MASTER DEGREE DISSERTATION IN MECHANICAL,
AERONAUTICAL ENGINEERING
Development of an
automatic shape
optimization platform
for a laminar profile
March - September 2013
Relatori :
Prof. Jan Pralits
Ing. Thomas Michon
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Studente :
Marcello Tobia Benvenuto
PROPRIETARY DAHER SOCATA
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Introduction
Daher Socata produces
the world’s fastest
single turboprop aircraft:
TBM 850.
As each aeronautic company,
it works every day to improve
Reduce the consumption
the aircraft performance.
Increase the max. speed
Reduce the drag
on the surfaces:
WING
Fluid mechanics
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Physical phenomenon
• When a body is in motion in a flow, the flow adhere to it because of
the viscosity.
A thin layer arises close to the
shape, called boundary layer.
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Physical phenomenon
External disturbances can enter the boundary layer and
generate a turbulent flow through a Transition process.
Skin Friction
X/C
• Laminar boundary layer:
• Turbulent boundary layer:
Thin with regular streamlines;
low skin friction.
Thick with irregular fluctuations;
high skin friction.
The transition phenomenon is very sensitive to the shape variations
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Objective
Reduce the friction drag on an airfoil by keeping the flow laminar over
the largest possible portion of the surface.
Automatic Shape Optimization
Advantages:
1) Save time during a process
2) Run multiple repetitive simulations
3) Analyze automatically the good results, finding the
optimum
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Contents
• Optimization platform for 2D Geometry
• 2D optimization High and High/Low speed
- results
- discussion
• Creation wing
- results
- discussion
• Conclusions
• Future works
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Why a 2D geometry?
The wing’s behaviors are given by its
profiles.
Relative Thickness: 16%
Chord: 1.675 m
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Optimization steps and tools
Create the 2D
geometry
Create the domain
and the mesh
Catia V 5
ANSYS: Design Modeler and Mesh
Optimization
platform
Mode Frontier
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Flow Solver
ANSYS: Fluent
Boundary layer and
its stability
bl3D and Nolot code
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Optimization steps and tools
Create the 2D
geometry
Create the domain
and the mesh
Catia V 5
ANSYS: Design Modeler and Mesh
Optimization
platform
Mode Frontier
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Flow Solver
ANSYS: Fluent
Boundary layer and
its stability
bl3D and Nolot code
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Create the 2D geometry
To limit the number of the geometric design variables
Describing the shape with a small set of inputs
9 Polynomial approximations of curves
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PROPRIETARY DAHER SOCATA
CAD Software: Catia V 5
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Create the 2D geometry
Design Parameters
Constraints
• Radius of the circle
• Chord = 1 meter
• Position of point 2 and 9 inside square
• Thickness at 25% and 75%
of the chord fixed.
• Tension of points 2,3,8,9
• Thickness of trailing edge
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Optimization steps and tools
Create the 2D
geometry
Create the domain
and the mesh
Catia V 5
ANSYS: Design Modeler and Mesh
Optimization
platform
Mode Frontier
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Flow Solver
ANSYS: Fluent
Boundary layer and
its stability
bl3D and Nolot code
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Create the domain and the mesh
Different domains and meshes have been investigated
to find the best grid in terms of time and quality
•O-type domain
•Radius = 90 meters
Grid close to the profile:
Grid
Profile
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Optimization steps and tools
Create the 2D
geometry
Create the domain
and the mesh
Catia V 5
ANSYS: Design Modeler and Mesh
Optimization
platform
Mode Frontier
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Flow Solver
ANSYS: Fluent
Boundary layer and
its stability
bl3D and Nolot code
PROPRIETARY DAHER SOCATA
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Flow solver
Numerical solution of the Navier-Stokes’s equations
FLUENT
Velocity and pressure distribution
Pressure Coefficient distribution on the root airfoil of TBM 850.
Cruise conditions.
Key point for the
stability analysis
Cp
X/C
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• Smoothness
• Good quality
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Optimization steps and tools
Create the 2D
geometry
Create the domain
and the mesh
Catia V 5
ANSYS: Design Modeler and Mesh
Optimization
platform
Mode Frontier
21/03/2014
Flow Solver
ANSYS: Fluent
Boundary layer and
its stability
bl3D and Nolot code
PROPRIETARY DAHER SOCATA
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Boundary layer and its stability: bl3D
bl3D code
Laminar Boundary Layer's
Equations
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It calculates the
parameters of the
boundary layer from the
Cp distribution
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Boundary layer and its stability: NOLOT
NOLOT is based on the Linear Stability:
Flow decomposed in mean flow and unsteady disturbances
u = U + u'
The unsteady disturbance is represented by a wave with
infinitesimal amplitude
Frequency
Streamwise Wave number
Spanmwise Wave number
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Boundary layer and its stability: NOLOT
Semi-empirical eN method
Mack’s Law:
Turbulence intensity
N factor
N = - 8.43 – 2.4 ln(Ti)
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0.0007 < Ti < 0.0298
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Objective functions
1. To maximize the position of transition
A change of the shape of a profile
can lead to different value of Cl
and Cm
1. To minimize ∆Cl = |Cl – ClTBM|
