10TH INTERNATIONAL SYMPOSIUM ON PARTICLE IMAGE VELOCIMETRY - PIV13 Delft, The Netherlands, July 1-3, 2013
Reduced frequency effects on Laminar Separation Bubbles
Kobra Gharali1and David Johnson21 − 2Department of Mechanical and Mechatronics Engineering, University of Waterloo, Waterloo, Canada
2da3johns@uwaterloo.ca
ABSTRACT
For further insight into the Laminar Separation Bubble characteristics for a dynamic airfoil, Particle Image Velocimetry (PIV) of a pitching SD7037 airfoil has been performed. All the experiments were completed for Re= 4 × 104 with a reduced frequency range of 0.05 ≤ k ≤ 0.12. The effects of the reduced frequency on the laminar separation bubble, leading edge vortex formation and lift coefficient are discussed in detail. Lift values from PIV measurements have been determined using the Control-Volume approach and compared with the simulated ones.
1. Introduction
For a low Reynolds number, when a laminar boundary layer transitions to a turbulent one, it may form a Laminar Separation Bubble (LSB) at certain angles of attack. Since the airfoil/object geometry is an important parameter determining the existence of an LSB and its size, there are many variations in the literature. For example, for different airfoils, Carmichael for 3 × 104≤ Re ≤ 7 × 104[4] and
Pelletier and Mueller for 6 × 104< Re < 2 × 105[23] reported that no LSB was observed while according to Ol et al. [21], an LSB was observed at Re = 6 × 104. Aerodynamic efficiency, the ratio of lift/drag, has resulted in a significant reduction in the presence of LSBs [2, 25]. Figure 1 shows a schematic of an LSB by Horton [11]. When laminar flow near the leading edge cannot resist the adverse pressure gradient, the attached flow starts to separate. Since the flow at the separated boundary layer is very sensitive to disturbances, laminar to turbulent transition occurs after separation close to the airfoil surface [2, 3, 28]. The turbulent flow improves momentum transfer causing reattachment and formation of a recirculation region called the LSB [2, 3, 24]. The turbulent boundary layer keeps the flow attached after the LSB [24].
even in generic two-dimensional test cases many effects like moving laminar turbulent transition [6,7], vortex shedding [8,9], and multimodal structural deformations [10] are influencing each other. The laminar-turbulent transition in this Reynolds number range takes place along laminar separation bubbles (LSB). Figure 2 describes the physics of a LSB. The oncoming laminar boundary-layer separates, which is caused by a pressure increase along the airfoil contour. According to Spalart and Strelets [11] and Rist [12], the separatedflow performs the transition process from laminar to turbulentflow following a gradual development of the primary instabilities from Tollmein–Schlichting instabilities toward Kelvin– Helmholtz instabilities [13]. The resulting turbulentfluctuations in theflow enhance momentum transport toward the wall, and the flow reattaches to the airfoil contour. The resulting region of circulating flow is called the LSB. LSBs are usually not desired in airfoil design because they increase the pressure drag of the airfoil due to a higher displacement thickness level of the boundary layer.
