Automatic Geometry Optimization of Exhaust Systems Based on Sensitivities Computed by a Continuous Adjoint CFD Method in OpenFOAM

Meeting backpressure and flow uniformity requirements within severe packaging constraints presents a particular challenge in the layout of catalyst inlet cones. In these cases, a parameterized optimization of the potentially complex cone geometries is inefficient (and inappropriate). Even assuming that a parameterization of the complex surface forms is possible, the choice of parametric shapes invariably affects the achievable results. Additionally, the long computation time for solving the flow fields limits the number of shape parameters that can be considered.

To overcome these restrictions, an optimization tool has been developed at EMCON Technologies that is based on the continuous adjoint method (augmented Lagrange method) of Othmer et al. The open source CFD toolbox OpenFOAM® is used as the platform for the implementation. Since the geometry itself is modeled using an immersed boundary method (in which finite volume cells are marked as fluid or solid), no geometry parameterization is required. The method allows computation of the sensitivity of flow uniformity and energy dissipation (or other target quantities) based on the instantaneous geometry. After the calculated surface sensitivities are combined and corrected for manufacturing and topological constraints, the location of the immersed boundary is automatically adjusted. It is thus possible to automatically determine a feasible catalyst cone geometry starting from an amorphous box (representing the packaging constraints) that is supplemented by definitions of inflow boundaries (for the flow coming from different manifold runners) and the outflow boundary (the catalyst surface). The calculation time associated with the process is on the same order of magnitude as the solution of the RANS equations itself. The optimization tool, its theoretical basis and some practical results are presented in the paper.