A finite volume unstructured mesh approach to dynamic fluid-structure interaction: an assessment of the challenge of flutter analysis

Computational modelling of dynamic fluid-structure interaction (DFSI) is problematical since conventionally computational fluid dynamics (CFD) is solved using finite volume (FV) methods and computational structural mechanics (CSM) is based entirely on finite element (FE) methods. Hence, progress in modelling the emerging multi-physics problem of dynamic fluid-structure interaction in a consistent manner is frustrated and significant problems in computation convergence may be encountered in transferring and filtering data from one mesh and solution procedure to another, unless the fluid-structure coupling is either one way, very weak or both. This paper sets out the solution procedure for modelling the multi-physics dynamic fluid-structure interaction problem within a single software framework PHYSICA, using finite volume, unstructured mesh (FV-UM) procedures and will focus upon some of the problems and issues that have to be resolved for time accurate closely coupled dynamic fluid-structure flutter analysis.

Flutter analysis including structural uncertainties

The common practice in industry is to perform flutter analyses considering the generalized stiffness and mass matrices obtained from finite element method (FEM) and aerodynamic generalized force matrices obtained from a panel method, as the doublet lattice method. These analyses are often reperformed if significant differences are found in structural frequencies and damping ratios determined from ground vibration tests compared to FEM. This unavoidable rework can result in a lengthy and costly process of analysis during the aircraft development. In this context, this paper presents an approach to perform flutter analysis including uncertainties in natural frequencies and damping ratios. The main goal is to assure the nominal system’s stability considering these modal parameters varying in a limited range. The aeroelastic system is written as an affine parameter model and the robust stability is verified solving a Lyapunov function through linear matrix inequalities and convex optimization

Aeroelastic stability of structures: flutter analysis using Computational Fluid Dynamics

Thanks to the increasing slenderness and lightness allowed by new construction techniques and materials, the effects of wind on structures became in the last decades a research field of great importance in Civil Engineering. Thanks to the advances in computers power, the numerical simulation of wind tunnel tests has became a valid complementary activity and an attractive alternative for the future. Due to its flexibility, during the last years, the computational approach gained importance with respect to the traditional experimental investigation. However, still today, the computational approach to fluid-structure interaction problems is not as widely adopted as it could be expected. The main reason for this lies in the difficulties encountered in the numerical simulation of the turbulent, unsteady flow conditions generally encountered around bluff bodies. This thesis aims at providing a guide to the numerical simulation of bridge deck aerodynamic and aeroelastic behaviour describing in detail the simulation strategies and setting guidelines useful for the interpretation of the results.

Wave dispersion and power flow analysis of an infinite aerofoil-shaped beam

Classic flutter analysis models an aerofoil as a two degree-of-freedom rigid body supported by linear and torsional springs, which represent the bending and torsional stiffness of the aerofoil section. In this classic flutter model, no energy transfer or dissipation can occur in the span-wise direction of the aerofoil section. However, as the aspect ratio of an aerofoil section increases, this span-wise energy transfer - in the form of travelling waves - becomes important to the overall system dynamics. This paper extends the classic flutter model to include travelling waves in the span-wise direction. Namely, wave dispersion and power flow analysis of an infinite, aerofoil-shaped beam, subject to bending, torsion, tension and a constant wind excitation, is used to investigate the overall system stability. Examples of potential applications for these high aspect ratio aerofoil sections include high-altitude balloon tethers, towed cables, offshore risers and mooring lines.

Aeroelastic stability analysis using linear matrix inequalities

The present work describes an alternative methodology for identification of aeroelastic stability in a range of varying parameters. Analysis is performed in time domain based on Lyapunov stability and solved by convex optimization algorithms. The theory is outlined and simulations are carried out on a benchmark system to illustrate the method. The classical methodology with the analysis of the system's eigenvalues is presented for comparing the results and validating the approach. The aeroelastic model is represented in state space format and the unsteady aerodynamic forces are written in time domain using rational function approximation. The problem is formulated as a polytopic differential inclusion system and the conceptual idea can be used in two different applications. In the first application the method verifies the aeroelastic stability in a range of air density (or its equivalent altitude range). In the second one, the stability is verified for a rage of velocities. These analyses are in contrast to the classical discrete analysis performed at fixed air density/velocity values. It is shown that this method is efficient to identify stability regions in the flight envelope and it offers promise for robust flutter identification.

