## Final Report Summary - FFAST (Future Fast Aeroelastic Simulation Technologies)

Unsteady loads calculations play anUnsteady loads calculations play an important role within the design of an aircraft, with dynamic gusts and manoeuvres leading to the largest aircraft loads. Unfortunately, a large number of conditions need to be investigated to ensure that the extreme cases for all aircraft components are identified. In the design of future aircraft there is therefore an industrial need to reduce the number of dynamic loads cases analysed, whilst simultaneously increasing the accuracy and reducing the cost/time for each unsteady aeroelastic analysis. In particular the new aircraft configurations that will be vital to meet 2050 performance targets are likely to possess design envelope boundaries and therefore critical loads cases that are very different from those previously found on conventional aircraft; and thus no previous experience is available to reduce the number of cases by engineering judgement. Hence the aim of the upstream FFAST project was to develop, implement and assess a range of candidate numerical simulation technologies to accelerate future aircraft design. To achieve this aim three main objectives were identified as offering major reductions in the total analysis cost/time: faster identification of critical loads cases, the extraction and implementation of aerodynamic and aeroelastic reduced order models (ROMs) from complex full order models; the use of reduced order models to accelerate full-order calculations.

Project Context and Objectives:

Introduction:

Unsteady loads calculations play an important role within the design and development of an aircraft, with dynamic gusts and manoeuvres leading to the largest aircraft loads. Unfortunately, a large number of conditions need to be investigated to ensure that the extreme cases for all aircraft components are identified. Furthermore, these analyses have to be repeated every time that there is an update in the aircraft structure. Within the modern civil airframe industry, each of these loads calculation cycles requires many weeks. This long lead time, together with the multiple times this calculation procedure needs to take place, has a detrimental effect on cost and time to market.

In the design of future aircraft there is therefore an industrial need to reduce the number of dynamic loads cases analysed, whilst simultaneously increasing the accuracy and reducing the cost/time for each unsteady aeroelastic analysis. For conventional designs reducing the cost and turnaround time of the loads process within the design cycle will lead to significant improvements to product development and manufacture, supporting the 2050 transport targets. In particular, identifying the flight conditions that give rise to the maximum loads on the aircraft structure and introducing more accurate methods at these conditions will allow the new and innovative designs, required for green aircraft, to be considered more rapidly and at significantly lower risk.

Background to project:

The impact of the loads process on each phase of the design process can be classified into:

-Concept phase - loads estimation plays an important role in assessing the structural weight of each concept under consideration and so influencing the design trade-offs between alternative options.

-Pre-Design phase - loads estimates are important to determine billet and forging sizes of long-lead items, and to contribute to the choice of alternative structural architectures (landing gear, position of the primary structural elements, two or three spar wing design etc.).

-Detailed Design phase - an accurate set of loads on which to base the design is critical, hence there is a high reliance on the preparatory mathematical modelling undertaken in pre-design. In practice there is often considerable pressure to seek loads decreases in order to facilitate weight saving. Hence the loads must be recalculated as the design progresses and the loads characteristics change.

-Validation and Certification phase - ground and flight-testing is performed in order to validate whether the characteristics built into the loads models are correct.

Project objectives:

FFAST has focused on three main objectives that were identified as offering major reductions in the total analysis cost/time:

-Faster identification of critical loads cases. Minimization of the total number of requested aeroelastic analyses to some representative key-points by formalising the process and reducing dependency on engineering judgment. This will allow non-conventional configurations to be evaluated at lower risk.

-The extraction and implementation of aerodynamic and aeroelastic reduced order models (ROMs), suitable for loads analysis, from complex full order models. Such models reproduce the dominant characteristics of higher fidelity models, but at lower cost than the full order simulation.

-The use of reduced order models to accelerate full-order models. Full order simulations are currently too expensive for routine use, but reduced order models offer potential cost savings through convergence acceleration.

Project Results:

1 Introduction

To achieve the three objectives and maximise the collaboration between partners, the technical work was split between three work packages: Critical Loads Identification; Reduced Order Aerodynamic Models; Reduced Order Aeroelastic Models. The presentation of the main Science and Technology (S&T) results is therefore divided between these three sections.

2 Critical Loads Identification

The work in critical loads identification within FFAST was aimed at reducing the number of test cases that needed to be considered in order to identify the critical loads cases through: faster identification of critical loads cases: minimization of the total number of requested aeroelastic analyses to some representative key-points by formalising the process and reducing dependency on engineering judgement. This will allow non-conventional configurations to be evaluated at lower risk.

Worst Cases '1-Cosine' Gusts:

Of interest is the gust wavelength Lg that produces the greatest maximum and minimum response of particular 'interesting quantities' (IQs), e.g. wingtip deflection, centre of gravity, wing root bending moment.

The response of the IQs are calculated not only for different gust lengths, but also variations of the whole range of parameters (speed, altitude, weight, c.o.g. position etc.) and the maximum and minimum values of each IQ are computed. There is also a need to compute 'correlated loads', which consider the variation of one IQ vs. another; this is important as for instance principal stresses may depend upon Bending Moments and Torques.

Test Models:

Most of the initial worst case gust loads work was developed using the 'NLR' model, a simple 5 DOF aeroelastic analytical model. The FFAST-2D, FFAST-Wing and FFAST models are based upon a typical civil aircraft, and were developed to provide test cases for the other work packages in FFAST. A number of test cases were required as the approaches being developed in the project ranged from those that built on pre-existing techniques to totally new methods. The comprehensive nature of the test cases mean they will continue to be useful beyond the end of the project as methods become more mature.

Surrogate Modelling Approaches :

The process for the definition of a meta-model can be summarised in the following three steps: sampling, meta-modelling and model validation.

Sampling aims to obtain the maximum amount of information related to the system behaviour with the minimum effort in terms of computation time, so with the minimum number of samples. The design space is sampled and the available sampling techniques differ in how they distribute these samples into the design domain.

Meta-modelling originated from the classical Design of Experiments (DOE) theory, where polynomial functions are used to build-up response surfaces, or meta-models. The polynomial coefficients are determined in a least square sense, so the effect is to smooth the peaks of the real behaviour. Alternative techniques have been used in FFAST that improve on this approach.

