Flow characteristics and drag force of a square cylinder in crossflow modulated by a slot jet injected from upstream surface

Experimental Thermal and Fluid Science 75 (2016) 235–248

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Flow characteristics and drag force of a square cylinder in crossflow modulated by a slot jet injected from upstream surface Ching Min Hsu a,⇑, Rong Fung Huang b, Hsiang Chun Chung b a b

Graduate Institute of Applied Science and Technology, National Taiwan University of Science and Technology, Taipei 10607, Taiwan, ROC Department of Mechanical Engineering, National Taiwan University of Science and Technology, Taipei 10607, Taiwan, ROC

a r t i c l e

i n f o

Article history: Received 4 August 2015 Received in revised form 13 December 2015 Accepted 22 February 2016 Available online 4 March 2016 Keywords: Square cylinder Flow control Flow visualization PIV

a b s t r a c t The flow characteristics and drag force of a square cylinder with a front jet injection were experimentally investigated in a wind tunnel. The evolution process of the characteristic flow patterns was recorded by the laser-assisted smoke flow visualization method. The time-averaged velocity fields measured by particle image velocimetry (PIV) were applied to analyze the velocity vectors, streamline patterns, vorticity contours, velocity distributions, and time histories of instantaneous velocities around the upstream region of the square cylinder. The drag force experienced by the square cylinder was obtained by measuring the surface pressures on the front and rear faces. The results show that the jet emitted from the upstream surface of the square cylinder periodically swings left-and-right in the experimental range of injection ratio 60.9. In the time-averaged velocity field, the jet flow impinges the freestream at a fourway saddle and subsequently bifurcates into two streams; one stream goes toward the left edge of the upstream surface, while the other stream directs toward the right edge of the upstream surface. Two recirculation regions formed above the upstream surface of the square cylinder are enclosed by those two streams. The vorticity contours around the upstream surface of the square cylinder are characterized by two adjacent vorticity-concentrated areas of opposite signs. The time histories of the instantaneous velocities around the four-way saddle, jet exit, and shear layer of the swinging jet represent periodic oscillation. This characteristic oscillation frequency is dominated by the wake instability. The recirculation regions formed above the cylinder’s upstream surface prevent impingement from the freestream. Consequently, the surface pressure coefficients on the upstream surface of the square cylinder are reduced. This reduction in the surface pressure coefficient decreases the drag force acting on the square cylinder. Ó 2016 Elsevier Inc. All rights reserved.

1. Introduction The study of the flow characteristics around the square cylinder in a uniform flow is important for industrial applications, such as architectural structures and heat exchangers. Many studies published in past decades have discussed the flow characteristics and aerodynamic performances of a square cylinder in freestream [1–9]. When a flow passes across a square cylinder, the flow characteristics, vortex-shedding frequency, and aerodynamic forces exhibit distinct behaviors at different ranges of incidence angles of the square cylinder. The flow behaviors are relatively insensitive to Reynolds numbers, but are more sensitive to the incidence

⇑ Corresponding author at: Graduate Institute of Applied Science and Technology, National Taiwan University of Science and Technology, 43 Keelung Road, Section 4, Taipei 10607, Taiwan, ROC. Tel.: +886 2 2737 6940; fax: +886 2 2730 3733. E-mail address: [email protected] (C.M. Hsu). http://dx.doi.org/10.1016/j.expthermflusci.2016.02.014 0894-1777/Ó 2016 Elsevier Inc. All rights reserved.

angle. The complex flow separation and recirculation behaviors around the square cylinder may induce large aerodynamic forces. Investigators, therefore, have developed some passive and active flow control methods to modulate the flow characteristics and to suppress the drag force asserting on the cylinder. Tamura and Miyagi [10] found that the separated shear layers approaching the side surface of the square cylinders with chamfered and rounded corners could promote reattachment and therefore reduce the drag force. Igarashi [11], Sarioglu et al. [12], and Zhang et al. [13] installed a rigid small circular rod at a distance upstream of the square cylinder to control the flow behaviors. They observed that the flow between the control rod and the square cylinder presented cavity and vortex shedding modes. When a cavity-flow pattern appeared between the rod wake and the square cylinder, the drag coefficient of the square cylinder was reduced. Huang et al. [14] developed a self-sustained vibration rod to control the flow around a square cylinder. The rod vibration

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Nomenclature Aj CD CD,j Cp f dslot Hj L Lslot Mj Qj R Rej Rew t t⁄ u

slot jet area (=dslot
Lslot) drag coefficient excluding jet momentum drag coefficient including jet momentum pressure coefficient frequencies of jet and wake width of slot for injecting a jet from upstream surface of square cylinder, 2 mm height of jet penetration length of square cylinder, 520 mm length of jet slot, 492 mm jet momentum (=qj
u2j
Aj) flow rate of jet injection ratio (=uj/uw) jet Reynolds number based on jet slot width dslot freestream Reynolds number based on side width of square cylinder w evolution time non-dimensional time (=tuw/w) instantaneous streamwise velocity

induced by fluid–solid interaction significantly changed the flow patterns around the square cylinder, and therefore reduced the drag by about 25%. Ali et al. [15,16] studied the flow around a square cylinder subject to the influence of a splitter plate by numerical method. The drag force decreased with an increase in the length of the splitter plate due to the suppression of vortex shedding in the cylinder wake. Koutmos et al. [17] performed computational and experimental studies on the wake flow of a two-dimensional square cylinder with a planar jet injected from the cylinder base into the vortex formation region. They confirmed that the periodic wake instabilities disappeared when the injection ratio (i.e. the jet to freestream velocity ratio) is greater than about one. Akansu and Firat [18] conducted experimental studies on the control of flow around a square prism by a slot jet emitted from the cylinder base. They found that increasing the injection ratio up to a certain value could cause important pressure recovery in the wake. Çuhadarog˘lu et al. [19], Çuhadarog˘lu [20], and Turhal and Çuhadarog˘lu [21] studied the effects of uniform injection and suction through a porous square cylinder on flow field and aerodynamic parameters. They found that increasing the injection/suction velocity would decrease the drag coefficient. The flow control method of using a slot jet injection from the upstream surface of the square cylinder was rarely found in the literature. A slot jet injected from the upstream surface of a square cylinder in a laminar freestream was studied by Kim et al. [22]. They reported that the high-pressure region on the upstream face of the square cylinder was pushed upstream by the control jet. As a result, the drag force exerted on the cylinder was reduced. Huang et al. [23] studied the flow behavior in the upstream and downstream regions of a square cylinder subject to the modulation of a planar jet issued from the cylinder’s upstream surface. Four characteristic flow modes were observed in the domain of the injection ratio and the freestream Reynolds number. The swinging jet mode appeared at the low injection ratios R smaller than about 1. The jet swung periodically leftward and rightward and formed a fluid bubble on the front surface. The fluid bubble contained a pair of counter-rotating vortices and presented a periodic variation in its height. The deflected oscillating jet mode appeared at the moderately low injection ratios within 1 < R < 4.3. The jet was deflected in either the left or the right direction and wrapped around one of the edges of the square cylinder. At the moderately high and

