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Characteristics of flow configurations around side-by-side twin wind blades
Experimental Thermal and Fluid Science 82 (2017) 302–313
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Characteristics of flow configurations around side-by-side twin wind blades Shun-Chang Yen a,⇑, Chu-Hsuan Wu a, Kuo-Ching San b a b
Department of Mechanical and Mechatronic Engineering, National Taiwan Ocean University, Keelung 202, Taiwan, ROC Department of Aeronautics and Astronautics, R.O.C. Air Force Academy, Kaohsiung 820, Taiwan, ROC
a r t i c l e
i n f o
Article history: Received 24 August 2016 Received in revised form 23 November 2016 Accepted 24 November 2016 Available online 25 November 2016 Keywords: Side-by-side wind blade Flow visualization Gap flow Gap ratio Aerodynamic performance
a b s t r a c t The effects of gap ratio (g⁄) and angle of attack (a) on side-by-side twin wind blades were investigated in an open-channel wind tunnel. Characteristic wake-flow patterns and aerodynamic performance were analyzed using smoke-streak flow visualization, hot-wire velocimetry, and six-force balancer. Seven smoke-streak flow patterns were defined – attached surface flow, wake instability wave, vortical wake, gap flow, bluff-body wake, anti-phase vortex shedding, and in-phase vortex shedding. For g⁄ 0, the flow characteristics were similar to those of a single wind blade. As g⁄ increased, these two wind blades induced the vortical wake, gap flow, and anti-phase vortex shedding modes. With further increase in g⁄, the wake-flow patterns were similar to those behind a single wind blade. The hot-wire velocimeter detected that the maximum velocity fluctuation occurred at g⁄ = 0.083. This velocity fluctuation decreased toward that of free stream as g⁄ increased. The vortex-shedding frequency decreased as a increased. For a single wind blade, the maximum lift occurred at a = 10° and the drag increased with a. The pitching momentum increased with a when a < 45°. The lift, drag, and pitching momentum on the lower wind blade decreased significantly due to the existence of upper wind blade. The effect of upper wind blade on the lower one deceased as g⁄ increased. Ó 2016 Elsevier Inc. All rights reserved.
1. Introduction The blades of a rotor were driven to rotate when a fluid flows through the rotor. A bluff-body blade caused a pressure difference around the rotor. The inner flow tube in gas turbines, blowers, and air compressors were utilized to generate the pressure difference. In daily applications, fans, wind turbines, and water turbines use the thrust induced from the pressure difference. In these applications, the gap width between the side-by-side blades has a significant effect on the machine performance. The previous study on single blade showed a significant relationship with the surface boundary-layer on the suction side [1–3]. These aerodynamic phenomena included flow separation, reattachment, and vortex formation. In addition, surface flow behavior has a significant effect on wake vortex shedding resulting from the shear instability wave in the boundary-layer separation [4]. Studies on surface flow and aerodynamic performance have showed a laminar boundary layer formed near the stagnation point ⇑ Corresponding author at: Department of Mechanical and Mechatronic Engineering, National Taiwan Ocean University, No. 2, Pei-Ning Road, Keelung 202, Taiwan, ROC. E-mail address: [email protected] (S.-C. Yen). http://dx.doi.org/10.1016/j.expthermflusci.2016.11.026 0894-1777/Ó 2016 Elsevier Inc. All rights reserved.
of a wind-blade leading edge. As the flow moves downstream, the flow separates at the minimum-pressure point. Behind the separation point, the shear layer transits to a turbulent flow. Subsequently, the separated flow reattaches on the wind-blade surface. Between the reattached point and wind-blade trailing edge, the surface flow formed a turbulent boundary layer. A bubble was generated between the separation point and reattached point. At a low chord-length Reynolds number and low angle of attack (AoA), the bubble occupied most of the wind-blade surface. This bubble changes the surface pressure distribution and aerodynamic characteristics. In the 1980s, most studies focused on surface-flow behaviors [5–7]. Lissaman [2] studied flow separation on the laminar boundary layers, boundary-layer transition, and boundary-layer reattachment. He found that the flow separation occurs near the point of the minimum surface pressure. A shear layer evolved downstream and transited to a turbulent flow. The turbulent kinetic energy increases and the separated boundary layer reattached on the wind-blade surface. This reattached turbulent boundary layer extended from the reattached point to the trailing edge. A study on unstable wake flow revealed that this flow was generated because of the boundary-layer separation and shear-layer instability wave [8]. Research topics included the periodic instabil-
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Nomenclature b C CL CD CM d D f g⁄ L M q Re s
half wind-blade span, 30 cm chord length, 6 cm lift coefficient (= L/qbC) drag coefficient (= D/qbC) quarter-chord moment coefficient (= M/qbC2) projection chord length drag wake vortex-shedding frequency (Hz) gap ratio (= s/C) lift quarter-chord momentum dynamic pressure of free-stream (= qu12/2) Reynolds number (= u1C/m) streamwise spacing between the centers of two wind blade cylinders
ity wave, the effect of coherent structure on wind-blade performance, and wind vibrations induced by the wake vortex (fluid– structure coupling) [9,10]. Previous studies focused on the wake flow behind a bluff body [11,12]. Roshko [13] found that the Strouhal number (St = fd/u) remained constant with values of 0.21, 0.18, and 0.14 for a cylinder, 90° wedge, and plain board, respectively, when the Reynolds number (Re) was in the range 103 < Re < 105. In addition, Roshko revealed that St was low for sharp and flat bodies. Huang and Lin [14] used wind and water tunnels to study the instable wake vortex-shedding frequency and behaviors behind wing airfoils. They found that the surface flow did not separate at a low AoA behind a sharp trailing-edge wing. However, such wings have a mixing-layer wake flow and a small-amplitude instability wave. These instability waves evolved into a wake vortex and subsequently a vortex street. Furthermore, in this wake flow, the viscous effect in the boundary layer was considered. At high AoA and high Reynolds numbers, the projection chord-length dominated the instability wake flow. In addition, the periodic vortex frequency displayed two trends: (1) at low Reynolds numbers, St decreases as Re increases, and (2) at high Reynolds numbers, St remains constant. Huang et al. found that St remained constant and Roshko number was proportional to St in the inertiadominated regime. However, in the viscosity-dominated regime, Roshko number remained constant and St was inversely proportional to Re [15]. In studies on multi-blade patterns, many researchers have numerically simulated flow structures and aerodynamic performance. Dong and Lu [16] used three fish-like profiles to numerically investigate the effect of gap ratio on aerodynamic performance. They found that the gap ratios influenced the formation of in-phase and anti-phase vortex streets. At low gap ratios, the upper and lower vortex series were close and then squeezed to form an anti-phase vortex street. In contrast, the high gap ratio caused an in-phase vortex street. Furthermore, the drag coefficient decreased with gap ratio. Hansen and Madsen [17] employed the blade element momentum method to determine the blade profiles and compute aerodynamic coefficients. Sieverding et al. [18] used a supersonic wind tunnel to study the surface-pressure distribution on side-by-side blades. They found the non-uniform pressure distribution near the blade trailing edge at subsonic speeds. Furthermore, the lowest pressure occurred at the trailing edge. On the suction side, the vortex formed near the trailing edge was influenced by the adjacent blade. Uzol et al. [19] studied a transient flow field by using particle image velocimetry and water tunnel. They found that the free-stream velocity changed by about 13%
St T.I. u1 u u0 v v0 x y
a q m
Strouhal number of vortex shedding (= fd/u1) turbulence intensity free-stream velocity x-component of mean velocity, m/s x-component of velocity fluctuation, m/s y-component of mean velocity, m/s y-component of velocity fluctuation, m/s streamwise coordinate originated at leading edge spanwise coordinate originated at the wing root angle of attack air density kinetic viscosity of air
due to the transverse velocity behind the blades. The gap ratio between blades has a significant effect on blade efficiency. Previous studies have investigated single bluff bodies and sideby-side cylinders/squares. In this study, the effects of gap ratio and AoA on a single bluff wind-blade and two side-by-side wind blades were investigated. Smoke-streak visualization was employed to observe the characteristic flow patterns. Hot-wire velocimetry was used to measure the wake vortex-shedding frequency and calculate the Strouhal number. Furthermore, the hot wire was used to measure the velocity contour around the wind blades. A six-force balancer was used to measure the aerodynamic loadings. 2. Experimental setup 2.1. Apparatus Fig. 1 shows the wind tunnel and experimental setup used in this study [20]. This open-loop wind tunnel was operated stably in the range of 1.64–28.28 m/s. This wind tunnel included seven parts: noise-filtering section, steady section (settling chamber), nozzle, test section, vibration absorber, expansion section (diffuser), and blower fan. The noise-filtering section comprised two parts: (1) an aluminum-made honeycomb for eliminating transverse flow fluctuations, and (2) a three-layer metal mesh for filtering the longitudinal flow noise. The nozzle contraction ratio was 3.24:1. The cross-section area and length of the test section were 50 50 cm2 and 120 cm, respectively. The downstream test section was connected to a vibration absorber, which was used to isolate the operation vibrations of the blower fan. The downstream expansion section was connected to a centrifugal blower fan driven using a three-phase and 20 horse-power motor. The motor rotation speed was adjusted using a inverter with the maximum rotating speed of 1160 rpm. The precision of inverter is 0.1 Hz and the operable range is 0–60 Hz, which corresponds to a flow speed of 1.64–28.28 m/s. 2.2. Blades An NACA 00122 [21] aerofoil was used to investigate the flow behavior. This wind blade was fabricated using solid chrome moly 4340 to reduce the wind resonance. The chord length (C) and windblade span (S) were 6 and 30 cm, respectively; and therefore, the aspect ratio was 5. The wind-blade surface was polished for reducing the surface roughness. An index plate was used to rotate the
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Fig. 1. Experimental setup.
