Exp Fluids (2011) 51:1605–1621 DOI 10.1007/s00348-011-1173-4
RESEARCH ARTICLE
Flow past two in-tandem airfoils undergoing sinusoidal oscillations T. Lee
Received: 24 April 2011 / Revised: 17 June 2011 / Accepted: 13 July 2011 / Published online: 4 August 2011 Ó Springer-Verlag 2011
Abstract The interaction of the wake, generated behind an upstream oscillating NACA 0012 airfoil, with the downstream NACA 0012 airfoil, oscillated at the same conditions but with / = 0° and 180° different phases (relative to the upstream airfoil), was investigated by particle image velocimetry and surface pressure measurements. The results show that the axial spacing and phase difference determined the strength of the undesirable interference effects and, subsequently, the behavior of the dynamic-load loops of the downstream airfoil. The boundary-layer events on the downstream airfoil were persistently different from those observed on the baseline oscillating airfoil. The downwash induced by the upstream airfoil disrupted leading-edge vortex (LEV) formation on the downstream airfoil. The absence of LEV-induced transient effects also led to a significantly lowered aerodynamic loading and Cl-hysteresis compared to the baseline airfoil. The aerodynamic performance of the / = 180° case, however, outperformed that of the / = 0° case. List of b c Cl Cl,max Cm Cm,min Cd Cp f
symbols Span Airfoil chord Section lift coefficient Maximum Cl Section pitching-moment coefficient about -c Minimum Cm Section drag coefficient Surface pressure coefficient Oscillation frequency
T. Lee (&) Department of Mechanical Engineering, McGill University, Montreal, QC, Canada e-mail:
[email protected]
L Re t u u? x,y,z j / a ads afr amax amin ass f m
Axial spacing Chord Reynolds number, = cu?/m Time Streamwise velocity Freestream velocity Streamwise, transverse and spanwise direction Reduced frequency, = pfc/u? Phase difference Angle of attack Dynamic-stall angle Angle at the onset of flow reversal Maximum angle Minimum angle Static-stall angle Vorticity Kinematic viscosity
Subscript d Pitch-down u Pitch-up
1 Introduction The interaction of the vortical wake, generated by an upstream oscillating airfoil, with a downstream airfoil at rest or oscillating is of great interest in various turbomachinery and rotorcraft applications. For rotorcraft, the control of the impulsive noise and aerodynamic loading generated by the interaction of rotor blades with the rotor wake, containing concentrated tip vortices during lowspeed powered descent flight, is always of great significance to rotor aerodynamicists. Different kinds of blade– vortex interactions (BVIs), according to different vortical system orientations, and their control has been examined
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(see, for example, Lorber and Covert 1982; Hardin and Lamkin 1987; Booth 1990; Straus et al. 1990; Lee and Bershader 1994; Foley et al. 1995; Leishman 2002; Wilder and Telionis 1998). Two BVI extremes occur when the vortex is either normal (which affects a small spanwise portion of the blade) or parallel (which affects most of the blade) to the blade. The most intense interaction, however, occurs when the axis of the vortex is parallel to the span of the blade. Meanwhile, research efforts were also made to study the interaction between a spanwise separated wake, generated by the retreating rotor blades, and the following advancing blades, that is, the so-called blade-wake interaction (BWI). Booth (1990) studied the parallel interaction between an isolated vortex, generated from an impulsively pitched wing, and a downstream interaction airfoil in a wind tunnel at Re = 1.61 9 105. The impact of vortex proximity, reduced frequency, and maximum pitch angle of the vortex generator on the surface pressures of the interaction stationary airfoil was investigated. The effects of the interaction process were shown to be increased by the reduction in blade-to-vortex spacing and/or the increase in blade loading. The most obvious effect of a parallel BVI was the growth and collapse of a large suction peak in the region of the leading edge of the interaction airfoil. Moreover, the largest change in the lift occurred when there was a direct encounter between the shed vortex and the downstream airfoil. Hardin and Lamkin (1987) suggested theoretically that the magnitude of the aeroacoustic pressure time history p(x,t) produced by the blade–vortex interaction can be expressed as p(x,t) * CLl/q?d2miss, where x is the observer position, C is the intensity of the incoming vortex, l the span over which essentially the 2-D interaction occurs, L is the lift of the interaction blade per unit span, q? is the freestream density, and dmiss is the miss or separation distance between the vortex center and the blade leading edge. One BVI noise reduction concept is therefore to decrease (or increase) the blade lift and, subsequently, the vortex strength (or the miss distance) at the blade–vortex encounters, which should reduce the intensity of the interaction and thus noise generated. For turbomachinery, the aerodynamic interaction between a rotor and a stator and the subsequent noise generation are always of significance to the designers and manufacturers of such engines (see, for example, Simonich and Lavrich 1993; Waitz et al. 1996; Hsu and Wo 1998; Brookfield and Waitz 2000; Tinetti et al. 2002). It is known that the rotor wake–stator interaction noise is mainly generated by the interaction between the downstream moving pressure wake from the upstream moving airfoil blades and the leading edges of the stationary airfoil vanes. The wake, which includes both pressure and velocity fluctuations, strikes the leading edge of the downstream stator vane,
