Effects of acoustic excitation at resonance Strouhal numbers on characteristics of an elevated transverse jet

Experimental Thermal and Fluid Science 35 (2011) 1370–1382

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Effects of acoustic excitation at resonance Strouhal numbers on characteristics of an elevated transverse jet Ching Min Hsu, Rong Fung Huang ⇑ Department of Mechanical Engineering, National Taiwan University of Science and Technology, Taipei 10672, Taiwan, ROC

a r t i c l e

i n f o

Article history: Received 26 September 2010 Received in revised form 7 May 2011 Accepted 10 May 2011 Available online 15 May 2011 Keywords: Jets in crossflow Acoustic excitation Jet-fluid dispersion

a b s t r a c t The effects of acoustic excitation on the flow behavior, penetration, and spread of the stack-issued and wall-issued transverse jets were studied experimentally. The jet flow was periodically excited by a loudspeaker that was driven with a square wave at resonance Strouhal numbers. The pulsed transverse jet was characterized by jet Reynolds number 2000. Streak pictures of the smoke flow patterns illuminated by the laser-light sheet in the median plane were recorded with a high-speed digital camera to illustrate the evolution process of the characteristic flow behavior within one excitation cycle. The binary edgedetection technique was used to determine penetration height and spread width. The tracer-gas concentration measurement provided jet dispersion information. The evolution processes of both the stackissued and wall-issued transverse jets were characterized by a leading vortex ring and swing motion of the jet column near the jet exit as the jets were forced at resonance Strouhal numbers. A leading vortex ring appeared near the jet exit during the leading phase of excitation cycle and evolved subsequently to puffs of jet fluids in the upwind shear layer of the deflected jet. The swinging motion of the near-tube tip jet column induced up/down oscillation of the deflected jet. The excited stack-issued transverse jet exhibited significantly larger penetration height and spread width than the excited wall-issued transverse jet. The tracer-gas detection experiment results showed that the excited transverse jet disperses significantly faster and wider than the non-excited transverse jet. Pulsating the transverse jet at low resonance Strouhal numbers produced higher mixing and dispersion effects than pulsating the transverse jet at high resonance Strouhal numbers. Ó 2011 Elsevier Inc. All rights reserved.

1. Introduction The study of jet in crossflow is important for its various practical engineering applications such as combustion, injection cooling, industrial mixing, and pollution transport. Depending on the jet configurations, the studies of jet-in-crossflow are conventionally classified into two categories: one is wall-issued transverse jet [1–4], and the other is stack-issued transverse jet [5–7]. The wall-issued transverse jet is characterized by three-dimensional flows, which are subject to the interactions between the jet, jet-wake, and wall boundary-layer. The flow structures in the stack-issued transverse jet are subject to the interactions between the jet, jet-wake, and stack-wake. The common feature in the timeaveraged flow structure of the wall-issued and the stack-issued transverse jets is the counter-rotating vortex pair associated with the jet cross section that appears in the far field. However, the characteristics of the flow field, the coherent structure along the ⇑ Corresponding author. Address: Department of Mechanical Engineering, National Taiwan University of Science and Technology, 43 Keelung Road, Section 4, Taipei, Taiwan, ROC. Tel.: +886 2 2737 6488; fax: +886 2 2737 6460. E-mail address: [email protected] (R.F. Huang). 0894-1777/$ - see front matter Ó 2011 Elsevier Inc. All rights reserved. doi:10.1016/j.expthermflusci.2011.05.005

upwind shear layer of the deflected jet, the trajectory of the deflected jet, and the wake properties of these two cases present prominent differences. During the past two decades, it has been found that the mixing process of the wall-issued transverse jet can be improved by pulsating the jet flow. Several methods, for example, acoustic excitation, piezoelectric actuator, and solenoid valve, have been employed to pulsate the jet velocity. Recent investigations [8–16] revealed that temporally varying the jet velocity allows jet penetration and spread to increase at specific excitation conditions. Vermeulen et al. [8] showed that acoustically forcing a jet in crossflow produces significant increase in jet spread, penetration, and mixing and a decrease in mixing length. Turbulence and penetration data showed that the responses of spread and penetration appeared to be optimum at a Strouhal number of about 0.22. Gogineni et al. [9] used piezoelectric actuators mounted on the interior walls of a square jet to modulate an air jet in crossflow. They found that manipulation of the upstream and downstream segments of the jet shear layer leads to an increase in the jet penetration into the crossflow and to substantial mixing enhancement. A solenoid valve operated by a square wave signal of variable frequency, injection time, and duty cycle was used to pulse

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Nomenclature Co Cco Cmax Cmax,n d D Eexc fexc fres h H R Rej Rew

carbon monoxide concentration at jet exit carbon monoxide concentration maximum carbon monoxide concentration maximum carbon monoxide concentration for nonexcited jet inner diameter of tube, 0.005 m outer diameter of tube, 0.0064 m RMS value of excitation voltage supplying the loudspeaker acoustic excitation frequency resonance frequency height of leading vortex ring visual penetration height of jet in z direction jet-to-crossflow momentum flux ratio (=qj u2j =qw u2w ) exit Reynolds number of jet (=ujd/mj) free-stream Reynolds number of crossflow (=uwD/mw)

