Complex damage mechanisms and roughness evolution of wind turbine blade surface: Multiphysics and stochastic effect modelling

Leading edge erosion of wind turbine blades is the most often observed damage mechanism of wind turbines. The surface erosion of blades is influenced by many multiphysics and stochastic factors including humidity and related degradation processes, rough uneven surface and roughness development, random defects in the materials. In this paper, the effects of these factors and possibilities of their computational modelling and prediction are discussed. Competing damage mechanisms in erosion, including debonding and impact damage, as well moisture ingress and weathering are investigated. A predictive model for roughness evolution of leading edge due to the surface damage is presented.


Introduction: Modeling of leading edge erosion beyond mechanistic analysis
Leading edge erosion of wind turbine blades is one or the main challenges compromising the development of the wind energy.In order to mitigate the blade erosion, and to find solutions to protect blades, detailed understanding of the erosion mechanisms and predictive models of erosion are necessary [1]- [3].
The main erosion mechanism is largely the material destruction, controlled by small scale impacts (by rain droplet, hail), stress wave propagation and material fatigue processes.That is why the majority of computational models of erosion are based on the methods of continuum mechanics, damage, fracture and fatigue theory [1], starting from the classical Springer model, and up to complex multi-element numerical models, considering liquid/solid contact, 3D stress wave propagation, viscoelastic materials behaviour and random fatigue [2]- [5].At the same time, leading edge erosion is a complex multiphysics process, which is strongly influenced by the many physical, stochastic effects(see schema Figure 1): • Materials structure: Micro-and nanoscale structure of the blade coatings, including the polymer chain behaviour, non-linear viscoelastic behaviour, internal structure of coatings, • Environmental effects: humidity, moisture flow, ultraviolet radiation, • Stochastic effects: rain scenario, material defects, roughening of the surface.
A solution of the blade erosion problem has to take into account these complex physical processes, going beyond the limits of classical materials mechanics and fracture/fatigue theory.In this paper, computational modelling of some of these effects is discussed.2. Environmental effects: moisture, temperature variations, radiation

Effect of environmental loading
Wind turbine blades are subject to both mechanical loading and environmental loading, including high humidity, temperature variation and ultraviolet (UV) radiation.These effects change material properties, interact with mechanical loads and reduce the lifetime of coatings.Combined mechanical loads, high humidity, and temperature variations can result in residual strain in coatings, hygroscopic swelling in polymers, reducing the materials strength and modulus, and eventually leading to debonding/delamination [6]- [8].The moisture diffusion in the polymer coatings can create the properties gradient in coatings.UV-radiation can cause photo-oxidation of the polymeric coatings, free radical excitation, coupling reaction, and lead to complicated degradation products, reduction of molecular weight, tensile strength, and impact resistance of polyurethane coating [8].Under combined UV, water and oxygen loading, polyurethane coatings tend to form blisters on the surface, then the chemical composition of the coatings surface can change (increase of urea and urethane group concentrations; build-up of hydrophilic groups), promoting the water absorption [9].
Fatigue and static strength of polyurethanes depends also on temperature, with decreasing fatigue performance and more cohesive failure at higher temperatures [10].In particular, degradation of polyurethanes in sea water depends on the degree of cross linking, with crosslinked polyurethanes very resistant to degradation in sea water, and slightly crosslinked polyurethanes only moderately resistant to degradation in sea water [11].

Humidity effect and coating debonding
In order to simulate the effect of moisture on the leading edge protection degradation, a computational model for moisture diffusion in the multilayered coating system was developed in [12] [13].
Several advanced tools were developed to simulate the moisture ingress and its influence on the liquid impact: o Moisture diffusion and formation of hygroscopic stress field in the coating sample were determined, using the coupled moisture-displacement problem solution, obtained using the thermal-moisture direct analogy in ABAQUS/Standard [14], [15].Saturation weight gain by the coating at 90% relative humidity and 60°C was approximately 2.5% of the initial weight.o Coating material changing properties due to moisture ingress is simulated using the Abaqus subroutine User Defined Field. Figure 2 shows von Mises (hygroscopic) stress distribution at the interfaces due to moisture ingress in multi-layer blade samples.The field variable is changed as a function of local moisture content and changes in turn the local material properties.Potentially, a model of changing material properties due to the external radiation (here, UV radiation) can be also developed, using the User Defined Field subroutine, with external field (with gradient along the vertical axis) and material properties influenced by local radiation level.o The enhanced interfacial stresses, caused by the polymer swelling and properties gradient due to the moisture diffusion, can lead to the interface debonding of coatings.It was observed in the simulation that stress changes between the polyurethane and putty layers cause additional shear stresses along interfaces caused by the moisture ingress.High humidity and moisture ingress, as well as thermal and ultraviolet loadings can potentially change drastically the material response, thus, influencing the lifetime and performance of the blade coatings.
Figure 2. Von Mises (hygroscopic) stress at the interfaces due to moisture ingress in multi-layer blade samples.Generally, the leading edge erosion process includes competing degradation processes, surface damage near the drop contact surface, and interface damage.A computational model developed allow simulation of both processes, damage due to contact impact and interface damage.It was observed that repetitive raindrop impact of different sizes at arbitrary locations causes damage accumulation and propagation faster at the interface, finally damaging the coating layer.Figure 3 shows the damage distribution on the top surface of the coating (left) and of the interface between coating and putty (right), obtained in the simulation.The validation of this work is underway.

