Effects of leading edge defects on aerodynamic performance of the S809 airfoil

Energy Conversion and Management 195 (2019) 466–479

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Energy Conversion and Management journal homepage: www.elsevier.com/locate/enconman

Effects of leading edge defects on aerodynamic performance of the S809 airfoil

T

⁎

Mingwei Gea,b, , Huan Zhangb, Ying Wub, Yuhua Lia a b

State Key Laboratory of Alternate Electrical Power System with Renewable Energy Sources, North China Electric Power University, Beijing 102206, PR China School of Renewable Energy, North China Electric Power University, Beijing 102206, PR China

A R T I C LE I N FO

A B S T R A C T

Keywords: Wind turbine airfoil Leading edge deep defects Leading edge shallow defects Aerodynamic performance Dynamic stall

Defects at the leading edge of blades are an important source of power loss for wind turbines. In the present work, a systematic study is carried out on two typical types of defects, i.e., the surface concaved deep defects and surface distributed shallow defects on the S809 airfoil. Different defect shapes, ranges, equivalent depths and their influence mechanisms are investigated via CFD. For deep defects, an enclosed vortex is formed in the defect cavity, which suppresses the momentum exchange between the external flow and internal flow, so that the airfoil aerodynamic performance is highly sensitive to the defect opening range and is little affected by the defect shape and equivalent depth. Flow around the leading edge is strongly hindered by the deep defects and an elongated leading-edge separation bubble is formed at the suction side of the airfoil. At large angles of attack, flow at the suction side is dominated by flow separation at both the leading edge and trailing edge. In contrast, for shallow defects, all the defect equivalent depth, opening range and shape can significantly influence the airfoil aerodynamic performance; and quantitatively, the effect of defect equivalent depth is the most significant. For the present simulation cases with defects, the maximum lift coefficient is notably decreased (by 35% to 61% ) accompanied by a sharp increase in drag coefficient (by 131% to 217% ). Under dynamic pitching motions, the opening of the dynamic lift (drag)-coefficient hysteresis curve is effectively enlarged. The present work aims to provide an important reference for the maintenance and management of turbine blade defects.

1. Introduction Wind turbine blades are exposed to complex high-altitude environmental conditions during operation, often eroded by rain, snow, hail, or ultraviolet rays. Zhang et al. [1] experimentally studied the erosion of wind turbine blade coatings caused by raindrop scouring and found that raindrops could hit coatings like bullets at the thin fast-rotating blade tip, causing damage to the protective layers. Similarly, the grains of sand carried in the wind can also cause severe erosion on the surface of wind turbine blades under high-speed rotation, resulting in an increased operation and maintenance costs for wind turbine blades [2,3]. In the initial stage of erosion, small shallow pits are usually formed near the leading edge of blades, which gradually grows and merges into surface gouges. If not repaired in time, they will continuously increase in size and depth, and eventually form surface deep defects. Leading edge defects severely affect the aerodynamic performance of blades, resulting in a great loss of power efficiency for large wind turbines [4–8]. 3 M Company studied the effects of leading edge

defects on a 1.5 MW wind turbine through field tests. Data from the tests showed that after five years operation, the unprotected wind turbine lost up to 20% of its energy production due to the blade defects [9]. Therefore, study on the leading edge defects is of great significance for the operation and maintenance of wind turbine blades. According to the degree and geometrical characteristics of leading edge defects, two typical types of defects are shown in Fig. 1. As illustrated in Fig. 1(a), surface concaved deep defects (SDD) on the airfoil leading edge represent the serious damage caused by severe impact or erosion. Such defects are more concentrated in distribution, with the equivalent depth of h ∼ t ; here, t represents the defect opening size, h = s / t indicates the defect equivalent depth, and s represents the defect area. As illustrated in Fig. 1(b), surface distributed shallow defects (SSD) on the airfoil leading edge is a kind of blade surface damage caused by slight erosion, usually composed of small shallow pits distributed on the leading surface, with h ≪ r ; here, the defect range r is defined by the length of defect along the airfoil profile, and the corresponding equivalent depth is defined as h = s / r .

⁎ Corresponding author at: State Key Laboratory of Alternate Electrical Power System with Renewable Energy Sources, North China Electric Power University, Beijing 102206, PR China. E-mail address: [email protected] (M. Ge).

https://doi.org/10.1016/j.enconman.2019.05.026 Received 18 February 2019; Received in revised form 19 April 2019; Accepted 8 May 2019 Available online 16 May 2019 0196-8904/ © 2019 Published by Elsevier Ltd.

