The Influence of Adaptive Camber on Dynamic Stall

Transcription

1 The Influence of Adaptive Camber on Dynamic Stall Ulrike Cordes *, Tobias Kehl, Klaus Hufnagel, Cameron Tropea Institute of Fluid Mechanics and Aerodynamics, Technische Universität Darmstadt, Germany * Corresponding author: cordes@sla.tu-darmstadt.de Keywords: TR PIV, dynamic stall, vortex identification, variable camber, gust load alleviation ABSTRACT The stall characteristics of a two-dimensional airfoil with variable camber based on a rigid Clark Y reference airfoil have been investigated experimentally in a wind tunnel. Dynamic stall is provoked by a continuous sinusoidal pure pitching motion around the airfoil s c/4-axis with a pitching amplitude of Δα = 6 around a mean angle of attack of α m = 14 at a reduced frequency of k = The chord based Reynolds number is Re=120,000. From time resolved particle image velocimetry (TR PIV) data, the circulation and position of coherent vortices are obtained, employing a vortex identification algorithm developed by Graftieaux et al. [3]. The variable airfoil model (adaptive camber airfoil) features mechanically coupled leading and trailing edge flaps and is designed to suppress gust loads by passively adapting the airfoil s camber to fluctuating inflow conditions. The concept entails enhanced fluid structure interaction, where flow conditions at the leading edge affect the airfoil shape and vice versa. Although the adaptive camber airfoil was designed to operate with attached flow, early tests indicated that it could also be used advantageously under conditions of dynamic stall. Therefore, the present study has the aim of quantifying the interaction of the adaptive camber airfoil s shape with the vortices associated with dynamic stall. Circulation and pathlines of the leading edge vortices for the case of the adaptive camber airfoil and the rigid reference airfoil are compared. The adaptive camber airfoil is found to alter the lifetime of the leading edge vortex significantly: the upward rotation of the flaps leads to smaller and weaker vortices that occur later in the pitch cycle and remain closer to the airfoil s surface. Since the circulation of the leading edge vortex is directly related to the lift overshoot typical for dynamic stall [1], an effective reduction of the vortex size and strength is beneficial in terms of gust load alleviation.

2 1. Introduction Wind turbines are subject to highly unsteady inflow conditions. Fluctuating aerodynamic loads are transmitted from the blades to the drive train and tower, where they increase structural fatigue and shorten component lifetime. Current research focuses on the development of mechanisms to reduce these fluctuating loads. The adaptive camber concept [7] (Figure 1), developed at TU Darmstadt, adapts its camber in a purely passive way to the fluctuating inflow conditions. Leading edge and trailing edge flaps are mounted rotatable and coupled in such a way, that the combined rotary motion of both flaps alters the airfoil s camber. The rotary motion is restrained by a restoring moment Mspring, which is applied via a pre-stressed spring system. High aerodynamic moments Maero around the leading edge, intrinsic to a flow of high angle of attack or high aerodynamic pressure, overcome the restoring moment M spring (Figure 1a). As a result, the leading edge is rotated upwards and its motion is transferred to the trailing edge flap, which is deflected by the trailing edge flap angle γ. This leads to a decreased camber and decreased load pick up (Figure 1b). (a) (b) Figure 1: Quasi steady considerations of the adaptive camber airfoil concept: High angles of attack provoke a high pressure difference around the leading edge (a). The resulting aerodynamic moment Maero is transferred to the trailing edge flap via a mechanical coupling mechanism (a) and the flaps rotate upward. This is quantified by the trailing edge angle γ (b). The airfoil s camber and the pressure distribution are reduced, until equilibrium between the aerodynamic forces and the restraining spring moment Mspring is attained. The aerodynamic response of the adaptive camber airfoil under steady flow conditions is shown in Figure 2 (a), where the potential of the adaptive camber concept is revealed: The lift L and trailing edge angle γ are measured at angles of attack α in the range of -10 < α < 20, after an

