Optimum 2d geometries that minimize drag for low Reynolds number flow.

Abstract

In this work, a two-dimensional Oseen’s approximation for Navier-Stokes equations is to be studied. As the theory applies only to low Reynolds numbers, the results are focused in this region of the flow regime, which is of interest in flows appearing in bioengineering applications. The investigation is performed using a boundary element formulation of the Oseen’s equation implemented in Matlab software package. The results are compared with simulations performed in COMSOL software package using a finite element approach for the full Navier-Stokes equations under the assumption of laminar and steady flow. Furthermore, experimental and numerical data from pertinent literature for the flow over a cylinder are used to verify the obtained results. The second part of the project employs the boundary element code in an optimization procedure that aims at drag minimization via body-shape modification with specific area constraints. The optimization results are validated with the aid of finite element simulations in COMSOL.