Sensitivity of wind turbine airfoil sections to geometry variations inherent in modular blades

Abstract

In the ongoing work to increase the efficiency of large-scale, horizontal-axis wind turbines, the modular blade concept has been proposed. This article works toward quantifying the aerodynamic performance of modular blades, whose baseline profile remains unchanged from conventional blades but which are susceptible to a larger degree of variation in both manufacturing tolerances and fabrication materials, by examining the effects of offsets in the leading edge and the use of a tensioned membrane-fabric as a flow surface over the aft. Wind tunnel tests were performed on modified DU00-W-212 and DU91-W2-250 sections and included standard pressure measurements, as well as surface deflection measurements of the fabric. For the case of offsets near the nose of the profile, the offsets produce up to 17% decrease in $C_{l} / C_{d}$ . For the case of fabric in the aft of the model, the $C_{l} / C_{d}$ variations are strongly dependent on the spanwise location of the measurement.

Keywords

Wind turbine modular blades surface imperfections membrane wings wind tunnel digital image correlation

Introduction

The modular blade concept has been proposed in order to ease transportation requirements of long blade sections, to allow for tailored blades depending on site-specific wind conditions, to lower the on-site heavy machinery installation requirements, and to increase the feasibility of repairing or replacing installed blades (Dutton et al., 2000; Saenz et al., 2014; Vionis et al., 2006). All these serve to reduce the overall cost of wind power, in addition to the direct savings reaped from lower material costs due to lower blade weight and cheaper manufacturing processes for modular blades than for the current fiber-glass blades. One modular blade concept consists of a central box-beam spar anchoring both a rigid leading edge section and aft section which is partially covered by tensioned fabric as rendered in Figure 1. The aerodynamic challenges of such a construction lie both in the likelihood for thickness-wise misalignment of the different spanwise-running sections and in the flexibility associated with a membrane-fabric flow surface.

Figure 1.

Conceptual design for a modular wind turbine blade including (listed from leading edge to trailing edge) a nose module, box-beam spar member, paneled aft module, and trailing edge stiffener. The panels in the aft module might alternatively be formed from fabric instead of the rigid case shown here.

Misalignments in flow

Misalignments of spanwise-running segments of a modular blade can manifest themselves as changes to the two-dimensional outer mold line at a given radial location along the blade. Flow over the profile of a misaligned section may encounter different mold line geometries including right-angled steps or sloped ramps, the latter of which are the focus of the current study given certain manufacturing processes foreseen for modular blades. The aerodynamic effects of such ramped offsets can be seen in the local pressure field as well as in the stability of the flow downstream of the offset.

Many authors have performed fundamental studies on discontinuities in a boundary layer; see the reviews included in Eaton and Johnston (1981) for the backward-facing step and Awasthi et al. (2014) for the forward-facing step. On a backward-facing step, a local dip in pressure exists at the leading edge due to the streamlines bowing around the convex corner, followed by a pressure spike as the flow turns through the concave corner and straightens after reattachment; all this producing a zig-zag shape in the pressure distribution. The forward-facing step has two rather than one separation regions and similar jaggedness as for the backward-facing step.

In addition to the changes in the mean pressure field, two-dimensional imperfections in a flow surface have been shown to affect the stability of the boundary layer. According to Braslow (1960), two-dimensional imperfections will result in turbulence at some location downstream of the roughness until the Reynolds number is high enough at which point the turbulence will move upstream to the imperfection location. This behavior is suggestive that two-dimensional imperfections contribute to the amplification of disturbances according to the Tollmien–Schlichting transition theory. The roughness Reynolds number is defined as in equation (1)

R e_{k} = μ_{k} k / ν_{k}

(1)

where $μ_{k}$ is the local velocity in the undisturbed boundary layer at the top of the roughness element, $k$ is the height of the element, and $ν_{k}$ is the kinematic viscosity of the flow at the roughness element. The critical roughness Reynolds number, $R e_{k, t}$ , is the value of $R e_{k}$ required to initiate premature transition relative to the un-rough flow surface transition (Braslow, 1960). Figure 2 illustrates the above effect for a backwards-facing ramp on the suction surface of an airfoil.

Figure 2.

Features of flow over the suction surface of an airfoil with (a) smooth geometry and (b) backward-facing ramp. Not drawn to scale.

Drake et al. (2010) tested isolated steps in the presence of laminar boundary layers with favorable pressure gradients in order to assess current manufacturing tolerance requirements for laminar-flow wings. The authors cite conventional manufacturing tolerances for laminar-flow wings of $R e_{k, t}$ values of 150 and 80 for forward- and backward-facing steps, respectively, but note that these previous values may be overly conservative given the favorable pressure gradients typically experienced by the laminar boundary layer over the forward region of airfoils. Instead, over a range of pressure gradients from zero to strongly favorable, the authors measured $R e_{k, t}$ values of 150 to 2100 for the forward-facing step and 75 to 800 for the backward-facing step.

Similarly, Duncan et al. (2014) made measurements on isolated two-dimensional steps at the 15% $x / c$ location on a swept, laminar-flow wing. The critical step height was defined to be the height at which there is a sudden jump in the laminar-flow fraction which indicates that the transition location has jumped forward to the step location. Shear layer instability was hypothesized to be the dominant factor in this critical transition regime.

Membrane-fabric surfaces in flow

The fabric in this study behaves as a membrane due to its small thickness relative to its other two dimensions. Smith and Shyy (1996) note that the static aeroelastic problem for the simplest case of a single-membrane wing in two dimensions can be fully described by five variables: Reynolds number, angle of attack, excess ratio (equal to zero for a taut membrane), non-dimensionalized elastic modulus

Π_{1} = {(\frac{E h}{q_{\infty} c})}^{1 / 3}

(2)

and non-dimensionalized pre-stress

Π_{2} = {(\frac{S h}{q_{\infty} c})}^{1 / 3}

(3)

where $E$ is the elastic modulus of the membrane, $S$ is the pretension of the membrane, $h$ is the thickness of the membrane, q_∞ is the freestream dynamic pressure, and $c$ is the chord of the wing. Depending on whether the membrane tension is dominated by elastic stress or pre-stress, the relative importance of $Π_{1}$ versus $Π_{2}$ in the out-of-plane equilibrium are interchanged. The three-dimensional membrane problem is furthermore complicated by the need for bi-axial tension, potential anisotropy in membrane properties, aspect ratio effects, and membrane wrinkling.

