6 IJAEST Volume No 3 Issue No 2 Effect of Maximum Thickness Location of an Aerofoil on Aerodynamic Characteristics 122 133

8/7/2019 6 IJAEST Volume No 3 Issue No 2 Effect of Maximum Thickness Location of an Aerofoil on Aerodynamic Characteristi

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Effect of Maximum Thickness Location of an Aerofoil on Aerodynamic

Characteristics

G MANIKANDAN M ANANDA RAO *

Professor Professor and PrincipalSS Institute of Technology SS Institute of TechnologyDundigal, Hyderabad Dundigal, HyderabadAndhra Pradesh, India Andhra Pradesh, [email protected] profanandarao @yahoo.com+91 9618190732 +91 9966049083

G MANIKANDAN et al. / (IJAEST) INTERNATIONAL JOURNAL OF ADVANCED ENGINEERING SCIENCES AND TECHNOLOGIESVol No. 3, Issue No. 2, 122 - 133

ISSN: 2230-7818 @ 2011 http://www.ijaest.iserp.org. All rights Reserved. Page 122


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Abstract Shape optimization of aerofoilfor aerodynamic analysis by changing the location of the maximum thicknesshas been carried out by GeneticAlgorithm Optimization technique.

NACA 0012 Symmetrical aerofoil waschosen as baseline aerofoil. CompositeWing models have been fabricated fromthe optimized aerofoils. Microcontrollerhas been designed and fabricated tochange the angle of attack. Effect of aerofoil profile on the co-efficient of Lift, Drag, Moment, and Pressure atsubsonic Mach number and low angle of attack have been investigated by Panelmethod using Mat Lab Program andvalidated by experimental analysis.Pressure and velocity distribution overaerofoils have been simulated byComputational Fluid Dynamic tool.

Keyword: Genetic Algorithm;Symmetrical Aerofoil; Composite Wing;Microcontroller; Wind Tunnel;

Nomenclature

D = DragL = LiftL/D = Lift/Drag ratioC p = Co-efficient of PressureCL = Co-efficient of Lift.CD = Co-efficient of Drag.CM = Co-efficient of Moment.F Set of Scalar Objective Function.

= Set of Generations.M = User specified vector with two

elements that controls modificationoperators.jth chromosome from n th GA

generation.ith gene from the j th chromosome

from the n th GA generation.Random number generator

which returns a random value between 0and 1.m pt = Pass through operator mrc = Random average cross over operator.

User specified maximum limitson the i th gene.

User specified minimum limits onthe i th gene.Subscriptsi = Gene Index

j = Chromosome IndexSuperscriptsn = Population Indext = Temporary chromosome and genevalues obtained after initial selection and

before modification operator.

I Introduction

The aerofoil profile variation hasdeterministic effect on the aerodynamiccoefficients. New designs can be gleanedwith enhanced aerodynamic characteristicsfrom the standard aerofoil profile (NACA)

by Genetic Algorithm (GA). There is anoverabundance of aerofoil designs andfamilies claimed right from the past tilltoday, and their effects have been used for various purposes that suit the requirementsof flight. The ideal shape of an aerofoildepends profoundly on the angle of attack,Reynolds number, Mach number, surface

roughness, and air turbulence [1].Increasing the angle of attack increases thelift and drag also. High lift wingsgenerally have a large convex curvature onthe upper surface and a concave lower curvature [2]. In this paper subsonic Machnumber and low angle of attack effects onsymmetrical aerofoils are considered.

Many research works have beenundertaken with various constraints, such

as on the aerofoil thickness, pitchingmoment, off-design performance and other unusual constraints [3-7]. The airfoildesign method is threefold: first, for thedesign of airfoils that fall outside the rangeof applicability of existing catalogs;second, for the design of airfoils that moreexactly match the requirements of theintended application; and third, for theeconomic exploration of many airfoilconcepts [8].




