The Application of Multi-Disciplinary Optimization Technologies to the Design of a Business Jet

Transcription

1 10th AIAA/ISSMO Multidisciplinary Analysis and Optimization Conference 30 August - 1 September 2004, Albany, New York AIAA The Application of Multi-Disciplinary Optimization Technologies to the Design of a Business Jet P. Piperni *, M. Abdo, and F. Kafyeke Bombardier Aerospace, Montreal, Quebec, H4S 2A9 This paper contains an outline of an engineering approach to multi-disciplinary design optimization and an application of it to a business jet. One of the most challenging issues in multi-disciplinary optimization is to bring together technologies and methodologies of various disciplines in a way that is both practical and inclusive of the expertise that must accompany these individual technologies. The approach taken by the Advanced Aerodynamics Department at Bombardier Aerospace is to build each component of the methodology in a stepwise fashion from the ground up and integrate the engineering analysis and design tools already in place at Bombardier. The methodology is based on the integration of low and high fidelity computational fluid dynamics codes into the multidisciplinary environment, the development of conceptual wing structural design codes, wing weight estimation codes, En Route fuel burn prediction models and codes for the prediction of wing static aeroelastic deformation under load. Once a multi-disciplinary optimum design is obtained using low fidelity codes, this preliminary design undergoes a second refinement stage of optimization using high fidelity codes. I. Introduction ircraft preliminary design comprises such a large number of complex trade studies that it has traditionally been Aaccomplished using a data base of semi-empirical relations in combination with experience and intuition. 1 Recently, as the technology for high-speed flight has matured, business jet manufacturers have developed faster aircraft for longer-range missions, 2-6 and the development of these advanced business jets requires the application of advanced multi-disciplinary technologies more commonly used on larger transport aircraft. 5,7,8 One of the most challenging issues in multi-disciplinary optimization is to bring together technologies and methodologies of various disciplines in a way that is both practical and inclusive of the expertise that must accompany these individual technologies. 9 Multi-disciplinary design and optimization (MDO) has become a discipline in itself, with hundreds of research papers and a growing recognition of its importance. Kroo, 10 addressed some of the difficulties that arise in largescale systems and focused on collaborative optimization methodology. Kroo and Manning, 11 Sobieski and Kroo, 12 Allwright, 13 and Altus and Kroo, 14 provide a comprehensive description of the application of collaborative optimization to aircraft design. The objective of reducing the design cycle of an aircraft has led to a major research effort into multi-disciplinary design and optimization methods. Sobieski and Haftka, 15 as well as Balling and Wilkinson, 16 presented some of these methodologies and recent developments. Morris and Gantois, 17 described a European Union funded research program into multi-disciplinary design and optimization, which involved the majority of the European aircraft industry together with university and research organizations. The target of the work was to create an optimized wing for the proposed A3XX aircraft. The objectives involved demonstrating and developing MDO methodologies able to combine aerodynamics, structures, aeroelastics and manufacturing disciplines. Wilkinson et al. 18 developed and evaluated several methods for sizing the finite elements of an aircraft structural idealization to achieve minimum-weight design under combined strength and flutter-speed requirements. * Group Leader, Advanced Aerodynamics, AIAA Senior Member. Engineering Professional, Advanced Aerodynamics, AIAA Member. Manager, Advanced Aerodynamics, AIAA Associate Fellow. 1 Copyright 2004 by the, Inc. All rights reserved.

2 Active flexible wing technology is a multi-disciplinary synergistic technology that integrates air vehicle aerodynamics, controls, and structures together to maximize air vehicle performance by allowing thinner, higher aspect ratio wings that are aeroelastically deformed into shapes for optimum performance The untwisted wing of elliptical spanwise chord variation, which is predicted by lifting-line theory (developed by Prandtl, 23 ) to generate minimum induced drag for a given lift at all angles of attack, represents one of the earliest optimized wings. However, Prandtl, 23 noted that the minimum induced drag was not necessarily the optimum span load distribution. Jones, 24 constrained the root bending moment in his analytical calculations for planar wings. Later, Jones and Lasinski, 25 constrained the area under the root bending moment curve (the same approach used by Prandtl, 23 ) for wings with winglets. More recently, numerical approaches have also been developed. Kroo, 26 developed a program to optimize span load distributions and induced drag for a given total lift, wing weight and trim. For a fixed wing weight and parasite drag, McGeer, 27 used an iterative scheme to find the optimum span load for minimum drag. Craig and McLean, 28 introduced fuselage interactions and aeroelastic effects while performing trade studies on wing weight and total drag, including profile drag. Wakayama and Kroo s, 29 MDO study combined the aerodynamics and structures fields without explicitly addressing the span load optimization step. A recent MDO study by Iglesias and Mason, 30 used a discrete vortex method to calculate optimum span load distributions. Changes in wing induced drag and weight were converted to aircraft total gross weight and fuel weight benefits, so that the span loads that give maximum take-off gross weight reduction can be found. However, the study does not include detailed structural analysis with aeroelastics effects (such as wing deformation) and needs to be extended to treat the case of strut-braced wing concepts which have recently been shown to be very promising. 31,32 Several authors such as Giesing and Wakayama, 33 have developed an objective function that is based on relative Direct Operating Costs (DOC) for the MDO of a transport aircraft. Johnson, 34 has compared the MDO results of optimizing a subsonic wing using various objective functions including MTOGW, fuel, acquisition costs and weight based DOC. Andersen and Venkayya, 35 investigated the use of the Tailored Structural Optimization (TSO) program and the Automated Structural Optimization System (ASTROS) in their airframe MDO efforts. Other authors such as Elliott and Leigh, 36 presented a methodology for developing a complete set of aircraft loads to be used in the structural optimization of an aircraft (a typical mid-size 100+ seat passenger aircraft) using ASTROS. A methodology that enables the investigation of static and dynamic nonlinear aeroelastic phenomena of flight vehicles was presented by Kolonay et al. 37 Browman et al. 38 performed an integrated design of aerodynamics and structures. In his study, static aeroelastic effects were considered and the design variables included cross-sectional dimensions of the structural members and the sweep angle of the wing structure. Several authors performed wing structural optimization using various levels of wing-box modeling for application to multi-disciplinary optimization. Giles, 39 developed an equivalent plate analysis formulation that is capable of modeling aircraft structures with a general planform. This procedure was used to calculate the static deflections, stresses and vibration frequencies and modes of an example wing configuration. Others such as Brooks and Meyer, 40 performed a multi-disciplinary trade study to select the best balance between weight and cost for the lower wing skin/stringer configuration and material for a proposed 550 seat commercial aircraft. More recently, Butler et al. 41 compared the optimization of metal and composite wings for a range of constraints and examined the interface between conceptual and preliminary design tools using the conceptual MDO program CALFUNOPT, 42 and the panel sizing program VICONOPT. 43 A computer code for obtaining the dimensions of optimum (least mass) stiffened composite structural panels was described by Anderson and Stroud. 44 The procedure is based on nonlinear mathematical programming and a rigorous buckling analysis. Isakson et al. 45 applied an optimality criteria in the iterative resizing of the elements of a finite-element model to achieve minimum weight for the cover-skin of the wing design. Several authors obtained minimum weight designs for wing-box panels using nonlinear finite element codes. 46 Speed and robustness of the optimization algorithms, and the quality of the analysis codes used in the optimization process, are major contributors to the success of multi-disciplinary optimization. In recent years, the development of aerodynamic shape optimization methods based on computational fluid dynamics (CFD) and the control theory approach (see Lions, 47 and Pironneau, 48 Reuther et al. 49, Jameson et al. 50,51, Nemec and Zingg, 52 Pulliam et al. 53 and Liu and Zingg, 54 ) has become an important topic of research. With the adjoint approach, the necessary gradients are obtained through the solution of an adjoint system of equations of the governing equations of interest. This approach is computationally efficient since the complete gradient is independent of the number of design variables, and can be used to incorporate higher-fidelity analysis codes into a multi-disciplinary optimization. 2