transverse jet in a water tunnel [10–13]. Hermanson et al. [10] and Johari et al. [11] found that the penetration of a fully modulated jet in a crossflow can be characterized in terms of injection time and duty cycle. The injection time influences the jet structure, and the duty cycle impacts the distance between jet puffs or vortices near the injector. A long injection time yields moderate enhancement for full pulsed jets, while a short injection time and a smaller duty cycle yield significant enhancement over the steady jet. Eroglu and Breidenthal [12] observed that the pulsed jet consists of a sequence of vortex rings that penetrate deeply into the crossflow, in comparison with the steady jet. A classification scheme proposed by Johari [13] demarcated the various flow regimes of a pulsed jet depending on the stroke ratio and duty cycle. A transverse jet forced by acoustic excitation has been investigated in a wind tunnel [14–16]. M’Closkey et al. [14] and Shapiro et al. [15] found that in some cases, forcing frequencies corresponding to the sub-harmonics of the upstream shear layer mode of the unforced transverse jet produces increased jet penetration. In other instances, merely exciting the jet at the optimal pulse width and at low excitation frequency yielded the best jet penetration and spread. At a jet-to-crossflow velocity ratio smaller than 4, largeamplitude sinusoidal excitation did not produce any significant jet response, compared with the significant jet response of the unforced jet in crossflow. Davitian et al. [16] forced a transverse jet at an excitation frequency that is 10% of the natural frequency of the shear-layer coherence structure of the unforced transverse jet. They found that the effect of the sinusoidal forcing on the jet’s penetration and spread is not significant when the jet-to-crossflow ratio is relatively low and the shear layer is globally unstable. As discussed above, the properties of a pulsed wall-issued transverse jet at various pulsating configurations have been extensively studied by investigators. However, investigations on the mixing enhancement and penetration characteristics of the pulsed stack-issued transverse jets are rarely found in the literature. The pulsating velocities at the exit of the acoustically pulsed jet at various resonance Strouhal numbers were first measured in order to characterize the responses of the jet to the acoustic excitation. The flow behaviors and characteristics of penetration and spread for the acoustically excited transverse jets at resonance condition were illustrated by using the laser-light sheet-assisted smoke flow visualization technique. Differences in the flow behaviors, penetration, and spread between the excited stack-issued transverse jet and the excited wall-issued transverse jet were presented. Then, the dispersion characteristics of the transverse jet were detected by measuring the concentration distributions of the carbon mon-

SPL Stres Stexc uj uw u0j0 W x, y, z

a qj qw mj mw

sound-pressure-level resonance Strouhal number (=fres d/u0j0 ) excitation Strouhal number (=fexc d/u0j0 ) average exit velocity of jet free-stream velocity of crossflow RMS value of the velocity pulsation at the jet exit under zero-crossflow condition visual spread width of jet in z direction Cartesian coordinates with origin at center of jet exit plane phase angle density of jet fluid density of crossflow viscosity of jet fluid viscosity of crossflow

oxide gas which was released from the tube exit. The effects of the jet velocity oscillating amplitude on the penetration height, spread width, and the dispersion characteristics were delineated. 2. Experiments The experiments were conducted in an open-circuit wind tunnel. The dimensions of the test section was 30  30  110 cm. The crossflow was conditioned by using honeycombs and screens mounted in the upstream chamber. A nozzle with a contraction ratio of 9:1 was used to accelerate the flow and further reduce turbulence intensities. The turbulence intensity of the crossflow in the test section was less than 0.25%. Two jet configurations investigated in this research are shown in Fig. 1. Fig. 1a shows the experimental setup of the stack-issued transverse jet. A stainless steel tube with an inner diameter d = 5 mm, an outer diameter D = 6.4 mm, and length L = 510 mm was normally protruded from the nozzle assembly into the test section. The protruding tube height measured from the test section floor was 160 mm. This tube-issued jet was located 220 mm downstream from the end of the wind tunnel contraction. Positions are described in terms of a rectangular coordinate system (x, y, z), as shown in Fig. 1a. The origin of the coordinate system is centered at the exit plane of the tube. In order to control the velocity profile at the inlet of the tube and in order to avoid generation of recirculation flows, the stack tube was adapted to a well contoured nozzle instead of a chamber. The contour of the nozzle (with a length of 300 mm and a contraction ratio of 900) was formed by a fifth-order polynomial contraction. This nozzle made the velocity profile at the inlet of the stack tube to approximate a ‘‘top hat’’; it also streamed the flow to eliminate vortex or recirculation which may induce acoustic emission. The cavity volume of the nozzle was 2.027  103 m3. As the tube was adapted to the nozzle, the velocity profile near the jet exit at z/d = 0.4 was measured by using a laser Doppler velocimeter, as shown in Fig. 2. The exit velocity within the range of x/d = 0.3 presents approximately a ‘‘top hat’’ profile. Since the flow evolved in the tube for 510 mm length after leaving the exit of the nozzle, the velocity profile outside the core region was influenced by the growth of the boundary layer. According to Chen [17] and Blevins [18], in order for the ‘‘entrance length’’ of the boundary layers that merge at the centerline of the tube to be fully developed, it should be about 122d for a Reynolds number smaller than 2000. Since the tube length that was used in the present study was 32d, which was much shorter than the critical tube entrance length, only the flow in the outer region near the

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Fig. 1. Experimental setup: (a) stack-issued transverse jet, (b) wall-issued transverse jet.

