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A Damage Assessment for Wind Turbine Blades from Heavy
Atmospheric Particles
Giovanni Fiore,∗Gustavo E. C. Fujiwara,†and Michael S. Selig‡
University of Illinois at Urbana-Champaign, Department of Aerospace Engineering, Urbana, IL 61801
A numerical study of how to simulate heavy atmospheric particle collisions with a 38-m, 1.5-MW
horizontal axis wind turbine blade is discussed. Two types of particles were considered, namely hail-
stones and rain drops. Computations were performed by using a two-dimensional inviscid flowfield
solver along with a particle position predictor code. Three blade sections were considered: at 35%
span and characterized by a DU 97-W-300 airfoil, at 70% span with a DU 96-W-212 airfoil, and
at 90% span using a DU 96-W-180 airfoil. The three blade sections are constituted by 8-ply car-
bon/epoxy panels, coated with ultra-high molecular weight polyethylene (UHMWPE). Hailstone
and raindrop simulations were performed to estimate the location of the striking occurrences and
the blade surface area subject to damage. Results show that the impact locations along the blade are
a function of airfoil angle of attack, local relative velocity, airfoil shape, aerodynamics and mass of
the particle. Hailstones were found to collide on nearly every portion of the blade section along their
trajectory due to their insensitivity to the blade flowfield. The damaged surface areas were found to
be small when compared to the overall impingement surface, and most of delamination damage was
localized on the blade leading edge. Moreover, panel delamination occurred for outboard sections,
when r/R≥0.90. The damage due to raindrops was divided in an erosive and a fatigue contribution
due to the impact force. It was observed that the erosive damage follows the cubic power of the
blade velocity, whereas the impact force follows the square power of the blade velocity. Moreover, it
was seen that the rain drops are sensitive to the blade flowfield, due to shape modifications through
the Weber number. In particular, a sensitive behavior of the damage with respect to the blade angle
of attack was observed.
Nomenclature
a= axial induction factor
A= particle reference area
AK = particle nondimensional mass
bC= coating constant related to the fatigue curve
c= airfoil chord length
C= speed of sound
COE = Cost of Energy
Cd= airfoil drag coefficient
CD= particle drag coefficient
Cl= airfoil lift coefficient
d= particle diameter
D= particle drag force
E= erosion rate
ED= particle damage efficiency
∗Graduate Student (Ph.D.), Department of Aerospace Engineering, 104 S. Wright St., AIAA Student Member.
†Graduate Student (Ph.D.), Department of Aerospace Engineering, 104 S. Wright St., AIAA Student Member.
‡Associate Professor, Department of Aerospace Engineering, 104 S. Wright St., AIAA Associate Fellow.
http://www.ae.illinois.edu/m-selig
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53rd AIAA Aerospace Sciences Meeting
5-9 January 2015, Kissimmee, Florida
AIAA 2015-1495
Copyright © 2015 by Giovanni Fiore. Published by the American Institute of Aeronautics and Astronautics, Inc., with permission.
AIAA SciTech
EI= particle impact efficiency
Fimp = particle impact force
F T E = failure threshold energy
FTV = failure threshold velocity
g= gravitational acceleration
GAEP = Gross Annual Energy Production
h= airfoil projected height perpendicular to freestream
k= number of coating stress wave reflections
m= particle mass
ni= number of droplet impacts per site during incubation period
P= impact pressure
r/R= blade section radial location
RD= damage surface ratio
RI= impingement surface ratio
Re = particle Reynolds number
Re∞= freestream Reynolds number
s= impact location in airfoil arc lengths
Se f f ,C= effective coating strength
stot = airfoil total arc length
t= time
t/c= airfoil thickness-to-chord ratio
U= chordwise flowfield velocity component
V= chord-normal flowfield velocity component
Vdam = hailstone damage velocity
Vimp = particle impact velocity
VN= particle normal impact velocity
Vr= blade relative wind velocity
Vrel = particle relative drop velocity
Vs= particle slip velocity
Vterm = particle terminal velocity
We = droplet Weber number
x= particle x-location
y= particle y-location
Z= impedance
α= angle of attack
αr= relative angle between flowfield and particle velocity
β= impingement efficiency
γ= parameter related to coating thickness
δ= thickness
ηD= particle damage ratio
λ= tip-speed ratio
θ= impact angle
µ= dynamic viscosity
ν= Poisson’s ratio
ρ= density
σ= surface tension
σC= coating average surface stress
σu,C= coating ultimate tensile strength
τ= nondimensional time
ψ= impedance ratio
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Subscripts and superscripts
0 = initial state
C= coating
H= hail
l= lower limit
P= particle
R= rain
S= substrate
u= upper limit
I. Introduction
Wind turbines used for eletrical power generation are subject to fouling and damage by airborne particles typical of
the environment where the wind turbine operates. Throughout the 20-year lifespan of a wind turbine, particles such as
rain, sand, ice crystals, hail, and insects are major contributors to a deterioration in turbine performances through local
airfoil surface alterations.1–6 Wind turbine blades accumulate dirt especially in the surroundings of the leading edge.
Moreover particle collision, temperature jumps and freeze-thaw cycles may cause smaller coating cracks to propagate,
promoting coating removal and eventually delamination and corrosion damage due to exposure of the internal com-
posite structure. The originally smooth surface of the blades may change considerably, and the increased roughness
will cause a drop of gross annual energy production (GAEP) and an increase in cost of energy (COE)7–13 .
