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.     

To formulating a nonlinear initial-boundary problem of an unsteady separated flow around an airfoil

A general formulation of a nonlinear initial-boundary problem of an unsteady separated flow around an airfoil by an ideal incompressible fluid is considered. The problem is formulated for a complex velocity. Conditions of shedding of vortex wakes from the airfoil are analyzed in detail. The proposed system of functional relations allows constructing algorithms for solving a wide class of problems of the wing theory. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 48, No. 2, pp. 48–56, March–April, 2007.     

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.     

EXPERIMENTAL INVESTIGATION ON LIFT INCREMENT OF A PLASMA CIRCULATION CONTROL AIRFOIL

利用等离子体激励器发展了新型的环量增升技术,并对二维NACA0012翼型绕流实施控制。由于NACA0012翼型为尖后缘构型,环量增升装置由2个非对称型介质阻挡放电等离子体激励器构成。一个等离子体激励器贴附于翼型吸力面靠近后缘处,其诱导的壁面射流沿来流方向指向下游;另一个等离子体激励器贴附于翼型压力面靠近后缘处,其诱导的壁面射流与来流方向相反指向上游。在风洞中通过时间解析二维PIV系统对翼型绕流流场进行了测量,基于翼型弦长的雷诺数Re=20 000。结果表明在等离子体激励器的控制下,翼型压力面靠近后缘处可以形成一个定常回流区,从而起到虚拟气动外形的作用,因此翼型吸力面的流场得到加速,压力面的流场得到减速,使得翼型压力面的吸力以及压力面的压力都得到增加,进而增加了翼型的环量。风洞天平测力实验进一步验证了该环量增升技术的有效性。在整个攻角范围内,施加控制的翼型的升力系数相比没有控制的工况有明显的提高。     

On the existence of three solutions for a supercritical steady flow of a heavy fluid over obstructions

The paper is devoted to the solution of the steady problem of ideal incompressible fluid flow over a semi-circular cylinder located at the bottom. Calculations showed that the problem has at least three solutions for the Froude number. In the absence of an obstruction at the bottom, the proposed algorithm allows one to construct solitary waves up to limiting waves. The paper reports the most important wave characteristics: circulation, mass, and potential and kinetic energy. Analysis of the calculation results leads to the conclusion that all maximum values of the solitary-wave characteristics are attained before the maximum amplitude and the maximum of the mass does not coincide with the maxima of the total energy and the Froude number. Kemerovo State University, Kemerovo 650043. Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 40, No. 1, pp. 27–35, January–February, 1999.     

Extension of the problem of designing a wing airfoil with active flow controls to the case of systems involving a screen

The solution of the inverse boundary-value problem for a wing airfoil with slot air suction from the outer flow on its upper surface and control jet injection from its rear is generalized to include the case of the flow around such an airfoil in the presence of a screen. The complications due to the double connectivity of the flow region are overcome by means of introducing a fictitious flow beneath the screen. The solution is constructed using a numerical-analytical iteration procedure. Formulas for recalculating the aerodynamic characteristics and the velocity distribution over the airfoil surface to different flight regimes and suction-injection device operation regimes are derived. The effect of the injected jet energy, the airfoil-screen spacing, and the slope of the rectilinear airfoil undersurface on the aerodynamic and geometric characteristics of the airfoil, namely, the shape and the lift coefficient, is studied. The reliability of the results is confirmed by the results of calculations using the Fluent program.     

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.     

Measurement of tonal-noise characteristics and periodic flow structure around NACA0018 airfoil

The characteristics of tonal noise and the variations of flow structure around NACA0018 airfoil in a uniform flow are studied by means of simultaneous measurement of noise and velocity field by particle-image velocimetry to understand the generation mechanism of tonal noise. Measurements are made on the noise characteristics, the phase-averaged velocity field with respect to the noise signal, and the cross-correlation contour of velocity fluctuations and noise signal. These experimental results indicate that the tonal noise is generated from the periodic vortex structure on the pressure surface of the airfoil near the trailing edge of the airfoil. It is found that the vortex structure is highly correlated with the noise signal, which indicates the presence of noise-source distribution on the pressure surface. The vorticity distribution on the pressure surface breaks down near the trailing edge of the airfoil and forms a staggered vortex street in the wake of the airfoil.     