Throughout the years, there have been a number of contributions assessing the performance of flexible sails and airfoils with varying degrees of both aerodynamic and structural non-linearity as reviewed by Newman (1987). Jackson and Christie (1987), for instance, applied an iterative, aeroelastic model to show that a single-membrane wing produced more lift than a rigid wing due to camber increases, especially at low angles of attack. A review focusing on micro-aerial vehicle applications of membrane wings at low Reynolds number is given by Shyy et al. (2007). One author, Galvao et al. (2006), measured increased $C_{l}$ for the membrane wing due to increased camber as well as increased $C_{d}$ due to both higher form drag (which is a by-product of the increased $C_{l}$ ) and possible membrane instability, the overall effect of these changes producing a $C_{l} / C_{d}$ for the membrane wing that is comparable to that of similar rigid wings.

Several authors also worked on the problem of double-membrane, or inflatable, membrane wings which has particular relevance to this study. The Princeton sailwing, proposed for applications both aeronautical (Fink, 1969; Fink et al., 1967; Ormiston, 1971) and related to wind energy (Maughmer, 1976; Sweeney et al., 1975), is a prime example of a double-membrane wing and consists of a fabric wrapped around a leading edge support and tensioned at the trailing edge by a wire. Due to the changes in induced tension in the fabric with angle of attack, the lift curve of the sailwing is non-linear. At low loading conditions, the fabric has low tension which allows the camber to change drastically over a short range of angles of attack. As loading and thus tension increase, the non-linear character of the tensioned fabric permits only small changes in the camber, so the lift curve has a slope more typical of a rigid wing. Approaching stall, the lift curve is more rounded than that of a typical rigid wing. The overall result is that the ${(C_{l} / C_{d})}_{m a x}$ of a well-designed sailwing approaches if not attains the same value as that of a rigid wing of the same aspect ratio.

Approach to present work

Consistent with the design of the proposed modular blade in Figure 1, the specific objectives of this work are to perform first-time analysis on the aerodynamic effects of a thickness-wise misalignment in the nose region and a flexible membrane-fabric surface in the aft region when applied to a wind turbine section.

To study the effects of misalignment of a nose module, the DU00-W-212 section, a 21.2% thick section designed at Delft University for wind turbine applications, was modified so that the region of the airfoil nose from $x / c = 0 - 0.200$ is offset from the main body in the thickness-wise direction as shown in Figure 3(a). The offset is imposed toward the suction side to simulate the more severe aerodynamic effect of the two potential offset directions. The offset nose module is connected to the main body on either side of the model by linear ramps running from $x / c = 0.200 - 0.225$ , thus producing isolated ramps similar to the isolated steps in Drake et al. (2010) and Duncan et al. (2014). The offset magnitude is based on an estimate of the manufacturing tolerance of a modular wind turbine blade which was then scaled for the wind tunnel testing using the ratio of the wind tunnel model’s chord to the full-scale chord at the radial location where airfoils of 21% thickness may be found on the wind turbine blade. Two offset magnitudes corresponding to a typical misalignment and a worst-case misalignment were tested which are 0.305 mm, or 0.0500% chord, and 0.610 mm, or 0.100% chord, respectively. The $R e_{k}$ values of these offsets on the suction side at the design angle of attack equate to roughly 1400 and 4400, respectively, as calculated from integral boundary layer profiles, which suggests that the ramps will indeed cause premature transition relative to the baseline case according to the literature. Wind tunnel measurements and analysis of mean surface pressure, lift, and drag are complimented by corresponding XFOIL simulations.

Figure 3.

Profiles of the (a) DU00-W-212 and the (b) DU91-W2-250 along with the geometry modifications tested in this study.

To study the effects of an aftwards membrane-fabric flow surface, the DU91-W2-250 profile was chosen which is a 25% thick section also designed at Delft University. Modification to the original profile has been made to replicate the geometry of a potential modular wind turbine blade as shown in Figure 3(b). The profile is straightened between $x / c = 0.461 - 0.823$ to replicate the flattened shape of an unloaded tensioned fabric. As seen in Figure 3(b), there are ramps leading into and out of the panel region so that the total extent of the modifications run from $x / c = 0.446 - 0.850$ . The effect of the straightening on both the pressure and suction sides is to produce a slight reduction in camber in the unloaded condition, although the flexible fabric changes camber in the presence of flow. To gauge the effects of such camber change, the panel region is alternatively fitted with rigid, aluminum panels, as well as the fabric panels. Measurements on this model include mean surface pressure, lift, drag, and wake cross-sections, as well as deflection of the fabric under wind loading via digital image correlation (DIC). Comparison of the experimental data is made with an aeroelastic simulation of the airfoil to support the analysis. Another modification to the DU91-W2-250 profile which was included on the model but is not a focus of this article is the ramped offset of the forward 25% chord of the nose by 0.590 mm, or 0.0738% chord, which is again made in the direction of the suction side.

Apparatus and techniques

Stability Wind Tunnel

The measurements presented in this study were taken at the Stability Wind Tunnel (SWT) on the campus of Virginia Tech. The tunnel, with its 1.85 m × 1.85 m × 7.3 m hardwall test section, is a closed-circuit, single return facility producing unblocked freestream velocities up to 80 m/s for chord Reynolds numbers exceeding 4 million. The tunnel has turbulence intensity levels ranging from 0.016% at 16 m/s to 0.031% at 57 m/s. Additional information on the tunnel circuit, test section specifications, and standard instrumentation are in Devenport et al. (2010).

