Designing wing airfoils with active flow controls

A method of designing wing airfoils in separationless flow with suction of a portion of the external flow and reactive jet injection from the rear of the body (the total pressure and the density in the jet are different from those in the freestream) within the framework of the ideal incompressible fluid model is proposed. It is shown that this method of active flow control makes it possible considerably to increase the airfoil lift as compared with the same airfoil with no suction or injection. Examples of the design of such airfoils in separationless flow are presented. The reliability of the results obtained is confirmed by a numerical experiment using the Fluent program.     

Design of a wing airfoil in a flow with a separated turbulent boundary layer

The problem of designing the contour of an airfoil in a viscous (incompressible and compressible) flow with a separated turbulent boundary layer from a pressure distribution given on the separationless part of the contour is solved using the boundary layer theory together with the separated flow model proposed in [1]. Numerical calculations are carried out to demonstrate the possibilities of the method.Kazan'. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No.3, pp. 83–91, May–June, 1994.     

Design and optimization of a two-element wing airfoil in a subsonic viscous flow

A numerical and analytical solution of the problem of designing a two-element wing airfoil providing maximum lift-drag ratio in a subsonic viscous flow is presented. In order to bring the theoretical results closer to the facts, viscosity and compressibility are taken into account within the framework of boundary layer theory and the Chaplygin gas model, respectively.     

Inverse problem of wing aerodynamics in a supersonic flow

The inverse problem of wing aerodynamics—the determination of the lifting surface shape from a specified load—is solved within the framework of linear theory. Volterra's solution of the wave equation is used. Solutions are found in the class of bounded functions if certain conditions imposed on the governing parameters of the problem are satisfied. Solutions of inverse problems of supersonic flow are presented for an infinite-span wing, a triangular wing with completely subsonic edges, and a rectangular wing. Institute of Theoretical and Applied Mechanics, Siberian Division, Russian Academy of Sciences, Novosibirsk 630090. Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 39, No. 3, pp. 86–91, May–June, 1998.     

The problem of supersonic flow over the lower surface of a triangular wing

In formulating the problem we make no assumption of smallness of the angle of attack; the attached three-dimensional compression shock which arises under the lower surface of the wing may be of arbitrary intensity, and in form is assumed to differ little from a plane shock; a finite yaw angle is allowed. We consider linear supersonic conical flow which is realized, with the exception of a characteristic linear dimension, in the portion of space bounded by the shock, the plane of the wing, and the surface of a disturbance cone with vertex at the discontinuity of the supersonic leading edge and which is a disturbance of the uniform flow behind the plane shock wave.The problem studied reduces to the homogeneous Hilbert boundary-value problem for an analytic function of a complex variable, whose real and imaginary parts are the partial derivatives of the unknown pressure disturbance with respect to the similarity coordinates.In the solution of the boundary-value problem, the effective method of Lighthill, developed with application to diffraction problems [1, 2], is generalized to the problem of an asymmetric region.The particular case of hypersonic flow about an unyawed triangular wing has been studied by Malmuth [3]; the author obtains the problem considered by Lighthill in [2] and writes out the solution contained in that work.     

Design of active flutter suppression and wind-tunnel tests of a wing model involving a control delay

In this study, a delayed controller was designed for active flutter suppression of a three-dimensional wing model. The design of controller can be divided into two steps. At the first step, a short time delay was artificially introduced into the control loop and the dynamic equations of the aeroelastic system with delayed control were converted into a set of delay-free state-space equations by using a state transformation. At the second step, the control law was synthesized by using the theory of optimal control for the delay-free state-space equations. To demonstrate the performance of the delayed controller, the margin of time delay was studied. The numerical results showed that the delayed controller had good robustness with respect to the time delay. Moreover, the delayed controller was digitally implemented and tested for the three-dimensional wing model in NH-2 subsonic wind-tunnel. The experimental results illustrated that the critical flow speed of flutter instability of the wing model could be effectively increased from 36.5 m/s to 39 m/s.     

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.     

Mathematical simulation of unsteady flow past a wing with jets

The various approximate approaches to the investigation of the unsteady aerodynamic characteristics of an airfoil with jet flap [1–3] are applicable only for an airfoil, low jet intensity, and low oscillation frequencies. In the present paper, the method of discrete vortices [4] is generalized to the case of unsteady flow past a wing with jets and arbitrary shape in plan. The problem is solved in the linear formulation; the conditions used are standard: no flow through the wing and jet, finite velocities at the trailing edges where there is no jet, and also a dynamical condition on the jet. The wing and jet are assumed to be thin and the medium inviscid and incompressible.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 3, pp. 139–144, May–June, 1982.     

