PhD thesis proposal in program MOPGA- Make-Our-Planet-Great-Again

Title of the PhD Project : Perpetual Mobile Wind-Turbine With Flexible Blades - System-of-Systems Approach to Analyzing and Optimizing Wind-Energy Farms

Thesis Advisors:

• Mr. Adnan Ibrahimbegovic, Professor Classe Exceptionnelle & IUF Membre Senior Laboratoire Roberval de Mécanique, Université de Technologie Compiègne Phone: +33 (0)3 44 23 45 34, E-mail: adnan.ibrahimbegovic@utc.fr

• Mr. Florian De Vuyst, Professor Laboratoire de Mathématiques Appliquées, Université de Technologie Compiègne Phone: +33 (0)3 44 23 43 61, E-mail: florian.de-vuyst@utc.fr

Abstract of the PhD Project (2000 char. max.): In this thesis we seek to elaborate a new concept of inland wind-turbines with respect to currently dominant system, which was, to a large extent, developed in Denmark and in Northern Germany. Both of these locations provide near steady winds close to optimal conditions for wind-turbines operation. For any other location, the system is far from optimal performance, mostly sitting idle waiting for optimal wind speed. This new concept to evaluate concerns the wind-turbines with flexible blades, which are easy to start for mild winds, like the leaves on a tree, but more difficult to control for strong winds, with large overall motion of flexible blades. There are multiple main scientific challenges in this work seeking a judicious combination of scientific progress in Mechanics, Control and Stochastics in order to provide the simulation tools for elaboration of such a new concept. In particular, we need to develop detailed models capable of describing the large displacements and rotations of flexible blades (including evaluation of risk to blades failure), the reduced basis approach that can furnish the optimal support for control algorithm of large overall motion of flexible blades and stochastic approach able to quantify the effects of variable wind conditions that can be obtained from measurements of wind-turbine deformations by solving an inverse problem. All these developments will be combined in simulation tools, which will be validated against experimental results and more elaborate predictive computations of underlying multi-physics problems. The main product to deliver is to achieve a novel concept of inland wind-turbines, referred to as Perpetual Mobile, which offers the optimal capacity for harvesting energy at large variations of wind speeds and for perfectly adapting to variable conditions inside wind-turbine farms. The side product to deliver concerns the simulation tools to be developed, which will also be of interest for other multi-physics problems.

Keywords (6): wind-turbines ; flexible blades ; nonlinear mechanics ; large motion control ; stochastic inverse problem ; multi-physics validation

Context and motivation (2000 char. max.) : In the quest for renewable energy by means of wind-turbine technology, SoS – System-of-Systems approach can have a significant potential for breakthrough with respect to currently dominant system that was developed in Denmark and in Northern Germany. These locations offer near steady winds providing the optimal conditions for wind-turbines. For any other location, the system is far from optimal performance, mostly sitting idle waiting for optimal wind speed.

We seek to (significantly) improve upon the Danish-German system and bring the optimal performance to in-land wind turbines, by using the flexible blades as the novel idea. The blades flexibility can be an advantage for starting the turbine operation for mild wind (like leaves on a tree), but a disadvantage for keeping the turbine operational and stable in the case of strong winds. Seeking to control the large overall motion and vibration of wind-turbines with flexible blades, is a way that can reduce the risk to failure, especially due to fatigue.

Next to flexible turbine blades and control of large overall motion, the biggest challenge is in quantifying the effect of variable wind speeds, from very small to stormy winds. The challenge is even bigger in seeking the optimal performance of in-land wind turbines placed within the wind farms, which further increases the wind conditions complexity, due to influence of turbulent wakes from closely spaced wind-turbines.

Instead of simulating the wind conditions directly, as the second novel idea, we will seek to quantify their effect indirectly through corresponding measurements of wind turbine deformations. The adequate decision-making procedure on motion control will have to account for stochastic aspects.

In summary, for this class of problems of interest for in-land wind turbines with flexible blades, we will seek to develop the most appropriate combination of computational modeling, control and measurement tools.

Scientific Objectives (2000 char. max.): Most current research related to interconnected technological systems requires a combined knowledge of more than one traditional scientific domain, and present multiple challenges. Here, we will face two main ones.