Die aeroelastische Stabilitätsanalyse – ein praxisnaher Ansatz zur intervalltheoretischen Betrachtung von Modellierungsunsicherheiten am Flugzeug

Die Untersuchung des dynamischen aeroelastischen Stabilitätsverhaltens von Flugzeugen erfordert sehr komplexe Rechenmodelle, welche die wesentlichen elastomechanischen und instationären aerodynamischen Eigenschaften der Konstruktion wiedergeben sollen. Bei der Modellbildung müssen einerseits Vereinfachungen und Idealisierungen im Rahmen der Anwendung der Finite Elemente Methode und der aerodynamischen Theorie vorgenommen werden, deren Auswirkungen auf das Simulationsergebnis zu bewerten sind. Andererseits können die strukturdynamischen Kenngrößen durch den Standschwingungsversuch identifiziert werden, wobei die Ergebnisse Messungenauigkeiten enthalten. Für eine robuste Flatteruntersuchung müssen die identifizierten Unwägbarkeiten in allen Prozessschritten über die Festlegung von unteren und oberen Schranken konservativ ermittelt werden, um für alle Flugzustände eine ausreichende Flatterstabilität sicherzustellen. Zu diesem Zweck wird in der vorliegenden Arbeit ein Rechenverfahren entwickelt, welches die klassische Flatteranalyse mit den Methoden der Fuzzy- und Intervallarithmetik verbindet. Dabei werden die Flatterbewegungsgleichungen als parameterabhängiges nichtlineares Eigenwertproblem formuliert. Die Änderung der komplexen Eigenlösung infolge eines veränderlichen Einflussparameters wird mit der Methode der numerischen Fortsetzung ausgehend von der nominalen Startlösung verfolgt. Ein modifizierter Newton-Iterations-Algorithmus kommt zur Anwendung. Als Ergebnis liegen die berechneten aeroelastischen Dämpfungs- und Frequenzverläufe in Abhängigkeit von der Fluggeschwindigkeit mit Unschärfebändern vor.

Aeroelastic characteristics of slender wing/bodies with freeplay non-linearities

This article presents a time domain approach to the flutter analysis of a missile-type wing/body configuration with concentrated structural non-linearities. The missile wing is considered fully movable and its rotation angle contains the structural freeplay-type non-linearity. Although a general formulation for flexible configurations is developed, only two rigid degrees of freedom are taken into account for the results: pitching of the whole wing/body configuration and wing rotation angle around its hinge. An unsteady aerodynamic model based on the slender-body approach is used to calculate aerodynamic generalized forces. Limit-cycle oscillations and chaotic motion below the flutter speed are observed in this study.

A influência do amortecimento viscoelástico na estabilidade aeroelástica de painéis aeronáuticos

Since the creation of supersonic vehicles, during the Second World War, the engineers have given special attention to the interaction between the aerodynamic efforts and the structures of the aircrafts due to a highly destructive phenomenon called flutter in aeronautical panel. Flutter in aeronautical panels is a self-excited aeroelastic phenomenon, which can occurs during supersonic flights due to dynamic instability of inertia, elastic and aerodynamic forces of the system. In the flutter condition, when the critical aerodynamic pressure is reached, the vibration amplitudes of the panel become dynamically unstable and increase exponentially with time, affecting significantly the fatigue life of the existing aeronautical components. Thus, in this paper, the interest is to investigate the possibility of reducing the effects of the supersonic aeroelastic instability of rectangular plates by applying passive constrained viscoelastic layers. The rationale for such study is the fact that as the addition of viscoelastic materials provides decreased vibration amplitudes it becomes important to quantify the suppression of plate flutter coalescence modes that can be obtained. Moreover, despite the fact that much research on the suppression of panel flutter has been carried out by using passive, semi-active and active control techniques, very few of them are adapted to deal with the problem of estimating the flutter speeds of viscoelastic systems, since they must conveniently account for the frequency- and temperature-dependent behavior of the viscoelastic material. In this context, two different model of viscoelastic material are developed and applied to the model of sandwich plate by using finite elements. After the presentation of the theoretical foundations of the methodology, the description of a numerical study on the flutter analysis of a three-layer sandwich plate is addressed.

