Initial Development of a Model to Predict Impact Ice

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Initial Development of a Model to Predict Impact Ice Adhesion Stress Conference Paper · June 2018 DOI: 10.2514/6.2018-3344

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AIAA AVIATION Forum June 25-29, 2018, Atlanta, Georgia 2018 Atmospheric and Space Environments Conference

10.2514/6.2018-3344

Initial Development of a Model to Predict Impact Ice Adhesion Stress David S. Thompson,1 Dong Meng,2 Amir Afshar,3 Randa Bassou,4 and Jing Zhong5 Mississippi State University, Mississippi State, MS, 39762, USA and

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Elmar Bonaccurso,6 Alexandre Laroche,7 and Vittorio Vercillo7 Airbus Central R&T, 81663 Munich, Germany Recent increasing interest in low ice adhesion surfaces has necessitated the development of a predictive model to ascertain their efficacy in the context of icing mitigation for aeronautical applications. We have formed an international team that is working to facilitate the use of advanced, low adhesion surfaces to mitigate ice accretion on N+2/N+3 generation aircraft by developing a semi-empirical, predictive technique through a combined experimental and computational effort. Experimental impact ice adhesion data is obtained using the vibrating cantilever method and employed to develop an empirical description of ice adhesion. This empirical description is augmented by first-principle simulations to include the effects of surface chemistry and micro- and nanoscale roughness on ice adhesion strength. The capstone version of the new model will couple simulations to define microscale (nanoscale and mesoscale) properties that can be correlated with the macroscale ice adhesion stress to produce an approximate functional relationship. In this paper, we provide a description of our approach along with sample results and conclude with a roadmap of the path forward.

I. Nomenclature CA d

H LWC

= = = = = = = = = = = = = = =

contact angle block separation distance Young’s Modulus of the bulk cantilever material Young’s Modulus of ice eccentricity of the neutral axis of the ice/metal beam with respect to the ice/metal interface ice adhesion strength from MD simulations thickness of the cantilever thickness of the ice block height block width block depth penetration depth initial penetration depth liquid water content simulation box size along the y dimension

1

Professor and Airbus Helicopters, Inc. Professor, Department of Aerospace Engineering, Associate Fellow. Assistant Professor, Dave C. Swalm School of Chemical Engineering. 3 Graduate Research Assistant, Dave C. Swalm School of Chemical Engineering. 4 Graduate Research Assistant, Center for Advanced Vehicular Systems, Student Member. 5 Postdoctoral Researcher, Dave C. Swalm School of Chemical Engineering. 6 Senior Scientist, Materials X. 7 Research Engineer, PhD Student, Materials X. 2

1 Copyright © 2018 by the American Institute of Aeronautics and Astronautics, Inc. All rights reserved.

MVD n P

TAT T

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t V

ε

= = = = = = = = = = = = = = = = = = = = = =

simulation box size along the z dimension length of the cantilever mean effective droplet diameter freezing fraction (nondimensional) pressure average roughness lateral correlation length peak-to-peak roughness total air temperature temperature total temperature time airspeed impinging velocity penetrating velocity of water linear position of the strain gauge with respect to the fixed end of the cantilever strain strain measured by the strain gauge interfacial ice adhesion stress relevant macroscale parameters relevant nanoscale parameters relevant microscale parameters

II. Introduction

A

IRCRAFT icing is a truly multiscale problem. Ice nucleation of impinging mesoscale, supercooled droplets is governed by processes that occur at the nanometer and nanosecond scales while the wetting of the surface is governed by processes that occur at the micron and millisecond scales. Finally, icing on aerodynamic surfaces occurs on the scale of meters with a time scale of minutes. At present, it is not possible to simulate aircraft icing, i.e., icing at the macroscale, from first principles due to the prohibitive computational cost. Our team is attempting to combine different methodologies (experimental, numerical, and theoretical) at multiple temporal and spatial scales to develop a semi-empirical, multiscale model for predicting the adhesion stress of impact ice on modern, engineered surfaces. The resulting capability will facilitate the analysis and design of surfaces with ice resistant properties to mitigate ice accretion on N+2/N+3 generation aircraft. The challenge associated with any multiscale modelling strategy is relating measurable macroscale properties to appropriate microscale (nanoscale and mesoscale) properties, which may not be measurable. Our strategy is to employ a surrogate variable approach to incorporate nanoscale and mesoscale ice-substrate interface effects at the macroscale. These characteristics, while not easily measured, can be computed using molecular dynamics (MD) simulations at the appropriate scales. We hypothesize that their effects are manifested in the measurable, macroscopic parameters. Our multiscale model will be based on correlations of the macroscale impact ice adhesion stress with macroscale icing parameters and predicted surrogate mesoscale and nanoscale parameters. Previous studies have investigated the effects of empirically chosen surface parameters such as contact angle, contact angle hysteresis, surface polarity, and surface roughness, etc.; however, findings about their effects on iceadhesion are inconclusive and often contradictory. The fundamental issues are: (a) the rationale for selecting a particular surface parameter for study is often not physics-based, but out of consideration of ready accessibility to experimental measurements; and (b) “surface properties” investigated in experiments are often multiscale in nature (e.g. contact angle), manifesting the properties of the surface at various length scales. The capstone result of this effort will be correlating the microscale and nanoscale properties, which are obtained via simulation, with the macroscale, experimentally-measured adhesive stress. Successful incorporation of these effects into a hybrid multiscale model will facilitate the development of a predictive, semi-empirical methodology for determining the effectiveness of a surface engineered for ice mitigation. Further, this effort has the potential to lay the groundwork for the development of more advanced predictive models for computing ice adhesion stress. In this paper, we describe our strategy for developing a predictive, semi-empirical model for estimating ice adhesion stress for an engineered surface. We first provide background information on icing mitigation and ice adhesion testing. Next, we describe our overall strategy while focusing on the details of vibrating cantilever method 2

for measuring ice adhesion stress and the rationale for the molecular dynamics (MD) simulations that we are performing. Then we present current results and conclude with a brief discussion of the path forward.