The weather conditions of a given wind farm site may vary substantially throughout the seasons. For geographical
locations subject to frequent precipitations, the repetitive impact with raindrops may increase the mechanical fatigue
in the blade surface materials14,15 and large droplets may cause potential panel delamination.16,17 A more severe sit-
uation is represented by hailstorms. High potential wind resource sites such as those found in the Great Plains of the
United States (north western Texas, eastern Colorado, north eastern Oklahoma, and southern Kansas), 18 are charac-
terized by larger hailstorm risk factors than any other location in the US territory.19 Anticyclonic supercells typical of
the Colorado Plains have been recorded to easily produce hailstones greater than 50 mm (1.97 in) in diameter.20 Soon
after the installation of large wind farms over the western Great Plains in early 2000, wind turbines were reported to
be damaged by heavy hailstorms.21 Hailstones are larger, heavier and harder than raindrops, and may strike in the
vicinity of the leading edge at relative velocities and impact energies capable of not only internal delamination, but
also permanent indentation, cracking and eventually penetration of the composite panel.6,22,23
Wind farm operators are forced to schedule blade inspection and maintenance to reduce the cost of ineffective elec-
tric power production due to degraded blade surfaces. Disassembling a wind turbine for factory inspection is costly,
so the majority of servicing is performed on site. Damaged areas are located through visual inspection of the blade,
surface alterations are smoothed through primer application and a protective polyurethane-based film is applied.11,24
However, because of the highly competitive nature of the wind turbine industry, the majority of wind turbine manu-
facturers are reluctant to share details of the construction materials with maintenance companies. Therefore, technical
expertise has a tremendous weight on blade repair success and effectiveness. 4,22 Moreover, repairs are mostly per-
formed in the vicinity of the leading edge and not necessarily on all areas exposed to damage. Farther downstream,
blade areas that do not manifest large damages may be left untreated, promoting the enlargement of surface imperfec-
tions starting where the coating is weaker. An estimated 6% of the overall repairs and maintenance resources for wind
turbines is dedicated to rotor blades.6,25 Moreover, an analysis of wind turbine reliability showed that tip break and
blade damage are the first and third most common failure modes for wind turbines, respectively.6
To complicate the blade maintenance scenario, the damage due to heavy particles is challenging to detect. An
emerging issue for damage assessment is posed by damage that is not visually evident. Barely visible impact damage
has large potential for not being detected during servicing.4,6,26 Spar caps that were damaged by severe hailstorms may
appear intact at a first look, but may have reduced maximum structural loads.27 Advanced nondestructive inspection
tools (NDI), such as ultrasound scan and shearography of the composite sandwich are currently increasing in popu-
larity but still represent a smaller fraction of actual servicing applications.26 Major technological challenges of NDI
tools are represented by poorly accessible conditions and large surface areas typical of wind turbines blades.6
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Since modern wind turbine designers make large use of composite materials,21,28 the investigation of the hailstone
damage problem follows an identical approach to assessing damage to modern composite aircraft and ship struc-
tures.17,22,26 Driven by such considerations, experimental and numerical studies of hailstone impact were performed
to simulate the damage tolerance of various aerospace-related composite materials.23,27,29 A variety of collision an-
gles and impact speeds were simulated, and such conditions are also typical for the hail-wind turbine scenario. These
studies show that the severity of panel damage is a function of hailstone kinetic impact energy and impact angle, along
with the structural characteristics of the composite panel.
The goal of this study was to numerically describe the trajectory of hailstones and rain drops and to characterize
the impact areas of three sections along a wind turbine blade, located at 35%, 70% and 90% of the span. Damage
models are implemented to characterize the blade for hailstone and droplet damage. A 3-blade, 38-m radius, 1.5-MW
HAWT has been chosen to be representative of existing wind turbine systems, being the most common configuration
in North America at present.18 This paper is divided into five sections: the numerical method used is explained in
Section II, the blade operating point, particle aerodynamics and damage models are introduced in Sec. III, while the
results obtained are discussed in Sec. IV. Finally, conclusions are proposed in Sec. V.
II. Methodology and Theoretical Development
Predicting the trajectory of impinging particles is critical when impact characteristics on the wind turbine blade
need to be determined. A lagrangian formulation code was developed in-house and named BugFoil.30 BugFoil inte-
grates a pre-existing insect trajectory code31 and a customized version of XFOIL.32 Local flowfield velocity compo-
nents are obtained by querying the potential flow routine built in XFOIL, from which the particle trajectory and impact
location on the airfoil are computed. Similarly, the capabilities of BugFoil have been expanded to simulate trajectories
of hailstones and raindrops as well.
In steady flight, the forces acting on the particle are perfectly balanced and perturbations to such forces are assumed
to be additive to the steady-state forces. For these reasons the equations of motion may be expressed by neglecting
the steady-state forces and may be written as functions of increments only.33 In the current study, both raindrops and
hailstones were treated as aerodynamic bodies whose only associated force is the aerodynamic drag D.
By applying Newton’s second law along the particle trajectory in both chordwise xand chord-normal ydirections,
the following equations are obtained30,34–37
mP
d2xP
dt2=ΣFx(1)
mP
d2yP
dt2=ΣFy(2)
By projecting the drag of the particle Din both chordwise xand chord-normal ydirections using the relative angle
between particle and flowfield velocity αr, the equations may be rewritten as
mP
d2xP
dt2=∆Dcos αr(3)
mP
d2yP
dt2=∆Dsin αr(4)
Given the particle velocity components UPand VPand given the velocity flowfield components Uand Vat a certain
point along the trajectory, the particle slip velocity Vscan be expressed as
Vs=q(U−UP)2+ (V−VP)2(5)
while the trigonometric functions in Eqs. (3) and (4) may assume the form
cosαr=U−UP
Vs
=Vrx
Vs
(6)
sinαr=V−VP
Vs
=Vry
Vs
(7)
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By expressing the particle aerodynamic drag Das a function of dynamic pressure and by substituting for the trigono-
metric functions, the Eqs. (3) and (4) may be rewritten as
mP
d2xP
dt2=1
2ρV2
sAPCD
Vrx
Vs
(8)
mP
d2yP
dt2=1
2ρV2
sAPCD
Vry
Vs
(9)
To scale this problem in a non-dimensional fashion, non-dimensional time, space, and mass parameters can be intro-
duced here
τ=t U
c(10)
xP=xP
c(11)
yP=yP
c(12)
AK =2mP
ρAPc(13)
Nondimensionalization of Eqs. (8) and (9) by a reference velocity Uyield
d2xP
dτ2=1
AK VrCDVrx (14)
d2yP
dτ2=1
AK VrCDVry (15)
which represents a set of second-order, nonlinear differential equations. Once the particle drag coefficient is evaluated,
the trajectory can be computed by numerically solving both xand yequations.
