JOURNAL OF AIRCRAFTVol. 36, No. 1, January-February 1999

Re-Engineering the Design Process Through Computation

Antony Jameson*Princeton University, Princeton, New Jersey 08544

I. Introduction

DURING the last 25 years, the entire process of engineer-ing design has been revolutionized as computational sim-

ulation has come to play an increasingly dominant role. At thepresent time engineers spend most of their time at worksta-tions.

Most notably, computer aided design (CAD) methods haveessentially replaced the drawing board as the basic tool fordefinition and control of the configuration. Software systemssuch as CATIA and Unigraphics provide a solid modeling ca-pability that enables designers to prepare complex layoutswithout the need to build mock-ups. The visualization pro-vided by three-dimensional graphics enables the designer toverify that there will be no interference between different partsin the layout, and greatly facilitates decisions on the routingof all the electrical wiring and hydraulic piping.

Similarly, structural analysis is now entirely carried out bycomputational methods typically based on the finite elementmethod. Commercially available software systems such asNASTRAN or ELFINI have been progressively developed andaugmented by new features, and can treat the full range ofrequirements for aeronautical structures, including analysis ofstressed skin structures into the nonlinear range.

They are also very carefully validated before each new re-lease against a comprehensive suite of test cases, and engineerscan place complete confidence in the results. Accordingly, thestructural design is routinely committed on the basis of com-putational analysis, while structural testing is limited to therole of verifying that the design truly meets its specified re-quirements of ultimate strength and fatigue life.

Computational simulation of fluid flow has not yet reachedthe same level of maturity. While commercial software for thesimulation of fluid flow is offered by numerous vendors, air-craft companies continue to make substantial investments onthe in-house development of their own methods, such asBoeing's TRANAIR program, or Lockheed's TEAM program.At the same time, there are major ongoing efforts to developthe science of computational fluid dynamics (CFD) in govern-ment research agencies such as NASA, Japan's ARL, or inEurope, France's ONERA, Germany's DLR, Holland's NLR,and Sweden's FFA, all of which are a source of industriallyused computer programs. This reflects the fact that fluid flowis generally more complex and harder to predict than the be-havior of structures. The complexity and range of phenomenaof fluid flow is well illustrated in Ref. 1.

The concept of a numerical wind tunnel, which might even-tually allow computers to supplant wind tunnels in the aero-

dynamic design and testing process, was already a topic ofdiscussion in 1970-1980. In their celebrated paper, Chapmanet al.2 listed three main objectives of computational aerody-namics:

1) To provide flow simulations that are either impractical orimpossible to obtain in wind tunnels or other ground-basedexperimental test facilities.

2) To lower the time and cost required to obtain aerody-namic flow simulations necessary for the design of new aero-space vehicles.

3) Eventually, to provide more accurate simulations of flightaerodynamics than wind tunnels can.

Chapman et al.2 also noted that the inherent limitations ofcomputational and wind-tunnel simulations are complemen-tary. Wind tunnels are limited by the size of the models thatcan be placed in them, and by the density, temperature, andvelocity of the flow that they can sustain, with the consequencethat flight-Reynolds numbers cannot be realized with completemodels. Their accuracy is also limited by wall and supportinterference, and by aeroelastic distortion. Computers are notlimited in any of these ways, but they are limited in speed andmemory, which in turn limit the attainable complexity and res-olution of the simulations.

CFD has matured to the point where it is widely acceptedas a key tool for aerodynamic design. Algorithms have beenthe subject of intensive development for the past two decades.The principles underlying the design and implementation ofrobust schemes that can accurately resolve shock waves andcontact discontinuities in compressible flows are now quitewell established. It is also quite well understood how to designhigh-order schemes for viscous flow, including compactschemes and spectral methods. Adaptive refinement of themesh interval h and the order of approximations p has beensuccessfully exploited both separately and in combination inthe h—p method.3

Despite these advances, CFD is still not being exploited aseffectively as one would like in the design process. This ispartially because of the long set-up times and high costs, bothhuman and computational, of complex flow simulations. Acontinuing obstacle to the treatment of configurations withcomplex geometry has been the problem of mesh generation.Several general techniques have been developed, including al-gebraic transformations and methods based on the solution ofelliptic and hyperbolic equations. In the last few years, meth-ods using unstructured meshes have also begun to gain moregeneral acceptance.

The fidelity of mathematical modeling of high Reynoldsnumber flows continues to be limited by computational costs.

Antony Jameson has been active in computational fluid dynamics since 1970, when he was at Grumman Aerospace. In 1972 he joinedthe Courant Institute of Mathematical Sciences at New York University, where he became a Professor of Computer Science in 1974. In1980 he moved to Princeton University, where he was McDonnell Professor of Aerospace Engineering from 1982 to 1996. He is currentlyThomas V. Jones Professor of Engineering at Stanford University. He has been a developer or codeveloper of a number of computerprograms that have been widely used in the aircraft industry, including FL022, FL027, FL057, FL067, and the AIRPLANE code. In thelast decade his research has been particularly focused on aerodynamic shape optimization.

Presented as Paper 97-0641 at the AIAA 35th Aerospace Sciences Meeting, Reno, NV, Jan. 6-9, 1997; received Oct. 26, 1997; revision receivedDec. 1, 1997; accepted for publication Aug. 9, 1998. Copyright © 1998 by A. Jameson. Published by the American Institute of Aeronautics andAstronautics, Inc., with permission.

36

JAMESON 37

Thus, accurate and cost-effective simulation of viscous flow athigh Reynolds numbers associated with full-scale flight re-mains a challenge. Several routes are available toward the re-duction of computational costs, including the reduction ofmesh requirements by the use of higher-order schemes, im-proved convergence to steady state by sophisticated accelera-tion methods, and the exploitation of massively parallel com-puters. In the present state of the art, however, it is still cheaperto obtain massive quantities of data such as the loads data overthe flight envelope by wind-tunnel testing, because the incre-mental cost of obtaining additional data is very small once awind-tunnel model has been built. With computational simu-lation, the cumulative cost of generating data for the full flightenvelope becomes very large because a separate run is requiredfor each data point. Computational simulation has the key ad-vantage, on the other hand, that it allows the rapid explorationof numerous alternative designs. Thus, CFD and wind-tunneltesting can be effectively used in complementary roles, withCFD being the prime tool for the initial design studies, andwind-tunnel testing the prime tool for final verification of thedesign concept and acquisition of the full aerodynamic datarequired for completion of the detailed design.

This paper examines ways to exploit computational simu-lation more effectively in the overall design process, with theprimary focus on aerodynamic design, while recognizing thatthis should be part of an integrated multidisciplinary process.The design process itself is surveyed in the next section. Thefollowing two sections examine the industrial requirements foreffective and trustworthy CFD software, and the way in whichoptimization techniques can be integrated with CFD. SectionV discusses recent industrial experience in the application ofCFD and optimization techniques to a major project for a com-mercial aircraft. Finally, Sec. VI discusses ways in which thedesign process might be re-engineered to exploit computa-tional simulation more effectively.

II. Design ProcessThe design process can generally be divided into three

phases: conceptual design, preliminary design, and final de-tailed design, as illustrated in Fig. 1. The conceptual designstage defines the mission in the light of anticipated marketrequirements, and determines a general configuration capableof performing this mission, together with first estimates of siz-ing, weight, and performance. In the preliminary design stage,the aerodynamic shape and structural skeleton progress to thepoint where detailed performance estimates can be made andguaranteed to potential customers. The design is sufficientlyrefined to provide the basis for making formal offers to cus-tomers and signing contracts. At this stage, the developmentcosts are still fairly moderate, in the range of 50—100 milliondollars. In the final design stage, the structure must be definedin complete detail, together with complete systems, includingthe flight deck, control systems (involving major software de-velopment for fly-by-wire systems), electrical and hydraulicsystems, landing gear, weapon systems for military aircraft,and cabin layout and systems for commercial aircraft. Majorcosts are incurred at this stage, during which it is also neces-sary to prepare a detailed manufacturing plan, together withappropriate facilities and tooling. The development costs toreach the point of initial production are in the range of 3 — 10billion dollars. Thus, the final design would normally be car-ried out only if sufficient orders have already been received toindicate a reasonably high probability of recovering the returnon the investment.

