Design of a separation-free airfoil with outer-flow suction over a certain range of angles of attack

The problem of the design of an airfoil with slot air suction from the outer flow for a prescribed velocity distribution over the airfoil contour that ensures the absence of flow separation over a given range of angles of attack is formulated and solved. The proposed combined numerical and analytical method of airfoil design within the framework of the inviscid incompressible fluid model is based on the theory of inverse problems of aerohydrodynamics. Separationless flow past the airfoil is achieved by eliminating the falling velocity intervals from the specified velocity distribution in two given flow regimes. The flow past an airfoil with outer-flow suction is determined not only by the angle of attack as for an impermeable airfoil but also by the value of the suction mass flow. The slot is modeled by an annular channel with constant velocities on the walls. To satisfy the problem solvability conditions, free parameters are introduced into the initial velocity distribution. Examples of airfoil design are given. Kazan, Moscow. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 4, pp. 185–191, July–August, 2000.     

Calculation of pressure on an airfoil contour in an unsteady separated flow

Simple formulas for calculating the pressure and the total hydrodynamic reactions acting on an arbitrarily moving airfoil are derived within the framework of the model of plane unsteady motion of an ideal incompressible fluid. Several vortex wakes may be shed from the airfoil owing to changes in velocity circulation around the airfoil contour. Cases with nonclosed and closed contours are considered. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 49, No. 3, pp. 109–113, May–June, 2008.     

Effect of asymmetric pulsed periodic energy supply on aerodynamic characteristics of airfoils

The possibility of controlling the aerodynamic characteristics of airfoils in transonic flight regimes by means of local pulsed periodic energy supply is considered. The numerical solution of two-dimensional unsteady equations of gas dynamics allowed determining the changes in the flow structure near a symmetric airfoil and its aerodynamic characteristics depending on the magnitude of energy in the case of its asymmetric (with respect to the airfoil) supply. The results obtained are compared with the calculated data for the flow around the airfoil at different angles of attack without energy supply. With the use of energy supply, a prescribed lift force can be obtained with a substantially lower wave drag of the airfoil, as compared with the flow around the airfoil at an angle of attack. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 48, No. 6, pp. 70–76, November–December, 2007.     

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.     

Design of a thin airfoil in a channel with permeable walls

A general solution is obtained for the boundary value problem of designing a thin airfoil in a channel with permeable walls from the given pressure distribution. A suitable choice of permeability coefficients makes it possible to construct a thin airfoil in a channel with impermeable walls, in a jet, etc. The effect of the wall permeability on the shape of the airfoil is studied. Cheboksary. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 4, pp. 28–34, July–August, 1994.     

Design of a two-element airfoil in a range of angles of attack

A numerical-analytical solution of an inverse boundary-value problem of aerohydrodynamics is obtained for a two-element airfoil in the full formulation, based on the velocity distribution defined on the sought airfoil contours in a range of angles of attack. It is demonstrated that flow separation does not occur in the entire range considered for a specified non-separated velocity distribution on the upper surfaces at the maximum angle of attack and on the lower surface at the minimum angle of attack. An example of constructing a sectional airfoil is given; verification of the results obtained is performed with the use of the Fluent software package. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 49, No. 6, pp. 107–114, November–December, 2008.     

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.     

Kinematic problem of an ideal incompressible fluid flow around an arbitrarily moving airfoil

An unsteady kinematic problem for arbitrary two-dimensional motion of an airfoil in an ideal incompressible fluid with formation of one and two vortex wakes is solved. The problem is solved by the method of conformal mapping of the flow domain onto a circle exterior; solution singularities in the vicinity of a sharp edge are analyzed, and the initial asymptotics of the solution is taken into account. The calculated results are found to be in good agreement with available experimental data on visualization of the flow pattern. The necessity of correct modeling of the initial stage of vortex-wake formation is demonstrated. A regular flow pattern is found to form after three and more periods of oscillations. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 50, No. 2, pp. 120–128, March-April, 2009.     

Experimental and numerical study of the stability of a pre-separated flow on an airfoil

The problem of the origin and evolution of two-dimensional waves of unstable disturbances in the boundary layer on an airfoil in the region of adverse pressure gradient in the preseparation flow region is solved numerically. The stability of the experimental velocity profiles, including the inflected profiles, is studied. As a result of the calculations, the boundaries of the instability region and the parameters of the maximally unstable disturbances (frequency, growth rate, wavelength, and propagation velocity) are determined for each velocity profile. The characteristics obtained in the present work are in good agreement with the real experimental parameters of instability waves. Institute of Theoretical and Applied Mechanics, Siberian Division, Russian Academy of Sciences, Novosibirsk 630090. Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 40, No. 1, pp. 126–132, January–February, 1999.     

Motion of an inclusion in uniformly and nonuniformly vibrating liquids

An approach to constructing the quantitative nonuniformity characteristics of liquid vibrations is proposed. A new problem of the motion of an inclusion in a vibrating liquid is considered. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 48, No. 1, pp. 79–85, January–February, 2007.     

Self-similar solution of the one-dimensional problem of thermocapillary motion of an emulsion

It is proved that the problem of one-dimensional motion of an emulsion under the action of thermocapillary forces has a self-similar solution in a semi-infinite interval. The behavior of the solution is illustrated by numerical examples for aluminum-lead emulsions, in which the carrier phase is lead or aluminum. The solution is compared with the solution of the self-similar problem linearized in the low impurity concentration. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 48, No. 5, pp. 61–70, September–October, 2007.     