III. Blade Damage Analysis
The selected wind turbine layout is a a 1.5-MW, 3-blade, 38-m radius, tip-speed ratio λ=8.7 HAWT. Starting at
the root of the blade and moving toward the tip, the airfoils utilized are the DU 97-W-300, -212, and -180 respectively.
The thickness of the blade sections (t/c) and chord length (c) decrease along the span of the blade, in accordance
to conventional wind turbine designs. A nominal wind speed of 10.5 m/s at the hub was proposed for quiet weather
conditions. However, due to the wind conditions during a rainstorm or hailstorm, the actual considered wind speed
was 18.4 m/s. Such wind speed augmentation was computed through an empirical formula, as explained in Ref.38.
Finally, an axial induction factor of a=1/3 was used for the relative inflow conditions. The blade properties and
airfoil operating conditions are summarized in Table 1.
During the unperturbed drop, hailstones and rain drops reach terminal velocity Vterm aligned with the gravitational
force. However, the total particle velocity will form an angle with the blade rotational plane. In fact the resultant
particle velocity Vtot,part icle will be the vector summation of Vwind and Vterm, as shown in Fig. 1. Depending on the
nature of the particle, Vterm may vary and may drive the particle to hit at steeper or shallower angles onto the blade
surface.
The materials used for estimating the blade damage are divided into two categories: blade coating and blade
composite structure. The blade coating was chosen to be ultra-high molecular weight polyethylene (UHMWPE). Such
choice was driven by a coherent approach with previous sand erosion studies.30 The material used for the composite
structure is carbon-epoxy T800/3900-2. Great interest is shown in the scientific literature for the hailstone damage
assessment of such composite materials.23,27,29,39,40
Since modern wind turbines are operated close to their maximum lift-to-drag ratios,3,41,42 the three blade sections
were analyzed with XFOIL and three values of Clwere determined in the proximity of (Cl/Cd)max. The operating
conditions for the three blade sections are reported in Table 2. Simulations for impingement and damage due to
hailstones and droplets were performed at three angles of attack corresponding to the Cl-values determined.
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Figure 1. Particle and blade velocities: a– axial induction factor, Ω– angular velocity, r– local span Vr– blade relative wind.
Table 1. Baseline blade parameters
Location r/RAirfoil c(m) Vr(m/s) Re
1 0.35 DU 97-W-300 3.13 34.30 7.39 ×106
2 0.70 DU 96-W-212 1.90 65.23 8.54 ×106
3 0.90 DU 96-W-180 1.20 83.28 6.88 ×106
A. Trajectory Evaluation
BugFoil is initialized using nondimensional input data. An equally-spaced array of particles is placed five chord-
lengths upstream of the blade section, with inital velocity components nondimensionalized with respect to the local
freestream velocity V∞. Each particle is evaluated individually throughout its trajectory by numerically solving the
particle equations of motion through a predictor-corrector algorithm. As the particle approaches the airfoil, the code
verifies whether impingment occurs, and the impact locations over the airfoil are determined. By taking the derivative
of the initial particle coordinate y0with respect to the particle impingement location in airfoil arc lengths s, the
impingement efficiency is defined in the following manner34
β=dy0
ds (16)
The parameter βis an index of probability for the particle to impact with the airfoil. By computing trajectories for a
vertical array of particles, the two outermost impacting trajectories correspond to β= 0. Those trajectories represent
the upper and lower limits of impingement. The fraction of striking particles out of the total number is evaluated
by localizing the initial upper and lower y-limits on the upstream array of particles, namely y0,u
Iand y0,l
I, as shown in
Fig. 2. By dividing the distance between these two locations by the projected height of the airfoil h, the nondimensional
impact efficiency parameter EIis introduced as
EI=y0,u
I−y0,l
I
h=∆y0
I
h(17)
The parameter EIrepresents the height of the particle array captured by the airfoil, relative to the airfoil projected
height. When simulating the trajectory of hailstones and droplets the local developed impact energy may cause damage
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Table 2. Blade sections operating conditions
r/Rα(deg) ClCl/Cd
0.35 3.5 0.83 101.81
5.5 1.09 126.52
7.5 1.34 142.32
0.70 4.0 0.81 151.80
6.0 1.04 151.24
8.0 1.24 119.83
0.90 4.0 0.79 162.35
6.0 1.02 175.21
8.0 1.21 123.60
in the panel depending on the panel strength characteristics. To assess damage in the panel, the particle impact velocity
can be compared to the failure threshold velocity FT V of the panel. A definition of damage efficiency EDfor hailstones
can be used to compute the fraction of damaging particles out of the total impinging number
ED=y0,u
D−y0,l
D
h=∆y0
D
h(18)
The relative quantity of damaging particles is given by the parameter damage ratio ηDdefined as follows
ηD=ED
EI
(19)
The parameter ηDrepresents a figure of merit of the airfoil since it incorporates the damage mechanism of hailstones.
An advantage of using ηDis the independency on airfoil projected height h, which may not have a linear relationship
with the angle of attack of the airfoil.
One way to estimate the extent of blade surface subject to particle collisions is to compute the airfoil arc length
within the upper and lower surface impingement limits, su
Iand sl
I, respectively, shown in Fig. 2. The result of this
operation is called ∆sI. By knowing the airfoil total arc length stot , the impingement surface ratio RIcan be computed
as
RI=su
I−sl
I
stot
=∆sI
stot
(20)
As RIapproaches the unity, a larger portion of the blade area is subject to particle collision. In a similar manner, when
considering the panel damage, the damage surface ratio RDmay be defined as
RD=su
D−sl
D
stot
=∆sD
stot
(21)
The parameter RDrepresents a direct measurement of the blade surface subject to damage.
Figure 2. Definition of impact and damage limits.
