Optimization in CFD and Case Studies

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Optimization in CFD
Presentation on different methods used for optimization
and case studies
V4
Prof GR Shevare

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©ZeusNumerixPvtLtd:ConfidentialDocument
Contents
 Motivation
 Optimization, Multi-disciplinary Analysis and Multi-disciplinary optimization
 Optimization of an airfoil
 Multi-disciplinary optimization of a winglet
 Closure
16 Sept 2020 Optimization in CFD: Zeus Numerix
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 Design optimization using current High-Performance Computing offers
 Faster solutions to more complex problems
 The results are more accurate and hence engineering systems offer improved performance
 The systems have enhanced safety & environmental acceptability
 The concept-to-market time is reduced for new products
 It is possible to reduce the development cost the overall development cost
 In fact, optimization using simulations is a reality
Motivation
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 No of wings requiring wind tunnel tests in Boeing airplanes company*
 Wind tunnels experiments cost much money; they require time
 CFD is a design tool capable of saving many wind tunnel tests
Motivation contd…
* Ref. : Thirty years of development and application of CFD at Boeing Commercial airplanes, Seattle,
by F. T. Johnson, E. N. Tinoco and N. Jong Yu, AIAA 2003-3439
1980 1990 2000 2011
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Tools other than CFD code
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Build Computational
Domain
Create
suitable Mesh
Boundary Conditions &
Initial conditions
Solution of discrete
equationsPlot flow FieldInterpret solution
Desktop simulations can take years for a real-life problem. HPC and automation may reduce time to months
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Definitions
 Optimization
 To arrive at the best candidate through automated repeated simulations
 Multi-disciplinary analysis
 A framework capable of executing two or more types of simulations (belonging to more than
one discipline) for finding out performance of an engineering design
 Multi-disciplinary Optimization
 A framework to identify the best design based on automated and repeated multi-disciplinary
analysis
 Searching the next design is important
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Optimisers
 Gradient based optimisers
 Adjoint equation
 Newton’s method
 Steepest gradient method
 Conjugate gradient method
 Sequential quadratic programming
 Gradient free optimisers
 Hooke-Jeeves pattern search
 Nelder-Mead method
 Population based optimisers
 Genetic algorithm
 Memetic algorithm
 Particle swarm based
 Harmony search
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Optimisation of an airfoil shape
Airfoil shape optimization using genetic algorithm approach
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Optimisation of a 2D airfoil
 Objectile: Design an airfoil with maximize lift/drag using genetic algorithm
 Design variables : Meanline and thickness
 Each is Bezier curve with fixed start and end points and positive thickness
 Control points can be anything more than 3 to less than 10
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Automation of Tools
 Geometry and meshing – About 2500 cells and Clustered around the body
 Flow Solver – Execution time 3 minutes / case
 Visualization – Automated Off-screen rendering
 Hardware – GA tool as client on Windows & 26 Linux desktops as compute server
 Optimiser – Genetic algorithm
Some candidate airfoil and meshes around them
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Random Initial Profiles
 Color plots show pressure variation
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Evolution over Generations
 Each dot is one candidate airfoil. 40 generations of population birth of 100 takes 10
hours (total ~4000 cases)
Target Fitting Function Band
Generations
Lift/drag
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Convergence to Robust Designs
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IncreasingFittingFunction(L/D)
Pressure variation Velocity variation

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Multi-disciplinary Optimisation of
Winglet
Case study of winglet optimization
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MDO Studies
 Engineering design is always multi-disciplinary. The designers are usually skeptical of
automation
 The cost function changes with time
 Some simulation tools may not be available on the platform being used. Workflow
must take care of such problems.
 The designer must specify the cost function (i.e. what to maximize or minimize)
 The fidelity of an analysis depends upon the sensitivity of cost function
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MDO of a winglet
 Winglets can reduce drag up to 15 %
 Savings depend on fuel cost. Therefore winglets can be an add-on
 Statement : Design a winglet (for a given wing) which produces maximum lift,
minimum drag and minimum weight
 This is multi-disciplinary optimisation
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 Design space: three out of six parameters that define a winglet
Winglet design parameterization
Winglet Wing
Front View
(showing Cant Angle)
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Cant
Angle
Sweep
Angle
Top View
winglet unfolded
(showing Sweep angle)
-ve twist +ve twist
Top View
winglet vertical
(showing Twist)
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Winglet Design Parameterization contd.
 Note that
 Winglet can be changed completely
 Outer shape of the wing exposed to air can not be changed
 Thickness of the skin, spars, ribs can be changed based on incremental loads that
winglet produces
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Winglet taper ratio Blend Span Wingspan
Wing-tip Chord
WTC
Wing-root Chord
WRC
Wing top view (winglet unfolded)