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Thicker aerofoil sections are goodat lower speeds of flight and weightcarrying applications. Thinner aerofoilsare suitable for higher speeds of flight.The thickness of the aerofoil is one of the

geometric parameters of the aerofoil thatstrongly affects the aerodynamiccharacteristics. The thickness distributionfor an aerofoil affects the pressuredistribution and the character of the

boundary layer [9]. As the position of maximum thickness moves aft of theaerofoil, the velocity gradient decreases,keeping the boundary layer flow to belaminar for a longer time. Designoptimization of aerofoils has been carriedout by various methods and computationaltechniques. [10-16]. The main feature of this paper was to reveal the effect of location of the maximum thickness fromthe leading edge of the aerofoil on theaerodynamic characteristics.

II Genetic Algorithm for Airfoil ShapeOptimization

The genetic algorithm optimization procedure adapted for airfoil shapeoptimization is discretely described by thedesign space using 35 decision variables(control points), G i. Each set of genes thatleads to the complete specification of anindividual airfoil profile is indicated by

( ) (1)

Real number encoding is used to represent

all genes. The population size consideredis 8. Each gene with each chromosome isassigned with an initial real number value

by random number generation betweenfixed upper and lower limits. The i th genein an arbitrary chromosome is computedusing

( ) (2)

The fitness function is denoted by

. (3)

The highest fitness functionchromosome is passed through the nextgeneration. In this paper two modificationoperators-pass through, random averagecross over are used. The number of chromosomes modified with each operator is controlled by M vector. The vector consists of 2 parameters The value of each M vector elementranges from 0 to 1. The first 50% of chromosomes are modified using passthrough operator. The next 50% aremodified using random average crossover. The chromosome with the highestindividual fitness value is passed to thenext generation. Thereby guaranteeing thatnone of the maximum fitness valuedchromosomes will get dropped during GAiteration. The random average cross over operator is applied on randomly selectedtwo chromosomes from the population.The gene by gene basis combination of thetwo selected chromosomes is achieved by:

( )

.. (4)The GA optimized aerofoil profiles are

shown in figure 1.

Figure 1: GA Optimized Aerofoilprofiles




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III Wind Tunnel Model preparation,Testing and Analysis

Using the eight optimized aerofoilsgenerated by GA, scaled wing models

having a chord of 15 cm and span of 21cm have been fabricated with Balsa woodreinforced by S fiber glass and epoxyresins. The wing is a single spar multi ribtype having one spar and 4 ribs (one in theroot and tip chord and one at the midchord). Various cross section of sparsused (I, C and Z) are shown in figure 2 to5.

Figure 2: C Section Spar Wing

Figure 3: I Section Spar Wing

Figure 4: Z Section Spar Wing

Figure 5: Dimensions of Various Spars.

The skin is made of two layers.First layer is 2mm balsa sheet and thesecond layer is 1 mm fiber glass reinforcedwith epoxy resins as shown in figure 6.

Figure 6: Wing model with S GlassFiber and Epoxy Resin.

Pressure tapings are provided inthe mid chord for the investigation of the

pressure distribution over the wing modelas shown in figure 7. Load cells are usedto find the aerodynamic characteristics.

Figure 7: Wing model with PressureTapping.




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The cross section of wing model with Isection spar is shown in figure 8.

Figure 8: Cross Section of Wing modelwith I Spar.

The wing model coupled to thestepper motor drive shaft is held firmly tothe base plate of the test section of the lowspeed wind tunnel. The angle of attack of the model is controlled by microcontroller with keypad and LED display board asshown in figure 9. The angle of attack can

be varied from 0 to 200 deg when the windtunnel is in operation.

Figure 9: Microcontroller for changingangle of attack dynamically.