Figure 2 provides a closer look at the conceptual designstage. In the case of commercial aircraft, the mission is definedon the basis of airline requirements. Desired payload-rangecharacteristics follow from route analysis between represen-tative city pairs such as Los Angeles-Tokyo, including dataon expected traffic volume, desired frequency, and prevailingweather patterns. At the same time it is necessary to consider

ConceptualDesign

Defines MissionPreliminary sizingWeight, performance

Final Design

Fig. 1 Overall design process.

MissionDefinition

AircraftSynthesis

Database forPreliminary

Design

Market captureAirline requirementsRoute analysisNoiseAirport compatibility

Preliminary sizingweight, performance,stability and control withassumed aerodynamic andstructural characteristics

Size, weight, number ofengines, engine thrust,control system concept,(fly by wire, relaxedstatic stability)noise constraints

Fig. 2 Conceptual design process.

issues of airport compatibility, including constraints on gatesize and noise regulations. A preliminary synthesis using sim-plified aerodynamic and structural models and statistical da-tabases provides an initial configuration and sizing, togetherwith performance estimates, taking into account requirementsfor stability and control. Software for aircraft synthesis suchas NASA Ames Research Center's ACSYNT program is avail-able to assist this process. For commercial aircraft it is nec-essary to estimate both the operating cost and the cost of own-ership, whereas for military aircraft the lifetime cycle cost maybe a determining factor. In either case it is generally assumedthat the selling price is likely to be proportional to the grossweight of the aircraft.

The result of the initial synthesis may confirm the feasibilityof the proposed mission. On the other hand, it may suggestthat it is too ambitious, requiring an excessively large and ex-pensive aircraft, or alternatively that an increased testing mis-sion could be accomplished with an aircraft of acceptable size.Thus, the process will generally be iterated until it arrives ata mission and corresponding design that can be expected toattain the desired market share and return on investment. Con-currently, discussions will proceed with potential customers toverify market interest and with major vendors such as the en-gine manufacturers to assure the availability of appropriatepowerplants and systems. These discussions may well lead tofurther iteration of the mission and design concept in an on-going process. Vendors may also be approached to share inthe development costs as risk-sharing partners, or to undertakesubstantial development costs of their own to provide com-ponents that meet the design requirements.

38 JAMESON

In the development of commercial aircraft, aerodynamic de-sign is in the lead during the preliminary design stage. Thedefinition of the external aerodynamic shape may actually befinalized in the preliminary design. The aerodynamic lines ofthe Boeing 777 were frozen, for example, when initial orderswere accepted before the initiation of detailed design of thestructure. Figure 3 illustrates the way in which the aerody-namic design process is embedded in the overall preliminarydesign. The starting point is an initial CAD definition resultingfrom the conceptual design. The inner loop of aerodynamicanalysis is contained in an outer multidisciplinary loop, whichis, in turn, contained in a major design cycle involving wind-tunnel testing. In recent Boeing practice, three major designcycles, each requiring about 4-6 months, were used to finalizethe wing design. Improvement in CFD, which would allow theelimination of a major cycle would significantly shorten theoverall design process and reduce costs. In the developmentof the MDXX, McDonnell Douglas planned to rely on high-level CFD together with the experimental database that hadbeen developed for the MD12; and expected to eliminate theneed for a sequence of major design cycles.

The inner aerodynamic design loop is used to evaluate nu-merous variations in the wing definition. In each iteration it isnecessary to generate a mesh for the new configuration priorto performing the CFD analysis. Computer graphics softwareis then used to visualize the results, and the performance isevaluated. The first studies may be confined to partial config-urations such as wing-body or wing-body-nacelle combi-nations. At this stage, the focus is on the design of the cleanwing. Key points of the flight envelope include the nominalcruise point, cruise at high and low lift to allow for the weightvariation between the initial and final cruise as the fuel is burntoff, and a long-range cruise point at lower Mach number,where it is important to make sure there is no significant dragcreep. Other defining points are the climb condition, whichrequires a good lift to drag ratio at low Mach number and highlift coefficient with a clean wing, and the buffet condition. Thisis typically taken as the high-lift cruise point increased to aload of 1.3 g to allow for maneuvering and gust loads. Bothwing section modifications such as the thickness to chord ratio,

ConceptuaDesign

U1

a •§

Out

er L

oop

I —— *>

Inne

r Loo

p

—

-*»•CAD I

Definition 1

*Mesh 1

Generation 1^

CFDAnalysis

fVisualization

tPerformance

Evaluation

f

Multi-DisciplinarEvaluation

1Wind Tunnel

Testing

T.

PropulsionNoiseStabilityControlLoadsStructuresFabrication

Fig. 3 Aerodynamic design process.

and planform variations such as the sweepback angle or aspectratio may be considered. While the detailed design of the high-lift system and control surfaces may be deferred to a laterstage, the planform must provide the necessary space for bothhigh-lift systems and control surfaces outside the main struc-tural box, and it must also accommodate the landing gear. Thisgenerally requires an extension of the inboard trailing edge toform a yehudi.

The aerodynamic analysis interacts with the other disciplinesin the next outer loop. These disciplines have their own innerloops (not shown in Fig. 3). For an efficient design process,the fully updated aerodesign database must be accessible toother disciplines without loss of information. For example, thethrust requirements in the powerplant design will depend onthe drag estimates for takeoff, climb, and cruise. To meet air-port noise constraints, a rapid climb may be required while thethrust may also be limited. Initial estimates of the lift andmoments allow preliminary sizing of the horizontal and ver-tical tail. This interacts with the design of the control system,where the use of a fly-by-wire system may allow relaxed staticstability and tail surfaces of reduced size.

First estimates of the aerodynamic loads allow the design ofan initial structural skeleton, which, in turn, provides an esti-mate of the structure weight. One of the main tradeoffs isbetween aerodynamic performance and wing structure weight.The requirement for fuel volume may also be an importantconsideration. An increase in the thickness to chord ratio in-creases fuel volume and allows the same bending moment tobe carried with reduced skin thickness, with an accompanyingreduction in weight. On the other hand, it will lead to a de-crease in the drag rise Mach number. The induced drag, whichtypically contributes around 40% of the cruising drag, variesinversely as the square of the span. Thus, a 5% increase in thewingspan could produce a total drag reduction of the order of4%, but would lead to an increase in wing weight because ofthe increase in the root bending moment. The wingspan mayin fact be limited by airport gate constraints.

The taper ratio and span load distribution also affect thetradeoff between aerodynamic performance and wing weight.While an elliptic span load distribution minimizes the induceddrag for a given span, a more triangular load distribution re-duces the root bending moment. A large root chord may bedictated by the need to accommodate the landing gear andflaps, but it also has the advantage of increasing the root thick-ness for a fixed thickness to chord ratio, yielding a weightreduction. For example, the root chord of the MDXX was in-creased at a late stage in the design to accommodate largerflaps, and this contributed a significant weight reduction. Tomaintain a moderately efficient span load distribution with ahighly tapered planform, the outboard wing must operate withhigher local section lift coefficient than the inboard wing. Thiscan have an adverse effect on the behavior near buffet, as theoutboard wing will incur a shock stall before the inboard wing,leading to a reduction of lift behind the e.g., and, consequently,a high-speed pitch-up. This is unacceptable for certification ifit is too severe.

An increase in the wing sweepback angle may be used toincrease the drag rise Mach number. Alternatively, it allows anincrease in the thickness to chord ratio for the same drag riseMach number, with a resulting weight reduction. This is par-tially offset by the increase in the length of the wing. More-over, an increase in the sweep-back angle will aggravate theproblem of high-speed pitch-up. Most modern highly loadedwings have sweep-back angles no greater than 35 deg at theone-quarter chord line.

Manufacturing constraints must also be considered in thefinal definition of the aerodynamic shape. For example, thesection changes in the spanwise direction must be limited. Thisavoids the need for shot peaning that might otherwise be re-quired to force curvature in both the spanwise and chordwisedirections.