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Fig. 1. Appearance of two typical types of defects on the airfoil leading edge: (a) SDD [10]; (b) SSD [11].

defect shape, investigated parameters and the research focus of the previous work is listed in Table 1. So far, significant insights into the airfoil leading edge defects have been gained. However, there still exist some questions needing to be further addressed: (i) most studies have been focused on specific types of defects or erosion, such as Gharali and Johnson [10] and Wang et al. [13] mainly focused on the rectangular defects, and Sareen et al. [14] mainly focused on pits and gouges on the leading edge surface. A systematic study on various defect types and shapes is still lacking. Especially, there is a lack of comparison between the two typical leading edge defects (SDD and SSD), which may deepen our understanding of the airfoil defects and be very useful to the maintenance of wind turbine blades; (ii) most studies have quantified the effects of leading edge defects on the airfoil lift and drag coefficients, but there lacks an in-depth elaboration on the flow structure and influence mechanism; (iii) due to the existence of wind shear, the attack angle of airfoil changes periodically during the operation of wind turbines. However, most of the current studies have been focused on the effects of leading edge defects under a static state. Studies on the dynamic aerodynamic performance of an airfoil with leading edge defects are still insufficient. To fill the above gaps, a systematic investigation is carried out on the leading edge SDD and SSD in the present study. Both the static and dynamic aerodynamic performances are investigated resorting to a Shear stress transport (SST) k − ω transition model. The influence of key parameters, such as the defect range, shape and equivalent depth, are studied in details. To show the main contributions of the present study more clearly, a comparison between the present and previous work is shown in Table 1. The present work aims to provide an important reference for the management of blade defects, and its results

A lot of work has been done on the leading edge deep defects: Gharali and Johnson [10] studied the effects of leading edge rectangular defects on the airfoil aerodynamic performance at different Reynolds numbers and reduced frequencies and found that in presence of SDD, both the mean and maximum lift coefficients were significantly reduced. Han et al. [12] have studied airfoils at the blade tip section, finding that SDD at the airfoil leading edge reduced the lift coefficient by 53% and increased the drag coefficient by 314%, which can result in a 2% to 3.7% reduction in the annual energy production of the NREL 5MW unit. Based on the S809 smooth airfoil, Wang et al. [13] have studied the effects of the opening size and equivalent depth of rectangular defects; the results indicated that for SDD on the leading edge, when h/ t > 0.5, the airfoil aerodynamic performance was mainly dependent on the defect opening size t. Besides SDD, SSD have also attracted extensive attention. Sareen et al. [14] studied the effects of SSD, such as shallow pits, gouges, and delamination by wind tunnel tests. The results showed that the increase of drag coefficient was strongly dependent on the leading edge roughness or defect degrees. In their cases, all the drags increased by more than 6%. Gaudern et al. [11] used different thickness films to simulate various erosion depths based on local roughness through wind tunnel experiments. The results showed that as the degree or depth of erosion increased, the aerodynamic performance of the wing was detrimentally affected. Ren et al. [15] numerically investigated the aerodynamic performance of a NACA 63-430 airfoil, finding that the blade surface roughness aggravated the transition from laminar to turbulence as well as the flow separation, thus degrading the airfoil aerodynamic performance. A more comprehensive summary, including the defect classification, Table 1 Summary of the main previous research. Relevant research

∗t

Defect classification

Defect shape

Investigated parameters

Research focus Aerodynamic performance

Flow structure and influence mechanism

Gharali & Johnson [10] Han et al. [12] Wang et al. [13] Sareen et al. [14] Gaudern et al. [11] Ren et al. [15] Wang et al. [8] Kadkhodapour et al. [16]

SSD SDD SDD SSD SSD, SDD SSD SSD SSD

Rectangular Irregular Rectangular Irregular Irregular Irregular Semicircle cavities Irregular

t, h – t, h – – – – –

Dynamic Static Static, dynamic Static Static Static Static, dynamic Static

No No No No No No No No

Present work

SSD, SDD

SSD: two different shapes SDD: three different shapes

SSD: r , h SDD: t , h

Static, dynamic

Yes

is the defect opening size, r is the length of defect along the airfoil profile, h is the defect equivalent depth. 467

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shown in Fig. 2. Following reference [17], about 250, 000 grids in total are used, with about 500 grid nodes distributing around the airfoil. In order to meet the requirement of calculation accuracy, y+ < 1 is ensured for the first-layer mesh above the airfoil wall. Grids with different densities are numerically tested. As the number of grids constantly increases, no obvious change appears in the airfoil aerodynamic performance, indicating that this mesh has converged.

will be very useful to evaluate the losses of power performance due to blade defects and help to make a decision on the maintenance strategy of wind turbines with defective blades. The contents are constructed as follows: the physical model and numerical method are presented in Section 2; the influence of the leading edge SDD on the aerodynamic performance of the S809 airfoil is illustrated in Section 3; and the effects of SSD are studied in Section 4, with conclusions drawn in Section 5.

2.2. Turbulence model 2. Physical model and numerical method Direct numerical simulation (DNS) and large eddy simulation (LES) are useful tools for fundamental research on low Reynolds number flows [31–36]; however, they are prohibitively costly for realistic engineering problems. The Reynolds-averaged Navier-Stokes (RANS) approach solves the Reynolds equations to determine the mean velocity field, and the Reynolds stresses are obtained from a turbulent viscosity model. Compared with DNS and LES, RANS is rather cheap, and is widely used for turbine blades and airfoils [37–43]. Leading edge defects break the original shape of the airfoil and increase the surface roughness. Thus, intense interaction occurs between the defects and the incoming flow near the leading edge. To capture these complex flow structures, an SST k − ω transition model (γ − Reθ model) is adopted in the present study. A host of practices have shown that the SST k − ω transition model is fairly sensitive to the adverse pressure gradient and capable of simulating complex flow with strong separation. Essentially, this model is a combined turbulence model, which uses the original form of k − ω turbulence model in the near wall region, but uses the k − ε model in the region far away from the wall. To simulate the flow transition from laminar to turbulence, the γ − Reθ transition model is coupled. Compared with the full turbulence model, the SST k − ω transition model can significantly improve the prediction accuracy of drag coefficient, dynamic flow, etc. For example, Sayed et al. [44] adopted the SST model for wind turbines airfoils and found that the aerodynamic load of wind turbine blades can be accurately evaluated by CFD. Rostamzadeh et al. [45] have used the model to numerically simulate a NACA0021 airfoil, finding that this model successfully captured the stall characteristics of the airfoil and accurately predicted the pressure distribution on the airfoil surface. Wang et al. [46] compared the standard k − ω model and the SST k − ω model in simulation of a NACA0012 airfoil at Rec = 105 and found that dynamic stall characteristics obtained by the SST k − ω model were in better agreement with those of the physical experiment. In the present study, numerical simulations are carried out by means of ANSYS-Fluent software. The regular SIMPLE (Semi-Implicit Method for Pressure Linked Equations) method is adopted in the solver and the finite volume method with a

