Abstract :
[en] Topology optimization in OpenFOAM: how to define the maximum inverse permeability to consider manufacturing constraint
Proton-Exchange Membrane Fuel Cells (PEMFC) are systems that directly convert chemicals into electricity by means of an electro-chemical reaction between hydrogen and oxygen. Following the concerns related to climate change, Hydrogen PEMFC are a promising option to contribute to a decarbonized society. Nevertheless, to rival the Internal Combustion Engine (ICE), PEMFC shall decrease their manufacturing cost, increase their lifetime and their efficiency, among others.
The INOXYPEM research project explores new designs of bipolar plates made of stamped coated steel. This work aims at increasing the efficiency of PEMFC by defining the channel network layout of bipolar plates using Fluid Flow Topology Optimization (FFTO) techniques, while simultaneously accounting for the manufacturing restrictions of the sheet metal forming process. We developed an in-house design environment that couples fluid simulations from OpenFOAM with Optimization Algorithms.
The flow is simulated using the Incompressible Navier Stokes equations in steady-state condition. These equations are combined with Darcy’s law by means of a Brinkman penalization, resulting in a density-based method to perform the Topology Optimization.
Our research addresses two of the main difficulties found in the topology optimization for fluid-based problems:
Firstly, the vast majority of the related publications is performed using the finite element method (76% of all publications), whilst the number of publications that use the finite volume method (the preferred for computational fluid dynamics) reach a surprisingly low level of use of only 7% (the other 16% goes to the lattice Boltzmann method and 1% to particle-based methods). Our research is developed using the finite volume method with a continuous adjoint formulation for the sensitivity analysis.
Secondly, when solving the modified Navier-Stokes equations, it’s necessary to define a maximum value for the inverse permeability that comes from the Brinkman penalization, which is the design variable in the problem (0 in the fluid zones and a large value in solid zone). This large value should be big enough to correctly penalize the velocity inside the solid regions, but not too big in order to avoid numerical problems. It’s common practice to either define a really big number by intuition or to define a value based on the Darcy number. However, when using the Darcy number, numerical simulations have shown that this method leads to highly-problem-dependent designs. Thus, our research proposes a new way of defining the maximum value of the inverse permeability based on the Reynolds number, principally because this is the main dimensionless number when working with the Incompressible Navier Stokes equations in steady-state condition.
In summary, our in-house developed solver performs the minimization of the total pressure loss considering constraints over the volume. In order to reflect manufacturing restrictions of the steel forming process, constraints on the maximum size of the channels and the separation between them are also implemented. The main contributions brings closer the world of the topology optimization to the computational fluid dynamics by considering the nature of the working fluid (using the Reynolds number to define the inverse permeability) and also by using the finite volume method.
