Separation impact of a circular disk floating on the surface of an ideal incompressible fluid of infinite depth

The three-dimensional mixed problem of the separation impact of a circular disk floating on the surface of an ideal incompressible unlimited fluid is considered. The position and shape of the contact area between the body and the fluid (and the separation zone) are not known and depend on the relation between the translational and angular velocities acquired by the disk upon impact. Because of this, the problem in question is nonlinear and belongs to the class of free-boundary problems. The problem is solved using the method of Hammerstein-type nonlinear boundary integral equations. This approach allows the fluid flow after impact and the unknown zone of separation of fluid particles to be determined simultaneously. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 50, No. 4, pp. 76–86, July–August, 2009.     

Modeling of the hydrodynamics of a facility for removing mechanical impurities from oil

The separation of a viscous fluid flow by means of a device operating on the centrifugal principle was modeled. Parameters of the device with a specified separation size were obtained in a series of numerical experiments. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 49, No. 4, pp. 108–112, July–August, 2008.     

Investigation of steady laminar flows with an initial disturbance

Results of a parametric study of steady asymmetric flows are analyzed. Three-dimensional unsteady equations of hydromechanics for a compressible medium are solved by a time-dependent method. The range of the characteristic Reynolds number Re = 60–350 is considered. It is shown that a symmetric flow becomes asymmetric at Re = 90. This value can be considered as a threshold value for air. In the examples considered, the upper separation region is always smaller than the lower separation region owing to flow asymmetry in the vicinity of the left boundary of the domain of integration. The dependence of the separation region size on the Reynolds number is found. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 49, No. 3, pp. 11–19, May–June, 2008.     

Effect of streamwise structures on heat transfer in a hypersonic flow in a compression corner

Coefficients of heat transfer to the surface in a laminar hypersonic flow (M _∞ = 21) over plane and axisymmetric models with a compression corner are presented. These coefficients are measured by an infrared camera. The parameters varied in the experiments are the angle of the compression corner and the distance to the corner point. Characteristics of the flow with and without separation in the corner configuration are obtained. The measured results are compared with direct numerical simulations performed by solving the full unsteady Navier-Stokes equations. Experiments with controlled streamwise structures inserted into the flow are described. A substantial increase in the maximum values of the heat-transfer coefficient in the region of flow reattachment after developed laminar separation is demonstrated. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 50, No. 4, pp. 112–120, July–August, 2009.     

Design of airfoils providing the absence of separation in a compressible flow in a specified range of angles of attack

A problem of modification of the classical airfoils that ensure the absence of separation in a subsonic ideal-gas flow in a specified range of angles of attack is solved by a numerical-analytical method based on the quasi-solution of inverse boundary-value problems of aerohydrodynamics and Kármán-Jiang formulas. Loitsyanskii’s criterion of the non-separated flow is used to determine the boundary-layer separation point. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 49, No. 6, pp. 99–106, November–December, 2008.     

Supersonic flow separation in planar nozzles

We present experimental results on separation of supersonic flow inside a convergent–divergent (CD) nozzle. The study is motivated by the occurrence of mixing enhancement outside CD nozzles operated at low pressure ratio. A novel apparatus allows investigation of many nozzle geometries with large optical access and measurement of wall and centerline pressures. The nozzle area ratio ranged from 1.0 to 1.6 and the pressure ratio ranged from 1.2 to 1.8. At the low end of these ranges, the shock is nearly straight. As the area ratio and pressure ratio increase, the shock acquires two lambda feet. Towards the high end of the ranges, one lambda foot is consistently larger than the other and flow separation occurs asymmetrically. Downstream of the shock, flow accelerates to supersonic speed and then recompresses. The shock is unsteady, however, there is no evidence of resonant tones. The separation shear layer on the side of the large lambda foot exhibits intense instability that grows into large eddies near the nozzle exit. Time-resolved wall pressure measurements indicate that the shock oscillates in a piston-like manner and most of the energy of the oscillations is at low frequency.      

Scanning PIV measurements of a laminar separation bubble

Scanning PIV is applied to a laminar separation bubble to investigate the spanwise structure and dynamics of the roll-up of vortices within the bubble. The laminar flow separation with turbulent reattachment is studied on the suction side of an airfoil SD7003 at Reynolds numbers of 20,000–60,000. The flow is recorded with a CMOS high-speed camera in successive light-sheet planes over a time span of 1–2 s to resolve the temporal evolution of the flow in the different planes. The results show the quasi-periodic development of large vortex-rolls at the downstream end of the separation bubble, which have a convex structure and an extension of 10–20% chord length in the spanwise direction. These vortices possess an irregular spanwise pattern. The evolution process of an exemplary vortex structure is shown in detail starting from small disturbances within the separation bubble transforming into a compact vortex at the downstream end of the separation bubble. As the vortex grows in size and strength it reaches a critical state that leads to an abrupt burst of the vortex with a large ejection of fluid into the mean flow.     

