Bifurcations of a Single-Support Elastic Thin-Walled Rotor

The bifurcations of a thin-walled shell rotor during simple and complex rotation are analyzed. The similarity and difference of the problem formulations and solution techniques are pointed out. In both cases, the buckling mode is described by the first circumferential harmonic. The dependence of rotor bifurcations on natural frequencies is studied__________Translated from Prikladnaya Mekhanika, Vol. 41, No. 3, pp. 127–134, March 2005.     

Convection in an oscillating force field and microgravity

Convective flows in a plane layer of viscous fluid in the presence of an oscillating external force are investigated numerically [1 – 8]. The layer is assumed to be placed in a gravitational field. The cases in which the external field oscillations are generated by rotation about the horizontal axis or by vibration in the longitudinal direction are considered. The Navier-Stokes equations and the Boussinesq approximation are used for describing the fluid motion. The flows developing in the layer in the presence of a transverse temperature gradient are determined, the stability boundaries of these flows are found, and the supercritical motion regimes are studied. These investigations are carried out using the averaging method (in order to find the stability limits for high rotation velocities and vibration frequencies) and the Galerkin method.Moscow. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 5, pp. 99–106, September–October, 1994.     

Vibrational Dynamics of a Centrifuged Fluid Layer

The dynamics of a low-viscosity fluid layer inside a rotating cylinder under transverse translational vibration relative to the rotation axis is investigated experimentally. A novel vibrational effect, the generation of intense azimuthal fluid flows with velocities comparable with the cavity rotation velocity, is revealed. The structure and intensity of the vibrational flows and the flow transformation with variation of the determining dimensionless parameters (frequency and vibrational acceleration) are studied.__________Translated from Izvestiya Rossiiskoi Academii Nauk, Mekhanika Zhidkosti i Gaza, No. 2, 2005, pp. 147–156.Original Russian Text Copyright © 2005 by Ivanova, Kozlov, and Polezhaev.     

Instability and breakup of capillary liquid jets in a parallel airstream

The problem of the development and interaction of nonlinear two-dimensional perturbations in a rotating capillary jet is solved. The main attention is devoted to the study of the nonuniform breakup of the jet with allowance for the influence of the parallel airstream and the rotation. The solution is found by Galerkin's method [1–3]. The nonlinear development and interaction of a large number of perturbations is considered. A significant influence of long-wavelength modulation on the nature of drop formation is established. It is shown that an increase in the velocity of the parallel stream leads to a decrease in the relative size of the satellite (for the characteristic wavelengths). It is also shown that the rotation extends the region of unstable wave numbers in the complete range of flow velocities and air densities.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 3, pp. 124–128, May–June, 1981.I am sincerely grateful to G. I. Petrov, V. Ya. Shkadov, and S. Ya. Gertsenshtein for constant interest in the work.     

DYNAMICS OF ROTORS IMMERSED IN ECCENTRIC ANNULAR FLOW. PART 2: EXPERIMENTS

In order to validate the theoretical approach described in Part 1, an extensive experimental study has been performed at Instituto Tecnológico e Nuclear (I.T.N.), using a test rig presenting some improvements over previous experiments by the authors. In agreement with the theoretical model, concentric configurations always display flutter instability of the forward mode only, at velocities much higher than the critical unbalance-excited rotor velocity. Also predicted by theory, an instability of the backward mode may occur at much lower spinning velocities, for some eccentric configurations—which is a conclusion of practical significance. Therefore, rotor-annulus eccentricity is a very important parameter, when stability of the system is addressed. The quantitative agreement of both modal frequencies and damping values, with respect to the rotor spinning velocity, is quite satisfactory at lower velocities. However, it deteriorates somewhat at higher velocities, even for concentric configurations. Discrepancies are discussed, in connection with experimental difficulties (some unavoidable three-dimensional flow effects in the test rig) or other possibly pertinent phenomena (dynamic flow nonlinearities)—which were not accounted for in the theoretical model. However, these problems should not be overstressed, as theoretical instability boundaries are usually fairly close to the experimental results.     

Stability of stationary motions of a gimbal gyro with an electric motor

A gimbal gyro on an immovable base in the gravity field and with vertical outer suspension axis is considered. The rotor is driven by an asynchronous or synchronous electric motor, and there is no friction or any controlling torques on the suspension axes. Such a systemhas a family of steady-state motions (regular precessions and the rotor uniform rotations). It is shown that a necessary and sufficient condition for stability of the steady-statemotions with respect to generalized velocities and the angle of rotation of the inner gimbal frame is the existence of an isolated minimum of the reduced potential energy with respect to the angle of rotation of the inner frame.     

