Modeling drag force acting on the individual particles in low Reynolds number flow

Abstract

We present a simple model for the hydrodynamic drag force acting on the individual N particles of aggregates in uniform flow with low Reynolds number. The present model predicts the shielding effect due to hydrodynamic interactions by considering the individual location and flow direction. The shielding effect of two particles was obtained from curve fitting with the exact solution. Furthermore, the shielding effect of N-particles was extended using scaling laws and curve fitting equations. The present model is advantageous in that it can predict the drag force without considering the fractal dimension. In addition, the hydrodynamic interaction between particles can be calculated without matrix operations. The presented model was verified by calculating the drag acting on aggregates with the Filippov method. Verification conditions were that the number of particles was less than 200, and the fractal dimension was in the range of 1.3 to 2.6. Validation results showed good agreement with Filippov's exact solution. The maximum error for the total drag force is within 5%. Finally, we not only applied the drag force model to the discrete element method, but also performed a numerical study of gravitational sedimentation problems at fixed depth.