The inverse problem of aerodynamics with Cartesian coordinates as dependent variables

The gas-dynamic equations are written in Cartesian coordinates in the potential plane. This approach to the inverse problem makes it possible to seek a quasisolution within a set of closed contours. To solve this problem an iterative procedure is developed using successive approximations and taking into account the fact that aerodynamic airfoils are elongated in the streamwise direction. In the case where an arbitrary pressure distribution is prescribed, the procedure determines the airfoil providing the best approximation to the design data. Moscow. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No.1, pp. 147–157, January–February, 1994.     

Effect of one-sided unsteady energy supply on aerodynamic characteristics of airfoils in a transonic flow

The possibility of controlling the aerodynamic characteristics of airfoils in transonic flight regimes by means of one-sided pulsed-periodic energy supply is studied. Based on the numerical solution of two-dimensional unsteady gas-dynamic equations, the change in the flow structure in the vicinity of a symmetric airfoil at different angles of attack and the aerodynamic characteristics of the airfoil as functions of the amount of energy supplied asymmetrically (with respect to the airfoil) are determined. The results obtained are compared with the data calculated for the flow past the airfoil at different angles of attack without energy supply. It is found that a given lift force can be obtained with the use of energy supply at a much better lift-to-drag ratio of the airfoil, as compared to the case of the flow past the airfoil at an angle of attack. The moment characteristics of the airfoil are found. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 49, No. 6, pp. 82–87, November–December, 2008.     

Stress-strain state of an anisotropic plate with an elliptic hole and thin rigid inclusions

The stress-strain state of an anisotropic plate containing an elliptic hole and thin, absolutely rigid, curvilinear inclusions is studied. General integral representations of the solution of the problem are constructed that satisfy automatically the boundary conditions on the elliptic-hole contour and at infinity. The unknown density functions appearing in the potential representations of the solution are determined from the boundary conditions at the rigid inclusion contours. The problem is reduced to a system of singular integral equations which is solved by a numerical method. The effects of the material anisotropy, the degree of ellipticity of the elliptic hole, and the geometry of the rigid inclusions on the stress concentration in the plate are studied. The numerical results obtained are compared with existing analytical solutions. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 48, No. 4, pp. 173–180, July–August, 2007.     

Rayleigh-Benard problem for an anomalous fluid

The stability of the state of rest of a heated infinite horizontal layer of a viscous heat-conducting fluid (the Rayleigh-Benard problem) is considered. The equation of state for the fluid takes into account the nonmonotonic temperature and pressure dependence of water density. Instability of the mechanical equilibrium with respect to small monotonic perturbations is studied. The effect of the problem parameters on the Rayleigh numbers and their corresponding critical motions is investigated numerically using linear theory. Numerical investigation of the spectral problem is based on the Godunov-Abramov orthogonalization method. The calculation results are compared with the well-known results for the limiting case where the density is considered a quadratic function of temperature and does not depend on pressure. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 48, No. 2, pp. 27–38, March–April, 2007.     

Eigenoscillations of an elastic body with a rough surface

Explicit presentations for the initial terms of the asymptotic solution of the spectral problem of the elasticity theory in a plane region with a rapidly oscillating boundary are obtained. Based on asymptotic formulas, two methods for problem modeling are proposed: with the use of Wenzel’s boundary conditions and with the use of the principle of a smooth image of a singularly perturbed boundary. Various approaches to justification of asymptotic presentations are discussed. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 48, No. 6, pp. 103–114, November–December, 2007.     

On an inverse problem of bending of a physically nonlinear inhomogeneous plate

An elastic plate with a physically nonlinear inclusion of an arbitrary shape is considered. This plate is subjected to pure bending under the action of transverse forces and bending moments applied at the external boundary of the plate. There are no loads distributed over the surface. The problem of finding external actions that provide a necessary uniform moment state in the inclusion, i.e., prescribed constant moments and curvatures, is formulated and solved. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 48, No. 5, pp. 104–107, September–October, 2007.     

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.     

Flow past an airfoil at an angle of attack to an oncoming sonic stream

Guderley [1] proposed a theoretical example of sonic flow of gas past a symmetric airfoil at zero angle of attack to an oncoming stream. The linear distribution of the velocity over the airfoil surface was found from the solution describing this flow. It is of interest to generalize this example to the case of nonsymmetric sonic flow past an airfoil. In the present paper a study is made of sonic flow past a Guderley airfoil at an angle of attack and a study is made of the dependence of the velocity over the surface of the airfoil on the angle of attack. This dependence is obtained by means of the parabolic method of Spreiter and Alksne [2], which makes it possible to solve this problem directly in the plane of the flow. For comparison, flow past a parabolic airfoil at an angle of attack is considered, and an expression is obtained for the dependence of the distribution of the velocity over the surface on the angle of attack, this being a generalization of the formula of Zierep [3], who considered sonic flow past a parabolic airfoil at zero angle of attack.Translated from Izvestlya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 5, pp. 81–86, September–October, 1982.     

Exact and approximate formulas for deflections of an elastically fixed rod under transverse loading

An exact solution is obtained for the nonlinear bending problem of a thin rod elastically fixed at one end and loaded by a transverse concentrated load of constant direction at the other end. The solution is written in parametric form and expressed in terms of the Jacobi elliptic functions. Based on the exact solutions, approximate formulas are proposed for the de.ection of the rod tip. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 48, No. 1, pp. 151–160, January–February, 2007.