Aerodynamic Forces Affecting the H-Rotor Darrieus Wind …turbines are designed as vertical axis...

Research ArticleAerodynamic Forces Affecting the H-Rotor DarrieusWind Turbine

Faris Alqurashi 12 and M H Mohamed23

1Mechanical Engineering Department College of Engineering University of Bisha Bisha 61922 Saudi Arabia2Mechanical Engineering Department College of Engineering and Islamic Architecture Umm Al-Qura University PO 5555Makkah Saudi Arabia3Mechanical Power Engineering Department Faculty of Engineering-Mattaria Helwan University PO 11718 Cairo Egypt

Correspondence should be addressed to Faris Alqurashi fars421hotmailcom

Received 15 April 2019 Revised 9 September 2019 Accepted 3 December 2019 Published 11 January 2020

Academic Editor Michele Calı

Copyright copy 2020 Faris Alqurashi and M H Mohamed -is is an open access article distributed under the Creative CommonsAttribution License which permits unrestricted use distribution and reproduction in anymedium provided the original work isproperly cited

Darrieus wind rotor is a vertical axis wind turbine that is a very promising kind of wind converters at remote and domesticlocations that have soft and weak wind potential and speed but from the quantitative comparison with horizontal axis windturbines this type of turbines has a weak performance Additional researches are still needed to develop its efficiency to identify allthe requirements of the generated power in low power demands -e aim of the current investigation is to analyze all the actingforces on the main parts of Darrieus rotor over the rotations as well as in maintenance and stationary conditions Aerodynamicforces assessment will be executed for 3 different blade shapes (nonsymmetric and symmetric airfoils) like the airfoil sectionshapes of the Darrieus rotor blades NACA 0021 LS413 and S1046 are selected as cross-sectional profile in this work CFDsimulations have been used in this work to get the different aerodynamic forces on the rotor blades of the Darrieus turbines -epresent results indicated that the symmetric S1046 blade has higher forces during the rotation and stagnant (static) conditionsMoreover the self-starting capability of NACA 0021 is better than S1046 due to low aerodynamic torsion on the S1046 blades

1 Introduction

Recently wind energy is a considerable and significantsource of power in the world Wind power must be classifiedas one of the significant growths in the 20th century Fewyears ago steam power stations played a large role in thetechnology of power generation and the fossil fuels wouldseem to have forever relegated to insignificance the role ofthe wind in energy generation Nowadays wind energy is aconsiderable source of electricity in a lot of countries Powerfields which used wind energy are installed with high ca-pacities in most countries of the world Converting thekinetic energy has been introduced by many devices whichcontained movable parts in the direction of wind stream toconvert it into mechanical work and then to electricity by thegenerators Aerodynamic characteristics are themain base inthe wind turbines classifications -e aerodynamic force

acting on an airfoil is conventionally resolved into itscomponents parallel (drag) and normal (lift) to the free-stream velocity vector -erefore the aerodynamic analysisof the turbine is characterized by the following (a) the windturbine that holds and seizes its mechanical energy from theaerodynamic drag force of the wind flow is called drag windturbine (b) the wind turbine that deals with the aerody-namic lift force over the blades airfoils is called lift windturbine By this classification and analysis both of theseturbines are designed as vertical axis wind turbines Inaddition the aerodynamic parameter called ldquotip-speed ratiordquois used to describe the wind turbines performance It isdivided into ldquolow speed turbinesrdquo and ldquohigh speed turbinesrdquoWind turbines classification is divided depending on thepositions and locations of the turbine axis of rotations-erefore it would be assorted into vertical axis windturbine (VAWT) rotating around this normal axis In

HindawiModelling and Simulation in EngineeringVolume 2020 Article ID 1368369 15 pageshttpsdoiorg10115520201368369

addition other patterns rotate about a horizontal axis-erefore they are called horizontal axis wind turbines andthese types are known to the public due to the commercialpervasion

Recently effective and efficient VAWTs were improvedand upgraded to be considerable wind converter Darrieusrotors were invented in the 3rd decade of the twentiethcentury in France Regularly Darrieus rotors consist of 2 or 3blades but these blades are positioned parallel to the rotoraxis -e vertical axis wind turbines (VAWTs) have char-acteristics of simplicity easy design mechanical housing noyaw systems gearboxes and generators and mechanical andelectrical elements are easily reached on ground level-erefore they are characterized by convenient installationsand suitable maintenance Meanwhile there are variousdisadvantages facing this wind rotor like low efficiencydisability and insufficiency to self-starting and no abilityto control the rotor power output -erefore the turbinescontrol speed by using variable pitch angles like other formsof blades Darrieus rotors (with H-shaped blade) are struc-tured instead of conventional curved blades called egg-shapedblades As represented in Figure 1 the designer linked theH-rotor blade to the rotating axis by struts [1]

After this display and definition it is obvious thatDarrieus turbines have a numerous potential for amplifi-cations that were not gained so far Extra money additionalefforts and further time are needed to fulfill optimum designfor this turbine

2 State of the Art and Previous Work Gaps

Recently a lot of interesting attempts and research papers indifferent countries were achieved in the scope area of windturbine to solve the energy problems and crisis in thosecountries In the last twenty years the horizontal axis windturbine received much attention in the development toincrease its performance Meanwhile there is no fine goodand valuable interest for vertical axis wind turbines thatoperate in the urban zones under low wind speed

Vertical axis wind turbine (VAWT) such as Darrieusturbine is particularly important and interesting for urbanzones but it has some drawbacks such as low efficiency andweak power output if it was compared with horizontal axiswind turbine bad self-starting capability is a main disad-vantage in VAWT

Straight blades Darrieus wind turbine which is an ap-propriate alternative and is obtained from the standardshape has even more engaging characteristics as easymanufacturing installation and construction-erefore theDarrieus turbine that has straight blades is called H-rotorDarrieus turbine -e H-rotor system has straight andvertical blades instead of standard shapes that have curvedblades of the Darrieus turbine Directly horizontal strutsconnect the blades and shaft -e position of these struts issometimes on the ends or the middle of the blades as shownin Figure 1 One of the major and essential characteristics ofthe vertical axis wind turbine is the ability to collect windfrom different directions Moreover straightforward andsimple design andmanufacturing lead to easy build as well as

easy installation and maintenance -ese features lead toconsiderably lower costs with comparison to other types ofwind turbines Aerodynamic simulation of this turbine isvery difficult quantitatively and quantitatively due to sep-aration and dynamic stall of the flow around the bladesOptimum design has not been gained yet even if a lot ofconsiderable and significant published researches have al-ready been introduced for this configuration

-rough calculation methods and experiments manypublications have attempted to recognize the major ap-propriate concepts of operation and to enhance the per-formance distinctive of the Darrieus rotor Takahashi et al[2] tried experimentally and numerically to improve theoutput power of the straight wing vertical axis wind turbines(SWVAWTs) by investigating several sectional profiles -edouble multiple stream tube model under transient con-ditions (analytical solution) is performed as a solutionmethod -at method was utilized to deduce the aerody-namic results by Mukinovic et al [3] for the performance ofDarrieus rotors Kumar et al [4] offered an appropriatesystem of Darrieus (H-rotor) turbines using both BEM andCFD methods

A CFD model was introduced by Castelli et al [5] toevaluate and assess the performance of a Darrieus wind rotorunder several conditions -at simulation used a sectionalprofile of NACA 0021 airfoil and the two-dimensionalcampaign to study the turbinersquos performance In order toestimate the aerodynamic efficiency of the H-rotor Darrieuswind turbines Sabaeifard et al [6] deduced some results thathave investigated experimentally and computationallyVarious designs and aerodynamic parameters like sectionalprofiles number of blades and solidities are investigated inthat paper -e optimum design was gained with an optimalpower output coefficient of 036

By testing 20 nonsymmetric and symmetric airfoilsMohamed [7] increased performance of Darrieus turbine

Figure 1 Straight rotor of Darrieus wind turbine

2 Modelling and Simulation in Engineering

He summarized that S1046 sectional profile is the optimalairfoil to construct Darrieus turbines with higher perfor-mance than the other sectional profiles in the current studyBy CFD methodology El-Baz et al [8] improved theaerodynamic power coefficient of the Darrieus H-rotors-is group deduced an optimal configuration with 15higher power coefficient than the conventional turbines

Mohamed evolved in [9] the self-starting capability byusing different methods to fix the problem of the turbinesrsquoself-starting which is the essential disadvantage of theDarrieus rotors Numerically the section profiles withseveral airfoils were studied by Kanyako and Janajreh [10]with the CFD techniques Kanyako and Janajreh tested someairfoils such as S1046 NACA 0015 NACA 0018 and DU-06-W-200 -ey deduced that NACA 0015 has an optimumpower coefficient within low tip-speed range -e effect ofthe Courant-Friedrichs-Lewy (CFL) criterion has beendiscussed by Trivellato and Castelli [11] and they studied theeffect of the angular marching time step on the numericalsimulation results on the accuracy of the Darrieus turbine-e sectional profile and the pitch angle have been examinedby Mohamed et al [12] -ey studied 25 different profiles ofnonsymmetric and symmetric airfoils using the numericalCFD simulations -e authors concluded that LS 413(nonsymmetric) and S1046 (symmetric) were the best air-foils to obtain optimum performance Bianchini et al [13]presented the influence of the chord length on the turbineradius ratio parameter in the tiny turbine utilizing CFDsimulations for three-sectional airfoil shapes in the Darrieusrotor motions Watanabe et al [14] clarified a main impactof the wind accelerations arrangement by calculating thepower coefficient like ldquowind-lensrdquo design

Wind-lens design factors like semiopen angles diffuserlengths and wind-lens locations have been studied as well asthe different section profile shapes -ese researchers con-cluded and deduced that the profile of NACA 0024 is theoptimum and convenient type for Darrieus turbines using awind lens