3 equilibrium between the aerodynamic moment M aero and the restraining spring moment M spring is established. For small α, where Maero is small, Mspring cambers the adaptive camber airfoil (γ > 0, flaps down), leading to a higher lift on the adaptive than for the rigid Clark Y reference airfoil. With increasing α, the adaptive camber airfoil de-cambers steadily. At α = 10, the adaptive camber airfoil takes the shape of the Clark Y reference airfoil (γ=0 ). The lift curves intersect. For α > 10, the adaptive camber airfoils camber is reduced compared to the rigid reference airfoil (γ < 0, flaps up) and the lift becomes smaller. This results in a reduced lift curve slope δc L/δα of the adaptive camber airfoil. Since fluctuating inflow in the rotating reference system of a wind turbine leads to a fluctuating angle of attack on the airfoil, the result is promising in terms of gust load alleviation. Further information on the adaptive camber airfoil and its response to steady inflow conditions can be found in Lambie [6]. Gusts are by definition unsteady events which alter the airfoil s response compared to the steady case. For this reason, unsteady experimental investigations have been carried out in the active grid wind tunnel at University of Oldenburg [2]. Both the adaptive camber airfoil and a rigid reference airfoil were submitted to a dynamic change in angle of attack due to a sinusoidal vertical gust. An active grid generates the fluctuating inflow, while the airfoil is fixed on a wind tunnel balance. Phase averaged temporal lift response curves of the adaptive camber airfoil and the rigid reference configuration are exemplary shown in Figure 2 (b) for one load cycle. Experiments were carried out for small mean angles of attack of αm=2, where the flow remains completely attached. The experimental results showed a reduction in fluctuating loads of up to 60% which is competitive with actively controlled gust load reduction mechanisms currently under investigation [5]. A clear correlation between the effectiveness of the adaptive camber airfoil in terms of gust load reduction and important factors of the unsteady flow (reduced frequency, gust amplitude) was observable.

4 a) Steady inflow b) Dynamic inflow Figure 2: Under steady inflow conditions (a), The adaptive camber airfoils trailing edge (TE) angle γ decreases from γ =15 (flaps down) to γ =-5 (flaps up) with increasing angle of attack α. This results in a reduced lift curve slope of the adaptive camber airfoil, compared to the rigid reference airfoil. Under dynamic inflow conditions (b), in attached flow regime, the de-cambering results in reduced lift fluctuations on the adaptive camber airfoil compared to the rigid reference airfoil. Both airfoils are submitted to the same angle of attack fluctuation, generated by an active grid. At high mean angles of attack beyond the static stall angle, the dynamic increase of the angle of attack leads to complex viscous phenomena, commonly known as dynamic stall. The predominant feature of dynamic stall is the lift force excursion experienced by the airfoil due to the presence of large coherent vortices forming at the airfoil s leading edge. They are known to be highly sensitive to the shear layer properties. The shear layer properties are in turn determined by the leading edge curvature and the relative velocity between surrounding flow and airfoil surface [11]. A rotating leading edge, as in the case of the adaptive camber airfoil, is thus expected to alter the vortex strength and behavior during dynamic stall. The leading edge of the adaptive camber airfoil is not driven by an actuator but rotates only due to the forces applied by the surrounding flow. Therefore, the presence of coherent vortices near the leading edge is in turn expected to alter the motion of the leading edge flap. In the present study, flow visualizations are carried out in order to investigate the interaction of an airfoil with adaptive camber and coherent vortical structures during dynamic stall. 2. Experimental Setup and Procedure Wind Tunnel Experiments are carried out in the open return wind tunnel at TU Darmstadt. The inlet has a cross section of 2.2 m x 2.2 m, a nozzle contraction ratio of 24:1 and cross-section of 0.45 m x 0.45 in the closed test section. The flow is driven by a 20 kw fan located 6 m downstream the test section, allowing maximum flow speeds in the empty tunnel of up to 60 m/s. Airfoil Model

