Deformation of liquid jets and drops injected into a gas stream

The process of deformation of liquid drops and jets is examined on a broad interval of two-phase flow parameters. The shape of a jet penetrating a gas stream directed at an angle to the jet-particle velocity vector is determined.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 3, pp. 82–88, May–June, 1971.In conclusion the authors thank A. K. Simonovskii for his useful comments.     

On the breakup of bubbles at high Reynolds numbers and subcritical Weber numbers

In this paper we propose a simplified two-dimensional model to describe some aspects of the turbulent breakage of bubbles at subcritical Weber numbers. In particular we focus on the breakup of bubbles owing to their interaction with an array of successive eddies, modeled by a train of straining flows. Our simulations show that, under certain conditions, a bubble accumulates energy due to its interaction with a sequence of turbulent structures until it eventually breaks, even if none of the eddies is sufficiently energetic to split the particle by itself. It is also shown that the different strain directions of the eddies acting on the surface of the bubble, and the resonance effect between their characteristic frequency and the natural oscillation frequency of the bubble immersed into the straining flow are the two key factors in the bubble deformation, and subsequent breakup mechanism. Moreover, the breakup patterns obtained from our simulations seem to agree qualitatively well with the experimental observations.     

Special characteristics of the breakup of liquid drops with a high gas pressure

In a majority of power plants, the conversion of a liquid fuel into combustion products takes place at high pressure and with a high velocity of the motion of the gas. It is natural that in the choice of the working scheme of the process account must be taken of the effect of possible changes in the characteristics of the atomization process of a liquid fuel, connected with a change in the density of the gas. Of particular importance is the effect of perturbations of the pressure and the velocity on the behavior of liquid drops in a high-density gas flow. The number of communications in which such questions are discussed is very limited, since an overwhelming number of experiments were made at atmospheric pressure [1–7]. Only articles [8, 9] give qualitative concepts with respect to the effect of perturbations of the pressure on the breakup of drops with a gas pressure up to 30 atm. From the information given in [8, 9] it is difficult to form a judgment with respect to the change in the critical conditions and the time parameters of the process of the breakup of drops with a rise in the initial pressure (density) of the gas.     

Shape and stability of a liquid drop moving at low Weber numbers

The equilibrium cross sectional shape and stability of a liquid drop moving in a gaseous medium is studied analytically. Such liquid drops appear as the final product in numerous industrial spraying and atomisation processes. Raindrops falling at their terminal speed can also be described by the present model. The equilibrium shape is formed by the interaction of two main factors; the dynamic pressure distribution in the gaseous medium which tends to deform the liquid drop into an oblate shape and the surface tension which tends to restore the spherical shape. The meridional shape of the liquid drop is obtained as a power series in the Weber number. The linear stability of the deformed shapes described above to small surface disturbances is studied. The stability analysis shows the effect of the surrounding gas flow on the natural frequencies of oscillation (vibration) of the liquid drop. The liquid drop is found to be stable in the region of low Weber numbers studied with a decrease in oscillation frequency proportional to the Weber number. This is in agreement with existing experimental data. Extrapolation of the results here lead to a Weber number of W=5.33 for breakup, again in agreement with experimental correlations.     

Deformation and breakup of viscoelastic drops in planar extensional flows

A computer-controlled four-roll mill was used to investigate the deformation and break-up of polymeric drops in the well-characterized flow of an immiscible Newtonian fluid. Aqueous polymer solutions ranging in concentration from 160 ppm to 3% by weight were examined. For zero-shear-rate viscosity ratios greater than order 1, the deformation of the drops closely followed that of Newtonian fluids, irrespective of the droplet material. However, drops with viscosity ratios less than order 1 had significantly smaller critical deformations and the critical capillary number was found to be substantially smaller. Two modes of drop break-up were discovered that differed substantially from that observed for Newtonian drops in the inclusion of cusped ends and tip streaming.     

Evaporation of spherical drops in a binary gas mixture at arbitrary Knudsen numbers

The quasisteady evaporation of drops in a binary gas mixture is investigated at arbitrary Knudsen numbers. The analysis is based on the solution of kinetic equations with collision integrals in the Boltzmann form by Lees's method [9]. The obtained solution makes it possible to consider an arbitrary model of intermolecular interactions. Formulas for the evaporation time of the drops are analyzed, the model of rigid elastic spheres being used for the interaction of the molecules.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 1, pp. 112–118, January–February, 1982.     

Experimental study of the atomization of drops of liquid at low Reynolds numbers

Some results of an experimental investigation into the deformation and atomization of drops of liquid at low Reynolds numbers are presented; these were obtained in a specially constructed apparatus in which a low-pressure flow of helium was used in order to reduce the Reynolds numbers. The values of the critical Weber numbers in a state of static deformation were equal to 15–22, in fair agreement with theory.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 2, pp. 182–186, March–April, 1971.     

Deceleration and deformation of a liquid drop in a gas stream

An analytic method is developed for calculating the nonstationary motion and spreading of two-dimensional and axisymmetric liquid drops in a gas stream. The method is based on an expansion of the Navier-Stokes equations in a small parameter.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 2, pp. 58–69, March–April, 1981.     

