Aerofólio S809 - 1 - s2 0 - s0142727x10001529 - main

Aerofólio S809 - 1 - s2 0 - s0142727x10001529 - main

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Fluid forces on a very low Reynolds number airfoil and their prediction

Zhou Y. a,⇑, Md. Mahbub Alam a,b, Yang H.X. c, Guo H. d, Wood D.H. e,1Department of Mechanical Engineering, The Hong Kong Polytechnic University, Hung Hom, Kowloon, Hong KongDepartment of Mechanical and Aeronautical Engineering, University of Pretoria, Pretoria 0002, South AfricaDepartment of Building Services Engineering, The Hong Kong Polytechnic University, Hung Hom, Kowloon, Hong KongSchool of Aeronautical Science and Engineering, Beijing University of Aeronautics and Astronautics, Xue Yuan Road No. 37, HaiDian District, Beijing, ChinaSchool of Engineering, The University of Newcastle, Callaghan NSW 2308, Australia article i nfo

Article history: Received 9 April 2009 Received in revised form 26 July 2010 Accepted 28 July 2010 Available online 17 September 2010

Keywords: Low Reynolds number airfoil Stall of airfoil Aerodynamics of airfoil Reynolds number effect abstra ct

This paper presents the measurements of mean and fluctuating forces on an NACA0012 airfoil over a large range of angle (a) of attack (0–90 ) and low to small chord Reynolds numbers (Rec), 5.3 103–5.1 104, which is of both fundamental and practical importance. The forces, measured using a load cell, display good agreement with the estimate from the LDA-measured cross-flow distributions of velocities in the wake based on the momentum conservation. The dependence of the forces on both a and Rec is determined and discussed in detail. It has been found that the stall of an airfoil, characterized by a drop in the lift force and a jump in the drag force, occurs at Rec P 1.05 104 but is absent at Rec = 5.3 103.A theoretical analysis is developed to predict and explain the observed dependence of the mean lift and drag on a. 2010 Elsevier Inc. All rights reserved.

1. Introduction

The aerodynamic characteristics of airfoils at a chord Reynolds number (Rec = qcU1/l, where q and l are the density and viscosity of the fluid, respectively, U1 is the free-stream velocity and c is the chord length of an aerofoil) of less than 5 105 are becoming increasingly important from both fundamental and industrial point of view, due to recent developments in small wind turbines, small unmanned aerial vehicles (UAVs), micro-air vehicles (MAVs), as well as researches on bird/insect flying aerodynamics (Brendel and Mueller, 1988; Hsiao et al., 1989; Dovgal et al., 1994; Lin and Pauley, 1996). For example, at the starting stage of a 500 W wind

1997; Wright and Wood, 2004). A similar variation in a occurs dur- ing insect flight, but Rec may be even lower (e.g. Wang, 2005). For UAVs and MAVs, Rec is commonly in the range of 1 105 –

6 105. However, such low Rec problems have not been addressed sufficiently in the literature, let alone when combined with large angle of attack. General researches on airfoil aerodynamics have focused on conventional aircraft design with Rec beyond 5 105 and a below stall. Carmichael (1981), Lissaman (1983) and Mueller and DeLaurier (2003) reviewed the available low Rec studies, with almost all the measured Rec higher than the wind turbine values quoted above.

The aerodynamics of hovering insect flight was explored

(Ellington, 1984a–e). Usherhood and Ellington (2002a,b) investigated forces acting on hawkmoth and bumblebee wings in ‘propel- ler-like’ revolution at Rec = 1.1 103–2.6 104. The steadily revolving wings produced high lift and drag, which was ascribed to the formation of a leading-edge vortex. Miklosovic et al. (2004) measured in a wind tunnel the lift and drag on a flipper of a humpback whale (Rec = 5.05 105–5.2 105). They observed that the stall angle of a flipper with a leading edge protuberance could be enlarged by approximately 40%, relatively to a flipper with a smooth leading edge, which led to increased lift and decreased drag. In spite of their importance, the experimental lift and drag data for low Rec are only available for some airfoils, and seldom beyond stall angle of attack. Among others, Critzos et al. (1955), Sheldahl and Klimas (1981), Michos et al. (1983) and Devinant et al. (2002) presented the test data of NACA0012 airfoil for a = 0–90 at drag at Rec =1 105–7 105 and a = 0–90 , Devinant et al. (2002) showed that lift grew from zero to a maximum for increasing a be- tween zero and stall, and then tumbled suddenly at stall, which oc- curred at a = 8–20 , depending on Rec. They further observed that lift grew with a and, after achieving the global maximum at a 45 ,droppedslowlyfroma =4 5 to90 .Ontheotherhand,drag increased monotonically with a, reaching a maximum at a 90 . Laitone (1997) measured the mean drag and lift forces successfully

0142-727X/$ - see front matter 2010 Elsevier Inc. All rights reserved. doi:10.1016/j.ijheatfluidflow.2010.07.008

