to study a plane turbulent jet of a viscous incompressible fluid flowing out through a narrow slot into a space filled with a fluid. The complete Navier—Stokes equations are considered. The characteristic Reynolds number is assumed to be large, while the jet thickness is small. In analyzing the problem the method of many scales is used, which makes it possible to determine and investigate a steady secondary flow within the turbulent jet. The secondary steady solutions are analytically obtained for the normal and longitudinal velocity components and the pressure. It is shown that the self-induced fluid outflow of the jet core toward the jet periphery is the main secondary flow ensuring the supply of the kinetic energy from a maximum velocity zone into the turbulence production zone. The solutions obtained are in good agreement with the available experimental data.

The outflow of a cold supersonic off-design jet with the nozzle pressure ratio of 21.8 is calculated using the high-resolution RANS/ILES method. For the nozzle under consideration and at the given nozzle pressure ratio the exit-to-ambient pressure ratio is 0.6. The jet is characterized by a long supersonic region with many “barrels.” The calculations are validated against the experimental data. The fluctuating and acoustic characteristics of the jet flow under consideration are compared with the characteristics of other supersonic jets. The geometric dimensions of the barrels and the acoustic properties of the jet are estimated from the known empirical relations for supersonic jets.

The solutions of initial and boundary value problems of the outflow of an ideal (inviscid and non-heat-conducting) gas from cylindrical and spherical sources into a vacuum are obtained. Time is measured from the moment, when the source is turned on; at this moment the source is surrounded by a vacuum. The entropy, flow rate, and the Mach number of the gas outflowing from the source are given, together with the source radius; the Mach number can be greater of or equal to unity. If the source radius is greater than zero, then the flow domain in the “radial coordinate–time” plane consists of the stationary source flow and adjoining non-self-similar centered expansion wave consisting of C−-characteristics. The stationary flow is described by the known formulas, while the expansion wave is calculated by the method of characteristics. The calculations by this method confirm the earlier obtained laws for large values of the radial coordinate. The interface between the vacuum and the expansion wave is the straight trajectory of particles and, at the same time, a unique rectilinear C−-characteristic. For the source of zero radius (“pointwise” source) the velocity, density, and speed of sound of the outflowing gas are infinite. The gas velocity remains infinite everywhere, while the density and speed of sound become zero for any non-zero values of the radial coordinate. For the pointwise source the problem of outflow into a vacuum is self-similar. In the plane of the “self-similar” velocity and speed of sound its solution is given by three singular points of a differential equation in these variables. At one of these points the self-similar velocity is infinite, the self-similar speed of sound is zero, and the self-similar independent variable varies from zero to infinity, with the exception of the extreme values.

The results of calculations of water vapor outflow from a source, in which the pressure and temperature are maintained constant, into a vacuum through an orifice in the infinitely thin wall are presented. The calculations are carried out using the direct simulation Monte Carlo method when the processes of water cluster formation/decay in the flow field are taken into account. The vapor flow regimes transient with respect to the Knudsen number are considered. The effect of the cluster formation processes on the parameters of flow which becomes significant for the mole cluster fraction above 4%is analyzed. The effect of “freezing” the mole cluster concentrations with increase in the distance from the source is demonstrated. The influence of the probabilities of monomer and dimer association during pair collisions, used in the model, on themole dimer fraction is investigated. The results obtained are compared with the available experimental data.

The results of an experimental investigation of the gasdynamic structure of supersonic underexpanded air jets flowing out of a sonic nozzle into a low-pressure medium are presented. This setting of the experimentmakes it possible to achieve high values of the nozzle-to-ambient pressure ratio at moderate outflow Reynolds numbers characteristic of underexpanded jets issuing from micronozzles. The data on the supersonic core length, the laminar-turbulent transition location, and the jet flow characteristics are obtained. The results are compared with those obtained in microjets flowing out of sonic nozzles. Emphasis is placed on the earlier discovered effect of inverse transition of a turbulent jet into the laminar flow regime with increase in the Reynolds number.

