Multi-Objective Optimization of a Boomerang Shape using...
Transcript of Multi-Objective Optimization of a Boomerang Shape using...
Alberto Clarich*, Rosario Russo ESTECO, Trieste, (Italy) Enrico Nobile, Carlo Poloni University of Trieste (Italy)
Multi-Objective Optimization of a
Boomerang Shape using
modeFRONTIER and STAR-CCM+
Summary
• A brief introduction to modeFRONTIER
• Description of modeFRONTIER direct interface for STAR-CCM+
• Application problem definition
• Optimization results
Introducing modeFRONTIER
is an integration platform for multi-objective optimization, automation of design processes
and analytic decision making providing seamless coupling with engineering tools
within various disciplines
User’s Community and short company history
ESTECO started in 1999 as a University spin-off.
modeFRONTIER was the first commercial tool that allowed a MULTI-OBJECTIVE optimization applied to ANY engineering design area
Now modeFRONTIER is used worldwide
1999 2001 2003 2004 2008 2010 2013
modeFRONTIER v. 1
Esteco establishment
in Europe
modeFRONTIER v. 2
Expansion to Asian markets
modeFRONTIER v. 3
Opening of ESTECO
North America
modeFRONTIER v. 4
modeFRONTIER v. 5
Automotive
Research Inst. and Uni
Electronics
Aerospace
Energy
Materials
Appliances
Defence and Space
No
Yes
OK?
Initial
Configuration
Simulate
Evaluate
Results
Accept
Modify
Configuration
Traditional Design Optimization Approach
Parametric
models Design Objectives
and Constraints
Optimal trade-off
Solution
The Concept behind modeFRONTIER
The Concept behind modeFRONTIER
The Black Box:
(ADAMS, ANSYS, GT-Suite, etc.)
Scheduler:
(DOE, optimization algorithms,..)
Input Variables:
Entities defining the
design space.
Output Variables:
Measures from the
system
modeFRONTIER can be coupled with most software (CAD, CAE or general application tools) and it enables the simultaneous use of a number of such software packages even on different machines
Modules of modeFRONTIER
Process Integration
Statistical Analysis Multivariate Analysis Decision Making Response Surface Tool
Design of Experiments Optimization Algorithms Robust Design
Direct interface with STAR-CCM+: how it works
• Input parameters (simulation or geometry modeled within) are automatically introspected
• Available output results are automatically introspected and can be selected
• Optimization variables nodes are automatically created in the workflow
• Optimization can be run changing the inputs and optimizing the selected outputs
Direct interface with STAR-CCM+ and external CAD
• Optimization setup with external CAD and Optimate (STAR-CCM+)
The application example: Boomerang Physics
The boomerang return is due to its interaction with the air that makes it work as a gyroscope. There are two kind of precessions: • W1 responsible for the boomerang return • W2 responsible for the boomerang plane of rotation change
To simulate accurately its trajectory, it is necessary to write its equations of motions, in which aerodynamics coefficients must be provided updated at each time step (since angle of attack and velocity changes)
W1 W2
w
Trailing edge
Leading edge
Boomerang motion equations
𝐹𝑥 , 𝐹𝑦 , 𝐹𝑧 external forces components
𝑇𝑥 , 𝑇𝑦 , 𝑇𝑧 external torques components
𝑉 boomerang center of mass velocity Ψ boomerang angle of attack
𝜔 𝑧 =
𝑇𝑧
𝐼3
𝑉 =1
𝑚(−𝐹𝑥 cosΨ − 𝐹𝑧 sinΨ)
Ψ =1
𝑚𝑉 𝐹𝑥 sinΨ − 𝐹𝑧 cosΨ +
𝑇𝑥
𝐼3𝜔𝑧
𝜗 =
1
𝐼3𝜔𝑧
−𝑇𝑦 cos𝜓 − 𝑇𝑥 sin𝜓
𝜑 =1
𝐼3𝜔𝑧
1
sin 𝜗 −𝑇𝑦 sin𝜓 + 𝑇𝑥 cos𝜓
𝜓 = −𝐹𝑦
𝑚𝑉 cosΨ − tanΨ
𝑇𝑦
𝐼3𝜔𝑧
− cos𝜗 ∙ 𝜑
𝑋 = 𝑉(− cosΨ(cos𝜓 cos𝜑 − sin𝜓 sin𝜑 cos𝜗) − sinΨ sin𝜑 sin 𝜗)
𝑌 = 𝑉(− cosΨ(cos𝜓 sin𝜑 + sin𝜓 cos𝜑 cos𝜗) + sinΨ cos𝜑 sin𝜗)
𝑍 = 𝑉(− cosΨ sin𝜓 sin𝜗 − sinΨ cos𝜗)
Purpose of this study is to find a boomerang geometry and a set of launching parameters in order to:
• 1. Minimize energy required for the launch obtaining a minimum launch range (>14m)
• 2. Maximize the accuracy of return
Optimization Objectives
Optimal return
Easiest throw
Optimization framework: Hierarchical Game Strategy
CAD parameterization A candidate boomerang geometry is
proposed
RSM analysis The 12 samples are used by mF to extrapolate aerodynamic coefficients for any Ψ,U pair
STAR-CCM+ analysis Boomerang aerodynamic coefficients are found
for 12 different angles Ψ and speed U
Trajectory evaluation (Matlab) Equations of motion are integrated by a
Matlab script – Aerodymics coefficients are exrapolated by RSM
Initial launching parameters A candidate set of launching parameters
Optimized launching parameters To reach return accuracy (<1m)
Optimal return accuracy?
