6-ijaest-volume-no-3-issue-no-2-effect-of-maximum-thickness-location-of-an-aerofoil-on-aerodynamic-c

Effect of Maximum Thickness Location of

an Aerofoil on Aerodynamic

Characteristics

G MANIKANDAN M ANANDA RAO*

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

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

ISSN: 2230-7818 @ 2011 http://www.ijaest.iserp.org. All rights Reserved. 22

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Abstract – Shape optimization of aerofoil

for aerodynamic analysis by changing the location of the maximum thickness

has been carried out by Genetic

Algorithm Optimization technique.

NACA 0012 Symmetrical aerofoil was

chosen as baseline aerofoil. Composite

Wing models have been fabricated from

the optimized aerofoils. Microcontroller

has been designed and fabricated to

change the angle of attack. Effect of

aerofoil profile on the co-efficient of

Lift, Drag, Moment, and Pressure at

subsonic Mach number and low angle of

attack have been investigated by Panel

method using Mat Lab Program and

validated by experimental analysis.

Pressure and velocity distribution over

aerofoils have been simulated by

Computational Fluid Dynamic tool.

Keyword: Genetic Algorithm;

Symmetrical Aerofoil; Composite Wing;

Microcontroller; Wind Tunnel;

Nomenclature

D = Drag L = Lift L/D = Lift/Drag ratio Cp = Co-efficient of Pressure CL = 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 modification operators. jth chromosome from nth GA

generation. ith gene from the jth chromosome

from the nth GA generation. ( ) Random number generator which returns a random value between 0 and 1. mpt = Pass through operator mrc = Random average cross over operator. User specified maximum limits on the ith gene.

User specified minimum limits on the ith gene. Subscripts i = Gene Index j = Chromosome Index Superscripts n = Population Index t = Temporary chromosome and gene values obtained after initial selection and before modification operator.

I Introduction

The aerofoil profile variation has deterministic effect on the aerodynamic coefficients. New designs can be gleaned with enhanced aerodynamic characteristics from the standard aerofoil profile (NACA) by Genetic Algorithm (GA). There is an overabundance of aerofoil designs and families claimed right from the past till today, and their effects have been used for various purposes that suit the requirements of flight. The ideal shape of an aerofoil depends profoundly on the angle of attack, Reynolds number, Mach number, surface roughness, and air turbulence [1]. Increasing the angle of attack increases the lift and drag also. High lift wings generally have a large convex curvature on the upper surface and a concave lower curvature [2]. In this paper subsonic Mach number and low angle of attack effects on symmetrical aerofoils are considered. Many research works have been undertaken with various constraints, such as on the aerofoil thickness, pitching moment, off-design performance and other unusual constraints [3-7]. The airfoil design method is threefold: first, for the design of airfoils that fall outside the range of applicability of existing catalogs; second, for the design of airfoils that more exactly match the requirements of the intended application; and third, for the economic exploration of many airfoil concepts [8].


ISSN: 2230-7818 @ 2011 http://www.ijaest.iserp.org. All rights Reserved. Page 123

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Thicker aerofoil sections are good at lower speeds of flight and weight carrying applications. Thinner aerofoils are suitable for higher speeds of flight. The thickness of the aerofoil is one of the geometric parameters of the aerofoil that strongly affects the aerodynamic characteristics. The thickness distribution for an aerofoil affects the pressure distribution and the character of the boundary layer [9]. As the position of maximum thickness moves aft of the aerofoil, the velocity gradient decreases, keeping the boundary layer flow to be laminar for a longer time. Design optimization of aerofoils has been carried out by various methods and computational techniques. [10-16]. The main feature of this paper was to reveal the effect of location of the maximum thickness from the leading edge of the aerofoil on the aerodynamic characteristics.

II Genetic Algorithm for Airfoil Shape

Optimization

The genetic algorithm optimization procedure adapted for airfoil shape optimization is discretely described by the design space using 35 decision variables (control points), Gi. Each set of genes that leads to the complete specification of an individual airfoil profile is indicated by (

)… (1) Real number encoding is used to represent all genes. The population size considered is 8. Each gene with each chromosome is assigned with an initial real number value by random number generation between fixed upper and lower limits. The ith gene in an arbitrary chromosome is computed using ( )( ) … (2) The fitness function is denoted by

(

) …. (3) The highest fitness function chromosome is passed through the next generation. In this paper two modification operators-pass through, random average cross 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 element ranges from 0 to 1. The first 50% of chromosomes are modified using pass through operator. The next 50% are modified using random average cross over. The chromosome with the highest individual fitness value is passed to the next generation. Thereby guaranteeing that none of the maximum fitness valued chromosomes will get dropped during GA iteration. The random average cross over operator is applied on randomly selected two chromosomes from the population. The gene by gene basis combination of the two selected chromosomes is achieved by:

(

)

….. (4) The GA optimized aerofoil profiles are shown in figure 1.