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.     

Stochastic estimation of flow near the trailing edge of a NACA0012 airfoil

A stochastic estimation technique has been applied to simultaneously acquired data of velocity and surface pressure as a tool to identify the sources of wall-pressure fluctuations. The measurements have been done on a NACA0012 airfoil at a Reynolds number of Re _c  = 2 × 10⁵, based on the chord of the airfoil, where a separated laminar boundary layer was present. By performing simultaneous measurements of the surface pressure fluctuations and of the velocity field in the boundary layer and wake of the airfoil, the wall-pressure sources near the trailing edge (TE) have been studied. The mechanisms and flow structures associated with the generation of the surface pressure have been investigated. The “quasi-instantaneous” velocity field resulting from the application of the technique has led to a picture of the evolution in time of the convecting surface pressure generating flow structures and revealed information about the sources of the wall-pressure fluctuations, their nature and variability. These sources are closely related to those of the radiated noise from the TE of an airfoil and to the vibration issues encountered in ship hulls for example. The NACA0012 airfoil had a 30 cm chord and aspect ratio of 1.     

Nonlinear effects caused by pulsed periodic supply of energy in the vicinity of a symmetric airfoil in a transonic flow

Changes in the structure of a transonic flow around a symmetric airfoil and a decrease in the wave drag of the latter, depending on the energy-supply period and on localization and shape of the energy-supply zone, are considered by means of the numerical solution of two-dimensional unsteady equations of gas dynamics. Energy addition to the gas ahead of the closing shock wave in an immediate vicinity of the contour in zones extended along the contour is found to significantly reduce the wave drag of the airfoil. The nature of this decrease in drag is clarified. The existence of a limiting frequency of energy supply is found. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 47, No. 3, pp. 64–71, May–June, 2006.     

Investigation of the control of the flow around a wing using mini-flaps

The flow around an airfoil with a mini-flap mounted on the lower or upper wing surface is investigated. The results are obtained by measuring the pressure distribution over the airfoil surface and the forces acting on it for Mach and Reynolds numbers M = 0.1?0.8 and Re = (0.6?3.8) × 10⁶. It is shown that, as distinct from known devices such as Gurney flaps, blunt trailing edge, etc., for controlling the flow in the vicinity of the trailing edge of an airfoil, a mini-flap mounted on the undersurface produces gas flow from the upper to the lower surface around a sharp edge. In this case the flow pattern is considerably affected not only near the trailing edge but also over the entire airfoil. The pressure redistribution over the airfoil makes it possible to increase or decrease the wing lift. Thanks to the low hinge moment, the mini-flap can serve as an effective means of low-inertia control of the flow around a wing.     

Some features of the flow around rapidly rotating bodies made of cellular-porous materials

Two types of gas flows arising near a rapidly rotating cellular-porous disk are studied numerically and experimentally. Steady-state limits for the flow around a disk rotating in free space and the type and scenario of the loss of stability are determined. Transitional flows are characterized by formation of a vortex sheet at the boundary of the exhausting jet. Numerical simulations of the flow around a cellular-porous disk rotating near a flat screen show that it is possible to form a closed swirl flow responsible for redistribution of swirl in the gap between the disk and the flat screen. The computed results offer an explanation for the experimentally observed excess of tangential velocity of the flow in the gap over the velocity of disk rotation. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 48, No. 1, pp. 86–96, January–February, 2007.     

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.     