Fig. 2. Near exit velocity profile measured at z/d = 0.4 in the median plane (y = 0).

tube exit of the cross-section was influenced by the boundary layer. Hence, the core region remained a ‘‘top hat.’’ Upstream of the nozzle assembly was a plenum on which was mounted a loudspeaker that was used for the acoustical excitation of the jet. The installation of the loudspeaker in the nozzle assembly was termed the ‘‘downstream longitudinal irradiation’’ by Ginevsky et al. [19]. The loudspeaker had a face diameter of 15 cm. The electrical resistance of the voice coil measured at the loudspeaker terminals was 6.6 X. The moving mass of the loudspeaker, which included the voice coil, dust cap, spider, and diaphragm, was 22.07 g. A square wave with a duty cycle of 50%, generated by a function generator and amplified by a power amplifier, was used to drive the loudspeaker. The conditions of acoustic excitation were controlled by driving the loudspeaker with a function generator and a power amplifier. Fig. 1b shows the experimental setup of the wall-issued transverse jet. The tube exit was mounted flush with the top surface of a flat plate. This plate was 30 cm in width, 30 cm in length, and 0.5 cm in thickness. The plate with sharp leading and trailing

edges was placed 160 mm over the floor of the test section to control boundary layer thickness. The jet exit was located 3 cm downstream from the leading edge of the plate. The boundary layer thickness at this location was about 1.5 mm [20]. The average wind velocity (uw) was measured by a Pitot tube associated with a high-precision electronic pressure transducer. The crossflow Reynolds number (Rew = uwD/mw) was based on the outer diameter of the tube and crossflow velocity. A calibrated rotameter was used to measure the flow rate of the jet. The average exit velocity of the jet (uj) was subsequently calculated by dividing the flow rate by the cross-section area of tube at the jet exit. The jet Reynolds number (Rej = ujd/mj), based on the inner diameter of the tube and the average exit velocity of the jet, was fixed at 2000. The jet-to-crossflow momentum flux ratio was defined by R ¼ qj u2j =qw u2w , where qj and qw are the densities of jet and crossflow, respectively. A one-component hot-wire anemometer was used to measure the velocities of the jet at the tube exit under the zero-crossflow condition. The hot-wire probe was TSI 1210-T1.5. The output signals of the hot-wire anemometer were transferred to a high-speed PC-based data acquisition system to analyze the jet velocity pulsations. A sound analyzer (Model 1358, TES Corp.) was used to measure the sound-pressure-level (SPL). The microphone was calibrated by a standard acoustic calibrator at the calibration frequency f = 1 kHz and calibration sound-pressure-level SPL = 94 dB. The measurement ranges of the SPL, accuracy, and frequency for this sound analyzer meter were 30–130 dB, ±1.5 dB, and A-weighting, respectively. The flow patterns were visualized by Mie scattering technique [21]. The air that was seeded with mineral-oil vapor mist was supplied through the nozzle assembly and issued into the transverse airstream. The laser light sheet generated from a dual-head diode-pumped Nd:YLF (Neodymium Doped Yttrium Lithium Fluorides) laser was used to illuminate the oil-mist particles on the median plane of the flow field. The wavelength of the light beams emitted from the laser head was 527 nm. The maximum pulse rate was 10,000 pulses per second. By using a set of optics, the laser beam was bundled in a planar laser sheet with a thickness of about 0.5 mm. The laser-light sheet was aligned vertically from a transparent glass-window on the top of the wind-tunnel test section’s ceiling so that the particles in the flowfield’s symmetry plane could

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be illuminated. Two digital cameras were used to record the flow visualization images. One high-speed digital camera (Model Xstream Version™ XS-4, IDT Inc.) was used to record instantaneous flow patterns. The camera had an array of CMOS sensor of monochrome 512  512 active pixels and had the ability to record up to 5145 frames per second at full resolution. The spatial resolution of the instantaneous flow images was 0.022 mm/pixel. The other digital camera (Model EOS 450D, Canon Inc.) was used to record long-exposure flow images. The camera had a CMOS sensor with a maximum resolution of 4272  2848 pixels. The spatial resolution of long-exposure flow images was 0.076 mm/pixel. The dispersion and mixing of the elevated transverse jet was characterized by the tracer-gas concentration detection technique. The carbon monoxide gas was used as the tracer gas. A gas mixture containing 10% carbon monoxide and 90% nitrogen was provided as the jet fluid. The properties of the mixture, such as its molecular weight, density, viscosity, and diffusivity, at 1 atm and 20 °C are, close to the properties of air. By considering the response to the acoustic excitation at resonance frequency, the jet flow supplied by the carbon monoxide/nitrogen mixture was similar to air. The carbon monoxide gas was detected by a non-dispersive infrared analyzer (Model 880A, Rosemount Inc.). The detectable range was from 0% to 4.74% and the uncertainty was within 1% of the full-scale reading. An L-shaped stainless probe with an outer diameter of 3 mm and inner diameter of 2.6 mm was used to sample the tracer gas. Before performing the concentration detection, the isokinetic situation of the flow field was confirmed by the flow visualization method. The optimized suction flow rate was 500 cm3/min.