Using the perturbation method to solve the problem of separated incompressible flow past thin airfoils

A model for separated incompressible flow past thin airfoils in the neighborhood of the “shockless entrance” condition is constructed based on the averaging of the vortex shedding flow past the airfoil edges. By approximation of the vortex shedding by two vortex curves, determination of the average hydrodynamic parameters is reduced to a twofold solution of an integral singular equation equivalent to the equation describing steady-state nonseparated airfoil flow. In this case, the calculation time is two orders of magnitude smaller than the time required for the solution of the corresponding evolution problem. The results of a test calculation using the proposed method are in fair agreement with available results of calculations and experiments. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 47, No. 3, pp. 49–63, May–June, 2006.     

Effect of a local stationary flow disturbance on separated boundary layer stability

The separated flow past a transverse barrier on a plate surface is modeled in a wind tunnel. The linear stability of the two-dimensional laminar flow in the separation zone is investigated in the presence of a stationary disturbance imposed on the flow and concentrated in a narrow spanwise region. It is experimentally shown that the local flow nonuniformity leads to a change in the flow stability features, such as the frequencies of the growing oscillations, their growth rate, and the dispersion characteristics. As a result, the transverse velocity gradients induced in the separation zone exert a strong destabilizing influence on the flow. Novosibirsk. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 1, pp. 174–178, January–February, 2000. The study was carried out with the support of the INTAS Foundation under grant No, 96-2225.     

Shallow and deep dynamic stall for flapping low Reynolds number airfoils

We consider a combined experimental (based on flow visualization, direct force measurement and phase-averaged 2D particle image velocimetry in a water tunnel), computational (2D Reynolds-averaged Navier–Stokes) and theoretical (Theodorsen’s formula) approach to study the fluid physics of rigid-airfoil pitch–plunge in nominally two-dimensional conditions. Shallow-stall (combined pitch–plunge) and deep-stall (pure-plunge) are compared at a reduced frequency commensurate with flapping-flight in cruise in nature. Objectives include assessment of how well attached-flow theory can predict lift coefficient even in the presence of significant separation, and how well 2D velocimetry and 2D computation can mutually validate one another. The shallow-stall case shows promising agreement between computation and experiment, while in the deep-stall case, the computation’s prediction of flow separation lags that of the experiment, but eventually evinces qualitatively similar leading edge vortex size. Dye injection was found to give good qualitative match with particle image velocimetry in describing leading edge vortex formation and return to flow reattachment, and also gave evidence of strong spanwise growth of flow separation after leading-edge vortex formation. Reynolds number effects, in the range of 10,000–60,000, were found to influence the size of laminar separation in those phases of motion where instantaneous angle of attack was well below stall, but have limited effect on post-stall flowfield behavior. Discrepancy in lift coefficient time history between experiment, theory and computation was mutually comparable, with no clear failure of Theodorsen’s formula. This is surprising and encouraging, especially for the deep-stall case, because the theory’s assumptions are clearly violated, while its prediction of lift coefficient remains useful for capturing general trends.     

Mathematical modeling of the motion of a portion of helium under pulsed injection over a fixed bed of cenospheres

A mathematical model is constructed and an analytical solution is obtained for the problem of a one-dimensional steady flow of a mixture of different gases with hollow permeable particles. The case of a one-dimensional unsteady flow of such a mixture is analyzed numerically. The numerical solutions are compared with experimental data on the motion of the peak concentration of helium in a fixed bed filled with cenospheres (solid hollow permeable spherical particles). The permeability of cenosphere walls and the drag coeficient of cenospheres in the gas flow are determined. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 48, No. 3, pp. 92–102, May–June, 2007.     

Experimental evaluation of side-loads in LE-7A prototype engine nozzle

During development tests of the LE-7A prototype engine, severe side-loads were observed. The side-load peaks appeared only in certain limited conditions during start-up and shut-down transients. To investigate phenomena causing those severe side-loads observed in the LE-7A prototype engine nozzle, series of cold-flow tests and hot-firing tests as well as CFD analyses were conducted. As a result of the hot-firing tests, two different phenomena were found to cause severe side-loads in the LE-7A prototype engine nozzle. One was a restricted shock separation (RSS) flow structure and the other was a phenomenon termed “separation jump,” the rapid movement of the separation location in the vicinity of the step. A step was installed in the LE-7A prototype to supply film-cooling gas. Hot-firing test results showed that RSS can occur for a limited mixture ratio. Detailed flow structure of RSS on the nozzle surface was revealed by the cold-flow tests. Measured pressures and visualized images of cold-flow tests clarified the mechanism causing the separation jump. The key phenomenon ruling the separation jump was found to be the base flow behind the step. Based on the results of the present study, the latest LE-7A engine nozzle design has been changed to eliminate the severe side-load.

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Criteria for the Separation of Unsteady Ideal Fluid Flow past a Smooth Airfoil

Criteria for the separation of unsteady flow past a closed smooth airfoil are studied using the ideal fluid model and the Brillouin-Villat criterion. The necessary separation conditions are formulated. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 47, No. 1, pp. 74–81, January– February, 2006.     