Airfoil flow instabilities induced by background flow oscillations

 The effect of background flow oscillations on transonic airfoil (NACA 0012) flow was investigated experimentally. The oscillations were generated by means of a rotating plate placed downstream of the airfoil. Owing to oscillating chocking of the flow caused by the plate, the airfoil flow periodically accelerated and decelerated. This led to strong variations in the surface pressure and the airfoil loading. The results are presented for two angles of attack, α=4° and α=8.5°, which correspond to the attached and separated steady airfoil flows, respectively. Received: 6 June 2000 / Accepted: 18 October 2001     

Numerical modeling of ideal incompressible fluid flow over a step

Results of calculations of fluid flow over a step located on a channel bottom are given. Numerical modeling is performed for the model of free-boundary potential flows of an ideal incompressible fluid using a finite-difference method with dynamically adaptive grids. The behavior of the free surface in the neighborhood of the step is studied as a function of the incident-flow velocity. The results are compared with experimental data. __________ Translated from PrikladnayaMekhanika i Tekhnicheskaya Fizika, Vol. 47, No. 6, pp. 17–22, November–December, 2006.     

Unsteady flow structure and vorticity convection over the airfoil oscillating at high reduced frequency

Unsteady vortex structures and vorticity convection over the airfoil (NACA 0012), oscillating in the uniform inflow, are studied by flow visualization and velocity measurements. The airfoil, pivoting at one-third of the chord, oscillates periodically near the static stalling angle of attack (AOA) at high reduced-frequency. The phase-triggering and modified phase-averaged techniques are employed to reconstruct the pseudo instantaneous velocity field over the airfoil. During the down stroke cycle, the leading-edge separation vortex is growing and the vortex near the trailing edge begins to shed into the wake. During the upstroke cycle, the leading-edge separation vortex is matured and moves downstream, and the counter clockwise vortex is forming near the trailing edge. Convection speeds and wavelength of the unsteady vortex structure over the airfoil equal to that of the counter clockwise vortex shed into the wake. This kind of vortex structure is termed as “synchronized shedding” type. The wavelength of unsteady vortex structure over the airfoil is significantly different from that at low reduced-frequency. Consistent convection speeds of the leading-edge separation vortex are acquired from the spatial-temporal variations of local circulation and local surface vorticity generation, and equals that predicted from flow visualization. Spatial-temporal variations of the local surface vorticity generation clearly reveal the formation and passage of the leading-edge separation vortex only in the region where the flow does not separate completely from the surface. Significant amounts of the surface vorticity are generated within the leading-edge region of the airfoil during the upstroke cycle. Only negligible amount of surface vorticity is produced within the region of complete flow separation. During the down stroke cycle, the surface vorticity generation is mild along the airfoil surface, except the leading-edge region where a small scale leading-edge separation vortex is forming and growing.     

Ideal incompressible flow around a wedge tip

A planar analog of conical flows is considered: an inviscid incompressible fluid flow around a wedge tip. A class of conical flows is found where vorticity is transported along streamlines by the potential component of velocity. Problems of a wave “locked” in the corner region and of a flow accelerating along the rib of a dihedral angle are considered. By analogy with an axisymmetric quasi-conical flow, a planar quasi-conical flow of the fluid is determined, namely, the flow inside and outside the region bounded by tangent curves described by a power law. Conditions are found where vorticity and swirl produce a significant effect. An approximate solution of the problem of the fluid flow inside a “zero” angle is obtained. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 48, No. 2, pp. 57–65, March–April, 2007.     

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.     

Bifurcation of self-similar solutions describing a thermocapillary flow of a fluid in a thin layer

Thermocapillary flows of a fluid in a lamina with a rigid lower wall and a free upper surface, along which the temperature gradient is given in the radial direction, are investigated for large Marangoni numbers. Self-similar solutions which describe the axisymmetric flow regimes of a fluid without the circumferential velocity component are constructed numerically and asymptotically for a system of Prandtl equations. It is shown that a pair of new self-similar flow regimes of a fluid with rotation branches off from the regimes obtained. The new regimes ere calculated numerically and asymptotically. Rostov State University, Rostov-on-Don 344090. Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 40, No. 3, pp. 137–142, May–June, 1999.