Robert M. Bennett

Time-marching transonic flutter solutions including angle-of-attack effects

Transonic aeroelastic solutions based upon the transonic small perturbation potential equation were studied. Time-marching transient solutions of plunging and pitching airfoils were analyzed using a complex exponential modal identification technique, and seven alternative integration techniques for the structural equations were evaluated. The HYTRAN2 code was used to determine transonic flutter boundaries versus Mach number and angle-of-attack for NACA 64A010 and MBB A-3 airfoils. In the code, a monotone differencing method, which eliminates leading edge expansion shocks, is used to solve the potential equation. When the effect of static pitching moment upon the angle-of-attack is included, the MBB A-3 airfoil can have multiple flutter speeds at a given Mach number.

Unsteady transonic flow calculations for realistic aircraft configurations

A transonic unsteady aerodynamic and aeroelasticity code has been developed for application to realistic aircraft configurations. The new code is called CAP-TSD which is an acronym for Computational Aeroelasticity Program - Transonic Small Disturbance. The CAP-TSD code uses a time-accurate approximate factorization (AF) algorithm for solution of the unsteady transonic small-disturbance equation. The AF algorithm is very efficient for solution of steady and unsteady transonic flow problems. It can provide accurate solutions in only several hundred time steps yielding a significant computational cost savings when compared to alternative methods. The new code can treat complete aircraft geometries with multiple lifting surfaces and bodies including canard, wing, tail, control surfaces, launchers, pylons, fuselage, stores, and nacelles. Applications are presented for a series of five configurations of increasing complexity to demonstrate the wide range of geometrical applicability of CAP-TSD. These results are in good agreement with available experimental steady and unsteady pressure data. Calculations for the General Dynamics one-ninth scale F-16C aircraft model are presented to demonstrate application to a realistic configuration. Unsteady results for the entire F-16C aircraft undergoing a rigid pitching motion illustrated the capability required to perform transonic unsteady aerodynamic and aeroelastic analyses for such configurations.

Modern wing flutter analysis by computational fluid dynamics methods

The application and assessment of the recently developed CAP-TSD transonic small-disturbance code for flutter prediction is described. The CAP-TSD code has been developed for aeroelastic analysis of complete aircraft configurations and was previously applied to the calculation of steady and unsteady pressures with favorable results. Generalized aerodynamic forces and flutter characteristics are calculated and compared with linear theory results and with experimental data for a 45 deg sweptback wing. These results are in good agreement with the experimental flutter data which is the first step toward validating CAP-TSD for general transonic aeroelastic applications. The paper presents these results and comparisons along with general remarks regarding modern wing flutter analysis by computational fluid dynamics methods.

NACA 0012 benchmark model experimental flutter results with unsteady pressure distributions

The Structural Dynamics Division at NASA Langley Research Center has started a wind tunnel activity referred to as the Benchmark Models Program. The primary objective of this program is to acquire measured dynamic instability and corresponding pressure data that will be useful for developing and evaluating aeroelastic type computational fluid dynamics codes currently in use or under development. The program is a multi-year activity that will involve testing of several different models to investigate various aeroelastic phenomena. This paper describes results obtained from a second wind tunnel test of the first model in the Benchmark Models Program. This first model consisted of a rigid semispan wing having a rectangular planform and a NACA 0012 airfoil shape which was mounted on a flexible two degree of freedom mount system. Experimental flutter boundaries and corresponding unsteady pressure distribution data acquired over two model chords located at the 60 and 95 percent span stations are presented.

Wing-flutter calculations with the CAP-TSD unsteady transonic small-disturbance program

The paper describes the application and assessment of the recently developed CAP-TSD transonic small-disturbance code for flutter predicition. The CAP-TSD program has been developed for aeroelastic analysis of complete aircraft configurations and was previously applied to the calculation of steady and unsteady pressures with favorable results. Flutter calculations are presented for two thin swept-and-tapered wing platforms with well-defined modal properties. The calculations are for Mach numbers from low subsonic to low supersonic values, including the transonic range, and are compared with subsonic linear theory and experimental flutter data. The CAP-TSD flutter results are generally in good agreement with the experimental values and are in good agreement with subsonic linear theory when wing thickness is neglected.

Experimental flutter boundaries with unsteady pressure distributions for the NACA 0012 Benchmark Model

The Structural Dynamics Division at NASA Langley Research Center has started a wind tunnel activity referred to as the Benchmark Models Program. The primary objective of the program is to acquire test data that will be useful for developing and evaluating aeroelastic type CFD codes currently in use of under development. This paper describes the progress achieved in testing the first model in the Benchmark Models Program. Experimental flutter boundaries are presented for a rigid semispan model (NACA 0012 airfoil section) mounted on a flexible mount system. Also, steady and unsteady pressure measurements taken at the flutter condition are presented. The pressure data were acquired over the entire model chord located at the 60 percent span station.

Experimental unsteady pressures at flutter on the Supercritical Wing Benchmark Model

This paper describes selected results from the flutter testing of the Supercritical Wing (SW) model. This model is a rigid semispan wing having a rectangular planform and a supercritical airfoil shape. The model was flutter tested in the Langley Transonic Dynamics Tunnel (TDT) as part of the Benchmark Models Program, a multi-year wind tunnel activity currently being conducted by the Structural Dynamics Division of NASA Langley Research Center. The primary objective of this program is to assist in the development and evaluation of aeroelastic computational fluid dynamics codes. The SW is the second of a series of three similar models which are designed to be flutter tested in the TDT on a flexible mount known as the Pitch and Plunge Apparatus. Data sets acquired with these models, including simultaneous unsteady surface pressures and model response data, are meant to be used for correlation with analytical codes. Presented in this report are experimental flutter boundaries and corresponding steady and unsteady pressure distribution data acquired over two model chords located at the 60 and 95 percent span stations.

