Lift-generated vortex wakes of subsonic transport aircraft

A new solution method for nonsimilarity boundary layers, applicable locally and independently of information from other stream wise positions, is described and implemented. The governing equations generated by the local nonsimilarity solution method are of the same type as those encountered in the treatment of similarity boundary layers. In addition to its local applicability, the utility of the new method is enhanced by its simplicity and directness, both in concept and in actual computations. Several nonsimilar velocity boundarylayer problems are solved herein with a view to illustrating the method, the participating nonsimilarities stemming from the freestream velocity distribution, surface mass transfer, and transverse curvature. On the basis of comparisons with available published information as well as of comparisons internal to the method itself, it may be concluded that the local nonsimilarity method provides results of high accuracy at all streamwise locations, except those near a point of separation.

Local nonsimilarity boundary-layer solutions

The state of the art in the formulation and solution of rotary-wing aeroelastic stability and response problems is reviewed in detail. The approximations used in the structural, inertia and aerodynamic operators are discussed. The important role of geometric nonlinearities, due to moderate deflections, and aerodynamic stall in the aeroelastic stability and response problem are identified. It is also shown that geometric nonlinearities are of primary importance in aeroelastic stability calculations, and have a more limited, though important, role in response calculations. Next, formulation of coupled rotor/fuselage problems is described, for both air and ground resonance type problems. Both topics, the isolated blade problem and the coupled rotor/fuselage problem, are treated for both hover and forward flight. Solution of aeroelastic stability and response problems proceeds in two stages. First, the spatial dependence is eliminated by using Galerkin's method, or by using the finite element method. Next the nonlinear, or linear, ordinary differential equation with periodic coefficients have to be solved for stability or response. Efficient numerical methods for accomplishing these objectives are presented in a comprehensive manner. The paper contains a number of illustrative numerical results which are intended to clarify various aspects of the modeling process and serve as representative results for both aeroelastic stability and response calculations for a variety of blade and rotor configurations.

Formulation and solution of rotary-wing aeroelastic stability and response problems

An experimental investigation was made of the gust field generated by a rotating slotted cylinder installed in the Duke University low-speed, closed-circuit wind tunnel. The system has a very simple configuration with low cost and can produce a controllable single or multiple harmonic gust wave in the lateral and longitudinal directions. It requires minimal power and torque input. A simplified theoretical aerodynamic model and a design estimation of the lateral and longitudinal gust flowfield is also proposed in this article. The design estimate is based on a two-dimensional dynamic lift coefficient that is given by the theoretical and experimental results. An interfering wake vortex effect is the major disadvantage of this system. Nomenclature C(k) = Theodorsen's function ICleql = magnitude of equivalent lift coefficient for rotating slotted cylinder/airfoil c = airfoil chord d = cylinder diameter dLa = airfoil lift force per span length dLrsc = rotating slotted cylinder lift force per span length e, e = gap between the o.d. of the rotating slotted cylinder and trailing edge of the airfoil, elc H, H = vertical position from tunnel bottom, HIHW Hw = height of the tunnel test section

Experiments and Analysis for a Gust Generator in a Wind Tunnel

The purpose of this review is to present the research done in rotary-wing aeroelasticity during the past eight years in a unified manner. The following topics are reviewed with considerable detail: (1) recent development in the aeroelastic modeling of the coupled flap-lag-torsional problem in hover (2) effect of unsteady aerodynamics on the coupled flap-lag-torsional aeroelastic problem in hover (3) the coupled flap-lag and the coupled flap-lag-torsional problem in forward flight (4) complete rotor and coupled rotor fuselage aeroelastic problems including both hingeless and teetering rotors.

Recent developments in rotary-wing aeroelasticity

: A theory is developed and used for determining the influence of compressibility on the aerodynamic forces acting on helicopter rotor blades when oscillating in hovering flight. The usual two-dimensional mathematical model of the flow is adopted in which a section of the reference rotor blade and its helical wake is replaced by an airfoil with a straight wake and a system of regularly spaced infinite wakes below, the amount of spacing depending on the downward flow induced by the rotor and the number of blades. (Author)

Compressibility effects on oscillating rotor blades in hovering flight

the pressure distributions and generalized aerodynamic forces on harmonically oscillating cylindrical shells having arbitrary radius-to-length ratio, axial and circumferential wave number for any supersonic Mach number and reduced frequency. Comparisons with Dowell and Widnall's solution of the complete linearized equation using Laplace-transform techniques showed excellent agreement. The present method is thought to be more easily applicable than methods requiring complex variable techniques. Also, it can readily be modified to include arbitrary (nonsinusoidal) axial deflection modes.

Simplified aerodynamic theory of oscillating thin surfaces in subsonic flow.

A study has been made of the amplitude and phase of the vertical osciUations in the wake behind 1) a cascade of airfoils oscillating in phase and 2) a cascade of airfoils at zero incidence with oscillating flaps. It was found that in both cases the amplitude of the flow oscillations in the wake remained approximately constant downstream for the values of frequency parameter and airfoil spacing considered. From the results of some preliminary experimental work it appears that sinusoidal gusts could be reproduced in an open jet wind tunnel fitted with either system, but the second type of airfoil-flap arrangement is preferable in practice. The difficulties resulting from flow separation and early stalling which arise with the first system do not appear until much higher angular amplitudes are used when only the flaps are oscillated.

Flow in the Wake of a Cascade of Oscillating Airfoils

Vortex-Elliptic Wing Interaction

The theory is developed in terms of the velocity potential rather than the acceleration potential, and a brief outline is given of the simple numerical technique used. The effects of varying airfoil spacing, frequency, Mach number, stagger angle, and phase difference between adjacent airfoils are discussed. Particular attention is given to variations in the aerodynamic damping for pure vertical translational and pitching motions. It is shown that the translational damping can become zero at certain discrete frequencies but that it never becomes negative. The pitching moment damping, however, can become negative over a wide range of frequencies of practical interest. The airfoils are assumed to be at zero mean incidence.

W. P. Jones

Papers

Compressibility effects on oscillating rotor blades in hovering flight

Simplified aerodynamic theory of oscillating thin surfaces in subsonic flow.

Flow in the Wake of a Cascade of Oscillating Airfoils

Vortex-Elliptic Wing Interaction

Aerodynamic theory for a cascade of oscillating airfoils in subsonicflow