The correlation between surface temperature and subsurface velocity during evaporative convection

The cross-correlation between surface temperature and subsurface velocity is presented for water undergoing evaporative convection. The surface temperature measurements were obtained via quantitative infrared imaging, and the velocity measurements were obtained using a two-component laser Doppler velocimetry (LDV) system. The water surface was covered with a surfactant monolayer, which did not impede evaporation. The largest measured correlation coefficient was 0.375. Correlation coefficients obtained after shifting the velocity and temperature time traces with respect to each other revealed a peak in the correlation coefficient very close to a zero time shift. The significance of these results and their implications for the remote sensing of underwater objects via infrared imaging are discussed. Received: 2 April 2001/Accepted: 30 November 2001     

Mixed convection of an incompressible viscous fluid in a porous medium past a hot vertical plate

This paper analyses steady two-dimensional mixed convection of an imcompressible viscous fluid in a porous medium past a hot vertical plate. Assuming Darcy-Brinkman model for the flow in a porous medium, the boundary layer equations are integrated numerically to obtain the non-similar solution for the velocity and temperature distribution for several values of the permeability and viscous dissipation parameters. It is shown that for a fixed value of Prandtl number Pr and dissipation parameter E, the skin-friction at the plate decreases with increase in the permeability parameter K₁. However for the same value or Pr and E, the heat transfer rate at the plate increases with increasing K₁. The dimensionlcss velocity and temperature functions in the flow are plotted for several values of E and K₁ with Pr = 0.73. It is also shown that for fixed values of K₁, and KPr, the skin-friction increases with increase in the dissipation parameter E.     

Low-level flow-induced acoustic resonances in ducts

Acoustic resonances are generated by air moving past a plate with a semi-circular leading edge located in a duct. The sound stimulates the small separation bubble near the leading edge to shed vortices into the boundary layer at the sound frequency. The acoustic energy required to sustain the resonances is generated as these vortices pass the trailing edge of the plate.     

Amplification of shock waves in a bubble-filled liquid with gas concentration gradient

The properties are studied of the propagation of unsteady shock waves in a gas-liquid system of bubble structure in the case when the volume concentration of the gas changes in the direction of motion of the shock wave. It is established that when there is a sufficiently rapid drop in the gas content, an effect of amplification of the shock wave is observed which is due to the deceleration of the medium behind the shock wave. A study is made of the laws of the evolution of long- and short-wave pulsed perturbations in such systems. The authors consider processes of reflection of waves from obstacles and their passage from a gas into a bubble liquid, from a two-phase mixture into a pure liquid. The contribution is determined of nonequilibrium effects to the process of amplification of a wave.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 1, pp. 49–54, January–February, 1988.The authors wish to express gratitude to R. I. Nigmatulin for his interest in the study and for useful discussions.     

Diffusion flux to a distorted gas bubble at large Reynolds numbers

The diffusion flux to a distorted gas bubble situated in a uniform viscous incompressible fluid flow is determined for large Reynolds and Péclet numbers and finite Weber numbers. The bubble has the shape of an ellipsoid of revolution, oblate in the flow direction, making it possible to use the flow field derived by Moore [1] in the form of a two-term expansion with respect to the flow parameter =R^–1/2 (R is the Reynolds number; the zeroth term of the expansion corresponds to potential flow). The dependence of the diffusion flux onto the bubble surface on the Weber and Reynolds numbers is determined. The results of Winnikow [2] and Sy and Lightfoot [3] are thus generalized to the case of finite Weber numbers and a broader range of Reynolds numbers.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 4, pp. 70–76, July–August, 1976.     

Slow motions of a rigid sphere in incompressible viscoelastic fluids

Problems concerned with the force of resistance and the moment of forces acting from the side of a viscoelastic fluid on a sphere moving with acceleration are considered in a linear formulation. Fairly simple relations are obtained for a fluid with a single relaxation time or a single after-action time. A discussion of the asymptotic expressions is given for a fluid with a large number of times.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 2, pp. 9–16, March–April, 1976.     

Radial oscillations of nonhomogeneous,thick-walled cylindrical and spherical shells subjected to finite deformations

The infinitesimal breathing motions of long cylindrical tubes and hollow spherical shells of arbitrary wall thickness subjected to a finite deformation field caused by uniform internal and/or external pressures are investigated. A neo-Hookean material with a material constant varying continuously along the radial direction is used. The shell is first subjected to finite static deformations and is then exposed to a secondary dynamic displacement field. Based on the theory of small deformations superposed on large deformations, closed form expressions are obtained for the frequency of small oscillations about the highly prestressed state. Frequency versus initial deformation parameter curves are given for several nohomogeneity functions and for various wall thicknesses.     

Ein Stoffgruppenmodell für die Berechnung der Diffusion in polynÄren Gasgemischen

A component group model for a simplified calculation of diffusion in multicomponent gaseous mixtures is developed. It is assumed, that the components of the mixture may be classified into groups in such way, that the binary diffusion coefficients between components of a group and also the binary diffusion coefficients between components of different groups may be approximated by averages. The application of the component group model is demonstrated for the mixture of dissociated air and for a 14-component H-C-N-O mixture. For many technically important gaseous mixtures a model with two or three groups of components yields a sufficient accurate approximation.     

Vibrations of a gas-filled spherical cavity in pseudoplastic and dilatant liquids

Questions of the dynamics of bubbles in a liquid are connected with problems of cavitation [1]. In connection with cavitation phenomena in non-Newtonian media, in particular in polymeric liquids [2, 3], a study is made of the pulsations of a bubble in a polymeric liquid with an exponential rheological law. The equation of the motion of the boundary of the gas cavity is integrated numerically; here, the cases of pseudo-plastic and dilatant liquids are discussed separately. The results obtained can be used in the analysis of acoustical cavitation in aqueous solutions of polymers.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 1, pp. 146–148, January–February, 1975.     

Bifurcational instability of an atomic lattice

In a recent article N.H. Macmillan and A. Kelly (1972) have confirmed on the basis of a linear eigenvalue analysis that a mechanically stressed perfect crystal can exhibit a bifurcational instability at stresses ranging to 20 per cent below that of the limiting maximum of the primary stress-strain curve. The question thus arises as to whether the branching point is in a non-linear sense either stable or unstable. In the former case, perfect and slightly imperfect crystals would be capable of sustaining stresses over and above the eigenvalue critical stress. In the unstable case, however, this eigenvalue stress would represent the ultimate strength of a perfect solid, while an imperfect crystal would fail at a limiting stress substantially below the eigenvalue.At 20 per cent below the limit point such a branching point is essentially distinct, and the non-linear stability analysis needed to answer this question is provided by a recently established general branching theory for discrete conservative systems. Often, however, the two critical equilibrium states are much nearer than this, and the branching theory is here suitably extended to cover the case of near-compound instabilities.An illustrative study of a close-packed crystal under uniaxial tension is next presented. A kinematically-admissible displacement field is employed and a bifurcation point is located on the primary equilibrium path just before the limiting maximum, the eigenvector being associated with a transverse shearing strain. Under these conditions a corresponding small transverse shearing stress would represent an ‘imperfection’, and the non-linear branching problem is next studied using the new general theory. This shows (in excellent quantitative agreement with an ad hoc numerical solution) that the branching point is non-linearly unstable with a quite severe imperfection-sensitivity which manifests itself as a sharp cusp on the failure-stress locus.