Global, regional, and national age–sex specifi c all-cause and cause-specifi c mortality for 240 causes of death, 1990–2013: a systematic analysis for the Global Burden of Disease Study 2013

Background Up-to-date evidence on levels and trends for age-sex-specific all-cause and cause-specific mortality is essential for the formation of global, regional, and national health policies. In the Global Burden of Disease Study 2013 (GBD 2013) we estimated yearly deaths for 188 countries between 1990, and 2013. We used the results to assess whether there is epidemiological convergence across countries. Methods We estimated age-sex-specific all-cause mortality using the GBD 2010 methods with some refinements to improve accuracy applied to an updated database of vital registration, survey, and census data. We generally estimated cause of death as in the GBD 2010. Key improvements included the addition of more recent vital registration data for 72 countries, an updated verbal autopsy literature review, two new and detailed data systems for China, and more detail for Mexico, UK, Turkey, and Russia. We improved statistical models for garbage code redistribution. We used six different modelling strategies across the 240 causes; cause of death ensemble modelling (CODEm) was the dominant strategy for causes with sufficient information. Trends for Alzheimer's disease and other dementias were informed by meta-regression of prevalence studies. For pathogen-specific causes of diarrhoea and lower respiratory infections we used a counterfactual approach. We computed two measures of convergence (inequality) across countries: the average relative difference across all pairs of countries (Gini coefficient) and the average absolute difference across countries. To summarise broad findings, we used multiple decrement life-tables to decompose probabilities of death from birth to exact age 15 years, from exact age 15 years to exact age 50 years, and from exact age 50 years to exact age 75 years, and life expectancy at birth into major causes. For all quantities reported, we computed 95% uncertainty intervals (UIs). We constrained cause-specific fractions within each age-sex-country-year group to sum to all-cause mortality based on draws from the uncertainty distributions. Findings Global life expectancy for both sexes increased from 65·3 years (UI 65·0–65·6) in 1990, to 71·5 years (UI 71·0–71·9) in 2013, while the number of deaths increased from 47·5 million (UI 46·8–48·2) to 54·9 million (UI 53·6–56·3) over the same interval. Global progress masked variation by age and sex: for children, average absolute differences between countries decreased but relative differences increased. For women aged 25–39 years and older than 75 years and for men aged 20–49 years and 65 years and older, both absolute and relative differences increased. Decomposition of global and regional life expectancy showed the prominent role of reductions in age-standardised death rates for cardiovascular diseases and cancers in high-income regions, and reductions in child deaths from diarrhoea, lower respiratory infections, and neonatal causes in low-income regions. HIV/AIDS reduced life expectancy in southern sub-Saharan Africa. For most communicable causes of death both numbers of deaths and age-standardised death rates fell whereas for most non-communicable causes, demographic shifts have increased numbers of deaths but decreased age-standardised death rates. Global deaths from injury increased by 10·7%, from 4·3 million deaths in 1990 to 4·8 million in 2013; but age-standardised rates declined over the same period by 21%. For some causes of more than 100 000 deaths per year in 2013, age-standardised death rates increased between 1990 and 2013, including HIV/AIDS, pancreatic cancer, atrial fibrillation and flutter, drug use disorders, diabetes, chronic kidney disease, and sickle-cell anaemias. Diarrhoeal diseases, lower respiratory infections, neonatal causes, and malaria are still in the top five causes of death in children younger than 5 years. The most important pathogens are rotavirus for diarrhoea and pneumococcus for lower respiratory infections. Country-specific probabilities of death over three phases of life were substantially varied between and within regions. Interpretation For most countries, the general pattern of reductions in age-sex specific mortality has been associated with a progressive shift towards a larger share of the remaining deaths caused by non-communicable disease and injuries. Assessing epidemiological convergence across countries depends on whether an absolute or relative measure of inequality is used. Nevertheless, age-standardised death rates for seven substantial causes are increasing, suggesting the potential for reversals in some countries. Important gaps exist in the empirical data for cause of death estimates for some countries; for example, no national data for India are available for the past decade.

A finite volume unstructured mesh approach to dynamic fluid–structure interaction: an assessment of the challenge of predicting the onset of flutter

