Sebastian Timme

Transonic Aeroelastic Stability Analysis Using a Kriging-Based Schur Complement Formulation

A method is described to allow searches for transonic aeroelastic instability of realistically sized aircraft models in multidimensional parameter spaces when computational fluid dynamics are used to model the aerodynamics. Aeroelastic instability is predicted from a small nonlinear eigenvalue problem. The approximation of the computationally expensive interaction term modeling the fluid response is formulated to allow the automated and blind search for aeroelastic instability. The approximation uses a kriging interpolation of exact numerical samples covering the parameter space. The approach, demonstrated for the Goland wing and the multidisciplinary optimization transport wing, results in stability analyses over whole flight envelopes at an equivalent cost of several steady-state simulations.

Model reduction for linear and nonlinear gust loads analysis

Time domain gust response analysis based on large-order nonlinear aeroelastic models is computationally expensive. An approach to the reduction of nonlinear models for gust loads prediction is presented in this paper. The method uses information on the eigenspectrum of the coupled system Jacobian matrix and projects the full order model through a series expansion onto a small basis of eigenvectors which is capable of representing the full order model dynamics. Linear and nonlinear reduced models derived from computational fluid dynamics and linear/nonlinear structural models are generated in this way. The novelty in the paper concerns the representation of the gust term in the reduced model in a manner consistent with standard synthetic gust definitions, allowing a systematic investigation of the influence of a large number of gusts without regenerating the reduced model. The methodology is illustrated by results for an aerofoil, with a combination of linear and nonlinear structural and aerodynamic models used, and a wing model with modal structural model.

Transonic Aeroelastic Instability Searches Using Sampling and Aerodynamic Model Hierarchy

DOI: 10.2514/1.J050509 A hierarchy of flow models is exploited for transonic aeroelastic stability analysis using the kriging interpolation technique applied within the Schur complement eigenvalue framework. In the Schur framework, a modified structural eigenvalue problem describes the coupled aeroelastic system with a precomputed interaction term depending on the response frequency. The interaction term, representing the influence of the high-dimensional computational fluid dynamics system, is approximated by reconstruction based on samples that can be computed using a frequency or time domain solver. The computationally cheap approximation model is developed and discussed in this paper for two-degree-of-freedom aerofoil cases. The approximation model is used for both the parametric blind search of aeroelastic instability and for updating predictions based on aerodynamic models of different fidelities.

Reynolds-Averaged Navier-Stokes Simulations of Shock Buffet on Half Wing-Body Configuration

This paper presents a numerical study of transonic flow over a wing representative of a large transport aircraft. Reynolds–averaged Navier–Stokes simulations are conducted on a half wing-body configuration, with a Mach number close to cruise conditions and different angles of attack. The flow physics are discussed with particular attention to the separated zone induced by the shock wave. For small angles of attack, this zone is limited to the vicinity of the shock foot, and steady simulations converge. With increasing angle of attack, the separated region increases in size and begins to oscillate. This phenomenon, known as transonic shock buffet, is characterised by shock motions on the outboard section of the wing. In contrast to previous publications, three-dimensional shock buffet is reproduced by such unsteady simulation, and much information can be extracted analysing frequency content, location of unsteadiness and amplitude. The results provide an insight into the mechanism which is responsible for the onset of the unsteadiness.

Solution of linear systems in Fourier-based methods for aircraft applications

Computational fluid dynamics Fourier-based methods have found increasing use for aircraft applications in the last decade. Two applications which benefit are aeroelastic stability analysis and flight dynamics for which previous work is reviewed here. The implicit solution of the methods considered in this work requires an effective preconditioner for solving the linear systems. New results are presented to understand the performance of an approach to accelerate the convergence of the linear solver. The computational performance of the resulting solver is considered for flutter and dynamic derivative calculations.

Semi-meshless stencil selection for anisotropic point distributions

Meshless methods are attractive for simulating moving body problems. The selection of the stencils over the domain for the meshless solver is crucial for the method to be competitive with established computational fluid dynamics techniques. Stencil selection is relatively straightforward if the point distributions are isotropic in nature, however, this is rarely the case in computations that solve the Navier–Stokes equations. In this paper, a fully automatic method of selecting the stencils from anisotropic point distributions, which are obtained from overlapping structured grids, is outlined. The original connectivity and the concept of a resolving direction are used to help construct good quality stencils with limited user input.