⇑ Corresponding author. Fax: +852 2365 4703. E-mail address: (Y. Zhou).Present address: Schulich School of Engineering, University of Calgary, Canada

International Journal of Heat and Fluid Flow 32 (2011) 329–339 Contents lists available at ScienceDirect

International Journal of Heat and Fluid Flow jou rnal homep ag e: w. el sevi er .co m/l oca te/ijhff

at Rec = 2.07 104, though with a <3 0 . The mean drag and lift forces at the same range of a were investigated for wings with an aspect ratio of around four at Rec =1 04 by Kesel (2000), and for 20 wings of higher aspect ratio by Sunada et al. (2002) at Rec =4 103. Selig and his co-workers have made a highly influential contribu- tion to low-speed aerodynamics of airfoils (e.g. Selig et al., 1989, 1995, 1996; Selig and McGranahan, 2004). Selig et al. (1989) noted a peculiar drag increase at a lift coefficient of 0.5 (Rec =6 104), where the drag coefficient reached a maximum of 0.032. They con- nected the observation to the laminar separation bubble, inferred fromsurfaceoilflowvisualization,andreferredtothisdragincrease as the ‘‘bubble drag”. Based on their DNS data, Hoarau et al. (2003) calculated the lift and drag coefficients of NACA0012 airfoil only at

higher a. Furthermore, studies pertaining to the fluctuating forces on an airfoil are very scant over the whole range of a, notwithstandingthefactthattheforcescausevibrationsonanairfoilandacoustic noise, even leading to structural fatigue failures. As a matter of fact, these forces have already been identified as the major cause for the relatively short life and damages that occur at the tip of wind turbine blades.

Aerodynamics of an airfoil is dependent appreciably on the airfoil model, in particular, at a <2 0 , but very slightly or negligibly at a >2 0 . A symmetric NACA 0012 airfoil is used presently as a model. This type of airfoil is used not only in low Re vehicles (Murthy, 2000) but also in large transport aircraft (Tan et al., 2005), yielding a large lift and having relatively high stability due to the symmetrical shape about the centerline. Our measurements were per-

formed at Rec = 5.3 103–5.1 104 and at a = 0–90 in a water tunnel. The work aims to document the lift and drag coefficients, using a highly sensitive force sensor, and to determine the depen- dence on a and Rec of the time-mean lift coefficient (CL), drag coef- ficient (CD), and root-mean-square (rms) values (CLrms and CDrms)o f fluctuating lift and drag coefficients for a unit depth of the airfoil.

Furthermore, a theoretical analysis is performed to predict CD and CL of an airfoil.

2. Experimental details 2.1. Test facility and setup

Experiments were conducted in a closed-loop water tunnel, with a test section of 0.3 m (width) 0.6 m (height) 2.4 m

(length), at The Hong Kong Polytechnic University. The flow speed in the test section ranges from 0.05 m/s to 4 m/s. NACA0012 airfoil was used as the test model with a chord length of c = 0.1 m and a span of 0.27 m. The tests were carried out at Rec = 5.3 103– 5.1 104, over which the free-stream turbulence level was


AD area of the airfoil (of unit length) projected on the y–z plane, c sin a

AL area of the airfoil (of unit length) projected on the x–z plane, c cos a

C chord length of airfoil

CDrms, CLrms fluctuating (root-mean-square) drag and lift coefficients

D, L mean drag and lift forces per unit length of airfoil

EL power spectral density functions of the lift signal fn natural frequency of the airfoil-fluid system fv vortex shedding frequency K–H Kelvin–Helmholtz

Pb base pressure

Rec chord Reynolds number, qU1c=l S ratio to c of distance between the leading edge and flow separation point

St Strouhal number, fvc/U1

U1 free-stream velocity U streamwise mean velocity urms, vrms streamwise (x-component) and lateral (y-component) rms velocities x, y, z Cartesian coordinates a angle of attack am a corresponding to the maximum CL l viscosity of fluid q density of fluid Superscript* denote normalization by c and/or U1


(a) Side view

(b) Front view(c) Zoom of the torque resisting system

Fig. 1. Sketches of experimental setup: 1—airfoil, 2—end plates, 3—airfoil support, 4—torque-resisting system, 5—setup base, 6—connection pole, 7—load cell, 8— working section walls of water tunnel, 9—cover plate, 4–1—U-shaped connectors, 4–2—circular plate, 4–3—pins around which the connectors can turn freely.

330 Y. Zhou et al./International Journal of Heat and Fluid Flow 32 (2011) 329–339 between 0.4% and 0.5%. This level may have an appreciable effect on the laminar boundary layer separation, which may account for, at least partly, the scattering in reported measurements at low Rec. The a, defined to be positive in the clockwise direction (Fig. 1a), was varied from 0 to 90 with an increment step of 5

The airfoil model spanned almost the whole width of the test section. Two square end plates, with size of 0.25 m 0.25 m, were fixed on each end of the airfoil model with no gap between them (Fig. 1) to ensure the two-dimensionality of the flow. The leading edge of the end plate was rounded to prevent flow separation, and its trailing edge was wedge-shaped to minimize the effect of the end-plate-generated wake on flow over the airfoil.