IV Results and Discussions

The NACA 0012 aerofoil has beenoptimized using GA by first considering9999 chromosome as initial seed generated

by random number generator. Out of which eight chromosomes have beenselected for first generation based on bestranked fitness function. For nextgenerations two modification operators areapplied and a total of 19998 chromosomeshave been generated out of which besteight chromosomes are selected based onfitness function. The shape converged atthe end of 128 th generation. From theoptimized last generation, eight aerofoilshave been chosen for the development of composite material wing for theexperimental investigation.

Effect of Aerofoil Shape on the Co-efficient of Lift :

Table 1 presents the effect of aerofoilshape on the Co-efficient of Lift for theMach number ranges from 0.2 to 0.7 at anangle of attack of 3 deg.

Table 1: Co-efficient of Lift of Optimized eight aerofoils at 3 deg angleof Attack.

It has been investigated that the C L varies from 0.2992 to 0.383. It has beenobserved that the C L increases as the Machnumber increases. For a particular subsonic Mach number, C L varies with thelocation of maximum thickness. Design 6




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aerofoil generated an average of 1 % hikeof C L than the NACA 0012 for the Machnumber considered.

Effect of Aerofoil Shape on the Co-

efficient of Drag:

The effect of aerofoil shape on the Co-efficient of Drag is presented in the table 2for the Mach number from 0.2 to 0.7 at anangle of attack of 3 deg.

Table 2: Co-efficient of Drag of Optimized eight aerofoils at 3 deg. angleof Attack.

It has been investigated that the C D increases as the Mach number increases.For a particular subsonic Mach number,CD varies with the location of maximumthickness. It has been observed that theDesign 6 aerofoil developed 26%reduction in drag than NACA 0012aerofoil at 0.7 Mach number due to theshifting of transition point towards thetrailing edge. Graph 1 presents C L vs.C D of eight aerofoils at 3 deg angle of attack.

Graph 1: Cl vs. Cd of eight aerofoils at3 deg angle of attack.

Effect of Aerofoil Shape on Lift/Dragratio:

Table 3 presents the effect of aerofoilshape on the L/D ratio for the Mach

number from 0.2 to 0.7 at an angle of attack of 3 deg.

Table 3: Lift/Drag of Optimized eightAerofoils at 3 deg. angle of Attack

It has been investigated that the L/Dratio varies from 7.66 to 30.32. It has beenobserved that the L/D ratio decreases as

the Mach number increases. For a particular subsonic Mach number, L/Dratio varies with the location of maximumthickness. It has been observed that theDesign 6 aerofoil developed 28% hike of L/D ratio than NACA 0012 at 0.4 Machnumber and 3 deg angle of attack.

Effect of Aerofoil Shape on PitchingMoment:

Table 4 presents the Moment Co-efficient of optimized aerofoils at 0.2Mach number. It has been observed thatthe moment coefficient varies severely asthe angle of attack increases. Even thoughthe Design 6 developed better lift anddrag, it fails to maintain stability due tomuch variation in the moment as the angleof attack increases. It has been observedthat the Design 2 aerofoil has better stability than the NACA 0012 aerofoil at0.2 Mach speed.




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Table 4: Moment Co-efficient of eightaerofoils at 0.2 Mach number.

Graph 2 presents the variation of Cmwith respect to angle of attack at 0.2Mach.

Graph 2: Cm vs. Angle of Attack at 0.2Mach number.

Effect of Aerofoil Shape on DifferentialPressure:

Variation of differential pressure withMach number at 2 deg angle of attack isshown in the graph 3.

Graph 3: Differentiate Pressure vs.Mach number of eight aerofoils at 3 deg

angle of attack .

It has been observed that the design6 aerofoil developed highest differential

pressure than NACA 0012 up to 0.4 Mach.Also it has been observed that the Design6 has severe pressure fluctuation at higher Mach number due to instability of transition point caused by pitchingmoments.

