ABSTRACTRecent advances in morphing, simulation, and optimizationtechnologies have enabled analytically driven aerodynamicshape optimization to become a reality. This paper willdiscuss the integration of these technologies into a singleprocess which enables the aerodynamicist to optimize vehicleshape as well as gain a much deeper understanding of thedesign space around a given exterior theme.

INTRODUCTIONEfforts are made periodically to understand the aerodynamicpotential of a given vehicle theme using designedexperiments and physical wind tunnel testing. The physicalmodel is typically constructed from a number modules, asillustrated in Figure 1, in order to support the multipleconfigurations within the designed experiment. A region suchas the greenhouse might be represented by two or moremodules. For example, one module representing variouswindshield angles, a second module to account for modifiedtumble home, and a third module representing different rearheader, rear pillar and backlight angles. This type of physicalexperiment also requires the multiple variations of eachmodule in order to evaluate different levels of each factor inthe design. The design and fabrication of these multiplemodules is costly and time consuming. The number of factorsthat can be evaluated is normally limited by the complexity ofthe modules and interfaces between modules. Theseconstraints and the cost of wind tunnel test time often limitthe extent of the investigation. (i.e.: two level vs. multiplelevel factor evaluation).

The value of the evaluation is frequently mitigated by the factthat the vehicle theme can evolve beyond the scope of theoriginal test by the time the wind tunnel experiment has been

completed. The cost and long lead time associated with thisexperimental approach coupled with the continuous reductionin vehicle development cycle time over the past decade limitthe benefits of this approach.

Computationally based designed experiments andoptimization studies have historically also been limited by thecost and time associated with configuration changes andsimulation times. The majority of computational studies inthe traditional processes have also tended to be sequential innature as illustrated in Figure 2.

Figure 1. Typical Test Vehicle Modular Construction

Figure 2. Traditional Process

Vehicle Aerodynamic Shape Optimization 2011-01-0169Published

04/12/2011

Robert Louis LietzFord Motor Co.

Copyright © 2011 SAE International

doi:10.4271/2011-01-0169

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More intensive analytically based processes have beenattempted in recent years with some success. Most have beenlimited to somewhat simplified models and/or constrained bythe need for manually driven model configuration changes.Recent advances in morphing, simulation, and optimizationtechnologies have opened the door to a new method ofaerodynamic shape optimization which is less costly and ableto keep pace with reduced vehicle design cycle times. Such aprocess is illustrated in Figure 3. The goal of the processdescribed in this paper is to deliver an aerodynamic shapeoptimization methodology capable of investigating the totaldesign space around a particular theme. The process definesthe minimum drag attainable from that shape, the optimumrange for each factor in the analysis, and provides theaerodynamicist with an interactive tool capable of supportingprogram trade-off discussions by rapidly evaluating theaerodynamic impact of any combination of factor levels.

Figure 3. Analytical Process

THE ANALYTICAL PROCESSBoth traditional and virtual optimization studies areintegrated into this analytical aerodynamic developmentprocess. Traditional optimization studies focus on dragreduction for either an exterior component such as the mirroror a particularly sensitive surface region of the vehicle suchas the rear header or on some combination of vehicleproportion changes. A limited number of samplingsimulations are required to initiate the process. Factor levelchanges and additional optimization simulations are thendriven by the simplex algorithm. This approach generates areduced drag configuration but provides little understandingof the broader design space of the problem.

The process described in this paper is a more holisticapproach that utilizes virtual optimization techniques. Thisapproach requires a larger number of initial samples evenlydistributed across the total design space. Design ofexperiment techniques are used to generate this initial set ofsamples. Simulations are performed for each sample/configuration. The simulation results are used to generate aresponse surface describing the mathematical relationships

between factors under evaluation. The response surface isvalid for any configuration whose factor levels are within therange of the initial designed experiment. A virtualoptimization (using standard optimization algorithms) is thenperformed in which alternate vehicle configurations areevaluated based on the relationships defined within theresponse surface. The accuracy of the response surface is afunction of the initial sampling distribution.

