A TWO-SCALE APPROACH TO ANALYZE CONSTITUTIVE DEPENDENCIES OF RIGID OBSTACLES IN FLUID FLOW ACCOUNTING INERTIAL EFFECTS

摘要

In this work, we present a multiscale model to characterize the constitutive behavior of a macroscale fluid accounting for microscale convective, transient, and obstacle effects. Thus, at the macroscale, a generalized continuum flow is considered, and the unsteady incompressible Navier-Stokes equation models the fine scale. From the concept of Representative Volume Element (RVE), we establish a connection between the macroscale and the RVE to perform computational homogenization of several scenarios accentuating the capabilities of the proposed two-scale model. The presented theory does not require classical homogenization constraints like periodicity of RVEs and separation of scales. Therefore, to analyze the constitutive relation provided by this approach, numerical simulations are performed, including several rigid obstacles with different geometries at the RVE level and the responses are compared with the classical principles.