Two-phase PIV method using two excitation and two emission spectra

To be able to characterize the airflow in the presence of liquid droplets in a confined geometry, a new two-phase particle image velocimetry (PIV) method is developed. It is based on a two-colour YAG laser and two different fluorescent dyes dissolved in the gas-phase tracers and droplets. This approach permits to separate the images (and thus the information) of the two phases optically and simultaneously. When experiments need to be carried out in a confined geometry (such as in a wind tunnel) with uniform droplet distribution and high turbulence, which are the case in the present investigation, one should be able to deal with continuous droplet deposition on the lateral walls through which the cameras acquire images. It requires the adaptation of the experimental conditions and the development of a dynamic background subtraction algorithm. The typical results reveal the influence of the presence of liquid droplets on the airflow by comparing single-phase flow field to the air-phase motion in two-phase flow configuration. Furthermore, by analysing the continuous-phase and the discrete-phase properties, some aspects of the interaction between the two phases are shown.     

Analysis of ellipsoid compressed by two axial concentrated forces at two ends

Integral equation method and photoelastic experiment are used for the stress analysis of an axial compressive ellipsoid. Let the concentrated forces and the centers of compression, with symmetrical unknown intensive functions X₁(c)=X₁(–c) and X₂(c)=X₂(–c) respectively, be distributed symmetrically to =0 plane along the axis z(=–c) in [a,) and [–a,–) of the elastic space, in addition to a pair of equal and opposite axial forces acting on z=a and z=–a. We can reduce the problem of an axial compressive ellipsoid to two coupled Fredholm integral equations of the first kind. Furthermore, numerical calculation is then made. Two photo-elastic models of ellipsoid were analysed by Freezing and Cutting method, and the results, in which ₂ is quite nearly to those obtained by integral equation method, had been used in the analysis of the data of compressive rock specimens.     

Squeeze flow of a second-order fluid between two parallel disks or two spheres

The normal viscous force of squeeze flow between two arbitrary rigid spheres with an interstitial second-order fluid was studied for modeling wet granular materials using the discrete element method. Based on the Reynolds‘ lubrication theory, the small parameter method was introduced to approximately analyze velocity field and stress distribution between the two disks. Then a similar procedure was carried out for analyzing the normal interaction between two nearly touching, arbitrary rigid spheres to obtain the pressure distribution and the resulting squeeze force. It has been proved that the solutions can be reduced to the case of a Newtonian fluid when the non-Newtonian terms are neelected.     

Motion of two vortex rings

It is well-known [1] that two coaxial rings which are moving in the same direction pass through each other alternately. In the case of thin vortex rings this phenomenon was first considered qualitatively in [2]. The assumption that the vortex rings are thin means that when their interaction is considered they can be assumed to be annular vortex filaments. In the present paper, on the basis of the approach suggested in [2], certain new properties are determined for a system of two coaxial vortex rings of the same intensity.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 5, pp. 176–177, September–October, 1985.The authors express their sincere thanks to A. A. Aleksandrov for his interest in their work.     

Richtmyer-Meshkov instability of an interface between two media due to passage of two successive shocks

The instability of a free surface of aluminum after passage of two shocks that follow one after the other at a certain time interval is studied numerically. The first shock is rather strong (the postshock pressure is about 75 GPa). It is shown that if at the moment when the second shock arrives at the free surface, the perturbation evolution is nonlinear, then, in contrast to the linear stage, the change in the growth rate of the amplitude depends weakly on the wavelength of the initial perturbation. A formula is proposed which describes the effect of the second shock on the amplitude growth rate and in which the main structure of Richtmyer's formula is preserved. It is demonstrated that the parameters of the second shock that ensure freezing of the instability can be determined using only the growth rate of the amplitude. Computing Center, Russian Academy of Sciences, Moscow 117967. Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 41, No. 1, pp. 28–37, January–February, 2000.     

