Numerical and computational simulation of the flow around a stationary sphere at moderate Reynolds numbers

Alessandra Ribeiro da Silva¹; Aristeu da Silveira Neto¹; Gustavo Borges Valim¹

¹ Universidade Federal de Uberlândia

doi:10.20906/CPS/CILAMCE2017-0209

Resumo

External flows are important in engineering due to the numerous existing applications: flows around automobiles, bridges, turbine blades, airplanes, submarines and buildings. The authors of the present paper intend to present a computational study of three-dimensional effects on the incompressible flow around a stationary sphere immersed in a fluid. Flows are simulated at moderate Reynolds numbers by the finite difference method. The domain of the problem is a rectangular parallelepiped defined by [0, 1.024] x [0, 0.512] x [0, 0.512]. It is considered a sphere within this domain with center in (0.36, 0.256, 0.256) and diameter of 0.04m. The behavior of the flow throughout the domain is described by the Eulerian formulation and the immersed boundary is characterized by a Lagrangian formulation. The Lagrangian domain was constructed with a mesh of triangular elements. It is intended to use the MFsim code developed in the Laboratory of Fluid Mechanics of the Faculty of Mechanical Engineering at Federal University of Uberlândia, which solves the Navier-Stokes equations in three-dimensional transient regimes, using multi-block structured mesh, with local adaptability. This code also allows parallel processing. The use of local refinement enables a reduction of the computational cost since the presence of more refined meshes is necessary only in specific regions of the flow where the fluid moves in complex form generating high gradients. For the solution of the linear systems, the Mutigrid-Multilevel method was adopted. For the time discretization, the semi-implicit scheme was used and for the coupling-pressure velocity the fractional step method was used. For a better flow modeling, the dynamic Smagorinsky model was used. The validation and verification of the proposed problem will be done through data available in the literature.

Palavras-chave: Adaptive mesh ; Immersed Boundary Method; Flow around a Sphere