Stability of a nonstationary round jet of an ideal incompressible fluid

The stability of transient flow in a cylinder of an ideal incompressible fluid with a free boundary is studied. There are 20 different cases of the behavior of small disturbances as a function of the parameters of the problem. In particular, if surface tension is not taken into account a round jet is stable with respect to axially symmetrical disturbances, but the introduction of capillary forces leads to a strong instability.Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 4, pp. 80–84, July–August, 1972.In conclusion the author thanks V. V. Pukhnachev for formulation of the problem and valuable advice.     

Motion of two pulsating spheres in an ideal incompressible fluid

The problem of the interaction of two pulsating spheres in an ideal incompressible fluid was first investigated in detail by Bjerknes [1]. However, his and subsequent studies on this subject [2–5] were restricted to the interaction forces between the spheres, whereas the law of their motion was not considered because of the much greater complexity of the corresponding problem. The aim of the present paper is to find an approximate analytic solution to the problem of the motion of two pulsating spheres in an ideal incompressible fluid filling the entire space exterior to the spheres under the assumption that the flow of the fluid is irrotational.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 3, pp. 159–162, May–June, 1983.     

New method for numerical simulation of a nonstationary potential flow of incompressible fluid with a free surface

New method for numerical simulation of potential flows with a free surface of two-dimensional fluid, based on combination of the conformal mapping and Fourier Transform is proposed. The method is efficient for study of strongly nonlinear effects in gravity waves including wave breaking and formation of rogue waves.     

Motion of a small sphere in a nonhomogeneous flow of an incompressible liquid

We consider the motion of a small sphere in an arbitrary potential flow of an ideal liquid. For the general case we obtain an integral of the equations of motion and a particular solution. We find flows in which the force acting on the sphere is central. We also obtain exact solutions of the equations of motion of the sphere for the cases of stationary flows around a cylinder and around a body of revolution when the forces are noncentral. N. E. Zhukovskii [1] calculated the force acting on a fixed sphere in an arbitrary nonstationary flow. Kelvin [2] obtained the equations of motion of a sphere in a stationary flow of a liquid circulating through a hole in a solid. A formula for the force F, acting on a fixed small body of volume V in a stationary flow with speed v, was obtained by Taylor [3]: F = (T ₀ / v)Vv + 1/2_V v ² Here T₀ is the kinetic energy of an unbounded liquid in which a body moves with velocity v. This problem was solved in [3] through a direct integration of the pressure forces over the surface of the body in a flow defined by multipoles of the first and second orders at infinity.Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 5, pp. 57–61, September–October, 1973.     

Steady flow of a viscous incompressible fluid around two particles of different dimensions

The study investigates the flow of an axisymmetric steady stream of a viscous incompressible fluid round two particles of spherical shape moving one after the other, on the assumption that the smaller in dimensions is in the wake of the first one.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 1, pp. 131–183, January–February, 1985.     

Steady flow of a viscous incompressible fluid past two particles at moderate Reynolds numbers

A study is made of axisymmetric flow past two particles of spherical shape at Reynolds numbers 1 R 80. The flow patterns, pressure distributions, and values of the drag are investigated for different distances between the spheres. It is found that the drag depends nonmonotonically on the parameters that determine the flow.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 1, pp. 167–171, January–February, 1982.     

Non-radial flow of an incompressible fluid of second grade in a contracting channel

The steady non-radial flow of an incompressible fluid of second grade in a contracting channel is studied. The dependence of the flow on the material parameters of the fluid and on the channel angle is investigated. A similarity transformation is introduced for the streamfunction which reduces the P.D.E. to a sequence of O.D.E.s. A series solution is employed to solve the problem.

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Sommario Si studia il flusso stazionario non radiale di un fluido di secondo grado incomprimibile in un canale convergente, esaminandone la dipendenza dai parametri materiali del fluido e dall'angolo di apertura del canale. Si introduce una trasformazione di similitudine per la funzione di corrente che riduce l'equazione di moto ad una serie di equazioni differenziali ordinarie, risolte numericamente.

     

Motion of discrete particles in a turbulent fluid

Summary Various approximations to Basset's equation for the motion of a particle in a viscous fluid have been applied to the complex phenomenon of dispersion in a turbulent fluid. The deviations of the particle motion from the fluid motion, as predicted by the various approximations, is explored, and the frequencies for which this deviation is large are described. The approximations are found to be invalid for such cases as sediment transport and motion of gas bubbles in liquids. For small, 7 micron, liquid or solid particles in air, however, all approximations are shown to be valid for turbulent frequencies below 812 cps.Nomenclature a parameter in equation (2.3) - b parameter in equation (2.3) - c parameter in equation (2.3) - d diameter of sphere - E _f energy spectrum of the fluid - E _p energy spectrum of the particle - F frequency of oscillation - f ₁ parameter defined by equation (2.10) - f ₂ parameter defined by equation (2.10) - g acceleration of gravity - N _S , Stokes number - s density ratio - t time - t ₀ initial time - u _f fluid velocity - u _p particle velocity - V velocity of sphere - phase angle - parameter in equation (2.8) - amplitude ratio - parameter in equation (2.8) - dynamic viscosity - kinematic viscosity - f density of the fluid - p density of the particle - parameter in equation (2.8) - parameter in equation (2.8) - circular frequency of the motion     

