Axisymmetric flow around bodies in the developed cavitation mode

As a rule, axisymmetric cavitation flows are investigated by means of numerical computations in the absence of analytic solutions. However, substantial difficulties are still encountered here which are discussed in detail in the survey report of Birkhoff [1]. One of the integral equation methods used earlier for numerical computations of a plane cavitation flow [2] is considered below. General considerations about its application for the computations of axisymmetric flows are presented in [3]. This method turns out to be effective for the numerical computations of axisymmetric flows, as well as for an analytical investigation of the curvature of the meridian section of the cavern boundary near the point of its separation from the body. This latter question has been examined earlier in [4], where it has been shown for the case of a circular cone with a rectilinear generator that the curvature becomes infinite. The order of the infinity has not been established.     

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.     

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.     

Simulation of the hypervelocity regime of flow past bodies in wind tunnels

The main features of the hypervelocity regime of flow past aircraft due to the influence of the real properties of an airstream and some criteria for simulating this regime in aerodynamic facilities of various types are considered. A comparative analysis reveals that there are definite advantages (from the point of view of reproducing the real flight conditions) of using facilities with the actual flow velocities, for example, wind tunnels with magnetogasdynamic acceleration of the gas. The development of rocket and space technology confronts experimental aerodynamics with the problem of reproducing more accurately the parameters of hypervelocity flow past bodies under laboratory conditions. The present paper considers the main requirements and some criteria for simulating the hypervelocity regime in aerodynamic facilities of various types.     

Conditions of supersonic flow around multiwedge bodies

An experimental study was made of some schemes for flow around multiwedge bodies at supersonic flow velocities. On the basis of data on the distribution of the pressure, on visualization of the flow, and on optical measurements, an analysis was made of the structure of the flow. Zones of breakaway of the flow were observed at the lateral surfaces of the lobes. In the nose part of a multiwedge body there is a three-dimensional configuration of attached plane shock waves, going over into a combined detached nonaxisymmetric wave directed toward the base of the body.     

The generalized theory of flow of plastic disperse systems with account of the wall effect

Summary This work is concerned with the generalized approach to an estimation of the influence of the wall effect on measurements of the viscous properties of plastic disperse systems in capillary and rotational instruments.Use is made of the model concept of the existence of a separate phase in the wall layer and of the equilibrium between this phase and the system in the bulk. Based on the conception of the activation mechanism of the flow process, the authors introduce characteristic parameters which have the dimensions of length and which depend on the shape and size of the measuring surfaces. The use of these parameters permits obtaining a linear relationship between the apparent rate of shear gradient and the characteristic sizes of the measuring surfaces. The angular coefficient of these relations determine the shear-rate-dependent apparent velocity of slippage, which makes it possible to calculate the rate of shear gradient for the system in the bulk and, hence, to find the true flow curves for PDS. The normalization of the slippage velocity and the walllayer thickness with respect to the characteristic parameters enables one to find the values of viscosity and the concentrations of the dispersed phase in the wall layers as a function of the shear rate on the surfaces of the measuring devices.

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Zusammenfassung Es wird ein verallgemeinertes Verfahren zur Abschätzung des Wandeinflusses auf die Messung der Viskositätseigenschaften von plastischen dispersen Systemen (PDS) in Kapillar- und Rotationsinstrumenten behandelt.Dabei wird die Modellvorstellung der Existenz einer separaten Phase in der Wandschicht und deren Gleichgewicht mit der Volumenphase in Ansatz gebracht. Mit Hilfe des Konzepts des Strömungsvorgangs als eines Aktivierungsmechanismus werden charakteristische Parameter eingeführt, welche die Dimension einer Länge besitzen und von der Gestalt und den Abmessungen der Oberflächen der Meßanordnung abhängen. Die Einführung dieser Parameter führt zu einer linearen Abhängigkeit der scheinbaren Schergeschwindigkeit von den charakteristischen Abmessungen der Meßflächen. Der hierin auftretende Koeffizient bestimmt die von der Schubspannung abhängige effektive Gleitgeschwindigkeit, wodurch die Berechnung der Schergeschwindigkeit im Volumen und somit auch die Bestimmung der wahren Fließkurven der PDS ermöglicht wird. Die Normierung der Gleitgeschwindigkeit und der Dicke der Wandschicht in bezug auf die charakteristischen Parameter ermöglicht es, den Wert der Viskosität und der Konzentration der dispersen Phase in den Wandschichten als Funktion der Schubspannung an den Oberflächen der Meßanordnung zu ermitteln.

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With 11 figures and 3 tables     

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.     

Supersonic unsteady-state flow around bodies of variable form

This paper discusses supersonic flow around a spherical blunt body, whose surface is deformed according to a known law over a certain period of time. An investigation is made of unsteady-state flows during the change in the form of the body as a function of the deflection and the rate of change in the form of the body. The calculations were made for Mach number M =2, 10. The solution is obtained by the grid-characteristic method [1].Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 6, pp. 187–191, November–December, 1978.     

Particle tracking velocimetry of the flow field around a collapsing cavitation bubble

The velocity field in the vicinity of a laser-generated cavitation bubble in water is investigated by means of particle tracking velocimetry (PTV). Two situations are explored: a bubble collapsing spherically and a bubble collapsing aspherically near a rigid wall. In the first case, the accuracy of the PTV method is assessed by comparing the experimental data with the flow field around the bubble as obtained from numerical simulations of the radial bubble dynamics. The numerical results are matched to the experimental radius–time curve extracted from high-speed photographs by tuning the model parameters. Trajectories of tracer particles are calculated and used to model the experimental process of the PTV measurement. For the second case of a bubble collapsing near a rigid wall, both the bubble shape and the velocity distribution in the fluid around the bubble are measured for different standoff parameters γ at several instants in time. The results for γ > 1 are compared with the corresponding results of a boundary-integral simulation. For both cases, good agreement between simulation and experiment is found.     