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III. Background Surface modification is recognized as an effective strategy for ice accretion mitigation. Icephobic surfaces are defined by low adhesion of already-formed ice, freezing drizzle, or snow on protected components, which leads to their spontaneous removal under the action of their own weight or by the relative wind. The creation of hydrophobic and superhydrophobic coatings has been one of the most promising advances in the development of icephobic surfaces [1, 2]. Superhydrophobic surfaces have significant potential for use as anti-icing coatings because of their demonstrated ability to reduce ice, frost, and wet snow buildup. They have significant water repellency along with a presumed, relatively weak ice-adhesion strength, and are characterized by contact angles greater than 150° and a small contact angle hysteresis. Superhydrophobicity typically requires surface texturing with hierarchical micro- and nanoscale roughness in addition to modification of the chemical composition of the surface through application of low surface energy coatings. However, research has demonstrated that adhesive shear strength correlates poorly with contact angle [3], and that varying hydrophobicity without varying the roughness of the surface had only a limited impact on the adhesive strength of the ice [4]. In general, three problems must be solved to produce a superhydrophobic surface: (1) decreasing the material’s surface energy by way of treating the surface with hydrophobic agents, (2) choosing a suitable shape for textural elements to increase the local contact angle, and (3) forming a texture with multimodal roughness on the surface, whether by treating a surface layer or applying texturing elements extracted from other materials [2,5-13]. Regardless, the majority of the literature focuses on icing under static conditions, i.e., a stationary droplet deposited carefully on a surface, or by low-speed impact conditions. There is significantly less information for conditions encountered in an aerodynamic application, i.e., a supercooled droplet impacting a surface at velocity 50 / that generates the so-called impact ice. This is a major drawback when trying to collect data for the design of ice protection systems for aircraft components. A recent review paper by Work and Lian [14] provides an excellent summary of the current state of the art regarding the measurement of ice adhesion. Among the more popular methods for measuring ice adhesion is the centrifuge adhesion test (CAT) [15,16]. CATs use centripetal force to estimate ice adhesion by rotating the sample at increasing angular velocity until the ice separates from the test specimen. Upon ice detachment, the adhesion strength is calculated knowing the rotation speed, the mass of the ice, and the contact area between ice and beam. The standard centrifuge test was developed in 2005 at the Anti-icing Materials International Laboratory (AMIL) [15]. Tests performed at AMIL use ice accreted at lowimpact speeds and simplified geometries [17], which are not intended for aircraft icing applications. Additionally, the samples are not accreted in-situ and must be transported to the CAT, which influences their mechanical and thermal histories and makes samples prone to pre-cracking at the interface, which in turn produces erroneous data. The AMIL CAT has other disadvantages, mainly that the stress-strain curves are not captured, that the samples are not preserved, which complicates the inspection of the sheared interface, and last but not least, the presence of aerodynamic loading and vibration may result in erroneous data. Itagaki developed the Calculated CAT (CCAT) [18]. Using the CCAT, the calculation of adhesion and tensile strength relies on the length of a piece of ice shed from the rotor. The CCAT addresses some of the shortcomings of the CAT; since the ice is tested in situ, there are no issues related to handling. Many researchers define the shear strength of ice adhered to a substrate as τint= F/A, where F is the force required to remove the sample and A is the area of the interface. Note that this assumes a uniform stress distribution at the ice/substrate interface; however, it has been proven that stress distributions at the interface are nonuniform even for a sample with simple geometry. One way this nonuniformity has been accounted for is through a comparative ice adhesion measure known as the Adhesion Reduction Factor (ARF), which is defined as the ratio of adhesion strength of a beam made of the baseline material to the adhesion strength of a beam covered by the icephobic material. The Adverse Environment Rotor Test Stand (AERTS) is an instrumented CAT designed to overcome some of the issues highlighted above. The AERTS is an in-situ test facility with an instrumented rotor that spins at a constant rotational speed. The rotor passes through a cloud that is produced within the AERTS. As ice accretes on the rotor, its mass increases until shedding occurs, after which the test is concluded, and the interfacial area is recorded. The instrumentation consists of a force transducer, which facilitates estimation of the mass of the ice. The obvious advantage is that the ice shedding occurs in the same environment in which the ice was created. The main disadvantages of this method are related to the complex geometries of the accreted ice that can produce significant variations in stress at the interface [19].

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Direct mechanical testing remains the method preferred by many authors, especially the push test. The push test applies a mechanical force to break the interface. Push tests are relatively straightforward for nonimpact ice; ice is frozen to a substrate, and then is pushed or pulled by a force probe. Push tests are more problematic for impact ice. A major shortcoming is that data is biased to lower values when multiple tests are performed, and strong stress concentrations on the interface result from the pusher, which is why a finite element analysis of the test geometries is needed to correct the data [20]. While limited in number, there have been several push tests using impact ice reported in the literature. Scavuzzo and Chu [21] developed one of the largest and perhaps most important sets of data. Their data used in the LEWICE ice accretion code [22,23]. These experiments were conducted in the NASA Glenn Research Center Icing Research Tunnel (IRT). The test article consisted of a set of two concentric cylinders; a thin outer cylinder with a window and a hollow inner cylinder. The assembly was rotated in the wind tunnel resulting in an almost uniform coating of ice being deposited on the inner cylinder. Then, the outer cylinder was rotated with respect to the inner cylinder until ice was shed. Two tests were performed: the first one used an inner cylinder made of aluminum, while the second used an inner cylinder made of steel. The data obtained for aluminum showed a strong correlation with both temperature and velocity; shear strength increased as temperature decreased, and velocity increased. However, the data for steel was unclear. A major drawback of using push tests on impact ice is that most of the tests existing in literature have been performed at speeds too low to be applicable to aircraft icing [24]. It should be noted that both cohesive and adhesive failures can be observed in many experiments [7,25]. The cohesive strength of ice in the temperature range relevant to aviation varies from approximately 100 kPa to 10 MPa [20]. Values of the measured adhesive strength vary from almost zero to the point where adhesive fracture is not observed due to preceding cohesive fracture. Indeed, in some experiments, traces of ice remain on the surface after the adhesion test. Thus, it is likely that the largest values of adhesion strength reported may be influenced by cohesive effects [20]. The inconsistencies in ice adhesive stress reported in the literature demonstrate: (1) the challenges associated with accurate measurement of ice adhesion, (2) the relatively poor state of understanding of the effects of traditional surface characterization parameters, e.g., contact angle, on ice adhesion, (3) the challenges associated with the handling of the samples, and (4) the difficulty associated with the preservation of the sample. Nevertheless, disregarding experimental differences between studies, some general trends can be recognized in literature [12]: 

