Quantitative planar Raman imaging through a spectrograph: visualisation of a supersonic wedge flow

Planar Raman imaging through a spectrograph is demonstrated as a diagnostic tool for quantitative flow visualisation of internal supersonic wedge flow. A dedicated Bayesian deconvolution filter is used to remove the spectral structure that is introduced by the spectrograph. The 2D density field is determined with ca. 10% precision using average images over 6,000 laser pulses, down to 0.5 mm from the surface of the wedge. Direct interpretations of Raman intensities provide more precise density data than indirect interpretations based on shock geometry in 2D inviscid flow.

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Validation of averaged equations for thermal vibrational convection in near-critical fluidsValidation d'équations moyennées pour l'étude de la convection vibrationnelle dans les fluides supercritiques.

Within an averaging approach, the governing equations and effective boundary conditions describing both the average and pulsation motion of a near-critical fluid subjected to high-frequency vibrations are obtained. Vibrations induce the non-homogeneities in average temperature. Owing to these non-homogeneities, the average flows can be generated even in isothermal cavity under weightlessness. These flows are examined for 1D and 2D configurations. The direct numerical simulations fulfilled earlier confirm the averaged model, we obtain the same flow structures by essentially smaller requirements for computational time. To cite this article: A.Vorobev et al., C. R. Mecanique 332 (2004).     

Unsteady-state flow of a gas in a channel,resulting from the motion of a piston,with magnetohydrodynamic offtake of energy and luminescence of the gas

The present paper discusses the one-dimensional unsteady-state flow of a gas resulting from the motion of a piston in the presence of weak perturbing factors, with which the investigation of the perturbed (with respect to the usual self-similar conditions) motion reduces to the solution of ordinary differential equations, is indicated. The distributions of the parameters of the gas between the piston and the shock wave are found. The conditions under which there is acceleration or slowing down of the shock front are clarified. As an example, this paper considers the unsteady-state motion of a conducting gas in a channel with solid electrodes under conditions where electrical energy is generated, and the flow of a gas taking radiation into account, under the assumption of optical transparency of the medium. The theory developed is used to solve the problem of the motion of a thin wedge with a high supersonic velocity in an external axial magnetic field, taking account of the luminescence of the layer of heated gas between the wedge and the shock wave.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 5, pp. 17–25, September–October, 1970.     

Numerical Simulation of Plasma Dynamics in a Nonuniform Magnetic Field

An efficient algorithm is proposed enabling numerical simulations of plasma dynamics in a nonuniform magnetic field. The present numerical data are in good agreement with experimental data obtained in a GOL-3 setup and with previous simulations. The experimentally observed effect of fast transfer of energy to ions is confirmed. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 47, No. 1, pp. 35–45, January–February, 2006.     

A note on line forces in gradient elasticity

The theory of gradient elasticity is applied to line forces. Line forces acting on a point within the body and a concentrated normal force (Flamant problem) which acts on a half plane are studied. Closed analytical solutions which have a simple form are obtained for displacement fields of these forces. The gradient elasticity solutions are free from undesirable displacement singularities predicted by classical elasticity.     

Forced and mixed convection boundary layer flow along a flat plate with variable viscosity and variable Prandtl number: new results

The steady laminar boundary layer flow along a flat plate is studied taking into account the variation of fluid viscosity and fluid Prandtl number with temperature. In the forced convection case the plate moves with constant velocity and its temperature varies in power law with x. In the mixed convection case the plate temperature is constant and the fluid moves upwards due to an external free stream and due to buoyancy forces. The results are obtained with the direct numerical solution of the boundary layer equations. The study concerns the wall heat transfer, the wall shear stress and velocity and temperature profiles across the boundary layer. The results of the present work are different from those existing in the literature, which have been obtained with the assumption of constant Pr number.     