5 18th International Symposium on the Application of Laser and Imaging Techniques to Fluid Mechanics LISBON PORTUGAL JULY 4 7, 2016 Figure 3 shows a picture of the two dimensional airfoil model used during the experimental investigations. The airfoil has a Clark Y profile with a chord length of c = 0.12 m and a span of s = 0.45 m. Its span covers the entire test section width. The blockage at zero mean angle of attack is 2% and the maximal blockage at maximal angle of attack of 20 is 10%. The airfoil is manufactured from polyamide by direct laser sintering. The surface of the airfoil is treated with Rhodamin 6g, which absorbs light at the wavelength of nm and fluoresces with 551 nm. The Rhodamin is dissolved in alcohol and blended with clear vanish to generate a heat resistant smooth surface. In combination with an optical bandpass filter, surface reflections on the airfoil from the PIV laser light sheet are effectively reduced. a) Rigid configuration b) Adaptive configuration Figure 3: 2D Model of the airfoil used in the experimental setup. (a) shows the model in rigid configuration, where the coupling between leading and trailing edge is blocked. (b) shows the adaptive configuration. The leading edge is coupled to the trailing edge flap via an external two-rod-coupling mechanism. The coupling is pre-tensioned by a spring system (not shown) and the trailing edge angle γ is monitored as a measure for the airfoil deformation with a rotary hall sensor. The coupling of leading and trailing edge flap is realized via an external two-rod system, which is fixed to both sides of the airfoil, see Figure 3(b). It is pre-tensioned by a mechanical spring system that counteracts the aerodynamic forces. By changing the spring system to a rigid block, the coupling of leading and trailing edge can be fixed in the original Clark Y position, see Figure 3(a). This corresponds to the reference configuration referred to as rigid. The position of the trailing flap γ is measured with an ams AS5162 rotary hall sensor on the trailing flap axis. For better resolution, the sensor is programmed to the limiting positions of the mechanical stopper. Pitch-Plunge Facility

6 Two linear actuators of type LinMotPS01-48x240F-C are installed underneath the test section. The airfoil model is mounted on the actuators pistons, allowing a simultaneous pitch and plunge movement of the airfoil with a maximal stroke of 240 mm and a maximal speed of 1.7 m/s (Figure 4). The actuators are controlled via LinMot LinTalk software and their actual position is traced with two acceleration sensors. The upstream motor is fixed and is only allowed to perform a vertical movement, whereas the downstream motor can be slightly tilted to account for the change in distance due to the pitching movement of the airfoil. Within the scope of this study, the airfoil is pitched continuously in a pure sinusoidal motion with a frequency f = 5 Hz around its c/4 axis. The inflow velocity is set to U = 15 m/s which results in a reduced frequency k = πfc/ U = 0.13 and a chord based Reynolds number of Re= 120,000. The mean angle of attack αm = 14 is chosen well beyond the static stall angle of 11. The pitching amplitude is set to Δα = +-6. This results in a total angle of attack α experienced by the airfoil of α(t)= αm + Δα(sin(2πft)). To avoid transient effects, the first and the last five pitch cycles are not considered in the post processing. Particle Image Velocimetry A Litron LDY-303 high speed Nd:YLF dual cavity laser with a wavelength of λ = 527 nm is operated in single frame mode at 10 khz with its maximum output of 21 mj pro pulse. A beam extender guides the laser beam to a light sheet optic installed above the wind tunnel. A 2 mm thick laser sheet is produced at quarter span, in the middle between wind tunnel wall and linear motors. The laser sheet illuminates DEHS seeding particles, which are atomized into the settling chamber. A Phantom v 12.1 high speed CMOS camera, controlled with the Phantom PCC 2.5 acquisition software, is synchronized to the laser pulse frequency of 10 khz and to the actuator motion via LabView and a NI PCI-6602 trigger card. It captures the flow field with a resolution of 800 x 600 pixels. The camera is equipped with a Carl Zeiss Makro Planar 2/50ZF lens and a bandpass filter of 20 nm bandwidth and 532 nm mid-band frequencies. The camera is installed at approximately 1 m distance from the measurement plane, which results in a field of view of 21x15.75 cm 2 and a resolution of approximately 40 pixels/mm.