Adhesive shear stress tends to increase on many materials when the test temperature decreases. The range is between 0.05 to 0.30 MPa as we move from -5 to -20°C. Other workers using alternative tests report larger values [26,27,28,29].



Adhesive shear stress slightly increases as the air velocity and particle/droplet momentum.



An increase in roughness results in an increase in adhesive shear stress.



Strain rate is an important factor that needs to be further investigated.



Influence of ice geometries on stress concentrations at the interface is accounted for using nonimpact ice.

droplet size increase, due to increased

IV. Approach A. Multi-scale Modeling Strategy Aircraft icing is a truly multiscale problem. The relevant icing processes occur at multiple spatial (three) and temporal (three) scales [30,31]. The effects of these scales must be considered in the development of a predictive model. 1) Ice nucleation of supercooled water is a process that occurs at the nanometer length scale, with size of critical nucleus being in the range of ~10-100 nm. The process is affected by intermolecular forces, interfacial energy, as well as nanoscale inhomogeneity on the substrate. 2) The ice profile formed by micron-sized impinging droplets is governed by processes that occur at the micron length scale (mesoscale). These processes include deformation, motion, and impact of droplets on a microstructured substrate and the concurrent heat transfer. 3) Icing on aerodynamic surfaces occurs at the macroscale at a time scale of minutes (traditional aircraft icing).

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We propose a relationship for the ice adhesion stress be expressed as ,…,

as a function of the various physical parameters that can ,

,…,

,

,…,

,

(1)

where 1, represent the relevant macroscale parameters, 1, represent the relevant 1, represent the relevant nanoscale parameters. The current effort seeks to microscale parameters, and combine different methodologies (experimental and numerical) at relevant scales to estimate this functional dependency. From conventional energy and mass balances, existing CFD models can be used to identify the effects of the icing environment (e.g. temperature, pressure, local humidity, wind shear, etc.). However, predicting stress-induced failure at the macroscale is extremely complicated and first principles-based modeling is not achievable at this time. Our modeling strategy is based on the hypothesis that the nano- and microscale adhesion strength parameters discussed above are manifested on the macroscale level. In other words, the quantities predicted by MD simulations at the nanoscale and mesoscale can be used as physics-based surrogate parameters for constructing an empirical macroscale model. The complexity in the dependence of ice adhesion strength on these surrogate parameters reflects the factors that were not included in the MD simulations (e.g. multiple-droplets; defects in the ice and surface structure, local strain conditions, etc.). These effects are incorporated through the fitting function of the macroscale ice adhesion stress obtained using the experimental data. Such an integrated approach leverages the capabilities of high-fidelity molecular modeling to identify and predict relevant physics-based surface parameters (often not readily accessible to experiments) and the relative computational simplicity of the empirical description of the experimental database to provide an efficient function that could be implemented in a code such as LEWICE [22,23]. The multiscale modeling strategy we employ consists of both predictive and empirical components, and balances fundamental understanding and practical applicability in modeling ice-adhesion at various length scales. Specifically, our multiscale approach consists of the following components: 1) MD simulations to provide the effects of microscopically well-defined surface parameters (e.g. molecular interactions, interfacial tensions, nanoscale structures, etc.,) on nanoscale mechanical properties of icesubstrate interface; 2) A mesoscale modeling scheme to provide the wetting and freezing kinetics of a single impacting droplet on the substrate; 3) An improved empirical model for predicting macroscale impact ice-adhesion strength, by incorporating quantities predicted in 1) and 3) as physics-based surrogate parameters for fitting to the experimental data. Appropriate parameters can be identified to incorporate into the multiscale model by investigating correlations between the experimentally-obtained macroscale ice adhesion data and the surrogate parameters obtained by analysis at the nanoscale and mesoscale. The key point is that the predicted surrogate parameters will be employed in the model, i.e., Eq. 1. As an example, instead of using contact angle as an independent variable in the fitting process, the calculated value of the selected microscale surrogate parameters could be employed. Several of the specific components of our model will now be briefly discussed. B. Determination of Macroscale Quantities An experimental approach is employed to determine the macroscale quantities of interest. All testing is done in the ice and COntamination REsearch (iCORE) facility at Airbus Central R&T (A-CRT). The iCORE facility consists of a closed-loop, primarily wooden structure (see Fig. 1 for a schematic and specifications). It is equipped with a centrifugal fan controlled by a frequency inverter. The air circulated within the wind tunnel is cooled by a triplecompressor system that regulates the temperature of the cooling fluid passing through the heat exchanger of the tunnel. An icing cloud is generated approximately 2 meters upstream of the test section. Three parallel horizontally aligned internal-mix air atomizing-nozzles generate individual full cones of droplets in the coaxial direction with the wind flow. The droplets are carried by the airflow through a converging section and into the test section. A pitot tube installed in the test section monitors the static pressure, total pressure, and total temperature of the air on-line. For further information on the iCORE icing wind tunnel, the reader is referred to Hauk et al. [32]. The in-situ testing protocol employed in this effort is the vibrating cantilever approach developed at A-CRT [33]. This test measures the shear stress at the interface between an accreted impact ice layer and a cantilever as shown in Fig. 2. The shear stress is applied by vibrating the cantilever with a fixed acceleration and sweeping the frequency until its resonant frequency is reached. When the interfacial shear stress due to cantilever bending exceeds the strength