3 II. Multi-Disciplinary Optimization at Bombardier Aerospace At Bombardier Aerospace, a multi-prong approach to the development of a multi-disciplinary capability has been adopted. One of the first initiatives was the development of a multi-disciplinary environment called VADOR (Virtual Aircraft Design and Optimization Framework) VADOR is an interface that enables the interaction of any number of codes, each of which may run on its own computing platform, and/or at a different site. VADOR is a data-centric environment that enables the management, storage, and retrieval of data, and maintains historical information of all processes that are executed within its framework. VADOR is thus a unified environment in which engineers from different disciplines can link their respective design and analysis codes to perform multi-disciplinary optimization (MDO). Various types of optimizers are employed at Bombardier Aerospace to perform wing design, including traditional gradient-based methods and inverse design methods. 55,63 More recently, this capability was expanded with the acquisition of EPOGY (formerly POINTER 81 ), a commercially available software developed by Synaps Inc. (recently acquired by Enginious Software). EPOGY provides a variety of optimization and search methods from linear simplex and sequential quadratic programming to genetic algorithms, which can be used individually or in combination. This software also provides an interface enabling the user to define the optimization variables, constraints, and other parameters. A suite of low and high-fidelity analysis codes have recently been linked to the optimization environment. The computational fluid dynamics (CFD) codes include a transonic small disturbance code developed in-house called KTRAN, and an Euler/Navier-Stokes code, also developed in-house, called FANSC developed by Zhu et al. 62 For the analysis and design of the wing structure, the codes currently used are TWSAP developed by Abdo et al and NASTRAN. 70 TWSAP is an in-house code that generates a beam FEM representation of the wing structure to calculate the wing structural properties. This code also includes a design module capable of performing a preliminary structural layout of the wing box, and a weight estimation module that uses the GASP (General Aviation and Synthesis Program) methodology, 71 to compute the total weight of the wing structure. The program was further developed to estimate the overall wing weight by using the wing structural components designed by TWSAP and by using the wing component weight factors method developed by Wakayama and Kroo. 72 The NASTRAN code is used when a more detailed, finite element model of the wing is desired. The linking of the above aerodynamic and structural analysis codes in a common design environment forms the basis upon which the MDO capability is being developed. In the sections that follow, each component of the system and its contribution to the overall capability is described in turn, followed by the application of the capability to the design of a business jet configuration. III. Computational Fluid Dynamics Codes for the MDO Environment Two CFD codes are currently linked to the multi-disciplinary environment. The first is a lower fidelity, fast turn-around code developed at Bombardier Aerospace called KTRAN KTRAN solves a modified transonic small disturbance equation using Cartesian grid embedding techniques. This program has traditionally been used to perform preliminary wing design ahead of higher-order CFD codes. However, despite its low order formulation, at design (aircraft typical cruise) conditions, KTRAN provides reliable predictions of wing pressure distributions and aerodynamic loads. This program can be used to model full aircraft configurations that include fuselage-mounted or wing-mounted nacelles, wing-tip winglets and horizontal tail components. KTRAN includes a mixture of semiempirical and CFD-based routines to compute the aircraft total drag (trimmed) to within engineering accuracy. A KTRAN solution on a typical Bombardier business jet configuration is shown in Fig. 1 below. In Fig. 2, the drag prediction capability of the code is illustrated on the well known DLR-F6 wing-body-engine configuration. The second CFD code linked to the design environment is an in-house Euler/Navier-Stokes code called FANSC (Full Aircraft Navier-Stokes Code). 62 FANSC is a multi-block structured, cell-centered, finite volume solver with explicit multi-stage Runga-Kutta time stepping. The code solves the Reynolds-Averaged Navier-Stokes (RANS) equations and it can be run in Euler, Euler-boundary-layer and Navier-Stokes modes. Turbulence modeling is implemented using either the Spalart-Almaras one equation model or the k two-equation model. 3

