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Users manual for 3 computer programs for predicting aerodynamic interference between lifting surfaces and lift and cruise fans in transport-type aircraft
Sequence of three computer programs predicts aerodynamic interference on lifting surfaces of transport-type aircraft which are equipped with lift and cruise fans; for example, high-bypass-ratio engine and wing-pylon tail configuration or fuselage-mounted lift-fan and wing-tail configuration.
The lifting-surface sidewash behind rolling triangular wings has been derived for a range of supersonic Mach numbers for which the wing leading edges remain swept behind the mark cone emanating from the wing apex. Variations of the sidewash with longitudinal distance in the vertical plane of symmetry are presented in graphical form. An approximate expression for the sidewash has been developed by means of an approach using a horseshoe-vortex approximate-lifting-line theory. By use of this approximate expression, sidewash may be computed for wings of arbitrary plan form and span loading. A comparison of the sidewash computed by lifting-surface and lifting-line expressions for the triangular wing showed good agreement except in the vicinity of the trailing edge when the leading edge approached the sonic condition. An illustrative calculation has been made of the force induced by the wing sidewash on a vertical tail located in various longitudinal positions.
A lifting surface theory based on a parallel shear flow model is presented for steady, incompressible flows. The theory is intended to account approximately for the presence of a boundary layer. The method of Fourier transforms is used to calculate the pressure on a surface of infinite extent and arbitrary contour. Immediately above the surface is a region of sheared flow (the boundary layer), outside of which the flow velocity is constant. The Fourier transform of the pressure on this surface is used to derive the shear flow equivalent to the kernel function of classical potential flow lifting surface theory. The kernel function provides an integral relation between the upwash at a given point on the surface and the pressure everywhere on the surface. This relation is treated as an integral equation for the pressure, and is solved numerically. Computations are presented for the lift and pitching moment on a flat plate in two-dimensional flow, and for flat, rectangular wings of aspect ratio 1, 2, and 5. As expected, the shear layer decreases the lift curve slope; however, the shear layer (whose thickness is constant along the wing chord) has little effect on the center of pressure.
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A new nonlinear, nonplanar lifting surface theory is presented. The method is regarded as a lifting surface theory in that the effects of wing thickness are neglected, but none of the usual small perturbation assumptions inherent in most other lifting surface theories are made. The method represents nonplanar lifting systems by distributed vorticity, including the leading edge singular behavior characteristic of thin wings. The method is well suited to the computation of induced drag of nonplanar systems because leading edge suction is calculated from the leading edge singularity. The method has been used to compute the induced drag benefit of winglets (vortex diffusers), and the agreement with NASA experimental data is excellent.
An improvement in the lift and drag characteristics of a lifting surface is achieved by attaching a serrated panel to the trailing edge of the lifting surface. The serrations may have a saw-tooth configuration, with a 60 degree included angle between adjacent serrations. The serrations may vary in shape and size over the span-wise length of the lifting surface, and may be positioned at fixed or adjustable deflections relative to the chord of the lifting surface.
A novel set of serrated-planform lifting surfaces produce unexpectedly high lift coefficients at moderate to high angles-of-attack. Each serration, or tooth, is designed to shed a vortex. The interaction of the vortices greatly enhances the lifting capability over an extremely large operating range. Variations of the invention use serrated-planform lifting surfaces in planes different than that of a primary lifting surface. In an alternate embodiment, the individual teeth are controllably retractable and deployable to provide for active control of the vortex system and hence lift coefficient. Differential lift on multiple serrated-planform lifting surfaces provides a means for vehicle control. The important aerodynamic advantages of the serrated-planform lifting surfaces are not limited to aircraft applications but can be used to establish desirable performance characteristics for missiles, land vehicles, and/or watercraft.
Subsonic lifting surface theory including leading edge, discussing singularities in solution of integral equation for determination of aerodynamic properties
Numerical lifting surface theory with spanwise distribution of control points
Subsonic lifting surface theory including leading edge, discussing singularities in solution of integral equation for determination of aerodynamic properties
The methods of the unsteady lifting surface theory are surveyed. Linearized Euler's equations are simplified by means of a Galileo-Lorentz transformation and a Laplace transformation so that the time and the compressibility of the fluid are limited to two constants. The solutions to this simplified problem are represented as integrals with a differential nucleus; these results in tolerance conditions, for which any exact solution must suffice. It is shown that none of the existing three-dimensional lifting surface theories in subsonic range satisfy these conditions. An oscillating elliptic lifting surface which satisfies the tolerance conditions is calculated through the use of Lame's functions. Numerical examples are calculated for the borderline cases of infinitely stretched elliptic lifting surfaces and of circular lifting surfaces. Out of the harmonic solutions any such temporal changes of the down current are calculated through the use of an inverse Laplace transformation.
