Home – Home – Jornals – Journal of Applied Mechanics and Technical Physics 2015 number 5

A mathematical model of motion of solid particles withselective permeability and a mixture of moving gases is developedwith the use of averaging principles of mechanics of multiphase media.The derived system of quasi-linear partial differential equations isstudied for a particular one-dimensional isothermal case.

Interaction of a shock wave with a system of motionlessor relaxing particles is numerically simulated. Regimes of the gas flowaround these particles are described, and the influence of the initialparameters of the examined phenomenon on the flow pattern is analyzed.The drag coefficient of particles is calculated as a function of theMach number behind the shock wave at a fixed Reynolds number. Thedynamics of heat exchange for particles of different sizes(10$\mu$m--1mm) is determined, and the laws of thermal relaxationafter passing of a shock wave over the system of particles are found.The times of thermal and velocity relaxation of particles are estimatedas functions of the Reynolds number, and the predicted relaxation timeis compared with the corresponding empirical dependences.

Currently available methods of computing thelaminar--turbulent transition (LTT), including methods used ingas-dynamic software packages, are analyzed from the viewpoint of LTTsimulation accuracy.

A three-dimensional supersonic turbulent flow withsymmetric normal injection of circular jets from the channel walls isnumerically simulated. The initial Favre-averaged Navier-Stokesequations closed by the $k$--$\omega$ turbulence model are solved by analgorithm based on an ENO scheme. The mechanism of the formation ofvortical structures due to the interaction of the jet with the freestream is studied for jet to crossflow total pressure ratios rangingfrom 3 to 50. It is known from experiments reported in the literaturethat, for $n\ge 10$, mixing of the jet with the high-velocity flowleads to the formation of a pair of vortices and of an additionalseparation zone near the wall behind the jet. It is demonstrated thatthe present numerical results are consistent with such findings andthat the pressure distribution on the wall ahead of the jet in theplane of symmetry is also in reasonable agreement with availableexperimental data.

This paper presents a numerical simulation of the flowresulting from transverse jet injection into a supersonic flow througha slot nozzle, at different pressures in the injected jet and mainflow. Calculations on grids with different resolutions use theSpalart--Allmaras turbulence model, the $k$--$\varepsilon$ model,the $k$--$\omega$ model and the SST model. Based on a comparison ofthe calculated and experimental data on pressure distribution on thewall, the length of the recirculation area and depth of penetration ofthe jet in the supersonic flow, conclusions are made about the accuracyof the calculation results of the different turbulence models and theapplicability of these models for solving similar problems.

A functional mathematical model of a hydrogen-driven combustion chamber for a scramjet is described. The model is constructed with the use of one-dimensional steady gas-dynamic equations and parametrization of the channel configuration and the governing parameters (fuel injection into the flow, fuel burnout along the channel, dissipation of kinetic energy, removal of some part of energy generated by gases for modeling cooling of channel walls by the fuel) with allowance for real thermophysical properties of the gases. Through parametric calculations, it is found that fuel injection in three cross sections of the channel consisting of segments with weak and strong expansion ensures a supersonic velocity of combustion products in the range of free-stream Mach numbers $\mboxM_\infty = 6\mbox--12$. It is demonstrated that the angle between the velocity vectors of the gaseous hydrogen flow and the main gas flow can be fairly large in the case of distributed injection of the fuel. This allows effective control of the mixing process. It is proposed to use the exergy of combustion products as a criterion of the efficiency of heat supply in the combustion chamber. Based on the calculated values of exergy, the critical free-stream Mach number that still allows scramjet operation is estimated.

The operation of an electromagnetic multirail launcher of solids powered from a pulsed magnetohydrodynamic (MHD) generator is studied. The plasma flow in the channel of the pulsed MHD generator and the possibility of launching solids in a rapid-fire mode of launcher operation are considered. It is shown that this mode of launcher operation can be implemented by matching the plasma flow dynamics in the channel of the pulsed \hboxMHD generator and the launching conditions. It is also shown that powerful pulsed MHD generators can be used as a source of electrical energy for rapid-fire electromagnetic rail launchers operating in a burst mode.

Theproblemofflowsinitiatedbyvertical lifting of a rectangular beam partially submerged in shallow water filling a rectangular prismatic channel with a horizontal bottom is studied in the long-wavelength approximation. The width of the beam is equal to the channel width, and its upper and lower planes are parallel to the channel bottom. In the first stage of the flow, the lower surface of the low beam is completely submerged in the liquid, which is lifted after it by hydrostatic pressure. Conditions for the well-posedness of this problem are obtained, and solutions describing the liquid flow in the region adjacent to the bottom surface of the beam and in outer regions with a free upper boundary are constructed for different laws of lifting of the beam.

A method of designing a supersonic axisymmetric tunnel air inlet based on the problem of an inverted flow in an annular nozzle with isentropic expansion is considered. The nozzle contour is constructed by the method of characteristics. Parameters of one inlet for viscous and inviscid gas flows are calculated.

The reflection and refraction of acoustic waves at different angles of incidence on the interface between a vapor--gas--droplet system and air are studied. From an analysis of analytical solutions, it has been found that in the case of incidence on the interface from the side of the vapor--gas--droplet medium, there is a critical angle of incidence at which the wave is completely reflected from the boundary, i.e., total internal reflection takes place. It is shown that for a certain angle of incidence on the interface both from the air side and from the mixture side and for a certain volume fraction of water in the disperse system, complete transmission of the acoustic wave through the medium is observed.