4 Figure 1. A KTRAN solution on a typical business jet configuration. FANSC requires body-fitted grids, and hence a mesh movement capability was recently developed, 63 to incorporate this code in the design environment. Currently, the mesh movement program, called MeshMover, can be applied to configurations that can include combinations of wing, fuselage, nacelle, and winglet components. Figure 3 shows the grid blocks on the upper surface of a wing geometry and Fig. 4 presents the grid lines on the wing-tip winglet before and after deformation as generated by the MeshMover code. This capability thus permits the linking of FANSC with all optimizers available at Bombardier Aerospace, including the INDES inverse design code, 63 and EPOGY. Figure 5 presents a sample aerodynamic optimization using a user specified target pressure distribution and the Euler/Navier-Stokes code FANSC CL DLR-F6 WBE Exp. KTRAN v Mach=0.75 Re=3.0 million Drag (counts) Figure 2. KTRAN drag prediction for the DLR-F6 wing-body-engine condifuration. 4

5 Figure 3. Grid blocks on the upper surface of a wing geometry. Figure 4. Grid lines on the wing-tip winglet before and after deformation. The green and red colors show the grid lines before and after deformation, respectively. IV. Structural Design and Analysis Codes To design the structure in an optimal sense, multi-disciplinary analysis must be considered to ensure that the computed aerodynamic loads match the structural deformation. However, for this process to be effective, wing structural models of sufficient detail are needed early in the design cycle. The subsequent phases of the design can then benefit from concepts, layouts, models and loads of higher fidelity. In this environment, the greatest potential benefits can be obtained by applying formal optimization at the preliminary design stage. 5

6 To achieve this, the development of a conceptual multi-disciplinary wing box design program was initiated at Bombardier. Several design modules were developed to size various essential components of the wing box. An overview of the wing box design components is shown in Fig. 6. A conceptual wing structure design code called TWSAP (Thin Wall Structural Analysis Program) was developed to layout the structure. The various modules of this program are described briefly below. section 2 : eta=0.260 section 3 : eta=0.401 Cp;Cptarget Starting point Final solution Target Cp;Cptarget z/c Starting point Final solution Target z/c x/c x/c section 6 : eta=0.954 Cp;Cptarget Starting point Final solution Target z/c x/c Figure 5. Aerodynamic optimization using the Full Aircraft Navier-Stokes Code (FANSC). 6

7 Conceptual Design Loads Module CFD Aircraft Model Skin-Stringer Design Module Spar-Cap Design Module Conceptual Wing Box Design Program Ribs-Spars Layout Module Wing Weight Prediction Module Thin-Walled Structures Analysis Program Bending Material Overall Wing Weight Wing Structural Stick Model Wing Aeroelasticity Input to MDO Environment Figure 6. Modules of the conceptual wing box design program. The design process begins by distributing the ribs within the wing box and designing the sections at the ribs locations one after the other along the wing span. The wing external geometry is assumed to be known at the beginning of the design process as well as the location of the front and rear spars for each section. A natural tendency is to locate the front spar at a constant chord location, between 5% to 20% chord. The front spar location should be selected to ascertain the space provisions in the leading edge for the leading edge device and to maximize the box volume for fuel containment and structural rigidity. The rear spar is usually located between 60% to 80% chord. The rear spar location is subject to as many or more influences as the front spar. Figure 7 shows two conceptual rib and spar layouts generated by the TWSAP program (for details see Abdo et al) The program is capable of generating streamwise, fanned and normal-to-rear spar ribs. 7

8 Normal to rear spar rib Front Spar Fanned rib Wing Planform Rear Spar Streamwise rib Airfoil sections Defining the ribs Extracted from the wing geometry Skin Stringer Cap Web- Rear Spar Figure 7. Two conceptual ribs and spars layouts generated by TWSAP. The structural layout at each rib location is idealized by the skin, stringers, spars and spar-caps. The skins, stringers, and caps are sized based on structural failure modes and design loads (load intensity curves). The process of generating the conceptual spanwise design loads, which are used in the sizing process of wing-box skin-stringer panels and spar-cap assemblies, was developed and transformed into a design module. 64 In TWSAP, the spars are considered as diagonal tension spars. The method most generally used for in-plane diagonal-tension spar analysis is given in detail in Ref. 73. A methodology was developed for the conceptual design of stringer stiffened compression panels. 64,65 The design method includes local (based on plate theory) and general (based on Euler-Engesser or Johnson-Euler column stress) failure modes common to aerospace compression structures. It also takes into account the panel beam-column analysis. A typical stringer-stiffened compression panel is shown in Fig. 8. The present skin-stringer design module is capable of sizing panels with different types of stringers such as the so-called J and Z types. Sample validation test cases are provided in Ref. 65. The design loads are extracted from the aerodynamic and inertial loads. The load intensity curves depend on the height and width of the box at the rib location, which in turn depend on the aerodynamic profile (airfoil shape) at that location. The preliminary weight of the wing (which is used to generate the preliminary inertial loads) is approximated from known empirical relations. Once the structural details (geometry of the box, skin thickness, stringer area, etc.) at each rib location have been sized, the thin-walled cross sectional properties of the box are then computed. The structure of a wing-box is complex in nature. It contains many elements that make the structural analysis process a very long and difficult one. 8