The unsteady outflow of a warm dense boiling compressiblemedium, initially at rest, from a plane layer, a cylinder, and a sphere into a vacuumis investigated in the approximation of an inviscid and non-heat-conducting two-parameter “gas-liquid”, whose thermodynamic properties are determined by the Van der Vaals equation of state. The expansion, the boiling, and the two-phase medium generation are assumed to be thermodynamically equilibrium, while the transition is instantaneous. The speed of sound suffers a discontinuity across the phase transition line of the second kind (binodal), whereas the pressure, the temperature, the density, the entropy, and the enthalpy remain continuous. The main issue in the thermodynamic calculations, which are the same for all the problems, is the construction of the binodal and, at the same time, an isentrope in an equilibrium two-phase mixture, reduced to the numerical integration of two ordinary differential equations. The one-dimensional problems of unsteady outflow are solved by means of the method of characteristics using the isentropes obtained in the thermodynamic calculations. As distinct from the plane problem, in the cylindrically and spherically symmetric problems there are no regions of homogeneous boiling liquid, which would be finite in space and time.

The process of precipitate formation during vapor outflow from a high-temperature geothermal reservoir saturated with a salt solution is investigated numerically. The evaporation regimes characterized by the formation of a phase transition front are considered. Comparison with the asymptotic solution obtained previously is performed. In the region of parameters where the self-similar solution exists the numerical solution approaches the asymptotic one in a short time. In the region where the asymptotic solution does not exist the numerical solution shows that the solid salt saturation monotonically increases with catastrophic growth in the last stage, which leads to the filling of the pores with solid salt and the total blocking of the flow.

After publication of the paper, the authors realized that the affiliation of the fourth author (Tiberiu Esanu) was given incorrectly. Its correct version appears above. Moreover, a second funding grant was missed in the acknowledgements. We give their complete correct version below.

The problem of the shape of an annular charged jet in an external electric field is considered. In the strong-field approximation, the formulation of the problem is reduced to a system of ordinary differential equations. The asymptotics of the solutions at large distances from the point of outflow are investigated. The condition of formation of the jet profile non-increasing along the streamwise coordinate is found.

The results of an investigation of the unsteady flow structure in a turbulent swirling jet obtained using the PIV technology are presented. The greater part of the measurements is carried out at the swirl intensity W 0 ≈ 1.7. A part of the data is obtained under other conditions of the swirl jet outflow. To establish the relation between disturbances of different types the phase averaging technique is employed with the pressure fluctuation in the acoustic field of the jet taken as a reference signal. The flow structure is numerically calculated. The results of the investigation show that a quasisteady inhomogeneity observable in the jet flow executes rotational motion relative to the mean flowfield in the jet cross-section, or “precession”. It causes disturbances in the flow ejected by the jet, which transform into acoustic disturbances far away from the jet. The frequencies of the dynamic disturbances near the jet and the acoustic disturbances far away from it coincide with the precession frequency.

The results of an experimental investigation of the self-oscillation regimes of liquid jet outflow into a plane channel with air injection in its dead end are presented. The effect of the volume of the cavity, or the air cushion, and its thickness (or channel width) on the flow is studied on a wide range of the gas injection rate and the liquid outflow velocity. The self-oscillation flow regimes are realized at a constant pressure of water in the supply tank and a constant mass flow rate of the air injected into the cushion. With increase in the air injection rate the self-oscillation regime realized at lower injection intensities is replaced by a higher-frequency regime. High-speed videofilming shows that the difference from the low-frequency regime consists in the absence of the direct interaction between the out flowing jet and the channel wall. It is found that in both low-frequency and high-frequency regimes the self-oscillation frequency and amplitude are independent of the cushion thickness but the moment of the regime changeover is determined by this parameter. It is established that there exists a threshold value of the cavity volume, behind which the low-frequency regime does not occur at any air injection rates.

