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Research Papers

Global Optimization Under Uncertainty and Uncertainty Quantification Applied to Tractor-Trailer Base Flaps

[+] Author and Article Information
Jacob A. Freeman

Department of Aeronautics and Astronautics,
Air Force Institute of Technology,
2950 Hobson Way,
Wright-Patterson AFB, OH 45433
e-mail: jacob.freeman@us.af.mil

Christopher J. Roy

Department of Aerospace and
Ocean Engineering,
Virginia Tech,
215 Randolph Hall,
Blacksburg, VA 24061
e-mail: cjroy@vt.edu

1Corresponding author.

Manuscript received August 7, 2015; final manuscript received March 30, 2016; published online May 3, 2016. Assoc. Editor: Luis Eca.This material is declared a work of the U.S. Government and is not subject to copyright protection in the United States. Approved for public release; distribution is unlimited.

J. Verif. Valid. Uncert 1(2), 021008 (May 03, 2016) (16 pages) Paper No: VVUQ-15-1033; doi: 10.1115/1.4033289 History: Received August 07, 2015; Revised March 30, 2016

Using a global optimization evolutionary algorithm (EA), propagating aleatory and epistemic uncertainty within the optimization loop, and using computational fluid dynamics (CFD), this study determines a design for a 3D tractor-trailer base (back-end) drag reduction device that reduces the wind-averaged drag coefficient by 41% at 57 mph (92 km/h). Because it is optimized under uncertainty, this design is relatively insensitive to uncertain wind speed and direction and uncertain deflection angles due to mounting accuracy and static aeroelastic loading. The model includes five design variables with generous constraints, and this study additionally includes the uncertain effects on drag prediction due to truck speed and elevation, steady Reynolds-averaged Navier–Stokes (RANS) approximation, and numerical approximation. This study uses the Design Analysis Kit for Optimization and Terascale Applications (DAKOTA) optimization and uncertainty quantification (UQ) framework to interface the RANS flow solver, grid generator, and optimization algorithm. The computational model is a simplified full-scale tractor-trailer with flow at highway speed. For the optimized design, the estimate of total predictive uncertainty is +15/−42%; 8–10% of this uncertainty comes from model form (computation versus experiment); 3–7% from model input (wind speed and direction, flap angle, and truck speed); and +0.0/−28.5% from numerical approximation (due to the relatively coarse, 6 × 106 cell grid). Relative comparison of designs to the no-flaps baseline should have considerably less uncertainty because numerical error and input variation are nearly eliminated and model form differences are reduced. The total predictive uncertainty is also presented in the form of a probability box, which may be used to decide how to improve the model and reduce uncertainty.