JAMESON 39

From the complexity of these tradeoffs it can be seen that acrucial requirement for aerodynamic analysis is to make trust-worthy predictions with a fast enough turnaround not to delaythe outer multidisciplinary cycle. To allow the completion ofthe major design cycle in 4—6 months, the cycle time for themultidisciplinary loop should not be greater than about 2weeks. Considering the need to examine the performance ofdesign variation at all the key points of the flight envelope,this implies the need to turn around the aerodynamic analysesin a few hours. The computational costs are also importantbecause the cumulative costs of large numbers of calculationscan become a limiting factor.

It is also evident that the number of possible design varia-tions is too large to permit their exhaustive evaluation, andthus, it is very unlikely that a truly optimum, solution can befound without the assistance of automatic optimization pro-cedures. Ultimately, there is a need for multidisciplinary designoptimization (MDO), but this can only be effective if it isbased on sufficiently high-fidelity modeling of the separate dis-ciplines. As a step in this direction there could be significantpayoffs from the application of optimization techniques withinthe disciplines, where the interactions with other disciplines istaken into account through the introduction of constraints. Forexample, the wing drag can be minimized at a given Machnumber and lift coefficient with a fixed planform, and con-straints on minimum thickness to meet requirements for fuelvolume and structure weight.

III. Industrial CFDTo carry out the inner loop of the aerodynamic design pro-

cess the main requirements for effective CFD software are 1)sufficient and known level of accuracy, 2) acceptable compu-tational and manpower costs, and 3) fast turn around time.Performance estimation in the cruise condition is crucial to thedesign of transport aircraft, and the error should be in the rangeof ±y%. The drag coefficient of a long-range transport air-craft, such as the Boeing 747, is in the range of 0.0275 (275counts), depending on the lift coefficient, which is in the rangeof 0.5. The drag coefficient of proposed supersonic transportdesigns is in the range of 0.0120-0.0150, at much lower liftcoefficients in the range of 0.1-0.12. Thus, one should aim topredict drag with an accuracy of the order of ±0.0001 (±1count). Manufacturers have to guarantee performance, and er-rors can be very expensive through the costs of redesign, pen-alty payments, and lost orders.

A first consideration is the choice of appropriate mathemat-ical models of fluid flow that are adequate for trustworthy flowpredictions. Many critical phenomena of fluid flow, such asshock waves and turbulence, are essentially nonlinear. Theyalso exhibit extreme disparities of scales. While the actualthickness of a shock wave is of the order of a mean free pathof the gas particles, on a macroscopic scale its thickness isessentially zero. In turbulent flow, energy is transferred fromlarge-scale motions to progressively smaller eddies until thescale becomes so small that the motion is dissipated by vis-cosity. The ratio of the length scale of the global flow to thatof the smallest persisting eddies is of the order Re3'4, where Reis the Reynolds number, typically in the range of 3 X 107 foran aircraft. To resolve such scales in all three space directions,a computational grid with the order of Re9'4 cells would berequired. This is beyond the range of any current or foresee-able computer. Consequently, mathematical models with var-ying degrees of simplification must be introduced to makecomputational simulation of flow feasible and to produce vi-able and cost-effective methods.

Figure 4 indicates a hierarchy of models at different levelsof simplification that have proven to be useful in practice. Ef-ficient flight is generally achieved by the use of smooth andstreamlined shapes that avoid flow separation and minimizeviscous effects, with the consequence that useful predictionscan be made using in viscid models. Inviscid calculations with

Fig. 4 Hierarchy of fluid flow models.

boundary-layer corrections can provide quite accurate predic-tions of lift and drag when the flow remains attached, butiteration between the inviscid outer solution and the innerboundary-layer solution becomes increasingly difficult with theonset of separation. Procedures for solving the full viscousequations are likely to be needed for the simulation of arbitrarycomplex separated flows, which may occur at high angles ofattack or with bluff bodies. To treat flows at high Reynoldsnumbers, one is generally forced to estimate turbulent effectsby Reynolds averaging of the fluctuating components. Thisrequires the introduction of a turbulence model. As the avail-able computing power increases, one may also aspire to largeeddy simulation (LES), in which the larger-scale eddies aredirectly calculated, whereas the influence of turbulence atscales smaller than the mesh interval is represented by a sub-grid scale model.

Computational costs vary drastically with the choice ofmathematical model. Panel methods can be effectively usedto solve the linear potential flow equation with higher-endpersonal computers (e.g., with an Intel 80486 microprocessor).Studies of the dependency of the result on mesh refinement,performed by this author and others (Ref, 42), have demon-strated that inviscid transonic potential flow or Euler solutionsfor an airfoil can be accurately calculated on a mesh with 160cells around the section, and 32 cells normal to the section.Using multigrid techniques, 10-25 cycles are adequate to ob-tain a converged result. Consequently, airfoil calculations canbe performed in seconds on a Cray Y-MP, and can also beperformed on Pentium-class personal computers. Correspond-ingly accurate three-dimensional inviscid calculations can beperformed for a wing on a mesh, say with 192 X 32 X 48 =294,912 cells, in about 5 min on a single processor CrayY-MP, or less than 1 min with eight processors, or in 1 or 2 hon a workstation such as a Hewlett Packard 735 or an IBM560 model.

Viscous simulations at high Reynolds numbers require vastlygreater resources. Careful two-dimensional studies of mesh re-quirements have been carried out by Martinelli and Jameson.4It was found that on the order of 32 mesh intervals were neededto resolve a turbulent boundary layer, in addition to 32 intervalsbetween the boundary layer and the far field, leading to a totalof 64 intervals. To prevent degradations in accuracy and con-vergence caused by excessively large aspect ratios (in excess of1000) in the surface mesh cells, the chordwise resolution mustalso be increased to 512 intervals. Reasonably accurate solutionscan be obtained in a 512 X 64 mesh in 100 multigrid cycles.Translated to three dimensions, this would imply the need formeshes with 5-10 million cells, e.g., 512 X 64 X 512 =16,777,216 cells as shown in Fig. 5. When simulations are per-formed on less fine meshes with, say, 500,000-1,000,000 cells,it is very hard to avoid mesh dependency in the solutions aswell as sensitivity to the turbulence model.

A typical algorithm requires approximately 5000 floatingpoint operations per mesh point in one multigrid iteration. With

40 JAMESON

512 cells around the wing to limitthe mesh aspect ratio (to about 1000)

Surface Mesh

512 cellsspan wise

Total: 512 x 64 x 512 = 16 777 216 cells

Fig. 5 Mesh requirements for a viscous simulation.

10 million mesh points, the operation count is of the order of0.5 X 1011 per cycle. Given a computer capable of sustaining1011 operations per second (100 Gflops), 200 cycles could thenbe performed in 100 s. Simulations of unsteady viscous flows(flutter, buffet) would be likely to require 1000-10,000 timesteps. A further progression to large eddy simulation of com-plex configurations would require even greater resources. Thefollowing estimate is from Jou.5 Suppose that a conservativeestimate of the size of eddies in a boundary layer that shouldbe resolved is one-fifth of the boundary-layer thickness. As-suming that 10 points are needed to resolve a single eddy, themesh interval should then be 1/50 of the boundary-layer thick-ness. Moreover, because the eddies are three dimensional, thesame mesh interval should be used in all three directions. Now,if the boundary-layer thickness is of the order of 0.01 of thechord length, 5000 intervals will be needed in the chordwisedirection, and for a wing with an aspect ratio of 10, 50,000intervals will be needed in the spanwise direction. Thus, of theorder of 50 X 5000 X 50,000 or 12.5 billion mesh pointswould be needed in the boundary layer. If the time-dependentbehavior of the eddies is to be fully resolved using time stepson the order of the time for a wave to pass through a meshinterval, and one allows for a total time equal to the timerequired for waves to travel three times the length of the chord,of the order of 15,000 time steps would be needed. Perfor-mance beyond the teraflop (1012 operations per second) willbe needed to attempt calculations of this nature, which alsohave an information content far beyond what is needed forengineering analysis and design. The designer does not needto know the details of the eddies in the boundary layer. Theprimary purpose of such calculations is to improve the calcu-lation of averaged quantities such as skin friction, and the pre-diction of global behavior such as the onset of separation. Thecurrent use of Navier-Stokes and large eddy simulations is totry to gain an improved insight into the physics of turbulentflow, which may, in turn, lead to the development of morecomprehensive and reliable turbulence models.

