Design of a Flapped Laminar Airfoil for High Performance Sailplane

Transcription

1 Design of a Flapped Laminar Airfoil for High Performance Sailplane Krzysztof Kubrynski 1 Warsaw University of Technology, Institute of Aeronautics and Applied Mechanics, Warsaw, Poland The paper discusses the following topics: opportunities to improve sailplane crosscountry flight performance, a quantitative assessment of the impact of the airfoil aerodynamic characteristics on the objective function adopted, way to solve the problem of aerodynamic design with an emphasis on correct determine the airfoil characteristics and finally presents the effects of aerodynamic design. Due to virtually no possibility for further reducing drag or improve L/D ratio of airfoil, the goal is mainly to increase the efficiency of energy extraction from the atmosphere. Aerodynamic design methodology is based on optimization technique using genetic algorithm and a modified program XFOIL to analyze the airfoil characteristics. An example of aerodynamic design of the airfoil, as well as computational and wind tunnel results of an optimized airfoil are presented. Nomenclature Hk N Re M boundary layer kinematic shape factor laminar boundary layer disturbance amplification exponent chord Reynolds number I. Introduction odern nowadays high performance gliders have reached very high level of aerodynamic efficiency measured by lift to drag ratio at large range of speeds. Maximum L/D ratio reached value over 60, which means glide angle below 1O. Thanks to modern aerodynamic concepts and advanced computational methods minimum drag of nowadays sailplane airfoils have reached value below at Reynolds number about 2.5-3mln. Fig. 1 presents typical drag contributions at variable lift coefficient (and speed) for high performance 15-meter class sailplane. All elements reach nearly minimum possible drag. It can be found opinions, that aerodynamic development of modern sailplanes have such high level, that it is no guarantee that the new sailplane will be better then the existing ones. Laminar flow extent is up to about 70% of an upper surface and up to 95% on lower wing surface. Farther improvement of aerodynamic efficiency is really nearly impossible without using new aerodynamic concepts (such as active boundary layer control) which must be costly and rather impractical for widespread operating. Figure 1. Sailplane components drag variation with lift coefficient. 1 Associate Professor, Faculty of Aerospace and Power, AIAA Member. 1

2 But there is still some space for improvement of overall performance by careful design and optimization of all elements (including some assistant devices, as speed flaps or winglets). On the other hand the main objective of modern sailplane design is the maximization of overall performance that can be measured by cross-country speed at specified thermal conditions, that depends not only on low drag or high lift to drag ratio of a plane. To address and study of such a problem, a mathematical model of cross-country flight must be established and used to optimize/determine of the sailplane design parameters. Such an approach must take into account the thermal model, sailplane aerodynamic characteristics (dependent on various design parameters and aerodynamic technology ), and mass (water ballast amount). The problem is very complicated (especially weather and thermal conditions), so only a very simplified approach can be used. The most clever method for improvement of ov erall sailplane performance is better extraction of atmospheric energy when circling inside thermal or due to vertical wind velocity gradient. Analysis of circling efficiency in a typical thermal (that have radial updraft gradient with maximum near center) shows that for better efficiency higher value of lift coefficient is required even in some cost of drag. Detailed analysis of this problem is presented in [4] and can be seen in Fig. 2. Figure 2. Sample dependency of sailplane rate of climb in thermal vs lift coefficient. Modern, highly laminarized airfoils utilize speed camber changing flaps that allow for some adoption of airfoil to current flow conditions and finally higher maximum lift at low speeds and lower drag at high speed. Such lowdrag glider airfoils currently in use have specific features [1,2,3,4]. The lift characteristics at higher angles of attack have a local decrease of lift with increasing angles of attack (has a local minimum). The reason of such a feature is the abrupt forward movement of transition point along the upper wing surface and the thickening of boundary layer on a highly laminarized airfoils. Typical characteristics of such a modern airfoil is shown in Fig. 3 [1,2]. Figure 3. Measured aerodynamic characteristics of airfoil DU97-127/15 at Re=1.5*10 6 and various flap settings [2] 2

