Wing Planform Optimization of a Transport Aircraft

22nd Applied Aerodynamics Conference and Exhibit 16-19 August 2004, Providence, Rhode Island AIAA 2004-5191 Wing Planform Optimization of a Transport Aircraft Paulo Ferrucio Rosin Bento Silva de Mattos Empresa Brasileira de Aeronáutica SA Embraer Av. Brigadeiro Faria Lima, 2170 12227-901 São José dos Campos São Paulo - Brazil Roberto da Mota Girardi Pedro Paglione Aeronautical Institute of Technology (ITA) São José dos Campos São Paulo - Brazil Abstract The present work deals with multi-disciplinary design and optimization (MDO) of a transport aircraft wing. The aircraft must fulfil a given mission requirements under restrictions imposed by different aeronautical disciplines. The mathematical model of the MDO framework includes the calculation of aircraft drag polar (based on geometrical characteristics), engine trust, aircraft structural weight, volume available for fuel tank (which is stored only in the wings), stability derivatives, and performance for some flight phases. MATLAB was used then to implement build the related computational routines. Some design tasks for a twinjet aircraft, carrying eight passengers and a crew of three, were carried out for some specified maximum ranges and the results are analyzed here. Copyright 2004 by the American Institute of Aeronautics and Astronautics, Inc. All rights reserved. 1

Introduction Each new generation of commercial airliner must present lower operational cost coupled with some degree of improvement in passenger comfort, to become a best seller among airlines. Future aircraft must also be carefully designed to achieve reductions in design cycle, maintenance, and manufacturing costs. The combination of efficient aerodynamic shapes with judicious use of new materials, structures, and systems is the way to design high-performance aircraft with low weight, and substantially reduced costs. In addition, today aircraft must be quiet and nonpolluting. However, despite of the utilization of numerical tools such as CAD systems and Computational Fluid Dynamics (CFD) in aircraft design, it is still a formidable task to integrate efficiently all of them and existing corporate expertise into the whole aircraft design process. Aircraft design is performed by a hierarchical sequence of steps. It begins with ideas, missions and concepts, takes successively developing shapes until the configuration can be frozen, continues with the practical considerations about hardware, certification issues, finally resulting in a set of drawings, manufacturing instructions and airworthiness documentation. This evolutionary process usually is split into conceptual, preliminary, detail design phases followed by manufacturing, flight tests and production. As this process evolves, design freedom decays rapidly while knowledge about the object of design is increasing. As the design process goes forward designers gain knowledge but lose freedom to act on that knowledge. It was demonstrated mathematically in that this natural evolution may lead to suboptimal designs. Recent transonic airliner designs have generally converged upon a common cantilever lowwing configuration. It is unlikely that further large strides in performance are possible without a significant departure from the present design paradigm. One such alternative configuration is the strut-braced wing 1, which uses a strut for wing bending load alleviation, allowing increased aspect ratio and reduced wing thickness to increase the lift to drag ratio. The thinner wing has less transonic wave drag, permitting lower wing sweep angles for increased areas of natural laminar flow and further structural weight savings. Such departure from conventional design and corporate knowledge poses cultural barriers in aircraft development, which can be lifted by the adequate utilization of MDO. Multi-disciplinary design and optimization (MDO) address the previously mentioned critical issues from earlier phases of aircraft design. Besides simply designing optimal configurations, MDO allows for the fulfillment of requirements, which are constrained by factors such as costs, material properties, wing thickness, and cabin height. The trend towards MDO was triggered by both high-performance low-cost computing systems and new efficient analysis and design 2

algorithms. Particularly, automatic design procedures have a significant impact on the design process by facilitating the decision making process. In the current highly competitive aircraft market, the most suited choice of the parameters that define an aircraft wing is the vital importance for performing the required mission with the highest efficiency, therefore, a matter of product success on the market. The goal of this work is the design of a civil transport aircraft wing suited to a specified mission, making use of the concepts of multi-disciplinary optimization. In a quest for performance and competitive products, aircraft conceptual design has become a highly integrated multi-disciplinary design. Some wing-design tasks were carried out in the present work for a twinjet aircraft (Fig. 1) carrying eight passengers and a crew of three with the turbofan engines located on pylons below the wing. The aircraft was required to cruise at 11,880 m (~39,000 ft) and at Mach number of 0.80. The optimization algorithm takes into account the climb, cruise, and loiter flight phases. The objective function was chosen to be the aircraft s specific range (SR). In order to execute a MDO tasks, routines were developed to represent the performance of the aircraft taking into account engine thrust output, drag polar formulas, fuel storage, and aircraft weight models, the later composed by structural and associated systems. Most of the models were developed using improved Torenbeek s and Roskan s correlations 5, 6. The routines, models, and formulas were implemented in MATLAB Language. Wing area, aspect Ratio, taper ratio, sweepback, airfoil maximum thickness at the basic wing stations, and wing break station position along the wingspan are the independent variables. Three basic airfoils compose the wing. They are located at the wing-fuselage junction, break station, and at the wingtip. The break and tip geometries are typical supercritical airfoils. The aftcamber of the airfoil at the wing root was reduced in order to reduce interference drag. The airfoils of the baseline wing configuration were designed by a multipoint genetic algorithm 2. They were properly reshaped according to value of the maximum thickness variable, which is calculated in each step of the MDO process. Sweeping the wing is not without drawbacks. Wing sweep increases the wing weight for fixed span since the length of the wing increases with sweep to get reach same wingspan. In addition, high-lift devices aren t as effective when the trailing edge is swept. Also, the wing tends to stall outboard first, leading to pitchup, a situation where the wing stops lifting well aft of the center of gravity, while continuing to lift ahead of the center of gravity. This results in a sudden nose up pitching moment, and an unstable slope. The pitching moment was a constraint in the design process of the present work, therefore enabling the design of aircraft with good flying qualities. However, the wing twist was not a design variable. By properly providing an adequate twist to the 3