A. Turbulence ModelingIt is doubtful whether a universally valid turbulence model,

capable of describing all complex flows, could be devised.6

Algebraic models7'8 have proven to be fairly satisfactory forthe calculation of attached and slightly separated wing flows.These models rely on the boundary-layer concept, usually in-corporating separate formulas for the inner and outer layers,and they require an estimate of a length scale that depends onthe thickness of the boundary layer. The estimation of thisquantity by a search for a maximum of the vorticity times adistance to the wall, as in the Bald win-Lomax model, canlead to ambiguities in internal flows, and also in complex vor-tical flows over slender bodies and highly swept or deltawings.9'10 The Johnson and King model,11 which allows fornonequilibrium effects through the introduction of an ordinarydifferential equation for the maximum shear stress, has im-proved the prediction of flows with shock-induced separa-tion.12'13

Closure models depending on the solution of transport equa-tions are widely accepted for industrial applications. Thesemodels eliminate the need to estimate a length scale by de-tecting the edge of the boundary layer. Eddy viscosity modelstypically use two equations for the turbulent kinetic energy kand the dissipation rate s, or a pair of equivalent quantities.14"20

Models of this type generally tend to present difficulties in theregion very close to the wall. They also tend to be badly con-ditioned for numerical solution. The k—l model21 is designedto alleviate this problem by taking advantage of the linear be-havior of the length scale / near the wall. In an alternativeapproach to the design of models, which are more amenableto numerical solution, new models requiring the solution ofone transport equation have recently been introduced.22'23 Theperformance of the algebraic models remains competitive forwing flows, but the one- and two-equation models show prom-ise for broader classes of flows. To achieve greater universality,research is also being pursued on more complex Reynoldsstress transport models, which require the solution of a largernumber of transport equations.

The selection of sufficiently accurate mathematical modelsand a judgment of their cost effectiveness ultimately rests withindustry. As the design progresses through the three phases ofconceptual, preliminary, and detailed designs, the appropriateCFD models will vary in complexity. In the conceptual andpreliminary design phases, the emphasis will be on relativelysimple models that can give results with very rapid turnaroundand low computer costs, to evaluate alternative configurationsand perform quick parametric studies. The detailed designstage requires the most complete simulation that can beachieved with acceptable cost.

B. Algorithms and Mesh GenerationThe computational simulation of fluid flow presents a num-

ber of severe challenges for algorithm design. At the level ofinviscid modeling, the inherent nonlinearity of the fluid flowequations leads to the formation of singularities such as shockwaves and contact discontinuities. Moreover, the geometricconfigurations of interest are extremely complex, and generallycontain sharp edges that lead to the shedding of vortex sheets.Extreme gradients near stagnation points or wing tips may alsolead to numerical errors that can have global influence. Nu-merically generated entropy may be convected from the lead-ing edge, for example, causing the formation of a numericallyinduced boundary layer that can lead to separation. The needto treat exterior domains of infinite extent is also a source ofdifficulty. Boundary conditions imposed at artificial outerboundaries may cause reflected waves that significantly inter-fere with the flow. When viscous effects are also included inthe simulation, the extreme difference of the scales in the vis-cous boundary layer and the outer flow, which is essentiallyinviscid, is another source of difficulty, forcing the use ofmeshes with extreme variations in mesh interval. For thesereasons CFD has been a driving force for the development ofnumerical algorithms.

An essential requirement for industrial CFD is the capabilityto treat extremely complex geometric configurations. A key

JAMESON 41

choice that must be made is the nature of the mesh used todivide the flowfield into discrete subdomains. The discretiza-tion procedure must allow for the treatment of complex con-figurations. The principal alternatives are Cartesian meshes,body-fitted curvilinear meshes, and unstructured tetrahedralmeshes. Each of these approaches has advantages that haveled to their use. The Cartesian mesh minimizes the complexityof the algorithm at interior points and facilitates the use ofhigh-order discretization procedures, at the expense of greatercomplexity, and possibly a loss of accuracy, in the treatmentof boundary conditions at curved surfaces. This difficulty maybe alleviated by using mesh refinement procedures near thesurface. With their aid, schemes that use Cartesian mesheshave recently been developed to treat very complex configura-tions.24"27

Body-fitted meshes have been widely used and are particu-larly well suited to the treatment of viscous flow because theyreadily allow the mesh to be compressed near the body surface.With this approach, the problem of mesh generation itself hasproved to be a major pacing item. To treat very complex con-figurations, it generally proves expedient to use a multiblockprocedure,28'29 with separately generated meshes in each block,which may then be patched at block faces, or allowed to over-lap, as in the Chimera scheme.30'31 While a number of inter-active software systems for grid generation have been devel-oped, such as EAGLE, GRIDGEN, GRAPE, and ICEM, thegeneration of a satisfactory grid for a very complex configu-ration may require months of effort.

The alternative is to use an unstructured mesh in which thedomain is subdivided into tetrahedra. This, in turn, requires thedevelopment of solution algorithms capable of yielding therequired accuracy on unstructured meshes. This approach hasbeen gaining acceptance, as it is becoming apparent that it canlead to a speed-up and reduction in the cost of mesh generationthat more than offsets the increased complexity and cost of theflow simulations. Two competing procedures for generatingtriangulations that have both proved successful are Delaunaytriangulation,32'33 based on the concepts introduced at the be-ginning of the century by Voronoi,34 and the moving frontmethod.35

For a detailed review of CFD algorithms in current use, thereader is referred to Ref. 36. Another key issue is the validationof CFD software for industrial use. For a better understandingof this issue it is important to distinguish the different sourcesof error. These include modeling errors because the mathe-matical model does not adequately represent the true physicsof the flow, numerical errors, and programming errors. Nu-merical errors include discretization errors, and errors in thenumerical solution of the discrete model, if, for example, aniterative procedure is not fully converged. The asymptotic be-havior of discretization errors may be estimated by numericalanalysis, and their magnitude in practice can be estimated bymesh refinement studies. It is hard to guarantee the eliminationof programming errors, but their likelihood can be reduced bythe use of modular programming. Then it should be possibleto obtain the same result when alternative implementations aresubstituted for each module. Mesh refinement studies may alsohelp the detection of programming errors by exposing discrep-ancies from the predicted asymptotic behavior as the meshspacing is reduced, or discrepancies from known results forspecial cases, such as the fact that the drag should be zero intwo-dimensional subsonic inviscid flow. It is only after thecorrectness of the program and the accuracy of the numericalsolution procedure have been independently verified that it ispossible to assess the modeling errors that may arise, for ex-ample, from the use of an inappropriate turbulence model. Fora more detailed discussion of validation procedures the readeris referred to Ref. 37.

IV. Aerodynamic Shape OptimizationTraditionally, the process of selecting design variations has

been carried out by trial and error, relying on the intuition and

experience of the designer. It is not at all likely that repeatedtrials in an interactive design and analysis procedure can leadto a truly optimum design. To take full advantage of the pos-sibility of examining a large design space, the numerical sim-ulations need to be combined with automatic search and op-timization procedures. This can lead to automatic designmethods that will fully realize the potential improvements inaerodynamic efficiency.

The simplest approach to optimization is to define the ge-ometry through a set of design parameters, which may, forexample, be the weights at applied to a set of shape functionsb{(x), so that the shape is represented as

/(*) = ̂ aMx)

Then a cost function / is selected, which might, for example,be the drag coefficient or the lift to drag ratio, and / is regardedas a function of the parameters a/. The sensitivities dT/da, maynow be estimated by making a small variation 6a, in eachdesign parameter in turn and recalculating the flow to obtainthe change in /. Then

dl I(at + Sa.) -—————— «-;

d ot-i da-i

The gradient vector dl/da may now be used to determine adirection of improvement. The simplest procedure is to makea step in the negative gradient direction by setting

n X= a — A —da

so that to first order

XT T+ * J 181 = I + — 8a = I — A — —da da da

More sophisticated search procedures may be used, such asquasi-Newton methods, which attempt to estimate the secondderivative d^/da/do, of the cost function from changes in thegradient dl/da in successive optimization steps. These methodsalso generally introduce line searches to find the minimum inthe search direction that is defined at each step. The maindisadvantage of this approach is the need for a number of flowcalculations proportional to the number of design variables toestimate the gradient. The computational costs can thus be-come prohibitive as the number of design variables is in-creased.