3. Results and discussion 3.1. Jet pulsations at tube exit A microphone placed at (x/d, y/d, z/d) = (0, 10, 0) was used to measure the SPL. The jet Reynolds number Rej was fixed at 2000 and the excitation frequency fexc varied from 60 to 1000 Hz. The measurements were made over a range of excitation voltages (Eexc) from 5 to 15 V. The variations of SPL with excitation frequency are shown in Fig. 3a. Larger excitation voltage induces higher SPL. The SPL increases by increasing the excitation frequency fexc. Fig. 3b shows the jet pulsation amplitude (the root-mean-square value of the jet velocity pulsation) under a zero-crossflow condition, u0j0 , measured at the near exit location (x/d, y/d, z/d) = (0, 0, 0.6) by using the single-component hotwire anemometer. The jet pulsation amplitude u0j0 varies with the excitation frequency. The responses of u0j0 at various excitation voltages behave similarly. Strong peaks of u0j0 appear at fexc = 270 Hz for all applied excitation voltages. The large peak values existing in the acoustically pulsed jet shown in Fig. 3b do not appear in the SPL shown in Fig. 3a. The pulsating sound waves induce resonance of the jet velocity at the specific excitation frequency fexc = 270 Hz under the present chamber geometry, but the sound-pressure-level is not affected as the jet fluids are subject to resonance excitation. For a tube where a sound-emitting source was located at one end, the maximum sound pressure radiation obtained at the other open end at specific harmonic frequencies are dependent on the tube length [22]. In the present case, since the nozzle assembly (including the nozzle and tube) was modeled as a tube, the resonance frequency which was calculated by using the theoretical formula of Kinsler and Frey [22] was 211 Hz, 22% lower than the experimental result of 270 Hz. Since the nozzle was modeled as a tube in estimating the theoretical resonance frequency, the difference was expected because the cross-section of the nozzle assembly was not really a constant. The theoretical results could be corrected

Fig. 3. Response characteristics of pulsed jet at zero-crossflow condition. Rej = 2000. (a) Sound-pressure-level, (b) amplitude of jet velocity pulsation.

by a factor of about 1.28, a value which was induced by the differences of volume and shape between the nozzle and the tube, to approximate the experimental value. Changing the apparatus geometry, certainly, will change the resonance frequency for the jet velocity. Fig. 4a shows the variations of jet pulsation amplitude u0j0 with the excitation voltage Eexc at various excitation frequencies. The jet pulsation amplitude at the resonance frequency fexc = 270 Hz presents significantly higher values than those at the off-resonance situation. A resonance Strouhal number, Stres (Stres = fres d/u0j0 , where fres is the resonance frequency), that is based on the resonance frequency 270 Hz and the jet pulsation amplitude u0j0 is introduced here in order to discuss the influence of resonance amplitude on the pulsed jet in crossflow. The jet pulsation intensity, u0j0 /uj, decreases quickly with the increase of the resonance Strouhal number Stres, as shown in Fig. 4b. At Stres = 0.22, u0j0 /uj attains about 1.0, while at Stres = 0.56, u0j0 /uj decreases significantly to a low value of about 0.4. The excitation signals at the output port of the function generator are square waves. After being coupled with the loudspeaker, the cyclic waveforms become distorted. Fig. 5a shows the distorted

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Fig. 5. Variations of excitation voltage and pulsation jet velocity at zero-crossflow condition. Rej = 2000. (a) Acoustical excitation signal, (b) jet velocity oscillation at tube exit.

Fig. 4. Jet pulsation characteristics at zero-crossflow condition. Rej = 2000. (a) Pulsation amplitudes, (b) pulsation intensities at resonance conditions.

waveforms, measured at the input terminals of the loudspeaker, as a function of the phase angle a at various resonance Strouhal numbers Stres. The oscillation amplitudes of the excitation signals decrease with increasing Stres. The responses of the jet velocities to the cyclic excitation signals are shown in Fig. 5b. The jet velocity oscillations look like distorted sinusoidal waves, and have a phase lag of about 45° behind the electronic excitation signals. Excitation signals of sinusoidal and triangular waves were ever tested by the authors. As the sinusoidal or triangular wave was applied, the jet velocity waveforms behaved similarly to Fig. 5b. However, the amplitude of the jet velocity pulsations became smaller than the amplitude of those excited by the square wave excitation signal. In order to demonstrate a more prominent case, the square wave excitation signal was employed in this study. 3.2. Flow patterns Fig. 6 shows the typical instantaneous flow patterns in the median plane of the non-excited stack-issued and wall-issued transverse jets. The jet issued from the tube tip is bent by the

crossflow. In Fig. 6a, the jet-type vortices travel on the upwind side shear-layer of the deflected jet. The jet-type vortices shown in Fig. 6a are not stable—they appear occasionally and disappear at other times, as shown in Fig. 6b. This behavior is consistent with the observations of Huang and Lan [7] for the range of jet-to-crossflow momentum flux ratio R > 1. Fig. 6c and d shows the flow instantaneous visualization pictures of the wall-issued transverse jet. The experimental conditions are the same as those of the elevated transverse jet shown in Fig. 6a and b. The up-wind side shear-layer of the wall-issued transverse jet exhibits intermittent appearance of coherent structures which are similar to those observed in the stack-issued transverse jet. However, the shear-layer vortices evolving in the upwind side shear-layer of the deflected wall-issued transverse jet shown in Fig. 6c are not as coherent as those observed in the stack-issued transverse jet shown in Fig. 6a. Besides, when the shear-layer coherent structure appears, the stack-issued transverse jet presents much higher frequency of the traveling vortices than the wall-issued transverse jet does. The above characteristic flow behavior for the wall-issued transverse jet has been observed by Fric and Roshko [3] as well. Fig. 7 shows the streak instantaneous flow patterns (i.e., the temporal evolution processes) in the median plane of the excited transverse jets as the acoustic excitation is applied at the resonance Strouhal number Stres = 0.28. The evolution process of the excited stack-issued transverse jet is shown in Fig. 7a–d. At the beginning of the excitation cycle (a = 0°), as shown in Fig. 7a, the