Lock-on characteristics behind two side-by-side cylinders of diameter ratio two at small gap ratio

The lock-on characteristics, the detailed interactions and downstream evolutions of the wakes behind side-by-side cylinders of unequal diameter (D/d?=?2), spaced by a gap ratio 0.75 (G/D?=?0.75), are investigated at Reynolds number 600 by the dye flow visualization, laser Doppler anemometry (LDA) and particle image velocimeter (PIV) velocity measurements. The lock-on frequency bands are studied by LDA and PIV at Reynolds number 2,000. The D, d and G are the diameters of the large, the small cylinders and the net gap between two cylinders, respectively. Periodic excitations, in form of rotary oscillation about the cylinder center, are applied to the large cylinder with the same amplitude. It is found that while the large cylinder is excited, two lock-on frequency bands of the wake behind the large cylinder are detected. These two lock-on frequency bands correspond to the primary and the one-third sub-harmonic lock-on of the wake behind large cylinder, respectively. These two lock-on frequency bands distribute symmetrically about the fundamental and the third superharmonic of the natural shedding frequency behind a single cylinder at the same Reynolds number. The left-shifted frequency band (1.8?≤?f _e /f _os ?≤?2.0) is not considered as a locked-on frequency band because the phase difference between two excitation frequencies across f _e /f _os ?=?2.0 vary significantly. While the wake behind the large cylinder is locked-on at f _e /3 (or f _os ), the gap flow becomes unbiased and the frequency of the wake behind small cylinder remains around the natural shedding frequency. Thus, the frequency band of 3.0?≤?f _e /f _os ?≤?3.22 is also not locked-on because the phase difference in the narrow wake excited at f _e /f _os ?=?2.93 and 3.07 changes significantly. Note f _e and f _os denote the excitation frequency and the natural shedding frequency behind a single large cylinder, respectively.     

The interface between two simple fluids between two oscillating vertical planes

The shape of the interface between two simple fluids having nearly the same densities which are contained between two oscillating vertical planes has been calculated by the method of domain perturbation pivoted about the rest state. The analysis has been carried out through second order in the amplitude of the oscillation velocity. The existence of the shearing motion on the interface has been considered by incorporating the spatial dependence of the primary motion on the vertical coordinate as well as on the transverse coordinate. This has led to an enhancement of the normal stress effect and thus results in predicting a higher rise in the interface than that in the case when no shearing motion is assumed to exist on the interface.     

Snap-through buckling of two simple structures

The snap-through buckling of two simple structures subjected to quasistatic loading is analyzed by use of the elastica theory of prismatic bars. In the first problem, the deformation of perfect and imperfect three-hinged deep trusses is considered and the results of the previous experimental observations are explained analytically. In the second problem, the snap-through behavior of a column restrained by an elastic wire is studied and a comparison of critical loads are made with the approximate solutions obtained recently by Nachbar [1].     

Thermal stresses around two parallel cracks in two bonded dissimilar elastic half-planes

Summary Thermal stresses around two parallel cracks in two bonded dissimilar elastic half-planes are determined. One of the cracks lies in the upper half-plane, while the other is in the lower half-plane. Uniform heat flow is assumed to be at right angles to the interface. Application of the Fourier transform technique reduces the problem to that of solving dual integral equations. To solve the equations, the difference of the crack surface temperature and those of the crack surface displacements are expanded in a series of functions which are automatically zero outside the cracks. The unknown coefficients in the series are solved by the Schmidt method. The stress intensity factors are calculated numerially for composite materials featuring a ceramic upper half-plane and a steel lower half-plane.

