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In order to reduce the danger of impact onto components caused by break-up, it is important to analyze the shape of shed ice accumulated during flight. In this paper, we will present a 3D finite element method (FEM) to predict the shed ice shape by using a fluid-solid interaction (FSI) approach to determine the loads, and linear fracture mechanics to track crack propagation. Typical icing scenarios for helicopters are analyzed, and the possibility of ice break-up is investigated. NomenclatureE = Young's modulus f, f cf = body force, centrifugal force G = shear modulus h = Neumann boundary conditions LWC = liquid water content MVD = droplet median volume diameter Nvector = normal vector p f = fluid pressure Rvector = propagation vector Tvector = tangential vector u = displacement field v = Poisson's ratio v = Eigen vector  = Cauchy stress tensor ij  = Kronecker delta  i = fluid/structure interface Ω s, Ω f = solid, fluid domain

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While CFD solutions of helicopter flow have increased in the last few years, icing simulations are rare and, to the best of our knowledge, none has modeled helicopter icing completely. In this work, we perform a 3D simulation of rotor-fuselage interaction for longterm in-flight ice accretion. For flow solution, the 3D compressible turbulent Navier-Stokes equations are solved, with the rotor modeled as an actuator disk that imparts radial and azimuthal distributions of pressure rise and swirl to the flow field. Our code, FENSAP-ICE is used to solve the 3D flow, impingement and ice accretion. The flow solutions for the ROBIN test case, at two forward speeds, are obtained and compared with published experimental results and then used to illustrate icing on the helicopter's fuselage. Nomenclature r = radius from disk center (m)  a = dynamic viscosity of air (N.s/m 2 ) R = radius of blade tip (m)  w = dynamic viscosity of water (N.s/m 2 )  = azimuthal angle (rad) d = droplet diameter (m) N = number of blades LWC = liquid water content (g/m 3 )  = rotor speed (rad/s) MVD = mean volumetric diameter (microns)  = rotor solidity  L = characteristic length (m) P = pressure difference (N/m 2 ) g = gravity vector r V = local swirl velocity (m/s) 0 g = magnitude of the gravity vector (m/s 2 ) dA = elemental area   . . r d dr  (m 2 ) Fr = Froude number 0 (U / L g )   dT = elemental thrust (N) K = droplet inertia parameter 2 ( /1 8 )     w w d U L dQ = elemental torque (N.m) Re d = droplet Reynolds number ( / ) a a d a dU     v v d  m = mass flow through elemental area (Kg/s)  = non-dimensional water volume fraction dL = lift produced by blade segment dr (N)  = collection efficiency dD = drag produced by blade segment dr (N) ice C = specific heat at constant pressure for ice (J/kgK)  = angle between thrust and lift forces (rad) w C = specific heat at const. pressure for water (J/kgK) p v = farfield vel. parallel to rotor plane (m/s) f h = film thickness (m) c v = farfield vel. perpendicular to rotor p. (m/s)  m ice = instantaneous mass of ice accretion (kg/s) i v = induced velocity (m/s)  m evap = instantaneous mass of evaporation (kg/s)  = advance ratio   / p v R evap L = latent heat of evaporation (J/kg)  = inflow ratio     / c i v v R  fusion L = latent heat of fusion (J/kg) P C = pressure coefficient       2 / 0.5 p p V      subl L = latent heat of sublimation (J/kg) 2 T C = thrust coefficient        2 2 / T R R     t = time (s) T  = temperature at infinity (°C) T  = temp. at wall/water/ice/air interface (°C)  U = air velocity at infinity (m/s) 0 T   = stagnation temperature at infinity (°C)  wall = air wall shear stress tensor (N/m 2 )  T d , = droplets temperature at infinity (°C) a u = air velocity vector f u = mean velocity across the water film (m/s) d u = droplets velocity vector  = solid emissivity  a = air density (kg/m 3 )  = Boltzmann constant  w = water density (kg/m 3 )

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 )