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of the adhesive bond between the ice and the coating, the ice layer will delaminate from the cantilever (Fig. 3). The advantages of this facility relative to other ice accretion and adhesion test rigs are as follows: 1) Impact ice from supercooled water droplets can be accreted on a coated cantilever at the desired “environmental” icing conditions. 2) The adhesion strength of the impact ice can be measured at the same environmental conditions at which it was accreted, which minimizes exposure to thermal shocks. It is known that even a temperature difference of 1-2 °C can induce cracks at the ice/coating interface [34,35], thus degrading the reliability of the subsequent ice adhesion measurement. 3) An additional advantage of this approach is that it avoids mechanical handling of the samples as is done in many other ice adhesion test rigs. The debonding process is illustrated more clearly in Fig. 4, which shows an enlarged region of Fig. 3 (right) just prior to and at the moment of debonding that is synchronized with frames from high-speed video of the vibrating cantilever. These images clearly demonstrate that the strain increases significantly at ice-substrate delamination.

Type: Test section size: Wind tunnel atmosphere: Test section Mach number: Test section static temperature: Size of (supercooled) water droplets:

Closed or Open Loop 150x100x450 mm³ Air Up to 0.4 Down to -35 °C 40 µm – 250 µm (single, monodisperse) 10 µm – 25 µm (MVD, polydisperse)

Fig. 1 (left) overview of the components of the iCORE; (center) ice accretion on NACA0012 profile inside test section; (right) iCORE operating conditions and icing envelope (blue line).

Fig. 2 (left) Test section with electromagnetic shaker fixed to one side-wall; (center) internal view of test section with cantilever fixed between the two side-walls; (right) view onto a cantilever with accreted impact ice.

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Fig. 3 (left) Electromagnetic shaker viewed outside of the test section with fixed cantilever; (right) shear strain acquired by a strain gage on the backside of the cantilever versus time: cantilever vibration amplitude increases until the curve shows a sudden increase in strain corresponding to the initial debonding of the ice. The Euler-Bernoulli beam theory is used to determine an equation from which the maximum interfacial shear stress between ice and metal can be calculated [33]: | | 2 1 | |

2

where is the interfacial shear stress, is the strain measured by the strain gauge, is the Young’s Modulus is the thickness of the ice, is the thickness of the cantilever, is the linear position of the strain gauge of ice, with respect to the fixed end of the cantilever, is the length of the cantilever, and is the eccentricity of the neutral axis of the ice/metal beam with respect to the ice/metal interface. The experimental values that must be input into the equation are the ice thickness and the strain at delamination. All other values are either constant or approximated. The eccentricity of the neutral axis may be computed from: 2

2

where is the Young’s Modulus of the bulk cantilever material. To date, there is no standard method for the determination of the Young’s Modulus of artificial impact ice. For this reason, the Young’s Modulus of ice obtained in prior research for fully dense ice is used for shear adhesion strength calculation; that is, until a satisfactory method is developed for the determination of the modulus of the specific ice formed in the ice adhesion study. Ice modulus measurement is an ongoing component of the current effort. C. Determination of Micro-and Nano-scale Characteristics 1. Molecular Dynamics Simulations on the Nanoscale Mechanical Response of Ice-Substrate Interface to Shear The aim of the molecular dynamics simulations is to achieve a quantitative understanding, at the nanometer and micrometer length scales, of the failure mechanisms of ice-substrate interfaces under shear stress. The significance of the microscale model is that it predicts the icing profile of a single droplet impacting a substrate. Together with the “microscopic adhesion strength” obtained from nanoscale simulations, the ice adhesion strength at the single droplet level can be calculated. Ice-Substrate Interfacial Structure: The nanoscale ice-substrate interfacial structure will first be characterized in simulations. The structure is mainly controlled by the nanoscale wetting behavior of liquid water phase on substrates. For static cases, the wetting structure is determined by the water-substrate interfacial tension. For impacting droplets, the momentum of the droplets (of diameter ~20-50 m, velocity ~10-50 m/s) needs to be taken into consideration. The wetting profile depends on both droplet momentum and surface roughness (characterized by the arithmetic and the lateral correlation length ). By introducing a collective initial momentum to the liquid average roughness water phase, the wetting profile on a substrate can be obtained as a function of time using MD simulations. Coupled with heterogeneous ice nucleation kinetics, this allows determination of whether the droplet momentum is able to overcome the resisting capillary force to alter the ice-substrate interfacial structure.

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Fig. 4 Output from strain gauge sychronized with still frames from high-speed video. Strain increase occurs simultaneous to crack initiation and debonding at ice-substrate interface.