2.1. Physical model and computational settings For a blade section far away from the root and tip, the flow is mainly dominated by the streamwise flow around the airfoil, while the spanwise flow as well as other three dimensional (3D) secondary flows are much less significant. Therefore, the influence of the 3D shape of defects are generally simplified to a 2D shape and investigated via an airfoil [8,10,13,17,18]. Following this simplification, the 3D flow characteristics of the leading edge defects are neglected in the present study. Both the SSD and SDD are studied via a wind turbine airfoil. As is known, many dedicated airfoils for wind turbines are developed, which are characterized by high lift coefficient, high lift-to-drag ratio, leading edge roughness insensitivity [19] and mitigated stall performance [20], such as the S-series airfoils developed by the National Renewable Energy Laboratory (NREL) [21], the DU-series airfoils [22], the FFA-series airfoils [23,24], the NACA6-series laminar airfoils [25], the RISØ wind turbine airfoils [26]. In this study, the S809 airfoil is selected as the research object, whose relative thickness is 20.95%. The chord length of the airfoil is 0.457 m, and the inflow wind speed u is 32 m / s , with the corresponding Reynolds number being 1 × 106 . As shown in Fig. 2, a Cshape computational domain is adopted in the present simulation, with the airfoil being located at the center of semi-circle. The radius of the semicircle is selected as 15c , and the length and height of the rectangle are selected as 20c and 30c , respectively. Compared with the computational domain used for similar problems [13,27–30], our computational domain is similar or even larger. Thus, the current C-shape computational domain is reasonably for the present study. On the boundary, the velocity Dirichlet condition is used for the far field upstream and both sides of the C-shape domain. Pressure outlet condition is used for the far field downstream boundary, and no-slip condition is adopted for the airfoil surface. A structured mesh is generated for the main computational domain and the airfoil defects are filled with unstructured mesh. Between the structured and unstructured meshes, an interface surface is set, as

Fig. 2. Computational domain and details of computational grids. 468

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Fig. 3. Variation of Cl and Cd of the S809 airfoil with the angle of attack under static state.

Fig. 4. Variation of Cl and Cd of the S809 airfoil with the angle of attack in dynamic pitching motion: (a) lift coefficient (αmean = 14°, αamp = 10°); (b) drag coefficient (αmean = 14°, αamp = 10°); (c) lift coefficient (αmean = 8°, αamp = 10°); (d) drag coefficient (αmean = 8°, αamp = 10°).

worth noting that flow separation at large angles of attack is very sensitive to experimental conditions, such as the inflow turbulent intensity, and the airfoil surface, and the measurements at large angles of attack have much larger uncertainty than those at small angles of attack [48]. Besides, the turbulence model also introduces an inevitable error in the numerical simulation. Even so, our simulation predicts the static aerodynamic performance of the airfoil with a reasonable accuracy. As can be observed, the static stall angle of attack by our numerical simulation is about 2° larger than the experimental result, and the average relative error between the numerically calculated drag coefficient and the experimental one is less than 8%. To further verify the capability of the proposed method for dynamic conditions, an airfoil with a periodic pitching motion is simulated here. The attack angle of

second-order upwind scheme is used for spatial discretization.

2.3. Numerical verification In this section, the numerical method is firstly validate under a static state. The experimental lift and drag coefficients of the S809 airfoil by Ramsay et al. [47] are introduced to make a comparison with the numerical prediction results. Considering the uncertainty of the wind tunnel measurements, an error band of 5% is superposed on the experimental data. As shown in Fig. 3, in the region of small angles of attack (α < 8°), the present numerical simulation accurately predicts the airfoil lift and drag coefficients; while in the region of large angles of attack, the simulation results slightly go beyond the error zone. It is 469

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the airfoil varies follows:

α = αmean + αampsin(2πft ),

Table 2 Simulation cases for SDD.