2.2. Force measurements

In view of very low lift and drag acted on the airfoil model at the test Rec range, a highly sensitive 3-component load cell (Kistler 9251A) including amplifiers (5011B) were used to measure the lift and drag forces. Given a pre-load to measured load ratio of larger than six, reasonably accurate force measurements may be obtained (So and Savkar, 1981). The present pre-load of the load cell was 25 kN, about 4.1 103 times the maximum forces measured (6 N), resulting in a very high signal-to-noise ratio in the measurement of fluid forces. As such, the present measurements are expected to yield accurate instantaneous forces. The test setup is sketched in Fig. 1. The co-ordinate system is shown in the figure, with the origin at the pivot point of the airfoil and x and y denoting the streamwise and cross-stream coordinates, respectively. The pivot was at the mid of airfoil thickness and 0.4c from the leading edge, which is approximately the mass center. The load cell was placed outside the test section. The force acted on the airfoil is transmitted to the sensor via two supports, marked by ‘3’, and a connection pole, marked by ‘6’. The force resulted in a torque, which influenced the output of the cell. To minimize this influence, a torque-resisting system, marked by ‘4’ (Fig. 1c), was designed, which is fixed at one end of the connection pole. The end of the connection pole on the load cell side could freely rotate relatively to the cell, thus preventing the torque from transmitting to the cell while allowing the force to be transmitted to the cell. Every joint of the system was adequately lubricated to eliminate the effects of friction.

The forces acting on the end plates and the supports (Fig. 1) were measured and subtracted to obtain the forces acting on the airfoil. The blockage effect of the airfoil at large a was corrected based on Maskell (1963). Hackett and Cooper (2001) examined in a wind tunnel a family of flat-plate wing models (a = 10 to 10 ) with blockage ratios of 4%, 7.1%, 1.1% and 16% (presently 16.7%) and demonstrated that this correction technique worked very well for both lift and drag estimates: all corrected curves for the four blockage ratios collapse to a single line. Other factors such as static pressure gradient and the boundary layer effects were not considered, whose contribution to experimental uncertainties was negligibly small. Static calibrations of the load cell in the lift and drag directions were carried out using dead weights. The load cell is characterized by high response, resolution and stiffness, and has a high linearity in the load/output relation. The force signals were digitized using a 12-bit A/D board at a sampling frequency of 4 Hz, about 14 times the maximum (0.29 Hz) vortex shedding frequency, measured during experiments.

The natural frequency fn of the combined airfoil-fluid system, including the load cell, needs to be measured. Furthermore, the tunnel vibration effect, if any, on the fluctuating forces must be determined in order to resolve the unsteady forces. To this end, the lift force (L) was measured using the load cell under four different conditions of the water tunnel: (i) filled with still water (the turbine was switched off), without mounting the airfoil; (i) filled with running water (the turbine was switched on and

Rec = 5.3 103), without mounting the airfoil; (i) filled with still water, with airfoil mounted at a =4 0 and hit slightly using a stick;

(iv) filled with running water (Rec = 5.3 103), with airfoil mounted at a =4 0 . The power spectral density functions, EL, of the lift signal are shown in Fig. 2. A comparison in EL (Fig. 2a) between conditions (i) and (i) suggests that there is no appreciable effect of the tunnel vibration on the load cell measurement. EL (Fig. 2b) under condition (i) displays a pronounced peak at

0.86 Hz, which was identified with fn. On the other hand, under condition (iv) EL (Fig. 2c) shows another even more pronounced peak at 0.12 Hz, which was determined to be the frequency (fv) of vortex shedding from the airfoil, as confirmed by the power spectral density function of the LDA-measured streamwise velocity (see Section 2.3).

The peak magnitude generated at fn, is no more than 12% of that at fv, which is evident if EL in Fig. 2c is re-plotted in linear scale

(Fig. 2d). Note that the measured fn may depend on the orientation of the airfoil and hence on the directions. For example, with the air- with still water (U1 = 0) is 0.68, 0.86 and 1.03 Hz, respectively, in the y-direction, and 0.97, 0.86 and 0.68 Hz, respectively, in the x-direction. Interestingly, with increasing a, fn increases in the y-direction but decreases in the x-direction. It is known that the damping force of still water on an airfoil oscillating with very small amplitude is directly proportional to the projected area of the airfoil normal to the direction of oscillation, and a higher damping force reduces fn. Therefore, the opposite trend in the variation of fn with a along the y-o r x-direction is due to the opposite change in the projected area normal to the corresponding directions. Since the damping force is smallest at a =9 0 along the y-direction and at a =0 along the x-direction, the correspond- ing fn is maximum.

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