Background

Marie Curie Excellence Teams are supported under the sixth Framework Programme of the European Union and are devoted to the promotion and recognition of scientific excellence. To quote from the FP6 work programme These [Grants] aim at providing support for the creation and development of European research teams which are considered to have the potential to reach a high level of excellence, more particularly for leading edge or interdisciplinary research activities.

The Marie-Curie Excellence team ECERTA was one of about 30 teams established from 280 proposals made in response to the call of January, 2006. The €1.6 million project started on 1st January, 2007 and will last for 4 years. The grant supports the efforts of 8 man years of experienced researchers, 6 man years of early stage researcher (PhD student) and the Team Leader, Prof. Ken J. Badcock. Prof. John Mottershead is contributing his expertise on structural model updating.

Foundations

ECERTA builds on two research programmes. First, work has been advancing on developing CFD based methods for predicting aeroelastic stability and response. These methods exploit knowledge of the discrete system eigenspectrum and have proved fast compared with the conventional time domain approach to CFD based aeroelasticity. Demonstration on in-service aircraft has been made successfully. Secondly, John Mottershead is a recognised expert in structural model updating, with a current interest in stochastic model updating.

Background Research

• Woodgate, M. and Badcock, K.J., "On the fast prediction of Transonic Aeroelastic Stability and Limit Cycles," AIAA Journal, Vol. 45, No. 6, pag. 1370-1381, 2007.
  doi: 10.2514/1.25604

• Mares, C., Mottershead, J.E., and Friswell, M.I., "Stochastic Model Updating: Part 1-Theory and Simulated Example," Mechanical Systems and Signal Processing, Vol. 20, No. 7, pag. 1674-1695, 2006.
  doi: 10.1016/j.ymssp.2005.06.006

• Woodgate, M., Badcock, K.J., Rampurawala, A., Richards, B., Nardini, D., and Henshaw, M., "Aeroelastic Calculations for the Hawk Aircraft Using the Euler Equations," Journal of Aircraft, Vol. 42, No. 4, pag. 1005-1012, 2005.
  doi: 10.2514/1.5608

Research Challenges

Simulation plays a crucial role in the development of aircraft. Simulation tools have reached an impressive level of maturity. For various reasons, including cost and increasingly feasibility, there is pressure to exploit simulation data for certification purposes. However, this application creates pressure to increase the certainty of the simulation tools, and to provide estimates of the uncertainties remaining in their predictions. The ECERTA project is looking to respond to this pressure in the area of Aircraft Aeroelasticity. The ultimate goal of ECERTA is to Advance simulation methods so that simulation data can play an increased role in flutter clearance, reducing the flight flutter testing required.

High Level Research Challenges

There are two key high level research challenges that arise from the Research Goal. First, an assessment of uncertainty is required together with the flutter simulation predictions. Secondly, the aircraft dynamics needs to be mapped out with very little prior guiding information.

Research Programme

To tackle these high level challenges the following research themes are being investigated:

• A hierarchy of aerodynamic modelling approaches is being developed, including linear potential, full potential, Euler and RANS. These balance cost and fidelity, potentially allowing searches over large parameter spaces.

• The uncertainty introduced by aerodynamic modelling needs to be quantified.

• Methods are being developed for Stochastic structural model updating from ground resonance tests and information on fleet variability. The impact of structural model uncertainty on the final flutter predictions will be minimised and quantified.

• Methods to extract structural damping information from ground resonance tests are being developed to allow improved representations in flutter simulations.

• Combination of aerodynamic and structural uncertainties into an aeroelastic uncertainty statement.

• Use of the simulation data to plan optimal validating flight tests.

Introduction

Certification is the most demanding potential application for simulation. For a decision about the safety of an aircraft to be based on calculations, a high degree of certainty in the results would be required. How this certainty might be established is the research topic of ECERTA. The goal is to establish methodology which can contribute to establishing confidence in simulation results. Aeroelastic certification is used as the particular example since this topic fits well with the team's past experience. It is expected that the conclusions of the research will be applicable more widely.

