- Email: [email protected]
Effects of crossflow on puff and oscillation modes of a pulsed elevated transverse jet
European Journal of Mechanics B/Fluids 31 (2012) 140–148
Contents lists available at SciVerse ScienceDirect
European Journal of Mechanics B/Fluids journal homepage: www.elsevier.com/locate/ejmflu
Effects of crossflow on puff and oscillation modes of a pulsed elevated transverse jet Ching Min Hsu, Rong Fung Huang ∗ Department of Mechanical Engineering, National Taiwan University of Science and Technology, Taipei 10672, Taiwan, ROC
article
info
Article history: Received 11 November 2010 Received in revised form 30 August 2011 Accepted 1 September 2011 Available online 13 September 2011 Keywords: Jets in crossflow Acoustic excitation Flow structure
abstract The effects of crossflow on the flow behaviour and mixing characteristics of an acoustically excited elevated transverse jet were investigated experimentally in a wind tunnel. The jet was excited at a frequency around the resonance condition by using a loudspeaker. The temporally varying flow structures of the excited elevated transverse jet in the median plane were captured by a high-speed digital camera. Visual penetration height and spread width were obtained by using an image processing method. The measured tracer-gas concentration revealed the dispersion characteristics. Forcing the transverse jet around the resonance frequency induced two distinct characteristic flow modes, puff and up–down oscillation of the deflected jet. A series of puffs travelling in the shear layer of the deflected jet were formed as the crossflow Reynolds number was lower than about 2300. For crossflow Reynolds numbers larger than 2300, large up–down oscillations of the deflected jet were observed. Acoustic excitation also eliminated the downwash effect induced by the shear of the transverse stream. The deflected transverse jet excited in the puff flow mode generated a significantly larger penetration height and spread width when compared with those in the oscillation flow mode and with the un-excited transverse jet. The measured tracer-gas concentration distributions demonstrated that the excited transverse jet has much better mixing and dispersion characteristics than the un-excited transverse jet. Besides, the puff flow mode has better mixing and dispersion characteristics than those in the oscillation flow mode. © 2011 Elsevier Masson SAS. All rights reserved.
1. Introduction A jet deflected in a crossflow, which is commonly referred to as a ‘‘transverse jet’’, has been studied for many years, and is important in various practical engineering applications such as combustion, industrial mixing, injection cooling, and pollution transport. According to the jet configurations, jet-in-crossflow studies were conventionally classified into two categories, wallissued [1–4] and stack-issued [5–7] transverse jets. A wall-issued transverse jet is characterized by three-dimensional flows, which are subject to interactions among the jet, the jet wake, and the wall boundary layer. Flow structures in the stack-issued transverse jet result from interactions among the jet, the jet wake, and the stack wake. A common feature of the time-averaged flow structure of wall-issued and stack-issued transverse jets is a counter-rotating vortex pair appearing in the far field. However, the characteristics of the flow field, the coherent structure along the upwind shear layer of the deflected jet, the trajectory of the deflected jet,
∗ Correspondence to: 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). 0997-7546/$ – see front matter © 2011 Elsevier Masson SAS. All rights reserved. doi:10.1016/j.euromechflu.2011.09.003
and the wake properties of these two cases represent prominent differences. The mixing process of the wall-issued transverse jet can be improved by pulsating the jet flow. Investigators have employed several methods, for instance, a loudspeaker, a piezoelectric actuator, and a solenoid valve, to generate jet velocity oscillation. Recent investigations [8–15] have revealed that the jet oscillation increased the jet penetration and spread when a transverse jet is subjected to some specific excitation conditions of acoustic waves. Vermeulen et al. [8] indicated that acoustic forcing of a jet in crossflow significantly increases the jet spread, penetration, and mixing and decreases the mixing length. The turbulence and penetration data showed that these responses were optimized at a Strouhal number of about 0.22. Gogineni et al. [9] utilized the piezoelectric actuators mounted on the interior walls of a square jet to modulate an air jet in the crossflow. They found that manipulating the upstream and downstream segments of the jet shear layer increased the jet penetration and mixing. A solenoid valve operated by a square wave signal of variable frequency, injection time, and duty cycle was used to pulse the transverse jet in a water tunnel [10–12]. Johari et al. [10] demonstrated that the penetration of a fully modulated jet in the crossflow can be characterized by injection time and duty cycle. A long injection time yielded a moderate increase in the mixing of a fully pulsed jet.
