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Engineering

ELSEVIER Procedia Engineering 56 (2013) 560 - 567 ;

www.elsevier.com/locate/procedia

5th BSME International Conference on Thermal Engineering

Investigation of improved aerodynamic performance of isolated airfoils

using CIRCLE method

M U Ahmeda, E J Avitala, T Korakianitisab *

aSchool of Engineering, Queen Mary University of London, London E1 4NS, UK bParks College of Engineering, Aviation and Technology, Saint Louis University, Missouri 63103, USA

Abstract

The Prescribed suRface Curvature distribution bLade dEsign (CIRCLE) method, proposed by T Korakianitis, is a direct method for designing (or redesigning) high efficiency turbomachinery and fan blades, and isolated airfoils. It was initially introduced to improve the design of high efficiency turbomachinery blades. It is now extended for use with 2D and 3D turbomachinery blades and isolated airfoils. The connection of the profile's leading edge (LE) to the trailing edge (TE), on both sides, is defined using continuity in the surface curvature and its derivatives. Improvements to the aerodynamic performance of the Eppler airfoil are presented in this paper. Improved geometries with continuous curvature have been produced using the CIRCLE method. The performances of Eppler and the redesigned A5 and A6 have been studied using CFD analysis. They are analyzed considering low subsonic flow condition (Reynolds number-105). These are compared to a previous airfoil A4. The redesigned blades' LE proved favorable as they succeeded in removing pressure 'spikes' on the suction side. Comparative analysis with the original results showed significant aerodynamic improvements. Airfoils A4, A5 and A6 have comparatively thicker TE section compared to Eppler. Despite the changes made to the geometry and continuous curvature distribution in A4, A5 and A6 (from Eppler), there appear a separated region on the suction side at about 60% of the chord downstream from the LE. The new blades exhibit higher aerodynamic efficiencies, in terms of overall lift-to-drag ratio up to 40% than the original. The investigations are performed at on and off design conditions.

© 2013 The Authors. Published by Elsevier Ltd.

Selection and peer review un der responsibility of the Bangladesh Society of Mechanical Engineers Keywords: aerodynamics; blade; CIRCLE method; design;

Nomenclature

Co, Cj... thickness coefficients Subscripts

C1,C2.. Bezier control points in inlet station

C=1/r curvature defined with its radius o stagnation point

k1,k2... exponential thickness polynomials ot outlet station

M Mach number P pressure side

o throat circle p2 pressure side TE circle to y1

P pressure pm pressure side y1 to y2

P points on airfoil pk pressure side y2 to y3

Cp/L/D Co-efficient of pressure/lift/drag pi pressure side y3 to LE circle

s suction side

Greek s2 suction side TE circle to y1

* Corresponding author. Tel.: (314) 977-8283

E-mail address: korakianitis@alum.mit.edu (T. Korakianitis)

1877-7058 © 2013 The Authors. Published by Elsevier Ltd.

Selection and peer review under responsibility of the Bangladesh Society of Mechanical Engineers doi: 10.1016/j .proeng .2013.03.160

a flow angle P blade surface angle X stagger angle _□_angle of throat diameter

suction side y1 to y2 suction side y2 to y3 suction side y3 to LE circle

1. Introduction

Gas turbines have been among the most efficient energy conversion devices developed so far. Wind and hydro turbines have also secured a good place in the category. With increasing advancements in fluid dynamics and thermodynamics, the overall performances of these devices have enhanced [1]. One of the major components in these devices is the blade or airfoil [1]. They are placed in the fluid flow either to work on, or to extract work out of the flow. The blades operate under complex harsh conditions [2]. Blade design process, therefore, has a significant influence on the performance of the whole machine [3]. In general, 3D blade geometry is obtained by arranging 2D geometries along the center of gravity considering the associated limitations [3]. And the relevant 2D profiles are defined by streamlined curvature calculations based on the flow angles from hub to tip at the leading edge (LE) and trailing edge (TE) [3]. In order to make the design process simpler 3D blade cascades are considered to be 2D geometries placed in stream-wise direction [3, 4].