An alternative approach is to cast the design problem as asearch for the shape that will generate the desired pressuredistribution. This approach recognizes that the designer usuallyhas an idea of the kind of pressure distribution that will leadto the desired performance. Thus, it is useful to consider theinverse problem of calculating the shape that will lead to agiven pressure distribution. The method has the advantage thatonly one flow solution is required to obtain the desired design.Unfortunately, a physically realizable shape may not necessar-ily exist, unless the pressure distribution satisfies certain con-straints. The difficulty that the target pressure may be unat-tainable may be circumvented by treating the inverse problemas a special case of the optimization problem, with a cost func-tion that measures the error in the solution of the inverse prob-lem. For example, if pd is the desired surface pressure, onemay take the cost function to be an integral over the bodysurface of the square of the pressure error

f = -

42 JAMESON

or possibly a more general Sobolev norm of the pressure error.This has the advantage of converting a possibly ill-posed prob-lem into a well-posed one. It has the disadvantage that it incursthe computational costs associated with optimization proce-dures.

Application of Control TheoryTo reduce the computational costs, it turns out that there are

advantages in formulating both the inverse problem and moregeneral aerodynamic problems within the framework of themathematical theory for the control of systems governed bypartial differential equations (PDEs).38 A wing, for example, isa device to produce lift by controlling the flow, and its designcan be regarded as a problem in the optimal control of theflow equations by variation of the shape of the boundary. Ifthe boundary shape is regarded as arbitrary within some re-quirements of smoothness, then the full generality of shapescannot be defined with a finite number of parameters, and onemust use the concept of the Frechet derivative of the cost withrespect to a function. Clearly, such a derivative cannot be de-termined directly by finite differences of the design parametersbecause there are now an infinite number of these. Using tech-niques of control theory, however, the gradient can be deter-mined indirectly by solving an adjoint equation that has co-efficients defined by the solution of the flow equations. Thecost of solving the adjoint equation is comparable to that ofsolving the flow equations. Thus, the gradient can be deter-mined with roughly the computational costs of two flow so-lutions, independently of the number of design variables,which may be infinite if the boundary is regarded as a freesurface.

For flow about an airfoil or wing, the aerodynamic proper-ties that define the cost function are functions of the flowfieldvariables (w) and the physical location of the boundary, whichmay be represented, for example, by the function F. Then

/ = 7(w, F)

and a change in F results in a change

dIT ,df81 = — 8w + — 8F (1)dw dF

in the cost function. Using control theory, the governing equa-tions of the flowfield are introduced as a constraint in such away that the final expression for the gradient does not requirere-evaluation of the flowfield. To achieve this, 8w must beeliminated from Eq (1). Suppose that the governing equationR that expresses the dependence of w and F within the flow-field domain D can be written as

R(w9 F) = 0

Then 8w is determined from the equation

(2)

(3)

Next, introducing a Lagrange multiplier i/f, we have

*r df x -u ̂ x* IT \(dR\ x + (dR\ **•!81 = — 8w + — 8F - ^ I — I 8w + I — \ 8F\dw dF L\dw/ \dF/ J

\dIT T(dR\] \dIT

TfdR\]= — - <A — } \ 8w + \ — - \f \ — 8F[dw * W/J [_dF * \dF/J

Choosing i/f to satisfy the adjoint equation

the first term is eliminated, and we find that

81 = G8F

where

(5)

dF dF

dl* = 7-dw/ dw

The advantage is that Eq. (5) is independent of 5w, with theresult that the gradient of / with respect to an arbitrary numberof design variables can be determined without the need foradditional flowfield evaluations. In the case that Eq. (2) is apartial differential equation the adjoint Eq. (4) is also a PDEand appropriate boundary conditions must be determined.

After making a step in the negative gradient direction, thegradient can be recalculated and the process repeated to followa path of steepest descent until a minimum is reached. To avoidviolating constraints, such as a minimum acceptable wingthickness, the gradient may be projected into the allowablesubspace within which the constraints are satisfied. In this wayone can devise procedures that must necessarily converge atleast to a local minimum, and which can be accelerated by theuse of more sophisticated descent methods such as conjugategradient or quasi-Newton algorithms. There is the possibilityof more than one local minimum, but in any case, the methodwill lead to an improvement over the original design.

The adjoint method can be applied to a variety of measuresof performance. It should be remembered, however, that gra-dient search methods depend on the assumption that the cost-function depends continuously on the design parameters. Thiscan be violated, if, for example, on attempts to calculate thesensitivity of the pressure at a fixed location, because there isthe possibility that a shape modification could result in a shockmoving over that location. The movement of the shock, how-ever, is continuous as the shape changes, with the consequencethat integrated quantities such as the drag coefficient also de-pend continuously on the shape. The adjoint equation allowsthe sensitivity of the drag coefficient without the explicit eval-uation of pressure sensitivities.

In Ref. 39, the author derived the adjoint equations for tran-sonic flows modeled by both the potential flow equation andthe Euler equations. The theory was developed in terms ofPDEs, leading to an adjoint PDE. To obtain numerical solu-tions, the flow and the adjoint equations must be discretized.The control theory might be applied directly to the discreteflow equations that result from the numerical approximationof the flow equations by finite element, finite volume, or finitedifference procedures. This leads directly to a set of discreteadjoint equations with a matrix that is the transpose of theJacobian matrix of the full set of discrete nonlinear flow equa-tions. On a three-dimensional mesh with indices 1,7, and k, theindividual adjoint equations may be derived by collecting allthe terms multiplied by the variation 8wijtk of the discrete flowvariable wijtk. The resulting discrete adjoint equations repre-sent a possible discretization of the adjoint PDE. If these equa-tions are solved exactly, they can provide the exact gradientof the cost function that results from the discretization of theflow equations, which is itself inexact. This may facilitate theasymptotic convergence of the search procedure. On the otherhand, any consistent discretization of the adjoint PDE willyield the exact gradient in the limit as the mesh is refined.

There are a number of benefits to be gained from developingthe theory for the PDEs of the flow. First, the true optimumshape belongs to an infinitely dimensional space of design pa-rameters, and the theory provides an indication, in principle,of how such a solution could be approached if sufficient com-putational resources are available. Second, it provides insightinto the nature of the adjoint equations, and the connectionbetween the formulation of the cost function and the boundary

JAMESON 43

conditions needed to assure a well-posed problem. Third, incertain circumstances, the discrete solution may lose the prop-erty of continuous dependence of the design parameters. Itmay, for example, contain nondifferentiable flux limiters. Also,if adaptive mesh refinement is used, there will be a discontin-uous change in the solution whenever a mesh point is addedor deleted. Finally, the differential equation theory provides aguideline for the design of iterative solution methods for theadjoint equation, in the case when the adjoint equation is sep-arately discretized and in the case when the discrete adjointequations are derived directly from the discrete flow equations.The theory for standard multigrid methods, for example, de-pends on the property that the discrete equations on a sequenceof meshes all represent the same differential equation. It turnsout that the same multigrid solution method can readily beused for both the flow and the adjoint equation.

The adjoint method has recently been extended to treat thecompressible Navier-Stokes equations.40 As an illustration ofthe power of the method Figs. 6 and 7 illustrate the redesignof a wing representative of wide-body transport aircraft in cur-rent use. The redesign was performed by modifying the wingsections with a fixed planform, subject to the constraint thatthe thickness could not be reduced. Because of the high com-putational costs of viscous design, a two-stage strategy wasadopted. In the first stage, a design calculation was performedwith the Euler equations on a mesh with 192 X 32 X 48 cellsto minimize the drag at a fixed lift coefficient. In the secondstage, the pressure distribution of the Euler solution was usedas the target pressure for inverse design with the Navier -Stokes equations, using a mesh with 192 X 64 X 48 cells,including 32 intervals normal to the wing concentrated insidethe boundary-layer region. Comparatively small modificationswere required in the second stage, so that it could be accom-plished with a small number of design cycles.

a) Initial Wing. Cp on Upper Surface.

b) Redesigned wing. Cp on Upper Surface.

