Study of Unsteady Flow Through and Around an Array of Isolated Square Cylinders

Flow past a porous square cylinder, which is constituted by an array of small square cylinders, was studied by simplified and highly stable lattice Boltzmann method (LBM) at Re = 4000. The effects of solid volume fractions (SVF) on the flow structure and important aerodynamic parameters were investigated and the internal fluid was described by phase-averaged method and its interaction with the near region. Several energy-contained Strouhal numbers come up in cylinder arrays, and mass flux through arrays is calculated to estimate the effects of blocking. The average total force on the array is found to decrease monotonically with decreasing SVF, and it has a dramatic drop as SVF decreasing from 0.062 to 0.036. The mass flux of array for SVF = 0.062 is smaller than that of 0.073 due to the stagger arrangement of isolated cylinders. The underlying Reynolds stresses reveal the increase in mean wake length as SVF decreases, and it behaves like the solid one for SVF = 0.132. Comparing with the other SVFs, the shear layer region at SVF = 0.132 indicates a significant decrease of curvature and a linear increase of growth rate, but a nonlinear growth rate for the other SVFs can be observed. The local maximum turbulent kinetic energy (TKE) and vorticity in shear layer region reveal the variation during the initial stages following separation. Moreover, detailed investigations of instantaneous wake dynamics provide an assistance to understand the flow physics of cylinder arrays for different SVF.