1 Introduction

In the last few decades, the need for a reduction in carbon emissions has led to developments in various areas of renewable energy production and in particular, onshore and offshore wind turbines. One area of particular concern with these turbines is their expected lifetime, including how much their output can be expected to decrease over time and how often maintenance and repair of the turbine blades is required. A major source of this degradation arises from erosion to the leading edge caused by forms of precipitation such as rain and hail, and this erosion can potentially have significant effects on the aerodynamic efficiency of the turbine blade—for example, wind tunnel testing has shown that roughness on the leading edge can increase aerodynamic drag by as much as 500%, with a significant loss in lift also measured, resulting in a loss in output of as much as 25% [1]. Since this results in a decrease in the turbine power output, it is of great interest to study the erosive effects of precipitation on typical wind turbine blade materials and coatings in order to predict and potentially mitigate this loss in output.

Whilst rain erosion on wind turbine blade materials has been studied in some depth [2], the effect that years of repeated hail impact could have on the leading edge of a wind turbine blade has not received the same level of study. Most of the experimental and modelling-based research into ice impact on composite material surfaces comes from the aerospace sector, where large ice particles pose a significant threat to the aerofoils used in vehicle wings. Kim et al. [3] performed an experimental investigation of hail impact using a gas cannon setup to fire Simulated Hail Ice (SHI) of multiple diameters at both a force transducer and a composite plate in order to probe both the impact mechanics of the ice sphere and the response of the composite material to the impact. In this work the authors also investigate the failure threshold energy (FTE) of the composite material, i.e. the minimum kinetic energy of a projectile that causes damage in the material, finding that smaller diameter hailstones result in a smaller FTE, as the impact force acts upon a smaller area of the target material. The experimental work of Tippmann et al. [4] is also noteworthy in that it includes detailed high-speed camera frames of multiple ice impacts, allowing the impact behaviour of the projectile to be seen in detail, including the way the sphere cracks and eventually shatter during the timescale of the impact.

The objective of this work is to use numerical modelling methods in order to greater explore the mechanics of a hailstone impact and how various parameters, such as projectile velocity, angle, and radius, of the impact affect the composite material response. The modelling method that has been chosen to tackle this problem is to use a Smooth Particle Hydrodynamics (SPH) approach to modelling the hailstone, which has been shown [5] to be advantageous to the use of solid elements both in terms of accuracy and computation time. The ice material model used is one introduced by Carney [6] that includes the significant dependence of the material behaviour on strain rate—an aspect that is very relevant when considering projectile impacts, where very high strain rates are observed—together with modifications as used by Tippmann [4]. A more in-depth description and discussion of this modelling method, as well as the results of preliminary test simulations, can be found in [7, 8].

This modelling method was used to simulate hail impacts under a range of impact conditions and parameters, with one parameter of particular importance being the diameter of the simulated ice projectile. In order to best reproduce the conditions found in real wind farms, the simulations will focus on projectiles of diameter less that 20 mm, since the majority of hailstones found UK weather events fall within that range [9]. The collected data can be used to produce maps of how various quantities measured from the simulation change with these parameters. It is intended that these maps, along with other data from the simulated impacts, can shed more light on the fundamental impact physics of a hailstone impact and allow us to better predict long-term damage to wind turbine blade materials as a consequence of hail precipitation.

2 Simulation Methodology

In order to explore the physical mechanism of a hail impact on a wind turbine blade, a simulation model was created in LS-DYNA, similar to that described in previous work [9], employing an SPH mesh together with the material model from Tippmann [4]. The ranges of the impact variables—projectile diameter, velocity, and impact angle—to be focussed on were chosen to be typical values seen in realistic hail impact scenarios. For instance, ice projectiles with diameters of 5, 10, 15, and 20 mm were simulated, as this is the range of hailstones most commonly seen in the UK and similar climates, with the larger end of this range giving rise to more characteristic impact physics. Initial impact velocities were also chosen to be approximate to the relative velocities between hailstones and turbine blades commonly seen. The impact angle was set via the ice sphere’s initial velocity components, with the initial velocity in the z-direction equal to the impact velocity multiplied by the cosine of the impact angle, and the velocity in the x-direction likewise with the sine of the impact angle.

When simulating the ice projectile, an SPH mesh containing approximately 40,000 nodes was determined to be sufficient for accuracy, whilst still resulting in a sufficiently low computation time. The composite material was chosen to be a 100 × 100 × 10 mm plate of a glass fibre composite, with the LS-DYNA material model MAT_COMPOSITE_DAMAGE. This material model allows for four different mechanisms of failure within the composite material, following the theoretical formulation of the Chang–Chang damage model of composites [10]. The bottom nodes of the solid mesh were given a boundary condition constraining their movement in all three directions, in order to prevent the sample moving during the impact.

3 Results

The completed simulations were analysed with LS-PrePost, with two particular outputs chosen in order to best illustrate how the impact mechanics and the subsequent material response changes over the impact parameters being studied: the peak deviatoric (Von Mises) stress observed in the material over the timescale of the impact, and the peak material strain in the x-direction over the impact. The maximum V-M Stress and X-Strain values present in the material over the first 200 ms of the simulation are shown plotted in Figs. 1 and 2, respectively, for a chosen illustrative example impact scenario of a 15-mm diameter projectile impacting the sample at 80 m/s at 90°. It can be seen that in this case, as is for the other simulated impacts, that the peak material response is seen during the very initial part of the impact, before most of the projectile has made contact with the surface—a frame from the simulation taken at the moment of peak V-M stress from the example simulation is shown in Fig. 3.

