Aerodynamic Optimization for a High-Lift Airfoil/Wing Configuration

S. Chen*, F. Zhang† and M. Khalid‡ Institute for Aerospace Research, National Research Council Canada, Ottawa, Ontario, K1A 0R6

This paper discusses the optimization procedures for a “2D wing” under cruise and take-off configurations. At cruise conditions, the complete wing was represented as a nested airfoil and a traditional optimization technique based on the genetic algorithm was applied to arrive at a shape best suited for drag performance. For the take-off configuration, the 2D wing was represented as a main airfoil with a deployed flap. For a more meticulous aerodynamic evaluation, the CFD Navier-Stokes code, WIND, was employed, where as a faster panel method based code USAERO was used for successive iterations towards a defined optimization goal. The USAERO code was evaluated for the multi-element airfoil computations in comparison against wind tunnel test data. In general, the numerical data agreed well with the test data, with only about a 5% difference between the two sets of data. The performance of the airfoil was improved at both flight conditions after the optimization operations.

Nomenclature CP = pressure coefficient CD = drag coefficient CL = lift coefficient c = airfoil chord, inch M = freestream Mach number Re = clean-chord-based Reynolds number, 1/ft x = streamwise coordinate direction, inch XF = flap gap from the main element in x direction, inch z = vertical coordinate direction, inch ZF = flap gap from the main element in z direction, inch α = angle of attack, degree δF = flap deflection angle, degree δS = slat deflection angle, degree

II. Introduction

Th

n 2001, an extensive experimental and numerical investigation 1,2 for a high lift system was performed at Institute for Aerospace Research (IAR), National Research Council Canada in collaboration with Bombardier Aerospace. e high-lift system included four elements: the main element, a slat, a flap and a vane. The numerical study

demonstrated IAR’s computational fluid dynamics (CFD) capability to predict the detailed flow features for this complex system. In order to design this system more efficiently, however, it is necessary to develop our aerodynamic optimization technology in this area. Aerodynamic optimization technology has advanced with the aid of rapid improvements in computing power over the past decades. At IAR, optimization techniques have been developed for the aerodynamic design of airfoil, wing and wing body configurations 3, 4. High fidelity CFD solvers have been used to perform Navier-Stoke and Euler flow optimizations. But for such a complex configuration as a multi-element airfoil, it is still a challenging

* Research Officer, AIAA Member † Research Officer, AIAA Member ‡ Research Officer, AIAA associate fellow

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22nd Applied Aerodynamics Conference and Exhibit16 - 19 August 2004, Providence, Rhode Island

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Copyright © 2004 by Suzhen Chen. Published by the American Institute of Aeronautics and Astronautics, Inc., with permission.

task to perform an aerodynamic optimization. The main challenges lie in two aspects: 1) the efficiency of the CFD analysis and 2) the automatic grid generation during the optimization operation. The USAERO code 5, a panel method-based CFD solver, however, is able to produce a steady aerodynamic solution much faster compared to Navier-Stoke CFD solvers. In addition, the panel method only requires a surface mesh. It is therefore quite feasible to couple this solver with an automatic mesh process for complex configurations.

.

For a given thickness to chord ratio (t/c) there is a finite amount of fuel that an aircraft can carry for a complete flight mission, including take-off and landing as well as the longer cruise phase. In particular, take-off and landing are crucial flight maneuvers in which elements such as a slat and flap may be deployed in order to generate sufficient lift at speeds lower than cruise flight conditions. Towards this end, optimization techniques were applied in conjunction with traditional aerodynamic CFD solvers to arrive at the most optimized shape of a basic airfoil design at conditions. The methodology was then taken a step further to arrive at a flap extended configuration of the ‘2D wing” that will provide the maximum lift value for take-off configurations. In this paper, an experimental airfoil was optimized during two phases: the cruise and take-off phases. A drag minimization optimization was performed for clean airfoil flight at cruise conditions. Based on this optimized airfoil, the position of the flap was optimized to provide the maximum lift performance at take-off flight conditions.

II. Numerical Procedure

A. Problem Definition A joint IAR/Bombardier Aerospace wind tunnel investigation of the flow around a typical two-dimensional four-

element high-lift section was performed in the IAR .15in 60 in× high-Reynolds-number facility 1. The same test model was used for the current study. Figure 1 shows the geometry of the model. It was based on a Bombardier Aerospace experimental supercritical airfoil. It had a clean airfoil chord of 10 inches and the airfoil maximum thickness-to-chord ratio t/c was 0.106. The shapes of the four elements are also shown in the figure.

XF

Figure 2. Definition of thFlap to the M

Based on the experimental database, the optimization for the cruise configuration was performed at flight conditions of freestream Mach number M = 0.53 and chord-based Reynolds number Re = 7×106. The objective was to minimize the airfoil drag. In this study, a 6th order B-spline curve was used to represent the airfoil geometry.

