Effect of Blade Inclination Angle.pdf

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Marco Raciti Castellie-mail: [email protected]

Ernesto Beninie-mail: [email protected]

Department of Mechanical Engineering,University of Padova, Via Venezia,

1-35131 Padova, Italy

Effect of Blade Inclination Angleon a Darrieus Wind TurbineThis paper presents a model for the evaluation of energy performance and aerodynamic forces acting on a small helical Darrieus vertical axis wind turbine depending on bladeinclination angle. It consists of an analytical code coupled to a solid modeling softwarecapable of generating the desired blade geometry depending on the desired design geo-metric parameters, which is linked to a nite volume CFD code for the calculation of rotor performance. After describing and validating the model with experimental data, theresults of numerical simulations are proposed on the bases of ve machine architectures,which are characterized by an inclination of the blades with respect to the horizontal plane in order to generate a phase shift angle between lower and upper blade sections of 0 deg, 30 deg, 60 deg, 90 deg, and 120 deg for a rotor having an aspect ratio of 1.5. Theeffects of blade inclination on tangential and axial forces are rst discussed and then theoverall rotor torque is considered as a function of azimuthal position of the blades.Finally, the downstream tip recirculation zone due to the nite blade extension is ana-lyzed for each blade inclination angle, achieving a numerical quantication of the inu-ence of induced drag on rotor performance, as a function of both blade element longi-tudinal and azimuthal positions of the blade itself. DOI: 10.1115/1.4003212

1 Introduction and Background

Recent instabilities of world economy, due to the increasingprice of carbon-derivative fuels along with connected sociopoliti-cal turbulences, have aroused the interest in the production of renewable energy among the most industrialized western nations.

In this scenario, the continuous quest for clean energy is nowfocusing on the local production of electric power, spread in awide area, so as to cooperate with the big electric power plantslocated in just few specic strategic locations of the countries.

One of the most promising resources is wind power associatedwith local production of clean electric power inside built environ-ment such as industrial and residential areas, which has lead to thedevelopment of the so called computational wind engineering.This new discipline has also renewed the interest in vertical axis

wind turbines VAWTs , which present several advantages if com-pared with the classical horizontal-axis wind turbines HAWTs ,primarily

lower cost; lower need of maintenance; lower sound emission; independence from wind directions due to rotor axial-

symmetry; better impact on the environment due to their

tridimensionality.

The vertical axis wind turbine has an inherently nonstationaryaerodynamic behavior mainly due to the continuous variation of the blade angle of attack during the rotation of the machine: Thispeculiarity involves the continuous variation both of the relativevelocity with respect to the blade prole andalthough to a lesserextentof the corresponding Reynolds number. This phenom-enon, typical of slow rotating machines, has a signicant effectboth on the dynamic loads acting on the rotor and on the gener-ated power and, therefore, on performance.

Among others, Templin 1 rst developed a blade element-momentum single streamtube numerical model to predict the per-

formance of a VAWT. Strickland 2,3 developed a blade element-momentum multiple streamtube numerical model to predict theperformance of a VAWT rotor. Paraschivoiu 47 developed ana-lytical and numerical aerodynamic models to investigate the per-formance of VAWT, focusing on the phenomenon of dynamicstall. Mertens 8 developed a blade element-momentum multiplestreamtube model to predict the performances of a fast rotatingVAWT in the skewed ow on a roof.

The complexity of the phenomena involved in the inherentlyunsteady behavior of vertical axis turbines is often impossible toinvestigate through classical aerodynamic tools, such as the theoryof the blade elements, and gives an account of the use of compu-tational uid dynamics CFD aimed at determining the structureof the ow eld vortices, three-dimensional effects, inuence of

spoke shape otherwise impossible to analyze, thanks to its inher-ent ability to determine the aerodynamic components of actionsthrough the integration of the Navier-Stokes equations in theneighborhood of the wind turbine.

Until now wind tunnel tests, involving considerable time andnancial resources, have been the only way to fully characterizethe behavior of a rotor in order to obtain the operating torquecurves for the implementation of the control system.