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References

Airy, G. B. , 1875, On the Algebraical and Numerical Theory of Errors of Observations and the Combination of Observations, 2nd ed., MacMillan, London.
Moffat, R. J. , 1988, “ Describing the Uncertainties in Experimental Results,” Exp. Therm. Fluid Sci., 1(1), pp. 3–17. [CrossRef]
Mason, W. T., Jr. , and Beebe, P. S. , 1978, “ The Drag Related Flowfield Characteristics of Trucks and Buses,” Symposium on Aerodynamic Drag Mechanisms of Bluff Bodies and Road Vehicles, General Motors Research Laboratories, Plenum Press, Warren, MI.
Cooper, K. R. , 2003, “ Truck Aerodynamics Reborn—Lessons From the Past,” SAE Technical Paper No. 2003-01-3376.
Leuschen, J. , and Cooper, K. R. , 2006, “ Full-Scale Wind Tunnel Tests of Production and Prototype, Second-Generation Aerodynamic Drag-Reducing Devices for Tractor-Trailers,” SAE Technical Paper No. 2006-01-3456.
SAE, 1981, “ SAE Wind Tunnel Test Procedure for Trucks and Buses,” SAE Recommended Practice, SAE International, Warrendale, PA, Standard No. SAE J1252_201207.
SAE, 2012, “ Fuel Consumption Test Procedure—Type II,” SAE International, Warrendale, PA, Standard No. J1321_201202.
STEMCO Ip, 2016, “ Aerodynamics 101,” Accessed Mar. 30, http://www.stemco.com/video-gallery/aerodynamics-101 and http://www.stemco.com/product/trailertail
Cooper, K. R. , 1985, “ The Effect of Front-Edge Rounding and Rear-Edge Shaping on the Aerodynamic Drag of Bluff Vehicles in Ground Proximity,” SAE Technical Paper No. 850288.
Storms, B. L. , Ross, J. C. , Heineck, J. T. , Walker, S. M. , Driver, D. M. , and Zilliac, G. G. , 2001, “ An Experimental Study of the Ground Transportation System (GTS) Model in the NASA Ames 7 by 10-ft Wind Tunnel,” Report No. NASA/TM-2001-209621.
Lanser, W. R. , Ross, J. C. , and Kaufman, A. E. , 1991, “ Aerodynamic Performance of a Drag Reduction Device on a Full-Scale Tractor/Trailer,” SAE Technical Paper No. 912125.
Visser, K. D. , Grover, K. , and Marin, L. E. , 2011, “ Sealed AFT Cavity Drag Reducer,” U.S. Patent No. 8,079,634.
Browand, F. , Radovich, C. , and Boivin, M. , 2005, “ Fuel Savings by Means of Flow Attached to the Base of a Trailer: Field Test Results,” SAE Technical Paper No. 2005-01-1016.
Hsu, T.-Y. , Hammache, M. , and Browand, F. , 2004, “ Base Flaps and Oscillatory Perturbations to Decrease Base Drag,” The Aerodynamics of Heavy Vehicles: Trucks, Buses, and Trains (Lecture Notes in Applied and Computational Mechanics), Vol. 19, R. McCallen , F. Browand , and J. Ross , eds., Springer, Berlin, pp. 303–316.
Ortega, J. M. , and Salari, K. , 2004, “ An Experimental Study of Drag Reduction Devices for a Trailer Underbody and Base,” AIAA Paper No. 2004-2252.
Hsu, F.-H. , and Davis, R. L. , 2010, “ Drag Reduction of Tractor-Trailers Using Optimized Add-On Devices,” ASME J. Fluids Eng., 132(8), p. 084504. [CrossRef]
Oberkampf, W. L. , and Roy, C. J. , 2010, Verification and Validation in Scientific Computing, Cambridge University Press, Cambridge, UK.
Roy, C. J. , and Oberkampf, W. L. , 2011, “ A Comprehensive Framework for Verification, Validation, and Uncertainty Quantification in Scientific Computing,” Comput. Methods Appl. Mech. Eng., 200(25–28), pp. 2131–2144. [CrossRef]
Freeman, J. A. , and Roy, C. J. , 2012, “ Application of Optimization Under Uncertainty: 2-d Tractor-Trailer Base Flaps,” AIAA Paper No. 2012-0671.
