Stationary Simple Waves on a Barotropic Liquid Shear Flow

Stationary threedimensional flows of a barotropic liquid in a gravity field are considered. In the shallowwater approximation, the Euler equations are transformed into a system of integrodifferential equations by the EulerLagrange change of coordinates. A system of simplewave equations is obtained, for which the theorem of existence of a solution attached to a given shear flow is proved. As an example, a particular solution analogous to the solution of the problem of a gas flow around a convex angle is given.     

On the Quasi‐Steadiness Hypothesis as Applied to Gas Exhaustion from a Receiver

A semiempirical method of determining the stabilization time for a quasisteady mode of gas exhaustion from a receiver after sudden opening of the nozzle and the time evolution of the real flow rate at the stage of the transitional process are considered. The numerical solution of the equations of exhaustion gas dynamics in a twodimensional formulation and the results of model experiments demonstrated that the method can be used to estimate the conditions of applicability of the quasisteadiness hypothesis and to determine the discharge coefficient of the nozzle with controlled accuracy.     

Evolution of the Diffusion Mixing Layer of Two Gases upon Interaction with Shock Waves

A mathematical model of mechanics of a twovelocity twotemperature mixture of gases is developed. Based on this model, evolution of the mixing layer of two gases with different densities under the action of shock and compression waves is considered by methods of mathematical simulation in the onedimensional unsteady approximation. In the asymptotic approximation of the full model, a solution of an initialboundary problem is obtained, which describes the formation of a diffusion layer between two gases. Problems of interaction of shock and compression waves with the diffusion layer are solved numerically in the full formulation. It is shown that the layer is compressed as the shock wave traverses it; the magnitude of compression depends on shockwave intensity. As the shock wave passes from the heavy gas to the light gas, the mixing layer becomes overcompressed and expands after shockwave transition. The wave pattern of the flow is described in detail. The calculated evolution of the mixinglayer width is in good agreement with experimental data.     

On the Propagation of Long‐Wave Perturbations in a Two‐Layer Free‐Boundary Rotational Fluid

A mathematical model for the propagation of longwave perturbations in a freeboundary shear flow of an ideal stratified twolayer fluid is considered. The characteristic equation defining the velocity of perturbation propagation in the fluid is obtained and studied. The necessary hyperbolicity conditions for the equations of motion are formulated for flows with a monotonic velocity profile over depth, and the characteristic form of the system is calculated. It is shown that the problem of deriving the sufficient hyperbolicity conditions is equivalent to solving a system of singular integral equations. The limiting cases of weak and strong stratification are studied. For these models, the necessary and sufficient hyperbolicity conditions are formulated, and the equations of motion are reduced to the Riemann integral invariants conserved along the characteristics.     

Adjoint problems of mechanics of continuous media in gas‐laser cutting of metals

A mathematical model of gaslaser cutting of metal plates in an inert gas is proposed. The formation and flow of the liquid metal melt film at the cutting front is considered within the framework of incompressible boundarylayer equations. Based on the resultant analytical solution, a local law of energy conservation on the cutting surface is derived, which takes into account the meltfilm thickness and the temperature dependence of thermophysical parameters of the metal. The problem of the cutting shape and depth is solved in the twodimensional formulation. A comparison with experimental data is made in terms of the cutting depth and maximum cutting velocity for carbon and alloy steel.     

Hyperbolicity of Steady‐State Equations of Gas Shear Flows in a Thin Layer

The steadystate threedimensional motion of an ideal gas in a thin layer of variable height is considered. In the longwave approximation, the equations of gas dynamics reduce to a system of integrodifferential equations. The generalized characteristics and hyperbolicity conditions of the obtained system are found.     

Viscous Film Flow down Corrugated Surfaces

A theoretical analysis of a downward viscous film flow on corrugated surfaces is reported. The study is based on Navier–Stokes equations (for one and twodimensional surfaces) and on an integral model (for a threedimensional surface with double corrugation). The calculations were carried out in a wide range of Reynolds numbers and geometric characteristics of the surface with due allowance for the surfacetension force. The shape of the free surface of the liquid film and other characteristics of the flow are calculated. It is shown that, in the case of a onedimensional surface, there exists a range of parameters where the flow is predominantly governed by surfacetension forces; this flow can be adequately treated with the integral approach. In this range of parameters, on the surface with double corrugation, the average quantities of the downward flow in wide corrugation valleys are determined by the finetexture geometry.     

A new approach to studying the dynamics of a thin curved vortex

The paper studies the dynamics of a thin curved vortex in a potential flow of an ideal incompressible fluid. The flow is specified by a number of geometrical restrictions and does not satisfy the Biot–Savart law. The form of the derived equation of the vortex dynamics coincides with the form of the wellknown equation of local induction for selfinduced vortex motion. The parameters of the new equation are simultaneously flow parameters, and in this sense, they do not show uncertainty typical of classical equations. The coefficient of the new equation can take any specified values (not necessarily much greater than unity, as required according to the concept of local induction) and generally is a function of a natural filament parameter.     

Interaction of an unsteady two‐phase jet with a layer of a disperse medium

Discharge of a twophase jet from a cylindrical channel into a bounded layer of a disperse medium is numerically simulated using the equations of the mechanics of heterogeneous media with allowance for the differences in velocity, temperature, and phase stresses. The effect of separation of the gas phase from the disperse phase in the layer is revealed and verified experimentally. A comparison with a similar process of gas discharge at equal initial pressures shows that in the interaction with the disperse layer, the twophase flow has a longer momentum and direction.     