In CFD simulations, the computer essentially replaces thephysical simulation in the wind tunnel, at least in principle. CFDmethods involve very large amounts of computation even for rela-tively simple problems and their accuracy is often difcult to as-sess when applied to a new problem where prior experimentalvalidation has not been done 9 .

Performing CFD calculations provide knowledge about theow in all its details, such as velocities, pressure, temperature, etc.Further, all types of useful graphical presentations, such as owlines, contour lines, and isolines, are readily available. This stagecan be compared with having completed a wind tunnel study or anelaborate full-scale measurement campaign 10 .

Ferreira et al. 11,12 investigated numerically the effect of dy-namic stall in a 2D single-bladed VAWT, reporting the inuenceof the turbulence model in the simulation of the vortical structuresspread from the blade.

In this work a numerical methodology was developed in orderto predict the performance of a Darrieus rotor model as a functionof the phase shift angle between lower and upper blade sections.

Contributed by the International Gas Turbine Institute of ASME for publication inthe JOURNAL OF TURBOMACHINERY . Manuscript received September 3, 2010; nalmanuscript received September 4, 2010; published online July 15, 2011. Editor:David Wisler.

Journal of Turbomachinery MAY 2012, Vol. 134 / 031016-1Copyright 2012 by ASME

wnloaded From: http://asmedigitalcollection.asme.org/ on 09/30/2014 Terms of Use: http://asme.org/terms


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2 Model Geometry

The aim of this work was to analyze numerically ve helicalDarrieus wind turbines, characterized by a different inclination of the blades with respect to the horizontal plane.

All the helical blades analyzed lye on the surface of a 515 mmradius cylinder, as shown in Fig. 1.

For the sake of clarity, the models were named according to thephase shift angle between lower and upper blade sections in thecase of an equivalent rotor having aspect ratio H / 2R =1.5. Thenumerically tested rotor architectures were instead characterizedby an aspect ratio equal to 1 in order to reduce the total number of mesh elements. Table 1 shows the name and description of theve models, together with their blade inclination with respect tothe horizontal plane.

A single-bladed rotor was analyzed, mainly for two reasons

to reduce the total number of mesh elements and thereafterthe computational time;

to highlight the behavior of a single-blade without the dis-torting effects due to the presence of other blades.

The common features of the tested rotors are summarized inTable 2, both for the real model characterized by an aspect ratioof 1.5 and for the computational one characterized by an aspectratio of 1 .

Figure 2 shows a comparison between Model 0, Model 60, andModel 120 blades.

The blade azimuthal position is identied by the angular coor-dinate of the pressure center of the blade midsection, as can beseen in Fig. 3. For Model 0 conguration, this coordinate alsoidenties the position of all blade sections.

Figure 4 shows a schematic of the survey methodology utilized,

consisting in the coupling of an analytical code to a solid model-

ing software, capable of generating the desired blade geometrydepending on the desired design geometric parameters, which islinked to a nite volume CFD code for the calculation of rotorperformance.

3 Computational Model and ValidationBefore analyzing the models described in the previous section,

a complete validation work based on wind tunnel measurementshas been conducted 13 . The experimental setup consisted in aclassical vertical-bladed Darrieus rotor made of aluminum andcarbon bers using a NACA 0021 blade prole with a chordlength of 85.8 mm, which was tested in Bovisas low turbulencefacility Milan .

A computational domain of rectangular shape has been chosen,having the same wind tunnel external size, as can be seen in Fig.

