Properties of similarity solutions for flows in turbulent vortex cores

A class of similarity solutions of the equations for turbulent vortex cores matching an external inviscid similarity flow with a power law of circumferential velocity variationv-r ^−m near the rotation axis and constant Bernoulli function is considered. Solutions are found to exist only in a certain range of the indexm of the exponential. For each suchm there are two solutions. The authors wish to apologise for a mistake which resulted in the figures in this paper corresponding to [1] and those in [1] corresponding to this paper. Moscow. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 3, pp. 60–64, May–June, 1998. The work was financially supported by the Russian Foundation for Basic Research (project No. 95-01-00483).     

Effect of volume energy supply on swirled flows in a subsonic cocurrent stream

The results of a numerical investigation of the effect of thermal energy supply on a swirling viscous heat-conducting gas flow in a subsonic cocurrent stream are presented. The initial stage of development of the swirling flow in the neighborhood of the vortex axis with constant circulation in the outer flow region is considered for two different distributions of the streamwise velocity vector component which simulate a swirling jet-type flow and a wake flow with a streamwise velocity deficit. The effect of local volume energy supply in the neighborhood of the vortex axis, the circulation of the azimuthal velocity component, and the longitudinal pressure gradient in the inviscid stream on the development of the swirling flow and the process of breakdown of cocurrent vortex flows is investigated. Moscow. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 6, pp. 47–53, November–December, 1998. The work was carried out with financial support from the Russian Foundation for Basic Research (project No. 96-01-00586).     

Plane configurations in a flow of a perfect gas with a maximum critical Mach number

The problems in the construction of bodies which, satisfying some geometric limitations, are exposed to a plane symmetric flow of a perfect (inviscid and heat-nonconducting) gas with a maximum critical Mach numberM* are considered. Solutions are found by a numerical-analytical method with the use of the variables of the velocity hodograph. The Mach numberM* is found as a function of the geometric characteristics of the sought bodies on the basis of approximation of numerical data. Institute of Mathematics and Mechanics at the Kazan' State University, Kazan' 420008. Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 39, No. 5, pp. 106–115, September–October, 1998.     

Investigation of transonic and supersonic flow past a pair of bodies

Transonic and supersonic flows past a pair of bodies have been experimentally investigated. The leading bodies were spheres, cylinders, and cones, while the trailing bodies were flat-ended circular cylinders. The leading and trailing bodies were joined by cylindrical rods of various lengths, aligned with the axis of symmetry. For these models, the pattern of flow between the bodies and the Mach number dependence of the drag coefficientC _x were determined in the acceleration and deceleration flow regimes in a wind tunnel. The experimental results are used to analyze the properties of the flow between the bodies and the variation of the aerodynamic coefficients of the models. The reasons for the hysteresis in the behavior of the coefficients in the acceleration and deceleration stages are discussed. The influence of the shape and dimensions of the leading body on the modelC _x is evaluated. Moscow. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 2, pp. 158–164, March–April, 1998.     

An analog of the Bernoulli and Cauchy-Lagrange integrals for a time-dependent vortex flow of an ideal incompressible fluid

An expression with a constant value over all space (including multiply connected domains) relating the pressure function to the square of the velocity and the characteristics of the traveling vortices is derived for a time-dependent ideal incompressible fluid flow with nonzero vorticity. When there are bodies in the flow, they must also be represented in the form of traveling vortices. For steady-state flow the formula obtained goes over into the Bernoulli integral and for time-dependent irrotational flow into the Cauchy-Lagrange integral. Moscow. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 1, pp. 31–41, January–February, 2000. The work was carried out with financial support from the Russian Foundation for Basic Research (project No. 98-01-00156 and project No. 96-15-9603 for the support of leading science schools).     

Certain features of similarity solutions for flows in viscous vortex cores

A class of steady similarity solutions of the equations for viscous vortex cores which correspond to external inviscid similarity solutions with a power-law variation of the circumferential velocityv-r ^−m near the rotation axis is considered. It is found that if the Bernoulli function in external flow is constant, then these solutions will exist only on a certain range of the indexm of the exponential. For eachm on this range there are two solutions. Moscow. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 1, pp. 38–43, January–February, 1998. The work was financially supported by the Russian Foundation for Fundamental Research (project No. 95-01-00483).     

