Wind tunnel effects on ice accretion over aircraft wings

Wind tunnel effects on ice accretion over aircraft wings Marta Zocca, Giulio Gori, Alberto Guardone Politecnico di Milano, Campus Bovisa, 2156 Milano, Italy Reference ice accretion experiments are reproduced numerically using the simulation framework PoliMIce to investigate solid blockage effects and wall-model boundary layer interaction at the wall-model juncture. The open-source OpenFOAM software is applied to the computation of the aerodynamic flow-field and of the trajectories of water droplets. The thickness of the iced layer is then determined using the PoliMIce ice accretion module, which solves the multi-phase ice, liquid water and air flow around the body surface. The iced geometry is updated in the aerodynamic solver to compute the aerodynamic forces, heat transfer and drop trajectories around the iced wing. The iterative process is carried out for the duration of the experiments. Wind tunnel wall effects are investigated for diverse operating conditions. Blockage effects on the measured lift coefficient of a twodimensional iced airfoil result into a variation of the corrected angle of attack during the experiment, due to the modification of the airfoil shape in time introduced by the accreting ice. Finally, icing tests on three-dimensional straight and swept wings are simulated. Water droplets impingement is heavily affected by flow separation at the juncture between the tunnel wall and the model wing: a shadow region where droplets do not hit the wing surface is observed. In pure rime icing conditions, the shadow region is free of ice. In glaze or mized rime-glaze conditions, instead, an ice build-up within the shadow region occurs, due to shear stresses driving the liquid film towards the wall-model juncture. Numerical results compare fairly well with available experimental data on ice accretion. Nomenclature z Vertical coordinate originating from the surface of the wing t Time, s T Temperature in the ice layer, K ϑ Temperature in liquid water layer, K B Ice layer thickness, m h Liquid water film thickness, m β Collection efficiency α Angle of attack, deg V Free-stream velocity, m/s T Free-stream temperature, K P Free-stream static pressure, Pa MVD Median Volume Diameter, mean droplets diameter, m LWC Liquid Water Content, kg/m 3 κ Thermal conductivity, W/mK ρ Density, kg/m 3 c P Specific heat at constant pressure, J/kgK L F Latent heat of fusion, J/Kg t ice Total icing exposure time, s t flow-field Aerodynamic flow-field update interval, s Student, currently PhD candidate, Department of Aerospace Science and Technology, Via La Masa 34, 2156 Milano, Italy Research Assistant (MSc Thesis co-advisor), Department of Aerospace Science and Technology, Via La Masa 34, 2156 Milano, Italy Associate Professor (MSc Thesis advisor), Department of Aerospace Science and Technology, Via La Masa 34, 2156 Milano, Italy 1 of 11

Subscript i Ice w Water I. Introduction In-flight ice accretion poses a key safety issue because of its detrimental effect on the performance of several components of the aircraft. Specifically, moderate to severe ice build-ups on aerodynamically critical surface regions determine substantial maximum lift penalty, stall angle reduction and parasite drag increase. 13 The icing phenomenon affects aircraft flying through clouds containing supercooled water droplets or in the presence of precipitations such as freezing rain or drizzle. 9 Among the droplets hitting the surface of the wing, those which freeze immediately upon impact originate a layer of so-called rime ice: this occurs in cold and dry environments, namely at low temperatures (below about 1 C) and low LWC. At temperatures near the freezing point of water and higher LWC, or after the rime ice layer has reached a critical thickness, 16 the freezing of the impinging droplets is not instantaneous. As a result, a thin film of unfrozen water driven by aerodynamic and gravitational forces lies on top of a previously accreted iced layer. This liquid layer, which either flows downstream or sheds off the body, is the distinguishing feature of the so-called glaze ice. A deep knowledge of the icing phenomenon and the related performance degradation is key to the design and validation of effective ice protection systems, which allow to gain an improved safety standard while