The problem of steady outflow of rarefied gas from a reservoir into vacuum through a long cylindrical tube of circular cross-section at a constant temperature is considered on the basis of the kinetic S-model. The kinetic equation is solved numerically using a conservative second-order method. The basic calculated quantity is the gas flow rate through the channel; the flowfields are also studied. The solutions obtained are compared with the known results.

Steady monatomic and diatomic gas flows from a spherical source into a vacuum in a gravitational field are studied using direct statistical simulation. The qualitative gravitation effect on the flow is shown to be independent of the intermolecular collision model. Three characteristic Jeans parameter ranges can always be distinguished, namely, the subcritical range, on which the flow in a weak gravitational field is similar with the outflow in the absence of gravitation, the supercritical range, on which the outflow velocity remains small even at large distances from the source, and a narrow transitional range between the two former ranges. The presence of internal degrees of freedom of gas molecules displaces the transitional range toward the greater values of the Jeans parameter and leads to an increase in the outflow velocity and the gas temperature; however, in the initial region the latter effect is expressed only slightly. The normalized escape flow is a nonmonotonic function of both the Jeans parameter and the Knudsen number and is different for monatomic and diatomic gases within 50% on the parameter range considered.

The results of an experimental investigation of self-oscillatory jet outflow into a plane channel with air injection in its dead-ended part are presented. It is found that at fixed channel geometry and water supply system the main flow parameters depend on the air injection rate and the relative cavity volume. It is shown that with increase in the gas injection at a fixed cavity volume the self-oscillation intensity monotonically increases and the oscillations considerably change in nature, whereas the Strouhal number varies only slightly. At a fixed air injection coefficient the self-oscillation amplitude decreases with increase in the cavity volume and the self-oscillations stop at a certain threshold value. The flow pattern evolution with increase in the injection coefficient is studied in detail using high-speed filming. The developed surge flow pattern is described in detail.

The instability of supersonic underexpanded submerged air jet outflow from a nozzle with a central cone in the form of two convergent interlaced spirals is described. A technique for controlling this structure by means of extending the central cone streamwise is proposed. It is shown that the central cone position makes it possible to control the gas outflow and to go over from the Mach reflection regime to the regime of wave spiral and gaseous phase condensation, which before were not observable. The results of the measurements of the dynamic head of jets issuing from the nozzle with and without the central cone are presented.

The results of a numerical simulation of slow free-boundary viscous-fluid outflow from a vessel are presented with account for jet formation. The problem is formulated in the creeping motion approximation. For solving the problem, a numerical algorithm for plane geometry, based on an indirect variant of the boundary-element method, is used. As a result of parametric studies, the evolution of the free surface inside the vessel and the jet shape is determined for different values of the governing parameters. Flow regimes with rapid funneling and film formation on the vessel walls are detected. The existence of an asymptotic flow regime is demonstrated using dimensional analysis and confirmed by calculation.

The process of inflow of an oil-bearing fluid from an infinite region of porous soil into a cavity (reservoir) and its subsequent pumping into a well located at the center of the reservoir is investigated. The cavity is chosen from the class of flattened ellipsoids of revolution. Thus, a combined problem of the optimization of the shape of a cavity of given volume for which the maximum seepage flow is achieved and the approximate determination of the additional constraints on the cavity dimensions necessary to ensure the outflow of the oil-bearing fluid is considered.

The process of funnel formation during unsteady outflow of initially still water under gravity through one or two circular holes in the bottom of a prismatic vessel rectangular in plan is analyzed experimentally and numerically. The process is studied for various locations of the sinkholes, for vessel bottoms and walls with areas that differ in roughness, and for several values of the initial water depth h0. A sufficient, but not necessary, condition for the absence of vortex funnels is formulated. On the basis of a method proposed for determining the fluid rotation direction in vortex funnels, regions are found such that above sinkholes located in them vortex funnels with a given rotation direction are formed, as well as lines such that for sinkhole centers positioned on them stable vortex funnels are not formed. These results are confirmed by numerical calculations and experiments. At different times t the structure of the circumferential velocity field in the sinkhole cross-section is investigated. In the sinkhole crosssection, at several levels above it, and in the outflowing jet the dependence of the integral moment of the circumferential velocities on time and the initial depth is found. The time dependences of the flow-rate characteristics (flow-rate coefficient and volume flow-rate) are obtained for various initial depths and compared with results known in hydraulics. On the range of determining parameters investigated it is established that the fluid depth in the vessel at which a vortex funnel begins to be formed is independent of the initial water depth. The numerical calculations were carried out using STAR-CD software (license of the Institute of Mechanics of Moscow State University) tested in experiments on water outflow from prismatic vessels circular and rectangular in plan.

