The document discusses two methods for aerodynamic optimization of vehicles: the parametric 50:50:50 method and the gradient-based adjoint method. The 50:50:50 method uses a design of experiments approach, parameterizing the vehicle shape with four parameters and running 50 design points with 50 million cell meshes and achieving results within 50 hours. Response surface modeling is used to analyze results and identify an optimized design with a 4% reduction in drag. The adjoint method computes sensitivities using a different approach than the traditional tangent method. It involves solving the flow equations, selecting an observation of interest like lift or drag, setting up and solving the adjoint problem for that observation, and processing the solution to obtain shape sensit

1. © 2011 ANSYS, Inc. July 17, 20131
Details of the
Automotive
Aerodynamics
Optimization work
featured in this
Bloomberg
Businessweek article
in the March 11-17,
2013 issue, are
presented here

2. © 2011 ANSYS, Inc. July 17, 20132
Automotive Aerodynamics Optimization
Sandeep Sovani, Ph.D.
Global Automotive Strategy and Marketing
ANSYS Inc, Detroit, USA
July 17, 2012
Ashok Khondge
Lead Technology Specialist
ANSYS India Pvt Ltd, Pune India

3. © 2011 ANSYS, Inc. July 17, 20133
Aerodynamics Optimization Methods
Parametric Method – 50:50:50 Method
Gradient Based Method – Adjoint Method
Agenda

4. © 2011 ANSYS, Inc. July 17, 20134
• Method 1 – Parametric Method
– Parameterize vehicle shape
– Change shape parameters and run numerous simulations
– Generate response surfaces and optimize vehicle shape
• Method 2 – Gradient Based Method
– Solve for flowfield of baseline shape
– Perturb shape and calculate derivative of drag w.r.t. to shape
– Identify shape changes yield most improvement in drag
Aerodynamics Optimization Methods

5. © 2011 ANSYS, Inc. July 17, 20135
Aerodynamics Optimization Methods
Parametric Method – 50:50:50 Method
Gradient Based Method – Adjoint Method
Agenda

6. © 2011 ANSYS, Inc. July 17, 20136
• Aerodynamic Optimization via shape exploration
– Parameterize vehicle shape
– Change shape parameters and run numerous simulations
– Generate response surfaces and optimize vehicle shape
• Ideal Aerodynamics Optimization Process
– Ability (to explore a large design space)
– Automatic (with least human effort)
– Fast (Fits in the vehicle development process)
– Accurate (High Fidelity Meshes, Physics Models)
Introduction

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7
Three
Essentials
PAPER 2012-01-0174
Introduction

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Introduction
The 50:50:50 Method
50 50 design points in the design space EXTENT
50
50 million cells used in CFD simulation
of each design point
ACCURACY
50
50 hours total elapsed time to
simulate all the design points
SPEED
“One – Click” – Entire design space is simulated and post-processed
completely automatically after the initial baseline case setup

9. © 2011 ANSYS, Inc. July 17, 20139
Methodology
Prepare Meshed Model for
Baseline Vehicle Shape
CFD Solver Setup,
Define Shape Parameters
Generate DOE using
Input Shape Parameters
Collate Data,
Perform Optimization
Morph Vehicle Shape
Run CFD Simulation
STEP 1
STEP 2
STEP 3
STEP 4
STEP 5

10. © 2011 ANSYS, Inc. July 17, 201310
• To Demonstrate 50:50:50
Method
– Volvo XC60 vehicle model
– Four shape parameters
– RBF Morph (Integrated within
FLUENT) to define shape
parameters
• ANSYS WorkBench (Frame Work
to Automate Process)
– To drive shape parameters
– To create DOE
– To perform Goal Driven
Optimization
Test Case Description

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Methodology – ANSYS WB
STEP 3
STEP 5
STEP 2
STEP 4

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• Surface mesh – ANSA
• Surface mesh size
– Front facia : 3.0 to 4.0 mm,
– Windshield : 4.0 to 5.0 mm
– Doors &windows : 5.0 to 6.0 mm
– Roof : 6.0 to 8.0 mm
– Rear : 4.0 to 5.0 mm
– Underbody : 5.0 to 6.0 mm
Step #1 : Baseline Model Creation

