Abstract
An improved topology optimization lattice Boltzmann model for porous structures is proposed for advection–diffusion chemical reaction systems. Nonlinear porous medium drag models related to the mesoscale porosities and velocities are introduced for the momentum and mass transport coupled with the topology structure evolution. The evolution of the temporal-spatially varying porosity field is governed by a mesoscale porosity transfer equation. At each evolution step, the porous structure is sharpened by the porosity adjustment of a transient deviation of the objective function relative to porosity, and is slightly smoothed by the porosity diffusion simultaneously. Adjustable weights for chemical reaction, mass diffusion, kinetic energy, and viscous shears are applied for calculation of the transient deviation fields, which control the evolution speeds of the topology structures due to local chemical reaction, mass diffusion, flow convection, and interface drag, respectively. The effects of governing parameters and objective weights on structure patterns are illustrated. Three topology structure patterns with natural shapes are observed: (i) trunk shaped convective flow induced channels, (ii) fractal-branch shaped diffusion enhanced sub-channels, and (iii) leaf shaped chemical reaction fins. The trunk–branch–leaf topology structures result from the dynamic balance of the mesoscale convection, diffusion, and reaction.
Published Version
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