5: The wall boundary conditions of the model consisted in twolateral walls spaced 2000 mm apart from the wind tunnel center-

Fig. 1 Exemplication of a helical blade developing on thesurface of a cylinder

Table 1 Main features of the ve models

Model name

deg

deg

0 0 90.0030 20 80.1060 40 70.7690 60 62.36

120 80 55.08

Table 2 Comparison between real model and computationalmodel

Real model Computational model

Horizontal section NACA 0021 NACA 0021Chord, c 85.8 mm 85.8 mmRotor radius, R 515 mm 515 mmRotor height, H 1545 mm 1030 mm

Fig. 2 Comparison between Model 0 , Model 60 , and Model 120 blade

Fig. 3 Azimuthal coordinate

031016-2 / Vol. 134, MAY 2012 Transactions of the ASME



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line the wind tunnel measured 4000 mm in width and 3880 mmin height . The rotor axis was placed on the symmetry position of the wind tunnel section. 3D simulations were performed in orderto take into account also the drag effect induced by the spokes.Only half of the experimental setup was modeled due to its verti-cal symmetry: In this case a symmetry boundary condition wasused. Anyway, the geometrical features of the model did not allowother simplications to be performed. Table 3 shows the valida-tion model main features. The effect of gravity on the rotor work-ing curves has not been contemplated, being considered not inu-ential for the scope of this work.

Inlet and outlet boundary conditions were placed respectively10 diameters upwind and 14 diameters downwind of the rotor,allowing a full development of the wake, as suggested by thework of Ferreira et al. 11 .

The correction due to wind tunnel blockage was not applied inorder to minimize any sources of error due to a wrong estimationof the blockage of the wind tunnel itself. Furthermore, this choicehas the signicant advantage of reducing the computational do-main, allowing a saving in the total number of mesh elements. Thecorrection of the friction resistive torque due to the bearings wastaken into account.

As the aim of the present work was to reproduce the operationof a rotating machine, the use of moving sub-grids was necessary.The simulation domain was divided in two sub-grids

Rotor sub-grid , rotating with angular velocity Fig. 6 ; Wind Tunnel sub-grid , xed.

An isotropic unstructured mesh was chosen for the Rotor sub-grid in order to guarantee the same accuracy in the prediction of rotors performance during the rotationaccording to the studiesof Commings, Forsythe, Morton, and Squires 14 and also inorder to test the prediction capability of a very simple grid. Con-sidering their features of exibility and adaption capability, un-structured meshes are in fact very easy to obtain, also for complex

geometries, and often represent the rst attempt in order to geta quick response from the CFD in engineering work.An unstructured mesh was chosen also for the Wind Tunnel

sub-grid in order to reduce engineering time to prepare the CFDsimulations. An interface boundary condition was assigned to theinterface between the Rotor sub-grid and the Wind Tunnel sub-grid .

In order to control the size of mesh elements near the surface of the blade, the latter was placed inside a 400 mm diameter controlcylinder Fig. 7 . An interior boundary condition was assigned tothe interface between the control cylinder and the remaining Rotor sub-grid mesh.

The computational grids were constructed from lower topolo-gies to higher ones, adopting appropriate size functions Fig. 8 , inorder to cluster grid points near the leading edge and the trailingedge of the blade prole, so as to improve the CFD code capabil-ity of determining lift, drag, and the separation of the ow fromthe blades itself. Mesh density was also based on the local curva-ture of the blade elements.

As a nal step, the mesh elements have been fully convertedinto polyhedra. This option, applicable to unstructured mesh of tetrahedral type, has the advantage of reducing the total number of grid elements, producing in the same time greater mesh regularity,as shown in Figs. 9 and 10.

Because conversion into polyhedra is a very resource intensiveprocess, two separate les were created for the Rotor sub-grid andthe Wind Tunnel sub-grid . It was thus possible to convert the two

Fig. 4 Schematic of the survey methodology

Fig. 5 Computational domain validation model

Table 3 Validation model main features

Prole type NACA 0021c 85.8 mmR 515 mmH 1456.4 mmA 1.236 m 2

0.25Spoke-blade connection 0.5 cWind tunnel dimensions 4000 3800 mm 2

Fig. 6 Rotor sub-grid mesh validation model

Fig. 7 Control cylinder validation model

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main grid areas independently and then to reassemble them into asingle le.

The conversion into polyhedra has achieved a 6070% reduc-tion in the total element number. On the other hand, a polyhedragrid occupies the memory of a tetraheda almost twice. The totalbudget is therefore favorable to polyhedra, even considering thefact that a polyhedral mesh shows more marked regularity fea-tures than the corresponding tetrahedral one and therefore allowsa much faster convergence.