Unsteady flow of an incompressible viscous fluid around a deformable spherical body

An unsteady flow of a viscous incompressible fluid around a deformable spherical body is considered in the approximation of low Reynolds numbers with a predetermined flow velocity. The hydrodynamic impact of the flow incoming onto the body is determined with allowance for small radial displacements of the body surface. The effect of spherical body surface deformation on the magnitude of the incoming flow impact force is taken into account, in particular, the dependence of small radial displacements of the body surface on the time is found, which makes it possible to minimize the physical impact of the incident flow.     

Fluctuations of the flow parameters of an incompressible viscous fluid in a collar-type flow throttling device

The flow in channels of the labyrinth seal type with one or two throttling stages is calculated on the interval of Reynolds numbers Re from 1.9·10⁴ to 4.5·10⁵. The nonsteady flow structure and the distribution and fluctuations of the pressure on the body of the labyrinth are investigated. The results are compared with the data of a physical experiment.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 1, pp. 3–8, January–February, 1990.     

Oblique stagnation-point flow of an incompressible visco-elastic fluid towards a stretching surface

An analysis is made of the steady two-dimensional stagnation-point flow of an incompressible viscoelastic fluid over a flat deformable surface when the surface is stretched in its own plane with a velocity cx, where x is the distance from the stagnation-point and c is a positive constant. It is shown that for a viscoelastic fluid of short memory (obeying Walters’ B model), a boundary layer is formed when the stretching velocity of the surface is less than ax, where ax+2by is the inviscid free-stream velocity and y is the distance normal to the plate, a and b being constants and the velocity at a point increases with increase in the elasticity of the fluid. On the other hand an inverted boundary layer is formed when the surface stretching velocity exceeds ax and the velocity decreases with increase in the elasticity of the fluid. A novel result of the analysis is that the flow near the stretching surface is that corresponding to an inviscid stagnation-point flow when a=c. Temperature distribution in the boundary layer is found in three cases, namely: (i) the sheet with constant surface temperature (CST); (ii) the sheet with variable surface temperature (VST) and (iii) the sheet with prescribed quadratic power law surface heat flux (PHF) for various values of non-dimensional parameters. It is found that in all the three cases when a/c>1, temperature at a point decreases with increase in the elasticity of the fluid and when a/c<1, temperature at a point increases with increase in the elasticity of the fluid. Further temperature at a point decreases with increase in the radiation parameter and wall temperature parameter.     

Cylinder in viscous incompressible fluid flow

We present a technique for calculating the temperature field in the vicinity of a cylinder in a viscous incompressible fluid flow under given conditions for the heat flux or the cylinder surface temperature. The Navier-Stokes equations and the energy equation for the steady heat transfer regime form the basis of the calculations. The numerical calculations are made for three flow regimes about the cylinder, corresponding to Reynolds numbers of 20, 40, and 80. The pressure distribution, voracity, and temperature distributions along the cylinder surface are found.It is known that for a Reynolds number R>1 the calculation of cylinder drag within the framework of the solution of the Oseen and Stokes equations yields a significant deviation from the experimental data. In 1933 Thom first solved this problem [1] on the basis of the Navier-Stokes equations. Subsequently several investigators [2, 3] studied the problem of viscous incompressible fluid flow past a cylinder.It has been established that a stable solution of the Navier-Stokes equations exists for R40 and that in this case the calculation results are in good agreement with the experimental data. According to [2], a stable solution also exists for R=44. The possibility of obtaining a steady solution for R>44 is suggested.Analysis of the results of [2] permits suggesting that the questions of constructing a difference scheme with a given order of approximation of the basic differential relations which will permit obtaining the sought solution over the entire range of variation of the problem parameters of interest are still worthy of attention.Calculation of the velocity field in the vicinity of a cylinder also makes possible the calculation of the cylinder temperature regime for given conditions for the heat flux or the temperature on its surface. However, we are familiar only with experience in the analytic solution of several questions of cylinder heat transfer with the surrounding fluid for large R within the framework of boundary layer theory [4].     

Hydraulic jump in the shear flow of an ideal incompressible fluid

Novosibirsk. Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, No. 1, pp. 11–20, January–February, 1995.     

Motion of a deformed contour in a flow of an ideal incompressible liquid with a constant vorticity

The article gives a solution to the plane problem of the motion of a deformed contour in a flow of an ideal incompressible liquid with a constant vorticity. An explicit expression is obtained for the hydrodynamic force when the velocity of the external flow depends linearly on the coordinates. In the case of a contour of small dimensions, this expression is valid also for an arbitrary external flow.