 u uw v V

v uj w x y z

qj mj mw U

Xz

time-averaged streamwise velocity freestream velocity instantaneous transverse velocity instantaneous velocities simultaneously detected at upor downstream regions of square cylinder time-averaged transverse velocity jet velocity at exit (=Qj/(Lslot
dslot)) side width of square cylinder, 60 mm Cartesian coordinate in axial direction Cartesian coordinate in cross-stream direction Cartesian coordinate along cylinder axis density of jet fluid viscosity of jet fluid viscosity of freestream power spectrum density function
of velocity fluctuation vorticity flow field in z-direction ¼ @@xv  @@yu

high injection ratios, the deflection jet mode (4.3 < R < 8.3) and penetrating jet mode (R > 8.3) appeared. The jet detached from the cylinder’s front surface and penetrated a long distance into the upstream region due to large jet momentum. The drag coefficient decreased with an increase in the injection ratio. The flow behavior, vortex shedding, and drag force of a square cylinder with a slot jet issued from the cylinder’s upstream surface have been investigated in the previous studies by flow visualization, hotwire anemometer, and pressure measurement. However, the detailed dynamics of the velocity field around the upstream surface of the square cylinder still remain unclear. In the present work, the qualitative and quantitative flow characteristics around the cylinder’s front surface are investigated in the range of swinging jet mode (R < 1) by using flow visualization and high-speed particle image velocimetry (PIV). The velocity vectors, streamline patterns, vorticity contours, velocity distributions, instantaneous velocities, surface pressure coefficient distributions, and drag coefficients are presented and discussed. The results will help to better understand the physical mechanism of the front jet injectioncontrolled square cylinder flow. 2. Experimental methods 2.1. Apparatus A closed-return wind tunnel was used for experiments. The test section of the wind tunnel was 600 mm
600 mm
1200 mm in width, height, and length, respectively. The bottom wall of the test section was made from one polished aluminum-alloy plate. For flow visualization, the upper and side walls of the test section were made from three transparent acrylic panels. A hot-wire anemometer, which was specially calibrated by a Pitot tube along with a high-precision pressure transducer, was used to detect the freestream velocity uw. The maximum freestream velocity uw used for the experiment was 0.54 m/s, which corresponded to a Reynolds number Rew = 2100. The selection of upper limit of Reynolds number in the study is to compare with the previous study of Huang et al. [23]. The turbulence intensity within the experimental range of uw was less than 0.6%. A hollow square cylinder, made of aluminum alloy (6061TET62), was mounted vertically in relation to the flow direction in the test section. The square cylinder had a side width of

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right side, and downstream surfaces of the square cylinder were designated as A, B, C, and D, respectively, as shown in Fig. 1(a). A slot was machined along the centerline of the upstream surface A for issuing a plane jet toward the upstream direction. The slot length Lslot spanned from z/w = 4.1 to 4.1. The slot width dslot was 0.033w. The aspect ratio Lslot/dslot was 264. The flow rate Qj of the air jet issued from the slot was metered by a calibrated rotameter. The jet velocity uj was calculated by Qj/Aj, where Aj was the area of the slot opening. The maximum jet velocity uj used for the experiments was 0.49 m/s, corresponding to the jet Reynolds number Rej = 65. The maximum injection ratio R used in the experiments therefore is 0.9. The presented data in this paper covered the range R < 1, which is in the swinging jet regime. The air supply system for the slot jet was specially designed to provide a uniform jet velocity distribution. A flow conditioning module was arranged in the cavity of the hollow square cylinder. Screens and a porous medium were installed in the flow conditioning module. By passing the airflow through the flow conditioning system, the uniformity of the slot jet at the front surface of the square cylinder could be conditioned. Fig. 2 shows a normalized velocity distribution (measured by a hot-wire anemometer) at the exit of the slot jet for Rej = 65. The normalized velocity distribution shown in Fig. 2 presented high uniformity. In the range of z/Lslot = 0.4 to 0.4, the maximum deviation between the local jet velocity (uj0) and the averaged jet velocity (uj) was less than 2%. The blockage ratio and the aspect ratio L/w of the square cylinder were 10% and 8.7, respectively. To minimize the effects of the wall boundary layer and three-dimensional flow around the cylinder ends, each end of the square cylinder was fitted with an end plate (i.e. a sharp-edged circular plate, 310 mm in diameter and 5 mm in thickness), as shown in Fig. 1(b), according to the suggestions of Stansby [24], Fox and West [25], Gerich and Eckelmann [26], and Szepessy and Bearman [27]. By installing these end plates, relatively uniform distributions of the vortex-shedding frequencies were detected in the range of 4 < z/w < 4. All experiments conducted in this study, including the flow visualization, PIV measurements, wake instability frequency detections, and surface pressure measurements, were performed around the central section of the cylinder within z/w = ±0.5, where the threedimensional effects were limited. Fig. 1. Experimental setup.

w = 60 mm and a span length of L = 520 mm. A top view of the arrangement of the square cylinder is shown in Fig. 1(a). A Cartesian coordinate system (x, y, z) was fixed to the mid-span at the center of the square cylinder, as shown in Fig. 1(b). The freestream velocity was aligned with the +x direction. The transverse and span directions were designated by y and z, respectively. The incidence angle of the square cylinder was fixed at 0°. The upstream, left side,

2.2. Flow visualization The laser-assisted smoke flow visualization method was employed to examine the behavior of the jet flow injected from the upstream surface of the square cylinder. A smoke generator that could continuously provide a large number of kerosene oil-mist particles was installed after the calibrated rotameters.

Fig. 2. Normalized velocity distribution of slot jet at Rej = 65.

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The smoke was released into the jet flow. The air seeded with the kerosene oil-mist particles was ejected through the slot toward the wind tunnel flow. The diameter of the condensed vapor aerosols, as measured by a Malvern 1600C Particle Analyzer, was 1.7 ± 0.3 lm. The Stokes number [28] of the oil aerosols was less than 0.5
103 when considering the density of the kerosene oil-mist to be 5.31 kg/m3. The Stokes number was sufficiently small to ensure that the particles followed the flow appropriately. A laser-light sheet generated from a continuous green-light laser was used to illuminate the particles of the flow field. The wavelength and the maximum power of the green-light laser were 532 nm and 3.3 W, respectively. The thickness of the laser-light sheet was about 0.5 mm. The laser-light sheet was aligned horizontally from the side of the test section so that the particles in the mid-span plane (i.e. the x–y plane) of the square cylinder were illuminated. One high-speed digital camera (Model Y4, Integrated Design Tools Inc.) was used to record the instantaneous flow patterns. The high-speed camera had a complementary metal oxide semiconductor (CMOS) array sensor of active monochrome 1024
1024 pixels and could record up to 3000 frames per second at full resolution. The spatial resolution of the instantaneous flow images was 0.10 mm/pixel. One still digital camera (Mode EOS 450D, Canon) was applied to record the long-exposure (2 s) flow images. This camera had a CMOS sensor with a maximum resolution of 4272
2848 pixels. The spatial resolution of the longexposure flow images was 0.18 mm/pixel. In order to determine the visual boundary of the jet penetration, an image processing method proposed by Shapiro and Stockman [29] was employed. The uncertainty of the boundary measurements for the jet penetration was estimated about 8% [30].