Figure 1: GA Optimized Aerofoil

profiles



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III Wind Tunnel Model preparation,

Testing and Analysis

Using the eight optimized aerofoils generated by GA, scaled wing models having a chord of 15 cm and span of 21 cm have been fabricated with Balsa wood reinforced by S fiber glass and epoxy resins. The wing is a single spar multi rib type having one spar and 4 ribs (one in the root and tip chord and one at the mid chord). Various cross section of spars used (I, C and Z) are shown in figure 2 to 5.

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 the second layer is 1 mm fiber glass reinforced with epoxy resins as shown in figure 6.

Figure 6: Wing model with S Glass

Fiber and Epoxy Resin.

Pressure tapings are provided in the mid chord for the investigation of the pressure distribution over the wing model as shown in figure 7. Load cells are used to find the aerodynamic characteristics.

Figure 7: Wing model with Pressure

Tapping.



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

Figure 8: Cross Section of Wing model

with I Spar.

The wing model coupled to the stepper motor drive shaft is held firmly to the base plate of the test section of the low speed wind tunnel. The angle of attack of the model is controlled by microcontroller with keypad and LED display board as shown in figure 9. The angle of attack can be varied from 0 to 200 deg when the wind tunnel is in operation.

Figure 9: Microcontroller for changing

angle of attack dynamically.

IV Results and Discussions

The NACA 0012 aerofoil has been optimized using GA by first considering 9999 chromosome as initial seed generated by random number generator. Out of which eight chromosomes have been selected for first generation based on best ranked fitness function. For next generations two modification operators are applied and a total of 19998 chromosomes have been generated out of which best eight chromosomes are selected based on fitness function. The shape converged at the end of 128th generation. From the optimized last generation, eight aerofoils have been chosen for the development of composite material wing for the experimental investigation. Effect of Aerofoil Shape on the Co-

efficient of Lift: Table 1 presents the effect of aerofoil shape on the Co-efficient of Lift for the Mach number ranges from 0.2 to 0.7 at an angle of attack of 3 deg. Table 1: Co-efficient of Lift of

Optimized eight aerofoils at 3 deg angle

of Attack.

It has been investigated that the CL varies from 0.2992 to 0.383. It has been observed that the CL increases as the Mach number increases. For a particular subsonic Mach number, CL varies with the location of maximum thickness. Design 6



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aerofoil generated an average of 1 % hike of CL than the NACA 0012 for the Mach number 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 2 for the Mach number from 0.2 to 0.7 at an angle of attack of 3 deg. Table 2: Co-efficient of Drag of

Optimized eight aerofoils at 3 deg. angle

of Attack.

It has been investigated that the CD increases as the Mach number increases. For a particular subsonic Mach number, CD varies with the location of maximum thickness. It has been observed that the Design 6 aerofoil developed 26% reduction in drag than NACA 0012 aerofoil at 0.7 Mach number due to the shifting of transition point towards the trailing edge. Graph 1 presents CL vs.CD of eight aerofoils at 3 deg angle of attack.

Graph 1: Cl vs. Cd of eight aerofoils at

3 deg angle of attack.

Effect of Aerofoil Shape on Lift/Drag

ratio:

Table 3 presents the effect of aerofoil shape 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 eight

Aerofoils at 3 deg. angle of Attack

It has been investigated that the L/D ratio varies from 7.66 to 30.32. It has been observed that the L/D ratio decreases as the Mach number increases. For a particular subsonic Mach number, L/D ratio varies with the location of maximum thickness. It has been observed that the Design 6 aerofoil developed 28% hike of L/D ratio than NACA 0012 at 0.4 Mach number and 3 deg angle of attack. Effect of Aerofoil Shape on Pitching

Moment:

Table 4 presents the Moment Co-efficient of optimized aerofoils at 0.2 Mach number. It has been observed that the moment coefficient varies severely as the angle of attack increases. Even though the Design 6 developed better lift and drag, it fails to maintain stability due to much variation in the moment as the angle of attack increases. It has been observed that the Design 2 aerofoil has better stability than the NACA 0012 aerofoil at 0.2 Mach speed.



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Table 4: Moment Co-efficient of eight

aerofoils at 0.2 Mach number.

Graph 2 presents the variation of Cm

with respect to angle of attack at 0.2 Mach.

Graph 2: Cm vs. Angle of Attack at 0.2

Mach number.

Effect of Aerofoil Shape on Differential

Pressure:

Variation of differential pressure with Mach number at 2 deg angle of attack is shown 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 design 6 aerofoil developed highest differential pressure than NACA 0012 up to 0.4 Mach. Also it has been observed that the Design 6 has severe pressure fluctuation at higher Mach number due to instability of transition point caused by pitching moments. Pressure and Velocity Distribution over

Aerofoil:

The shape of the pressure distribution graph is directly related to the airfoil performance as indicated by some of the features like the adverse pressure gradients leading to flow transition, separation and a minimum Cp. The Cp variation along the chord of optimized aerofoils is plotted in the graph 4 to 12. The pressure and velocity distribution over optimized aerofoils are shown in the figure 10 to 15.