Aerodynamically most of the above publications haveattempted to raise and boost the efficiency and self-start ofDarrieus turbine Almost all of the experimental and the-oretical publications mentioned above in this section areonly interesting for using traditional symmetric NACA00XX sectional profiles Despite that there is no argument orevidence that NACA sectional profiles are the optimumprofile shapes for these types of VAWTs (H-rotor Darrieusturbines) In addition none of these papers studied thedifferent forces around the blades and whether these bladesconsist of symmetric or nonsymmetric airfoils -erefore inthe preset work the authors investigated the static and thedynamic forces around the blades with different sectionalprofiles such as NACA 0021 LS413 and S1046 to help thedesigners and the manufacturers to select and design thedifferent mechanical parts of the Darrieus turbine

3 Operation Principles

During the air flow of the wind across the turbine and itsblades through the sectional profiles of H-rotor the blade

generates beneficial torque and power Like all rotatingblades in the turbomachinery velocity triangles will beproduced on all points of the blades -ese triangles consistof the relative velocity W that has been created between theflow velocity Va and the peripheral blade speed u asrepresented in Figure 2 -ere is another significant pa-rameter that can be defined as speed ratio λ Speed ratio is aratio between the blade peripheral speed ωR and the freestream wind velocity Uinfin and this ratio is defined as

λ ωR

Uinfin (1)

A straightforward relation is governing the angle ofattack αwith the azimuth angle θ and the speed ratio λ It canbe calculated by (2) -at equation will be deduced from theanalysis of velocity triangles (as shown in Figure 3) asfollows

α tanminus 1 sin θλ + cos θ

1113890 1113891 (2)

where

w

V2c + V2

n

1113969

(3)

where Vc is the velocity (chord base) and Vn are the normalvelocity components

Different aerodynamic forces can be generated on thesectional profile of the blades due to air flow stream throughthe turbine rotors Mainly those forces were called drag andlift forces the drag force FD in the direction of the air flowand the lift force FL perpendicular to the air flow Aero-dynamically these forces have deep relations with the angleof attack α of the wind Occasionally these angles in ir-regular conditions or in pitching cases are called incidenceangles With solving those forces normal forces FN and thetangential forces FT are accountable forces of the torque andpower outputs are gained as shown in Figure 2

-e function between the attack angles azimuth anglesand the speed ratio was formulated by (2) Figure 3 presentsa distinction and singularity of the attack angles as a result ofa variation of the azimuth angles and the speed ratiosthrough all revolutions of the rotations of the H-rotor

-e figure indicates also that within higher speed ratiosλ the attack angle range variations become lower -isimpact is very substantial and it can be considered in thesimulation of Darrieus turbines

Another major parameter that influences the forces onthe sectional profile is the rotor solidity -e solidity is theessential factor to determine shape dimensions of theDarrieus turbines it can be defined as

σ Nc

2R (4)

where N is the number of blades c is length of chord of anyairfoil and R is turbinersquos radius

Several forces and performances of Darrieus H-rotorturbines depend on various factors such as the free streamwind velocity Uinfin output of power P aerodynamic positivetorque T on the axis of rotation and effective rotor area A

Modelling and Simulation in Engineering 3

Via grouping those factors we will obtain some equations ofthe aerodynamic forces torques and power coefficients asfollows

Cm T

(12)ρARU3infin

(5)

Cp P

(12)ρAU3infin

(6)

Cx Fn

(12)ρAU2infin

(7)

CT FT

(12)ρAU2infin

(8)

Cms Ts

(12)ρARU2infin

(9)

where Cp and Cm are the power coefficients and torquecoefficients respectively Furthermore Cx is an axial forcecoefficient and CT is a tangential force coefficient Readersmust pay attention to the fact that all of these factors aredynamic parameters -is means that all of these factorshave been studied through the rotations of the rotorAlthough Cms is the static torques coefficient it was de-fined within the static cases of the turbines like mainte-nance situations Additionally Cms is a very remarkableindex to the self-starting capabilities of the turbines In therecent study all of these factors have been determined toget the complete force analysis over the sectional profileduring the rotation and static conditions (as shown inFigure 4)

4 Methodology and Model Validation

-e modeling plan and the strategy were introduced in thissection to clarify the objectives of simulation estimation ofthe aerodynamic conduct of a Darrieus rotor using severalprofile sections of airfoil -e present work deals withsymmetric and nonsymmetric airfoil shapes (3 airfoils)NACA 0021 (symmetric airfoil) S1046 (symmetric airfoil)and LS413 (nonsymmetric airfoil) as represented in Fig-ure 5 -e target of this work is to obtain the different forcesand torsion dynamically and statically around the blades ofthe turbine -is will help the mechanical designers andmanufacturers to build and construct a Darrieus turbinesafely -e analysis of the turbine is introduced at differentangular velocities with a fixed wind flow velocity equal to

FRFNFL FD

W

Wind

Wind

R

Vc

Va

Vn

u

w

FTRotation

α

α

θ

θ

ω

Figure 2 Velocities and forces distributions of Darrieus turbine airfoils

λ = 2λ = 3λ = 4

λ = 6λ = 8

ndash40ndash30ndash20ndash10

010203040

Ang

le o

f atta

ck α

(deg)

60 120 180 240 300 3600Azimuth angle θ (deg)

Figure 3 -e change of azimuth angle θ with incident angle α forone revolution at various speed ratios λ


9ms -e major geometrical characteristics of the turbinestudied were summarized in Table 1

In the first step in this work an important task is to studythe full numerical models with deep concern -e com-mercial ANSYS software (Fluent) has been applied in thepresent paper for all calculations that have been performedIn CFD techniques a transient case study called ldquoReynoldsAveraged NavierndashStokesrdquo equations (URANS) was studiedusing the ldquoSIMPLE algorithmrdquo for the coupling of pressurevelocity Discretizations were executed by using the finitevolume analysis with second-order upwind scheme for allfactors Incompressible continuity equation of unsteady flowcan be written in tensorial formula as

zui

zt+

zui

zxi

0 (10)

and the momentum equation can be written as

zui

zt+ ui

zui

zxj

minus1ρ

zp

zxi

minusz

zxj

]zui

zxj

+zuj

zxi

minus23δij

zui

zxi

1113888 11138891113890 1113891

+z

zxj

minus ui uj1113872 1113873

(11)

Tangential force

Axial force (thrust)

Wind

TorqueInterface

Blade

BladeBlade Shaft

Figure 4 Distribution of various forces and torque impacting the Darrieus rotor

yc

0 02 04 06 08 1xc

ndash015ndash01

ndash0050

00501

015

NACA 0021

(a)

yc

ndash012ndash008ndash004

0004008012

S1046

0 02 04 06 08 1xc

(b)

ndash008ndash004

0004008012

yc LS(1)ndash0413

0 02 04 06 08 1xc

(c)

Figure 5 Airfoil shapes

Table 1 Darrieus turbine descriptions

Parameter SpecificationsBlade profile NACA 0021 S1046 LS413Number of blades N 3Blade chord length c 00833mRotor radius R 05mRotor height H 1m (two-dimensional simulation)Rotor solidity σ 025Tip-speed ratio λ 1 35Wind speed Uinfin 9ms


During the dynamic forces calculation and by using thesliding mesh model (SMM) the 2D transient flow was ex-ecuted to behold the physics of turbine rotations impactsHowever in the static case slidingmeshmodel (SMM) is notrequired Double tests on convergence were fulfilled -efirst check is relying on the torque coefficients Cm con-vergence criteria that it must be lower than 1 -e secondone is achieved by the residuals that should be lower than10minus 5 at any physical time step (iteration) All the simulationsintroduced that five revolutions are needed to obtain thesteady convergence states Via the mean value the results ofthe last revolution power coefficient and torque coefficienthave been determined -e current study with ultimatesubiterations of 70 to obtain the solutions convergence at allphysical time steps was utilized Computation accomplishedby 8-processor 280GHz clock frequency PC needs a wholeCPU time of about 350 minutes during five cycles -eaccurate mesh evaluation was performed on one configu-ration that has three-blades NACA 0021 sectional profileblades at λ 3 An unstructured mesh was chosen for the fullflow domain with accurate qualities

Mesh on both sides of the interfaces boundaries has thesame number of cell sizes to obtain quicker convergencesexceptionally and the continuity equation Density andquality of unstructured cells in 2D CFD domain werestudied and read through different cell sizes ranging ap-proximately within 55000 and 200000 cells -is workpresents that more than 153200 cells lead to a relativevariance of the output quantities less than 1049 as rep-resented in Figure 6 A reasonable grid of 164200 cells hasbeen held over all the further results due to the calculatingtime

A certain square CFD domain form with convenientdimensions was employed with a considerable ratio betweenthe turbine diameter and the CFD domain lengths that ratioequals 25 as represented in Figure 7 Within the stationaryand rotating zones the grids have been picked out as un-structured grid (see Figure 8) Six layers on the blades wallboundary with a growth rate of 14 have been accomplishedto obtain a small normalized wall distance of y+lt 3 Wallfunctions have been used to be y+lt 3 through the simu-lations of the flow field with a fixed wind speed of 9ms andit will be constant in the whole simulation in the presentproject -ese techniques ware utilized in various

applications by one of the authors of this paper in the dragand lift vertical turbines [15ndash19] Calı et al [20] offered amethod that enhanced recognizing of the influences of panelarrangements and fibre orientations on sail performancesFluid-structure-interaction (FSI) in a symmetric spinnakerwas studied through an integrated CFD-CSM (Computa-tional Structural Mechanics) analysis Numerical simula-tions are also used to compare sail designs and to optimizesail parameters [21]

-e CFD boundary conditions utilized in the simula-tions are given in Figures 7 and 8 Symmetry boundariesvelocity inlet pressure outlet and interfaces between therotating and fixed boundaries were required as shown inFigures 7 and 8 In Table 2 a summery of the CFD boundaryconditions and flow domain dimensions is introduced