wind blade, and the operation resolution was 0.0333/div. Fig. 1 shows the experimental configuration for the side-by-side twin wind blades. 2.3. Free-stream velocity The free-stream velocity was obtained using a commercial Pitot tube (Dwyer Instruments, Inc.) and a U-tube pressure indicator; and then calculated using the Bernoulli equation. The pressure signals were detected using a Huba 694 pressure transducer (JETEC Electronics Co.). The Pitot tube consists of a total pressure hole and four symmetrical static pressure holes. The diameters of the total and static pressure holes were 2.3 and 0.3 mm, respectively. Further, the diameter of Pitot tube is 8 mm and the resolution of Huba 694 is less than 0.002 mmAq. 2.4. Smoke-streak visualization The smoke-streak visualization method utilized in this study was developed and proposed by Raspet and Moore. Fraxinus oil, used for coating the wind blades, was heated using an electric wire. The average diameter of the fraxinus particles was 1.7 ± 0.2 lm. Flagan and Seinfeld [22] indicated that a particle group can be treated as a continuous medium when the Knudsen number 1; in such a case, the random motion of flow particles can be neglected. The Stokes number for fraxinus particles is 1.28 104 (i.e., 1); this shows that the flow particles can follow the flow motion. The properties of vaporized fraxinus oil showed that the slip phenomenon induced by the turbulent diffusion effect was negligible and the interactions between fraxinus oil particles could also be neglected. In addition, the experimental results showed that the smoke streak width was less than 0.1 mm and the Reynolds number (Re) was smaller than 40. The smoke vortex street vanished and did not interfere with the flow field. In this study, the free stream velocity was maintained in the range of 1.96–3.23 m/s (i.e., 16 < Re < 27). The flow photos were captured using a Nikon D70s digital camera at a shutter speed of 1/1000s. 2.5. Velocity characteristics and turbulence intensity The velocity characteristics and turbulence intensity (T.I.) were detected using the hot-wire velocimetry and a two-dimensional constant-temperature hot-wire probe (TSI 1240-T1.5 X-type). The
diameter and length of the hot-wire probe were 5 lm and 1.5 mm, respectively, yielding a response frequency of 15–25 kHz. The hot-wire velocimeter was corrected using a Pitot tube sensor. In this experiment, the detection position (z) was set at z = 2.5C located in the wake region of the side-by-side twin wind blades. The detected signals were transferred from the probe to a high-speed data logger. Furthermore, the velocity data were used to calculate the turbulence intensity. 2.6. Wake shedding frequency The wake vortex-shedding frequency was detected using the hot-wire velocimetry and a normal-type one-dimensional constant-temperature hot-wire probe (TSI 1218-T1.5). The hotwire probe was installed at z = 2.5C (i.e., in the wake region). The detected signals were transferred to a fast-Fourier transform (FFT) analyzer (CF-920, Ono Sokki Co.). The FFT analyzer recorded the frequency spectrum and then calculated the vortex-shedding frequency. The precision of FFT analyzer depends on the FFT resolution. As the resolution is 1 Hz, its precision is 0.0025 Hz. In addition, the precision is 5 Hz when the FFT resolution is 2 kHz. 2.7. Aerodynamic loadings The aerodynamic loadings were measured using a JR3 universal force–moment system (NITTA) associated with a six-degree-offreedom force sensor (UFS-2012A015). The maximum sensible loadings were 6, 6, and 9 kg along the x, y, and z coordinates. The maximum torque was 30 kg cm. The detected force and torque voltage signals were transferred to a high-speed data acquisition system (NI USB-6251 BNC, National Instruments Co.). This acquisition system transformed the detected voltage into the loadings of force and momentum. 2.8. Error analysis The relative positions of the Pitot tube and pressure sensor have great influence on the measurement of free-stream velocity. For reducing the uncertainty of free-stream velocity measurement, a synchronized micropressure calibration system was employed in the Pitot tube measurement system. The uncertainty in freestream velocity measurement was around 3%. A dividing head was used to adjust the angle of attack (AoA) of the wind blades.
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The rotation resolution was 0.0333° per division. The accuracy of AoA was about 0.5%. The aerodynamic loadings (i.e., lift, drag, and quarter pitching momentum) were calculated using the calibration-matrix method. The accuracies of these loadings were as follows: ±1.5% for lift, ±2% for drag, and ±2.5% for pitching momentum. The sampling rate of the hot wire is 16 kHz, and the measurement accuracy of free-stream velocity is around 3%. Furthermore, the accuracy of the vortex-shedding frequency is about 0.75%. 3. Results and discussion 3.1. Smoke-streak flow patterns 3.1.1. Side-by-side twin wind blades at a = 0° Fig. 2 shows the smoke-streak flow patterns and schematic plots for side-by-side twin wind blades using various gap ratios at a = 0° and Re = 7550. Fig. 2(a) shows the wake vortex-shedding structures at low gap ratio (i.e. g⁄ = 0). These two wind blades
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can be viewed as one bluff-body wind blade as shown in Fig. 2 (f). In Fig. 2(f), 0 6 g⁄ 6 0.04167, the reverse pressure in the wake cause a pseudo-Kármán vortex-shedding flow structure. This flow structure is called the ‘‘vortical wake” mode blades and causes a surface-pressure redistribution on the two inner blade surfaces. As g⁄ increased to 0.05, as show in Fig. 2(b), the pressure distribution induces a instability wave in the wake downstream. Therefore, these flow patterns are named the ‘‘wake instability wave” mode. For 0.04167 < g⁄ 6 0.2, Fig. 2(g) shows a sketched plot of this mode. For high gap ratios (i.e., g⁄ > 0.2), Fig. 2(c)–(e), shows the flow interaction between these two wind blades is weak. The flow structures around these two wind blades can be viewed as two independent wind blades. This characteristic flow structures are named the ‘‘attached surface flow” mode. Fig. 2(h) reveals the sketched plot of this flow pattern. 3.1.2. Side-by-side twin wind blades at a = 15° Fig. 3 shows the smoke streak and sketched flow patterns around side-by-side twin wind blades using various gap ratios at
Fig. 2. Smoke-streak flow patterns and schematic plots at a = 0° and Re = 7550.
