Charles M. Denegri

Limit Cycle Oscillation Flight Test Results of a Fighter with External Stores

Oscillatory wing response data were measured on an F-16A aircraft during flutter tests of several external store configurations. Previous testing had shown the F-16 to exhibit limit cycle oscillations (LCO) in the transonic regime, During the present tests, LCO were encountered as well as the sudden onset of high-amplitude oscillations. This sudden high-amplitude response closely resembled that of classical flutter. In all, three distinct categories of response behavior were seen during these tests: classical flutter, typical LCO, and nontypical LCO. These categories are representative of the broad spectrum of aeroelastic responses encountered by fighter aircraft with external stores. Theoretical flutter analyses are shown to adequately identify flutter- or LCO-sensitive store configurations and their instability oscillation frequencies. In addition, a strong correlation between the flight test response and the modal composition of the analytical flutter mechanism is evident. However, the linear analysis fails to provide insight into the oscillation amplitude or onset velocity, which are of primary importance for external store certification on fighter aircraft. Flutter analysis results are presented along with details of the analytical model, the store configurations, and the store mass properties for use as realistic check cases for the validation of nonlinear flutter analysis methods.

In-Flight Wing Deformation Characteristics During Limit-Cycle Oscillations

Oscillatory wing response data were measured on an F-16C aircraft during limit-cycle-oscillation (LCO) testing of an external store configuration. The configuration tested exhibited typical LCO response in the transonic flight regime. Deformation characteristics were measured at 11 locations on the wing and missile launchers during various LCO events. These measurements allowed viewing of the aeroelastic mode of instability for various flight conditions. Details of a linear flutter analysis model are presented, and the predicted eigenmode from the linear flutter analysis is compared to the in-flight measured mode. The measured LCO modes are also compared for level flight vs elevated load factor flight and subcritical LCO vs critical LCO conditions. At the onset of LCO, the mode shape bears a strong resemblance to the flutter mode predicted by linear flutter analysis. Further, the wing deformation characteristics during LCO vary significantly with respect to Mach number and load factor. The nonsynchronous motion of the LCO diminishes and becomes more synchronous as the Mach number increases beyond 0.90. This contradicts the trends predicted by linear flutter analyses and suggests that a change in the oscillation bounding mechanism occurs over the flight region examined.

Further Invesitgation of Modeling Limit Cycle Oscillation Behavior of the F-16 Fighter Using a Harmonic Balance Approach

A computational investigation of limit cycle oscillation behavior of the F-16 fighter configuration using a nonlinear frequency-domain harmonic-balance approach is presented. The research discussed in this latest paper is a follow-on to our work presented at the 2004 SDM conference. Our latest eorts have been directed toward assessing the eects of mean angle-of-attack, wingtip geometry, wing twist, and static aeroelastic deformation on flutter onset and LCO response.

Theoretical Predictions of F-16 Fighter Limit Cycle Oscillations for Flight Flutter Testing

A computational investigation of the flutter onset and limit cycle oscillation behavior of various F-16 fighter weapons and stores configurations is presented. A nonlinear harmonic balance compressible Reynolds-averaged Navier–Stokescomputational fluiddynamic flowsolverisusedtomodeltheunsteadyaerodynamicsoftheF-16wing. Slender body/wing theory is used as an approximate method for accounting for the unsteady aerodynamic effects of wing-tip launchers and missiles. Details of the computational model are presented along with an examination of the sensitivity of computed aeroelastic behavior to characteristics and parameters of the structural and fluid dynamic model. Comparisons with flight-test data are also shown. I. Introduction T HE SEEK EAGLE Office at Eglin Air Force Base performs an essential task in clearing new aircraft/stores configurations through flight tests for safe and effective operation. Many of these flighttestsarefortheF-16aircraftwhichcontinuestobeaworkhorse for the U.S. Air Forcewith continually new stores (missiles, bombs, and fuel tanks) being considered for aircraft operations. Similar aeroelastic flight tests are expected for future fighter aircraft as they go into service in the coming years. The number of needed flight tests is projected to be well beyond the financial and staff resources available. Hence there is a pressing need to identify the most critical aircraft/store configurations for the limited flight-test resources available and also insofar as possibly reduce the number of flight tests needed. Virtual flight testing may be the answer. Using new improved computational capability that provides much more rapid solutions, computational simulation can help identify the most critical aircraft/ store configuration and also hasthe potential of reducingthe number ofneeded flighttestsifconfidencecanbeestablishedinthecapability of simulations to correlate with flight-test data. A new methodology has been developed to produce these computer simulations based upon the notion that because the response is periodic in time, the solution need only be obtained over a single period of oscillation in time. By avoiding the traditional time marching solution which computes the long transient before a steady-state periodic oscillation is reached, computational times are reduced by a factor of 10–100. This enables a sufficiently rapid solutiontomakesuchsimulationsapracticalrealityforthe flight-test engineer and support team. Future developments of this methodology hold the promise of further substantial reductions in computational cost and are being vigorously pursued. Also further refinements in the physical fidelity of the simulation models are being considered.