In this contribution, we want to provide validated and efficient numerical tools, which cover all the above-mentioned challenges of fluid-structure interactions at transitional low Reynolds numbers. This is done in three steps:
1) Generating an Airfoil: We want to draw on naturally evolved airfoils. Therefore, the shape of the hand pinion of a seagull was our design paradigm, also because the hand pinion of bird wings is known to be the thrust producing part [14], which is favorable for future MAV design. As a result, the SG04 airfoil was developed;
2) Defining the Approach and Setting up Numerical Simulations: To understand the influence of flexibility, a comparison between a flexible and a rigid SG04 airfoil is necessary. This comparison, with its optimization problem of maximizing the propulsive efficiency, can only be done economically by means of computational methods. For the aerodynamics of the rigid airfoil, the validation of the transition prediction is of particular interest. In this connection, Radespiel et al. [7] contributed a generalized eN method for a flapping SD7003 airfoil. To simulate flow phenomena interacting on a highly-flexible thin structure and involving laminar separation bubbles, high qualitative and time resolved coupling schemes for fluid-structure interaction problems are adopted [10,15]. Using a partitioned coupling approach, well-validated fluid as well as structural solvers are linked together in a simulation environment with the aid offlexible data transfer libraries [16]. Three coupling
aspects need to be addressed: the data transfer across nonmatching interface grids, the time integration and equilibrium iteration of the whole coupled system and the grid deformation of thefluid grid to take the updated geometry into account. For thefirst aspect, a conservative data transfer scheme based on the Lagrange multipliers and the Galerkin discretization is developed. Further, theflow solver needs the capability to solve the governing equation on moving grids; 3) Validation Case: The computational methods have to be validated. Therefore, rigid andflexible models of the SG04 airfoil were manufactured in lightweight design. High-resolution particle image velocimetry (PIV) of the boundary layer was used to capture velocityfields and turbulent shear-stress distributions around the airfoils. Investigations were performed both for steady cases at constant angle of attack and for an unsteady case with the oscillating airfoils at a reduced frequency of k 0:2. To capture structural modes of the flexible airfoil, deformation measurements were applied.
II. Birdlike Airfoils
A. Aerodynamic Design
Compared with conventional airfoils, two major design aspects can be found when examining the airfoil of a seagull in the vicinity of its hand pinion: first, a large maximum camber compared with artificial airfoils, and second, the position of maximum thickness is situated close to the leading edge, see also Fig. 3.
There are several reasons why the position of maximum thickness is located near the leading edge. Considering the wing anatomy, the skeleton and muscles run in this section, whereas at the trailing-edge region of the airfoil, only the feathers determine the airfoil shape. From an aerodynamic point of view, there are also advantages of this design. On the one hand, the adverse pressure gradients along the upper surface can be kept reasonably small. This yields thin laminar separation bubbles with low-pressure drag losses, which can be seen in the drag polar of the airfoil discussed later on in Sec. VI.A.2. On the other hand, thin airfoils have normally a small range of applicable angles of attack where no stall occurs. Airfoils with their position of maximum thickness in the vicinity of the leading edge exhibit an increased nose radius, which results in a relatively large angle of attack range with attachedflow.
A large relative camber of 8% was measured by BILO using narcotized birds [17]. However, observations in nature revealed that this value is usually smaller for glidingflight, although in wind-tunnel experiments with living birds the maximum camber during oneflapping stroke was found to vary from 8 to 12%.
Based on these design aspects, a new birdlike airfoil, the SG04, was developed [18], see Fig. 4. This profile has a maximum thickness and a maximum camber of 4%, where the maximum camber is located at x=c 40%. At operational angles of attack between 0 and
Fig. 1 Sketch of the generic airfoil by Heathcote and Gursul [4].
Fig. 2 Sketch of a LSB by Horton [40](corrected).
1960 BANSMER ET AL.
Downloaded by University of Waterloo on October 8, 2012 | http://arc.aiaa.org | DOI: 10.2514/1.J050158
Figure 1: LSB sketch by Horton [11].
Angle of attack also influences LSB characteristics. As the angle of attack increases, the laminar separation moves forward [12, 22]. As the Reynolds number is increased, the height of the bubble is decreased while the reduction rate of the height is higher than the reduction of the length [6, 22].
For the dynamic case, as the incidence increases, the airfoil shows similar characteristics as in the static case [13, 15, 17]. The LSB length of a dynamic airfoil decreases significantly compared to that of the static case [15]. A higher reduced frequency delays transition, while the LSB length is not sensitive to the frequency of the oscillations [15]. Although LSB characteristics are not yet fully understood, for an unsteady airfoil, the temporal aspect makes the study of the LSB even more complicated.
Table 1: Experimental setup details.
