Reduced order models for nonlinear aerodynamics

40th Structures, Structural Dynamics, and Materials Conference and Exhibit, 1999

A review of the status of reduced order modeling of unsteady aerodynamic systems is presented. Reduced order modeling is a conceptually novel and computationally efficient technique for computing unsteady flow about isolated airfoils, wings, and turbomachinery cascades. For example, starting with either a time domain or frequency domain computational fluid dynamics (CFD) analysis of unsteady aerodynamic flows, a large, sparse eigenvalue problem is solved using the Lanczos algorithm. Then, using just a few of the resulting eigenmodes, a Reduced Order Model of the unsteady flow is constructed. With this model, one can rapidly and accurately predict the unsteady aerodynamic response of the system over a wide range of reduced frequencies. Moreover, the eigenmode information provides important insights into the physics of unsteady flows. Finally, the method is particularly well suited for use in the aeroelastic analysis of active control for flutter or gust response. As an alternative to the use of eigenmodes, Proper Orthogonal Decomposition (POD) is also explored and discussed. In general POD is an attractive alternative and/or complement to the use of eigenmodes in terms of computational cost and convenience. Balanced modes, a concept widely used in control engineering, are also briefly discussed, as are input/output models. Numerical results presented include a discussion of the effects of discretization and a finite computational domain in the CFD model on the eigenvalue distribution, the effects of the Mach number and viscosity on reduced order models and representative results from linear and nonlinear aeroelastic analysis. Recent results for transonic flows with shock waves including viscous and nonlinear effects are emphasized.

Computer Methods in Applied Mechanics and Engineering, 2006

... the exclusive use of linear aerodynamic theories for predicting the unsteady aerodynamic forces. ... Because of this computational cost, the potential of CFD-based nonlinear aeroelastic codes ... possible however to address this limitation with the use of reduced-order models (ROMs ...

& Proceedings 저널· 프로시딩즈| 기술보고서| 해외 …, 2008

Reduced-order models (ROMs) are usually thought of as computationally inexpensive mathematical representations that offer the potential for near real-time analysis. Indeed, most ROMs can operate in near real-time. However, their construction can be computationally intensive as it requires accumulating a large number of system responses to input excitations. Furthermore, ROMs usually lack robustness with respect to parameter changes and therefore must often be rebuilt for each parameter variation. Together, these two issues underline the need for a fast and robust method for adapting pre-computed ROMs to new sets of physical or modeling parameters. To this effect, this paper reports on recent advances in this topic. In particular, it describes a recently developed interpolation method based on the Grassmann manifold and its tangent space at a point that is applicable to structural, aerodynamic, aeroelastic and many other ROMs based on projection schemes. This method is illustrated here with the adaptation of CFD-based aeroelastic ROMs of complete fighter configurations to new values of the free-stream Mach number. Good correlations with results obtained from direct ROM reconstruction and high-fidelity linear and nonlinear simulations are reported, thereby highlighting the potential of the described ROM adaptation method for near real-time aeroelastic predictions using pre-computed ROM databases. example, in the transonic regime. This cost is such that CFD-based nonlinear aeroelastic codes are applied nowadays to the analysis of a few, carefully chosen configurations, rather than routine analysis.

AIAA Journal, 2014

The paper presents a novel nonlinear reduced-order modeling approach for multi-input/multi-output aerodynamic systems. The nonlinear reduced-order model for an aerodynamic system includes a finite sum of Wiener-type cascade models. The nonlinear reduced-order model approach starts with fitting a Wiener-type cascade path between the inputs and outputs of the aerodynamic system first. Then, the approach computes the outputs of the path and subtracts them from the measured outputs. The second path is then fitted between the inputs and the output residuals. This process is repeated until the residuals contain only noise. To obtain an optimal path at each stage, a novel nonlinear model, a linear dynamic state-space element followed by a single-layer neural network model, is selected as the Wiener-type cascade model. The Wiener-type cascade model can be optimized by using the Levenberg-Marquadt algorithm. To demonstrate the performance of the proposed nonlinear reduced-order model in modeling the statically nonlinear and dynamically linearized behavior of a nonlinear aerodynamic system, the unsteady transonic compressible flow over a two-degree-of-freedom wing section with the NACA 64A010 airfoil is presented. The numerical results indicate that the proposed nonlinear reduced-order model can accurately identify the outputs of aerodynamic systems subject to a weak excitation. Then, the nonlinear reduced-order model is applied to the transonic flutter analysis of the Isogai wing model. Compared with the direct computational fluid dynamics and linear reduced-order model, the proposed nonlinear reduced-order model is accurate and efficient for transonic flutter prediction of nonlinear aeroelastic systems.

CEAS Aeronautical Journal, 2015

We implement reduced order modelling techniques for aeroelastic predictions of the HIRENASD and S 4 T wings in order to represent CFD based high-fidelity solutions efficiently. Model reduction techniques such as non-intrusive Polynomial Chaos Expansion and Proper Orthogonal Decomposition are applied to both static and dynamic aeroelastic cases. The high-fidelity solutions are obtained by fluid structure interaction analysis using a 3D Euler unsteady aerodynamic solver and structural modal solution from a finite element solver. The model order reduction strategy is based on a multidisciplinary approach since both structural and aerodynamic input parameters are employed. The model order reduction is performed not only to represent the high-fidelity computational analyses when small variations of input parameters are considered but also to characterize the flutter responses of the S 4 T wing in a broad range of input values over the entire flight regime for Mach numbers between 0.60 and 1.20. The efficient aeroelastic analyses performed using the developed reduced order models agreed well with the high-fidelity computational analyses.

