Motion of gas bubbles in a liquid under the influence of a temperature gradient

This study deals with the motion of a gas bubble developing under the influence of surface-tension forces in an imponderable viscous liquid with a temperature gradient. A theory of steady-state motion of a bubble in a field with constant temperature gradient is given for the case of small Reynolds numbers. Experimental results that show qualitative agreement with the theory are presented.The authors wish to thank M. A. Lavrent'ev for formulating the problem and giving constant attention to their work.     

Uniform expansion of a gravitating gas in the presence of a pressure gradient

Within the framework of the Newtonian mechanics, we studied the possibility of the formation of a uniformly expanding gravitating gas due to the passage of a detonation wave through a freely compressible medium (dust). The formulation of the problem is associated with the modeling of the large-scale expansion of the Universe. At the same time, the results obtained can also be applied to the calculation of the consequences of the spherical collapse of other gaseous masses. A class of exact solutions taking the pressure gradient into account is derived. Possible changes in the system behavior, as compared to with case of uniform pressure studied in [1], are analyzed. Moscow. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 4, pp. 176–182, July–August, 1998. The study was carried out with the support of the Russian Foundation for Basic Research (project No. 97-01-00196).     

The reduction of skin friction by riblets under the influence of an adverse pressure gradient

In this paper we address the effectiveness of riblets on skin friction reduction under the influence of an adverse pressure gradient. The measurements were taken in a wind tunnel. Skin friction was observed with a drag balance which has a reproducibility of better than 1%. The accuracy of the balance is estimated to be less than 1% for the case of zero-pressure gradient and at most 3% for a pressure gradient. The data on skin friction reduction at zero pressure gradient were consistent with previous results and amount to 5% at dimensionless riblet width of s ⁺ = 13. We find that at all adverse pressure gradients the skin friction reduction by riblets persists. At moderate pressure gradients the reduction increases somewhat to 7%. The velocity profile which is also measured, exhibits the characteristic shape for a boundary layer with an adverse pressure gradient and agrees well with theory. From the velocity profiles measured at two stations we estimated with the help of a momentum balance the skin friction and skin friction reduction. The results differ from the drag-balance data. Due to the poor accuracy of the momentum balance method which we estimate in our case, we conclude that the results obtained with this method are less reliable than those obtained with the drag balance. This throws some doubt on previous results on drag reduction under the influence of a pressure gradient which were based on the momentum balance method.     

The stability of a revolving non-newtonian liquid in the presence of an axial pressure gradient

Summary The effect of cross-viscosity on the stability in fluids has been investigated. It is found that this effect destabilizes the flow of an incompressible non-newtonian liquid between coaxial rotating cylinders when an axial pressure gradient is applied.     

Asymptotic theory of the occurrence of recirculation zones in an axisymmetric wake under the influence of an adverse pressure gradient

An integrodifferential equation is obtained which describes the process of formation of recirculation zones near the axis of a thin axisymmetric wake in an incompressible fluid. The equation contains a parameter which characterizes the degree of influence of an adverse pressure gradient. It is shown that for values of the parameter less than a definite critical value there exist two different steady solutions, and for values exceeding the critical one there are no steady solutions.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 5, pp. 54–60, September–October, 1987.The author is grateful to V. Ya. Neiland and Vik. V. Sychev for information about their work and useful advice.     

Motion of a piston in a cylindrical tunnel with allowance for the additional mass of the gas

We propose to derive relations for the motion of a piston, taking into account the variation of its mass due to the additional mass of the gas entrained by the motion of the piston. We show that the gas entrained by the piston has an appreciable effect on the acceleration of the piston and the acceleration length, with the piston attaining a velocity close to the limiting value.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 5, pp. 167–169, September–October, 1971.     

