Quasi-Unsteady Icing Simulation of an Oscillating Airfoil

Abstract

Over the last two decades, steady-state and quasi-steady computational techniques have been proposed and used to model ice accretion on helicopter rotors in both hover and forward flight. These methods cannot accurately predict ice shapes or their aerodynamic impact on rotor performance, particularly in forward flight due to its unsteady nature. The current study proposes a methodology to predict ice accretion on oscillating airfoils with varying angles of attack. The computation of the airflow, droplet impingement, and ice accretion is carried out in an unsteady framework that preserves the characteristics of air, water droplets and ice accretion with respect to time. Application of this approach to an oscillating airfoil shows good agreement with experiments. Nomenclature l C = lift coefficient d C = drag coefficient f = oscillation frequency ( Hz ) i = time step number k = the total number of icing time step at each shot ( * k n m  ) LWC = liquid water content ( 3 / g m ) m = total number of saved multiphase solutions of a cycle MVD = droplet mean volumetric diameter ( m  ) n = total number of cycles of a shot h Q  = convective heat flux ( / j s ) T = oscillation period ( s ) T  = air temperature at infinity ( C  ) . total t = total exposure time to icing condition ( s ) U  = air speed at infinity ( / m s ) u a = air velocity vector ( / m s ) u d = droplet velocity vector ( / m s )  = pitching angle ( deg ) . ave  = average pitching angle ( deg ) . osc  = oscillating pitching angle ( deg )  = collection efficiency 1 Ph.D. Candidate, Member AIAA. 2 total  = total collection efficiency t  = prescribed time step of ice accretion (s) a  = air density ( 3 / kg m ) wall  = air wall shear stress tensor ( 2 / N m )  = azimuthal angle ( rad )