Performance of the blade profiles is expressed by blade surface and cascade passage property (such as Mach number, pressure, velocity, etc.) distribution along the chord [5]. Numerous techniques have been applied in blade designing, such as, direct method, inverse and semi-inverse method, optimization methods and etc. [5]. The objective of any method is to define the best profile which exhibits good aerodynamic and heat transfer performance with adequate structural integrity. This means disturbances upstream and downstream the profile should be minimized while complying with the constraints within the design conditions. For 3D profile generation, compromises are made to allow location of cooling and hollow passages. This paper presents a blade design approach using direct method. The process is defined by analyzing the aerodynamic performance of a specified blade profile. On the other hand, a typical inverse blade design method is defined as a method in which the preferred blade performance is defined and the geometry satisfying this performance is calculated [4].

Numerous works [3,4,6,7] have shown that it is difficult to obtain a desirable aerodynamic blade profile using inverse method. The inverse method has difficulties in both the LE and TE due to zero velocity at the stagnation points [3,4]. Inverse method can be applicable for generating compressor blades with very thin TE, but not to define a blade with thicker TE. Any blade which is designed with zero thickness TE becomes difficult to manufacture [4].

The work presented here, depicts a way of designing blades using Prescribed suRface Curvature distribution bLade dEsign (CIRCLE) method. It defines both turbomachinery and isolated profiles with continuous surface curvature and slope of curvature from the LE to TE for the suction and pressure sides. It can be used to design and redesign (improve) blades with higher efficiencies than their contemporaries, and can also be coupled with genetic algorithm based optimization method. CIRCLE method has evolved from a 2D turbomachinery blade design method to a 3D turbomachinery and isolated profile design method. Past studies [4,5] showed its applications in gas turbine blade redesign. Here the method's robustness in redesigning isolated wind turbine airfoils is presented. Following the global growing concern to switch to renewable energy source for the longevity of world's natural resources and environmental sustainability, wind turbine is one of the best choices for power plants. Results of redesigned wind turbine isolated airfoil, using CIRCLE method, is presented and discussed with few examples of other turbomachinery blades.

2. Background theory

The CIRCLE method defines each side of a 2D shape in three parts: yi near the LE; y2 in the middle part of the surface; and y3 near the TE. The stream-wise surface and slope of the curvature distribution is manipulated to optimize the aerodynamic performance. 2D shapes are designed near the hub, mean and tip regions and then the 3D shape is designed by maintaining continuity in the 2D parameters from hub to tip. This method does not use the traditional maximum thickness and maximum camber principles. It is guided by the surface pressure and Mach number distribution with their relation to continuous surface curvature distribution, and the outcome is the blade profile. Theoretical and experimental evidences

presented in [5] show curvature and slope of curvature affects aerodynamic performance of blade profiles. Continuous slope of curvature requires continuous third derivative of the splines used in the method. It is illustrated in the following two equations for curvature C and slope of curvature C', where y=f(x) as: 1 v"

C=l = —— (!)

c, _ dC _ y'"[l+y,2]-3yy"2

Figure 1 depicts CIRCLE method's background and its modification for generating compressor and isolated profiles. The LE and TE shapes are circular geometries defined by their corresponding radii, and inlet and outlet flow angles aj and a2 (Fig 1). Blade pitch plays an important parameter in turbomachinery profile while it is not used in isolated airfoils. Turbomachinery blades are set at their stagger angle 1 (Fig 1a-c) while it is set to zero for isolated profiles. Turbomachinery blades are defined on the suction by the distribution of the flow area and the minimum area along the passage (Fig 1). The throat circle o and its angle □ determine the suction side blade control point Psm and the corresponding blade angle fism. The corresponding input values for the pressure side control point Ppm and blade angle ppm are arbitrary values. The Psm and psm, for isolated airfoils, are independent of the passage area. The LE and TE circles are very difficult to connect with the other blade segments, as the circles have continuous curvature and rest of the surface have locally varying curvature. The TE radius and the A locate the TE circle. The two sides disengage from the TE circle at Ps2 and Pp2. This is controlled by fis2 and

Fig. 1. CIRCLE method's blade geometry development process [3]