The methods implemented are as follows:

-Radial Basis Function (RBF)

-Kriging

--Optimal Sampling for the Kriging predictor

-Optimization Approaches

--Binary Genetic Algorithm (BGA)

--Continuous Genetic Algorithm (CGA)

-Neural Networks

Sample Results from the NLR model:

The RBF method, Kriging method, Optimisation approaches and various forms of Neural Networks have been used to determine the response of different IQs from a set of test points across the flight envelope, gust lengths and varying parameters.

It was found that good estimates of the worst values (max and min) could be determined using around 800 test points, and this accuracy could be increased if the sampling points were taken towards the edges of the response surfaces. For example these figures show the variation of maximum wing root bending moment versus gust length and air velocity and the variation of minimum wing root torsion moment versus gust length and altitude. The purpose of this part of the work was to obtain a meta-model capable of representing the true values of 10 IQs within the whole space of variation for the input parameters. Therefore 810 samples were required to achieve this goal. However, if only maximum/minimum values of IQs are sought then the optimal sampling techniques may be used. In this case the optimal sampling method selected only 179 samples from the space of parameters variations, less than 25% of the previous sample size. The meta-model constructed using optimal sampling is not a good global fit of the true function but the accuracy of the fit is significantly improved around the region with global maximum/minimum IQs.

Results of Neural Network Approach Applied to FFAST Full Aircraft:

The Neural Network-based procedure has been applied to the FFAST Full Aircraft, an A350-like representative aircraft. Typical models describing the geometry, the fuel distribution, the structural model (stick) and the aerodynamic model (DLM approach). Ten mass configurations have been created and a suitable, realistic flight envelope has been assumed for the validation of the proposed procedure.

Reanalysis:

The above work has investigated the use of several surrogate modelling and optimization methods for fast and efficient prediction of the worst case gust loads for each IQ. It has been shown that significant savings in computational time can be made without sacrificing accuracy. However, these studies have not considered any changes to the actual aircraft structure itself as part of the evolving design process. It would be desirable for the response of a modified structure to be obtainable from the responses of the original structure. This may be achieved by using an exact reanalysis technique (e.g. Sherman-Morrison-Woodbury formula) or an approximate reanalysis method (e.g. perturbation). There is a body of work in the field of civil engineering considering fast static structural reanalysis; however, the application of such an approach to aeroelastic analysis has received no attention.

System Identification Approach for Correlated Gust Loads:

As well as determining the maximum and minimum response for each IQ, it is also of interest to determine 'correlated loads' as the critical stresses / strains will be dependent upon a combination of SMT (shear, moment and torque) loads. The correlated responses (or correlated loads) can be plotted against each other and the outlying points of a convex hull are used to define the critical load cases.

The use of system identification methods for the estimation of modal parameters from Ground Vibration Testing and also Flight Flutter Testing is well established. Bearing in mind the requirement of being able to produce models that can be applied across a wide range of flight, gust and aircraft parameters, it was decided to perform an iterative frequency domain fit that includes out of frequency range contributions.

3 Reduced Order Aerodynamic Models

The focus of this work was the development and novel use of aerodynamic Reduced Order Models that can be coupled to a structural model to accelerate aeroelastic simulations. ROMs are designed to capture the behaviour of high order aerodynamic models (high fidelity computational models) and once constructed, are computationally inexpensive to use in analysis and require less storage. Aerodynamic ROMs may be used as a complete replacement for the high order models from which they have been derived, or in hybrid methods which use the ROMs to accelerate higher order methods. The methodologies developed within FFAST for fluids are generic and can be applied to other non-linear sets of equations. The approaches being developed in FFAST ranged from those that built on pre-existing techniques to totally new methods.

-DLR focused on the development of both single point and global POD based unsteady ROMs in the transonic regimes. Two frameworks for this were considered within the flow solver TAU, the first uses the main compressible unsteady RANS solver and the second linear frequency domain solver that already existed in TAU.

-The work of the University of Bristol concentrated on the construction of low order models from CFD, using the Eigensystem Realisation Algorithm (ERA), for aerofoils and wings undergoing motions and gusts. In these cases the changes in force coefficients on the bodies can be assumed to be approximately linear, when taken about the non-linear baseline (steady state) flow. The dynamic behaviour of the system can then be represented by a linear state-space model. The method has also been extended to include nonlinear steady state behaviour for gusts.

-INRIA and Optimad have collaboratively developed systematic hybrid ROM technologies to accelerate high order unsteady simulations based on the POD method. This work required the investigation of both a hybrid zonal approach and a basis enhancement technique.

-Numeca has developed a ROM based on a Fourier decomposition of the unsteady signals, called the Non-Linear Harmonic (NLH) method. This ROM allows the computation of unsteady flows for the cost of a steady computation multiplied by a factor. This approach has previously been implemented by Numeca for internal flows and has been extended to external flows around moving structures in FFAST. This necessitated work on deterministic stresses and harmonic interaction for transonic flows.

POD-based ROM:

Unsteady transonic aerodynamic predictions based on the compressible unsteady RANS equations were made for a pitching aerofoil using a dimensionality reduction technique, coupled with another technique for the estimation of the time dependent coefficients. The two dimensionality reduction methods followed were Proper Orthogonal Decomposition (POD) and kernel Principal Component Analysis (kPCA). For the estimation of the POD or kPCA coefficients, three different methods were pursued namely, fuzzy logic, radial basis functions and Kriging.