-e turbulence models validation was the second stepin the simulations after accomplishing the grid inde-pendence tests -e aerodynamic rapprochement andproximity of power coefficients Cp between the currentmodel and experimental results have been published byCastelli et al [5] It was carried out as well as other CFDoutputs [5 7 12 18 22] as shown in Figure 9 -ecomparison was quantitative and qualitative Further-more it is noted that there are accurate reasonable andconsiderable agreements between the present CFD sim-ulations and the experimental results [5] in the deter-minations of the power output coefficients -e realizablek minus ε turbulence model is used in the present CFD modelwith the aid of standard wall function From this com-parison it is noted that the current CFD methodology isan acceptable strategy to calculate and simulate theperformance of the H-rotor Darrieus turbines -estudied H-rotor blade vertical axis wind turbines in thiswork operate in Reynolds number flow field of the order of105 -e flow speed Uinfin is 9ms during the simulations andthe Reynolds number is equal to approximately 03times105established (chord base) c 005m-e inlet flow turbulenceintensity equals 5 and turbine hydraulic diameter is 1m

-is turbulence model (realizable k minus ε turbulencemodel) was introduced and improved by Shih et al [23]-ismodel is relying on new transport equations for the tur-bulent dissipation rates that upgrade the features of theturbulence model A model critical coefficient (Cmu) that isalready constant in the standard k minus ε model is variable in

0005

01015

02025

03035

Pow

er co

effic

ient

Cp (

ndash)

50000 100000 150000 200000 2500000Grid size (elements)

Figure 6 Mesh independence study by changing the power coefficient Cp with grid size at λ 33


the realizable k minus ε turbulence model -is variable coeffi-cient is function in the mean flow conditions and turbulenceproperties

In the rotating flows separated flow and flow streamunder strong levels of adverse pressure gradient the real-izable k minus ε turbulence model introduces a superb

performance In addition this turbulence model also solvesessential problems in the standard k minus ε model especiallywhen the flow features includes rotation vortices and ex-treme curvature in the streamline

-e word ldquorealizablerdquo means that the model accepts theflow constraints and the mathematical analysis on

Stationary zone Rotating zone

Turbine shaft

Turbine blades

Figure 8 Unstructured grid

Table 2 Mesh and boundary conditions used in the current CFD work

Parameter DescriptionFlow domain Square (50Rtimes 50R)Interfacetype SlidingconformalGridtype UnstructuredtriElements 164200Fluid AirTurbulence model k-ε realizableInlet Velocity inletOutlet Pressure outletShaft No-slip wallBlades No-slip wallSide SymmetryResiduals RMS criteria 1times 10minus 5

Rotating zone

Rotating zoneStationary zone

Blade

BladeBlade

Side (symmetry)

Side (symmetry)

Interface

Interface

Out

let

Inle

t

50R

50R

Shaft

Figure 7 Flow domain


harmonious and normal stresses with the turbulent flowphysics By using vt μtρ the result introducing negativevalues for the normal stress is obtained u2 that are positivequantities ldquononrealizablerdquo To get the realizability (Cμ) mustbe variable by considering it to be a function of the tur-bulence characteristics Transport equations of k and ε in therealizable k minus ε model are written as follows

z

zt(ρk) +

z

zxi

ρkuj1113872 1113873 z

zxi

μ +μt

σk

1113888 1113889zk

zxj

1113890 1113891 + Gk + Gb

minus ρε minus YM + Sk

z

zt(ρε) +

z

zxj

ρεuj1113872 1113873 z

zxj

μ +μt

σε1113888 1113889

zεzxj

1113890 1113891 + ρC1St

minus ρC2ε2

k +vε

radic + C1εεk

C3εGb + St

(12)

where

C1 max 043η

η + 51113890 1113891

η Sk

ε

(13)

where Gk is a function of the generated turbulence kineticenergy Gb is a function of the generated turbulence kineticenergy YM is the fluctuating incompressible diffusion σk

and σε are functions of the turbulent Prandtl numbers Sk

and Sε are user-defined source terms

5 Results and Discussions

A lot of parameters are influencing aerodynamically theperformance of the vertical axis wind turbines -e es-sential forces created over any airfoil are the drag forces andlift forces Lift forces to drag forces ratio is a function ofturbines solidities airfoil section profiles speed ratios andwind speeds -is paper studies the dynamic and staticforces on the airfoils of the turbines through the rotationsand during the static condition like axial forces coefficient(Cx) tangential forces coefficient (CT) torque coefficient(Cm) and static torque coefficient (Cms) -e followingresults can assist the designers and manufacturers tochoose appropriate materials and convenient dimensionsof different elements of the turbines All of those coeffi-cients will be determined from the equations [5ndash9] for theseveral sectional airfoil sectional profiles NACA 0021LS413 and S1046

In Figure 10 the results indicate that turbines thatconsist of LS413 airfoil have higher torque coefficientsEquation (5) is used to calculate the torque coefficient thatis a dynamic moment So this shows that turbines intro-duce larger power outputs that were determined by (6)Moreover readers here should not pay attention to neg-ative signs showing the direction of turbine rotationHowever static torques can be calculated by (9) and itintroduces the capability of turbine self-starting Addi-tionally and at the maintenance terms turbines will bestationary and the static torques (Cms) static thrusts (Cxs)and static tangential forces (CTs) will impact the severalparts and probably failures will occur Figure 11 introducesa rapprochement between the turbines with several

1 2 3 4Speed ratio (λ)

0

01

02

03

04

05

06

Pow

er co

effic

ient

(Cp)

σ = 025(Experimental) Castelli et al [5]Present work(CFD) Castelli et al [5](CFD) Hashem and Mohamed-[18](CFD) Mohamed et al [12](CFD) Sun et al [22](CFD) Mohamed [7]

Figure 9 Present CFD study versus the experimental results of [5] and other CFD results for a Darrieus turbines [5 7 12 18 22]


σ = 025NACA 0021S1046LS413

ndash01

ndash008

ndash006

ndash004

ndash002

0

002

Stat

ic to

rque

coef

ficie

nt (C

ms)

60 120 180 240 300 3600Azimuth angle (θ)

(a)

σ = 025NACA 0021S1046LS413

05

06

07

08

09St

atic

axia

l for

ce co

effic

ient

(Cxs

)

60 120 180 240 300 3600Azimuth angle (θ)

(b)

σ = 0 25NACA 0021S1046LS413

ndash015

ndash01

ndash005

0

005

01

Stat

ic ta

ngen

tial c

oeffi

cien

t (C T

s)

60 120 180 240 300 3600Azimuth angle (θ)

(c)

Figure 11 Static torque static axial force and static tangential force coecient on the Darrieus turbine

0 60 120 180 240 300 360Azimuth angle (θ)

ndash012

ndash01

ndash008

ndash006

ndash004

ndash002

0

Torq

ue co

effic

ient

(Cm

)

σ = 025S1046NACA 0021LS413

Figure 10 Instantaneous dynamic torque coecient on the Darrieus turbine


NACA 0021 LS413 S1046

Pressure distribution at fixed conditions 0 degrees





Figure 12 Pressure distribution at fixed conditions at different configurations


Velocity distribution at fixed conditions 90 degrees





NACA 0021 LS413 S1046

Figure 13 Velocity distribution at fixed conditions at different configurations


sectional prole airfoils (NACA 0021 LS413 and S1046)for that aerodynamic forces coecient It is clear that thereis no massive variation in the static force coecients be-tween the various H-rotor Darrieus turbines apart from thestatic torque coecient of S1046 which is less than theother is gives the advantage that the static torsion on theturbine is smaller with S1046 however the turbine thatconsists of S1046 has the disadvantage of less self-startingability In Figures 12 and 13 the pressure and velocitydistributions are introduced respectively for the dierentturbine designs of the static conditions (0 30 60 90 and105 degrees)

e dynamic loads also are very signicant and im-portant during the mechanical design and manufacturingof the Darrieus turbine therefore the authors investigatedthe instantaneous tangential force and axial force coe-cients as presented in Figures 14 and 15e study analyzedthe forces at every one degree of the azimuth angle for arevolution and also studied the forces for every blade in theturbine individually to show the dynamic stresses and loadson every blade instantaneously Form the gures it is alsonoted that the S1046 blades have higher maximum tan-gential force and axial force coecients than the otherairfoils is means that if the designer selects the turbine

0 60 120 180 240 300 360Azimuth angle (θ)

ndash08

ndash04

0

04

08

12Ta

ngen

tial c

oeffi

cien

t (C T

)

Blade 1λ = 3

S1046LS413NACA 0021

(a)

0 60 120 180 240 300 360Azimuth angle (θ)

Tang

entia

l coe

ffici

ent (C T

)

Blade 2λ = 3

S1046LS413NACA 0021

ndash08

ndash04

0

04

08

12

(b)

0 60 120 180 240 300 360Azimuth angle (θ)

Tang

entia

l coe

ffici

ent (C T

)

Blade 3λ = 3

S1046LS413NACA 0021

ndash08

ndash04

0

04

08

12

(c)

Figure 14 Instantaneous dynamic tangential force coecients on the Darrieus rotor located at every blade


that consists of S1046 he should take into consideration thehigher dynamic loads

6 Conclusions

Vertical axis wind turbine (VAWT) especially Darrieusturbine has the eligibility to work at low and weak windspeed conditions However it has the weakness of minimalaerodynamic performances with comparison to horizontalaxis wind turbines e current paperrsquos target is to assess theaerodynamic performance of the Darrieus H-rotors underthe optimal blade airfoils selected by the previous work andintroduce some details about the dierent forces generated

on the turbine blades during either the rotation or thestagnant (static) conditions CFD simulations based anddepending on the nite volume analysis have been used inthis work under the interface of the ANSYS uent com-mercial code Accordingly some ndings have beenconcluded

(i) ree airfoils that are appropriate for Darrieusturbine (H-rotor) are examined which have higherand suitable aerodynamic performance It is foundthat NACA 0021 S-1046 and LS413 are the mostsuitable airfoils in the literatures ese airfoils aresymmetric airfoils such as NACA 0021 and S-1046however LS413 is a nonsymmetric one

0 60 120 180 240 300 360Azimuth angle (θ)

Blade 1λ = 3

S1046LS413NACA 0021

ndash02

0

02

04

06

08

1

12

14

16A

xial

coef

ficie

nt (C

x)

(a)

0 60 120 180 240 300 360Azimuth angle (θ)

Blade 2λ = 3

S1046LS413NACA 0021

Axi

al co

effic

ient

(Cx)

ndash02

0

02

04

06

08

1

12

14

16

(b)