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Fig. 6. Instantaneous flow patterns in median plane of non-excited stake-issued and wall-issued transverse jets. R = 1.4, Rej = 2000. Exposure time: 1/10000 s. (a and c) Shear layer vortices traveling in upwind shear layer, (b and d) shear layer vortices vanish.

jet velocity at the exit of the elevated tube starts to increase from the lowest velocity level (as has been shown in Fig. 5b). The exit jet column, therefore, starts to tilt upstream because of the increase in the instantaneous jet-to-crossflow momentum flux ratio [6]. At the excitation phase angle a = 90°, as shown in Fig. 7b, a ‘‘leading vortex ring’’, as indicated by the arrowhead, is formed in the upwind shear layer of the tilting exit jet column. At the excitation phase angle a = 180°, as shown in Fig. 7c, the leading vortex ring deforms, enlarges, becomes less coherent, and travels downstream with a vortex chain trailing behind. The exit jet column tilts up at its most upstream posture. At the excitation phase angle a = 270°, as shown in Fig. 7d, the leading vortex ring travels further downstream and becomes a ‘‘puff’’ due to the effects of entrainment and turbulent diffusion. The exit jet column tilts downstream because the jet exit velocity at a = 270° decreases from its maximum at a = 180°. This process of initiation of leading vortex ring near the jet exit and evolving to turbulent puff in the downstream area repeats periodically and therefore makes the scenarios in Fig. 7a–d occupied by series of puffs. The swinging motion of the jet column near the tube exit produces the up/down oscillating motion of the deflected jet in the crossflow. The frequencies of the puff generation and the oscillation of the deflected jet estimated by observing the video images are the same as the resonance frequency. Johari et al. [23] and Gharib et al. [24] have observed a phenomenon of ‘‘leading vortex ring’’ or ‘‘starting vortex ring’’ when they studied the impulsively started free jet. A starting vortex ring appears near the jet exit at the beginning period of the jet injection. The starting vortex ring evolves subsequently to the downstream area and is ‘‘followed’’ by a series of upstream vortices which are created during the jet evolution process. When studying the excited wall-issued transverse jet, Johari et al. [11], Eroglu and Breidenthal [12], Johari [13], and M’Closkey et al. [14] revealed three distinct characteristic flow modes (i.e., distinct vortex ring, vortical structures with trailing column, and turbulent puffs) of the shear-layer coherent structures and used the definition of the stroke length L for a pulse of temporal width s through a nozzle of area A to characterize the pulsation characteristics by employing the ‘‘leading vortex ring’’ observation. The evolution process of the excited wall-issued transverse jet are shown in Fig. 7e–h. The formation mechanism of the puffs in

the excited wall-issued transverse jet is the same as that observed in the excited stack-issued transverse jet—a leading vortex ring appears near the jet exit and evolves subsequently to puff in the downstream area of the up-wind side shear layer. However, at the same phase angle, the leading vortex ring in the excited wallissued transverse jet appears at an elevation lower than that of the excited stack-issued transverse jet. Besides, the sizes of the puffs in the excited wall-issued transverse jet are apparently smaller than those of the excited stack-issued transverse jet. The effect of duty cycles on the flow behavior of the excited transverse jet was preliminarily studied. Referring to the investigation of Hermanson et al. [10], jet penetration increased significantly by decreasing the duty cycle. The vortical structures in the shear layer of the transverse jet changed by varying the duty cycle. A larger duty cycle (50%) produced puff-like structures, while a smaller duty cycle (17%) produced ring-like structures. Fig. 8 shows the flow patterns of the transverse jet excited by the square waves with various duty cycles at fexc = 270 Hz and Eexc = 10 V. It was found that jet penetration was not remarkably increased by decreasing the duty cycle. As the transverse jet was excited at various duty cycles, the puff structures appeared in the shear layer of the transverse jet. The pulsed transverse jet at the excitation condition of 50% duty cycle had deeper jet penetration and larger puff structures when compared to the other duty cycles. The puffs indicated intense interaction between the jet and the crossflow. Since the large puff flow structures exhibited better mixing and dispersion than the small ones, the 50% duty cycle was therefore applied in this study. Fig. 9 shows that the height of the leading vortex ring varies with resonance Strouhal numbers at different excitation phase angles. A low resonance Strouhal number that results from a large jet pulsation amplitude generates the tallness of a leading vortex ring within the excitation cycle. The height of the leading vortex ring is short at a high-resonance Strouhal number because the jet pulsation amplitude at high-resonance Strouhal number is low (as shown in Fig. 4b). At the same phase angle, the height of the leading vortex ring of the excited stack-issued transverse jet is larger than that of the excited wall-issued transverse jet. Typical instantaneous flow patterns in the horizontal plane at z/d = 3 are shown in Fig. 10. The flow pattern of the non-excited

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Fig. 7. Temporal evolution processes of excited transverse jets in median plane. R = 1.4, Rej = 2000, Stres = 0.28. Exposure time: 1/10000 s. (a–d) Excited stack-issued transverse jet, (e–h) excited wall-issued transverse jet.