Pressure measurements on the airfoil for this test included sectional lift and drag. The former is accomplished through the integration of airfoil surface pressure data measured via taps near the model’s midspan. These pressure data are measured by an Esterline 9816/98RK pressure scanner with a range of ±2.5 psi and accuracy of ±0.15% full scale. Each measurement consists of an average of at least 16 external samples, each of which is the result of 100 internal averages inside the pressure scanner. Drag measurements are performed with a wake rake located 1.75 m downstream of the model’s center of rotation that runs the entire width of the test section. The wake stagnation pressure is measured by an array of 127 Pitot tubes, 7 of which are additionally capable of measuring static pressures across the test section. The wake pressures are sensed with a set of 16TC/Digital Temperature Compensated (DTC) Gen 2 scanners by Pressure Systems, Inc. with a range of ±2.5 psi and a rated accuracy of ±0.03% full scale.

Wall-interference corrections to global coefficients and local static pressures are calculated from a panel method solution of the flow in the test section which yields interference velocities and their derivatives at the model location that are then used with the method of Allen and Vincenti (1944) to make corrections to the measured quantities. These corrections account for streamline curvature, solid blockage, and wake blockage. In addition, correction is made for the static pressure drop through the test section due to wall boundary layer growth and for the removal of mass flow from the test section due to the boundary layer control system (Joseph, 2014), when applicable.

Airfoil models

Tests were conducted on modified DU00-W-212 and DU91-W2-250 models as detailed in the following.

Modified DU00W-212 model

The 610 mm chord DU00W-212 shown in Figures 4 and 5 spans the full 1.85 m height of the test section and is constructed from 64 aluminum laminates of 25.2 mm thickness in addition to sections at the span ends that have the profile of the airfoil and fittings for the boundary layer control system. The CNC-machined laminates are aligned to mating laminates with dowel pins and compressed together by threaded rods running the span of the model. Aluminum shafts near the quarter-chord location protrude through the boundary layer control system and into turntables on both ends of the model, the upper shaft being connected to the turntable for angle of attack control.

Figure 4.

Bird’s-eye (above) and planform (below) views of the DU00W-212 model with the locations of the pressure taps as indicated by the “x” symbols.

Figure 5.

In-tunnel views of (a) the suction side of the DU00W-212, (b) a close-up view of the chordwise-running interface of the nose module and main body, and (c) a close-up view of the spanwise-running interface of the nose module and main body.

The DU00W-212 model has a removable nose module as shown in Figure 5(b) and (c) with span length of 1.01 m and chord length of 0.24 m or 40% chord. Each nose module fits into the cavity in the main body so that any spanwise or chordwise gap formed by the interfaces depicted in Figure 5(b) and (c) are typically no more than 1 mm or 0.13 mm, respectively. Such gaps are filled with sealing putty and smoothed over before being covered with 0.040-mm-thick tape prior to testing. Due to machining tolerances, the interface between the nose module and main body, which is more than 15% chord downstream of the designed ramps in Figure 3, also has a discontinuity associated with it on the pressure and suction sides that was treated on the pressure side with layers of 0.040 mm tape. The resulting height of these discontinuities was typically 0.15 mm (backward-facing) on the pressure side and 0.30 mm (forward-facing) on the suction side for the 0.3 mm offset model. The 0.6 mm offset model and baseline model had similar discontinuities at the interface location, the exact height of these not being measured. The effect of the discontinuities, which will be noted in the discussion of the airfoil pressure distributions surrounding Figure 11, should be borne in mind when interpreting the results, and the measured airfoil performance might be considered a lower bound for the nominal geometry.

Each of the nose modules noted above are instrumented with 45 pressure taps which complement the 28 taps on the main body of the airfoil. The taps are drilled to a diameter of 0.5 mm and are spread at an angle of 15° to the chordline to avoid contamination of downstream taps by the wake of upstream taps. Beneath the surface the taps connect to 1.6 mm internal diameter pressure tubing which leads out of the model through the shafts and to the pressure scanner.

Modified DU91W2-250 model

The 800-mm-chord modified DU91W2-250 has similar laminate construction to the DU00W-212 with 34 aluminum laminates each of thickness 49.1 mm. The model is similar to the DU00W-212 described previously in most respects; however, the offset in the nose region is machined into the profile rather than contained on a removable nose module, and there are no fittings for the boundary layer control system which was not used for this model.

Also unique to this model are the fittings for six removable, rectangular panels, three of which are visible on the suction side in Figure 6(a). The 6.4 mm deep panel cavities are 0.26 m spanwise and 0.29 m or 0.30 m chordwise for the suction and pressure sides, respectively, and are centered around the midspan of the model as indicated in Figure 7. Adjacent cavities are separated by a distance of 28.6 mm spanwise, the gap of which is occupied by a rigid plastic flow surface. The top and bottom panel cavities on each side of the model have no path for air to enter or exit the cavity, whereas the center panels on each side have channels into the interior of the model (and thus eventually to the control room) through which pressure tubing is routed. As a consequence of the channels to the center panels, the pressure difference and thus deflection across the center panels will in general be larger than that across the top and bottom panels. With the exception of the drag rake measurements, all data are taken over the center panels with the top and bottom panels working to create a near periodic boundary condition for the center panels.

Figure 6.

Cutaway rendering of the modified DU91W2-250 laminate model displaying the arrangement of the three suction-side cavities for panel mounting as shown in (a). One of the laminates near midspan has been removed and enlarged as shown in (b). A close-up view of the cavity region is shown in (c).

Figure 7.

Bird’s-eye (above) and planform (below) views of the modified DU91W2-250 model with the locations of the pressure taps as indicated by the “x” symbols.

Each of the cavities described above are fitted with panels consisting of an impervious, glass-fiber-reinforced membrane stretched over steel frames as seen in Figure 8(a) and (b). The outer dimensions of the frames are the same as those of the cavities described above minus twice the thickness of the fabric thus giving a panel aspect ratio of 1.1 to 1.2, and the width of each leg of the rectangular frames is 25.4 mm. To fabricate a panel, the fabric is stretched over the steel frames to a pretension of 900 ±230- N/m by a tensioning jig and glued in-place on both the top and bottom sides of the frames with a polyurethane/polyoxysilane all-purpose glue. After curing for 24 hours, each frame is removed and 14 mounting bolt holes and counterbores are machined around the perimeter.

Figure 8.

Tensioned fabric panel with pressure taps. Views of the (a) flow-side surface with speckling, (b) back-side surface with six pressure ports, and (c) sample of the facing quality of the flow-side pressure taps which were punched by the punch head shown in the top image.

