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NASA NTRS1997

Identification of Linear and Nonlinear Aerodynamic Impulse Responses Using Digital Filter Techniques

This paper discusses the mathematical existence and the numerically-correct identification of linear and nonlinear aerodynamic impulse response functions. Differences between continuous-time and discrete-time system theories, which permit the identification and efficient use of these functions, will be detailed. Important input/output definitions and the concept of linear and nonlinear systems with memory will also be discussed. It will be shown that indicial (step or steady) responses (such as Wagner's function), forced harmonic responses (such as Theodorsen's function or those from doublet lattice theory), and responses to random inputs (such as gusts) can all be obtained from an aerodynamic impulse response function. This paper establishes the aerodynamic impulse response function as the most fundamental, and, therefore, the most computationally efficient, aerodynamic function that can be extracted from any given discrete-time, aerodynamic system. The results presented in this paper help to unify the understanding of classical two-dimensional continuous-time theories with modern three-dimensional, discrete-time theories. First, the method is applied to the nonlinear viscous Burger's equation as an example. Next the method is applied to a three-dimensional aeroelastic model using the CAP-TSD (Computational Aeroelasticity Program - Transonic Small Disturbance) code and then to a two-dimensional model using the CFL3D Navier-Stokes code. Comparisons of accuracy and computational cost savings are presented. Because of its mathematical generality, an important attribute of this methodology is that it is applicable to a wide range of nonlinear, discrete-time problems.

Silva, Walter A.↗

NASA NTRS1952

Investigation in the Ames Supersonic Free-Flight Wind Tunnel of the Static Longitudinal Stability of the Hermes A-3B Missile at a Mach Number of 5.0

Models of the Hermes A-3B missile were tested in the Ames supersonic free-flight wind tunnel to determine the static-longitudinal-stability characteristics at a Mach number of 5.0 and a Reynolds number based on body length of 10 million. The results indicated that the model center of pressure was 45.3 percent of the body length aft of the nose and the lift-curve slope based on body frontal area was 0.064 per degree. Estimates indicated that the effect on these characteristics of aeroelastic twisting of the model fins was small but important if a precise location of center of pressure is required. A comparison of the test results with predictions based on available theory showed that the theory was useful only for rough estimates, The drag coefficient at zero lift, based on body frontal area, was found to be 0.155.

Denardo, Billy Pat↗

NASA NTRS1977

Unsteady aerodynamic modeling for arbitrary motions

A study is presented on the unsteady aerodynamic loads due to arbitrary motions of a thin wing and their adaptation for the calculation of response and true stability of aeroelastic modes. In an Appendix, the use of Laplace transform techniques and the generalized Theodorsen function for two-dimensional incompressible flow is reviewed. New applications of the same approach are shown also to yield airloads valid for quite general small motions. Numerical results are given for the two-dimensional supersonic case. Previously proposed approximate methods, starting from simple harmonic unsteady theory, are evaluated by comparison with exact results obtained by the present approach. The Laplace inversion integral is employed to separate the loads into 'rational' and 'nonrational' parts, of which only the former are involved in aeroelastic stability of the wing. Among other suggestions for further work, it is explained how existing aerodynamic computer programs may be adapted in a fairly straightforward fashion to deal with arbitrary transients.

Edwards, J. W.↗

NASA NTRSDate not supplied

Transition Analysis for the Pazy Wing

The Pazy wing, designed as a benchmark for highly flexible wings that experience large deformations, presents intriguing nonlinear phenomena due to its unique geometry with spanwise varying static deformation and low Reynolds number flow conditions. These phenomena include limit cycle oscillation related to laminar separation bubbles, boundary-layer transition, and dynamic stall. The primary focus of this study is to investigate transition behavior on the sagged Pazy wing under static loading by using the shear-stress-transport (SST)-based Langtry-Menter 𝜸 − 𝑹𝒆𝜽𝒕 transition model in the NASA OVERFLOW and FUN3D solvers. Based on the steady-state results obtained via different variants of the Langtry-Menter model, we investigate the likely transition behavior over a range of incidence angles. The predicted flowfield on the sagged Pazy wing is strongly three dimensional and the application of turbulence index as a viable indicator of the transition front in such flows is also explored. The study demonstrates the limitations of the Langtry-Menter model when applied to low Reynolds number flows. We introduce a spanwise periodic configuration to simulate a narrow-span section of the Pazy wing, specifically centered on one of the 14 nearly equidistant ribs spanning the wing. The computational results demonstrate that the spanwise periodic configuration provides a straightforward environment for studying transition characteristics as well as demonstrating systematic grid convergence and successful code-to-code comparisons. The research offers useful insights into the transition characteristics of flexible wings under various loading conditions, contributing to the field of aeroelastic simulations.