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Mechanical Response of Ice-Substrate Interface under Shear Stress: With the interfacial structure identified, we also investigate the mechanical response of the interface under shear stress. The shear stress is imposed in simulations by deforming the simulation box in the shear direction (at a certain strain rate). The stress-strain curve will be recorded during deformation, from which the failure stress can be identified. If there are no structural features at a longer length scale (e.g. microscale roughness, ice structural defects), the recorded shear stress at failure can be interpreted as the microscopic ice adhesion strength on a substrate. We plan to investigate in further detail the dependence of failure mode (“adhesive” vs. “cohesive”) on molecular interactions (e.g. van der Waals, covalent, electrostatic, and hydrogen bonding), as well as surface roughness. We will also determine the structural correlation length during stress failure, which measures the extent to which stress failure involves the ice structure further away from the substrate. It has been commonly assumed that ice shedding occurs “at” the ice-substrate contact. Such a macroscopic view does not account for the surface roughness and stress propagation in the solid state. The failure mechanism and stress revealed by simulations will help to identify the microscopic surface parameters most critical in determining the adhesion strength, which is beyond the reach of experiments. 2. Mesoscale Model of Ice Formation of Impacting Droplets on Substrates This modeling describes the phenomenon of a micron-sized supercooled droplet impacting a substrate and the concurrent thermal and nucleation processes during the spreading and retraction stages of droplet impact. Three submodels will be employed to integrate ice nucleation theory with heat transfer and fluid dynamics: Droplet Impact Dynamics Model: This submodel predicts the spreading and retraction dynamics of a droplet impacting a surface. Upon impact, the droplet tends to spread and penetrates the surface microstructure because of inertia. The maximum spread and penetration can be determined by assuming the conversion of all inertial energy into surface interfacial energy under the constraint of conserved volume. It has been experimentally observed [36] that pinning and freezing of the droplet occur during the retraction stage. Thus, the motion of air-droplet interface needs to be tracked during the retraction. Heat Transfer Model: During the time interval over which the droplet spreads and retracts, heat will be transferred from the droplet to the substrate. The temperature profile at time t can be calculated using the “heat equation” based on the wetting profile at t. A first-order approximation regarding heat transfer can be made considering the fact that the droplet is in a supercooled state. In this condition, ice formation proceeds rapidly as soon as the nucleation activation barrier is overcome. Therefore, heat transfer plays a secondary role in driving ice formation compared to the heterogeneous nucleation initiated by the substrate. Heterogeneous Nucleation Model: With the wetting and temperature profile determined as a function of time in 1) and 2), an ice nucleation model can be used to determine the ice formation in a single droplet during its retraction on the substrate. Given that the degree of supercooling of droplets, typically -5C to -15C, which is “shallow quenched” in comparison to the spinodal limit of pure liquid water (-39C), the classical heterogeneous nucleation theory should be applicable. From here, we can proceed with two levels of complexity. For the more general case, the onedimensional freeze front propagation model [37] can be used together with the nucleation rate model to predict the extent of ice formation during droplet retraction. But even with this model, direct comparison with experiments is problematic because of undetermined constants in the model. Alternatively, we can make approximations based on existing experimental observations. Experiments [36] show that for ~mm sized droplets the time from onset of nucleation to completion of freezing is ~s. For a ~10m droplet this time will be in the order of 10-6s. On the other hand, the nucleation time is a weak function of droplet volume but strongly depends on the temperature and the free energy barrier. For practical purpose, both the environmental temperature and the activation energy (types and numbers of nucleation sites) exhibit variations. We therefore expect that droplet either freezes “instantaneously” upon spreading on the substrate or retracts to recover the state of minimum surface interfacial energy.

V. Results A. Experimental Ice Adhesion Data The icing conditions considered to date are shown in Table 1. Nine surfaces, characterized in Table 2, were tested using the vibrating cantilever method. Two anodized aluminum and titanium samples were designated as hydrophilic, hydrophobic, or superhydrophobic based on their interaction with water droplets. Despite the higher roughness measurements of the superhydrophobic “TiO2-nanotubes w/ Episurf” surface, it was the only surface to yield a value less than 90° for water roll-off-angle using a 5-µL droplet. The polyurethane surfaces showed mid-range water contact angles. The highest water contact angle on polyurethane was for “Polyurethane Coating 5, structured” in the direction perpendicular to the artificial surface structures. 9

Fig. 5 shows the results of the ice adhesion test for the samples mentioned above. The reference surface results are coloured in red. The results are discussed below grouped as metal surfaces without/with Episurf (reference, hydrophobic, and superhydrophobic) and polyurethane surfaces. The “hydrophobic old” sample refers to an aluminium cantilever which was functionalized with the silane coating, Episurf, seven months prior to being tested for ice adhesion, whereas the sample designated “hydrophobic” was a separate cantilever with the same treatment but tested two months following surface treatment. Table 1. Icing wind tunnel test conditions.

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Icing conditions

Total Air Temperature (TAT)

Airspeed

Liquid Water Content (LWC)

Ice type

(°C)

(m/s)

(g/m )

(µm)

(mm)

Rime

-20

50

0.3

20

4.55

1.0

Mixed/Rime

-20

50

0.8

20

4.55

0.55

Mixed/Glaze

-5

50

0.3

20

4.55

0.7

Glaze

-5

80

1.0

20

4.55

0.2

3

Mean effective droplet diameter (MVD)

Ice Approx. Thickness Freezing Fraction

1. Reference, Hydrophobic, and Superhydrophobic Surfaces Ice adhesion on the reference surface was on average in the range 40 kPa – 60 kPa. For the rime and mixed conditions, the hydrophobic surface showed lower ice adhesion strengths than the reference surface, and the superhydrophobic surface showed much lower adhesion strengths than the reference anodized aluminum sample. Under the glaze ice condition, however, the behavior was reversed. The relatively high adhesion strength on the superhydrophobic surface under glaze ice conditions is believed to be caused by the high surface roughness. Unlike low-impact energy droplets, the higher impact velocity droplets tend to engulf small surface structures which would, under less severe conditions, result in a Cassie-Baxter state. The influence of impact energy is more evident under glaze ice conditions where droplets take more time to freeze than in rime ice conditions, and therefore have more time for mobility; that is, more time to penetrate surface troughs and form stronger mechanical grips onto the surface. 2. Polyurethane Coatings Six different polyurethane coatings were tested; however, only three icing conditions were considered due to time constraints. The coatings did not appear to differ noticeably from each other in terms of ice adhesion strength, except for “Polyurethane 2,” which showed slightly higher values than the reference surface for both mixed/rime and glaze ice conditions. One of the coatings, “Polyurethane 5” was included to study the effects of surface structure on the adhesion strength. The structured surface had more surface area in contact with ice; therefore, it was expected to exhibit higher adhesion strengths than the non-structured version. On average, and considering the range of data measured, roughly the same adhesion strength was seen on both the structured and non-structured surfaces. High-speed camera images revealed that ice never actually separated from the structured surface as it did from the non-structured surface, but the ice did separate from itself. Such observations are evidence of cohesive failure in the ice at its surface where its ultimate tensile stress was reached before the ultimate shear stress was reached at the ice/substrate interface. Since the ultimate tensile stress of ice is difficult to predict, it is of interest here to study the influence of ice thickness on the measured shear strength results. The goal is to identify if and, if so, for what range of ice thicknesses does cohesive failure become the dominant failure mode. 3. Potential Sources of Experimental Error The cause of the largest deviations in the results is in the experimental conditions. The most common is error in equipment operation or equipment malfunction. Specifically, water could freeze in the water-feed line to the air

