1, Mingyao Gu1, David A. Johnson1* - ULisboa

16th Int Symp on Applications of Laser Techniques to Fluid Mechanics Lisbon, Portugal, 09-12 July, 2012

A PIV Study of a Low Reynolds Number Pitch Oscillating SD7037 Airfoil in Dynamic Stall with CFD comparison

Kobra Gharali1, Mingyao Gu1, David A. Johnson1*

1: Department of Mechanical and Mechatronics Engineering, University of Waterloo, Waterloo, Canada

* Corresponding author: [email protected] Abstract The unsteady flow field in the vicinity of a pitch oscillating SD7037 airfoil at a Reynolds number of 40,000 was investigated experimentally and numerically. The mean and amplitude of the oscillatory motion were both 11º with a reduced frequency (k) of 0.085. The airfoil undergoes dynamic stall phenomena associated with a highly separated unsteady boundary layer and energetic vortex formation and shedding. The main characteristic of the dynamic stall phenomena is lift overshoot at the stall point which is a result of the low pressure region on the suction side. The post-stall airfoil experiences highly separated vortices with a thick wake resulting in rapid decline in lift performance. The experimental part of the current study employed particle image velocimetry (PIV). The PIV results were based on averaging 500 images for each angle of attack. A computational fluid dynamics (CFD) simulation was performed for the same flow field with ANSYS Fluent 12, simulating laminar-turbulent transition using the transition SST method. Reasonable agreement was observed between the PIV and CFD methods in capturing both qualitative and quantitative flow characteristics. Generation, development, and separation of the leading edge vortices from the suction side of the airfoil as well as the creation and roll up of the trailing edge vortices from the pressure side of the airfoil were evident in the experimental and numerical results, which agreed well with the literature regarding the general features of dynamic stall. The post-processed PIV data used for calculating the pressure field based on the phase averaged Navier-Stokes equations demonstrated that the first low pressure wave leading edge vortex was energetic enough to cause a significant pressure difference, giving rise to an increased lift coefficient. The succeeding leading edge vortices did not carry pressure waves of the same low magnitude and thus in turn did not bring about as dramatic a lift increase. 1. Introduction Investigating unsteady events on airfoils is challenging for both experimental and numerical simulations particularly when dynamic stall occurs and the flow and pressure fields are dramatically altered, giving rise to a significant lift adjustment. Unsteady angle of attack motion delays stall and the lift coefficient rises until dynamic stall occurs. Dynamic stall phenomena are associated with a highly separated unsteady boundary layer and energetic vortex formation and shedding. Modeling dynamic stall with pitch oscillating airfoils has been considered for many years because of its wide range of applications such as helicopter blade rotors, wind turbines, and maneuverable wings. Extensive experimental studies have been reported [1-5] since the two important reviews given by McCroskey [6,7], but the physics of dynamic stall is not yet fully understood as a result of the numerous parameters involved. Most of the literature reports have studied high Reynolds numbers. Experiments aimed to measure aerodynamic loads for low Reynolds number flows as well as numerical simulations of these cases including laminar-turbulent transition are lacking. Due to progress in image processing and post processing of the laser based particle image velocimetry (PIV) technique, it is now possible to obtain in-depth information on dynamic stall phenomena at low Reynolds numbers.


This study focuses on highly separated regions on the suction surface of SD7037 airfoil using non-intrusive phase averaged PIV measurements. Since no study on a pitch oscillating SD7037 airfoil exists in the literature, a transient numerical computational fluid dynamics (CFD) simulation was carried out in conjunction with the experimental work for comparison of flow features in dynamic stall. Aerodynamic loads are calculated from the CFD analysis. 2. Methodology Experimental Setup A SD7037 airfoil was pitch oscillated at one quarter of the chord according to the sinusoidal motion prescribed by