Computational modelling of dynamic fluid–structure interaction (DFSI) is a considerable challenge. Our approach to this class of problems involves the use of a single software framework for all the phenomena involved, employing finite volume methods on unstructured meshes in three dimensions. This method enables time and space accurate calculations in a consistent manner. One key application of DFSI simulation is the analysis of the onset of flutter in aircraft wings, where the work of Yates et al. [Measured and Calculated Subsonic and Transonic Flutter Characteristics of a 45° degree Sweptback Wing Planform in Air and Freon-12 in the Langley Transonic Dynamic Tunnel. NASA Technical Note D-1616, 1963] on the AGARD 445.6 wing planform still provides the most comprehensive benchmark data available. This paper presents the results of a significant effort to model the onset of flutter for the AGARD 445.6 wing planform geometry. A series of key issues needs to be addressed for this computational approach. • The advantage of using a single mesh, in order to eliminate numerical problems when applying boundary conditions at the fluid-structure interface, is counteracted by the challenge of generating a suitably high quality mesh in both the fluid and structural domains. • The computational effort for this DFSI procedure, in terms of run time and memory requirements, is very significant. Practical simulations require even finer meshes and shorter time steps, requiring parallel implementation for operation on large, high performance parallel systems. • The consistency and completeness of the AGARD data in the public domain is inadequate for use in the validation of DFSI codes when predicting the onset of flutter.

Transonic aeroelastic simulation for instability searches and uncertainty analysis

In this paper the use of eigenvalue stability analysis of very large dimension aeroelastic numerical models arising from the exploitation of computational fluid dynamics is reviewed. A formulation based on a block reduction of the system Jacobian proves powerful to allow various numerical algorithms to be exploited, including frequency domain solvers, reconstruction of a term describing the fluid–structure interaction from the sparse data which incurs the main computational cost, and sampling to place the expensive samples where they are most needed. The stability formulation also allows non-deterministic analysis to be carried out very efficiently through the use of an approximate Newton solver. Finally, the system eigenvectors are exploited to produce nonlinear and parameterised reduced order models for computing limit cycle responses. The performance of the methods is illustrated with results from a number of academic and large dimension aircraft test cases.

Reducing Uncertainty in Aeroelastic Flutter Boundaries Using Experimental Data

Flutter prediction as currently practiced is usually deterministic, with a single structural model used to represent an aircraft. By using interval analysis to take into account structural variability, recent work has demonstrated that small changes in the structure can lead to very large changes in the altitude at which
utter occurs (Marques, Badcock, et al., J. Aircraft, 2010). In this follow-up work we examine the same phenomenon using probabilistic collocation (PC), an uncertainty quantification technique which can eficiently propagate multivariate stochastic input through a simulation code,
in this case an eigenvalue-based fluid-structure stability code. The resulting analysis predicts the consequences of an uncertain structure on incidence of
utter in probabilistic terms { information that could be useful in planning
flight-tests and assessing the risk of structural failure. The uncertainty in
utter altitude is confirmed to be substantial. Assuming that the structural uncertainty represents a epistemic uncertainty regarding the
structure, it may be reduced with the availability of additional information { for example aeroelastic response data from a flight-test. Such data is used to update the structural uncertainty using Bayes' theorem. The consequent
utter uncertainty is significantly reduced across the entire Mach number range.

The use of Gramian matrices for aeroelastic stability analysis

Most of the established procedures for analysis of aeroelastic flutter in the development of aircraft are based on frequency domain methods. Proposing new methodologies in this field is always a challenge, because the new methods need to be validated by many experimental procedures. With the interest for new flight control systems and nonlinear behavior of aeroelastic structures, other strategies may be necessary to complete the analysis of such systems. If the aeroelastic model can be written in time domain, using state-space formulation, for instance, then many of the tools used in stability analysis of dynamic systems may be used to help providing an insight into the aeroelastic phenomenon. In this respect, this paper presents a discussion on the use of Gramian matrices to determine conditions of aeroelastic flutter. The main goal of this work is to introduce how observability gramian matrix can be used to identify the system instability. To explain the approach, the theory is outlined and simulations are carried out on two benchmark problems. Results are compared with classical methods to validate the approach and a reduction of computational time is obtained for the second example. © 2013 Douglas Domingues Bueno et al.

Aeroelastic stability analysis considering a continuous flight envelope

This paper presents a new methodology to analyze aeroelastic stability in a continuous range of flight envelope with varying parameter of velocity and altitude. The focus of the paper is to demonstrate that linear matrix inequalities can be used to evaluate the aeroelastic stability in a region of flight envelope instead of a single point, like classical methods. The proposed methodology can also be used to study if a system remains stable during an arbitrary motion from one point to another in the flight envelope, i.e., when the problem becomes time-variant. The main idea is to represent the system as a polytopic differential inclusion system using rational function approximation to write the model in time domain. The theory is outlined and simulations are carried out on the benchmark AGARD 445.6 wing to demonstrate the method. The classical pk-method is used for comparing results and validating the approach. It is shown that this method is efficient to identify stability regions in the flight envelope. (C) 2014 Elsevier Ltd. All rights reserved.