Numerical Modeling of Unsteady Radiative–Convective Heat Transfer on a Flat–Plate Boundary Layer in a Selectively Emitting and Scattering Medium

A conjugation problem for radiative–convective heat transfer in a turbulent flow of a high–temperature gas—particle medium around a thermally thin plate is considered. The plate experiences intense heating from an outside source that emits radiation in a restricted spectral range. Unsteady temperature fields and heat–flux distributions along the plate are calculated. The results permit prediction of the effect of the type and concentration of particles on the dynamics of the thermal state of both the medium in the boundary layer and the plate itself under conditions of its outside heating by a high–temperature source of radiation.     

Dynamics of a spherical particle in a laminar boundary layer

The problem of the motion of an individual spherical particle in a laminar boundary layer is considered for small Reynolds numbers determined from the relative velocity and the transverse velocity gradient of the flow undisturbed by the particle. The dependence of the transverse force acting on the particle, which results from the nonuniformity of the free stream, on the distance of the particle from the surface of a flat plate is calculated. It is shown that the direction of the transverse force changes with the distance of the particle from the plate: near the surface the force is positive, i.e., directed away from the plate, and at greater distances negative.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 6, pp. 91–96, November–December, 1990.The author wishes to thank M. N. Kogan and N. K. Makashev for useful discussions.     

The effects of shadowing and interference from the rotation of a plate

The effects are considered of shadowing and interference which arise during tumbling motion of a plate in a free molecule flow. The particle fluxes are found together with the pressure and the tangential intensities acting on the plate, with allowance for these effects. For a purely diffuse scheme of interaction of the gas with the surface of the plate, estimates are obtained of the relative contribution of shading and interference to the drag and the damping moment of the plate.Translated from Ivestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 2, pp. 140–148, March–April, 1985.     

Motion of a dusty gas at the entrance to a flat channel and a circular pipe

It is shown that at large Reynolds numbers, calculated from the entrance velocity and the half-width of the channel, four characteristic flow regions are formed in the entrance section. The equations describing the motion of the mixture in each of these regions are constructed by the method of matched expansions. An expression relating the particle concentration distribution at points remote from the entrance section to the particle concentration distribution in the boundary layer on a flat plate at points remote from the beginning of the plate is obtained. The dependence of the dispersed-phase concentration profile formed on the governing parameters is studied on the basis of a numerical solution. It is shown that as the contribution of the Saffman force to the interphase momentum transfer increases, the rise in particle concentration in the direction of the wall is replaced by a fall. A qualitative correspondence between the calculated particle concentration profiles and certain known experimental data is noted.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 6, pp. 80–87, November–December, 1988.     

Two-phase couette flow

A study is made of plane laminar Couette flow, in which foreign particles are injected through the upper boundary. The effect of the particles on friction and heat transfer is analyzed on the basis of the equations of two-fluid theory. A two-phase boundary layer on a plate has been considered in [1, 2] with the effect of the particles on the gas flow field neglected. A solution has been obtained in [3] for a laminar boundary layer on a plate with allowance for the dynamic and thermal effects of the particles on the gas parameters. There are also solutions for the case of the impulsive motion of a plate in a two-phase medium [4–6], and local rotation of the particles is taken into account in [5, 6]. The simplest model accounting for the effect of the particles on friction and heat transfer for the general case, when the particles are not in equilibrium with the gas at the outer edge of the boundary layer, is Couette flow. This type of flow with particle injection and a fixed surface has been considered in [7] under the assumptions of constant gas viscosity and the simplest drag and heat-transfer law. A solution for an accelerated Couette flow without particle injection and with a wall has been obtained in [6]. In the present paper fairly general assumptions are used to obtain a numerical solution of the problem of two-phase Couette flow with particle injection, and simple formulas useful for estimating the effect of the particles on friction and heat transfer are also obtained.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 3, pp. 42–46, May–June, 1976.     

Propagation of two-dimensional plastic waves in a thick plate

A study is made of the propagation and interaction of two-dimensional waves of high amplitude in a thick plate. A monotonically decreasing pressure is applied to the surface of the plate. Deformations are assumed to be large; the problem is formulated and solved in Lagrangian variables. An approximate method for constructing the fronts of the shock waves is proposed. The pressure and particle velocity at an arbitrary point and at an arbitrary instant of time are determined by the method of characteristics. A numerical example is given.Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 1, pp. 100–106, January–Febraury, 1971.     

Effect of the Conductance and Thickness of a Conducting Plate on the Signal from a Material–Velocity Inductive Transducer

The perturbation problem of the magnetic field of a constant–current turn located above a conducting plate set into motion by a plane shock wave with a rectangular profile is considered. It is shown that not only the velocity of the plate but also its dynamic conductivity can be determined on the basis of the electromotive force of induction recorded by means of the turn. For the case where the conductance of the plate is known for both the conducting half–space and for a plate whose thickness is comparable with the skin–layer thickness, approximatecalculated dependences for the velocity of the plate are obtained. A comparison with experimental data and the clarification of the calculated dependences allows one to conclude that the approaches proposed can be used for determining the conductance of metals in shock–wave processes.     

