Computational analysis of cross-flow of power-law fluids through a periodic square array of circular cylinders

The steady flow of non-Newtonian power-law fluids across a periodic square array of infinitely long circular cylinders is studied numerically using an unstructured finite volume method. The local and global flow characteristics have extensively been explored by the systematic variations of the pertinent dimensionless parameters as follows: fluid volume fraction (phi(f) = .70-.99), Reynolds number (Re = 1-40), and power-law index (n = .4-1.8). Qualitatively, the dense and curved streamlines are seen with the increasing inertial forces and shear-thinning behavior across all the fluid volume fractions. Further, the pressure coefficient over the surface of periodic cylinders is significantly influenced by the governing parameters and found to be maximum and minimum for the upstream and downstream cylinders, respectively. The individual and total drag coefficients have shown complex dependence on n, phi(f), and Re. For shear-thinning fluids (n < 1), the pressure drag coefficient dominates over the friction drag coefficient, whereas an opposite response is seen for the shear-thickening fluids (n > 1) except at Re = 40. Further, both individual and total drag coefficients are observed to increase and decrease in the ranges of phi(f) of .70-.90 and .92-.99, respectively, with increasing n. The strong interactions between the periodic cylinders, at smaller phi(f), diminish with a corresponding increase in phi(f). In addition, simple predictive correlations for the pressure, friction, and total drag coefficients have been developed to gain further physical insights into the detailed flow kinematics. Finally, the present findings display a good agreement with the available literature.

Automated summary

In this study, the flow characteristics of non-Newtonian power-law fluids across a periodic square array of infinitely long circular cylinders were numerically investigated using an unstructured finite volume method. The effects of fluid volume fraction, Reynolds number, and power-law index on the flow behavior were explored. The results show that with increasing inertial forces, the flow becomes more dense and curved. Furthermore, the pressure coefficient over the surface of periodic cylinders is significantly influenced by the governing parameters.