The ROMs were applied to the two-dimensional pitching NLR7301 supercritical aerofoil. All investigations were performed at a Mach number of 0.753 a Reynolds number of 1.727e6 and a mean angle of attack of 0°. The pitch amplitude was 4°. Different pitching frequencies as described below were simulated. The flow conditions (operating point) were chosen such that they coincide with those where Limit-Cycle Oscillations were observed in experimental and numerical investigations. A series of unsteady CFD snapshots were generated using the TAU flow solver for a pitching NLR 7301 aerofoil between +/- 4° angle of attack as described above. The values considered for the reduced frequency k were 0.2301 0.2429 0.2557 0.2685 and 0.2813. For each frequency, 3 complete periods of oscillation were generated, each period incorporating 100 snapshots. In our analysis only the last period from each frequency was considered. By considering four reduced frequencies only, a solution was predicted for the other intermediate reduced frequency at 0.2557 using the POD and kPCA methods coupled with the interpolation procedures. Two different approaches to the POD were adopted. In one method, which we refer to it as the local method, the POD was conducted on only four snapshots at a time that are at the same angle of attack and at different reduced frequencies. The POD procedure was carried out for each and every angle of attack throughout the whole periodic motion.

Improving ERA:

The method used at Bristol for Model Order Reduction (MOR) is the Eigensystem Realisation Algorithm (ERA). Work has focused on the implementation and extension of this technique to improve robustness and allow the formation of reduced order models for gusts. CFD codes are implemented in discrete time space for a particular time step size and this approach requires the calculation of discrete time pulse or step responses to characterise all the solutions of the dynamically linear system. These responses are then used with the ERA to reduce the model order. It should be noted that as well as model order reduction, ERA can be used for system identification. In a system identification implementation sufficient terms in the response must be computed to enable the full order system to be found. However in the present study the high order system is large and known, with only small defined sets of inputs and outputs (surface pressures or integrated body forces) being of interest. In this case, the only requirement is to capture the dominant behaviour of the known system for which only truncated responses are required.

Extending ERA methods to gusts:

In order to create a reduced order model for the response of an aerofoil or wing to a gust, it is first necessary to have an accurate and efficient high order CFD code for gusts. The drawback of introducing the gust through the far field boundary conditions is that a very fine mesh is needed all the way to the far field to convict disturbances; such as vortices and gusts; through the computational domain without dissipating them. This high cost limits the use of the full simulations in loads calculations to a few flight conditions. The requirement for a fine mesh can be reduced by refining the mesh local to the disturbance as it moves through the domain. This approach has been used by Tang and Baeder to model a vortex impinging on an aerofoil. The difficulty with this approach is that it needs the CFD solver to be coupled to a mesh generator that can suitably refine the mesh locally.

In this project a new method for modelling the interaction of an aerofoil with a gust called the Split Velocity Method was developed. It involves only a rearrangement of the Euler or Navier-Stokes equations and thus is able to capture the effect of the aerofoil or wing on the gust as well as the effect of the gust on the aerofoil and wing. This contrasts with the existing prescribed velocity approach called the Field Velocity Method (disturbance velocity approach) which does not include the effect of the aerofoil or wing on the gust. The two prescribed velocity approaches agree well for longer gusts. For shorter gusts were the gust length is close to chord of the aerofoil the new approach produces better results. A linearised version of the Split Velocity Method has also been developed and has been shown to agree well with the full method for cases when the gust does not result in large shock motions.

Hybrid ROM/Full Order Technology:

The idea of 'Drag and Drop' simulation tools to drastically reduce the turn-around time for CFD results in complex aerodynamic configurations is attractive. One area that may contribute to achieving this long term objective is the development of systematic hybrid ROM technologies for unsteady simulations. Within FFAST, INRIA and Optimad have worked collaboratively to investigate hybrid fusion-basis methods based on POD.

The main idea of the hybrid fusion-basis method relies on:

i) a domain decomposition or zonal approach that uses a high-fidelity model close to the body surface, where the flow is changing rapidly and a POD ROM for the outer flow region;

ii) a pseudo-time method to enrich the solution space from which the ROM basis is derived.

The pseudo-time approach consists of a non-linear interpolation in the parameter space obtained using an optimal transportation approach.

The hybrid zonal approach was applied to the AGARD test case CT1. The case is for a NACA0012 aerofoil at Mach number of 0.6 that is oscillating in pitch angle. The computational time savings for the hybrid method compared to a fully high order solution are of the order of 100. The reduced frequency is 0.0808 for this case.

Model Order Reduction Using Fourier-Decomposition Method:

Numeca has developed a ROM based on a Fourier decomposition of the unsteady signals, called the Non-Linear Harmonic (NLH) method. Within this ROM, the flow variables are written as a time-mean plus a sum of unsteady perturbations. Each of these perturbations is decomposed into several Fourier harmonics. This decomposition leads to two different sets of equations. The first one corresponds to the time-averaged conservation laws, where all the effects of the unsteadiness are taken into account by the introduction of deterministic stresses similar to the Reynolds stress tensor. The second one corresponds to the conservation laws for the complex amplitudes of the harmonic flow variables. They are derived by considering a first order linearization of the unsteady Navier-Stokes equation, in the frequency domain. This ROM allows, therefore, the computation of unsteady flows for the cost of a steady computation multiplied by a factor (1 plus twice the number of harmonics). For applications such as Contra-Rotating Open Rotor, it leads to a reduction of three orders of magnitude in CPU time, compared to full-order sliding grid techniques.

4 Reduced Order Aeroelastic Models

The focus of the reduction of the computational cost of performing the aeroelastic simulations, required in aircraft design, using reduced order simulation techniques. A number of new approaches have been developed and implemented for use in external aeroelastic problems. Aeroelastic ROMs may be used as a complete replacement for the high order models from which they have been derived, or in hybrid methods which use the ROMs to accelerate higher order methods. The approaches being developed in this work package ranged from those that built on pre-existing techniques to totally new methods.

-The objective of the work at TU Delft was the development and assessment of hybrid full/reduced order modelling techniques. This work was not based on any pre-existing research knowledge or techniques and thus will require further work beyond FFAST to reach its potential.

-The objective of the work of the University of Cape Town and CSIR was to investigate the construction of reduced order models from a unified non-linear aeroelastic system. With the unified fluid-structure-interaction (FSI) technology as base, a hybrid ROM was developed consisting of separate structural and aerodynamic ROMs coupled in an iterative way.

-The Non-Linear Harmonic Method was extended by Numeca to model 1-cosine gusts and their effects on aircraft wings with an aeroelastic formulation. This test case revealed some limitations of the baseline NLH method, therefore work was done to improve the method by considering non-linear harmonic interactions.

