This paper presents the results of a numerical study of the unsteady flow around a leading-edge iced airfoil. At first, we demonstrate the efficiency of the numerical model used for the unsteady computations, a Zonal Detached Eddy Simulation (ZDES), validated by experimental data. Then, the degradation of the aerodynamic performance due to the ice accretion is better predicted by the ZDES than by steady RANS-SA method. Besides the paper aims at improving the understanding of the unsteady phenomena related to the turbulent separated flows. Nomenclature ZDES : Zonal Detached Eddy Simulation RANS-SA : Reynolds-Averaged Navier-Stokes equations with Spalart-Allmaras turbulent model PIV : Particle Image Velocimetry c = airfoil chord length L y = airfoil span length h = height of the upper ice ridge x = chordwise position along the airfoil from the leading edge y = spanwise position (between -L y and 0) z = normal position from the airfoil chord line α = airfoil angle of attack P i = stagnation pressure in the wind tunnel U 0 = free stream velocity M = Mach number Re = Reynolds number based on chord length dt = time step df = frequency resolution for spectral analyses v x , v y , v z = x-, y-and z-components of the flow velocity C D= drag coefficient C y = force coefficient in the spanwise direction C L = lift coefficient C P = pressure coefficient Q = Q-criterion measuring vorticity in the flow C corrY = coefficient measuring the averaged correlation degree in the spanwise direction

a b s t r a c tFlow dynamics, in-line and transverse forces exerted on an oscillating circular cylinder in a fluid initially at rest are studied by numerical resolution of the two-dimensional Navier-Stokes equations. The Keulegan-Carpenter number is held constant at KC = 10 and Re is increased from 40 to 500. For the different flow regimes, links between flow spatio-temporal symmetries and force histories are established. Besides simulations of long duration show that in two ranges of Re, forces exhibit low frequency fluctuations compared to the cylinder oscillation frequency. Such observations have been only mentioned in the literature and are more deeply examined here. In both ranges, force fluctuations correspond to oscillations of the front and rear stagnation points on the cylinder surface. However, they occur in flow regimes whose basic patterns (V-shaped mode or diagonal mode) have different symmetry features, inducing two distinct behaviors. For 80 r Re r 100, fluctuations are related to a spectral broadening of the harmonics and to a permutation between three vortex patterns (V-shaped, transverse and oblique modes). In the second range 150 r Re r 280, amplitude fluctuations are correlated to the appearance of low frequency peaks interacting with harmonics of the cylinder frequency. Fluctuations are then a combination of a wavy fluctuation and an amplitude modulation. The carrier frequency corresponding to the wavy fluctuation depends on Re and is related to a fluid characteristic time; the modulation frequency is independent of Re and equal to 1/4 of the cylinder oscillation frequency.

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This paper deals with a vibratory problem of fluid-structure interaction. It considers the two-dimensional case of a rigid, smooth and circular cylinder undergoing transverse sinusoidal oscillations and immersed in a viscous fluid otherwise at rest. Our work is focused on the in-line force acting on the cylinder in unsteady laminar flow. The aim is to understand the variations of the force with time according to the configuration of the physical system. For that the analysis will also use an energetic approach based on the power balance. The physical system can be characterized by two non-dimensional numbers: the Reynolds number (Re) compares the importance of the fluid viscosity to its inertia, and the Keulegan-Carpenter number (Kc) measures the amplitude of the cylinder displacement compared to its diameter. First the incompressible Navier-Stokes equations are solved numerically by means of a finite elements method. The flow structure is analyzed by determining the evolution with time and throughout the computational domain of flow quantities, such as pressure field, vorticity field or stream lines. We also calculate the values versus time of the different terms occurring in the mean force balance and power balance. We compare these results for several pairs (Kc, Re) of “extreme” values. Thus it appears three characteristic configurations: the inertial Euler case (Kc≪1 and inviscid fluid), the Stokes case (Kc≪1 and Re≫1) and the drag case (Kc≫1). For these three reference configurations the physical mechanisms operating in the system are identified. But in intermediate cases, particularly when Kc>1, every mechanisms interact. Consequently the evolution of the force acting on the cylinder versus time is more complex and its interpretation becomes less straightforward. That is why a quantitative energetic analysis is carried out. We define a measure of the dissipative energy present in the flow. Then we compare the values of that coefficient for different cases throughout the map (Kc, Re).