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Fitness Evaluation function
Cruise Induced
Drag
Cdicruise
Climb Induced
Drag
CdiClimb
Maneuver Bending
Moment
MxManeuver
Structural weight estimation model
Penaltystructural = Δwing-weight / ktrade-off
Averaged ΔCdi (in drag counts)
ΔCdiavg = 0.5 ( ΔCdicruise + ΔCdiclimb)
Aero-Structural trade-off
coefficient
Ktrade-off
(kg per drag count)
Final Fitness Value
J=ΔCdiavg+Penaltystructural
GA optimizer
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Genetic Algorithm Optimizer
 The following flow diagram represents the basic algorithm for GA
Create a population of winglet by varying
the 3 design parameters
(generation = 0)
Job Scheduler
Select designs with best
characteristics
Perform reproduction using crossover
and mutate creating new population
Output Latest population
of Design
If required number of generations
completed
NextGeneration
Fitness
Evaluation
(Design 1)
Fitness
Evaluation
(Design 2)
Fitness
Evaluation
(Design 3)
Fitness
Evaluation
(Design n)
Parallel Fitness Calculation
for all individual of a
generation
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WOS Flow Diagram
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Input Structure
Bezier Control Point Array for:
 Wingtip to winglet-tip chord taper variation
 Sweep variation along winglet span
Real number values for
 Ratio of winglet span to wing span (ESR)
 Ratio of Blend span to Winglet span (BSR)
 Cant angle for Winglet
 Toe angle for Winglet
Simulation
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Total Cruise Drag
Total Cruise Lift
Bending Moment
Horizontal Span
Penalty based
Fitness
Calculation
FitnessValue
Other
Constraints
• Wing geometry
• Airfoil Shapes
• Cruise conditions.
Other Inputs
Garuda
Grid
Simulation
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Simulation
3
Optimization
Client
Simulation
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Simulation
5
n Simulations
CFD Execution Server
(HTTP Server)
GridWay Jobs

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Need for Grid Consistency Study
 Initial CFD runs for determination drag were performed over a grid size of 1.2 million
 Time required for simulations ~ 26 hours on 8 CPU
 Need lesser grid size for use in optimization cycle for faster CFD execution time
 Perform grid-consistency study (grids which do not alter the merit of wing geometry,
actual drag values may differ) to find out lower grid sizes that can be used in
optimization calculation
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1.2 Million vs. 0.2 Million Grids
0.2 million Mesh 1.2 million Mesh
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1.2 Million vs. 0.2 Million Grids
 Geometric fidelity of winglet is not lost by reducing the grid size by a factor of 10!
 But the computations will be 10 times faster!!
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0.2 million Mesh 1.2 million Mesh

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Comment 1 Comment 2
 It can be observed that the relative
merit, as measured in the induced
drag values, remains unchanged for
all the six geometric configurations
in cruise as well as climb conditions
 In optimisation cycles only coarse
grids will be used for induced drag
 The coarse grid values will be scaled
up by an averaged scaling factor to
convert them into realistic values
Comparison of Grid Consistency Results
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Bending Moment Variation around Wing-tip
 Bending moment around wing-tip calculated for the first winglet
 Bending moment calculated for each of the random winglet design ( case 0 – 5)
 Compare with benchmark case to find effect of variation on moment
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FEM Modelling Of Wing-box
 Wing is modeled as a wing box consisting of ribs, spars and skin as shown below.
 FEM Mesh included skin, spars, stringers with Element Type : 8–noded Shell element
 No. of DoF : 5 –DoF (3 Translation +2 –Rotation)
 Boundary Condition – All DoF at root of wing is constrained
 Loading Conditions:
 Pressure Distribution
 Forces and moment due to winglet
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Z
Y
X

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Loads on Structure – I
 Distributed Pressure force is applied on the upper and lower surface of the wing-skin
as obtained from CFD simulations
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Lower Surface
Upper Surface