In order to test the code sensitivity to the number of grid points,three unstructured meshes were adopted for the Rotor sub-grid ,while the Wind Tunnel sub-grid remained substantially the same.

After some corrections to take into account spoke drag, theaverage torque values measured in the wind tunnel for a 9 m/swind speed and different tip speed ratios were compared withthose obtained from CFD analysis for the three different gridscharacterized by different blade size function values and three

different turbulence models k- SST, k- realizable, and SpalartAllmaras Table 4 .

Figures 11 and 12 show the evolution of the instantaneoustorque coefcient, dened as

CT =M

1/ 2 A V2 R1

as a function of the azimuthal position for two different meshesand for the three adopted turbulence models.

The nal choice was mesh mod A, based on a better distributionof the blade y + parameter and k- SST turbulence model becauseof its better ability to describe ow separation 1517 , whichoccurs in ow elds dominated by adverse pressure gradients,even if it has shown a certain sensitivity to grid size 18 . Stan-dard wall functions were used to model the boundary layer.

The temporal discretization has been achieved by imposing atime step equal to the lapse of time the rotor takes to make a 1 degrotation. An improved spatial-discretization simulation did notshow any signicant variation.

The commercial CFD package used was FLUENT 6.3.26, whichimplements 3-D Reynolds-averaged NavierStokes equations us-ing a nite volume-nite element based solver. The uid was as-

Fig. 8 Blade size functions

Fig. 9 Improved mesh regularity after conversion into polyhe-dra 1

Fig. 10 Improved mesh regularity after conversion into poly-hedra 2

Table 4 Grid and turbulence models used for calculations

MeshMaximum blade element size

mm Turbulence model

Mod 0 2 k- k- SST S-AMod A 3 k- k- SST S-AMod B 3.5 k- k- SST S-A

Fig. 11 Effect of grid resolution on the instantaneous torquefor a single-bladed rotor turbulence model: k- SST

Fig. 12 Effect of turbulence model on the instantaneoustorque for a three-bladed rotor mod A mesh




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sumed to be incompressible, being the maximum uid velocity onthe order of 60 m/s.

The simulations, performed on an 8 processor, 2.33 GHz clock frequency computer, have been run until the instantaneous torquevalues showed a deviation of less than 1% compared with thecorresponding values of the previous period. Total CPU time hasbeen about 20 days for each simulation.

4 Model AnalysisThe ve helical models have kept some common points with

the validation model, particularly as far as the chord length andthe rotor radius are concerned. The blade-spoke connection pointhas been changed, since it had been placed in the center of pres-sure of the prole, corresponding to 25% of the chord lengthbehind the blade leading edge, while in the validation model it hadbeen placed close to 50%. The analysis of the impact of thisvariation on the parameter y + showed no signicant effect, mainlydue to the fact that in fast rotating machines, the values of bladerelative velocity are determined primarily by the angular velocityof the rotor itself and to a lesser extent by the speed of undis-turbed air ow.

In order to control the size of mesh elements near the surface of the blade, the latter was placed inside a control cylindroid, whichwas in turn subdivided into 20 equal subvolumes, numbered from1 to 20 from top downward Fig. 13 . This choice has also provedextremely useful in order to study blade tip effects, allowing toanalyze the contributions to torque generation of any single bladesubelement.

The validation model was made of straight blades: It was there-fore possible to proceed to the analysis of only half the model,exploiting the symmetry with respect to the median horizontalplane. The helical models do not show any symmetry: It wastherefore necessary to simulate the whole rotor.

The external size of the computational domain was changed: In

the validation model the Wind Tunnel sub-grid had to reproducethe geometry of the wind tunnel Table 5 . In order to avoid block-

age effects due to the proximity to wind tunnel walls, the compu-tational domain for the ve helical models has been enlarged,allowing to analyze the behavior of the rotor in an open ow eld.This additional change from validation model was limited to theouter portions of the computational domain and it was thereforeconsidered negligible with respect to the values of blade y + Figs.14 and 15 .

