Subsonic gas-liquid cavitation flow past a disk

The problem of axisymmetric subsonic gas-liquid cavitation flow past a disk in accordance with the Riabouchinsky scheme is solved using the method of [1]. Formulas relating the main flow parameters with the cavitation number, the Mach number on the free boundary and the gas/liquid volume ratio under stagnation conditions are presented.Kazan'. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 2, pp. 202–206, March–April, 1996.     

Modeling and computation of cavitation in vortical flow

The paper presents an investigation of Euler–Lagrangian methods for cavitating two-phase flows. The Euler–Euler methods, widely used for simulations of cavitating flows in ship technology, perform well in regions of moderate flow changes but fail in zones of strong, vortical flow. Reasons are the strong approximations of cavitation models in the Euler concept. Alternatively, Euler–Lagrangian concepts enable more detailed formulations for transport, dynamics and acoustic of discrete vapor bubbles. Test calculations are performed to study the influence of different parameters in the equations of motion and in the Rayleigh–Plesset equation for bubble dynamics. Results confirm that only Lagrangian models are able to describe correctly the bubble behavior in vortices, while Eulerian results deviate strongly. Lagrangian formulations enable additionally the determination of acoustic pressure of cavitation noise. Two-way coupling between the phases is required for large regions of the vapor phase. A new coupling concept between continuous fluid flow and discrete bubble phase is developed and demonstrated for flow through a nozzle. However, the iterative coupling between the phases via volume fractions is computationally expensive and should therefore be applied only in regions where Eulerian treatment fails. A corresponding local concept for combination with an Euler–Euler method is outlined and is in progress.     

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.     

Operation of a fluid jet amplifier in the cavitation regime

It is established that a Coanda-effect fluid jet amplifier continues to function in the initial and intermediate stages of cavitation. However, in the separation stage, which extends to the output channels, the effect is disrupted and the amplifier can no longer function normally.Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 5, pp. 147–150, September–October, 1970.     

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.     

Motion of a liquid-gas bubble mixture in the incipient cavitation stage

This article is concerned with the nonsteady motion of a mixture of an ideal incompressible liquid with gas bubbles in the incipient stage of cavitation. Solutions are obtained in the first and second approximations. The solutions are applied to pipe flow situations.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 5, pp. 151–153, September–October, 1976.The author is indebted to L. I. Sedov for valuable comments.     

Approximate solution of the three-dimensional inverse problem for nonlifting bodies with optimum cavitation characteristics

A formulation and method of solving the three-dimensional inverse problem of ideal fluid mechanics are proposed and examples of their application to the design of bodies of revolution with optimum cavitation characteristics for given overall dimensions are presented.St. Petersburg. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No.3, pp. 92–100, May–June, 1994.     

A scheme of developed cavitation flow past a wedge

A scheme is proposed for studying the symmetric steady flow with developed cavitation of an ideal incompressible and weightless fluid past a wedge in a channel. This scheme generalizes the existing schemes of cavitation flow past bodies and describes flow that is intermediate between the flow past obstacles in the Riabouchinsky and Efros schemes. Detailed calculations have been made for the drag coefficient and the cavity size in the case of a plate in an unbounded flow. The results of the calculations are tabulated.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 1, pp. 165–170, January–February, 1983.I thank P. M. Ivanov, Kh. Kh. Kalazhokov, and T. Sokhov for assistance in the computer calculations.     

Allowance for the unsteadiness of the flow in determining the critical cavitation number for marine propellers

A method of estimating the critical cavitation number for marine propeller blades is proposed. This method is based on the reduction of the three-dimensional unsteady problem to the three-dimensional steady problem and a series of two-dimensional unsteady problems.Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No.1, pp. 78–85, January–February, 1993.The authors are grateful to S. V. Kaprantsev for assisting with the experiments.     

Initiation of cavitation by injection of hot steam into a cold liquid jet

The problem of the dynamics of a hot steam bubble in the nonuniform flowfield of a plane cold liquid jet is considered. The motion of the bubble along the symmetry axis is analyzed with allowance for nonequilibrium condensation and heat conduction by the steam and the liquid. The domain of jet and steam parameters corresponding to the dynamic cavitation bubble initiation mode, is evaluated.Moscow. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 5, pp. 91–100, September–October, 1995.     