2.3. PIV measurement A high-speed PIV system was used to measure the instantaneous flow velocities. The PIV system consisted of a pulsed laser, a high-speed digital camera, an electronic synchronizer, an image acquisition system, and PIV analysis software. The pulsed laser was a dual-head diode-pumped pulsed Neodymium-doped Yttrium Lithium Fluoride (Nd:YLF) laser (Model LDY 301, Litron Laser Ltd.). The wavelength of the light beams emitted from the laser head was 527 nm. The maximum pulsing rate was 20,000 Hz. The high-speed digital camera used for the PIV measurement was the same as that used in the flow visualization. The pulsed laser and the camera were triggered and synchronized by the electronic synchronizer. The pixel array of the CMOS camera was mapped to a physical region of 30
96 mm2 so that the spatial resolution was about 110 lm/pixel. The double-exposure mode was used. The frame rate was adjusted to 1000 image pairs per second. The time interval between the two consecutive laser pulses was 180 ls. To scatter the laser light, kerosene oil-mist particles were seeded in the jet and the freestream. The single exposed double frame images were analyzed with a cross-correlation technique [31] embedded in the PIV analysis software. The software was a commercial code developed by Integrated Design Tools Inc. The software calculated the average displacement of the local groups of particles in consecutive images. The interrogation window was set to 32
32 pixels. The displacement of the particles in the consecutive double-exposed images was kept at less than one-fourth of the length of the interrogation area to reduce velocity bias in the regions of large velocity gradients, as suggested by Keane and Adrian [32]. The seeding density was adjusted to keep the number of particle image pairs per interrogation spot at no less than four so that the measurement reliability would not become significantly poor. The number of vectors

(i.e. grids) predetermined for the PIV analysis results was set to 91
33 in the median plane of the transverse jets. Error check and interpolation routines identified outliers. Regenerated interpolated values replaced the identified outliers. The percentage of outliers in a vector map usually depends on factors such as seeding density, seeding homogeneity, out-of-plane motion, pulse separation, and analysis parameters (e.g. the size of the interrogation area). Even for well-optimized PIV images analyzed with appropriate parameters, there was still a finite probability of getting some outliers. In general, spurious vectors were less than 0.6%. 2.4. Instability frequency and mean velocity detection The one-component hot-wire anemometer was used to detect the instabilities of the front jet and wake and the mean velocity in the wake. In order to detect the frequency of the instability motions properly, the probe position underwent careful adjustment to enable it to capture the oscillation signals caused by the swinging motion of the slot jet in the upstream region and the vortex shedding in the wake region. To analyze the dynamic behaviors and to calculate the flow statistics, the current study simultaneously fed the output signals of the hot-wire anemometer into both an FFT analyzer and a high-speed PC-based data acquisition system. The FFT analyzer monitor the time history output signals of the hot-wire anemometer and converted the time-domain data to frequency domain, thereby ensuring the appropriateness of the probe position at all times. The hot-wire probes used were TSI 1210-T1.5. The original tungsten wire was replaced by platinum wire; the wire diameter and length were 5 lm and 1.5 mm, respectively. The dynamic response corresponding to the electronic square-wave test was adjusted to 20 kHz. The sampling rate and the elapsed time of the data acquisition system were set to 10000 samples per second and 10 s, respectively. The accuracy for the hot-wire probe positioning was 0.2 mm. The accuracy of the instability frequency measurements depended not only on the response of the hot-wire anemometer, but also on the record length and sampling rate of the FFT analyzer. The uncertainty of the frequency detection was estimated to be within ±0.75% of the reading. 2.5. Pressure distribution measurement To obtain the drag coefficient of the square cylinder, the timeaveraged surface pressure distributions on the square cylinder were measured. Fourteen pressure taps were drilled around the mid-plane of the square cylinder. The diameter of the tap holes was 1 mm. Eight taps were made on the downstream surface D with equal spacing. The spacing between two neighboring taps was 6.67 mm. Six taps were made on the upstream surface A at the same distribution as that on the downstream surface D, with the exception that two taps near the slot jet were not drilled. A short stainless-steel tube was tightly inserted into the hole of each tap from the inside of the hollow cylinder and connected to a plastic polyester tube. The polyester tube was connected to a homemade ‘linear pressure scanner.’ The pressure transducer (Model 264, Setra Corp.), with a maximum measurable pressure of 2.54 mm Aq, was utilized to measure the surface pressure. Since the surface pressure was very low at low freestream Reynolds numbers, the pressure transducer could not resolve the surface pressure to a satisfactory accuracy. As the freestream Reynolds number increased to 8000, the surface pressure became large enough for the resolution of the pressure transducer. Therefore, the Reynolds number was set at 8000 when performing the surface pressure measurement. The smoke flow visualization can clearly reveal flow patterns only at low Reynolds numbers. We therefore

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presented the flow visualization pictures in the range of Rew = 2100. According to the previous observation by Huang et al. [23], in the freestream Reynolds number ranged within 1600–13,000, the flow presented the same characteristic modes in the same injection ratios. Although the flow visualizations and pressure measurements were performed in different ranges of Reynolds number, the pressure data are correlated to the characteristic flow modes. A computer was utilized to control the pressure scanner to detect the distribution of surface pressure. The output voltages of the pressure transducer were fed into a data acquisition card (Model PCL-818L-12, Advantech Co.) and were converted to pressure data by a calibration curve installed in the computer. The sampling rate and record length were 250 Hz and 5000 samples, respectively. The present method of using pressure taps and transmitting tubes was incapable of detecting the fluctuating surface pressures because the long extension tube and small sensing holes induced phase lag and smaller root-mean-square values for the pressure fluctuations. Therefore, only the time-averaged surface pressure and drag coefficient are presented. 2.6. Uncertainty estimation The uncertainty estimates for each variable in the figures were based on Steele et al.’s method [33]. The total uncertainty E of the variables can be found by combining systematic and random errors as E = [B2 + (DSD)2]1/2, where B is the systematic uncertainty, SD is the standard deviation of the mean, and the degrees of freedom D are set at 2 for the 95% confidence level. The systematic uncertainty B was estimated based on the calibration data and previous test experiences. The standard deviation of the mean SD was computed from the raw measurement data. The measured accuracy of