-The objective of the work of IRIAS and IITP was to investigate global aeroelastic surrogate models for use in the early design phase. This used mathematical approximation methods and a data base of results. The resulting surrogate model was assessed by comparison with available test case data.

Aeroelastic Full/Reduced Order Model Fusion:

Transient response due to gust loads can lead to structural failure despite the fact that the aero-elastic system is asymptotically stable. Unsteady aeroelastic analysis should therefore be included in the load calculation cycle of the aircraft design process. Using engineering experience and lower fidelity models, often corrected with costly wind tunnel data, the current load calculation cycle requires more than 6 weeks. The replacement of these low fidelity models with more accurate aeroelastic simulations is attractive because of the reduced tunnel testing costs and the decreased risk of design modification in the later design phases. However, the computational effort associated with high fidelity aeroelastic models currently precludes their direct use in industry. This motivates the development of methods that aim to reduce the cost of time-accurate high fidelity simulations.

The aim of the work of TU Delft in FFAST has been the development of a numerical technique that accelerates time-accurate high fidelity Fluid-Structure Interaction simulations with the following constraints:

-Maintaining software modularity / Non-intrusiveness

-Maintaining Robustness

Within this context TU Delft has carried out research into the acceleration of high fidelity aeroelastic simulations using aeroelastic reduced order models and developed a generic coupling shell, thus allowing CFD and CSM communities to implement the present approach using their own codes and expertise.

ROM for Unified Aeroelastic Systems:

A unified aeroelastic simulation framework for the effective modelling of non-linear aeroelastic phenomenon has been considered. The 'Elemental' computational fluid dynamics (CFD) code was employed for this purpose. Rather than consider the fluid and structure in isolation, high resolution modelling of the complete non-linear system via Elemental enables model reduction to be done in a more natural and intuitive manner. The initial work focussed on the development of a fully-coupled hybrid-unstructured fluid-structure-interaction (FSI) modelling technology for non-linear aeroelastics.

With the unified FSI technology as base, a hybrid ROM was developed consisting of separate structural and aerodynamic ROMs coupled in an iterative way. This allowed the most appropriate for each to be used.

For the aerodynamic ROM, a surrogate based method with Kriging was used as this has been shown to be effective for strongly non-linear flows. The input parameters to interact with the non-linear structural ROM are Mach number, heave and pitch, as well as heave and pitch rates and accelerations. The outputs are the coefficients of lift and moment.

The required training cases are chosen using Latin Hypercube Sampling (LHS), a modified version of Monte Carlo Sampling. If the physics of the problem is understood before the generation of the training cases however, a computationally less expensive strategy is possible with appropriate cases being selected strategically. For the purpose of this work we consider the variation in aeroelastic response as a function of Mach number, and therefore simply select the latter for the purpose of prescribed parameter variation. It has been found that choosing the Mach number range to include the flutter boundary is essential. Interpolation between samples is accomplished using Kriging.

Fully coupled parallel solution was employed in the interest of robustness and accuracy, and the methodology rigorously validated via application to a range of benchmark problems. Having proven the high fidelity technology in 2D, a quadratic modal ROM was next developed to describe the wing structure. The simulation technology was subsequently applied to modelling non-linear flutter in 2D, and the proposed quadratic ROM shown to offer dramatic improvements in accuracy over the more conventional linear modal method. This concluded the contribution by the CSIR.

Following on from the 2D work, a unified modelling technology was developed at UCT for 3D applications. The Elemental software again served as base for the work. An Arbitrary Lagrangian-Eulerian (ALE) reference frame was employed, and transonic shocks accounted for in the fluid. The solid was described via non-linear beam ROMs with 6 degrees-of-freedom per node, therefore accounting for translations as well as rotations. The solver was again parallelized for efficient distributed memory computing. Robustness was demonstrated via application of the technology to FFAST benchmark test-cases.

Having validated the unified FSI methodology, the final step in the completion of the aeroelastic ROM was the development of the aerodynamic model. A surrogate ROM with Kriging interpolation was established for this purpose. This could then be solved in a fully coupled manner with the structural ROM to predict the unsteady response of a wing in a truly fast and efficient manner. The application study involved the FFAST wing undergoing flutter response. For ROM training purposes, the developed high fidelity code was run for three transonic Mach numbers viz. 0.7 0.73 and 0.8. The coupled aerodynamic and structural ROMs were then solved simultaneously to predict the system response at a range of Mach numbers which lie within the range of the training data. The solutions were achieved within seconds.

The non-linearity of the problem is clearly visible from the results, with the ROM achieving an accurate solution. Similar results were achieved for all other flow speeds tested. This successfully demonstrated the marked potential of the developed ROM framework in achieving significant cost savings in non-linear gust load predictions.

ROM based on Fourier-Decomposition Method:

The Non-Linear Harmonic Method was extended to model 1-cosine gusts and their effects on aircraft wings with an aeroelastic formulation. This method is not suited to discrete gusts, because it relies on flow periodicity to enable efficient system reduction. Hence gusts are repeated and a Fourier transform is applied to get their harmonic definition. The analyses of the results reveal some limitations of the NLH method for the accurate prediction of flow solution in presence of strong nonlinearities such as sonic shock motions. Therefore work has been done to improve the method by considering non-linear harmonic interactions.

To apply the NLH method to a discrete gust, it is necessary to assume this repeats periodically with a sufficiently large period. This period must be rather large in order to avoid some interaction effects between two consecutive gusts. In order to limit the number of harmonics to compute, and hence reduce the computational cost, the spectrum has been restricted to lower frequencies. The quality of the retained spectrum can be checked by performing an inverse Fourier transform.

Initially this gust representation was used in the baseline NLH method for a rigid aerofoil with two different periods for the repeat. Analysis of the pressure profile around the aerofoil showed that the shock is displaced from 20% to 60% of the chord due to the gust in the full order method. With the NLH method, this shock did not move, remaining fixed at an averaged position around 40% of the chord. Only its amplitude varied with time. This behaviour of the baseline NLH method for the gust case is similar to the issue encountered for pitching aerofoils in transonic flow, see above.