Fig. 1
figure 1

A chosen illustrative example impact scenario of a 15-mm diameter projectile impacting the sample at 80 m/s at 90° for maximum of effective stress versus time

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Fig. 2
figure 2

A chosen illustrative example impact scenario of a 15-mm diameter projectile impacting the sample at 80 m/s at 90° for maximum of X-strain versus time

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Fig. 3
figure 3

A frame from the simulation at the moment of peak V-M stress

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Contour plots of the maximum observed Von Mises stress as a function of impact velocity and projectile diameter for six values of impact angle are shown in Fig. 4a–f showing significant differences as a function of impact angle. Impact angle variation was also observed for the maximum observed X-strain as shown in Fig. 5a–f. In order to better illustrate the nature of the evolution of the forces in the material directly following the beginning of the impact, the Von Mises stresses present at the impacted surface is shown in a colour plot at six different times, spaced 1 μs apart throughout the first 5 μs of the impact, as shown in Fig. 6a–f.

Fig. 4
figure 4

a–f Contour plots of the maximum observed Von Mises stress as a function of impact velocity and projectile diameter for six values of impact angle from left to right. a 90 degrees, b 75 degrees, c 60 degrees, d 45 degrees, e 30 degrees, and f 15 degrees

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Fig. 5
figure 5

a–f Fig. 4a–f shows contour plots of the maximum observed X-strain as a function of impact velocity and projectile diameter for six values of impact angle from left to right. a 90 degrees, b 75 degrees, c 60 degrees, d 45 degrees, e 30 degrees, and f 15 degrees

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Fig. 6
figure 6

a–f Von Mises stresses present at the impacted surface is shown in a colour plot at six different times, spaced 1 μs apart throughout the first 5 μs of the impact. a 0.5 μs, b 1 μs, c 2 μs, d 3 μs, e 4 μs, and f 5 μs

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4 Discussion

The results have indicated that at the lower-velocity impacts, the material response varies linearly with diameter and velocity. However, at higher velocities, more complicated behaviour arises due to the interaction between the initial stress wave and the remainder of the impacting projectile. Hence, this indicates two distinct regime transitions for the material as indicated by the simulation process.

It is expected that higher-velocity impacts and those with larger projectiles will result in larger induced stresses in the material, since these projectiles impart greater momentum to the composite material. It can be seen from the impact map plots, Figs. 4 and 5, however, that the variation in both observed peak stress and strain in the material with these parameters is far from simple, with particularly complex behaviour seen in the impact of 15 mm and 20 mm diameter projectiles at the various impact angles. This pattern has important implications for design of materials for resistance to hail erosion impact as very different behaviour is observed at the various impact angles. It should be noted furthermore that this is the first attempt to develop such maps for hail impact using theoretical methods.

A possible explanation for this behaviour is how the impacting projectile as illustrated in Fig. 3 interacts with the shockwave from the impact. During the initial phase of the impact, a shockwave is created travelling outwards from the initial impact point, as can be seen in the illustrative example simulation in Fig. 6a–f. Whilst this wave is travelling outwards, the remainder of the projectile begins to make contact with the material, imparting further energy to the material at that point. The energy dissipation processes can be clearly observed over the given time interval. It can be seen that under certain conditions, the outward travelling wave and the still impacting ice material form a larger total stress in the material.

The scenario modelled in the simulations presented involves an impacting ice projectile that is monolithic, i.e. a sphere consisting of a single, continuous solid with constant mechanical properties throughout. Real hailstones have been shown to not conform to this property, instead being composed of multiple radial layers of ice with slightly different compositions, around a central core, marking different stages of the hailstone formation process within a storm cloud [11]. Essentially this “onion like” configuration presents challenges to modelling the solid particle impact of such materials. This property has potential to significantly alter the impact properties of the hailstone, by changing the way the impact energy dissipates through the projectile. Further modelling work aiming to properly simulate this layered hail particle, and to determine what effect this has on the impact properties and therefore, the forces arising within the target material, is recommended.

This work only simulates the impact on an uncoated glass fibre composite plate. Wind turbine blades in use are often treated with some coating, usually a gelcoat or paint consisting of one of a number of materials [12]. The purpose of this coating is primarily to provide some degree of protection against wear and erosion caused by atmospheric conditions, including precipitation. However due to the relative lack of literature treating the impact of hail on wind turbine blades, it is possible that one or multiple hailstone strikes have the potential to cause damage to the surface of the coating, allowing impingement of rain and potentially causing the formation of incubation sites, speeding up the rain erosion process.

Other outcomes of the hail impact process could also affect the resistance of the blade to rain erosion, such as delamination of the underlying composite material layers [13], which was found as a result of aerospace sector experimental ice impact tests [3]. It is felt that further insight into this potential synergistic wear effect is necessary to fully understand and quantify the threat that hailstorms pose to the lifetime of wind turbine blades.

It should be noted that due to limitations in the version of LS-DYNA used in this analysis, the models used were limited in the total number of elements. This, together with limitations in available computing power and computational time, resulted in difficulties in reaching a satisfactory level of convergence. One area that further work in this area will focus on is to verify that this result holds whilst using a larger number of elements to represent the impacted material.

5 Conclusion

The general background and goal of predicting erosion in composite materials undergoing impact with ice projectiles has been outlined, with reference to the literature and already completed experimental and modelling work in the area. In order to better understand the potentially complex physics of such an interaction, this work aimed to characterise the response of the composite material during such an interaction. The method of modelling the impact, adapted from well-established techniques in this and similar areas of study, was described.

From these simulations two sets of impact maps were created, showing the peak deviatoric (Von Mises) stress and directional strain observed in the simulated composite material over the timescale of the impact. These maps showed a more complicated dependence on impact velocity and impact angle than expected, with potential explanations of this behaviour, involving the initial shockwave through the material caused by the impact, presented and discussed.