Reduced-order fluid/structure modeling of a complete aircraft configuration

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Abstract

The proper orthogonal decomposition (POD) method is applied to the computational fluid dynamics (CFD)-based reduced-order aeroelastic modeling of a complete F-16 fighter configuration, in order to assess its potential for the solution of realistic aeroelastic problems. The limitation of such a computational approach to a fixed free-stream Mach number is addressed by a Mach-adaptation strategy that interpolates the angle between two POD subspaces rather than the POD basis vectors directly. The predicted aeroelastic frequencies and damping ratio coefficients are compared with counterparts obtained from full-order nonlinear simulations and from flight test data. The results of these comparisons, including in the transonic regime, reveal a good potential of POD-based reduced-order modeling for the near real-time prediction of aircraft flutter using CFD technology.

Introduction

The ability to accurately predict flutter is essential for developing high-performance, safe, aircraft designs. There are a number of computational methods for achieving this objective. The advantages and disadvantages of each of them depend primarily on the flight regime of interest. Many computational methods are based on the linear aeroelastic theory which assumes that the aerodynamic forces can be reliably predicted by a linear operator. In the subsonic regime, this operator is often computed using the doublet-lattice method [1], while methods derived from the piston theory [2] are more suitable in the supersonic regime. In both cases, such linear methods are attractive because they appear to offer an accurate and yet fast computational mean for identifying flutter speeds.

However, most modern aircraft, especially high-performance fighters, operate in the transonic regime where complex nonlinear flow patterns preclude the exclusive use of linear aerodynamic theories for predicting the unsteady aerodynamic forces. Consequently, scaled wind tunnel testing is often performed to obtain corrections to the flutter speeds predicted by linear theories. However, the design of scaled wind tunnel models and the subsequent data analysis typically require more than one year of time [3]. State-of-the-art, computational fluid dynamics (CFD)-based, nonlinear aeroelastic simulation capabilities have shown that for low to moderate angles of attack, they can be a reliable alternative to scaled wind tunnel testing provided that adequate computing resources are made available. For example, using a 128-processor computing system, the AERO code was reported to accurately predict the aeroelastic parameters of a complete F-16 configuration at five different Mach numbers in the transonic regime, and in less than one day [4], [5], [6]. More practically, an engineer with access to a six-processor computing platform can meet the same objective using AERO in less than three days. Hence, nonlinear simulation technologies such as AERO and others [7], [8] seem to offer a partial viable alternative to scaled wind tunnel testing for flutter prediction in the transonic regime.

The major computational cost incurred by CFD-based nonlinear aeroelastic simulations is attributable to the need for high-fidelity fluid models in order to resolve the complex flow patterns present in the transonic regime. Because of this computational cost, the potential of CFD-based nonlinear aeroelastic codes is currently limited to the analysis of a few, carefully chosen configurations rather than routine analyses. In some instances such as those discussed in this paper, it is possible however to address this limitation with the use of reduced-order models (ROMs). For example, it was recently shown [9], [10], [11], [12], [13], [14], [15], [16], [17], [18] that ROMs constructed by a variety of methods, including the popular proper orthogonal decomposition (POD) method [19], [20], can produce numerical results that compare well with those generated by full-order nonlinear models. However, since its first application to aeroelastic problems [9], the POD method was primarily applied to simple airfoils [10], [11], [12], [13], panels [21], wings [14], [15], [16], turbine blades [17], [18], but not to complete aircraft configurations. Furthermore, a ROM constructed by POD or any other similar technique is usually not robust with respect to change in a model parameter [11], [22]. Some progress in this area has been recently reported for the case of structural parameters [15]; however, little has been reported for changes in the free-stream Mach number.

Hence, the objectives of this paper are two fold: (a) to demonstrate the potential of a POD-based ROM methodology for the CFD-based aeroelastic analysis of a complete fighter configuration, including in the transonic regime, and (b) to present an algorithm for rapidly adapting aeroelastic ROMs to different free-stream Mach numbers. To this effect, the remainder of this paper is organized as follows. In Section 2, the computational framework adopted for constructing a POD-based ROM is presented. In Section 3, a novel algorithm for adapting two given ROMs to a varying free-stream Mach number is described. In Section 4, both computational technologies are applied to the aeroelastic analysis of a complete F-16 configuration at a low angle of attack, and the aeroelastic parameters obtained using the ROMs are compared with those obtained using full-order nonlinear simulations and flight test data. Finally, conclusions pertaining to the performance characteristics, merits, limitations, and potential of the described computational methodologies are formulated in Section 5.

Section snippets

Computational framework

In order to construct a POD subspace, an ensemble of sample data representative of some physical system, in this case a flexible aircraft, is required. This sample data is generated here by numerical simulation in the frequency domain of the linearized flows associated with a set of displacement-based excitations of the modeled structure. To this effect, the transient aeroelastic problem is first formulated as a coupled, nonlinear, fluid–structure interaction problem. However, in order to

Adaptation of the aeroelastic ROM

The main drawback of a POD-based ROM, and for that matter any similarly constructed ROM, is the lack of robustness over an entire parameter space. Essentially, this is because the data samples are collected only within a small region of the state space. While this focused data sampling leads to a very accurate ROM, it does not lead to a reduced-order basis that can accurately capture the solution space for a range of the parameter space. In particular, since the steady-state, non-dimensional

Aeroelastic parametric identification of a complete F-16 configuration

In this section, the two ROM methodologies described in the previous sections are applied to the aeroelastic parametric identification of a complete F-16 configuration with clean wings. To the best knowledge of the authors, this is the first time the potential of an aeroelastic ROM methodology is assessed for such a realistic aeronautical engineering problem. The full-order aeroelastic computational model chosen here consists of a 168,799-dof FE structural model built with bar, beam, solid,

Conclusions

In recent years, significant progress has been made in advancing the state-of-the-art of computational fluid dynamics (CFD)-based aeroelastic reduced-order modeling (ROM), to the point where the introduction of this computational technology in a design environment is often discussed in the literature. To this effect, this paper contributes the first demonstration and discussion of the application of a CFD-based aeroelastic ROM methodology to a complete aircraft configuration—namely, an F-16

Acknowledgements

The authors acknowledge the support by the Air Force Office of Scientific Research under Grant F49620-01-1-0129. They also thank ICEM CFD Engineering Inc. for providing its mesh generation software.

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