(1)

Deep defect shape

where, αmean is the mean angle of attack for sinusoidal oscillation, αamp is the amplitude, and f is the oscillating frequency. To quantify the characteristic frequency of airfoil oscillation, a dimensionless reduced frequency is defined as:

k = πfc / U∞,

(2)

where, c is the airfoil chord length, and U∞ is the inflow velocity. The parameter k takes into account the interaction of oscillating motion in the longitudinal axis with the main inflow. In ANSYS-Fluent software, a user-defined function (UDF) is used, enabling the entire computational domain and mesh to sinusoidally oscillate around the point at a quarter of the chord length. The simulation parameters are exactly the same as those set in the experiment [47]. To verify the reliability of the present numerical method, both the data from physical experiment and the prediction results from the L-B model [48] are introduced for comparison. Two sets of dynamic experimental data are selected for quantitative comparison. For the first set, αmean = 14°, αamp = 10°, and the corresponding angle of attack ranges from 4° to 24°; for the second set, αmean = 8°, αamp = 10°, and the corresponding angle of attack ranges from − 2° to 18°. For both sets of experiments, the dimensionless reduced frequency is 0.077 . Fig. 4 shows the variation of dynamic lift and drag coefficients with the angle of attack for the above two experimental cases. Both the lift and drag coefficients change periodically in the pitching motion of airfoil, and they form a hysteresis loop in the upstroke and downstroke stages. For the first set of experimental parameters, several time steps are tested for the calculations, as shown in Fig. 4(a) and (b), when the time step reduces from 5 × 10−4 s to 5 × 10−5 s, the prediction results are significantly improved, but when the time step is further reduced, the results is not improved. Hence, the time step of 5 × 10−5 s, corresponding to 3.5 × 10−3c / u , is used for all the subsequent simulation of the dynamic cases. As shown in Fig. 4, for the first validation case, the numerical results show good agreement with the experimental ones in the upstroke stage, but the lift coefficient is slightly overestimated in the downstroke stage; for the second validation case, the simulation results and the experimental ones show an even larger discrepancy when compared with the first case. However, compared with the results from the L-B model that are widely used in engineering, our simulation results are much more accurate with a mean error less than 15%. Considering the uncertainty and strong unsteadiness of the dynamic stall, the airfoil dynamic performance is predicted by the present method with a reasonable accuracy, and is well accepted in engineering.

Opening size

Equivalent depth

t * = t / ta

h* = h/ c

Rectangular defect

6% 12% 25%

1%, 2%, 3% 1%, 2%, 3% 3%, 4%, 5%

Smooth sunken deformation

6% 12% 25%

1%, 2%, 3% 1%, 2%, 3% 3%, 4%, 5%

Random deep pits

6% 12% 25%

1%, 2%, 3% 1%, 2%, 3% 3%, 4%, 5%

Fig. 5. Schematics of SDD on the leading edge: (a) Rectangular defect; (b) Smooth sunken deformation; (c) Random deep pits.

3.2. Aerodynamic performance under static state 3.2.1. Effects of defect equivalent depth and opening size Fig. 6 shows the curves of lift coefficients, drag coefficients and liftto-drag ratios for defective airfoils with different defect shapes, opening sizes and equivalent depths. As is shown, at small angles of attack, the lift-coefficient curve of defective airfoil overlaps that of the smooth airfoil. As the angle of attack increases, the lift-coefficient curve of defective airfoil begins to deviate from that of the smooth airfoil. Here, the corresponding angle of attack is defined as the lift-coefficient curve deviation angle αd . In presence of the defects, the static stall angle of attack αd of the airfoil and the maximum lift-to-drag ratio (Cl/ Cd )max reduces significantly. At large angles of attack, the lift coefficient of the defective airfoil substantially decreases with a remarkable enhanced drag coefficient. By comparing the lift (drag) curves with different colors in Fig. 6, it can be concluded that the aerodynamic performance of airfoil with SDD is strongly dependent on the defect opening size. Gharali et al. [10] and Wang et al. [13] have also found the similar result, which provides a clear support to our current finding. For SDD of a specific shape, when the defect opening range is constant, the airfoil performance is fairly insensitive to the defect depth. Table 3 lists the maximum lift coefficient Clmax , maximum lift-to-drag ratios (Cl/ Cd )max , αd and αs of the defective airfoil with different defect opening sizes when the defect equivalent depth h*=3%. It can be observed from the table that as the defect opening size increases, the Clmax , (Cl/ Cd )max and αd of the defective airfoil show a monotone and sharp decreasing. For the 27 SDD cases in the present study, compared with that of the smooth airfoil, Clmax reduces by about 19% to 61%, (Cl/ Cd )max reduces by about 23% to 72%, and αd reduces by 2° to 8°. At a small angle of attack, such as when α = 0°, the drag increases by 0.5% to 36%, while at a large angle of attack, such as when α = 18°, the drag increases by 50% to 217% . The degradation of the airfoil performance due to SDD agrees well with that of the previous studies [10,12,13,11].

3. Effects of surface concaved deep defects on the aerodynamic performance of an airfoil 3.1. Simulation cases SDD on the leading edge of airfoil is numerically simulated in this section, and then SSD is studied in Section 4. To reveal the effects of defect key parameters, three defect shapes (rectangular defect, smooth sunken deformation and random deep pits), three opening sizes (t * = t / ta = 6%, 12% , and 25%), and three equivalent depths (h* = h/ c = 1%, 2%, and 3% for t * = 6%;h* = 1%, 2%, and 3% for t * = 12%;h* = 3%, 4%, and 5% for t * = 25%) are considered, with specific cases shown in Table 2. Here, the airfoil maximum thickness ta and chord c are used to quantify the defect opening size and equivalent depth, respectively. Similarly, the corresponding dimensionless defect area s * = s / cta . For clarification, schematics of the three defect shapes are shown in Fig. 5.