Airfoil SD7037 Field of view xc= yc≈ 1.4
Chord length, c 2.6 cm Time interval between images 4 ∼ 10 µs
Reynolds number, Re 4 × 104 Spatial Resolution 1500 pix/c
Number of image pairs 500 Interrogation size 16 × 16 pix2
Camera sensor format 2048 × 2048 pix2
pitch oscillated according to the sinusoidal mode:
α = 11o+ 11osin (2π f t), (1)
where f is the oscillation frequency. The reduced frequencies (k) of 0.05, 0.08 and 0.12 are chosen where the reduced frequency is based on the airfoil chord, c, and freestream velocity, U∞, introduced as
k=π f c U∞
. (2)
For all cases, the Reynolds number of 4×104was fixed. The experimental part of the current study employed particle image velocimetry (PIV) while for lift comparison a computational fluid dynamics (CFD) simulation was performed for the same flow field with the transition SST method.
2. Methodology 2.1 Experimental setup
Experiments have been performed in a low speed closed circuit wind tunnel with the turbulence intensity of less than 1%. For the PIV setup, the flow was illuminated with a New Wave Gemini Nd:YAG laser. A 50% − 50% beam splitter was used to separate the laser light in order to illuminate the top and bottom surfaces of the airfoil equally. Images were captured with a Dantec Dynamics FlowSense EO 4M camera. Due to the small field of view, a 60mm f /2.8 Nikkor lens was selected. For each angle of attack, 500 triggered images were captured and phase averaged. A summary of the experimental setup is provided in Table 1. Image pairs were processed with the adaptive correlation of the Dantec DynamicStudio software with a final interrogation area size of 16x16 pixels. The 80N77 Timer Box synchronized the laser and camera when it is triggered with a TTL signal. The TTL signal came from the motor controller which controls the pitching motion of the airfoil. Information regarding the motion system can be found in Gharali et al.[9]. For the highest frequency of oscillation, the maximum error of triggering is around 0.2o. It should be noted that since the airfoil is small, one camera was sufficient for capturing the entire field of view. Thus, the errors associated with multiple cameras and lasers are removed. Because of the small field of view, the spatial resolution has also been increased. Post processing to determine the aerodynamic loads and the pressure field was completed with in-house codes.
2.2 Numerical setup
For comparison, a numerical simulation was performed to predict the lift values. A C-type mesh with a resolution of 2.5 × 105cells was created. All the computational domain boundaries were placed about 20c from the airfoil surface while the entire numerical domain oscillates according to Equation 1 [10]. ANSYS Fluent 13, [1], predicted the flow field using 16 parallel CPUs. For the turbulence model, the γ − Reθmodel (or the transition SST model) has been used. In this model, two equations the intermittency, γ, and transitional onset criteria, Reθare added to the SST κ − ω equations. For more details see [19, 20].
3. PIV-base lift determination
Measuring unsteady aerodynamic loads on small wind tunnel models is very challenging; thus, the importance of calculating aerodynamic loads based on velocity fields from new techniques such as the PIV method is obvious. The control-volume approach has been applied recently to PIV velocity fields to determine the aerodynamic forces on an object. Load calculation based on the control-volume approach of PIV velocity fields has been extensively validated for static objects [5, 14, 27, 29, 30, 31, 32]. The dependency of the unsteady forces of dynamic airfoils on many parameters makes applying this technique for dynamic airfoils more complicated. Based on linear momentum, the phase averaged aerodynamic loads on an object, surrounded by a control volume (CV) of unit depth fixed in space and bounded by control surface (CS), (Figure 2), are determined indirectly by integrating flow variables inside the control volume: ~F= −Z Z Z V d dt(ρ~U)dV − Z Z s ρ~U(~U· ˆn)dS − Z Z s PndSˆ + Z Z s (¯¯τ · ˆn)dS, (3)
where ˆnis the unit normal vector, ~U the velocity vector and ¯¯τ the viscous stress tensor. The flow pressure, P, can be determined by integrating the phase averaged Navier-Stokes equations. The tensor form of the phase-averaged pressure is
−∂ ¯P ∂xi = ρ ¯Uj ∂ ¯Ui ∂xj + ρ∂U 0 iU0j ∂xj − µ ∂ 2U¯ i ∂xj∂xj . (4)
To avoid error propagation associated with integration methods for calculating aerodynamic loads, pressure was calculated through the Bernoulli relation for the upstream and the lower sides of the control surface. The Navier-Stokes equations are integrated numerically by a forward-differencing method in the x-axis direction for the suction side of the control surface. Finally, in the wake the downstream side is integrated by a second order central-differencing (standard five-point) scheme while the first and last nodes were known.