C.M. Hsu, R.F. Huang / European Journal of Mechanics B/Fluids 31 (2012) 140–148
141
Nomenclature Cco Cmax Co D d Eexc f fexc fres H Ipul R Rej Rew St Stexc Stres uj uw uj0 u′j0 W x, y , z
ρj ρw νj νw
carbon monoxide concentration maximum carbon monoxide concentration carbon monoxide concentration at the jet exit outer diameter of the tube, 0.0064 m inner diameter of the tube, 0.005 m root-mean-square value of excitation voltage supplied to the loudspeaker frequency of vortical flow structure (puff or oscillation) acoustic excitation frequency resonance frequency of nozzle/tube/loudspeaker assembly visual penetration height of jet in the z direction jet pulsation intensity (= u′j0 /uj )
jet-to-crossflow momentum flux ratio (= ρj u2j /ρw u2w ) exit Reynolds number of jet (= uj d/νj ) free-stream Reynolds number of crossflow (= uw D/νw ) Strouhal number of vortical flow structure in upper shear layer of bent jet (St = fd/uj ) Strouhal number of acoustic excitation (= fexc d/uj ) Strouhal number based on fres (= fres d/uj ) average exit velocity of the jet free-stream velocity of crossflow velocity at the jet exit under zero-crossflow condition root-mean-square of jet pulsation velocity visual spread width of jet in the z direction cartesian coordinates with origin at the centre of the jet exit plane density of jet fluid density of crossflow viscosity of jet fluid viscosity of crossflow
Eroglu and Breidenthal [11] observed that the pulsed jet consists of a sequence of vortex rings that penetrate deeply into the crossflow. A classification scheme proposed by Johari [12] demarcated the various flow regimes of a pulsed jet depending on the stroke ratio and duty cycle. M’Closkey et al. [13], and Shapiro et al. [14] demonstrated that in some cases, applying forcing frequencies corresponding to sub-harmonics of the upstream shear layer mode for the unforced transverse jet increases the jet penetration. In other scenarios, merely exciting at the optimal pulse width and low excitation frequency yielded the best jet penetration and spread. At jet-to-crossflow velocity ratios smaller than 4, largeamplitude excitation did not produce a significant jet response when compared to that of the unforced jet in crossflow. Davitian et al. [15] forced a transverse jet at an excitation frequency of ten percent of the natural frequency of the unforced transverse jet. They found that the effect of acoustic excitation 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. Although the pulsed wall-issued transverse jet at various pulsating configurations has been studied extensively, investigations of flow behaviour and mixing for the pulsed stack-issued transverse jet are rare. In this study, a flow visualization technique was applied to characterize the effect of crossflow on the vortical flow behaviour of a pulsed stack-issued transverse jet. Penetration height and spread width were measured by an image processing method. Dispersion of the transverse jet was measured by detecting the tracer-gas concentration. The aim of this study was to identify the characteristic flow modes of a transverse jet subjected to
Fig. 1. Experimental setup.