The TE segmenty3 from PS2 to PSm is defined by an analytic polynomialy=f(x) of exponential form [5]:

y3 = f(x) = C0 + CjX + c2x2 + c3x3 + c4fe1[x — %(Ps2)] + £5^21* — ^C^)]

where, k1 and k2 are exponential functions depending on Ps2. The six coefficients c0 to c5 are evaluated from the slope and other derivatives' continuity at Ps2 and Psm. The line segment y2 between Psm and Psk is defined by mapping the curvature C vs X to the plane Y vs X using multiple point Bezier spline (e.g. Fig 1d). The curvature segment corresponding from Ps2 to Psm is evaluated from analytic polynomialy1 using Eq. (3). It is plotted on the C vs. X plane, from the TE at X = 1.0 and to point C6s (Fig 1d). The slope of the curvature Cs(x) at point C6s is computed from Eq. (3) and becomes an input to further calculations. Using central difference Eq. (1) is written for curvature at airfoil point I as a function of (x,y). Then the Bezier spline is iteratively computed until the slope and the y coordinate at Psk, and the shape of the curvature distribution matches reasonably. The LE circle similarly disengages at Ps1 and Pp1, defined by fis1 and ¡ip1. Then a parabolic construction line y and a thickness distribution yt are defined from the LE origin or circle center. They are defined to have continuous point and derivatives of the curvature at points Ps1 and Psk. For instance, construction line y may be defined as:

where, k11, k12, k13 and k14 are exponential polynomials and are dependent on Ps1 and Psk. And similar to Eq. (3) the c0 to c7 are evaluated from the continuity in y and its derivatives at Ps1 and Psk. Thus the whole approach ensures that continuity of curvature and slope of curvature from the TE circle to the main part of the blade surface through the LE yt and into the LE circle, for both surfaces of the blade. The control parameters C1, C2, C3 and C4 (Fig. 1) are specified smoothly to vary along the curvature's radius with the Bezier curves. Desired changes in 2D surface pressure or streamlines are compared with changes in 2D curvature distributions and the location of the 2D blade surfaces. After the first iteration (i.e. first geometric design and analysis) the user examines the resulting blade loading distributions, and decides where to alter local curvature and loading. After the second iteration the user gains an understanding of the magnitude of the required changes in curvature to cause the desired changes in Mach number or pressure distribution. The procedure is repeated until a desirable profile and aerodynamic performance are obtained.

3. 2D turbomachinery blade redesign

Performance of four redesigned cascades L25, L30, L35 and L40 was presented in [5]. For all cases, the cascades have been designed by changing the stagger angle while keeping the other variable constant. The computed results showed that increasing the k, while keeping other parameters constant, results in thinner and more front loaded cascades. As k increases, the o pushes both the blade surfaces farther down. This located the throat of the blade farther upstream on the suction side making the blade thinner. Consequently, this increased the curvature of the suction side and in turn increases the Mach number while loading the front accordingly [5]. It is predicted that there is one optimum k for which the wake thickness is minimum.

The LE has significant effects on the aerodynamic performance of an airfoil. Defining airfoil's LE with any method is very difficult. The approach in CIRCLE method is discussed earlier. Hodson [8] detected spikes on the LE experimentally due to discontinuity in the curvature. They experimentally tested HD blade. The redesigned HD blade, in Fig. 2, shows that the leading edge seperation spikes have been removed. This improvement is depicted with CFD computations in Fig. 2. I1, I4 and I9 are the redesigned stages of the original HD blade. The modified blades are restricted to have the same LE circle diameter and chord length. Therefore they ended up being a bit thinner near the LE, due to the reduction in the wedge angle. The curvature distribution (Fig. 2b) shows smoother lines for the redesigned profile than the original HD profile, obtained from [9]. The Mach number plot shows successful removal of suction side discrepancies and pressure side diffusion in the

y = f(x) = Ax2 +Bx + C

yt = c0 + ctx + c2x2 + c3x3 + c4ku[x - x(Psl)] + c5k12[x - x(Psk)] + c6k13[x - x(Psl)] + c7k14[x -

x{Psk)]

LE region of the redesigned profiles compared to the experimental results obtained from [9]. Experimental and computational results for Kiock blade show the existence of significant disorders on both surfaces [10]. Fig. 3a shows the surface curvature distribution of Kiock and S1, which is evident enough to show the improvements in the surface curvature discontinuity. Fig.3b indicates a variation in the thickness to compensate for a smooth continuous curvature around the profile. This resulted in the removal of small disturbances in the blade's Mach number distribution (Fig. 3c). This has resulted in smoother boundary layer displacement thickness and reduced the local entropy generation [3].

