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Adjoint-based optimization is used to passively improve the mixing characteristics of a micro T-mixer thanks to the design of an improved geometry of the device. Besides the technological interest of the specific problem, the procedure is also meant to assess the practical usability and robustness of adjoint techniques in the con- text of existing finite-volumes CFD libraries for incompressible flow problems.
The choice of a geometrically simple case, like that of the T-mixer, should be considered natural, being this work a first step towards more complex applications. A futher simplification is given by the laminar nature of the flow regime taken into account.
A continuous adjoint formulation is adopted; after the introduction of a properly selected objective function for the problem at hand, adjoint equations and boundary conditions are implemented in the open-source software OpenFOAM to compute the surface sensitivity to the degree of mixing. We specifically target the laminar flow regime (i.e. the vortex flow regime) where the T-mixer shows a low mixing efficiency. It is well know that, in this regime, the numerical diffusion affects the results, and in particular leads to an overestimate of the degree of mixing.
Several calculations on meshes of different size are used to keep resolution effects under control; a threshold, corresponding to cell lenght of 3.0 μm, is identified, below which the solution does not present further qualitative changes, and the results are marginally affected by further increases in spatial resolution. With only one optimization step, and rather small geometry changes, we are able to increase the degre of mixing by more than two orders of magnitude, while the pressure drop across the device remains basically unchanged.