The equations of long nonlinear waves in round jets and channels of arbitrary cross section are considered with account for the transverse acceleration of the fluid particles (Boussinesq approximation). In the general case of steady flows, the equations in the form of shallow water equations with the pressure expressed in terms of the variational derivative of the kinetic energy of a thin transverse fluid layer, have three first integrals with three arbitrary constants. Examples of solutions of the equations for solitary capillary-gravitation waves in rectangular and triangular channels are presented and compared with the higher approximations. The shape of the free boundary of the round jet is determined. In the case of outflow from a conical nozzle an analytical dependence of the jet contraction ratio on the conicity angle is obtained. The dependence is in agreement with the experimental data for angles of less than 45°.

The main features of the unsteady outflow of a fluid from a cylindrical vessel rotating together with it at a constant angular velocity through a central drain hole in the bottom are studied. The software package STAR-CD tested on the results of experiments with water in the absence of rotation is used. Certain important features of the phenomenon under consideration related with the formation of vortex funnels in the fluid are established. The effect of the main control parameters of the problem, namely, angular velocity, viscosity, initial depth, etc., is analyzed.

The problem of interaction between the intraocular pressure and the hydrodynamic processes in the eye is investigated. A lumped-parameter model taking into account a wide range of physically permissible mechanisms of the inflow and outflow of intraocular fluid is proposed. In the cases of stationary and nonstationary flow regimes, the consequences of various assumptions are analyzed. The flow in the presence of an external load is considered. It is shown that the physical interpretation of measurements used in ophthalmology strongly depends on the hypotheses adopted, the choice between which needs further investigation.

It is shown that the core of a swirled helical flow can be described using a novel exact nonstationary solution of the hydrodynamic equations for a viscous incompressible fluid, which generalizes the rigid-body asymptotics for the Burgers and Sullivan vortices in the form of rigid-body rotation with a finite helicity. An estimate of the pressure fluctuations corresponding to this nonstationary vortex regime, which is proportional to the frequency of the swirled-jet core rotation as a rigid body and also depends on the parameters of the initial velocity field structure, is obtained. It is noted that this frequency may correspond to the frequency observed in the pressure fluctuation spectrum, which is almost proportional to the swirled flow rate in vortex acoustic emitters.

The effect of the sinkhole position on the formation of nonstationary vortex funnels during fluid outflow from a tank whose diameter is much greater than the sinkhole diameter is studied experimentally. The devices for filling the tank were so designed that the opening of a sinkhole on the axis of a cylindrical tank immediately after it had been filled did not lead to the formation of a vortex funnel during fluid outflow. The formation of vortex funnels, when before the sinkhole was opened a disk immersed in the fluid was rotated, is investigated. In this case, a certain time after the outflow started, above the sinkhole a vortex funnel was formed. This time measured by means of digital filming depended on the sinkhole position and increased with the distance between the sinkhole and the axis. The results obtained make it possible to conclude that the symmetry strongly affects the process of vortex funnel formation.

The variation of the flow-rate of a fluid flowing out of a prefilled cylindrical vessel through sinkholes with a diameter less than 0.1 of the vessel diameter has been studied experimentally. The study was carried out in both the presence and the absence of a vortex funnel around the sinkhole. In these experiments the vessel was filled in such a way that a funnel was formed only when a disk immersed in the fluid was rotated before the sinkhole was opened. The time dependence of the flow-rate is found for various initial heights and rates of artificial swirl. Four different outflow stages were detected. It is shown that for certain flow parameters there is a time interval on which the fluid flow-rate is independent of the column height. A critical rotation velocity W 0* below which (W 0 < W 0*) an intense funnel is not formed is found. A limiting curve approached by all the flow-rate curves in the final stage of outflow is obtained.