3.2.2. Effects of defect shape By comparing the lift and drag coefficient curves of airfoils with different defect shapes at a certain defect opening size in Fig. 6, it can 470

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Fig. 6. Variation of Cl, Cd and Cl/ Cd with the angle of attack for SDD airfoils with different defect shapes, opening sizes and equivalent depths.

and contours for the smooth airfoil are also shown. Fig. 8 gives a clear scenario that SDD can significantly alter the flow structure near the airfoil leading edge. Since the defect equivalent depth is relatively large, the airflow blows into the defect cavity and forms an enclosed vortex system, which blocks the momentum exchange between the external flow and cavity flow. In other words, because of this effect mechanism, the internal surface of SDD is unable to fully interact with the ambient flow, which gives a reasonable explanation why the aerodynamic performance of SDD airfoils is insensitive to both the defect depth and shape. Behind the sharp corner of the defects, an elongated leading-edge separation bubble forms at the suction side of the airfoil. Under negative pressure gradient, the flow reattaches on the airfoil surface downstream of the bubble. After the reattachment, the momentum of boundary-layer flow on the airfoil suction side is reduced obviously, which consequently weakens the capability of viscous flow attaching on the surface. Due to the leading edge defects, flow separation at the trailing edge of the SDD airfoil remarkably intensifies and the separation point substantially moves forward. Obviously, with the expansion of the separation vortex, more fluids are involved into the separation region. Because of different defect shapes, flow on the airfoil leading edge varies greatly, such that a pair of counter-rotating spanwise vortexes are formed in the rectangular defect, a single separation vortex is formed in the smooth sunken deformation defect, while a complex vortex system presents inside the random deep pits. The vortex systems vary with the geometry of defects; however, they interact with the ambient flow in a similar way, that is, a relative isolated region is formed inside the defect cavity, which makes the aerodynamic performance of the airfoil only sensitive to the opening size that directly interacts with the outer flow.

Table 3 Aerodynamic performance coefficients of SDD airfoils. Defect opening size (dimensionless)

Smooth airfoil

t * = 6%

t * = 12%

t * = 25%

Rectangular defect

Clmax (Cl/ Cd )max αd αs

1.24 48.6 – 16°

0.98 35.54 4° 14°

0.72 28.53 2° 12°

0.50 16.3 0° 8°

Smooth sunken deformation

Clmax (Cl/ Cd )max αd αs

1.24 48.6 – 16°

0.92 37.28 4° 14°

0.72 27.77 2° 12°

0.54 15.61 0° 8°

Random deep pits

Clmax (Cl/ Cd )max αd αs

1.24 48.6 – 16°

0.94 37.32 4° 14°

0.71 28.37 2° 12°

0.55 15.48 0° 8°

be observed that both the lift and drag coefficients of airfoil with leading edge SDD are insensitive to the defect shape. It means that for SDD, the defect opening size is the key parameter, while the defect equivalent depth and the defect shape only have very limited influences. To reveal the mechanism of SDD, Fig. 7 presents the streamlines and contours of the streamwise velocity for SDD airfoils with different shapes at α = 12°. For the defective airfoil, the opening range of t * = 12% and the equivalent depth of h* = 2% are selected here. These cases attempt to first illustrate the effect mechanism of SDD and then the differences among three shapes. For comparison, the streamlines

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Fig. 7. Streamlines and contours of the streamwise velocity for smooth airfoil and SDD airfoils (t * = 12%, h* = 2% ) at α = 12°: (a) smooth airfoil; (b) airfoil with rectangular defect; (c) airfoil with smooth sunken deformation; (d) airfoil with random deep pits.

Fig. 8. Distribution of surface pressure coefficient for smooth airfoil and defective airfoils with the same equivalent depth (h* = 3% ) but different shapes at α = 8°: (a) t * = 6% ; (b) t * = 12% ; (c) t * = 25% .

at the suction side for x > 0.5c . As the defect opening size enlarges, the above trend becomes more obvious. When t * = 25%, the pressure coefficient of the pressure side in the middle of the airfoil declines even smaller than that of the suction side, further reducing the airfoil lift coefficient.

Fig. 8 shows the surface pressure coefficient of smooth airfoil and SDD airfoils. Three different defect shapes are compared under the same equivalent depth of h* = 3% at α = 8°. As is shown, the leading edge SSD significantly reduce the differential pressure between the pressure side and the suction side, resulting in a reduction of the lift coefficient. At a certain opening size of SDD, pressure coefficients of the defective airfoils with different shapes are almost the same. The result agrees well with that of Fig. 8, further indicating that for the leading edge SDD, the airfoil aerodynamic performance is not much influenced by the defect shape. When t * = 6%, the surface pressure coefficient of the SDD airfoil varies little, but a slight increase of the pressure coefficient can be observed at the suction side. When t * = 12%, for the leading part of the airfoil ( x < 0.5c ), the momentum of boundary-layer flow reduces significantly at the suction side, and the pressure coefficient increases notably, implying a higher possibility of flow separation

3.3. Dynamic performance Fig. 9(a) and (b) plot the dynamic lift and drag coefficients of SDD airfoils under the pitching oscillating motion. Results for the three different defect shapes are compared at t * = 12% and h* = 1%. A similar conclusion as that under static state is demonstrated: the defect shape only slightly influences the dynamic performance of the airfoil. Further, SDD airfoils with different equivalent depths also illustrate similar results that both the lift-coefficient curve and drag-coefficient curve only 472

