Shape optimization of flow channels based on lattice Boltzmann method

Abstract

A new optimality criterion algorithm is presented for producing modified shape designs for fluid flow inside channels. To compute the fluid motion in a channel, the lattice Boltzmann method (LBM) was used based on D2Q9 and D3Q15 lattice spaces associated with the Bhatnagar-Gross-Krook (BGK) collision term. An experiential optimality method to design channels with the lowest pressure drop along the passage is introduced. The positions of solid cells and fluid cells are exchanged based on the strain rate tensor at the solid-fluid interface. To obtain the optimized shape, the cells are changed until the optimality condition is obtained with the restriction of constant fluid volume. Examples are presented to validate the algorithm, including an elbow tube as well as symmetrical and nonsymmetrical Tjunction channels. The validation exercises demonstrate that the algorithm is suitable for optimal channel design.