To investigate whether this deficiency was due to the linearisations within the baseline NLH, a new formulation that includes non-linear harmonic interactions was developed. This was initially tested on a channel flow, before being applied to the FFAST rigid gust test case 4. It can be seen that the agreement with the full order solution is improved. However some spurious oscillations remain after the passage of the gust. These are due to the restriction of the harmonic spectrum of the gust imposed in the free stream. Remaining differences with the Bristol results may be due to the fact that the NLH is viscous and the full order solution is inviscid.

Surrogate Computational Unsteady Fluid Models for Early Stage Design:

The problem of predicting the integral and distributed aerodynamic time characteristics of aerofoils under unsteady flow conditions for large amplitude disturbances is a common problem in industry. These large disturbances which may contain dynamic stall events are considered when modelling: passenger aircraft penetration in high turbulence zones, light aircraft manoeuvres, Helicopter rotor blade flow under various regimes, and so on.

Traditionally, aerodynamic characteristics of an aerofoil in unsteady flow are found by carrying out extremely complex and expensive experiments in wind tunnels or numerical simulation, which is also costly. Traditionally, aerofoil characteristics are only obtained in wind tunnels under steady conditions and unsteady predictions are predicted using simple models. Numerical simulation applied to detached viscous unsteady flow, requires extensive computational resources which limits its use in design and object dynamics simulation.

The IITP/IRIAS activities within the FFAST project concerned the construction of fast reduced order aeroelastic models for complex configurations and physical phenomena under unsteady conditions. This work extended the predictive meta-modelling technology previously developed by IITP/IRIAS for steady flow. The constructed models are based on the results of numerical experiments performed with higher order initial models.

During the FFAST project, the original technology was successfully adapted and improved. The effectiveness for constructing a Surrogate Computational Unsteady Fluid Model (SCUFM) has been demonstrated through the practical case of predicting the time-varied aerodynamic characteristics of aerofoils (aircraft wing cross-section, helicopter rotor blade, etc.) under unsteady flow conditions with dynamic stall.

The resulting reduced order SCUFM model was validated against experimental data and shows good performance (small operating time, satisfactory accuracy).

SCUFM consists of four steps:

-choosing the high order training data model

-experiments to obtain the training data (DoE strategy)

-constructing the surrogate model from training data

-evaluation of the quality of the surrogate model

The particular problem shown here requires a description of the aerofoil geometry, angle of attack variation with time and the unperturbed flow parameters: Mach number, Reynolds number and Strouhal number.

The full order experiments to produce training data have used the FlowVision CFD code on the National Research Centre 'Kurchatov Institute' supercomputers. This CFD code can model 3D laminar and turbulent steady and unsteady gas and liquid flows in complex geometries. Every experiment produced exactly two periods of aerofoil oscillation with the same number of time steps. The training data used was the second period of the lift coefficient value and pressure distribution over both sides of the aerofoil, as the first period contains strong transients.

The SCUFM surrogate model was built using the MACROS (Multidisciplinary Aeronautic Capability Research On Simulation) toolkit developed by the Datadvance research company whose theoretical basis (predictive meta-modelling technology) was developed by IITP and IRIAS. Within FFAST, the basic MACROS data handling procedures were further developed to include special time-series analysis and dimension reduction.

For the purposes of validation some sets of the training data were excluded. A root mean square error metric gave an average error lower than 5%. The surrogate model execution time is less than one second compared to 24 hours of the original high order model.

The Surrogate Computational Unsteady Model is implemented as a web service available to project participants and industrial partners. One may test the method and software developed to evaluate its speed and accuracy.

It has been demonstrated that the developed software SCUFM is able to approximate the lift coefficient data in the presence of dynamic stall with a standard deviation of less than 5% and a calculation time of less than 1 second once the training data sets have been produced.

5 Potential Efficiency Savings

All the methods developed in FFAST offer savings in computational effort compared to full order methods. The savings offered by the various approaches compared to the corresponding full order methods are summarised as follows:

-Surrogate modelling and optimization techniques. Reanalysis methods - 50% efficiency saving for existing aircraft designs. Potentially significantly greater for novel configurations

-POD and kPCA plus nonlinear interpolation, POD + SID / Fuzzy Identification,

POD plus Galerkin projection - 90% efficiency saving for URANS based ROM compared to URANS solutions. 99% for linear frequency domain based ROM compared to URANS solutions

-Improved ERA - 90% efficiency saving compared to full order Euler solutions

-Hybrid POD/full-order model plus nonlinear interpolation - 90-99% efficiency saving compared for the Cartesian mesh solutions considered.

-Nonlinear harmonic method based on Fourier decomposition - 80% to 99% efficiency saving compared to full order solutions depending on number of harmonics required.

-Space mapping - 50% efficiency saving over best available solver.

-Reduced order models of aerodynamics and structured implemented in a unified solver - 90-99% efficiency saving over full order unified method.

These values are based purely on the range of test cases considered by each partner and further work is required to validate these speed ups for a wide range of industry relevant test cases. It should be noted that the full order methods differ between partners. The work of IRIAS and IITP has a slightly different focus, being aimed at very early design for a range of possible aircraft configurations. It can take data from numerous sources both numerical and experimental. The efficiency gains in the table above are easy to quantify because they are based on a specific code and a single aircraft configuration. Applying the same criteria for this surrogate model is not reasonable. The high initial costs of construction can be justified by the trivial costs of exploring the design space.

It should be noted that the methods of TU Delft and Bristol/Liverpool/Polimi could be used in conjunction with the other methods, bringing greater savings to the loads process. If an average value of 90% speed up for the other methods (individually) is assumed, then adding these technologies could be expected to produce a commensurately greater speed up of the order of 97.5%.

6 Conclusions

A number of different Design of Experiments, surrogate modelling and optimization techniques have been applied to '1-cosine' gust response data in order to determine the worst case gust loads for both 1D and correlated loads. Further work has considered the analysis following changes to the aircraft structure. The methodologies have been demonstrated on a number of different test cases. It has been shown that for conventional configurations, a saving of around 50% in the test cases that need to be considered can be achieved. This saving is likely to be much more substantial for novel aircraft configurations.