13. © 2011 ANSYS, Inc. July 17, 201313
13 PAPER 2012-01-0174
Prism Layer
• 10 Layers (First Aspect Ratio 10, Growth 1.1)
• 24.4 million cells (about half of total cells are in prism layer
Cell size
needed if
using
cartesian cells
with same cell
count
Number of cartesian cells needed to achieve same
near wall resolution 550 million!
Step #1 : Baseline Model Creation

14. © 2011 ANSYS, Inc. July 17, 201314
• Volume Mesh – TGrid
• Cell Count : 50.2 Million Cells
• Prism Layers : 10 (First Aspect Ratio 10,
Growth 1.1)
• Prism Count : 24.4 Million Cells
• Skewness < 0.9
Step #1 : Baseline Model Creation
Prism Layers
Cut Plane Y=0
Cut Plane Z = 1.4 m

15. © 2011 ANSYS, Inc. July 17, 201315
• Boundary Conditions
– Inlet : Velocity Inlet 100 kmph
– Outlet : Pressure Outlet, 0 Pa (Gage)
– Side walls : Wall, no-slip
– Top wall : Wall, no-slip
• Solver Settings
– Steady, PBCS, Green Gauss Node
Based Gradient
– Fluid : Incompressible air,
– Density = 1.225 kg/m3
– Turbulence : Realizable K-epsilon,
Non-equilibrium wall treatment
– Discretization :
• Pressure – Standard
• Momentum, TKE, TDR – 2nd Order
Step #2 : CFD Setup
• Solution Controls
– Courant Number = 200
– ERF
Momentum, Pressure = 0.7
– URFs
Density = 1.0, Body Forces = 1.0
TKE, TDR = 0.8
TR = 1.0

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Step #2 : RBF Morph
• RBF Morph : Add-On Module
– Fully Integrated within ANSYS
FLUENT with GUI/TUI
• Uses Radial Basis Function
Technique for Mesh
Morphing
– System of radial basis function
is used to produce solution for
mesh movement
– List of source points and their
displacements are used as
input
– Valid for both surface shape
change and volume mesh
smoothing
• Developed by RBF Morph
http://www.rbf-morph.com/
RBF GUI

17. © 2011 ANSYS, Inc. July 17, 201317
Step #2 : Shape Parameters - Definition
1. Boat Tail Angle (P2)
Constraint :
Point “B” to move upto 20 mm in
+ve /-ve Y-direction about the
Pivot axis
2. Long Roof Drop Angle (P3)
Constraint :
Rear edge to move
Upto 30 mm in +ve Z-direction
Upto 45 mm in -ve Z-direction
about the Pivot axis

18. © 2011 ANSYS, Inc. July 17, 201318
Step #2 : Shape Parameters - Definition
3. Green House (P4)
Constraint:
Point “A” to move 20 mm in
+ve /-ve Y-direction about the
Pivot axis
4. Front Spoiler Angle (P5)
Constraint:
Point “C” to move 30 mm in
+ve Z direction

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Axis about which selected
surface set gets morphedEncapsulation RegionSurface set selection
Step #2 : Setup – Boat tail angle (P2)

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Step #2 : Setup – Long roof drop angle (P3)
Encapsulation RegionSurface set selection Axis about which selected surface set gets morphed

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P2 – Boat Tail Angle

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P3 – Long Roof Drop Angle

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P4 – Green House Angle

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P5 – Front Spoiler Angle

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• RBF Morph shape parameters
– Define in FLUENT
– Available in WB for
• Input Shape Parameters
– P2 : Boat tail angle
– P3 : Long roof drop angle
– P4 : Green house
– P5 : Front spoiler
• Output Parameter
– P1: Drag Force on vehicle
• DOE Algorithm
– Central Composite Design
– Design Type : Face Centered with
Enhanced Template
– 49 DOE Points Generated
Step #3 : Design Space
Design Space Bounds
Parameter Min Baseline Max
Boat tail angle - 1.85 0.0 + 1.85
Long roof drop angle - 2.30 0.0 + 1.50
Green House Angle - 0.70 0.0 + 0.70
Front Spoiler Angle 0.0 + 3.80