Quantitative results for the thrust and flow-rate performance of axisymmetric nozzles in highly overexpanded regimes are presented. Estimates for the lateral component of the reactive force and its range of possible existence are obtained for axisymmetric nozzles differing in the divergent region geometry. Empirical formulas for the gas flow rate in the subcritical outflow regime and the pressure range on which this regime can take place are proposed.

The results of a numerical simulation of the three-dimensional outflow of a system of circular supersonic turbulent jets into a cocurrent supersonic (or subsonic) air flow in a partially bounded region are given. Solutions are obtained by the splitting method using a matrix sweep of the parabolized Navier-Stokes equations. Assuming that the flow is nonseparated in the boundary layer, features of the three-dimensional structure of the jet system are investigated as functions of the pressure ratio number and the jet and cocurrent flow Mach numbers.

The problem of steady viscous flow in a convergent channel is analyzed analytically and numerically for small, moderately large and asymptotically large Reynolds numbers over the entire range of allowed convergence angles. Attention is focused on regularly extendable problem solutions, for which purpose a high-accuracy hybrid numerical-analytical method of accelerated convergence and extension in a parameter is developed. For sufficiently large angles, the existence of tri-modal regimes symmetrical about the bisectrix and containing in- and outflow regions is established. The evolution of the velocity profiles with unbounded increase in the Reynolds number is investigated. Flow regimes for the critical convergence angle, which cannot be regularly extended in the parameter, are also studied. Several novel hydromechanical effects are noted.

Using the numerical method of direct statistical simulation (Monte-Carlo method), the effect of the intermolecular potential exponent on the dependence of the stress and the heat flux on the stress rate tensor components and the temperature gradient is analyzed for the nonequilibrium, spherically symmetric outflow of a monatomic gas into a vacuum. Analytical approximations of the constitutive relations are presented. The dependence of the macroscopic parameters on the distance from the source is found.

The effect of accumulation of reversible strains on the pressure head is analyzed theoretically for elastic and viscoelastic liquid flow from convergent channels. It is shown that, depending on the rheological features of the liquids, the pressure head can both increase and decrease as compared with the pressure determined by the Bernoulli formula. In particular, a situation in which a liquid flows out without any pressure head applied (paradox of “self-outflow”) is possible within the framework of the model. Transition to different viscoelastic liquid flow regimes as a function of the constitutive parameters is considered with reference to a channel with a sharp bottleneck (abrupt decrease in the cross-section).

On the basis of the method of matched asymptotic expansions, the problem of the outflow of a nonswirling axisymmetric laminar jet from a hole in a plane is solved for large Reynolds numbers. Since directly matching the leading terms of the asymptotic expansions for the axial boundary layer and the main flow region is impossible, the problem is solved by introducing an intermediate region. In the axial region the solution is the Schlichting solution [1] for an axisymmetric jet in the boundary-layer approximation, in the intermediate region the solution is found analytically, and in the main flow region the problem is reduced to that of viscous flow induced by a sink line in the presence of a transverse wall [2].

The transport processes in the nonequilibrium outflow of a monatomic gas into a vacuum are investigated using direct numerical statistical simulation. The quantitative dependence of the macroscopic parameters, such as the density, velocity, temperature, stress, and heat flux, on the distance from the source is determined. In the case of a gasdynamic source the dependence of the stress and the heat flux on the strain rate tensor components and the temperature gradient is established. The applicability range of the well-known hypersonic approximation is determined.

The variational problem of optimizing the energy supplied to the discharge channel of a pulsed water jet in order to maximize the mean jet outflow velocity is considered. The problem is solved in the gasdynamic formulation using the general method of indefinite Lagrange multipliers. The optimality conditions are derived by considering the smeared flow. Both the direct and conjugate problems are solved by the shock-capturing method. An example of the calculation is presented.