A range of aerodynamic reduced order modelling methods have been developed in FFAST, including methods based on proper orthogonal decomposition of solution snapshots, Fourier decomposition of the governing equations, the Eigensystem Realisation Algorithm and a hybrid zonal approach. All ROM methods have been shown to speed-up the prediction of aerodynamic response data and to compare well to the corresponding full order results. However, a direct comparison of the different ROM approaches has not been performed due to different physical modelling (unsteady Euler vs. URANS) and different levels of maturity. The speed up produced depends on the problem but are all in the range of a 90 to 99% reduction in the cost compared to the full order model.

A non-linear interpolation method based on the solution of an optimal transport problem has allowed accurate interpolation in the parameter space of the flow snapshots. These can be used either to enrich the database of a ROM or directly estimate performance.

The Linear and Non-Linear Harmonic methods have been extended to the computation of external flow configurations including moving boundaries. These harmonic methods produce a drastic reduction of the CPU cost and can also be applied to the calculation of discrete gusts. A major enhancement in accuracy for flows with large shock displacements has also been introduced in the NLH method with the consideration of the harmonic interactions.

As well as the developed reduced order technologies, a split velocity method has been developed which allows the convection of defined gusts through the computational domain without numerical diffusion.

A range of aeroelastic methods have been developed in FFAST. A new multi-fidelity coupling algorithm has been developed in order to reduce the cost of high fidelity time-accurate fluid-structure interaction simulations. The new algorithm - called space-mapping - is capable of exploiting a lower fidelity model in order to accelerate high fidelity simulations while maintaining software modularity. The observed speedup increases with the time step size. It is therefore expected that the space-mapping algorithm can be efficiently combined with higher order time integration schemes that maintain accuracy over a large range of time step sizes.

Reduced models have been constructed in a natural and efficient manner by modelling a small number of gust responses via a unified high fidelity FSI code developed for this purpose. The hybrid ROM accurately predicts gust responses for transonic flow conditions at a range of untried Mach numbers with the computational cost savings of an order of magnitude.

It has been demonstrated that the developed software SCUFM is able to approximate the lift coefficient data in the presence of dynamic stall with a standard deviation of less than 5% and a calculation time of less than one second once the training data sets have been produced.

Potential Impact:

1 Potential Impact

The FFAST project will contribute to the goals of improving European industrial competitiveness by developing capabilities to design an aircraft concept that will have significantly lower fuel burn levels than today's best standard. Lowering aircraft fuel burn will result in reductions in CO2 emissions that will go a significant way to meeting the FLIGHTPATH 2050 vision targets. In order to meet these targets the aircraft design process must evolve rapidly to allow a number of concepts to be retained and assessed from top level definition through to high levels of maturity whilst also reducing lead times. Two approaches that could impact on this aim are reducing the number of load cases to be calculated and by increasing accuracy for the calculations through greater use of CFD.

FFAST has developed a range of methods for critical loads identification, which will reduce the number of loads cases that need to be calculated. The key advantage of the methods over the existing approach is that they apply to both conventional and novel configurations. In the latter case the engineering judgment based on previous experience is not available; this means one of the main stumbling blocks to new designs has been overcome. The methods are currently being evaluated within industrial projects and if successful on real aircraft will immediately impact on future aircraft design.

The aerospace industry continues to push forward the use of CFD for loads to provide both a reduction of timescales and an improved aircraft design through taking proper account of nonlinear effects. However, considerable technical progress is needed in two areas to achieve this aim: CFD methods and reduced order modelling. The focus of FFAST has been on reduced order modelling since it will still be many years before computing power is sufficient to enable the full flight regime to be studied using full CFD. However, a reduced order model can only be as good as the CFD from which it is derived and thus CFD methods must be capable of predicting correct behaviour throughout the flight regime which can only be assessed using currently insufficient test data. The reduced order models will improve as the CFD improves and will provide substantial savings in terms of computational effort and hence lead time.

FFAST has developed a number of ROMs which give a good representation of the CFD response curves. Each method has shown large speed ups in computational time and some methods could be combined in future to give even greater efficiency gains. Though not yet fully mature, these methods have the potential to allow high fidelity methods to be used earlier and more extensively in aircraft design. This will lead to a more efficient process.

Exploitation post project completion will have a number of different phases. The first is follow-on research and technology projects that will: advance the maturity of the technologies developed in FFAST so that they can become industrial standard tools suitable for use in real industrial design application or investigate the research areas that have been identified by FFAST as lacking knowledge and which therefore need further academic focus . This will be followed in the longer term by a second exploitation phase with the application and evaluation of beta release version of codes developed in the project by industrial partners.

2 Dissemination

The dissemination strategy for FFAST promotes the transfer of skills, expertise and knowledge both internally within the consortium and externally to the wider community. During the project all the major dissemination targets have been achieved ensuring that the knowledge developed is being utilised in industrial, research and educational communities. In addition to conference and journal publication, which are detailed below, dissemination to the wider community has taken place through the public web site (see http://www.ffastproject.org online) and presentations to industry, academia and research students. The web site will continue to be maintained beyond the end of the project. It is also worth noting that the South African Department of Science and Technology (DST) has selected FFAST as a project of high ranking national importance. This will result in wide-spread media coverage as well as the project being brought under the attention of high ranking South African and European Union officials.