Temporal analysis of breakup for a power law liquid jet in a swirling gas

The breakup mechanism and instability of a power law liquid jet are investigated in this study. The power law model is used to account for the non-Newtonian behavior of the liquid fluid. A new theoretical model is established to explain the breakup of a power law liquid jet with axisymmetric and asymmetric disturbances, which moves in a swirling gas. The corresponding dispersion relation is derived by a linear approximation, and it is applicable for both shear-thinning and shear-thickening liquid jets. Analysis results are calculated based on the temporal mode. The analysis includes the effects of the generalized Reynolds number, the Weber number, the power law exponent, and the air swirl strength on the breakup of the jet. Results show that the shear-thickening liquid jet is more unstable than its Newtonian and shear-thinning counterparts when the effect of the air swirl is taken into account. The axisymmetric mode can be the dominant mode on the power law jet breakup when the air swirl strength is strong enough, while the non-axisymmetric mode is the domination on the instability of the power liquid jet with a high We and a low Re _n . It is also found that the air swirl is a stabilizing factor on the breakup of the power law liquid jet. Furthermore, the instability characteristics are different for different power law exponents. The amplitude of the power law liquid jet surface on the temporal mode is also discussed under different air swirl strengths.     

Steady and transient liquid sphere heating in a convective gas stream

 A finite-difference scheme has been developed to solve the equations governing the laminar forced convection heat transfer around and inside a spherical fluid droplet moving steadily in another immiscible fluid for both steady and transient thermal conditions. For large values of the external flow Reynolds number (Re), results not available in the literature have been obtained for circulating droplets at intermediate and high interior-to-exterior viscosity ratios (μ^*). Detailed results over a wide range of viscosity ratio (μ^*) and for 200≤Re≤1000 are presented for the temperature profiles outside and inside the sphere, Nusselt number, the time required to attain a uniform surface temperature and the time required to reach the steady-state temperature. Results show that convective heating is dependent on the external flow Reynolds number (Re) and the interior-to-exterior viscosity ratio (μ^*) where increasing Re or decreasing μ^* result in increasing heat transfer rate convected to the liquid sphere. Received on 1 March 1999     

Wave propagation in three-phase mixtures of a gas with particles and liquid drops

Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 4, pp. 74–81, July–August, 1991.     

Numerical prediction of breakup mode of contracting gas filament in liquid

The breaking up of gas filament in liquid is important in many industrial and scientific applications. In this study, a transient axisymmetric model with the level set method is built up to examine the dynamics of a contracting gas filament, and to determine the effects of the aspect ratio, Ohnesorge (Oh) number, and viscosity ratio on its breakup mode. The filament undergoes no break, middle break, or end-pinching modes with increasing aspect ratio at either a low or a high Oh number, and one critical initial aspect ratio is observed for each Oh number. The fate of the filament is determined by the interaction of capillary waves on its surface, and can be predicted accurately by using the one-dimensional wave superposition method. The decreasing viscosity ratio of liquid over gas reduces the critical initial aspect ratio for the fate transition between the no break and breakup modes, and this effect is reduced at a low viscosity ratio. These findings may be helpful in fabricating gas bubbles and their breakup suppression.     

Interaction of a turbulent stream of gas with a liquid film

We consider the turbulent motion of a gas in contact with a liquid film next to a wall. We assume that the stream of gas excites in the liquid a complex system of motions which are analogous in principle to the motions in the near-wall zone of a homogeneous turbulent stream with transverse shear. As a result of these motions, the gas stream has considerable turbulence even at the gas-film boundary. On this assumption, we calculate the relation between the pressure drop and the average gas velocity and find that it is in satisfactory qualitative and quantitative agreement with experimental results. As our scale of turbulence at the boundary, we took a linear variation as a function of the film thickness, which enabled us to describe the available experimental results satisfactorily, making use of two empirical constants.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 2, pp. 67–74, March–April, 1976.In conclusion, the authors take this opportunity to express their grateful recollection of conversations with the late Professor P. A. Semenov, who drew their attention to this problem, and also to thank G. G. Chernyi and G. A. Lyubimov for their comments and their interest in the work.     

液滴在气体介质中剪切破碎的数值模拟研究

液滴变形和破碎是燃料抛撒问题的重要过程.本文将VOF方法和标准k-ε湍流模型组合,建立了计算液滴在气流中变形破碎过程的数值方法.数值模拟了相关的实验,计算得到的液滴破碎过程与实验结果符合较好.在此基础上,分析了几个关键参数(Weber数、Ohnesorge数、液气密度比)对液滴破碎过程的影响.计算结果表明,Weber数...     

Nonlinear waves in a liquid film entrained by a turbulent gas stream

In the long-wavelength approximation and on the basis of a simplified system of equations analogous to the one considered by Shkadov and Nabil' [1, 2], an investigation is made into waves of finite amplitude in thin films of a viscous liquid on the walls of a channel in the presence of a turbulent gas stream. A bibliography on the linear stability of such plane-parallel flows can be found in [3–5]. The nonlinear stability is considered in [6]. A stationary periodic solution is sought in the form of a Fourier expansion whose coefficients are found near the upper curve of neutral stability by Newton's method and near the lower branch of the stability curve by the method of Petviashvili and Tsvelodub [7, 8].Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No, 2, pp. 37–42, March–April, 1981.I thank V. Ya. Shkadov for supervising the work and all the participants of G. I. Petrov's seminar for a helpful discussion.