Transonic isentropic imperfect gas flows* were investigated in the one-dimensional formulation in [2–5]. The problem of the transonic outflow of a jet of thermally perfect gas with equilibrium excitation of the vibrational degrees of freedom of the molecules (calorically imperfect gas) was investigated in the two-dimensional formulation in [6]. Below the problem of the transonic outflow of a real (thermally and calorically imperfect) gas from a vessel with plane walls is considered. A method of solution is proposed. Calculation results characterizing the effect of the angle between the walls and the stagnation parameters on the transonic outflow of air are presented.

Below, a flow model and a method of calculating the flow in a narrow plane channel of finite length in the presence of evaporation or sublimation on one wall induced by radiative-conductive heat transfer from the other hot wall are proposed. The Prandtl approximation is employed. The pressure difference between the center and the exit section of the channel is of the order of the characteristic value of the pressure in it. Subcritical and critical vapor outflow regimes are considered. The effect of the problem parameters on the evaporation rate and pressure distributions in the channel is investigated numerically.

The article discusses the outflow of a nonviscous gas from a strongly unexpanded supersonic nozzle into a supersonic wake. Under the assumption that the radius of the outlet cross section of the nozzle is negligibly small in comparison with the characteristic dimensions of the jet, expressions are obtained for the transverse and longitudinal dimensions of the jet, as well as similarity criteria determining the dimensionless gasdynamic functions. The satisfaction of the similarity criteria was verified by comparison with numerical calculations. Similarity with the outflow of strongly unexpanded jets was discussed in [1–3], where, specifically, the characteristic dimension of the flow was determined. In [4] it was demonstrated that the experimentally observed structure of the jet can be best described with the introduction of two characteristic dimensions, longitudinal and transverse. The effective construction of these two characteristic dimensions for the case of nonviscous outflow into a flooded space was carried out in [5], in which it was shown that using the longitudinal and transverse dimensions the geometries of the flow and the gasdynamic parameters are found to depend on the adiabatic index of the outflowing gas and on a parameter formed from the integral characteristics of the nozzle. The present work is a generalization of the results of [5] for the outflow of a jet into a hypersonic wake.

The presence of circulation in an outflowing gas leads to a change in the working parameters of a nozzle. The question of the mass flow rate and the draft of a nozzle without a diffusor (a point) for twisted flows has been studied theoretically and experimentally [1–6]. The use of nozzles with a supersonic part introduces a considerable degree of complication into the method for the analytical calculation of the draft characteristics and the program for their experimental investigation. In [2, 7], a theory of a nozzle is formulated for a model of a potential circulating flow of gas; in [5, 8], an electronic computer was used to solve the complete system of the equations of gasdynamics for the motion of a rotating flow along a nozzle; in [7, 9], an investigation was made of a variational problem of the shaping of a diffusor for a circulation flow. The calculation of the draft, carried out in the above-mentioned communications (with the exception of [2], in which a study was made of a partial model of an eddyless rotational motion), is bound up with labor-consuming computer calculations. In the present article, in a development of [3, 6], a quasi-one-dimensional theory of a supersonic nozzle for a vortical flow of gas is formulated and verified experimentally.

In [1–3], a class of self-similar solutions was considered for the flow of incompressible fluid in a plane channel with porous walls, through which there is homogeneous symmetric inflow or outflow. An analogous class of self-similar solutions for flow between porous disks with natural homogeneous conditions at the periphery was considered in [4], where the asymptotic behavior of these solutions at a small Reynolds number of the outflow R was investigated, and the limiting form of the solution for symmetric outflow with R=∞ was noted. In the present paper, the boundary-function method is applied to the singular problem corresponding to the flow between porous disks for asymmetric inflow and outflow characterized by large R.