7 Figure 4: Schematic view of the experimental setup. The two dimensional airfoil is mounted on two linear motors and pitched around its c/4 axis. A laser sheet illuminates the flow around the airfoil. Images of the field of view (FoV) are captured with a camera (not shown) normal to the laser sheet. Flow is from left to right. Data Analysis The images are analyzed using MATLAB and PIVview. After masking the airfoil in all recordings with MATLAB, an adaptive cross-correlation is performed in PIVview2C. Interrogation areas of 16 x 16 pixels and an overlap of 50% lead to a grid spacing of 2 mm. Outliers were identified with a normalized median test and a size of 3 x 3 interrogation area s. The outliers are replaced via bi-linear interpolation. On the obtained vector fields, a vortex identification method, developed by Graftieaux et al. [3] is used to quantify the location and size of the vortical structures of the rigid and the adaptive camber airfoil. The method allows to track centers of large rotating coherent structures and provides a measure for the vortex size: Two scalar functions Γ1 and Γ2 are derived for each velocity vector field. According to its definition, local extrema of Γ1 indicate vortex centers, with values typically between 0.9 and 1. The sign of Γ1 gives the sense of rotation. Γ2 takes the value of 2/π at a point of pure shear. This serves as the criterion for a vortex boundary if the rotating structure is circular. 3. Experimental Results Qualitative Description of Vortex Life During one Pitch Cycle

8 All presented results are displayed over the dimensionless time t*, which is obtained by normalization with the pitching period T=1/f. The pitch cycle begins at the minimum angle of attack of 8 (t* = 0). The airfoil pitches upwards to its maximum angle of attack of 20 (t* = 0.5) and afterwards pitches downwards to the minimum angle of attack (t* = 1). The flow structure around the adaptive camber airfoil differs significantly from that around the rigid airfoil. Figure 5 gives a schematic representation of the flow situations on the rigid and the adaptive camber airfoil for several stages in the pitch cycle. The corresponding dimensionless times in the pitch cycle are defined in Figure 6. Figure 5: Schematic display of the dynamic stall process on the rigid (top) and the adaptive camber airfoil (bottom). During the pitch cycle, the rigid airfoil experiences the flow phenomena typically associated with dynamic stall: a cycle of formation of a leading edge vortex (b) growth and convection of the vortex over the airfoil (c), interaction with the trailing edge vortex and separation (d), followed by full stall, well behind the static stall angle (e). The flow around the adaptive camber airfoil features smaller vortices (b-d), while the airfoil de-cambers, followed by full stall (e).

9 Figure 6: Effective angle of attack on the airfoil for one pitch cycle (0 < t*=t/t < 1). The airfoil pitches around a mean angle of attack αm = 14, with an amplitude Δα = 6. The cycle starts at minimum angle of attack and follows a harmonic sinusoidal motion. Important positions in the pitch cycle are highlighted and later described. The flow structure on the rigid airfoil is similar to that observed by other authors (for example [8], [9]): During the upstroke, the shear layer feeds into a coherent vortical structure at the front part of the airfoil, the so-called leading edge vortex (Figure 5b). This vortex grows in size as it convects over the airfoil, with a velocity smaller than the main flow, staying close to the airfoil surface (Figure 5c). At the aft part, it interacts with a counter rotating trailing edge vortex (Figure 5d). The leading edge vortex is deflected from the airfoil surface and is drawn away by the outer flow. A new coherent vortex is formed at the leading edge and the vortex life cycle of formation, growth and convection is repeated two to three times before the airfoil stalls completely (Figure 5e). The full stall persists during down stroke. Smaller vortices sprout in the shear layer between undisturbed mean flow and the stalled region. This vortex layer moves closer to the airfoil as deep stall passes to light stall with decreasing angle of attack. The vortices in the vortex layer become less distinct and the flow reattaches from the leading edge as the airfoil passes its minimum angle of attack. A new coherent leading edge vortex forms, and the cycle is repeated. At the beginning of the pitch cycle, the flexible airfoil s shape is close to the original Clark Y with a trailing edge angle of about γ = 1 (Figure 7). During the first stage of the upstroke, where the aerodynamic moment around the leading edge is not sufficient to overcome the restraining spring moment, the adaptive camber airfoils shape remains unchanged. Midway during the upstroke, the adaptive camber airfoil de-cambers to a trailing edge angle of γ = 9. The adaptive camber airfoil maintains its shape as the airfoil passes its maximum angle of attack and returns to its original shape during down stroke, proportional to the airfoil pitch motion.