excitation by acoustic waves, and the effects of flow modes on jet mixing and dispersion. 2. Experiments The experiments were conducted in an open-circuit wind tunnel. The test section was 30 × 30 × 110 cm. In order to visualize the flow behaviour in the test section, the lateral walls and ceiling were constructed of glass plates that transmit the laser lights. The crossflow was conditioned using honeycombs and screens mounted in the upstream chamber of the wind tunnel. The turbulence intensity of the crossflow in the test section for Rew from 1800 to 3500 was less than 0.25%. A nozzle with a contraction ratio of 9:1 was utilized to accelerate the flow and to further reduce the turbulence intensity. The turbulence intensity of the jet flow in the experimental range Rej = 800–2000 continuously increases from 0.2% to 2% and no abrupt change was observed. An acoustic excitation device, as shown in Fig. 1, was used to pulse the jet. A stainless steel tube with an inner diameter d = 5 mm, outer diameter D = 6.4 mm, and length L = 510 mm was protruded normally from the nozzle assembly into the test section. The protruding tube height measured from the test-section floor was 160 mm. A loudspeaker installed in the nozzle assembly excited the jet flow. The method for installing the loudspeaker in the nozzle assembly was called ‘‘downstream longitudinal irradiation’’ by Ginevsky et al. [16]. The jet velocity pulsation conditions were controlled by a loudspeaker driven with a function generator and power amplifier. According to the investigations of M’Closkey et al. [13] and Shapiro et al. [14], the square-wave excitation had a better effect on the jet penetration and spread than a sinusoidal excitation. Therefore, the square wave forcing was used in this study to force the transverse jet. The square waves created from the function generator with a duty cycle of 50% was first amplified by a power amplifier, and then transmitted to the loudspeaker.
142
C.M. Hsu, R.F. Huang / European Journal of Mechanics B/Fluids 31 (2012) 140–148
provided as the jet flow. Properties, such as molecular weight, density, viscosity, and diffusivity, of this carbon monoxide/nitrogen mixture at 1 atm and 20 °C were Mmix = 28.01, ρmix = 1.164 kg/m3 , µmix = 1.747 × 10−5 kg/s-m, and Dmix-air = 1.982 × 10−5 m2 /s, respectively; these values were close to those of air (Mair = 28.97, ρair = 1.205 kg/m3 , µair = 1.801 × 10−5 kg/sm, and Dair −air = 1.981 × 10−5 m2 /s). By considering the response to acoustic excitation, the carbon monoxide/nitrogen mixture jet flow was similar to air. The carbon monoxide gas was detected by a non-dispersive infrared analyser (Model 880A, Rosemount Inc.) with a detectable range 0%–4.74% and an uncertainty within 1% of the full-scale reading. An L-shaped stainless steel probe with an outer diameter of 3 mm and inner diameter of 2.6 mm detected the tracer gas. Before concentration detection, the isokinetic status of the flowfield was confirmed by using the flow visualization method for inserting the probe with a suction flow rate of 500 cm3 /min into the test section. The CO concentration values presented in this paper were the mean values of concentration measurement recorded within 2 min. Fig. 2. Velocity histories of jet at the tube exit. fexc = 275 Hz, Rew = 0.