The first task of the project was to define more precisely what "establishing confidence" involves, and to translate this into expanded methodology for simulation. At a high level we might identify the following as the requirements for confidence: we should be able to

• simulate the complete aircraft problem, with the minimum of simplifications required. For aeroelastic certification, this means having the option to include CFD based aerodynamic predictions, nonlinear structural effects, trimming and the flight control system, full geometry and structural damping;

• predict undesired behaviour in small regions of the flight envelope without any prior knowledge of its existence;

• identify the important weaknesses in the simulation, including the influence of uncertainties in input parameters;

• design physical tests that would provide data to remove the main uncertainties in the predictions.

At a lower level of detail, research was targetted at the following areas:

• Complete aircraft modelling: - how can the representation of structural damping be improved?

• Flight envelope search: - how can CFD based flutter tools be made to run order of magnitude more efficiently than time domain tools to allow flight envelope search? - how can a hierarchy of aerodynamic tools be coordinated to search the flight envelope?

• Accomodate uncertainties - develop methodologies that allow structural parameter uncertainty to be propagated to the uncertainty in flutter speed through CFD based simulations - how can an aerodynamic model be parameterised to allow uncertainty in the aerodynamic predictions to be propagated to the flutter speed.

Flight Envelope Search

Computational aeroelasticity is often used to analyse behaviour that has already happened in flight. A greater challenge is presented by predicting behaviour before it happens, without guiding information. Since we are interested in exploiting high fidelity models, including CFD aerodynamic models, the computational cost of exploring a flight envelope defined by many parameters, is potentially prohibitive. Research is being carried out into two ways of defeating the problem of computational cost.

First, over several years Badcock and Woodgate have been developing eigensystem based approaches to analysing stability and doing model reduction of CFD based aeroelastic models. These approaches have been found to be one to two orders of magitude faster than traditional time domain approaches to calculating stability. Under the ECERTA project these methods have been extended to allow robust parallel large scale eigenvalue calculations for multiple modes. The resulting method is called the Schur complement method, and involves linear frequency domain forced calculations to build a response matrix, and the solution of a nonlinear eigenvalue problem to track aeroelastic modes. This method has been applied to calculate the influence of structural variability on stability through Monte-Carlo, perturbation and interval analysis.

Finally, work is ongoing to use the system critical eigenvector to develop a nonlinear reduced order model which can predict limit cycle oscillations.

Background Papers

• Woodgate, M. and Badcock, K.J., "On the fast prediction of Transonic Aeroelastic Stability and Limit Cycles," AIAA Journal, Vol. 45, No. 6, pag. 1370-1381, 2007.
  doi: 10.2514/1.25604

• Woodgate, M., Badcock, K.J., Rampurawala, A., Richards, B., Nardini, D., and Henshaw, M., "Aeroelastic Calculations for the Hawk Aircraft Using the Euler Equations," Journal of Aircraft, Vol. 42, No. 4, pag. 1005-1012, 2005.
  doi: 10.2514/1.5608

• Badcock, K.J., Woodgate, M.A., and Richards, B.E., "Direct Aeroelastic Bifurcation Analysis of a Symmetric Wing Based on the Euler Equations," Journal of Aircraft, Vol. 42, No. 3, pag. 731-737, 2005.
  doi: 10.2514/1.5323

• Badcock, K.J., Woodgate, M., and Richards, B.E., "Hopf Bifurcation Calculations for a Symmetric Airfoil in Transonic Flow," AIAA Journal, Vol. 42, No. 5, pag. 883-892, 2004.
  doi: 10.2514/1.9584

Structural Model Updating and Variability

The ability to analyse the influence of uncertainty in the structural model parameters is a vibrant research area. Uncertainty arises for example from the modelling of joints. A ground vibration test provides data on the vibratory response, which is then used to update key parameters in the structural model to better match the measurements. This is a crucial step in a flutter certification.