9 The present method for structural analysis depends on a numerical procedure that is applied to determine the torsional and flexural properties of multi-cellular cross sections, which are used frequently in modern wing structures The TWSAP program uses thin-walled, single cell sections to represent the wing-box. Each wing box section is modeled with a set of skin-stringer panels, front and rear spars and upper and lower spar caps, as shown in Fig. 8. Bending Moment Distributed Pressure Axial Load Figure 8. A typical stringer stiffened compression wing panel. Airfoil Geometry Wing -Box Skin Pad-up Web Upper -Stringer Rear -Spar Boom Equivalent Wing-Box Figure 9. Equivalent wing box extracted from the actual structure. Upon completion of the numerical calculations of the stiffness properties for all the box sections at the rib locations (along the wing span), a finite element beam model of the conceptual structure is generated. This model can be used to predict the deformation of a wing that has yet to go through detailed design. The difficulty in preliminary design is to find or develop aeroelastic models that are sufficiently simple to be called thousands of times during optimization, but are sophisticated enough to accurately predict wing deformations. Simplified beam finite element models of aircraft wing structures, also known as stick models, are often used for aerodynamics-structures interaction. Such models can be used for both static or dynamic aeroelastic analysis. 9

10 The stick model of a wing structure is a series of tapered or uniform beam or bar elements, as shown in Fig. 10. The TWSAP program automatically generates the stick finite element model of the conceptually designed wing. 66,67 Rib station 2 Skin-stringer model 1 Beam element 1 Skin-stringer model 2 Rib station 1 Figure 10. A typical stick FEM beam element. A second methodology (Fig. 11) was also developed to create wing stick models for known wing structures. 66,67 This method extracts the stiffness properties of the beam model from the complete finite element model of the wing. However, this method cannot be used at the conceptual design stage when the wing structure has yet to be defined. In that case, one has to rely on historical data. The stiffness distributions of four of Bombardier s existing aircraft was normalized and fitted with linear relations. Some of the results are shown in Fig. 12. These empirical relations can then be used to create a stick model for a new aircraft early in its development phase. The accuracy of the empirical relations was verified and was found to be acceptable. 66 Rib Position Rigid Bar Elements Full Finite Element Model of the Wing Elastic Axis Node Elastic Axis Definition Stick FEM of the Wing Figure 11. Extracting the stick finite element model of the wing from the full FEM. The objective of coupling aerodynamic and structural models is to compute the flow over flexible wings. The aerodynamic forces computed by aerodynamic analysis codes are integrated to obtain the shear forces. The shear forces are then applied to the stick model to obtain the deformed condition of the wing. Figure 13 shows the static aeroelastic equilibrium state of a test wing obtained using the present method. 10

11 ( EI ) 1 FEM ( EI ) 1 CATIA Global Express CRJ 200 Challenger 300 CRJ 700 Global Express_line CRJ 200_line Challenger 300_line CRJ 700_line Figure 12. Vertical bending stiffness of four of Bombardier s wings fitted with straight line segments. a) The undeformed condition b) The deformed condition Figure 13. The static aeroelastic equilibrium state of a test wing. 11

12 The TWSAP program, was validated by computing the stiffness of a conceptual wing structure designed by TWSAP to simulate the Bombardier Global Express aircraft wing. Figure 14 shows the comparison of the spanwise stiffness distribution of the actual and conceptual wings, showing an excellent agreement. This result illustrates how a very good estimate of the wing stiffness can be obtained with a preliminary design tool. A wing weight estimation module based on the General Aviation Synthesis Program, GASP, 71 was also developed. This method uses semi-empirical relationships to determine the structural weight of wings, applicable to a wide range of subsonic aircraft. TWSAP was further developed to estimate the overall wing weight by using the wing structural components designed by TWSAP, the ribs weight estimated by Farrar s method, 74 the high-lift devices weight predicted by GASP, 71 and by using the wing component weight factors method developed by Wakayama and Kroo. 72 Bending Moment of Inertia, I1 Global Express Present Design Method Wing Station Figure 14. Comparison between the bending moment of inertia of the Global Express and the conceptually designed one. V. En Route Performance Model A series of prediction algorithms suitable for the pre-design stage of industrial conceptual transport aircraft design were incorporated in the present MDO environment. The methods have been devised by hybridizing statistical correlation of design variables, synthetic functions and macro-objective functions with fractional change analytical constructs (for details see Isikveren, 75,76 ). Applicability of these prediction algorithms encompasses personal/micro turbofans, business aircraft from very light to ultra-long range categories to commercial aircraft from commuters to narrow-body transports of around 100 PAX. The suite of fractional change algorithms cover six sub-spaces: atmospheric and general properties, geometric characteristics, weights, low-speed and high-speed aerodynamics, engine performance and operational performance. Operational field and En Route performance prediction can still become quite complex even with greatly simplified empirical methods. For instance, issues related to take-off second segment climb capability become of increasing concern particularly whenever a derivative/variant aircraft with modest thrust augmentation is investigated (see Ref. 75 for details). To address this requirement, existing simple methods found in literature have been utilized but with some pertinent enhancements. A complete mission flight profile trajectory consists of three consecutive segments: climb, cruise and descent. Each segment is subject to transversality conditions that are additional and depend on the end point constraints of state variables, thus the entire flight must be analyzed as a global problem wherein the links between all the phases are considered concurrently. A sector mission is the operation of an aircraft from the end of initial climb to the end of descent, with both nodes corresponding to a height of 1500 ft pressure altitude. Flight time and flight fuel include allowances required for takeoff, initial climb, approach and landing. The block time and block fuel includes additional allowances for start- 12