0 60 120 180 240 300 360Azimuth angle (θ)

Blade 3λ = 3

S1046LS413NACA 0021

Axi

al co

effic

ient

(Cx)

ndash02

0

02

04

06

08

1

12

14

16

(c)

Figure 15 Instantaneous dynamic axial force coecients on the Darrieus rotor located at every blade


(ii) -e k minus ε turbulence model has been utilized in thepresent CFD study with the support of standardwall function

(iii) Quantitatively and qualitatively validation is in-troduced in this paper and it is noted that there isan agreeable approbation between the present CFDsimulations and experimental data [5] during thecalculation of the power output coefficients Fromthis comparison it is noted that current compu-tational fluid dynamic methodology is a precisestrategy to calculate aerodynamically the perfor-mance of a Darrieus turbine

(iv) Axial force coefficients (Cx) tangential force co-efficients (CT) torque coefficients (Cm) and statictorque coefficients (Cms) have been checked in thecurrent work as dynamic and static forces indi-cators on the blades during the rotation and thestatic conditions

(v) -e results indicated that turbines that consist ofLS413 sectional profiles have higher dynamictorque coefficients this deduces that turbines willintroduce a high power output in the normalrotation conditions

(vi) In the maintenance time and the static conditionsthe turbines will be stationary and the static tor-ques (Cms) static thrusts (Cxs) and static tan-gential forces (CTs) are the indicators for thedifferent stress affecting the different parts of theturbine -e results indicated that apart from theS1046 static torque coefficients there is no massivedifference in the aerodynamic static force betweenthe two turbines which is less than the other

(vii) Low static torque gives an advantage that the statictorsion on the turbine is smaller with S1046however the turbine that has been constructedwith S1046 has some disadvantages such as thereduced ability of self-starting

(viii) -e results represented that the S1046 blades havehigher maximum tangential force and axial forcecoefficients than the other airfoils -is means thatif the designer selects the turbine that consists ofS1046 he should take into consideration the higherdynamic loads

Nomenclature

Cm Torque coefficient (ndash)Cp Power coefficient (ndash)c Blade chord length (m)

A Projected area of rotor (m3)T Mechanical torque (Nmiddotm)R Rotor radius (m)Uinfin Wind speed (ms)s Clearance (m)y+ Normalized wall distance (ndash)k Turbulence kinetic energy (Jkg)H Rotor height (m)

N Number of blades (ndash)P Mechanical power (W)u Blade speed (ms)w Relative velocity (ms)Va Free stream velocity (ms)Vn Normal velocity (ms)Vc Chordal velocity (ms)FL Lift force (N)FD Drag force (N)FN Normal force (N)P Mechanical power (W)u Blade speed (ms)w Relative velocity (ms)Va Free stream velocity (ms)

AbbreviationsURANS Unsteady Reynolds Averaged NavierndashStokesSMM Sliding mesh modelVAWT Vertical axis wind turbineHAWT Horizontal axis wind turbineCFL Courant-Friedrichs-LewyCFD Computational fluid dynamicsDMST Double multiple stream tubeSIMPLE Semi-implicit method for pressure-linked

equationsCFL Courant-Friedrichs-Lewy

Greek Symbolsα Angle of attack (deg)σ Rotor solidity (ndash)μ Dynamic viscosity (kgmmiddots)μt Eddy viscosity (kgmmiddots)λ Tip-speed ratio (ndash)θ Azimuth angle (deg)ω Angular velocity (rads)ε Turbulence dissipation rate (Jkgmiddots)]t Turbulence kinematic viscosity (m2s)c Inlet semiopen angle (deg)ρ Density (kgm3)

Subscriptsi j Temporal and spatial tensors

Superscripts Mean Fluctuating

Data Availability

-e data used to support the findings of this study areavailable from the corresponding author upon request

Conflicts of Interest

-e authors declare that they have no conflicts of interest

Acknowledgments

-is project and corroboration were supported financially bythe University of Bisha


References

[1] E Hau Wind Turbines Fundamentals Technologies Appli-cation Economics Springer-Verlag Berlin Heidelberg 3rdedition 2006

[2] S Takahashi J Hamada and Y Takashi ldquoNumerical andexperimental studies of airfoils suitable for vertical axis windturbines and an application of wind-energy collectingstructure for higher performancerdquo in Proceedings of theBeFourth International Symposium on Computational WindEngineering pp 327ndash330 Yokohama Japan July 2006

[3] M Mukinovic G Brenner and A Rahimi ldquoAnalysis ofvertical axis wind turbinesrdquo in New Results in Numerical andExperimental FluidMechanics VII Springer Berlin Germany2010

[4] V Kumar M Paraschivoiu and I Paraschivoiu ldquoLow Rey-nolds number vertical axis wind turbine for marsrdquo WindEngineering vol 34 no 4 pp 461ndash476 2010

[5] M R Castelli A Englaro and E Benini ldquo-e Darrieus windturbine proposal for a new performance prediction modelbased on CFDrdquo Energy vol 36 no 8 pp 4919ndash4934 2011

[6] P Sabaeifard H Razzaghi and A Forouzandeh ldquoDetermi-nation of vertical axis wind turbines optimal configurationthrough CFD simulationsrdquo in Proceedings of the 2012 In-ternational Conference on Future Environment and Energyvol 28 pp 109ndash113 Singapore November 2012

[7] M H Mohamed ldquoPerformance investigation of H-rotorDarrieus turbine with new airfoil shapesrdquo Energy vol 47no 1 pp 522ndash530 2012

[8] A M El Baz A R Refaey Y Mohannad andA W Y Mohammed ldquoComputational modelling of H-typeDarrius vertical axis wind turbine with multi element airfoilbladesrdquo in Proceedings of the IICFD112013 InternationalConference of Fluid Dynamics pp 1ndash9 Alexandria EgyptDecember 2013

[9] M H Mohamed ldquoImpacts of solidity and hybrid system insmall wind turbines performancerdquo Energy vol 57 pp 495ndash504 2013

[10] F Kanyako and I Janajreh ldquoNumerical investigation of fourcommonly used airfoils for vertical axis wind turbinerdquoICREGArsquo14mdashRenewable Energy Generation and ApplicationsSpringer Proceedings in Energy Springer Berlin Germa-nySpringer 2014

[11] F Trivellato and M R Castelli ldquoOn the courant-Friedrichs-Lewy criterion of rotating grids in 2D vertical-axis windturbine analysisrdquo Renewable Energy vol 62 pp 53ndash62 2014

[12] M HMohamed A M Ali and A A Hafiz ldquoCFD analysis forH-rotor Darrieus turbine as a low speed wind energy con-verterrdquo Engineering Science and Technology an InternationalJournal vol 18 no 1 pp 1ndash13 2015

[13] A Bianchini F Balduzzi G Ferrara and L Ferrari ldquoVirtualincidence effect on rotating airfoils in Darrieus wind tur-binesrdquo Energy Conversion and Management vol 111pp 329ndash338 2016

[14] K Watanabe S Takahashi and Y Ohya ldquoApplication of adiffuser structure to vertical-axis wind turbinesrdquo Energiesvol 9 no 6 p 406 2016

[15] A Ramadan K Yousef M Said andM HMohamed ldquoShapeoptimization and experimental validation of a drag verticalaxis wind turbinerdquo Energy vol 151 pp 839ndash853 2018

[16] M Mohammadi M Lakestani and M H Mohamed ldquoIn-telligent parameter optimization of savonius rotor using ar-tificial neural network and genetic algorithmrdquo Energyvol 143 pp 56ndash68 2018

[17] I Hashem M H Mohamed and A A Hafiz ldquoAero-acousticsnoise assessment for wind-lens turbinerdquo Energy vol 118pp 345ndash368 2017

[18] I Hashem and M H Mohamed ldquoAerodynamic performanceenhancements of H-rotor Darrieus wind turbinerdquo Energyvol 142 pp 531ndash545 2018

[19] M H Mohamed G Janiga and D -evenin ldquoPerformanceoptimization of a modified Wells turbine using non-sym-metric airfoil bladesrdquo in Proceedings of the ASME Turbo Expo2008 Power for Land Sea and Air Berlin Germany June2008

[20] M Calı S M Oliveri U Cella M Martorelli A Gloria andD Speranza ldquoMechanical characterization and modeling ofdownwind sailcloth in fluid-structure interaction analysisrdquoOcean Engineering vol 165 pp 488ndash504 2018

[21] J B Braun and L Imas ldquoHigh fidelity CFD simulations inracing yacht aerodynamic analysisrdquo in Proceedings of the 3rdHigh Performance Yacht Design Conference pp 2ndash4 Auck-land New Zealand December 2008

[22] X Sun Y Wang Q An Y Cao G Wu and D HuangldquoAerodynamic performance and characteristic of vortexstructures for Darrieus wind turbine I Numerical methodand aerodynamic performancerdquo Journal of Renewable andSustainable Energy vol 6 no 4 Article ID 043134 2014

[23] T-H Shih W W Liou A Shabbir Z Yang and J Zhu ldquoAnew K-ϵ Eddy viscosity model for high Reynolds numberturbulent flows model development and validationrdquo Com-puters amp Fluids vol 24 no 3 pp 227ndash238 1995


International Journal of

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VLSI Design



Shock and Vibration


Civil EngineeringAdvances in

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Journal of

Advances inOptoElectronics

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Volume 2018

Hindawi Publishing Corporation httpwwwhindawicom Volume 2013Hindawiwwwhindawicom

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Journal of



Journal ofEngineeringVolume 2018

SensorsJournal of



RotatingMachinery


Modelling ampSimulationin EngineeringHindawiwwwhindawicom Volume 2018


Chemical EngineeringInternational Journal of Antennas and

Propagation




Navigation and Observation


Hindawi

wwwhindawicom Volume 2018

Advances in

Multimedia

Submit your manuscripts atwwwhindawicom

addition other patterns rotate about a horizontal axis-erefore they are called horizontal axis wind turbines andthese types are known to the public due to the commercialpervasion