A total of 19 international conferences and 5 workshops will have been attended by FFAST representatives. At these events the results from FFAST have been presented. Interactive sessions have enabled feedback from the wider community, which has directly benefited the project progression. The number of conference publications is likely to increase over the forthcoming months. Publications have been written for submission to journals with many more in the developmental stages. Details of the venues for publications are:

Conferences:

Aerodays, Spain 2011

AIAA/SDM, USA 2011

IFASD, France 2011

Coupled Problems, Greece 2011

ASME Turbo Expo 2011

Finite Volumes for complex applications V1 FVCA6 2011

Eurogen 2011

Wouschoten Conference 2011

CHPC- Centre for High Computing 2011

CECAM 2012

ICIAM 2011

10th World Congress on Computational Mechanics, 2012

Set for Britain, UK 2012

S2MRSA, France 2012

SACAM 2012

AIAA/SDM, USA 2012

ISMA 2012

7th ICCFD 2012

SMSMEO 2012

HYP2012

ECCOMAS 2012

AIAA/SDM USA 2013

Workshops:

Airbus DiPaRT (2010, 2011, 2012)

ALEF and FFAST (2011)

1st DLR-NPU Joint Workshop

FFAST final workshop (2013)

Journals:

IJNMF

AIAA Journal of Aircraft

Journal of Computational Physics

Journal Européen des Systèmes Automatisé

Journal of Aeroelasticity and Structural Dynamics

Finite Volumes for complex applications VI-problems and perspectives

The implementation of the dissemination strategy has continued throughout the project and post project there will be continued dissemination by partners.

3 Exploitation

Exploitation is an integral part of the research project life cycle. The aim is to ensure that a number of tangible and intangible results become available for economic, technological and social benefit of industry and society. As the project comes to an end the focus is on the efficient exploitation of the project results, to achieve these aims. Although some exploitation activities have already been demonstrated the majority of the foreground application will occur after the completion of the project.

Exploitation post project completion will have a number of different phases. The first is follow-on research and technology projects that will: advance the maturity of the technologies developed in FFAST so that they can become industrial standard tools suitable for use in real industrial design application or investigate the research areas that have been identified by FFAST as lacking knowledge and which therefore need further academic or industrial focus.

Individual statements from all project partners outlining the exploitable results developed within their organisation are presented below. These statements highlight individual exploitation activities that will utilise these results ensuring that economic, technological and social benefits are attained.

University of Bristol Exploitation Activities:

The main ROM algorithms that have been developed by Bristol in FFAST are generic, being applicable to any CFD code after minor input/output modifications. Hence the methods can be utilised within the wider European aerospace industry, with the technology being well suited for further development and integration with other developments in FFAST and CFD.

The developed technology will provide the foundation for future research platforms. For instance, results developed in FFAST directly fed into the recently awarded ALPES IITN; a PhD directly funded by industry and the MMGUST proposal submitted in the Seventh Framework Programme (FP7) 2012 call addressing the AAT.2012.4.1-1 Design systems and tools topic.

Knowledge transfer will be a key consideration as the technologies have been developed within a teaching and research organisation. The results from FFAST have already, and will continue, to directly influence the teaching of both undergraduate research projects and PhD students. Furthermore it is planned to include the loads analysis techniques developed in FFAST into the software used by undergraduates in the airframe design project. Inclusion of state of the art developments within teaching will enhance the student experience and promote future research.

INRIA Exploitation Activities:

INRIA's contribution to technology transfer will be implemented via the development of durable simulation libraries that will be used in subsequent research projects. Transfer to industry will be indirect, through the communication of the new methods during public events, such as conferences and workshops, as well as during dedicated training sessions or seminars. The simulation libraries developed are now available for direct transfer to industry in future joint projects.

Moreover, the methods and schemes developed in the framework of FFAST are sufficiently general to be employed for a larger set of applications in which INRIA is involved: naval industry, and wind turbine reduced flow models and simulations, patient-specific models in medicine.

UCT Exploitation Activities:

At an early stage in development, the newly developed unified CFD/aeroelastic software showed clear industrial potential. In terms of exploitation, the following activities have resulted: the developed modelling technology is being commercialised via a UCT technology spin-out company (Numerous Technologies Ltd); a research project applying the developed ROM technology with Airbus (UK) Flights Physics as part of the South African National Aerospace Council (NAC) programme; the developed technology will also be used as a base for on-going collaborative research and exploitation activities with the other FFAST partners.

TU DELFT Exploitation Activities:

The main exploitation of the results for university is at the educational level by teaching the new knowledge to students and at the academic/industrial level by integrating the results in FLECS which provides a software toolbox for portability of developments to the industrial level.

At an educational level a MSc student from TU Delft will perform her MSc thesis at Numeca, possibly in cooperation with OpenEngineering to incorporate strong coupling algorithms based on the work performed in FFAST into the industrial FSI code of Numeca/OpenEngineering.

Further exploitation of the developed methodologies is through new research projects in different research fields (in particular wind energy): AVATAR (FP7 project) and a project within the Computational Science and Engineering program initiated by Shell and arranged by the Dutch national funding agency FOM.

DLR Exploitation Activities:

The ROM methods that have been investigated in the scope of WP2 of this project have all been implemented into official release versions of DLR's Surrogate Modelling for AeroData Toolbox (SMART), which is in use at Airbus Germany for modelling aerodynamic data for loads and for data fusion purposes. SMART is also being used for research purposes by EADS / Cassidian and several German universities. The necessary changes to the LFD solver, which is part of TAU, have also been made to official release versions of TAU. Therefore, there will be a direct transfer of the technology developed in the scope of the FFAST project into the release versions of both SMART and TAU. The release of the new version of SMART containing the FFAST developments are available in a branch of the SMART repository The changes in TAU have already been released with the TAU release 2012.

As SMART is already interfaced with the FlowSimulator software, a parallel simulation environment for large scale applications currently being developed for Airbus and other EADS business units by DLR, the new ROM approaches can fully exploit existing data structures in FSDM for parallel reading, partitioning, storing, repartitioning, grids and snapshots, among other functionalities. This is an important aspect for the industrialization of the new ROM technology, as FlowSimulator is considered the future simulation backbone of the European aeronautics industry.

At DLR, the LFD-ROM capability in the extended SMART toolbox will also be made available to and be used by the DLR Institute of Aeroelasticity for efficient flutter predictions. Students who perform their PhD or MSc thesis work at DLR will be able to perform further research based on the innovative methods that have been implemented into SMART in FFAST.

Finally, DLR will use its gained expertise to apply for new projects and contracts and to enhance its network consisting of other European research organisations, universities and industry. DLR will further exploit the results to further its outstanding academic and scientific reputation by publishing in scientific journals and by enhance its competitiveness as a supplier of aerospace simulation solutions.

