On the convergence of unsteady generalized aerodynamic forces
Previously cited in issue 12, p. 1923, Accession no. A81-29500
Engineering topics
Publications and source records attributed to Cunningham, H. J..
Previously cited in issue 12, p. 1923, Accession no. A81-29500
A generalized subsonic unsteady aerodynamic kernel function, valid for both growing and decaying oscillatory motions, is developed and applied in a modified flutter analysis computer program to solve the boundaries of constant damping ratio as well as the flutter boundary. Rates of change of damping ratios with respect to dynamic pressure near flutter are substantially lower from the generalized-kernel-function calculations than from the conventional velocity-damping (V-g) calculation. A rational function approximation for aerodynamic forces used in control theory for s-plane analysis gave rather good agreement with kernel-function results, except for strongly damped motion at combinations of high (subsonic) Mach number and reduced frequency.
Computer program SOUSSA-P (Steady, Oscillatory, and Unsteady Subsonic and Supersonic Aerodynamics--Production Version) accurately and efficiently evaluates steady and unsteady aerodynamic loads on aircraft having arbitrary shapes and motions, including structural deformations.
The SOUSSA (steady, oscillatory, and unsteady subsonic and supersonic aerodynamics) program is the computational implementation of a general potential flow analysis (by the Green's function method) that can generate pressure distributions on complete aircraft having arbitrary shapes, motions and deformations. Some applications of the initial release version of this program to several wings in steady and oscillatory motion, including flutter are presented. The results are validated by comparisons with other calculations and experiments. Experiences in using the program as well as some recent improvements are described.
The influence of the trailing wake at each wing panel center is investigated. The effect of the wake is calculated by analyzing the wake as being subdivided into trailing wake strips. With the improved program there are two optional ways of calculating the wake effect, and the choice is controlled by an added parameter KANW that is part of the input data.
Several applications of the steady, oscillatory, and unsteady subsonic and supersonic aerodynamics (SOUSSA) computer program to wings with steady and oscillatory motion, including flutter, are discussed. The program employs a generalized Green's function to the full, time-dependent potential-flow equation to obtain an integral equation for the velocity potential at any point in a flow, even points on a body or whole bodies in a flow. Aerodynamic calculations are provided for two rectangular wings, a clipped-tip delta wing, and two swept wings with and without a fuselage. The number and distribution of the finite element panels are varied in order to demonstrate the convergence of the results. The results are shown to be close to those of lifting-surface theory, and further applications with bodies having deformities, arbitrary shapes, motions, and deformations are indicated.
Variations in generalized forces calculated by different computer programs are traced to improper mathematical modeling techniques. Comparisons of generalized forces calculated by three theoretical methods are presented to illustrate difficulties involved in obtaining prediction convergence for increasing wave number. Use of a sufficiently dense chordwise paneling arrangement, in finite panel methods, results in predictions that are essentially identical to predictions of converged solutions. Procedural modifications are suggested for application in finite panel methods to increase prediction accuracy and reduce computer usage costs.
An aspect ratio 10.8 supercritical wing with oscillating control surfaces is described. The wing is instrumental with 252 static orifices and 164 in situ dynamic pressure transducers for studying the effects of control surface deflection on steady and unsteady pressures at transonic speeds. Results from initial wind tunnel tests conducted in the Langley Transonic Dynamics Tunnel are discussed. Unsteady pressure results are presented for two trailing edge control surfaces oscillating separately at the design Mach number of 0.78. Some experimental results are compared with analytical results obtained by using linear lifting surface theory.
An aspect-ratio 10.8 supercritical wing with oscillating control surfaces is described. The wing is instrumented with 252 static orifices and 164 in situ dynamic pressure transducers for studying the effects of control surface deflection on steady and unsteady pressures at transonic speeds. Selected results from initial wind-tunnel tests conducted in the Langley Transonic Dynamics Tunnel are discussed. Unsteady pressure results are presented for two trailing-edge control surfaces oscillating separately at the design Mach number of 0.78. Some experimental results are compared with analytical results obtained by using linear lifting-surface theory.
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.
A Galerkin modal analysis is presented that accounts for the effects of both solid friction and viscous structural damping on panel flutter, based on unsteady aerodynamic forces from supersonic potential flow. The eigensolutions are made by complex eigenvalue computer routines. Markedly different effects on the flutter boundary of the two types of structural damping are obtained. This result establishes that there is not, in general, an "equivalent viscous" damping for solid-friction damping. For the limiting case of the static-aerodynamic approximation, a substantially different flutter dynamic pressure is obtained for solid friction identically zero compared with solid friction approaching zero as a limit. Use of the quasi-static aerodynamic approximation eliminates that difference.
The Level 16 flutter analysis capability was applied to an aspect-ratio-6.8 subsonic transport type wing, an aspect-ratio-1.7 arrow wing, and an aspect-ratio-1.3 all movable horizontal tail with a geared elevator. The transport wing and arrow wing results are compared with experimental results obtained in the Langley transonic dynamic tunnel and with other calculated results obtained using subsonic lifting surface (kernel function) unsteady aerodynamic theory.
This report describes a computer program (program D2180) that has been prepared to implement the analysis described in (N71-10866) for calculating the aerodynamic forces on a class of harmonically oscillating planar lifting surfaces in supersonic potential flow. The planforms treated are the delta and modified-delta (arrowhead) planforms with subsonic leading and supersonic trailing edges, and (essentially) pointed tips. The resulting aerodynamic forces are applied in a Galerkin modal flutter analysis. The required input data are the flow and planform parameters including deflection-mode data, modal frequencies, and generalized masses.
Analysis of the panel flutter characteristics of a candidate thermal protection system (TPS) for the space shuttle, using piston theory aerodynamics and Lagrange equations. The results show the TPS candidate panel array to be deep in the 'no-flutter' region during launch and, therefore, safe from panel flutter.
Defense of damping theory applications in flutter analysis, discussing energy dissipation
Flutter analysis for thin lifting surfaces by application of supersonic kernel function procedure
Three dimensional pressure distribution functions for lifting surfaces with trailing-edge controls based on integral equations for subsonic flow
Flutter analysis of flat rectangular panels based on three-dimensional supersonic unsteady potential flow