Structure of artificial disturbances induced by an external acoustic field in a supersonic boundary layer

The wave structure of the artificial disturbances generated by an external acoustic field in a supersonic boundary layer is investigated. The disturbances are classified with respect to phase velocity. Disturbances whose phase velocity in the direction of flow is greater than unity and waves located at the boundary of the discrete and continuous spectra are detected.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 3, pp. 82–86, May–June, 1989.     

Effect of homogeneous shear flow on small long-lived perturbations in a stratified fluid

Conclusions In the transitional stage of the evolution of small perturbations in a flowing stratified fluid various structures may be formed. The form of these structures will depend on the initial conditions, the velocity shear, the stratification, and the dissipative characteristics of the fluid. In some cases in the intermediate stage the perturbations may increase.However, at large times in the final dissipative stage all the perturbations decay and the structure of the longest-lived of them is fairly simple. Owing to the shear effect the surviving perturbations are highly elongated in the direction of flow. However, under the influence of the stratification, from all the perturbations with _h L/g in the transverse plane perturbations of two types are gradually filtered out: internal waves and thin horizontal layered structures.In the presence of shear flow the layered structure in a stratified fluid is not only preserved but even becomes more sharply expressed owing to the suppression by the shear if many of the competing perturbations.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 2, pp. 94–102, March–April, 1988.     

The propagation of nonlinear waves in a bidisperse fluidized bed

A study is made of the propagation of nonlinear kinematic waves of concentrations of solid particles in a fluidized bed of particles of two different sizes. A hyperbolic system of quasilinear equations is obtained which describes the propagation of the waves. A dependence of the characteristic velocities on the concentrations of the phases and the ratio of the sizes of the particles is found. The influence of an admixture of fine particles on the propagation of porosity waves in the fluidized bed is analyzed. The nature of the formation of jumps in the porosity depending on the concentration of the admixture is studied, as is the process of the transfer of the admixture of fine particles in the bed. The nature of the propagation of nonlinear waves in a fluidized bed of identical particles is clarified. A characteristic velocity is found and conditions are determined for the formation of discontinuities of concentration of the dispserse phase in rarefaction compression waves.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 1, pp. 49–58, January–February, 1985.     

Hypersonic multicycle gas jet with a high degree of underexpansion at the nozzle exit

Experimental research on highly underexpanded gas jets flowing from supersonic nozzles into an ambient medium has shown that for fairly large Mach and Reynolds numbers at the nozzle exit the jet consists of several cycles or barrels [1–3]. The authors have made a theoretical study of these jets, using the nonstationary analogy method (law of plane sections). An approximate model of the flow is constructed and an analytic solution is obtained for the location of the boundary of the multicycle jet. The corresponding equivalent nonstationary problem of the expansion of a cylindrical slug of gas is solved numerically. The results are found to be consistent with the experimental data and make it possible to explain a number of observations. It is shown, for example, that the experimentally observed decrease in the amplitude of the cycles (maximum radius of the barrels) as they progress downstream is due to the dissipation of energy in shock waves. It appears that the length of the cycles is more or less independent of the dissipation and almost constant. The effect of the removal (supply) of heat, for example, due to radiation, the relaxation of internal degrees of freedom, etc., on the geometry of the jet is examined. It is shown that the removal of heat leads to a decrease in the amplitude of the cycles and the supply of heat to an increase, but, like dissipation, neither affects the length of the cycles. The problem of a jet in a weakly inhomogeneous atmosphere is solved. It has shown that the jet geometry possesses an adiabatic invariant linking the length and amplitude of the cycles.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 6, pp. 27–35, November–December, 1984.     

Propagation of an ion jet near a dielectric surface

Difficulties in determining experimentally the local electrical parameters of unipolar-charged jets are arousing interest in the theoretical investigation of electrogasdynamic (EGD) flows. Free EGD jets were examined, for example, in [1–3]. In order to control the charge on the dielectric parts of aircraft surfaces, which results from their static electrification and may have certain negative consequences [4], and, moreover, to influence the flow in the boundary layer use is being made of unipolar-charged jets propagating near the dielectric [5, 6]. In [6] the case of an ion jet near a dielectric surface possessing surface conductivity was investigated. In these circumstances it is possible to neglect charge diffusion, which considerably simplifies the problem. Space charge diffusion was taken into account in [7], but subject to certain very important simplifications. The author has calculated the electrical parameters of a unipolar-charged jet propagating in a viscous incompressible gas near an ideal dielectric plate, with allowance for surface and polarization charges and, moreover, the diffusion processes near the surface. An asymptotic solution is obtained for the equations of the ionic diffusion layer as the ratio of the thickness of the diffusion layer to the thickness of the hydrodynamic boundary layer tends to zero.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 5, pp. 174–180, September–October, 1984.The author is grateful to V. V. Mikhailov and A. V. Kazakov for valuable advice and comments.     

Inhomogeneous inverse problem in finite elasticity

For a class of materials for which the principal strain directions always coincide with the principal stress directions one can determine the stress field in an inhomogeneously deformed body from given boundary conditions and a known strain field without knowing the constitutive equations. Each point of the inhomogeneously deformed body contains information such as that derived from an individual homogeneous identification test. The practically important two-dimensional case leads to a problem of solving a linear hyperbolic system where two differential equations describe the principal stress components. The problem can be reduced to that of integration along characteristics.Under a certain globality condition the existence, uniqueness, and correctness of the solution are guaranteed in the whole test piece. It is shown that the globality condition is closely related to whether or not the test piece is isotropic and elastic. The influence of experimental error on the correctness of problem formulation is discussed.

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Abstrakte Für die Klasse der Materialen, für welche die Grundspannungsrichtungen und die Grundverformungsrichtungen gleich sind, kann man das Spannungsfeld in einem inhomogen deformierten Körper für gegebene Randbedingungen und einem bekannten Verformungsfeld ohne Kenntnis der detailierten Form der Dehnungs-Spannungsgleichung bestimmen. Jeder Punkt des inhomogen deformierten Körpers liefert dieselbe Information wie ein individueller homogener Test. Der praktisch wichtige zweidimensionale Fall führt zu einem Problem der Lösung eines linear hyperbolischen Systems von zwei Differentialgleichungen für die Grundspannungskomponenten. Das Problem kann auf die Integration entlang der Charakteristik des Systems reduziert werden.Unter einer Bedingung der Globalität das die Existent, Eindeutigkeit und Richtigkeit der Lösung in der ganzen Testprobe gewährleistet sind. Es wird gezeigt, dass diese Globalitätsbedingung damit zusammenhängt eng, ob die Testprobe isotrop und elastisch ist. Der Einfluss der experimentellen Fehler auf die Richtigkeit der Formulation des Problems wird auch analysiert.

     

An approximate method of orthotropic photoelastic analysis

An approximate strain-optic law has been derived for photoelastic analysis of orthotropic model materials. Principal-strain difference and the direction of major principal strain can be obtained from only two photoelastic measurements (isochromatic-fringe order and isoclinic angle) by means of this strain-optic law. Limited experiments on models subjected to uniaxial and biaxial stresses indicate good agreement between the experimental results and predictions of the strain-optic law. A parametric study demonstrates that the direction of major principal strain can be predicted to within a few degrees of the exact value and that the principalstrain difference can be predicted within ±20 percent for most practical values of degree of orthotropy and ratio of principal strains. The error levels are quite acceptable considering the significant ease in analysis provided by the new law and the fact that such error levels are not uncommon in experimental investigations.