transverse jet, as shown in Fig. 10a, revealed that jet-type vortices appear at x/d = 2. As the vortices move toward the downstream area, the vortices enlarge and become less coherent due to the effect of entrainment. Therefore, the penetration in the downstream area is larger than that in the near-tube area. The flow pattern of the pulsed transverse jet at Stres = 0.28 is shown in Fig. 10b. Because the puff structure induces intense interaction between the jet and the crossflow, the jet flow leaving the elevated tube immediately penetrates into the crossflow in the near field. The pulsed transverse jet thus spreads laterally earlier and wider in a spanwise direction (y-direction) than the non-excited transverse jet. 3.3. Jet penetration and spread The long-exposure images for the stack-issued and wall-issued transverse jets at no excitation and at resonance Strouhal number Stres = 0.28 are shown in Fig. 11. The white area in the image indicates the mixture of smoke jet flow and crossflow. For the stack-issued transverse jet, the smoke spreads to the area below the horizontal level across the tube tip, as shown in Fig. 11a and c. While in the case of the wall-issued transverse jet, as shown in Fig. 11b and d, the smoke dispersion cannot attain the levels lower

than the jet exit plane due to the blockage of the wall. The penetration height and spread width of the excited stack-issued transverse jet (Fig. 11c) are larger than those of the non-excited case (Fig. 11a). The penetration height and spread width of the excited stack-issued transverse jet shown in Fig. 11c are significantly larger than those of the excited wall-issued transverse jets shown in Fig. 11d. In order to quantify the penetration and spread characteristics of the transverse jet, an image processing method called edgedetection technique [25] was utilized to identify the upper and lower boundaries of the deflected jet from long-exposure images. With the digitized locations of jet boundaries, the penetration height and spread width of the elevated transverse jet were determined. The long-term average values of the upper and lower boundaries were calculated because the upper and lower boundaries of the transverse jet varied slightly with time. The exposure time for each image was 2 s. In total, 20 images were used for analysis. By analyzing the gray level distribution of the long-exposure images, the critical gray level (about 60) of the smoke boundaries was determined to be where the gradient of the gray level in the grayscale images changed abruptly. The grayscale image was transformed to a binary image by a thresholding operation. For

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Fig. 8. Instantaneous flow patterns of elevated transverse jet excited at various duty cycles. R = 1.4, Rej = 2000, fexc = 270 Hz, Eexc = 10 V. Exposure time: 1/10000 s.

Fig. 10. Instantaneous flow patterns of elevated transverse jet in horizontal plane at z/d = 3. R = 1.4, Rej = 2000 (a) non-excited, (b) excited, Stres = 0.28. Exposure time: 1/ 10000 s. Fig. 9. Height of leading vortex ring. R = 1.4, Rej = 2000.

the long-exposure time image, all the pixels whose gray-level values were greater than or equal to the critical gray level became foreground pixels, and all the rest became background pixels. Typically, a foreground pixel was given a value of ‘‘1’’ while a background pixel was given a value of ‘‘0’’. After the upper and lower edges of the transverse jet were identified, the penetration heights and spread widths were calculated by counting the foreground pixels. The data taken from 20 long-exposure images were averaged to obtain final results because the average values converged to almost a constant when the image number used as an average was more than 15. By considering the uncertainties of the image grabbing de-

vices and image processing algorithms, the uncertainties of the penetration and spread values were estimated as 4% [26]. Fig. 12a shows the normalized penetration height H/d of the stack-issued transverse jet; this normalized penetration height varies with the normalized streamwise distance x/d. The jet penetration height H was measured from the level z = 0 up to the identified upper boundary of the deflected jet. At no excitation condition, as well as Stres = 0.37 and 0.56, the normalized penetration height increases slightly with increasing x/d. At Stres = 0.22, 0.25, and 0.28, H/d increases faster with the increase of x/d. Stres  0.3 seems to be a critical value below which the penetration height could be increased significantly. Reducing the resonance Strouhal number would enhance the jet penetration height; for

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Fig. 11. Long-exposure flow patterns of the transverse jets. R = 1.4, Rej = 2000. Exposure time: 2 s.

Fig. 12. Normalized penetration height. R = 1.4, Rej = 2000.

instance, the penetration height at x/d = 20 increases from 6 to 10.7 as Stres decreases from 0.56 to 0.22. In order to make a comparison between the non-excited and excited transverse jets, the penetration height H of the excited stack-issued transverse jet was normalized by the penetration height Hn of the non-excited stack-issued transverse jet. The results are shown in Fig. 12b. The

penetration heights of the stack-issued transverse jet excited at resonance frequency are drastically greater than the penetration heights of the non-excited stack-issued transverse jet. For instance, the stack-issued transverse jet excited at Stres = 0.22 presents a penetration height of about 230% of penetration height of the non-excited stack-issued transverse jet at x/d = 20. The normalized