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B. Hailstone Background
1. Aerodynamics of the Hailstone
Hailstones are significantly larger and heavier than other airborne particles such as sand grains and insects. Hence,
their aerodynamic behavior is significantly different from the behavior of other particles considered in previous stud-
ies.30,43 The hailstone impacting trajectories largely deviate from the aerodynamic streamlines around the blade and
impact occurs on a range of steep impact angles.
Choosing the representative hailstone characteristics for aerodynamic drag computation is somewhat subjective.
In fact, hailstone dimensions and weight may vary significantly in different storms and geographic regions.19 From
a conservative standpoint, however, one can choose large and heavy hailstones as a reference. The chosen values of
diameter and weight are 50.8 mm (2 in) and 61.8 g (2.18 oz), respectively, in accordance with U.S. weather reports,20
along with experimental and numerical impact investigations.23,29,39 Also, these hailstone characteristics are in good
agreement with modern wind turbine design and maintenance recommendations outlined in Ref.44.
During the unperturbed drop, hailstones reach terminal velocity Vterm as a function of the aerodynamic drag coef-
ficient CD,H, ice density ρHand stone diameter dH. If the aerodynamic drag is equated to the gravitational force acting
on the particle, the following expression of Vterm,His obtained
Vterm,H=s4g dHρH
3CD,Hρ(22)
The underlying assumption is that the drag does not vary throughout the unperturbed drop. Hence, a typical value of
CD,H=0.83 is assumed until the trajectory is influenced by the wind turbine flowfield. Assuming the particle to be
horizontally transported by the wind, the hailstone relative velocity Vrel will be the vector summation of Vterm,Hand
wind speed.
When the hailstone finally encounters the aerodynamic flowfield generated by the wind turbine, the aerodynamic
forces acting on the particle change according to the particle relative flow, and hence relative Reynolds number. An
equation for the sphere drag coefficient in the Reynolds number range typical of falling hailstones is given by45
CD,H=24
Re +6
1+Re1/2+0.4 (23)
Note that in order to use such a formula, it is first computed the relative flow seen by the hailstone and hence the
relative Reynolds number. Also, because Eq. 23 is valid for Re ≤2.5×105, the hailstone drag coefficient is set to 0.1
past that range.45,46 The lift coefficient of the hailstone is assumed to be negligible for this study.
As opposed to insects and sand grains,30 hailstone approach the blade with a velocity that is the combination of
Vterm,Hand Vwind. It is assumed here that an increase in wind intensity is observed during the hailstorm. A way to
estimate such an increase is by correcting the incoming wind speed (Vwind =10.5 m/s (23.5 mph)) with appropriate
gust factors.38 The relation to correct for Vwind is the following
∆Vwind = (FgFs−1)Vwind (24)
where Fgand Fsare the empirical mean gust factor and the empirical statistical factor, respectively. By selecting a gust
duration of 10 s for a standard deviation above mean wind speed equal to 1, the resulting values are Fg=1.195 and
Fs=1.465.
C. Hailstone Damage
The prediction of damage due to hailstones is derived from the definition of failure threshold velocity (FT V ),23,29
defined as the lowest velocity at which a composite panel is subject to delamination upon impact. Using this velocity,
a failure threshold energy (FT E ) can be defined as the kinetic energy of the damaging hailstone at impact
F T E =1
2mHF TV 2(25)
By measuring the failure threshold velocity at normal impact FT E90 , the following trigonometric relationship holds
F T E (θ) = F T E90
sinθ=
1
2mHF TV 2
90
sinθ(26)
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Table 3. Hailstone computational parameters
r/R Re AKHdH/c V 0
x,H/VrV0
y,H/VVrFTV90/Vr
0.35 207740 15.9 1.62 ×10−21.73 -0.088 2.65
0.70 316150 26.2 2.67 ×10−21.39 0.022 1.39
0.90 379000 41.4 4.23 ×10−21.30 0.029 1.09
where θis the hailstone impact angle. Since mass of hailstone mHis known, FT V90 can be determined and the
nondimensional damage velocity can be estimated dividing by the relative drop velocity Vrel . Finally, the computed
velocity at impact Vimp can be compared to the corresponding F T V of the panel for a given impact angle, and the blade
section may be flagged with hailstone damage when an excessive velocity Vdam is reached, i.e.
Vdam =Vimp −FTV >0 (27)
This evaluative damage criteria allows for quick analysis of wind turbine configurations during the design phase, or for
a posterior damage assessment for existing installations. In general, drivers of F TV are the structural characteristics of
the composite material and impact angle of the particle. The materials used for this study are 8-ply, 1.59 mm (0.062 in)
thick carbon/epoxy panels.27,39
Note that Eq. 22 gives an absolute terminal velocity of the hailstone. However, when considering the rotative
motion of turbine blades, the relative velocity Vrel is the vector summation of the local blade translational velocity
and hailstone terminal velocity. From a damage evaluation standpoint, the most restrictive case is represented by the
blade travelling upward, with the leading edge perpendicular to the hailstone trajectory. In this situation the highest
velocities and thus impact energies are developed.
An additional way to characterize the damage due to hailstones is by computing the peak impact force Fimp on the
blade surface. A proposed form to estimate Fimp is given by the formula17
Fimp =mH
(Vimp sin θ)2
dH
(28)
Such formula was used in the literature to estimate the force due to water droplets47,48 and it is here extended to
hailstones for simplicity. The advantage of using Eq. 28 lies in the ease of implementation. In fact, implementing a
more accurate formula would require a deep ballistic characterization of the target material. Despite these observations,
results show that applying such formula brings to reasonable estimates of Fimp, when compared with instantaneous
measurements from experimental setups.23
The computational parameters and initial conditions for hailstones are summarized in Table 3, where the relative
hailstone drop velocity Vrel and failure threshold velocity FTV90 are nondimensionalized with respect to the blade
relative wind Vr.
D. Raindrop Background
1. Aerodynamics of the Raindrop
In order to establish the initial conditions for the droplet simulations, the motion of a water droplet in its unperturbed
descent needs to be evaluated. As opposed to the hailstone, the terminal velocity of a droplet follows the empirical law
as49–51
Vterm,R=943 h1−e−(dR/1.77)1.47 i(29)
Again, the relative droplet velocity Vrel will be the vector summation of Vterm,Rand the wind speed.