Adams, B. M. , Bohnhoff, W. J. , Dalbey, K. R. , Eddy, J. P. , Eldred, M. S. , Gay, D. M. , Haskell, K. , Hough, P. D. , and Swiler, L. P. , 2009, “ DAKOTA, a Multilevel Parallel Object-Oriented Framework for Design Optimization, Parameter Estimation, Uncertainty Quantification, and Sensitivity Analysis: Version 5.0 User's Manual,” Sandia Technical Report No. SAND2010-2183.
Pointwise, 2006, “ Gridgen Version 15 User Manual,” Pointwise, Fort Worth, TX.
Cobalt Solutions, LLC, 2011, “ Cobalt Version 5.2 User's Manual,” 2011, Cobalt Solutions, LLC, Springfield, OH.
“ Freight Performance Measures Integrated Query Tool (FPMweb),” Federal Highway Administration and American Transportation Research Institute, Accessed Mar. 30, 2016, https://www.freightperformance.org/fpmweb/default.aspx
Gutierrez, W. T. , Hassan, B. , Croll, R. H. , and Rutledge, W. H. , 1996, “ Aerodynamics Overview of the Ground Transportation Systems (GTS) Project for Heavy Vehicle Drag Reduction,” SAE Technical Paper No. 960906.
Dellinger, D. , 2008, “ Average Wind Speed,” National Oceanic and Atmospheric Administration, Accessed June 19, 2012, http://lwf.ncdc.noaa.gov/oa/climate/online/ccd/avgwind.html
Doyle, J. B. , Hartfield, R. J. , and Roy, C. J. , 2008, “ Aerodynamic Optimization for Freight Trucks Using a Genetic Algorithm and CFD,” AIAA Paper No. 2008-0323.
Federal Highway Administration, 2004, “Truck Size and Weight, Route Designations—Length, Width and Weight Limitations: Exclusions From Length and Width Determinations, Code of Federal Regulations, 23,” U.S. Department of Transportation, Washington, DC, Chap. 1, Part 658.
Grismer, M. J. , Strang, W. Z. , Tomaro, R. F. , and Witzeman, F. C. , 1998, “ Cobalt: A Parallel, Implicit, Unstructured Euler/Navier–Stokes Solver,” Adv. Eng. Software, 29(3–6), pp. 365–373. [CrossRef]
Forsythe, J. R. , Strang, W. Z. , and Hoffmann, K. A. , 2000, “ Validation of Several Reynolds-Averaged Turbulence Models in a 3-D Unstructured Grid Code,” AIAA Paper No. 2000-2552.
Freeman, J. A. , and Roy, C. J. , 2014, “ Verification and Validation of Reynolds-Averaged Navier–Stokes Turbulence Models for External Flow,” Aerosp. Sci. Technol., 32(1), pp. 84–93. [CrossRef]
Basara, B. , and Tibaut, P. , 2004, “ Time Dependent Versus Steady State Calculations of External Aerodynamics,” The Aerodynamics of Heavy Vehicles: Trucks, Buses, and Trains (Lecture Notes in Applied and Computational Mechanics), Vol. 19, R. McCallen , F. Browand , and J. Ross , J., eds., Springer, Berlin, pp. 107–117.
Roy, C. J. , Payne, J. L. , and McWherter-Payne, M. A. , 2006, “ RANS Simulations of a Simplified Tractor/Trailer Geometry,” ASME J. Fluids Eng. 128(5), pp. 1083–1089. [CrossRef]
Maddox, S. , Squires, K. D. , Wurtzler, K. E. , and Forsythe, J. R. , 2004, “ Detached-Eddy Simulation of the Ground Transportation System,” The Aerodynamics of Heavy Vehicles: Trucks, Buses, and Trains (Lecture Notes in Applied and Computational Mechanics), Vol. 19, R. McCallen , F. Browand , and J. Ross , eds., Springer, Berlin, pp. 89–104.
Pointer, D. , Sofu, T. , Chang, J. , and Weber, D. , 2009, “ Applicability of Commercial CFD Tools for Assessment of Heavy Vehicle Aerodynamic Characteristics,” The Aerodynamics of Heavy Vehicles II: Trucks, Buses, and Trains (Lecture Notes in Applied and Computational Mechanics), Vol. 41, F. Browand , R. McCallen , and J. Ross , eds., Springer, Berlin, pp. 349–361.