Hypersonic similitude in the case of flow past a combination of a circular cone and a delta-shaped wing

The validity of the well-known law of hypersonic similitude [1, 2] for a combination of a circular cone and a delta-shaped wing has hitherto been verified only for the integral characteristics [3]. The law is verified in this paper for both the integral and local parameters of the flow. The posed problem has been solved numerically using the stationary analog of Godunov's method [4]. The shock waves and characteristic surfaces bounding the region of the properly conical flow were separated. As in the paper of Ivanov and Kraiko [5], the required distributions of the parameters were found by stabilization with respect to the coordinate.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 2, pp. 188–190, March–April, 1984.I thank A. N. Kraiko for his interest in the work and for discussing the results.     

Hypersonic flow past an airfoil with a mach system of shock waves

A method based on the use of the two-approximation theory developed in [1, 2] is proposed for the computation of hypersonic flow past a conical wing with a Mach-type shock configuration.Moscow. Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 3, pp. 104–116, May–June, 1972.     

On the theory of a wing with small aspect ratio in a hypersonic flow

A study is made of flow over three-dimensional wings of small aspect ratio with shape close to that of a flat delta-shaped wing. The obtained results make it possible to estimate the influence of the plan shape of the leading edge and the curvature of the wing on the pattern of the flow over its windward surface and on the corresponding gas-dynamic functions.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 4, pp. 112–117, July–August, 1980.     

Aeroelastic stability of a wing with bracing struts (Keldysh problem)

The problem of the influence of bracing struts of two types on the aeroelastic stability of a wing is studied. The formulation of the problem follows that considered by M. V. Keldysh [1]. The behavior of the eigenvalues is studied in the complex plane and the stability, flutter, and divergence domains are constructed. Moscow. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 1, pp. 151–162, January–February, 1998.     

Extension of a combined analytical/numerical initial value problem solver for unsteady periodic flow

Here we describe analytical and numerical modifications that extend the Differential Reduced Ejector/ mixer Analysis (DREA), a combined analytical/numerical, multiple species ejector/mixing code developed for preliminary design applications, to apply to periodic unsteady flow. An unsteady periodic flow modelling capability opens a range of pertinent simulation problems including pulse detonation engines (PDE), internal combustion engine ICE applications, mixing enhancement and more fundamental fluid dynamic unsteadiness, e.g. fan instability/vortex shedding problems. Although mapping between steady and periodic forms for a scalar equation is a classical problem in applied mathematics, we will show that extension to systems of equations and, moreover, problems with complex initial conditions are more challenging. Additionally, the inherent large gradient initial condition singularities that are characteristic of mixing flows and that have greatly influenced the DREA code formulation, place considerable limitations on the use of numerical solution methods. Fortunately, using the combined analytical–numerical form of the DREA formulation, a successful formulation is developed and described. Comparison of this method with experimental measurements for jet flows with excitation shows reasonable agreement with the simulation. Other flow fields are presented to demonstrate the capabilities of the model. As such, we demonstrate that unsteady periodic effects can be included within the simple, efficient, coarse grid DREA implementation that has been the original intent of the DREA development effort, namely, to provide a viable tool where more complex and expensive models are inappropriate. Copyright © 2002 John Wiley & Sons, Ltd.     

Sound generation and flow interaction of vortices with an airfoil and a flat plate in transonic flow

The mechanisms of sound generation and the kind of interaction of vortices with airfoils in an airflow are investigated. Experiments have been performed in stationary flow with vortices of a Kármán vortex street and in a shock tube flow with a starting vortex of a lifting airfoil. Depending on the dimensions of vortices and airfoils, their distance, and the flow Mach numbers, different kinds and amplitudes of upstream propagating steep sound waves occur.     

Experimental analysis of the flow field over a novel owl based airfoil

The aerodynamics of a newly constructed wing model the geometry of which is related to the wing of a barn owl is experimentally investigated. Several barn owl wings are scanned to obtain three-dimensional surface models of natural wings. A rectangular wing model with the general geometry of the barn owl but without any owl-specific structure being the reference case for all subsequent measurements is investigated using pressure tabs, oil flow pattern technique, and particle-image velocimetry. The main flow feature of the clean wing is a transitional separation bubble on the suction side. The size of the bubble depends on the Reynolds number and the angle of attack, whereas the location is mainly influenced by the angle of attack. Next, a second model with a modified surface is considered and its influence on the flow field is analyzed. Applying a velvet onto the suction side drastically reduces the size of this separation at moderate angles of attack and higher Reynolds numbers.