13 up, taxi-out and taxi-in. Each sector mission analysis will have with it an associated reserve fuel that is carried to destination. The method of fractional change was used in the present MDO program to predict En Route performance attributes of initial cruise altitude, optimal speed schedule identification, integrated range and block fuel for given sector mission. A Cash Operating Cost (COC) model for multi-disciplinary optimization studies has been developed with the aid of an En Route performance model, 75,76. The En Route performance model is a closed form algorithm whereby a complete mission profile is taken into consideration. The foundations of the COC and En Route performance models were derived from fractional change operators. The analytical component of the present method operates with the underlying premise that the designer/analyst begins with a seed condition or aircraft. Once a basic list of fundamental design variables and functions are known, prediction of minimum goals for variations away from the seed aircraft can then be conducted. In the present analysis, the COC model for North American operations comprises crew, block fuel, maintenance and landing fee cost constituents. Assuming a fixed block time (same speed schedule), neglecting adjustments in maintenance cost due to changes in engine derate, and since the fees cost constituent now explicitly related to fractional change in MTOW (Maximum Takeoff Operating Weight) is small, the final model for COC is found to be directly proportional to the fractional change in mission fuel. Thus, the MDO statement is now the reduction of the mission fuel mass which represents the major component in the COC model. VI. Present MDO Methodology A realistic multi-disciplinary optimization of an aircraft wing must take into account all factors impacting both the aerodynamics and the structure of the wing. This includes not only high-speed aerodynamic considerations, such as lift-to-drag ratio, buffet boundary and stability and control issues, but also low speed issues such a maximum lift coefficient and stall characteristics, etc. On the structural side, a proper design of the wing structure can only be achieved when all the critical load cases are considered. However, in the stepwise approach adopted here, the MDO problem is simplified by taking into consideration only two flight conditions to design a conceptual wing: a high-speed cruise condition (Mach 0.8, C L =0.5) and a single critical load case. In the application included herein, the 2.5g maneuver at Mach 0.5 was chosen as the dimensioning load case. The statement of the MDO problem was formulated as the minimization of the Cash Operating Cost (COC) of the aircraft for a fixed range mission, assuming a constant maximum take-off weight. In this setup, the lift-to-drag ratio is computed by KTRAN, and the changes in wing structural weight are calculated using TWSAP. The changes in structural weight and fuel weight are fed into the En Route performance model described above to compute an objective function proportional to the aircraft COC. For the cruise case, an initial wing deformation is assumed and the aerodynamic loads are calculated using KTRAN. These loads are then used to compute the wing deformation (twist and bending) using NASTRAN. For the dimensioning load case (2.5g maneuver at Mach 0.5), a wing twist distribution is initially assumed in order to run KTRAN. This is done by computing an expected twist, which is assumed to be a function of the cruise twist. The loads are then obtained by running KTRAN at the dimensioning load case flow conditions. Once the wing is resized for stress constraints, the wing deformations are obtained by running NASTRAN. This process is repeated until the computed twist and the expected twist converge to within a specified tolerance, in which case the static aeroelastic equilibrium condition is reached. In order to minimize the overall computational effort, the 2.5g wing deformation is not computed at every design iteration. Instead, based on the first calculation of the 2.5g wing loading, scale factors are computed, as a function of span position, to permit the calculation of the 2.5g wing loading directly from the 1g cruise loading. However, during the optimization process, the scale factors are updated periodically with a full flexible wing calculation to ensure an accurate representation of the loading at all times. The use of scale factors was validated and shown to provide sufficiently accurate results while greatly reducing the overall computational effort. Since the optimization is done for an assumed constant maximum take-off weight, the wing reference area is held fixed during the optimization. However, the wing planform shape is allowed to vary, and it is parameterized in terms of the wing aspect ratio, taper ratio, and quarter-chord sweep. The optimization process is decomposed into three distinct steps. In the first step, the wing planform shape and spanwise loading are held fixed (an elliptic loading is initially assumed). The wing sectional profiles are optimized and the thickness-to-chord ratios are allowed to vary. In the second step, the wing profiles and planform are held constant, and the wing span loading is optimized. The wing loading is represented by a classical Fourier series limited to four coefficients which are used as design variables. In the third and final step, the wing profiles and 13

14 spanwise loading are held constant, while the wing planform parameters are optimized. At the end of the three steps, the scale factors used to compute the 2.5g wing loading from the 1g loading are updated with a full analysis the latest flexible wing geometry. This process is then repeated a number of times to achieve a satisfactory convergence of the objective function. VII. MDO Application The test case presented here involves the simultaneous optimization of the wing planform shape and the wing sectional profiles for a business jet-type aircraft configuration (Fig. 15) at Mach 0.8, C L =0.52. The optimization environment used for this application is the EPOGY software (of Synaps Inc., now Engineous Software). KTRAN was used as the aerodynamic analysis code, and TWSAP was used to compute the wing structural layout and properties. A complete aerodynamic representation of the aircraft, including winglets, rear-mounted engines, and a T-tail configuration, was used in the KTRAN analysis. One full aircraft (trimmed) KTRAN solution takes about 3 minutes CPU on an 800 mhz R16000 SGI workstation. During the optimization, the code automatically trims the aircraft at the user-requested lift coefficient for every new wing design iteration. In the optimization exercise presented here, the horizontal tail, winglets, fuselage and engine geometries were held fixed. The results of this optimization are illustrated in Figures 16 to 26. The initial wing profiles for this optimization exercise were intentionally chosen to have poor performance characteristics in order to test the capability of the optimizer to improve the design. Figure 16 shows the evolution of the lift-to-drag ratio for this configuration. As shown, the entire optimization process was run for about 3400 function calls (~ 7 days), although convergence was achieved after about 1500 function calls. The optimization was run for an extended period of time was to verify that the optimizer had not settled into a local minimum. Figure 17 shows the evolution of the objective function (fuel weight required for a constant range mission) relative to the reference aircraft. As shown, the increase in L/D results in substantial fuel savings. An examination of the data shows that the performance improvement for this configuration comes from a 43% increase in the wing aspect ratio, a 2% decrease in wing average thickness, and improved wing profiles. Figure 18 shows the initial and final wing planform shape associated with this optimization. The new wing has an aspect ratio of AR=10.6 compared to 7.4 for the initial wing (Fig. 19 shows the evolution of the aspect ratio). Based on this large increase in aspect ratio and reduction in wing thickness, one would expect that the structural weight of the new wing would be significantly greater. However, as shown in Fig. 20, the wing structural weight only increased by roughly 300 pounds. The reason for this is that the optimizer compensated by reducing the wing sweep (by 10 inboard of the planform break, and by 7 outboard), by reducing the wing taper ratio (Fig. 21), and by shifting the wing loading significantly further inboard (Fig. 22). In the latter figure, the span load distributions include the winglet (i.e. =0 at the wing root, =1 at winglet tip). This figure indicates that the optimizer not only shifted the load inboard to reduce the structural weight, but also to reduce trim drag by generating more downwash at the tail, thereby increasing the tail thrust (which is computed by KTRAN). Figures 23 to 25 show the wing pressure distributions at three wing stations before and after the optimization. As shown, the optimization produced very benign, virtually shock free, pressure distributions. Figure 26 shows a KTRAN solution of the optimized configuration. An interesting characteristic of the new design is the forward trailing sweep inboard of the wing break. This is an illustration of how a sophisticated optimization tool can lead to unexpected designs, or at least to designs one would not normally consider with conventional methods. This forward trailing sweep helps reduce weight as well as reduce the adverse effect of the rear-mounted engines on the wing aerodynamics by increasing the distance between engine inlet planes and the local wing trailing edge. Another interesting result is the fact that the optimizer chose reduce sweep in favor of a 2% reduction in wing thickness, rather than the reverse choice, which was also plausible. (Perhaps if a C Lmax requirement had been included as a constraint in the problem statement, the optimizer would have found a different optimum.) It would be clearly impossible to manually replicate the 3400 candidates the optimizer evaluated, and simultaneously trade span load distribution against aspect ratio, and sweep angle against taper ratio and profile thickness. It must be noted that the results presented here are only valid in the limited scope of the problem statement (i.e. only high-speed drag was considered, and only one dimensioning load case was used), and only as accurate as the preliminary analysis codes employed. A post-optimality analysis with higher-fidelity tools is required to evaluate the actual performance improvements resulting from the optimization. 14