Recently effective and efficient VAWTs were improvedand upgraded to be considerable wind converter Darrieusrotors were invented in the 3rd decade of the twentiethcentury in France Regularly Darrieus rotors consist of 2 or 3blades but these blades are positioned parallel to the rotoraxis -e vertical axis wind turbines (VAWTs) have char-acteristics of simplicity easy design mechanical housing noyaw systems gearboxes and generators and mechanical andelectrical elements are easily reached on ground level-erefore they are characterized by convenient installationsand suitable maintenance Meanwhile there are variousdisadvantages facing this wind rotor like low efficiencydisability and insufficiency to self-starting and no abilityto control the rotor power output -erefore the turbinescontrol speed by using variable pitch angles like other formsof blades Darrieus rotors (with H-shaped blade) are struc-tured instead of conventional curved blades called egg-shapedblades As represented in Figure 1 the designer linked theH-rotor blade to the rotating axis by struts [1]

After this display and definition it is obvious thatDarrieus turbines have a numerous potential for amplifi-cations that were not gained so far Extra money additionalefforts and further time are needed to fulfill optimum designfor this turbine

2 State of the Art and Previous Work Gaps

Recently a lot of interesting attempts and research papers indifferent countries were achieved in the scope area of windturbine to solve the energy problems and crisis in thosecountries In the last twenty years the horizontal axis windturbine received much attention in the development toincrease its performance Meanwhile there is no fine goodand valuable interest for vertical axis wind turbines thatoperate in the urban zones under low wind speed

Vertical axis wind turbine (VAWT) such as Darrieusturbine is particularly important and interesting for urbanzones but it has some drawbacks such as low efficiency andweak power output if it was compared with horizontal axiswind turbine bad self-starting capability is a main disad-vantage in VAWT

Straight blades Darrieus wind turbine which is an ap-propriate alternative and is obtained from the standardshape has even more engaging characteristics as easymanufacturing installation and construction-erefore theDarrieus turbine that has straight blades is called H-rotorDarrieus turbine -e H-rotor system has straight andvertical blades instead of standard shapes that have curvedblades of the Darrieus turbine Directly horizontal strutsconnect the blades and shaft -e position of these struts issometimes on the ends or the middle of the blades as shownin Figure 1 One of the major and essential characteristics ofthe vertical axis wind turbine is the ability to collect windfrom different directions Moreover straightforward andsimple design andmanufacturing lead to easy build as well as

easy installation and maintenance -ese features lead toconsiderably lower costs with comparison to other types ofwind turbines Aerodynamic simulation of this turbine isvery difficult quantitatively and quantitatively due to sep-aration and dynamic stall of the flow around the bladesOptimum design has not been gained yet even if a lot ofconsiderable and significant published researches have al-ready been introduced for this configuration

-rough calculation methods and experiments manypublications have attempted to recognize the major ap-propriate concepts of operation and to enhance the per-formance distinctive of the Darrieus rotor Takahashi et al[2] tried experimentally and numerically to improve theoutput power of the straight wing vertical axis wind turbines(SWVAWTs) by investigating several sectional profiles -edouble multiple stream tube model under transient con-ditions (analytical solution) is performed as a solutionmethod -at method was utilized to deduce the aerody-namic results by Mukinovic et al [3] for the performance ofDarrieus rotors Kumar et al [4] offered an appropriatesystem of Darrieus (H-rotor) turbines using both BEM andCFD methods

A CFD model was introduced by Castelli et al [5] toevaluate and assess the performance of a Darrieus wind rotorunder several conditions -at simulation used a sectionalprofile of NACA 0021 airfoil and the two-dimensionalcampaign to study the turbinersquos performance In order toestimate the aerodynamic efficiency of the H-rotor Darrieuswind turbines Sabaeifard et al [6] deduced some results thathave investigated experimentally and computationallyVarious designs and aerodynamic parameters like sectionalprofiles number of blades and solidities are investigated inthat paper -e optimum design was gained with an optimalpower output coefficient of 036

By testing 20 nonsymmetric and symmetric airfoilsMohamed [7] increased performance of Darrieus turbine

Figure 1 Straight rotor of Darrieus wind turbine









λ ωR

Uinfin (1)



1113890 1113891 (2)

where

w

V2c + V2

n

1113969

(3)






σ Nc

2R (4)





Cm T

(12)ρARU3infin

(5)

Cp P

(12)ρAU3infin

(6)

Cx Fn

(12)ρAU2infin

(7)

CT FT

(12)ρAU2infin

(8)

Cms Ts

(12)ρARU2infin

(9)




FRFNFL FD

W

Wind

Wind

R

Vc

Va

Vn

u

w

FTRotation

α

α

θ

θ

ω


λ = 2λ = 3λ = 4

λ = 6λ = 8


010203040

Ang

le o

f atta

ck α

(deg)






zui

zt+

zui

zxi

0 (10)


zui

zt+ ui

zui

zxj

minus1ρ

zp

zxi

minusz

zxj

]zui

zxj

+zuj

zxi

minus23δij

zui

zxi

1113888 11138891113890 1113891

+z

zxj

minus ui uj1113872 1113873

(11)

Tangential force


Wind

TorqueInterface

Blade

BladeBlade Shaft


yc

0 02 04 06 08 1xc

ndash015ndash01

ndash0050

00501

015

NACA 0021

(a)

yc


0004008012

S1046

0 02 04 06 08 1xc

(b)

ndash008ndash004

0004008012

yc LS(1)ndash0413

0 02 04 06 08 1xc

(c)












0005

01015

02025

03035

Pow

er co

effic

ient

Cp (

ndash)









Turbine shaft

Turbine blades




Rotating zone


Blade

BladeBlade

Side (symmetry)

Side (symmetry)

Interface

Interface

Out

let

Inle

t

50R

50R

Shaft




z

zt(ρk) +

z

zxi

ρkuj1113872 1113873 z

zxi

μ +μt

σk

1113888 1113889zk

zxj

1113890 1113891 + Gk + Gb


z

zt(ρε) +

z

zxj

ρεuj1113872 1113873 z

zxj

μ +μt

σε1113888 1113889

zεzxj

1113890 1113891 + ρC1St

minus ρC2ε2

k +vε

radic + C1εεk

C3εGb + St

(12)

where

C1 max 043η

η + 51113890 1113891

η Sk

ε

(13)








0

01

02

03

04

05

06

Pow

er co

effic

ient

(Cp)




σ = 025NACA 0021S1046LS413

ndash01

ndash008

ndash006

ndash004

ndash002

0

002

Stat

ic to

rque

coef

ficie

nt (C

ms)

60 120 180 240 300 3600Azimuth angle (θ)

(a)

σ = 025NACA 0021S1046LS413

05

06

07

08

09St

atic

axia

l for

ce co

effic

ient

(Cxs

)

60 120 180 240 300 3600Azimuth angle (θ)

(b)

σ = 0 25NACA 0021S1046LS413

ndash015

ndash01

ndash005

0

005

01

Stat

ic ta

ngen

tial c

oeffi

cien

t (C T

s)

60 120 180 240 300 3600Azimuth angle (θ)

(c)


0 60 120 180 240 300 360Azimuth angle (θ)

ndash012

ndash01

ndash008

ndash006

ndash004

ndash002

0

Torq

ue co

effic

ient

(Cm

)

σ = 025S1046NACA 0021LS413



NACA 0021 LS413 S1046













NACA 0021 LS413 S1046





0 60 120 180 240 300 360Azimuth angle (θ)

ndash08

ndash04

0

04

08

12Ta

ngen

tial c

oeffi

cien

t (C T

)

Blade 1λ = 3

S1046LS413NACA 0021

(a)

0 60 120 180 240 300 360Azimuth angle (θ)

Tang

entia

l coe

ffici

ent (C T

)

Blade 2λ = 3

S1046LS413NACA 0021

ndash08

ndash04

0

04

08

12

(b)

0 60 120 180 240 300 360Azimuth angle (θ)

Tang

entia

l coe

ffici

ent (C T

)

Blade 3λ = 3

S1046LS413NACA 0021

ndash08

ndash04

0

04

08

12

(c)




6 Conclusions




0 60 120 180 240 300 360Azimuth angle (θ)

Blade 1λ = 3

S1046LS413NACA 0021

ndash02

0

02

04

06

08

1

12

14

16A

xial

coef

ficie

nt (C

x)

(a)

0 60 120 180 240 300 360Azimuth angle (θ)

Blade 2λ = 3

S1046LS413NACA 0021

Axi

al co

effic

ient

(Cx)

ndash02

0

02

04

06

08

1

12

14

16

(b)

0 60 120 180 240 300 360Azimuth angle (θ)

Blade 3λ = 3

S1046LS413NACA 0021

Axi

al co

effic

ient

(Cx)

ndash02

0

02

04

06

08

1

12

14

16

(c)










Nomenclature









Data Availability




Acknowledgments



References



























RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia









λ ωR

Uinfin (1)



1113890 1113891 (2)

where

w

V2c + V2

n

1113969

(3)






σ Nc

2R (4)





Cm T

(12)ρARU3infin

(5)

Cp P

(12)ρAU3infin

(6)

Cx Fn

(12)ρAU2infin

(7)

CT FT

(12)ρAU2infin

(8)

Cms Ts

(12)ρARU2infin

(9)




FRFNFL FD

W

Wind

Wind

R

Vc

Va

Vn

u

w

FTRotation

α

α

θ

θ

ω


λ = 2λ = 3λ = 4

λ = 6λ = 8


010203040

Ang

le o

f atta

ck α

(deg)






zui

zt+

zui

zxi

0 (10)


zui

zt+ ui

zui

zxj

minus1ρ

zp

zxi

minusz

zxj

]zui

zxj

+zuj

zxi

minus23δij

zui

zxi

1113888 11138891113890 1113891

+z

zxj

minus ui uj1113872 1113873

(11)

Tangential force


Wind

TorqueInterface

Blade

BladeBlade Shaft


yc

0 02 04 06 08 1xc

ndash015ndash01

ndash0050

00501

015

NACA 0021

(a)

yc


0004008012

S1046

0 02 04 06 08 1xc

(b)

ndash008ndash004

0004008012

yc LS(1)ndash0413

0 02 04 06 08 1xc

(c)