Pressure and Velocity Distribution overAerofoil:

The shape of the pressuredistribution graph is directly related to theairfoil performance as indicated by someof the features like the adverse pressuregradients leading to flow transition,separation and a minimum Cp. The Cpvariation along the chord of optimizedaerofoils is plotted in the graph 4 to 12.The pressure and velocity distribution over optimized aerofoils are shown in the figure10 to 15.




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Graph 4: Cp vs. x/c of NACA 0012Aerofoil at Mach number 0.2 and 2 degangle of attack

Graph 5: Cp vs. x/c of Design 1 Aerofoilat Mach number 0.2 and 2 deg angle of attack

Graph 6: Cp vs. x/c of Design 2 Aerofoilat Mach number 0.2 and 2 deg angle of attack.


Graph 8: Cp vs. x/c of Design 4 Aerofoilat Mach number 0.2 and 2 deg angle of

attack





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Graph 10: Cp vs. x/c of Design 6Aerofoil at Mach number 0.2 and 2 degangle of attack.

Graph 11: Cp vs. x/c of Design 7

Aerofoil at Mach number 0.2 and 2 degangle of attack

Graph 12: Cp vs. x/c of Design 8Aerofoil at Mach number 0.2 and 2 degangle of attack

Figure 10: Pressure Distribution overDesign 1 Aerofoil at Mach number 0.2and 2 deg angle of attack.

Figure 11: Velocity Distribution over

Design 1 Aerofoil at Mach number 0.2and 2 deg angle of attack.





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Figure 13: Velocity Distribution overDesign 2 Aerofoil at Mach number 0.2and 2 deg angle of attack.


Figure 15: Velocity Distribution overDesign 3 Aerofoil at Mach number 0.2and 2 deg angle of attack

V Conclusion

In this paper, eight aerofoils have been developed for experimental

investigation by Genetic AlgorithmOptimization technique. Wing models

have been developed for wind tunneltesting using Composite material.Microcontroller has been designed andfabricated to vary the angle of attack of theaerofoil. Mat Lab program has been

developed for finding the aerodynamiccharacteristics of aerofoils. Pressure andvelocity distribution simulation over aerofoil profiles have been achieved byusing Computational Fluid Dynamic Tool.

The following are the variousobservations made in the experimentalinvestigation of optimized aerofoils.

Design 6 aerofoil generated anaverage of 1 % hike of C L than the

NACA 0012 for the Mach number and angle of attack considered for the investigation.

Design 6 aerofoil developed 26%reduction in drag than NACA 0012aerofoil at 0.7 Mach number and 3deg angle of attack due to theshifting of transition point towardsthe trailing edge.

Design 6 aerofoil developed 28%hike of L/D ratio than NACA 0012at 0.4 Mach number and 3 degangle of attack.

Even though the Design 6developed better lift and drag, itfails to maintain stability due tomuch variation in the moment asthe angle of attack increases.Design 2 aerofoil has better stability than the NACA 0012

aerofoil at 0.2 Mach speed and 3deg angle of attack.

Design 6 aerofoil developedhighest differential pressure than

NACA 0012 up to 0.4 Mach. It hassevere pressure fluctuation athigher Mach number due toinstability of transition pointcaused by pitching moments.




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References

[1] P. B. S. Lissaman, LowReynolds Number Aerofoils ,

Annual review of FluidMechanics, Vol 15, pages223- 239, January 1983,AeroVironment Inc.,California,

[2] The Pilots Handbook of Aeronautical Knowledge byPaul E Illman, pages 220-248, 2008

[3] P.A. Henne, AppliedComputational Aerodynamics,Progress in AIAA series, pages434-440, 1990, Douglas AircraftCompany.