reducing costs and environmental impact. Over the years, complementary approaches to the study of ice accretion have been adopted: flight and wind tunnel tests and numerical simulations. From the numerical standpoint, several ice-prediction codes have been developed by many research agencies and serve as valuable design and certification tools for the aircraft industry: among others, they are NASA LEWICE, 26 FENSAP-ICE, 7, 5 ICECREMO, 17 CIRA Multi-ICE 15, 21 and ONERA 11 icing prediction codes. As regards the assessment of the performance penalties associated to ice accretion and the phenomenological study of the flow around iced aerodynamic surfaces, wind tunnel tests performed in dedicated facilities 1 play a leading role. Since the early years of aviation, 4, 6 scaling issues arising from the use of subscale models and wind tunnel blockage effects have been widely studied in the range of dry testing and specific corrections have been devised. 22 However, during an ice accretion wind tunnel test, the geometry of the model and hence the flowfield varies over time due to the accreted ice. The goal of the present work is to study windtunnel effects in an icing experiment by applying the PoliMIce ice prediction software 1 to the numerical reproduction of exemplary experimental runs in diverse environmental conditions. In order to evaluate the influence of solid blockage in two-dimensional airfoil testing, ice shapes and force coefficients obtained in flight conditions and for different values of the ratio of the chord of the airfoil to the height of the test section are compared. Numerical simulations of three-dimensional geometries are carried out to quantify the relevance of wing-wall interference at the tunnel side-walls. The present paper is structured as follows. A brief overview of the numerical procedure for the numerical simulation of wind tunnel test within PoliMIce is presented in Sec. II. Numerical results quantifying blockage effects in two-dimensional airfoil tests and wing-wall interference at the wall-model juncture are discussed in Sec. III. Concluding remarks are provided in Sec. IV. II. Numerical simulation of ice accretion The software PoliMIce is a simulation framework for ice accretion prediction developed at the Department of Aerospace Science and Technology of Politecnico di Milano. 1 In a dedicated ice accretion module, a stateof-the-art ice accretion model is implemented to compute the ice build-up over a two- or three-dimensional geometry. Namely, a modified version of the extended Messinger model 14 for aircraft icing is implemented, 1 allowing the simulation of both rime and glaze ice accretions. The ice accretion module is made interact with diverse open-source and commercial CFD solvers, following a well-established procedure usually found in ice prediction codes. 7 The flowchart presented in Fig. 1 summarizes the calculation procedure. Given the total icing exposure time, the freestream velocity vector V, the liquid water content (LWC) of the cloud (grams of water contained in a cubic meter of air), the ambient temperature T a, the droplet median volume diameter (MVD) 9, 19 and the initial clean geometry, the flowfield around the body is computed. To this purpose, a steady-state solver for incompressible turbulent flows, included in the open-source CFD suite 2 of 11

flight data cloud data OpenFOAM/PoliMIce Interface Aerodynamic Solver OpenFOAM flow-field OpenFOAM/PoliMIce Interface PoliMIce initial geometry clean airfoil/wing domain and mesh trajectories of water droplets ice accretion parameters ice accretion calculation geometry update data saving Figure 1: Flowchart of calculation procedure within the PoliMIce framework. OpenFOAM 3 is adopted. Specifically, the OpenFOAM solver simplefoam is complemented with Spalart- Allmaras turbulence model. 24, 2 In order to determine the shape and the thickness of the ice layer over the surface of the airfoil/wing, the water distribution on the body surface is required. The impact point of each water droplet on the body result from the calculation of water droplet trajectories via a Lagrangian approach. Starting from an initial state in which equally spaced droplets are arranged at a plane 5 7 airfoil chords upstream of the body, immersed within the previously determined velocity field, a force balance in differential form involving inertia, aerodynamic drag, gravity and buoyancy 9 is integrated in time by the OpenFOAM Lagrangian solver uncoupledkinematicparcelfoam. 