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Fig. 3. Smoke-streak flow patterns and schematic plots at a = 15° and Re = 7550.
a = 15° and Re = 7550. At low gap ratios (i.e., g⁄ = 0), Fig. 3(a) shows that these two wind blades are identical to one bluff-body wind blade (as shown in Fig. 3(f)). For 0 6 g⁄ 6 0.04167, the reverse wake pressure induces a pseudo-Kármán vortex-shedding flow structure in the wake. This characteristic flow pattern is called the ‘‘vortical wake” mode. Fig. 3(b) reveals that the central flow moves between the inclined wind blades and causes a intricate flow behavior near the trailing edge at g⁄ = 0.0667. In addition, the sketched diagram of the downstream (as shown in Fig. 3(g)) reveals a pseudoKármán vortex-shedding flow structure for 0.04167 < g⁄ 6 0.675. This flow pattern is named as the ‘‘gap flow” mode. Fig. 3(c) and (d) shows the flow structure at g⁄ = 0.5 and 1.0. The flow behaviors around these two wind blades are influenced by the gap spacing. The phase difference between the upper and lower wind blades cause the anti-phase pseudo-Kármán vortex-shedding behaviors. For 0.675 < g⁄ 6 1.375, Fig. 3(h) schematically plotted the characteristic flow structure. This characteristic flow behavior is named as the ‘‘anti-phase vortex shedding” mode. As the gap ratio increases to 2.0, Fig. 2(e) shows that the pseudo-Kármán vortexshedding behaviors are independent. This flow patterns is called the ‘‘in-phase vortex shedding” mode. Fig. 3(i) schematically plotted this characteristic flow structure for g⁄ > 1.375.
3.1.3. Side-by-side twin wind blades at a = 30° Fig. 4 shows the smoke streak and sketched flow patterns around side-by-side twin wind blades using various gap ratios at a = 30° and Re = 7550. In Fig. 4, the high AoA causes a significant bluff-body effect. These flow behaviors and schematic plots are similar to those shown in Fig. 3 except that there is a high reverse-pressure region at a = 30°. This high reverse pressure causes the more complicate flow behaviors than those occurred in Fig. 3. Therefore, the flow patterns are also classified as the ‘‘vortical wake” mode (Fig. 4(a)), the ‘‘gap flow” mode (Fig. 4(b)), the ‘‘anti-phase vortex shedding” mode (Fig. 4(c) and (d)), and the ‘‘in-phase vortex shedding” mode (Fig. 4(e)). Furthermore, the schematic plots shown in Fig. 4(f)–(i) reveal the relationship between mode distribution and gap ratio as that vortical wake mode: 0 6 g⁄ 6 0.04167, gap flow mode: 0.04167 < g⁄ 6 0.458, anti-phase vortex shedding mode: 0.458 < g⁄ 6 1.375 and in-phase vortex-shedding mode: g⁄ > 1.375. 3.1.4. Side-by-side twin wind blades at a = 90° Fig. 5 shows the smoke streak and sketched flow patterns for side-by-side twin wind blades using various gap ratios at Re = 7550 and a = 90°. The high AoA causes a strong bluff-body
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Fig. 4. Smoke-streak flow patterns and schematic plots at a = 30° and Re = 7550.
effect. In Fig. 5(a), g⁄ = 0, the flow behavior is not like those of one wind blade at a = 90°. This flow pattern is called the ‘‘single-flow” mode. Fig. 5(e) schematically plotted this flow characteristics. As the gap spacing increases, the flow moves through the gap and moves irregularly in the wake (as shown in Fig. 5(b) and (c) for g⁄ = 0.0333 and 0.0667, respectively). These flow patterns are called the ‘‘gap flow” mode. Furthermore, Fig. 5(f) reveals that this gap flow mode occurs in the range of 0 < g⁄ 6 0.2. In Fig. 5(d), g⁄ = 0.25, the flows move straightly through the gap and form a symmetric shear-flow vortex-shedding pair. These characteristic flow behaviors are called the ‘‘jet flow” mode. Fig. 5(g) schematically shows this characteristic flow modes occurring at g⁄ > 0.2. 3.2. Flow mode distribution Fig. 6 shows the distribution of the characteristic flow modes. The control parameters are the AoA, Reynolds number and gap ratio. Fig. 6(a) shows the mode distribution for a = 0°. The vortical
wake mode located in the low gap-ratio region and the attached surface flow occurs at the high gap ratio. At high Reynolds numbers, the mode distribution was delayed toward the high gap ratio. The high Reynolds number yields a high inertial force. Fig. 6(b) and (c) shows a similar mode distribution for a = 15° and 30°, respectively. The vortical wake mode occurs at low gap ratio, and the in-phase vortex shedding mode occurs at high gap ratio. The gap flow mode located at 0.05 < g⁄ < 0.45 and the anti-phase vortex shedding mode is 0.45 < g⁄ < 1.4. The high AoA yields the high bluff-body effect. Fig. 6(d) shows the mode distribution for a = 90°. The single flow mode occurs at low gap ratio and the inphase vortex shedding mode occurs at high gap ratio. The gap flow mode occurs between these two modes. In summary, as g⁄ 0, the flow characteristics of side-by-side twin wind blades show the flow properties of single wind blade. As g⁄ increased, the interaction between upper and lower wind blades induce the vortical wake, gap flow and anti-phase vortex shedding modes. Furthermore, the wake-flow patterns behind the side-by-side twin wind
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Fig. 5. Smoke-streak flow patterns and schematic plots at a = 90° and Re = 7550.
blades are similar to those behind the single wind blade as g⁄ increased to some specific values. In Fig. 6, the effect of Reynolds number on the mode distribution is weak when Re < 9 103. Furthermore, the in-phase vortex shedding mode occurs when Re < 1.1 104 for a > 15°. In addition, the in-phase vortexshedding mode occurs at high gap ration (i.e., g⁄ > 1.35) except that g⁄ > 0.2 at a = 90° due to the high bluff-body effect. 3.3. Velocity properties The normalized longitudinal/transverse velocities, nondimensional normal Reynolds stress, non-dimensional Reynolds
shear stress, and turbulence intensity were used to indicate the velocity properties. The detection position was set at x/D = 2.5. For Re = 7550, Fig. 7(a) shows that the normalized longitudinal velocity increased with the gap ratio and approached a constant of 0.95. For single wind blade at a = 0°, Fig. 7(a) also shows that u/u1 approaches toward 0.95. This physical phenomenon reveals that the flow behavior of side-by-side twin wind blades is similar to single one when g⁄ > 2.0 (i.e., high gap ratio). Fig. 7(b) also shows that the normalized transverse velocity increased with the gap ratio and approached a constant at high gap ratios. In Fig. 7(c) and (d), the non-dimensional Reynolds normal stress in the longitudinal and transverse directions decreased with gap ratio and
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Fig. 6. Distribution of characteristic flow modes. (a) a = 0°, (b) a = 15°, (c) a = 30° and (d) a = 90°.
approached a constant at high gap ratios. Similarly, the curves of non-dimensional Reynolds shear stress shown in Fig. 7(e) decreases with the gap ratio and approached a constant at high gap ratios. Additionally, Fig. 7(f) shows the turbulence intensity (T.I.) decreased with the gap ratio and approached a constant at high gap ratios. The high gap ratio decreases the perturbed strength of flow field and approached the values of the flow field for one wind blade. Consequently, except at a = 0°, the maximum velocity fluctuation occurred at g⁄ = 0.083 and the velocity fluctuation decreased toward that of free-stream as g⁄ increased. In Fig. 7 (f), the maximum T.I. of 30% occurs at a = 90° and g⁄ = 0.083. The low gap ratio induces a high bluff-body effect and forms the gapflow mode. This high bluff-body effect generates the high T.I. Moreover, the minimum T.I. of 3% occurs at a = 0° and g⁄ > 0.5. For this flow condition, the flow structure on these twin wind blades is attached surface-flow mode when g⁄ > 0.5. At a = 0°, the g⁄ = 0.5 is enough high and the flow behaviors on these two wind blades are independent.