0005

01015

02025

03035

Pow

er co

effic

ient

Cp (

ndash)









Turbine shaft

Turbine blades




Rotating zone


Blade

BladeBlade

Side (symmetry)

Side (symmetry)

Interface

Interface

Out

let

Inle

t

50R

50R

Shaft




z

zt(ρk) +

z

zxi

ρkuj1113872 1113873 z

zxi

μ +μt

σk

1113888 1113889zk

zxj

1113890 1113891 + Gk + Gb


z

zt(ρε) +

z

zxj

ρεuj1113872 1113873 z

zxj

μ +μt

σε1113888 1113889

zεzxj

1113890 1113891 + ρC1St

minus ρC2ε2

k +vε

radic + C1εεk

C3εGb + St

(12)

where

C1 max 043η

η + 51113890 1113891

η Sk

ε

(13)








0

01

02

03

04

05

06

Pow

er co

effic

ient

(Cp)




σ = 025NACA 0021S1046LS413

ndash01

ndash008

ndash006

ndash004

ndash002

0

002

Stat

ic to

rque

coef

ficie

nt (C

ms)

60 120 180 240 300 3600Azimuth angle (θ)

(a)

σ = 025NACA 0021S1046LS413

05

06

07

08

09St

atic

axia

l for

ce co

effic

ient

(Cxs

)

60 120 180 240 300 3600Azimuth angle (θ)

(b)

σ = 0 25NACA 0021S1046LS413

ndash015

ndash01

ndash005

0

005

01

Stat

ic ta

ngen

tial c

oeffi

cien

t (C T

s)

60 120 180 240 300 3600Azimuth angle (θ)

(c)


0 60 120 180 240 300 360Azimuth angle (θ)

ndash012

ndash01

ndash008

ndash006

ndash004

ndash002

0

Torq

ue co

effic

ient

(Cm

)

σ = 025S1046NACA 0021LS413



NACA 0021 LS413 S1046













NACA 0021 LS413 S1046





0 60 120 180 240 300 360Azimuth angle (θ)

ndash08

ndash04

0

04

08

12Ta

ngen

tial c

oeffi

cien

t (C T

)

Blade 1λ = 3

S1046LS413NACA 0021

(a)

0 60 120 180 240 300 360Azimuth angle (θ)

Tang

entia

l coe

ffici

ent (C T

)

Blade 2λ = 3

S1046LS413NACA 0021

ndash08

ndash04

0

04

08

12

(b)

0 60 120 180 240 300 360Azimuth angle (θ)

Tang

entia

l coe

ffici

ent (C T

)

Blade 3λ = 3

S1046LS413NACA 0021

ndash08

ndash04

0

04

08

12

(c)




6 Conclusions




0 60 120 180 240 300 360Azimuth angle (θ)

Blade 1λ = 3

S1046LS413NACA 0021

ndash02

0

02

04

06

08

1

12

14

16A

xial

coef

ficie

nt (C

x)

(a)

0 60 120 180 240 300 360Azimuth angle (θ)

Blade 2λ = 3

S1046LS413NACA 0021

Axi

al co

effic

ient

(Cx)

ndash02

0

02

04

06

08

1

12

14

16

(b)

0 60 120 180 240 300 360Azimuth angle (θ)

Blade 3λ = 3

S1046LS413NACA 0021

Axi

al co

effic

ient

(Cx)

ndash02

0

02

04

06

08

1

12

14

16

(c)










Nomenclature









Data Availability




Acknowledgments



References



























RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia



Cm T

(12)ρARU3infin

(5)

Cp P

(12)ρAU3infin

(6)

Cx Fn

(12)ρAU2infin

(7)

CT FT

(12)ρAU2infin

(8)

Cms Ts

(12)ρARU2infin

(9)




FRFNFL FD

W

Wind

Wind

R

Vc

Va

Vn

u

w

FTRotation

α

α

θ

θ

ω


λ = 2λ = 3λ = 4

λ = 6λ = 8


010203040

Ang

le o

f atta

ck α

(deg)






zui

zt+

zui

zxi

0 (10)


zui

zt+ ui

zui

zxj

minus1ρ

zp

zxi

minusz

zxj

]zui

zxj

+zuj

zxi

minus23δij

zui

zxi

1113888 11138891113890 1113891

+z

zxj

minus ui uj1113872 1113873

(11)

Tangential force


Wind

TorqueInterface

Blade

BladeBlade Shaft


yc

0 02 04 06 08 1xc

ndash015ndash01

ndash0050

00501

015

NACA 0021

(a)

yc


0004008012

S1046

0 02 04 06 08 1xc

(b)

ndash008ndash004

0004008012

yc LS(1)ndash0413

0 02 04 06 08 1xc

(c)












0005

01015

02025

03035

Pow

er co

effic

ient

Cp (

ndash)









Turbine shaft

Turbine blades




Rotating zone


Blade

BladeBlade

Side (symmetry)

Side (symmetry)

Interface

Interface

Out

let

Inle

t

50R

50R

Shaft




z

zt(ρk) +

z

zxi

ρkuj1113872 1113873 z

zxi

μ +μt

σk

1113888 1113889zk

zxj

1113890 1113891 + Gk + Gb


z

zt(ρε) +

z

zxj

ρεuj1113872 1113873 z

zxj

μ +μt

σε1113888 1113889

zεzxj

1113890 1113891 + ρC1St

minus ρC2ε2

k +vε

radic + C1εεk

C3εGb + St

(12)

where

C1 max 043η

η + 51113890 1113891

η Sk

ε

(13)








0

01

02

03

04

05

06

Pow

er co

effic

ient

(Cp)




σ = 025NACA 0021S1046LS413

ndash01

ndash008

ndash006

ndash004

ndash002

0

002

Stat

ic to

rque

coef

ficie

nt (C

ms)

60 120 180 240 300 3600Azimuth angle (θ)

(a)

σ = 025NACA 0021S1046LS413

05

06

07

08

09St

atic

axia

l for

ce co

effic

ient

(Cxs

)

60 120 180 240 300 3600Azimuth angle (θ)

(b)

σ = 0 25NACA 0021S1046LS413

ndash015

ndash01

ndash005

0

005

01

Stat

ic ta

ngen

tial c

oeffi

cien

t (C T

s)

60 120 180 240 300 3600Azimuth angle (θ)

(c)


0 60 120 180 240 300 360Azimuth angle (θ)

ndash012

ndash01

ndash008

ndash006

ndash004

ndash002

0

Torq

ue co

effic

ient

(Cm

)

σ = 025S1046NACA 0021LS413



NACA 0021 LS413 S1046













NACA 0021 LS413 S1046





0 60 120 180 240 300 360Azimuth angle (θ)

ndash08

ndash04

0

04

08

12Ta

ngen

tial c

oeffi

cien

t (C T

)

Blade 1λ = 3

S1046LS413NACA 0021

(a)

0 60 120 180 240 300 360Azimuth angle (θ)

Tang

entia

l coe

ffici

ent (C T

)

Blade 2λ = 3

S1046LS413NACA 0021

ndash08

ndash04

0

04

08

12

(b)

0 60 120 180 240 300 360Azimuth angle (θ)

Tang

entia

l coe

ffici

ent (C T

)

Blade 3λ = 3

S1046LS413NACA 0021

ndash08

ndash04

0

04

08

12

(c)




6 Conclusions




0 60 120 180 240 300 360Azimuth angle (θ)

Blade 1λ = 3

S1046LS413NACA 0021

ndash02

0

02

04

06

08

1

12

14

16A

xial

coef

ficie

nt (C

x)

(a)

0 60 120 180 240 300 360Azimuth angle (θ)

Blade 2λ = 3

S1046LS413NACA 0021

Axi

al co

effic

ient

(Cx)

ndash02

0

02

04

06

08

1

12

14

16

(b)

0 60 120 180 240 300 360Azimuth angle (θ)

Blade 3λ = 3

S1046LS413NACA 0021

Axi

al co

effic

ient

(Cx)

ndash02

0

02

04

06

08

1

12

14

16

(c)










Nomenclature









Data Availability




Acknowledgments



References



























RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia




zui

zt+

zui

zxi

0 (10)


zui

zt+ ui

zui

zxj

minus1ρ

zp

zxi

minusz

zxj

]zui

zxj

+zuj

zxi

minus23δij

zui

zxi

1113888 11138891113890 1113891

+z

zxj

minus ui uj1113872 1113873

(11)

Tangential force


Wind

TorqueInterface

Blade

BladeBlade Shaft


yc

0 02 04 06 08 1xc

ndash015ndash01

ndash0050

00501

015

NACA 0021

(a)

yc


0004008012

S1046

0 02 04 06 08 1xc

(b)

ndash008ndash004

0004008012

yc LS(1)ndash0413

0 02 04 06 08 1xc

(c)












0005

01015

02025

03035

Pow

er co

effic

ient

Cp (

ndash)









Turbine shaft

Turbine blades




Rotating zone


Blade

BladeBlade

Side (symmetry)

Side (symmetry)

Interface

Interface

Out

let

Inle

t

50R

50R

Shaft




z

zt(ρk) +

z

zxi

ρkuj1113872 1113873 z

zxi

μ +μt

σk

1113888 1113889zk

zxj

1113890 1113891 + Gk + Gb


z

zt(ρε) +

z

zxj

ρεuj1113872 1113873 z

zxj

μ +μt

σε1113888 1113889

zεzxj

1113890 1113891 + ρC1St

minus ρC2ε2

k +vε

radic + C1εεk

C3εGb + St

(12)

where

C1 max 043η

η + 51113890 1113891

η Sk

ε

(13)








0

01

02

03

04

05

06

Pow

er co

effic

ient

(Cp)




σ = 025NACA 0021S1046LS413

ndash01

ndash008

ndash006

ndash004

ndash002

0

002

Stat

ic to

rque

coef

ficie

nt (C

ms)

60 120 180 240 300 3600Azimuth angle (θ)

(a)

σ = 025NACA 0021S1046LS413

05

06

07

08

09St

atic

axia

l for

ce co

effic

ient

(Cxs

)

60 120 180 240 300 3600Azimuth angle (θ)