3 A C++ interface between the CFD/Lagrangian solver and the ice accretion module computes all the aerodynamic and thermodynamic parameters entering the thermal analysis needed to compute the thickness of the iced layer, namely the convective heat transfer coefficient, the recovery factor and the collection efficiency. The latter expresses the fraction of the free-stream water concentration impacting on each surface cell. Within the ice accretion model, the complex mass and energy exchanges involved in the icing phenomenon are summarized in a set of four partial differential equations expressing mass conservation, heat transfer in ice and water and the energy balance relating the heat fluxes involved in the phase changes. ρ i B t + ρ w T t = κ i 2 T ρ i c Pi z 2 h t = β LWC V ϑ t = κ w 2 ϑ ρ w c Pw z 2 B ρ i L F t = κ T i z κ ϑ w z On each surface element, elementary control volumes containing an ice and a water layer are defined. The local solution of the aforementioned set of equations gives the thickness and the temperature of the two layers. For the complete formulation of the problem, see the original paper by Myers. 16 In the PoliMIce simulation framework, a so-called multi-step procedure 25 is implemented, to account for the modification of the aerodynamic flowfield and hence of the accretion parameters caused by ice progressively accumulating during the assigned exposure time. By periodically updating the iced geometry into the CFD/Lagrangian solver, the collection efficiency, the convective heat transfer coefficient and the recovery factor are calculated on the basis of up-to-date aerodynamic variables. On the contrary, a single-step procedure adopts their clean-configuration counterparts over the entire duration of the simulation. (1) 3 of 11

III. Numerical Results A. Reference problem Similarly to wind tunnel testing of clean airfoils/wings, wind tunnel testing in icing conditions has to cope with scaling issues arising from the use of subscale models and the presence of walls confining the flow inside the test section. A precise quantification of the performance degradation undergone by an aircraft in full-scale icing conditions is the outcome of an accurate analysis of both the effects of Mach and Reynolds number on the aerodynamics of iced airfoils and of the influence of wind tunnel walls on force measurements. It is not the scope of this paper to describe Mach and Reynolds number effects on the behavior of the flow over iced airfoils. For a thorough discussion, see Ref. 8. As far as our analysis is concerned, suffice it to say that the maximum lift coefficient of two-dimensional iced airfoils is almost independent on the Reynolds number, especially in the presence of large ice shapes, which can attain a size comparable to the thickness of the wing section. In this case, flow separation is imposed by singularities in the geometry of the ice layer. Moreover, Mach number effects on force coefficients are smaller than the performance degradation due to ice accretion. In accordance to the above observations, it is common practice to apply results from low-reynolds tests to actual operating conditions, with no excessive approximation. That said, the quantification of wind tunnel wall effects assume a key role in the assessment of iced airfoil performance degradation. A survey of the diverse features characterizing wall-model interactions is presented in Sec. B and C, where the numerical reproduction of three icing experiments described in public-domain literature is discussed. Specifically, three different experimental campaigns conducted at the NASA Icing Research Tunnel 1 are considered. The NASA Icing Research Tunnel (IRT) 1 is a closed-loop and closed-test-section refrigerated wind tunnel. The test section is 6.1 m long, 1.83 m high and 2.74 m wide. The facility is capable of guaranteeing continuous operations at airspeeds up to 192 m/s and temperatures up to 4 C in the test section. Spray bars placed upstream of the test section can simulate a 1.22 m high and 1.83 m wide cloud of supercooled droplets. MVDs range from 15 to 5 µm and LWCs from.2 to 2.5 g/m 3. In Fig. 2, an exemplary experimental setup is reported: a two-dimensional airfoil model