The excitation voltage, Eexc , defined by measuring the root-meansquare value of excitation signals across the loudspeaker terminals, was fixed at 10 V. The excitation frequency, fexc , driving the loudspeaker was 275 Hz. The crossflow velocity (uw ) was measured by a Pitot tube associated with a high-precision electronic pressure transducer. The accuracy of the freestream velocity measurement was affected primarily by the alignment of the Pitot tube and the calibration of the pressure transducer. With the help of an on-line micropressure calibration system and the aforementioned careful alignment of the Pitot tube, the uncertainty in the crossflow velocity was estimated [17] to be as large as 3% of reading. A rotameter calibrated by a micro-pressure calibration system was used to monitor the jet velocity (uj ) with an accuracy of about 1% of the full-scale reading. The crossflow Reynolds number is defined as Rew = uw D/νw , where D is the outer diameter of the tube and νw denotes the kinematic viscosity of the crossflow. The jet Reynolds number is defined as Rej = uj d/νj , where d is the inner diameter of the tube and νj is the kinematic viscosity of the jet fluid. The jet-to-crossflow momentum flux ratio is defined as R = ρj u2j /ρw u2w , where ρj and ρw are the densities of the jet and the crossflow, respectively, which were in the range of 0.1–1.4. The subset in Fig. 1 shows the coordinate system. As no crossflow was applied, the velocity (uj0 ) of the jet flow at the tube exit was measured by using a one-component hot-wire anemometer. Output signals of the hot-wire anemometer were transferred to a high-speed PC-based data acquisition system to analyse the feature of jet velocity pulsation. Flow patterns were visualized using the Mie scattering technique [18]. Air seeded with mineral-oil 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 oilmist particles on the median plane of the flow field. Streak images of the smoke-traced flow patterns on the median plane y = 0 were captured by a high-speed digital CCD camera. The camera had an array of CMOS monochrome sensor with 512 × 512 active pixels. The camera frame rate at full resolution was 5145 fps. The dispersion and mixing of the elevated pulsed transverse jet was characterized using the tracer-gas concentration detection technique. Carbon monoxide gas was used as the tracer gas. A gas mixture containing 10% carbon monoxide and 90% nitrogen was
3. Results and discussion 3.1. Pulsation of the jet velocity A one-component hotwire anemometer placed near the tube exit at (x/d, y/d, z /d) = (0, 0, 0.6) measured the temporal variation of the pulsating jet velocity under the zero-crossflow condition. Measurements were made over a range of 800–2000 of jet Reynolds numbers (Rej ). The resonance frequency of the tube/nozzle/loudspeaker assembly (hereafter simply termed ‘‘resonance frequency’’), which produced the highest jet velocity pulsation amplitude, was observed at 270 Hz. Forcing the jet in the frequency range 265–285 Hz around the resonance frequency fres = 270 Hz, the jet pulsating velocities near the tube exit present drastically large values. A specific acoustic excitation frequency, fexe = 275 Hz, was used in this study. Fig. 2 shows velocity histories of the pulsed jet induced by acoustic excitation at fexc = 275 Hz. Acoustic excitation produces periodic oscillations of the jet velocity uj0 at the tube exit. The maximum and time-averaged jet pulsating velocities increased as the jet Reynolds number Rej increased. For instance, the maximal jet pulsating velocities increase from 10.6 m/s to 13 m/s, the time-averaged jet velocities increase from 4.81 m/s to 5.94 m/s, and the root-mean-square values of the jet pulsation velocities u′j0 increases from 3.93 m/s to 4.81 m/s when Rej increases from 820 to 1200. The jet pulsation intensities Ipul are therefore 82% and 81% for Rej = 820 and 1200, respectively. The frequency of the jet pulsation was 275 Hz which was the same as the excitation frequency. The Strouhal number values of the acoustic excitation Stexc measured 0.54 and 0.37 for Rej = 820 and 1200, respectively. 3.2. Characteristic flow modes Fig. 3 shows the typical instantaneous flow pattern in the median plane of the non-excited transverse jet at R = 0.25, Rew = 2100, Rej = 820. The jet issued from the tube tip is deflected by the crossflow. A vortex ring evolved from the tube tip rotates clockwise. As the vortex travelled downstream, the head of the vortex turns up-right and the outline of the coherent structure looks like an asymmetric ‘‘mushroom’’. The right hand side of the mushroom vortex rotates clockwise, while the left hand side of it rotates counterclockwise. When the mushroom structure is turned over towards the right, only the vortices rotating counterclockwise appear in the shear layer in the downstream area. Additionally, some smoke particles emitted from the tube tip are entrained into the tube wake because of the downwash effect. The flow behaviour
C.M. Hsu, R.F. Huang / European Journal of Mechanics B/Fluids 31 (2012) 140–148
Fig. 3. Instantaneous flow pattern in the median plane of non-excited transverse jet. R = 0.25, Rew = 2100. Exposure time: 1/10 000 s.