Fig. 6 Redesign of the wing of a wide transport aircraft. Stage1: inviscid design. Sixty design cycles in drag reduction mode withforced lift, a) M = 0.83, C, = 0.5498, Cd - 0.0196; a = 2.410 degand b) M = 0.83, C, = 0.5500, Cd » 0.0181; a = 1.959 deg.

3) Initial Wing.

b) Redesigned wing. on Upper Surface.

Fig. 7 Redesign of the wing of a wide transport aircraft. Stage2: viscous redesign. Ten design cycles in inverse mode, a) M =0.83, C, - 0.5506, Cd - 0.0199; a = 2.317 deg and b) M = 0.83, C,= 0.5508, Cd = 0.0194; a = 2.355 deg.

The design point was taken as a lift coefficient of 0.55 at aMach number of 0.83. Figure 6 illustrates the Euler redesign,displaying both the geometry and the upper surface pressuredistribution, with negative Cp upward. The initial wing showsa moderately strong shock wave across most of the top surface,as can be seen in Fig. 6a. Sixty design cycles were needed toproduce the shock-free wing shown in Fig. 6b, with an indi-cated drag reduction of 15 counts from 0.0196 to 0.0181. Fig-ure 7 shows the viscous redesign at a Reynolds number of 12X 106. In Fig. 7a, it can be seen that the Euler design producesa weak shock as a result of the displacement effects of theboundary layer. Ten design cycles were needed to recover theshock-free wing shown in Fig. 7b. It is interesting that thewing section modifications between the initial wing of Fig. 6aand the final wing of Fig. 7b are remarkably small.

V. Industrial Experience: A Case StudyDuring the summer a group, consisting of the author, J.

Alonso, J. Reuther, and L. Martinelli, participated in designstudies for the McDonnell Douglas MDXX. We interfacedwith the project principally through J. Vassberg. The MDXXwas a promising successor to the MD11. Despite significantairline interest, it was canceled by the McDonnell DouglasBoard in late October.

We were brought into the project to augment the Douglasdesign effort by applying advanced CFD and aerodynamic op-timization techniques. These methods were used to evaluateattainable values of Mach number and LID in cruise whilesatisfying other design constraints, including 1) drag creep, 2)buffet (>\3 g to buffet from the maximum cruise CL), 3)maximum cruise CL, 4) high-speed pitch-up, 5) suitability for

44 JAMESON

high lift, 6) low-speed characteristics, 7) fuel volume, and 8)wing weight.

In particular, the goals of the study were as follows:1) To prove the validity and feasibility of adjoint-based de-

sign methods in the context of a real design environment.2) To improve the existing DAC configuration, which is rec-

ognized to be highly refined, by small modifications to extractmaximum performance.

3) To independently design a family of optimized wings asan alternative to the DAC configuration.

These goals could provide DAC with options for alternativedesigns that may yield improvements in LID, cruise Machnumber, and thickness (for fuel volume and structural weight).They could also establish a bound on attainable limits thatcould be used as a yardstick to measure the DAC configurationand to determine whether or not there was room for significantimprovement. From our side we also recognized that directexposure to a project environment could give us the insightand awareness of practical requirements that could enable usto develop better software for future use.

The two design improvement criteria used in this study wereas follows:

1) Improvements in M^LID.2) Reduction in weight: 3300 Ib was estimated to be equiv-

alent to 1 percentage point in M^L/D.The existing McDonnell Douglas wing design was used as

the baseline against which any improvements were to be mea-sured.

Some of the key questions to be addressed were as follows:1) Could LID be increased by either reducing the shock

drag, varying the spanload, or improving the wing-body-en-gine integration? Possible improvements to LID would yield asignificant improvement in fuel efficiency and aircraft range.

2) Could the cruise Mach number be increased? This couldproduce both a reduction of airline operating costs and an in-crease in passenger comfort derived from shorter flight times.

3) Could the wing thickness be increased without penalizingthe current design? Several options are available in order totake advantage of a wing with increased thickness. Amongthem one has decreased structure weight for the same wingloading, increased fuel volume, optimized span loading for thesame structural weight, or the possibility of installing largerwinglets.

4) Could the loading be moved forward to reduce trim dragand reduce hinge moments on control surfaces?

5) Could the design be made less sensitive to small changesin CL, Mach number, and Reynolds number?

6) Would a shock-free design necessarily have undesirableoff-design characteristics?

7) Could the benefits of the divergent railing-edge technol-ogy developed by McDonnell Douglas41 be combined with op-timization?

8) What compromises are needed to ensure satisfactory ma-neuver and buffet margins, as well as good high-lift charac-teristics?

9) Would there be any benefits in planform variations(sweep, taper)?

10) Could capacity for stretch be built into the system?Would span extensions be necessary for this purpose?

To support the project, we used a variety of computer pro-grams for flow analysis and aerodynamic design. Some ofthese tools were very recent, and were the subject of ongoingdevelopment during the study, as we tried to respond to theproject requirements within the very short time available. Be-cause of the cancellation of the MDXX, the study was notbrought to full fruition. Prior to the cancellation, there hadbeen plans to carry out wind-tunnel tests to evaluate an alter-nate wing designed by optimization in comparison with theMcDonnell Douglas baseline design. Nevertheless, a numberof valuable lessons were learned from the experience.

In the initial phase of the study we focused on the devel-opment of the optimization tools for isolated wings. Asidefrom difficulties with data handling, file conversation, and ob-servation of the same conventions as McDonnell Douglas, forexample, in the definition of reference quantities such as thewing area, it proved necessary to modify the codes in variousways. In particular, the visualization was greatly improved byincorporating an interface to Vassberg's COMPPLOT program.The codes had to be modified to allow for thick trailing edges.It also proved worthwhile to introduce terms measuring thepressure gradient into the cost function to prevent the pressuregradients in the optimized designs from becoming unaccepta-bly large in the rear upper surface. Access to off-site super-computers was limited, and was subject to serious delays be-cause of the queues from many users. It was demonstrated,however, that optimizations could be completed overnight onworkstations.

During the initial study three major issues soon became ap-parent:

1) The body effect was too large to be ignored and must beincluded for the optimizations to be useful.

2) Supercritical wings of the type contemplated for theMDXX are sensitive to viscous effects, which should also beincluded in the optimization.

3) Single-point designs could be too sensitive to small var-iations in the flight condition.

Therefore, in the second phase of the study, we concentratedon the optimization of wing—body combinations, proceeded tothree-point optimizations, and carried out optimizations withthe Reynolds-averaged Navier-Stokes equations. Only a pre-liminary version of a viscous design code was available, andit had to be pressed into action. To enable quick turnaroundthe strategy was adopted of first carrying out a three-pointwing-body optimization with SYN 88, which models the flowwith the Euler equations. This could be accomplished in about2y days on a C-H mesh with 256 X 32 X 48 cells using aworkstation. The preliminary Euler design was then fed toSYN 107 for Navier-Stokes redesign, using the pressure dis-tribution of the Euler result at the principal design point as atarget, with the constraint that the thickness could be increasedbut not reduced. The inverse mode was preferred because ofdoubts about the accuracy of viscous drag prediction. TheNavier-Stokes calculations are much more expensive, requir-ing a mesh with at least twice as many points, and 5-10 timesas many iterations at each design cycles. Usually a fairly clos.eapproximation to the Euler target pressure could be obtainedin 10-20 design cycles. This could be accomplished in about3 days on a workstation.