0.00 0.01 0.G1 ».03

(*) X (t>) (c)

Fig. 2. Original and redesigned HD blade's (a) LE, (b) curvature distribution and (c) Mach number distribution [4]

Fig. 3. Comparison of original Kiock blade with modified S1 blade (a) curvature distribution (b) geometry and (c) Mach number plot [3]

Fig. 4. (a) Geometries of Eppler, A4, A5 and A6; Curvature distribution of: (b) Eppler and A4, (c) A5 and A6

4. 2D isolated airfoil redesign

Isolated airfoils appear to be sparsely arranged, e.g. wind turbine airfoils, compared to clustered turbomachinery blades, i.e. turbine/compressor blades. Eppler 387 is a wind turbine airfoil candidate. From Fig. 4b, curvature discontinuity on its surface appears apparent. The CFD (depicted in Fig 4 and 5) and the experimental results [11] clearly show the LE disturbances on Eppler. Isolated airfoil appears to have 'curved-out' pressure side; therefore a slight modification in the CIRCLE method to define the pressure side has been used to redesign Eppler. Fig. 4a shows the geometries of Eppler with its stages of redesign: A4, A5 and A6. The redesigned blades appear thicker in the LE and TE regions. This removed the LE curvature disturbances that exist in Eppler. A4 shows better continuity in curvature compared to Eppler (Fig. 4b). A5 shows further improvement than A4 and A6 more than A5 (Fig. 4c and 5). The computations are based on typical wind turbine flow conditions [3], unlike high speed unsteady turbulent flow in turbomachinery. It was computed in a flow with Reynolds number 105; turbulence intensity 0.5% at various incidences, i.e. on and off design points. The Cp contours are plotted using CFD RANS model - Transition SST in ANSYS 13.0, with a 2D structured C grid, giving a y+<1.5. Figs 5a, b and c refer to computational and experimental Cp of Eppler and the redesigned blades. Figs 5b and c show the removal of the Eppler's LE noise from all the redesigned blades at a=4D (comparison to experimental data [11]) and a=8D (design point), respectively. Despite smooth curvature there exist boundary layer separation bubbles at 65-70% of the chord on the suction-side at a=4D, and 45-60% of the chord on the suction-side at a=8D; but reattaches turbulent soon after. This is due to the aerodynamic behavior of flow at such low Reynolds number. The laminar boundary layer becomes too weak to remain attached at that Reynolds number for those incidences. Nevertheless, suitable active or passive flow control method can be used to investigate further and optimize the aerodynamics at those instances. The polars results for the airfoils, which are obtained using XFoil [12], (Fig 5h, i & j) show the incremental aerodynamic improvement among the stages of Eppler's redesign. They exhibit a trend where A6 has overall better CL, CD and CL/CD performances, with a slight deviation near a=7D where A4 dominated till a=8D.

Percentage improvements in CD, CL and CL/CD calculated as, for CD: (ACD/CD_Eppler) x 100; for CL: (ACL/CL_Eppler) x 100; and for CL/CD: (A(Cl/Cd)/( CL/CD)Eppler) x 100 at design point. The following table depicts the implicit values from the polar calculations.

Table 1 Showing the polar results for CD, CL and CL/CD and their percentage improvements

Items Eppler A4 A5 A6

CD 0.031494 0.025046 0.02373 0.023304

CL 1.156052 1.196228 1.177495 1.196925

Cl/CD 36.70733 47.76206 49.62153 51.36147

% improvements from Eppler in CD -- 20.47451 24.65324 26.00452

% improvements from Eppler in CL -- 3.475276 1.854847 3.635568

% improvements from Eppler in CL/CD -- 30.11587 35.18153 39.92156

5. Conclusion

The paper presents the effect of CIRCLE method on airfoil design and redesign. It successfully comprehended the improvement of the Eppler 387 isolated airfoil. The references to the turbomachinery blade redesign show its overall proficiency in this field. From the polar results, it is found comparing with Eppler, the drag reduced 20.5% in A4, 24.7% in A5 and 26% in A6 at design point, and the lift improved 3.5% in A4, 1.9% in A5 and 3.6% in A6. These indicate an overall CL/CD performance improvement of 30.1% in A4, 35.2% in A5 and 40% in A6. It is deemed necessary for a paradigm shift to sustainable energy systems to meet global energy demand and emission targets. And it can be concluded from here, CIRCLE method can contribute in to the solution to current global energy crisis and emission problems.