is mounted vertically within the test section and connected to an external balance for the measurement of lift, drag, and pitching moment. Diverse configurations of the test section are analyzed in Sec. B and the ice shapes and lift coefficients are compared to investigate the blockage effect offered by the lateral walls of Fig. 2. The reference case for the study of wall blockage effects is taken from an experimental campaign carried out in the early 199s: a NACA 12 airfoil was tested in a wide range of enviromental conditions, the results presented in Ref. 23. Sec. C deals with the interference between the model and the upper and lower walls of Fig. 2: complex three-dimensional flow features lead to a peculiar conformation of the ice shape at the wall-model juncture. The analysis of three-dimensional wall-model interference effects is carried out by considering a constantchord model a swept wing. Test conditions are extracted from two more recent databases, providing a comprehensive overview of ice shapes and performance degradation over currently used airfoils 12 and on three-dimensional swept wings, 18, 2 respectively. Figure 2: Photograph of a Cessna Tail Wing Section installed in the test section of the NASA Icing Research Tunnel (IRT). 1 4 of 11

B. Influence of wind tunnel blockage A mixed rime-glaze ice accretion test over a constant-chord NACA 12 airfoil, 23 performed within the reference setup of Fig. 2, is analyzed here to study the blockage offered by the lateral walls of the wind tunnel. With reference to the same figure, and consistently with the available literature about wind tunnel corrections, 22 the ratio of the chord of the model c to the width of the test section h is adopted here to quantify the relevance of wall blockage. Table 1: Mixed rime-glaze icing conditions for the study of wind tunnel wall blockage on a constant-chord model of a NACA-12 airfoil. 23 c α V T P MVD LWC t ice t flow-field [m] [deg] [m/s] [K] [Pa] [µm] [g/m 3 ] [s] [s].533 4 67 262.4 1 5 2 1 36 1 In order to evaluate the influence of wind tunnel walls on measured ice shapes, the test conditions given in Tab. 1 are simulated within a number of different domains: a free air flow representing flight conditions (FC) and wind tunnel flows (WT) at four different values of the ratio c/h. At c/h =.2, the simulation domain closely reproduces the test section of the NASA IRT. At c/h =.3,.5,.7, the simulation domains are obtained by virtually varying the height of the test section of the NASA IRT, while the airfoil chord is held constant, as well as the input parameters, including grid refinement in boundary layer regions and boundary values of turbulence variables. A complete icing simulation requires numerous evaluations of the flow-field. For this reason, computing the flow-field inside the test section by means of three-dimensional viscous simulations can turn out to be excessively burdensome in terms of CPU-time. A number of solutions aimed at minimizing the influence of the wall boundary layer on the flow within the test section are usually devised in the design and construction of a wind tunnel test section (e.g. the upper and lower walls are often slightly divergent in the direction of the flow). This fact is exploited here to achieve a reduction of CPU-time: by assuming that the layout of the test section accommodates the thickening of the boundary layer on the lateral walls, inviscid-like slip boundary conditions can be imposed on the tunnel walls instead of no-slip boundary conditions, thus avoiding to resolve the boundary layer on the tunnel walls themselves. To grasp the net effect of the blockage offered by the lateral walls, an accurate representation of the flow and the ice shape at the middle section of the wind tunnel is required. That said, another workaround to the excessive computational cost is to perform two-dimensional simulations instead of three-dimensional ones. The validity of this approach can be assessed by inspecting the evident agreement between the two ice shapes shown in Fig. 3, which result from a two-dimensional and a three-dimensional simulation of a GLC 35 airfoil at an angle of attack of 6 degrees in rime ice conditions. The ice shape obtained from the simulation of the wind tunnel flow at c/h =.2 is shown in Fig. 4, together with the corresponding IRT data. z [m].2.1 -.1 -.2 3D