Numerical modelling of step–strain for stretched filaments

This article addresses the modelling of filament-stretching/step–strain deformation under viscoelastic capillary break-up configurations of the CaBER-type. Start-up, prior to step–strain, is conducted under constant stretch-rate synchronous plate retraction with impulsive sessation of plate motion. The study encompasses variation in material rheology, appealing to Oldroyd, Geisekus and Phan-Thien/Tanner-type models, which display differences in shear and extensional viscosity properties (shear thinning/extension hardening). Two different viscosity ratio settings are considered to reflect high- and low-solvent viscosity constituent components; the former representing typical Boger fluids, the latter high-polymer concentration fluids. We compare and contrast results for three alternative filament aspect ratios at the onset of step–strain. Throughout the step–strain period, we have been able to successfully capture such physical features as drainage to the filament feet, necking at the filament centre, and periods with travelling waves through the axial filament length. In addition, we have identified the suppressive influence that larger capillary forces have upon radial fluctuations, and the minor impact that gravitational forces have upon the ensuing deformation. From this study, estimates for rheometrical data have been derived in terms of characteristic material relaxation time and apparent extensional viscosity. The computational techniques employed include a compressed-mesh (CM) procedure, an Arbitrary Lagrangian–Eulerian scheme (ALE) and a free-surface particle tracking technique. Spatial discretisation of the problem is accomplished through a hybrid finite element/finite volume algorithm implemented in the form of a time-stepping incremental pressure-correction formulation.     

Mathematical construction of a Reissner–Mindlin plate theory for composite laminates

A Reissner–Mindlin theory for composite laminates without invoking ad hoc kinematic assumptions is constructed using the variational-asymptotic method. Instead of assuming a priori the distribution of three-dimensional displacements in terms of two-dimensional plate displacements as what is usually done in typical plate theories, an exact intrinsic formulation has been achieved by introducing unknown three-dimensional warping functions. Then the variational-asymptotic method is applied to systematically decouple the original three-dimensional problem into a one-dimensional through-the-thickness analysis and a two-dimensional plate analysis. The resulting theory is an equivalent single-layer Reissner–Mindlin theory with an excellent accuracy comparable to that of higher-order, layer-wise theories. The present work is extended from the previous theory developed by the writer and his co-workers with several sizable contributions: (a) six more constants (33 in total) are introduced to allow maximum freedom to transform the asymptotically correct energy into a Reissner–Mindlin model; (b) the semi-definite programming technique is used to seek the optimum Reissner–Mindlin model. Furthermore, it is proved the first time that the recovered three-dimensional quantities exactly satisfy the continuity conditions on the interface between different layers and traction boundary conditions on the bottom and top surfaces. It is also shown that two of the equilibrium equations of three-dimensional elasticity can be satisfied asymptotically, and the third one can be satisfied approximately so that the difference between the Reissner–Mindlin model and the second-order asymptotical model can be minimized. Numerical examples are presented to compare with the exact solution as well as the classical lamination theory and the first-order shear-deformation theory, demonstrating that the present theory has an excellent agreement with the exact solution.     

Boundary layer on a flat plate with strong longitudinal magnetic field

The influence of a magnetic field on the boundary layer on a flat plate in a sufficiently strongly ionized gas stream is studied. The magnetic field is parallel to the plate and to the velocity of the free stream, and it is so strong that the transport coefficients become anisotropic (the cyclotron rotation frequency of the charged particles is greater than or equal to the order of the frequency of the particle collisions). Using the results of [1–3] it is shown that the effect of the strong longitudinal magnetic field with a sufficiently high degree of gas ionization leads to a reduction in the thermal flux to the plate. For low degrees of ionization this effect is very small, since the viscosity and heat conduction in this case are determined by the neutral component of the gas.Results are presented of numerical calculations of the considered problem with account for the dependence of the transport coefficients on the thermodynamic parameters. It is assumed throughout that the magnetic Reynolds number is small (R_m1).     

Delamination effects on cracked steel members reinforced by prestressed composite patch

Prestressed composite patch bonded on cracked steel section is a promising technique to reinforce cracked details or to prevent fatigue cracking on steel structural elements. It introduces compressive stresses that produce crack closure effect. Moreover, it modifies the crack geometry by bridging the crack lips and reduces the stress range at crack tip. Fatigue tests were performed on notched steel plate reinforced by CFRP strips as a step toward the validation of crack patching for fatigue life extension of riveted steel bridges. A debond crack in the adhesive–plate interface was observed by optical technique. Debond crack total strain energy release rate is computed by the modified virtual crack closure technique. A parametric analysis is performed in order to investigate the influence of some design parameters such as the composite patch Young’s modulus, the adhesive thickness and the pretension level on the adhesive–plate interface debond.     

