Multi-Objective Optimization of a Boomerang Shape using modeFRONTIER - PowerPoint PPT Presentation

Multi-Objective Optimization of a Boomerang Shape using modeFRONTIER and STAR-CCM+ Alberto Clarich*, Rosario Russo ESTECO, Trieste, (Italy) Enrico Nobile, Carlo Poloni University of Trieste (Italy)

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 modeFRONTIER modeFRONTIER modeFRONTIER modeFRONTIER modeFRONTIER v. 1 v. 2 v. 3 v. 4 v. 5 1999 2001 2003 2004 2008 2010 2013 Esteco Opening of Expansion to establishment ESTECO Asian markets in Europe North America Automotive Research Inst. and Uni Electronics Aerospace Energy Materials Appliances Defence and Space

The Concept behind modeFRONTIER Traditional Design Optimization Approach Initial Parametric Design Objectives models Configuration and Constraints Simulate Evaluate Modify Results Configuration No OK? Yes Optimal trade-off Solution Accept

The Concept behind modeFRONTIER Scheduler: (DOE, optimization algorithms,..) The Black Box: Input Variables: Output Variables: (ADAMS, ANSYS, GT-Suite, etc.) Entities defining the Measures from the design space. 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 Design of Experiments Optimization Algorithms Robust Design Response Surface Tool Statistical Analysis Multivariate Analysis Decision Making

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: W 1 responsible for the boomerang return • W 2 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) Trailing edge w W 2 W 1 Leading edge

Boomerang motion equations 𝐺 𝑦 , 𝐺 𝑧 , 𝐺 𝑨 external forces components 𝑨 = 𝑈 𝑈 𝑦 , 𝑈 𝑧 , 𝑈 𝑨 external torques components 𝑨 𝜕 𝐽 3 𝑊 boomerang center of mass velocity 𝑊 = 1 𝑛 ( −𝐺 𝑦 cos Ψ − 𝐺 𝑨 sin Ψ ) Ψ boomerang angle of attack = 1 𝑨 cos Ψ + 𝑈 𝑦 𝑛𝑊 𝐺 Ψ 𝑦 sin Ψ − 𝐺 𝐽 3 𝜕 𝑨 1 𝜘 = −𝑈 𝑧 cos 𝜔 − 𝑈 𝑦 sin 𝜔 𝐽 3 𝜕 𝑨 1 1 sin 𝜘 −𝑈 𝑦 cos 𝜔 𝜒 = 𝑧 sin 𝜔 + 𝑈 𝐽 3 𝜕 𝑨 𝐺 𝑈 𝑧 𝑧 𝜔 = − 𝑛𝑊 cos Ψ − tan Ψ − cos 𝜘 ∙ 𝜒 𝐽 3 𝜕 𝑨 𝑌 = 𝑊 ( − cos Ψ (cos 𝜔 cos 𝜒 − sin 𝜔 sin 𝜒 cos 𝜘 ) − sin Ψ sin 𝜒 sin 𝜘 ) 𝑍 = 𝑊 ( − cos Ψ (cos 𝜔 sin 𝜒 + sin 𝜔 cos 𝜒 cos 𝜘 ) + sin Ψ cos 𝜒 sin 𝜘 ) 𝑎 = 𝑊 ( − cos Ψ sin 𝜔 sin 𝜘 − sin Ψ cos 𝜘 )

Optimization Objectives 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 Easiest throw Optimal return

Optimization framework: Hierarchical Game Strategy CAD parameterization A candidate boomerang geometry is proposed STAR-CCM+ analysis Boomerang aerodynamic coefficients are found for 12 different angles Ψ and speed U RSM analysis The 12 samples are used by mF to extrapolate aerodynamic coefficients for any Ψ, U pair Trajectory evaluation (Matlab) Equations of motion are integrated by a Matlab script – Aerodymics coefficients are Initial launching parameters exrapolated by RSM A candidate set of launching parameters Optimized launching parameters New launching parameters To reach return accuracy (<1m) A different set of launching parameters no Optimal return accuracy? Minimum no Launch energy ? yes yes Optimized boomerang

modeFRONTIER main Workflow (Leader Optimization) CAD CFD RSM Matlab - tuning 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

Boomerang geometry parametric model via CATIA (direct interface) The boomerang shape is modified by a CAD parametric model CAD 9 geometry parameters have been considered, including: • Blade profiles (9 Bezier control points) • Dihedral angle • Angle between arms

modeFRONTIER sub-Workflow to run STAR-CCM+ samples CFD 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 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 RSM 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

modeFRONTIER inner workflow (Follower Optimization) Launching parameters: Matlab - tuning • Velocity • Spin • Aim angle (from horizontal plane) • Tilt article (from normal axis) The internal objective for each candidate geometry is to find the launching parameters which minimize the arrival distance (returning accuracy)

modeFRONTIER Optimization Results • Simplex algorithm (39 designs only) is used to find the optimal solutions • One solution is selected as optimal compromise Selected result

Results: Optimal configuration Optimal geometry Optimal launching parameters • The initial spin is about 4Hz • The initial velocity is 15m/s • The tilt angle is about 0° • The aim is about 20° Optimal performances • The launch energy is 3.5J • The range is 14.5m • The return accuracy is 1m

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: engineering@esteco.com ESTECO North America 3955 Orchard Hill Place , Suite 430 Novi, MI 48375 e-mail: na@esteco.com www.esteco.com