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Loads on Structure – II
 Forces Fz and Fy generated by winglet is transferred to the wing tip as forces and
moment as shown in figure below.
 Moment is modeled as a couple. Equal and opposite forces acting on the lower and
upper nodes at the wing tip
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Wing Winglet
Fixed wing root
Wing
Fixed wing root
Mxwinglet
Mxwinglet = a . Fzwinglet - b . Fywinglet
Z
Y
X
Fzwinglet
Fywinglet
a
b
Fzwinglet
Fywinglet

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Thickness Estimation Procedure
 Thickness of all ribs except the one at tip is kept constant (1.6mm)
 Rib thickness at the tip is kept as (5 mm) to avoid local deformation
due to moment.
 Thickness of spars is kept as (7 mm)
 Table shows span-wise skin thickness variation
 Wing root is thicker than the tip because of higher stress and to
avoid any buckling
 The thickness of the structural elements were varied by equal
percentage to achieve the target stress value that satisfy failure
criteria for corresponding change in bending moment
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Panel No Thickness
(mm)
1 (root) 6.4
2 6.3
3 5.9
4 5.6
5 5.4
6 5
7 4.7
8 4.3
9 4.2
10 4
11 3.7
12 3.4
13 3.1
14 2.8
15 2.5
16 2.2
17 2
18 1.7
19 1.6
20 1.6
21 (tip) 1.6

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Post Process for Benchmark Configuration
 Normal Stresses in Y - direction
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Wing Deflection (Dmax = 1.5 m)
Stress on spar
Note:
1) Compression and tension on upper and lower surface can be seen
2) Stress on centerline of spar is mostly 0 and increasing as going towards width

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Von-Mises Stresses
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Von Mises stress is maximum

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Comparison of Stress Distribution
 The percentage increase in Bending moment due to winglet results in higher
stresses. The thickness of the all part has been increased in equal proportion that
satisfy failure criteria
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%Bending Moment v/s %Weight Change
 Model of percentage variation in wing-tip bending moment v/s weight change is
formulated and is shown in the following plot
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Equation for change in weight estimation
ΔW = (( 0.182 x %ΔMx ) + 0.1451 ) / 100 x 481.793
ΔW = change in weight
%ΔMx = percent change in Moment
Comparable curve from
ONERA-MDO work

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Details of Optimizer Execution
 No. Individual in a generation : 40 individuals
 No. of CFD runs for a design : 7 runs
 Computational Nodes used : 20 nodes
 Generations Completed : 12 generations
 Total CFD simulations : 2160
 CFD mesh size : 0.45 million
 Optimization target : MINIMIZING fitness value
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Scatter of Individual over 9 Generations
 The band of fitness of individuals in successive generation demonstrates the
reduction of the spread due to Genetic Algorithm Optimization
 The difference in fitness between the best individuals of 1st generation and 12th
generation is ~ 7 units. This signifies that the optimizer is able to give better designs
This is also seen by the drop in the Green line that denotes the average fitness
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Each of these short-thick horizontal dashes represent a design
individual
Blue Line denotes the least fit individual
Green Line denotes the average fitness per generation
Orange Line denotes the best fit individuals

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Best Design: 9th Generation
 The following figure gives a comparison between the nominal winglet and the
winglet with best fitness after 8th generation, in 9th generation
 Notice the comparison of winglet span between the two pictures
 The span of lower winglet is nearly double that of above design
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Nominal Design
Design 70
Fitness:-54.16

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Best Design: 12th Generation
 The following figure gives a comparison between the nominal winglet and the
winglet with best fitness after 11th generation, in 12th generation
 This figure shows that the winglet design obtained after 12th generation is similar to
that obtained in 9th generation
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Nominal Design
Design 105
Fitness:-54.57

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Closure
 In aerodynamic optimisation studies automation of all the processes is a must.
Choosing the next design candidate is as important as the analysis
 An optimisation of 2D airfoil is explained
 A framework for data transfer and controlling simulations is essential for multi-
disciplinary optimisation of aerodynamic shapes
 The framework has been explained for optimising a winglet for a short-range aircraft.
The framework is capable of reducing the induced drag of an aircraft without
compromising structural integrity
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www.zeusnumerix.com
+91 72760 31511
Abhishek Jain
abhishek@zeusnumerix.com
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