Laminar boundary layer on blunt bodies with account for vorticity of the external flow

This paper presents the technique for and results from numerical calculations of the hypersonic laminar boundary layer on blunted cones with account for the vorticity of the external flow caused by the curved bow shock wave. It is assumed that the air in the boundary layer is in the equilibrium dissociated state, but the Prandtl number is assumed constant, =0.72. The calculations were made in the range of velocities 3–8 km/sec, cone half-angles _k=0°–20°. With account for the vortical interaction of the boundary layer with the external flow, the distribution of the thermal flux and friction will depend on the freestream Reynolds number (other conditions being the same). In the calculations the Reynolds number R, calculated from the freestream parameters and the radius of the spherical blunting, varies from 2.5·10³ to 5.10⁴. For the smaller Reynolds numbers the boundary layer thickness on the blunting becomes comparable with the shock standoff, and for R<2.5·10³ it is apparent that we must reconsider the calculation scheme. With R>5·10⁴ for cones which are not very long the vortical interaction becomes relatively unimportant. The results of the calculations are processed in accordance with the similarity criteria for hypersonic viscous gas flow past slender blunted cones [1, 2].     

Features of the turbulent flow around symmetric elongated bluff bodies

The flow fields around three elongated bluff bodies with the same chord-to-thickness ratios but distinct leading and trailing edge details were measured at a Reynolds number of 3×10⁴. These models each represent a case where: leading edge shedding dominates, trailing edge shedding dominates and a case where there is a balance between the two. The results show that the vortex street parameters vary between the models, and in particular, the shedding frequencies are significantly altered by the geometry. However, contrary to the current understanding for shorter bluff bodies, the scale of the recirculation region is found to be similar for each model, even though the shedding frequency changes within the range from 0.15 to 0.24. Also, the base pressure does not follow trends with shedding frequency expected from shorter bluff bodies. A force balance of the recirculation region shows that the near wake of each body is significantly affected by the Reynolds shear stress distribution and the resultant force due to the pressure field in the mean recirculation region. These differences infer that the distinct vortex formation characteristics depend on the state of the trailing edge shear layers. The boundary layers at the trailing edge have been quantified, as have the leading edge separation bubbles, and the marked differences in the wake details are shown to depend on the leading edge separation.     

Plane problem of cavitation flow around an oblique cascade of profiles

The solution of the direct and inverse problems of the flow around a plane cascade of profiles with partial and supercavitation for closure of the caverns on one vortex singularity is presented. A method of designing an optimal cascade from the viewpoint of hydrodynamic quality is given on the basis of this solution.     

The influence of surface roughness on cloud cavitation flow around hydrofoils

The aim of this study is to investigate experimentally the effect of surface roughness on cloud cavitation around Clark-Y hydrofoils. High-speed video and particle image velocimetry(PIV) were used to obtain cavitation patterns images(Prog. Aerosp. Sci. 37: 551–581, 2001), as well as velocity and vorticity fields. Results are presented for cloud cavitating conditions around a Clark-Y hydrofoil fixed at angle of attack of α = 8?for moderate Reynolds number of Re = 5.6 × 10~5. The results show that roughness had a great influence on the pattern, velocity and vorticity distribution of cloud cavitation. For cavitating flow around a smooth hydrofoil(A) and a rough hydrofoil(B), cloud cavitation occurred in the form of finger-like cavities and attached subulate cavities, respectively. The period of cloud cavitation around hydrofoil A was shorter than for hydrofoil B.Surface roughness had a great influence on the process of cloud cavitation. The development of cloud cavitation around hydrofoil A consisted of two stages:(1) Attached cavities developed along the surface to the trailing edge;(2) A reentrant jet developed, resulting in shedding and collapse of cluster bubbles or vortex structure. Meanwhile, its development for hydrofoil B included three stages:(1) Attached cavities developed along the surface to the trailing edge, with accumulation and rotation of bubbles at the trailing edge of the hydrofoil affecting the flow field;(2) Development of a reentrant jet resulted in the first shedding of cavities. Interaction and movement of flows from the pressure side and suction side brought liquid water from the pressure side to the suction side of the hydrofoil, finally forming a reentrant jet. The jet kept moving along the surface to the leading edge of the hydrofoil, resulting in large-scale shedding of cloud bubbles. Several vortices appeared and dissipated during the process;(3) Cavities grew and shed again.     

Diffraction of solitary water waves around three-dimensional floating bodies

By using the matched asymptotic expansion method and the idea of edge layer, a mathematic model for describing the interaction between weakly nonlinear shallow-water waves and three-dimensional floating bodies is formed in the paper. As a numerical example, the diffraction of a solitary wave around a vertically floating circular cylinder has been investigated and the results are presented. The present method can further be extended to the study of wave diffraction around floating bodies of general shape. The project is supported by the National Natural Science Foundation of China.     

Calculation of supersonic air flow about blunt bodies with account for equilibrium physicochemical transformations

Air flow with separated shock wave about blunt axisymmetric bodies with a smooth contour is considered on the assumption of equilibrium of the physicochemical transformations. The method of Telenin [1] is used to calculate the flow in the subsonic and transonic regions.