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the freestream velocity was influenced by the alignment of the Pitot tube and the calibration of the pressure transducer. The uncertainty of the freestream velocity was estimated to be as large as 3% of the reading. The jet velocity was measured with a rotameter calibrated through a micro-pressure calibration system to an accuracy of 1% of the full scale. The uncertainty of the injection ratio was estimated to be about 4%. The uncertainty of the velocity components measured with the PIV technique was evaluated within 2% [31]. The uncertainty of the derivative vorticity was estimated to be as large as 4% [34]. The uncertainty of the pressure measurement was estimated to be about 3%. 3. Results and discussion 3.1. Characteristic flow evolution processes Typical instantaneous time-evolving flow patterns of the injected jet fluids around the upstream surface A of the square cylinder at R = 0.9 and Rew = 2100 are shown in Fig. 3. The symbol t⁄ denotes the non-dimensional time defined as t⁄ = tuw/w, where t is the evolving time. At t⁄ = 0, as shown in Fig. 3(a), the jet emitted from the slot is deflected toward the y direction and attached to the left side of face A at around y/w = 0.4. At t⁄ = 1.5, as shown in Fig. 3(b), a recirculation bubble rotating counterclockwise is formed near the left side of the jet exit. The jet emitted from the slot follows the outer contour of the recirculation bubble so that the deflected jet column tilts upward. The attached point of the deflected jet moves toward the center line of face A and locates at around y/w = 0.18. At t⁄ = 2.4, as shown in Fig. 3(c), the height of the recirculation bubble increases. The jet column emitted from the slot continuously tilts upward and becomes almost vertical.

Fig. 3. Evolution process of jet flow around upstream surface of square cylinder with a front jet injection at R = 0.9 and Rew = 2100. Framing rate: 30 fps; exposure time: 30 ms.

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A recirculation bubble rotating clockwise is evolved on the right side of the jet exit. At t⁄ = 3.0, as shown in Fig. 3(d), the jet column deflects toward the +y direction. The recirculation bubble on the right side of the jet exit enlarges, while the recirculation bubble on the left side of the jet exit gradually reduces in size. At t⁄ = 4.2, as shown in Fig. 3(e), the recirculation bubbles on both the right and left sides of the jet exit disappear. The jet column emitted from the slot tilts downward and attaches to face A at around y/w = 0.4. When t⁄ larger than around 5, the evolution process of the jet flow characteristics shown in Fig. 3(f) and (e) mirrorreflects the evolution process shown in Fig. 3(a)–(d). At t⁄ > 6.9, the jet flow subsequently evolves back to a flow pattern similar to that shown in Fig. 3(a). The video recordings of the flow visualization show that the slot jet periodically swings left-and-right around the upstream surface of the square cylinder. The oscillation frequency of Fig. 3, estimated by means of observing the video images and counting the number of jet oscillations within the time period 6 s, was about 1.12 Hz. The characteristic flow behavior shown in Fig. 3 appears in the range of an injection ratio R approximately smaller than 1.1 and is termed the ‘swinging jet’ mode, which is consistent with the observation of Huang et al. [23]. Fig. 4 shows the long-exposure images of the jet flow around the upstream surface A of the square cylinder at R = 0.5 and 0.9. The white color in the long-exposure images indicates the penetration area of the jet flow. The jet emitted from the slot swings leftand-right periodically so that face A is covered with white smoke. The penetration height of the front jet (Hj), which was defined as the vertical distance from face A to the upper boundary of the white smoke jet, was measured by using the binary image processing method mentioned in Section 2.2. The variation of the normalized penetration height (Hj/w) with injection ratio R at various freestream Reynolds numbers is shown in Fig. 5. The slot jet with a larger injection ratio produces a larger jet momentum to sustain the impingement of the freestream. Therefore, the jet penetration height increases as the injection ratio increases. The increased rate is almost linear. At R = 0.2, Hj/w = 0.04. At R = 1.0, Hj/w = 0.25. The slope (Hj/w)/R is about 0.26. The typical instantaneous time-evolving flow patterns in the near wake of the square cylinder corresponding to Fig. 3 are shown in Fig. 6. To observe the near wake flow structure, the smoke was released into the freestream. The flow patterns in Figs. 3 and 5 are synchronous. At t⁄ = 0, as shown in Fig. 6(a), a counterclockwiserotating vortex (indicated by V1) appears near face D. This vortex

Fig. 5. Variation of normalized penetration height with injection ratio at various freestream Reynolds numbers.

was evolved from the shear layer separated from the left edge of face A. At t⁄ = 1.5, as shown in Fig. 6(b), the vortex deforms and detaches from face D. At t⁄ = 2.4, as shown in Fig. 6(c), a small vortex (indicated by V2) rotating clockwise appears around the right part of face D. The vortex V1 moves toward the downstream area. In Fig. 6(d)–(f), the vortex V2 grows in size as time elapses. At t⁄ = 5.1, as shown in Fig. 6(f), the vortex V2 deforms and is ready to detach from face D. A small vortex (indicated by V3) rotating counterclockwise appears at around the left part of face D. As the time elapses, the vortex V2 moves toward the downstream and the vortex V3 enlarges, as shown in Fig. 6(g) and (h). After this, the flow pattern returns to that similar to Fig. 6(a). The evolution process of the characteristic flow behavior in Fig. 6 repeats periodically. It is similar to a typical vortex shedding of a square cylinder. The vortex shedding frequency of Fig. 6, estimated by observing the video images and counting the number of vortex within the time period 6 s, was about 1.12 Hz. The vortex shedding frequency of Fig. 6 coincides with the jet oscillation frequency of Fig. 3. The results of the upstream and downstream flow patterns (Figs. 3 and 6) demonstrate that the upstream jet is deflected toward the left side of face A (y direction) when a vortex evolves at the left part of face D. In contrast, the upstream jet is deflected toward the right side of face A (+y direction) when a vortex evolves at the left part of face D. 3.2. Time-averaged velocity fields

Fig. 4. Long-exposure flow images of jet flow around upstream surface of square cylinder at Rew = 2100. (a) R = 0.5, (b) R = 0.9. Exposure time = 2 s.

