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At least 235 records · Page 13
All sourcesNASA NTRSDOE OSTI
NASA NTRS1976

Arrangement of vortex lattices

A new method is developed for solving the lifting-surface equation for thin wings. The solution requires the downwash equation to be in the form of Cauchy integrals which can be interpreted as a vortex lattice with the positions of the vortices and control points dictated by the finite sum used to approximate the integrals involved. Lan's continuous loading method is employed for the chordwise integral since it properly accounts for the leading-edge singularity, Cauchy singularity, and Kutta condition. Unlike Lan, the spanwise loading is also continuous and the Cauchy singularity in the spanwise integral is also properly accounted for by using the midpoint trapezoidal rule and the theory of Chebyshev polynomials. This technique yields the exact classical solution to Prandtl's lifting-line equation.The solution to the lifting-surface equation for rectangular wings was found to compare well with other continuous loading methods, but with much smaller computational times, and to converge faster than other vortex lattice methods.

Dejarnette, F. R.↗
NASA NTRS1989

Development and application of a program to calculate transonic flow around an oscillating three-dimensional wing using finite difference procedures

A finite difference method for solving the unsteady transonic flow about harmonically oscillating wings is investigated. The procedure is based on separating the velocity potential into steady and unsteady parts and linearizing the resulting unsteady differential equation for small disturbances. The differential equation for the unsteady potential is linear with spatially varying coefficients and with the time variable eliminated by assuming harmonic motion. Difference equations are derived for harmonic transonic flow to include a coordinate transformation for swept and tapered planforms. A pilot program is developed for three-dimensional planar lifting surface configurations (including thickness) for the CRAY-XMP at Boeing Commercial Airplanes and for the CYBER VPS-32 at the NASA Langley Research Center. An investigation is made of the effect of the location of the outer boundaries on accuracy for very small reduced frequencies. Finally, the pilot program is applied to the flutter analysis of a rectangular wing.

Weatherill, Warren H.↗
NASA NTRS1991

A unified viscous theory of lift and drag of 2-D thin airfoils and 3-D thin wings

A unified viscous theory of 2-D thin airfoils and 3-D thin wings is developed with numerical examples. The viscous theory of the load distribution is unique and tends to the classical inviscid result with Kutta condition in the high Reynolds number limit. A new theory of 2-D section induced drag is introduced with specific applications to three cases of interest: (1) constant angle of attack; (2) parabolic camber; and (3) a flapped airfoil. The first case is also extended to a profiled leading edge foil. The well-known drag due to absence of leading edge suction is derived from the viscous theory. It is independent of Reynolds number for zero thickness and varies inversely with the square root of the Reynolds number based on the leading edge radius for profiled sections. The role of turbulence in the section induced drag problem is discussed. A theory of minimum section induced drag is derived and applied. For low Reynolds number the minimum drag load tends to the constant angle of attack solution and for high Reynolds number to an approximation of the parabolic camber solution. The parabolic camber section induced drag is about 4 percent greater than the ideal minimum at high Reynolds number. Two new concepts, the viscous induced drag angle and the viscous induced separation potential are introduced. The separation potential is calculated for three 2-D cases and for a 3-D rectangular wing. The potential is calculated with input from a standard doublet lattice wing code without recourse to any boundary layer calculations. Separation is indicated in regions where it is observed experimentally. The classical induced drag is recovered in the 3-D high Reynolds number limit with an additional contribution that is Reynold number dependent. The 3-D viscous theory of minimum induced drag yields an equation for the optimal spanwise and chordwise load distribution. The design of optimal wing tip planforms and camber distributions is possible with the viscous 3-D wing theory.

Yates, John E.↗
NASA NTRS1973

The application of laser Doppler velocimetry to trailing vortex definition and alleviation

A laser Doppler velocimeter whose focal volume can be rapidly traversed through a flowfield has been used to overcome the problem introduced by excursions of the central vortex filament within a wind tunnel test section. The basic concepts of operation of the instrument are reviewed and data are presented which accurately define the trailing vortex from a square-tipped rectangular wing. Measured axial and tangential velocity distributions are given, both with and without a vortex dissipator panel installed at the wing tip. From the experimental data, circulation and vorticity distributions are obtained and the effect of turbulence injection into the vortex structure is discussed.

Orloff, K. L.↗
NASA NTRS1973

The effects of leading-edge serrations on reducing flow unsteadiness about airfoils.

High frequency surface pressure measurements were obtained from wind-tunnel tests over the Reynolds number range 1.2 x 1,000,000 to 6.2 x 1,000,000 on a rectangular wing of NACA 63-009 airfoil section. A wide selection of leading-edge serrations were also added to the basic airfoil. Under a two-dimensional laminar bubble very close to the leading edge of the basic airfoil there is a large peak in rms pressure, which is interpreted as an oscillation in size and position of the bubble. The serrations divide the bubble into segments and reduce the peak rms pressures. A low Reynolds number flow visualization test on a hydrofoil in water was also conducted. A von Karman vortex street was found trailing from the rear of the foil. Its frequency is at a much lower Strouhal number than in the high Reynolds number experiment, and is related mathematically to the airfoil trailing-edge and boundary-layer thicknesses.