Calculating the Influence of Structural Uncertainty on Aeroelastic Limit Cycle Response

Previous work by the authors has considered the impact on aeroelastic stability of uncertainty in structural parameters. Particular consideration has been given to how large dimensional systems like those arising from computational fluid dynamics can be made tractable for the stability analysis. There is considerable practical interest in evaluating the impact of structural parameter variability on limit cycle responses. This is a demanding task since nonlinearity must be involved in some form (which tends to render model reduction through methods like proper orthogonal decomposition less effective than for linear problems). The best current approach seems to be that described in reference, which contains a good review of the current state of the art. The current paper has the objective of reconsidering the (nonlinear) model reduction presented in references 6 for application to parametric variability studies. The approach is to calculate the critical eigenspace of the linearised system and use this as a basis for model reduction. The full order system is manipulated using a Taylor expansion which is then projected onto the critical eigenspace basis. The extra step here is to add the influence of an uncertain parameter to the Taylor Series. This allows the reduced model (two degrees-of-freedom) to be precomputed, and then exploited for the variability analysis. The feasibility of this approach was demonstrated in a recent paper, where the application was made to a two degree of freedom system with a structural nonlinearity, and a linear model for the aerodynamics. Results showed that the nonlinear reduced model was effective for computing the LCO probability density function when a distribution for one of the structural parameters was assumed. In the current paper this work is extended to a three dimensional case with a nonlinearity introduced into the structural model of a wing/tip store test case.

Reduced Order Gust Response Simulation using Computational Fluid Dynamics

© 2016, American Institute of Aeronautics and Astronautics Inc, AIAA. All rights reserved. The investigation of gust response problems is a crucial and, if high accuracy is desired, time consuming task. Since linear frequency domain methods have previously shown significant reduction in computational cost for motion-induced aerodynamics, an extension towards gust excitation is proposed. Time-domain signals are reconstructed by a super- position of responses at several discrete frequencies. Once frequency domain solutions are available, a reduced order model is constructed projecting the linearised Reynolds-averaged Navier-Stokes equations on a combined modal basis. While eigenmodes are accurate in predicting structural vibration, additional modes from proper orthogonal decomposition capture aerodynamic effects due to gust excitation. For all methods a two-dimensional NACA0012 aerofoil is investigated at sub- and transonic conditions. Limitations of the linearised approach are first outlined by increasing the gust amplitude at both operating points. Subsequently, a worst case gust length search is performed and it is shown that the computational cost is reduced case dependent by several orders of magnitude compared to the original system.

Delayed Detached–Eddy Simulation of Shock Buffet on Half Wing–Body Configuration

This paper presents a numerical study of the transonic flow over a half wing–body configuration representative of a large civil aircraft. The Mach number is close to cruise conditions, whereas the high angle of attack causes strong separation on the suction side of the wing. Results indicate the presence of shock-wave oscillations inducing unsteady loads that can cause serious damage to the aircraft. Transonic shock buffet is found. Based on exploratory simulations using a baseline grid, the region relevant to the phenomenon is identified and mesh adaptation is applied to significantly refine the grid locally. Time-accurate Reynolds-averaged Navier–Stokes and delayed detached–eddy simulations are then performed on the adapted grid. Both types of simulation reproduce the unsteady flow physics, and much information can be extracted from the results when investigating frequency content, the location of unsteadiness, and its amplitude. Differences and similarities in the computational results are discussed in...

Oscillatory Behavior of Transonic Aeroelastic Instability Boundaries

T HE use of computational aeroelasticity employing high-fidelity CFD-based (computational fluid dynamics-based) nonlinear aerodynamics has matured from a research exercise to a powerful tool in engineering applications. The stability of an aeroelastic system can be inferred froma time-marching simulation following an initial excitation. Calculations of complete aircraft configurations have been made [1,2]. The time-accurate approach is very capable due to its generality. However, it carries significant computational costs, in particular to solve for the unsteady, nonlinear transonic aerodynamics. One alternative approach uses the theory of dynamic systems to predict aeroelastic instabilities. An eigenvalue-based calculation solves the stability problem for a steady-state solution of the aeroelastic system instead of performing unsteady simulations [3–6]. The “typical section” aerofoil of Isogai [7,8], used to represent the bending and torsional behavior of a wing structure, is a benchmark case for methods predicting aeroelastic instabilities. Figure 1 shows a comparison between results from different numerical methods [7–11] illustrating the instability boundary as flutter speed index VF vs freestream Mach number. The s-shape of the curve in the deep transonic region, giving a second stable branch for higher values of the flutter speed index, is distinct for the inviscid aerodynamic modeling approaches. The current solver (BIFOR) allows the instability boundary to be resolvedwith small steps inMach number. The averageMach number increment in the “transonic dip” region is 2:0 10 , giving a total number of more than 200 individual points on the shown boundary, which required less than 4 h of computation on a desktop computer. Taking a close-up view, the small steps inMach number reveal an oscillatory behavior in the transonic regime. These oscillations merit a closer investigation, and, therefore, the NACA 0012 aerofoil configuration defined in [3] as “heavy case” is considered in the current note. II. Numerical Method