Small parameter effects and rain scenarios
The surface degradation of blades is strongly influenced by small parameters, factors, which are often out-idealized in continuum mechanical problems.In [16], it was demonstrated that changing the shape of a rain droplet before the impact (from spherical to ellipsoidal) changes drastically the stress field in the coating after the impact, thus, influencing the damage mechanism.The shape of rain droplet changes during its flight, is dependent on the cloud height, wind velocity, and other random factors.Further, availability of small voids or particles in the coating can reduce the coating lifetime by order of magnitude [5].On the other side, the availability of water film on the surface of a blade can reduce the stresses, thus, extending the coating lifetime [16].Further, the sequence of rainy periods (strong/weak or vice versa) has strong effect on the blade erosion, according to the results by ORE Catapult team [17].In this section, some critical stochastic factors, influencing the blade erosion, are listed.A rain scenario and droplet distributions represent important starting points in all erosion analyses.Many models of rain erosion are based on the Best droplet size distribution [4].However, Prior and colleagues [18] analysed the precipitation intensity, droplet size distributions (DSD), hydrometeor phase and the wind turbine rotational speed, and concluded that neither Best distribution, nor Marshall Palmer approximation represent realistic atmosphere-relevant drop distribution.Thus, correct, data based rain scenario should be used, when modelling the blade surface degradation.

Roughness formation and effect of roughness
The blade erosion leads to the roughening of blade surface.The rough surfaces change the droplet impact conditions, and the roughness increases over time, reducing the aerodynamic performance of the blades.Even initially, the blade surface is not ideally plane, while most of the computational models of the droplet impact still assume the plane surface [4] [5]. Figure 4a shows 3D reconstruction of small region of rough blade surface, obtained using the photogrammetry approach from [12].The digitized rough surface model was introduced into finite element model of liquid impact.Figure 4b shows the stress distribution in the rough surface hit by a rain droplet.In order to predict the roughness evolution of the blade surface, a computational model based on the finite element method, coupled Eulerian-Lagrangian approach, and damage mechanics was developed in [20].The model uses the stress amplitude calculation method of fatigue damage analysis, and is therefore relatively expensive in computational resources.
Another approach of the roughness is based on simplified model of the material removal.This model simulates material removal by setting a threshold value for the absorbed impact energy of the coating material.Once the absorbed energy from multiple impacts exceeds this threshold, the coating material is removed from that point (see schema Figure 5).A rain event is generated by randomly distributed impact positions of liquid droplets over the surface area.The absorbed impact energy is calculated by summing the contribution of each droplet impact, if the impact occurs close enough to the point.The impact energy is defined as the kinetic energy of the droplet relative to the moving blade.The shape of this area is assumed to be a 3D ellipsoid.If a point of the coating material is within this ellipsoid, then it absorbs an energy amount equal to the droplet's impact energy.Figure 6 shows the examples of the roughness evolution, obtained using the simplified method.

Conclusions
Leading edge erosion of wind turbine blades is controlled by complex multiphysics, stochastic processes.These processes include environmental loading, temperature, moisture and load variations, ultraviolet radiation, stochastic variations of mechanical loading and combination of all these factors.In this paper, we consider methods of computational modeling of effects of these effects.Examples of computational simulations of the effect of moisture, roughness evolution, role of defects in blade coatings on the blade erosion are demonstrated.

2 Figure 1 .
Figure 1.Schema: from idealized model of blade erosion (left) to the analysis taking into account stochastic and multiphysics effects(right).

Figure 3 .
Figure 3. Damage distribution on the top surface of the coating (left) and of the interface between coating and putty (right), obtained in the simulation.

Figure 4 .
Figure 4. Reconstructed 3D surface of rough blade surface (left) and computational model of droplet impact on rough surface (Reprinted from [12])