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DOE Table

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Step #4 : Running Simulations
• Current Study
– Simulations were run outside of
WorkBench using journal file in
batch mode
– Output the drag force
– DOE table updated by
importing output parameters
• Five Runs Using
– 768, 384, 288, 240, 144 Cores
• Convergence Monitors
– Drag force
– Pressure /velocity at few points
in wake
Design point # 1
Design point # 2
Design point # 50

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Step #4 : Running Simulations
768 Cores 384 Cores 288 Cores 240 Cores 144 Cores
Task Time (Seconds) Time (Seconds)
Time
(Seconds)
Time
(Seconds)
Time
(Seconds)
Baseline Case (i.e. Design Point 1)
Read volume mesh of baseline
case into the CFD solver and
apply solver settings
225 340 365 481 228
CFD Solution 6979 11153 14409 17256 27246
Writing CFD data file 681 538 558 600 532
Each Subsequent Design Point
Morph vehicle shape 84 59 65 69 100
CFD Solution 1284 1754 2208 2630 4100
Writing CFD data file 734 559 572 621 532
Total Run Time (Wall Clock)
Needed for All 50 Design
Points (Hours)
30.80 35.63 42.98 50.28 72.19
If data file is not written at each data point, then 50
hours target is achieved in less than 200 cores
Same study was repeated with newer hardware.
50 hours target is achieved in roughly 150 cores

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Step #4 : Running Simulations
Compute Cluster Details
1. Intel’s Endeavor Cluster
2. Intel Xeon X5670 (dual socket)
3. Clock speed 2.93 GHz
4. Six cores per socket
(12 cores per node)
5. 24 GB RAM @ 1333 MHz, SMT
ON, Turbo ON
6. QDR Infiniband
7. RHEL Server Release 6.1

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Updated DOE Table

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• Response Surface Analysis
– Non Parametric Regression (NPR) Algorithm
– Plots
• Goodness of fit
• 2d / 3d Response surface plots
• Sensitivity plots
• Parallel Co-ordinates (Pareto) Plots
• Trade-Off plots
• Optimization Study
– Goal driven optimization
– Screening algorithm (no of samples = 5000)
– NLPQL (Non-Linear Programming by Quadratic Lagrangian)
• Flow Results
Results

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Results : Response Surface Plots

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Results : Response Surface Plots

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Results : Response Surface Plots

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Results : Sensitivity Plots
Local Sensitivity Global Sensitivity

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Results : Parallel Co-ordinates (Pareto) Plot

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Results : Trade-off Plots

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Results : Goal Driven Optimization

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Results : Goal Driven Optimization

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Flow Results
Design
Points
Boat Tail Angle
(P2)
Long Roof Angle
(P3)
Green House
(P4)
Front Spoiler
Angle (P5)
Drag Force (N)
(P1)
1 0.000 0.000 0.000 0.000 388.01
9 0.000 1.500 0.000 1.900 393.01
19 1.850 -2.300 -0.700 0.000 372.30
25 -1.850 1.500 -0.700 0.000 397.33
• Flow Results Discussion
– Design point 1, 9, 19 & 25
– Velocity contours
– Iso-surface of total pressure = 0.0

41. © 2011 ANSYS, Inc. July 17, 201341
Summary of 50:50:50 Method
The 50:50:50 Method
50 50 design points in the design space EXTENT
50
50 million cells used in CFD simulation
of each design point
ACCURACY
50
50 hours total elapsed time to
simulate all the design points
SPEED
“One – Click” – Entire design space is simulated and post-processed
completely automatically after the initial baseline case setup

42. © 2011 ANSYS, Inc. July 17, 201342
• The 50:50:50 Method
– An extensive, fast, and accurate DOE method
– In case study: 4% drag reduction achieved in 1 week of work
• Fully automated workflow (after baseline case setup)
using industry leading technologies
– FLUENT Solver (With High Performance Computing)
– RBF Morph (Fast, User-Friendly, Accurate Mesh Morpher)
– ANSYS WorkBench (Integration Platform)
– Design Xplorer (Optimization)
– CFD Post (Flow Visualization)
Summary of 50:50:50 Method

43. © 2011 ANSYS, Inc. July 17, 201343
Aerodynamics Optimization Methods
Parametric Method – 50:50:50 Method
Gradient Based Method – Adjoint Method
Agenda