3.4. Vortex shedding In this study, the wake vortex-shedding frequency (f) was detected at four different positions (i.e., (x/C, y/C) = (2.5, 1s/2C), (x/C, y/C) = (2.5, 1s/2C), (x/C, y/C) = (2.5, s/2C) and (x/C, y/C) = (2.5, 1 + s/2C)). The effects of gap ratio and AoA on the wake vortex shedding were considered. The relationships between non-dimensional frequency (Strouhal number, St) and gap ratio were plotted in Fig. 8. The definition of Strouhal number is St = fd/u1 where d is the projection chord length and u1 presents the free-stream velocity. In Fig. 8, at g⁄ = 0, this twin wind blades can be considered as a bluff body. Therefore, the St increases with the projection chord length. At a = 0°, the lowest St occurs at g⁄ = 0.0833. While increasing the gap ratio, the St in the wake increases toward that of single wind blade. Fig. 8(a) and (b) shows that the St is higher than those of g⁄ = 0.5 and 1. The wake vortexshedding behind wind blade-II is compressed by wind blade-I. As g⁄ P 1.5, the St of single wind blade and side-by-side wind blades
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Fig. 7. Velocity properties. (a) Normalized streamwise velocity, (b) normalized spanwise velocity, (c) non-dimensional streamwise normal Reynolds Stress, (d) nondimensional spanwise normal Reynolds Stress, (e) non-dimensional Reynolds shear stress and (f) turbulence intensity.
approach a constant. Specifically, at a = 0°, St is 0.418, at a = 15°, St is 0.206, at a = 30° St is 0.21; and at a = 90°, St approaches 0.133. With comparing St at a = 0° and a = 90°, the bluff-body effect decreases the St about 68.2% (i.e., decreasing St from 0.418 to 0.133). These experimental results show a similar conclusion obtained from Yen et al. [20,23]. At different AoA, the vortexshedding frequencies behind these side-by-side twin wind blades are almost the same as that of single wind blade and these vortex-shedding frequency decreased as a increased. 3.5. Aerodynamic performance The aerodynamic performance of lift, drag, quarter-chord momentum and the lift-to-drag ratio was tested at Re = 7550, as shown in Fig. 9. At g⁄ = 0, these two wind blades formed a bluff body and increased the projection width. The aerodynamic loading on
these two wind blades was lower than those of single wind blade. In Fig. 9(a) and (e), at low AoA, the pressure direction on wind blade-I is in the y direction. Therefore, the lift coefficient on wind blade-I is negative at low AoA. However, the lift coefficient on wind blade-II is positive. When increasing AoA, the projection width increased; lift and drag all increased, as shown in Fig. 9(a), (b), (e) and (f). When g⁄ > 0, the aerodynamic loadings on wind blade-I were similar to those for single wind blade. Specifically, the lift coefficient and lift-to-drag ratio at g⁄ = 0.833 were higher than those of single wind blade. The aerodynamic loading on wind blade-II was affected by wind blade-I and acts in the y direction. At high AoA, the pressure component acts in the x direction and causes a loss of drag on wind blade-II. Therefore, the lift-to-drag ratio on wind blade-II was lower than that of the single wind blade, as shown in Fig. 9(c) and (g). On blade-I, the maximum CL/CD of 3.19 occurs at a = 8°. However, the maximum CL/CD of 1.54 occurs at
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Fig. 8. Distributions of Strouhal numbers.
a = 15° due to the effect of blade-I. Fig. 9(d) and (h) shows that the quarter-chord momentum coefficient on wind blade-I was similar to that of single wind blade with the effect of gap ratio. However, the momentum coefficient on wind blade-II increased with increasing the gap ratio. The decrease of lift and drag at high AoA caused the decrease of momentum coefficient. In conclusion, for single wind blade, the maximum lift occurs at a = 10° and the drag increased with a. The quarter-chord momentum increased with a when a < 45° and decreased with a when a > 45°. For side-by-side twin wind blades, the flow characteristics on the upper wind blade are similar to those on single wind blade. The lift, drag and quarterchord momentum on the lower wind blade decreased significantly due to the pressure distribution of upper wind blade. The effect of upper wind blade on the lower wind blade deceased as g⁄ increased. 4. Conclusions This study explored the effects of the gap ratio (g⁄) and angle of attack (a) on side-by-side twin wind blades. The wake-flow
patterns and aerodynamic performances around these two wind blades were probed and classified using the smoke-streak flow visualization, hot-wire velocimetry and six-force balancer. The following conclusions are summarized from the experimental results and discussions. (1) Seven characteristic smoke-streak flow patterns were defined – Attached surface-flow, Wake instability wave, Vortical wake, Gap flow, Bluff-body wake, Antiphase vortex shedding and In-phase vortex shedding. As g⁄ 0, the flow characteristics of side-by-side twin wind blades show the similar flow properties of single wind blade. As g⁄ increased, the interaction between upper and lower wind blades induces vortical wake, gap flow and anti-phase vortex shedding modes. Furthermore, the wake-flow patterns behind side-by-side twin wind blades are similar to those behind single wind blade as g⁄ increases to the specific values. (2) At a = 15°, 30° and 90°, the maximum velocity fluctuation occurs at g⁄ = 0.083 and the velocity fluctuation decreases toward that of free-stream as g⁄ increased.
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Fig. 9. Aerodynamic performances of wind blade-I and II. (a) and (e) Lift coefficient, (b) and (f) drag coefficient, (c) and (g) lift-to-drag ratio, (d) and (h) quarter-chord momentum coefficient. Re = 7550.
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(3) The vortex-shedding frequencies at different AoA behind these side-by-side twin wind blades were nearly equivalent to those for single wind blade and the vortex-shedding frequency decreased as a increased. (4) For single wind blade, the maximum lift occurs at a = 10° and drag increased with a. The quarter-chord momentum increased with a when a < 45° and decreased when a > 45°. For side-by-side twin wind blades, the flow characteristics on the upper wind blade were similar to those on single wind blade. The lift, drag and quarter-chord momentum on the lower wind blade decreased significantly due to the pressure distribution of upper wind blade. The effect of upper wind blade on the lower wind blade deceased as g⁄ increased.
Acknowledgment This research was supported by the National Science Council of the Republic of China, under Grant No. NSC 102-2221-E-019-018. References [1] S.M. Batill, T.J. Mueller, Visualization of transition in the flow over an airfoil using the smoke-wire technique, AIAA J. 19 (1981) 340–345. [2] P.B.S. Lissaman, Low Reynolds number airfoils, Annu. Rev. Fluid Mech. 15 (1983) 223–239. [3] T.J. Mueller, Flow visualization by direct injection, in: R.J. Goldstein (Ed.), Fluid Mechanics Measurements, second ed., Taylor & Francis, Washington DC, 2000, pp. 367–450. [4] L.F. Crabtree, Effect of leading edge separation on thin wings in twodimensional incompressible flow, J. Aeronaut. Sci. 24 (1957) 597–604. [5] J.R. Ward, The behavior and effects of laminar separation bubbles on airfoils in incompressible flow, J. R. Aeronaut. Soc. 67 (1963) 783–790.