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Fig. 9. Variation of the dynamic (a) lift coefficient and (b) drag coefficient with the angle of attack for defective airfoils with the same opening size (t * = 12% ), same equivalent depth (h* = 1% ) but different shapes; variation of the dynamic (c) lift coefficient and (d) drag coefficient with the angle of attack for rectangular defect airfoils with the same equivalent depth (h* = 3% ) but different opening sizes.

separation area of the defective airfoil are integrated, covering the entire suction side; and the airfoil enters the deep stall condition, resulting in a sharp drop in the dynamic lift coefficient. Correspondingly, for the smooth airfoil, flow separation mainly occurs at the trailing edge; as the angle of attack increases, the stall region gradually enlarges and the flow separation point moves forward. In the initial of the downstroke stage, periodic vortex shedding appears in the large separation region of the defective airfoil, causing the lift and drag coefficients to oscillate up and down. In contrast, flow on the smooth airfoil is relatively simple. As the angle of attack decreases, flow in the separation area gradually reattaches on the airfoil surface, but at similar angles of attack, the stall area is larger than the separation region in the upstroke stage. Corresponding to the dynamic hysteresis loops of the lift (drag) coefficient, a hysteresis phenomenon occurs in the evolution of separation flow on the airfoil suction side in the downstroke stage. By comparing the dynamic flow structure of three defective airfoils with different defect opening sizes, it can be observed that when the defect opening range is larger, the leading separation is enhanced, and the evolution of the separation vortex system becomes more complicated. Compared with the airfoil under static state, the evolution of dynamic flow is more intensely affected by the leading edge SDD. In this section, the SDD airfoils are investigated systematically, including the static and dynamic aerodynamic performance, the flow structures as well as the influence mechanisms. In the following, we will carry out study on the SSD airfoils.

differ slightly at different equivalent depths. For brevity, the results are not shown here. In the following, we will select a certain parameter combination (rectangular defect, h* = 3%) and focus on the influence of the defect opening size. Fig. 9(c) and (d) exhibit the dynamic lift and drag coefficients of the airfoil with rectangular SDD of different opening sizes. As can be observed, at 2° < α < 7°, the lift and drag coefficients of the defective airfoil overlap those of the smooth airfoil in the upstroke stage; at α > 7°, both the lift and drag coefficients of the defective airfoil start to differ from those of the smooth airfoil. Due to SDD, the dynamic stall angle of attack reduces notably; the lift coefficient decreases sharply after dynamic stall and exhibits an obvious oscillation at the initial of the downstroke stage (at large angles of attack). It is worth noting that the dynamic drag coefficient of the defective airfoil increases much more significantly when compared with that under static state (the maximum static drag coefficient increases by about 216% , but the maximum dynamic drag coefficient increases by 565%). Correspondingly, the lift coefficient reduces to a very low level at this stage, and the opening of hysteresis loop formed by the lift (drag) coefficients substantially enlarges. As the opening size of SDD increases, the dynamic performance of the airfoil becomes worsen, i.e. in the upstroke stage, the deviation angle of attack further reduces, the dynamic stall advances, the lift (drag) coefficient further decrease (increases), and the aerodynamic force coefficients oscillate more strongly in the initial of the downstroke stage. Fig. 10 illustrates the streamlines and contours of the streamwise velocity around rectangular SDD airfoils under dynamic motion. Flow structures for SDD with different opening sizes (t * = 6%, 12% and 25%) under a certain equivalent depth (h* = 3%) are compared in details. For clarification, the same plots for smooth airfoil at the same instant are also presented. As is shown, in the upstroke stage, at α = 12.8°, the smooth airfoil possesses good flow attaching characteristics, but the defective airfoil shows a small range of flow separation at both the leading edge and trailing edge. As the angle of attack increases, flow separation on the suction side of the defective airfoil gradually deepens; at α = 18°, the leading edge separation area and trailing edge

4. Effects of surface shallow defects on the aerodynamic performance of airfoils 4.1. Simulation cases Different from SDD, SSD are mainly distributed along the airfoil profile around the leading edge. Such defects are often found in the leading edge coating shedding or surface pits caused by rain or sand erosion. Though SSD are various in shape, two typical leading edge 473

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Fig. 10. Streamlines and contours of the streamwise velocity for rectangular defect airfoils with the same equivalent depth (h* = 3% ) but different opening sizes under pitching motion.