Aerodynamic drag of a pair of bodies in transonic and supersonic flow

The aerodynamic characteristics of models of pairs of bodies on the flow acceleration and deceleration intervals are investigated experimentally at transonic and supersonic flow velocities. The dependence of the drag coefficient of the pair model on the relative drag of the leading body is determined for supersonic velocities.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 3, pp. 152–156, May–June, 1990.     

A numerical modelling of stator–rotor interaction in a turbine stage with oscillating blades

In real flows unsteady phenomena connected with the circumferential non-uniformity of the main flow and those caused by oscillations of blades are observed only jointly. An understanding of the physics of the mutual interaction between gas flow and oscillating blades and the development of predictive capabilities are essential for improved overall efficiency, durability and reliability. In the study presented, the algorithm proposed involves the coupled solution of 3D unsteady flow through a turbine stage and the dynamics problem for rotor-blade motion by the action of aerodynamic forces, without separating the outer and inner flow fluctuations. The partially integrated method involves the solution of the fluid and structural equations separately, but information is exchanged at each time step, so that solution from one domain is used as a boundary condition for the other domain. 3-D transonic gas flow through the stator and rotor blades in relative motion with periodicity on the whole annulus is described by the unsteady Euler conservation equations, which are integrated using the explicit monotonous finite volume difference scheme of Godunov–Kolgan. The structural analysis uses the modal approach and a 3-D finite element model of a blade. The blade motion is assumed to be constituted as a linear combination of the first natural modes of blade oscillations, with the modal coefficients depending on time. A calculation has been done for the last stage of the steam turbine, under design and off-design regimes. The numerical results for unsteady aerodynamic forces due to stator–rotor interaction are compared with results obtained while taking into account blade oscillations. The mutual influence of both outer flow non-uniformity and blade oscillations has been investigated. It is shown that the amplitude-frequency spectrum of blade oscillations contains the high-frequency harmonics, corresponding to the rotor moving past one stator blade pitch, and low-frequency harmonics caused by blade oscillations and flow non-uniformity downstream from the blade row; moreover, the spectrum involves the harmonics which are not multiples of the rotation frequency.     

Experimental study of the mean wake of a tidal stream rotor in a shallow turbulent flow

The mean wake of a three-bladed horizontal axis tidal stream turbine operating at maximum power coefficient has been investigated experimentally in a wide flume with width 11 times the depth, providing minimal restriction to transverse wake development and behaviour of large-scale horizontal turbulence structures. This is an important first stage for understanding wake interaction in turbine arrays and hence large-scale power generation. The rotor diameter has a typical value of 60% of the depth and the thrust coefficient is representative of a full-scale turbine. The shear layers originating from the rotor tip circumference show classic linear expansion downstream, with the rate of a plane shear layer vertically and 1.5 times that horizontally. These shear layers merge by around 2.5 diameters downstream forming a self-similar two-dimensional wake beyond eight diameters downstream with a virtual origin at two diameters downstream of the rotor plane. The spreading rate is somewhat less than that for solid bodies. The detailed velocity measurements made in the near wake show rotation and vorticity similar to that measured previously for wind and marine turbines although with asymmetry associated with bed and surface proximity. The longitudinal circulation in a transverse plane is conserved at about 1% of the swept circulation from the blade tip within two diameters downstream, the extent of detailed measurement. Turbines are usually designed using blade element momentum theory in which velocities at the rotor plane are characterised by axial and tangential induction factors and it is now possible to see how this idealisation relates to actual velocities. The axial induction factor corresponds to velocity deficits at 0.4–0.8 radii from the rotor axis across the near wake while the tangential induction factor at the rotor plane corresponds to velocities at 0.4–0.6 radii between 1–2 diameters downstream, indicating some general correspondence. For the two-dimensional self-similar far wake the two parameters defining the centreline velocity deficit and the transverse velocity profiles are likely to be insensitive to Reynolds number in turbulent conditions.     

Visualization study of the flow in and around a Savonius rotor

Flow in and around a Savonius rotor has been studied by flow visualization experiments, and the rotation effect is discussed in comparison with the measured pressure distributions on the blade surfaces. It is observed that the flow separating regions on the blade surfaces are fairly reduced by the rotation effect and the flow through the overlap is weakened by the appearance of resisting flow. The former contributes to the torque production of the rotating rotor while the latter acts as a resistance. These phenomena together with the stagnation effect on the front side of the rotor contribute to the power producing mechanism of the Savonius rotor.     

