On determining the power-law fluid friction factor in a partially porous channel using the lattice Boltzmann method

In the present work, the power-law fluid flow in a channel partially filled with a porous medium is numerically investigated using the lattice Boltzmann method (LBM). The porous domain, placed in the lower half of the channel, is represented according to a heterogeneous approach by a matrix of solid square disconnected blocks. The apparent viscosity of the power-law fluid is computed by locally varying the LBM relaxation factor. The results show the influence of geometry (porosity, number of obstacles, and hydraulic diameter), inertia (Reynolds number), and fluid properties (power-law index) over the partially porous-to-impermeable channel friction factor ratio. In general, the higher the porosity and the lower the number of obstacles, Reynolds number, and power-law index, the lower the friction factor. Finally, a correlation for the friction factor ratio as a function of the free region hydraulic diameter, permeability, and power-law index is presented for a specific channel configuration.