yes
New launching parameters A different set of launching parameters
no
Optimized boomerang
Minimum
Launch energy? no
yes
modeFRONTIER main Workflow (Leader Optimization)
The main objective is to find a boomerang geometry which minimizes the Energy required for its thrown, satisfying at the same time a constraint on the range
CAD CFD RSM Matlab - tuning
Boomerang geometry parametric model via CATIA (direct interface)
The boomerang shape is modified by a CAD parametric model 9 geometry parameters have been considered, including:
• Blade profiles (9 Bezier control points) • Dihedral angle • Angle between arms
CAD
modeFRONTIER sub-Workflow to run STAR-CCM+ samples
The main workflow launches for each candidate geometry a new mF workflow that executes a DOE of (12) STAR-CCM+ analysis changing the value of angle Ψ and speed U
CFD
CFD simulation via STAR-CCM+: Mesh
• Two domains are defined: a sphere around the boomerang which rotates with it at each time step of its spin (Ψ,U are fixed , and a fixed domain in the rest of domain
• The mesh (2.5 millions of cells) is polyhedral within the sphere around the boomerang, with prisms layers at the boomerang walls, and hexahedral in the rest of the domain
• The STAR-CCM+ General Grid interface is used to merge the two domains
Ψ,U fixed
Spin w
CFD simulation via STAR-CCM+: CFD analysis
• The two-equations RANS SST (Shear Stress Transport) turbulent model, with wall functions, is chosen and a segregated solver with constant density is employed
• A full not-stationary analysis is run over a proper interval of time until the flow becomes periodic (after about 5-6 spin periods)
Ψ,U fixed
spin period
Response Surfaces for Aerodynamic coefficients
The set of (12) STAR-CCM+ analysis (yellow points) is used to train a Response Surface (Radial Basis Function) available in modeFRONTIER, to extrapolate the response for any value of angle Ψ and speed U
RSM
modeFRONTIER inner workflow (Follower Optimization)
The internal objective for each candidate geometry is to find the launching parameters which minimize the arrival distance (returning accuracy)
Launching parameters: • Velocity • Spin • Aim angle (from horizontal plane) • Tilt article (from normal axis)
Matlab - tuning
modeFRONTIER Optimization Results
Selected result
•Simplex algorithm (39 designs only) is used to find the optimal solutions • One solution is selected as optimal compromise
Results: Optimal configuration
• The initial spin is about 4Hz • The initial velocity is 15m/s • The tilt angle is about 0° • The aim is about 20°
• The launch energy is 3.5J • The range is 14.5m • The return accuracy is 1m
Optimal geometry
Optimal launching parameters
Optimal performances
Conclusion
• The boomerang shape optimization here proposed shows how efficiently and powerfully a complex and multi-disciplinary optimization problem can be set up in modeFRONTIER
• In particular, the new direct interface with STAR-CCM+ allows to define the automatic integration and execution of any STAR model in the optimization workflow
• Any problem of industrial relevance can be optimized with modeFRONTIER, as confirmed by many of our customers including many leading companies working with STAR-CCM+ (please check www.esteco.com for more details)
Thank you!
ESTECO Area Science Park
Padriciano, 99
34149 Trieste - Italy
e-mail: [email protected]
ESTECO North America 3955 Orchard Hill Place , Suite 430
Novi, MI 48375
e-mail: [email protected]
www.esteco.com