Simulation and optimisation of unsteady aerodynamic performance of a 2D VAWT rotor

105 Pages·2017·3.63 MB·English

by  Greeshma Boohalli Shivamallegowda

Simulation and optimisation of
unsteady aerodynamic per-
formance of a 2D VAWT rotor
With emphasis on airfoil design
Greeshma Boohalli Shivamallegowda
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Simulation and optimisation of unsteady
aerodynamic performance of a 2D VAWT
rotor
With emphasis on airfoil design
by
Greeshma Boohalli Shivamallegowda
to obtain the degree of Master of Science
at the Delft University of Technology,
to be defended publicly on April 23, 2018.
Student number: 4518691
Project duration: April 2017 – April 2018
Thesis committee: Dr. ir. C. J. Simão Ferreira, TU Delft, Wind Energy
Ir. W. A. Timmer, TU Delft, Wind Energy
Dr. R. Dwight, TU Delft, Aerodynamics
Ir. D .A .M De Tavernier, TU Delft, Wind Energy
Cover Image: https://goo.gl/P69SHW.
An electronic version of this thesis is available at https://repository.tudelft.nl/

Abstract
AirfoildesignplaysanimportantroleinimprovingtheperformanceofVerticalAxisWindTur-
bines(VAWTs). The aim of this thesis is to arrive at optimal airfoil geometries to enhance the
performance of VAWTs and analyse the performance of these optimal airfoils under steady
andunsteadyoperationconditionsoftherotor. Theairfoildesignisaimedatrotorsoperating
in the Reynolds number range of 10(cid:4800). The inverse airfoil design approach is used to arrive
at the airfoil geometries. The design process involves formulating a multiobjective optimisa-
tion problem with the aerodynamic and structural performance of the airfoil as objectives.
Afteracomprehensiveliteraturestudy,theobjectivederivedbyFerreiraandGeurts[25]was
chosen for its suitability to the current work. The aerodynamic performance of the airfoil is
gauged by the ratio of lift slope and drag coefficient. The structural objective is limited to
theflapwisebendingstiffness. Toaccountfortheweatherimpact,theaerodynamicobjective
also includes the effect of surface roughness.
An effective optimisation framework is built with the Non-dominated Sorting Genetic
Algorithm(NSGA-II) to arrive at the Pareto front with best suitable airfoils for VAWTs. This
frameworkiscoupledwithXFOILwhichevaluatesthegeometriesandanotherpythonbased
framework, Distributed Evolutionary Algorithms in Python(DEAP) which helps in setting up
the genetic algorithm. Once the convergence is reached, few airfoils from the final Pareto
front are chosen for further analysis.
Based on the literature study, the Actuator Cylinder Model(ACM) was chosen to simulate
theperformanceoftheairfoilsinaVAWTrotor. Theperformanceoftheselectedairfoilswere
analysed under steady flow conditions with the ACM. To account for the effects of unsteady
flow over the airfoil, a Beddoes-Leishman type dynamic stall model formulated by the Risø
national laboratories was integrated into the AC Model loop along with a correction to the
effectiveangleofattack. TheinviscidpartofthismodelwasvalidatedwithanotherACModel
code from Li [42] and the inviscid panel method 𝑈2𝐷𝑖𝑉𝐴 [65].
The performance of the optimised airfoils is an improvement over the performance of the
NACA airfoils of similar thicknesses which proves that the optimisation process has been
successful. The performance of the airfoils in steady flow indicates that the power perfor-
mance of the airfoil suffers more from the surface roughness as the thickness of the airfoil
increases. The thicker airfoils perform better at high solidity applications at low tip speed
ratios. The range of operational tip speed ratios decreases as the airfoils become thicker.
The performance of these airfoils under the effects of unsteady flow under the inviscid flow
assumption provides an overview of the differences in the performance of the airfoils under
unsteadyflowconditions. Therangeoftipspeedratioswheretheairfoilsshowtheirbestper-
formancemovestowardshighervaluesindicatingthatunderunsteadyfloweffects,therotor
needs to operate at a higher rotational velocity to achieve its best performance. However, to
obtainabetterinsightontheperformancesoftheairfoilunderunsteadyfloweffects,further
studies with the complete validated Risø model have to be carried out.
iii