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resulting in the generation of an acoustic pressure wave which, in certain frequency ranges, is perceived as noise. A significant difference in transient response, depending on the direction of the passage of the wakes (i.e., whether the suction or the pressure surface of the cascade vane was struck first), was, however, observed. Unsteady pressure difference was found to be a maximum near the leading edge and was dominated by blade passing frequency. In addition, peak unsteady lift occurred when the leading edge of the vane was near the wake centerline. Maresca et al. (1979) and Favier et al. (1985) investigated the aerodynamic interaction between an impinging static airfoil and a vortical wake, generated by a 2-D airfoil oscillated in longitudinal motion through dynamic-stall conditions. Different axial and transversal distances were examined. The influence on a downstream fixed airfoil (simulating the following stator blades) was analyzed by means of aerodynamic loads and wake measurements in conjunction with smoke-flow visualizations. They reported that the simultaneous variations of the velocity and airfoil incidence in the incident wake flow were found to greatly modify both the steady and the unsteady aerodynamic behavior of the downstream static airfoil. The interaction effects were also shown to be dependent on the geometric incidence of the downstream airfoil, as well as on its lateral position in the impinging wake. Investigations of the interaction between two in-tandem oscillating airfoils are, however, needed. Yao and Liu (1998) and Rival et al. (2010) investigated the interaction between an oscillating leading airfoil and a trailing airfoil (held fixed with a specific angle of attack and vertical spacing in its wake), i.e., the parallel blade– vortex interaction for a Schmidt-propeller configuration, both theoretically and experimentally. In the particle image velocimetry experiment of Rival et al., the leading airfoil was oscillated with a pure-plunge motion: h(t) = hocos(2pft) with j = 0.2 at Re = 3 9 104, where ho = 50%c is the plunge amplitude and f is the frequency of the period. The vortex wake was found to be similar to that produced by an equivalent pure-pitch motion with a mean angle of attack of 8° and pitch amplitude of 14.1°. Time-averaged aerodynamic loads were determined via control-volume analysis and pressure-integration of the respective velocity fields. Rival et al. reported that the nature of the interaction was found be dictated by the leading airfoil incidence and not the vertical spacing to the incoming vertical wake, and that for cases where vortex-blade offset was small and the trailing airfoil was loaded, vortex distortion and vortex-induced separations were observed. An extensive review on vortex–body interaction is given by Rockwell (1998). The objective of this study was to investigate the interaction of the wake, generated by an upstream
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oscillating NACA 0012 airfoil, with a downstream NACA 0012 airfoil oscillated at the same conditions but with different phases relative to the upstream airfoil. The impact of the axial spacing between these two airfoils was also examined. The nature of airfoil–wake interaction was examined by using particle image velocimetry (PIV) technique. The dynamic-load loops of the downstream airfoil were also obtained to supplement the PIV flowfield measurements. Physical mechanisms responsible for the observed phenomena were also discussed.
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The particle image velocity (PIV) experiment was carried out in a suction-type subsonic wind tunnel with a test section of 20 9 20 9 120 cm3. Two identical NACA 0012 airfoils, each with a chord of c = 7.5 cm and a span of b = 19 cm, were used as the test models. The origin of the coordinate was located at the leading edge of the upstream airfoil. The chord Reynolds number was fixed at 8.5 9 104. Two identical specially designed four-bar-linkage and flywheel oscillation mechanisms, capable of oscillating the airfoils sinusoidally at various amplitudes and frequencies, were used in the present experiment (Fig. 1a). The pitch axis was located at -chord. Both mechanisms were driven by Maxon RE-35 servomotors, each one being equipped with a Maxon MR encoder and having its own Maxon EPOS 70/10 motion controller. The controllers were programmed with the desired motion profile via a PC using a home-developed program. The program was capable of checking the encoder output at 80 kHz to guarantee the accuracy of the motion. In addition, the angles of attack and phases of both airfoils were monitored using potentiometers. Both airfoils were oscillated with a(t) = 8° ? 5°sinxt at a reduced frequency j = 0.05 with an uncertainty of ±0.2°. The downstream airfoil was oscillated at two phase differences / (=0° and 180°; i.e., in-phase and 180° out-of-phase), relative to the upstream airfoil motion (Fig. 1b). The axial spacing in the PIV experiment was fixed at L = 0.3c, and the vertical distance was kept at 0c (Fig. 1c). Note that when the phase angle is within the range of -0.5p B s B 0.5p and 0.5p B s B 1.5p, the airfoil is described to be in pitch-up and pitch-down motion, respectively. Also, in the following discussion, the suffix u is used to indicate pitch-up when a is increasing and d is used to denote pitch-down when a is decreasing. The flowfield was illuminated by two 1.7-mm-thick laser light sheets, generated by a dual head Continuum Nd:YAG laser (Model SureLite II), separated by a time delay of 49.4 ls. The particle images were digitally acquired using a TSI PowerView 4MP Plus CCD camera (Model 630059), with a resolution of 2,048 9 2,048 pixels,
