Modelagem matemática e computacional de camada limite laminar utilizando a metodologia mista pseudoespectral de fourier e fronteira imersa

Abstract

Computational Fluid Dynamics is a tool that can assist in the understanding and optimization of wind farms. The modeling of complex phenomena, such as the interaction of wind turbines with the atmospheric boundary layer, is achieved through a well-developed solid knowledge base. Based on this argument, the present dissertation employs a hybrid methodology combining the pseudospectral Fourier method (MPF) with the immersed boundary method (MFI), called IMERSPEC, for the two-dimensional modeling of the laminar boundary layer over a flat plate. IMERSPEC is a high-order convergence methodology with low computational cost compared to other high-order methods. It decouples the pressure from its numerical-computational solution process. It is worth noting that IMERSPEC is the pioneering approach in modeling the Blasius boundary layer using the spectral Fourier domain in all flow directions. To achieve the proposed objective, numerical-computational verification steps of the methodology are performed, along with understanding its functioning and typical implementation techniques. The two-dimensional code verification is conducted for Taylor-Green vortices, demonstrating the high accuracy of IMERSPEC. Virtual experiments representing developing two-dimensional plane jets in temporal and spatial domains are conducted to verify the accuracy of this methodology in representing physical phenomena and to become familiar with the application of flow periodicity methods for spatial modeling, where the computational domain is subdivided into complementary and useful domains. The imposition of white numerical noise is necessary to develop instabilities in free shearing flows transitioning to turbulence. The spatially developing Blasius boundary layer is modeled with IMERSPEC using the fringe method, the best alternative for periodicity in this type of modeling. Mesh refinement and CFL analyses are performed, indicating that the most significant computational errors are due to the fringe method. Subsequently, an optimization of computational implementation parameters is carried out, including the flat plate imposition method, possible boundary conditions at the top of the useful domain, and the evaluation of the size of the non-modeled domain. Overall, the computational results indicate a satisfactory modeling of the laminar boundary layer over a flat plate.