10 Figure 7: De-cambering of the adaptive airfoil over one pitch-period. During the first half of the upstroke, the aerodynamic forces are not sufficient to overcome the restraining spring moment. The adaptive camber airfoils shape resembles the rigid airfoils Clark Y profile (trailing edge angle γ = 1 ). During the second half of the upstroke, the adaptive camber airfoil de-cambers rapidly until a maximum trailing edge angle of γ = 9. The airfoil returns to its original shape during down stroke, consistent with the change in angle of attack. During the first stage of the upstroke, the flow structure of the adaptive camber airfoil resembles the topology of the rigid airfoil: a light stall with a layer of small vortices between the stalled region and the outer flow (Figure 5a). During the formation period of the first distinct LEV in the rigid airfoil case, the adaptive camber airfoil de-cambers rapidly. During this process, coherent structures are formed, but these structures remain smaller than the ones formed on the rigid airfoil and are less stable. Most disappear before they reach the airfoil s trailing edge. Because of the smaller size of the vortices, the outer flow stays closer to the upper surface of the adaptive camber airfoil compared to the rigid case (Figure 5b-d). The adaptive camber airfoil stalls as it reaches its maximum angle of attack, slightly later in the pitch cycle than the rigid airfoil. Similar to the rigid airfoil, the flow around the adaptive camber airfoil stays stalled during the downstroke (Figure 5e). When the airfoil passes the minimum angle of attack, the flow reattaches from the leading edge and the cycle repeats. Quantitative Description of Vortex Life During one Pitch Cycle These qualitative observations are quantified by tracking the amount of circulation present in the large coherent structures. Figure 8 compares exemplarily a time resolved snapshot of the flow

11 field around the rigid (left) and the adaptive camber airfoil (right) for one instant in time t* = 0.34, which corresponds approximately to stage (c), Figure 5. Vectors indicate the local flow direction. The background is color coded with Γ2 values. The boundaries of the coherent structures are detected with the Γ2= 2/π criteria of the vortex identification algorithm of Graftieaux et al. [3]. The two biggest coherent structures are highlighted in blue for the rigid and in red for the adaptive camber airfoil and their centers a tagged with marker sympols. The vorticity inside the Γ2 = 2/π boundaries is integrated to obtain the circulation of each coherent structure. The circulation of all detected coherent structures is summed up. Normalization with the chord length c and the inflow velocity U yields a normalized circluation of Γ/cU =1.89 for the rigid and Γ/cU =1.26 for the adaptive camber airfoil at the exemplary shown snapshot at t* = This quantifies the qualitative observation, that the coherent structures on the rigid airfoil are bigger in size and stronger than on the adaptive camber airfoil. a) Rigid airfoil, Γ/cU = 1.89 b) Adaptive camber airfoil, Γ/cU = 1.26 Figure 8: Exemplary representation of the scalar values Γ1 and Γ2 for one snapshot it time at t* = 0.34, which corresponds approximately to stage (c) in Figure 5. The boundaries of the coherent structures are identified at Γ2 = 2/π, the vorticity inside the coherent structures is integrated and normalized to obtain the normalized circulation Γ/cU of each coherent structure. The procedure is repeated for every snapshot of the pitch cycle and the resulting values of Γ/cU are displayed over the dimensionless time t* in Figure 9. Γ/cU values for the rigid airfoil are displayed in blue, for the adaptive camber airfoil in red. Figure 9 a) shows the time resolved evolution of Γ/cU over one complete pitch cycle while Figure 9 b) gives a close up on the second