Fig. 7 shows the time-averaged velocity vectors and streamline patterns in the upstream region of the square cylinder with front jet injections at R = 0.5 and 0.9. The time-averaged velocity fields were obtained by averaging 3000 instantaneous velocity maps. The measurement points are dense; thus, in Fig. 7, superfluous velocity vectors were removed for the clarity of presentation. The streamlines were obtained by using the shooting method. At R = 0.5, along the centerline (y/w = 0) the freestream flows downward and the jet directs upward, as shown in Fig. 7(a). The freestream and the slot jet impinge each other at a four-way saddle, then bifurcate into two streams: one stream goes toward the left edge of face A, while the other stream goes toward the right edge of face A. This four-way saddle locates at (x/w, y/w) = (0.57, 0). The jet flow emitted from the slot approaches the four-way saddle and bifurcates into two streams. One stream goes toward the left, while the other goes toward the right. Two

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Fig. 6. Evolution process of flow patterns in near wake region of square cylinder with a front jet injection at R = 0.9 and Rew = 2100. Framing rate: 30 fps; exposure time: 30 ms.

recirculation regions marked by the green shadow appear above face A. In the left recirculation region, the streamlines emitted from the jet exit deflect toward the y direction; in the right recirculation region, the streamlines emitted from the jet exit deflect toward the +y direction. As the freestream impinges against the jet, the freestream momentum counterbalances the jet momentum. Therefore, the velocity vectors around the four-way saddle are almost null. The velocity vectors within the recirculation regions are smaller than those outside the recirculation regions. At R = 0.9, as shown in Fig. 7(b), the characteristics of the velocity vectors and streamline patterns are similar to those in Fig. 7(a). However, at R = 0.9, two counter-rotating vortices are formed within the recirculation regions. The vortex in the right recirculation region rotates clockwise, while the vortex in the left recirculation region rotates counterclockwise. The four-way saddle locates at (x/w, y/w) = (0.62, 0). The altitude of the four-way saddle at R = 0.9 is higher than that at R = 0.5. In the time-averaged velocity field, the four-way saddle locates at where the freestream momentum counterbalances the jet momentum. The freestream Reynolds number is fixed. The jet momentum at R = 0.9 is larger than that at R = 0.5. The larger jet momentum can sustain more impingement

from the freestream so that the four-way saddle in Fig. 7(b) appears more upstream than that in Fig. 7(a). The recirculation regions in Fig. 7(b) are larger than those in Fig. 7(a). The time-averaged vorticity contours in the upstream region of the square cylinder are shown in Fig. 8. The iso-vorticity contours are computed from the time-averaged velocity fields shown in Fig. 7. The vorticity Xz is normalized by uw/w. Positive vorticity contours denotes a counterclockwise rotation, while negative vorticity denotes a clockwise rotation. In Fig. 8(a), for R = 0.5, the vorticity contours are represented by two adjacent vorticityconcentrated areas with opposite signs appearing above face A. To the right of the jet exit, the normalized vorticities have a peak value of 1.2. To the left of the jet exit, the normalized vorticities have a peak value of 1.3. The peak values of those two vorticityconcentrated areas locate near the right and left edges of face A. The characteristics of the time-averaged vorticity contours at R = 0.9, as shown in Fig. 8(b), are similar to those shown in Fig. 8 (a). The right part of the jet exit has negative vorticities with a peak value of 1.1, while the left part of the jet exit has positive vorticities with a peak value of 1.0. The peak values of the right and left parts of the vorticity-concentrated areas locate at the regions

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Fig. 7. Velocity vectors and streamline patterns around upstream surface of square cylinder with a front jet injection at Rew = 2100. (a) R = 0.5, (b) R = 0.9.

Fig. 8. Vorticity contours around upstream surface of square cylinder with a front jet injection at Rew = 2100. (a) R = 0.5, (b) R = 0.9.

ranging within 0.3 < y/w < 0.5 and 0.5 < y/w < 0.3, respectively. The peak values of the vorticity-concentrated areas at R = 0.9 are lower than those at R = 0.5.  ) and transverse (v  ) velocities The time-averaged streamwise (u in the upstream region of the square cylinder with a front jet injection at R = 0.9 are extracted from the time-averaged velocity vector field shown in Fig. 7(b). The variations of the streamwise and transverse velocities distributions normalized by freestream velocity (uw) with the normalized axial distance (x/w) at various transverse distances (y/w) are shown in Figs. 9 and 10. Fig. 9 shows the normalized streamwise velocity distributions  =uw ) along x/w at various transverse distances at R = 0.9 and (u Rew = 2100. At y/w = 0 (i.e. the central line of face A), the normalized streamwise velocity distribution is positive at x/w < 0.62 and is negative at about x/w > 0.62. The position of x/w = 0.62 coincides with the location of the four-way saddle shown in Fig. 7(b). The positive normalized streamwise velocity distribution is induced by the freestream, while the negative normalized

velocity is caused by the slot jet. The values of the normalized streamwise velocities induced by the freestream and the slot jet gradually decrease to null as the streamwise position approaches x/w = 0.62 because the counterbalance of the momentum between the freestream and the slot jet appears at the four-way saddle (x/w, y/w) = (0.62, 0). At y/w = 0.13, 0.26, 0.39, and 0.50, the normalized streamwise velocities gradually decay with increasing streamwise distance because the freestream deflects toward the +y direction. The normalized streamwise velocity distribution at the transverse distance close to the central line of face A is smaller than that farther away from the central line of face A. For example, the normalized streamwise velocity distribution at x/ w = 0.13 is smaller than that at x/w = 0.50. At y/w = 0.63, the normalized streamwise velocity that appears within the range 1.0 < x/w < 0.76 is about constant. At x/w > 0.76, the normalized streamwise velocity increases with increasing streamwise distance. The time-averaged velocity field is almost symmetric with respect to the central line of face A, so that the streamwise velocity

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Fig. 9. Streamwise velocity distributions around upstream surface of square cylinder with a front jet injection at various transverse levels. Rew = 2100, R = 0.9.

Fig. 10. Transverse velocity distributions around upstream surface of square cylinder with a front jet injection at various transverse levels. Rew = 2100, R = 0.9.

distributions at y/w = 0.13, 0.26, 0.39, 0.50, and 0.63 approximately overlap with those at y/w = 0.13, 0.26, 0.39, 0.50 and 0.63, respectively. Fig. 10 shows the normalized transverse velocity distributions  =uw ) along x/w at various transverse distances y/w at R = 0.9 (v and Rew = 2100. At y/w = 0, the normalized transverse velocities are null because the velocity vectors along the central line of face A direct upward or downward, as shown in Fig. 7(b). At y/ w = 0.13, 0.26, and 0.39, the normalized transverse velocities gradually increase with increasing streamwise distance until they reach a specific streamwise position, after which they decrease quickly with further increases in x/w. For each y/w, the specific streamwise position approximately locates at the upper border of the recirculation region, as marked by green shadow in Fig. 7(b). The normalized transverse velocity at this specific position is the peak value of the normalized transverse velocity distribution. For example, at y/w = 0.13, the peak value of the normalized transverse velocity