The general process involves 8 steps. The first step is thecreation of the analytical model and identification of thefactors to be studied. Step 2 is the development andapplication of the morphing strategies to the base model. Thethird step focuses on the design of the experiment. Step 4 isthe performance of the simulations for each configuration.Step 5 uses the data from the numerical experiment togenerate a response surface. The sixth step utilizes theresponse surface as the engine to perform a virtualoptimization. A simulation is performed in Step 7 to confirmthe performance of the optimized configuration predictedfrom the response surface. The data analysis required tounderstand the physics driving the Cd reduction is performedin Step 8.

The process is totally automated and shown in simplifiedform in Figure 4. Overall process integration andoptimization algorithms are provided by the ModeFrontiersoftware application.

All model configuration changes are automatically generatedfrom a single initial model surface mesh using morphingstrategies developed at the beginning of the project. Themorphing strategies are developed within ANSA. Eachmorphing strategy is checked for the quality of meshgenerated before it is incorporated into the process. Thesequencing of morphing combinations is also checked toensure quality meshing. Each morphing strategy created iscataloged and available for deployment on future vehicleprograms. The morphing strategies are deployed in batchmode during the process.

The process is not dependent upon a particular computationalsolver. This is definitely an advantage. It enables the processto be deployed early in a vehicle program using a steady statesolver (faster simulation times but less accurate) or later inthe vehicle program with a transient solver (longer simulationtimes with increased accuracy).

The Enliten software application is used to generate dynamic(ELS) images for each configuration simulated. These imagesare useful in communicating potential surface changes toother attributes such as styling and package engineering.

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STEP 1: ANALYTICAL VEHICLEMODELFront end opening size & location is not typically known atthe beginning of a vehicle program. At this point in theprogram closed front end models have typically been used.This makes it difficult to accurately predict the flow splitaround the vehicle. To address this issue the closed front endmodels now incorporate boundary condition mapping. In thisprocess closure surfaces are first created for both the frontend openings and the bottom of the engine bay. A mass flowboundary condition is mapped onto the front end closurepanels and set of velocity boundary conditions are mappedonto the engine bay closures. This approach results in a morerealistic flow split prediction without the additionalcomputational expense incurred by detailed under hoodgeometry modeling. This does, however, prevent theinclusion of under hood components as factors within thestudy. All models include fully detailed underbodiesincluding suspension, exhaust, etc. This process has beensuccessfully applied at Ford Motor Company across a broadrange of vehicle topologies including trucks, cross-overutility (CUV) vehicles, B-cars, and sedans as illustrated inFigure 5.

Each study typically targets up to 14 proportionality factors.This upper bound is strictly a function of available computerresources and vehicle program timing requirements. Typicalfactors are shown in Table 1. Examples from a recent truckapplication are included in this paper for illustrative purposes.Factors specific to the truck study are identified in Table 2.

Table 1. Common Design Factors

Figure 4. ModeFrontier Process Workflow

Figure 5. Example vehicle applications

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Table 2. Truck Specific Design Factors

STEP 2: MORPHING STRATEGIES;AUTOMATED MODELCONFIGURATION CHANGESAutomated morphing is a critical part of the analyticalprocess. It requires some amount of development time at thebeginning of a new study but ensures consistency in approachacross all configuration changes. The strategies are then alsoavailable to rapidly generate any configuration defined duringthe virtual optimization phase of the process.

Strategies initially developed are applied to the base modeland the quality of the morphed meshes is evaluated across the

full level range of each factor. Several iterations are typicallyrequired to ensure consistently high quality mesh morphing.The morphing strategies developed are archived and availablefor reference/application on future programs. The combinedmorphing strategies for truck are shown in Figure 6.

Figure 6. Complex Truck Morphing Strategy

Dynamic images (Enliten .els images) are created of eachconfiguration in the designed experiment during themorphing stage of the process. The images have zoomcapability and can be rotated. This provides a method forquick inspection prior to the performance of any simulations.It also serves as a good visual communication tool with thevehicle program development teams. The images specificallyexclude all underbody components and focus on the upperbody where the morphing was performed. An example ofsuch an image is shown in Figure 7.