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[6] A.V. Arena, T.J. Mueller, Laminar separation, transition, and turbulent reattachment near the leading edge of airfoils, AIAA J. 18 (1980) 747–753. [7] J. Katz, Wing/vortex interactions and wing rock, Prog. Aerosp. Sci. 35 (1999) 727–750. [8] K.B.M. Zaman, D.J. McKinzie, C.L. Rumsey, A natural low-frequency oscillation of the flow over an airfoil near stalling conditions, J. Fluid Mech. 202 (1989) 403–442. [9] R.D. Blevins, Flow-Induced Vibration, Van Nostrand Reinhold, New York, 1990, pp. 43–104. [10] J.H. Lienhard, Synopsis of Lift, Drag and Vortex Frequency Data for Rigid Circular Cylinders, Research Division Bulletin 300, Washington State University, 1966. [11] C.H. Ho, P. Huerre, Perturbed free shear layers, Annu. Rev. Fluid Mech. 16 (1984) 365–424. [12] E. Levi, A universal Strouhal law, ASCE J. Eng. Mech. 109 (1983) 718–727. [13] A. Roshko, On the wake and drag of bluff bodies, J. Aerospace Sci. 22 (1955) 124–135. [14] R.F. Huang, C.L. Lin, Vortex shedding and shear-layer instability of wing at lowReynolds numbers, AIAA J. 31 (1995) 1398–1430. [15] R.F. Huang, H.W. Lee, Turbulence effect on frequency characteristic of unsteady motions in wake of wing, AIAA J. 38 (2000) 87–94. [16] G.J. Dong, X.-Y. Lu, Characteristics of flow over traveling wavy foils in a sideby-side arrangement, Phys. Fluids 19 (2007) 057107. [17] O.L. Hansen, H.A. Madsen, Review paper on wind turbine aerodynamics, J. Fluids Eng. ASME Trans. 133 (2011) 114001. [18] C.H. Sieverding, H. Richard, J.M. Desse, Turbine blade trailing edge flow characteristics at high subsonic outlet Mach number, J. Turbomach. ASME Trans. 125 (2003) 298–309. [19] O. Uzol, Y.C. Chow, J. Katz, C. Meneveau, Experimental investigation of unsteady flow field within a two-stage axial turbomachine using particle image velocimetry, J. Turbomach. ASME Trans. 124 (2002) 542–552. [20] S.C. Yen, J.H. Liu, Wake flow behind two side-by-side square cylinders, Int. J. Heat Fluid Flow 32 (2011) 41–51. [21] I.H. Abbott, A.E. Von Doenhoff, Theory of Wing Section, Dover Publications, New York, 1959, pp. 113–115. [22] R.C. Flagan, J.H. Seinfeld, Fundamentals of Air Pollution Engineering, PrenticeHall, Englewood Cliffs, NJ, 1988, pp. 295–307. [23] S.C. Yen, C.M. Hsu, Investigation on vortex shedding of a swept-back wing, Exp. Thermal Fluid Sci. 31 (2007) 849–855.
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Characteristics of flow configurations around side-by-side twin wind blades Shun-Chang Yen a,⇑, Chu-Hsuan Wu a, Kuo-Ching San b a b
Department of Mechanical and Mechatronic Engineering, National Taiwan Ocean University, Keelung 202, Taiwan, ROC Department of Aeronautics and Astronautics, R.O.C. Air Force Academy, Kaohsiung 820, Taiwan, ROC
a r t i c l e
i n f o
Article history: Received 24 August 2016 Received in revised form 23 November 2016 Accepted 24 November 2016 Available online 25 November 2016 Keywords: Side-by-side wind blade Flow visualization Gap flow Gap ratio Aerodynamic performance
a b s t r a c t The effects of gap ratio (g⁄) and angle of attack (a) on side-by-side twin wind blades were investigated in an open-channel wind tunnel. Characteristic wake-flow patterns and aerodynamic performance were analyzed using smoke-streak flow visualization, hot-wire velocimetry, and six-force balancer. Seven smoke-streak flow patterns were defined – attached surface flow, wake instability wave, vortical wake, gap flow, bluff-body wake, anti-phase vortex shedding, and in-phase vortex shedding. For g⁄ 0, the flow characteristics were similar to those of a single wind blade. As g⁄ increased, these two wind blades induced the vortical wake, gap flow, and anti-phase vortex shedding modes. With further increase in g⁄, the wake-flow patterns were similar to those behind a single wind blade. The hot-wire velocimeter detected that the maximum velocity fluctuation occurred at g⁄ = 0.083. This velocity fluctuation decreased toward that of free stream as g⁄ increased. The vortex-shedding frequency decreased as a increased. For a single wind blade, the maximum lift occurred at a = 10° and the drag increased with a. The pitching momentum increased with a when a < 45°. The lift, drag, and pitching momentum on the lower wind blade decreased significantly due to the existence of upper wind blade. The effect of upper wind blade on the lower one deceased as g⁄ increased. Ó 2016 Elsevier Inc. All rights reserved.
1. Introduction The blades of a rotor were driven to rotate when a fluid flows through the rotor. A bluff-body blade caused a pressure difference around the rotor. The inner flow tube in gas turbines, blowers, and air compressors were utilized to generate the pressure difference. In daily applications, fans, wind turbines, and water turbines use the thrust induced from the pressure difference. In these applications, the gap width between the side-by-side blades has a significant effect on the machine performance. The previous study on single blade showed a significant relationship with the surface boundary-layer on the suction side [1–3]. These aerodynamic phenomena included flow separation, reattachment, and vortex formation. In addition, surface flow behavior has a significant effect on wake vortex shedding resulting from the shear instability wave in the boundary-layer separation [4]. Studies on surface flow and aerodynamic performance have showed a laminar boundary layer formed near the stagnation point ⇑ Corresponding author at: Department of Mechanical and Mechatronic Engineering, National Taiwan Ocean University, No. 2, Pei-Ning Road, Keelung 202, Taiwan, ROC. E-mail address: [email protected] (S.-C. Yen). http://dx.doi.org/10.1016/j.expthermflusci.2016.11.026 0894-1777/Ó 2016 Elsevier Inc. All rights reserved.
of a wind-blade leading edge. As the flow moves downstream, the flow separates at the minimum-pressure point. Behind the separation point, the shear layer transits to a turbulent flow. Subsequently, the separated flow reattaches on the wind-blade surface. Between the reattached point and wind-blade trailing edge, the surface flow formed a turbulent boundary layer. A bubble was generated between the separation point and reattached point. At a low chord-length Reynolds number and low angle of attack (AoA), the bubble occupied most of the wind-blade surface. This bubble changes the surface pressure distribution and aerodynamic characteristics. In the 1980s, most studies focused on surface-flow behaviors [5–7]. Lissaman [2] studied flow separation on the laminar boundary layers, boundary-layer transition, and boundary-layer reattachment. He found that the flow separation occurs near the point of the minimum surface pressure. A shear layer evolved downstream and transited to a turbulent flow. The turbulent kinetic energy increases and the separated boundary layer reattached on the wind-blade surface. This reattached turbulent boundary layer extended from the reattached point to the trailing edge. A study on unstable wake flow revealed that this flow was generated because of the boundary-layer separation and shear-layer instability wave [8]. Research topics included the periodic instabil-
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Nomenclature b C CL CD CM d D f g⁄ L M q Re s
half wind-blade span, 30 cm chord length, 6 cm lift coefficient (= L/qbC) drag coefficient (= D/qbC) quarter-chord moment coefficient (= M/qbC2) projection chord length drag wake vortex-shedding frequency (Hz) gap ratio (= s/C) lift quarter-chord momentum dynamic pressure of free-stream (= qu12/2) Reynolds number (= u1C/m) streamwise spacing between the centers of two wind blade cylinders
