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!

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