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 =uw = 0.24 and is located at about x/w = 0.58. The distribution is v normalized transverse velocity distribution at the transverse distance near the central line of face A has smaller normalized transverse velocity than that far away from the central line of face A. For example, the normalized streamwise velocity distribution at y/ w = 0.13 is smaller than that at y/w = 0.39. At y/w = 0.50 and 0.63, the normalized transverse velocities increase with increasing streamwise distance at x/w < 0.54. The normalized transverse velocities approach constant at x/w > 0.54. The normalized transverse velocity distributions for negative (i.e. y/w = 0.13, 0.26, 0.39, 0.50, and 0.69) and positive (i.e. y/w = 0.13, 0.26, 0.39, 0.50, and 0.69) transverse distances exhibit similar magnitudes but opposite signs because the time-averaged velocity field is almost symmetric with respect to the central line of face A. The velocity vectors at the positive transverse distances direct toward +y direction so that the normalized transverse velocity distributions are positive. The typical time histories of the instantaneous streamwise velocity (u) and transverse velocity (v) around the upstream region of the square cylinder with a front jet at R = 0.9 and Rew = 2100 were simultaneously measured at (x/w, y/w) = (0.62, 0), (0.56, 0), (0.56, 0.42), and (0.56, 0.42), as shown in Figs. 11 and 12. The time histories of the instantaneous velocities in Figs. 11 and 12 were extracted by PIV measurement. The position (x/w, y/ w) = (0.62, 0) locates at the four-way saddle. The position (x/w, y/w) = (0.56, 0) locates around the exit of the slot jet. The positions (x/w, y/w) = (0.56, 0.42) and (x/w, y/w) = (0.56, 0.42) locate around the shear layer of the slot jet that deflected toward the left and right sides of the jet exit, respectively. The instantaneous streamwise and transverse velocities, as shown in Figs. 11 and 12, are normalized by the freestream velocity (uw). In Fig. 11(a), at (x/w, y/w) = (0.62, 0), the normalized streamwise velocity periodically oscillates between 0.37 and 0.1. The normalized streamwise velocity presents positive values when the jet emitted from the slot is deflected toward y and +y directions, as shown in Fig. 3(a), (b), (e), and (f). However, the normalized streamwise velocity becomes negative when the slot jet tilts upward and becomes almost vertical, as shown in Fig. 3 (c) and (g). In Fig. 11(b), at (x/w, y/w) = (0.56, 0), the normalized streamwise velocity periodically oscillates with negative values. The minimum value of the velocity oscillation appears at the instant when the slot jet tilts upward and becomes almost vertical, as shown in Fig. 3(c) and (g). The maximum value of the velocity oscillation forms at the instant when the slot jet is completely deflected toward the y and +y directions and no recirculation vortices are formed, as shown in Fig. 3(a) and (e). The waveforms of Fig. 11(a) and (b) oscillate in phase. As the slot jet swings leftand-right in one oscillation cycle, two oscillating waveforms are formed in the time histories of the instantaneous streamwise velocity at (x/w, y/w) = (0.62, 0) and (0.56, 0). In Fig. 11(c) and (d), at (x/w, y/w) = (0.56, 0.42) and (0.56, 0.42), respectively the normalized streamwise velocities present the same periodic oscillations with a phase lag of about half a cycle. When the slot jet is deflected toward the -y direction, as shown in Fig. 3(a), the normalized streamwise velocity at (x/w, y/w) = (0.56, 0.42) presents the crest of the oscillation waveform because the jet is deflected toward the y direction to accelerate the streamwise velocity. Meanwhile, the normalized transverse velocity at (x/w, y/w) = (0.56, 0.42) exhibits the trough of the oscillation waveform. On the contrary, when the slot jet is deflected toward +y direction, as shown in Fig. 3(c), the normalized streamwise velocity at (x/w, y/w) = (0.56, 0.42) appears as the trough of the oscillation waveform, while the normalized streamwise velocity at (x/w, y/w) = (0.56, 0.42) exhibits the crest of oscillation waveform. As the slot jet swings left-and-right in one oscillation cycle, one oscillating waveform is formed in the time

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Fig. 11. Typical time histories of instantaneous streamwise velocity (u) around upstream surface of square cylinder with a front jet injection at R = 0.9 and Rew = 2100.

Fig. 12. Typical time histories of instantaneous transverse velocity (v) around upstream surface of square cylinder with a front jet injection at R = 0.9 and Rew = 2100.

histories of the instantaneous streamwise velocity at (x/w, y/w) = (0.62, 0) and (0.56, 0). In Fig. 12(a) and (b), at (x/w, y/w) = (0.62, 0) and (0.56, 0), respectively the normalized transverse velocities periodically oscillate between negative and positive values. The sign of the velocity values depends on the deflected direction of the slot jet.

For example, as the slot jet is deflected toward the y direction, as shown in Fig. 3(a), the normalized transverse velocities at (x/ w, y/w) = (0.62, 0) and (0.56, 0) are negative. In Fig. 12 (c) and (d), at (x/w, y/w) = (0.56, 0.42) and (0.56, 0.42), respectively the normalized transverse velocities present similar periodic oscillations with a phase lag of about half a cycle, but the signs are

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opposite; the transverse velocity is negative at (x/w, y/w) = (0.56, 0.42) and is positive at (x/w, y/w) = (0.56, 0.42). The appearance of maximum transverse velocity oscillations depends on the deflected direction of the slot jet. For example, when the slot jet is deflected toward the y direction, the transverse velocity appears at the maximum value of the oscillation waveform at (x/ w, y/w) = (0.56, 0.42). Simultaneously, the transverse velocity appears at the minimum value of the oscillation waveform at (x/ w, y/w) = (0.56, 0.42). 3.3. Instability frequency and velocity distribution To study the jet and wake instabilities of the square cylinder with a front jet, two hot-wire probes were simultaneously placed at the upstream and downstream regions of the square cylinder to measure the time histories of velocity V. The typical hot-wire signals and the corresponding power spectrum density functions in the upstream and downstream regions are shown in Fig. 13. In the upstream region, the hot-wire probe was placed at (x/w, y/w) = (0.6, 0.4). The velocity history, as shown in Fig. 13(a), is a periodic sinusoid-like waveform. The periodic oscillation of the velocity history is induced by the periodically swinging motion of the slot jet, as shown in Fig. 3. To obtain the characteristic frequency of the jet instability, the velocity history in the time domain was transformed to the power spectrum density function in the frequency domain by using the discrete fast Fourier transform (DFFT) technique. The characteristic frequency of the jet instability identified in the power spectrum density function, as shown in Fig. 13(b), is 1.15 Hz. The jet instability obtained by PIV measurement is slightly different from that observed by flow visualization method (as shown in Fig. 3) by about 2.6% because the time resolutions of those two experimental methods are different. The time resolution of PIV measurement was much higher than that of flow visualization. In the downstream region, the hot-wire probe was placed at (x/w, y/w) = (1.0, 1.0). The velocity history, as shown in Fig. 13 (c), is a periodic oscillating waveform superimposed by turbulent fluctuations. The periodic oscillation of the velocity history is induced by vortex shedding in the wake of the square cylinder [9]. The characteristic frequency of the wake instability identified

