Self-oscillatory regimes of the penetration of vertical free turbulent jets through a liquid surface

The results of an experimental investigation of the penetration of vertical plane and round free turbulent jets through the surface of a liquid contained in a relatively narrow channel are presented. It is established that there exist the ranges of jet thicknesses, their velocities, and free region lengths, on which regular self-oscillatory regimes of the displacement of submerged jet regions and two-phase flow regions are observable. The mechanism of the generation of these regimes and the special features of the observable flows are discussed. The dependences of the self-oscillation periods on the main control parameters of the problem are established.     

Self-oscillatory spouting regimes of plane vertical submerged heavy-fluid jets in setups with near-bottom discharge

New results of the series of experimental and numerical investigations of the self-oscillatory regimes of plane vertical jet spouting from beneath the free surface of a heavy incompressible fluid in reservoirs of limited dimensions are presented. The experiments were performed on a rectangular-in-plan setup with near-bottom regime of fluid discharge. For several widths of the near-bottom orifices in the end walls of the setup the dependence of the self-oscillation period on the jet flow rate is studied. A considerable difference of these dependences from those earlier obtained in the case of the spouting with fluid discharge over a weir is found to exist. On certain ranges of control parameters it is established that the fountain self-oscillation periods are similar in value to those of natural oscillations of standing waves in the setup. A fairly narrow jet velocity range is revealed on which a hysteresis effect, that consists in the difference between the flow-rate-dependences of the self-oscillation period with gradual increase or decrease in the flow rate, is observable. The results of numerical calculations carried out using the STAR-CD software package are in good agreement with the experimental data.     

Some problems of axisymmetric cavitation flows

The equations for the shape of a slender axisymmetric cavity [1–3] are used to consider problems relating to pulsations of the cavity shape, the drag of a slender cavity-forming body, and the influence of surface tension on the shape of a steady cavity.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 1, pp. 28–34, January–February, 1982.I thank V. P. Karlikov and Yu. L. Yakimov for helpful discussions of the results.     

Cavitation interaction between fluid counterflows

Some features of self-oscillatory regimes for the cavitation interaction of coaxial water and annular gas jets with a water counterflow are studied. The dependencies of the self-oscillation frequency, the maximum displacement of a cavity toward the incident flow, and the displacement amplitude on the pipe diameter and the Froude number are found. A conclusion on the onset of self-oscillations is substantiated. The possibility of a significant increase in the counterflow range due to the gas injection in the vicinity of the counterflow is shown.     

Time-dependent interaction between two inviscid fluid flows separated by a semi-infinite non-rigid plate in a flat-walled channel

The problem of the time-dependent interaction between two inviscid weightless fluids separated by a semi-infinite non-rigid plate in a channel with fixed rigid walls is solved in the linear approximation. The general case of deformation and harmonic oscillations of the plate (flapping mover) are considered. The time-dependent hydrodynamic reaction forces, the position of the interface, and the dynamic characteristics of the mover are determined. Kazan’. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 1, pp. 67–76, January–February, 1997.     

Time-dependent interaction of two fluid flows separated by a semi-infinite non-rigid plate

In this paper the following problem is solved in the linear approximation. Let a flat plate separate two uniform inviscid fluid flows with different steady-state densities and velocities. These flows are subject to small time-dependent disturbances due to plate deformation. This problem is solved for arbitrary deformations as well as in the case of the angular harmonic oscillations of a flapping mover. The time-dependent forces acting on the plate are determined, together with the dynamic characteristics of the mover and the position of the fluid-fluid interface. Kazan'. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 1, pp. 55–64, January–February, 1994.     