Simulation 2D Simulation -.1.1.3.5.7.9 x [m] Figure 3: Two-dimensional and three-dimensional results of a rime ice simulation on a GLC 35 airfoil, c =.9144 m, α = 6 deg, V = 9 m/s, P = 1 5 Pa, T = 263.15 K, MVD = 2 µm, LWC =.43 g/m 3, t ice = 12 s, t flow-field = 5 s. In Fig. 5, the collection efficiency obtained from the same flight and environmental conditions in a wind tunnel at c/h =.2 and in flight conditions is expressed as function of the non-dimensional curvilinear abscissa along the airfoil, the origin being placed at the leading edge. Graph (a) refers to the clean configuration, while (b) to the iced one. No significant difference between the two curves is observed in the case of the clean airfoil, while for the iced airfoil a non negligible deviation occurs only away from the stagnation 5 of 11

z [m].2.1 -.1 -.2 PoliMIce NASA IRT -.1.1.2.3.4.5 x [m] Figure 4: Numerical simulation of wind tunnel flow at c/h =.2 compared to the experimental ice shape. Test conditions are given in Tab. 1. region. A similar insight emerges from Fig. 6, where the ice shapes obtained for four different values of the blockage coefficient are compared. The four ice shapes overlap in the stagnation region and show little deviations from each other immediately downstream..7.6.5 WT, c/h =.2 FC, Uncorrected 1.8 WT, c/h =.2 FC, Uncorrected.4.6 β.3.2.1 β.4.2 -.1.1.2.3.4.5 (a) s/c -.1.1.2.3.4 (b) s/c Figure 5: Collection efficiency versus non-dimensional curvilinear abscissa along the airfoil: clean airfoil (a) and iced airfoil (b). The origin is placed at the leading edge..2 z [m].1 -.1 -.2 WT, c/h =.2 WT, c/h =.3 WT, c/h =.5 WT, c/h =.7 -.1.1.2.3.4.5 x [m] Figure 6: Ice shapes resulting from the simulation of wind tunnel flows at varying blockage coefficient c/h. The remainder of this paragraph is dedicated to the analysis of blockage effects on the performances of the iced airfoils. In icing tests, the geometry of the model changes over time due to ice growth. Therefore, a time-variation of the corrected angle of attack is expected to occur. In addition to the simulations reported in Fig. 6, four free-air-flow simulations are carried out, namely those reproducing flight conditions at the corrected angles of attack associated to the four different blockage coefficients. The corrected angle of attack is evaluated on the baseline un-iced configuration and then it is 6 of 11

held constant over the entire duration of the test. To assess the validity of such correction, the trend of lift coefficient over time is monitored. For each value of the ratio c/h, the corrected angle of attack, i.e. the free-air-flow angle of attack associated to the wind-tunnel lift coefficient, is retrieved by interpolation of a the piecewise linear C l (α) curve referred to flight conditions. C l.44.42.4.38.36.34 1-5 5 1 15 2 25 3 35-1 t [s] 5 Relative error [%] C l.46.44.42.4.38 1.36 5 1 15 2 25 3 35-1 t [s] 5-5 Relative error [%] WT, c/h =.2 FC, Corrected (a) Rel. error WT, c/h =.3 FC, Corrected (b) Rel. error C l.5.48.46.44.42.4.38 1-1 5 1 15 2 25 3 35 WT, c/h =.5 FC, Corrected t [s] (c) Rel. error 5-5 Relative error [%] C l.54.52.5.48.46.44.42 1-1 5 1 15 2 25 3 35 WT, c/h =.7 FC, Corrected t [s] (d) Rel. error 5-5 Relative error [%] Figure 7: Lift coefficients and relative correction errors (y-axis) as function of the duration of the experiment (x-axis) for four values of c/h:.2 (a),.3 (b),.5 (c),.7 (d). Dashed lines: wind tunnel flows at the reference angle of attack. Continuous lines: flight conditions at the reference angles of attack. Dotted lines: correction errors. In Fig. 7 (a)-(d), the lift coefficient and the percentage difference between the wind-tunnel and the corrected lift coefficients (y-axis) are given as function of the duration of the experiment (x-axis) for each value of the blockage coefficient c/h. The dashed lines refer to the wind tunnel flow simulations, while the continuous lines represent flight conditions at the corrected angles of attack. In all cases, a significant deviation between the two C l (t) curves for increasing time is observed. This behavior is common to all the examined blockage coefficients, from.2 to.7, thus confirming the expectation of a time dependence of blockage correction angle due to ice build-up. The sole correction of blockage effects can significantly affect performance estimation of iced