3 Such a local minimum in the lift curve can have significant influence on sailplane s behavior during entering thermal and flying in a turbulent thermal. The situation is explained schematically in Fig.4. In a case of angle of attack during circling near local maximum of CL (and close to the low drag bucket upper limit) a downward gust (one that decreases the angle of attack) leads to some loss of lift and some loss of altitude. An upward gust (one that increases the angle of attack) leads to additional lift in the case of a monotone lift-angle of attack relationship, and an increase in climb rate. However, in the case when the lift curve has a local minimum as noted, an increase in angle of attack leads to a loss of lift and altitude. A variation of angle of attack due to a gust during circling can reach up to about 8 deg. Thus, there can be a significant problem in circling at such a value of the lift coefficient due to both the loss of climb efficiency and the danger of stall. This means that circling at lower C L is necessary for in case of an airfoil with lift characteristics containing local minimum. Figure 4.. Sketch of airfoil behavior at angle of attack changes due to vertical gust. Additionally the local minimum in lift character produces additional problems with safety (possible unintended stall) as example it is possible (and quite frequent) hard landing due to sudden stall just before reaching ground. The next problem is high sensitivity of highly laminarized airfoils with flaps on non-smooth surface/insects/rain. In a case of turbulent flow starting near a leading edge (due to insects/rain) usually boundary layer separates in a pressure recovery region having high pressure gradient, that significantly deteriorate aerodynamic efficiency of a sailplane (lift lost, drag rise). The first high-performance sailplane that was equipped with flapped airfoil without local lift decreasing (at least in intentions) was Diana-2, designed by the author [4,5] that up to now reaches nearly all top locates in 15-m class glider competitions. Design of airfoil was performed using computational methods only: XFOIL [6] and MSES [7] programs of Mark Drela and inverse boundary layer design code [8]. Computational results were enthusiastic: basic wing airfoil KL f - Fig. 5 (really airfoils because different sections along a span) seams to have monotone lift character up to high flap angles and (compared to best competitors) higher max. lift coefficient, lower min. drag and weaker sensitivity for turbulent flow (insects/rain) in entire range of lift coefficients and flap deflections at a cost of stronger sensitivity for proper flap position (narrower low drag bucket). Computational results were successfully implemented in practice, result in the best currently 15-m class competition sailplane [9]. On the other hand there was no check of real characteristics in a wind tunnel tests. Current work contains further investigation (both theoretical and experimental) on such airfoils type. The main points of investigations are: 1) 2) 3) 4) 5) 6) detailed investigations of an influence of airfoil lift characteristics on final sailplane performance wind tunnel tests of pneumatic turbulator system, used on lower wing surface in order to force transition design reconstruction and detailed investigations of a typical high performance airfoil [1] further investigations (computational and wind tunnel) of basic basic Diana-2 and other flapped airfoils modification of aerodynamic software used in order to improve computational predictions developing of a new aerodynamic design methodology and preparation possible better sailplane airfoil. The paper describes basic elements of the first point and detailed effects of the investigations performed at last two points of the project. 3

4 Figure 5. Computational characteristics of Diana-2 airfoil and typical modern airfoil clean and wet conditions simulated, a) no flaps, b) flaps down. Influence of airfoil character on final sailplane performance was studied via simple (two-dimensional) flight simulator that calculate sailplane dynamics in specified atmospheric gusts/turbulence (vertical and/or horizontal) including pilot influence via joystick. It was found, that in a case of local CL minimum increment of vertical velocity produce negative vertical acceleration, initially lost of altitude and horizontal speed increment. Also there is no clever pilot input that could improve net rate of climb. In a case of monotone CL character positive gust produces positive load (important for pilot filling of thermal air-masses structure) and smaller horizontal velocity increment (increase time spent in stronger lift compared to non-monotone case). Additionally there is possible pilot action improving energy extraction due to some extra lift margin. Similar opinions are expressed by competition pilots but only using simulation it was possible to get quantitative results! Typical simulation (gust along a path) for non-monotone case and monotone one presents Fig. 6 (without influence of pilot and without additional atmospheric turbulence ). Gain in this case is about 3%. With pilot influence can be even better (up to about 5%). In the case of atmospheric turbulence sailplane experience additionally Katzmayr effect [10], which allows for additional extracting of turbulent energy. Detailed studies show that the efficiency of this depends on both the sailplane design parameters (mass, moment of inertia, longitudinal stability margin etc.) and the wing lift slope value. Monotonicity of lift characteristics allows for additional profit. Additionally non-monotonic lift characteristic result in greater variation of the instantaneous angle of attack value, increasing losses. The information obtained based on the above analysis (both static and dynamic behavior of the glider) allowed to determine the sensitivity of various parameters and factors (also not described here glider design parameters) on the final efficiency expressed as a cross-country speed obtained in specified thermal conditions. They were used as background for design procedure used to develop new, optimized airfoil for high performance sailplane. Figure 6. Simulation of a sailplane dynamics in vertical gust for non-monotone (left) and monotone (right) lift case. 4