CFD Modeling↗

NASA NTRSDate not supplied

Transition Analysis for the Pazy Wing

CFD Modeling↗

NASA NTRS1986

Unsteady transonics of a wing with tip store

The presence of tip stores influences both the aerodynamic and the aeroelastic performance of wings. Such effects are more pronounced in the transonic regime. In this study, a theoretical method is developed, for the first time, to compute unsteady transonics of oscillating wings with tip stores. The method is based on the small-disturbance, aerodynamic equations of motion from the potential-flow theory. To validate the method, subsonic and transonic aerodynamic computations are made for a lower-aspect-ratio wing, and they are compared with the available experimental data. Comparisons are favorable. The strong effects of the tip store on the transonic aerodynamics of the wing are also illustrated. The method developed in this steady can be used for transonic, aeroelastic computations of wings with tip stores.

Guruswamy, G. P.↗

NASA NTRS1986

Unsteady Transonics of a Wing With Tip Store

The presence of tip stores influences both the aerodynamic and aeroelastic performances of wings. Such effects are more pronounced in the transonic regime. In this study, a theoretical method is developed, for the first time, to compute unsteady transonics of oscillating wings with tip stores. The method is based on the small-disturbance aerodynamic equations or motion from the potential-flow theory. To validate the method, subsonic and transonic aerodynamic computations are made for a wing of low aspect ratio, and they are compared with the available experimental data. The comparisons are favorable. The strong effects of the tip store on the transonic aerodynamics on the wing are also illustrated. The method developed in this study can be used for transonic aeroelastic computations of wings with tip stores.

Guruswamy, Guru P.↗

NASA NTRS1986

Arbitrary motion unsteady aerodynamics and its application to rotary-wing aeroelasticity

This paper presents in a unified manner recent research on arbitrary motion unsteady aerodynamics with an emphasis on applications to a number of rotary wing aeroelastic problems. The term arbitrary motion is used to denote growing or decaying oscillations with a certain frequency. The specific topics treated in this paper are: (1) generalization of Greenberg's theory and its application to hingeless rotor aeroelastic stability; (2) description of a new technique for formulating finite state approximations to steady aerodynamic theories, which are suitable for both fixed-wing and rotary-wing applications, and its application to generalize Loewy's theory; (3) comparison of fixed wing and rotary-wing indicial response functions; (4) influence of arbitrary motion aerodynamics, as represented by dynamic inflow on a helicopter in ground resonance. From the discussion of these topics a number of useful conclusions on the fundamental nature of arbitrary motion aerodynamics and its role in rotary-wing aeroelasticity are obtained.

Friedmann, P. P.↗

NASA NTRS1989

Effects of nonlinear aerodynamics and static aeroelasticity on mission performance calculations for a fighter aircraft

During conceptual design studies of advanced aircraft, the usual practice is to use linear theory to calculate the aerodynamic characteristics of candidate rigid (nonflexible) geometric external shapes. Recent developments and improvements in computational methods, especially computational fluid dynamics (CFD), provide significantly improved capability to generate detailed analysis data for the use of all disciplines involved in the evaluation of a proposed aircraft design. A multidisciplinary application of such analysis methods to calculate the effects of nonlinear aerodynamics and static aeroelasticity on the mission performance of a fighter aircraft concept is described. The aircraft configuration selected for study was defined in a previous study using linear aerodynamics and rigid geometry. The results from the previous study are used as a basis of comparison for the data generated herein. Aerodynamic characteristics are calculated using two different nonlinear theories, potential flow and rotational (Euler) flow. The aerodynamic calculations are performed in an iterative procedure with an equivalent plate structural analysis method to obtain lift and drag data for a flexible (nonrigid) aircraft. These static aeroelastic data are then used in calculating the combat and mission performance characteristics of the aircraft.