wing, the problem with pitchup can be minimized, while reducing the induced drag and contributing to tip stall avoidance. However, a weight penalty is inherent when twisting the wing. The proper balance of all these factors can be only satisfactorily accomplished by under a MDO framework. The multi-disciplinary optimization process of the present work is tailored to generate a wing geometry that will produce the highest specific range for a chosen altitude and cruising Mach number. An optimization routine written in MATLAB language was used in the wing-design process. The optimization routine is called fgoalattain. A searching routine was developed by the authors to ensure that a global maximum/minimum could be attained. Fig. 1 Artistic view of a typical aircraft configuration. Theoretical Modelling In this section, the theoretical models necessary to the calculation of the aircraft performance are described. The climb and cruise phases of the flight were considered for the calculation of the specific range. The formulation for the climb and cruise modeling assumes that the aircraft is in steady state and angles are small. The following equations can be derived T D Climb rate (CR) = V W T D (Eq. 2) with the Trajectory angle (γ) given by, W where, T is the engine thrust, D is the drag force, V is the indicated airspeed, and W is the aircraft weight. The climb path was divided into segments where some flight parameters were considered constant. Therefore, the time Δt necessary to climb a segment with a variation of altitude Δh is Δt=Δh/CR (Eq. 3) and the fuel consumption within that segment is obtained by solving the relation fuel = m & f t (Eq. 4) with m& f being the fuel flow. For the cruise phase, the same approach of a segmented calculation was adopted. The Breguet equation was employed 4

C R = V C L D 1 c j Wi ln W f (Eq.5), with c j is the engine s specific consumption. Additionally, T = D (Eq. 6) and L = W (Eq. 7). Figures 2, 3 present the engine thrust and fuel flow chart for the climb phase, respectively. Different airspeeds and altitude for the flight envelope under consideration are taken into account. 14000 Engine Trust Climb 12000 10000 8000 Airspeed (KTAS) 100 150 200 250 300 350 6000 400 450 500 4000 2000 0 0 5000 10000 15000 20000 25000 30000 35000 40000 45000 Altitude (ft) Figure 2 - Engine Trust during the climb phase. 7000 Fuel Flow flow during climb 6000 5000 Airspeed (KTAS) 100 150 4000 200 250 300 350 3000 400 450 500 2000 1000 0 0 5000 10000 15000 20000 25000 30000 35000 40000 45000 Altitude (ft) Figure 3 - Fuel flow during the climb phase. 5

Fig. 4 Basic structural layout of a typical aircraft configuration. The basic structural layout of a typical configuration is shown in Fig. 4. The wing contains two main and one auxiliary spars. The rear spar is located at 55% of the wing chord. Fig. 5 presents the wing structural weight sensitivity to sweepback, the keeping remaining variables unchanged. The structural wing weight was calculated based on wing s geometry variables such as sweepback, area and aspect ratio (Eq. 8). (Eq. 8) where λ is the taper ratio; Λ 1/2 is the sweepback angle of the wing s mid chord line; W MZF is the maximum zero fuel weight; b is the wingspan; S the wing area; n ult is the critical design load factor. In order to include aircraft stability in the computations, the stability derivatives of the aircraft must be first calculated, reflecting their geometric characteristics. Afterwards, a study of short-period and phugoid modes is performed. The main objective of incorporating the stability study into the present MDO framework is to design an aircraft with Class I flying qualities. The stability derivatives implemented here follow the methodology outlined by Roskam 5. 6