ity wave, the effect of coherent structure on wind-blade performance, and wind vibrations induced by the wake vortex (fluid– structure coupling) [9,10]. Previous studies focused on the wake flow behind a bluff body [11,12]. Roshko [13] found that the Strouhal number (St = fd/u) remained constant with values of 0.21, 0.18, and 0.14 for a cylinder, 90° wedge, and plain board, respectively, when the Reynolds number (Re) was in the range 103 < Re < 105. In addition, Roshko revealed that St was low for sharp and flat bodies. Huang and Lin [14] used wind and water tunnels to study the instable wake vortex-shedding frequency and behaviors behind wing airfoils. They found that the surface flow did not separate at a low AoA behind a sharp trailing-edge wing. However, such wings have a mixing-layer wake flow and a small-amplitude instability wave. These instability waves evolved into a wake vortex and subsequently a vortex street. Furthermore, in this wake flow, the viscous effect in the boundary layer was considered. At high AoA and high Reynolds numbers, the projection chord-length dominated the instability wake flow. In addition, the periodic vortex frequency displayed two trends: (1) at low Reynolds numbers, St decreases as Re increases, and (2) at high Reynolds numbers, St remains constant. Huang et al. found that St remained constant and Roshko number was proportional to St in the inertiadominated regime. However, in the viscosity-dominated regime, Roshko number remained constant and St was inversely proportional to Re [15]. In studies on multi-blade patterns, many researchers have numerically simulated flow structures and aerodynamic performance. Dong and Lu [16] used three fish-like profiles to numerically investigate the effect of gap ratio on aerodynamic performance. They found that the gap ratios influenced the formation of in-phase and anti-phase vortex streets. At low gap ratios, the upper and lower vortex series were close and then squeezed to form an anti-phase vortex street. In contrast, the high gap ratio caused an in-phase vortex street. Furthermore, the drag coefficient decreased with gap ratio. Hansen and Madsen [17] employed the blade element momentum method to determine the blade profiles and compute aerodynamic coefficients. Sieverding et al. [18] used a supersonic wind tunnel to study the surface-pressure distribution on side-by-side blades. They found the non-uniform pressure distribution near the blade trailing edge at subsonic speeds. Furthermore, the lowest pressure occurred at the trailing edge. On the suction side, the vortex formed near the trailing edge was influenced by the adjacent blade. Uzol et al. [19] studied a transient flow field by using particle image velocimetry and water tunnel. They found that the free-stream velocity changed by about 13%
St T.I. u1 u u0 v v0 x y
a q m
Strouhal number of vortex shedding (= fd/u1) turbulence intensity free-stream velocity x-component of mean velocity, m/s x-component of velocity fluctuation, m/s y-component of mean velocity, m/s y-component of velocity fluctuation, m/s streamwise coordinate originated at leading edge spanwise coordinate originated at the wing root angle of attack air density kinetic viscosity of air
due to the transverse velocity behind the blades. The gap ratio between blades has a significant effect on blade efficiency. Previous studies have investigated single bluff bodies and sideby-side cylinders/squares. In this study, the effects of gap ratio and AoA on a single bluff wind-blade and two side-by-side wind blades were investigated. Smoke-streak visualization was employed to observe the characteristic flow patterns. Hot-wire velocimetry was used to measure the wake vortex-shedding frequency and calculate the Strouhal number. Furthermore, the hot wire was used to measure the velocity contour around the wind blades. A six-force balancer was used to measure the aerodynamic loadings. 2. Experimental setup 2.1. Apparatus Fig. 1 shows the wind tunnel and experimental setup used in this study [20]. This open-loop wind tunnel was operated stably in the range of 1.64–28.28 m/s. This wind tunnel included seven parts: noise-filtering section, steady section (settling chamber), nozzle, test section, vibration absorber, expansion section (diffuser), and blower fan. The noise-filtering section comprised two parts: (1) an aluminum-made honeycomb for eliminating transverse flow fluctuations, and (2) a three-layer metal mesh for filtering the longitudinal flow noise. The nozzle contraction ratio was 3.24:1. The cross-section area and length of the test section were 50 50 cm2 and 120 cm, respectively. The downstream test section was connected to a vibration absorber, which was used to isolate the operation vibrations of the blower fan. The downstream expansion section was connected to a centrifugal blower fan driven using a three-phase and 20 horse-power motor. The motor rotation speed was adjusted using a inverter with the maximum rotating speed of 1160 rpm. The precision of inverter is 0.1 Hz and the operable range is 0–60 Hz, which corresponds to a flow speed of 1.64–28.28 m/s. 2.2. Blades An NACA 00122 [21] aerofoil was used to investigate the flow behavior. This wind blade was fabricated using solid chrome moly 4340 to reduce the wind resonance. The chord length (C) and windblade span (S) were 6 and 30 cm, respectively; and therefore, the aspect ratio was 5. The wind-blade surface was polished for reducing the surface roughness. An index plate was used to rotate the
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Fig. 1. Experimental setup.
wind blade, and the operation resolution was 0.0333/div. Fig. 1 shows the experimental configuration for the side-by-side twin wind blades. 2.3. Free-stream velocity The free-stream velocity was obtained using a commercial Pitot tube (Dwyer Instruments, Inc.) and a U-tube pressure indicator; and then calculated using the Bernoulli equation. The pressure signals were detected using a Huba 694 pressure transducer (JETEC Electronics Co.). The Pitot tube consists of a total pressure hole and four symmetrical static pressure holes. The diameters of the total and static pressure holes were 2.3 and 0.3 mm, respectively. Further, the diameter of Pitot tube is 8 mm and the resolution of Huba 694 is less than 0.002 mmAq. 2.4. Smoke-streak visualization The smoke-streak visualization method utilized in this study was developed and proposed by Raspet and Moore. Fraxinus oil, used for coating the wind blades, was heated using an electric wire. The average diameter of the fraxinus particles was 1.7 ± 0.2 lm. Flagan and Seinfeld [22] indicated that a particle group can be treated as a continuous medium when the Knudsen number 1; in such a case, the random motion of flow particles can be neglected. The Stokes number for fraxinus particles is 1.28 104 (i.e., 1); this shows that the flow particles can follow the flow motion. The properties of vaporized fraxinus oil showed that the slip phenomenon induced by the turbulent diffusion effect was negligible and the interactions between fraxinus oil particles could also be neglected. In addition, the experimental results showed that the smoke streak width was less than 0.1 mm and the Reynolds number (Re) was smaller than 40. The smoke vortex street vanished and did not interfere with the flow field. In this study, the free stream velocity was maintained in the range of 1.96–3.23 m/s (i.e., 16 < Re < 27). The flow photos were captured using a Nikon D70s digital camera at a shutter speed of 1/1000s. 2.5. Velocity characteristics and turbulence intensity The velocity characteristics and turbulence intensity (T.I.) were detected using the hot-wire velocimetry and a two-dimensional constant-temperature hot-wire probe (TSI 1240-T1.5 X-type). The
diameter and length of the hot-wire probe were 5 lm and 1.5 mm, respectively, yielding a response frequency of 15–25 kHz. The hot-wire velocimeter was corrected using a Pitot tube sensor. In this experiment, the detection position (z) was set at z = 2.5C located in the wake region of the side-by-side twin wind blades. The detected signals were transferred from the probe to a high-speed data logger. Furthermore, the velocity data were used to calculate the turbulence intensity. 2.6. Wake shedding frequency The wake vortex-shedding frequency was detected using the hot-wire velocimetry and a normal-type one-dimensional constant-temperature hot-wire probe (TSI 1218-T1.5). The hotwire probe was installed at z = 2.5C (i.e., in the wake region). The detected signals were transferred to a fast-Fourier transform (FFT) analyzer (CF-920, Ono Sokki Co.). The FFT analyzer recorded the frequency spectrum and then calculated the vortex-shedding frequency. The precision of FFT analyzer depends on the FFT resolution. As the resolution is 1 Hz, its precision is 0.0025 Hz. In addition, the precision is 5 Hz when the FFT resolution is 2 kHz. 2.7. Aerodynamic loadings The aerodynamic loadings were measured using a JR3 universal force–moment system (NITTA) associated with a six-degree-offreedom force sensor (UFS-2012A015). The maximum sensible loadings were 6, 6, and 9 kg along the x, y, and z coordinates. The maximum torque was 30 kg cm. The detected force and torque voltage signals were transferred to a high-speed data acquisition system (NI USB-6251 BNC, National Instruments Co.). This acquisition system transformed the detected voltage into the loadings of force and momentum. 2.8. Error analysis The relative positions of the Pitot tube and pressure sensor have great influence on the measurement of free-stream velocity. For reducing the uncertainty of free-stream velocity measurement, a synchronized micropressure calibration system was employed in the Pitot tube measurement system. The uncertainty in freestream velocity measurement was around 3%. A dividing head was used to adjust the angle of attack (AoA) of the wind blades.