Global stability analysis of parametrically excited cylindrical shells through the evolution of basin boundaries

In the present study, the large-amplitude vibrations and stability of a perfect circular cylindrical shell subjected to axial harmonic excitation in the neighborhood of the lowest natural frequencies are investigated. Donnell's shallow shell theory is used and the shell spatial discretization is obtained by the Ritz method. An efficient low-dimensional model presented in previous publications is used to discretize the continuous system. The main purpose of this work is to discuss the use of basins of attraction as a measure of the reliability and safety of the structure. First, the nonlinear behavior of the conservative system is discussed and the basin structure and volume is understood from the topologic structure of the total energy and its evolution as a function of the system parameters. Then, the behavior of the forced oscillations of the harmonically excited shell is analyzed. First the stability boundaries in force control space are obtained and the bifurcation events connected with these boundaries are identified. Based on the bifurcation diagrams, the probability of parametric instability and escape are analyzed through the evolution and erosion of basin boundaries within a prescribed control volume defined by the manifolds. Usually, basin boundaries become fractal. This together with the presence of catastrophic subcritical bifurcations makes the shell very sensitive to initial conditions, uncertainties in system parameters, and initial imperfections. Results show that the analysis of the evolution of safe basins and the derivation of appropriate measures of their robustness is an essential step in the derivation of safe design procedures for multiwell systems.     

Local flows of a deformable damageable medium under impact interaction with a cavitating fluid

Local viscoplastic-flow and damage processes in a deformable medium induced by the collapse of dispersed vapor-gas bubbles in the near-wall layer of a cavitating fluid in the presence of propagating shock waves are investigated. The study is based on a generalized model developed for describing nonlinear deformations and flow of damageable media and on the results obtained earlier for local fluid flows induced by limiting transitions of vapor-gas bubbles.     

On the propagation of elastic waves through composite media II

Summary The propagation of elastic waves (both longitudinal and transverse) through polyurethane rubbers filled with different amounts of sodium chloride particles was studied at 0.8 MHz and 5 MHz. At a constant filler concentration (∼10% by volume), the velocity of these waves appeared to be independent of filler size. On the other hand, both velocities were found to increase with filler content. From the wave velocities, the effective modulus for longitudinal waves, L, bulk modulus, K, and shear modulus, G, were calculated according to the relations for a homogeneous isotropic material. All three moduli appear to be monotonically increasing functions of filler content, c, over the whole experimentally accessible temperature range (−80°C to +80°C for L and K; −80°C to about −30°C for G) and they, moreover, reflect the glass-rubber transition of the binder. Poissons ratio, μ, was found to decrease with increasing filler content and shows a rise at about −30°C as a result of the approach of the glass-rubber transition. The attenuation of the elastic waves was also measured in the temperature ranges mentioned. For filler particles beyond a critical size both tan δ_L and tan δ_G in the hard region are independent of the filler content within the accuracy of the measurements. The critical size depends on the type of wave and on its frequency. In the rubbery region, however, tan δ_L increases with particle size (at a constant content of 10% by volume) and even shows an enhancement with the smallest particles (1–5 μ) at 0.8 MHz. Moreover, it is found that for the same filler size tan δ_L increases with filler content. In some cases an anomalous damping behaviour was found, such that in the rubbery region the attenuation rises indefinitely with temperature. For filler particles larger than the above-mentioned critical size, tan δ_G and tan δ_L increase in the hard region as well. Finally, the experimental results are compared with existing theories on the elastic properties of and wave propagation through composite media.     

Elementary solutions of plane nonlinear filtration problems

In the solution of plane problems of filtration theory it is important to study the behavior of the solution near the singular points of the boundary of the flow region (corner points, points of boundary-condition change, and so on) and at infinity (see, for example, [1]). In the present study, this analysis is made for nonlinear filtration problems.Just as in the analogous problems of gasdynamics [2, 3] and nonlinear elasticity theory [4], to find the singular solutions we make the transformation to the filtration velocity hodograph plane. Examples relating basically to filtration with the limiting gradient are presented.The authors wish to thank I. I. Eremlna, T. N. Ericheva, and T. N. Ivanova for assistance in the calculations.