The first challenge in the present study pertains to modeling and control of flexible structures and systems, such as typical of wind turbines with flexible blades. The wide variety of numerical models based upon the finite element method (Ibrahimbegovic [2009]) can be adapted to provide the discrete approximation of overall large vibrations of structures and mechanical systems, including the most recent models of wind turbines with flexible blades (Ibrahimbegovic et al. [2018]). The main challenge is to provide reduced basis (DeVuyst [2016]) in order to be able to control such a flexible system, and also large overall motion where the equations of motion are no longer linear (Ibrahimbegovic et al. [2004]). Thus, we have to reexamine the system stability with respect to the latest advances in adaptive control (e.g. Brogliato et al. [2008]), with the latter being typical of geometrically exact structural models.

The second challenge is in thorough understanding of the loading conditions of variable winds and the risk to wind turbine failure, especially in fatigue. In this work we formulate novel observers of the structural flexible states of a wind turbine, as well as of the wind incident on its rotor (Botasso [2009]). Stochastic filtering processes (Matthies et al. [2016]) will reconstruct states, with the estimates on the wind-over-the-rotor distribution, seeking to approximate vertical and horizontal wind shear, yawed flow and a vertical wind component. The stochastic estimate procedure will be validated against the refined multi-physics computations (Ibrahimbegovic et al. [2014], Ibrahimbegovic [2016]) and the case studies for the wind conditions measurement for Picardie.

Candidate Desired profile: The successful candidate must hold a Master degree in Mechanical or Civil Engineering, Applied Mathematics, Computational Science or other relevant discipline. He or she will be engaged in tool developments for modeling and numerical simulation of underlying multi-physics problem. Candidates with experience in the multiscale computational modeling of solids and fluids are encouraged to apply. Computer programming experience is required.

International Partnership (optional): The international collaboration in the framework of jointly funded ANR-DFG project with Mr. Hermann Matthies, Professor at TU Braunschweig and laureate of Gay-Lussac-Humboldt Award for France in 2016, will also concern this PhD thesis. This collaboration will in particular deal with stochastic aspects of this analysis, starting with and further extended the results in (Matthies and Ibrahimbegovic [2012]).

Position of the project in relation with the MOPGA scientific domains: Among different themes targeted by MOPGA program, this PhD thesis belongs to the domain of transition towards renewable energy.

Methodology and Planning (3000 char. max.): The smart grid of in-land wind turbines with flexible blades, which can remain in motion for very variable wind speeds, with reduced cost of the control system (Moreno et al. [2018]) is the domain of excellence at UTC developed by Labex MS2T.

The first phase of the present study pertains to modeling and control of flexible structures and systems. The first task is to adapt so-called geometrically exact models based upon the finite element method (Ibrahimbegovic [2009]) that can be used to provide the discrete approximation of overall large vibrations of structures and mechanical systems, such as beams

To be eligible, students must possess a master’s degree or be enrolled in a master-level program, must not be French nationals, and must not have resided in France after April 1, 2016. (see: www.campusfrance.org/en/co-financing-of-3-year-doctoral-contracts)

(Ibrahimbegovic [2002]), shells (Ibrahimbegovic [1997]), or solid models of wind turbines with flexible blades (Ibrahimbegovic [2018]). The model of this kind has to be sufficiently refined in order to provide the most reliable interpretation to the risk of blade failure in fatigue. The next phase is to control such a flexible system, and also large overall motion where the equations of motion are no longer linear (Ibrahimbegovic et al. [2004]). The reduced-order models have to be developed before one attempts to control such flexible system, along with the most appropriate method for long-term computations among those presently available (deVuyste [2016], Matthies [2003]).

The chosen model for large overall motion of flexible system has to be formulated and handled in agreement with passive control framework (Brogliato et al. [2008]). The main advantage of various geometrically exact models of this kind that we can use for flexible blade modeling, is in using efficient representation of finite rotations in terms of quaternion. Interestingly enough, the latter was also used recently (Castillo et al. [2017]) to develop a passive control framework for large overall motion of UAVs (or drone), as 0-d model making use of a (single) large rotation matrix described in terms of quaternion.

The final phase concerns the development of thorough understanding of the loading conditions and the risk to wind turbine failure, especially in fatigue. In this work we want to develop and test a novel approach where the studies of this problem will be placed within the framework of smart systems, with active and sensor-like capabilities (Botasso [2009]). Stochastic filtering processes will reconstruct on-line optimal estimates of the wind states which, improving on the commonly used mean hub-height wind estimates or the point measurements available from on-board anemometers, also include information on the wind-over-the-rotor distribution.

The stochastic estimates of the wind turbine states on the bases of performed measurements will be compared against the results of numerical simulations, where the (artificial) wind conditions can be quantified through corresponding fluid-structure interaction problems. (Kassiotis et al. [2011], Zienkiewicz [2005]), The proposed approach should provide validation and verification of our inverse procedure.