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atomizing nozzles causing an imbalance in water pressure to the three nozzles and produce a non-uniform spray. This event results in an unpredictable liquid water content, which influences the density and modulus of the ice formed. Table 2. Sample surface roughness and water interaction angles. Average Roughness, Ra (µm)

Peak-toPeak Roughness, Rz (µm)

Water Contact Angle (°)

Water Rolloff-Angle (°)

AL2024 Anodized1 (Reference)

0.01

0.2

59.3

>90

AL2024 Anodized w/ Episurf2 (Hydrophobic)

0.01

0.2

110.2

>90

TiO2-nanotubes w/ Episurf (Superhydrophobic)

0.58

4.40

165.7

24

Polyurethane Coating 1

0.613

3.761

82.3

>90

Polyurethane Coating 2

0.507

3.279

89.5

>90

Polyurethane Coating 3

0.007

0.037

72.9

>90

Polyurethane Coating 4

0.006

0.037

68.6

>90

Polyurethane Coating 5, non-structured

0.22

1.40

71

>90

Polyurethane Coating 5, structured

21

42

69 / 116

>90

0.006

0.061

101.9

>90

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Material and Surface Description

Polyurethane Coating 6 1 2

Tartaric Sulfuric Acid anodization. Commercially available perfluoropolyether phosphonate compound in a HFO solvent.

The size of water droplets that freeze on the surface plays an important role in shear ice adhesion strength. Small water droplets trapped as humidity in the air surrounding the substrate can freeze on the surface and act as nucleation and anchor points for ice. Precautions were taken during wind tunnel operation to lower the relative humidity of air circulating in the wind tunnel prior to freezing by using a slow cooling rate; that is, air would be circulated in the wind tunnel for 5-10 minutes between +5 °C to +10 °C prior to going below 0 °C. In addition, a humidity casing was designed to fit over the test section wall where the cantilever was held to prevent warm air in the room from entering the tunnel. A negative effect of introducing warm air is that ice could melt at the ice/substrate interface, which would significantly influence the test. Under test conditions, improper sealing of the humidity cover resulted in thick frost build-up in the port of the test section wall where the cantilever passed through. The frost build-up was sufficient to obstruct the motion of the cantilever. In some cases, the frost was not visible from outside the test section but could be detected in the strain gauge data by a slight bias to negative or positive strains. There was some concern about fatigue failure in the ice. Delamination typically occurs after less than 4 x 103 cycles, but with only 101 – 102 cycles at the frequency of interest, i.e., the frequency where the deformation is “large.” At low forces, the number of cycles experienced during this vibration test is not in the range typical of fatigue failure in ice [38].

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Fig. 5 Ice adhesion shear strength database developed to date. 4. Empirical Model for Ice Adhesion Stress The ice adhesion stress data is employed with multiple linear regression [39] to produce a purely empirical model. The first step is to perform a sensitivity analysis to determine which variables should be included in the surface fitting. We note several general trends: (1) the adhesive stress increased with increasing liquid water content, surface temperature, and droplet velocity; (2) the adhesive stress decreased with increasing contact angle and freezing fraction; and (3) the relationship between adhesive stress and surface roughness was mixed. It was also noted that that data were obtained at only three partial conditions for liquid water content and only two conditions for surface temperature and droplet velocity. For this reason, and because the trend for surface roughness was not clear, the independent variables taken for the surface fitting were contact angle and freezing fraction. Multiple Linear Regression (MLR) [39] is a statistical technique that uses several explanatory variables to predict the outcome of a response variable. The purposes of the MLR are three-fold: (1) model a relationship between the response variable and explanatory variables (regressors) , , … , ; (2) predict based on the regressors , , … , ; and (3) screen the variables , , … , to determine which variables are more important for explaining the dependent variable so that the causal relationship can be determined more efficiently and accurately. Fig. 6 shows a surface fitting of the interfacial shear stress as a function of the freezing fraction and contact angle. The resulting equation is 99.8918

0.2641

27.6085

(3)

is the adhesive stress (kPa), CA is the contact angle (degrees), and n is the freezing fraction where (nondimensional). While the shear stress does correlate to a certain degree with those variables, it still does not correlate well enough to produce a good fit. One reason for this could be that, while shear stress may linearly correlate with contact angle, velocity, surface temperature, and liquid water content, it does necessarily correlate with those variables in the freezing fraction. Another reason could be that these variables do not correlate linearly, but rather nonlinearly, in a function that can be determined from the experimental data once more is available. B. Nanoscale Characteristics based on MD Simulation Results In this section, we focus on simulation of the wetting behavior at droplet impact and briefly introduce simulation of fracture at an ice-substrate interface, both of which are being performed to gain an understanding of these phenomena at the nanoscale. Recall that our strategy is based on correlating measured macroscale properties with computed nanoscale surface characteristics and chemical composition. Although not described here, we performed an extensive verification and validation study to determine which atomistic force field was most appropriate for the simulations in question. Based on these results, we selected the TIP4P/Ice model [40], which is used in the simulations described below. All MD simulation were performed using the LAMMPS (Large-scale Atomic/Molecular Massively Parallel Simulator) package [41]. More details regarding the simulations and other results are contained in Afshar et al. [42]. Graphene was employed as the substrate in both simulations because of the availability of a well-defined force field. 12