After installing the tensioned fabric panels on the model, it was noticed that the fabric had in some places wrinkles which were believed to be due to deformation of the tensioning frame imposed by slight misalignment of the mounting holes on the airfoil. To the touch, the tension in the wrinkled areas was noticeably lower than when the tension measurements were performed, and the direction of the wrinkles indicated that most of the tension loss occurred in the spanwise direction. By comparing measured fabric deflections from this study with corresponding simulation results, Brown et al. (2015) indicate that the actual tension in the fabric was likely two orders of magnitude lower than the original measurements. In terms of equations (2) and (3), the effect of lowering $Π_{2}$ at a given value of $Π_{1}$ will be larger deflections of the fabric under loading and more pronounced effects of the flexible camber on aerodynamic performance. While the wrinkles acted as indicators of tension loss when there was no loading on the fabric, the wrinkles were smoothed away when the fabric was placed under aerodynamic load, so there was not believed to be any adverse aerodynamic effects due to undulations in the fabric surface.

Figure 9 shows the paneled model in the wind tunnel, including close-up views of the transitions into the panel region for the fabric case and aluminum case in Figure 9(b) and (d), respectively. For the fabric case, some small spanwise-running steps in the profile, which usually stemmed from the surface of the fabric sitting just below the corresponding surface of the airfoil, created steps in the outer mold line which were generally no more than 0.25 mm, or 0.031% chord, and there were no associated gaps of any measurable width between the fabric and the model. For the aluminum case, any spanwise-running steps were generally smaller than those of the fabric model, though small gaps between the panels had to be taped over with 0.040-mm-thick tape as visible in Figure 9(c) to prevent air seepage.

Figure 9.

In-tunnel views of (a) the suction side of the model and (b) a close-up view of the transitions into and out of the fabric sections for the fabric-paneled model. (c and d) Corresponding views for the rigid-paneled model.

The center-span panels on both sides of the model such as the one in Figure 8 were instrumented with pressure taps, the spanwise and chordwise arrangement consistent with Figure 7. Both of the center-span fabric panels had six pressure taps as visible in the back-side view of a panel in Figure 8(b). Orifices through the fabric were made with a 1.0-mm-diameter circular punch that produced holes with the facing quality seen in Figure 8(c). Each pressure tap is made from a 9.5-mm-diameter, 4.8-mm-thick plastic disk glued to the backside of the fabric by epoxy glue. Each disk has an internally drilled 90° corner that leads from the back surface of the fabric out to a fitting for a 1.6 mm inner diameter pressure tube. Pressure-checking of the fabric-mounted pressure lines revealed some leakage, and upon investigation with soap and water, the leakage was discovered to be at least in part due to a small degree of porosity in the cross section of the fabric itself which vents to the cavity behind the fabric (the front side of the fabric that is exposed to the flow is, in fact, impervious to all flow). This small amount of leakage is not thought to have had a perceivable effect on the pressure data. Including both the panel-mounted taps described above and the conventional taps in the model laminates, the model contains a total of 64 pressure taps.

Fabric deflection measurements

To understand the aerodynamic impact of the flexible flow surface on the aft portion of the airfoil, DIC was employed which involves correlating patterns between undeformed and deformed images to calculate the local strain across a surface and also the out-of-plane deformations in the case of stereo-DIC (Sutton et al., 2009).

Measurements were performed with a pair of cameras from LaVision, type VC-Imager Pro 4M. The cameras have 2048 × 2048 pixel resolution for a total of 4 megapixels, as well as 7.4 × 7.4 µm pixel size and 14-bit digital output. Lenses from Nikkor with a focal length of 50 mm were found sufficient to capture the whole measurement space, which for this test was limited to the center-span panel on the suction side of the model. This panel was speckled with permanent black marker to provide the necessary non-reflective contrast for the correlation algorithm. Since it was not practical to refocus the cameras at each angle of attack, the cameras were mounted to an overhead camera rig that was directly coupled to the angle-of-attack rotation of the model. Because of varying refraction effects as the angle of attack was varied, it was necessary to perform a separate calibration of the cameras for each angle of attack; the details of which may be found in Brown et al. (2015). The camera positions on the overhead rig, selected with consideration for maximizing the depth resolution (Grewe and Kak, 1994), amounted to a stereo angle of 49°, providing an out-of-plane resolution of 40 µm. The data presented in this article consist of a time-average of 12 images at each condition which were processed with LaVision’s DaVis 8.2.1 software.

Results and discussion

The following subsections describe the aerodynamic performance of the modified profile models first in the forward offset region and then in the aftward panel region. In preparation, two considerations are here noted related to the comparison of data between different models.

Subsequent to the test, it was discovered that the pitching moment and lift of the models had caused torsional deflection of up to 1° within the model mounting system. This was corrected for by using the relationship between the angle error and the dimensional pitching moment and lift as determined from subsequent tests of similar airfoil models. Use of this relationship reduced the relative uncertainty within a polar to ±0.15°, and the absolute uncertainty between polars of the same airfoil at a given point in the lift curve is estimated at ±0.50° which originates from torsional slippage that occurred over the duration of the testing.

The coupled invicid/viscous flow solver XFOIL was used as a supporting resource in this investigation to offer insight into the boundary layer behavior and other flow physics around the ramps and paneled regions. In all cases, the simulations were run with a critical N-value of 9 and at the same Reynolds and Mach numbers as those measured experimentally. Meaningful comparison of the pressure distributions with XFOIL using the exact measured angles of attack was frustrated by the residual absolute angle of attack error resulting from the torsion correction noted above. To avoid this, the XFOIL pressure distributions have been interpolated between angles of attack to match the experimental data as closely as possible, and the interpolated XFOIL angles of attack are reported along with the measured angles, where applicable.

Effect of offsets on aerodynamic performance

The DU00W-212 model was the focus of the analysis on the misalignment offsets in the nose region. After applying the angle of attack torsion correction referenced above, angle of attack increments were added, within the ±0.50° absolute uncertainty, to each polar of the offset models according to the angle of attack increment predicted between models by XFOIL in the linear region.