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in the power spectrum density function, as shown in Fig. 13(d), is 1.15 Hz, which is the same as that of the jet instability. According to Huang et al. [23], it is reasonable to infer that the wake instability dominates the frequency characteristic of the jet instability. Fig. 14 shows the distributions of the normalized mean velocity (V/uw) and fluctuation intensity (V0 /uw) at the downstream location x/w = 1. Fig. 14(a) and (b) show the natural case, while Fig. 14(c)– (f) show the front jet injection-controlled cases under various jet injection ratios. The mean velocity distribution of the natural square cylinder (R = 0) presents an inverse Gaussian-like profile, as shown in Fig. 14(a). The mean velocities within the region 1 < y/w < 1 are smaller than the freestream velocity. The lowest mean velocity locates at around the center line (i.e. y/w = 0) of the square cylinder. The mean velocity increases with increasing the transverse distance from the central line of the square cylinder. For Fig. 14(b), the distribution of the fluctuation intensity for the natural case shows a dual-hump profile. Both humps indicate the shear layers separated from the leading edge of the faces B and C. They locate at y/w = 0.7 and y/w = 0.7. A trough locating between the two humps represents the wake center. In Fig 14 (c)–(f), the distributions of the normalized mean velocity and fluctuation intensity in the wake of square cylinder with a front jet injection at R = 0.5 and R = 0.9 are similar to those of the nature case. The lowest mean velocity at the center line of the front jetcontrolled cases increases with increasing R. This phenomenon denotes that the momentum deficit in the wake of the controlled cases is recovered a little which is beneficial to reduce the drag coefficient. 3.4. Pressure and drag coefficients The surface pressure coefficient Cp, as measured on face A and face D of the square cylinder at various R, is shown in Fig. 15 (a) and (b), respectively. The Reynolds number of the freestream is 8000. For Fig. 15(a), the values of Cp around the central part of face A for a natural square cylinder are about 1.0 because of the impingement effect of the freestream on face A. When the jet is injected from face A, a recirculation region formed on face A (as shown in Fig. 7) reduces the impingement effect of the freestream

Fig. 13. Instability waves in upstream and downstream region of square cylinder with a front jet injection at Rew = 2100 and R = 0.9. Velocity histories (a, c) and power spectrum density functions (b, d).

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Fig. 14. Distributions of the normalized mean velocity (V/uw) and fluctuation intensity (V0 /uw) at the downstream location of x/w = 1 of the square cylinder. Rew = 2100, (a, b) R = 0, (c, d) R = 0.5, (e, f) R = 0.9.

so that the values of Cp across face A decrease significantly by about 28 to 49%. The square cylinder with the larger jet injection produces the smaller Cp on face A. For Fig. 15(b), the values of Cp around face D for a natural square cylinder are about 1.6. As the jet is injected from face A, the values of Cp across face D increase slightly. To calculate the drag force for the square cylinder, the pressure drag and viscous drag should be considered. However, the viscous drag in this case is difficult to estimate and since the lateral face areas are not large the viscous drag is ignored for calculation. The drag coefficient (CD) asserting on the square cylinder without considering the viscous drag can be calculated by integrating the pressure coefficients shown in Fig. 15 over faces A and D by using the following expression:

Z



Z

C p dy 

C p dy

A

CD ¼

D

ð1Þ

w

The front jet injection reduces the drag force because of the improvement of flow characteristics around face A, but it also produces an additional drag force induced by reaction of jet momentum. Should the jet momentum be considered, the drag coefficient should be calculated by

Z

C D;j ¼

Z

C p dy  A

C p dy D

w

þ1

Mj

q u2 A 2 j j j

ð2Þ

Fig. 16 shows the calculated CD and CD,j. The filled circles in Fig. 16 show the drag coefficients CD calculated by using Eq. (1). The empty circles in Fig. 16 denote the drag coefficients including the jet momentum CD,j calculated by using Eq. (2). For the case excluding the jet momentum, the drag coefficient CD of the natural square cylinder (i.e. R = 0) is about 1.88, which is almost the same as that obtained by Yen and Yang [9]. When the slot jet is issued from face A, the values of CD decrease to 1.53 and 1.36 at R = 0.5 and R = 0.9, respectively. The pressure coefficients on face A decrease significantly when the front jet injection is applied, as shown in Fig. 15; therefore, the cases with front jet injection have a smaller drag coefficient as compared to the cases without front jet injection. The front jet injection forms the recirculation regions above the upstream surface (i.e. face A) of the square cylinder to avoid the direct impingement of the freestream. Consequently, the surface pressure coefficients on face A are reduced. This reduction in the surface pressure coefficients decreases the drag force acting on the square cylinder. For the drag coefficients including the jet-momentum-induced drag, the drag coefficients CD,j are a little higher than CD. Since the jet width and the jet velocities employed in the study are small, the differences between CD and CD,j are insignificant. The increase of the additional drag is proportional to jet momentum. A higher injection ratio produces a larger jet momentum. The benefit of improving drag by front jet injection reduces with increasing the jet injection ratio. For example, the increasing rate of the additional jet-momentum-induced drag coefficient at R = 0.3 is about 0.5%,

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4. Conclusions The characteristic flow patterns, time-averaged velocity fields, time histories of instantaneous velocities, and surface pressure distributions around the upstream of a square cylinder with a planar jet injected from the cylinder’s upstream surface were studied using the laser-assisted smoke flow visualization method, the high-speed PIV technique, hot-wire anemometer, and pressure measurement. The conclusions described below are drawn from the experimental results.

Fig. 15. Pressure coefficient distributions on face A (a) and face D (b) of square cylinder at various R. Rew = 8000.

1. At R 6 0.9, the slot jet injected from the upstream surface of the square cylinder presents a ‘swinging jet’ mode. The slot jet periodically swings left-and-right around the upstream surface of the square cylinder. 2. In the time-averaged velocity field, the slot jet impinges the freestream at a four-way saddle, then bifurcates into two streams; one stream goes toward the left edge of the upstream face, while the other stream directs toward the right edge of the upstream surface. Two recirculation regions are enclosed by those two streams. As the jet impinges against the freestream, the freestream momentum counterbalances the jet momentum. Therefore, the velocity vectors around the four-way saddle are almost null. The velocity vectors within the recirculation regions are smaller than those outside the recirculation regions. 3. The vorticity contours around the upstream of the square cylinder are characterized by two adjacent vorticity-concentrated areas with opposite signs. The peak values of the vorticityconcentrated areas at large injection ratios are lower than those at small injection ratios. 4. The time histories of the instantaneous velocities at the fourway saddle, jet exit, and shear layer of the swinging jet present periodic oscillations. The characteristic oscillation frequency in the upstream region is dominated by the wake instability. 5. A slot jet injected from the cylinder’s front surface forms the recirculation regions above the upstream surface of the square cylinder to avoid the impingement effect of the freestream. Consequently, the surface pressure coefficients on the upstream surface are reduced. This reduction of surface pressure coefficients decreases the drag force acting on the square cylinder.