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 Overview
 Application Areas and Associated
Technologies
 R14.5 New Features
 Solved Examples using R14.5
 Summary
Agenda

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What is It ?
• Different methods for computing derivatives – sometimes
referred to as sensitivities.
• Consider a high-level view of a fluid system
ADJOINT METHOD
Inputs c Quantities q
Flow Solver Flow variables
Integral quantities
Mesh
Boundary conditions
Material properties
Transfer matrix j
i
c
q
Tangent method
Adjoint method

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Overview of the adjoint method
Workflow
• Solve the flow equations and post-process the results as usual.
• Pick an observation that is of engineering interest.
• Lift, drag, total pressure drop?
• Set up and solve the adjoint problem for this observation
• Define solution advancement controls
• Set convergence criteria
• Initialize
• Iterate to convergence
• Post-process the adjoint solution to view
• Shape sensitivity
• Sensitivity to boundary condition settings
• Contour & vector plots

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Overview of the adjoint method
Shape sensitivity: Sensitivity of the observed value with respect to
(boundary) grid node locations
mesh
nn
xwDrag .)(
Shape sensitivity coefficients:
Vector field defined
on mesh nodes
Node displacement
Visualization of shape sensitivity
• Uses vector field visualization.
• Identifies regions of high and low
sensitivity.
• These are the places where
changes to the shape can have a
big impact on the quantity of
interest.
• The guidance is specific to the
quantity of interest, and the current
flow state.
Drag sensitivity for NACA0012

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Associated Technologies
Mesh Morphing
• Use a Bernstein polynomial-based morphing scheme for freeform mesh
deformation.
• Select portions of the geometry to be modified by specifying a rectilinear
deformation region.
• Define a uniform distribution of control points in space in each coordinate
direction.
• Movement of any control point leads to a smooth deformation field throughout
the deformation region.
• Can be driven by non-gradient based algorithm – e.g. Simplex.

49. © 2011 ANSYS, Inc. July 17, 201349
Increase the downforce on the vehicle
Look for regions of high sensitivity of downforce to shape
Downforce enhancement for a generic race car

50. © 2011 ANSYS, Inc. July 17, 201350
Front wing redesign to generate more downforce
Downforce enhancement for a
generic race car
Downforce (N)
Geometry Predicted Result
Original --- 425.7
Modified 447.4 (+5.1%) 451.1 (+6.0%)

51. © 2011 ANSYS, Inc. July 17, 201351
Rear wing redesign to generate more downforce
Lift enhancement for a generic race car
Downforce (N)
Geometry Predicted Result
Original --- 425.7
Modified 481.3 (+13.1%) 492.5 (+15.7%)

52. © 2011 ANSYS, Inc. July 17, 201352
• What are the major factors affecting
the uniformity in the mass flow rates
at the 4 outlets?
• Material is air
• Solve the flow problem.
• Set up and solve the adjoint problem
with the variance in mass flow rates
as the quantity of interest.
• Post-process the field to identify
important influences.
Robust Design Example: Internal Flow
Total pressure (pascal)
60 cm
1
2
3
4
m1: 0.0020 Kg/s
m2: 0.0023 Kg/s
m3: 0.0028 Kg/s
m4: 0.0025 Kg/s
var: 7.52e-08
4
14
1
i
imm
24
14
1
var
i
i mm
inlet

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• Variance computed to be
7.52e-08 (Kg/s)^2
• Plot the displacements of the
surface that, based on linear
extrapolation, would drive
the variance to zero.
• Geometry far upstream is
dictating the flow split.
• Manufacturing variances of
the order of 3mm in the inlet
region can cause O(1) flow
variance variations.
Robust Design Example: Internal Flow
Surface normal displacements that
Induce O(1) change in variance

54. © 2011 ANSYS, Inc. July 17, 201354
Appendix

55. © 2011 ANSYS, Inc. July 17, 201355
Design Point #1

56. © 2011 ANSYS, Inc. July 17, 201356
Design Point #9

57. © 2011 ANSYS, Inc. July 17, 201357
Design Point #19

58. © 2011 ANSYS, Inc. July 17, 201358
Design Point #25