I 00 0.50 0.00 •0.50 -1.00

PpplcT conputatKMi Fpplcf fVfflïwitd (tu

0.00 0.10 0.40 0.60 0.80 1,00

- - A4

\ - Ai

.......-AÖ

Eppler - - A4 --- A5 -----A6

0 ......... ffl

Fig. 5. Comparison of Eppler and the redesigned airfoils: (a) Cp distributions of Eppler computational with experimental and A4 computational results; Cp distributions of Eppler computational vs A4, A5 and A6 for: (b) a=4 □ , (c) a=8Q (design point); (d) LE Cp contour plot of Eppler; (e) LE Cp contour plot of A4; (f) LE Cp contour plot of A5; (g) LE Cp contour plot of A6; (h) CL variation against a; (i) CD variation against Ot;

(j) Cl/Cd variation against a;

Acknowledgements

The authors acknowledge the contributions of MSc and PhD students, and postdocs, who over two decades have contributed to coding various aspects of the CIRCLE blade design method in FORTRAN, C++ and MATLAB, and on various platforms and operating systems: George Pantazopoulos; Nick Vlachopoulos; Paschalis Papagiannidis; Dequan Zou; Richard Binzley; Sean Spicer; Brandon Wegge; Yan Tan; Mingyu Shi; Akbar Rahideh, M. Amin Rezaienia and Idres Hamakhan. The PhD research of Moin U Ahmed is partly sponsored by Cummins Turbo Technologies Ltd and partly by Queen Mary University of London.

Reference

[1] Fast M, Assadi M, De S, 2009, Development and multi-utility of an ANN model for an industrial gas turbine, Applied Energy, 86(1): pp 9-17

[2] Massardo A, Satta A, 1990, Axial-flow compressor design optimization. Part 1. Pitchline analysis and multivariable objective function influence. Trans ASME, J Turbomach, 112(3): pp 399-404

[3] Korakianitis T, Hamakhan I, Rezaienia M, Wheeler A, Avital E, and Williams J, 2012, Design of High-Efficiency Turbomachinery Blades for Energy Conversion Devices With the Three-Dimensional Prescribed Surface Curvature Distribution Blade Design (CIRCLE) Method, Appl. Energy, 89: pp

215-227

[4] Hamakhan IA, Korakianitis T, 2010, Aerodynamic performance effects of leading edge geometry in gas turbine blades. Appl Energy, 87(5): pp 1591601

[5] Korakianitis T, 1993, Prescribed-Curvature Distribution Airfoils for the Preliminary Geometric Design of Axial Turbomachinery Cascades, ASME J. Turbomachinery, 115(2): pp 325-333

[6] Dang T, Damle S, Qiu X, 2000, Euler-Based Inverse Method for Turbomachinery Blades, Part 2: Three-Dimensional Flows, AIAA J, 38(11): pp 2007-2013

[7] Phillipsen B, 2005, A Simple Inverse Cascade Design Method, 50th ASME Turbo-Expo, ASME Paper No. 2005-GT-68575

[8] Hodson H P, Dominy R G, 1987, Three-Dimensional Flow in a Low Pressure Turbine Cascade at its Design Condition, ASME J. Turbomachinery, 109(2): pp. 177-185

[9] Hodson H P, Dominy R G, 1987, The Off-Design Performance of a Low-Pressure Turbine Cascade, ASME J. Turbomachinery, 109(2): pp. 201-209

[10] Kiock R, Lehthaus F, Baines N C, Sieverding C H, 1986, The transonic flow through a turbine cascade as measured in four European wind tunnels. Trans ASME, J Eng Gas Turb and Power, 108(2): pp 277-284

[11] McGhee R J, Walker B S, 1988, Experimental results for the Eppler 387 airfoil at low Reynolds numbers in the Langley Low Pressure Turbine Tunnel, NASA-TM- 4062

[12] Drela M, Giles M B, 1987, Viscous-inviscid analysis of transonic and low Reynolds number airfoils, AIAA J, 25(10): pp 1347-55