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The rotation resolution was 0.0333° per division. The accuracy of AoA was about 0.5%. The aerodynamic loadings (i.e., lift, drag, and quarter pitching momentum) were calculated using the calibration-matrix method. The accuracies of these loadings were as follows: ±1.5% for lift, ±2% for drag, and ±2.5% for pitching momentum. The sampling rate of the hot wire is 16 kHz, and the measurement accuracy of free-stream velocity is around 3%. Furthermore, the accuracy of the vortex-shedding frequency is about 0.75%. 3. Results and discussion 3.1. Smoke-streak flow patterns 3.1.1. Side-by-side twin wind blades at a = 0° Fig. 2 shows the smoke-streak flow patterns and schematic plots for side-by-side twin wind blades using various gap ratios at a = 0° and Re = 7550. Fig. 2(a) shows the wake vortex-shedding structures at low gap ratio (i.e. g⁄ = 0). These two wind blades
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can be viewed as one bluff-body wind blade as shown in Fig. 2 (f). In Fig. 2(f), 0 6 g⁄ 6 0.04167, the reverse pressure in the wake cause a pseudo-Kármán vortex-shedding flow structure. This flow structure is called the ‘‘vortical wake” mode blades and causes a surface-pressure redistribution on the two inner blade surfaces. As g⁄ increased to 0.05, as show in Fig. 2(b), the pressure distribution induces a instability wave in the wake downstream. Therefore, these flow patterns are named the ‘‘wake instability wave” mode. For 0.04167 < g⁄ 6 0.2, Fig. 2(g) shows a sketched plot of this mode. For high gap ratios (i.e., g⁄ > 0.2), Fig. 2(c)–(e), shows the flow interaction between these two wind blades is weak. The flow structures around these two wind blades can be viewed as two independent wind blades. This characteristic flow structures are named the ‘‘attached surface flow” mode. Fig. 2(h) reveals the sketched plot of this flow pattern. 3.1.2. Side-by-side twin wind blades at a = 15° Fig. 3 shows the smoke streak and sketched flow patterns around side-by-side twin wind blades using various gap ratios at
Fig. 2. Smoke-streak flow patterns and schematic plots at a = 0° and Re = 7550.
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Fig. 3. Smoke-streak flow patterns and schematic plots at a = 15° and Re = 7550.
a = 15° and Re = 7550. At low gap ratios (i.e., g⁄ = 0), Fig. 3(a) shows that these two wind blades are identical to one bluff-body wind blade (as shown in Fig. 3(f)). For 0 6 g⁄ 6 0.04167, the reverse wake pressure induces a pseudo-Kármán vortex-shedding flow structure in the wake. This characteristic flow pattern is called the ‘‘vortical wake” mode. Fig. 3(b) reveals that the central flow moves between the inclined wind blades and causes a intricate flow behavior near the trailing edge at g⁄ = 0.0667. In addition, the sketched diagram of the downstream (as shown in Fig. 3(g)) reveals a pseudoKármán vortex-shedding flow structure for 0.04167 < g⁄ 6 0.675. This flow pattern is named as the ‘‘gap flow” mode. Fig. 3(c) and (d) shows the flow structure at g⁄ = 0.5 and 1.0. The flow behaviors around these two wind blades are influenced by the gap spacing. The phase difference between the upper and lower wind blades cause the anti-phase pseudo-Kármán vortex-shedding behaviors. For 0.675 < g⁄ 6 1.375, Fig. 3(h) schematically plotted the characteristic flow structure. This characteristic flow behavior is named as the ‘‘anti-phase vortex shedding” mode. As the gap ratio increases to 2.0, Fig. 2(e) shows that the pseudo-Kármán vortexshedding behaviors are independent. This flow patterns is called the ‘‘in-phase vortex shedding” mode. Fig. 3(i) schematically plotted this characteristic flow structure for g⁄ > 1.375.
3.1.3. Side-by-side twin wind blades at a = 30° Fig. 4 shows the smoke streak and sketched flow patterns around side-by-side twin wind blades using various gap ratios at a = 30° and Re = 7550. In Fig. 4, the high AoA causes a significant bluff-body effect. These flow behaviors and schematic plots are similar to those shown in Fig. 3 except that there is a high reverse-pressure region at a = 30°. This high reverse pressure causes the more complicate flow behaviors than those occurred in Fig. 3. Therefore, the flow patterns are also classified as the ‘‘vortical wake” mode (Fig. 4(a)), the ‘‘gap flow” mode (Fig. 4(b)), the ‘‘anti-phase vortex shedding” mode (Fig. 4(c) and (d)), and the ‘‘in-phase vortex shedding” mode (Fig. 4(e)). Furthermore, the schematic plots shown in Fig. 4(f)–(i) reveal the relationship between mode distribution and gap ratio as that vortical wake mode: 0 6 g⁄ 6 0.04167, gap flow mode: 0.04167 < g⁄ 6 0.458, anti-phase vortex shedding mode: 0.458 < g⁄ 6 1.375 and in-phase vortex-shedding mode: g⁄ > 1.375. 3.1.4. Side-by-side twin wind blades at a = 90° Fig. 5 shows the smoke streak and sketched flow patterns for side-by-side twin wind blades using various gap ratios at Re = 7550 and a = 90°. The high AoA causes a strong bluff-body
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Fig. 4. Smoke-streak flow patterns and schematic plots at a = 30° and Re = 7550.
effect. In Fig. 5(a), g⁄ = 0, the flow behavior is not like those of one wind blade at a = 90°. This flow pattern is called the ‘‘single-flow” mode. Fig. 5(e) schematically plotted this flow characteristics. As the gap spacing increases, the flow moves through the gap and moves irregularly in the wake (as shown in Fig. 5(b) and (c) for g⁄ = 0.0333 and 0.0667, respectively). These flow patterns are called the ‘‘gap flow” mode. Furthermore, Fig. 5(f) reveals that this gap flow mode occurs in the range of 0 < g⁄ 6 0.2. In Fig. 5(d), g⁄ = 0.25, the flows move straightly through the gap and form a symmetric shear-flow vortex-shedding pair. These characteristic flow behaviors are called the ‘‘jet flow” mode. Fig. 5(g) schematically shows this characteristic flow modes occurring at g⁄ > 0.2. 3.2. Flow mode distribution Fig. 6 shows the distribution of the characteristic flow modes. The control parameters are the AoA, Reynolds number and gap ratio. Fig. 6(a) shows the mode distribution for a = 0°. The vortical
wake mode located in the low gap-ratio region and the attached surface flow occurs at the high gap ratio. At high Reynolds numbers, the mode distribution was delayed toward the high gap ratio. The high Reynolds number yields a high inertial force. Fig. 6(b) and (c) shows a similar mode distribution for a = 15° and 30°, respectively. The vortical wake mode occurs at low gap ratio, and the in-phase vortex shedding mode occurs at high gap ratio. The gap flow mode located at 0.05 < g⁄ < 0.45 and the anti-phase vortex shedding mode is 0.45 < g⁄ < 1.4. The high AoA yields the high bluff-body effect. Fig. 6(d) shows the mode distribution for a = 90°. The single flow mode occurs at low gap ratio and the inphase vortex shedding mode occurs at high gap ratio. The gap flow mode occurs between these two modes. In summary, as g⁄ 0, the flow characteristics of side-by-side twin wind blades show the flow properties of single wind blade. As g⁄ increased, the interaction between upper and lower wind blades induce the vortical wake, gap flow and anti-phase vortex shedding modes. Furthermore, the wake-flow patterns behind the side-by-side twin wind
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Fig. 5. Smoke-streak flow patterns and schematic plots at a = 90° and Re = 7550.