The process of forming of a fiber can be represented in a simplified manner as the outflow of a solution or melt of a polymer injected by a certain pressure device from a convergent nozzle (a draw plate) with the subsequent coiling of the jet formed at the exit (the filament) onto a drum rotating at constant velocity. The coupled nature of the problem, i.e., the presence of a back reaction of the fiber on the conditions of outflow of the liquid from the draw plate, is fundamental for the forming. The working solutions are usually viscoelastic liquids, capable of the accumulation of significant reversible deformations. It is well known that this leads to the appearance of specific instabilities of the flow which restrict the productivity of the forming. At present there is no hydrodynamic theory capable of explaining the occurrence of these instabilities without using additional hypotheses. In the present paper an attempt is made to construct a hydrodynamic theory of the process of forming as a coupled flow of viscoelastic liquid in a pressure-device-nozzle-fiber system, in a one-dimensional (hydraulic) approximation. Such an approach makes it possible to carry out a detailed analysis and to obtain reasonably transparent results. It is fully justified at present, when the imperfection of rheological models and methods of hydrodynamic calculation of flows of elastic fluids does not give reason to hope for the serious development of a two-dimensional description. Analysis of the coupled problem leads, in particular, to the conclusion that the appearance of a falling section of the flow characteristic of the nozzle and the auto-oscillatory conditions of formation due to this are possible. The question of the identification of this instability with the experimentally observed instability of the process of forming remains open.

The flow structure for which the Karman hypothesis is valid is explored experimentally and theoretically. It is established that there exists not a point but a region of finite size, adjacent to the upper generator of the tube and including the moving line of contact between the phase interface and the wall, in which the fluid is stationary relative to the line of contact, i.e., in which the no-slip condition is not satisfied. The dimensions of the region depend on the surface tension. The action of this stagnant zone on the flow is fully explained by the effect of the surface tension in experiments [1]. It is established that depending on the ratio of the tube diameter to the dimension of the stagnant zone two flow regimes are possible: in sufficiently wide tubes, an inertial regime for which Karman's hypothesis holds and the no-slip condition is not satisfied, and, in sufficiently narrow tubes, a creep regime in which the no-slip condition continues to apply. The values of the determining dimensionless parameter corresponding to the change of regime and the cessation of flow are calculated. They are similar to the experimental values.

Flow of a liquid in collapsing pipes is of great interest for problems in the mechanics of blood circulation, since collapse can take place in many blood vessels. This effect forms the basis for a large number of diagnostic and therapeutic methods, and also for methods of investigating the system of blood circulation. Consequently the mechanics of collapsing pipes has been studied intensively of late [1], but the available studies are far from exhausting the theoretical or the applied aspects of the problem. This applies also to the study of discontinuous solutions such as shock waves which describe steep fronts of opening or narrowing of a blood vessel. The most studied phenomenon is unsteady flow caused by change in the external pressure [2]. There is an explanation in [3–6] of the effect on the process of formation of discontinuities in collapsing pipes due to such factors as friction on the wall, distributed lateral outflow, the presence of a stagnant zone in the flow, and viscoelasticity of the wall. The origin of some acoustic phenomena in the arteries is connected by some with the propagation of discontinuities; these phenomena include Korotkov sounds, used in the determination of the arterial pressure of blood [1, 7]. The present study considers quasione-dimensional flow of a viscous incompressible liquid in a collapsing pipe of finite length and made of a nonlinear viscoelastic material; there is a study of the conditions in which discontinuities arise in such systems, and an investigation of the structure of shock waves with allowance for the effect of the surrounding tissues.

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.

The flow structure and impurity distribution in an axisymmetric cylindrical space is obtained from the system of equations of convective heat and mass transfer in the Boussinesq approximation for different variants of the gas inflow and outflow conditions. The variation of the average impurity concentration in the space investigated, obtained as a result of numerical calculations, is compared with two limiting cases of expulsion of the contaminated gas: the “gas piston” case and total mixing. The dependence of the velocity and impurity concentration fields on the regime parameters (Reynolds, Grashof, and Schmidt numbers, velocity profiles at the gas inlet and outlet) and the geometric and design parameters (elongation of cylinder, inflow and outflow geometry) is investigated numerically.