of shear-layer vortices is consistent with observations obtained by Huang and Lan [7]. They referred this type of shear-layer vortices as ‘‘backward-rolling vortices’’. The backward-rolling vortices appear in the shear layer as the jet-to-crossflow momentum flux ratio R is 0.15–0.34. Fig. 4 shows the typical instantaneous flow patterns in the median plane of the transverse jet in the crossflow at R = 0.25, Rew = 2100, Rej = 820, and fexc = 275 Hz (Stexc = 0.54, Ipul = 82%). The dimensionless time in the evolution is defined as t ∗ = t /T , where t is the evolving time starting from the beginning of an excitation cycle and T is the period of the acoustic excitation cycle. At the beginning of the jet velocity pulsation (t ∗ = 0), as shown in Fig. 4(a), the exit jet column bends towards the right at a large angle deviating from the tube centreline. The smoke flow near the tube tip is nearly invisible because the instantaneous jet-to-crossflow momentum flux ratio R near the tube exit at the beginning of the cycle is not large [6]. At t ∗ = 0.28, as shown in Fig. 4(b), the jet column issued from the tube tip tilts up because the instantaneous jet velocity is increased by the positive pulsation phase of the acoustic excitation. A leading vortex ring is formed in the upwind shear layer of the tilting exit jet column. At t ∗ = 0.55, as seen in Fig. 4(c), the leading vortex ring enlarges and deforms. At t ∗ = 0.83, as shown in Fig. 4(d), the leading vortex ring travels farther downstream and becomes a ‘‘puff’’ due to entrainment and turbulent diffusion effects. The exit jet column tilts downstream because the instantaneous jet-to-crossflow momentum flux ratio reduces in the negative pulsation phase of the acoustic excitation. This process continues for each excitation cycle and thus a series of puffs appears in the upper part of the deflected jet in the pictures of Fig. 4. As the pulsating jet is deflected in the crossflow, no images of smoke particles emitted from the tube tip are observed near the tube wake. Comparisons between the flow patterns of the acoustically excited case (Fig. 4) with those of the non-excited case (Fig. 3) yield that the acoustic excitation eliminates the downwash effect induced by the shear effect of the transverse stream. This flow behaviour is termed the ‘‘puff mode’’.
143
Fig. 5 shows the typical instantaneous flow patterns in the median plane of the elevated transverse jet at R = 0.25, Rew = 3000, and fexc = 275 Hz (Stexc = 0.37, Ipul = 81%). To keep R constant, the jet Reynolds number is changed with the change of the crossflow Reynolds number. In this situation, Rej is varied to 1200. The jet-to-crossflow momentum flux ratio R and the acoustic excitation frequency fexe are the same as those used in Fig. 4. The only difference is the crossflow Reynolds number Rew . At the beginning of the jet velocity pulsation (t ∗ = 0), as shown in Fig. 5(a), the jet smoke near the tube is nearly invisible. At t ∗ = 0.28, as seen in Fig. 5(b), a vortex ring appears in the upwind shear-layer of the jet column emitted from the elevated tube as the exit jet column tilts up towards the upstream direction. The behaviour of the jet column illustrated in Fig. 5(a) and (b) is similar to that shown in Fig. 4(a) and (b). At t ∗ = 0.55, as shown in Fig. 5(c), the initial vortex enlarges and deforms. This vortex is bent over in the downstream direction. At t ∗ = 0.83, as shown in Fig. 5(d), the exit jet column tilts downstream due to the reduction in the instantaneous jet momentum. The shearlayer vortex travels farther downstream and follows an up/down wavy path. The up/down wavy appearance of the deflected jet can be attributed to the periodical swinging motion of the jet column near the tube exit. The crossflow Reynolds number in the case of Fig. 5 is 3000, which is greater than 2100 of Fig. 4. A large crossflow momentum may have the effect of suppressing the ‘‘over-shoot’’ of the jet. The puff mode appearing in Fig. 4 therefore is hardly observed in Fig. 5. The flow structure like the