Schwind, R. G.↗
NASA NTRS1973

The effects of leading-edge serrations on reducing flow unsteadiness about airfoils, an experimental and analytical investigation

High frequency surface pressure measurements were obtained from wind-tunnel tests over the Reynolds number range 1.2 times one million to 6.2 times one million on a rectangular wing of NACA 63-009 airfoil section. Measurements were also obtained with a wide selection of leading-edge serrations added to the basic airfoil. Under a two-dimensional laminar bubble very close to the leading edge of the basic airfoil there is a large apatial peak in rms pressure. Frequency analysis of the pressure signals in this region show a large, high-frequency energy peak which is interpreted as an oscillation in size and position of the bubble. The serrations divide the bubble into segments and reduce the peak rms pressures. A low Reynolds number flow visualization test on a hydrofoil in water was also conducted. A von Karman vortex street was found trailing from the rear of the foil. Its frequency is at a much lower Strouhal number than in the high Reynolds number experiment, and is related to the trailing-edge and boundary-layer thicknesses.

Schwind, R. G.↗
NASA NTRS1974

Comparison of interference-free numerical results with sample experimental data for the AEDC wall-interference model at transonic and subsonic flow conditions

Numerical results obtained from two computer programs recently developed with NASA support and now available for use by others are compared with some sample experimental data taken on a rectangular-wing configuration in the AEDC 16-Foot Transonic Tunnel at transonic and subsonic flow conditions. This data was used in an AEDC investigation as reference data to deduce the tunnel-wall interference effects for corresponding data taken in a smaller tunnel. The comparisons were originally intended to see how well a current state-of-the-art transonic flow calculation for a simple 3-D wing agreed with data which was felt by experimentalists to be relatively interference-free. As a result of the discrepancies between the experimental data and computational results at the quoted angle of attack, it was then deduced from an approximate stress analysis that the sting had deflected appreciably. Thus, the comparisons themselves are not so meaningful, since the calculations must be repeated at the proper angle of attack. Of more importance, however, is a demonstration of the utility of currently available computational tools in the analysis and correlation of transonic experimental data.

Newman, P. A.↗
NASA NTRS1974

The Vortex Lattice Method for the Rotor-Vortex Interaction Problem

The rotor blade-vortex interaction problem and the resulting impulsive airloads which generate undesirable noise levels are discussed. A numerical lifting surface method to predict unsteady aerodynamic forces induced on a finite aspect ratio rectangular wing by a straight, free vortex placed at an arbitrary angle in a subsonic incompressible free stream is developed first. Using a rigid wake assumption, the wake vortices are assumed to move downsteam with the free steam velocity. Unsteady load distributions are obtained which compare favorably with the results of planar lifting surface theory. The vortex lattice method has been extended to a single bladed rotor operating at high advance ratios and encountering a free vortex from a fixed wing upstream of the rotor. The predicted unsteady load distributions on the model rotor blade are generally in agreement with the experimental results. This method has also been extended to full scale rotor flight cases in which vortex induced loads near the tip of a rotor blade were indicated. In both the model and the full scale rotor blade airload calculations a flat planar wake was assumed which is a good approximation at large advance ratios because the downwash is small in comparison to the free stream at large advance ratios. The large fluctuations in the measured airloads near the tip of the rotor blade on the advance side is predicted closely by the vortex lattice method.

Padakannaya, R.↗
NASA NTRS1973

Experimental studies of turbulent aircraft wake

Review of wind tunnel test data obtained for tip vortex studies on a square-tipped rectangular wing. The results include wing surface pressure distributions, three-dimensional velocity components in the wake, and principal vortex characteristics such as peak tangential velocity and core size distributions. The wind tunnel measurements are compared with flight test data. These comparisons show that the magnitudes of circumferential velocities, normalized by flight speed and lift coefficient, as well as the vortex core radius, normalized by wing span, are in close agreement. The data obtained make possible the calculation of turbulence stress distributions and the formulation of models for the prediction of downstream flow fields.

Chigier, N. A.↗
NASA NTRS1974

Steady incompressible potential flow around lifting bodies immersed in a fluid

The refinement was investigated of a method for evaluating the pressure distribution on a body surface of arbitrary shape in incompressible flow. The solution was obtained in terms of the velocity potential, through numerical approximations which require the use of a high speed digital computer. The box method and the modal method are described in detail, and were applied to a very thin, rectangular wing in incompressible, steady flow. The box method is found to be more practical as it is applicable to more general geometries (the modal method requires a new set of functions for each geometry), and requires less computer time (fifty percent of that required by the modal method for the same problem).

Chiuchiolo, E. A.↗
NASA NTRS1975

Shear flow aerodynamics - Lifting surface theory

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.