Development of a bluff body wake under the combined influence of curvature and pressure gradient

The present experimental investigation deals with the behaviour of a wake generated by a square cylinder developing in a curved diffuser, a curved duct, a straight duct and a straight diffuser having a same pressure gradient as in the curved diffuser. This enables a systematic study of the effects of curvature and pressure gradient on wake development. It is seen that the curvature makes the wake asymmetric; the wake half width increases on the inner side and decreases on the outer side; the inner side being the region between the centreline and the wall closer to the centre of curvature and the outer side being the region between the centreline and the other wall. It causes a higher entrainment in the inner side as compared to the outer side. An adverse pressure gradient, on the other hand, causes a higher wake growth and velocity defect but reduces the rate of decay of the velocity defect. These are not altered significantly when the curvature and pressure gradient effects are combined. The curvature enhances the Reynolds stresses and the kinetic energy on the inner side and suppresses them on the outer side which makes their profiles asymmetric. These profiles become more and more asymmetric with increase in the streamwise distance. When the effects of curvature and adverse pressure gradient are combined, the profiles become further asymmetric.Department of Aerospace Engineering     

Laminar mixing of homogeneous currents in the presence of a pressure gradient

The problem of the mixture of a current with a quiescent gas was solved by Chapman [1]. In this study, the results of certain calculations on the laminar mixing zone of homogeneous gas currents with a pressure gradient will be presented. On the basis of the data calculated and evaluations, it is shown that the concept of similarity, formulated by Less [2], is applicable to the problem of mixture with a pressure gradient. In variable similarities, the velocity profiles for gradient flow practically coincide with the profiles of nongradient flow for the same parameter values at the interior and exterior boundaries of the mixture zone. Moreover, it proves to be the case that the excess velocity profile depends weakly on the specific parameters of the problem.Moscow. Translated from Izvestiya Akademii Nauk SSSR. Mekhanika Zhidkosti i Gaza, No. 2, pp. 67–71, March–April, 1972.     

Change in the thickness of an incompressible turbulent boundary layer in the presence of a longitudinal pressure gradient

Dimensional analysis is used to find the change in the thickness of a turbulent boundary layer that develops under conditions of a strong positive or negative pressure gradient. Comparison of the expression for the thickness with the available experimental data makes it possible to determine the universal constant in the expression. An interpolation dependence is proposed, this holding for all not too rapidly varying velocity distributions on the outer boundary of the turbulent boundary layer. The results of calculations made with this dependence are compared with numerous experimental data on the change in the thickness of turbulent boundary layers.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 2. pp. 150–156, March–April, 1979.     

Nonlinear subresonance oscillations of a gas in a pipe under the influence of periodically varying pressure

A study is made of one-dimensional nonlinear oscillations of an ideal gas in a pipe one end of which is closed, the pressure being given at the other end and periodically varying with the time. For frequencies close to the subresonance ones, asymptotic equations are obtained which govern the periodic motions of the gas. Solutions containing shock waves are constructed.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 2, pp. 151–157, March–April, 1988.The author is grateful to A. N. Kraiko and V. E. Fortov for considering the study and for their support.     

Flow of elastico-viscous liquids in channels under the influence of a periodic pressure gradient,part 1

Summary The flow of a non-Newtonian incompressible liquid in a straight pipe of circular cross-section under the influence of a periodic pressure gradient is investigated; the viscous and elastic properties of the liquid are defined in terms of a spectrum of relaxation times. Such a flow is of interest to the experimentalist, because the flow could be readily attained and controlled in practice. A solution is obtained which determines the variation in the mean-square velocity over the section of the pipe. In the numerical illustrations given, it is shown that the general nature of the flow is similar to that of a purely viscous liquid of constant viscosity, a high peak of average velocity occurring near the wall of the pipe. However, it is shown that elasticity of the type considered could strongly affect the value and position of this peak of the average velocity.     

Motion of a gas bubble in fluid under vibration

This paper is concerned with the analysis of motion of a gas bubble in a uniformly oscillating incompressible fluid. A theoretical model explaining the effect of sinking of gas bubbles in the absence of a standing pressure wave is validated experimentally. The conditions under which this effect occurs are determined, and a simple formula is derived for the average velocity of a gas bubble in the fluid.     

Motion of a flat piston in a gas at high Reynolds numbers taking account of chemical reactions

One-dimensional flows originating during motion of a heat-conducting piston in a gas at high values of the Reynolds number are studied. The influence of diffusion and chemical reactions is considered in the case of a binary gas mixture. A binomial external expansion taking account of the boundary-layer-displacement thickness formed ahead of the piston is found. A solution is obtained which describes the boundary layer, which includes accommodation effects. An analogous problem about plane shock reflection from a heat-conducting wall has been considered in [1–3], but without taking account of diffusion and chemical reactions. Accomodation effects were taken into account in later work, which improved the agreement between theoretical and experimental results for short times.