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Fig. 1 Schematics of a experimental setup and b airfoil motion profile, and c two-airfoil arrangement
via a 64-bit frame grabber installed in a Dell Precision 690 workstation. Timing and control of the PIV system, which include the lasers, CCD camera, frame grabber, and synchronizer, was accomplished by a programmable LaserPulse synchronizer (Model 610035) with a time resolution of 1 ns. The airfoil phase angles at which the pulses were generated and PIV data were acquired could be modified using the computer program. Seeding of the flow with particles of propylene glycol (Fisher P355-1) was accomplished by using a TSI 6-jet atomizer (Model 9306) in conjunction with a custom-built diffuser. The airfoil models were also coated with a thin layer of fluorescent paint, prepared by mixing 3 grams of Rhodamine 6G with 100 ml of ethanol and 500 ml of water soluble transparent acrylic paint, to reduce the amount of reflection (by 70–80%) from the airfoil surface. A 532 ± 2 nm narrow band-pass interference filter (Edmund model NT 43-174) was also installed on the CCD camera to block the higher
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wavelength. The PIV images were analyzed by using the Insight 3G software package developed by TSI Inc. The size of the interrogation window was set to either 24 9 24 or 32 9 32 (representing a physical size of roughly 1.5 and 2 mm, or 2 and 2.6%c, respectively), with a 50% overlapping of the interrogation windows. The velocity vector resolution was found to be accurate to within 1 and 1.3% for the 24 and 32 pixel interrogation windows, respectively. The field of view was 126 mm by 86 mm with a total of 28,200 vectors, which gave a vector density of 2.6 vectors/mm2. Vorticity values were obtained by centrally differentiating the velocity field. These values were expected to be within 5% accuracy. Details of the PIV setup are given in Gerontakos and Lee (2008) and Lee (2011). Two NC-machined NACA 0012 airfoils, each with c = 15 cm and b = 37.5 cm, were also used in a 0.9 9 1.2 9 2.7 m3 wind tunnel for surface pressure measurements. Circular end disks, of a diameter of 30 cm, with sharp leading edges were fitted to the airfoils to mitigate the free end effects. The airfoil pitch axes were located at -c location. The downstream airfoil was equipped with 61 pressure taps, of 0.35 mm in diameter, distributed over the upper and lower surface of the downstream airfoil. The pressure signals were obtained via a 48-channel Scannivalve system in conjunction with a fast-response miniature pressure transducer (Type YQCH-250-1). The orifices were 1.5 mm apart in the streamwise direction to avoid the wake effect from an upstream orifice on orifices further downstream. The pressure signals were phase-locked ensembleaveraged over 100 cycles of oscillation and were integrated numerically to compute the lift Cl and pitching-moment Cm coefficients. The effects of the 28-cm long and 0.75-mm i.d. Tygon tubing, separating the surface tap and the pressure transducer, on the unsteady pressure signals were examined by comparing the transducer output level and the phase with a controlled acoustic sound source. The effect of the length of the Tygon tubing was a simple time constant delay on all pressure signals with frequency above 2.05 Hz, which rendered a limited reduced frequency j of 0.088 at u? = 11 m/s. Details of this method can be found in the work of Chen and Ho (1987) and Jumper et al. (1989). Three axial spacings with L = 0.3, 0.6 and 1.6c were tested. Also, an uncertainty analysis gave a typical total uncertainty ±0.013 in Cp (see Moffat 1985).
3 Results and discussion To better illustrate the complex airfoil–wake interaction of the two-airfoil configuration, the velocity and vorticity flowfields around the baseline, or isolated, oscillating airfoil were re-examined first and serve as a comparison. The
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aerodynamic load characteristics of the baseline airfoil were also obtained to supplement the PIV flowfield measurements. 3.1 Baseline oscillating airfoil Figure 2 shows the normalized instantaneous iso-contours of streamwise velocity and vorticity of the baseline NACA 0012 airfoil oscillated with a(t) = 8° ? 5°sinxt at j = 0.05. Also included in this figure are the static airfoil results at a = 10.5° and 11° (Fig. 2j–k, u–v), which suggests a static stalling at ass & 11°. The results show that, for the baseline oscillating airfoil, the boundary layer remained mainly attached up to au = 9°, as a consequence of pitch-induced boundary-layer improvements (see Fig. 2a, l). For 9° \ au \ 11°, the turbulent boundary layer, in the aft portion of the airfoil, became significantly thickened (see, for example, at au = 10.5°; Fig. 2b, m), as a consequence of the streamwise accumulation of fluid in the flow reversal. This thickened low-velocity layer grew and progressed upstream as a was increased. Note that, unlike for steady flow, for the unsteady case, flow reversal does not necessarily imply a significant departure of the boundary layer from the wall. Thus, while the boundary layer on the rear portion of the airfoil thickened, the flow seemed to remain mostly attached with no apparent breakaway of the boundary-layer flow from the surface. The thin layer of flow reversal was, however, not detected due to the lack of seeding particles in the near-wall region. Nevertheless, the presence of the flow reversal can be inferred from the drastic thickening of the