Numerical analysis of axisymmetric buckling of conical shells

Nonlinear boundaryvalue problems of axisymmetric buckling of conical shells under a uniformly distributed normal pressure are solved by the shooting method. The problems are formulated for a system of six firstorder ordinary differential equations with independent rotation and displacement fields. Simply supported and clamped cases are considered. Branching solutions of the boundaryvalue problems are studied for different pressures and geometrical parameters of the shells. The nonmonotonic and discontinuous curves of equilibrium states obtained show that collapse, i.e., snapthrough instability is possible. For a simply supported shell, multivalued solutions are obtained for both external and internal pressure. For a clamped thinwalled shell, theoretical results are compared with experimental data.     

Model of a plastically compressible material and its application to the analysis of the compaction of a porous body

This paper considers a model of a plastically compressible porous medium with a cylindricaltype yield condition and its associated constitutive relations, which ensure independent mechanisms of shear and compaction of the porous material. This allows one to use the wellknown theorems of plastic theory to analyze plastically compressible media and obtain analytical solutions for a number of boundaryvalue problems, including those taking into account conditions on strongdiscontinuity surfaces. Results from fullscale studies of the structural periodicity of noncompact materials using wavelet analysis were employed to choose a physical model for a porous body and determine the properties and dimensions of a representative volume. The problem of extrusion of a porous material through a conical matrix was solved.     

Exact solutions and mathematical properties of boundary‐value problems for dynamic‐diffusion boundary layers

The paper studies boundaryvalue problems for dynamicdiffusion boundary layers occurring near a vertical wall at high Schmidt numbers and for dynamic boundary layers whose inner edge is adjacent to the dynamicdiffusion layers. Exact solutions for boundary layers at small and large times are derived. The wellposedness of the boundaryvalue problem for a steady dynamicdiffusion layer is studied.     

A Numerical Study of the Critical Gas Saturation in a Porous Medium

We use porenetwork simulations to study the dependence of the critical gas saturation in solutiongas drive processes on the geometric parameters of the porous medium. We show that for a variety of growth regimes (including global and local percolation, instantaneous and sequential nucleation, and masstransfer driven processes), the critical gas saturation, Sgc, follows a powerlaw scaling with the final nucleation fraction (fraction of sites activated), fq. For 3D processes, this relation reads Sgcfq0.16, indicating a sensitive dependence of Sgc to fq at very small values of fq.     

Numerical Analysis of Branched Shapes of Arches in Bending

Nonlinear boundaryvalue problems of plane bending of elastic arches under a uniformly distributed load are solved by the shooting method. The problems are formulated for a system of six firstorder ordinary differential equations with a finiterotation field independent of displacements. Simply supported and clamped cases are considered. Branching solutions of the boundaryvalue problems are obtained. For a simply supported arch, a set of solutions describes symmetric and nonsymmetric shapes of bending, which correspond to positive, negative, and zero loads. For a clamped arch, the set of solutions consists of symmetric shapes that occur only for positive loads.     

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.     

Mixing Layer on the Lee Side of an Obstacle

Twolayer miscible flow above an uneven bottom is considered. A mathematical model in the shallowwater approximation is constructed for the development of a turbulent layer between homogeneous layers of different density in a twolayer channel flow over a local obstacle. The influence of the mixing process on the formation of an initial segment of the steadystate densitystratified flow on the leeward side of the obstacle is studied.     

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.     

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.     

Analytical Modeling of Nonaqueous Phase Liquid Dissolution with Green's Functions

Equilibrium and bicontinuum nonequilibrium formulations of the advection–dispersion equation (ADE) have been widely used to describe subsurface solute transport. The Green's Function Method (GFM) is particularly attractive to solve the ADE because of its flexibility to deal with arbitrary initial and boundary conditions, and its relative simplicity to formulate solutions for multidimensional problems. The Green's functions that are presented can be used for a wide range of problems involving equilibrium and nonequilibrium transport in semiinfinite and infinite media. The GFM is applied to analytically model multidimensional transport from persistent solute sources typical of nonaqueous phase liquids (NAPLs). Specific solutions are derived for transport from a rectangular source (parallel to the flow direction) of persistent contamination using first, second, or thirdtype boundary or source input conditions. Away from the source, the first and thirdtype condition cannot be expected to represent the exact surface condition. The secondtype condition has the disadvantage that the diffusive flux from the source needs to be specified a priori. Near the source, the thirdtype condition appears most suitable to model NAPL dissolution into the medium. The solute flux from the pool, and hence the concentration in the medium, depends strongly on the mass transfer coefficient. For all conditions, the concentration profiles indicate that nonequilibrium conditions tend to reduce the maximum solute concentration and the total amount of solute that enters the porous medium from the source. On the other hand, during nonequilibrium transport the solute may spread over a larger area of the medium compared to equilibrium transport.     