15 Figure 15. KTRAN model of reference business jet configuration. Figure 16. Convergence history of the lift/drag ratio. 15

16 VIII. Conclusion The development and application of an MDO capability was presented herein. In this approach, automated aerodynamic and structural analysis codes were developed and linked to the MDO environment and applied to the optimization of a business jet-type wing. The results presented here are preliminary in nature, but clearly illustrate the significant potential of an automated multi-disciplinary optimization capability. It is also shown that low fidelity analysis codes, such as in this case a transonic small disturbance flow solver and a thin-wall structural analysis program, are very useful tools for the multi-disciplinary optimization of a complete aircraft. The speed of execution of these codes allows for the rapid investigation of numerous candidate designs in a practical time frame. As computer power continues to increase, higher-fidelity analysis codes will be incorporated in the MDO environment, while lower order formulations will continue to be used to optimize configurations with an increasing number of design cases and constraints, thereby increasing the realism of the simulation. Acknowledgments The authors would like to thank Dr. Askin T. Isikveren, of the Advanced Product Development Department of Bombardier Aerospace, for contributing the En Route performance model used in the optimization exercise presented here. Figure 17. Evolution of the objective function (lbs). 16

17 X Y (a) Wing planform before optimization X Y (b) Wing planform after optimization Figure 18. Wing planform before and after MDO. 17

18 Figure 19. Evolution of the wing aspect ratio. Figure 20. Evolution of the structural mass (lbs). 18

19 Figure 21. Evolution of the wing outboard taper ratio. C L c/cav Before MDO After MDO Eta Figure 22. Wing spanwise lift distribution before and after optimization. 19

20 (a) Before optimization (b) After optimization Figure 23. Sectional pressure at = (a) Before optimization (b) After optimization Figure 24 Sectional pressure at =0.4. (a) Before optimization (b) After optimization Figure 25. Sectional pressure at =

21 Figure 26. Business jet configuration after MDO. References 1 Ashely, H., On making things the best- aeronautical uses of optimization, AIAA Aircraft Systems and Technology Conference, AIAA , Ohio, August 1981, pp Dornheim, M. A., Dassault s Falcon 2000: New Big Cabin Twinjet, Aviation Week & Space Technology, March 29, 1993, pp North, D. M., IAI Launches Galaxy into Crowded Market, Aviation Week & Space Technology, September 27, 1993, p Goritschnig, G., Isikveren, A., Lamothe, M., and Munger, E., The evolution of civil aircraft design at Bombardier: A historical perespective, CASI conference proceedings, 2003, pp Gallman, J. W., Madson, M. D., Chandrasekharan, R., Hawke, V., Hinson, M., Saunders, D., Mendoza, D., Reuther, J., Optimization of a transonic business jet wing, 33 rd Aerospace Sciences Meeting and Exhibit, AIAA , January 1995, Reno, pp Gallman, J. W., Reuther, J., Pfeiffer, N., Forrest, W., and Bernstorf, D., Business jet wing design using aerodynamic shape optimization, 34 th Aerospace Sciences Meeting and Exhibit, AIAA , January 1996, Reno, pp Gallman, J. W., Kaul, R., Chandrasekharan, R., and V., Hinson, Optimization of an advanced business jet, Journal of Aircraft, Vol. 34, No. 3, May-June 1997, pp Kelm, R., and Grabietz, M., Aeroelastic effects on the weight of an aircraft in the pre-design phase, SAWE paper 2407, 56 th Annual Conference of Weight Engineers, Bellevue WA, May Kafyeke, F., Abdo, M., Pépin, F., Piperni, P., and Laurendeau, Challenges of aircraft design integration, Reduction of Military Vehicle Acquisition Time and Cost Through Advanced Modeling and Virtual Product Simulation, NATO RTO, Applied Vehicle Technology (AVT) Symposium, MP-89-P-48, Paris, France, April Kroo, I., MDO for large-scale systems, in Multidisciplinary design optimization: State of the Art, N. M. Alexandrov and M. Y. Hussaini, eds., SIAM, 1997, pp Kroo, I., and Manning, V., Collaborative optimization: status and directions, AIAA paper, AIAA , 2000, pp Sobieski, I., and Kroo, I., Collaborative optimization using response surface estimation, 36 th Aerospace Sciences Meeting and Exhibit, AIAA , January 1998, Reno, pp Allwright, S., Technical data management for collaborative multi-discipline optimization, AIAA Paper, AIAA ,