turbulent boundary layer. As the airfoil continued to pitch up, the arrival of the upstream progression of flow reversal disrupted the laminar separation bubble and initiated the formation of the leading-edge vortex (LEV) at au = 11.5°, as shown in Fig. 2c and n, with an initial length of around 30%c. The LEV formation can also be identified from the increasingly large suction pressure footprint developed on the airfoil upper surface, as shown later in the Cp data. The LEV grew rapidly in both its dimensions (i.e., streamwise and transverse) with its center shifting downstream with increasing a. At au = 128 (Fig. 2d, o), the center of the LEV had reached about x/c & 45% along the airfoil chord and it spanned a length of about 60%c. The downstream spreading and convection of the LEV not only produced a rapid increase in Cl but also produced a severe nose-down Cm, a characteristic of an oscillating airfoil. For au \ ads = 12.5°, the flow downstream of the LEV was unable to persist in an attached state and separated. ads is the dynamic-stall angle. At au = ads, the LEV reached a size equivalent to the airfoil chord as it was finally shed into the wake (Fig. 2e, p). For au [ ads, for example, at
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Fig. 2 Normalized instantaneous iso-velocity and vorticity contours. a–i and l–t: oscillating baseline airfoil; j–k and u–v static airfoil
au = amax = 13° (Fig. 2f, q), the upper-surface boundary layer was in a state of complete separation, leading to a catastrophic drop in lift. The post-stall flow condition was indicated by a massive flow separation over the airfoil upper surface (Fig. 2g, r). As the airfoil continued its pitch-
down motion, the separated boundary-layer flow began to reattach to the airfoil upper surface at ad around 9.5° (Fig. 2h, s), which caused a narrowing of the wake and a restructuring of the boundary layer. For ad \ 8°, the leading-edge suction peak and the presence of the laminar
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suction footprint and the flat Cp distribution developed on the airfoil upper surface, respectively. Meanwhile, the dynamic-stall angle was delayed to ads = 14.6° with a Cl,max of 1.39 compared to ass = 12.5° with Cl,max = 1.08 of its static counterparts. As the airfoil continued to pitch down, the LEV-induced massive flow separation caused a sharp drop in Cl accompanied by a rapid rise in the nosedown Cm value (Fig. 3b). The during-stall and post-stall flow regimes were also characterized by a flat Cp distribution (Fig. 4e–f). The pitch-down flow reattachment was indicated by a sharp recovery in Cl (Fig. 3a) and the re-establishment of the laminar separation bubble (Fig. 4g). Note that in order to compensate for the discrepancy in the Reynolds numbers tested in the PIV measurements (at Re = 8.45 9 104 with ass & 11°) and in the Cp measurements (at Re = 1.06 9 105 with ass = 12.5°), the pressure-orifice equipped airfoil was therefore oscillated with a(t) = 10° ? 5°sinxt instead of a(t) = 8° ? 5°sinxt employed in the PIV experiment. The present experiment also shows that there was a 3.4 times increase in the Cm,min value compared to the static airfoil (Fig. 3b). It is noteworthy that the alleviation of the nose-down Cm-induced negative damping and the associated pitch control load has
separation bubble were re-established (Fig. 2i, t), and the wake and boundary-layer flow were on their way to returning to pre-stall conditions. A more detailed analysis of the flowfields and the behavior of the boundary layer developed on an oscillating airfoil can be found in the works of Lee and Gerontakos (2004) and Gerontakos and Lee (2008). The PIV measurements of the baseline-airfoil flowfields can be further reinforced by the dynamic Cl and Cm loops and the Cp distributions displayed in Figs. 3 and 4. The locations of the end of attached flow or the onset of flow reversal, the initiation of LEV, LEV spillage/detachment, and the onset of pitch-down flow reattachment occurred on the baseline-airfoil upper surface during an oscillation cycle are denoted by points , `, ´, and ˆ, respectively, in Fig. 3a. For the baseline oscillating airfoil, the attachedflow regime is denoted by the linear portion of the lift curve. The static lift curve is also included in Fig. 3a. The increase in the leading-edge suction pressure with a and the presence of a laminar separation bubble (characterized by the pressure plateau) of the baseline airfoil are evident in Fig. 4a and b. The LEV formation (Fig. 4c) and detachment (Fig. 4d) are characterized by the large
Fig. 3 Impact of axial spacing on the dynamic-load loops of the downstream airfoil for / = 180°. Thick line: pitch-up; thin line: pitch-down
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1612 Fig. 4 Impact of / on Cp distribution at selected a for L = 0.3c. LSB laminar separation bubble; LEV leadingedge vortex
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-2
Cp -2
-1
-1
0
0 0.2
0.4
0.6
0.8
1
1.0
0.0
0.2
0.4
(g)
αu = 14º
Suction peak
Cp -2
-1
-1
0
0
0.2
0.4
0.6
0.8
1.0
x/c
(d)
1.0
αd = 8º
LSB re-establishment
-3
Cp -2
1 0.0
0.8
-5 -4
LEV
-3
0.6
x/c
-5 -4
1.0
Post stall
x/c
(c)
0.8
αd = 12º
Suction peak -4
-3
1 0.0
0.6
x/c
-5 -4
αd = 14º
Suction peak
-4
1 0.0
0.2
0.4
0.6
0.8
1.0
x/c
-5 -4
αu = 15º
Suction peak
LEV detachment
-3
Cp -2 -1 0 1 0.0
0.2
0.4
0.6
0.8
1.0
x/c
always posed a challenge to helicopter aerodynamicists. On the other hand, in the case of highly maneuverable aircraft, advantage could be made of the increased dynamic lift if the LEV is allowed to form but is delayed in its detachment and shedding from the airfoil suction surface, thereby delaying dynamic stall.