airfoils, to an extent expressed by the percentage difference between the wind-tunnel and the corrected lift coefficients. As expected, the wind tunnel correction retrieved from the analysis of the clean-airfoil configuration well represents the iced airfoil performances only at the first stages of ice accretion. For longer exposure times, the shape variation caused by ice accretion worsens the estimate of the iced-airfoil lift coefficient, leading to errors up to about 1%. A well-defined trend of the lift coefficients versus time is not observed, neither for each single value of blockage, nor at varying blockage coefficient. Moreover, the relative error associated to the lowest value of blockage coefficient, c/h =.2, reveals that, counter-intuitively, a low blockage does not necessarily imply small errors in iced-airfoil lift coefficient estimation. 7 of 11

C. Wall-wing interference In wind tunnel testing, the interaction between the boundary layer on the tunnel sidewalls and the one on the wing affects both the maximum lift achievable and the spanwise stall initiation. An alternative explanation of the fact that as mentioned in Sec. A the maximum lift coefficient of two-dimensional iced airfoils is almost independent on Reynolds number is proposed in Ref. 13 : the strong interaction between the boundary layer on the tunnel sidewalls and the wing boundary layer is the factor controlling stall initiation, and hence the observed Reynolds number independence, instead of the geometrical irregularities of the large ice shapes. In flight conditions, similar phenomena take place at the wing-fuselage junction. Therefore, simulating the behavior of the flow at a wall-wing juncture and the resulting ice accretion is of paramount importance when assessing maximum lift penalties caused by ice accretions. Wind tunnel tests of a constant-chord model 12 and of a swept wing 2 in the rime icing conditions given in Tab. 2 and 3 are simulated within the experimental setup shown in Fig. 2. Table 2: Mixed rime-glaze icing conditions for the study of wall-wing interference effects on a constant-chord model of a GLC 35 airfoil. 12 c α V T P MVD LWC t ice t flow-field [m] [deg] [m/s] [K] [Pa] [µm] [g/m 3 ] [s] [s].9144 6 9 263.15 1 5 2.43 12 12 Table 3: Mixed rime-glaze icing conditions for the study of wall-wing interference effects on a swept wing model. 2 α V T P MVD LWC t ice t flow-field [deg] [m/s] [K] [Pa] [µm] [g/m 3 ] [s] [s] 6 9 261.87 1 5 2.51 12 12 A comprehensive evaluation of the performances of three-dimensional wings exposed to icing conditions is not carried out in this paper. Difficulties arising from both the droplet insemination of the flow and the control of the sidewall boundary layer have led to a substantial lack of qualitative and quantitative experimental data documenting ice shapes at a wall-wing juncture. Therefore, three-dimensional simulations aimed at capturing the peculiar ice geometries at the wall-wing juncture are accomplished. Figure 8: Distribution of the spanwise component of the shear stress on the surface of a constant-chord model of a GLC 35 airfoil. The case of the constant-chord model is analyzed first. Fig. 8 shows the streamlines and the y-component of the shear stress on the wing surface. The y-axis is directed from the middle section of the wind tunnel towards the tunnel wall. At the wall-model juncture, there is a region of separated flow that originates from the interaction between the boundary layer at the sidewall and the model boundary layer. This feature is clearly visible from the streamlines at the wall-model juncture, but is also suggested by the fact that the flow 8 of 11

at the leading edge of the model, near the juncture between the model and the tunnel wall, is characterized by a velocity component directed from the middle section of the wind tunnel towards the sidewall. (a) (b) Figure 9: Collection efficiency and resulting ice shape on the surface of a constant-chord model of a GLC 35 airfoil (a). Ice accretion at the wall-model juncture on a constant-chord model of a GLC-35 airfoil (b). In Fig. 9 (a), a view of the ice accreted on the model is superposed to the collection efficiency distribution, while in Fig. 9 (b), the ice shape at the wall-model juncture is reported. A shadow zone in which water droplets do not impinge is seen to occur. This phenomenon