Application of Homogenization Theory to the Flow Over and Through Micro-Structured, Porous and Elastic Surfaces

This research is aimed to develop a homogenized model for practical applications of the fluid flow over and through the microstructured surfaces, which prescribed reliable estimates of the linear response of overall structures. The up-scaling method based on asymptotic theories is used to treat the fluid flow problems where various spatial scales (microscopic and macroscopic) are present. The goal of this work is to provide an in-expensive high-order homogenized framework for the flows over complex textures such as elastic and rigid rough surfaces, isotropic and orthotropic porous media, with periodic internal distributions, independent of the material properties and the constituent's geometrical arrangement in a reliable way. The framework includes effective conditions corrected up to the high-order as a replacement of the micro-textured surfaces, producing sizeable effects on the overlaying flow as compared to the classical Navier's conditions. These effective conditions contain parameters that are non-empirical and stems from the numerical solution of auxiliary Stokes-like problems. These conditions developed for different applications are tested on the classical problems such as Hiemenz stagnation point flow over a rough plate, Hiemenz stagnation point flow over isotropic and orthotropic porous bed, backward-facing step with porous step region, and flow over the permeable channel, to test the accuracy and working capability of the framework for different flow situations. For simulation purposes, commercial software COMSOL academic version 5.4, open-source solver FreeFEM, and commercial software Star-CCM+ by are used. The outcomes of the model simulations are compared with exact simulations of our own and with literature. The overall results suggested that the homogenized model is computationally inexpensive compared to the feature-resolving simulations and can provide a quick design of drag-altering micro-textured surfaces. Moreover, the present model is flexible for further amendments to tackle complex engineered and industrial fluid flow problems.