Figure 2: Left: Sketch of the 2D control volume and control surface definitions for determining integral aerodynamic forces; Right: control volume boundaries for a pitching airfoil during post stall superimposed with the vorticity field.
3.1 Verification
For the static case, as another alternative, XFOIL [7] has been used to calculate loads of a subsonic airfoil. The experimental results of Selig et al. [26] exist for Re= 6 × 104; thus XFOIL has been used for both Re = 4 × 104and 6 × 104. In Figure 3, the static lift values from the PIV method are compared with those of XFOIL [7] and the experimental results of Selig et al. [26]. For Re = 6 × 104 at higher angles, XFOIL overpredicts the lift values compared to the experimental method of Selig et al. [26]. The same condition was applied for Re = 4 × 104; the XFOIL load values are higher than the current PIV results and the stall points are at the same angle. The trends of the lift curves after stall are almost the same. This figure shows that the calculated PIV lift values are reliable for the static case. For the dynamic case, a numerical simulation has been used for comparison which has been described above.
4. Results and discussion 4.1 Vorticity field
Figure 4 shows the vorticity contours for k = 0.05, 0.08 and 0.12 for two angles of attack. At α = 9oduring upstroke, for all k values,
the flow field contains a LSB. Since the LSB is very small, it is not clear in the vorticity fields. As the angle of attack increases a Leading Edge Vortex (LEV) replaces the LSB. The LEV is a main characteristic of the dynamic stall phenomena which occurs at high angles of attack (after the static stall angle) for a dynamic airfoil. At α = 15o↑ in Figure 4, for all k values, vortical structures show a LEV. As k decreases, the size of the LEV increases. For k = 0.05, the LEV covers more than half of the airfoil suction surface. That means, increasing k postpones LEV formation; thus, the LSB remains longer for higher k values. In the next section, by analyzing the shear layer of the airfoil, the details of the LSB will be discussed in detail.
4.2 Shear layer analysis
Since a LSB is smaller in dynamic cases compared to that found in static cases [15], capturing the laminar-to-turbulent transition and the LSB characteristics shows the ability of high resolution PIV to detect the details of the boundary layer. For the location of transition, normalized Reynolds shear stress −u0v0/U∞2has been used as an indicator, similar to the study of Bansmer and Radespiel [2] who used −u0v0/U2
∞≥ 0.1% as an indicator. The laminar turbulent transition location (XT) based on the chord length is shown in Figure 5.
Moreover, the streamlines in this figure indicate the separation location (XS) based on the chord length. The figure also shows the
strong dependency of the separation and transition locations on the reduced frequency. The trends of the transition location variation are shown in Figure 6a. Increasing the reduced frequency moves the transition location upstream. Moreover, a higher angle of attack results in an earlier transition location which is consistent with the results of other studies [8, 13, 17, 22]. The transition point moves upstream faster when the corresponding angle is closer to the LEV formation angle; thus in Figure 6a, a significant drop in the k = 0.05 curve exists. The height of the LSB (hb) (the height of the LSB at the transition location) is a good indicator for the LSB size for a
dynamic airfoil. Figure 6b as well as Figure 5 show that a reduced frequency increase results in a thin LSB; therefore, the contribution of the LSB to aerodynamic effects is reduced when the reduced frequency is increased. It is obvious that higher Reynolds shear stress dominates the shear layer at a higher reduced frequency. The higher shear stress increases the energy of the boundary layer and then the separated bubble reattaches faster resulting in a smaller LSB. Figure 6b also indicates an almost linear trend of the hbaugmentation
versus the angle increase. The hbdifference between the two angles is also visible in Figure 7 which agrees with the level of the shear
stress magnitude. The hbaugmentation versus angle of attack increment is very similar to the trend of the bubble length versus angle
Figure 3: Static lift coefficient of the SD7037 airfoil versus angle of attack including XFOIL results for Re = 4 × 104and 6 × 104and experimental results of Selig et al. for Re = 6 × 104[26] and current PIV results for Re = 4 × 104.
