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All sourcesNASA NTRSDOE OSTI
NASA NTRS1978

User's Guide for a Modular Flutter Analysis Software System (Fast Version 1.0)

The use and operation of a group of computer programs to perform a flutter analysis of a single planar wing are described. This system of programs is called FAST for Flutter Analysis System, and consists of five programs. Each program performs certain portions of a flutter analysis and can be run sequentially as a job step or individually. FAST uses natural vibration modes as input data and performs a conventional V-g type of solution. The unsteady aerodynamics programs in FAST are based on the subsonic kernel function lifting-surface theory although other aerodynamic programs can be used. Application of the programs is illustrated by a sample case of a complete flutter calculation that exercises each program.

Desmarais, R. N.↗
NASA NTRS1978

Analysis of preflutter and postflutter characteristics with motion-matched aerodynamic forces

The development of the equations of dynamic equilibrium for a lifting surface from Lagrange's equation is reviewed and restated for general exponential growing and decaying oscillatory motion. Aerodynamic forces for this motion are obtained from the three-dimensional supersonic kernel function that is newly generalized to complex reduced frequencies. Illustrative calculations were made for two flutter models at supersonic Mach numbers. Preflutter and postflutter motion isodecrement curves were obtained. This type of analysis can be used to predict preflutter behavior during flutter testing and to predict postflutter behavior for use in the design of flutter suppression systems.

Cunningham, H. J.↗
NASA NTRS1978

Advanced panel-type influence coefficient methods applied to unsteady three dimensional potential flows

A panel method for solving unsteady, subsonic wind-body-tail flow problems is formulated and partially verified. The method is applicable to general aircraft configurations consisting of arbitrary arrangements of wings, bodies, tails, and nacelles. The wake may be located arbitrarily and the unsteady, transverse component of vorticity in the wake may be assigned any covection velocity. The wake in the unsteady flow problem, therefore, can be given the location and convection velocity of the wake produced by a steady flow which is the mean flow of the unsteady flow problem. The panel method has been used as a basis for expanding the unsteady kernel function in a power series to obtain panel influence coefficients which can be integrated in closed form.

Dusto, A. R.↗
NASA NTRS1980

Interfering surfaces in subsonic, transonic, and supersonic flow

Computer program provides analysis method based on kernel-function technique that uses assumed pressure functions with unknown coefficients. With technique, generalized forces are calculated in unsteady flow, and pressure distributions are obtained in steady and unsteady flow.

Cunningham, A. M., Jr.↗
NASA NTRS1982

Unsteady Subsonic Loadings Due to Control-Surface Motion

RHOIV computer program predicts unsteady lifting-surface loadings caused by motions of leading edge and trailing-edge control surfaces having sealed gaps at hinge lines and side edges. Analysis is based on linear, subsonic, potential-flow theory using kernel function method. Linear combinations of pressure distributions are used that are continuous except at planform edges and hinge lines. Loading solution is obtained by downwash collocation for deflection or motion of main wing and control surfaces.

Rowe, W. S.↗
NASA NTRS1981

Transonic flutter study of a wind-tunnel model of an arrow-wing supersonic transport

A 1/20-size, low-speed flutter model of the SCAT-15F complete airplane was tested on cables to simulate a near free-flying condition. Only the model wing and fuselage were flexible. Flutter boundaries were measured for a nominal configuration and a configuration with wing fins removed at Mach numbers M from 0.76 to 1.2. For both configurations, the transonic dip in the wing flutter dynamic pressure q boundary was relatively small and the minimum flutter q occurred near M = 0.92. Removing the wing fins increased the flutter q about 14 percent and changed the flutter mode from symmetric to antisymmetric. Vibration and flutter analyses were made using a finite-element structural representation and subsonic kernel-function aerodynamics. For the nominal configuration, the analysis (using calculated modal data) predicted the experimental flutter q levels within 10 percent but did not predict the correct flutter mode at the higher M. For the configuration without wing fins, the analysis predicted 16 to 36 percent unconservative (higher than experimental) flutter q levels and showed extreme sensitivity to mass representation details that affected wing tip mode shapes. For high subsonic M, empennage aerodynamics had a significant effect on the predicted flutter boundaries of several symmetric modes.

Ruhlin, C. L.↗
NASA NTRS1981

Transonic flutter study of a wind-tunnel model of an arrow-wing supersonic transport

A 1/20-size, low-speed flutter model of the SCAT-15F complete airplane was tested in a wind-tunnel on cables to simulate a near free-flying condition. Only the model wing and fuselage were flexible. Flutter boundaries were measured for a nominal configuration and a configuration with wing fins removed at Mach numbers M from 0.76 to 1.2. For both configurations, the transonic dip in the wing flutter dynamic pressure q boundary was relatively small and the minimum flutter q occurred near M = 0.92. Removing the wing fins increased the flutter q about 14 percent and changed the flutter mode from symmetric to antisymmetric. Vibration and flutter analyses were made using a finite-element structural representation and subsonic kernel-function aerodynamics. For the nominal configuration, the analysis (using calculated modal data) predicted the experimental flutter q levels within 10 percent but did not predict the correct flutter mode at the higher M. For the configuration without wing fins, the analysis predicted 16 to 36 percent unconservative (higher than experimental) flutter q levels and showed extreme sensitivity to mass shapes.

