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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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. 4

Framework of optimization algorithm, preprocessing, simulation, and postprocessing

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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. 1

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

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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. 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. 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. 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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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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