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Wärmespannungen um zwei parallele Risse in zwei verbundenen, verschiedenen, elastischen Halbunendlichplatten

Übersicht Es werden die Wärmespannungen um zwei parallele Risse in zwei verbundenen, verschiedenen, elastischen Halbunendlichplatten bestimmt. Einer der beiden Risse liegt in der oberen Halbunendlichplatte, der andere in der unteren. Es wird angenommen, daß ein gleichmäßiger Wärmefluß senkrecht zur Grenzfläche erfolgt. Die Anwendung der Fourier-Transformation reduziert das Problem auf die Lösung dualer Integralgleichungen. Zur Lösung der Gleichungen werden die Temperatur-sowie die Verschiebungsdifferenzen an der Rißoberfläche in eine Reihe von Funktionen entwickelt, die außerhalb der Risse automatisch zu Null werden. Die unbekannten Koeffizienten dieser Reihe werden dann über das Schmidt-Verfahren bestimmt. Anschließend werden für Verbundmaterialien, bei denen die obere Halbunendlichplatte aus Keramik und die untere aus Stahl besteht, die Spannungsintensitätsfaktoren numerisch berechnet.

     

Conservation laws of two coupled non-linear oscillators

This paper presents a novel approach to obtaining a complete set of time-dependent expressions for approximate conservation laws of two weakly non-linear coupled oscillators. The procedure developed for a non-resonant case is based on the field method concept of deriving a conservation law from an incomplete solution of a partial differential equation. Due to the non-linearity of the system being considered, this concept is combined with the multiple variable expansion procedure.     

Growth predictions of two interacting cracks

The elastic fracture behavior of a plate subjected to uniform stress surrounding two equal cracks inclined at an angle is investigated. The orientation of the crack plane with applied stress can be varied. Among the cases are: (1) two cracks inclined symmetrically with respect to the vertical and horizontal applied stress, and (2) one crack is horizontal while the other is inclined to the vertical applied stress. The strain energy density criterion is used for determining the combined crack and load arrangement that correspond to the lowest critical load at global instability. The direction of crack initiation is also determined. Quantitative results pertaining to the fracture characteristics are given in graphical forms.     

Free vibration of two coupled nonlinear oscillators

An analytical investigation is carried out on the free vibration of a two degree of freedom weakly nonlinear oscillator. Namely, the method of multiple time scales is first applied in deriving modulation equations for a van der Pol oscillator coupled with a Duffing oscillator. For the case of non-resonant oscillations, these equations are in standard normal form of a codimension two (Hopf-Hopf) bifurcation, which permits a complete analysis to be performed. Three different types of asymptotic states-corresponding to trivial, periodic and quasiperiodic motions of the original system-are obtained and their stability is analyzed. Transitions between these different solutions are also identified and analyzed in terms of two appropriate parameters. Then, effects of a coupling, a detuning, a nonlinear stiffness and a damping parameter are investigated numerically in a systematic manner. The results are interpreted in terms of classical engineering terminology and are related to some relatively new findings in the area of nonlinear dynamical systems.     

Transitions between two pictorial attractors

Two experiments exploring similarity judgments on pairs and triplets of stimuli drawn from pictorial series are described. The stimuli are the Man-Woman and Gypsy-Girl pictures that slowly change from one prototype to the other as one progresses along the series. These have been used previously to demonstrate hysteresis of category judgments on ambiguous figures; the Man Woman series has been both modelled as a problem in neural network theory and mapped onto part of a cusp catastrophe surface. It. is shown that the transition process is complicated with a zone of uncertainty and prevalence of bimodality in many of the pairwise similarity judgments. The dynamics are interpreted in terms of transitions between two saddle-node attractors that are themselves not a discrete pair but have some overlap in their composition.     