Figure 5 Wing Structural Weight. Fig. 7 displays a drag polar chart. The drag-polar estimation algorithm is inputted by wing geometry parameters, flight altitude and speed. Care was taken to ensure that consistent drag polars at the design conditions could be elaborated. The drag components considered in the present modeling are parasite, induced, interference and wave drag. To calculate the parasite drag, form factors are applied to the equivalent flat plate skin friction drag of all exposed surfaces on the aircraft. The flow is forced to transition at 5% of the chord of the lifting surfaces. Drag Polar - Mach 0.7 to 0.8 0.055 0.05 CD 0.045 0.04 0.035 Mach 0.7 0.72 0.74 0.76 0.78 0.8 0.03 0.025 0.02-0.8-0.6-0.4-0.2 0 0.2 0.4 0.6 0.8 CL Figure 5 Drag polar chart. 7

Specific Range- Mach : 0.8 0.15 0.14 0.13 0.12 0.11 0.1 0.09 weight 25 t 28 t 31 t 34 t 37 t 40 t 0.08 0.07 0.06 140 190 240 290 340 Flight level (ft) Figure 8 Specific Range. Fig. 8 represents specific range output. This function receives inputs of flight level, airspeed converted to Mach number, weight, and the output is the aircraft s specific range in nautical miles per pound, the later constitutes the objective function of the optimization carried out in the present work. Results The aircraft under consideration cruises at a chosen constant cruise altitude and at a fixed Mach number. Two missions with two different maximum ranges with maximum payload, 2,000 nm (~ 3,700 km) and 3,000 nm (5,556 km), were selected to perform the design tasks. The objective function is the specific range. Engine and aerodynamics limits as well as minimum and maximum values for the independent wing geometry variables were imposed. For the mentioned missions, two kinds of geometries were designed: rectangular wings and ones with a break station. Figure 9 presents the wing area historic along the iterative process for the wing with a break station. It can be easily seen that during the optimization task, the wing area was reduced in order to lower the friction drag. However, it is limited to a certain value due to the necessary volume to store fuel. Figure 10 shows the aspect ratio log along the optimization process. In a similar fashion that occurred with the wing area, the necessary volume of fuel required to perform the mission imposed some limits to the allowable values of wing aspect ratio. 8

Wing Area (m 2 ) 120 100 80 60 40 20 0 0 500 1000 1500 2000 2500 3000 Iteration Figure 9 Wing Area history. Aspect Ratio 12 10 8 6 4 2 0 0 500 1000 1500 2000 2500 3000 Iteration Figure 10 Wing Aspect Ratio history. Figures 11 and 12 display the historic of the basic operational weight (BOW) and wing structural weight. The search for the optimal value of the wing structural weight was biased by drag and fuel volume requirements, the same being valid for the BOW. Figure 13 shows the specific range during the optimization. The specific range constitutes the function to be maximized. 9

The final planform of the rectangular wings can be seen in Fig. 14. The wing for the 3,000- nm range aircraft presented a wing with higher area than the 2,000-nm range one. Once more, the need to store the required fuel volume drove the final shape of the wings, considering that no fuel is stored in the fuselage. The final parameters for both designed wings are can be seen in Table I. Table I Final parameters for the rectangular designed wings. Basic Operational Weight - Kg 29500 29000 28500 28000 27500 27000 26500 26000 25500 25000 0 500 1000 1500 2000 2500 3000 Iteration Figure 11 Basic operational weight history. 10

Wing Structural weight - Kg 7000 6000 5000 4000 3000 2000 1000 0 0 500 1000 1500 2000 2500 3000 Iteration Figure 12 Wing structural Weight. Specific Range 0.1160 0.1140 0.1120 0.1100 0.1080 0.1060 0.1040 0.1020 0.1000 0.0980 0 500 1000 1500 2000 2500 3000 Iteration Figure 13 Aircraft Specific Range evolution. 11

Fig. 14 Final planform of the rectangular wings. 15 10 5 0-15 -10-5 0 5 10 15 3000 nm 2000 nm -5-10 -15 Figure 15 Designed wings for two specified maximum ranges. The planform of the final wings with a break station can be seen in Figure 15. The wing designed for the aircraft with shorter range, 2000 nm, once more presented a higher span when compared to the wing for the 3,000-nm range aircraft. Both wings present almost the same sweepback angle. 12

Concluding Remarks Two low-fidelity multi-disciplinary design optimization tasks were performed for a commercial transport aircraft. The wing shape is strongly dependent on the aircraft maximum range for the 2,000-3,000 nm range (max. payload) sector that was considered in the present work. The need for the storage of the required fuel volume to accomplish the mission biased the design. If part of the fuel could be stored in the fuselage, certainly more efficient wings could be designed. Further development will incorporate wing twist for improving flying qualities, with additional reduction of induced drag. A full-potential code is being considered as the best compromise for calculating the accurately induced drag for different wing-fuselage combinations and computing requirements. That is a way to increase the fidelity of the present simulations. The takeoff and landing flight phases must be also considered in future work in order to design more realistic aircraft. 13

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