Roy, C. J. , and Ghuge, H. A. , 2009, “ Detached Eddy Simulations of a Simplified Tractor/Trailer Geometry,” The Aerodynamics of Heavy Vehicles II: Trucks, Buses, and Trains (Lecture Notes in Applied and Computational Mechanics), Vol. 41, F. Browand , R. McCallen , and J. Ross , eds., Springer, Berlin, pp. 363–381.
Sreenivas, K. , Mitchell, B. , Nichols, S. , Hyams, D. , and Whitfield, D. , 2009, “ Computational Simulation of the GCM Tractor-Trailer Configuration,” The Aerodynamics of Heavy Vehicles II: Trucks, Buses, and Trains (Lecture Notes in Applied and Computational Mechanics), Vol. 41, F. Browand , R. McCallen , and J. Ross , eds., Springer, Berlin, pp. 325–338.
Fluent, Inc., 2006, “ Determining Turbulence Parameters, Fluent 6.3 User''s Guide,” Fluent, Canonsburg, PA, Section 7.2.2.
Holmes, J. D. , “ Atmospheric Boundary Layers and Turbulence,” Hurricane Engineering, Louisiana State University, Accessed Sept. 27, 2011, http://www.hurricaneengineering.lsu.edu/CourseMat/03Lect6BoundLayer.ppt
Socolofsky, S. A. , and Jirka, G. H. , “ Atmospheric Mixing,” Coastal and Ocean Engineering Division, Texas A&M University, Accessed Mar. 30, 2016, http://ceprofs.civil.tamu.edu/ssocolofsky/cven489/Downloads/Book/Ch6.pdf
Arora, J. S. , 2004, Introduction to Optimum Design, 2nd ed., Elsevier Academic Press, San Diego, CA.
Eddy, J. , and Lewis, K. , 2001, “ Effective Generation of Pareto Sets Using Genetic Programming,” ASME Paper No. DETC2001/DAC-21094.
Janiga, G. , 2008, “ A Few Illustrative Examples of CFD-Based Optimization: Heat Exchanger, Laminar Burner and Turbulence Modeling,” Optimization and Computational Fluid Dynamics, D. Thévenin , and G. Janiga , eds., Springer-Verlag, Berlin, pp. 17–59.
Dumas, L. , 2008, “ CFD-Based Optimization for Automotive Applications,” Optimization and Computational Fluid Dynamics, D. Thévenin , and G. Janiga , eds., Springer-Verlag, Berlin, pp. 191–215.
“ Consolidated Hardware,” Department of Defense High-Performance Computing Modernization Program, Accessed Mar. 30, 2016, https://centers.hpc.mil/consolidated/hardware.html
Schetz, J. A. , 1993, Boundary Layer Analysis, Prentice-Hall, NJ.
“ Annual Vehicle Miles of Travel by Highway Category and Vehicle Type,” 2013, Table VM-1, Highway Statistics, Office of Highway Patrol Information, Federal Highway Administration, U.S. Department of Transportation, Accessed Oct. 29, 2015, http://www.fhwa.dot.gov/policyinformation/statistics/2013/vm1.cfm
“ U.S. On-Highway Diesel Fuel Prices,” 2015, U.S. Energy Information Administration, Accessed Oct. 29, 2015, http://www.eia.gov/petroleum/gasdiesel
McCallen, R. , Couch, R. , Hsu, J. , Browand, F. , Hammache, M. , Leonard, A. , Brady, M. , Salari, K. , Rutledge, W. , Ross, J. , Storms, B. , Heineck, J. T. , Driver, D. , Bell, J. , and Zilliac, G. , 1999, “ Progress in Reducing Aerodynamic Drag for Higher Efficiency of Heavy Duty Trucks (Class 7–8),” Office of Scientific and Technical Information, U.S. Department of Energy, SAE Paper No. 1999-01-2238.
Cummings, R. M. , Morton, S. A. , and McDaniel, D. R. , 2008, “ Experiences in Accurately Predicting Time-Dependent Flows,” Prog. Aerosp. Sci., 44(4), pp. 241–257. [CrossRef]
Freeman, J. A. , 2012, “ Optimization Under Uncertainty and Total Predictive Uncertainty for a Tractor-Trailer Base-Drag Reduction Device,” Ph.D. dissertation, Virginia Polytechnic Institute and State University, Blacksburg, VA.
He, J. , Watson, L. T. , and Sosonkina, M. , 2009, “ Algorithm 897: VTDIRECT95: Serial and Parallel Codes for the Global Optimization Algorithm DIRECT,” ACM Trans. Math. Software, 36(3), p. 17. [CrossRef]

