Unsteady Transonic Small Disturbance Research Articles

Transonic flutter analysis of aerodynamic surfaces in the presence of structural nonlinearities

The influence of structural nonlinearities on the transonic aeroelastic behavior of a two-degree-of-freedom system consisting of an airfoil which is plunging and pitching is considered. The preload and freeplay nonlinearity in the spring model are treated using the asymptotic expansion method which takes into account the influence of the higher harmonics. The aerodynamic load vector is obtained by solving the unsteady transonic small-disturbance (TSD) equation using an alternating-direction implicit (ADI) finite-difference algorithm. The frequency domain solution of the aeroelastic equation is obtained using the U-g method, and the aeroelastic response is carried out by applying Newmark-β and Wilson-ϑ methods. A comparison is made between the results obtained from these two solutions. The effects of preload and freeplay magnitudes on the stability of the system and the corresponding reduced frequency and mass density ratio at neutrally stable response are studied.

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.

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.

Efficient algorithm for solution of the unsteady transonic small-disturbance equation

A time accurate approximation factorization (AF) algorithm is formulated for solution of the three-dimensional unsteady transonic small-disturbance equation. The AF algorithm consists of a time linearization procedure coupled with a Newton iteration technique. Superior stability characteristics of the new algorithm are demonstrated through applications to steady and oscillatory flows at subsonic and supersonic freestream conditions for an F-5 fighter wing. For steady flow calculations, the size of the time step is cycled to achieve rapid convergence. For unsteady flow calculations, the AF algorithm is sufficiently robust to allow the step size to be selected based on accuracy rather than on stability considerations. Therefore, accurate solutions are obtained in only several hundred time steps yielding a significant computational cost savings when compared to alternative methods.

Unsteady transonic flow calculations for wing/fuselage configurations

Unsteady transonic flow calculations are presented for wing/fuselage configurations. Calculations are performed by extending the XTRAN3S (version 1.5) unsteady transonic small-disturbance code to allow the treatment of a fuselage. The research was conducted as part of a larger effort directed toward developing the capability to treat a complete flight vehicle. Details of the XTRAN3S fuselage modeling are discussed in the context of the small-disturbance equation. Transonic calculations are presented for two wing/fuselage configurations with leading-edge sweep angles of 0 and 36.65 deg, the results of which compare well with available experimental steady-pressure data. Unsteady calculations are performed for simple bending and torsion modal oscillations of the wing. Comparisons of sectional lift and moment coefficients for the wing-alone and wing/fuselage cases reveal effects of fuselage aerodynamic interference on the unsteady wing loading. Tabulated generalized aerodynamic forces, typically used in flutter analyses, indicate small changes in the real (in-phase) component and as much as a 30% change in the imaginary (out-of-phase) component when the fuselage is included in the calculation. These changes result in a 2-5% increase in total magnitude and a several degree increase in phase.

Unsteady transonic flow calculations for interfering lifting surfaceconfigurations

Unsteady transonic flow calculations are presented for aerodynamically interfering lifting surface configurations. Calculations are performed by extending the XTRAN3S (Version 1.5) unsteady transonic small-disturbance code to allow the treatment of an additional lifting surface. The research was conducted as a first-step toward developing the capability to treat a complete flight vehicle. Grid generation procedures for swept tapered interfering lifting surface applications of XTRAN3S are described. Transonic calculations are presented for wing-tail and canard-wing configurations for several values of mean angle of attack. The effects of aerodynamic interference on transonic steady pressure distributions and steady and oscillatory spanwise lift distributions are demonstrated. Results due to wing, tail, or canard pitching motions are presented and discussed in detail.

Unsteady transonic flow calculations for two-dimensional canard-wingconfigurations

Unsteady transonic flow calculations for aerodv namically interfering airfoil configurations are performed as a first step toward solving the three-dimensional canard-wing interaction problem. These calculations are performed by extending the XTRAN2L two-dimensional unsteady transonic small-disturbance code to include an additional airfoil. Unsteady transonic forces due to plunge and pitch motions of a two-dimensional canard and wing are presented. Results for a variety of canard-wing separation distances reveal the effects of aerodynamic interference on unsteady transonic airloads. Aeroelastic analyses employing these unsteady airloads demonstrate the effects of aerodynamic interference on aeroelastic stability and flutter. For the configurations studied, increases in wing flutter speed result with the inclusion of the aerodynamically interfering canard. p C* D h k m M q qF

Flow instabilities in transonic small-disturbance theory

The dynamics of unsteady transonic small disturbance flows about two-dimensional airfoils is examined, with emphasis on the behavior in the region where the steady state flow is nonunique. It is shown that nonuniqueness results from an extremely long time scale instability which occurs in a finite Mach number and angle of attack range. The similarity scaling rules for the instability are presented and the possibility of similar behavior in the Euler equations is discussed.

Nonreflecting boundary conditions for the complete unsteady transonic small-disturbance equation

Nonreflecting far-field boundary conditions that are consistent with the complete transonic small-disturbance (TSD) equations are derived. They are implemented in a new code for solving the complete TSD equation and are tested for a harmonically oscillating NACA 64A010 airfoil in transonic flow and for a flat-plate airfoil with a pulse in the angle of attack. Using the new boundary conditions on a relatively small grid, solutions for the airfoil that are obtained that agree with large-grid calculations, resulting in a 44 percent savings in computer time. Frequency responses for the flat plate show that most of the disturbances incident on the computational boundaries are absorbed by the boundary conditions.

Unsteady transonic small disturbance approximation with strong shockwaves

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Unsteady transonic flow over wings including inviscid/viscous interaction

A numerical procedure is presented for computing the unsteady transonic flowfield about swept wings undergoing time-dependent motions. The outer inviscid portion of the flow is assumed to be governed by the modified unsteady transonic small disturbance potential equation which is integrated in the time domain by means of an alternating direction implicit algorithm. Dominant effects of the shock/boundary-layer interaction are accdunted for by a simple empirically defined model. Viscous flow regions adjacent to the wing surface and in the trailing wake are described by a set of integral equations appropriate for compressible turbulent shear layers. The two-dimensional boundary-layer equations are applied quasistatically stripwise across the span. Coupling with the outer inviscid flow is implemented through use of the displacement thickness concept. Validity of the assumptions underlying the method is established by comparison with experimental data for the flow about a high aspect ratio transport wing having an advanced airfoil section.

Invariance groups and reduction of the unsteady transonic small disturbance equation

A geometric approach is undertaken towards the solution of the unsteady transonic small disturbance equation describing the low frequency flow field about a thin airfoil. From group properties given in Anderson and Ibragimov, Lie-Bäcklund Transformations in Applications (1979) we derive three invariance groups for the equation. Based on these groups a reduction of the equation is performed. The reduction leads to a steady equation and to an ordinary differential equation from which group invariant solutions of the unsteady transonic small disturbance equation can be obtained.