Acknowledgements
”Allwehavetodecideiswhattodowiththetimethatisgiventous.”
-J.R.RTolkien
And I decided to venture to a land far far away from home to pursue postgraduate studies.
As I stand staring at the denouement of my student life in TU Delft, the realisation that I
could not have made it this far on my own hits me harder than usual. So, I will take this as
anopportunitytoacknowledgetheoneswhosepresencewasimperativetothecompletionof
my postgraduate studies.
IwouldliketoexpressmysinceregratitudetomysupervisorDr. Ferreiraforhisguidance
and valuable inputs during the course of my thesis. It is apt to mention that his work on
the VAWTs which I followed during my undergraduate studies was one of my inspirations
to study at TU Delft and I am thankful for that. On the same note, I would like to extend
my gratitude to Delphine De Tavernier for guiding me through the tasks of my thesis with
immensepatience. Herkindwordswereashelpfulashertechnicaladvicewhilecarryingout
my thesis.
I have been fortunate enough to have warm and supportive parents who have always in-
spired me to strive towards bettering myself. I am eternally grateful for their unconditional
love and encouragement which fuel my endeavours. My friend of six years, Geetha Rani has
been putting up with my peevishness and keeping my spirits up throughout these years. I
would like to thank her for her continual efforts to make me stop and smell the roses.
Ithank Deepak, Naina, Ram, and Yeshwanthfor alwaysbeing thereto helpme overcome
the roadblocks I faced during my thesis even when they had very little time to spare. I also
thank Adri, Chinmay, Jaydeep,Marco, Pranav, and Rimit for their support. I found a home
far from home in my friends.
I extend my appreciation to all the members of the former masters’ room, 6.08 which has
acquired a special significance in the past year. Besides the ones I have mentioned, many
others have been helpful in different ways during the last few months. I thank each one of
them for their time and patience.
Lastinorderofoccurrencebutnotofimportance,Iwouldliketothanktheloveofmylifefor
never letting me down. Coffee, I couldn’t have done this without you.
Image: https://goo.gl/DnF982
Greeshma Boohalli Shivamallegowda
Delft, April 2018
v

Contents
ListofFigures ix
1 Introduction 1
1.1 Motivation. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.2 Overviewofthereportstructure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2
2 LiteratureStudyandResearchObjectives 3
2.1 VerticalAxisWindTurbines . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
2.1.1 WorkingPrinciples . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
2.2 SimulationModels . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
2.2.1 DoubleMultipleStreamTubeModel. . . . . . . . . . . . . . . . . . . . . . . . . . 7
2.2.2 VortexModel . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
2.2.3 ComputationalFluidDynamics . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
2.2.4 ActuatorCylinderModel . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8
2.2.5 Comparisonbetweenthemodels . . . . . . . . . . . . . . . . . . . . . . . . . . . 8
2.3 UnsteadyFlowEffects . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9
2.3.1 Flowcurvaturemodeling. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9
2.3.2 DynamicStallModeling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10
2.4 OptimisationofAirfoilDesign . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11
2.5 Researchquestion,aimsandobjectives . . . . . . . . . . . . . . . . . . . . . . . . . . . 12
3 MultiobjectiveOptimisation 15
3.1 MultiobjectiveOptimisation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15
3.2 GeneticAlgorithms. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16
3.3 Non-dominatedSortingGeneticAlgorithm-II . . . . . . . . . . . . . . . . . . . . . . . . . 17
3.4 OptimisationFramework. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19
4 AirfoildesignandOptimisation 21
4.1 InitialPopulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21
4.2 Parametrisationofairfoils . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21
4.3 EvaluationFunction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23
4.3.1 AerodynamicEvaluationFunction. . . . . . . . . . . . . . . . . . . . . . . . . . . 23
4.3.2 StructuralEvaluationFunction. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25
4.4 XFOIL. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26
4.5 ConstraintsandInputs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27
4.5.1 Constraints . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27
4.5.2 Inputs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27
4.6 StructureoftheOptimiser . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29
5 ActuatorCylinderModel 33
5.1 FormulationofACM . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33
5.2 ImplementationofACM . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36
5.3 SteadystateperformanceoftheActuatorCylinderModel . . . . . . . . . . . . . . . . . . 38
6 EffectsofUnsteadyOperationoftherotor 41
6.1 FlowCurvatureEffects. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41
6.1.1 ImplementationofFlowCurvatureEffects . . . . . . . . . . . . . . . . . . . . . . 41
6.2 DynamicStall. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44
6.2.1 DynamicStallModellingwithRisøModel. . . . . . . . . . . . . . . . . . . . . . . 46
6.2.2 Pirrung’sModificationtotheRisøModel . . . . . . . . . . . . . . . . . . . . . . . 49
6.2.3 Directionofapplicationofliftforce. . . . . . . . . . . . . . . . . . . . . . . . . . . 50
6.2.4 Validationofthedynamicstallmodel . . . . . . . . . . . . . . . . . . . . . . . . . 50
vii
viii Contents
7 ResultsandDiscussions 53
7.1 ResultsofOptimisation. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53
7.1.1 EvolutionoftheParetofrontandselectionofAirfoils. . . . . . . . . . . . . . . . . 53
7.2 PerformanceofoptimisedAirfoils . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59
7.2.1 Performanceundersteadyflow . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59
7.2.2 Performanceundertheeffectsofunsteadyflow . . . . . . . . . . . . . . . . . . . 63
7.2.3 Comparisonbetweentheperformancesundersteadyandunsteadyflow. . . . . . 68
8 FinalRemarks 73
8.1 Conclusions. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73
8.2 Recommendations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 75
A LoadDistributiononselectedairfoils 77
A.1 SteadyFlowCondition . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 77
A.2 UnsteadyFlowEffects . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 79
A.3 Comparisonbetweenloadsundersteadyandunsteadyfloweffects . . . . . . . . . . . . 81
B PirrungModificationtotheRisøDynamicStallModel 83
C Implementationofflowcurvatureeffectsintotheoptimisationloop 85
Bibliography 87