SSD has a predominate effect on the airfoil aerodynamic performance. As the defect depth increases, the lift coefficient and the maximum liftto-drag ratio decrease, the drag coefficient rises, and the stall angle of attack reduces. Another distinction from SDD is that the aerodynamic performance of SSD is also fairly sensitive to the defect shape and range. When h* = 0.5%, the aerodynamic performance of airfoils with random shallow pits is worse. But quantitatively, the effect of the defect shape or range is inferior to that of the equivalent depth, indicating that at the initial stage of defects, the equivalent depth plays a critical role. Among the 18 SSD cases in the present study, the maximum lift coefficient of the airfoil reduces by 1% to 35%,the maximum lift-to-drag ratio reduces by about 2% to 45%, and the maximum drag coefficient increases by 54% to 131% . Taking a certain defect range (r * = 25%) and equivalent depth (h* = 0.1%), the streamlines and contours of the streamwise velocity around defective airfoils with different defect shapes are compared in Fig. 13(b) and (c). As is illustrated, SSD distribute along the profile of leading edge with h ≪ r , and the defect surface can fully interact with the incoming flow. Thus, the retardation effect of SSD on the incoming flow is closely related with the defect shape. Different flow structures can also be observed at the airfoil leading edge due to different defect shapes. For example, when flowing from the leading edge to the suction side, flow separation appears at the forward-facing step of the concave defect, while small-size vortexes form inside the small gouges of the random pits. Due to SSD, the momentum in the suction side boundary layer lessens, which thickens the boundary layer and reduces the capability of the flow attaching on the airfoil. In contrast to the elongated leading separation bubble induced by SDD, no apparent leading separation occurs for SSD cases. Fig. 13(c)–(e) compare the streamlines and contours of the streamwise velocity around SSD airfoils with different equivalent depths. Here, the defect of random shallow pits is only focused. Similar results can be obtained as the cases with concave defect, but for brevity, they are not plotted. When the defect depth increases, leading separation bubbles of the airfoil start to occur at the suction side (see Fig. 13(e)). At the present angle of attack (α = 14°), flow separation intensifies as the defect depth increases and the flow on the suction side is mainly dominated by the trailing-edge separation.

Fig. 11. Schematics of leading edge SSD: (a) concave defect; (b) random shallow pits. Table 4 Surface-defect airfoil parameters. Surface shallow defect shape

Opening size

Equivalent depth

r * = r / ta

h* = h/ c

Concave defect

15% 25% 35%

0.1%, 0.25%, 0.5% 0.1%, 0.25%, 0.5% 0.1%, 0.25%, 0.5%

Random shallow pits

15% 25% 35%

0.1%, 0.25%, 0.5% 0.1%, 0.25%, 0.5% 0.1%, 0.25%, 0.5%

defect shapes, i.e. concave defect and random shallow pits, are selected to study the effects of SSD on the airfoil aerodynamic performance, with the schematics shown in Fig. 11. Specific simulation cases are listed in Table 4. 4.2. Aerodynamic performance under static state Fig. 12 presents curves of the lift coefficients, drag coefficients and lift-to-drag ratios of SSD airfoils. Unlike SDD, the equivalent depth of 474

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Fig. 12. Variation of Cl, Cd and Cl/ Cd with the angle of attack for SSD airfoils with different defect opening ranges, equivalent depths and shapes.

Similar to the static-state aerodynamic performance, the dynamic aerodynamic performance of the airfoil is sensitive to the equivalent depth of SSD. As the defect depth increases, the dynamic stall angle of attack reduces, and the opening of hysteresis loop formed by lift (drag) coefficient enlarges. As is shown, when h* = 0.5%, the airfoil stall angle of attack reduces by about 3° than that for h* = 0.1%, and the aerodynamic coefficient is oscillated slightly in the downstroke stage. The corresponding drag coefficient also increases remarkably, and the maximum drag coefficient is about twice than that for h* = 0.1%. Fig. 15(c)–(f) shows the effects of defect range and shape on the dynamic lift and drag characteristics. It is clear that both the defect range and shape can effectively impact the airfoil dynamic performance. For SSD in the present study (h ≪ r ), similar to that under static state, the defect equivalent depth predominates the dynamic performance of the defective airfoils. Fig. 16 shows the streamlines and contours of the streamwise velocity around SSD airfoils with different defect equivalent depths under pitching motion. All the plots are made at a certain defect opening range (r * = 25%). The figure shows that in the upstroke stage, at α = 12.8°, flow of the defective airfoil is similar to that of the smooth airfoil, and no flow separation occurs; at α = 18°, the airfoil enters deep stall condition with a large flow separation at the trailing edge and the separation bubble enlarges with the defect equivalent depth. In the initial of the downstroke stage, as the defect equivalent depth increases, the separation point of the defective airfoil moves forward substantially, and more fluids are involved into the separation region. Correspondingly, the lift (drag) coefficient undergoes a sharp decline (enhancement).

Fig. 14(a)–(c) show the surface pressure distribution on airfoils with random shallow pits. Three different defect equivalent depths are compared in the figure. With the increase of defect depth, the retardation effect of SSD on flow at the leading edge is enhanced, which induces a raise in the pressure at the suction side. Similar to the roughness element, the retardation effect of leading edge SSD on the flow may be predominantly attributed to the pressure drag caused by the defect geometry, and the friction drag only plays a secondary role. For SSD with an equivalent depth h* = 0.25%, the protrusion height [49,50] of concave-defect forward-facing step corresponds to y+ ∼ 18, while the maximum protrusion height of random shallow pits corresponds to y+ ∼ 14 . Both are greater than y+ = 5 ( y+ < 5 is thought to be hydraulically smooth, where y denotes the grain size [51,52] of the roughness). Considering that for SSD, h ≪ r , the protrusions of SSD are fully exposed to the incoming flow and fully interact with the boundary-layer around the leading edge. Therefore, one possible explanation for the current results is that the protrusion height of SSD as well as their form drags increase with the defect equivalent depth, and thus the aerodynamic performance of the SSD airfoil is highly sensitive to the equivalent depth. It should be noted that for a certain defect equivalent depth, the airfoil with random shallow pits generates a slightly smaller (larger) lift (drag) coefficient than the one with concave defect, as shown in Fig. 12. This may be because the airfoil with random shallow pits contains a number of tinny protrusions, and a stronger interaction occurs between the protrusions and the incoming flow. 4.3. Aerodynamic performance under dynamic motion Fig. 15(a) and (b) present the lift and drag coefficients of SSD airfoils with different equivalent depths under pitching oscillating motion. 475