is due both to flow separation at the wall-model juncture, and to the fact that the motion of droplets of small diameter, such as those considered in this simulation, is affected more by aerodynamic forces proportional to the square of droplet radius than by buoyancy and inertia which vary as the cube of the radius. Moreover, Fig. 9 (a) reveals ice build-ups even where the collection efficiency is zero. The ice observed both downstream of the region of non-zero collection efficiency and at the model-wall juncture is mostly of glaze type; it results from the freezing of liquid water driven towards the root of the model by shear stresses acting on the surface of the model itself. Even more prominent three-dimensional effects are observed in the case of the swept wing. Especially at the wall-wing juncture, where a strong interaction between the boundary layer on the wall and that on the wing exists, a significant variation in the ice shape along the span is observed. The reference experimental setup is again that shown in Fig. 2, but the model is now a 28 -leading edge sweep angle wing. Figure 1: Distribution of the spanwise component of the shear stress on the surface of a GLC 35 swept wing model. The same arguments addressed in the case of the constant-chord model still apply to the distribution of the spanwise component of the shear stress on the model surface, of the collection efficiency and of the three-dimensional ice shape (Fig. 1 to 12). In all the mentioned figures, the z-axis is normal to the sidewall and it is oriented from the root towards the tip of the wing. A region of separated flow is observed to occur on the suction side of the wing, close to the juncture to the tunnel sidewall. Flow separation in this region affects droplet impingement, leading to an irregular 9 of 11

(a) (b) Figure 11: Collection efficiency and resulting ice shape on the surface of a GLC 35 swept wing model (a). IIce accretion at the wall-model juncture on a GLC-35 swept wing model (b). distribution of the collection efficiency at the wall-wing juncture, as shown in Fig. 11 (a). (a) (b) Figure 12: Ice accretion at the wall-model juncture on a GLC-35 swept wing model: suction side (left) and pressure side (right) of the wing. Outside the separated flow region, ice build-ups of the so-called streamwise type 8 are observed, as expected from a test carried out in rime icing conditions. In the near-wall region, instead, a larger amount of ice of the glaze type accumulates due to shear stresses driving liquid water towards the root of the model (cf. Fig. 11 (b) and 12). Moreover, a large spanwise variation in the ice shape is observed (Fig. 12) on the pressure side of the wing, where the module of the shear stresses is larger than its suction-side counterpart. Differently from the case of the constant-chord model, a large shadow zone where ice does not accumulate is not observed. Instead, numerical results show only a smooth decrease in the ice thickness at the wall-wing juncture. IV. Conclusions Two-dimensional simulations of icing experiments over airfoil sections carried out in free air flows and in wind tunnel domains at varying blockage coefficient exposed for the first time a dependence of the blockage correction angle on time and showed that a standard blockage correction could lead up to a 1% error on the estimation of the lift coefficient of the iced airfoil. Therefore, a reassessment of all the experimental results obtained so far is suggested, in order to quantify their dependence on wall blockage. Numerical simulations were proven to be a valuable tool to accomplish this task, as well as to grasp complex accretion phenomena in three-dimensional wing testing. Three-dimensional simulations on a constant-chord model and on a swept wing in rime icing conditions revealed a peculiar conformation of the ice shape at the wall-model juncture. 1 of 11