Effect of Streamwise Streaky Structures on Turbulization of a Circular Jet

Experimental investigations of the influence of streamwise streaky structures on turbulization of a circular laminar jet are described. The qualitative characteristics of jet evolution are studied by smoke visualization of the flow pattern in the jet and by filming the transverse and longitudinal sections of the jet illuminated by the laser sheet with image stroboscopy. It is shown that the streaky structures can be generated directly at the nozzle exit, and their interaction with the Kelvin–Helmholtz ring vortices leads to emergence of azimuthal beams ( structures) by a mechanism similar to threedimensional distortion of the twodimensional Tollmien–Schlichting wave at the nonlinear stage of the classical transition in nearwall flows. The effect of the jetexhaustion velocity and acoustic action on jet turbulization is considered.     

Wave regimes on a ferromagnetic viscous‐fluid film flowing down a vertical cylinder

Axially symmetrical waves on the surface of a ferromagnetic viscousfluid film flowing down a cylindrical conductor with alternating current are considered. In this case, in addition to the gravitational force, the film is affected by a spatially nonuniform timedependent magnetic field. The film thickness was assumed to be small compared to the radius of the conductor. In the longwave approximation, a model equation for the deviation of the film thickness from its undisturbed value is obtained. Some numerical solutions of this equations are reported.     

Transverse Decay of Solutions in an Elastic Cylinder

In a semiinfinite cylinder composed of anisotropic linearised elastic material, loaded on the base and clamped along the lateral surface, it is known that the solution as measured, for example, by the strainenergy flux through a plane crossection decays longitudinally at most exponentially with respect to the axial distance from the base. There is, however, also a transverse radial decay of the solution, again measured for example by the strainenergy, occurring from the region close to the cylinder's axis to the region near the lateral surface, where the energy vanishes.This problem is considered in the present paper which discusses a circular semiinfinite cylinder and derives an estimate for the strainenergy contained in a cylindrical annulus at a given distance from the base and of variable height, and whose outer surface coincides with the lateral surface of the cylinder. It is shown that the strainenergy decays at most algebraically to zero as the inner radius of the annulus increases to that of the cylinder.Sommario. E'noto che in un cilindro semiinfinito composto da materiale elastico lineare anisotropo, caricato sulla base ed incastrato lungo la superficie laterale, la soluzione elastica, misurata, per esempio, dal flusso di energia di deformazione attraverso una sezione trasversale piana, decade con legge al più esponenziale con la distanza dalla base. C'è tuttavia, anche un decadimento radiale della soluzione, misurato, per esempio, dall'energia di deformazione che passa dalla regione vicina all'asse del cilindro a quella vicin alla superficie laterale dove l'energia si annullaQuesto problema è qui studiato. Si discute in particolare un cilindro circolare semiinfinito e si deduce una stima per l'energia di deformazione contenuta in un anello cilindrico ad una distanza assegnata dalla base e di altezza variabile, e la cui superficie esterna coincide con la superficie laterale del cilindro. Si dimostra che l'energia di deformazione decade al più con legge algebrica a zero quando il raggio interno del cilindro si avvicina a quello esterno.     

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.     

Hartmann Effect. Region of Existence and Oscillation Frequencies

Data of experiments on determining the region of existence for autooscillations (Hartmann effect) with a frequency of approximately 450 Hz with variation in the distance from the nozzle to the resonator. Results of these experiments differ from the wellknown results of Hartmann and his followers obtained for shallow resonators. It is shown that the region of autooscillations exists for large distances between the nozzle and the resonator. The results obtained are explained using the modern knowledge of the gasdynamic structure of a supersonic underexpanded jet. It is shown that in determining the frequency of lowfrequency oscillations, it suffices to allow for the resonator length and its added mass.     

Effects of magnetic field and variable viscosity on forced non‐darcy flow about a flat plate with variable wall temperature in porous media in the presence of suction and blowing

This paper presents a study of the effect of a magnetic field and variable viscosity on steady twodimensional laminar nonDarcy forced convection flow over a flat plate with variable wall temperature in a porous medium in the presence of blowing (suction). The fluid viscosity is assumed to vary as an inverse linear function of temperature. The derived fundamental equations on the assumption of small magnetic Reynolds number are solved numerically by using the finite difference method. The effects of variable viscosity, magnetic and suction (or injection) parameters on the velocity and temperature profiles as well as on the skinfriction and heattransfer coefficients were studied. It is shown that the magnetic field increases the wall skin friction while the heattransfer rate decreases.     

Spatial Simple Waves on a Shear Flow

The paper studies simple waves of the shallowwater equations describing threedimensional wave motions of a rotational liquid in a freeboundary layer. Simple wave equations are derived for the general case. The existence of unsteady or steady simple waves adjacent continuously to a given steady shear flow along a characteristic surface is proved. Exact solutions of the equations describing steady simple waves were found. These solutions can be treated as extension of Prandtl–Mayer waves for sheared flows. For shearless flows, a general solution of the system of equations describing unsteady spatial simple waves was found.     

Calculation of Ionization and Radiative Characteristics of Air in the Shock Layer on the Basis of Various Models of Vibration–Dissociation Interaction

Models of vibrationdissociation interaction are verified on the basis of results of numerical simulation of nonequilibrium air flow in the shock layer near vehicles flying in the atmosphere and data of inflight and windtunnel experiments on measurement of ionization and radiative characteristics of the shock layer.