Proceedings of the Institution of Mechanical Engineers, Part G: Journal of Aerospace Engineering

Reduced order models of computational fluid dynamics codes have been developed to decrease computational costs; however, each reduced order model has a limited range of validity based on the data used in its construction. Further, like the computational fluid dynamics from which it is derived, such models exhibit differences from experimental data due to uncertainty in boundary conditions and numerical accuracy. Model updating provides the opportunity to use small amounts of additional data to modify the behaviour of a reduced order model, which means that the range of validity of the reduced order model can be extended. Whilst here computational fluid dynamics data have been used for updating, the approach offers the possibility that experimental data can be used in future. In this work, the baseline reduced order models are constructed using the Eigensystem realisation algorithm and the steps used to update these models are given in detail. The methods developed are then applied t...

AIAA Journal, 2015

Recently, the parallel cascade reduced-order modeling approach has been successfully used for the flutter prediction of a two-degree-of-freedom wing section. However, this approach has been less successful when applied to reveal other important aeroelastic phenomena, such as the transonic aeroservoelastic behaviors of a threedimensional wing with a trailing-edge control surface. Because of the complexity introduced by the forced controlsurface deflection, effects of oscillating shock waves, and aerodynamic viscosity, the stability of the dynamic linear parts of the parallel cascade reduced-order model cannot be guaranteed. In this paper, a novel, stable representation of the parallel cascade reduced-order model is explored in which the linear part is identified by using a predictorbased subspace scheme. To demonstrate the performance of the present parallel cascade reduced-order model in modeling the aeroservoelastic behaviors of a three-dimensional wing with a trailing-edge control surface, the Benchmark Active Control Technology wing is used as an illustrative example. The numerical results demonstrate that the parallel cascade reduced-order models are capable of modeling open/closed-loop aeroservoelastic behaviors. Moreover, the effects of the aerodynamic nonlinearity on the dynamic behaviors of the aeroservoelastic systems are investigated always based on the proposed reduced-order model.

AIAA Journal, 2010

ABSTRACT A novel nonlinear reduced-order-modeling technique for computational aerodynamics and aeroelasticity is presented. The method is based on a Taylor series expansion of a frequency-domain harmonic balance computational fluid dynamic solver residual. The first- and second-order gradient matrices and tensors oft he Taylor series expansion are computed rising automatic differentiation via FORTRAN 90/95 operator overloading. A Ritz-type expansion using proper orthogonal decomposition shapes is then used in the Taylor series expansion to create the nonlinear reduced-order model. The nonlinear reduced-order-modeling technique is applied to a viscous flow about an aeroelastic NLR 7301 airfoil model to determine limit cycle oscillations. Computational times are decreased from hours to seconds using the nonlinear reduced-order model.

45th AIAA Aerospace Sciences Meeting and Exhibit, 2007

The proper orthogonal decomposition (POD) method has been shown to produce accurate reduced-order models (ROMs) for unsteady aerodynamic analyses at fixed flight conditions. However, changes in aerodynamic parameters such as the Mach number or angle of attack often necessitate the re-construction of the ROM in order to maintain accuracy, which destroys the sought-after computational efficiency. Straightforward approaches to ROM adaptation — such as the global POD method and the direct interpolation of the POD basis vectors — are known to lead to inaccurate POD bases in the transonic flight regime. Alternatively, a new ROM adaptation scheme is described in this paper and evaluated for changes in the free-stream Mach number and/or angle of attack. This scheme interpolates the subspace angles between two POD subspaces, then generates a new POD basis through an orthogonal transformation based on the interpolated subspace angles. The resulting computational methodology is applied to unsteady flows for both aerodynamic and aeroelastic applications involving a complete F-16 configuration in various airstreams. The predicted aerodynamics loads and aeroelastic frequencies and damping coefficients are compared with counterparts obtained from full-order nonlinear simulations and flight test data. Good correlations are observed, including in the transonic regime. The obtained computational results reveal a significant potential of the adapted ROM computational technology for accurate, near-real-time, numerical, predictions.

Proceedings of the 3rd South-East European Conference on Computational Mechanics – SEECCM III, 2013

We investigate model reduction techniques through computational aeroelastic analyses of the HIRENASD and S 4 T wings. The aim of the present work is to construct accurate and computationally efficient reduced order models for high-fidelity aeroelastic computations. Firstly, the aeroelastic analyses of the specified wings are performed by high-fidelity structural and aerodynamic models to substantiate the fluid-structure interaction. Concerning high amount of computational time required to perform such high-fidelity fluid-structure interaction analyses, the model orders are reduced by introducing relevant reduction techniques such as Polynomial Chaos Expansion and Proper Orthogonal Decomposition. The final aeroelastic analyses performed on these reduced models agree well with the initial high-fidelity computational analyses.