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Graph 4: Cp vs. x/c of NACA 0012

Aerofoil at Mach number 0.2 and 2 deg

angle of attack

Graph 5: Cp vs. x/c of Design 1 Aerofoil

at Mach number 0.2 and 2 deg angle of

attack



attack.



attack



attack



attack



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Graph 10: Cp vs. x/c of Design 6


angle of attack.



angle of attack



angle of attack

Figure 10: Pressure Distribution over

Design 1 Aerofoil at Mach number 0.2

and 2 deg angle of attack.

Figure 11: Velocity Distribution over








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and 2 deg angle of attack

V Conclusion

In this paper, eight aerofoils have been developed for experimental investigation by Genetic Algorithm Optimization technique. Wing models

have been developed for wind tunnel testing using Composite material. Microcontroller has been designed and fabricated to vary the angle of attack of the aerofoil. Mat Lab program has been developed for finding the aerodynamic characteristics of aerofoils. Pressure and velocity distribution simulation over aerofoil profiles have been achieved by using Computational Fluid Dynamic Tool. The following are the various observations made in the experimental investigation of optimized aerofoils.

Design 6 aerofoil generated an average of 1 % hike of CL 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 0012 aerofoil at 0.7 Mach number and 3 deg angle of attack due to the shifting of transition point towards the trailing edge.

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

Even though the Design 6 developed better lift and drag, it fails to maintain stability due to much variation in the moment as the angle of attack increases. Design 2 aerofoil has better stability than the NACA 0012 aerofoil at 0.2 Mach speed and 3 deg angle of attack.

Design 6 aerofoil developed highest differential pressure than NACA 0012 up to 0.4 Mach. It has severe pressure fluctuation at higher Mach number due to instability of transition point caused by pitching moments.



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References

[1] P. B. S. Lissaman, “Low Reynolds Number Aerofoils ”, Annual review of Fluid Mechanics, Vol 15, pages 223- 239, January 1983, AeroVironment Inc., California, [2] The Pilot’s Handbook of Aeronautical Knowledge by Paul E Illman, pages 220- 248, 2008 [3] P.A. Henne, “Applied Computational Aerodynamics”, Progress in AIAA series, pages 434-440, 1990, Douglas Aircraft Company. [4] Higgins, George J.: The Prediction of Airfoil Characteristics. T.R. No. 312, N.A.C.A., 1929. [5] Knight, Montgomery, and Harris, Thomas A.: Experimental Determination of Jet Boundary Corrections for Airfoil Tests in Four 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 from Tests in the Variable- Density Wind Tunnel. T.R. No. 391, N.A.C.A., 1931. [7] Theodorsen, Theodore: On the Theory of Wing Sections with Particular Reference to the Lift Distribution. T.R. No. 383, N.A.C.A., 1931. [8] “Subsonic airfoil design – A historical background”, NACA Report to Congress of US. [9] Aerodynamics for Engineers, 5th 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 Density Wind 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 Design Optimization”, In Proceedings of The International Gas Turbine and Aero Engine Congress and Exposition, Bermingham, UK, June 1996

[13] D.H.Huddleston and CW Mastin “Optimization Methods Applied to Aerodynamic Design Problems in Computational Fluid Dynamics”, in Proceedings of the 7th International Conference of Finite Element Methods in Fluid Flow, Huntsville, Ala, USA, 1989

[14] A. Jameson, “Optimum Aerodynamic Design using Control Theory”, Computational Fluid Dynamics Review, Vol.3, Pages 495-528, 1995

[15] C Sung and JH Kwon, “Aerodynamic Design Optimization Using the Navier- Stokes and Adjoined Equations”, AIAA Paper 2001-0266

[16] B Mialon, T Fol and C Bonnaud, “ Optimization of High Subsonic Blended Wing Body Configurations”, AIAA Paper 2002- 5666.

G. Manikandan was born on 12th January 1969 from the famous big temple city Thanjavur, Tamil Nadu. He obtained his Engineering 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 put up 16 years of colorful service in Indian Air Force. In his credit, he overhauled 365 Rolls Royce Viper Turbojet Engine fitted on Kiran Aircraft and Carried out Structural Repairs and maintenance of Cheetah and Chetak helicopters and Kiran aircraft. He was team leader for several Structural re-fabrications of Ardhra and Rohini Gliders. He developed number of Un-manned Aerial Vehicles (UAV). Presently, his contributions are in the area of aerofoil shape optimization and flutter analysis. He was awarded best in trade and all-rounder for Kiran Aircraft in the year 2000.

M. Ananda Rao obtained B.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 “Machine Dynamics” in the year 1987. He worked over 33 years in Andhra University at various capacities. He worked in the Link Interchange Program with UK Universities for about 03 years sponsored by British Council and Government of India. He published more than 200 papers in International Journals and more than 50 papers in International and National Conferences. He was awarded three times “The Best Researcher Award” in the year 1992, 1999 and 2001. He worked as a technical adviser for Altair Company for the development of software in the domain of solvers. He is one of the renowned researchers in the area of Vibration and Condition Monitoring in the World. He was 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-c

Documents

aerofoil thickness

baseline aerofoil

effect of aerofoil profile

aerofoil profile variation

coefficient of lift

coefficient of pressure

standard aerofoil profile

ith gene