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Direct Finite Element Simulation of the Turbulent Flow Past a Vertical Axis Wind Turbine
KTH, School of Electrical Engineering and Computer Science (EECS), Computational Science and Technology (CST).ORCID iD: 0000-0002-3213-0040
KTH, School of Electrical Engineering and Computer Science (EECS), Computational Science and Technology (CST).ORCID iD: 0000-0002-1695-8809
Uppsala University, Uppsala, Sweden. (Ångström Laboratory)
KTH, School of Electrical Engineering and Computer Science (EECS), Computational Science and Technology (CST).ORCID iD: 0000-0003-4256-0463
2019 (English)In: Renewable energy, ISSN 0960-1481, E-ISSN 1879-0682, Vol. 135, p. 238-247Article in journal (Refereed) Published
Abstract [en]

There is today a significant interest in harvesting renewable energy, specifically wind energy, in offshore and urban environments. Vertical axis wind turbines get increasing attention since they are able to capture the wind from any direction. They are relatively easy to install and to transport, cheaper to build and maintain, and quite safe for humans and birds. Detailed computer simulations of the fluid dynamics of wind turbines provide an enhanced understanding of the technology and may guide design improvements. In this paper, we simulate the turbulent flow past a vertical axis wind turbine for a range of rotation angles in parked and rotating conditions. We propose the method of Direct Finite Element Simulation in a rotating ALE framework, abbreviated as DFS-ALE. The simulation results are validated against experimental data in the form of force measurements. We find that the simulation results are stable with respect to mesh refinement and that we capture well the general shape of the variation of force measurements over the rotation angles.

Place, publisher, year, edition, pages
Elsevier, 2019. Vol. 135, p. 238-247
Keywords [en]
VAWT, Direct FEM simulation, ALE
National Category
Energy Systems
Research subject
Computer Science; Applied and Computational Mathematics; Vehicle and Maritime Engineering
Identifiers
URN: urn:nbn:se:kth:diva-224801DOI: 10.1016/j.renene.2018.11.098ISI: 000459365600021Scopus ID: 2-s2.0-85058018814OAI: oai:DiVA.org:kth-224801DiVA, id: diva2:1193114
Note

QC 20180326

Available from: 2018-03-26 Created: 2018-03-26 Last updated: 2019-11-01Bibliographically approved
In thesis
1. High-Performance Finite Element Methods: with Application to Simulation of Diffusion MRI and Vertical Axis Wind Turbines
Open this publication in new window or tab >>High-Performance Finite Element Methods: with Application to Simulation of Diffusion MRI and Vertical Axis Wind Turbines
2018 (English)Licentiate thesis, comprehensive summary (Other academic)
Abstract [en]

The finite element methods (FEM) have been developed over decades, and together with the growth of computer engineering, they become more and more important in solving large-scale problems in science and industry. The objective of this thesis is to develop high-performance finite element methods (HP-FEM), with two main applications in mind: computational diffusion magnetic resonance imaging (MRI), and simulation of the turbulent flow past a vertical axis wind turbine (VAWT). In the first application, we develop an efficient high-performance finite element framework HP-PUFEM based on a partition of unity finite element method to solve the Bloch-Torrey equation in heterogeneous domains. The proposed framework overcomes the difficulties that the standard approaches have when imposing the microscopic heterogeneity of the biological tissues. We also propose artificial jump conditions at the external boundaries to approximate the pseudo-periodic boundary conditions which allows for the water exchange at the external boundaries for non-periodic meshes. The framework is of a high level simplicity and efficiency that well facilitates parallelization. It can be straightforwardly implemented in different FEM software packages and it is implemented in FEniCS for moderate-scale simulations and in FEniCS-HPC for the large-scale simulations. The framework is validated against reference solutions, and implementation shows a strong parallel scalability. Since such a high-performance simulation framework is still missing in the field, it can become a powerful tool to uncover diffusion in complex biological tissues. In the second application, we develop an ALE-DFS method which combines advanced techniques developed in recent years to simulate turbulence. We apply a General Galerkin (G2) method which is continuous piecewise linear in both time and space, to solve the Navier-Stokes equations for a rotating turbine in an Arbitrary Lagrangian-Eulerian (ALE) framework. This method is enhanced with dual-based a posterior error control and automated mesh adaptation. Turbulent boundary layers are modeled by a slip boundary condition to avoid a full resolution which is impossible even with the most powerful computers available today. The method is validated against experimental data of parked turbines with good agreements. The thesis presents contributions in the form of both numerical methods for high-performance computing frameworks and efficient, tested software, published open source as part of the FEniCS-HPC platform.