Thermoelastic problem of two collinear cracks

A two-dimensional problem of two collinear cracks influenced by concentrated heat sources is studied. The considerations are limited to a problem of normal opening of the crack (Mode I) assuming that cracks of different lengths are thermally insulated and free of loads. The formulas describing displacements and stresses at any point of the body are given. The stress intensity factors at the crack tips and the openings of the cracks are obtained. To avoid possible overlapping of the cracks boundaries, the position of the heat sources and the lengths of the cracks are analyzed to ensure non-negative stress intensities factors (SIF's) at all the crack tips. The solution to the above problem has been derived using the method given by Panasuyk et al. [V.V. Panasuyk, M.P. Savruk, A.P. Datshshyn, Stress Distribution around Cracks in Plates and Shells, Naukova Dumka, Kiev, 1976 (in Russian); V.V. Panasuyk, M.P. Savruk, A.P. Datsyshyn, A general method of solution of two-dimensional problems in the theory of cracks, Eng. Fracture Mech. 9 (1977) 481–497.     

Interaction of two supersonic radial gas flows

The flow resulting from the collision of two spherically symmetric supersonic gas streams generated by three-dimensional sources has been studied within the framework of the inviscid perfect gas model. When the characteristics of both sources are the same, the problem reduces to that of the interaction between a spherically symmetric flow and a plane barrier [1, 2]. By means of a certain passage to the limit, the flow from one of the sources can be reduced to a uniform supersonic gas flow. In this case the problem reduces to the problem of uniform gas flow past a source considered in [1, 3, 4]. The resulting flows are investigated with reference to all the parameters characterizing the two sources. The shock wave structure, both in the neighborhood of and at points remote from the axis of symmetry, is studied, together with the distributions of the gas dynamic quantities in the shock layers; certain similarity laws are established. The astrophysical applications of the problem associated, in particular, with a certain x-ray radiation mechanism in binary stellar systems [5] are of particular interest.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 4, pp. 159–165, July–August, 1990.The authors are grateful to V. B. Baranov for his constant interest and to S. A. Zhekov and V. V. Usov for useful discussions.     

Merging of two independent diffracting shock waves

A preliminary experimental and numerical investigation into the interaction between two independent shock waves emerging perpendicular to each other into a common space is presented. It is arranged that two shock tubes have a common diffracting edge, so that the two waves arrive at the edge simultaneously. The shock Mach number was 1.31. The merging three-dimensional diffracting shocks reflect regularly off each other, but as they become more curved due to diffraction the angle between them changes and Mach reflection develops. L-shaped vortices are shed at the two free edges of each tube exit. As they meet, they merge and interact in a complex manner with each other.     

DYNAMIC BEHAVIOR OF TWO COLLINEAR PERMEABLE CRACKS IN A PIEZOELECTRIC LAYER BONDED TO TWO HALF SPACES

IntroductionIn the fracture mechanics studies for piezoelectric materials,differently electricboundary conditions at the crack surfaces have been proposed by many researchers.Forexample,for the sake of analytical simplification,the assumption that the cra…     

Fluid-dynamic interaction between two spheres

Experiment of fluid-dynamic interaction between two spheres was conducted to obtain basic information concerning the two-phase flow, especially in dense phase. Two or three spheres were set up in a water tunnel in the longitudinal or transverse direction with Reynolds numbers less than 10³. The flow behind the sphere was visualized by the use of condense milk and change in vortex structure due to the interaction was observed in detail. Additionally, drag force on the sphere was measured by a pendulum method which was developed to detect small drag, and the range of distance in which the drag is affected by the interaction was shown.     

Collision of two plane free streams with division of one of them into two flows

The collision of two streams of ideal incompressible fluid with the division of one stream into two flows in opposite directions along the boundary of the other is considered. The second stream is shifted from its initial direction due to the collision. The ratio of the total pressure heads of the separated and shifted streams is 1. The flow regions corresponding to each of these streams map conformally onto the first and fourth quadrants of the complex plane so that the streamline separating the streams corresponds to the real semiaxis in both cases. By using the dynamic and kinematic conditions for this streamline, nonlinear relations are found linking the boundary values of the logarithms of the complex velocity in each of the two flow regions. These analytic functions are computed approximately by linearization at small values of .Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 1, pp. 3–7, January–February, 1975.