When approaching the wind turbine blade section, a water droplet is subject to a progressive shape modification
due to the magnitude of aerodynamic forces with respect to the surface tension forces.17,52–54 In fact, the relative
flow seen by the droplet may cause deformation and even fragmentation before impact. The physical parameter that
represents the ratio of aerodynamic forces with respect to the droplet surface tension is the Weber number (We), that
is
We =ρV2
rel dR
σR
(30)
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Table 4. Material constants
Phase Material ρ(kg/m3)C(m/s)
Raindrop (R) Water 1000 1464
Coating (C) UHMWPE 930 861
Substrate (SS) T800/3900-2 1590 2375
Because of the droplet shape modification throughout the flowfield, the particle drag coefficient needs to be estimated
accordingly. In particular, it was observed that a steep increase in CDjust prior to impact occurred, and values of
drag coefficient greater than of a circular disk appeared.55 A quasi-steady model to describe the drag coefficient is
proposed. The particle drag coefficient is computed as an additive correction ∆CD,Rto the spherical drag, as a function
of We, that is 56
∆CD,R=We 0.2319 −0.1579 logRe +0.047 (log Re)2−0.0042 (logRe)3(31)
Such a formula is an empirical correction that allows for simple drag computation, greatly simplifying the mathemat-
ical approach. The considered raindrop diameter for the simulations is 2 mm (0.079 in) and represents a typical value
found in other experimental studies and reviews.53,54,57,58 Note that similarly to hailstones, Vwind is augmented by a
gust representing an increment in wind intensity due to the rain storm (see Eqn.24).
2. Raindrop Damage
Upon impact with a solid surface, a droplet is subject to a complex system of shock waves which lead to compressible
behavior.47,59,60 The instantaneous pressure Pgenerated by the impact of a water raindrop with the blade solid surface
may be evaluated through the modified water hammer pressure,17,47,58,59,61–63 that is
P=ZRVimp sin θ
1+ (ZR/ZC)(32)
where Zare the impedances for raindrop (R), and coating (C). By introducing also the impedance for the substrate
(SS), the expressions for Zare
ZR=ρRCR;ZC=ρCCC;ZSS =ρSS CSS (33)
Note that ZSS is composed by a matrix and a fiber phase, depending on the fiber content of the material. The physical
constants for raindrop, coating, and substrate are reported in Table 4. Once the droplet impact velocity Vimp and impact
angle θare known, the computation of the instantaneous pressures developed upon impact is complete. However, due
to the largely subsonic impact speeds, it is likely that a single impact of a raindrop would not promote damage in
the blade coating or substrate. For such reasons, it would be of particular interest being able to estimate the damage
due to multiple raindrop impacts. In fact, the blade coating may weaken and be removed over time due to a fatigue
mechanism imposed by numerous impacts on the same target.15 The repetitive raindrop striking results in an erosion
of the blade coating.
The approach implemented in the current study makes use of the damage model developed by Springer for coated
composite materials subject to liquid droplet impact.57 The advantage of doing so is in the ability to estimate the blade
coating erosion rate, given the average stress on the coating surface. The erosion rate is a physical property associated
with wear, and it is defined as the ratio of removed target material with respect to the unit mass of erodent.64 In order
to find an expression for the erosion rate, the average stress on the coating surface σCis derived from the modified
waterhammer pressure, that is
σC=P1+ψSC
1−ψSC ψRC 1−ψSC
1+ψRC
1+ψSC
1−e−γ
γ(34)
where the impedance ratios ψare computed as
ψSC =ZSS −ZC
ZSS +ZC
;ψRC =ZR−ZC
ZR+ZC
(35)
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Table 5. Raindrop computational parameters
r/R Re AKRdR/c V 0
x,R/VrV0
y,R/VrVrel /VrWe
0.35 5870 0.695 6.39 ×10−41.239 0.099 1.243 60.7
0.70 10030 1.142 1.05 ×10−31.115 0.074 1.117 177.1
0.90 12484 1.810 1.66 ×10−31.087 0.061 1.089 274.4
while the expression for γis given in the following form
γ=CC
CR
dR
δC
1+ (ZR/ZSS)
1+ (ZC/ZSS)
2
1+ (ZR/ZC)(36)
Springer developed an empirical formula to express the erosion rate of a coating layer on top of a composite substrate
as a function of σC, the material impedances Z, and other structural parameters of the coating and of the composite
substrate. The expression for the coating erosion rate Edue to multiple raindrop impacts is written as
E=0.023 1
ni,C0.7
(37)
where ni,Crepresents the number of impacts per site during the incubation period on the coating. It is expressed as
ni,C=7×10−6Sef f ,C
σC5.7
(38)
while the effective coating strength Sef f ,Cis computed as
Se f f ,C=4σu,C(bC−1)
(1−2νC)1+2k|ψSC |(39)
where σu,Cis the coating ultimate tensile strength and bCis a dimensionless constant related to the coating fatigue
curve. Finally, the expression for kis the following
k=1−e−γ
1−ψSC ψRC
(40)
Note that once the erodent, coating, and substrate materials are chosen, the values of Z,ψ,γ,k, and Se f f ,Care constants
and are evaluated only once at the beginning of the computations.
Similar to hailstones, an additional way to characterize the damage due to raindrops is by computing the impact
force Fimp on the blade surface. A proposed form to estimate Fimp is given by the formula47,48
Fimp =mR
(Vimp sin θ)2
dR
(41)
Such a formula represents the average impact force due to a liquid droplet on a solid, motionless target.
The computational parameters and initial conditions for raindrops are summarized in Table 5, where the initial
velocity components (V0
x,Rand V0
y,R), and the relative droplet velocity (Vrel ) are nondimensionalized with respect to Vr.
IV. Results and Discussion
All simulations were performed by initializing BugFoil with the input parameters for hailstone and raindrop re-
ported in Tables 3 and 5, respectively. Each location along the blade span was analyzed at three operating points
corresponding to three angles of attack, as reported in Table 2. A single simulation required an average of 2 sec of
computation time on an Intel Core i7 machine with 8 GB RAM running LinuxMint OS.