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penetration height H/d of the wall-issued transverse jet is shown in Fig. 12c. Obviously forcing the wall-issued transverse jet at resonance condition increases the jet penetration height. The normalized penetration height H/d increases with decreasing resonance Strouhal number. Fig. 12d shows the penetration height H of the excited wall-issued transverse jet normalized by the penetration height Hn of the non-excited wall-issued transverse jet. The penetration heights of the excited wall-issued transverse jet are larger than those of the non-excited wall-issued transverse jet. The penetration height of the excited wall-issued transverse jet may attain values 55% larger than those of the non-excited wall-issued transverse jet as the transverse jet is excited at Stres = 0.22. Comparisons between the stack-issued case (Fig. 12a and b) and the wall-issued case (Fig. 12c and d) show that the stack-issued transverse jet excited at resonance condition produces drastically larger penetration height than the wall-issued transverse jet. Fig. 13 shows the spread width of the stack-issued and wall-issued transverse jets. The jet spread width W is defined as the vertical distance between the identified upper and lower boundaries of the deflected jet. Fig. 13a shows the normalized spread width W/d of the excited stack-issued transverse jet. The normalized spread width increases quickly with increasing axial distance. Forcing the jet at resonance frequency, W/d does not differ drastically at different resonance Strouhal numbers. The normalized spread widths at various resonance Strouhal numbers are significantly larger than the normalized spread widths of the non-excited transverse jet. Comparisons between the excited and non-excited cases of the stack-issued transverse jet are shown in Fig. 13b, in which Wn denotes the spread width of the non-excited transverse jet. At x/d = 8 and 20, the spread width of the stack-issued transverse jet excited at Stres = 0.22 could attain about 142% and 136% respectively of the spread width of the non-excited transverse jet. Fig. 13c and d shows the normalized spread width of the wall-issued transverse jet. Forcing the wall-issued transverse jet

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at resonance conditions increases the spread width of the deflected jet. The spread width of the excited wall-issued transverse jet may present values 55% larger than those of the non-excited wall-issued transverse jet as the wall-issued jet is excited at Stres = 0.22. Comparisons between the stack-issued case (Fig. 13a) and the wall-issued case (Fig. 13c) show that the excited wall-issued transverse jet has a narrower spread width than the excited stack-issued transverse jet because the wall restricts the spread of the deflected jet in the negative z direction. An acoustically excited transverse jet issued from a slightly elevated stack with a height of 3.75 stack inner diameters were investigated by Davitian et al. [16] in a wind tunnel. They studied the variation of the penetration height and spread width with various effective non-dimensional stroke lengths. They found that the pulsed elevated transverse jet at R = 1.3 had the maximum penetration height and spread width, as the elevated transverse jet was characterized by a non-dimensional stroke length of 3.70. The experimental results of Davitian et al. were added to Figs. 12a and 13a for comparison with the present results. Since a non-dimensional stroke length (L/d) instead of the Strouhal number was used by Davitian et al., the present work calculated the values of a non-dimensional stroke length by employing the velocity data measured at the tube tip (Fig. 5b), and listed the calculated values of L/d in Figs. 12 and 13. In Fig. 12a, the normalized penetration height (H/d) of the present results for L/d = 4.33 are significantly larger than that of Davitian et al. for L/d = 3.70. In Fig. 13a, the normalized spread width (W/d) of the present results is larger than that of Davitian et al. for x/d > 12. The stack tube of Davitian et al.’s experiments extruded from the lower wall by a small height of only 3.75d (equivalent to 1.5 cm), while the present study employed a stack tube extruded out of the lower wall by 32d (equivalent to 16 cm). A small extrusion of stack tube may be subject to the restriction of the lower wall and therefore induces smaller penetration and spread.

Fig. 13. Normalized spread width. R = 1.4, Rej = 2000.

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Fig. 15. Carbon monoxide concentration distributions at various axial stages.

3.4. Dispersion

Fig. 14. Normalized penetration height and spread width at various jet-tocrossflow momentum flux ratios. Stres = 0.28, Rej = 2000.

In order to study the effect of the jet-to-crossflow momentum flux ratio on the characteristics of the jet penetration and spread, the normalized penetration height H/d and spread width W/d for the excited stack-issued and wall-issued transverse jets at various jet-to-crossflow momentum flux ratios are shown in Fig. 14. Fig. 14a shows that the penetration height increases with increasing the jet-to-crossflow momentum flux ratio. At low momentum flux ratios, H/d of the excited stack-issued transverse jet is larger than that of the excited wall-issued transverse jet. As the jet-tocrossflow momentum flux ratio is increased to about 10, H/d of the excited stack-issued transverse exhibits similar value to that of the excited wall-issued transverse jet. The restriction of the wall seems not to significantly influence the penetration of the transverse jet at large jet-to-crossflow momentum flux ratios. Fig. 14b shows that the spread width increases with increasing the jet-tocrossflow momentum flux ratio. In the near field (x/d = 4), W/d of the excited stack-issued transverse jet presents values close to those of the excited wall-issued transverse jet. At x/d greater than 4, W/d of the excited stack-issued transverse jet becomes apparently larger than that of the excited wall-issued transverse jet. The smaller the jet-to-crossflow momentum flux ration is, the larger the difference presents.

Fig. 15 shows the typical distributions of the measured carbonmonoxide concentration (CCO) in the median planes of the non-excited and excited stack-issued transverse jets. The tracer gas containing 10% CO in Nitrogen gas was ejected out of the tube tip. Therefore the carbon monoxide concentration at the tube exit should be 10%. All the carbon-monoxide concentration profiles shown in Fig. 15 show that the maximum concentration values are located at the latitudes above the jet-exit plane and, from there, gradually decrease to nulls at the latitudes higher or lower than the levels with the maximum values. The maximum concentration values of the non-excited transverse jet at all streamwise stages are apparently higher than those of the excited transverse jet, particularly within the distance of x/d < 10. As the jet flow goes downstream, the maximum values of the concentration distribution profiles become smaller, and the spread width of CO concentration

Fig. 16. Comparison of jet trajectories.