Ruhlin, C. L.↗
NASA NTRS1982

On the power output of some idealized source configurations with one or more characteristic dimensions

The calculation of power output from a (finite) linear array of equidistant point sources is investigated with allowance for a relative phase shift and particular focus on the circumstances of small/large individual source separation. A key role is played by the estimates found for a twin parameter definite integral that involves the Fejer kernel functions, where N denotes a (positive) integer; these results also permit a quantitative accounting of energy partition between the principal and secondary lobes of the array pattern. Continuously distributed sources along a finite line segment or an open ended circular cylindrical shell are considered, and estimates for the relatively lower output in the latter configuration are made explicit when the shell radius is small compared to the wave length. A systematic reduction of diverse integrals which characterize the energy output from specific line and strip sources is investigated.

Levine, H.↗
NASA NTRS1979

Reduction of computer usage costs in predicting unsteady aerodynamic loadings caused by control surface motions: Computer program description

A digital computer program was developed to calculate unsteady loadings caused by motions of lifting surfaces with leading edge and trailing edge controls based on the subsonic kernel function approach. The pressure singularities at hinge line and side edges were extracted analytically as a preliminary step to solving the integral equation of collocation. The program calculates generalized aerodynamic forces for user supplied deflection modes. Optional intermediate output includes pressure at an array of points, and sectional generalized forces. From one to six controls on the half span can be accomodated.

Petrarca, J. R.↗
NASA NTRS1982

Chordwise and compressibility corrections for arbitrary planform slender wings

The Lomax and Sluder method for adapting slender-wing theory to delta or rectangular wings by making chordwise and compressibility corrections is extended to cover wings of any arbitrary planform in subsonic and supersonic flows. The numerical accuracy of the present work is better than that of the Lomax-Sluder results. Comparison of the results of this work with those of the vortex-lattice method and Kernel function method for a family of Gothic and arrowhead wings shows good agreement. A universal curve is proposed for the evaluation of the lift coefficient of a low aspect ratio wing of an arbitrary planform in subsonic flow. The location of the center of pressure can also be estimated.

Levin, D.↗
NASA NTRS1983

Transonic pressure distributions on a rectangular supercritical wing oscillating in pitch

Steady and unsteady aerodynamic data were measured on a rectangular wing with a 12 percent thick supercritical airfoil mounted in the NASA Langley Transonic Dynamics Tunnel. The wing was oscillated in pitch to generate the unsteady aerodynamic data. The purpose of the wind-tunnel test was to measure data for use in the development and assessment of transonic analytical codes. The effects on the wing pressure distributions of Mach number, mean angle of attack, and oscillation frequency and amplitude were measured. Results from the newly-developed XTRAN3S program (a non-linear transonic small disturbance code) and from the RHOIV program (a linear lifting surface kernel function code) were compared to measured data for a Mach number of 0.7 and for oscillation frequencies ranging from 0 to 20 Hz. The XTRAN3S steady and unsteady results agreed fairly well with the measured data. The RHOIV unsteady-result agreement was fair but, of course, did not predict shock effects.

Ricketts, R. H.↗
NASA NTRS1983

Transonic pressure distributions on a rectangular supercritical wing oscillating in pitch

Steady and unsteady aerodynamic data were measured on a rectangular wing with a 12 percent thick supercritical airfoil mounted in the NASA Langley Transonic Dynamics Tunnel. The wing was oscillated in pitch to generate the unsteady aerodynamic data. The purpose of the wind-tunnel test was to measure data for use in the development and assessment of transonic analytical codes. The effects on the wing pressure distributions of Mach number, mean angle of attack, and oscillation frequency and amplitude were measured. Results from the newly-developed XTRAN3S program (a nonlinear transonic small disturbance code) and from the RHOIV program (a linear lifting surface kernel function code) were compared to measured data for a Mach number of 0.7 and for oscillation frequencies ranging from 0 to 20 Hz. The XTRAN3S steady and unsteady results agreed fairly well with the measured results. The RHOIV unsteady-result agreement was fair but, of course, did not predict shock effects.

Ricketts, R. H.↗
NASA NTRS1984

Two-dimensional splines

Noteworthy properties of one-dimensional splines are presented. Stochastic processes, kernel functions, interpolation, and data smoothing were discussed. Theorems and concomitant proofs are provided.