Figure 7. Example of a Dynamic Image generatedduring a truck DOE

STEP 3: DESIGNED EXPERIMENTA well designed experiment tries to balance 3 criteria. It isdesired to minimize the number of required simulations,minimize the correlation between factors, and generatesufficient data to enable a reliable statistical analysisincluding RSM. Establishing the criteria for a well designedexperiment is a compromise. In industrial applications costand timing concerns lead away from pure academic criteriaand toward a more subjective approach. For example,although zero correlation between factors would be the ideal

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situation, a less demanding value of 0.2 is normally accepted.The acceptability of this value has been established through anumber of confirmation simulations.

Latin HypercubeA number of sample generation schemes were evaluatedduring the development of this process. The Latin Hypercubeapproach was selected based on its ability to consistentlygenerate the most even distribution across the design spacewhile providing reasonable independence between factors.

This process begins with a Latin Hypercube design with atotal sample size of approximately 20 times the number offactors in the study. The initial sample set is subjectivelychecked for distribution and factor independence. Reductionof the initial data set is performed manually using toolswithin ModeFrontier. The reduced data set is visuallychecked for distribution and factor correlation. The size of theinitial data is typically set at 200 for a ten factor designedexperiment and randomly reduced to 150, 100, 75, 50 and 25.A sample set of 50 for a 9-10 factor experiment has beenfound to be the minimum required to generate a reasonablequality response surface (RSM). The quality criteria for theresponse surface are based on equivalent directionality ascompared to the 200 sample case. The Scatter Matrix shownin Figure 8 provides a graphical depiction of the design spacedistribution, the numerical correlation value between factors,and histograms of factor level distributions.

Figure 8. Scatter Matrix is used to check factorcorrelation and design space distribution

STEP 4: SIMULATIONSThe process is designed to be “solver independent”.Commercially available Lattice Boltzmann transient andRANS steady state solvers have been used in this process.

The size of the models used during a transient analysistypically ranged 50 and 75 million cells. Simulation timeswere on the order of 24 hours running across a 96cpu cluster.Post-processing for each simulation is performedautomatically as part of the overall process.

The size of the models used during steady state simulationsranged from 25 to 40 million cells. Typical simulation timeswere 5 hours running across a 64 cpu cluster. Post-processingfor each simulation is performed automatically as part of theoverall process.

All post-processing is performed automatically and providesthe aerodynamicist with images of flow structures, pressuredistributions, velocity distributions, surface flow lines, anddrag development plots. In addition, the relative significanceon vehicle drag of each factor in the study is quantified in aFactor Correlation Table as shown in Table 3 below.

Table 3. Correlation of Factors to Drag Coefficient

STEP 5: RESPONSE SURFACEMETHODOLOGYA quality response surface serves as the engine for virtualoptimization studies which minimize (vs. a traditionaloptimization approach) the total number of requiredsimulations.

The analytical process described in this paper uses the RadialBasis Function for response surface generation. Thisapproach was selected for its ability to best fit to theunderlying data. The maximum expected error range forpredicted Cd values based on empirical results is on the orderof 0.002. The validity of this approach has been establishedthrough a number of confirmation simulations. In theseconfirmation studies, CFD detailed simulations of the designconfigurations associated with the RSM predicted minimumand maximum Cd values are performed and the resultscompared against the RSM predictions.

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Graphical User InterfaceA graphical user interface (GUI) was developed specificallyto support this process. The GUI is totally interactive andprovides the aerodynamicist with a tool for rapid evaluationof design alternatives within the original design space. TheGUI is divided into two major sections. The first section,shown in Figure 9, presents a function plot for each of thefactors (a total of 10 in this case). The function plot acts as asensitivity indicator. The vertical axis of each function plotshows the range of each factor in the study. The horizontalaxis shows the corresponding range of potential Cd changes.Each set of function plots is valid for a single point(configuration) within the design space. Relative sensitivityof a given factor at one point in the design space will varyversus other points in the design space.