A limited number of lifting-surface-theory solutions for wings with chordwise loadings resulting from angle of attack, parabolic-ac camber, and flap deflection are now available. These solutions were studied with the purpose of determining methods of extrapolating the results in such a way that they could be used to determine lifting-surface-theory values of the aspect-ratio corrections to the lift and hinge-moment parameters for both angle-of-attack and flap-deflection-type loading that could be used to predict the characteristics of horizontal tail surfaces from section data with sufficient accuracy for engineering purposes. Such a method was devised for horizontal tail surfaces with full-span elevators. In spite of the fact that the theory involved is rather complex, the method is simple to apply and may be applied without any knowledge of lifting-surface theory. A comparison of experimental finite-span and section value and of the estimated values of the lift and hinge-moment parameters for three horizontal tail surfaces was made to provide an experimental verification of the method suggested. (author)
The energetics of oscillating flexible lifting surfaces in two and three dimensions is calculated by the use of integral conservation laws in inviscid incompressible flow for general and harmonic transverse oscillations. Total thrust is calculated from the momentum theorem and energy loss rate due to vortex shedding in the wake from the principle of conservation of mechanical energy. Total power required to maintain the oscillations and hydrodynamic efficiency are also determined. In two dimensions, the results are obtained in closed form. In three dimensions, the distribution of vorticity on the lifting surface is also required as input to the calculations. Thus, unsteady lifting-surface theory must be used as well. The analysis is applicable to oscillating lifting surfaces of arbitrary planform, aspect ratio, and reduced frequency and does not require calculation of the leading-edge thrust.
The problem of steady incompressible flow for lifting surfaces is considered. An integral equation is solved relating the values of the potential discontinuity on the lifting surface and its wake to the values of the normal derivative of the potential which are known from the boundary conditions. The lifting surface and the wake are divided into small quadrilateral surface elements. The values of the potential discontinuity and the normal derivative of the potential are assumed to be constant within each lifting surface element and equal to their values at the centroids of the lifting surface elements. This yields a set of linear algebraic equations. An iteration procedure is used to obtain the wake geometry: the velocities at the corner points of the wake elements are calculated and the wake streamlines are aligned to be parallel to the velocity vector. The procedure is repeated until convergence is attained.
Nonplanar wing tip mounted lifting surfaces reduce lift induced drag substantially. Winglets, which are small, nearly vertical, winglike surfaces, are an example of these devices. To achieve reduction in lift induced drag, winglets produce significant side forces. Consequently, these surfaces can seriously affect airplane lateral directional aerodynamic characteristics. Therefore, the effects of nonplanar wing tip mounted surfaces on the lateral directional stability and control of low speed general aviation airplanes were studied. The study consists of a theoretical and an experimental, in flight investigation. The experimental investigation involves flight tests of winglets on an agricultural airplane. Results of these tests demonstrate the significant influence of winglets on airplane lateral directional aerodynamic characteristics. It is shown that good correlations exist between experimental data and theoretically predicted results. In addition, a lifting surface method was used to perform a parametric study of the effects of various winglet parameters on lateral directional stability derivatives of general aviation type wings.
Unsteady transonic flow calculations are presented for aerodynamically interfering lifting surface configurations. Calculations are performed by extending the XTRAN3S (Version 1.5) unsteady transonic small-disturbance code to allow the treatment of an additional lifting surface. The research was conducted as a first-step toward developing the capability to treat a complete flight vehicle. Grid generation procedures for swept tapered interfering lifting surface applications of XTRAN3S are described. Transonic calculations are presented for wing-tail and canard-wing configurations for several values of mean angle of attack. The effects of aerodynamic interference on transonic steady pressure distributions and steady and oscillatory spanwise lift distributions are demonstrated. Results due to wing, tail, or canard pitching motions are presented and discussed in detail.
Unsteady transonic flow calculations are presented for aerodynamically interfering lifting surface configurations. Calculations are performed by extending the XTRAN3S (Version 1.5) unsteady transonic small-disturbance code to allow the treatment of an additional lifting surface. The research was conducted as a first-step toward developing the capability to treat a complete flight vehicle. Grid generation procedures for swept tapered interfering lifting surface applications of XTRAN3S are described. Transonic calculations are presented for wing-tail and canard-wing configurations for several values of mean angle of attack. The effects of aerodynamic interference on transonic steady pressure distributions and steady and oscillatory spanwise lift distributions are demonstrated. Results due to wing, tail, or canard pitching motions are presented and discussed in detail.