Modeling of developed cavitation flows in water tunnels

An approximate dependence between cavitation numbers in an unbounded flow and in an experimental section of a water tunnel, at which the equality of the maximum transverse dimensions of the cavities formed behind identical cavitators is ensured, is obtained in the framework of a model of a viscous, weightless, incompressible liquid. On the basis of an analysis of the well-known numerical calculations of developed cavitation flows for cavitators of different shape in the two-dimensional and axisymmetric cases, and those carried out by the authors, an estimate is made showing that when the found relation between these cavitation numbers is satisfied the relative lengths, the relative maximum transverse dimensions, and the elongations of the cavities are also equal in unbounded and bounded flows. These values are equal in the considered cases, correct to 6%, for all the cavitation numbers in the tunnel which differ from the limiting values by not less than 5%. This conclusion is verified by experiments of the authors and other investigators.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 2, pp. 73–80, March–April, 1987.     

Quasihomogeneous model of cavitation flows in diffuser channels

Starting with the experiments carried out by Reynolds in 1894, the flow in Venturi tubes has traditionally been used to study and demonstrate various forms of cavitation. Numerous authors have carried out experimental research on the various flow regimes in diffuser channels [1–7] or have investigated theoretical models of such flows [6, 8]. The occurrence and development of cavitation is closely associated with the phenomenon of turbulent separation complicated by the presence of two-phase flow in the dissipation zone. For a long time these effects were considered separately, until Gogish and Stepanov [9] proposed a single model of cavitation and separation based on the theory of intense interaction of an incompressible potential flow and a turbulent cavitation layer of variable density and embracing the various stages of cavitation. The object of this study is to demonstrate the possibilities of this model with reference to the simple example of flows accompanied by cavitation and separation in plane and axisymmetric diffuser channels of the Venturi tube type with straight and curved walls. The dissipative flow near the walls is described by a quasihomogeneous model of turbulent two-phase flow, in which the presence of two phases is taken into account only by varying the mean density. The potential core of the flow is considered in the one-dimensional formulation. The displacement thickness serves as the flow interaction parameter. The conditions of ocurrence and development of circulatory flows are determined. Examples of symmetrical and nonsymmetrical flows are presented.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 5, pp. 47–54, September–October, 1986.     

Axisymmetric flows of an incompressible fluid between movable rotating disks

Within the Karman family of exact solutions of the Navier-Stokes equations, some non-selfsimilar solutions are considered to the problem of unsteady incompressible flow between two rotating disks one of which moves along a common rotation axis. Three classes of the flow regimes are studied: (i) a flow between the non-rotating disks, (ii) a flow between the disks rotating with identical angular velocities, and (iii) a flow between the disks rotating with opposite velocities. Examples of exact rotationally symmetric solutions for the inviscid-fluid equations, satisfying the no-slip conditions, are given.     

General arrangement of regimes for spatial local flows

Different local features at the surface of a body are breaks or sharp changes in boundary conditions, separation or joining of a flow, irregularities, etc., and they may have a marked effect on local and global characteristics of flow over it [1]. This situation stimulates continued interest towards to flow in local regions, which apart from considerable practical importance, often exhibit considerable theoretical novelty (see, e.g., [2–6], where a systematic study was carried out of planar local regions of flow). However, the majority of local regions are spatial, and whereas in studying flat regions considerable success have been achieved, for spatial regions only individual solutions have been obtained, often using considerable simplifications [7–19]. In addition, due to the absence of systematic studies it is difficult to determine the boundaries for existence of different flow regimes in local spatial regions, and limiting transitions which make it possible to changeover from one flow regime to another. In this work systematic studies are carried out for flow regimes in local spatial regions for each of the boundary problems formulated, the main properties of their solution are studied, and a general classification for the arrangement of flow regimes is built up.Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 6, pp. 80–91, November–December, 1986.     