The decision to increase the size of the computational domainhas led to an unusual hourglass shape for the Rotor sub-grid . In

order to avoid a rotating cylindrical grid as tall as the whole com-putational domain, a short cylindrical grid was connected to theupper and lower surfaces using two truncated cone elements. Themesh element inside these cones are characterized by the samegrowth rate from the lateral surface of the central cylinder to theouter surface of the computational domain.

Figure 16 shows the central element of the Rotor sub-grid . Theclustering of grid points inside the Rotor sub-grid can be seen.

The choice to extend the rotating mesh to the upper and lowersurfaces of the computational domain was dictated by the need not

Fig. 13 Blade subdivision into 20 zones, numbered from 1 to20 from top downward

Table 5 Comparison between validation model and computa-tional model

Validation model Computational model

c 85.8 mm 85.8 mmR 515 mm 515 mmH 1456.4 mm 1030 mmSpoke-blade connection 0.5 c 0.25 c

Fig. 14 Computational domain and relative mesh computa-tional model, 1

Fig. 15 Computational domain and relative mesh computa-tional model, 2

Fig. 16 Rotor sub-grid mesh for Model 0 computationalmodel




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to create interfaces parallel to the principal ow direction, whichcould cause numerical problems especially with regard to Omegaresiduals, as can be seen in Figs. 17 and 18.

5 Results and Discussion

Figure 19 represents the ve helical model power curves for anincident wind speed of 9 m/s as a function of the tip speed ratio,dened as

= R / V 2

The power coefcients do not show signicant differencessince the phase shift angle between lower and upper blade sec-tions is lower than 60 deg. For Model 90 and Model 120 thepower coefcients show a marked decrease and the optimum tipspeed ratios show a small increase.

Figure 20 shows the distribution of instantaneous torque coef-cient as a function of azimuthal position of rotor Model 0 , Model60 , and Model 120 , for a tip speed ratio of 3.36. Once more,

signicant differences depending on the phase shift angle betweenlower and upper blade sections are visible.

The rst maximum torque peak at 96 deg azimuthal positionis however the same for the three models, while the second peak close to 276 deg azimuthal position is slightly spaced backward

for Model 60 and Model 120 .Table 6 shows the values of instantaneous torque coefcient for

the two corresponding azimuthal positions 92 deg and 276 deg .The peak value decrease is very low about 5% between Model 0and Model 60 but increases up to 24% between Model 0 and Model 120 .

Figures 2123 compare the contributions of instantaneoustorque in each of the 20 blade zones for the two described abovepeak torque azimuthal positions and for a third intermediate azi-muthal position 48 deg .

The Model 0 straight blade exhibits a symmetrical torque pro-

Fig. 17 Numerical problems caused by parallel to principalow direction interfaces and problem solution using extendedrotating mesh 1

Fig. 18 Numerical problems caused by parallel to principalow direction interfaces and problem solution using extendedrotating mesh 2

Fig. 19 Power curves for the ve models

Fig. 20 Instantaneous torque coefcient as a function of azi-muthal coordinate

Table 6 Instantaneous torque coefcients for azimuthal posi-tions of 92 deg and 276 deg Model 0 , Model 60 , and Model 120

Azimuthal position deg 92 276 Model 0 C T 0.201 0.049 Model 60 C T 0.191 5% 0.046 Model 120 CT 0.152 24.4% 0.042

Fig. 21 Contribution of instantaneous torque in each bladezone for Model 0 and Model 120 azimuthal coordinate 92 deg




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le with respect to the blade centerline a decrease in blade per-formance can also be registered due to vortex shedding in corre-spondence to the upper and lower blade tips . This is not the casefor helical blades as a consequence of the choice for the referencesystem in dening the blade azimuthal position: In a straightblade, each zone features the same azimuthal position with respectto the relative ow eld, while in the case of helical blades it hasa different angular position with respect to the blade centerline.