12 half of the upstroke, the region typically associated with the presence of coherent vortex structures. a) Complete pitch cycle b) Vortex shedding region Figure 9: Total normalized circulation Γ/cU on the rigid and the adaptive camber airfoil over the dimensionless time t* during the first pitch cycle. a) Shows the complete pitch cycle, b) is a close up of the second half of the upstroke, where coherent structures mainly occur. The pitch angle of attack is plotted as a gray thick line in the background in order to provide orientation of the position in the motion cycle. On the rigid airfoil, high variations of the normalized circulation Γ/cU are observed, especially in the second half of the upstroke. This is caused by the typical cycle of formation, growth and convection of large coherent structures, during which Γ/cU increases steadily. When the coherent structure reaches the airfoil s trailing edge, it interacts with a counter rotating trailing edge vortex and is shed. The coherent structure is convected downstream and leaves the field of view, Γ/cU decreases. A new cycle of formation, growth and convection begins which results in cyclic variations of Γ/cU. On the adaptive camber airfoil, the variation of Γ/cU is less pronounced: vortices are formed at the leading edge and are convected downstream but stay generally smaller in size and are less stable. An equivalent behavior is seen for each of the other three investigated pitch cycles. Mean and maximal values of Γ/cU as well as the standard deviation are given in Table 1. Although dynamic stall is a highly turbulent phenomena and the temporally resolved data exhibits a high variability, mean and maximum values as well as the standard deviation agree well from pitch cycle to pitch cycle.

13 Table 1: Quantification of Γ/cU for all four investigated pitch cycles by their respective mean and maximum values and standard deviation. Pitch Cycle mean(γ/cu ) max(γ/cu ) std(γ/cu ) rigid adaptive rigid adaptive rigid adaptive It was stated above that the coherent structures stay close to the airfoil surface of the adaptive camber airfoil. This observation can be quantified when tracking the vortex centers of the coherent structures, identified by the local maxima of Γ1 values. Figure 10 (a) shows the pathline of the vortex centers for the first cycle of formation, growth and convection during one pitch cycle on the rigid and the adaptive camber airfoil. The vortex is formed at the airfoil s leading edge at x/c 0. As it grows and convects downstream, the airfoil pitches upward. On the adaptive camber airfoil, the vortices stay closer to the airfoil s surface than on the rigid airfoil. Figure 10 (b) shows the same data for each of the four investigated pitch cycles. Again, the data scatters due to the turbulent nature of the phenomena, but a clear difference between the pathlines on the rigid and the adaptive camber airfoil is detectable.

14 (a) Pitch cycle 1 (b) Pitch cycle 1-4 Figure 10: Pathlines of the vortex centers, identified with the Γ1 criteria for the first cycle of vortex generation, growth and convection during (a) the first pitch cycle and (b) for all evaluated pitch cycles. 4. Conclusions Time resolved PIV data of a two-dimensional rigid and adaptive camber airfoil in continuous pure sinusoidal pitch motion has been collected. A vortex identification algorithm is applied to the TR PIV data to identify boundaries and centers of large coherent vortical structures. The vorticity inside the detected boundaries is integrated and normalized to obtain a normalized circulation Γ/cU. The flow field on both airfoils varies significantly: The rigid airfoil undergoes the process of leading edge vortex formation, convection and abrupt separation, typically associated with dynamic stall and a lift overshoot. High fluctuations and high peak values of Γ/cU are observed, especially in the second half of the upstroke where dynamic stall typically occurs. The flexible airfoil de-cambers rapidly during this phase of the pitch cycle. The upward rotation of the leading edge results in smaller and less stable vortical structures, that stay closer attached to airfoil resulting in smaller and less varying Γ/cU values. The experimental results indicate an effective damping of the fluctuating loads on a pitching airfoil by the adaptive camber mechanism as it was shown by Cleaver [1] that the strength of the coherent vortices on a plunging span wise flexible airfoil is directly related to the experienced lift force. References [1] Cleaver, D. J., Wang, Z. and Gursul, I. "Oscillating Flexible Wings at low Reynolds Numbers." 51st AIAA Aerospace Sciences Meeting; Grapevine, Texas, USA [2] Cordes, U., Hufnagel, K., Tropea, C., Kampers, G., Hölling, M. and Peinke, J. Experimental Investigation of Passive Load Reduction under Dynamic Inflow Conditions, 33rd AIAA Applied Aerodynamics Conference, Dallas, June 2015.

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