Changes of global
repartition of lift
• Stability problems
• Stalling problems
1. To minimize ∆Cm = |Cm – CmTBM|
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Optimization steps and tools
Create the 2D
geometry
Create the domain
and the mesh
Catia V 5
ANSYS: Design Modeler and Mesh
Optimization
platform
Mode Frontier
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Flow Solver
ANSYS: Fluent
Boundary layer and
its stability
bl3D and Nolot code
PROPRIETARY DAHER SOCATA
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Optimization platform: Mode Frontier
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Optimization platform: Mode Frontier
Lift and Mom. coeff
∆Cl ∆Cm
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Contents
• Optimization platform for 2D Geometry
• 2D optimization High and High/Low speed
- results
- discussion
• Creation wing
- results
- discussion
• Conclusions
• Future works
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Optimization 2D High speed
• high speed (cruise): M=0.51; h=26000 feet; aoa=0 degrees
• Strategy optimization
- explore all the domain of input parameters DOE
- optimize the best profiles found by DOE with genetic algorithm
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Pareto front opt. 2D high speed
•
399 profiles have been explored in 8 days
Max ∆Cl 3%
∆Cl
Max trans. 47% of the chord
TBM (trans. 26% of the chord)
Transition location
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Best solution opt. 2D high speed
BLACK = TBM
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RED = BEST
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Robustness solution for manufacturing?
0.07% of 1765 mm = 1.19 mm
c A big influence of the leading edge on the transition
Solution not robust
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Drag evaluation with transition model
To evaluate the difference of drag, the SST-transition model is used in
Fluent to study the natural transition:
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Optimization 2D High/Low speed
To analyze stall characteristics at low speed,
the profile has been optimized also at take-off conditions
- High speed (cruise): M=0.51; h=26000 feet; aoa=0 degrees
- Low speed (take-off): M=0.18; h=0; aoa= > 15 degrees
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Objective functions
Cruise condition:
1. To maximize the transition location
2. To minimize ∆Cl and ∆Cm
Take-off condition:
1. Maximize the max Lift coefficient
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Pareto front 2D opt. High/low speed
Pareto front
Cl low speed
Transition high speed
The objective functions are in opposition one with the other
The same optimization has been done for the tip profile of the
wing
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Discussion optimization 2D
High speed
•
•
•
•
Big sensibility of the phenomenon by the shape variations
Transition moved from 26% to 47% of the chord
Viscous drag reduced of 14.26%
Improvements limited by the constraints of the shape: transition
occurs close to the maximum thickness
High/low speed
• Each flight condition requires a different optimal shape
• The presence of a new O.F. has not penalized the transition
(42%)
• Improvements limited by the constraints of the shape
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Contents
• Optimization platform for 2D Geometry
• 2D optimization High and High/Low speed
- results
- discussion
• Creation wing
- results
- discussion
• Conclusions
• Future works
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Creation wing
Creation of a wing with the optimal root and tip profile obtained
previously
Wing parameters:
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The same of the wing of TBM 850
- span: 12161.3 mm
- dihedral: 6.5 degree
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CFD Simulation 3D
To compare the wing of the TBM 850 with the wing using the optimal
profiles.
NEW
TBM
Skin Friction
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Results 3D
Wing
Visc. drag
Press. drag
Total drag
Lift coeff
TBM
0.00273
0.00754
0.01027
0.1919
New
0.00279
0.00755
0.01035
0.1903
Skin Friction
New
TBM
Chord
Skin friction on profile at 50% of the span
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Discussion
• The validation on the wing has given unexpected results in terms of
drag:
The effects of the flows on 2D and 3D geometry are different
- trailing vortex
- cross flow disturbances
X - Wall shear stress
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Discussion
• The validation on the wing has given unexpected results in terms of
drag:
The effects of the flows on 2D and 3D geometry are different
- trailing vortex
- cross flow disturbances
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Contents
• Optimization platform for 2D Geometry
• 2D optimization High and High/Low speed
- results
- discussion
• Creation wing
- results
- discussion
• Conclusions
• Future works
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Conclusions
I am familiar with software like Catia V 5, Fluent (2D and 3D), Fortran,
Python, modeFRONTIER

I created an automatic shape optimization for 2D geometry

•
The strategy used, has allowed to obtain good results for 2D geometry
- transition phenomenon delayed from 26% to 47% of the chord
- Viscous drag reduced more than 14%
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Future work and suggestions
Optimization 2D:
1. New parameterization (CST) with other constraints can be tested
2. More time for the iterations can lead a better results
3D Validation:
1. To consider 3D effects we can run the following loop:

Study the flow around the wing

Take Cp distribution of three profiles of the wing (root, middle, tip)

Run optimization platform for the three profiles

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To rebuild the wing with the three new profiles and study the flow on the
wing
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Thank you for your attention
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