Numerical investigation of natural convective motions in a rotating cube

On the basis of a numerical integration of the Navier-Stokes equations in the Boussinesq approximation, the natural thermal convection in a rotating cube heated from below is investigated for three values of the Rayleigh number. The effect of the rotation velocity on the establishment of various forms of convection flows is studied. The existence of several types of convection flows is noted. Each of the motions is realized on a specific range of the rotation velocity of the cube. The domains of existence of the different types are determined. The results obtained are compared with experimental data.Moscow. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 4, pp. 53–60, July–August, 1995.     

The effects of shadowing and interference from the rotation of a plate

The effects are considered of shadowing and interference which arise during tumbling motion of a plate in a free molecule flow. The particle fluxes are found together with the pressure and the tangential intensities acting on the plate, with allowance for these effects. For a purely diffuse scheme of interaction of the gas with the surface of the plate, estimates are obtained of the relative contribution of shading and interference to the drag and the damping moment of the plate.Translated from Ivestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 2, pp. 140–148, March–April, 1985.     

Theory of the hydromagnetic generator

It is shown that in a homogeneous medium, a magnetic field may generate helical motion in a cylinder with constant angular and axial velocities. The generation problem is solved exactly, and analytic expressions for the magnetic field are found. At high velocities the increment of field growth is maximal when the ratio of the velocities is of the order of unity. The maximum increment and frequency are of the order of the velocity to the two-thirds power. The field distribution has the form of a surface wave. The field decay decrement for departure from the cylinder surface is proportional to the square root of its increment.Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 6, pp. 47–51, November–December, 1973.     

Velocities and structure of convective motions in a rotating fluid

The velocities in various rotating fluid regimes are investigated.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 4, pp. 165–168, July–August, 1989.The author wishes to thank G. S. Golitsyn for his constant interest in the work.     

High-velocity cumulative gas jets

The author examines the theory of the cumulation effect [1] in axisymmetric inviscid perfect gas flows and the possibility of creating cumulative gas jets with velocities considerably in excess of the speed of sound.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 4, pp. 148–152, July–August, 1989.     

Effect of the Coriolis force on the onset of convection in a layer with a fixed heat flux on the boundaries

The effect of the Coriolis force on the onset of convection in a plane horizontal layer of viscous fluid with a fixed heat flux on the rigid lower and free upper boundaries is investigated. Expressions for the critical Rayleigh numbers and wave number are obtained analytically in the rapid rotation limit.Perm'. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 3, pp. 42–46, May–June, 1994.     

Determination of elastic and plastic characteristics of TiC–TiNi alloys by the ultrasonic resonance method

Elastic characteristics and propagation velocities of ultrasonic waves in a TiC–TiNi composite material are determined by the ultrasonic resonance method. The values of the elastic moduli of the solid composite obtained are used to estimate its plastic properties. The effect of various additives on the elastic and plastic properties of the composite is studied.     

Effect of the percolation heat transfer component on the temperature field and thawing dynamics of soils

The effect of the convective heat transfer component on the temperature field and thawing front dynamics of soils is investigated for high fluid percolation velocities in the thawed zone. The steady state interchange and approximate self-similarity methods are used to obtain upper and lower bounds of the solution of the Stefan problem with a convective heat transfer component in a porous medium. From the results of the calculations conclusions are drawn concerning the accuracy and limits of applicability of the solutions obtained.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 2, pp. 166–171, March–April, 1987.     

A class of exact solutions of a nonlinear boundary-value problem for fluid flow in a rotating cylinder

The flow of an ideal incompressible weightless fluid that fills a rotating cylinder is investigated. The rotation axis of the cylinder is outside it and parallel to the cylinder generator, and the form of the cylinder section is determined in the process of solution of the problem. In the paper, a class of exact solutions of the problem is obtained in terms of elementary functions for different angular velocities of the cylinder. In these solutions, the flow field is formed by two straight vortex filaments parallel to the cylinder generator. The intensities of the vortex filaments are determined by the angular velocity . Investigations of ideal fluid flow in rotating vessels were begun already in the last century by Stokes and Zhukovskii [1]. The subject has been reviewed in monographs [2, 3].Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No, 1, pp. 71–75, January–February, 1984.