Influence of an elastic plate on the motion of an inhomogenfous fluid

The influence of a thin elastic isotropic plate on the wave motion of an inhomogeneous fluid originating under the effect of external periodic perturbations is investigated. The fluid density increases constantly with depth. Analogous problems have been examined for an inhomogeneous fluid without a plate in [1, 2] and with a plate on the surface of a homogeneous fluid in [3–5].Sevastopol'. Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 1, pp. 60–67, January–February, 1972.     

Shock Compression of a Plate on a Wedged–Shaped Target

Problems of compression of a plate on a wedge–shaped target by a strong shock wave and plate acceleration are studied using the equations of dissipationless hydrodynamics of compressible media. The state of an aluminum plate accelerated or compressed by an aluminum impactor with a velocity of 5—15 km/sec is studied numerically. For a compression regime in which a shaped–charge jet forms, critical values of the wedge angle are obtained beginning with which the shaped–charge jet is in the liquid or solid state and does not contain the boiling liquid. For the jetless regime of shock–wave compression, an approximate solution with an attached shock wave is constructed that takes into account the phase composition of the plate material in the rarefaction wave. The constructed solution is compared with the solution of the original problem. The temperature behind the front of the attached shock wave was found to be considerably (severalfold) higher than the temperature behind the front of the compression wave. The fundamental possibility of initiating a thermonuclear reaction is shown for jetless compression of a plate of deuterium ice by a strong shock wave.     

Pressure pulsations on an obstacle in a jet

At the present time, much attention is devoted to auto-oscillations that arise from the interaction between a supersonic underexpanded jet and an obstacle that it encounters at right angles [1, 2]. There are far fewer data on the pressure pulsations on an obstacle in the absence of auto-oscillations [3–6]. However, in many cases the highest total levels of the pressure pulsations are observed when the barrier is situated at fairly large distances from the nozzle opening and the pressure pulsations have a random nature. We have investigated the pressure pulsations on a plate normal to a supersonic strongly underexpanded jet. The pulsation characteristics were measured for an arrangement of the obstacle when auto-oscillations are absent. We have established dependences that generalize the results of measurement of the pulsation characteristics at both subsonic and supersonic velocities on the jet axis directly in front of the obstacle. We have also investigated the correlation between the pressure pulsations on the plate and external acoustic noise. We have obtained the dependence of the level of the acoustic noise on the value of the maximal pressure pulsations on the plate.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 1, pp. 163–167, January–February, 1980.     

Action of an explosive plastic wave on a plate

The action of a transient loading on an infinitely elastic plate, freely covering the surface of an ideal compressible liquid, was discussed in [1–3]. A review of work on the dynamics of a plate under the action of a transient loading is given in [4].Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 4, pp. 131–136, July–August, 1976.     

Mathematical models of particle crystallization in two-phase flows

The results of an analytic and numerical investigation of individual particle crystallization regimes are presented and it is shown that the equilibrium crystallization model [1, 2] is a limiting case of the nonequilibrium crystallization model [3]. An approximate method of solving the problem of nonuniform particle heating, which must be taken into account in determining the onset of particle crystallization, is described.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 6, pp. 77–84, November–December, 1989.     

Thermal effect of a freely expanding gas jet on a flat plate

An experimental investigation was made into the thermal effect of a single gas jet on a plate at Mach numbers of the nozzles in the range 2–6.1, specific heat ratio = 1.4, total pressure difference up to 6·10⁷, gas temperature 450–520 °K in the forechamber, and pressure in the forechamber (10–20)· 10⁵ Pa. The proposed dimensionless numbers made it possible to obtain generalized dependences of the distribution of the heat flux to the plate on the conditions of the problem. A method of approximate calculation of the heat fluxes is proposed.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 4, pp. 119–126, July–August, 1981.     

The problem of plane flow of ideal liquid around a shell filled with gas

The plane flow of an ideal liquid around a certain volume of gas bounded by a rigid rectilinear plate perpendicular to the incident flow and by an absolutely elastic film fastened at the ends of the plate is examined. The existence of a solution is demonstrated in a certain range of variation of the parameters, and a method of finding it is indicated.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 3, pp. 108–117, May–June, 1971.     

Solution of Navier-Stokes equations near the trailing edge of a plate

The appearance of a local singularity in the solutions for the neighborhood of the trailing edge of a plate in a sub- or supersonic flow makes it necessary to consider the flow in the local region which is described in the first approximation by the Navier-Stokes equations for an incompressible gas. In this paper numerical solutions are obtained for such a region for both a thin plate and a plate with thickness. The streamline patterns and the distributions of the flow functions over the surface of the plate and in the wake behind it are presented. For the plate with finite thickness, a numerical solution is obtained in a wide range of variation of the local Reynolds number.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 4, pp. 173–176, July–August, 1985.