F-16 Limit Cycle Oscillation Analysis Using Transonic Small-disturbance Theory

Earlier work presented an F-16 limit cycle oscillation (LCO) test case where the flutter mode shape predicted by linear analysis was compared to the in-flight measured wing deflections. A similar evaluation of this test case is accomplished in the present work using a medium-fidelity transonic small-disturbance aerodynamic model. The wing-tip launcher aerodynamics were found to have a significant influence on the computed aeroelastic instability speed. A simplified F-16 computational aerodynamic model consisting of the full-span wing and tip launchers was used for this study and was validated with data from a wind tunnel test and a computational fluid dynamics model. The nonlinear aeroelastic analysis results show that the onset of LCO occurs at a slightly higher Mach number and velocity than seen in flight test. The computed frequency and deflection characteristics show good correlation to flight test results but the transitions from stable to unstable oscillations and the LCO amplitude variations do not appear to be as dramatic. Deficiencies in the aerodynamic model and the absence of underwing store aerodynamics may be the primary causes of the observed differences between the computational and flight test results.

An Investigation of the Sensitivity of F-16 Fighter Flutter Onset and Limit Cycle Oscillations to Uncertainties

A computational investigation of utter onset and limit cycle oscillations of the F-16 gh ter using a nonlinear frequency-domain harmonic-balance approach is presented. In this latest study, we examine the sensitivity of computed aeroelastic behavior to characteristics and parameters of the structural and uid dynamic model. Three dieren t F-16 weapons and stores congurations are considered. Results indicate that the utter onset Mach number is very sensitive to the structural natural frequencies, and, more specically , the dierence between the natural frequencies, of the rst two antisymmetric structural mode shapes. Wing mean angle-of-attack is also shown to be very important. The results presented herein may prove useful and provide insight to other researchers modeling F16 gh ter aeroelastic behavior, and who also may be observing large sensitivities in their computational solutions.

Comparison of Static and Dynamic Neural Networks for Limit Cycle Oscillation Prediction

A dynamic artificial neural network in the form of a multilayer perceptron with a delayed recurrent feedback connection is investigated to determine its ability to predict linear and nonlinear flutter response characteristics. Flight-test results show that limit cycle oscillation (LCO) response characteristics are strongly dependent on Mach number in the transonic flight regime. This effect is also evident in the classical transonic small-disturbance theory governing equations. A dynamic network is considered in order to examine the effects of sequential Mach-number dependence on the networks predictive capability. The architecture of a dynamic network allows for modeling data dependent on a sequentially or linearly increasing parameter (usually time, but in this case Mach number). The predictive capabilities are compared to those of a static artificial neural network. The network is developed and trained using linear flutter analysis and flight-test results from a fighter test. Eleven external store carriage configurations are used as training data, and three configurations are used as test cases. The dynamic network was successful in predicting the aeroelastic oscillation frequency and amplitude responses over a range of Mach numbers for two of the test cases. The dynamic network showed slightly better correlation to flight-test results for the typical LCO test case but slightly worse correlation for the flutter case. Predictions for the nontypical LCO test case were not good for either network.

Virtual Aeroelastic Flight Testing for the F-16 Fighter with Stores

In the following, we present computational aeroelastic flutter onset and limit cycle oscillation response trends for various stores and weapons configurations of the F-16 fighter. A nonlinear harmonic balance compressible Reynolds averaged Navier-Stokes computational fluid dynamic flow solver is used to model the unsteady aerodynamics of the F-16 wing. However, slender body/wing theory is used as an approximate method in accounting for the unsteady aerodynamic effects of wingtip launchers and missiles.

A New Solution Method for Unsteady Flows Around Oscillating Bluff Bodies

This paper briefly summarizes a body of work that describes a combination of methods that have been found useful in greatly increasing the speed of dynamic simulation of complex dynamical systems of very high dimensions. These were initially developed with fluid-structure interaction phenomena in mind for streamlined bodies that are elastically deforming in a flowing fluid. However they have also been applied to bluff body oscillations, the primary subject of the present paper, as well as to the dynamics of biological molecules. In each of these areas of interest, the traditional time marching simulations of spatially discretized models of the fluid, elastic structure, or atoms comprising a molecule simply take too long for most research purposes, not to mention design and optimization studies. Hence the common challenge is to reduce the cost and time of computation. The methods described here have been developed to achieve this goal. For a classical and recent summary of the literature on bluff body dynamics of fluid-structure interaction, please see references [1,2]. For a recent summary of the nonlinear dynamics of fluid-structure interaction (aeroelasticity) for streamlined bodies, please see references [3,4,5].

Reduced Order Models in Unsteady Aerodynamic Models, Aeroelasticity and Molecular Dynamics

The state of reduced order modeling of unsteady aerodynamic flows for the efficient calculation of fluid-structure interaction (aeroelasticity) is discussed. Reduced order modeling is a set of conceptually novel and computationally efficient techniques for computing unsteady flow about airfoils, wings, and turbomachinery cascades.