VLab - Simulation, Optimisation & Design Numérique

 Optimisation du design d’un profil d’aile suivant une fonction coût aérodynamique choisi par l’ingénieur comme la maximisation de la portance, de la finesse, la minimisation de la traînée ou de tout autre fonction exprimable à partir des résultats d’une simulation numérique.

• Exemple maximisation de la finesse aérodynamique ou de la portance d’un profil d’aile de la famille des NACA 4 digits. Il s’agit d’une optimisation mono-objectif à 4 paramètres (cambrure, position de la cambrure, épaisseur et incidence). Si l’on se donne 20 valeurs pour chaque paramètre on recherche les profils optimums parmi 20^4 = 160 000 configurations aérodynamiques.
• question 1 : quelle forme maximise la portance ?
• question 2 : quelle forme maximise la finesse aérodynamique ?

• Après un calcul sur maillages fins (2h de calcul sur un ordinateur portable standard) voici les résultats :

 The analysis of the flow is based on 2D RANS simulations with Spalart-Allmaras turbulence model
 The optimization is based on CMA-ES evolutionary algorithm developped by N. Hansen from LRI, University Paris-Sud, Orsay. One great advantage of this algorithm is that in contrast to most other evolutionary algorithms, the CMA-ES is quasi parameter-free. It has been empirically successful in many applications and is useful in particular on non-convex, non-separable, ill-conditioned, multi-modal or noisy objective functions. The search space dimension ranges typically between two and a few hundred. Assuming black-box optimization, where gradients are not available and function evaluations are the only considered cost of search, the CMA-ES method is likely to be outperformed by other methods in the following scenarios.

• on low-dimensional functions, say n < 5, for example by the downhill simplex method or surrogate-based methods (like kriging with expected improvement)
• on separable functions without or with only negligible dependencies between the design variables in particular in the case of multi-modality or large dimension, for example by differential evolution
• on (nearly) convex-quadratic functions with low or moderate condition number of the Hessian matrix, where BFGS or NEWUOA are typically ten times faster
• on functions that can already be solved with a comparatively small number of function evaluations, say no more than 10n, CMA-ES is often slower than, for example, NEWUOA or Multilevel Coordinate Search (MCS).

 Optimization of a synthetic jet (location, frequency, angle, jet velocity and diameter) to maximize airfoil lift by decreasing the extend of the suction surface separation.

 Optimal shape and trim of 2D interacting sails

• Lift optimization :

• Lift-to-Drag ratio optimization :

 Analysis of the three-dimensional sail flow

 Optimization of 3D sail shape through 3D RANS

Comparison ofVLab, Xfoil, Javafoil with NASA wind-tunnel tests on the aerodynamic airfoil polar plot.

 NACA 0012 at Re=6e6 is chosen for validation purposes because it is a well documented test case. As an example detailed validations may be found from http://turbmodels.larc.nasa.gov/

 A comparison of our prediction by RANS 2D on VLab through FLUENT is made in the following figure with experimental datas :

 This test case has been done during the CFD course & project (3A ENSICA in 2009-2010 by Gerhard Zumbil & Tanguy Kervern). Comparisons between VLab-FLUENT, Xfoil & Javafoil have been done.

 For more details : see the following student report :