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.     

Design of airfoils stall-free on a given range of angles of attack

A general formulation of the inverse boundary-value problem of aerohydrodynamics for v(s) is given for two angles of attack. This formulation includes that given in [10] as a particular case. An integral representation of the solution is constructed, and the conditions of consistency of the initial data and the solvability conditions are written down. For satisfying the latter the method of quasisolutions of inverse boundary-value problems [11, 12] is employed. A criterion is obtained for the absence of boundary layer separation as the angle of attack varies over a given range. This criterion is expressed in terms of the velocity distributions for the limiting positions. A method of specifying hydrodynamically expedient velocity distributions that takes into account the nonstalling conditions obtained is proposed. Questions of lift maximization are considered. The results of numerical calculations are presented.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 3, pp. 157–164, May–June, 1990.The authors are grateful to G. Yu. Stepanov and N. B. Il'inskii for their constant interest and useful comments.     

Calculation of the flow around wings of arbitrary planform over a wide range of angles of attack

A numerical method is described for the calculation of the distributed and total aerodynamic characteristics of a thin wing of any planform. We use only the generally accepted hypotheses-smoothness of flow around the wing and the Chaplygin-Zhukovskii condition of finite velocity at the trailing edges. The medium is considered ideal and incompressible.The development of a nonlinear theory for the wing of small aspect ratio in a compressible medium is one of the most important and difficult problems of wing theory. It has long attracted the attention of the aerodynamiscists. Chaplygin touched on this question in his 1913 report On the vortex theory of the finite span wing, presented to the Moscow Mathematical Society. Several interesting ideas and schemes were proposed by Golubev (see, for example, [2]). The first adequately correct and effective attempt to determine theoretically the nonlinear variation of wing normal force with angle of attack was that of Bollay [3]. In this work he studied rectangular wings of very small aspect ratio. The circulation variation law along the span was taken to be constant, and along the chord it was taken the same as for a flat plate of infinite span. It was also assumed that the centerlines of the free vortices trailing from the wing tips are straight lines and form the same angle with the plane of the wing. The magnitude of this angle was calculated from the average value of the relative velocity. The boundary condition at the wing was satisfied at a single point.In several later studies [4–8] attempts have been made to extend this approach somewhat. In [7] the circulation variation law along the wing chord is calculated, and the boundary conditions are satisfied more exactly. However, attempts to convert to the study of wings of more complex planform, when the circulation can no longer be considered constant along the span, are hydrodynamically incorrect [5, 6, 8]. In these studies schemes are used in which with smooth flow around the wing the free vortices stand off from the wing surface. The angles which the vortex centerlines form with the wing surface are assumed or are calculated on the basis of very arbitrary hypotheses.In the present paper the vortex layer which simulates the wing surface, just as in the linear theory [9, 10], is replaced by a system of discrete vortices. The free vortices away from the wing then are discrete curvilinear vortex filaments. Each of them is replaced by a series of rectilinear vortex segments. The number of bound and free discrete vortices may be increased without limit. The position of the free vortex segments is determined in the computation process, which is carried out sequentially for a series of angles of attack , beginning with 0 when the linear theory scheme holds. We note that the question of accounting for the effect of the leading-edge free vortex sheet is not considered here, although the method described may also be used to obtain results for this problem.The proposed method turned out to be very general, flexible and convenient for the digital computer. It permits studying the practical convergence of the solution, and also permits obtaining not only the total and distributed characteristics of the wing of arbitrary planform, but also studying such delicate questions as the rollup of the vortex sheet behind the wing.The author wishes to thank O. N. Sokolov and T. M. Muzychenko for the example calculations.     

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.     

Experimental investigation of the distribution of the pressure on a triangular airfoil with blunt edges at small angles of attack

The article gives the results of an experimental investigation of the pressure on a triangular airfoil with blunt edges with a half aperture angle =45° under angles of attack =0,5,10°, with M=11.6 and Re1.5×10⁶. It has been observed that in a region adjacent to the axis of symmetry, at a certain distance from the apex, there is observed a considerable lowering of the pressure.Moscow. Translated from Izvestiya Akademii Nauk SSSR. Mekhanika Zhidkosti i Gaza, No. 2, pp. 166–169, March–April, 1972.     

Hypersonic flow over a narrow delta plate at large angles of attack

The problem of hypersonic flow over a flat delta plate with a high sweepback anglex at angles of attack close to /2 is solved using a numerical algorithm based on transition to the conical solution. The existence of conical flow at /2 with the velocity vector directed towards the apex of the plate is established. Values ofC _p/sin² and the thickness of the shock layer in the plane of symmetry of the plate are given as functions of the hypersonic similarity parameterk=tan tanx. A comparison of the calculated and experimental data shows that they are in good agreement.Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No.5, pp. 183–185, September–October, 1992.     

Numerical modeling of supersonic flow over wings with varying aspect ratio on a broad range of angles of attack using the law of plane sections

A method and a program based on it for solving the problem of flow in the neighborhood of bodies of different shapes introduced into a high-supersonic stream at arbitrary angles of attack are proposed. The equations of the law of plane sections are integrated by Godunov's method. It is shown that the region of applicability of Sychev's theory is much broader than indicated in [1].Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No.2, pp. 113–120, March–April, 1992.     

Separated flow over a strongly cambered conical wing at small angles of attack

The interference of supersonic flows on the concave surface of conical wings was experimentally investigated in [1] for various values of the camber and angles of attack. In order to establish the detailed structure of the interference flow the laminar flow past a wing model in the form of half the surface of a circular cone with vertex angle 2_k = 34° was numerically modeled within the framework of the quasiconical approximation for the three-dimensional Navier-Stokes equations [2]. Under this assumption, confirmed by analysis of the experimental data [1], it was found that the displacement of the external inviscid flow as a result of intense flow separation beyond the leading edges leads to flow patterns similar to those realized on V wing's with a break in the transverse contour [3]. At nonzero angles of attack weak secondary separation was detected beneath the flattened regions of primary separation located in the shaded parts of the concave surface.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 4, pp. 130–136, July–August, 1989.     