Giles, Gary L.↗

NASA NTRS2008

Rotorcraft Technology for HALE Aeroelastic Analysis

Much of technology needed for analysis of HALE nonlinear aeroelastic problems is available from rotorcraft methodologies. Consequence of similarities in operating environment and aerodynamic surface configuration. Technology available - theory developed, validated by comparison with test data, incorporated into rotorcraft codes. High subsonic to transonic rotor speed, low to moderate Reynolds number. Structural and aerodynamic models for high aspect-ratio wings and propeller blades. Dynamic and aerodynamic interaction of wing/airframe and propellers. Large deflections, arbitrary planform. Steady state flight, maneuvers and response to turbulence. Linearized state space models. This technology has not been extensively applied to HALE configurations. Correlation with measured HALE performance and behavior required before can rely on tools.

Young, Larry↗

NASA NTRS1982

Comparison of analytical and wind-tunnel results for flutter and gust response of a transport wing with active controls

Two flutter suppression control laws wre designed and tested on a low speed aeroelastic model of a DC-10 derivative wing. Both control laws demontrated increases in flutter speed in excess of 25 percent above the passive wing flutter speed. In addition, one of the control laws was effective in reducing loads due to turbulence generated in the wind tunnel. The effect of variations in gain and phase on the closed-loop performance was measured and is compared with predictions. In general, both flutter and gust response predictions agree reasonably well with experimental data.

Abel, I.↗

NASA NTRS2020

Passive Aeroelastic Tailored Wing Modal Test Using the Fixed Base Correction Method

In modal testing and finite element model correlation, analysts desire modal results using free-free or rigid boundary conditions to ease comparisons of test versus analytical data. It is often expensive both in cost and schedule to build and test with boundary conditions that replicate the free-free or rigid boundaries. Static test fixtures for load testing are often large, heavy, and unyielding, but do not provide adequate boundaries for modal tests because they are dynamically too flexible and often contain natural frequencies within the frequency range of interest of the test article. Dynamic coupling between the test article and test fixture complicates the model updating process because significant effort is required to model the test fixture and boundary conditions in addition to the test article. If there were a way to correct the modal results for fixture coupling, then setups used for other structural testing could be adequate for modal testing. In the case described in this paper, a partial static loads testing setup was used, which allowed significant schedule and cost savings by eliminating a unique setup for a modal test. A fixed base correction technique was investigated during modal testing of a flexible wing cantilevered from part of a static test fixture. The technique was successfully used to measure the wing modes de-coupled from the dynamically active test fixture. The technique is promising for future aircraft applications, but more research is needed.

structural dynamics↗

NASA NTRSDate not supplied

Gradient-Based Optimization of the Common Research Model Wing Subject to CFD-Based Gust and Flutter Constraints

The linearized frequency-domain method was recently implemented in the stabilized finite element solver in NASA’s FUN3D code. Previous work by the authors used this method for enforcing flutter constraints during gradient-based optimizations. More recently, the solver was expanded to account for continuous (also known as stochastic) gust responses. This paper expands on recent Common Research Model wing optimization work, which demonstrated gradient-based optimization with flutter and stochastic gust constraints, among others. While that work utilized FUN3D for static aeroelastic solutions but relied on doublet lattice aerodynamics for gust and flutter responses, the present work replaces these unsteady aerodynamic analyses with those of FUN3D’s linearized frequency-domain solver. With analytic derivatives available, gradient-based optimization is performed through the use of the OpenMDAO/MPhys libraries with over 700 shape, structural, and aerodynamic design variables and over 10 nonlinear constraints. Comparisons of analysis results and optimized designs are made between doublet lattice and linearized frequency-domain solutions.