blades are similar to those behind the single wind blade as g⁄ increased to some specific values. In Fig. 6, the effect of Reynolds number on the mode distribution is weak when Re < 9 103. Furthermore, the in-phase vortex shedding mode occurs when Re < 1.1 104 for a > 15°. In addition, the in-phase vortexshedding mode occurs at high gap ration (i.e., g⁄ > 1.35) except that g⁄ > 0.2 at a = 90° due to the high bluff-body effect. 3.3. Velocity properties The normalized longitudinal/transverse velocities, nondimensional normal Reynolds stress, non-dimensional Reynolds
shear stress, and turbulence intensity were used to indicate the velocity properties. The detection position was set at x/D = 2.5. For Re = 7550, Fig. 7(a) shows that the normalized longitudinal velocity increased with the gap ratio and approached a constant of 0.95. For single wind blade at a = 0°, Fig. 7(a) also shows that u/u1 approaches toward 0.95. This physical phenomenon reveals that the flow behavior of side-by-side twin wind blades is similar to single one when g⁄ > 2.0 (i.e., high gap ratio). Fig. 7(b) also shows that the normalized transverse velocity increased with the gap ratio and approached a constant at high gap ratios. In Fig. 7(c) and (d), the non-dimensional Reynolds normal stress in the longitudinal and transverse directions decreased with gap ratio and
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Fig. 6. Distribution of characteristic flow modes. (a) a = 0°, (b) a = 15°, (c) a = 30° and (d) a = 90°.
approached a constant at high gap ratios. Similarly, the curves of non-dimensional Reynolds shear stress shown in Fig. 7(e) decreases with the gap ratio and approached a constant at high gap ratios. Additionally, Fig. 7(f) shows the turbulence intensity (T.I.) decreased with the gap ratio and approached a constant at high gap ratios. The high gap ratio decreases the perturbed strength of flow field and approached the values of the flow field for one wind blade. Consequently, except at a = 0°, the maximum velocity fluctuation occurred at g⁄ = 0.083 and the velocity fluctuation decreased toward that of free-stream as g⁄ increased. In Fig. 7 (f), the maximum T.I. of 30% occurs at a = 90° and g⁄ = 0.083. The low gap ratio induces a high bluff-body effect and forms the gapflow mode. This high bluff-body effect generates the high T.I. Moreover, the minimum T.I. of 3% occurs at a = 0° and g⁄ > 0.5. For this flow condition, the flow structure on these twin wind blades is attached surface-flow mode when g⁄ > 0.5. At a = 0°, the g⁄ = 0.5 is enough high and the flow behaviors on these two wind blades are independent.
3.4. Vortex shedding In this study, the wake vortex-shedding frequency (f) was detected at four different positions (i.e., (x/C, y/C) = (2.5, 1s/2C), (x/C, y/C) = (2.5, 1s/2C), (x/C, y/C) = (2.5, s/2C) and (x/C, y/C) = (2.5, 1 + s/2C)). The effects of gap ratio and AoA on the wake vortex shedding were considered. The relationships between non-dimensional frequency (Strouhal number, St) and gap ratio were plotted in Fig. 8. The definition of Strouhal number is St = fd/u1 where d is the projection chord length and u1 presents the free-stream velocity. In Fig. 8, at g⁄ = 0, this twin wind blades can be considered as a bluff body. Therefore, the St increases with the projection chord length. At a = 0°, the lowest St occurs at g⁄ = 0.0833. While increasing the gap ratio, the St in the wake increases toward that of single wind blade. Fig. 8(a) and (b) shows that the St is higher than those of g⁄ = 0.5 and 1. The wake vortexshedding behind wind blade-II is compressed by wind blade-I. As g⁄ P 1.5, the St of single wind blade and side-by-side wind blades
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Fig. 7. Velocity properties. (a) Normalized streamwise velocity, (b) normalized spanwise velocity, (c) non-dimensional streamwise normal Reynolds Stress, (d) nondimensional spanwise normal Reynolds Stress, (e) non-dimensional Reynolds shear stress and (f) turbulence intensity.
approach a constant. Specifically, at a = 0°, St is 0.418, at a = 15°, St is 0.206, at a = 30° St is 0.21; and at a = 90°, St approaches 0.133. With comparing St at a = 0° and a = 90°, the bluff-body effect decreases the St about 68.2% (i.e., decreasing St from 0.418 to 0.133). These experimental results show a similar conclusion obtained from Yen et al. [20,23]. At different AoA, the vortexshedding frequencies behind these side-by-side twin wind blades are almost the same as that of single wind blade and these vortex-shedding frequency decreased as a increased. 3.5. Aerodynamic performance The aerodynamic performance of lift, drag, quarter-chord momentum and the lift-to-drag ratio was tested at Re = 7550, as shown in Fig. 9. At g⁄ = 0, these two wind blades formed a bluff body and increased the projection width. The aerodynamic loading on
these two wind blades was lower than those of single wind blade. In Fig. 9(a) and (e), at low AoA, the pressure direction on wind blade-I is in the y direction. Therefore, the lift coefficient on wind blade-I is negative at low AoA. However, the lift coefficient on wind blade-II is positive. When increasing AoA, the projection width increased; lift and drag all increased, as shown in Fig. 9(a), (b), (e) and (f). When g⁄ > 0, the aerodynamic loadings on wind blade-I were similar to those for single wind blade. Specifically, the lift coefficient and lift-to-drag ratio at g⁄ = 0.833 were higher than those of single wind blade. The aerodynamic loading on wind blade-II was affected by wind blade-I and acts in the y direction. At high AoA, the pressure component acts in the x direction and causes a loss of drag on wind blade-II. Therefore, the lift-to-drag ratio on wind blade-II was lower than that of the single wind blade, as shown in Fig. 9(c) and (g). On blade-I, the maximum CL/CD of 3.19 occurs at a = 8°. However, the maximum CL/CD of 1.54 occurs at
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Fig. 8. Distributions of Strouhal numbers.
a = 15° due to the effect of blade-I. Fig. 9(d) and (h) shows that the quarter-chord momentum coefficient on wind blade-I was similar to that of single wind blade with the effect of gap ratio. However, the momentum coefficient on wind blade-II increased with increasing the gap ratio. The decrease of lift and drag at high AoA caused the decrease of momentum coefficient. In conclusion, for single wind blade, the maximum lift occurs at a = 10° and the drag increased with a. The quarter-chord momentum increased with a when a < 45° and decreased with a when a > 45°. For side-by-side twin wind blades, the flow characteristics on the upper wind blade are similar to those on single wind blade. The lift, drag and quarterchord momentum on the lower wind blade decreased significantly due to the pressure distribution of upper wind blade. The effect of upper wind blade on the lower wind blade deceased as g⁄ increased. 4. Conclusions This study explored the effects of the gap ratio (g⁄) and angle of attack (a) on side-by-side twin wind blades. The wake-flow
patterns and aerodynamic performances around these two wind blades were probed and classified using the smoke-streak flow visualization, hot-wire velocimetry and six-force balancer. The following conclusions are summarized from the experimental results and discussions. (1) Seven characteristic smoke-streak flow patterns were defined – Attached surface-flow, Wake instability wave, Vortical wake, Gap flow, Bluff-body wake, Antiphase vortex shedding and In-phase vortex shedding. As g⁄ 0, the flow characteristics of side-by-side twin wind blades show the similar flow properties of single wind blade. As g⁄ increased, the interaction between upper and lower wind blades induces vortical wake, gap flow and anti-phase vortex shedding modes. Furthermore, the wake-flow patterns behind side-by-side twin wind blades are similar to those behind single wind blade as g⁄ increases to the specific values. (2) At a = 15°, 30° and 90°, the maximum velocity fluctuation occurs at g⁄ = 0.083 and the velocity fluctuation decreases toward that of free-stream as g⁄ increased.
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Fig. 9. Aerodynamic performances of wind blade-I and II. (a) and (e) Lift coefficient, (b) and (f) drag coefficient, (c) and (g) lift-to-drag ratio, (d) and (h) quarter-chord momentum coefficient. Re = 7550.
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(3) The vortex-shedding frequencies at different AoA behind these side-by-side twin wind blades were nearly equivalent to those for single wind blade and the vortex-shedding frequency decreased as a increased. (4) For single wind blade, the maximum lift occurs at a = 10° and drag increased with a. The quarter-chord momentum increased with a when a < 45° and decreased when a > 45°. For side-by-side twin wind blades, the flow characteristics on the upper wind blade were similar to those on single wind blade. The lift, drag and quarter-chord momentum on the lower wind blade decreased significantly due to the pressure distribution of upper wind blade. The effect of upper wind blade on the lower wind blade deceased as g⁄ increased.
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