Mixed Formulations of Bending Problems for Homogeneous Elastic Plates and Beams

Mixed formulations of bending problems for homogeneous plates (beams) are proposed, whose essence is that the deformation of a plate (beam) near its fixed boundary is described by the threedimensional elasticity equations, and the remaining part by the conventional equations of plate (beam) bending. At the interface between these regions, the solutions of these equations are joined. The mixed formulation allows one to describe the threedimensional stress state in the neighborhood of the fixed boundaries of plates (beams) and take into account the complex nature of the fixing conditions. Finiteelement implementation is more efficient for the mixed formulations of plate (beam) bending problems than for the wellknown threedimensional formulations.     

Electrical Characteristics of Three‐Component Dielectric Composites with Close‐Packed Inclusions

The electric field and effective permittivity are calculated for a twodimensional threecomponent dielectric material reinforced by cylindrical fibers. A composite material with a square close packing of inclusions is considered. The field in the periodic system is investigated using the exact solution of the model problem of interaction of two dissimilar cylindrical inclusions in an external homogeneous electric field. A diagram of the relative effective permittivity is constructed.     

Case Method Employed for Solving the Problem of Thermal Creep of a Rarefied Gas along a Solid Cylindrical Surface

An analytical solution of a halfspace boundaryvalue problem is constructed for an inhomogeneous kinetic Boltzmann equation with the collision operator in the form of an operator of an ellipsoidal statistical model in the problem on thermal creep of a rarefied gas along a solid cylindrical surface. Corrections to the thermal creep coefficient are obtained for the cases of longitudinal and transverse flow past a straight circular cylinder in the approximation linear with respect to the Knudsen number, allowing for the interfacial curvature. The results are compared with available data.     

Evaluation of the energy efficiency of heat addition upstream of the body in a supersonic flow

Criteria for evaluating the energy efficiency of heat addition upstream of the body in a supersonic gas flow are obtained. Based on the functional objectives of flying vehicles and the thermodynamic model of the process, estimates are obtained for missile and aircrafttype vehicles. The minimum Mach numbers at which heat addition upstream of the body is reasonable are evaluated. The increase in the flight range in the cruising regime for an aircrafttype vehicle and on the active trajectory for a missiletype vehicle is evaluated. Estimates for fuel economy in launching an aerospace plane into an Earth orbit are given. It is shown that a significant part of the fuel should be spent on producing energy for gas heating in order to obtain a noticeable effect. The minimum necessary efficiency" of conversion of the fuel energy into the gasheating energy is evaluated.     

Velocity Measurements in a One‐Dimensional Steady Flow by Methods of Emission Tomography

A new method for velocityfield measurements in a onedimensional steady flow is proposed. The method is based on principles of laserinduced fluorescence combined with emission tomography. Results of a numerical experiment are presented.     

Asymptotic Modeling of Nonlinear Wave Processes in Shock‐Loaded Elastoplastic Materials

Nonlinear wave processes in shockloaded elastoplastic materials are modeled. A comparison of the results obtained with experimental data and numerical solutions of exact systems of dynamic equations shows that the model equations proposed qualitatively describe the stressdistribution evolution in both the elasticflow and plasticflow regions and can be used to solve one and twodimensional problems of pulsed deformation and fracture of elastoplastic media.     

Origination of In‐Phase Oscillations of Thin Plates with Aeroelastic Interaction

Synchronization of oscillations of thin elastic plates that are walls of a gasfilled channel is considered. The gas motion is described by a system of Navier–Stokes equations, which is solved using the secondorder MacCormack method with time splitting. The motion of the channel walls is described by a system of geometrically nonlinear dynamic equations of the theory of this plates, which is solved by the finitedifference method. Kinematic and dynamic contact conditions are imposed at the interface between the media. A numerical experiment is performed to determine typical dynamic regimes and study the transition of the aeroelastic system to inphase oscillations.     

Effect of Surfactant Added in Small Amounts on Nonisothermal Absorption: an Experimental Study

Results of an experimental study of watervapor absorption by a stagnant layer of the aqueous solution of LiBr with admixed octanol, used as a surfactant, are described. Time dependences of temperature at various heights of the layer, time dependences of absorbed mass, and temperature and concentration profiles at various times are reported. A comparison with experimental data for surfactantfree solutions reveals an enhanced action of octanol on watervapor absorption and an increase in the absorbent surface temperature at the initial stage of the process.     

Effect of Porous Coatings on Stability of Hypersonic Boundary Layers

The influence of ultrasoundabsorbing coatings on stability of hypersonic boundary layers is considered. Two types of coatings were used in experiments: feltmetal with a random porous microstructure and a sheet perforated by blind cylindrical microchannels. The experiments were performed in a wind tunnel at a Mach number M = 5.95 on sharp cones with a 7° apex halfangle. Evolution of natural disturbances and artificially induced wave packets in the boundary layer was studied with the help of hotwire anemometry. Spatial characteristics of artificial disturbances were obtained. It is demonstrated that such coatings exert a stabilizing effect on secondmode disturbances.     

Heat Transfer on the Surface on a Spherically Blunted Cone Exposed to a Supersonic Spatial Flow with Injection of a Coolant Gas

The heattransfer processes in a supersonic spatial flow around a spherically blunted cone with allowance for heat overflow along the longitudinal and circumferential coordinates and injection of a coolant gas are studied numerically. The prospects of using highly heatconducting materials and injection of a coolant gas for reduction of the maximum temperatures at the body surface are demonstrated. The solutions of the direct and inverse problems in one, two, and threedimensional formulations for different shell materials are compared. The error of the thinwall method in determining the heat flux on the heatloaded boundary of the body is estimated.