On particle dynamics in steady axial rotor flows

We investigate the effect of rotor velocity induction on the distribution of particles impinging on rotor blades and model the delayed response of a particle to the rotor-induced velocity field. We consider as reference a wind turbine rotor and a small-scale propeller in axial flow conditions. We first show that the classical two-dimensional (2-D) modelling of the multiphase flow can generate a systematic error with respect to the three-dimensional (3-D) solution. We consider two limiting cases: particles in equilibrium with the rotor-induced velocity field, where the carrier phase is computed using the section’s aerodynamic velocity vector, and induction-independent particles, where the geometric velocity vector is used. The 3-D solution differs from the two limiting cases when particles are in partial equilibrium with the induced velocity. We introduce an induction Stokes number Stkind and identify a transition regime between the two limiting solutions for 0.1 Stkind 10. We support this by presenting a simple one-dimensional delay model to evaluate the induced component of the particle velocity at the rotor disk as a function of Stkind. We validate the model by showing that it allows capturing the transition regime in 2-D simulations. The model only requires knowledge of the aerodynamic and geometric velocity vectors, i.e. of the axial and tangential induction factors and rotor operating conditions.