Ventres, C. S.↗
NASA NTRS1977

Numerical solutions of Navier-Stokes equations for the structure of a trailing vortex

The structure and decay of a trailing vortex were analyzed during the numerical solutions of the full Navier-Stokes equations. Unsteady forms of the governing equations were recast in terms of circulation, vorticity, and stream function as dependent variables, and a second upwind finite difference scheme was used to integrate them with prescribed initial and boundary conditions. The boundary conditions at the outer edge and at the outflow section of the trailing vortex were considered. Different models of the flow were postulated, and solutions were obtained describing the development of the flow as integration proceeds in time. A parametric study was undertaken with a view to understanding the various phenomena that may possibly occur in the trailing vortex. Using the Hoffman and Joubert law of circulation at the inflow section, the results of this investigation were compared with experimental data for a Convair 990 wind model and a rectangular wing. With an exponentially decaying law of circulation at the inflow section and an adverse pressure gradient at the outer edge of the trailing vortex, solutions depict vortex bursting through the sudden expansion of the core and/or through the stagnation and consequent reversal of the flow on the axis. It was found that this bursting takes place at lower values of the swirl ratio as the Reynolds number increases.

Jain, A. C.↗
NASA NTRS1982

Comparison between computations and experimental data in unsteady three-dimensional transonic aerodynamics, including aeroelastic applications

Comparisons were made of computed and experimental data in three-dimensional unsteady transonic aerodynamics, including aeroelastic applications. The computer code LTRAN3, which is based on small-disturbance aerodynamic theory, was used to obtain the aerodynamic data. A procedure based on the U-g method was developed to compute flutter boundaries by using the unsteady aerodynamic coefficients obtained from LTRAN3. The experimental data were obtained from available NASA publications. All the studies were conducted for thin, unswept, rectangular wings with circular-arc cross sections. Numerical and experimental steady and unsteady aerodynamic data were compared for a wing with an aspect ratio of 3 and a thickness ratio of 5% at Mach numbers of 0.7 and 0.9. Flutter data were compared for a wing with an aspect ratio of 5. Two thickness ratios, 6% at Mach numbers of 0.715, 0.851, and 0.913, and 4% at Mach number of 0.904, were considered. Based on the unsteady aerodynamic data obtained from LTRAN3, flutter boundaries were computed; they were compared with those obtained from experiments and the code NASTRAN, which uses linear aerodynamics.

Guruswamy, P.↗
NASA NTRS1982

An initial look at the supersonic aerodynamics of twin-fuselage aircraft concepts

Results of two studies into the supersonic aerodynamics of twin-fuselage aircraft configurations are summarized. In the first study, a set of experimental data was obtained on a simple rectangular-wing twin-fuselage wind-tunnel model; this data was then used to evaluate prediction methods, assess favorable interference effects, and identify any unexpected or unpredictable aerodynamic phenomena. Results are presented which show that significant reductions in wave drag are possible through optimum body positioning and that existing aerodynamic prediction methods are adequate for making preliminary aerodynamic estimates. Several configuration concepts were theoretically explored in the second study, and results are presented which indicate the sensitivity of the twin-fuselage concept to various methods of integrating the aircraft components.

Wood, R. M.↗
NASA NTRS1984

Characteristic boundary conditions for three-dimensional transonic unsteady aerodynamics

Characteristic far-field boundary conditions for the three-dimensional unsteady transonic small disturbance potential equation have been developed. The boundary conditions were implemented in the XTRAN3S finite difference code and tested for a flat plate rectangular wing with a pulse in angle of attack; the freestream Mach number was 0.85. The calculated force response shows that the characteristic boundary conditions reduce disturbances that are reflected from the computational boundaries.

Whitlow, W., Jr.↗
NASA NTRS1984

Wind tunnel wall interference in closed, ventilated and adaptive test sections

A wall interference correction method for closed rectangular test sections was developed which uses measured wall pressures. Measurements with circular discs for blockage and a rectangular wing as a lift generator in a square closed test section validate this method. These measurements are intended to be a basis of comparison for measurements in the same tunnel using ventilated (in these case, slotted) walls. Using the vortex lattice method and homogeneous boundary conditions, calculations were performed which show sufficiently high pressure levels at the walls for correction purposes in test sections with porous walls. In Gottingen, an adaptive test section (which is a deformable rubber tube of 800 mm diameter) was built and a computer program was developed which is able to find the necessary wall adaptation for interference-free measurements in a single step. To check the program prior to the first run, the vortex lattice method was used to calculate wall pressure distributions in the nonadapted test section as input data for the one-step method. Comparison of the pressure distribution in the adapted test section with free-flight data shows nearly perfect agreement. An extension of the computer program can be made to evaluate the remaining interference corrections.

Holst, H.↗
NASA NTRS1984

On the flow processes in sharply inclined and stalled airfoils in parallel movement and rotation

The purpose of this study is to obtain a deeper insight into the complicated flow processes on airfoils in the region of the buoyancy maxima. To this end calculated and experimental investigations are carried out on a straight stationary, a twisted stationary and a straight rotating rectangular wing. According to the available results the method gives results which can be applied sufficiently for flow applied firmly on all sides for all rotation values. The reliability of the method may be questioned for a flow undergoing transition from the attached to the separated state or for totally separated flow and higher rotation values.

Kohler, M.↗