Recent advances in transonic computational aeroelasticity

Abstract A transonic unsteady aerodynamic and aeroelasticity code called CAP-TSD has been developed for application to realistic aircraft configurations. The code permits the calculation of steady and unsteady flows about complete aircraft configurations for aeroelastic analysis in the flutter critical transonic speed range. The CAP-TSD code uses a time-accurate approximate factorization (AF) algorithm for solution of the unsteady transonic small-disturbance potential equation. The paper gives an overview of the CAP-TSD code development effort and presents results which demonstrate various capabilities of the code. Calculations are presented for several configurations including the General Dynamics one-ninth scale F-16C aircraft model and the ONERA M6 wing. Calculations are also presented from a flutter analysis of a 45° sweptback wing which agree well with the experimental data. The paper presents descriptions of the CAP-TSD code and algorithm details along with results and comparisons which demonstrate these recent developments in transonic computational aeroelasticity.

Application of transonic small disturbance theory to the active flexible wing model

The CAP-TSD code, developed at the NASA Langley Research Center, is applied to the active flexible wing windtunnel model for prediction of transonic aeroelastic behavior. A semispan computational model is used for evaluation of symmetric motions, and a full-span model is used for evaluation of antisymmetric motions. Static aeroelastic solutions using the computational aeroelasticity program-transonic small disturbance, are computed. Dynamic (flutter) analyses are then performed as perturbations about the static aeroelastic deformations and presented as flutter boundaries in terms of Mach number and dynamic pressure. Flutter boundaries that take into account modal refinements, vorticity and entropy corrections, antisymmetric motions, and sensitivity to the modeling of the wingtip ballast stores are also presented and compared with experimental flutter results.

USING TRANSONIC SMALL DISTURBANCE THEORY FOR PREDICTING THE AEROELASTIC STABILITY OF A FLEXIBLE WIND-TUNNEL MODEL

The CAP-TSD (Computational AcroelasticityProgram -Transonic Small Disturbance) code, developedat the NASA -Langley Research Center, is applied to theActive Flexible Wing (AFW) wind-tunnel model forprediction of the models transonic aeroelastic behavior.Static aeroelastic solutions using CAP-TSD arecomputed. Dynamic (flutter) analyses are then performedas perturbations about the static aeroclastic deformationsof the AFW. The accuracy of the static aeroelasticprocedure is investigated by comparing analytical resultsto those from previous AFW wind-tunnel experiments.Dynamic results are presented in the form of root loci atdifferent Mach numbers for a heavy gas and air. Theresultant flutter boundaries for both gases are alsopresented. The effects of viscous damping and angle-of-attack, on the flutter boundary in air, are presented aswell.INTRODUCTIONAn understanding of the aeroelastic behavior of flightvehicles in the transonic regime is of great importance forflight safety. For example, it is well known that aircraftflying into or through the transonic regime may encountera region of reduced flutter speed known as the transonicflutter dip. Valuable insight into the nature of thistransonic flutterdip phenomena is provided by Isogai I fora two-dimensional airfoil, while comparison ofaerodynamic theory with the experiments reported byDavis and Malcolm 2 reveal the limitations of lineartheory applied in the transonic regime. Linearacrodynamics, although highly successful in the subsonicand supersonic regimes, cannot normally be used toaccurately predict transonic aeroelastic behavior,Transonic flow equations capable of modelling flow* Principal Engineer, Member AIAA.** Senior Research Engineer, UnsteadyAerodynamics Branch, Associate Fellow AIAA.nonlinearities (shocks, boundary layer, separation andvorticity) and boundary condition nonlinearities (airfoilthickness and shape, and large deflections) must thenbe solved. The surveys by Edwards and Thomas 3 andBallhaus and Bridgeman 4 review recent computationaldevelopments in the field of transonic aeroelasticity.Some of these developments include modelling of theNavier-Stokes equations 5 and the Euler equations 6 forflutter analysis. Application of these higher orderformulations, however, has primarily been limited to two-dimensional configurations, due to the largecomputational costs incurred. Certain assumptionsregarding the flow can be made to yield reduced orderformulations such as the full-potential equation 7 and thecomputationally efficient transonic small-disturbance(TSD) equation. Research efforts involving the TSDformulation include the development of the XTRAN3Scode 8, the work by Yang, Guruswamy, and Striz 9, andmany others.A transonic aerodynamics code known as CAP-TSD(_t_omputational Aeroelasticity Program-Transonic SmallDisturbance) has been developed at the NASA -LangleyResearch Center (LaRC). CAP-TSD is capable ofhandling multiple lifting surfaces with control surfaces,bodies (nacelles, pylons, stores), vertical surfaces, and afuselage, and solves the TSD equation using an efficientapproximate factorization scheme 10. References 11-12verified the codes ability to accurately predict steady andunsteady pressures for wings and configurations atsubsonic, transonic, and supersonic Mach numbers.Flutter prediction using CAP-TSD for two thin, swept-and-tapered wings compared well with experimental flutterresults 13. The goal of the present study was to define thetransonic flutter boundary of the Active Flexible Wing(AFW) wind-tunnel model 14,15, for use as guidanceduring flutter testing, and to evaluate CAP-TSDs flutterprediction capability for a complete and realistic aircraftconfiguration.The Active Flexible Wing (Fig. 1) model is a full-span, sting-mounted wind-tunnel model designed and builtby the Rockwell International Corporation. The main