aeroelasticity↗

NASA NTRS2014

Static Aeroelastic Analysis with an Inviscid Cartesian Method

An embedded-boundary, Cartesian-mesh flow solver is coupled with a three degree-of-freedom structural model to perform static, aeroelastic analysis of complex aircraft geometries. The approach solves a nonlinear, aerostructural system of equations using a loosely-coupled strategy. An open-source, 3-D discrete-geometry engine is utilized to deform a triangulated surface geometry according to the shape predicted by the structural model under the computed aerodynamic loads. The deformation scheme is capable of modeling large deflections and is applicable to the design of modern, very-flexible transport wings. The coupling interface is modular so that aerodynamic or structural analysis methods can be easily swapped or enhanced. After verifying the structural model with comparisons to Euler beam theory, two applications of the analysis method are presented as validation. The first is a relatively stiff, transport wing model which was a subject of a recent workshop on aeroelasticity. The second is a very flexible model recently tested in a low speed wind tunnel. Both cases show that the aeroelastic analysis method produces results in excellent agreement with experimental data.

Aeroelastic↗

NASA NTRS1980

Wind-tunnel/flight correlation study of aerodynamic characteristics of a large flexible supersonic cruise airplane (XB-70-1). 3: A comparison between characteristics predicted from wind-tunnel measurements and those measured in flight

A program was undertaken by NASA to evaluate the accuracy of a method for predicting the aerodynamic characteristics of large supersonic cruise airplanes. This program compared predicted and flight-measured lift, drag, angle of attack, and control surface deflection for the XB-70-1 airplane for 14 flight conditions with a Mach number range from 0.76 to 2.56. The predictions were derived from the wind-tunnel test data of a 0.03-scale model of the XB-70-1 airplane fabricated to represent the aeroelastically deformed shape at a 2.5 Mach number cruise condition. Corrections for shape variations at the other Mach numbers were included in the prediction. For most cases, differences between predicted and measured values were within the accuracy of the comparison. However, there were significant differences at transonic Mach numbers. At a Mach number of 1.06 differences were as large as 27 percent in the drag coefficients and 20 deg in the elevator deflections. A brief analysis indicated that a significant part of the difference between drag coefficients was due to the incorrect prediction of the control surface deflection required to trim the airplane.

Arnaiz, H. H.↗

NASA NTRS1996

Overset Grid Methods for Multidisciplinary Applications in Rotorcraft Problems

A methodology for the coupling of an advanced computational fluid dynamics method based on an overset grid flow-solver and an advanced computational structural dynamics method based on a finite element analysis is presented. Various procedures for the fluid-structure interactions modeling along with their limitations are also discussed. The flight test data for the four-bladed UH-60A Blackhawk helicopter rotor is chosen for the validation of the results. Convergence and accuracy are tested by numerical experiments with a single-bladed rotor. A comparison of airload predictions with flight test data as well as with a rigid blade case is presented. Grid and interpolation related issues for this aeroelastic application are described.

Ahmad, J. U.↗

NASA NTRS1996

Modeling the Benchmark Active Control Technology Wind-Tunnel Model for Application to Flutter Suppression

This paper describes the formulation of a model of the dynamic behavior of the Benchmark Active Controls Technology (BACT) wind-tunnel model for application to design and analysis of flutter suppression controllers. The model is formed by combining the equations of motion for the BACT wind-tunnel model with actuator models and a model of wind-tunnel turbulence. The primary focus of this paper is the development of the equations of motion from first principles using Lagrange's equations and the principle of virtual work. A numerical form of the model is generated using values for parameters obtained from both experiment and analysis. A unique aspect of the BACT wind-tunnel model is that it has upper- and lower-surface spoilers for active control. Comparisons with experimental frequency responses and other data show excellent agreement and suggest that simple coefficient-based aerodynamics are sufficient to accurately characterize the aeroelastic response of the BACT wind-tunnel model. The equations of motion developed herein have been used to assist the design and analysis of a number of flutter suppression controllers that have been successfully implemented.

Waszak, Martin R.↗

NASA NTRS1982

AGARD three-dimensional aeroelastic configurations

The calculation of unsteady aerodynamic forces in the critical transonic speed regime is investigated. The development of such methods is be enhanced by the availability of a limited number of test cases for the comparison of competing methods. Test cases for five clean, isolated wings are presented. Wing geometric descriptions, airfoil coordinates, and suggested aerodynamic conditions for each are included.

Bland, S. R.↗