5 II. Design methodology T he basic design methodology used in presented studies is based on optimization techniques using genetic algorithm. In the present computations standard PGAPack library [11] was used for this purposes. The objective function, cross-country speed, was evaluated at given thermal conditions and some basic sailplane design data: span, aspect ratio, mass, fuselage and empennage drag etc. [4,5]. Sensitivities of various parameters: airfoil drag polar, CL at circling (defined at specified minimum local dcl /dα value), dcl /dα above circling CL, CL_max, L/D at circling, etc. have to be prepared as input. Particular values of sensitivity parameters were calculated using analysis of both: static and dynamic sailplane characteristics in flight. Static aerodynamic characteristics have strong influence on altitude loses (sink) during entire flight - mainly at inter-thermal flight, but also during circling. Lift coefficient value at circling determine net climb rate in a given thermal as describe earlier (Fig.2). Dynamic influences comes from the analysis described in the previous point, as a result of flight simulations performed for various airfoil characteristics and fixed sailplane design parameters. Airfoil geometry was decomposed into thickness distribution and camber line. Both were expressed in a parametric manner. Optimum airfoil geometry, flap chord size, flap deflections and turbulator location on the lower airfoil surface (used in order to prevent laminar separation) were found as a result of using genetic optimization method. Penalty function was added to the objective function in order to fit thickness and other parameters in a reasonable limits. Presented later results were obtain using 4-core PC. Scalar PGAPack library version was used, but objective function (the most costly part of the computational algorithm)was evaluated applying parallel processing. Flow over airfoils was calculated using variable Reynolds number, that corresponds to level flight (load factor n=1) at sea level equal to Re = / CL. This value is slightly lower then most sailplanes have (corresponds to slightly lighter sailplane or smaller chord higher wing aspect ratio). Entire airfoil polar was calculated in order to evaluate single value of objective function. Flow analysis was performed using well known, but modified XFOIL program of Mark Drela [6], that was used in a batch mode without screen output. A special effort was put into the accurate determination of computational aerodynamic characteristics of an airfoil, as the design effect depends mainly on the correctness of this analysis. III. Flow analysis T he airfoil flow analysis code XFOIL is probably one of the most efficient and popular for low Reynolds number computations. It is based on strong viscous-inviscid interaction, that allows to determine characteristics with small amount of trailing edge separation and with laminar separation bubbles. Laminar-turbulent transition point is calculated using envelope e^n method. The main drawback of the program is usually underprediction of a drag [12] and over-prediction of a maximum lift. A great effort was undertaken to improve the estimation of aerodynamic coefficients of the airfoil, in particular to improve the estimation of maximum lift, lift characteristics at higher angles of attack (in order to determine the possible local minimum in CL) and to improve the drag estimation. The work was based not on an extensive analysis of the formulation used in the original XFOIL, but rather on the calibration of the method in order to achieve better consistency with experimental results in the widest possible range of the calculation /measurement conditions. In the Figure 7a a comparison of Althaus wind tunnel tests results (extracted from [13]) of SM-701 airfoil and basic XFOIL results is presented for Re=1.5 million. Quite a large discrepancy is seen. Slightly better results can be obtain using smaller critical amplification ratio NCR=6, but still character of drag polar is not satisfactory. The first attempt to improve results was implementation of full e^n method for transition determination. Applying default value of N=9 result in slightly better result of upper CL limit of low drag bucket, but even much worse prediction on lower surface transition and lower CL limit of drag bucket Fig. 7b. Correct location of low drag region can be obtained by specification of the critical N value separately for lower and upper surface in a full e^n method Fig. 7c. A large differences in NCR for both surfaces is required in order to reconstruct proper laminar bucket limits: NCR_UPP=11, NCR_LOW=5.2. Improvement in drag prediction can be achieved by modifying expression for friction coefficient in turbulent boundary layer. Simple multiplier for turbulent friction was currently applied. Really it was used XFOIL option CFAC provided but hidden by author in the original code. In the Fig. 7d it is seen effect of simple enhancement of friction coefficient1 by 50% (CFAC=1.5). A great improvement is seen in all: drag, maximum lift and moment prediction. Some differences still exist in CL_MAX prediction. It was found, that large dissipation in the wake just behind the trailing edge produce rapid reduction of the wake displacement thickness (equivalent to strong sing distribution along a wake near the trailing edge) producing lower pressure just at the trailing edge, suppressing tendency for flow separation on the upper surface. 5

6 Figure 7a. XFOIL computational analysis of SM-701 airfoil - results for default formulation (NCR=9) and for lower critical amplification rate (NCR=6) Figure 7b. Comparison of basic envelope e^n method for transition location and full e^n method (NCR=9) Figure 7c. Airfoil polar for full e^n method and two NCR (11 & 5.2) and individual values for upper and lower surface (upper NCR=11 / lower NCR=5.2) Figure 7d. Airfoil characteristics calculated with enhanced turbulent friction coefficient 6