Influence of cavitation on blade characteristics

An experimental study of flow around a blade with a modified NACA 4418 profile was conducted in a water tunnel that also enables control of the cavitation conditions within it. Pressure, lift force, drag force and pitching moment acting on the blade were measured for different blade angles and cavitation numbers, respectively. Relationships between these parameters were elaborated and some of them are presented here in dimensionless form. The analysis of results confirmed that cavitation changes the pressure distribution significantly. As a consequence, lift force and pitching moment are reduced, and the drag force is increased. When the cavitation cloud covers one side of the blade and the flow becomes more and more vaporous, the drag force also begins to decrease. The cavity length is increased by increasing the blade angle and by decreasing thé cavitation number.List of symbols A (m²) blade area,B ·L - B (m) blade width - C _D (–) drag coefficient,F _D /(p _d ·A) - C _L (–) lift coefficient,F _L /(P _d ·A) - C _M (–) pitching moment coefficient,M/(P _d ·A ·L) - C _p (–) pressure coefficient, (p-p _r )/p _d - F (N) force - L (m) blade length - M (Nm) pitching moment - p (Pa) local pressure on blade surface - p _d (Pa) dynamic pressure, ·V ²/2 - p _r (Pa) reference wall pressure at blade nose position if there would be no blade in the tunnel - p _v (Pa) vapor pressure - p ₁ (Pa) wall pressure 350 mm in front of thé blade axis - Re (–) Reynolds number,V ·L/v - V (m/s) mean velocity of flow in the tunnel - x (m) Cartesian coordinate along thé blade profile cord - x _c (m) cavity length,x-coordinate of cavity end - (°) blade angle - v (m²/s²) kinematic viscosity - (kg/m³) fluid density - (–) cavitation number, (p _r –p _v )/p _d - (°) angle of tangent to thé blade profile contour     

Generation and evolution of cavitation in magma under dynamic unloading

The full system of equations for the problem of rarefaction-wave passage over the magma-melt column in the gravity field is derived with the use of the kinetic theory of phase transformations, and the problem is numerically solved. With allowance for diffusion zones and nucleation frequency as a function of supersaturation, the dependence of the number of cavitation nuclei formed in the course of phase transformations behind the rarefaction-wave front is found. The dynamics of the size distribution of cavitation bubbles along the magma-melt column (1 km) whose viscosity varies dynamically as a function of the concentration of dissolved water is studied.Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 46, No. 2, pp. 71–80, March–April, 2005.     

Study of cavitation phenomena based on a technique for visualizing bubbles in a liquid pressurized chamber

In this paper, the influence of nozzle geometry on cavitation and near-nozzle spray behavior under liquid pressurized ambient is studied. For this purpose, eight steel drilled plates, with different diameters and degrees of conicity of their holes, are analyzed. A special near-nozzle field visualization technique, using a test rig pressurized with fuel, is used. Due to the difference in refractive index between liquid and vapor phase, bubbles present at the outlet of the orifice are visualized. The pressure conditions at which bubbles start appearing at the orifice outlet are compared with those at which choked flow appears. The results showed that pressure conditions for inception of cavitation obtained in the visualization tests differs from those seen for choked flow (5–8% in terms of cavitation number). In addition to this, the images taken are analyzed to get the angle of the jet formed by fuel bubbles, showing that it increases significantly for those conditions more prone to cavitate. Furthermore, comparison of bubbles generation when increasing or decreasing backpressure indicates the presence of hysteresis in cavitation inception phenomena.     

Axisymmetric cavitation flow around a body in a tube

The problem of the axisymmetric flow around a body in a circular tube with arbitrary shape of the meridian section is reduced to the numerical solution of a system of two integral equations to determine the shape of the cavern and the intensity of the vortex rings arranged on the solid boundaries and the cavern boundary. Results of computations of the cavitation flow around a sphere, ellipsoid of revolution, and cone in a cylindrical tube, and also for a cone in converging and expanding tubes and in a hydrodynamic tunnel with the actual shape of the converging and working sections, are presented.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 4, pp. 50–55, July–August, 1976.     

Symmetric cavitation flow past a wedge in the presence of a source on the wedge or in the flow

A solution is found to the problem of symmetric cavitation flow over a wedge by an ideal incompressible fluid (in accordance with Efros's scheme [1]) in the presence of a point source in the flow or on the wedge. Expressions are obtained for the forces exerted on the source and the wedge by the fluid, the conditions under which there is a negative resistance (thrust) are indicated, and the profiles of the free streamlines are constructed for different values of the flow parameters.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Shidkosti i Gaza, No. 6, pp. 137–141, November–December, 1979.We thank L. I. Sedov for his interest in the work.     

