MATHEMATICAL MODELING AND NUMERICAL SIMULATION OF A THREE-DIMENSIONAL FLOW OVER COMPLEX GEOMETRIES USING THE IMMERSED BOUNDARY METHOD

João Marcelo Vedovoto¹; Karina Mayumi Tsuruta¹; Sigeo Kitatani Júnior¹; Aristeu da Silveira Neto¹

¹ Faculty of Mechanical Engineering - Federal University of Uberlândia

Resumo

The mathematical modeling and numerical simulation of real problems in engineering has a fundamental importance. However, the search for accurate and viable solutions constitutes in a great challenge. The goal of this paper is to present the Immersed Boundary methodology for modeling and simulating flows over complex three-dimensional geometries, and also characterize the generation of wingtip vortices. This methodology is being developed in the Laboratory of Heat and Mass Transfer and Fluid Dynamics (LTCM). The Immersed Boundary method uses two independent domains in the solution of the flows over complex geometries: An 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. The Lagrangian domain is represented by a superficial unstructured mesh, composed by triangles. 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. Three-dimensional flow over airfoils NACA-0012 were simulated aiming to accurately study wingtip vortices. The results present a good agreement with literature, and it is possible to understand the generation and development of the vortices.

Palavras-chave: Immersed Boundary Method; Virtual Physical Model; complex geometries; wingtip vortices