SHAPE OPTIMIZATION AT MODERATE REYNOLDS NUMBER USING IMMERSED BOUNDARY METHOD AND META-MODELING

João Marcelo Vedovoto¹; Felipe Antonio Chegury Viana¹; José dos Reis Vieira de Moura Jr.¹; Valder Steffen Jr.¹; Aristeu da Silveira Neto¹

¹ School of Mechanical Engineering - Federal University of Uberlândia

Resumo

Regarding the design of aircraft components, the state-of-art involves the use of extensive mathematical modeling and numerical simulation as well as optimization techniques. However, due the high computational costs in fluid dynamics, the search for accurate and viable solutions using numerical optimization constitutes a great challenge. This work has to main goals: (i) the use of the Immersed Boundary Method as a strategy of modeling and simulation of flows over complex three-dimensional geometries; and (ii) the optimization of a winglet using meta-modeling techniques. The Immersed Boundary Method has been developed by the Laboratory of Heat and Mass Transfer and Fluid Dynamics (LTCM) of the Federal University of Uberlandia. This technique makes use of two independent domains in the solution of the flows over complex geometries: a Eulerian domain, which is discretized using Finite Volume Method over a non-uniform mesh to integrate the Navier-Stokes equations and a second-order approximation for time and space derivatives. Another important remark is that the Lagrangian domain, which represents the immersed boundary, is represented by a superficial unstructured mesh, composed by triangles. In this scenario, meta-modeling is used as a way to overcome the high computational cost when dealing with fluid dynamics. The meta-models represent a low-cost approximation which can be easily dealt by numerical optimization codes. The in-house parallel code runs on a Beowulf-class cluster, a viable and reliable alternative to solve problems that demand very large computational resources. Finally, numerical results show the simulation of a three-dimensional flow over several airfoils NACA-0012 and design optimization of winglets aiming the maximum lift and minimum drag coefficients.

Palavras-chave: Immersed Boundary Method; Virtual Physical Model; Meta Modeling; Numerical Optimization