Two torque peaks are visible in Fig. 22 for Model 0 , locatedclose to zone 3 and zone 18 because Model 0 0 is symmetrical,the torque distribution is also symmetrical : The cause of thisphenomenon is not yet clear; however, we suggest that for someazimuthal locations, a vertical air suction into the rotor occurs,which accelerates the ow eld in the proximity of blade tips.

A more appropriate representation of the torque generated byeach blade zone can be ascertained in Fig. 24, where the averagevalue of the torque coefcient generated during a complete 360deg rotation is represented as a function of the blade zone itself:Most of the torque in a helical blade is produced from the bottomblade zones, while the upper blade zone contribution is negative.

The cause of this phenomenon is not easy to understand; how-ever, it can be argued that tip effects play a dominant role at the

top than at the bottom of the blade. This aspect is analyzed in thefollowing.

Figure 25 shows the instantaneous torque values as a functionof azimuthal position for zone 1 and zone 20 for Model 0 and Model 120 .

As can be clearly seen, the torque generated by the lower bladezone is much higher than the torque generated by the correspond-ing upper blade zone Fig. 26 . However, the velocity-vector vi-

sualizations of Figs. 27 and 28 for upper and lower blade tip zonesshow no appreciable differences in the vortex shedding.

The explanation of the phenomenon lies therefore in other fac-tors. Figures 29 and 30 visualize the pathlines for Model 0 and Model 60 in correspondence to the blade centerline zone 10 ,which is far from the perturbed areas due to tip effects. Model 0streamlines are parallel to the horizontal plane, while Model 60streamlines clearly deviate upward.

The above description shows that, close to the blade, the oweld takes a direction perpendicular to the leading edge, accordingto Fig. 31.

The reduced contribution to torque generation of the upperblade element is caused by the fact that pathlines are unable to



Fig. 24 Average torque for each blade zone for Model 0 andModel 120 0

Fig. 25 Instantaneous torque coefcient values as a functionof azimuthal position for Model 0 and Model 120 zone 1

Fig. 26 Instantaneous torque coefcient values as a functionof azimuthal position for Model 0 0 and Model 120 zone 20




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fully develop along a blade prole because of an abrupt halt dueto the horizontal cut in the blade itself, as can be seen in Fig. 32.

Even the lower blade element presents a similar cut, but sincethe pathlines bend upward, it does not affect the continuity of owalong the blade element itself: Therefore, no reduction in thetorque is seen.

The deviation of streamlines is also responsible for the markeddecrease in rotor performance for high values of phase shift anglebetween lower and upper blade sections. Figure 33 shows thedistortion of the blade section in direction perpendicular to theleading edge due to blade curvature, compared with the originalNACA 0021 blade section in the horizontal plane.

For high phase shift angle, the ow eld is no more interactingwith a NACA prole but with a deformed one, with consequentdecrease of overall rotor efciency.

Blade deformation can also be seen from Table 7, comparing

the chord length of the blade section interacting with the ow eldwith the original NACA 0021 section for the ve analyzed modelsFig. 34 .

The reduction of chord length, and the consequent reduction of rotor solidity, are also responsible for the slight increment in op-timum tip speed ratio values with the phase shift angle betweenlower and upper blade sections, as described in Fig. 19.

Figure 35 shows the axial thrust coefcient acting on blades for Model 0 and Model 120 , dened as

CFz =Fz

1 / 2 A V2 3

as a function of the azimuthal position for a tip speed ratio of 3.36. While there is no straight blade axial thrust, the helicalblades produce a downward axial thrust increasing the axial bear-ing load.

Fig. 27 Velocity vectors visualization for upper and lowerblade tip zones 1

Fig. 28 Velocity vectors visualization for upper and lowerblade tip zones 2

Fig. 29 Model 0 0, zone 10: streamlines are parallel to the hori-zontal plane

Fig. 30 Model 0 , zone 10: streamlines deviate upward

Fig. 31 Streamlines deviation in a direction perpendicular tothe leading edge

Fig. 32 Horizontal cut on the top of helical blades




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The explanation for this phenomenon lies once more in the factthat pathlines bend upwards in a direction orthogonal to the lead-ing edge. This causes, for Newtons laws of motion, a uid down-ward thrust on the blade.