References

Fig. 16. Variation of drag coefficient with jet injection. Rew = 8000.

while the increasing rate of the additional jet-momentum-induced drag coefficient at R = 0.9 is about 3.6%. However, the drag coefficients of the front jet injection-controlled square cylinder are still much lower than those of the natural case.

[1] A. Okajuma, Strouhal numbers of rectangular cylinders, J. Fluid Mech. 123 (1982) 379–398. [2] F. Lesage, I.S. Gartshore, A method of reducing drag and fluctuating side force on bluff bodies, J. Wind Eng. Ind. Aerodyn. 25 (2) (1987) 229–245. [3] D.F.G. Durão, M.V. Heitor, J.C.F. Pereira, Measurements of turbulent and periodic flows around a square cross-section cylinder, Exp. Fluids 6 (5) (1988) 298–304. [4] M.A.Z. Hasan, The near wake structure of a square cylinder, Int. J. Heat Fluid Flow 20 (6) (1989) 339–348. [5] C. Norbert, Flow around rectangular cylinders: pressure forces and wake frequencies, J. Wind Eng. Ind. Aerodyn. 49 (1993) 187–196. [6] D.A. Lyn, S. Einav, W. Rodi, J.-K. Park, A laser-Doppler velocimetry study of the ensemble-averaged characteristics of the turbulent near wake of a square cylinder, J. Fluid Mech. 304 (1995) 285–319. [7] A.K. Saha, K. Muralidhar, G. Biswas, Experimental study of flow past a square cylinder at high Reynolds numbers, Exp. Fluids 29 (2000) 553–563. [8] R.F. Huang, B.H. Lin, S.C. Yen, Time-averaged topological flow patterns and their influences on vortex shedding of a square cylinder in crossflow at incidence, J. Fluids Struct. 26 (3) (2010) 406–429. [9] S.C. Yen, C.W. Yang, Flow patterns and vortex shedding behavior behind a square cylinder, J. Wind Eng. Ind. Aerodyn. 90 (2011) 868–878. [10] T. Tamura, T. Miyagi, The effect of turbulence on aerodynamic forces on a square cylinder with various corner shapes, J. Wind Eng. Ind. Aerodyn. 83 (1999) 135–145. [11] T. Igarashi, Drag reduction of a square prism by flow control using a small rod, J. Wind Eng. Ind. Aerodyn. 67–71 (1997) 141–153. [12] M. Sarioglu, Y.E. Akansu, T. Yavuz, Control of flow around square cylinders at incidence by using a rod, AIAA J. 43 (7) (2005) 1419–1426.

248

C.M. Hsu et al. / Experimental Thermal and Fluid Science 75 (2016) 235–248

[13] P.F. Zhang, J.J. Wang, S.F. Lu, J. Mi, Aerodynamic characteristics of a square cylinder with a rod in a staggered arrangement, Exp. Fluids 38 (4) (2005) 494– 502. [14] R.F. Huang, J.C. Cheng, J.-K. Chen, C.M. Hsu, Manipulating flow to reduce drag of a square cylinder by using a self-sustained vibrating rod, J. Fluids Eng. 133 (5) (2011) 051202. [15] M.S.M. Ali, C.J. Doolan, V. Wheatley, Low Reynolds number flow over a square cylinder with a splitter plate, Phys. Fluids 23 (2011) 033602. [16] M.S.M. Ali, C.J. Doolan, V. Wheatley, Low Reynolds number flow over a square cylinder with a detached flat plate, Int. J. Heat Fluid Flow 36 (2012) 133–141. [17] P. Koutmos, D. Papailiou, A. Bakrozis, Experimental and computational study of square cylinder wakes with two-dimensional injection into the base flow region, Eur. J. Mech. B/Fluids 23 (2) (2004) 353–365. [18] Y.E. Akansu, E. Firat, Control of flow around a square prism by slot jet injection from the rear surface, Exp. Thermal Fluid Sci. 34 (7) (2010) 906–914. [19] B. Çuhadarog˘lu, Y.E. Akansu, A.Ö. Turhal, An experimental study on the effects of uniform injection through one perforated surface of a square cylinder on some aerodynamic parameters, Exp. Thermal Fluid Sci. 31 (2007) 909–915. [20] B. Çuhadarog˘lu, A numerical study on turbulent flow around a square cylinder with uniform injection or suction, Int. J. Numer. Meth. Heat Fluid Flow 19 (6) (2009) 708–727. [21] A.Ö. Turhal, B. Çuhadarog˘lu, The effects of surface injection through a perforated square cylinder on some aerodynamic parameters, Exp. Thermal Fluid Sci. 34 (2010) 725–735. [22] D.-H. Kim, K.-S. Yang, J.-S. Eom, Confined vortex shedding past a square cylinder with a planar jet, JSME Int. J. Ser. B 46 (2) (2003) 316–325.

[23] R.F. Huang, C.M. Hsu, P.C. Chiu, Flow behavior around a square cylinder subject to modulation of a planar jet issued from upstream surface, J. Fluids Struct. 51 (2014) 362–383. [24] P.K. Stanby, The effects of end plates on the base pressure coefficient of a circular cylinder, Aeronaut. J. 78 (1974) 36–37. [25] T.A. Fox, G.S. West, On the use end plates with circular cylinders, Exp. Fluids 9 (1990) 237–239. [26] J.H. Gerich, H. Eckelmann, Influence of end plates and free ends on the shedding frequency of circular cylinders, J. Fluid Mech. 122 (1982) 109–121. [27] S. Szepessy, P.W. Bearman, Aspect ratio and end plate effects on vortex shedding from a circular cylinder, J. Fluid Mech. 234 (1992) 191–217. [28] R.C. Flagan, J.H. Seinfeld, Fundamentals of Air Pollution Engineering, Prentice Hall, Englewood Cliffs, New Jersey, 1988. [29] L.G. Shapiro, G.C. Stockman, Computer Vision, Prentice Hall, Upper Saddle River, New Jersey, 2001. [30] R.F. Huang, S.R. Jufar, C.M. Hsu, Flow and mixing characteristics of swirling double-concentric jets subject to acoustic excitation, Exp. Fluids 54 (1) (2013) 1421. [31] R.D. Keane, R.J. Adrian, Theory of cross-correlation analysis of PIV images, Appl. Sci. Res. 49 (1992) 191–215. [32] R.D. Keane, R.J. Adrian, Optimization of particle image velocimeters. Part I: double pulsed systems, Meas. Sci. Technol. 1 (1990) 1202–1215. [33] W.G. Steele, R.P. Taylor, R.E. Burrell, H.W. Coleman, Use of previous experience to estimate precision uncertainty of small sample experiments, AIAA J. 31 (10) (1993) 1891–1896. [34] J.D. Luff, T. Drouillard, A.M. Rompage, M.A. Linne, J.R. Hertzberg, Experimental uncertainties associated with particle image velocimetry (PIV) based vorticity algorithms, Exp. Fluids 26 (1999) 36–54.