7 Figure 7e. Airfoil characteristics with original and reduced dissipation in a wake Figure 7f. Default XFOIL formulation and finally modified formulation results comparison for SM-701 airfoil In the original program simple multiplier for dissipation in the wake is used in order to double dissipation relative wall boundary layer. MSES code of the same author uses the same boundary layer formulation, but wake layer is calculated in slightly different manner. Comparison of both results shows, that in a case of high angle of attack and strongly non-symmetrical upper and lower layers at a trailing edge XFOIL uses much larger dissipation. Reducing multiplier used in XFOIL it is possible to increase compatibility of the two methods and further improvement of CL_MAX estimation Fig. 7e. In the present formulation wake dissipation multiplier varies along the wake and depends on local value of a wake shape factor Hk. Such formulation produces too low dissipation at small angles of attack, but it does not cause any noticeable disturbances in the pressure distribution or aerodynamic coefficients. Final results compared to original formulation and wind tunnel results are presented in Figure 7f. It is worth noting that default XFOIL transition formulation and settings does not reconstruct wind tunnel results as overpredict laminar flow zone. But seting in the envelope e^n method the N CR to 7 on upper surface and 6 for lower allows to get proper characteristics. For better recognition the applicability of the presented modifications, and even better calibration of the method, based on available wind tunnel tests, a number of comparisons of computational results with the experimental results (from various wind tunnels) were performed. Particularly interesting was the calibration of the method based on the wind tunnel data of modern, high-performance glider airfoils. The multipliers for turbulent friction coefficient and wake dissipation were determined due to calibration using such airfoil. Friction coefficient was enhancement by 50% (CFAC=1.5) and wake dissipation multiplier was 1.0 just near the trailing edge and 1.4 down. Due to the rather interesting results of the study and comparison, results of the analysis are presented below. It is worth noting that the increase of friction by 50% causes usually much smaller increase of airfoil drag, which results both from a limited area of turbulent flow, and changes in the velocity distributions in the boundary layer (its thickness and shape factor Hk). Sometimes differences due to higher friction coefficient produce nearly no drag chances but significant maximum lift reduction. The presented cases come from the wind tunnel tests of DU89-138/14 airfoil, designed and tested in a low turbulence wind tunnel at Delft University of Technology [3]. Tests were performed at Reynolds numbers 0.7 million to 3 million and flap deflections changes from -4 deg to +25 deg. Chord of the tested wing was 500mm. The 7

8 ZIG-ZAG turbulator was used on the lower airfoil surface at 82% of the chord in order to prevent laminar separation. It is worth noting that due to forced transition on the lower airfoil surface, drag above lower C L limit of low drag bucket depends only on correct transition prediction on the upper surface significantly reducing ambiguity of correct computational parameters choice in order to ensure compatibility of computational and experimental results. The lower limit of the angle of attack and lift coefficient at which there is an increase of drag means the movement of the transition point below the 82% chord on the lower surface. The turbulence level in the test section varied from about 0.02% for the Reynolds number 0.7 million to slightly below 0.1% for Re = 3 million. Fig. 8a presents drag comparison for flap 4 deg. and Re=3 million using default XFOIL formulation and using above presented modifications (the same amount of turbulent friction enhancement and the same dissipation reduction). In order to reconstruct wind tunnel result full e^n method was used with N CR=10.5 for upper surface and very low NCR=4.2 for lower surface. It is worth to notice, that original XFOIL envelope method predict rather correctly lower limit of drag bucket using NCR=9 for both surfaces (best correlation is obtained using NCR=8). It is well known [14], that envelope method underpredict amplification ratio in a case of non-simmilar decelerating flow (increasing the value of shape factor) and overpredict in a case of accelerating flow (decreasing the value of shape factor). High performance sailplane airfoils have rather special geometry and pressure distribution. Typically in order to get as wide low drag bracket as possible special pressure distribution is applied on lower airfoil surface at low angle of attack. A large negative pressure peak occurs near a leading edge followed by rapid pressure rise just behind it. Due to the very thin boundary layer there is no tendency for laminar separation, and the shape factor decreases the value (despite the increase in pressure). In the rear part of the airfoil it is applied zero or slightly negative pressure gradient for further reduction the shape factor, reduction of rapid growing of Tollmien-Shlichting waves and finally to prevent tendency for natural transition. Near the trailing edge in front to the pressure recovery zone turbulator (mechanical or pneumatic) is applied in order to force transition and prevent laminar separation. Envelope e^n method adopted in original XFOIL code generally rather accurately predicts lower C L limit of low drag bracket (despite the fact of overpredicting the real amplification ratio), but usually produce to large region of laminar flow on upper surface at larger angles of attack. Figure 8b present results using previous modification in friction coefficient and dissipation, but using original envelope method using default value of NCR=9(that underpredict drag) and NCR= 7/8. Figure 8a. Drag polar, flap: -4 deg, Re=3 mln Original XFOIL formulation and modified one with full e^n method and selected NCR. Figure 8b. Drag polar, flap: -4 deg, Re=3 mln Original XFOIL modified formulation with original envelope e^n method: NCR=9 and NCR= 7(upper) / 8(lower) 8