Global aerodynamic performance

In order to clearly pronounce the effects of the offset ramps on the global aerodynamic coefficients such as $C_{l}$ , $C_{d}$ , and $C_{l} / C_{d}$ , these coefficients are plotted in Figure 10 as the difference of each between the modified model and the baseline model.

Figure 10.

Variation in (a) $C_{l}$ , (b) $C_{d}$ , and (c) $C_{l} / C_{d}$ from the baseline case plotted versus angle of attack, $α$ , at 2.5 million Reynolds number for the DU00W-212.

Figure 10(a) plots this difference for $C_{l}$ , and while the absolute location of the experimental data along the $C_{l}$ axis is dependent on the aforementioned angle of attack correction which invokes the aid of XFOIL, the relative behavior of the lift across different angles of attack is independent of the simulation. The lift is mostly flat throughout the linear range of angles of attack in both the experimental data and XFOIL predictions, thus indicating that the effect of the offsets can essentially be considered an increment in angle of attack between the baseline and modified models. Such an increment is consistent with the concept of the offset models having an effective increase in camber over the baseline model since camber’s effect on lift in the limit of thin-airfoil theory is to alter the zero-lift angle of attack. The magnitude of the $C_{l}$ increase for both modified models shown in the linear region of Figure 10(a) is roughly 0.008 or 0.7% of $C_{l, m a x}$ . Moving higher into the linear range toward the design angle of attack at ${(C_{l} / C_{d})}_{m a x}$ , the $C_{l}$ of the 0.6 mm model falls by −0.006, or 0.5% of $C_{l, m a x}$ , below the baseline value for the experimental data, and a similar drop is seen for the XFOIL simulation. Based on transition data from XFOIL simulations (Brown et al., 2015), this drop appears to be the result of tripping by the ramp which prematurely moves the transition location on the suction side of the 0.6 mm model up to the ramp in the same critical manner noted by Duncan et al. (2014).

It is important to keep in mind that the differences in lift between the baseline and modified models amount to small percentage changes in the overall lift. While these changes are of the same order as the repeatability of the facility which is quoted for the lift measurement at 0.6% $C_{l}$ , the consistency of the relative behavior with XFOIL, as well as between different nose modules, builds a case that the above-noted lift effects are not only plausible but true.

Figure 10(b) shows the $C_{d}$ results for the modified profile models. As with the lift results, the drag changes relative to the baseline are mostly flat with angle of attack throughout the linear region. The first perceivable drag increase relative to the baseline begins at 4.7° for the 0.6 mm offset model. At 7.7°, the rise in drag reaches a maximum of 19 counts, or 17% of $C_{d}$ , which is consistent with the theory of premature transition and the observed drop in lift at the same angle. Similarly, the 0.3 mm offset model sees a spike in drag though smaller and more delayed, confirming the prediction that the $R e_{k}$ for both offset geometries are critical.

Figure 10(c) shows the $C_{l} / C_{d}$ results for the modified profile models. The aforementioned transition behavior around ${(C_{l} / C_{d})}_{m a x}$ returns as reductions in $C_{l} / C_{d}$ relative to the baseline. At ${(C_{l} / C_{d})}_{m a x}$ , the 0.6 and 0.3 mm offsets result in a decrease of $C_{l} / C_{d}$ of 21.9 and 6.6, respectively, or 17% and 5% of ${(C_{l} / C_{d})}_{m a x}$ . These reductions are strongly dominated by the $C_{d}$ term rather than the $C_{l}$ term. The unintentional discontinuities at 40% chord mentioned above are notably more than 15% chord downstream of the designed ramps and thus should not play a strong role in the presumed premature transition of the offset models. These discontinuities could, however, act to increase the perceived drag of the offset models, so drag estimates for the offsets may tend toward overprediction, if anything. The 17% and 5% reductions of ${(C_{l} / C_{d})}_{m a x}$ are thus thought to be representative of the upper bound of that to be expected for offsets of the given height under the given flow conditions.

$C_{p}$ versus $x / c$ comparisons

We now examine the effect of the ramped offset in light of mean surface pressure measurements on the airfoil. Figure 11 shows the $C_{p}$ distribution over the DU00W-212 for the baseline and two modified profile cases at 6.29° angle of attack. It is seen that the modified profiles result in perturbations to the baseline flow while maintaining the same overall character of the flow around the airfoil. The presence of the ramps is discernible in the pressure data as a sequential peak and dip in $- C_{p}$ for the suction side and vice versa for the pressure side, according to the convexity and concavity of the flow surface at the beginning and end of the ramp, respectively. In addition to the jaggedness around the ramps, the effect of the unintentional discontinuities on the suction side around the 40% chord location is discernible for the two offset cases. The higher −C_p’s of the offset models in the pre-ramp region might be understood as increases in circulation which appear to be a result of the effective camber increase of the offset models over the baseline model.

Figure 11.

$- C_{p}$ versus $x / c$ at 6.29° angle of attack and 2.5 million Reynolds for the DU00W-212.

Effect of flexible camber on aerodynamic performance

The modified DU91W2-250 profile including both fabric and rigid panels was used for the analysis of modular blades with camber changes in the aft of the profile. This section includes analysis of the flexible camber with regard to global coefficients, airfoil pressure distributions, wake profiles, and fabric deflection distributions.

The same angle of attack correction procedure outlined above for the DU00W-212 was also used for the modified DU91W2-250 data. Namely, the angle-of-attack torsion correction was applied to the raw angles, followed by correction of the absolute angle of attack using offsets obtained by comparison with XFOIL predictions over the low lift portions of the polars. Throughout the below analysis, a static aeroelastic model designed to capture the fluid-structure coupling of the fabric is employed as a comparison to the measured behavior of the flow and fabric. This model, described in detail in Brown et al. (2015) and denoted below simply as XFOIL, is an iterative solver that uses XFOIL to solve for the aerodynamic solution via a strip theory approach and uses a membrane finite difference formulation to solve the structural solution of the fabric deformation. The model simulates the panel deflection and surface pressure distributions over the center-span panel on the pressure and suction sides and is especially helpful in the case of the pressure side where no deflection measurements were made.