It is possible to perform this analysis in a stochastic manner. If multiple vibration tests, or tests on multiple structures are available, then the measurements form a probability distribution. If the parameters are assumed to have some distribution also then the mean and variance can be set to match the mean and variance in the measurements. This is called stochastic model updating.

Taking the model updating ideas one step further, methods can be used to propagate structural parameter distributions through to flutter speed distributions. Different methods are being investigated: Monte-Carlo simulation, first and second order perturbation analysis and interval analysis. Initial investigations have been based on linear aeroelastic methods. For CFD based analysis. the Schur complement framework for flutter calculation is powerful for this type of analysis.

Aerodynamic Hierarchy

The aerodynamic model which has received widespread application for aeroelasticity is the Doublet-Lattice method. This model is based on potential theory and its main advantage is speed of computation. However, potential flow cannot represent important flow physics. In addition, the assessment of the impact of the modelling assumptions on the aeroelastic predictions is likely to be important for practical application and physical insight. Structural model sensitivity is relatively easy to evaluate if the structural model uncertainty is assumed to be due to parametric uncertainty. Methods for considering uncertainty introduced by the model form are much less clear.

Several methods have been considered to attack this problem. Efforts were made to parametrise the influence of aerodynamic structures through POD modes. The next attempt tried to use coupled models (eg full potential model + shock model + boundary layer model) to expose parameters related to individual physical features (see D2.1). Finally, the method fixed upon uses the Schur eigenvalue framework to evaluate sensitivity to matrix elements and to update matrix elements using different model levels.

The example being investigated is to use the simplest model possible being able to predict shock waves. The model of choice is the full potential equation. This baseline model is coupled with an integral boundary layer model to correct for viscous effects such as the displacement effect of the boundary layer as well as shallow separation. Besides the integral boundary layer formulation, a Clebsch variable model to correct for entropy and vorticity effects caused by strong shock waves violating the isentropic assumption of the full potential formulation is a future possibility. Euler and RANS codes are available for higher level models.

Modelling of Structural Damping

The oscillation of elasto-mechanical systems involves the exchange of kinetic and potential energies as well as the dissipation of energy by damping. Methods are generally well established for modelling the inertial and stiffness properties of most systems but often there remains very considerable doubt on how the damping behaviour should be represented. The most common method is to assume viscous damping, which is attractive computationally because it results in systems of second-order differential equations with solutions that are readily available by well-understood techniques. A regular approach is to simplify the assumption of viscous damping still further by selecting a damping matrix, C, diagonalizable by the classical normal modes of the system. This form of damping, usually known as classical damping, includes proportional damping as a special case.

The viscous damping approximation may not be very representative of reality, since the mechanisms that remove energy from a system (material damping, friction, gas pumping at interfaces, energy radiation, etc.) are very different both in nature and amplitude, and they could be often nonlinear. However, if the damping is light the dynamical behavior is principally determined by the relatively large elastic or inertial forces so this approach can represent a valid approximation in many cases.

The literature on the subject includes several different methods to identify the linear viscous damping matrix in multiple degree-of-freedoms systems. In the recent review paper [1] we compare the philosophy and performances of the main strategies in the identification of linear viscous damping, namely the perturbation method, Lancaster formula, the imaginary part of the inverse receptance matrix and the energy method. In [1] is shown that the last two strategies are in principle identical when dealing with linear viscous damping only and they perform better than the others when modal incompleteness is present in the measurements.

For these reasons, a method is developed based on the energy strategy with some variations that allow the identification of damping without the need to estimate the mass and the stiffness matrices. The energy-based method is able to locate the main sources of damping and it is intended to be used practically in real structures and to be able to identify both viscous and non-viscous damping. The method is validated by a numerical simulation [2] and gives good results in the first experimental tests [3]. Further tests are currently running to confirm the good performance of the method for both viscous damping and Coulomb friction identification.

This work is being carried out in collaboration with our project partners at Politecnico di Torino.