9 In the Fig. 9 pressure, shape factor and amplification exponent distributions on the airfoil are presented at CL=0.184 (lower limit of low drag). Along the airfoil chord on the upper surface flow initially accelerate then decelerate. There is exactly opposite situation on the lower surface. Shape factor growth along chord in the laminar part of upper surface and decrease on the lower. As a result it is seen that envelope e^n method significantly overpredicts amplification of initial disturbances on the lower surface and underpredicts on the upper (at correct transition point it evaluates slightly above N=6). It is worth to notice that modes of all frequencies on upper surface are amplified up to transition point, while on the lower are initially amplified and then sharply damped until they disappeared. Transition on the lower surface is really not possible to predict properly using full e^n method. Specifying unusually low NCR it is possible to get proper value of drag bucket, but the predicted transition point jumps in a discontinuous manner toward the leading edge and drag rise is much faster for lower angles of attack then that observed in the experiment. a) b) Figure 9. Flow analysis at CL=0.184, Re: 3.0mln. flaps: -4 deg. a) pressure distribution, b) shape factor, c) amplification factor N c) Even more interesting case is presented in the Fig. 10 flap deflection -4 deg, Re=0.7 mln. Experimental lift value at low drag limit is CL= Transition on a lower surface occurs in a healthy laminar boundary layer (Hk ~ 2.4). Maximum amplification exponent obtained from full e^n method is only about 4 with maximum near the leading edge. Towards the tailing edge all modes lost amplitude and at true transition point maximum amplification reached value slightly over 2. This is in a total contrast with envelope method N factor rise monotonically and reaches value 8 at transition. On the upper surface there is a strong laminar separation bubble and in order to reconstruct proper drag very large critical N factor (15) must be used. Envelope N factor have at proper transition point value 10. It was found that every time there occurs loss of modes that had previously reached the large amplification value, in order to reconstruct correctly lower C L limit of a low drag (and thus correctly identifying the condition of a rapid movement of transition toward the leading edge) it is necessary to use very low value of N CR in a full e^n method. Additionally there seems to be no correlation between proper value of N CR and turbulence level for such a case. In some cases the correct movement of transition point is not possible at all (Fig. 10) as there is rapid jump in predicted transition location from turbulator position to the leading edge. Wind tunnel results suggest fast but gradual drag rise in this case. A simplified envelope method, despite the obvious error in determining the amplification envelope, provides a reasonably good prediction of transition in such cases and compatibility with the experiment. 9

10 a) b) Figure 10. Flow analysis at CL=0.045, Re: 0.7mln. flaps: -4 deg. a) pressure distribution, b) shape factor, c) amplification factor N c) Subsequent Figures shows comparison of predicted computational results using original XFOIL formulation with default control parameters and modified one using both full e^n method for transition location with the best choice of critical N value separately for lower and upper surface. Figure 11 presents comparison of results for Re=2.5mln and flaps= 0 deg using default XFOIL formulation and modified one with full e^n and NCR =10.5 & 6 for upper and lower surface respectively. The same characteristics can be obtain using envelope method with NCR =8 & 9. It is seen correct reconstruction of experimental results. Figure 11. Airfoil characteristics at Re= 2.5 mln, flap deflection: 0 Slightly more interesting case is presented in Fig. 12, for Re=1mln and flaps 10 deg. Generally it is seen good agreement between experiment and computations using NCR =11 & 6. Additionally it is seen that enhancement of local turbulent friction coefficient produces nearly no airfoil drag increment. But it is possible to get even better resolution of the first local maximum of C L (and corresponding drag) decreasing gradually NCR for upper surface when increasing angle of attack above 4 deg. For this range of angles of attack it is altered character of T-S modes 10

