# TsAGI Science Journal, Issue 2, Year 2013

**TO THE ASYMPTOTIC THEORY OF A FLOW OVER A SMALL THREE-DIMENSIONAL HUMP**

*Vic. V. Sychev*

*A steady flow of incompressible fluid at high Reynolds number over a small hump embedded in a three-dimensional boundary layer is considered. The flow regime with a new type of interaction inherent only in three-dimensional flows is investigated. The solution of the linearized problem is obtained.*

**KEY WORDS: ***three-dimensional boundary layer, jet, interaction*

**HEAT FLUX TO THE CYLINDER SURFACE AT THE THREE-DIMENSIONAL PERTURBATIONS OF SUPERSONIC FLOW**

*I. V. Egorov** & V. V. Shvedchenko*

*Three-dimensional flow in the shock layer at a supersonic flow over the cylinder frontal surface under imposed small space-periodic perturbations was studied in this work. On the basis of the numerical solution of the unsteady three-dimensional Navier-Stokes equations it was demonstrated that the small imposed perturbations of the incoming flow in the transversal coordinate result in the distortion of the shock wave front, in the generation of the significantly three-dimensional flow in the region of the shock wave, and in the formation of large heat flux perturbations on the surface.*

**KEYWORDS: ***supersonic flow, spatial perturbations, cylinder, heat flux*

**NUMERICAL SIMULATION OF HYPERSONIC BOUNDARY-LAYER RECEPTIVITY TO ENTROPY AND VORTICITY WAVES**

*V. G. Soudakov*

*Receptivity of a hypersonic boundary layer (free-stream Mach number 6) over a flat plate with a sharp leading edge is investigated on the base of numerical simulation of the Navier—Stokes equations for two-dimensional (2D) unsteady flows. The physical mechanisms of receptivity to 2D monochromatic entropy and vorticity waves of a wide range of angles of inclination to the plate surface are considered. Initially, small perturbations introduced into the free-stream flow pass through the bow shock. This interaction generates acoustic waves downstream of the shock, which penetrate into the boundary layer together with passing entropy and vorticity waves. In this case, the acoustic waves generate unsteady disturbances in the boundary layer with essentially higher amplitudes than the entropy and vorticity waves.*

**KEY WORDS: ***hypersonic boundary layer, receptivity, entropy and vorticity waves, acoustics*

**THE PRINCIPLES OF SEPARATED FLOW AT THE INLET OF THE PROTRUDING DUCT WITH SCREENS**

*O. A. Averkova, I. N. Logachev, K. I. Logachev,** & A. K. Logachev*

*The direct problem of separated flow at the inlet of a suction duct is solved within the framework of the theory of ideal incompressible fluid jets. The sucking torch of the duct is constraint by thin screens and divided into two areas by a vertical board with a central aperture. The orthogonal grid of equal potential lines and streamlines, the velocity field, and the factor of compression of a jet are defined. Optimal removal of the board is found, in which the minimum thickness of the jet and the maximum factor of drag of the soaked-up medium at the inlet of the duct are observed.*

**KEY WORDS: ***separated flow, ideal incompressible fluid, conformal mapping method, Joukowski method, discrete vortex method, local drag coefficient*

**ANALYSIS OF INTERACTION OF LONGITUDINAL AND LATERAL MOTION OF THE MANEUVERABLE AIRCRAFT WHEN REACHING HIGH ANGLE OF ATTACK**

*Yu. B. Dubov*

*The reasons for aircraft roll and yaw rate overshoot are analyzed when being piloted at large angles of attack. Approximate analytical expressions for estimation of the overshoot values are given.*

**KEY WORDS: ***inertia coupled maneuver, gyroscope torque, roll rate and yaw rate, angle of attack, sideslip angle*

**PROPORTIONAL-INTEGRAL ALGORITHMS FOR CONTROL OF LONGITUDINAL AND LATERAL MOTION OF MANEUVERABLE AIRCRAFT**

*Yu. B. Dubov,** Yu. G. Zhivov, A. N. Mitrichenko, & A. M. Poedinok*

*A structure of the aircraft control system based on the use of proportional-integral laws along all three control axes is proposed. The results of motion of the aircraft with such a control system are presented.*

**KEY WORDS: ***a system of the aircraft stability and controllability augmentation, compensation of inherent characteristics of the aircraft, model motion, integral limiter of sideslip angle*

**NUMERICAL SIMULATION OF HELICOPTER CONSTRUCTION AT EARLY STAGES OF DESIGN**

*E. V. Kasumov*

*A numerical simulation technique at the stage of conceptual design of aircraft mechanical systems is considered. The results of a kinematic analysis and load design using the light helicopter mathematical model and calculations of rotor blade flutter are given. Examples of bench and flight test simulations are presented. Using the prediction of the routine flying trajectory of a light helicopter, the possibility of determining cyclically alternating loadings in rotor system elements is considered.*

**KEY WORDS: ***mathematical model, numerical experiment, kinematic analysis, load design, stain-stress state, flutter, helicopter, design*

**SOME ANALYTICAL MODELS OF THE PLATE BENDING THEORY**

*J. F. Yaremchuk*

*Three versions of equilibrium equations of a plate, which are alternative to the well-known biharmonic equation for deflection function w*(*x, y), have been derived on the assumption of the bending theory of a thin homogeneous plate at small deflections. These new equilibrium equations are given for moments M _{x}, M_{y}, and M_{xy} in which the integrability conditions of deflection are fulfilled. The correctness of the proposed equations is confirmed by two calculation examples of a rectangular simply supported plate under a uniform load and a load that can be represented by a double trigonometric series.*

**KEY WORDS: ***bending of a thin plate, equilibrium equations, deflection function, bending moments*

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