The McDonnell Douglas design team were using the OVER-FLOW program, originally developed by P. Buning, forNavier-Stokes analysis. This could treat complete configura-tions if enough time was taken to generate the required over-lapping meshes over all of the components. The use of over-lapping meshes also facilitates the concentration of meshpoints to resolve the viscous regions, and results obtained withOVERFLOW had been validated against wind-tunnel data ob-tained from tests of earlier McDonnell Douglas designs. How-ever, each OVERFLOW run required about 25 h of CPU timeon a Cray C90, and had to be broken up into 6-h shifts onseparate nights. A proper evaluation of the designs emergingfrom the optimization would require analyses at numerouspoints through the flight envelope, including a series of pointsto establish the drag rise characteristics. It was clear that thiswas impossible in the time available. In fact, it was impossibleeven with the Douglas baseline design to achieve turnaroundtimes compatible with the attempt to complete the multidisci-plinary design loop in 2 weeks.

To alleviate the situation we accelerated the development ofa parallel implementation of our own multiblock analysis pro-gram FLO 107MB, which solves the full Reynolds-averagedNavier-Stokes (RANS) equations. With this we were able to

JAMESON 45

complete a RANS analysis in a mesh with 1.5-2 million meshcells in about 1 % h using 32 processors of an IBM SP2. Thisenabled us to evaluate the performance of four different can-didate designs over the flight envelope with the aid of 60Navier-Stokes calculations during the weekend Sept. 6-8,1996. The results allowed us to eliminate one design. We alsolearned that the wings were carrying too much outboard loadnear the buffet point, and would be susceptible to shock stallnear the tip. This led us to increase the wing twist to reducethe angle of attack of the tip.

It also became apparent that there were discrepancies be-tween the results of the RANS design calculations, which hadbeen performed on coarser meshes with about 600,000 meshcells, and the analysis on finer meshes. Therefore, we alsoimplemented a parallel version of the single-block design codeSYN107, which enabled us to carry out RANS designs onmeshes with 1.8 million mesh points. Twenty design cycleswere usually found to be sufficient, and these could be com-pleted in a run of about 7y h using 48 processors of the IBMSP2.

As an illustration of the results that could be obtained, Figs.8-13 show an alternate wing-body design with increasedsweep back of about 38 degrees at the one-quarter chord. Start-ing from the result of an Euler design, the RANS optimizationproduced an essentially shock-free wing at a cruise designpoint of Mach 0.86, with a lift coefficient of 0.6 for thewing-body combination. Figure 8 shows the design point,whereas the evolution of the design is shown in Fig. 9, usingJohn Vassberg's COMPPLOT. In this case the pressure con-tours are for the final design. This wing is quite thick, actuallythicker than the McDonnell Douglas baseline design across thespan, with a thickness to chord ratio of more than 14% at theroot and 9% at the tip. The design offers excellent performanceat the nominal cruise point. Figures 10 and 11 show the resultsof a Mach number sweep to determine the drag rise. It can beseen that a double shock pattern forms below the design point,while there is actually a slight increase in the drag coefficientof about ly counts at Mach 0.85. The drag is still low, how-ever, and the double shocks remain quite weak. Figure 13

shows a comparison of the design point with alternate cruisepoints at lower and higher lift. Finally, Fig. 12 indicates thatthe pressure distribution at the buffet point is acceptable. Pro-vided that the high-speed pitch-up associated with the highsweepback angle is controllable, this is a promising candidatedesign. It is a subject of ongoing research whether the sensi-tivity near the design point could be reduced by forcing thepresence of a shock at the design point.

One difficulty of the study was that there were discrepanciesbetween the predictions of OVERFLOW and FLO 107MB.These can be attributed to a combination of mesh effects, tur-bulence modeling, and differences in the discretization scheme.FLO 107MB was normally run with the CUSP scheme,42 whichwe considered to be more accurate. We were able to verifythis by mesh refinement studies in which the CUSP solutionon a mesh with 1 X 106 mesh points was found to approachclosely the solution with the standard scalar dissipation43 on 2X 106 mesh points. A weakness of the present implementationof FLO 107MB is its use of the Bald win-Lomax turbulencemodel. This model is generally considered to be reasonablyaccurate for attached flows in the neighborhood of the cruisepoint, but unsuitable for the prediction of separated flows. Infuture work it is planned to provide options for a variety ofturbulence models.

The prediction of fuselage drag was another source of dif-ficulty. The pressure drag on the fuselage can be quite large,of the order of 40 counts, because the fuselage contributesabout 15% of the lift, and the down wash distribution of aswept wing causes a transfer of the induced drag to the inboardpart of the wing, while the tip region experiences a thrust. Withthe C-H mesh used in the wing—body design codes, the fu-selage pressure drag was drastically overpredicted. In the dragoptimization studies only the wing drag was included. Thisleads to the possibility that the optimization might transfer dragfrom the wing to the fuselage. The multiblock analysis cal-culations indicated that drag savings on the wing were partiallyoffset by an increase in fuselage drag, but further studies areneeded to clarify this issue.

REN= 101.00 , MACH = 0.860

SYMBOL SOURCE ALPHA CL CDSYN107PDESIGN40 2.094 0.610 0.01126

Solution 1Upper-Surface Isobars

( Contours at 0.05 Cp )

Fig. 8 Pressure distribution of the MPX5X at its design point.

46 JAMES ON

REN = 101.00 , MACH = 0.860 , CL = 0.610

SYMBOL

-•-• —— •

SOURCE

SYN107P DESIGN 0

ALPHA

2.251

CD

0.01131

-1.0-0.8-0.5-0.2

0.00.20.50.81.0

Solution 1Upper-Surface Isobars

( Contours at 0.05 Cp )

Fig. 9 Optimization Sequence in the design of the MPX5X.

-1.0-0.8-0.5-0.2

U 0.0

0.2

0.5

0.8

1.0

.....OJZ.....04.....QJJ&....Ji x / c ;

""":"""""44."3<7f"Span

REN= 101.00 , CL = 0.610

SYMBOL

v-SOURCE

MPX5X DESIGN 40MPX5X DESIGN 40MPX5X DESIGN 40

MACH

0.8500.8450.840

ALPHA

2.2312.2802.326

CD

0.01 14f~~0.011/00.01W4

/

-1.0-0.8-0.5-0.2

0.2 -0.5 -0.8 -1.0

Fig. 10 Off-design performance of the MPX5X below the design point.

The final phase of the study, which was truncated bythe cancellation of the MDXX, addressed the performanceof the wing-body combination with engines and wingletsincluded. Using GRIDGEN, several weeks were needed togenerate a mesh with 234 blocks and more than five millionmesh cells. RANS calculations could then be performed in5 or 6 h with 48 processors of an IBM SP2. An example of

such a calculation is presented in Figs. 14 and 15, in whichthe shading indicates the surface pressure, with darker shadingcorresponding to higher pressure. The overall turnaround formesh generation and flow analysis is still too slow. A multi-block optimization code in which the flow is modeled bythe Euler equations is already operational. A multiblockviscous design code is clearly needed and we plan to under-

JAMESON 47

REN= 101.00 , CL = 0.610

_ ._ ._ ._ . MPX5X DESIGN 40• • - • • - • - MPX5X DESIGN 40

Solution 1Upper-Surface Isobars

( Contours at 0.05 Cp )

Fig. 11 Off-design performance of the MPX5X above the design point.

-1.0

-0.8 --0.5-0.2 -

& 0.00.2 -0.5 -0.8 -1.0

..0;2......04.....0:j6......0j^......l.i x / c i

""";"" '""44 .39f Span

REN= 101.00 , MACH = 0.860

SYMBOL

------

SOURCE

MPX5X DESIGN 40

ALPHA

2.380

CL

0.661

CD

0.01314 /

-1.0

-0.8-0.5 '-0.2 -

r o.o

Solution 1Upper-Surt'ace Isobars

( Contours at 0.05 Cp )

Fig. 12 Comparison of the MPX5X at its design point and at lower and higher lift.

take its development. In the long run, unstructured meshes maybe needed to treat complete configurations with rapid turna-round.

Two major lessons of the studies were as follows:1) Useful simulations in the design of a wing for a com-

mercial transport must treat at least wing-fuselage combina-

tions and include viscous effects: more complete simulationsshould treat the engines, and also winglets if they are featuredin the design.

2) To be fully accepted by the design team, both CFD andoptimization methods need to be validated before their use inthe project.