In the case of the constant-chord model, a shadow zone where droplets do not impinge and ice does not accrete was observed to occur. In the case of the swept wing, similar environmental conditions led to a typical mixed rime-glaze ice build-up at the wall-wing juncture: the presence of more intense shear stresses driving the liquid film towards the root of the model prevented the occurrence of an ice-free region even in the shadow zone. Outside from the separated-flow region, so-called streamwise ice formations were observed along the wing span. Further research is required to improve the estimation of performance degradation of aerodynamic surfaces exposed to ice accretion and to attain a complete understanding of wall-wing interference phenomena. These goals can be achieved via an extensive use of numerical tools. Suitable blockage corrections can be devised and the effect of boundary layer interaction at the sidewalls can be isolated by comparing the force coefficients obtained from a simulated flight condition to wind-tunnel flow simulations. From the phenomenological standpoint, diverse geometrical configurations and environmental conditions can be simulated and the resulting ice accretions analyzed and classified. References 1 Nasa Icing Research Tunnel. http://facilities.grc.nasa.gov/irt/. 2 NASA Langley Research Center Turbulence Modeling Resource. http://turbmodels.larc.nasa.gov/. 3 The OpenFOAM Foundation. http://www.openfoam.org/. 4 I. H. Abbott, A. E. Von Doenhoff, and Jr. L. S. Stivers. Summary of airfoil data. NACA Report 824, 1945. 5 C. N. Aliaga, M. S. Aubé, G. S. Baruzzi, and W. G. Habashi. FENSAP-ICE-Unsteady: Unified In-Flight Icing Simulation Methodology for Aircraft, Rotorcraft, and Jet Engines. Journal of Aircraft, 48(1):119 126, 211. 6 H. J. Allen and W. G. Vincenti. Wall interference in a two-dimensional-flow wind tunnel, with consideration of the effect of compressibility. NACA Report 782, 1948. 7 H. Beaugendre, F. Morency, and W. G. Habashi. FFENSAP-ICEs Three-Dimensional In-Flight Ice Accretion Module: ICE3D. Journal of Aircraft, 4(2):239 247, 23. 8 M. B. Bragg, A. P. Broeren, and L. A. Blumenthal. Iced-airfoil aerodynamics. Progress in Aerospace Sciences, 41:323 362, 25. 9 R. W. Gent, N. P. Dart, and J. T. Cansdale. Aircraft icing. Philosophical Transactions of The Royal Society A, 358:2873 2911, 2. 1 G. Gori, M. Garabelli, M. Zocca, A. Guardone, and G. Quaranta. PoliMIce: A Open Simulation Framework for Threedimensional Ice Accretion. Submitted for publication to the Special Issue of Applied Mathematics and Computation, 214. 11 T. Hedde and D. Guffond. ONERA Three-Dimensional Icing Model. AIAA Journal, 33(6):138 145, 1995. 12 H. E. Addy Jr. Ice Accretions and Icing Effects for Modern Airfoils. Technical Publication NASA/TP-2-2131, 2. 13 F. T. Lynch and A. Khodadoust. Effects of ice accretions on aircraft aerodynamics. Progress in Aerospace Sciences, 37:669 767, 21. 14 B. L. Messinger. Equilibrium Temperature of an Unheated Icing Surface as a Function of Air Speed. Journal of the Aeronautical Sciences, pages 29 42, January 1953. 15 G. Mingione and V. Brandi. Ice Accretion Prediction on Multielement Airfoils. Journal of Aircraft, 35(2):24 246, 1998. 16 T. G. Myers. Extension to the Messinger Model for Aircraft Icing. AIAA Journal, 39(2):211 218, February 21. 17 T. G. Myers and J. P. F. Charpin. A mathematical model for atmospheric ice accretion and water low on a cold surface. International Journal of Heat and Mass Transfer, 47:5483 55, 24. 18 M. Papadakis, M. Potapczuk, H. Addy, D. Sheldon, and J. Giriunas. Ice Accretions on a Swept GLC-35 Airfoil. Technical Memorandum NASA/TM-22-211557, 22. 19 M. Papadakis, A. Rachman, S. C. Wong, K. E. Hung, G. T. Vu, and C. S. Bidwell. Experimental Study of Supercooled Large Droplet Impingement Effects. FAA Technical Report DOT/FAA/AR-3/59, 23. 2 M. Papadakis, H. W. Yeong, S. C. Wong, M. Vargas, and M. Potapczuk. Experimental investigation of ice accretion effects on a swept wing. Technical Report DOT/FAA/AR-5/39, 25. 21 F. Petrosino, G. Mingione, A. Carozza, T. Gilardoni, and G. D Agostini. Ice Accretion Model on Multi-Element Airfoil. Journal of Aircraft, 48(6):1913 192, 211. 22 J. B. Barlow W. H. Rae Jr. A. Pope. Low-speed wind tunnel testing, 3rd Edition. John Wiley & Sons, Inc., 1999. 23 J. Shin and T. H. Bond. Experimental and Computational Ice Shapes and Resulting Drag Increase for a NACA 12 Airfoil. Technical Memorandum NASA/TM-15743, 1992. 24 P. R. Spalart and S. R. Allmaras. A One-Equation Turbulence Model for Aerodynamic Flows. Recherche Aerospatiale, 1:5 21, 1994. 25 P. Verdin, J. P. F. Charpin, and C. P. Thompson. Multistep Results in ICECREMO2. Journal of Aircraft, 46(5):167 1613, 29. 26 W. Wright. User s Manual for LEWICE Version 3.2. Contractor Report NASA/CR-28-214255, 28. 11 of 11