Effects of particle arrangements on the drag force of a particle in the intermediate flow regime

Abstract

The drag force of a single particle in the presence of other equal-sized particles arranged in specific configurations is measured directly for Re from 30 to 106. Four particle arrangements are investigated: a two-particle configuration (Model I), a three-coaligned particle configuration (Model II), a hexagonal particle configuration (Model III) and a cubic particle configuration (Model IV). Variables studied include the particle Reynolds number (Re) and the separation distance. The effect of pipe wall on the measurement results is also examined. The measured drag force, expressed in terms of the drag ratio, is compared with the theoretical values at zero Re and the experimental values for 100 < Re < 10 3 reported in the literature. Comparisons of the experimentally determined drag ratios with numerically simulated values are also conducted. Because of the Re effect, the drag ratio curves for Model I are no longer symmetrical with respect to θ = 90° as observed for the Stokes flow. The results for Model I at θ = 90° show that the drag ratio increases with the separation distance and then decreases with further increasing separation distance, and the combination of the Re and wall effects causes the drag ratios higher than unity. For Model II, the drag ratio of the middle particle is lower than that of the upper particle at small separation distances but becomes slightly higher beyond a certain separation distance. The computational results provide detailed information on the flow field around each particle, and the pressure and the shear stress distributions on particle surfaces. The numerically simulated drag ratios compare reasonably well with the experimental data. The drag ratio behavior for Model IV is found to be similar to Models I and III; however, the Re does not seem to affect the drag ratio. The results of the flow visualization conducted in this study clearly demonstrate a significant change of the wake structure of Models I and III at different separation distances.