In order to characterize the particle impact locations along the airfoil, an appropriate figure of merit is the particle
collection efficiency β, over the airfoil arc length s. The parameter sis defined as the length of the arc starting at the
particle impact location and ending at the airfoil leading edge, normalized by the airfoil chord c. Note that sis negative
for impingement locations on the lower side of the airfoil, while it is positive on the upper side. Also, the leading edge
of a finite-thickness airfoil is located at s≡0, while the trailing edge corresponds to values of |s| ≥ 1. Results for
impact of hailstone and raindrop are discussed in Sections B and C respectively.
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(a) (b)
Figure 3. Comparison of BugFoil and LEWICE: βcurves for rain at (a) r/R= 0.70, and (b) 0.90.
A. Code Validation
In order to evaluate the performance of BugFoil, it was performed a validation against the well-established droplet-
icing code LEWICE.65–67 LEWICE was used as a comparison of the water droplet trajectory against two airfoils at
two different blade locations. In particular, it was chosen a rain drop diameter d=2 mm, α=6 deg, and the blade
locations at r/R=0.70 and 0.90. The input conditions for the particles were identical to the conditions used for the
blade analysis, and shown in Table 5. Note that LEWICE does not allow for a vertical component of the droplet
velocity, and therefore both codes were initialized by neglecting such component.
Due to the different capabilities of the two codes, it was apparent to use the collection efficiency βas a benchmark.
Figure 3 shows the comparison between the two codes for r/R=0.70 [Fig. 3(a)], and r/R=0.90 [Fig. 3(b)]. As it can
be seen, BugFoil can predict closely the location and shape of the peaks at both bladespan locations. In particular, β
has an excellent agreement in the region of s=±0.1, where the largest damage on the blade is observed. However, the
impingement limits appear to be consistently shifted toward smaller values of sat both bladespan locations. Moreover,
during the validation procedure it was observed that a variation in angle of attack ∆α≈2 deg would allow for the tails
of the β-curves to overlap. In particular, BugFoil displays very similar βcurves for a reduced angle of attack, when
compared with LEWICE. Such consideration suggested a substantial difference in the computed circulation around
the airfoil, driven by differences in local pressure. However, as it can be noticed in Fig. 4, the coefficient of pressure
CPappears similar for both codes, and it rules out the hypothesis of differences in circulation.
Multiple tests of BugFoil were run using various resolutions for the impinging particles. Because LEWICE does
not allow the user to fix the vertical spacing between particles upstream the airfoil, such parameter was varied in
BugFoil to match the number of striking occurrences. However, even when this was accomplished, the shift in βcurve
was still present. Finally, the code was tested by perturbing the initial droplet input parameters, such as rain drop mass
and diameter, but no appreciable convergence of the curves was observed.
By reading the manual for LEWICE,65 it was found that the two codes handle the particle equations of motion
differently. In particular, LEWICE makes use of the particle lift and gravitational force, whereas BugFoil neglects
both. Unfortunately, a thorough treatment of the particle lift is not given in the manual, hence it was concluded that the
two codes may have substantial differences in predicting the particle position, which drive the observed differences in
βcurves.
B. Hail Simulation
Hailstone trajectory is evaluated at the three locations along the blade span. Impingement efficiency βand damage
velocity Vdam are plotted versus airfoil arc length sin Figs. 5, and 6. The β-curves of hailstones appear to reach a
maximum at s= 0 for all three locations, as shown in Figs. 5(a), 5(b) and 5(c). Moreover, the maximum of βappears
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0 0.2 0.4 0.6 0.8 1
−2
−1.5
−1
−0.5
0
0.5
1
x/c
CP
BugFoil through XFOIL
LEWICE
Figure 4. Comparison of codes – BugFoil vs. LEWICE; pressure coefficient CPon a DU 96-W-180 airfoil, α=6deg.
to be insensitive in amplitude and location with respect to angle of attack α. In fact, β=1 is observed at all blade
sections and for all considered angles of attack. The small sensitivity of the hailstones to the aerodynamic flowfield
generated by the wind turbine blade is apparent. Because the hailstone mass is several orders of magnitude larger
than particles such as sand grains, the observed behavior is physical. As a further proof of aerodynamic insensitivity,
a fairly symmetrical shape of the βcurve about s= 0 can be observed. The effect of the blade flowfield on both the
blade suction and pressure sides has a limited effect on the impact s-location of hailstones.
Damage velocity Vdam along the blade is plotted in Fig. 6. The hailstone impact velocity reaches and exceedes the
failure threshold velocity FTV at r/R=0.90, promoting panel damage [Figs. 6(b) and 6(c)]. Peak values of Vdam are
reached in the near proximity of s= 0 at that blade section, with a narrow range of s-values. Even though no damage
was detected at r/R=0.35 [Fig. 6(a)] and 0.70 [Fig. 6(b)], it should be noticed that a higher resolution of blade
sections along the span would determine accurately the earliest panel delamination when moving toward the balde tip.
The absence of damage for inboard sections is explainable when considering the local blade rotational velocity, which
decrease linearly moving toward the blade hub.
Variations in angle of attack have little or no effect on Vdam at all three blade locations (Fig. 6), and such phe-
nomenon follows the rationale previously explained about the hailstone β-curve sensitivity to α. In general, a narrow
range of damaged panel surface is observed. This result is due to the F T E trigonometric function dependency on θ,
shown in Eq. 26. Steeper impact angles occur at the blade leading edge, which corresponds to lower values of F T E.
When moving downstream of the leading edge, θdecreases, causing FT E to increase, and therefore making it more
difficult for hailstones to cause damage in the panel.