Figure 9. Response Surface GUI Function Plots

The second section of the GUI, shown in Figure 10, is theuser interface. It is in this section that the user interrogates thedesign space by adjusting individual factor levels. The effecton Cd of any configuration change is calculated andimmediately available for review by the engineer or programteam members.

Figure 10. Response Surface GUI User Interface

STEP 6: VIRTUAL OPTIMIZATIONAs stated earlier, this process utilizes virtual optimizations inlieu of traditional optimization approaches. Time, cost,efficiency and a desire to understand the entire design spaceare the main drivers in selecting the virtual optimizationapproach. A number of optimization algorithms are availablewithin ModeFrontier. Non-dominated Sorting GeneticAlgorithm II, (NSGAII) has been applied with a good level ofsuccess. The virtual optimization is only as accurate as theunderlying response surface. The response surface is anapproximation of the relationships between the factors understudy. It provides direction in terms of factor levels andapproximate Cd values. Virtual optimization is deployedearly in the vehicle development process when directionalityis more important than absolute accuracy of predicted Cd.Virtual optimization has shown itself capable of providingvery good directionality. Confirmation simulations areultimately used to provide accurate Cd predictions forspecific configurations of interest to the vehicle program.

There are three major deliverables from this process as shownin the flow chart in Figure 11. Those deliverables are:

1. Determine the minimum Cd attainable within the givendesign space

2. Quantify the optimum ranges for each factor

3. Provide a GUI to support trade-off discussions acrossvehicle attributes

Figure 11. Process Flow Chart

The GUI was described previously. The minimum attainableCd and the optimum range for each factor are determinedfrom the parallel coordinates plot. A typical parallelcoordinates plot is shown in Figure 12.

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Figure 12. Parallel Coordinates Chart

The plot defines the factor levels and Cd values for eachconfiguration evaluated during the virtual optimization.Factors are identified across the horizontal axis. Factor levelranges are identified along the vertical axes. Cd valuescorresponding to each configuration evaluated are plotted onthe far right vertical axis. Each configuration is represented inthe plot by a single unique curve formed by connecting thefactor levels for that configuration. The NSGA IIoptimization algorithm evaluates an additional 100generations from each of the configurations in the originaldesigned experiment. This algorithm would thus evaluate10,000 additional configurations from a 100 configurationdesigned experiment. Optimum ranges for each factor areidentified by areas of clustering in the parallel coordinateschart. The effect of the clustering can also be visuallyenhanced by filtering the Cd values. The ability to defineoptimum ranges rather than a point target for each factor levelis important. It provides the aerodynamicist with multiplefactor level combinations that can all generate a minimizedCd. This is a valuable tool in trade-off discussions.

The minimum attainable Cd value appears as the lowest valueshown in the far right hand axis. Filtering can also be appliedto any and all vertical axes to evaluate potential Cdreductions under any combination of factor constraints.

STEP 7: CONFIRMATIONSIMULATIONConfirmation simulations, as stated earlier, are an importantcomponent of this system. The response surface is capable ofaccurately predicting Cd directionality and relative valuesonly. It is not used for absolute vehicle Cd predictions.Confirmation simulations are ultimately required to provideaccurate Cd predictions for specific configurations of interestto the vehicle program.

STEP 8: ANALYSIS OF RESULTSOne of the strengths of CFD is the ability to analyze the flowphysics and understand the driver behind predicted Cdchanges. A series of images illustrating flow structures,pressure distributions, surface flow visualizations, and Cddevelopment are automatically generated as part of theoverall process. An abbreviated set of comparison images fortwo different design levels from a recent truck optimizationstudy are presented below for illustration purposes.

Geometry

Cd Development Curves

The Cd development curves plot cumulative Cd on thevertical axis against vehicle position on the horizontal axis.Comparison of the plots shows a significant difference in Cdoccurs at the rear of the cab.