Documents required to apply: Send to adnan.ibrahimbegovic@utc.fr , florian.de-vuyst@utc.fr • Curriculum vitae • Motivation letter • At least two references and/or recommendation letters • A statement of research experience and interests

Location: Université de Technologie de Compiègne (UTC) Laboratory Roberval de Mécanique (Plateform Meca-Math between laboratories Roberval & LMAC)

References: Bottasso C.L., A. Croce, ‘Cascading Kalman Observers of Structural Flexible and Wind States for Wind Turbine Control’, Report DIA-SR 09-02, Dipart. Ingegneria Aerospaziale, Politecnico di Milano, 1-17, (2009) Brogliato, B., Lozano, R., Maschke, B., Egeland, O., ‘Passivity-based control system analysis and design’, Springer Series in Communications and Control Engineering, (2008) Ben Belgacem F., A. Buffa, Y. Maday, ‘The mortar finite elements for 3D Maxwell equations: first results’, SIAM J. Numer. Analysis, 39, 880-901, (2001) Castillo P., M.E. Guerrero-Sanchez, H. Abaunza, R. Lozano, C. Garcia-Beltran and A. Rodriguez-Palacios, ‘Passivity-Based Control for a Micro Air Vehicle Using Unit Quaternions’, J. Appl. Sciences, 7, 1-17, (2017) DeVuyst F., ‘Efficient solvers for time-dependent problems: review of IMEX, LATIN, PARAEXP and PARAREAL algorithms with potential use of exponential type integrators and reduced-order models’, Advanced Modeling and Simulation in Engineering Sciences, 3, 1-14, (2016) Ibrahimbegovic A., 'Stress Resultant Geometrically Exact Shell Theory for Finite Rotations and Its Finite Element Implementation', ASME Applied Mechanics Reviews, 50, 199-226 (1997) Ibrahimbegovic A., R.L. Taylor, ‘On the role of frame-invariance of structural mechanics models at finite rotations’, Computer Methods in Applied Mechanics and Engineering, 191, 5159-5176, (2002) Ibrahimbegovic A., C. Knopf-Lenoir, A. Kucerova, P. Villon, ‘Optimal design and optimal control of elastic structures undergoing finite rotations and deformations’, International Journal for Numerical Methods in Engineering, 61, 2428-2460, (2004) Ibrahimbegovic A., ‘Nonlinear solid mechanics: theoretical formulations and finite element solution methods’, Springer, (2009)

Ibrahimbegovic A., R. Niekamp, C. Kassiotis, D. Markovic, H. Matthies, ‘Code-coupling strategy for efficient development of computer software in multiscale and multiphysics nonlinear evolution problems in computational mechanics’, Advances in Engineering Software, 72, 8-17, (2014) Ibrahimbegovic A., ‘Computational Methods for Solids and Fluids: Multiscale Analysis, Probability Aspects and Model Reduction’, Springer, pp. 1-493, (2016) Ibrahimbegovic, A., Boujelben, A., ‘Long-term simulation of wind turbine structure for distributed loading describing long-term wind loads for preliminary design’, Coupled Systems Mechanics, 7, 233-254, (2018) Kassiotis C., A. Ibrahimbegovic, R. Niekamp, H. Matthies, ‘Partitioned solution to nonlinear fluid-structure interaction problems. Part I: implicit coupling algorithms and stability proof’, Computational Mechanics, 47, 305-323, (2011) Kassiotis C., A. Ibrahimbegovic, R. Niekamp, H. Matthies, ‘Partitioned solution to nonlinear fluid-structure interaction problems. Part II: CTL based software implementation with nested parallelization’, Computational Mechanics, 47, 335-357, (2011) Matthies H., M. Meyer, ‘Nonlinear Galerkin Methods for the Model Reduction of Nonlinear Dynamical Systems’, Computers and Structures 81, 1277–1286, (2003) Matthies H., A. Ibrahimbegovic, ‘Stochastic Multiscale Coupling of Inelastic Processes in Solid Mechanics’, in (eds. M. Papadrakakis, G. Stefanou) ‘Multiscale Modeling and Uncertainty Quantification of Materials and Structures’, Springer, 135-157, (2014) Moreno-Navarro P., A. Ibrahimbegovic, J.L. Perez-Aparicio, ‘Linear elastic mechanical system interacting with coupled thermo-electro-magnetic fields’, Coupled Systems Mechanics, 7, 5-25, (2018) Zienkiewicz O.C., R.L. Taylor, The Finite Element Methods, vols I, II, III, Elsevier, (2005)