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Fig. 6 Linear least-squares surface fitting of interfacial shear stress as a function of contact angle and freezing fraction. 1. Wetting Behavior of Supercooled Droplets on Nanostructured Substrates The in-flight icing conditions encountered in aviation involve droplets impacting a substrate at high speed. The resulting ice-substrate interfacial structure, especially in the case of a structured substrate, affects the ice adhesion strength significantly. Studies have found that initially icephobic surfaces can become icephilic once exposed to impinging water droplets. The reasons behind this change are unclear; however, it is generally understood as being the result of a different wetting behaviour exhibited by impinging droplets. This difference is attributed to the high momentum of the droplets, which enables them to overcome the surface energy barrier leading to a larger watersubstrate contact area. The objective of this task is to develop a simulation protocol that allows us to elucidate in a quantitative manner the dependence of wetting behaviour of supercooled water droplets on the impingement velocity, substrate structural features, and substrate chemistry. Fig. 7 schematically shows the system studied in our wetting simulations. Details of simulation methods are provided in the Appendix. Penetration Profiles: Fig.8 shows snapshots taken at different times during a wetting simulation with graphene block distance d=50 A. Clearly, after impinging droplet comes into contact with the substrate, a water front develops between the two graphene blocks. This water front penetrates deeper into the substrate with simulation time. If we define the penetration depth to be the largest value of the coordinate for all water molecules (a more sophisticated way of measuring is under development) and plot it as function time, a typical penetration curve is obtained as shown in Fig. 9. All penetration curves obtained from the simulations can be fit reasonably well by linear functions. characterizes the extent of initial Two quantities can be derived from such linear fittings. The intercept parameter penetration by water within a short period of time immediately after droplet comes into contact with the substrate. The characterizes the penetrating velocity of water, i.e., the apparent velocity of the water front slope parameter moving between graphene blocks. In the next sections, we discuss the effects of impinging velocity, temperature, and and . substrate structure on Effects of Impinging Velocity : Fig. 10(a) shows the initial penetration depth as a function of impinging velocity at two temperatures. It shows that at 0.1 and 0.5, is measured to be on the order of the size of one water molecule, while at 2 , significant initial penetration is achieved with increasing to ~5 water molecule sizes. The increase in with exhibits a threshold character, i.e., there seems to be a threshold value of over which strong initial penetration is observed. More simulations will be required to allow a more informed conclusion on why and what value the threshold limit is. Fig. 10(b) depicts the effects of on the penetrating velocity for two droplet temperatures. First of all, for all systems studied in our simulations, the penetration speed is found to be ~10 times smaller than ! At both temperatures, the variation in is ~ 0.1m/s as

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increases from 0.1 to 2. Furthermore, results from the two studied temperatures exhibit somewhat opposite trends. This may indicate that variations in reported in Fig. 10(b) are likely due to uncertainties in our measurements (e.g. the method used in identifying the water front. A better and reliable way of defining penetration is under development). Nevertheless, the three-order magnitude difference between and implies that has a fairly weak dependence on (if at all), and plausibly, the motion of the water front in-between the graphene blocks is controlled mostly by thermodynamic effects (such as interfacial tension, fluid viscosity, etc.) that does not depend on the initial velocity.

Fig. 7 Schematic showing the setup for our wetting simulations.

Fig. 8 Snapshots taken from simulations showing penetration profiles of water into blocks of graphene sheet at different times. The simulation condition is . , T=250 K, 265 K, and d=50 A.

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Fig. 9 A typical penetration curve measured from simulations, showing variation of penetration depth H (see text for definition) with simulation time. Effects of Droplet Temperature: The effects of droplet temperature can be inferred by comparing the two curves shown in Fig. 10(a) and (b). Fig. 10(a) suggests that droplet temperature only has a small effect on the initial (again, the difference in may be due to uncertainties in measurements). This is a physically penetration depth intuitive outcome in the sense that during the short period of time at the beginning of droplet penetration, it is the ) that plays the determining role rather than thermodynamics. On the initial momentum of droplets (related to other hand, temperature has a significant effect on the penetrating velocity as shown in Fig. 10(b), showing an increase in (by ~3 times) as increases from 250 to 265K. Thus, is mostly controlled by thermodynamic effects rather than initial momentum. In this case, the increase in is likely a result of lower viscosity of the fluid at the higher temperature. The interfacial structure (molecular structure of the contact layer between water and graphene) may also contribute to this increase. 2. Characterization of Fracture at Ice-Substrate Interface The “ice adhesion strength” reported in experiments is often based on macroscopic measurements, meaning that obtained values are influenced by phenomena at multiple length scales. Measurements are often found to be inconsistent and scattered [43]. Atomistic scale simulations of ice fracture at an interface offer the potential for direct correlations between the mechanical properties and various molecular-scale parameters. Therefore, we want to develop a simulation protocol that can be used to probe the fracture mechanism at the ice-substrate interface at the nanometer length scale under various loading conditions. Fig. 11 shows the schematic of the system setup used in this study for simulating fracture of ice layer at icegraphene interface. Please refer to the Appendix for details of simulation method. The MD simulation results indicate that there exists a region in the vicinity of the water-graphite interface where ice crystal structure is disrupted (Fig. 11), showing reduced order parameter but high number density. The stress distribution analysis suggests that stresses are concentrated in this disordered interfacial region, and therefore its structure has direct effects on measured adhesion strength. Fig. 12 shows the ice adhesion strengths on graphite substrates with different grooves widths measured from MD simulations. More details regarding this simulation, as well as results, are included in Afshar et al. [42]. C. Ongoing/Future Work 1. Ice Adhesion Testing In addition to expanding the test matrix to include additional icing conditions and surface treatments, several issues identified during testing will be investigated. Investigate influence of ice thickness: In the vibrating cantilever ice adhesion test, strain gauge data reveal both the time when there is a sudden change in the stiffness of the ice/metal composite cantilever and the strain value at that moment; that is, the crack initiation time and strain. It does not, however, reveal the crack propagation vector. Depending on where the crack initiates, the mode of failure could be either adhesive or cohesive. In some cases, it is believed that the thickness of accreted ice may have an influence on the mode of ice fracture detected and measured; 15

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particularly for surfaces where a large interfacial shear strength is expected. A systematic study of the influence of ice thickness on the results of the vibrating cantilever ice adhesion test is planned.