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Surface Pressure Distributions

The surface pressure distributions show a significantly lowerpressure on the back face of the cab and along the rear headerand pillars of the cab in design level 9.

Flow Structures

Iso-surfaces of total pressure show wake structure differencesbetween design levels but the effect of these differences onCd can be difficult to quantify.

Flow Field Pressure Distributions

A lower pressure region directly behind the cab in designlevel 9 is clearly seen in these centerline slices and supportsthe differences in the two design levels highlighted in the Cddevelopment curves.

SUMMARY/CONCLUSIONSA process has been developed that is capable of:

1. Determining minimum Cd attainable within a specifiedsurface envelope at the beginning of the vehicle program

2. Quantifying effect on Cd of key upper body surfaceparameters and establishing optimum ranges for each.

3. Providing a graphical user interface enabling rapidevaluation of the effect on Cd of any configuration within thespecified surface envelope.

◦ Rapid feedback to Design Studios

◦ Supports program trade-off discussions

That process has been successfully deployed in support ofvehicle aerodynamic development in a productionenvironment. The process continues to evolve and improvewith each new vehicle application.

REFERENCES1. Ortiz, J., Guerrero, J., Rosa, E., Conde, F., “AerodynamicSimulation Integration in the Development Process at SEATS. A.” SAE Technical Paper 2004-05-0127.

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2. Singh, R. “Automated Aerodynamic Design OptimizationProcess for Automotive Vehicle,” SAE Technical Paper2003-01-0993, 2003, doi:10.4271/2003-01-0993.

3. Breitling, T., Jehle, E., Reister, H., and Schwarz, V.,“Development and Evaluation of a Numerical SimulationStrategy Designed to Support the Early Stages of theAerodynamic Development Process,” SAE Technical Paper2002-01-0571, 2002, doi:10.4271/2002-01-0571.

4. Joshi, D.S., Zhu, X., and Singh, K., “Parametric ShapeOptimization,” SAE Technical Paper 2008-01-1431, 2008,doi:10.4271/2008-01-1431.

5. Pediroda, V., Parussini, L., Poloni, C., Parashar, S. et al.,“Efficient Stochastic Optimization using Chaos CollocationMethod with modeFRONTIER,” SAE Technical Paper2008-01-1429, 2008, doi:10.4271/2008-01-1429.

6. Rubio, P., Jacquet, B., Bouwman, R., “Validation of OpenSource CFD Methods used for Race Cars,” MIRA 2010, UK

7. Campos, F., Geremia, P., Skaperdas, E., “AutomaticOptimization of Automotive Designs Using Mesh Morphingand CFD,” EACC 2007

8. Narayanan, A., Einstein, A., “Morphing andParameterization Technologies for CFD Applications,” SAETechnical Paper 2007-01-0597, 2007, doi:10.4271/2007-01-0597.

9. Bosmans, I., Brughmans, M., Brizzi, P., Shiozaki, H.,Yanase, J., Application of Morphing in Concept Phase ofVehicle Development,” SAE Technical Paper 2005-08-0023.

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CONTACT INFORMATIONRobert LietzFord Motor CompanyDearborn MichiganRLIETZ@FORD.COM

ACKNOWLEDGMENTSSpecial thanks to Sunil Earla and Ravi Nimbalkar of Beta-CAE Systems, Sumeet Parashar of Esteco Corporation, andDena Hendriana of Exa Corporation for their support in thedevelopment of the process. Also like to acknowledge thecontribution from Kevin Disotell in the development of theGUI. Support from the following engineers was instrumentalin deploying this process in a production environment: MarkTessmer, John Romig, Rafael Silveira, Debra Hands, SteveParks, Jodi McGrew, Shaoyun Sun, Ken Anderson, andHojun Ahn.

DEFINITIONS/ABBREVIATIONSCFD

Computational fluid dynamics

CdCoefficient of drag

GUIGraphical User Interface

DOEDesign of Experiment

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