Figures

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Fig. 1

Example of straight trailer base flaps and other aerodynamic drag-reduction devices [8] (used with permission, ATDynamics/STEMCO)

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Fig. 2

Time-averaged 3D computational solutions of simplified tractor-trailer with and without base flaps, showing reduced region of low pressure. Horizontal slice at y/W = 0.695 for β = 9.1 deg showing velocity streamlines atop contours of gauge pressure (for (a) and (b)). β = 0 deg for (c) and (d). Highway speed, V = 57.2 mph (92.1 km/h), and trailer-width-based Reynolds number, ReW = 4.4 × 106. (a) baseline configuration, no flaps, CD = 0.329, (b) side flaps deflected inward 20 deg, CD = 0.201, (c) stream traces, no flaps, and (d) stream traces, all flaps deflected inward 18 deg.

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Fig. 3

Time-averaged 3D computational solutions of simplified tractor-trailer showing sensitivity of base-flap boundary layer to flap deflection angle. Horizontal slice at y/W = 0.695 for β = 2.0 deg showing velocity streamlines atop contours of velocity in the x-direction. Highway speed, V = 57.2 mph (25.6 m/s), and ReW = 4.4 × 106: (a) attached flow for δ = 20 deg, CD = 0.208 and (b) separated flow for δ = 29 deg, CD = 0.267.

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Fig. 4

Framework of optimization algorithm, preprocessing, simulation, and postprocessing

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Fig. 5

Trailer-base flaps with design-variable values for one possible configuration: (a) 2D side flap with variable labels; view looking down from top and (b) 3D flaps at trailer base

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Fig. 6

Computational mesh for simplified 3D tractor-trailer geometry (GTS model), 5.75 × 106 hexahedral cells, average first-cell y+≈ 1.3 (for combined GTS and flaps): (a) complete computational domain, (b) surface geometry with base flaps, (c) surface mesh with base flaps, and (d) base and flaps, horizontal slice at y/W = 0.69

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Fig. 7

Convergence history of iterative residuals and forces for 3D simplified tractor-trailer, 5.75 × 106 cell structured grid, Cobalt v5.2, SST turbulence model. History shown for design 45, β = 2 deg. (a) Seven orders of magnitude for continuity and turbulence and (b) body-axis force.

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Fig. 8

C¯Dδ±2 deg results for 3D simplified tractor-trailer using the DAKOTA-implemented COLINY EA and five design variables (L1, θ1, θ2, δside, and δtop); seven generations represent 130 feasible design candidates and 1560 flow solutions; compared with straight flap design at various deflection angles. 5.75 × 106 cell structured grid, Cobalt v5.2 flow solver, SST turbulence model. (a) Design tracking over seven generations and (b) graphic of best design, EA.127.

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Fig. 9

Design variable tracker by generation for EA base flaps on 3D GTS. Filled shapes highlight the ten best-performing designs: (a) axial length of flap; (b) slope at trailer-flap interface; (c) slope at flap trailing edge; (d) inward deflection angle for top, bottom flaps; and (e) inward deflection angle for both side flaps.

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Fig. 10

Negative angle at flap trailing edge results in large regions of separated flow and larger CD. Horizontal slice at y/W = 0.695 for β = 5.8 deg showing velocity streamlines atop contours of gauge pressure. Highway speed, V = 57.2 mph (25.6 m/s), and ReW = 4.4 × 106: (a) design 1, θ2 = 35 deg, CD = 0.232 and (b) Design 24, θ2 = −34 deg, CD = 0.313.

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Fig. 11

Three-dimensional simplified tractor-trailer design progression by EA generations; percent improvement over no-flaps baseline C¯D shown in parentheses. Seven generations are completed. ReW = 4.4 × 106, cobalt SST turbulence model. (a) Side flaps and (b) top/bottom flaps.

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Fig. 12

Ensemble of EDFs of CD for model-input uncertain parameters: wind speed and direction (aleatory), truck speed and elevation (aleatory treated as epistemic), and flap deflection variation (epistemic). All results are from 3D simplified tractor-trailer with base flaps design EA.90, 5.75 × 106 cell grid, Cobalt SST turbulence model.

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Fig. 13

Time-step sensitivity study, showing CD for the 5.75 × 106 cell grid at β = 2.036 deg, Cobalt SST turbulence model

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Fig. 14

Probability box showing total predictive uncertainty that includes uncertainty due to model input, model form, and numerical approximation, for the 3D simplified tractor-trailer with base flaps design EA.90, ReW = 4.4 × 106, Cobalt SST turbulence model

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