Fig. 10 Effects of impinging velocity

on (a) the initial penetration depth , at T=250, 265K, and d=50A.

Fig. 11 A simulation snapshot showing the system setup of ice fracture simulation.

, and (b) penetrating velocity

Fig. 12 Ice adhesion strength on graphite substrates with structured grooves of different width d, measured at T=250 and 265K.

Estimate Young’s modulus for impact ice: Eq. 1 requires a value for Young’s modulus of the accreted ice; however, this value may differ from that for nonimpact ice. The natural frequencies of a composite cantilever may be calculated using the expression for a homogenous beam with equivalent mechanical properties. Values for the equivalent mechanical properties may be found by determining the first natural frequency experimentally. Afterward, the modulus of the ice may be determined. Since both the ice density and the elastic modulus are used to calculate interfacial shear stress, it is of interest for the study of ice adhesion strength to know those properties of each individual ice formation. 2. Multiscale Modeling and Simulation Having established initial simulation protocols, these protocols will be employed to perform simulations to investigate the behavior of ice accretion on a substrate. These investigations will inform the development of the hybrid technique for estimating the adhesive stress, which is based on a correlation between observed macroscopic parameters and computed microscopic and nanoscopic quantities, as well the initial development of a multi-scale, purely physicsbased approach.

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Conduct systematic simulations based on the developed simulation protocols:  Study other types of substrate materials, larger systems, and two-dimensional substrate structures.  Simulate ice crystallization on substrates of different chemistry and nanoscale structure to probe the equilibrium ice-substrate interfacial structure.  Conduct nonequilibrium simulations under shear and tension loading conditions to characterize fracture mechanisms using the obtained equilibrium structures as inputs.  Simulate of wetting behavior of impinging droplets on substrates of different chemistry and nanoscale structure. Identify the principle nano- and micro-scale parameters: The quantitative correlations between these computed parameters and measured mechanical strength of ice-substrate interfaces will be investigated. These correlations will be employed to develop a hybrid empirical/physics-based relationship that includes the effects of macroscale, microscale, and nanoscale parameters.

VI. Conclusion The current effort represents an attempt to estimate the adhesion stress of impact ice for aeronautical applications. Computing the adhesion stress from first principles is not currently a tractable problem due to computational hardware limitations. To circumvent this shortcoming, our approach seeks to combine experimental, numerical, and analytical techniques to develop a functional description of ice adhesion stress using parameters at multiple length scales. Our underlying hypothesis is that the effects of characteristics at the nanoscale and mesoscale are manifested in measurable macroscopic variables such as adhesion stress. These microscopic parameters that characterize the surface and the accreted ice, while not easily measured, can be estimated using MD simulations. What remains is to identify the mechanism for coupling these easily predicted microscopic quantities with the currently impossible-to-predict macroscopic adhesion stress. In this, our first attempt, we are using simple correlation; however, we believe that the understanding obtained from this effort will lead to improved models with less empiricism in the future.

Appendix Wetting Simulation Protocol: In each wetting simulation, graphene blocks are created by stacking multiple layers of graphene sheets along the z direction with an interlayer distance of 3.5 A. A vacuum is introduced between adjacent graphene blocks to mimic the nanoscale “roughness” of a substrate. Structural properties of such created substrates and h , and block height can thus be characterized by four parameters, block separation distance , block width . In our simulations, we fix 5 nm, 5 nm and , where is simulation box size along the y dimension, while is varied from 1~10nm. A layer of water molecules is introduced at a distance of 2 nm away from the top layer of graphene sheets along the direction. The water layer is created in a way that under the periodic boundary condition it recovers bulk water properties along y and z directions. This is necessary given that the droplet size of interest is in the order of 5~20μm, which is 10 ~10 times greater than our simulation box size. Therefore, the unnecessary vacuum-water interfaces at simulation length scale need to be removed to prevent their interference on the wetting behavior. In performing simulations, an nPT ensemble is used with pressure and temperature fixed at desired values using a Norse-Hoover style baro- and thermostat. In order to simulate an impinging water droplet, is added to all water molecules on top of the thermos-velocity at the beginning of an initial collective velocity simulations. In the results below, the collective velocity is expressed in terms of a nondimensional Mach number. The motion and distribution of water molecules are then tracked during simulations that facilitates the characterization of wetting behaviors such as water density profiles and water penetration velocities. Fracture Simulation Protocol: In each fracture simulation, an Ih ice layer pre-equilibrated at 250 K is placed on top of a substrate made of graphene sheets. Extra care had been taken to ensure that the size of the Ih ice layer along and the lateral dimensions (y and z) are the same as that of graphene sheets (which equal to simulation box size ). This is necessary because we aim to investigate fracture of an ice layer with a bulk property along the lateral dimensions. Furthermore, it is also important to relax the initial stresses induced by placing the prefabricated graphene and ice layer into contact. For this purpose, the region of the ice layer that is located within 1 nm from the graphene sheet is melted and then brought into supercooled state at 250K. A pre-developed “seeding” protocol is then applied to the system to induce crystallization in the interfacial region “naturally” at a constant pressure. In this way, stresses artificially introduced during the initiation of the simulation will be removed.

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Acknowledgments D. S. Thompson, D. Meng, A. Amir, R. Bassou, and J. Zong acknowledge the support of NASA Glenn Research Center through the Advanced Aircraft Icing Subproject of the Advanced Air Transport Technology (AATT) Project (Cooperative Agreement NNX16AN20A, Richard E. Kreeger Technical Monitor). The support of the MSU Center for Advanced Vehicular Systems is also gratefully acknowledged. E. Bonaccurso, A. LaRoche, and V. Vercillo acknowledge the support of the European Commission Horizons 2020 program (Project Phobic2Ice, Grant Agreement 690819, H2020-MG-2015).

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