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turns wider. It is evident that the CO concentrations of the excited transverse jet present much wider distributions in z direction than the CO concentrations of the non-excited transverse jet. The increase in the dispersion effect induced by the excitation is dramatically significant. The jet trajectory was obtained from the locus of maximum CO concentrations. In order to make a meaningful comparison with steady transverse jet, the jet trajectory of the excited stack-issued transverse jet was normalized by the jet trajectory of the non-excited stack-issued transverse jet, as shown in Fig. 16. The parameters zn and Rv were respectively the latitude of the maximum CO concentration of the non-excited transverse jet and the jet-tocrossflow velocity ratio. The results of Johari et al. [11] (which were obtained by locating the maximum scalar concentration of the averaged PLIF images) were compared with the present normalized jet trajectories. Johari et al. performed the experiments on a solenoid-valve excited wall-issued transverse water jet in a water tunnel. It is apparent that the trajectories of the excited wall-issued transverse jet are drastically lower than the trajectories of the excited stack-issued transverse jet. The restriction of the lower wall in the case of the wall-issued jet may be one of the reasons causing the low trajectories. Fig. 17 shows the normalized maximum concentration, Cmax/Co, where Co denotes the concentration of CO at the jet exit. The normalized maximum concentration decreases with increasing streamwise distance. The maximum CO concentrations of the excited transverse jet are lower than the maximum CO concentrations of the non-excited transverse jet. Forcing the elevated transverse jet at the resonance frequency reduces significantly the values of Cmax/Co in the near field. It can be attributed to the up-down oscillation motion of the transverse jet which is brought about by the swinging mechanism of the jet column near the tube exit. Huang and Chang [27] reported that by transforming the momentum of the jet in the jet transport direction to the lateral self-sustained oscillation by a fluidic oscillator, the axial momentum of the jet is quickly dissipated in a short distance. The turbulence intensity and entrainment of the jet are significantly increased. The up-down oscillating motion of the transverse jet induced by the acoustic excitation transforms axial momentum to lateral momentum. The excited transverse jet, therefore, presents drastically larger dispersion properties than the non-excited transverse jet.

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Fig. 18. Carbon monoxide concentration distributions of elevated transverse jet under acoustic excitation at resonance frequency. x/d = 20, R = 1.4, Rej = 2000.

Fig. 19. Variation of maximum carbon monoxide concentration with Stres at x/ d = 20. R = 1.4, Rej = 2000.

Fig. 17. Variation of maximum carbon monoxide concentration with streamwise distance. R = 1.4, Rej = 2000.

The CO concentration distribution profiles at x/d = 20 at various resonance Strouhal numbers are given in Fig. 18. The gradient of the concentration distribution profile decreases when the resonance Strouhal number is reduced. The latitude of the maximum concentration was marked by arrowheads. The locations of the maximum concentrations denote the locus of the jet trajectory. It was found that the jet trajectory penetrates deeply into the crossflow by reducing the resonance Strouhal number. Fig. 19 shows the normalized maximum concentration, Cmax/Cmax,n, where Cmax,n denotes the maximum concentration of the non-excited. The normalized maximum concentration increases abruptly with increasing resonance Strouhal number, for resonance Strouhal number below about 0.3. As the resonance Strouhal number exceeds about 0.3, the normalized maximum concentration increases slowly with increasing resonance Strouhal number. The results reveal that pulsating the transverse jet at low resonance Strouhal numbers

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produces higher mixing and dispersion effects than pulsating at high resonance Strouhal numbers. 4. Conclusions The effects of acoustic excitation on the flow behavior, penetration, and spread of the stack-issued and wall-issued transverse jets were studied experimentally at various resonance Strouhal numbers. The temporal evolution images of the transverse jets excited at the resonance Strouhal numbers showed that the jet column near the tube exit proceeds in a swinging motion with the pulsation of the jet velocity due to the variation of the instantaneous jet-to-crossflow momentum flux ratio. At the beginning of the pulsating cycle, a leading vortex ring is formed in the shear layer of the jet column near the jet exit. The leading vortex ring finally evolves into a large puff and subsequently travels downstream. The formation mechanism of the puff in the excited wall-issued transverse jet is the same as that in the excited stack-issued transverse jet. However, at the same phase angle, the leading vortex ring in the excited wall-issued transverse jet appears at a smaller height when compared with that of the excited stack-issued transverse jet. Besides, the puff size of the excited wall-issued transverse jet is much smaller than that of the excited stack-issued transverse jet. The swinging motion and traveling puffs of the excited transverse jets produce larger penetration height and spread width when compared with those of the non-excited jet. The transverse jet excited at lower resonance Strouhal numbers presented larger penetration height and spread width. The stack-issued transverse jet presents significantly higher jet penetration and wider spread when compared with the wall-issued transverse jet. The dispersion of the jet fluids, quantitatively measured by using the tracer-gas detection method, therefore, presents a drastic improvement in the near field when a transverse jet is excited at resonance Strouhal numbers. Pulsating the transverse jet at low Strouhal numbers produces higher mixing and dispersion effects than pulsating at high Strouhal numbers. References [1] Y. Kamotani, I. Greber, Experiments on a turbulent jet in a crossflow, AIAA Journal 10 (11) (1972) 1425–1429. [2] B.D. Pratte, W.D. Baines, Profiles of the round turbulent jet in a crossflow, Journal of Hydraulics Division ASCE 93 (1967) 53–64.

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