𝛼 = 𝛼!"#$ + 𝛼!"# sin(2𝜋𝑓𝑡) (1) where 𝛼!"#$, 𝛼!"# and 𝑓 represent mean angle of attack, pitch oscillation amplitude, and oscillation frequency, respectively. For the current study 𝛼!"#$ =11o, 𝛼!"# =11o, and a reduced frequency k (𝜋𝑓𝑐 𝑈) of 0.085 were considered. The airfoil motion was actuated using a servo motor with a 2000 line encoder. A Galil CDS-3310 motion controller was used to interface with the servo motor and trigger the PIV image acquisition at user specified angles. The airfoil was mounted in a closed loop wind tunnel with a mean air velocity of 25.5 m/s. The blockage ratio of the airfoil at the highest angle of attack was 7%, and the Reynolds number was fixed at 40,000. Images were obtained with a Dantec Dynamics PIV system utilizing a Nd:YAG laser. A beam splitter was used to separate the laser light in order to illuminate the top and bottom surfaces of the airfoil equally. The field of view was 8 cm by 8 cm with an image resolution of 2048 pixels by 2048 pixels. The time interval between frames was set to 4 µs with 500 images captured for each angle of attack. Image pairs were processed with adaptive correlation in two steps with a final interrogation area size of 32 pixels by 32 pixels. Post processing was done with codes developed in-house. Numerical Setup For the numerical simulation a commercial CFD flow solver package, ANSYS Fluent 12, was employed. A grid independence study was performed, concluding that a mesh resolution of 200,000 cells with 500 nodes around the airfoil was suitable. The whole computational domain was oscillated around the one quarter chord of the airfoil to serve as a dynamic mesh. The transition SST model [8] was applied as a viscous model for simulating laminar-to-turbulent transitional behaviour. In order to render the simulation results temporally independent the time step size for the transient simulation was chosen in accordance with the characteristic time of the airfoil, 𝑑𝑡 = 𝜏(𝑐 𝑈!), where 𝜏 is on the order of 10-2. All simulations were run over 16 CPUs in parallel. From the CFD analysis aerodynamic loads were computed based on pressure distribution.


Pressure Field Determination The pressure field is generally not available in a PIV experiment. One approach is to integrate the phase averaged Navier-Stokes equations to determine the mean pressure acting on the flow field. The tensor form of the phase-averaged pressure is

−𝜕𝑃𝜕𝑥!

= 𝜌𝑈!𝜕𝑈!𝜕𝑥!

+ 𝜌𝜕𝑈!𝑈!𝜕𝑥!

− 𝜇𝜕!𝑈!𝜕𝑥!𝜕𝑥!

(2)

To avoid error propagation associated with integration methods, a two dimensional integration was used. 3. Results and Discussion Dynamic stall can be divided into three stages, namely pre-stall, full stall and post-stall. All these stages are shown by the streamline plots in Figures 1 and 2 for varying upstroke and downstroke angles. During upward pitch motion the flow starts to separate from the trailing edge at α = 5°. As the angle of attack increases, laminar separation bubbles (LSB) are created close to the leading edge. Figure 1 demonstrates that at α = 15° a LSB occurs in both PIV and numerical results, but the trailing edge vortex is more dominant in the numerical results. A further increase in the angle of incidence turns the LSB into a leading edge vortex (LEV). At α = 17° the clock-wise LEV covers half of the suction side. Static pressure contours scaled by the static pressure of the incoming flow calculated at one chord length ahead of the airfoil are plotted in Figure 5, which shows vortices affiliated with the low pressure waves. Hence, at α = 17° the LEV yields a large pressure difference between the pressure and suction sides, resulting in high lift. The lift coefficient reaches the absolute maximum at the dynamic stall point. The stall angle is 18.8° by numerical prediction (Figure 4) or 19° according to PIV data. The numerical approach predicts the airfoil stall 0.2° earlier. Consequently, the subsequent aerodynamic events are advanced. Figures 1 and 3 illustrate that at the dynamic stall point the LEV covers the entire suction side with very low pressure. After the airfoil stalls, shedding of the clockwise vorticity transfers the low pressure waves to the wake, leading to a quick drop in lift (Figure 4) and full stall stage. During full stall a counter-clockwise vortex from the pressure surface forms and gradually rolls up at the trailing edge. At the end of full stall it reaches its maximum size and sheds into the wake. Although the pressure inside the trailing edge vortex is low, it cannot increase the lift coefficient (Figures 1 and 3). Following the numerical streamline plots, emergence of a second LEV is evident at α = 20.5°. The growth of the second LEV enhances the lift performance during the upstroke motion though its strength subsides in comparison with the first LEV (Figure 3), as is evidenced by the higher inner pressure. At α = 21°, the first LEV separates while the second LEV undergoes further development (Figure 1). At α = 21.5° the first trailing edge vortex is shed while a third LEV emerges. At the same time the second LEV reaches the end of the airfoil, corresponding with a second lift peak during the upstroke motion (Figure 4). After this angle, the second LEV is separated fully, and the third LEV covers the whole suction side. Since the numerical simulation slightly advances the aerodynamic events, at α = 22° it shows the separation of the LEV and formation of the next trailing edge vortex whereas the PIV streamline plot shows only the developed LEV over the upper surface (Figure 2).