[4] Higgins, George J.: ThePrediction of AirfoilCharacteristics. T.R. No. 312,

N.A.C.A., 1929.[5] Knight, Montgomery, and Harris,

Thomas A.: ExperimentalDetermination of Jet BoundaryCorrections for Airfoil Tests inFour Open Wind Tunnel Jets of Different Shapes. T.R. No. 361,

N.A.C.A., 1930.[6] Jacobs, Eastman N.: The

Aerodynamic Characteristics of Eight Very Thick Airfoils fromTests in the Variable- DensityWind Tunnel. T.R. No. 391,

N.A.C.A., 1931.[7] Theodorsen, Theodore: On the

Theory of Wing Sections withParticular Reference to the LiftDistribution. T.R. No. 383,

N.A.C.A., 1931.[8] Subsonic airfoil design A

historical background, NACAReport to Congress of US.

[9] Aerodynamics for Engineers, 5 th edition, John J.Bertin, pages 120-147, 2008.

[10] Jacobs, Eastman N., and Anderson,

Raymond F, Large Scale Aero-dynamic Characteristics of

Airfoils as Tested in the Variable DensityWind Tunnel, T.R. No. 352, N.A.C.A.,1930.[11] M Drela and M B Giles, Viscous

Inviscid Analysis of Transonic and

Low Reynolds Number Airfoils,AIAA Journal, Vol.25, Issue 10,Pages 1347-1355

[12] S. Goel, J.I.Cofer, and H.Singh,Turbine Airfoil DesignOptimization, In Proceedings of The International Gas Turbine andAero Engine Congress andExposition, Bermingham, UK,June 1996

[13] D.H.Huddleston and CW MastinOptimization Methods Applied toAerodynamic Design Problems inComputational Fluid Dynamics,in Proceedings of the 7 th International Conference of Finite Element Methods inFluid Flow, Huntsville, Ala,USA, 1989

[14] A. Jameson, OptimumAerodynamic Design using ControlTheory, Computational FluidDynamics Review, Vol.3, Pages495-528, 1995

[15] C Sung and JH Kwon,Aerodynamic DesignOptimization Using the Navier-Stokes and AdjoinedEquations, AIAA Paper 2001-0266

[16] B Mialon, T Fol and C Bonnaud, Optimization of High Subsonic

Blended Wing BodyConfigurations, AIAA Paper 2002- 5666.

G. Manikandan was bornon 12 th January 1969 fromthe famous big temple cityThanjavur, Tamil Nadu.He obtained hisEngineering Graduation(Mech) in the year 1994

from Institution of Engineers (India),Calcutta and M.Tech (CAD/CAM) in the




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year 2002 from JNTU, Hyderabad. He putup 16 years of colorful service in IndianAir Force. In his credit, he overhauled 365Rolls Royce Viper Turbojet Engine fittedon Kiran Aircraft and Carried out

Structural Repairs and maintenance of Cheetah and Chetak helicopters and Kiranaircraft. He was team leader for severalStructural re-fabrications of Ardhra andRohini Gliders. He developed number of Un-manned Aerial Vehicles (UAV).Presently, his contributions are in the areaof aerofoil shape optimization and flutter analysis. He was awarded best in tradeand all-rounder for Kiran Aircraft in theyear 2000.

M. Ananda Rao obtainedB.E (Mech) in 1968,M.Tech (Machine Design)in 1970 and M.Tech(Industrial Engg) in 1984.He was awarded PhD from

IIT, Madras in the area of MachineDynamics in the year 1987. He workedover 33 years in Andhra University atvarious capacities. He worked in the Link Interchange Program with UK Universitiesfor about 03 years sponsored by BritishCouncil and Government of India. He

published more than 200 papers inInternational Journals and more than 50

papers in International and NationalConferences. He was awarded three timesThe Best Researcher Award in the year 1992, 1999 and 2001. He worked as atechnical adviser for Altair Company for

the development of software in the domainof solvers. He is one of the renownedresearchers in the area of Vibration andCondition Monitoring in the World. Hewas the nucleus in the starting of Condition Monitoring Society of India.



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6 IJAEST Volume No 3 Issue No 2 Effect of Maximum Thickness Location of an Aerofoil on Aerodynamic Characteristics 122 133