Optimization of micromixer with staggered herringbone grooves on top and bottom walls

Multi-objective shape optimization of a micromixer with staggered herringbone grooves on the top and bottom walls has been performed through three-dimensional Navier-Stokes analysis, surrogate method and multi-objective evolutionary algorithm. Mixing index and friction factor are selected as objective functions, and four design variables, viz., number of grooves per half cycle (N), angle of groove (θ), groove depth to channel height ratio (d/h), and groove width to pitch ratio (Wd/pi) are chosen out of the various geometric parameters which affect the performance of the micromixer for the shape optimization. Numerical analysis has been performed with two working fluids, viz., water and ethanol at Reynolds number 1. The variance of the mass fraction at various nodes on a plane is used to quantify the mixing performance in the micromixer. The design space is explored through some preliminary calculations and a Latin hypercube sampling method is used as a design of experiments to exploit the design space. Response surface approximation model is constructed using numerical solutions at the designed-sites. The trade-off between the two competing objective functions has been found and discussed in the light of the distribution of Pareto-optimal solutions in the design space. It is observed that the Pareto-optimal solutions shift towards lower values of the design variables θ and wd/pi, and towards higher value of the design variable d/h whereas the design variable N remains insensitive along the Pareto-optimal front in the direction of higher mixing index.