Utreras, F. I.↗
NASA NTRS1985

Exploratory flutter test in a cryogenic wind tunnel

A model consisting of a rigid wing with an integral, flexible beam support that was cantilever mounted from the wall in the NASA LaRC 0.3-m transonic cryogenic tunnel was used in a flutter analysis study. The wing had a rectangular planform of aspect ratio 1.5 and a 64A010 airfoil. Various considerations and procedures for conducting flutter tests in a cryogenic wind tunnel were evaluated. Flutter onset conditions were established from extrapolated subcritical response measurements. A flutter boundary was determined at cryogenic temperatures over a Mach number M range from 0.5 to 0.9. Flutter was obtained at two different Reynolds numbers R at M = 0.5 (R = 4.4 and 18.4 x 10 to the 6th power) and at M = 0.8 (R = 5.0 and 10.4 x 10 to the 6th power). Flutter analyses using subsonic lifting surface (kernel function) aerodynamics were made over the range of test conditions. To evaluate the Reynolds number effects at M = 0.5 and 0.8, the experimental results were adjusted using analytical trends to account for differences in the model test temperatures and mass ratios. The adjusted experimental results indicate that increasing Reynolds number from 5.0 to 20.0 x 10 to the 6th power decreased the dynamic pressure by 4.0 to 6.5 percent at M = 0.5 and 0.8.

Cole, S. R.↗
NASA NTRS1986

Divergence study of a high-aspect ratio, forward-swept wing

An experimental wind-tunnel study to determine the divergence characteristics of a high-aspect ratio, forward-swept wing has been conducted in the NASA Langley Research Center (LaRC) Transonic Dynamics Tunnel (TDT). The rectangular wing used for this study had a panel aspect ratio of 9.16 (lambda = 0 deg.) and the sweep angle could be set at lambda = 0 deg., -15 deg., -30 deg., -45 deg., or -60 deg. A rectangular wing tip shape was tested at each of these sweep angles. In addition, a tip shape parallel to the freestream flow was tested for a wing sweep angle of lambda = -45 deg. The root of the wing was cantilever mounted to the wall of the wind tunnel. Divergence conditions were measured at M = 0.4 for each sweep angle and tip configuration tested. Subcritical response techniques were used to extrapolate to the divergence conditions during the wind-tunnel test. The primary objective of this test was to obtain data which could be used to verify for this configuration the divergence prediction capability of an aeroelastic analysis code. Subsonic lifting surface theory (kernel function) aerodynamics are utilized by this particular code. The analytical predictions of divergence were found to be significantly conservative at all forward sweep angles. At lambda = -45 deg., the analysis was 14 percent conservative. The effect of the two tip shapes on the divergence dynamic pressure was predicted accurately by the analysis. The divergence condition for the tip shape parallel to the flow occurred at a dynamic pressure 14 percent higher than the divergence condition with a rectangular tip shape.

Cole, S. R.↗
NASA NTRS1986

Divergence study of a high-aspect ratio, forward-swept wing

A study has been conducted in the NASA-Langley Transonic Dynamics wind tunnel to determine the divergence characteristics of a high aspect ratio forward swept wing of rectangular planform, for sweep angles of zero, -15, -30, -45, and -60 deg. In addition to a rectangular wingtip, a tip whose geometry lay parallel with the freestream flow was tested at a sweep angle of -45 deg. The primary objective was to obtain data that could be used to verify the divergence prediction capabilities of an aeroelastic analysis code employing kernel function aerodynamics. The analytical predictions of convergence were found to be conservative for all forward sweep angles, and the effect of the two tip shapes on divergence dynamic pressure were accurately predicted.

Cole, S. R.↗
NASA NTRS1987

Some numerical calculations by using linear classical sonic theories approached from sub- or supersonic speeds

The unsteady aerodynamics of a two-dimensional wing at sonic speed are studied by using so-called classical sonic theories (linear), approached from supersonic flow (M=1+0) or subsonic flow (M=1-0). In the former approach, the exact expressions of lift and lift distribution are obtained in terms of Fresnel integrals, while in the latter approach an integral equation must be solved, the kernel function of which is obtained from the subsonic Possio's equation and has a root singularity. The discrete analysis is adopted on the basis of the semicircle method (SCM) and the weighting function for subsonic-flow-Gauss-quadrature, as well as modified characteristics obtained from both approaches agree quite well with each other. The results obtained by the present computations are compared with those of DLM-C (subsonic 2D code) developed by ANDO et al, and are found to give a reasonable outer boundary for subsonic unsteady aerodynamics.

Yamamoto, Y.↗
NASA NTRS1988

Flutter analysis of highly swept delta wings by conventional methods

The flutter boundaries of six thin highly-swept delta-platform wings have been calculated. Comparisons are made between experimental data and results using several aerodynamic methods. The aerodynamic methods used include a subsonic and supersonic kernel function, second order piston theory, and a transonic small disturbance code. The dynamic equations of motion are solved using analytically calculated mode shapes and frequencies.

Gibbons, M. D.↗