IRIAS/IITP Exploitation Activities:

IITP and IRIAS activities have focused on the adaptation of the general Surrogate modelling technology for problems with unsteady flow conditions. The adaptation is based on the inclusion into the technology of emerging mathematical topics such as dimensionality reduction, time-series techniques and manifold learning methods. As the base IITP and IRIAS technology is widely used in EADS projects, there will be a direct transfer of the adapted technology to the customers (majority of which are EADS Business Units).

The adapted surrogate modelling technology will allow the creation of new surrogate models with reasonable accuracy and outstanding computation time that enable usage of optimization techniques at the early stages of aircraft design.

Expertise gained during the project will be used for further development of the technology and its applications in the aerospace industry. The technology will be included into software packages for engineering modelling and optimisation tasks.

The scientific results obtained during the project are included into the courses of lectures ('Predictive modelling', 'Multidimensional statistical analyses', and other) which Prof. Alexander Kuleshov and Prof. Alexander Bernstein give in the Moscow Institute of Physics and Technology and National Research University Higher School of Economics.

University of Liverpool and University of Bristol Exploitation Activities:

It is intended to explore the application of the developed technologies for the efficiently determination of worst case gust loads within the European Aerospace Industry. The University of Bristol is involved in the following projects that will exploit these methodologies:

-ETRIOLLA - FP7 CLEAN-SKY project aimed at designing, manufacturing and testing a transonic wind tunnel model with flow control and load control devices

-ESICAPIA - FP7 CLEAN SKY project aiming at the experimental optimization of a regional jet configuration with the wing designed for natural laminar flow, fuselage mounted engines and a T tail. The project involves design and test of a wind tunnel model

-CONGA - UK TSB funded Aerodynamics Centre project aimed at developing design methodologies for novel aircraft configurations.

Politechnico di Milano Exploitation Activities:

POLIMI will implement indirect exploitation by pursuing its institutional mission, i.e. by training the students with the approaches and tools developed during the FFAST project. Indeed, today's students will be, hopefully, the employees of the Aerospace Industry of tomorrow. More specifically, the techniques made available by FFAST project will be included into graduate courses like Aircraft Design and Aeroelasticity, and will be more deeply developed and implemented in future PhD theses.

NUMECA International S.A. Exploitation Actions:

Two sectors are targeted for exploiting the FFAST results: the aeronautical industry and the turbomachinery industry. The developed ROM-NLH methodology will be communicated at various NUMECA user meetings over the world, with reference to the FFAST project. It will also be exploited in various communication actions through dedicated training sessions and webinars. Since NUMECA is hosting many students in their final years of study as trainees, these actions will also be extended to the student level. NUMECA is involved in several current EU projects, and will communicate and exploit the FFAST ROM-NLH methodology in these projects, where appropriate.

The method developed in the FFAST project forms a basis for future developments. It is already applied, and extended, in a Marie Curie ITN project on the aeroelastic behaviour of off-shore wind turbines. Moreover it will be made available for the industrial sector according to the Fine(TM)/Turbo release plan.

Optimad Engineering S.r.l. Exploitation Activities:

Optimad engineering as a CFD solution provider especially to small and medium-sized entreprises (SME)s will propose this method to its clients to be integrated in their optimization cycle in order to use at their best available solution databases. Reusing available information and still allowing the method to predict the performance of new configurations will reduce development times and cost significantly and will assure that the industry will not remain trapped in the basin of their empirical knowledge. Consequently the continuous quest for competitive products is not biased by this method. These methods are particularly attractive to the automotive industry, for environmental science and engineering and to simulate the interaction between devices in industrial processes.

The knowledge gained in this project has been a seed for development activities within the company. These methods are being included in an optimization toolbox developed by Optimad engineering. Furthermore the positive results encouraged the company to propose research projects in collaboration with universities and industry on bilateral basis and in the framework of regional, national or European initiatives.

Airbus UK Ltd Exploitation Activities:

The FFAST project has always been seen as an upstream research endeavour aimed at exploring the current ideas and methods for using ROMs with unsteady CFD codes, with a view to directing research to provide a robust capability to enhance advanced CFD developments. The research performed in FFAST has shown that the ROMs can be used to enhance CFD capability although the required future CFD developments may prove more challenging. Current CFD/CSM coupling developments being undertaken at Airbus will be reviewed to look for opportunities to investigate some of the FFAST ROM technologies. The worst case load identification technology will be evaluated within projects considering rapid early design developments starting in 2013.

EADS-MAS (Cassidian) Exploitation Activities:

The method of detecting a 'worst case gust' will be considered for structural optimization as a step beyond the obligatory gust analysis. FFAST can be seen as an intermediate research project for achieving the 'big goal' of the future, to calculate fast arbitrary high quality unsteady loads aerodynamic databases, ideally on a laptop. As such, the project may guide research investment.

Conclusion:

The above statements indicate an array of applications for the methods and tools developed in FFAST. For instance the industrial applications are as follows; after minor modifications the developed ROM algorithms are applicable to any CFD code, the technologies can be directly transferred into the release versions of SMART and TAU, the SCUFM tool can be utilized in early aircraft design, the ROM-NHL methodology has industrial relevance, finally the unified solver and quadratic modal ROM technology has the potential contribute to the competitiveness of European Aerospace design. These statements have shown the vast potential to exploit the methods and tools developed by the FFAST project within the aerospace industry.

From a research view point the technologies developed in the FFAST project provide the foundations for future research. The project foreground will be implemented in future research projects aiming to achieve the big goal of developing fast arbitrary unsteady aerodynamic loads databases.

With numerous partners being educational establishments, the exploitation of FFAST result for educational purposes is inevitable. The results from FFAST are being included in teaching programmes for undergraduate design projects, MSc and PhD students. The project partners also include small and medium-sized entreprises (SME)s which employ students in their final years; the results from FFAST therefore may also be used for educational purposes within these companies.

List of Websites:

http://www.ffastproject.org;

http://www.bris.ac.uk/aerodynamics-research/ffast/