123
3.2 Two-airfoil configuration with / = 180° The effects of the upstream airfoil-generated wake on the flow and aerodynamic characteristics of the downstream airfoil, oscillated at the same conditions but with / = 180° phase difference (relative to the upstream airfoil), were
Exp Fluids (2011) 51:1605–1621
investigated first for L = 0.3c and are summarized in Figs. 3, 4, 5, 6 and 7. The results show that, for two intandem oscillating airfoils, the aerodynamic loads developed on the downstream airfoil were strongly influenced by the upstream interference effect, including its shed LEV. For / = 180°, the upstream airfoil and the downstream airfoil were always at opposite incidences or directions of motion at any given time instant. This gave rise to a continuous rise in the suction peak in the leading-edge region of the downstream airfoil during its pitch-up motion for afr \ au B amax (Fig. 4b–d), due to the fact that as the angle of attack of the downstream airfoil was increased, the upstream interference became progressively smaller, thus allowing the higher suction peaks to develop. afr denotes the angle at which the onset of flow reversal occurred on the baseline airfoil. The corresponding interferences of the upstream-airfoil wake with the downstream airfoil are illustrated in Figs. 5d–g and 6c–e. These figures reveal that the upstream airfoil-generated wake mainly impinged on the lower surface of the downstream airfoil, especially in the leading-edge region, leaving the upper surface of the downstream airfoil largely unaffected. This explains the observed increase in the leading-edge suction peak with increasing a (for afr \ au B amax) and the lowered pressure on the lower surface of the downstream airfoil, compared to the baseline airfoil. For au \ afr of the downstream airfoil, the large separated wake generated by the upstream airfoil (which was undergoing LEV formation, growth and shedding process), however, was found to produce the most detrimental interference effects on the downstream airfoil (see Figs. 5a–c, 6a–b), rendering a flat Cp distribution on the upper surface of the downstream airfoil (see, for example, Fig. 4a), and subsequently a greatly lowered Cl value (denoted by the red line in Fig. 3a). It should be noted that the presence of the downstream airfoil could cause the upstream-airfoil wake to be deflected upwards and separate slightly earlier. Nevertheless, the interaction of the upstream airfoil-generated wake with the downstream airfoil unavoidably led to boundary-layer events significantly different from those observed on the baseline oscillating airfoil. The downwash induced by the upstream airfoil disrupted the LEV formation such that it never developed over the downstream airfoil. As a result, the LEV-induced transient effects typical of dynamic-stall oscillation, as observed on the baseline airfoil, were not realized and the Cl-hysteresis was significantly reduced. As can be seen in Fig. 3a, the Cl, including its maximum value, of the downstream airfoil (with / = 180°) was therefore of a smaller magnitude during its pitch-up motion compared to the baseline airfoil. The reduction in Cl, as a result of the upstream induced downwash, can also be viewed as a reduction in effective incidence. For L = 0.3c, a Cl,max of 1.28 and a Cm,min of -0.0096 (see Fig. 3b),
1613
compared to 1.39 and -0.0256 of the baseline airfoil, were observed. The Cm loop of the downstream airfoil (with / = 180°) was shifted downward with a lower value during pitch-up than during pitch-down (Fig. 3b), which had a trend opposite to that of the baseline airfoil. The present measurements also show that during pitchdown motion of the downstream airfoil, the interferences remained insignificant (see Figs. 5h–k, 6f–h) and that the suction peak on the downstream airfoil began to recede with decreasing a (see Fig. 4e–g). The presence of the suction peak on the downstream airfoil during its pitchdown motion can be attributed to the absence of the LEV formation and detachment on its upper surface as it pitched through its maximum angle of attack. The upstream-airfoil wake mainly impinged upon the lower surface of the downstream airfoil, rendering a further decrease in the lower-surface pressure compared to the baseline airfoil. The downwash also eliminated the re-establishment of the laminar separation bubble on the downstream airfoil during its pitch-down flow reattachment process. The absence of the LEV-induced massive flow separation and the presence of the