11 amplifications curve, and there is a strong suppression of previously amplified mods. In such a case it is not possible to reconstruct experimental results using single value of NCR for entire range of angles of attack in full e^n method. Figure 12 Airfoil characteristics at Re=1.0mln and flap deflection 10 deg. The problem is better explained in the next example, for Re=0.7 mln. and flaps 18 deg. The lift force has local minimum near CL_MAX and there is a concave drag character in the low drag bucket. In order to reconstruct all characteristic features of the airfoil properties it is required to use different critical amplification ratio values in full e^n method in various ranges of angle of attack. In order to get concave drag character it is required large value of NCR=14 on both airfoil surfaces. In order to get proper lower C L limit of low drag it is required to use low NCR=8 for lower surface at this conditions. In order to reconstruct lift and drag near C L_MAX it is required decreasing NCR on upper airfoil surface when increasing angle of attack. It can be observed that the reduced value of NCR is required whenever there is damping of T-S modes that had previously reached significant amplification Fig On the other hand it is seen that amplification ratio N calculated using envelope method have at free transition location in all cases rather similar value close to The same airfoil characteristics calculated with modified XFOIL formulation and envelope method using NCR = 10.5 & 9 are presented in the Fig. 13. So in the summary it can be concluded that the envelope method used for linear stability analysis in XFOIL, despite its approximate nature, like automatically adjusts requirements for relevant conditions without having to change the critical N value! In the example calculations the best choice of NCR used in envelope method was This is in contrast to the full e^n method, the application of which require a detailed knowledge of flow conditions, changing value even when changing the angle of attack. The presented study shows the possibility to get correct values of aerodynamic characteristics of an airfoil using slightly modified XFOIL code at least for the case of quite specific sailplane airfoils. Still incomplete analysis suggests however that a modification of the method is effective also in a wider range of applications. Fig. 13 Re: 0.7 mln, flaps 18 deg, envelope method, NCR = 10.5 / 9. 11

12 Figure 14. Characteristics, pressure distribution and T-S amplification ratio at Re=0.7 mln and flaps 18 deg. 12

13 IV.Airfoil design T he previously shortly described design methodology, required sensitivities to estimate objective function and modified XFOIL computer program were used to find airfoil shape, turbulator location, flap chord and deflections that maximizes the objective function (cross-country speed) at typical weather conditions (wide thermals, updraft at a center slightly above 3.5 m/s, that provide net climb rate about 2 m/s). Sailplane mass was specified as 500 kg, all other design parameters were adopted from Diana-2 plane. Reynolds number for various angles of attack varies as Re = / CL. It was used full e^n method for transition location while critical amplification exponent was specified individually for each point of airfoil polar. Friction coefficient multiplier CFAC used in the computations was also slightly smaller: 1.3 (as initial estimate of the best value of CFAC was just such) and dissipation in a wake was slightly larger (near the trailing edge 1.2, currently used 1.0). As the initial geometry the airfoil KL f was specified the basic airfoil of the Diana-2 wing. In the Fig. 15 history of optimization process using genetic algorithm is presented. The expected objective function for the initial airfoil is about 109 km/h cross-country speed. Results of optimization is objective function about 2.5 km/h higher compared to the starting airfoil, that was created using inverse design method. The presented results required almost 120 hours of computations on a 4-core PC computer. Red points express objective function. The blue points include penalty function due to exceeding constraints. Figure 15. Airfoil optimization history chart. Subsequent Figures show influence of various geometrical and aerodynamic parameters on the objective function and trends for the population of airfoils. In the Fig. 16a it is seen influence of relative thickness on efficiency. A flat maximum exist in the thickness range 12.6 to 13.7 % with the extreme at 13.2%. In the next Figure (16b) influence of flap axis position is presented. A rather sharp optimum exist at 87% of a chord (equivalent to 13% flap chord). This is in contrast to existing solutions, in which the relative flap chord ranges from 14 to 17%. Baseline airfoil KL f has 17% flap size and apparently obtained by him objective function is the maximum the optimization program was able to found for this parameter value. Turbulator location seems to be not so important for final airfoil efficient provided that is behind 90% of a chord. Designed airfoil have forced transition at 91% of the chord, which seems to be a mild maximum. Lift coefficient at circling (defined as lift coefficient at which lift slope lost 30% of its initial value) reaches rather high value,as have strong impact on rate of climb efficiency in a thermal. The best airfoil have such defined C L value equal about 1.55 really high. Lift slope just above the circling conditions (Fig. 16e), defined as minimum local value of dcl/dα in some range of angles of attack just above circling conditions is slightly positive and thus prevents the appearance of a local minimum of CL on the characteristics and ensures monotonicity of lift. Minimum airfoil drag at low lift conditions is slightly larger then one would get but reducing it has a negative impact on other important properties of the airfoil and lowers its final effectiveness. Maximum lift coefficient (Fig. 16f) for the optimal airfoil was estimated at approximately 1.65, which is a very promising result. 13