Figure 5: LSB characteristics versus reduced frequency based on normalized shear stress superimposed with the streamlines; XT:
laminar-turbulent transition location based on the chord length; XS: separation location based on the chord length.
Figure 6: Reduced frequency effects on (a) Laminar-turbulent transition location, XT, and (b) LSB height, hb(the height of the LSB at
the transition location); lines for visualization only.
Figure 7: LSB characteristics versus angle of attack (k = 0.08) based on normalized shear stress superimposed with the streamlines; XT: laminar-turbulent transition location based on the chord length; XS: separation location based on the chord length.
(
a)
(
b)
Figure 8: Effects of the reduced frequency on determined lift coefficients; (a) PIV results, (b) Simulation results.
4.3 Lift coefficient
Since pitch oscillating airfoils provide load variation in one cycle, understanding the details is critical for designing and controlling systems operating under these conditions. Load variation will be more significant if an unsteady angle of attack passes the static stall angle. If the angle of attack of a lifting surface subject to unsteady motion exceeds its static stall angle, dynamic stall occurs [16, 18]. The combination of stall phenomena, inherently unsteady, and unsteady angle of attack motion results in delay of stall, the development of a LEV and the loads exceeding the static one.
Experimental and numerical lift coefficients from different reduced frequency values are shown in Figure 8. The values are shown for upstroke cycles for low angles of attack. Compared to the static case, Figure 3, the dynamic case postpones the stall; after the static stall angle α ≈ 10o, the lift is augmenting linearly. In these angles, a LSB is formed and then it is replaced with a LEV. The lift curves are shown before the LEV increases the slope of the lift curve [10]. The reduced frequency does not change the overall behavior of the curves and there is no significant lift differences between curves. Increasing the reduced frequency postpones the LEV formation; thus, at higher reduced frequencies, the LSB remains longer. Overall, there is a good agreement between numerical and experimental results showing that the PIV-load determination method is a good method for calculating lift coefficients even at high reduced frequencies. 5. Conclusions
For the SD7037 airfoil with Re= 4 × 104, the LSB appears in the oscillating cycles before LEV formation. Here the effects of the reduced frequency, 0.05 ≤ k ≤ 0.12, on the LSB characteristics and the laminar-turbulent transition are investigated with the aid of the PIV method. The PIV velocity fields were post-processed to determine the lift values based on the control-volume approach. Because there is no literature regarding the dynamic SD7037 airfoil, a numerical simulation is considered as an alternative method of lift comparison.
Based on the vortical structure analysis, the LEV advances at lower angles of attack with the reduction of k. That means, the LSB disappears faster for low k values.
Normalized shear stress contours show that the transition location is moving upstream when either the reduced frequency or angle of attack is increased. The transition point moves upstream faster when the corresponding angle is closer to the LEV formation angle. The height of the bubble was introduced as an indicator for studying the behavior of the LSB versus reduced frequency variation. Increasing the angle of attack results in a thicker bubble, but increasing k reduces the height of the bubble. Since the LSB usually affects the overall performance of the airfoil, LSB height reduction with increased reduced frequency is possible.
Analyzing the lift curves indicates that there is no significant differences between the lift values during upstroke before dynamic stall. There is a good agreement between the PIV lift curves and simulation lift values indicating that the control-volume approach is a good method for determining the lift values for a pitching airfoil even at high reduced frequencies. For a further study, the drag values should be calculated to show the performance of the airfoil during LSB formation.
6. Acknowledgements
We acknowledge the support of the Natural Sciences and Engineering Research Council of Canada (NSERC), Ontario Centres of Excellence (OCE), the facilities of the Shared Hierarchical Academic Research Computing Network (SHARCNET) and Compute/Calcul
Canada, which made this work possible. The assistance of Mingyao Gu for taking PIV images and Vivian Lam for the motion control setup is deeply appreciated.
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