22 14 Altus, S., and Kroo, I., Concurrent wing design and flight-path optimization using optimizer based decomposition, AIAA paper, AIAA , 1998, pp Sobieski, J., and Haftka, R. T., Multidisciplinary aerospace design optimization: survey of recent developments, 34 th AIAA Aerospace Sciences Meeting and Exhibition, AIAA , Reno, Balling, R. J., and Wilkinson, C. A., Execution of multidisciplinary design optimization approaches on common test problems, 6 th AIAA/NASA/ISSMO symposium on Multidisciplinary Analysis and Optimization, AIAA CP, 1996, pp Morris, A. J., and Gantois, K., Combined MDO optimization including drag, mass and manufacturing information, 7 th AIAA/USAF/ISSMO symposium on Multidisciplinary Analysis and Optimization, AIAA , St. Louis, September, 1998, pp Wilkinson, K., Lerner, E., and Taylor, R., Practical design of minimum-weight aircraft structures for strength and flutter requirements, Journal of Aircraft, Vol. 13, No. 8, August, 1976, pp Miller, G. D., Active flexible wing technology, AFWAL-TR , February Miller, G. D., An active flexible wing multi-disciplinary design optimization method, AIAA paper, AIAA CP, 1994, pp Vanderplaats, G. N., Sugimoto, H., and Sprague, C. M., ADS-1: A new general purpose optimization program, AIAA Journal, Vol. 22, No. 10, Vanderplaats, G. N., Numerical optimization techniques for engineering design: with applications, McGraw-Hill Book Company1984, Chaps. 4, 5, 9, Prandtl, L., Applications of modern hydrodynamics to aeronautics, translated as NACA Report 116 (original sources dated ). 24 Jones, R. T., The spanwise distribution of lift for minimum induced drag of wings having given lift and root bending moment, NASA TN-2249, Jones, R. T., and Lasinski, T., Effect of winglets on the induced drag of ideal wing shapes, NASA TM-81230, Kroo, I., A general approach to multiple lifting surface design and analysis, AIAA paper, AIAA , McGeer, T., Wing design for minimum drag with practical constraints, Journal of Aircraft, Vol. 21, Nov. 1984, pp Craig, A., and McLean, J., Spanload optimization for strength designed lifting surfaces, AIAA Paper, AIAA , Wakayama, S., and Kroo, I., Subsonic wing planform design using multidisciplinary optimization, Journal of Aircraft, Vol. 32, No. 4, July-August, 1995, pp Iglesias, S., and Mason, W. H., Optimum spanloads incorporating wing structural weight, First AIAA Aircraft Technology, Integration, and Operations Forum, AIAA , Los Angeles, October 2001, pp Grasmeyer, J.M., Naghshineh, A., Tetrault, P.A., Grossman, B., Haftka, R.T., Kapania, R.K., Mason, W.H., and Schetz, J.A., Multidisciplinary design optimization of a strut-braced wing aircraft with tip-mounted engines, MAD Center Report, MAD , January Gern, F. H., Gundlach, J.F., Ko, A., Naghshineh, A., Sulaeman, E., Tetrault, P.A., Grossman, Kapania, R.K., Mason, W.H., and Schetz, J.A., Multidisciplinary design optimization of a transonic commercial transport with a strut-braced wing, SAE paper , 1999 World Aviation Conference, San Francisco, October, Giesing, J. P., and Wakayama, S., A simple cost related objective function for MDO of transport aircraft, 35 th Aerospace Sciences Meeting and Exhibit, AIAA , Reno, January 1997, pp Johnson, V. S., Minimizing life cycle cost for subsonic commercial aircraft, Journal of Aircraft, Vol. 27, No. 2, February Andersen, G., and Venkayya, V., The roll of conceptual and preliminary design in airframe MDO, AIAA CP, 1996, pp Elliott, W. G., and Leigh, B. R., Aircraft loads methodology for MDO, AIAA paper, AIAA Kolonay, R., Dindar, M., Love, M., and Garza, A., A methodology of large scale computational aeroelasticity for the MDA/MDO environment, 8 th AIAA/NASA/USAF/ISSMO Symposium on MDO, AIAA , September Browman, K., Grandhi, R., Eastep, F., Integrated design of aerodynamics and structures, AIAA/AHS/ASEE Aircraft Design, Systems and Operations Conference, AIAA , Seattle, August Giles, G. L., Equivalent plate analysis of aircraft wing box structures with general planform geometry, Journal of Aircraft, Vol. 23, No. 11, November 1986, pp Brooks, C., and Meyer, E., New aircraft lower wing skin trade study, 36 th AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics and Materials Conference, AIAA , New Orleans, April 1995, pp Butler, R., Lillico, M., Banerjee, J., Patel, M., and Done, G., Sequential use of conceptual MDO and panel sizing methods for aircraft wing design, The Aeronautical Journal, Paper No. 2422, August 1999, pp Lillico, M., Butler, R., Guo, S., and Banerjee, J.R., Aeroelastic optimization of composite wings using the dynamic stiffness method, The Aeronautical Journal, Vol. 101, No. 1002, 1997, pp Butler, R., and Williams, F. W., Optimum design using VICONOPT, a buckling and strength constraint program for prismatic assemblies of anisotropic plates, Computers and Structures, Vol. 43, No. 4, 1992, pp Anderson, M., and Stroud, W., General panel sizing computer code and its application to composite structural panels, AIAA Journal, Vol. 17, No. 8, August 1979, pp