Gas-dynamic colliders: Numerical simulations

A collision of supersonic flows of gas mixtures with disparate molecular weights, which are limited in their cross-sectional size, in vacuum leads to formation of a cloud with an elevated concentration and elevated temperature of the heavy gas. Under certain conditions, the governing factor is the collision of molecules of the heavy gas being compressed at the center of the collision of the flows. The generator of such a flow can be called a collider. Results of studying the flows in jet-type, cylindrical, and mixed two-stage colliders are described. The main attention is paid to separation of gases in terms of energy and composition. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 48, No. 3, pp. 142–151, May–June, 2007.     

Regimes of laminar lateral flow separation due to jet exhaust

Numerical simulation of the separation flow on the lateral surface of an aircraft due to interaction between the engine exhaust plume and the external air-stream is carried out on the basis of the full Navier-Stokes equations. Three separated flow regimes are revealed, namely, closed, open and periodic. The conditions under which each of these three regimes may exist are determined. Moscow. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No.1, pp. 132–138, January–February, 1994.     

The effect of roughness on separating flow over two-dimensional hills

Two new experimental data sets for turbulent flow over a steep, rough hill are presented. These include detailed laser Doppler anemometry measurements obtained at the separation and reattachment points and, in particular, within the reverse flow region on the lee side of the hill. These results allow the development of a new parametrization for rough wall boundary layers and validate the use of Stratford’s solution for a separating rough flow. The experiments were conducted in a water channel for two different Reynolds numbers. In the first set of rough wall experiments, the flow conditions and the hill shape are similar to those presented in Loureiro et al. (Exp. Fluids, 42:441–457, 2007a) for a smooth surface, leading to a much reduced separation region. In the second set of experiments, the Reynolds number is raised ten times. The region of separated flow is then observed to increase, but still to a length shorter than that recorded by Loureiro et al. (Exp. Fluids, 42:441–457, 2007a). Detailed data on mean velocity and turbulent quantities are presented. To quantify the wall shear stress, global optimization algorithms are used. The merit function is defined in terms of a local solution that is shown to reduce to the classical law of the wall far away from a separation point and to the expression of Stratford at a separation point. The flow structure at the separation point is also discussed.     

Calculation of dynamic stall on an oscillating airfoil

A mathematical model of an unsteady separated flow around an oscillating airfoil is considered. This model is based on a viscid-inviscid approach. The points of separation and the intensity of vorticity displaced into the external flow are determined using boundary-layer equations in an integral form. Dynamic stall on an oscillating airfoil is studied. The mechanism and nature of antidamping are discovered. Novosibirsk State Technical University, Novosibirsk 630092. Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 41, No. 3, pp. 81–85, May–June, 2000.     

Flow pattern in the vicinity of an annular system of transverse jets in a supersonic stream

The pattern of the flow in the vicinity of an annular system of jets exiting into a supersonic stream from orifices on a cylindrical surface with a turbulent boundary layer is experimentally investigated Four typical flow regimes are recorded The effect of the jet number and the nozzle-to-outer pressure ratio on the extent of the separation zone and its structure ahead of and behind the jet system is determined Moscow. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 1, pp. 21–27, January–February, 1999.     

One problem of the theory of dimensional electrochemical machining of metals

A method is proposed for determining the shape of the anode-article boundary for a given shape of the cathode-tool in plane problems of the theory of dimensional electrochemical machining of metals. Under the assumptions used, the boundary of the anode-article is divided into the working zone, where metal dissolution occurs, and an adjacent zone, where the treatment (dissolution) is terminated. The initial problem is reduced to a problem of a fictitious plane-parallel potential flow of an ideal fluid with a nonlinear condition on the free surface. The point of separation of the fictitious flow from the solid boundary corresponds to the point separating these two zones of the anode boundary. The Brillouin-Will condition of smooth separation is imposed at the separation point to construct a closed system of equations determining the problem solution. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 50, No. 3, pp. 214–220, May–June, 2009.     

Stabilization and evolution of parameters of a symmetric laminar flow in a plane channel with sudden expansion

A problem is formulated for computing the fields of parameters of a stationary laminar symmetric flow. A two-dimensional flow in a channel with a sudden change in the cross-sectional area is computed. The evolution of a three-dimensional perturbation inserted into the channel at the initial stage of computations is analyzed. It is demonstrated that the parameters of a two-dimensional flow in the channel at a Reynolds number Re = 50 become stabilized at a dimensionless time t > 20, whereas the steady state is reached under the same conditions at t ≈ 100. At a distance of approximately 10h (h is the channel width at the entrance), the flow becomes one-dimensional, but the streamwise component of the velocity vector remains a function of the streamwise coordinate owing to flow compressibility. __________ Translated from PrikladnayaMekhanika i Tekhnicheskaya Fizika, Vol. 48, No. 1, pp. 35–42, January–February, 2007.