Dual characters of interaction between particles and fluid

The unique characteristics of gas-solids two-phase flow and fluidization in terms of the flow structures and the apparent behavior of particles and fluid-particle interactions are closely linked to physical properties of the particles, operating conditions and bed configurations. Fluidized beds behave quite differently when solid properties, gas velocities or vessel geometries are varied. An understanding of hydrodynamic changes and how they, in turn, influence the transfer and reaction characteristics of chemical and thermal operations by variations in gas-solid contact, residence time, solid circulation and mixing and gas distribution is very important for the proper design and scale-up of fluidized bed reactors. In this paper, rather than attempting a comprehensive survey, we concentrate on examining some important positive and negative impacts of particle sizes, bubbles, clusters and column walls on the physical and chemical aspects of chemical reactor performance from the engineering application point of view with the aim of forming an adequate concept for guiding the design of multiphase fluidized bed chemical reactors.One unique phenomenon associated with particle size is that fluidized bed behavior does not always vary monotonically with changing the average particle size. Different behaviors of particles with difference sizes can be well understood by analyzing the relationship between particle size and various forces. For both fine and coarse particles, too narrow a distribution is generally not favorable for smooth fluidization. A too wide size distribution, on the other hand, may lead to particle segregation and high particle elutriation. Good fluidization performance can be established with a proper size distribution in which inter-particle cohesive forces are reduced by the lubricating effect of fine particles on coarse particles for Type A, B and D particles or by the spacing effect of coarse particles or aggregates for Type C powders.Much emphasis has been paid to the negative impacts of bubbles, such as gas bypassing through bubbles, poor bubble-to-dense phase heat & mass transfer, bubble-induced large pressure fluctuations, process instabilities, catalyst attrition and equipment erosion, and high entrainment of particles induced by erupting bubbles at the bed surface. However, it should be noted that bubble motion and gas circulation through bubbles, together with the motion of particles in bubble wakes and clouds, contribute to good gas and solids mixing. The formation of clusters can be attributed to the movement of trailing particles into the low-pressure wake region of leading particles or clusters. On one hand, the existence of down-flowing clusters induces strong solid back-mixing and non-uniform radial distributions of particle velocities and holdups, which is undesirable for chemical reactions. On the other hand, the formation of clusters creates high solids holdups in the riser by inducing internal solids circulations, which are usually beneficial for increasing concentrations of solid catalysts or solid reactants.Wall effects have widely been blamed for complicating the scale-up and design of fluidized-bed reactors. The decrease in wall friction with increasing the column diameter can significantly change the flow patterns and other important characteristics even under identical operating conditions with the same gas and particles. However, internals, which can be considered as a special wall, have been used to improve the fluidized bed reactor performance.Generally, desirable and undesirable dual characteristics of interaction between particles and fluid are one of the important natures of multiphase flow. It is shown that there exists a critical balance between those positive and negative impacts. Good fluidization quality can always be achieved with a proper choice of right combinations of particle size and size distribution, bubble size and wall design to alleviate the negative impacts.     

A numerical method for simulation of attached cavitation flows

A new numerical algorithm for attached cavitation flows is developed. A cavitation model is implemented in a viscous Navier–Stokes solver. The liquid–vapour interface is assumed as a free surface boundary of the computation domain. Its shape is determined with an iterative procedure to match the cavity surface to a constant pressure boundary. The pressure distribution, as well as its gradient along the wall, is taken into account in updating the cavity shape iteratively. A series of computations are performed for the cavitating flows across three kinds of headform/cylinder bodies: conic, ogival and hemispheric heads. A range of cavitation numbers is investigated for each headform/cylinder body. The obtained results are reasonable and the iterative procedure of cavity shape updating is quite stable. The superiority of the developed cavitation model and algorithm is demonstrated. Copyright © 2006 John Wiley & Sons, Ltd.     