There were 8 control points for each of the lower and upper sides of the airfoil. The dvalues of the x and y coordinates of the control nodes for the B-spline curves. To obtminimum allowable maximum thickness (>8% chord) and the range of the traconstraints were imposed.

For the take-off configuration, usually the slat device is not used and only the flapthe lift required for the take-off performance. A typical case was selected based on thdeflection was zero degrees and the flap deflection was 8.89 degrees. The flight condchord Re = 7 × 106. Figure 2 illustrates the definition of the relative position of the f

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ZF δF

e Relative Position of the ain Element

Figure 1. Wind Tunnel Experimental Models

esign variables were the actual ain a realistic airfoil geometry, iling edge angle (>5o, <20o)

device is deployed to increase e experimental design: the slat itions were M = 0.2 and clean-lap to the main element. A lift

maximization was performed to find the optimized position of the flap. The design variables in this optimization problem were the flap position FX and FZ .

B. Optimization Method The variation of the objective functions for aerodynamic optimization can be highly non-linear and non-convex.

Therefore, the genetic algorithm (GA) 6 was chosen to find the global optima for the current optimization study. The GA utilizes three operators: reproduction, crossover and mutation. Fitness evaluation is the basis for the GA

search and selection procedure. The GA aims to reward individual combinations of design parameters with high fitness values and to select them as “parents” to reproduce “offspring”. For the cruise phase, the objective of the optimization was to reduce the drag of the airfoil for a given lift. Therefore, the ratio of the lift to drag coefficients was used as the fitness value (objective function). For the take-off phase, the objective was to maximize the lift generated by the main element and the flap. Therefore the total lift coefficient was used as the fitness value. During the GA operation process, parents were chosen based on the Roulette wheel method where the probability of a parent being chosen was proportional to its fitness value. Each pair of parents produced one offspring by crossover. Then, mutation was applied to the offspring. After a new population was produced, the fitness of each member was compared to that of the parent generation, the best and the second best members in the generation were assigned to the new generation without crossover or mutation (elitism). Using this technique guaranteed that the best member in all the populations would not be filtered out by using the GA operators during the optimization procedures.

For the cruise phase optimization, the IAR in-house developed GA program was used. The population size was set to 10 based on previous optimization experience for a wing/airfoil 3, 4. The starting population was generated from a mutation of the original airfoil (the experimental model). A simple one-point crossover scheme was applied. The probability of the crossover was set at 80%, as the use of smaller values was observed to deteriorate the GA performance. Mutations were created by randomly selecting a gene and changing its value by an arbitrary amount within a prescribed range (1% chord). A high mutation rate of 80% was chosen for better GA performance with real number coding.

For the take-off phase optimization, a GA toolbox 7 developed by the University of Sheffield was used in a MATLAB environment. The population size was set to 20. The initial airfoil was the optimized airfoil from the cruise optimization result. The crossover rate was set to 70%. The generation gap was set at 90%.

C. Grid Generation and CFD Analysis Methods 1. Cruise Phase A hyperbolic 2D grid generator HYGRID was used to

generate the grids. A typical C-H grid on the experimental clean airfoil is shown in Figure 3. There are 169 mesh points distributed around the airfoil and 49 points in the direction normal to the airfoil surface. The computations were performed using ARC2D. This code makes use of the implicit pentadiagonal form of the approximate factorization scheme due to Beam and Warming 8 for solving the Euler/Navier-Stokes equations. The multi-step Runge-Kutta scheme proposed by Jameson et al. 9 based on cell-vertex control volume is also available. Second and fourth order artificial dissipations were used in both schemes and the corresponding dissipation coefficients were set at 0.25 and 0.64 for fast convergence. The Baldwin-Lomax turbulence model is available in this code to consider the viscous effects. The flow solver calculated the objective function (CL/CD) and sent it to the GA, which used it as a fitness value.

Figure 3. Mesh around a Clean Airfoil for theARC2D Calculations

2. Take-off phase The take-off configuration consisted of the main airfoil and a flap. To solve the flow details past this type of

configuration, Navier-Stoke/Euler computations are quite time-consuming from an optimization point of view because the optimization process generally involves hundreds of CFD analysis calls. Besides, automatic grid generation for this type of configuration is also a challenging task. A panel method-based CFD solver USAERO, therefore, was used for the take-off phase optimization.

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USAERO computes the unsteady subsonic flow characteristics for multiple bodies in general motion. The basis of the method is a time-stepping, surface singularity method that uses quadrilateral panels of uniformly distributed doublets and sources. For the current study, the flow was at a steady state. To obtain a steady flow solution using USAERO, we simply used the same initial and final positions of the calculated configuration. Also, we defined a time step value that was large enough to produce a stable solution.