Impact efficiency EIand damage ratio ηDversus αare plotted in Fig. 7. Values of EIare consistently near unity
for all blade sections and angles of attack, as shown in Fig. 7(a). This result is caused by the insensitivity of hailstones
to aerodynamic perturbations due to the blade flowfield. In other words, hailstones impinge at nearly every location
that the blade section shows along the particle path. However, by observing Fig. 7(b) a small portion of the impacting
hailstones appear to promote delamination. In fact, ηDis greater than zero only for r/R=0.90 where the impact ve-
locity is high. Results show also that a variation in angle of attack reduces linearly the fraction of damaging hailstones
when moving toward the blade tip. All the results are presented in Table 6 in terms of average and standard deviation
of EIand ηD.
The contours of damage velocity Vdam are plotted over the blade sections in Fig. 8. It can be observed that the
extent of surface subject to hailstone impact is fairly large [Figs. 8(a), 8(b), and 8(a)]. However, FTV is reached only
on a small region of the blade surface at r/R=0.90, where the relative speed is high. Moreover, the whole lower side
of the blade is exposed to hailstone impact at α=6 deg, even if the impact velocity is modest.
The hailstone impact force Fimp contours are shown in Fig. 9 for the three blade sections. At the inboard section
(r/R=0.35) [Fig. 9(a)] Fimp is modest, but it increases rapidly moving toward the blade tip [Figs. 9(b) and 9(c)]. In
particular, Fimp can be approximated as ∝V2
r. By analyzing Fig. 9 it can be seen that the highest impact forces occur
at the very leading edge of the blade and the whole bottom surface is invested by hailstones, with modest values of
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−1.2 −1 −0.8 −0.6 −0.4 −0.2 0 0.2 0.4
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
s
β
α = 3.5 deg
α = 5.5 deg
α = 7.5 deg
(a)
−1.2 −1 −0.8 −0.6 −0.4 −0.2 0 0.2 0.4
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
s
β
α = 4 deg
α = 6 deg
α = 8 deg
(b)
(c)
Figure 5. βcurves for hail at (a) r/R= 0.35, (b) 0.70, and (c)
0.90.
−1.2 −1 −0.8 −0.6 −0.4 −0.2 0 0.2 0.4
0
0.05
0.1
0.15
0.2
0.25
0.3
s
Vdam/Vr
α = 3.5 deg
α = 5.5 deg
α = 7.5 deg
(a)
−1.2 −1 −0.8 −0.6 −0.4 −0.2 0 0.2 0.4
0
0.05
0.1
0.15
0.2
0.25
0.3
s
Vdam/Vr
α = 4 deg
α = 6 deg
α = 8 deg
(b)
−1.2 −1 −0.8 −0.6 −0.4 −0.2 0 0.2 0.4
0
0.05
0.1
0.15
0.2
0.25
0.3
s
Vdam/Vr
α = 4 deg
α = 6 deg
α = 8 deg
(c)
Figure 6. Vdam curves for hail at r/R= 0.35, (b) 0.70, and (c)
0.90.
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3 4 5 6 7 8 9
0
0.2
0.4
0.6
0.8
1
1.2
α (deg)
EI
r/R = 0.35
r/R = 0.70
r/R = 0.90
(a)
3 4 5 6 7 8 9
0
0.01
0.02
0.03
0.04
0.05
0.06
0.07
0.08
0.09
0.1
α (deg)
ηD
r/R = 0.35
r/R = 0.70
r/R = 0.90
(b)
Figure 7. (a) Hail impingement efficiency EIand (b) damage ratio ηDalong the blade.
Fimp at the trailing edge. However, it is well known that blades are fairly weak with respect to strong impacts on the
trailing edge, hence a valuable information comes from the present analysis.
C. Rain Simulation
The trajectory of falling raindrops is considered in this section. The curves of impingement efficiency βand erosion
rate Eare plotted versus airfoil arc length sin Figs. 10, and 11. Similarly to the hailstone case [see Fig. 5], the β-
curves of raindrops have a maximum at s=0 for all three locations, as shown in Figs. 10(a), 10(b) and 10(c). However,
as opposed to the hailstone case, the maximum value of βnever reaches the value of unity. Also, the peak of βis
somewhat sensitive to variations in angle of attack α. In fact, for increasing α, the β-peak decreases in magnitude
and moves toward the blade lower side (s<0), following the stagnation point movement. By examining the upper
impingement limits of raindrops, one can observe a consistent shift toward the blade leading edge for large values
of α[Figs. 10(a), 10(b) and 10(c)]. The emerging information from this analysis is that the impingement pattern of
raindrops is strongly correlated to the blade angle of attack and flowfield, as opposed to hailstones.
The erosion rate Eof the coating for three blade sections is plotted in Fig. 11. The most apparent result of
the computations is that Eincreases rapidly when moving from the blade inboard sections [Fig. 11(a)] toward more
outboard sections [Figs. 11(b) and 11(c)]. Moreover, Eis appreciable only on a small portion of the blade within the
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(a)
(b)
(c)
Figure 8. Contours of hailstone damage velocity Vdam at (a)
r/R= 0.35 (α= 5.5 deg), (b) 0.70 (α= 6 deg), (c) and 0.90
(α= 6 deg); circles placed at impingement locations and red
segments at maximum Vdam .
(a)
(b)
(c)
Figure 9. Contours of hailstone impact force Fimp at (a)
r/R= 0.35 (α= 5.5 deg), (b) 0.70 (α= 6 deg), (c) and 0.90
(α= 6 deg); circles placed at impingement locations and red
segments at maximum Fimp .
impingement limits. In fact, negligible values of Eappear on the majority of blade surface subject to impingement,
while most of the erosion is concentrated in the vicinity of the leading edge. Also, the shape of the E-curves suggests
that the geometry of the leading edge modifies the pattern of the E-peaks. Blade sections with smaller leading edge
radii have sharper peaks of E[Figs. 11(b) and 11(c)], compared with more inboard sections [Fig. 11(a)]. Finally, the
effect of an increased αhas a sensitive influence on the maximum value of E. In particular, at r/R=0.90 [Fig. 11(c)]
the erosion rate is about one third smaller when αis increased from 4 deg to 8 deg.