Global aerodynamic performance

Figure 12(a) displays the lift coefficients and lift coefficient differences for the fabric and rigid cases at a Reynolds number of 2.5 million. While the variations outside of the linear range are seemingly uncorrelated, there is a discernible trend of the lift variation within the linear region. That is, moving from negative to positive angles, the fabric model has a higher lift curve slope than the rigid model which directly follows from the earlier discussion where the slope increase of flexible models over their rigid counterparts at low loading is attributed to the compliance of the camber. The largest measured positive deviation of the fabric model $C_{l}$ from that of the rigid model is 0.007 or 0.7% of $C_{l}$ , which occurs at 4.14°. The increased lift of the fabric over the rigid case at this angle and the angles surrounding it is a result of the deflection of both the pressure- and suction-side fabric panels toward the suction-side direction which increases the camber over the aft region of the model as will be described in later sections. This lift gain is also evident in the aeroelastic simulation, whose predictions have been plotted for two spanwise locations that cover the spanwise extent of the experimental pressure taps.

Figure 12.

Values of (a) $C_{l}$ , (b) $C_{d}$ , and (c) $C_{l} / C_{d}$ versus angle of attack, $α$ , as well as differences between the fabric and rigid cases, for the modified DU91W2-250 at 2.5 million Reynolds number. The error bars in (b) and (c) show the range of spanwise variation measured from cross-sectional wake profiles. The aeroelastic simulation results (labeled XFOIL) have been plotted for two spanwise locations that cover the spanwise extent of the experimental pressure taps.

While the fabric deflection does not produce large non-linearity in lift such as seen in the literature for Princeton sailwings, it is interesting that the greatest increase in lift of the fabric model over the rigid model occurs near the design angle of attack. With some tuning of the fabric structural properties such as the values $Π_{1}$ and $Π_{2}$ in equations (2) and (3), respectively, the fabric model should be able to produce similar lift performance not only to that of the rigid case of this study but also to that of the carefully designed original DU91W2-250 profile, at least near the design angle of attack.

The $C_{d}$ data are presented in Figure 12(b). The upper plot of this subfigure contains data from multiple experimental runs: polar sweeps with a fixed wake rake position as well as wake cross section sweeps at select angles, all data for the case of 2.5 million Reynolds number. There is quite large spanwise variation in $C_{d}$ as shown by the margin bars, especially for the fabric model at high angles of attack. For instance, the range of $C_{d}$ values measured across the fabric panels at 6.6° is 21 counts. The drag values of the polar sweeps fall at the low end of the range of the cross-sectional drag measurements because the spanwise location of the wake rake for the polar sweeps was between panels where the drag is lowest. Considering the polar data, the $C_{d}$ of the fabric model is higher than that of the rigid model between −7° and 4° in both the experiment and simulation which according to the simulation is primarily due to form drag increases. For the three angles just around ${(C_{l} / C_{d})}_{m a x}$ , the drag difference between models falls to smaller values without a clear trend. However, it is reiterated that a spanwise-average drag is required in order to get a meaningful picture of the drag from a model with flexible panels. More discussion of the drag variation is included further below in the discussion of the wake profiles.

Figure 12(c) shows the $C_{l} / C_{d}$ results which are again dominated by the $C_{d}$ term rather than the $C_{l}$ term as with the DU00W-212. The differences between models are small in the case of the polar data which is in agreement with the previously noted literature that observed only small perturbations of $C_{l} / C_{d}$ performance due to the insertion of flexible flow surfaces into wings. Considering the data of the cross-sectional wake sweeps, the high sensitivity of the $C_{l} / C_{d}$ to the spanwise location of the drag measurement is again evident. It is believed that future testing of modular blade designs with flexible surfaces should include significant consideration toward how to accurately represent the average drag across the span.

$C_{p}$ versus $x / c$ comparisons

The results of the previous section are further informed by examining the mean surface pressure distributions over the airfoils in Figure 13. Although the ramped nose offset creates slight deviations in the −C_p’s between x/c = 0.225–0.250, the analysis below focuses on the paneled region, with $x / c$ limits of 0.446 and 0.850, as shown in detail in Figures 14 and 15.

Figure 13.

−C_p versus $x / c$ at 6.59° angle of attack and 3.0 million Reynolds number for the DU91W2-250.

Figure 14.

Section profiles and baseline-subtracted section profiles for the (a) suction side and (b) pressure side of the modified DU91W2-250 at 3.0 million Reynolds number. Baseline subtraction is relative to the modified rigid profile. The experimental data is at 6.59° angle of attack and the aeroelastic simulation (labeled XFOIL) is at 6.37°.

Figure 15.

−C_p and baseline-subtracted −C_p versus $x / c$ for the (a) suction side and (b) pressure side of the modified DU91W2-250 at 3.0 million Reynolds number. Baseline subtraction is relative to the modified rigid profile. The experimental data is at 6.59° angle of attack and the aeroelastic simulation (labeled XFOIL) is at 6.37°. The simulation results have been plotted for two spanwise locations that cover the spanwise extent of the experimental pressure taps.

At the beginning and end of the panels, the abrupt changes in pressure in Figures 13 and 15 are due to the discontinuity of the ramps leading into and out of the panel region. Over the width of the panels, the behavior of the pressure closely corresponds to the measured profile shape as seen by comparing subplots a(ii) between Figures 14 and 15, for instance. On the suction side, the flow’s local static pressure is lower than the internal model pressure (which is at or near freestream static pressure) which causes the fabric to bow into the flow relative to its original position. The suction panel’s deflection into the flow as shown in Figure 14(a) causes the flow to accelerate and raises the $- C_{p}$ in Figure 15(a). The reverse is true on the pressure side. Here, the pressure difference across the fabric causes it to deflect out of the flow, resulting in the observed lower $- C_{p}$ values.

It is interesting to consider the deflected fabric profile of Figure 14 versus the shape of the original DU91W2-250 profile. At the 6.59° angle of attack plotted in the figures, the shape of the fabric on the suction side turns out to be quite similar to that of the original profile, the same being true but to a lessor extent on the pressure side according to the simulation results. Thus, it is suspected that the aerodynamic performance of the fabric model near the design condition may approach that of a model with the carefully designed original profile, granted that the spanwise variation in flow across a fabric panel will alter the performance somewhat relative to the original profile.