suction peak on the upper surface of the downstream airfoil also led to an improved Cl during pitch-down compared to the baseline airfoil (see Fig. 3a). For a more straightforward evaluation of the impact of the BWI effects on the aerodynamic characteristics of the downstream airfoil oscillated with / = 180°, the changes in DCl (= Cl,downstream airfoil - Cl,baseline airfoil) and DCm (= Cm,downstream airfoil - Cm,baseline airfoil) for L = 0.3c are also displayed in Fig. 7a and d. The BWI clearly led to a lowered Cl of the downstream airfoil during its pitch-up motion but an improved Cl during the first half of its pitchdown motion (Fig. 7a). The change in Cm, however, remained largely inferior to the baseline-airfoil value, except around au = amax (Fig. 7d). Figure 3a further shows that, for L = 0.3c and / = 180°, there was virtually no hysteresis in the Cl value between pitch-up and pitch-down motion of the downstream R airfoil. The magnitude of the Cl-hysteresis or CH (¼ Cl ðaÞda) was found to be 0.16 compared to 2.73 of the baseline airfoil (see Table 1), which translates into a 94% reduction in Cl-hysteresis over that of the baseline airfoil. The large Cl-hysteresis (or CH value) generally observed on a baseline oscillating airfoil is of great significance since it is the source of reduced aerodynamic damping, which can potentially lead to a variety of aeroelastic problems on the rotor. The impact of the upstream-airfoil wake on the aerodynamic loads of the downstream airfoil can be further R evaluatedR via the torsional R damping factor Cw (¼ Cm ðaÞda ¼ ccw Cm ðaÞda þ cw Cm ðaÞda; Leishman (2002)). Cw is positive when it corresponds to a counterclockwise (CCW) loop while negative for a clockwise (CW) loop in the Cm versus a curve. Table 1 shows that, for / = 180°,
123
1614
Exp Fluids (2011) 51:1605–1621
Φ =180˚
(a)
Φ =0˚
(a1)
0.40
0.30 0.30
0.20 0.20 0.10
y/c
y/c
0.10
α u=3˚
0.00
0.00
-0.10 -0.10
-0.20
-0.20
-0.20 -0.20
0.00
0.20
0.40
0.60
0.80
0.30
0.30
y/c
y/c
0.10
-0.20
0.00
0.20
0.60
0.80
0.30
0.30
0.20
0.20
0.10
0.10
0.40
1.00
(c1) 1.5
0.00
0.00
-0.10
-0.10
-0.20
1 -0.20
-0.20 0.00
0.20
0.40
0.60
0.80
0.00
0.20
0.40
0.60
0.80
1.00
x/c
(d)
0
(d1)
0.20
0.20
0.10
0.10
0.00
0.00
-0.10
-0.5 -1
-0.10 -0.20
-0.20 -0.20
0.00
0.20
0.40
0.60
0.80
-0.20
1.00
0.00
0.20
0.40
0.60
0.80
1.00
0.60
0.80
1.00
0.60
0.80
1.00
x/c
x/c
(e1)
(e)
0.40 0.30
0.10
0.20
0.00
0.10
y/c
0.20
-0.10
0.00
-0.20
-0.10 -0.20 -0.20
0.00
0.20
0.40
0.60
0.80
1.00
-0.30
x/c
-0.20
0.00
0.20
0.40
x/c
(f1)
(f)
0.40
0.20
0.30 0.10 0.00
y/c
y/c
0.20
α u=12.5˚
-0.10
0.10 0.00
-0.20
-0.10 -0.30
-0.20
0.00
0.20
0.40
x/c
0.60
0.80
1.00
-0.20 -0.20
0.00
0.20
0.40
x/c
Fig. 5 Impact of / on iso-u/u? contours for L = 0.3c. a–k: / = 180°; a1–k1: / = 0°
123
0.5
x/c
1.00
y/c
y/c
0.20
x/c
0.40
-0.20
0.00
1.00
y/c
y/c
0.40
x/c
(c)
y/c
0.80
-0.20
-0.20
-0.30
0.60
(b1)
0.10
-0.20
α u=12˚
1.00
-0.10
-0.10
-0.30
0.80
0.00
0.00
α u=11˚
0.60
0.20
0.20
0.30
0.40
x/c
0.40
α u=8˚
0.20
x/c
(b)
α u=6˚
0.00
1.00
Exp Fluids (2011) 51:1605–1621
1615
Φ =180˚
(g)
0.50
0.30
0.40
0.20
0.30
y/c
y/c
0.10
α u=13˚
0.00
0.20 0.10
-0.10
0.00
-0.20 -0.30
Φ =0˚
(g1)
-0.10
-0.20
0.00
0.20
0.40
0.60
0.80
1.00
-0.20
x/c
-0.20
0.00
0.20
0.40
0.60
0.80
1.00
0.60
0.80
1.00
x/c 0.60
(h1)
0.50
0.30
0.40
0.20
0.30
y/c
α d=12˚
y/c
0.40
(h)
0.10
0.20 0.10
0.00 -0.10
0.00
-0.20
-0.10
-0.20
0.00
0.20
0.40
0.60
0.80
-0.20
1.00
-0.20
x/c
0.00
0.20
0.40
1.5
x/c 0.50
0.30
0.40
0.20
0.30
0.10
0.20
y/c
α d=10˚
y/c
(i)
0.00
0.00
-0.20
-0.10
-0.20
0.00
0.20
0.40
0.60
0.80
0.5 0
0.10
-0.10
-0.30
1
(i1)
-0.5
-0.20
1.00
-0.20
x/c
0.00x/c
0.20
0.40
0.60
0.80
1.00
0.60
0.80
1.00
0.60
0.80
1.00
-1
x/c 0.30
(j1)
(j) 0.40
0.20
0.30
y/c
α d=9˚
y/c
0.10 0.00 -0.10
0.10 0.00
-0.20 -0.30
0.20
-0.10 -0.20
0.00
0.20
0.40
0.60
0.80
1.00
-0.20
x/c
0.30
0.10
0.20
y/c
y/c
0.20
0.40
x/c
0.40
0.20
0.00 -0.10
0.10 0.00
-0.20 -0.30
0.00
(k1)
(k)
α d=7˚
-0.20
-0.10 -0.20
0.00
0.20
0.40
x/c
0.60
0.80
1.00
-0.20 -0.20
0.00
0.20
0.40
x/c
Fig. 5 continued
123
1616
Exp Fluids (2011) 51:1605–1621
Φ =180˚
0.40
0.30
0.30
0.20
0.20
0.10
0.10
0.00
0.00
-0.10
-0.10
-0.20 -0.20
-0.20 -0.20
0.00
0.20
0.40
Φ =0˚
(a1)
y/c
α u=3˚
y/c
(a)
0.60
0.80
0.00
0.20
0.40
0.60
0.80
1.00
x/c
1.00
x/c 0.50
(b) 0.30
0.40
0.20 0.10
0.20
y/c
y/c
0.30
α u=8˚
0.10
0.00
60
-0.10
0.00
-0.20
-0.10 -0.20
(b1)
-0.20
-0.20
0.00
0.20
0.40
0.60
0.80
0.00
0.20
0.40
0.60
0.80
1.00
x/c
1.00
40 20
x/c
0 0.30
(c)
(c1)
y/c
y/c
0.00 -0.10
0.00
-60
-0.10 -0.20
-0.20 -0.30
-40
0.10
0.10
α u=11˚
-20
0.20
0.20
-0.30
