Numerical study of low-Reynolds number flow over rotating rigid helix: an investigation of the unsteady hydrodynamic force

Abstract

A helical flagellum filament can be modeled as a rigid helix. Numerical simulations of the unsteady flow around a rigid, finite length rotating helix are performed to examine the characteristics of the hydrodynamic force exerted on the helix by the fluid medium. Newtonian and non-Newtonian fluid models are used. The Reynolds numbers of the flows simulated range between and Where appropriate, the calculated mean thrusts, obtained by using three different numerical solvers, are compared with that based on theoretical prediction. The simulated mean thrusts agree well with the theoretical predictions. Analyses show that hydrodynamic force variations, although of small amplitudes, are dominated by distinct discrete modes that are higher harmonics of the rotation frequency of the helix for the low-Reynolds number flows simulated. Simple correlations are developed for the dominant frequencies, where present, observed in the simulations of the helix with different sizes, rotation frequency, and fluid viscosity.