(b)

σ = 0 25NACA 0021S1046LS413

ndash015

ndash01

ndash005

0

005

01

Stat

ic ta

ngen

tial c

oeffi

cien

t (C T

s)

60 120 180 240 300 3600Azimuth angle (θ)

(c)


0 60 120 180 240 300 360Azimuth angle (θ)

ndash012

ndash01

ndash008

ndash006

ndash004

ndash002

0

Torq

ue co

effic

ient

(Cm

)

σ = 025S1046NACA 0021LS413



NACA 0021 LS413 S1046













NACA 0021 LS413 S1046





0 60 120 180 240 300 360Azimuth angle (θ)

ndash08

ndash04

0

04

08

12Ta

ngen

tial c

oeffi

cien

t (C T

)

Blade 1λ = 3

S1046LS413NACA 0021

(a)

0 60 120 180 240 300 360Azimuth angle (θ)

Tang

entia

l coe

ffici

ent (C T

)

Blade 2λ = 3

S1046LS413NACA 0021

ndash08

ndash04

0

04

08

12

(b)

0 60 120 180 240 300 360Azimuth angle (θ)

Tang

entia

l coe

ffici

ent (C T

)

Blade 3λ = 3

S1046LS413NACA 0021

ndash08

ndash04

0

04

08

12

(c)




6 Conclusions




0 60 120 180 240 300 360Azimuth angle (θ)

Blade 1λ = 3

S1046LS413NACA 0021

ndash02

0

02

04

06

08

1

12

14

16A

xial

coef

ficie

nt (C

x)

(a)

0 60 120 180 240 300 360Azimuth angle (θ)

Blade 2λ = 3

S1046LS413NACA 0021

Axi

al co

effic

ient

(Cx)

ndash02

0

02

04

06

08

1

12

14

16

(b)

0 60 120 180 240 300 360Azimuth angle (θ)

Blade 3λ = 3

S1046LS413NACA 0021

Axi

al co

effic

ient

(Cx)

ndash02

0

02

04

06

08

1

12

14

16

(c)










Nomenclature









Data Availability




Acknowledgments



References



























RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia









0005

01015

02025

03035

Pow

er co

effic

ient

Cp (

ndash)









Turbine shaft

Turbine blades




Rotating zone


Blade

BladeBlade

Side (symmetry)

Side (symmetry)

Interface

Interface

Out

let

Inle

t

50R

50R

Shaft




z

zt(ρk) +

z

zxi

ρkuj1113872 1113873 z

zxi

μ +μt

σk

1113888 1113889zk

zxj

1113890 1113891 + Gk + Gb


z

zt(ρε) +

z

zxj

ρεuj1113872 1113873 z

zxj

μ +μt

σε1113888 1113889

zεzxj

1113890 1113891 + ρC1St

minus ρC2ε2

k +vε

radic + C1εεk

C3εGb + St

(12)

where

C1 max 043η

η + 51113890 1113891

η Sk

ε

(13)








0

01

02

03

04

05

06

Pow

er co

effic

ient

(Cp)




σ = 025NACA 0021S1046LS413

ndash01

ndash008

ndash006

ndash004

ndash002

0

002

Stat

ic to

rque

coef

ficie

nt (C

ms)

60 120 180 240 300 3600Azimuth angle (θ)

(a)

σ = 025NACA 0021S1046LS413

05

06

07

08

09St

atic

axia

l for

ce co

effic

ient

(Cxs

)

60 120 180 240 300 3600Azimuth angle (θ)

(b)

σ = 0 25NACA 0021S1046LS413

ndash015

ndash01

ndash005

0

005

01

Stat

ic ta

ngen

tial c

oeffi

cien

t (C T

s)

60 120 180 240 300 3600Azimuth angle (θ)

(c)


0 60 120 180 240 300 360Azimuth angle (θ)

ndash012

ndash01

ndash008

ndash006

ndash004

ndash002

0

Torq

ue co

effic

ient

(Cm

)

σ = 025S1046NACA 0021LS413



NACA 0021 LS413 S1046













NACA 0021 LS413 S1046





0 60 120 180 240 300 360Azimuth angle (θ)

ndash08

ndash04

0

04

08

12Ta

ngen

tial c

oeffi

cien

t (C T

)

Blade 1λ = 3

S1046LS413NACA 0021

(a)

0 60 120 180 240 300 360Azimuth angle (θ)

Tang

entia

l coe

ffici

ent (C T

)

Blade 2λ = 3

S1046LS413NACA 0021

ndash08

ndash04

0

04

08

12

(b)

0 60 120 180 240 300 360Azimuth angle (θ)

Tang

entia

l coe

ffici

ent (C T

)

Blade 3λ = 3

S1046LS413NACA 0021

ndash08

ndash04

0

04

08

12

(c)




6 Conclusions




0 60 120 180 240 300 360Azimuth angle (θ)

Blade 1λ = 3

S1046LS413NACA 0021

ndash02

0

02

04

06

08

1

12

14

16A

xial

coef

ficie

nt (C

x)

(a)

0 60 120 180 240 300 360Azimuth angle (θ)

Blade 2λ = 3

S1046LS413NACA 0021

Axi

al co

effic

ient

(Cx)

ndash02

0

02

04

06

08

1

12

14

16

(b)

0 60 120 180 240 300 360Azimuth angle (θ)

Blade 3λ = 3

S1046LS413NACA 0021

Axi

al co

effic

ient

(Cx)

ndash02

0

02

04

06

08

1

12

14

16

(c)










Nomenclature









Data Availability




Acknowledgments



References



























RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia







Turbine shaft

Turbine blades




Rotating zone


Blade

BladeBlade

Side (symmetry)

Side (symmetry)

Interface

Interface

Out

let

Inle

t

50R

50R

Shaft




z

zt(ρk) +

z

zxi

ρkuj1113872 1113873 z

zxi

μ +μt

σk

1113888 1113889zk

zxj

1113890 1113891 + Gk + Gb


z

zt(ρε) +

z

zxj

ρεuj1113872 1113873 z

zxj

μ +μt

σε1113888 1113889

zεzxj

1113890 1113891 + ρC1St

minus ρC2ε2

k +vε

radic + C1εεk

C3εGb + St

(12)

where

C1 max 043η

η + 51113890 1113891

η Sk

ε

(13)








0

01

02

03

04

05

06

Pow

er co

effic

ient

(Cp)




σ = 025NACA 0021S1046LS413

ndash01

ndash008

ndash006

ndash004

ndash002

0

002

Stat

ic to

rque

coef

ficie

nt (C

ms)

60 120 180 240 300 3600Azimuth angle (θ)

(a)

σ = 025NACA 0021S1046LS413

05

06

07

08

09St

atic

axia

l for

ce co

effic

ient

(Cxs

)

60 120 180 240 300 3600Azimuth angle (θ)

(b)

σ = 0 25NACA 0021S1046LS413

ndash015

ndash01

ndash005

0

005

01

Stat

ic ta

ngen

tial c

oeffi

cien

t (C T

s)

60 120 180 240 300 3600Azimuth angle (θ)

(c)


0 60 120 180 240 300 360Azimuth angle (θ)

ndash012

ndash01

ndash008

ndash006

ndash004

ndash002

0

Torq

ue co

effic

ient

(Cm

)

σ = 025S1046NACA 0021LS413



NACA 0021 LS413 S1046













NACA 0021 LS413 S1046





0 60 120 180 240 300 360Azimuth angle (θ)

ndash08

ndash04

0

04

08

12Ta

ngen

tial c

oeffi

cien

t (C T

)

Blade 1λ = 3

S1046LS413NACA 0021

(a)

0 60 120 180 240 300 360Azimuth angle (θ)

Tang

entia

l coe

ffici

ent (C T

)

Blade 2λ = 3

S1046LS413NACA 0021

ndash08

ndash04

0

04

08

12

(b)

0 60 120 180 240 300 360Azimuth angle (θ)

Tang

entia

l coe

ffici

ent (C T

)

Blade 3λ = 3

S1046LS413NACA 0021

ndash08

ndash04

0

04

08

12

(c)




6 Conclusions




0 60 120 180 240 300 360Azimuth angle (θ)

Blade 1λ = 3

S1046LS413NACA 0021

ndash02

0

02

04

06

08

1

12

14

16A

xial

coef

ficie

nt (C

x)

(a)

0 60 120 180 240 300 360Azimuth angle (θ)

Blade 2λ = 3

S1046LS413NACA 0021

Axi

al co

effic

ient

(Cx)

ndash02

0

02

04

06

08

1

12

14

16

(b)

0 60 120 180 240 300 360Azimuth angle (θ)

Blade 3λ = 3

S1046LS413NACA 0021

Axi

al co

effic

ient

(Cx)

ndash02

0

02

04

06

08

1

12

14

16

(c)










Nomenclature









Data Availability




Acknowledgments



References



























RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia



z

zt(ρk) +

z

zxi

ρkuj1113872 1113873 z

zxi

μ +μt

σk

1113888 1113889zk

zxj

1113890 1113891 + Gk + Gb


z

zt(ρε) +

z

zxj

ρεuj1113872 1113873 z

zxj

μ +μt

σε1113888 1113889

zεzxj

1113890 1113891 + ρC1St

minus ρC2ε2

k +vε

radic + C1εεk

C3εGb + St

(12)

where

C1 max 043η

η + 51113890 1113891

η Sk

ε

(13)








0

01

02

03

04

05

06

Pow

er co

effic

ient

(Cp)




σ = 025NACA 0021S1046LS413

ndash01

ndash008

ndash006

ndash004

ndash002

0

002

Stat

ic to

rque

coef

ficie

nt (C

ms)

60 120 180 240 300 3600Azimuth angle (θ)

(a)

σ = 025NACA 0021S1046LS413

05

06

07

08

09St

atic

axia

l for

ce co

effic

ient

(Cxs

)

60 120 180 240 300 3600Azimuth angle (θ)

(b)

σ = 0 25NACA 0021S1046LS413

ndash015

ndash01

ndash005

0

005

01

Stat

ic ta

ngen

tial c

oeffi

cien

t (C T

s)