The results discussed above are repeated for the case of a lower Reynolds number of 2.5 million except that the $- C_{p}$ values on the suction side for the fabric model are slightly lowered due to the lower dynamic pressure acting on the panels and thus less deflection of the panels. The lowering of dynamic pressure can alternatively be considered as an increase in the value of $Π_{1}$ and $Π_{2}$ , which in the limit of high $Π_{1}$ and $Π_{2}$ returns the flexible airfoil performance to that of the rigid airfoil.

Wake profiles

Wake cross sections are shown in Figure 16 for the fabric case at 2.0°, 6.6°, and 8.5° angle of attack. Over the center third of the span that is pictured, the contours of stagnation $C_{p}$ reveal the velocity deficit increasing in magnitude and extent moving toward higher angles of attack. As indicated by the horizontal black lines at the panel centers, there is a spanwise periodicity in the wake profile that aligns with the locations of the panel centers, at least for the 6.6° and 8.5° angle of attack cases. The spanwise periodicity can also be seen in the traces of the drag coefficient on the right-hand side of Figure 16.

Figure 16.

Cross-sectional wake profiles of stagnation pressure coefficient and drag coefficient traces for the modified DU91W2-250 model with fabric panels at a Reynolds number of 2.5 million and angles of attack of (a) 2.0°, (b) 6.6°, and (c) 8.5°. The black horizontal lines indicate the spanwise centers of each panel.

The suction-side wake profile in Figure 16(b) and (c) widens at the center of each of the three spanwise panels and narrows at the transition between panels in conjunction with the deflection of the panels into the flow as will be described in the following section. This relatively large increase in thickness of the wake at the panel spanwise-centers points to higher form drag at the centers, as well as stronger adverse pressure gradients on the aft side of the deflected panels nearer the center than the spanwise ends. Although not yet confirmed with flow visualization, the stronger adverse gradient on the aft of the central panel regions on the suction-side may cause separation to lead from these regions. There is likely also to be a component of three-dimensional flow created as higher pressure flow from the streamlines above and below the spanwise center of a particular panel is drawn toward the more cambered and thus lower pressure central region. In contrast to Figure 16(b) and (c), there is significantly less spanwise variation in the wake profile at the 2.0° angle of attack in Figure 16(a), the smaller magnitude of the pressure loading on the panels understandably making their deflection and thus aerodynamic impact more benign.

Fabric deflection

Measurements of the fabric deflection distribution were made using the DIC system described previously with data taken at 4.7°, 6.6°, and 8.5° angle of attack on the suction side of the airfoil for a Reynolds number of 3 million, as well as data at 2.5 million Reynolds number for similar angles. Over the course of the 10 second image capture time, the root mean square (RMS) variation in the maximum deflection was no more than 0.05 mm in any of the measurements, the value being much lower at 4.7° and 6.6° angle of attack and increasing at the higher angle due to the unsteadiness of partially separated flow.

Figure 17 shows the deflections of the fabric panels in the thickness-wise direction for the three angles of attack measured on the suction side of the model at Reynolds numbers of 2.5 and 3.0 million. The direction of deflection is everywhere into the flow, and the deflected fabric is generally symmetric about the midspan of the panel. The maximum deflection among the three angles of attack for each Reynolds number occurs at the middle rather than at the highest angle of attack as the effects of trailing edge separation at the highest case apparently reduce the local loading in the aft section. The maximum deflection for the 2.5 million Reynolds number is 4.12 mm, or 0.52% chord, and that for the 3.0 million Reynolds number is 4.60 mm, or 0.58% chord. According to the non-linearity associated with out-of-plane loading of membrane-fabrics, the difference in dynamic pressure between the two Reynolds number cases is 30%, while the difference in maximum deflection between the cases is just 9%–11%.

Figure 17.

Contours of thickness-wise deflection of the fabric panels on the suction-side of the model for (a) 2.5 million Reynolds number and (b) 3.0 million Reynolds number, including the point of maximum y-deflection. The y-direction is that which is perpendicular to the chordline.

Conclusion

A wind tunnel experiment was designed to assess the aerodynamic consequences of imperfections in prospective modular wind turbine blades and of constructing portions of the blade using fabric panels. The specific features used to simulate a modular blade were a suction-direction offset in the profile’s nose region and the insertion of fabric panels in the aft of the profile. Two wind turbine airfoil sections were selected to test these modifications: the DU00W-212 for the nose offset and the DU91W2-250 for the fabric panels. Wind tunnel measurements of lift, drag, wake cross sections, mean airfoil surface pressures, and mean surface deflection of the fabric material revealed the effects of such features on the aerodynamic performance of the modified models. The two nose offsets tested, whose offset heights were scaled to represent a typical and worst-case manufacturing misalignment, produced 5%–17% loss of $C_{l} / C_{d}$ relative to the baseline at the design angle of attack, this loss being attributed to $C_{d}$ increases stemming from premature transition caused by the flow disturbance of the offsets on the suction side. For the fabric panels, deflection of the fabric and the resulting spanwise $C_{d}$ variability was shown to be an important characteristic of flow over fabric models, and thus, the $C_{l} / C_{d}$ performance of the fabric model relative to the rigid model is largely dependent on the spanwise location of the measurement. The upper bound of the fabric $C_{l} / C_{d}$ is similar at most angles of attack to that of the modified rigid model, and tuning of the fabric properties including elastic modulus and pretension may allow the fabric profile to have comparable performance relative to the original DU91W2-250 profile. Correlations were evident between the measured deflection shapes of the fabric and the mean surface pressure distributions over the fabric. Such results provide introductory quantification of the risk associated with the aerodynamic performance of modular blades.

Footnotes

Acknowledgements

This work comes out of a collaborative project between Virginia Tech and GE Power and Water titled Understanding The Aerodynamics And Aeroacoustics Of Fabric-Covered Wind Turbine Blades under the parent project titled Tensioned Fabric Wind Blades.

Declaration of conflicting interests

The author(s) declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.

Funding

The author(s) disclosed receipt of the following financial support for the research, authorship, and/or publication of this article: The information, data, or work presented herein was funded in part by the Advanced Research Projects Agency-Energy (ARPA-E), U.S. Department of Energy (Award Number DE-AR0000293).