23 45 Isakson, G., Pardo, H., Lerner, E., Venkayya, V., ASOP-3: a program for optimum structural design to satisfy strength and deflection constraints, Journal of Aircraft, Vol. 15, No. 7, July 1978, pp Bushnell, D., and Bushnell, W. D., Minimum-weight design of a stiffened panel via PANDA2 and evaluation of the optimized panel via STAGS, Computers and Structures, Vol. 50, No. 4, 1994, pp Lions, J. L., Optimal Control of Systems Governed by Partial Differential Equations, Springer-Verlag, New York, 1971, Translated by S.K. Mitter. 48 Pironneau, O., Optimal Shape Design for Elliptic Systems, Springer-Verlag, New York, Reuther, J.J., Jameson, A., Alonso, J.J., Rimlinger, M.J., and Saunders, D., Constrained multipoint aerodynamic shape optimization using an adjoint formulation and parallel computers, Part 1 & 2, Journal of Aircraft, Vol. 36, No. 1, January- February 1999, pp Jameson, A., Kim, S., Shankaran, S., Leoviriyakit, K., Aerodynamic shape optimization: Exploring the limits of design, KSAS 1 st International Sessions in 2003 Fall Conference, KSAS 03, Korea, November 2003, pp Jameson, A., Shankaran, S., Martinelli, L., Haimes, B., Aerodynamic shape optimization of complete aircraft configurations using unstructured grids, 42 nd Aerospace Science Meeting, AIAA , Reno, 2004, pp Nemec, M., Zingg, D., Optimization of high-lift configurations using a Newton-Krylov algorithm, 16 th AIAA Computational Fluid Dynamics Conference, AIAA , June 2003, pp Pulliam, T.H., Nemec, M., Holst, T., and Zingg, D., Comparison of evolutionary (genetic) algorithm and adjoint methods for multi-objective viscous airfoil optimization, 41 st Aerospace Sciences Meeting, AIAA , January 2003, pp Liu, P., and Zingg, D., Comparison of optimization algorithms applied to aerodynamic design, 42 nd Aerospace Science Meeting, AIAA , Reno, 2004, pp Kafyeke, F., Abdo, M., Pépin, F., Piperni, P., Laurendeau, E., Challenges of Aircraft Design Integration, 3 rd International Workshop on Numerical Simulation Technology for Design of the Next Generation Supersonic Civil Transport, Tokyo, Japan, December Ndiaye, A., Trépanier, J.Y., Guibault, F., Ozell, B., Mahdavi, B., Database Requirements for an MDO Framework, Conference of the Canadian CFD Society, Montreal, June Chen, B., Bouhemhem, D., Ndiaye, A., Guibault, F., Ozell, B., Trépanier, J.Y., An Object-Oriented Application Framework for Distributed Engineering Analysis and Optimization, 15 th Annual International Symposium on High Performance Computing Systems and Applications, Windsor University, Ontario, Canada, June Kafyeke, F. and Piperni, P. Applications of KTRAN Transonic Small Disturbance code to the Challenger Business Jet Configuration with Winglets, SAE Paper , October Piperni, P. and Kafyeke, F., "Applications of the KTRAN Transonic Small Disturbance Code to the Complete CF-18 Aircraft with Stores," Canadian Aeronautics and Space Institute (CASI) Journal, Vol. 36, No. 3, September Piperni, P. and Stokoe, K., "Estimation of store interference loads using transonic small disturbance Theory and Influence Function Method," AGARD-CP-570, February Piperni, P., Patel, K., and Kafyeke, F., The prediction of aircraft trim drag in transonic flight using CFD, 46 th Annual CASI Conference, Montreal, May Zhu Z., Laurendeau E., Mokhtarian F., Cell-Centered and Cell-Vertex algorithm for complex flow configurations, 8 th Annual Conference of the CFD Society of Canada, Montreal, June 11-13, Sadri R., Leblond D., Piperni, P., Coupling of a wing inverse design code to a Euler/Navier-Stokes flow solver using mesh movement capabilities, CASI 50 th Annual General Meeting and Conference, Montreal, April Abdo, M., Sadri, R., and Piperni, P., Multi-Disciplinary Optimization of Wings, Bombardier Report, MAA Abdo, M., Piperni, P. and Kafyeke, F. Conceptual design of stringer stiffened compression panels, CASI 16 th Aerospace Structures & Materials Symposium, Abdo, M., L Heureux, R., Pépin, F., and Kafyeke, F., Equivalent finite element wing structural models used for aerodynamics-structures interaction, CASI 16 th Aerospace Structures & Materials Symposium, Abdo, M., Kafyeke, F. and Pépin, F., Transonic aerodynamics of flexible wings, CASI 48 th Annual Conference Proceedings, Abdo, M. and Pépin, F., Transonic Aerodynamics of Flexible Wings, Bombardier Report, MAA Abdo, M., Leblond, D., Sadri, R., and Piperni, P., Multi-Disciplinary Wing Optimization Methods, Bombardier Report, MAA Reymond, M. and Miller, M. MSC/NASTRAN, Quick Reference Guide, Version 68, General Aviation Synthesis Program- GASP, NASA CR , Cosmic Program ARC Wakayama, S and Kroo, I., Subsonic wing planform design using multidisciplinary optimization, Journal of Aircraft, Vol. 32, No. 4, July-August Kuhn, P., Peterson, J., and Levin, L., A summary of diagonal tension, Part I- methods of analysis, NACA Technical Note Farrar, D. J., The design of compression structures for minimum weight, Journal of The Royal Aeronautical Society, November 1949, pp Isikveren, A., Identifying economically optimum flight techniques of transport aircraft, Journal of Aircraft, Vol. 39, No. 4, July-August 2002, pp Isikveren, A., Parametric modeling techniques in industrial conceptual transport aircraft design, 2003 World Aviation Congress, Montreal, SAE Paper , September