14 Figure 16a. impact on population. Relative thickness efficiency of airfoil Figure 16b. Influence of flap axis location on efficiency of airfoil population. Figure 16c. Influence of turbulator location on efficiency of airfoil population. Figure 16b. Influence of obtainable lift coefficient at circling in thermal on efficiency of airfoil population. 14

15 Figure 16e. Optimum value of airfoil lift slope above circling conditions for airfoil population. Figure 16f. Minimum airfoil drag coefficient tendency for optimized airfoils Figure 16g. Maximum lift coefficient for optimized airfoils. The final airfoil, designed as KL f, has been derived from the best one obtain in optimization process, by using the inverse method - mainly to remove any possible waves on the surface. The shapes of three airfoils: a typical flapped sailplane (having design principles similar to the presented in [1]), the airfoil of Diana-2 wing (KL f) and the new design KL f are shown in Fig. 19. Calculated aerodynamic characteristics for these three airfoils at Reynolds number Re = / CL (slightly higher then the used in optimization, but more closed to the design Re numbers of first two airfoils) are shown in Figure 20, for the flaps not deflected, for flaps 20 deg. and flaps 25 deg. It is seen that minimum drag with no flap deflection is nearly the same for all airfoils. At higher flaps all three airfoils have similar values of usable lift coefficient (for circling) at given flap deflection. The only difference is lift slope above this value. DU-type airfoil have rather strong local lift minimum at 20 and 25 deg. flap deflection. KL f airfoil shows local closed to zero slop at 20 deg. flap and small negative slope (mild local minimum in lift confirmed in wind tunnel tests) at 25 deg flap angle. The new airfoil shows no such problems have monotone lift curve. Predicted by the optimization program flap deflection for circling conditions was even higher then 25 deg. - nearly 30 deg. Calculations show that the monotonicity of the lift force is kept to a flap 15

16 deflection angle even above 30 degrees, despite the mild separation already present on the flap. In the Fig. 18d calculated characteristics are presented for the new airfoil at 25, 30 and 35 degree of flap deflections. Great improvement in characteristics can be seen in the light of the objectives pursued under the overall assessment of the impact of the airfoil on the final glider performance in flight. a) b) Figure 17. Geometry considered airfoils: a) DU-type [1] b) KL f c) KL f of three c) Figure 18a. Calculated airfoils characteristics, flap angle 0 deg. Figure 18b. Calculated airfoils characteristics, flap angle 20 deg. 16

17 Figure 18c. Calculated airfoils characteristics, flap angle 25 deg. Figure 18d. Calculated KL airfoil characteristics, flap angle 25, 30 and 35 deg. T V. Wind tunnel tests he final verification of the designed airfoil are wind tunnel tests. Some preliminary results were obtained in the two-dimensional low speed wind tunnel at Warsaw University of Technology, Institute of Aeronautics and Applied Mechanics Figure 19. It is relatively small tunnel of closed-return type: closed test section have dimensions 0.46 m X 0.67m. Maximum speed is about 90 m/s. It is equipped with single stage fan, cooling system, 8 anti-turbulence screens and contraction ratio about 10. As it was recently rebuilt and modernized not been carefully tested the quality of the stream. The results indicate that up to a speed of about 50 m/s have a very low level of turbulence. Two models of a chord 260mm and 390mm were prepared. The second mainly to test at small angles of attack only in order to get higher Reynolds numbers. The models have a camber changing flap. A total of 64 pressure orifices were drilled (0.3mm diameter) to measure pressure distribution on the wing and flap. Additional pipe is mounted in a flap at 89% of wing chord and drilled (0.4 mm diameter and 4 mm intervals for 260 mm chord) that is used as pneumatic turbulator. A total pressure and static pressure wake rake is located at 80% chord distant behind model trailing edge. Pressure distribution on a model, wake, in a setting chamber and confusor are read using automatic multi-tube liquid manometer. Standard low-speed wind tunnel corrections [15] were used with second order terms (mainly in a case of higher chord). No streamlines curvature correction was applied to present aerodynamic coefficients in pressure distribution data. Figures 20(a-e) present test results of 260 mm model at Reynolds number 0.7 million, that correspond to flight conditions near maximum lift. Additionally there are presented computational results obtained using modified XFOIL program using default envelope e^n method for transition prediction and NCR = 9. Generally satisfactory results were obtained in wide range of angles of attack. For angles of attack above 7-8 deg there occur rapid decrease in lift coefficient, which is not reproduced in calculations. Computational results predict long plateau in the CL that does not exists in wind tunnel test results, but which is in principle beyond the useful range of angles of attack. In general there was obtained also a satisfactory agreement in the pressure distributions for the basic range of angles of attack and flap deflections, including conditions with flow separation. In the Figures 21(a-c) wind tunnel results obtained for a model having higher chord (390 mm) in a limited range of angles of attack are presented. Flap is set at neutral position and Reynolds number is varying in a range 1.5 to 2.4 million. A good agreement with computational results is also seen. Figure 22 shows sample pressure distribution on a model at Reynolds number 0.7 million, flaps 30 deg and angle of attack -5 and 12 deg. 17