Before this method was used for the optimization, the solver was evaluated for a clean airfoil and a typical two-element take-off configuration. The clean airfoil computation was run at M = 0.2 and Re = 7×106 with an angle of attack of α = 3.750. As shown in Figure 4, the CFD pressure results agree with the experimental data very well. The USAERO code was executed with the viscous corrections as available in the solver. The solution produced a CL value of 0.802 as compared to a measured CL value of 0.852.

For the take-off configuration, the slat deflection was δS = 0o and the flap deflection was δF = 8.89o. All the necessary modifications to the main element cove region were made in order to run the USAERO panel code. In Figure 5, the red curves represent the test model and the blue dashed curves represent the modified configuration. Computations were carried outRe = 7×106 with an angle of attack of α = 80. A conumerical and experimental data is shown in Figure 6.data very well. The pressure slope was slightly over-prnose part of the flap. Perhaps this numerical error wasmain element, which was located immediately upstrea

this configuration was 1.619, which was 5% higher thathe take-off phase was the airfoil lift performance, by cof the solution, USAERO should be able to predict the can be used to perform the CFD analysis for the lift opt

Figure 5. Geometry Modifications in the Cove Region of the Main Element for a Panel Method

Computation

American Institute of A

O Exp. USAERO WIND: Euler

Figure 4. Pressure Distributions for a Clean Airfoil at

0 6

with 250 panels on the main element and flap at M = 0.2 and mparison of the surface pressure distribution between the In general, the numerical data agreed with the experimental edicted only on the surfaces of the flap, especially around the caused by the shape modifications to the cove region of the m of the flap. The lift coefficient predicted by USAERO for

n theomptrendimiz

α = 3.75 , . , Re∞ = = ×M 0 2 7 10

FiA

ero

4

gure 6. Pressure Distributions for a Two-Element

0 o 6

experimental value of 1.541. Since the main concern for romising the efficiency of the computations and accuracy of the lift change at the take-off position and, therefore,

ation of this high-lift airfoil system.

irfoil at α =8 , . ,=F 8 89δ M 0.2, Re = 7 10∞ = ×

nautics and Astronautics

III. Results and Discussion

A. Cruise Phase During the process of the cruise phase optimization, the lift coefficient of the clean airfoil was required to remain

at a steady state value. The constant lift coefficient was calculated from the experimental clean

airfoil flight at M = 0.53. The angle of attack was allowed to vary in a small range during the course of the optimization process

.LC 0 70= 3

10. The Baldwin-Lomax turbulence model in ARC2D was used to perform the CFD analysis.

The convergence history for the computations with the experimental model as the initial airfoil is shown in Figure 7. The maximum fitness reached its converged value after about 500 CFD calls. Figure 8 compares the original experimental airfoil with the optimized airfoil. Their corresponding surface pressure distributions are shown in Figure 9. The drag coefficient decreased from 0.0125 for the experimental model to 0.0113 for the optimized model. The angle of attack was adjusted from 2.32o to -1.48o. Compared with the experimental model, the radius of curvature of the optimized model at the leading edge became smaller. This resulted in a decrease of the pressure peak value on the suction surface.

CFD solver calls

Fitness

200 400

20

40

60

80maximum fitnessaveraged fitness

Figure 7. Convergence History of the Cruise Phase Optimization

x (in.)

Cp

0 2 4 6 8 10

-2.5

-2

-1.5

-1

-0.5

0

0.5

1

EXP., Alpha=2.32 Deg., CD=0.0125Optimized, Alpha= - 1.48 Deg., CD=0.0113

Figure 9. Pressure Distributions of the Initial and F

FiguEx

igure 8. Experimental and Optimized Clean

Airfoils at Cruise Conditions

Figure 11. Mach Number Contours around the Optimized Airfoil at Cruise Conditions

Optimized Airfoil at Cruise Conditions

re 10. Mach Number Contours around the perimental Airfoil at Cruise Conditions

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At the rearward portion of the airfoil, the curvature on the both lower and upper surfaces was increased, which created a larger pressure difference between the two surfaces. This compensated for the lift lost at the forward part of the airfoil in order to keep the lift coefficient constant. The Mach number contours for both the original and optimized airfoils are displayed in Figures 10 and 11, respectively. The maximum local Mach number was reduced from 1.039 for the experimental airfoil to 0.827 for the optimized airfoil.

B. Take-off Phase The optimized airfoil during the cruise phase was used to perform the take-off phase lift optimization at M = 0.2

and δF = 8.89o. First, the airfoil was divided into two parts: the main element and the flap. The modified experimental flap dimensions and leading edge shape shown in Figure 5 were used as the model to divide the airfoil into a main element and a flap.

