Computational Aeroelasticity Program - Transonic Small Disturbance Research Articles

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.

Application of nonlinear systems theory to transonic unsteady aerodynamic responses

A methodology is presented for using the Volterra-Wiener theory of nonlinear systems in aeroservoelastic (ASE) analyses and design. The theory is applied to the development of nonlinear aerodynamic response models that can be defined in state-space form and are, therefore, appropriate for use in modern control theory. The Volterra-Wiener theory relies on the identification of nonlinear kernels that can be used to predict the response of a nonlinear system due to an arbitrary input. A numerical kernel identification technique, based on unit impulse responses, is presented and applied to a simple bilinear, single-input-single-output (SISO) system. The linear kernel (unit impulse response) and the nonlinear second-order kernel of the system are numerically identified and compared with the exact, analytically defined linear and second-order kernels. This kernel identification technique is then applied to the computational aeroelasticity program-transonic small disturbance (CAP-TSD) code for identification of the linear and second-order kernels of a NACA64A010 rectangular wing undergoing pitch at M = 0.5, M = 0.85 (transonic), and M = 0.93 (transonic). Results presented demonstrate the feasibility of this approach for use with nonlinear, unsteady aerodynamic responses.

Mach number effects on transonic aeroelastic forces and flutter characteristics

Transonic aeroelastic stability analysis and flutter calculations are presented for a generic transport-type wing based on the use of the CAP-TSD (Computational Aeroelasticity Program - Transonic Small Disturbance) finite-difference code. The CAP-TSD code was recently developed for transonic unsteady aerodynamic and aeroelastic analysis of complete aircraft configurations. A binary aeroelastic system consisting of simple bending and torsion modes was used to study aeroelastic behavior at transonic speeds. Generalized aerodynamic forces are presented for a wide range of Mach number and reduced frequency. Aeroelastic characteristics are presented for variations in freestream Mach number, mass ratio, and bending-torsion frequency ratio. Flutter boundaries are presented which have two transonic dips in flutter speed. The first dip is the usual transonic dip involving a bending-dominated flutter mode. The second dip is characterized by a single degree-of-freedom torsion oscillation. These aeroelastic results are physically interpreted and shown to be related to the steady state shock location and changes in generalized aerodynamic forces due to freestream Mach number.

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

The application and assessment is described of CAP-TSD (Computational Aeroelasticity Program - Transonic Small Disturbance) code for flutter prediction. The CAP-TSD program was developed for aeroelastic analysis of complete aircraft configurations and was previously applied to the calculation of steady and unsteady pressures. Flutter calculations are presented for two thin, swept-and-tapered wing planforms 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.

Unsteady transonic small-disturbance theory including entropy and vorticity effects

Modifications to unsteady transonic small-disturbance theory to include entropy and vorticity effects are presented. The modifications have been implemented in the CAP-TSD (Computational Aeroelasticity Program - Transonic Small Disturbance) code developed recently at the NASA Langley Research Center. The code permits the aeroelastic analysis of complete aircraft configurations in the flutter critical transonic speed range. Entropy and vorticity effects have been incorporated within the solution procedure to more accurately analyze flows with strong shock waves. The modified code includes these effects while retaining the relative simplicity and cost efficiency of the TSD formulation. The paper presents detailed descriptions of the entropy and vorticity modifications along with calculated results and comparisons which assess the modified theory. These results are in good agreement with parallel Euler calculations and with experimental data. Therefore, the present method now provides the aeroelastician with an affordable capability to analyze relatively difficult transonic flows without having to solve the computationally more expensive Euler equations.