Place, publisher, year, edition, pages
KTH Royal Institute of Technology, 2018. p. 34
Series
TRITA-EECS-AVL ; 2018:3
Keywords
High performance finite element method, computational diffusion MRI, turbulent flow, vertical axis wind turbine.
National Category
Computer and Information Sciences Mathematics
Research subject
Computer Science
Identifiers
urn:nbn:se:kth:diva-225952 (URN)978-91-7729-708-6 (ISBN)
Presentation
2018-05-08, Q33, Osquldas väg 6B, Stockholm, 10:15 (English)
Opponent
Supervisors
Note

QC 20180411

Available from: 2018-04-11 Created: 2018-04-11 Last updated: 2018-05-02Bibliographically approved
2. High Performance Finite Element Methods with Application to Simulation of Vertical Axis Wind Turbines and Diffusion MRI
Open this publication in new window or tab >>High Performance Finite Element Methods with Application to Simulation of Vertical Axis Wind Turbines and Diffusion MRI
2019 (English)Doctoral thesis, comprehensive summary (Other academic)
Abstract [en]

Finite element methods have been developed over decades, and together with the growth of computer power, they become more and more important in dealing with large-scale simulations in science and industry.The objective of this thesis is to develop high-performance finite element methods, with two concrete applications: computational fluid dynamics (CFD) with simulation of turbulent flow past a vertical axis wind turbine (VAWT), and computational diffusion magnetic resonance imaging (CDMRI). The thesis presents contributions in the form of both new numerical methods for high-performance computing frameworks and efficient, tested software, published open source as part of the FEniCS/FEniCS-HPC platform. More specifically, we have four main contributions through the thesis work.

First, we develop a DFS-ALE method which combines the Direct finite element simulation method (DFS) with the Arbitrary Lagrangian-Eulerian method (ALE) to solve the Navier-Stokes equations for a rotating turbine. This method is enhanced with dual-based a posteriori error control and automated mesh adaptation. Turbulent boundary layers are modeled by a slip boundary condition to avoid a full resolution which is impossible even with the most powerful computers available today. The method is validated against experimental data with a good agreement.

Second, we propose a partition of unity finite element method to tackle interface problems. In CFD, it allows for imposing slip velocity boundary conditions on conforming internal interfaces for a fluid-structure interaction model. In CDMRI, it helps to overcome the difficulties that the standard approaches have when imposing the microscopic heterogeneity of the biological tissues and allows for efficient solutions of the Bloch-Torrey equation in heterogeneous domains. The method facilitates a straightforward implementation on the FEniCS/ FEniCS-HPC platform. The method is validated against reference solutions, and the implementation shows a strong parallel scalability.

Third, we propose a finite element discretization on manifolds in order to efficiently simulate the diffusion MRI signal in domains that have a thin layer or a thin tube geometrical structure. The method helps to significantly reduce the required simulation time, computer memory, and difficulties associated with mesh generation, while maintaining the accuracy. Thus, it opens the possibility to simulate complicated structures at a low cost, for a better understanding of diffusion MRI in the brain.

Finally, we propose an efficient portable simulation framework that integrates recent advanced techniques in both mathematics and computer science to enable the users to perform simulations with the Cloud computing technology. The simulation framework consists of Python, IPython and C++ solvers working either on a web browser with Google Colaboratory notebooks or on the Google Cloud Platform with MPI parallelization.