This paper is a review of studies carried out on the basis of two-dimensional boundary-value problems of filtration theory. The role of critical regimes determining the specifics of filtration flows with moving boundaries is noted.

A mathematical model for hydraulic fracturing is proposed. The model is based on the presentation of the fractured portion of the stratum adjacent to the well as a heterogeneous fractured porous medium. Assumptions usually used in the theory of elastic flow are applied. Formulas for determining the size of the hydraulic fracturing zone and the degree of fracture opening under conditions of relative equilibrium are derived.

Gas filtration from an underground reservoir through a layer of a porous medium due to an instantaneous increase in the gas pressure in the reservoir is studied. The problem is considered in a one-dimensional formulation in the general case where the temperatures of the gas and the porous medium are different and unstable, and in the case of a high specific heat of the solid phase and a high interfacial heat-transfer rate. The dynamics of the gas flow at the inlet and outlet of the underground reservoir is analyzed, the time of unloading of the system is estimated as a function of the permeability of the porous medium. It is shown that, depending on the properties of the porous layer, two characteristic gas flow regimes are possible: a fast discharge regime and a slow regime which is determined mainly by barodiffusion.

This paper describes an experimental study of heat transfer in a channel behind a backward-facing step in the presence of a disturbance in front of it in the form of a single rib in the range of the Reynolds numbers $\Re = 5000\mbox--15\,000$. The influence of the rib position and height on heat transfer intensity behind the backward-facing step is investigated. It is shown that reattachment of the flow disturbed by the obstacle intensifies the heat transfer on the surface behind the backward-facing step.

An analysis of a second-grade fluid in a semi-porous channel in the presence of a chemical reaction is carried out to study the effects of mass transfer and magnetohydrodynamics. The upper wall of the channel is porous, while the lower wall is impermeable. The basic governing flow equations are transformed into a set of nonlinear ordinary differential equations by means of a similarity transformation. An approximate analytical solution of nonlinear differential equations is constructed by using the homotopy analysis method. The features of the flow and concentration fields are analyzed for various problem parameters. Numerical values of the skin friction coefficient and the rate of mass transfer at the wall are found.

The influence of two nanomodifiers with different compositions during their homogenization in the AL7 aluminum melt and moulding on the properties of the modified aluminum alloy is studied. Experiments are performed with the use of a centrifugal conductive magnetohydrodynamic pump. The melt is poured into a graphite mould with three cylindrical channels 38 mm in diameter and 160 mm long, which are designed for a metal mass of 500g. Two compositions are used as modifying agents: nano-scale particles of the aluminum nitride powder 40--100nm in size and metallized carbon nanotubes smaller than 25 nm, which are clad with aluminum to improve wetting of their surface. The analysis of the structure of the experimental and reference samples shows that the use of modifiers leads to refinement of the grain structure of the cast metal. According to the Hall--Petch theory, this effect may result in improvement of mechanical characteristics of the cast metal.

The microscopic behavior of nanofluids in the Poiseuille flow in a nanochannel is examined by means of molecular dynamics simulation through visual observations and statistic analysis. For nanofluid flows inside the nanochannel, a clustering effect is observed during the time evolution of the system. The cluster moves along the centerline of the nanochannel due to the maximum velocity in the middle part of the Poiseuille flow. The attractive force is believed to be the primary culprit behind the agglomeration of nanoparticles.

The dependence of a scalar measure of the structural changes occurring in a material under plastic deformation on a plastic strain measure and the dependence of a free energy measure on a structural change measure are constructed using experimental data that allow the expended plastic work to be divided into a latent part and a thermal part. The obtained dependences, kinematic relations, a constitutive equation, and a heat-conduction equation that satisfy the principles of thermodynamics and objectivity are used to construct a model of thermo-elastic--inelastic processes in the presence of finite deformations and structural changes in the material. The model is tested on the problem of temperature changes in the process of adiabatic elastic--plastic compression, which has experimental support.

A program of experiments to identify the type of elastic anisotropy of material is proposed. The position of the principal axes of material anisotropy is determined by measuring the strains resulting from compression of a cubic sample along three of its faces. For the subsequent identification of the type of anisotropy, samples oriented along definite principal axes are used.

We consider the linear unsteady motion of an IL-76TD aircraft on ice. Water is treated as an ideal incompressible liquid, and the liquid motion is considered potential. Ice cover is modeled by an initially unstressed uniform isotropic elastic plate, and the load exerted by the aircraft on the ice cover with consideration of the wing lift is modeled by regions of distributed pressure of variable intensity, arranged under the aircraft landing gear. The effect of the thickness and elastic modulus of the ice plate, takeoff and landing regimes on stress-strain state of the ice cover used as a runway.

The processes of high-velocity oblique collision of metal plates which lead to the formation of their joints (seizure) are considered. It is found that the cleaning of the plate surface necessary for seizure results from a jet flow (particle stream), whose source is at least one of the welded materials or an interlayer of ductile material located in the initial region of collision. It is shown that additional cleaning may occur due to the emergence of rotating microregions in intense gradient flows localized in the joint area; seizure on cleaned surfaces is due to reduction of the surface energy of the system.