LBM simulation of fluid flow in a viscous micropump with non-circular rotors and RSM approach for multiple response optimization

A numerical simulation is performed to analyze the performance of viscous micropumps with elliptic and rectangular rotors with variable aspect ratios by lattice Boltzmann method (LBM). The influences of three effective geometrical parameters of viscous micropump namely rotor aspect ratio (AR), microchannel height (S) and rotor eccentricity (epsilon) in the ranges of 0.2-1, 1.5-3.5 and 0.1-0.9, respectively, are investigated on the cross sectional instantaneous dimensionless averaged velocity ((U) over bar) and the instantaneous area averaged total entropy generation ((S) over bar (F)) as well as their time-averaged values (U-ave and S-F, (ave)). A five-level central composite design (CCD), which is one of the most important response surface method (RSM) schemes, is adopted for the analysis of main and interaction effects as well as the optimization of these parameters. Results show that the U-ave increases with the increase of AR and epsilon in all aspect ratios while decreases as S increases at high aspect ratios for both rotors. However, this trend is reversed at low aspect ratios. Furthermore, results indicate that S-F, (ave) increases with the increase of all three geometrical parameters for both rotors. Finally, a numerical optimization is employed to simultaneously optimize both responses of U-ave and S-F, (ave) for elliptic and rectangular rotors. Overall desirability values of 0.701 and 0.758 are obtained for elliptic and rectangular rotors, respectively. For elliptic rotor, the obtained optimal values of geometrical parameters are 0.884, 1.5 and 0.744, respectively, for aspect ratio, microchannel height, and eccentricity, while the respective values for rectangular rotor are 1, 1.5 and 0.694.