In order to reduce axial bearing loads, the helical blade should

develop so that the lower sections meet the ow before the upperones.

6 Conclusions and Future WorkIn this paper, a model for the evaluation of energy performance

and aerodynamic forces acting on a small helical Darrieus verticalaxis wind turbine depending on blade inclination angle has beendeveloped, based on an analytical code coupled to a solid model-ing software that was linked to a nite volume CFD code for thecalculation of rotor performance.

The obtained results, based on ve machine architectures,which are characterized by an inclination of the blades with re-spect to the horizontal plane in order to generate a phase shiftangle between lower and upper blade sections of 0 deg, 30 deg, 60

deg, 90 deg, and 120 deg for a rotor with aspect ratio of 1.5,demonstrate that the average torque does not change substantiallyfor lower phase shift angle but shows a marked decrease for highvalues of phase shift angle between upper and lower blade sec-tions.

Up to 60 deg phase shift angle, torque peaks showed a slightdecrease, depending on blade inclination, but no signicant reduc-tion of pulsating torque depending on the phase shift angle be-tween lower and upper blade sections has been proved.

The obtained results demonstrate also that, close to the blade,the ow eld takes a direction perpendicular to the leading edge,with streamlines clearly deviating upward for a helical blade de-veloping so that the upper sections meet the ow before the lowerones.

The obtained results demonstrate also that a signicant contri-bution to the mean torque in a helical blade is produced from thebottom blade zones. Although the reason for this phenomenon isnot easy to understand, it has been assumed to be caused by thefact that pathlines are unable to fully develop along a upper bladeprole because of an abrupt halt due to the horizontal cut in theblade itself.

Finally, it has been demonstrated that helical blades developedso that the upper sections meet the ow before the lower ones

produce a downward axial thrust increasing the axial bearing load.The explanation for this phenomenon lies once more in the factthat pathlines bend upward in a direction orthogonal to the leadingedge. This causes, for Newtons laws of motion, a uid downwardthrust on the blade.

Some aspects still remain to be investigated: First of all, nu-merical analysis need to be extended in order to examine theeffect of constructing the blade prole using inclined normal toleading edge airfoil sections, which could achieve better perfor-mance, due to streamline inclination.

Also, the cause of the two torque peaks close to tip blades forsome azimuthal position and the corresponding possible verticalair suction into the rotor remain to be further investigated.

Finally, an accurate analysis is needed to investigate axial loadsacting on a helical blade developed so that the lower sections meetthe ow before the upper ones, thus reducing the total loads actingon the bearings.

NomenclatureA rotor swept area, m 2

c blade chord, mmCFz axial thrust coefcientCp rotor power coefcient

CT instantaneous torque coefcientF rotor axial force, NH rotor height, mmP rotor power, W

Fig. 33 Blade section interacting with the ow eld dark blue compared with the original NACA 0021 horizontal section lightblue for phase shift angle of 120 deg

Table 7 Comparison between chord lengths of the blade sec-tion interacting with the ow eld for the ve models analyzed

Model namecnormal to blade

mm Variation %

0 85.8 0.0030 84.5 1.5160 81.0 5.5990 76.0 11.42

120 70.3 18.06

Fig. 34 Blade section distortion dark blue for phase shiftangle of 60 deg and 120 deg, compared with the original NACA0021 section light blue

Fig. 35 Axial forces acting on Model 0 and Model 60 blades fora tip speed ratio of 3.36




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R rotor radius, mmT rotor torque, Nm

V undisturbed ow velocity, m/s phase shift angle between lower and upper

blade sections, deg blade inclination with respect to the horizontal

plane, deg tip speed ratio blade azimuthal coordinate, deg air density assumed 1.225 kg / m3 , kg / m3

rotor solidity rotor angular velocity, rad/s

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18 Bardina, J. E., Huang, P. G., and Coakley, T. J., 1997, Turbulence ModelingValidation, Testing and Development, NASA, Technical Report 110446.


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