Solution of the linear problem of cavitation flow around a curvilinear arc

A method is proposed for the construction, without quadratures, of a solution to the linear problem of the flow of a gradientless stream around an arc of the curve y_n=f(x), whose derivativef(x)=g(x) at x=z is a meromorphic function in the plane z=x+iy. For flow around the arc of a parabola, with fully developed and partial cavitation, convenient finite formulas are obtained and numerical calculations are made. An analogous method may be used to construct, without quadratures, the solution of a number of other problems (a hydroplane, a grid, etc.).Cheboksary. Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 1, pp. 34–38, January–February, 1972.     

Flow past a plate lattice with developed cavitation

Problems of streamline cavitation flow past a lattice were studied in [1–8] using the Kirchhoff scheme. In this scheme the magnitude of the velocity at the free surface is equal to the stream velocity behind the lattice, and the cavitation number is zero (for a lattice the relative velocity and the cavitation number are defined from the stream velocity behind the lattice). In [4, 7] a solution is given of the problem of flow past a lattice using a scheme with an Efros-Gilbargreturn streamline, which permits considering arbitrary cavitation numbers; however, a unique solution is not given. Some other streamline schemes are mentioned in [8].In the following we consider the cavitational flow of an ideal incompressible inviscid and weightless fluid past an infinite lattice of flat plates, using the streamline wake model previously utilized by Wu [9] in studying cavitational flow past an isolated obstacle. In accordance with this model, the streamlines which separate from the body and bound the cavity behind it pass into two curvilinear infinitely long walls, along which the pressure increases and approaches the pressure in the undisturbed stream.It is further assumed that in the hodograph plane there corresponds to the curvilinear walls a cut along some line and that the complex potential takes the same values at points lying on opposite sides of the cut. In particular, at the points of contact of the streamlines with the curvilinear walls the complex potential is the same. In the Wu scheme the latter condition leads to vanishing of the velocity circulation along the contour CABC₁ (Fig. 1).In conclusion the author wishes to thank N. V. Yurtaeva for the accurately performed numerical work.     

Axially symmetric cavitation flow at small cavitation numbers

A method for computing the drag coefficient of a body in an axially symmetric, steady-state cavitation flow is presented. A ‘vortex ring’ distribution along the wetted body surface and along the cavity interface is assumed. Since the location of the cavitation interface is unknown a priori, an iterative procedure is used, where, for the first stage, an arbitrary cavitation interface is assumed. The flow field is then solved, and by an iterative process the location of the cavitation interface is corrected. Even though the flow field is governed by the linear Laplace equation, strong non-linearity resulting from the kinematic boundary conditions appears along the cavitation interface. An improved numerical scheme for solving the dual Fredholm integral equations is obtained by formulating high-order approximations to the singular integrals in order to reduce the matrix dimensions. Good agreement is found between the numerical results of the present work, experimental results and other solutions.     

Dynamics of cavitational demolition in the interaction of a shock wave with a free surface

The problem of cavitation in the tension wave associated with the reflection of a shock wave from a free fluid surface is considered. A method of calculating the cavitation zone dynamics which makes it possible to determine the structure of the cavitation front, including for large space scales, is developed. A procedure for determining the dispersity of the fragment-drops of dispersed fluid, which takes into account the initial size distribution of the cavitation nuclei and the parameters of the incident shock wave, is proposed.Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No.6, pp. 73–80, November–December, 1992.     

Method of approximate account for the wall effect in cavitation flow around bodies in water tunnels

One of the basic questions in the study of advanced cavitation in water tunnels of the closed-circuit type is the establishment of the correspondence between the flow patterns observed in the channel and in an unbounded stream. The objective of the study of the wall effect must be the determination of a connection between the basic characteristics of the phenomenon, i. e., the cavitation numbers, the cavity dimensions, the drag coefficients, etc., for the unbounded flow and the channel flow. A large number of works devoted to this question are known [1–7], but in the majority of them only two-dimensional flows are considered. These studies contain either exact solutions obtained with the aid of the apparatus of functions of a complex variable or solutions in the linearized formulation.At the present time there is urgent need to obtain at least approximate solutions for axisymmetric cavitation flows in a tunnel.In several studies [1, 2, 4] it has been shown that in the case of two-dimensional flows the presence of solid boundaries influences the drag coefficient only through the mechanism of a change of the magnitude of the cavitation number, while the variation of the drag coefficient itself with the cavitation number is not changed in comparison with the unbounded flow. It may be assumed that an analogous situation obtains for the axisymmetric case as well. Then the question of the wall effect may be reduced to establishing the connection between the corresponding cavitation numbers.The present paper makes an attempt to establish the correspondence between the cavitation numbers in the unbounded flow and in the tunnel for which the cavities behind the same body have the same areas of the maximal cross section.