18 Figure 20. General view of low speed wind tunnel at Warsaw University of Technology and aerodynamic models of flapped airfoil. a) b) c) d) e) Figure 20. Calculated and measured aerodynamic characteristics at Re=0.7 million and various flap angles: a) flap 0 deg b) flap 10 deg c) flap 20 deg. d) flap 30 deg. e) flap 35 deg. 18

19 a) b) Figure 21. Calculated and measured aerodynamic characteristics for flap position 0 deg and and various Reynolds numbers: a) Re = 1.5 million b) Re = 2.0 million c) Re = 2.4 million. c) a) b) Figure 22. Calculated and measured pressure distribution on KL airfoil at Re=0.7 mln, flap: 30 deg a) alfa: -5 deg, b: alfa: 12 deg VI. Conclusion The paper presents an efficient methodology for aerodynamic airfoil design, which should provide improved in overall performance of sailplane in thermal flight. Assessment of requirements was carried out using a simple flight simulator, which allows for quantitative evaluation the impact of airfoil on the sailplane performance. The paper presents a simple modification of the XFOIL program that significantly improves, at least for the considered category of airfoils, evaluation of aerodynamic characteristics of airfoil. The optimized airfoil was designed and wind tunnel tested, demonstrating the efficiency and effectiveness of the proposed approach. 19

20 Acknowledgments The research was supported by Polish Ministry of Science, Research Contract 2867/B/T02/2008/35. References 1 Boermans L.M.M, van Garrel A., Design and Windtunnel Test Results of a Flapped Laminar Flow Airfoil for HighPerformance Sailplane Applications ICAS Congress, 1994, ICAS Boermans L.M.M, Research on sailplane aerodynamics at Delft University of Technology. Recent and Present developments, NVvL presentation Boermans L.M.M,, Heijma P.M., Two-Dimensional Aerodynamic Characteristics of Airfoil DU89-138/14, Delft University of Technology, Low Speed Laboratory, Internal Report LSW 90-4 (SZD Factory, Bielsko-Biala), June, Kubrynski K., Aerodynamic design and cross-country flight performance analysis of Diana-2 sailplane OSTIV Congress, Eskilstuna 2006, Technical Soaring, Vol. 30, No. 3, July, 2006, pp Kubrynski K., High Performance Sailplane Design Strategy Using Inverse Design and Optimization Techniques Inverse Problems, Design and Optimization Symposium, Miami, Florida,U.S.A., April 16-18, Drela M., XFOIL: An Analysis and Design System for Low Reynolds Number Airfoils, Low Reynolds Number Aerodynamics, Ed. T.J. Mueller, Lecture Notes in Eng. 54 (1989) 7 Drela M., Design and Optimization method for Multi-Element Airfoils, AIAA Pap , Feb Kubrynski K., Inverse Treatment of Design Problems in Low Speed Aerodynamics, Fifth World Congress on Computational Mechanics, Eds. H.A.Mang, F.G.Rammerstorfer, J.Eberhardsteiner, Vienna (2002) 9 Johnson R.H., A Flight Test Evaluation of the SZD-56-2 Diana-2 Racing Class Sailplane, Soaring Magazine, March Katzmyer R., Effect of periodic changes in angle of attack on behavior of airfoils. NACATM-147, Levine D., Users Gade to the PGAPack Parallel Genetic Algorithm Library,. T. R. ANL-95/18, January Würz W., Wagner S. Experimental Investigations of Transition Development in Attached Boundary Layers and Laminar Separation Bubbles Körner H., Hilbig R. (Eds.), New Results in Numerical and Experimental Fluid Mechanics, NNFM, Vol.60, Vieweg-Verlag Braunschweig, 1997 ( ) 13 Steen G., Nicks O., Heffner M., Further wind tunnel investigation of the SM701 airfoil with aileron and turbulators, NASA CR , Dini, P., Selig M.S., Maughmer M.D., A Simplified e n method for Separated Boundary Layers AIAA Pap , Wind Tunnel Wall Correction, AGARDograph AG-336, Ewald B.F.R. (Eds.) Oct