A cavitation model for computations of unsteady cavitating flows

A local vortical cavitation(LVC) model for the computation of unsteady cavitation is proposed.The model is derived from the Rayleigh–Plesset equations,and takes into account the relations between the cavitation bubble radius and local vortical effects.Calculations of unsteady cloud cavitating fows around a Clark-Y hydrofoil are performed to assess the predictive capability of the LVC model using well-documented experimental data.Compared with the conventional Zwart's model,better agreement is observed between the predictions of the LVC model and experimental data,including measurements of time-averaged fl w structures,instantaneous cavity shapes and the frequency of the cloud cavity shedding process.Based on the predictions of the LVC model,it is demonstrated that the evaporation process largely concentrates in the core region of the leading edge vorticity in accordance with the growth in the attached cavity,and the condensation process concentrates in the core region of the trailing edge vorticity,which corresponds to the spread of the rear component of the attached cavity.When the attached cavity breaks up and moves downstream,the condensation area fully transports to the wake region,which is in accordance with the dissipation of the detached cavity.Furthermore,using vorticity transport equations,we also fin that the periodic formation,breakup,and shedding of the sheet/cloud cavities,along with the associated baroclinic torque,are important mechanisms for vorticity production and modification When the attached cavity grows,the liquid–vapour interface that moves towards the trailing edge enhances the vorticity in the attached cav-ity closure region.As the re-entrant jet moves upstream,the wavy/bubbly cavity interface enhances the vorticity near the trailing edge.At the end of the cycle,the break-up of the stable attached cavity is the main reason for the vorticity enhancement near the suction surface.     

Local flows of a deformable damageable medium under impact interaction with a cavitating fluid

Local viscoplastic-flow and damage processes in a deformable medium induced by the collapse of dispersed vapor-gas bubbles in the near-wall layer of a cavitating fluid in the presence of propagating shock waves are investigated. The study is based on a generalized model developed for describing nonlinear deformations and flow of damageable media and on the results obtained earlier for local fluid flows induced by limiting transitions of vapor-gas bubbles.     

Two-dimensional flows of a viscous binary fluid between moving solid boundaries

A class of exact solutions of hydrodynamic equations with additional Korteweg stresses is obtained which is characterized by a linear dependence of part of the velocity components on the space variable. In this class, exact solutions of two problems of binary fluid flow between moving flat solid boundaries was found. A family of particular exact solutions is obtained for the problem of viscous fluid flow between planes which approach or move away from each other according to a special law.     

绕三维水翼云状空化现象的实验研究

为了研究云状空化阶段空穴发展和脱落的机理,采用实验的方法对绕三维水翼云状空化流动进行了研究.实验在高速水洞中进行,采用高速摄像技术研究了不同空化阶段的空穴形态,并测量了翼型所受的升阻力,并对上述数据进行了频谱分析.结果发现:在云状空化阶段,观测到空穴的产生-发展-脱落-溃灭的准周期性变化;并捕捉到空泡脱落时附着在翼型前...     

Turbulence and cavitation models for time-dependent turbulent cavitating flows

Cavitation typically occurs when the fluid pressure is lower than the vapor pressure at a local thermodynamic state,and the flow is frequently unsteady and turbulent.To assess the state-of-the-art of computational capabilities for unsteady cavitating flows,different cavitation and turbulence model combinations are conducted.The selected cavitation models include several widely-used models including one based on phenomenological argument and the other utilizing interface dynamics.The kε turbulence model with additional implementation of the filter function and density correction function are considered to reduce the eddy viscosity according to the computed turbulence length scale and local fluid density respectively.We have also blended these alternative cavitation and turbulence treatments,to illustrate that the eddy viscosity near the closure region can significantly influence the capture of detached cavity.From the experimental validations regarding the force analysis,frequency,and the cavity visualization,no single model combination performs best in all aspects.Furthermore,the implications of parameters contained in different cavitation models are investigated.The phase change process is more pronounced around the detached cavity,which is better illus-trated by the interfacial dynamics model.Our study provides insight to aid further modeling development.     

A model of cavitational flows for initial stages of cavitation

Initial stages of cavitation onset in a stream of liquid flowing past a body is considered. A certain pattern of hydrodynamic phenomena related to the onset of cavitational flows is porposed. It is based on the assumption of a comparatively high cavitation number and that a liquid with a relatively low content of gas-vapor bubbles moves within a certain zone.Results of calculations are compared with experimentally determined dimensions of the cavitation zone. As an example, the flow past a step in a plane channel is considered.