Rain impact efficiency EIand impact surface ratio RIare plotted versus αin Fig. 12. The most striking information
obtained from EI[Fig. 12(a)] is that large blade sections promote a more consistent deviation of rain drops, which is
reflected by values of EIsmaller than unity at r/R=0.35 and 0.70. In fact, thick blade sections perturb the flow early,
allowing for rain drops to deviate from their path sooner. This observation is a further confirmation of the susceptibility
of rain drops to the flowfield, through the local blade chord length and thickness. However, the blade angle of attack
does not have a significant effect on EI.
By examining Fig. 12(b) a mixed behavior of RIcan be observed with respect to α. In particular, the surface of
the blade section that is mostly invested by rain drops is located at r/R=0.90, and in general such value decreases
when moving toward the hub. It can be concluded that at r/R=0.9, the airfoil has the slimmest leading edge of those
analyzed, allowing for larger surface areas exposed to rain impingement. On the contrary when moving inboard, the
large leading edge radius shades the downstream parts of the blade, allowing for smaller values of RI.
The contours of erosion rate Edue to raindrops are displayed over the three blade sections in Fig. 13. First, a
strong increase in Eis evident when moving toward the blade tip. Also, the contours show that the extent of impinged
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−1.2 −1 −0.8 −0.6 −0.4 −0.2 0 0.2 0.4
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
s
β
α = 3.5 deg
α = 5.5 deg
α = 7.5 deg
(a)
(b)
(c)
Figure 10. βcurves for rain at (a) r/R= 0.35, (b) 0.70, and (c)
0.90.
(a)
(b)
(c)
Figure 11. Ecurves for rain at (a) r/R= 0.35, (b) 0.70, and (c)
0.90.
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Table 6. Average Values and Standard Deviations of Hail Impact Efficiency and Damage Ratio
Particle r/R(EI)avg σEI(ηD)avg σηD
Hail 0.35 0.995 3.50×10−30.0 0.0
0.70 1.011 1.03×10−20.0 0.0
0.90 1.050 2.79×10−20.015 3.2×10−3
blade surface is greater for the lower side of the blade, compared with the upper side. An explanation of such behavior
comes from the sensitivity of raindrops to the blade flowfield and the geometry of the blade. In fact, once the blade
is set at a given angle of attack, the incoming droplet may approach the upper side only tangentially, while striking a
larger portion of the blade lower side.
The contours of droplet impact force Fimp are shown in Fig. 14. Similarly to hailstones [Fig. 9], Fimp is modest when
considering the inboard section (r/R=0.35) [Fig. 14(a)]. However, when moving toward the blade tip [Figs. 14(b)
and 14(c)], Fimp increases rapidly. It has to be noted that the largest blade portion subject to rain impact lies below
the blade stagnation point. Such behavior was explained in the previous paragraph, regarding the erosion rate E. As a
further support of this observation, the blade sections with the bulkier leading edge [Figs. 14(a) and 14(b)] show larger
portions of blade lower surface exposed to rain, when compared to the section with thinner leading edge [Fig. 14(c)].
A quick estimate of the rain drop damage with respect to blade velocity is proposed. From the E-contours [Fig. 13]
it appears that the erosion rate is related to the cube of the local blade velocity, whereas Fim p shows a square power
correlation to it [Fig. 14].
Finally, a comparison of the rain drop impact force is proposed at r/R=0.90 for three angles of attack, as shown
in Fig. 15. For all angles of attack, values of Fimp ≈10 N are reached. However, by looking closely an increase in α
causes a drop in Fimp . In particular, the maximum Fimp recorded at α=8 deg is about 1/3 smaller than the maximum
Fimp observed for α=4 deg. An explanation of such behavior is due to shape deformations of the rain drop as it
approaches the blade surface while varying Weber number We. In fact, close to the stagnation point, the high-pressure
regions of the lower surface will cause a relative flow that deforms the rain drop, increasing the drag coefficient. In
other words, rain drops that impinge on the blade lower side will be slowed down more than rain drops impinging
on the upper side of the blade. Such behavior will cause a more prominent damage when small angles of attack are
considered.
V. Conclusions
The present work described a model to assess damage for wind turbine blades due to water-based atmospheric
particles. Two types of particles were considered, namely hailstones and raindrops. Trajectories of impinging particles
were evaluated through a numerical code and the properties at impact were computed. For both hailstones and rain
drops, higher values of impingement efficiency EIwere observed for thinner airfoils, meaning a larger amount of
particles were captured by the blade section when compared to thicker airfoils. Such behavior is physical, since small
blade sections perturb the flow less upstream than thick and wider blade sections.
The simulations of hailstones showed that few particles promoting panel delamination were observed by moving
toward the blade hub. This is due to the reduced local blade velocity at such locations. In fact, the impact velocity
promoted panel damage when moving toward outboard blade sections, for r/R≥0.90. Finally, the impact forces
developed by hailstones show prominent values on the very leading edge the blade, due to the incoming trajectory
with respect to the blade surface. An estimate of the impact forces with respect to the blade relative wind shows that
Fimp ∝V2
r.
Table 7. Average Values and Standard Deviations of Rain Impact Efficiency
Particle r/R(EI)avg σEI(RI)avg σRI
Rain 0.35 0.861 0.022 0.265 0.014
0.70 0.893 0.023 0.370 0.135
0.90 0.988 0.046 0.500 0.094
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3 4 5 6 7 8 9
0
0.2
0.4
0.6
0.8
1
1.2
α (deg)
EI
r/R = 0.35
r/R = 0.70
r/R = 0.90
(a)
3 4 5 6 7 8 9
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
α (deg)
RI
r/R = 0.35
r/R = 0.70
r/R = 0.90
(b)
Figure 12. (a) Rain impingement efficiency EIand (b) impact surface ratio RIat three blade spanwise locations.
The analysis of rain drop impact showed that rain drops have a stronger sensitivity to the blade flowfield, when
compared to hailstones. Such observation is reflected in the sensitivity of the impact force with respect to the blade
angle of attack. It was also observed that the erosion rate due to rain drops follows the cubic power of the blade relative
wind, whereas the impact force is related with a square power-law.
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