Non-Newtonian flow over a wedge with suction

A pseudo-similarity solution is obtained for the flow of an incompressible fluid of second grade past a wedge with suction at the surface. The non-linear differential equation is solved using quasi-linearization and orthonormalization. The numerical method developed for this purpose enables computation of the flow characteristics for any values of the parameters K, a and b, where K is the dimensionless normal stress modulus of the fluid, a is related to the wedge angle and b is the suction parameter. A significant effect of suction on the wall shear stress is observed. The present results match exactly those from an earlier perturbation analysis for Kx^2a ? 0·01 but differ significantly as Kx^2a increases.     

Numerical investigation of three-dimensional laminar boundary layer flow over spheroids at angles of attack

The flow in the laminar boundary layers on spheroids with axial ratios of 611 (prolate ellipsoid of revolution) and 616 (circular wing) at angles of attack of 5 and 10° is investigated numerically. The implicit finite-difference method described in [1] is employed. The results obtained are compared with the measurements reported in [2–4].Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 6, pp. 59–68, November–December, 1990.     

Input-output reduced-order modeling of unsteady flow over an airfoil at a high angle of attack based on dynamic mode decomposition with control

Due to the damage caused by stall flutter, the investigation and modeling of the flow over a wind turbine airfoil at high angles of attack are essential. Dynamic mode decomposition (DMD) and dynamic mode decomposition with control (DMDc) are used to analyze unsteady flow and identify the intrinsic dynamics. The DMDc algorithm is found to have an identification problem when the spatial dimension of the training data is larger than the number of snapshots. IDMDc, a variant algorithm based on reduced dimension data, is introduced to identify the precise intrinsic dynamics. DMD, DMDc and IDMDc are all used to decompose the data for unsteady flow over the S809 airfoil that are obtained by numerical simulations. The DMD results show that the dominant feature of a static airfoil is the adjacent shedding vortices in the wake. For an oscillating airfoil, the DMDc results may fail to consider the effect of the input and have an identification problem. IDMDc can alleviate this problem. The dominant IDMDc modes show that the intrinsic flow for the oscillating case is similar to the unsteady flow over the static airfoil. Moreover, the input–output model identified by IDMDc can give better predictions for different oscillating cases than the identified DMDc model.     

Large injection rates on unsteady compressible boundary layer flow over cones at angles of attack

Summary Three-dimensional unsteady laminar boundary layer near the planes of symmetry of sharp cones at angles of attack subject to large rates of injection is obtained numerically by using an implicit finite difference scheme in combination with the quasi-linearization technique. Several model gases are considered with Mach numbers, wall-to-total-enthalpy ratios, and cross-flow parameters spanning the ranges of main engineering interest. A detailed study has been made of the solutions in the symmetry plane, in order to increase the understanding of the problem. Various cases are considered, when the free-stream velocity and the surface mass transfer (injection) vary arbitrarily with time. The effects of viscous dissipation and the cross-flow parameter have also been discussed.This research has been partially supported by the Research and Development Centre for Iron and Steel, Steel Authority of India Ltd. The constructive comments of Professor G. Nath and Professor A. K. Lahiri are sincerely appreciated.     

The restoration coefficient and Reynolds analogy in a boundary layer with injection and suction over the entire Prandtl number range

The restoration and Reynolds analogy coefficients are calculated for a laminar self-similar boundary layer on a permeable plate over the entire possible range of variation in the Prandtl number and the injection and suction parameter.     

Supersonic flow past a cylindrical body with transverse jets at large angles of attack

Supersonic flow past a cylindrical body with a system of transverse jets ejected from its surface at angles of attack α=60–120^o is characterized by a complicated gasdynamic flow pattern [1]. The body surface is affected by both the oncoming flow and the ejected jets which shield a portion of the surface from the external flow. This results in considerable transverse and longitudinal pressure gradients appearing on the body surface. The experimental pressure distributions over a cylindrical model with four transverse jets at a Mach number M=4 and α=60°, 90°, and 120° make it possible to study the specific features of the flowfield and derive correlations for the "jet obstacle" dimensions. Moscow. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 1, pp. 179–183, January–February, 1998.     

Supersonic flow over delta wings and elements of star-shaped bodies at angles of attack and roll

Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 1, pp. 81–87, January–February, 1989.     

Hypersonic flow past a wing at large angles of attack with detached shock wave

The thin shock layer method [1–3] has been used to solve the problem of hypersonic flow past the windward surface of a delta wing at large angles of attack, when the shock wave is detached from the leading edge (but attached to the apex of the wing) and the velocity of the gas in the shock layer is of the same order as the speed of sound. A classification of the regimes of flow past a delta wing at large angles of attack has been made. A general solution has been obtained for the problem of three-dimensional hypersonic flow past the wing allowing for nonequilibrium physicochemical processes of thermal radiation of the gas at high temperatures.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 3, pp. 149–157, May–June, 1985.     

Design of an airfoil with a flap of finite dimensions

A method of designing mechanized profiles is proposed. This method preserves the advantages of inverse boundary-value problems for simply connected domains and makes it possible to use quasi-solutions for satisfying the conditions of solvability. The problems of designing a profile with an infinitely thin flap of finite length and an airfoil with a flap of finite thickness are considered.Kazan'. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 1, pp. 173–180, January–February, 1995.