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Navier-Stokes Modelling of Offshore Wind Turbines Using the SPH Method

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Navier-Stokes Modelling of Offshore Wind Turbines Using the SPH Method Navier-Stokes modelling of offshore wind turbines using the SPH method Jean-Marie Le Goff Master of Science Thesis KTH School of Industrial Engineering and Management Energy Technology EGI_2017-0071-MSC EKV1197 Division of Heat & Power SE-100 44 STOCKHOLM Master of Science Thesis EGI_2017-0071-MSC EKV1197 Navier-Stokes modelling of offshore wind turbines using the SPH method Jean-Marie Le Goff Approved Examiner Supervisor 2017-08-15 Miroslav Petrov - KTH/ITM/EGI Miroslav Petrov Commissioner Contact person EDF R&D, France Agnès Leroy Christophe Peyrard ABSTRACT This Master Thesis has been realized as a result of an internship supervised by Agnès Leroy and Christophe Peyrard.at LNHE (Laboratoire National d'Hydraulique et Environnement), a part of EDF R&D in Chatou, France. The aim was to use the Smoothed Particle Hydrodynamics (SPH) method in order to study the forces generated by ocean waves on two different offshore wind turbine structures. The SPH method is a Lagrangian computational method, first used in astrophysics but soon extended to the study of free surface flows. Developed by EDF R&D and in cooperation with other institutes and universities, GPUSPH is an open source software based on the SPH method to simulate complex free surface flows. The first part of the internship was dedicated to the study of the forces applied on a monopile structure by breaking waves, while the second part was dedicated to the study of the forces induced on a gravity-based foundation by regular waves. Both studies were done using GPUSPH, and the numerical results are compared to experimental results obtained in 2003 and 2015 within EDF R&D facilities. SAMMANFATTNING Detta examensarbete har resulterat efter en praktikperiod hos LNHE (Laboratoire National d'Hydraulique et Environnement), en del av EDF R&D i Chatou, Frankrike, under handledning av Agnès Leroy och Christophe Peyrard. Syftet var att använda metoden för smoothed particle hydrodynamics (SPH) för att studera krafterna som genereras av vågor på två typer av fundament till havsbaserade vindkraftverk. SPH-metoden är en Lagrange beräkningsmetod, som först användes i astrofysik men snart utvidgades också till studier av fria ytflöden. Vidare har GPUSPH utvecklats av EDF R&D i samarbete med andra institut och universitet, som är en öppen källkodsprogram baserad på SPH- metoden för att simulera komplexa fria ytflöden. Den första delen av arbetet ägnades åt att studera de krafter som brytande vågor tillämpar på en monopile-struktur, medan den andra delen var avsedd för studien av de krafter som inducerades på en tyngdbaserad grundfundament som utsätts för vanliga vågor. Båda studierna gjordes med hjälp av GPUSPH, och de numeriska resultaten jämfördes med tidigare experimentella resultat som uppnåddes år 2003 och 2015 inom EDF:s forskningsanläggningar. Contents Introduction 10 1 Background on offshore wind turbines 11 1.1 Historical reminder about offshore wind power . 13 1.1.1 Offshore wind power in the world and in Europe . 13 1.1.2 Offshore wind power in France . 19 1.2 Questions about fluid dynamics while studying offshore turbine . 20 1.2.1 Simplified mathematical model . 20 1.2.2 Numerical model based on potential flows . 21 1.2.3 Computational fluid dynamics (CFD) . 22 1.2.4 New numerical methods . 22 2 The SPH method 23 2.1 Navier-Stokes equations for weakly compressible flows . 23 2.2 Mathematical principles of the SPH method . 24 2.2.1 Continuous interpolation . 25 2.2.2 Discrete interpolation . 26 2.2.3 Choice of discrete operators . 28 2.2.4 Boundary conditions . 28 2.2.5 Moving objects . 30 3 First studied case : waves breaking on a monopile structure 31 3.1 Description of the experiments . 31 3.2 Description of the shoaling phenomemon . 32 3.3 Features of the GPUSPH simulations . 34 3.3.1 Configurations of the several cases . 34 3.3.2 Numerical options . 35 3.3.3 Construction of the geometry files . 35 3.4 Results and analysis . 37 3.4.1 Computational times . 37 3.4.2 Mean free surface elevation results . 37 3.4.3 Mean horizontal force results . 39 4 Second studied case : waves impacting on a gravity-based foundation (GBF) 43 4.1 Description of the experiments . 43 4.2 Features of the GPUSPH simulations . 43 4.2.1 Configuration of the several cases . 43 4.2.2 Numerical options . 45 4.3 Results and analysis . 45 4.3.1 Computational times . 45 4.3.2 Mean free surface elevation results . 46 4.3.3 Mean horizontal force results . 54 4.3.4 Mean overturning moment results . 59 4.4 Possible improvements . 63 4.4.1 Computational times . 63 1 4.4.2 Mean free surface elevation results . 63 4.4.3 Mean horizontal force results . 64 4.4.4 Mean overturning moment results . 65 Appendix A Consistency of the continuous SPH interpolation 67 Appendix B Plan of the gravity-based foundation 69 Bibliography 71 2 List of Figures 1.1 The Smith-Putnam turbine prototype in Vermont, USA (1940)................ 