On Optimal Designs Using Topology Optimization for Flow Through Porous Media Applications

Topology optimization (TopOpt) is a mathematical-driven design procedure to realize optimal material architectures. This often used automate the of devices involving flow through porous media, such as micro-fluidic devices. TopOpt offers layouts that control fluids materials, providing desired functionalities. Many prior studies in this application area have Darcy equations for primal analysis and minimum power theorem (MPT) drive problem. But both these choices (Darcy MPT) are restrictive not valid general working conditions modern Being simple linear, model media. However, two inherent assumptions are: viscosity fluid constant, inertial effects negligible. There irrefutable experimental evidence fluid, especially organic liquids, depends on pressure. Given typical small pore-sizes, dominant Next, MPT principle (nonlinear) models relax model. paper aims overcome mentioned deficiencies by presenting strategy using TopOpt. First, we will consider nonlinear take into account pressure-dependent effects, study effect nonlinearities under Second, explore rate mechanical dissipation, even models, an alternative objective function. Third, present analytical solutions designs canonical problems; only possess research pedagogical values, but also facilitate verification computer implementations. We considered pressure-driven problem with axisymmetry got topology maximizing total dissipation. The left figure shows unphysical finger-like patterns when does enforce explicitly underlying radial symmetry. right one can avoid numerical pathologies if invokes conditions.