ORCID iD

Kenneth Brown

References

Allen

Vincenti

(1944) Wall interference in a two-dimensional-flow wind tunnel, with consideration of the effect of compressibility. Technical report, NACA-TR-782. Available at: https://ntrs.nasa.gov/search.jsp?R=19930091861

Awasthi

Devenport

Glegg

SAL

et al . (2014) Pressure fluctuations produced by forward steps immersed in a turbulent boundary layer. Journal of Fluid Mechanics 756: 384–421.

Braslow

(1960) Review of the effect of distributed surface roughness on boundary-layer transition. Technical report, DTIC document. Available at: http://www.dtic.mil/dtic/tr/fulltext/u2/262487.pdf

Brown

Molinaro

Meyers

et al . (2015) Sensitivity of wind turbine airfoil sections to geometry variations inherent in modular blades. In: Proceedings of the 33rd AIAA applied aerodynamics conference, Dallas, TX, 22–26 June, AIAA-2015-3389. Available at: https://doi.org/10.2514/6.2015-3389

Devenport

Burdisso

Camargo

et al . (2010) Aeroacoustic testing of wind turbine airfoils. Subcontract report, NREL/SR-500–43471. Available at: https://www.nrel.gov/docs/fy10osti/43471.pdf

Drake

Bender

Korntheuer

et al . (2010) Step excrescence effects for manufacturing tolerances on laminar flow wings. In: Proceedings of the 48th AIAA aerospace sciences meeting, Orlando, FL, 4–7 January, AIAA-2010-375. Available at: https://doi.org/10.2514/6.2010-375

Duncan

Jr Crawford

Tufts

et al . (2014) Effects of step excrescences on a swept wing in a low-disturbance wind tunnel. In: Proceedings of the 52nd AIAA aerospace sciences meeting, National Harbor, MD, 13–17 January, AIAA-2014-0910. Available at: https://doi.org/10.2514/6.2014-0910

Dutton

Kildegaard

Dobbe

et al . (2000) Design, structural design, structural testing, and cost effectiveness of sectional wind turbine blades (publishable final report). Technical report. Brussels: The European Commission. Available at: https://wmc.eu/pdf/sectional_blades_publishable.pdf

Eaton

Johnston

(1981) A review of research on subsonic turbulent flow reattachment. AIAA Journal 19(9): 1093–1100.

10.

Fink

(1969) Full-scale investigation of the aerodynamic characteristics of a sailwing of aspect ratio 5.9. Technical report, NASA-TN-D-5047. Available at: https://ntrs.nasa.gov/search.jsp?R=19690009905

11.

Fink

Statio

Stiampton

(1967) Full-scale investigation of the aerodynamic characteristics of a model employing a sailwing concept. Technical report, NASA-TN-D-4062. Available at: https://ntrs.nasa.gov/search.jsp?R=19670021814

12.

Galvao

Israeli

Song

et al . (2006) The aerodynamics of compliant membrane wings modeled on mammalian flight mechanics. In: Proceedings of the 36th AIAA fluid dynamics conference, San Francisco, CA, 5–8 June, AIAA2006–2866. Available at: https://doi.org/10.2514/6.2006-2866

13.

Grewe

Kak

(1994) Stereo vision. In: Young

(ed.) Handbook of Pattern Recognition and Image Processing, vol. 2. Orlando, FL: Academic Press, pp. 239–317.

14.

Jackson

Christie

(1987) Numerical analysis of three-dimensional elastic membrane wings. AIAA Journal 25(5): 676–682.

15.

Joseph

(2014) Transition detection for low speed wind tunnel testing using infrared thermography. MSc Thesis, Virginia Tech. Available at: http://hdl.handle.net/10919/78145

16.

Maughmer

(1976) Optimization and characteristics of a sailwing windmill rotor. Technical report, January. Princeton, NJ: Princeton University.

17.

Newman

(1987) Aerodynamic theory for membranes and sails. Progress in Aerospace Sciences 24(1): 1–27.

18.

Ormiston

(1971) Theoretical and experimental aerodynamics of the sailwing. Journal of Aircraft 8(2): 77–84.

19.

Saenz

Nuin

Montejo

et al . (2014) Development and validation of a new joint system for sectional blades. Wind Energy 18(3): 419–428. Available at: https://doi.org/10.1002/we.1704

20.

Shyy

Lian

Tang

et al . (2007) Aerodynamics of Low Reynolds Number Flyers. Cambridge: Cambridge University Press.

21.

Smith

Shyy

(1996) Computation of aerodynamic coefficients for a flexible membrane airfoil in turbulent flow: A comparison with classical theory. Physics of Fluids 8(12): 3346–3353.

22.

Sutton

Orteu

Schreier

(2009) Image Correlation for Shape, Motion and Deformation Measurements: Basic Concepts, Theory and Applications. New York: Springer Science & Business Media.

23.

Sweeney

Nixon

Maughmer

et al . (1975) Sailwing windmill characteristics and related topics. Technical report, AMS report no. 1240. Princeton, NJ: Princeton University.

24.

Vionis

Lekou

Gonzalez

et al . (2006) Development of a MW scale wind turbine for high wind complex terrain sites; the MEGAWIND project. In: 2006 European wind energy conference, Athens, 27 February–2 March.

Sensitivity of wind turbine airfoil sections to geometry variations inherent in modular blades

Abstract

Keywords

Introduction

Misalignments in flow

Membrane-fabric surfaces in flow

Approach to present work

Apparatus and techniques

Stability Wind Tunnel

Airfoil models

Modified DU00W-212 model

Modified DU91W2-250 model

Fabric deflection measurements

Results and discussion

Effect of offsets on aerodynamic performance

Global aerodynamic performance

C p versus x / c comparisons

Effect of flexible camber on aerodynamic performance

Global aerodynamic performance

C p versus x / c comparisons

Wake profiles

Fabric deflection

Conclusion

Footnotes

Acknowledgements

Declaration of conflicting interests

Funding

ORCID iD

References

$C_{p}$ versus $x / c$ comparisons

$C_{p}$ versus $x / c$ comparisons