13 1.2 The Gedser turbine prototype in Gedser, Denmark (1957)................... 14 1.3 Evolution of the size and the power capacity of wind turbine from the 1980’s up to now.. 14 1.4 Share of main countries in European offshore wind power capacity [9]............ 15 1.5 Picture of the different existing offshore wind turbine structures [2]............. 16 1.6 Share of foundations in the European offshore wind farms [2]................. 16 1.7 Hywind, the first tested floating structure from the Norvegian company Statoil (2001)... 17 1.8 Picture of the different existing floating offshore wind turbine structures [26]........ 17 1.9 Windfloat, the structure from the American company Principle Power (installed in 2011). 18 1.10 Floatgen, the floating structure from Ideol, installed by the end 2017............ 18 1.11 The floating structure proposed by the Dutch company SBM Offshore............ 19 1.12 Map presenting the different locations of the French awarded site, and the companies in charge of each project....................................... 20 1.13 Numerical model of the GBF studied by EDF R&D and Innosea [23]............ 21 2.1 Illustration of a 2D-kernel function................................ 25 2.2 Illustration of a 2D-kernel function for discrete particles. The particles b ∈ F are in blue. 27 2.3 Illustration of a 2D-kernel near a boundary ∂Ω......................... 29 2.4 Illustration of a 2D-kernel near a boundary ∂Ω with discrete particles and boundary segments.............................................. 30 3.1 Sketch of the experimental facilites [13]............................. 31 3.2 Scheme of the propagating regular waves arriving in a non constant depth area....... 33 3.3 Representation of the shoaling phenomemon.......................... 34 3.4 Visualization of the 3D modelling of EOL95 case in ParaView................ 35 3.5 Visualization of the 3D particle filling from Crixus for EOL95 case in ParaView. Red particles are fluid particles, blue and gray particles are boundary particles.......... 36 3.6 Visualization of the 3D particle filling around the monopile in ParaView........... 36 3.7 Visualization of the pressure field in the flow induced by the wavemaker in EOL95 case, t = 60 s............................................... 37 3.8 Mean free surface elevation near the pile in EOL95 case.................... 38 3.9 Mean free surface elevation near the pile in EOL96 case.................... 38 3.10 Mean force Fx applied on the pile in EOL95 case........................ 39 3.11 Mean force Fx applied on the pile in EOL96 case........................ 39 3.12 Mean force Fx applied on the pile in EOL54 case........................ 40 3.13 Mean force Fx applied on the pile in EOL79 case........................ 40 4.1 Scheme of the experimental facilites [23]............................. 43 4.2 Visualization of the 3D modelling of GBF02R case in ParaView............... 44 4.3 Visualization of the 3D modelling of the GBF in ParaView.................. 45 4.4 Free surface elevation near the GBF in GBF02R case..................... 46 4.5 Mean free surface elevation near the GBF in GBF02R case.................. 47 4.6 Mean wave height evolution before the GBF in GBF02R case................. 47 4.7 Fourier analysis of the free surface elevation in GBF02R case................. 48 4.8 Free surface elevation near the GBF in GBF04R case..................... 48 3 4.9 Mean free surface elevation near the GBF in GBF04R case.................. 49 4.10 Mean wave height evolution before the GBF in GBF04R case................. 49 4.11 Fourier analysis of the free surface elevation in GBF04R case................. 50 4.12 Free surface elevation near the GBF in GBF05R case..................... 50 4.13 Mean free surface elevation near the GBF in GBF05R case.................. 51 4.14 Mean wave height evolution before the GBF in GBF05R case................. 51 4.15 Fourier analysis of the free surface elevation in GBF05R case................. 52 4.16 Free surface elevation near the GBF in GBFU1R case..................... 52 4.17 Mean free surface elevation near the GBF in GBFU1R case.................. 53 4.18 Mean wave height evolution before the GBF in GBFU1R case................ 53 4.19 Fourier analysis of the free surface elevation in GBFU1R case................. 54 4.20 Forces Fx applied on the GBF in GBF02R case........................ 54 4.21 Mean force Fx applied on the GBF in GBF02R case...................... 55 4.22 Forces Fx applied on the GBF in GBF04R case........................ 56 4.23 Mean force Fx applied on the GBF in GBF04R case...................... 56 4.24 Forces Fx applied on the GBF in GBF05R case........................ 57 4.25 Mean force Fx applied on the GBF in GBF05R case...................... 57 4.26 Over-turning moments My applied on the GBF in GBFU1R case............... 58 4.27 Forces Fx applied on the GBF in GBFU1R case........................ 58 4.28 Mean force Fx applied on the GBF in GBFU1R case....................
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