The pattern and restructuring of supersonic flow past a pair of bodies

The pattern of symmetric and asymmetric supersonic flow past a pair of isolated/connected bodies is analyzed. Semiempirical dependences of the critical parameterl ^*, determining direct and reverse flow restructuring, on the geometry and permeability of the bodies and the Mach and Reynolds numbers are derived using experimental data. Moscow. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 1, pp. 158–165, January–February, 1994.     

Stability of a compressible swirling flow in a circular pipe

The stability of an axisymmetric flow of viscous gas in a circular pipe, which models the Burgers vortex in the pipe axis neighborhood, is studied within the linear theory framework. Neutral curves for the most unstable disturbances are calculated. The influence of the characteristic Mach number on the flow stability is investigated. It is shown that for a given model velocity distribution the Mach number affects only the temperature and pressure profiles of the main undisturbed flow. In this case, for the disturbance types considered, as the Mach number increases, the critical Reynolds number corresponding to loss of stability decreases. Moscow. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 1, pp. 35–41, January–February, 1999. The work received financial support from the Russian Foundation for Basic Research (project No. 96-01-00586).     

Effect of acoustic disturbances on a free convective flow

A gas-dynamic flow in an axisymmetric convective jet is studied experimentally. It is demonstrated that the jet flow with Grashof numbers Gr = (0.4–2.0) · 10⁶ is self-similar. Acoustic oscillations directed perpendicular to the axis of symmetry transform the profiles of the gas-flow parameters; two temperature maximums located outside the axis can appear. The results obtained indicate that flow instability is generated in high-gradient regions. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 47, No. 5, pp. 27–33, September–October, 2006.     

Effect of the height of a melted layer on its thermal structure in growing single crystals by the stockbarger method with the use of the accelerated crucible rotation technique

The effect of the height of a melted layer on its thermal structure is examined. The maximum velocities of ascending and descending flows during crystal growth by the Stockbarger method with the use of the accelerated crucible rotation technique in crucibles100 mm in diameter at Taylor numbersTa>10 ⁸ are estimated. A sudden increase in the amplitude of temperature oscillations with diminution of the height of the melted layer caused by unsteady rotation of the crucible is found. With decreasing height of the melted layer, the velocity of both ascending and descending flows at the axis of a cylindrical ampoule decreases. Institute of Mineralogy and Petrography, Siberian Division. Russian Academy of Sciences, Novosibirsk 630090. Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 41, No. 3, pp. 133–138, May–June, 2000.     

Stabilization of the Rotation Axis of a Solid by Coupled Perfectly Rigid Bodies

The problem of stabilizing the axis of a solid by coupled perfectly rigid bodies (PRBs) is solved. The solid executes a plane-parallel motion. The PRBs can rotate as a single rigid body about the centroidal axis of the solid and counterrotate about its transverse axes through equal angles. There is a particle inside the solid which causes its imbalance. It is established that the principal state (if any) of the system—rotation about the centroidal axis—is stable, whereas the rest (unwanted) states are unstable __________ Translated from Prikladnaya Mekhanika, Vol. 41, No. 8, pp. 122–129, August 2005.     

Rebounding of a shaped-charge jet

The phenomenon of rebounding of a shaped-charge jet from the armour surface with small angles between the jet axis and the target surface is considered. Rebounding angles as a function of jet velocity are obtained in experiments for a copper shaped-charge jet. An engineering calculation technique is developed. The results calculated with the use of this technique are in reasonable agreement with experimental data. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 48, No. 5, pp. 17–20, September–October, 2007.     

The flow in a planar-radial vortex chamber. 2. Vortex structure of the flow

A vortex structure of an air flow with a characteristic size of vortices comparable with the primary vortex size was observed in a vortex chamber of planar-radial geometry for the first time. The vortex component of the flow velocity along the chamber radius and its axis was calculated. Lavrent'ev Institute of Hydrodynamics, Siberian Division, Russian Academy of Sciences, Novosibirsk 630090. Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 41, No. 1, pp. 41–49, January–February, 2000.     