As for the downward pitch motion, at α = 21.5° the LEV from the numerical simulation is fully separated while the LEV from PIV starts to shed. The most marked discrepancy between the PIV and numerical results occurs during the downstroke motion at high angles of attack since the flow is significantly unsteady in this range of angles of attack and the development and subsequent separation of the LEV could happen within 0.5°. The LEVs during the downstroke motion are not as energetic as the upstroke counterparts and in turn do not significantly increase the aerodynamic loads (Figure 4). At α = 7° there is no sign of vortex formation, and the flow remains attached until the end of the cycle α = 0°. 4. Conclusion Facilitated by the PIV technique with recent post processing methods, the current study explored the dynamic stall phenomena of a pitch oscillating SD7037 airfoil at low Reynolds number (40,000). During oscillation the airfoil experiences formation, development, and separation of pressure side and suction side vortices, which give rise to a severely separated boundary layer, as observed by both experimental and numerical methods. Although the latter predicts the stall point 0.2° earlier during the upstroke motion, there is reasonable agreement between both methods in qualitatively and quantitatively capturing the flow characteristics. The calculated lift coefficient peaks to an absolute maximum at the stall point. Subsequently a rapid drop in lift to full stall is observed when the low pressure LEV is separated from the suction surface and enters the wake, followed by lift recovery due to the development of another LEV. Although there is a marked discrepancy between experimental and numerical results at relatively high angles of attack during the downstroke motion, overall the PIV technique was successful in identifying and analyzing the flow behavior associated with the dynamic stall phenomena.


Figure 1. Time averaged streamlines during upstroke at increasing angles of attack


Figure 2. Time averaged streamlines during downstroke at decreasing angles of attack


Figure 3. Dimensionless static pressure in the vicinity of the airfoil

Figure 4. Aerodynamic loads from numerical simulation.

(deg) (deg)

Upstroke Upstroke

Downstroke

Downstroke


References [1] Kurtulus D, Scarano F, and David L (2007) Unsteady aerodynamic forces estimation on a square cylinder by TR-PIV. Exp. Fluids 42(2):185–196. [2] Rival D, Manejev R, Tropea C (2010) Measurement of parallel blade-vortex interaction at low Reynolds numbers. Exp. Fluids 49(1):89–99. [3] Van Oudheusden BW, Casimiri EWF, Scarano F (2007) Aerodynamic load measurement of a low speed airfoil using particle image velocimetry. AIAA 45th Aerospace Science Meeting and Exhibit, Reno, Nevada, USA. [4] Van Oudheusden BW, Scarano F, Casimiri EWF (2006) Non-intrusive load characterization of an airfoil using PIV. Exp. Fluids 40: 988–992. [5] Van Oudheusden BW, Scarano F, Roosenboom EWM, Casimiri EWF, Souverein LJ (2006) Evaluation of integral forces and pressure fields from planar velocimetry data for incompressible and compressible flows. 13th Int Symp on Applications of Laser Tech to Fluid Mechanics, Lisbon, Portugal. [6] McCroskey W (1981) The phenomenon of dynamic stall. NASA TM-81264. [7] McCroskey W (1982) Unsteady airfoils. Ann. Rev. Fluid Mech. 14(1): 285–311. [8] Menter FR, Langtry R, Volker S (2006) Transition modeling for general purpose CFD codes. Flow Turbul. Combust. 77:277–303.

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1, Mingyao Gu1, David A. Johnson1* - ULisboa