60 120 180 240 300 3600Azimuth angle (θ)

(c)


0 60 120 180 240 300 360Azimuth angle (θ)

ndash012

ndash01

ndash008

ndash006

ndash004

ndash002

0

Torq

ue co

effic

ient

(Cm

)

σ = 025S1046NACA 0021LS413



NACA 0021 LS413 S1046













NACA 0021 LS413 S1046





0 60 120 180 240 300 360Azimuth angle (θ)

ndash08

ndash04

0

04

08

12Ta

ngen

tial c

oeffi

cien

t (C T

)

Blade 1λ = 3

S1046LS413NACA 0021

(a)

0 60 120 180 240 300 360Azimuth angle (θ)

Tang

entia

l coe

ffici

ent (C T

)

Blade 2λ = 3

S1046LS413NACA 0021

ndash08

ndash04

0

04

08

12

(b)

0 60 120 180 240 300 360Azimuth angle (θ)

Tang

entia

l coe

ffici

ent (C T

)

Blade 3λ = 3

S1046LS413NACA 0021

ndash08

ndash04

0

04

08

12

(c)




6 Conclusions




0 60 120 180 240 300 360Azimuth angle (θ)

Blade 1λ = 3

S1046LS413NACA 0021

ndash02

0

02

04

06

08

1

12

14

16A

xial

coef

ficie

nt (C

x)

(a)

0 60 120 180 240 300 360Azimuth angle (θ)

Blade 2λ = 3

S1046LS413NACA 0021

Axi

al co

effic

ient

(Cx)

ndash02

0

02

04

06

08

1

12

14

16

(b)

0 60 120 180 240 300 360Azimuth angle (θ)

Blade 3λ = 3

S1046LS413NACA 0021

Axi

al co

effic

ient

(Cx)

ndash02

0

02

04

06

08

1

12

14

16

(c)










Nomenclature









Data Availability




Acknowledgments



References



























RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia


σ = 025NACA 0021S1046LS413

ndash01

ndash008

ndash006

ndash004

ndash002

0

002

Stat

ic to

rque

coef

ficie

nt (C

ms)

60 120 180 240 300 3600Azimuth angle (θ)

(a)

σ = 025NACA 0021S1046LS413

05

06

07

08

09St

atic

axia

l for

ce co

effic

ient

(Cxs

)

60 120 180 240 300 3600Azimuth angle (θ)

(b)

σ = 0 25NACA 0021S1046LS413

ndash015

ndash01

ndash005

0

005

01

Stat

ic ta

ngen

tial c

oeffi

cien

t (C T

s)

60 120 180 240 300 3600Azimuth angle (θ)

(c)


0 60 120 180 240 300 360Azimuth angle (θ)

ndash012

ndash01

ndash008

ndash006

ndash004

ndash002

0

Torq

ue co

effic

ient

(Cm

)

σ = 025S1046NACA 0021LS413



NACA 0021 LS413 S1046













NACA 0021 LS413 S1046





0 60 120 180 240 300 360Azimuth angle (θ)

ndash08

ndash04

0

04

08

12Ta

ngen

tial c

oeffi

cien

t (C T

)

Blade 1λ = 3

S1046LS413NACA 0021

(a)

0 60 120 180 240 300 360Azimuth angle (θ)

Tang

entia

l coe

ffici

ent (C T

)

Blade 2λ = 3

S1046LS413NACA 0021

ndash08

ndash04

0

04

08

12

(b)

0 60 120 180 240 300 360Azimuth angle (θ)

Tang

entia

l coe

ffici

ent (C T

)

Blade 3λ = 3

S1046LS413NACA 0021

ndash08

ndash04

0

04

08

12

(c)




6 Conclusions




0 60 120 180 240 300 360Azimuth angle (θ)

Blade 1λ = 3

S1046LS413NACA 0021

ndash02

0

02

04

06

08

1

12

14

16A

xial

coef

ficie

nt (C

x)

(a)

0 60 120 180 240 300 360Azimuth angle (θ)

Blade 2λ = 3

S1046LS413NACA 0021

Axi

al co

effic

ient

(Cx)

ndash02

0

02

04

06

08

1

12

14

16

(b)

0 60 120 180 240 300 360Azimuth angle (θ)

Blade 3λ = 3

S1046LS413NACA 0021

Axi

al co

effic

ient

(Cx)

ndash02

0

02

04

06

08

1

12

14

16

(c)










Nomenclature









Data Availability




Acknowledgments



References



























RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia


NACA 0021 LS413 S1046













NACA 0021 LS413 S1046





0 60 120 180 240 300 360Azimuth angle (θ)

ndash08

ndash04

0

04

08

12Ta

ngen

tial c

oeffi

cien

t (C T

)

Blade 1λ = 3

S1046LS413NACA 0021

(a)

0 60 120 180 240 300 360Azimuth angle (θ)

Tang

entia

l coe

ffici

ent (C T

)

Blade 2λ = 3

S1046LS413NACA 0021

ndash08

ndash04

0

04

08

12

(b)

0 60 120 180 240 300 360Azimuth angle (θ)

Tang

entia

l coe

ffici

ent (C T

)

Blade 3λ = 3

S1046LS413NACA 0021

ndash08

ndash04

0

04

08

12

(c)




6 Conclusions




0 60 120 180 240 300 360Azimuth angle (θ)

Blade 1λ = 3

S1046LS413NACA 0021

ndash02

0

02

04

06

08

1

12

14

16A

xial

coef

ficie

nt (C

x)

(a)

0 60 120 180 240 300 360Azimuth angle (θ)

Blade 2λ = 3

S1046LS413NACA 0021

Axi

al co

effic

ient

(Cx)

ndash02

0

02

04

06

08

1

12

14

16

(b)

0 60 120 180 240 300 360Azimuth angle (θ)

Blade 3λ = 3

S1046LS413NACA 0021

Axi

al co

effic

ient

(Cx)

ndash02

0

02

04

06

08

1

12

14

16

(c)










Nomenclature









Data Availability




Acknowledgments



References



























RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia







NACA 0021 LS413 S1046





0 60 120 180 240 300 360Azimuth angle (θ)

ndash08

ndash04

0

04

08

12Ta

ngen

tial c

oeffi

cien

t (C T

)

Blade 1λ = 3

S1046LS413NACA 0021

(a)

0 60 120 180 240 300 360Azimuth angle (θ)

Tang

entia

l coe

ffici

ent (C T

)

Blade 2λ = 3

S1046LS413NACA 0021

ndash08

ndash04

0

04

08

12

(b)

0 60 120 180 240 300 360Azimuth angle (θ)

Tang

entia

l coe

ffici

ent (C T

)

Blade 3λ = 3

S1046LS413NACA 0021

ndash08

ndash04

0

04

08

12

(c)




6 Conclusions




0 60 120 180 240 300 360Azimuth angle (θ)

Blade 1λ = 3

S1046LS413NACA 0021

ndash02

0

02

04

06

08

1

12

14

16A

xial

coef

ficie

nt (C

x)

(a)

0 60 120 180 240 300 360Azimuth angle (θ)

Blade 2λ = 3

S1046LS413NACA 0021

Axi

al co

effic

ient

(Cx)

ndash02

0

02

04

06

08

1

12

14

16

(b)

0 60 120 180 240 300 360Azimuth angle (θ)

Blade 3λ = 3

S1046LS413NACA 0021

Axi

al co

effic

ient

(Cx)

ndash02

0

02

04

06

08

1

12

14

16

(c)










Nomenclature









Data Availability




Acknowledgments



References



























RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia




0 60 120 180 240 300 360Azimuth angle (θ)

ndash08

ndash04

0

04

08

12Ta

ngen

tial c

oeffi

cien

t (C T

)

Blade 1λ = 3

S1046LS413NACA 0021

(a)

0 60 120 180 240 300 360Azimuth angle (θ)

Tang

entia

l coe

ffici

ent (C T

)

Blade 2λ = 3

S1046LS413NACA 0021

ndash08

ndash04

0

04

08

12

(b)

0 60 120 180 240 300 360Azimuth angle (θ)

Tang

entia

l coe

ffici

ent (C T

)

Blade 3λ = 3

S1046LS413NACA 0021

ndash08

ndash04

0

04

08

12

(c)




6 Conclusions




0 60 120 180 240 300 360Azimuth angle (θ)

Blade 1λ = 3

S1046LS413NACA 0021

ndash02

0

02

04

06

08

1

12

14

16A

xial

coef

ficie

nt (C

x)

(a)

0 60 120 180 240 300 360Azimuth angle (θ)

Blade 2λ = 3

S1046LS413NACA 0021

Axi

al co

effic

ient

(Cx)

ndash02

0

02

04

06

08

1

12

14

16

(b)

0 60 120 180 240 300 360Azimuth angle (θ)

Blade 3λ = 3

S1046LS413NACA 0021

Axi

al co

effic

ient

(Cx)

ndash02

0

02

04

06

08

1

12

14

16

(c)










Nomenclature









Data Availability




Acknowledgments



References



























RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia



6 Conclusions




0 60 120 180 240 300 360Azimuth angle (θ)

Blade 1λ = 3

S1046LS413NACA 0021

ndash02

0

02

04

06

08

1

12

14

16A

xial

coef

ficie

nt (C

x)

(a)

0 60 120 180 240 300 360Azimuth angle (θ)

Blade 2λ = 3

S1046LS413NACA 0021

Axi

al co

effic

ient

(Cx)

ndash02

0

02

04

06

08

1

12

14

16

(b)

0 60 120 180 240 300 360Azimuth angle (θ)

Blade 3λ = 3

S1046LS413NACA 0021

Axi

al co

effic

ient

(Cx)

ndash02

0

02

04

06

08

1

12

14

16

(c)










Nomenclature









Data Availability




Acknowledgments



References



























RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia









Nomenclature









Data Availability




Acknowledgments



References



























RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia


References



























RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia




RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia


Aerodynamic Forces Affecting the H-Rotor Darrieus Wind …turbines are designed as vertical axis...

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Transcript of Aerodynamic Forces Affecting the H-Rotor Darrieus Wind …turbines are designed as vertical axis...