Abstract [sv]

Finita elementmetoder har utvecklats under årtionden, och har, till- sammans med tillväxten i datorkraft, blivit allt viktigare för att utföra storskaliga simuleringar inom både akademin och industrin. Målet med denna avhandling är att utveckla finita elementmetoder med högprestanda, med särskilt fokus på två konkreta applikationer; beräknings- strömningsdynamik (eng. Computational Fluid Dynamics (CFD)) för simulering av turbulent flöde runt en vindturbin, och beräkningar inom diffusionsmagnetresonanstomografi (eng. Computational diffusion magnetic resonance imaging (CDMRI)). Denna avhandling innehåller bidrag till ovanstående områden i form av såväl nya numeriska metoder för högprestandaberäkningsramverk och testad effektiv programvara vilken publicerats som öppen källkod som del av plattformen FEniCS/FEniCS-HPC. Mer specifikt presenterar vi fyra huvudbidrag i detta avhandlingsarbete.

Först utvecklar vi en DFS-ALE-metod som kombinerar Direkt Fini- ta Elementsimulering (DFS) med den Arbiträra Lagrange-Eulermetoden (ALE) för att lösa Navier-Stokes ekvationer för en roterande turbin. Vår metod är en förbättrad variant med dualbaserad a posteriori felkontroll och automatiserad adaptering av beräkningsnätet. Turbulenta gränsskikt modelleras med ett sliprandvillkor för att undvika full upplösning av problemet, vilket är omöjligt även med de mest kraftfulla datorer som finns att tillgå idag. Metoden valideras mot experimentell data, med god överensstämmelse.

Därnäst föreslår vi en enhetspartitions finita element metod för att tackla interfaceproblem. Inom CFD möjliggör detta att påtvinga ett sliprandvillkor på konforma inre interface för en fluidstrukturinter-kationsmodell. Inom CDMRI bidrar det med att överkomma svårigheterna med att påtvinga mikroskopisk heterogenitet av den biologiska vävnaden, och möjliggör effektiv lösning av Bloch-Torrey ekvationen i heterogena domäner. Metoden gör det enklare att göra en rättfram implementering i FEniCS/FEniCS-HPC. Metoden valideras mot referenslösnignar, och implementationen visar på stark parallel skalning (eng. strong parallel scaling).

Sedan föreslår vi en finita elementdisktretisering på mångfalder för att effektivt kunna simulera diffusions-MRI-signaler i områden med en tunn geometrisk struktur. Metoden bidrar med att signifikant reducera simuleringstiden, minnesåtgång och svårigheter associerade med genereringen av beräkningsnät, utan att påverka precisionen i beräkningarna. Detta öppnar för möjligheter att simulera komplicerade strukturer till låg kostnad, för att bättre förstå diffusionsmagnettomografi i hjärnan.

Tilll sist föreslår vi ett effektivt portabelt simuleringsramverk som integrear nya avancerade tekniker inom både matematik och datave- tenskap för att möjliggöra för användaren att utföra simuleringar med datormolnberäkningsteknologin. Simuleringsramverket består av Python, IPython och C++-lösare som används tillsammans antingen i en webbläsare med Google Colaboration notebooks eller på Google Cloud-plattformen med MPI-parallellisering.

Place, publisher, year, edition, pages
KTH Royal Institute of Technology, 2019. p. 53
Series
TRITA-EECS-AVL ; 2019:76
Keywords
High performance finite element method, computational diffusion MRI, turbulent flow, vertical axis wind turbine, Cloud computing., högprestanda finita elementmetod, beräkningsdiffusionsmagnetresonanstomografi, turbulent flöde, vertikalaxlad vindturbin, datormolnberäkning
National Category
Natural Sciences Medical and Health Sciences
Research subject
Applied and Computational Mathematics; Biological Physics; Computer Science; Engineering Mechanics; Mathematics; Physics, Biological and Biomedical Physics
Identifiers
urn:nbn:se:kth:diva-263200 (URN)978-91-7873-337-8 (ISBN)
Public defence
2019-12-04, F3, Lindstedtsvägen 26, Stockholm, 10:15 (English)
Opponent
Supervisors
Note

QC 20191105

Available from: 2019-11-05 Created: 2019-11-01 Last updated: 2019-11-11Bibliographically approved

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Nguyen, Van DangJansson, JohanHoffman, Johan

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