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To study ice adhesion at the droplet scale, a strategy is presented to simulate the impact and solidification of a supercooled water droplet on a cooled substrate. Upon impact, nucleation is assumed to occur instantaneously, and properties of the droplet are chosen to account for the nucleation process. Simulations are performed in ANSYS Fluent using a coupled volume-of-fluid and level-set method to capture the air-water interface, and an enthalpyporosity method is used to capture the liquid-solid interface. Calibration of a simulation parameter A mush is performed in order to match experimental data for different ideal surface types and surface temperatures. The simulation strategy successfully predicts the overall droplet response for several droplet impact conditions. Nomenclaturewidth on the surface, m d = signed distance to level-set interface f liquid = any physical property of the liquid material f mixture = any physical property of the liquid-solid mixture f solid = any physical property of the solid material k = thermal conductivity, W∕m · K L = specific latent heat of phase change, J∕kg L mixture = specific latent heat of phase change of the ice-water mixture, J∕kĝ n = normal unit vector for level-set interfacê n wall = unit vector normal to wall Oh = Ohnesorge number R = area ratio of droplet on surface Re = Reynolds number r = droplet radius, m r max = maximum droplet radius on surface, m r mixture = droplet radius of ice-water mixture, m St = Stefan number St mixture = Stefan number of the ice-water mixture T freezing = freezing temperature,°C T supercooled = supercooling temperature,°Ct wall = unit vector tangential to wall V 0 = droplet impact velocity, m∕s v = fluid velocity vector, m∕s We = Weber number α = volume fraction α p = volume fraction of primary phase α s = volume fraction of secondary phase β = liquid fraction ΔH = specific latent heat in a computational cell, J∕kg ΔT = degree of supercooling, deg θ = contact angle, deg θ wall = contact angle assigned to wall, deg κ = curvature of level-set interface μ= droplet viscosity, kg∕m · s ρ = density, kg∕m 3 ρ liquid = density of the liquid material, kg∕m 3 ρ p = density of the primary phase, kg∕m 3 ρ s = density of the secondary phase, kg∕m 3 ρ solid = density of the solid material, kg∕m 3 σ = surface tension coefficient, N∕m ϕ = liquid mass fraction φ = level-set function

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A key design factor impacting the utilization of electrical power to drive aircraft systems and subsystems is energy efficiency. With the design of an all-electric, hybrid ice protection system, energy consumption can be reduced to a large extent. The hybridization is achieved through an intentional partitioning of the ice at the stagnation line by melting via surface heating and ice shedding in the unheated regions of the airfoil surface via an electromechanical deicing system based on piezoelectric multilayer actuators. In addition, to reduce energy consumption, the adhesion forces between the ice and the airfoil surface can be reduced using an ultrasmooth, nanostructured surface with water and ice repellent properties that encourages ice shedding. Experimental investigations, performed in a laboratory-scale icing wind tunnel for a small-scale system configuration, reveal that the hybrid approach for ice protection reliably sheds the ice accreted on the airfoil surface. Compared to conventional state-of-the-art systems for ice protection, the hybrid approach is able to reduce power consumption up to 95 %. Beyond the laboratory tests, numerical simulations of the hybrid strategy analogous to the one used for the experiments are performed. The time history of the residual ice shapes aft of the heated region are simulated using the ice accretion prediction software LEWICE2D for a wet-running anti-icing subsystem. Finite element analyses of the effects of the piezoelectric actuators are then performed using Abaqus to investigate the ice shedding capability in the unheated regions of airfoil surface. It is shown that the variation in the thickness of the different ice shapes affects the stiffness of the model, and the ice shedding capability, respectively. Simulation results correlate well with experimental results obtained with the icing wind tunnel. It can be concluded that reliable operation of the hybrid system for ice shedding can be guaranteed when using a harmonic sweep excitation able to excite the structure at its resonance. NomenclatureA = surface area α = mass proportional Rayleigh damping coefficient β = stiffness proportional Rayleigh damping coefficient C3D8E = 8-node three-dimensional linear piezoelectric brick elements C3D8R = 8-node three-dimensional linear brick elements EDM = electro-discharge machining f = frequency FEA = finite element analysis 2 IPS = ice protection system LWC = liquid water content MVD = median volume diameter NACA = National Advisory Committee for Aeronautics p d = power density q = heater density Q m = mechanical quality factor R a = arithmetic mean value of surface roughness SEM = scanning electron microscope T = air temperature  = shear stress V air = velocity of the airstream Subscripts exp = experimental FEA = finite element analysis heater = carbon fiber cord heater int = interface n = natural piezo = piezoelectric st = static condition surf_ice = surface of the ice tot = total condition