Extension of Ovsyannikov's Analytical Solutions to Transonic Flows

The solution of the equation of the velocity potential of a steady axisymmetric ideal-gas flow in the neighborhood of a given point at the axis of symmetry in the form of a double series in powers of the distance to the axis of symmetry and its logarithm is considered. Recurrent chains of equations with arbitrariness in two analytical functions of the streamwise variable are obtained for coefficients of the series. Convergence of the constructed series is proved by the method of special majorants. The theorem of existence and uniqueness of the solution of the initial-boundary problem for this nonlinear differential equation in partial derivatives with a singularity at the axis of symmetry is obtained as an analog of Kovalevskaya's and Ovsyannikov's theorems. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 46, No. 6, pp. 14–25, November–December, 2005.     

Separationless flow past a body of revolution with simultaneous suction and ejection of fluid

The problem of the axisymmetric potential flow past a body of revolution with a channel along the axis in the presence of a recirculation flow zone near the body, first proposed by G. Yu. Stepanov, is solved. Kazan’. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 1, pp. 14–21, January–February, 2000. The study was carried out with the support of the Russian Foundation for Basic Research (project No. 96-01-00123).     

Interaction of a shaped-charge jet with a target possessing an axial orifice

Interaction of a shaped-charge jet with a target possessing an axial orifice is studied experimentally. For an orifice diameter approximately equal to 0.2D, where D is the shaped-charge diameter, the shaped-charge penetration depth is found to be substantially reduced owing to deviation of the shaped-charge jet axis from the shaped charge axis because of imperfections of the manufacturing technology. A diameter of the target orifice providing unconstrained penetration of the shaped-charge jet is determined. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 49, No. 6, pp. 13–16, November–December, 2008.     

The plane problem on vertical impact of a rotating circular cylindrical shell against the surface of a liquid

The plane nonsymmetric problem on impact against and immersion into a compressible fluid of a thin electic cylindrical shell is considered. The shell rotates about its axis with a given angular velocity. The boundary-value problem is reduced to an infinite system of integral Volterra equations of the second kind. Translated from Prikladnaya Mekhanika, Vol. 36, No. 5, pp. 103–113, May, 2000.     

Circulation flow around airfoils by a steady plane-parallel flow of a heavy liquid of finite depth with a free surface

Steady problems of a circulation flow around bodies by a flow of a heavy liquid bounded by a free surface and a straight bottom are solved. The method of complex boundary elements is used, which is based on the integral Cauchy formula written for a complex-conjugate velocity. Results of numerical calculations of the flow around a circular contour and the Joukowski airfoil are presented. Shapes of the free surface and the most important hydrodynamic characteristics of the process (velocity circulation over the airfoil and the lifting force and its moment relative to the sharp edge of the airfoil) are given. Kemerovo State University, Kemerovo 650043. Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 41, No. 3, pp. 101–110, May–June, 2000.     

The stability of a compressed rotating rod

The classical stability problem of a compressed hinged elastic rod rotating with constant angular velocity about the axis that passes through the hinges is considered. It is assumed that the compressive force is constant and the line of its action coincides with the axis of rotation of the rod. The stability of a solution of the nonlinear problem that describes deformation of the rod under the action of the compressive force and the distributed centrifugal load is studied within the framework of the stability theory of dynamic systems with distributed parameters. The buckling paramcters of the problem are determined. Calculation results are given. Technology Institute, Altai State Technical University, Biisk 659305. Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 41, No. 4, pp. 190–197, July–August, 2000.     

Passive deployment of a tether between two bodies in orbit

The authors consider the problem of deployment in orbit of a small tether that can serve as a standard of length for calibration of both onboard and ground optical and radar tracking systems, as an integrated sensor of the force fields of planets, etc. A tether for two bodies is examined. Possible methods for compact placement of a tether in orbit in operating condition are discussed. The main method is that of use of the centrifugal forces resulting from imparting to the tether an initial angular velocity in its deployment from the spacecraft. Various methods for creating moments of friction forces in hinges are considered. Numerical modeling of the dynamic processes is carried out within the framework of the theory of systems of bodies. Problems associated with determination of the required initial angular velocity and of the “cone of departure” of the tether from the spacecraft are examined. Translated from Prikladnaya Mekhanika, Vol. 35, No. 10, pp. 87–92, October, 1999.