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Fig. 13. Streamlines and contours of the streamwise velocity of smooth airfoil and SSD airfoils with the same opening range (r * = 25% ) at α = 14°: (a) smooth airfoil; (b) concave defect (h* = 0.1% ); (c) random shallow pits (h* = 0.1% ); (d) random shallow pits (h* = 0.25%); (e) random shallow pits (h* = 0.5% ).

Fig. 14. Surface pressure coefficient distribution for smooth airfoil and random shallow pits airfoils with different defect equivalent depths at α = 12°: (a) r * = 15%; (b) r * = 25% ; (c) r * = 35% .

5. Summary and conclusions

impact the airfoil aerodynamic performance. At large angles of attack, the lift (drag) coefficient of defective airfoils decreases (increases) dramatically, and both the static and dynamic stall angles of attack reduce. In the present study, for airfoils with SDD, the maximum lift coefficient decreases by about 19% to 61% , the maximum drag coefficient increases by about 50% to 217% , the static stall angle of attack reduces by 2° to 8°, and the dynamic stall angle of attack reduces by 1° to 3°, when compared with that of the smooth airfoil. For airfoils with SSD, the maximum lift coefficient decreases by about 1% to 35%, the maximum drag coefficient increases by about 54% to 131% , the static stall angle of attack reduces by 2° to 6°,

In the present study, a systematic study is carried out on two typical types of defects (SDD and SSD) on the leading edge of the S809 airfoil. Influences of the defect shape, opening size and depth are quantitatively investigated under both the static and dynamic state by using a SST k − ω transition model. An in-depth elaboration on the flow structures and influence mechanisms is presented for both types of defects. The main conclusions are as follows: (i) Both SDD and SSD on the airfoil leading edge can significantly 476

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Fig. 15. Variation of the dynamic (a) lift coefficient and (b) drag coefficient with the angle of attack for random shallow pits airfoils with the same defect opening range (r * = 25% ) but different defect equivalent depths; variation of the dynamic (c) lift coefficient and (d) drag coefficient with the angle of attack for random shallow pits airfoils with the same defect equivalent depth (h* = 0.25%) but different opening ranges; variation of the dynamic (e) lift coefficient and (f) drag coefficient with the angle of attack for airfoils with the same defect opening range (r * = 25%), the same defect equivalent depth (h* = 0.25%), but different shapes.

separation bubble is formed at the suction side of the airfoil. Downstream of the bubble, the flow reattaches on the airfoil with a remarkable momentum reduction. Because of this retardation effect, the tailing-edge separation is intensified at large angles of attack, and in the stall condition, flow at the suction side of the airfoil is dominated by flow separation at both the leading edge and trailing edge. (iii) Under dynamic pitching motion, the opening of the lift-coefficient (drag-coefficient) hysteresis curves is increased substantially due to the leading edge SDD. Compared with that on the static

and the dynamic stall angle of attack reduces by 1° to 2°, when compared with that of the smooth airfoil. (ii) The aerodynamic performance of airfoils with SDD on the leading edge is highly sensitive to the defect opening size. An enclosed vortex (system) is formed in the defect cavity, which suppresses the momentum exchange between the external flow and the cavity flow. Because of this mechanism, the internal surface of SDD cannot fully interact with the ambient flow, thus the defect shape and equivalent depth less affect the airfoil aerodynamic performance. Due to the sharp corner of SDD, an elongated leading-edge

Fig. 16. Streamlines and contours of the streamwise velocity of random shallow pits airfoils with the same defect opening range (r * = 25% ) but different defect equivalent depths. 477

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aerodynamic performance of an airfoil, more significant effects on the dynamic aerodynamic performance are observed, particularly in the downstroke stage. In the initial of the downstroke stage, periodic vortex shedding occurs in the large separation region of the defective airfoil, accompanied by strong oscillation of the lift (drag) coefficient. As the defect opening enlarges, the separation region at the leading edge increases, the evolution and periodic shedding of vortexes become more complicated. (iv) SSD is distributed along the leading edge of the airfoil, with the equivalent depth h ≪ r ; therefore, they can fully interact with the incoming flow. And all the defect equivalent depth, range and shape can significantly affect the airfoil aerodynamic performance. SSD slows down the external flow by a mechanism similar to that of the roughness element. The protrusion height of SSD as well as their form drags increase with the equivalent depth, which thus predominates the aerodynamic performance of the SSD airfoil. In contrast to SDD, only a slight leading-edge separation occurs at small angles of attack, and flow on the suction side of the airfoil is only dominated by the trailing-edge separation under the critical stall condition. Under dynamic pitching motion, the opening of lift coefficient (drag-coefficient) hysteresis curves also enlarges, but quantitatively, the increase is smaller than that for the SDD airfoil with the same defect opening size.

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