48 JAMESON

REN = 101.00 , MACH = 0.860

SYMBOL SOURCE ALPHA CL CDMPX5X DESIGN 40 3.436 0.845 0.02808

Solution 1Upper-Surface Isobars

( Contours at 0.05 Cp )

0i2--oi4---oi6---oi8....:.........7R.lS.Saa.......

Fig. 13 Off-design performance of the MPX5X at the buffet point.

VI. Opportunity to Re-Engineer theDesign Process

In the long run, computational simulation should becomethe principal tool for aerodynamic design because of the flex-ibility it provides for the rapid and comparatively inexpensiveevaluation of alternative designs, and because it can be inte-grated with a multidisciplinary design process. To be effectivein this role, high-fidelity aerodynamic simulation needs to beused at an early stage in the process, when it can be used tomake crucial tradeoff decisions before the principal features ofthe design have been frozen.

Presently available computer programs for design integra-tion incorporate only crude and simplified aerodynamic modelssuch as vortex lattice methods. Long setup and turnaroundtimes continue to restrict the use of high-fidelity simulationmethods. The opportunity now exists to take advantage of de-velopments in information technology to completely reorgan-ize the design process. The basic flow simulation software isonly one of the needed ingredients. The flow solver must beembedded in a user-friendly system for geometry modeling,output analysis, and data management that will provide a com-plete numerical design environment. The objective should beto provide fast, cost-effective computational analysis and op-timization capabilities at an early stage in the design cycle.Some of the principal goals are as follows:

1) Analysis turnaround of less than 1 h for a full aircraftconfiguration.

2) Geometry manipulation via a CAD system with access toa central database.

3) Automated optimization of the design.4) Multidisciplinary analysis.An important element in an integrated system is the need

for good geometry modeling. When computational simulationswere first attempted, geometric definitions of aircraft were stillgenerally provided by drawings. This made it very difficult toobtain an adequate digital description of the configuration.Modern developments in computational geometry, such as Be-zier patches and nonuniform rational B-splines (NURBS), have

made it possible to provide a complete and precise digital def-inition of the geometry. In principle, this should allow manu-facturing engineers, structural designers, and aerodynamiciststo access the same unique definition of the design in a centraldatabase. The definitions provided by current CAD systemsare intended to meet appropriate manufacturing tolerances.Unfortunately, they sometimes prove to be inadequate for aero-dynamic analysis because they do not always guarantee a suf-ficient degree of smoothness across boundaries of geometricpatches. Moreover, accurate viscous simulations require meshpoints to be placed extremely close to the surface to resolvethe inner part of the boundary layer. The first mesh pointshould be at a distance of the order of v+ = 1, where v+ is adimensionless coordinate based on the viscous length scale,and this distance may be smaller than the usual manufacturingtolerances.

Given an adequate geometric model, it becomes cruciallyimportant to compress the time spent in mesh generation.There has been rapid progress in methods based on overlayingseparately generated meshes for different components, includ-ing the development of software that automatically calculatesthe coefficients needed to transfer data between the meshes. Itseems difficult, however, to automate the choice of the com-ponent meshes, though expert systems might prove useful forthis purpose. At the same time, the use of unstructured meshesis becoming an increasingly attractive option through the emer-gence of improved triangulation techniques, which are bothfast and can also assure the satisfaction of various criteria ofmesh quality. These methods should make it possible to com-pletely automate the mesh generation process, removing oneof the principal bottlenecks of current flow simulation systems.Ultimately, one can anticipate the use of hybrid meshes thatallow the use of beneficial combination of hexahedral, pris-matic, and tetrahedral cells in the same simulation.

Turnaround times, even of viscous simulations for complexconfigurations can now be reduced to at most a few hoursthrough the emergence of stable and reliable parallel comput-ing systems, together with the software needed to support com-

JAMESON 49

MPX3R wlng-bo<ly-iiace!!e-wliig!et combination at Maeli., ~ 0.6. View from, below.

Fig. 15 MFX3E wing-body-iiacelle-wlnglet combination at Mach0.85, CL = 0.6. View from above,

pilation, message passing, and memory management. In ad-dition to the availability of powerful central servers withhundreds of processors, it is now possible to link large num-bers of workstations through fast networks to operate in groupsas parallel computers. This allows the more effective utiliza-tion of workstations which might otherwise be idle at night,and can significantly increase the available computational re-sources at a moderate cost. The costs of software conversionfor parallel use can be very large, however. Therefore it iscrucially important to establish uniform standards for parallelsoftware, and the new message passing interface (MPI) pro-tocol is rapidly gaining acceptance.

Advanced geometry modeling, automatic mesh generation,and parallel computing provide the basic building blocks foran integrated system. Figures 16 and 17 illustrate the way inwhich a numerical wind tunnel might evolve from currenttechniques to a fully integrated numerical design environment.Figure 16 is representative of current practice, both at theNASA Ames National Aerodynamic Simulation system, and atthe Japanese National Aeronautical Laboratory's NumericalWind Tunnel. The massive data-handling activities in the left-hand box are human intensive. In the advanced system shownin Figure 17, many of these tasks have been automated andtransferred to the right-hand box of numerically intensive ac-tivities. An advanced system should also eventually providefor optimization and multi-disciplinary analysis. Adjoint meth-ods based on control theory can provide the capability of aero-dynamic shape optimization with quite moderate computa-tional costs. Effective design optimization must, however,account for tradeoffs in the complete system. The design of awing, for example, must include tradeoffs between drag, struc-ture weight, fuel volume, takeoff, and landing field lengths,the need to retract the undercarriage, and gate-width restric-tions. As a first step multi-disciplinary analysis requires thelinkage of the relevant disciplines through a uniform integrateddatabase. This will provide the basis for a tighter couplingwhere it is needed. For example, integrated aerodynamic andstructural analysis would allow engineers to take early accountof aeroelastic effects, such as structural deflection under aer-odynamic load, which vary as the weight changes with fuelburnoff.

Proceeding beyond multidisciplinary analysis, a future goalis the development of effective tools for MDO. This subject is

Fig. 16 Concept for a numerical wind tunnel.

__________

Fig. 17 Advanced numerical wind tunnel.

becoming the focus of extensive research. The results of nu-merical optimizations that use low-fidelity models of the dif-ferent disciplines should be treated with caution, as they maybe quite misleading. To establish confidence in the conclu-sions, it is therefore important to determine the sensitivity ofthe results to modeling inaccuracies.

VII. ConclusionsThe basic techniques of computational flow simulation are

now quite well established. Simulation techniques can com-press the design process and enhance it by allowing engineersto explore a larger range of options. This potential can onlybe fully realized by improved integration of the whole processfrom geometry definition to analysis of the final output. De-velopments in a broad spectrum of information technology in-cluding CAD, geometry modeling, database control, and par-allel computing can all contribute to the re-engineering of thedesign process.

Companies can become more competitive through reducedcycle times and improved products. In the long run, the inte-gration of computational simulation with information technol-ogy may also have a significant social impact on the engi-neering profession. Historically, many engineers wereemployed on large projects to perform routine calculations.Engineers of the future, relieved of the burden of computing,will be able to spend more of their time in creative thinkingto find innovative solutions to problems, and to produce newdesign concepts.

As the power of microprocessors continues to increase, itwill become possible to perform most engineering simulationson inexpensive workstations, and comparatively small groupswill be able to afford competitive computational resources.This may facilitate the emergence of small independent groupsto take over specialized design tasks. It is already a commonpractice, for example, for independent studios to design auto-mobile bodies for the major manufacturers. Thus in the future,an increasing number of engineers may fill a role more likethat played today by architects and consulting engineers in theconstruction industry.

AcknowledgmentsThe research described in this paper has benefited greatly

from the sponsorship of the U.S. Air Force Office of Scientific

50 JAMESON

Research under Grant AFOSR F49620-95-1-0259, monitoredby Scott Schreck. In the development of parallel implemen-tations, we have been very fortunate to have the support ofIBM and NASA through the Cooperative Research Agreement.We are also very grateful for the support of the McDonnellDouglas Corporation and the opportunity to experience at firsthand the realities of an industrial project. Thanks go to PradeepRaj of the Lockheed Martin Corporation for providing Fig. 4.

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