Figure 12. Wake Developm Model Flight at α

Figure 13. Mach NumberExperimental Model Fligh

During the optimization call, USAERO required uselines for both the main elemedeveloped to generate automatically according to thtwo elements and the freedevelopment of the experimconditions is shown in Figurthe Mach number streamlinequation turbulence model shown in Figure 13. The Figure 12 indicates compacomputed by WIND as show

By selecting 20 populatioconverged after about 50 gprocess. The optimization coFigure 14. The optimized flapand ZF = 0.2795 in. At thisimproved from 1.759 to 1.913

ent for the Experimental

= 80 and δ = 8.89o

F

process, at each CFD analysis r inputs of the wake shedding nt and the flap. A program was

these wake shedding lines e relative position between the

stream flow angle. The wake ental model flight at take-off

e 12. For comparison purposes, es computed by the SST two-in the CFD solver WIND 11 is wake development shown in rable features to the wake

n in Figure 13.

M = 0.2, Re = 7×10 ,

ns in the GA, the lift coefficient enerations of the optimization nvergence history is shown in position was at XF = 0.2771 in. position, the lift coefficient .

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Flow Streamlines for the t at α = 80 and δ = 8.89o

F

Figure 14. Optimization Convergence History for Take-off Phase of a Two-element Airfoil at

6 0 o

α = 8 and δF = 8.89

To evaluate the optimized results, WIND was used to compute the flow past the two-element airfoil at the initial and optimized flap positions. The mesh for the viscous flow computation was generated by ICEMCFD HEXA. A non-contiguous grid generation technique 12 was used and a C-type two-block mesh was generated as shown in Figure 15. The pressure coefficients of the experimental, cruise-optimized and take-off-optimized configurations are shown in Figures 16 in black, blue and red curves, respectively. The pressure suction peak on the leading edge of the upper surface of the main element was reduced with the optimized configurations. The pressure loss in that region was then compensated for on the rear surface of the main element and the surface of the flap. The take-off-optimized model produced similar pressure distributions on the main element surface as the cruise-optimized model. However, at the optimized flap position, the pressure slope on the flap surface was larger than that at its initial flap position.

Figure 15. Viscous Mesh for the Initial Take-off Airfoil at α =80 and δF=8.89o

Figure 16. Pressure Coefficients for the initial

and optimized Take-off Airfoil at α =80 and δF=8.89o

USAERO CL

WIND CL

EXP CL

Experimental model

1.619 1.649 1.541

Cruise-optimized model

1.759 1.675 X

Take-off- optimized model

1.913 1.724 X

Table 1. Lift Coefficients of the Three Models at

the Take-off Flight Condition Table 1 summarizes the lift coefficients for the three models, the experimental, the cruise-optimize and the take-

FiguCrui -

Figure 18. Mach number contours for the Cruise Optimized Model at the Optimized Take-

0 o

re 17. Mach number contours for the se Optimized Model at the Original Take

Off Position at α =80 and δ =8.89o

F Off Position at α =8 and δF=8.89

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off-optimized models, for flight at α = 80 and δF = 8.89o. At the take-off-optimized position, the difference between the USAERO and WIND results was slightly greater than the other two cases. Figures 17 and 18 show the Mach number contours for the cruise-optimized model at the initial and the optimized flap positions, respectively. The region above the upper surface of the flap at the take-off optimized position was larger than at its initial position. Separation phenomenon should be present in that region so that the USAERO code may not be able to predict the results as well as it did for the other two cases. In general, however, USAERO had predicted the right trend of the lift performance.

IV. Conclusions A Bombardier Aerospace supercritical airfoil was optimized during both cruise and take-off phases. A viscous

CFD solver ARC2D was used to perform the aerodynamic analysis at the cruise conditions of M = 0.53 and Re = 7×106, and a panel method solver USAERO was used at the take-off conditions of M = 0.2 and Re = 7×106. Both flight conditions were chosen based on the wind tunnel test information. The USAERO code was evaluated for the multi-element airfoil computations based on the wind tunnel test data. In general, the numerical data agreed with the test data very well at both flight conditions.

The GA was then successfully applied to optimize this airfoil system during two phases. The drag coefficient of the airfoil flight at cruise conditions was reduced from 0.0125 to 0.0113, while maintaining its lift coefficient at the constant value of the experimental model. The cruise-optimized airfoil was then used to perform the take-off phase optimization. The lift coefficient was improved from 1.759 to 1.913 with the optimized flap position at

FX = 0.2771 in. and FZ = 0.2795 in. The results were then evaluated using the high fidelity CFD code WIND, which indicated that the optimized results using USAERO were able to give the right trend of the lift performance.

The high lift airfoil system during the landing phase utilizes both slat and flap devices to provide the desired maximum lift performance. The flow past a multi-element configuration involving a slat deflection is, however, very complex. It is quite challenging to implement the CFD computations for such a complex high-lift system into the optimization process. To investigate the high-lift system completely, the aerodynamic optimization involving the slat deployment during the landing phase must also be developed further in the future.

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