-0.20
0.00
0.20
0.40
0.60
0.80
1.00
-0.20
0.00
0.20
0.40
0.60
0.80
1.00
0.60
0.80
1.00
x/c
x/c
(d1) 0.40
0.20
0.30
0.10
0.20
0.00
y/c
α u=12˚
y/c
(d)
0.10
-0.10
0.00
-0.20
-0.10
-0.30
-0.20
0.00
0.20
0.40
0.60
0.80
1.00
x/c
-0.20 -0.30
-0.20
0.00
0.20
0.40
x/c
Fig. 6 Impact of / on iso-fc/u? contours for L = 0.3c. a–h: / = 180°; a1–h1: / = 0°
there was a substantial improvement in the net Cw value (Cw,net = Cw,cw ? Cw,ccw) of the downstream airfoil compared to the baseline airfoil. 3.3 Two-airfoil configuration with / = 0° For / = 0° and L = 0.3c, both upstream and downstream airfoils were at the same incidence, the interference effects from the upstream airfoil and its turbulent wake therefore caused a significantly reduced pressure on both the upper
123
and the lower surfaces of the downstream airfoil throughout the entire oscillation cycle (see Fig. 4a–g). For most of the oscillation cycle, the downstream airfoil was completely embedded in the upstream airfoil-generated turbulent wake. This resulted in a considerably decreased lift and lift-curve slope compared to the baseline airfoil and the / = 1808 case with L = 0.3c (Fig. 8a). The Cm value was also found to be persistently lower than that of the baseline airfoil (Fig. 8b). A Cl,max of 0.58 accompanied by a Cm,min of -0.0116 was observed. The interaction of the upstream-
Exp Fluids (2011) 51:1605–1621
Φ =180˚
0.30
0.40
0.20
0.30
0.10
0.20
0.00
0.10
-0.10
0.00
-0.20
-0.10
-0.30
-0.20
0.00
0.20
0.40
Φ =0˚
(e1) 0.50
y/c
y/c
(e)
α u=13˚
1617
0.60
0.80
-0.20
1.00
-0.30
x/c
-0.20
0.00
0.20
0.40
0.60
0.80
1.00
x/c
(f1) 0.40
(f)
0.50 0.40
0.30
0.30
y/c
α d=12˚
y/c
0.20 0.10 0.00
0.20 0.10 0.00
-0.10
60
-0.10
-0.20 -0.20
0.00
0.20
0.40
0.60
0.80
-0.20
1.00
-0.20
0.00
0.20
x/c
1.00
40 20 0
0.50 0.40
0.20
-20
0.30
y/c
0.10
y/c
0.80
(g1)
(g)
0.00
-40
0.20 0.10
-0.10
-60
0.00
-0.20 -0.30
0.60
x/c
0.30
α d=9˚
0.40
-0.10
-0.20
0.00
0.20
0.40
0.60
0.80
1.00
-0.20
x/c
-0.20
0.00
0.20
0.40
0.60
0.80
1.00
0.60
0.80
1.00
x/c
(h1) 0.40
0.20
0.30
0.10
0.20
y/c
α d=7˚
y/c
(h)
0.00
0.10
-0.10
0.00
-0.20
-0.10
-0.30
-0.20
0.00
0.20
0.40
0.60
0.80
1.00
x/c
-0.20 -0.20
0.00
0.20
0.40
x/c
Fig. 6 continued
airfoil LEV-induced wake with the downstream airfoil (for au C 11° and ad C 9°), position at L = 0.3c, and the resulting massive flow separation on the downstream airfoil can be illustrated from the iso-u/u? and fc/u? contours presented in Figs. 5d1–j1 and 6c1–g1, respectively. The flowfields corresponding to au \ afr and after the pitchdown flow reattachment flow regimes are illustrated in Fig. 5a1–c1 and k1, and Fig. 6a1–b1 and h1, respectively.
These figures reveal that, for / = 0°, the degree and extent of upstream airfoil interference on the downstream airfoil was greatly reduced due to the narrow wake (thus a smaller downwash) produced by the upstream airfoil. The substantially lowered Cl value over the entire oscillation cycle of the downstream airfoil with / = 0° also led to 71% reduction in CH compared to the baseline airfoil (see Table 1). A Cw,net of 0.034 compared to -0.036 of the
123
1618
Exp Fluids (2011) 51:1605–1621
0.02
0.2
0.01
-0.1
0.00
ΔCm
-0.4
-1.0 -π/2
0
π/2
π
τ
-0.03 -π/2
3π/2
(b) L = 0.6c
0.03
0.2
0.02
-0.1
0.01
-0.4
0.00
-0.7
-0.01
π/2
π
3π/2
(g) L = 0.6c
(e) L = 0.6c
0.1 0.0 -0.1 -0.2
-1.0 -π/2
π/2
0
π
τ
-0.02 -π/2
3π/2
0.03
0.2
0.02
-0.1
0.01
ΔCm
0.5
-0.4
π/2
π
3π/2
π
3π/2
0
-π/2
π/2
π
τ
3π/2
(f) L = 1.6c
0.00 -0.01
-0.7 -1.0 -π/2
-0.3 0
τ
(c) L = 1.6c
ΔCl
0
τ
ΔCm
ΔCl
-0.01 -0.02
-0.7
0.5
(d) L = 0.3c
ΔCd
ΔCl
(a) L = 0.3c 0.5
0
π/2
π
τ
3π/2
-0.02 -π/2
0
π/2
τ
Fig. 7 Variation in lift, pitching-moment, and drag coefficients, relative to the baseline airfoil, with axial spacing and phase difference. Solid line / = 0°; dashed line / = 180°
Table 1 Impact of / and L on Cl,max, ads, Cm,min, CH, Cw,cw, Cw,ccw, and Cw,net Configuration
/ (°)
L
Cl,max
ads (°)
Cm,min
CH
Cw,cw –
Cw,ccw –
Cw,net
SA
–
–
1.08
12.5
-0.0580
–
BA
–
–
1.39
14.6
-0.0256
2.73
-0.061
0.025
-0.036
–
TA
180
0.3c
1.28
15
-0.0096
0.16
-0.034
0.051
0.017
TA
180
0.6c
1.13
15
-0.0028
0.39
-0.015
0.002
0.013
TA
180
1.6c
1.05
15
-0.0011
0.42
-0.013
0.001
0.010
TA
0
0.3c
0.58
13.9
-0.0116
0.78
-0.032
0.068
0.034
TA
0
0.6c
0.79
14.2
-0.0062
1.00
-0.014
0.039
0.022
TA
0
1.6c
0.94
14
-0.0051
1.08
-0.011
0.030
0.019
SA, BA, and TA denote static airfoil, baseline airfoil, and two airfoils, respectively
baseline airfoil was also noticed. The improvement in CH of the / = 08 case was, however, of a lesser extent in comparison with the / = 1808 case.
123
The effects of axial spacing (for L B 1.6c) on the aerodynamic characteristics of the downstream airfoil were also investigated. The variation of Cl,max, Cm,min, CH, Cw,cw,
Exp Fluids (2011) 51:1605–1621 Fig. 8 Impact of axial spacing on the dynamic-load loops of the downstream airfoil for / = 0°. Thick line pitch-up; thin line pitch-down
1619
(a)
1.5
(c) 0.4
3 2
1.2
1
0.3
0.9
Cl
Cd 0.2
4 0.6
0.1 0.3
0.0
(b)
0.0 4
6
8
10
α
12
14
16
12
14
16
4
6
8
10
12
14
16
α
0.01
0.00
Cm -0.01 , baseline airfoil , L = 0.3c , L = 0.6c , L = 1.6c , static airfoil
-0.02
-0.03
4
6
8
10
α
Cw,ccw, and Cw,net with L and / is summarized in Table 1. For both / tested, the axial spacing appeared to play a strong role in the Cl and Cm values (see Figs. 3, 7, 8). The combination of phase difference and axial spacing determined not only the type of interaction but also the strength of the undesirable interference effects on the downstream airfoil. The LEV-induced transient effects were persistently not realized, rendering a significantly lowered Cl-hysteresis compared to the baseline airfoil. A consistently lowered Cl and Cm value, compared to the baseline airfoil, regardless of / and L, was observed. For / = 0°, the Cl and Cl,max of the downstream airfoil were found to improve with increasing axial spacing, likely because the interference effects were most dominant. Thus, as L was increased, the wake deficit and the downwash were reduced leading to a less significant interaction, or interference, of the upstream airfoil with the downstream airfoil. The opposite trend was, however, observed for the / = 180° case. For both / tested, the CH value was, however, found to increase with increasing L (for L B 0.6c), while the Cw,net value showed an opposite trend as L was increased. For L C 0.6c, both CH and Cw,net values appeared to be a weak function of the axial spacing for L C 0.6c.
Finally, the near-wake mean u and fluctuating u0 velocity profiles were also measured by using a miniature hot-wire probe, located at x/c = 0.6 behind the trailing edge of the downstream airfoil, for L = 0.6c (Fig. 9a,b). The various aerodynamic and boundary-layer flow characteristics of the downstream oscillating airfoils (with / = 0° and 180°), as described in Figs. 3, 4, 5, 6, 7 and 8, can also be reflected from the observed changes in the wake width and deficit (Fig. 9a) and the associated velocity fluctuations (Fig. 9b), behind the downstream airfoil, over one cycle of oscillation. The phase-averaged mean wake velocity profiles were also used to estimate the drag coefficient of the downstream airfoil (Figs. 3c, 8c). Figures 3c and 8c show that the Cd value was generally increased during pitch-up but decreased during pitch-down compared to the baseline airfoil. The / = 0° case, however, had a higher Cd than the / = 180° case. Note that because of the convection time required for the wake flow, including the LEV, to propagate from the airfoil to the downstream sensor location, which translates into a phase lag between any sensors readings at that instant, a correction, or compensation, scheme was therefore needed in interpreting the wake measurements. In the present experiment,
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Exp Fluids (2011) 51:1605–1621
(a)
αu = 5º
0.5
αu = 11º
αu = 13º
αu = 14º
αu = 15º
αd = 14º
αd = 12º
αd = 7º
y/c
0.2 -0.1
-0.4 -0.7
1.0
0.8
0.6
u/uo
(b)
0.5
y/c
0.2 -0.1
-0.4 -0.7 0.0 0.1 0.2 0.3
u'/uo
Fig. 9 Wake velocity profiles behind the downstream airfoil at x/c = 0.6 for L = 0.6c. Solid line, baseline airfoil; dashed line, / = 0°; dotted line, / = 180°
a convection speed uconv approximated as the 50% of the freestream speed, similar to the phase compensation suggested by Park et al. (1990) in their study of the near wake behind a sinusoidally oscillating airfoil, was employed to minimize the axial spacing-induced phase lag for L [ 0.3c.
aerodynamic performance of the / = 1808 case, however, outperformed that of the / = 08 case.
4 Conclusions
References
The interaction of the wake, generated by an upstream NACA 0012 airfoil, with a downstream airfoil, oscillated with both / = 0° and 180° phase differences (relative to the upstream airfoil), was investigated. The results show that the axial spacing L and phase difference determined the strength of the undesirable interference effects and, subsequently, the behavior of the dynamic-load loops of the downstream airfoil. The boundary-layer events on the downstream airfoil were persistently different from those observed on the baseline oscillating airfoil, regardless of / and L. The downwash induced by the upstream airfoil disrupted LEV formation such that it never developed over the downstream airfoil. As a result, the LEV-induced transient effects (as observed on a baseline oscillating airfoil) were not realized, which gave rise to a considerably lowered Cl-hysteresis compared to the baseline airfoil. A consistently lowered Cl, Cm, CH, and Cw,net value, compared to the baseline airfoil, was observed. For / = 08, the Cl value appeared to improve with axial distance. The opposite trend was observed for the / = 1808 case. The
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Acknowledgments The author would like to thank L.S. Ko and Y.Y. Su for their help with the PIV experiment and J. Pereira for her help with the surface pressure measurement.
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