flow pattern shown in Fig. 5 is termed the ‘‘oscillation mode’’. Fig. 6 shows the flow patterns at excitation conditions out of the range fexc = 265 − 285 Hz. The oscillation mode appears in Fig. 6(a) and shear-layer organized vortices can be observed in Fig. 6(b). The puff flow structure is not observed in the experimental range R = 0.1 − 1.4 because the excitation frequency is not within the range around the resonance frequency. Fig. 7 shows the effect of the crossflow Reynolds number Rew on the characteristic jet flow modes. The symbols, empty and filled circles, in the domain of the jet-to-crossflow momentum flux ratio R vs. the crossflow Reynolds number Rew denote the conditions for the experimental observations (assisted by video recordings). All flows with conditions located in the regime to the left of the narrow band marked by the short slashed lines represent the puff flow pattern, which is similar to those shown in Fig. 4. All flows with conditions located in the regime to the right of the narrow band marked by short slashed lines represent the oscillation flow pattern, which was similar to those shown in Fig. 5. The width of the band indicates the uncertainty in the flow mode identification. The critical crossflow Reynolds number Rew,cri is about 2300. As the crossflow Reynolds number is lower than 2300, the flow structure of the elevated pulsating transverse jet represents the puff mode. As the crossflow Reynolds number is higher than 2300, the flow structure of the elevated pulsating transverse jet shows an up–down oscillation mode. According to the results of the wide-range search conducted in this study, the mode-bifurcation phenomenon occurs only within the range of excitation frequency fexe = 265 − 285 Hz, which is around the resonance frequency of 270 Hz. As discussed in above paragraphs, when the jet is excited around the resonance frequency at crossflow Reynolds number lower than about 2300, the velocity pulsation significantly produces a series of puff flow structures evolving in the upwind shear layer of the deflected jet. As the crossflow Reynolds number is increased to exceed the critical crossflow Reynolds number, the flow behaviour changes from puff flow structures to up–down oscillation in the downstream direction of the deflected jet. The above discussed phenomenon of the puff flow mode appears as two conditions coexist: (1) the excitation frequency must
144
C.M. Hsu, R.F. Huang / European Journal of Mechanics B/Fluids 31 (2012) 140–148
Fig. 4. Temporal evolution of flow patterns (puff mode) in the median plane of pulsed elevated transverse jet. fexc = 275 Hz (Stexc = 0.54 and Ipul = 82%), R = 0.25, Rew = 2100. Exposure time: 1/10 000 s.
Fig. 5. Temporal evolution of flow patterns (oscillation mode) in the median plane of pulsed elevated transverse jet. fexc = 275 Hz (Stexc = 0.37 and Ipul = 81%), R = 0.25, Rew = 3000. Exposure time: 1/10 000 s.
be around the resonance frequency so that the jet pulsation velocity is large and (2) the crossflow Reynolds number must be low enough (Rew < 2300 in this study). Under these two conditions, the pulsating jet can shoot up periodically to a high altitude before it is deflected by the crossflow. If the crossflow Reynolds number is larger than 2300, the pulsating jet cannot attain a high altitude periodically because it is deflected earlier by large crossflow momentum. However, the up-shooting pulsating jet near the jet exit swings back and forth (because the jet-tocrossflow momentum flux ratio varies periodically) and induces an up–down oscillation of the bent jet. The oscillation mode therefore appears. Davitian et al. [15] found that forcing a transverse jet at an acoustic excitation frequency fexc = 88 Hz and for a low jetto-crossflow momentum flux ratio (R = 1.44) would induce little effect on the jet structure, penetration, and spread. The excitation frequency fexc = 88 Hz used in their study was not near the resonance frequency to induce a large enough jet pulsation velocity
and the crossflow Reynolds number (Rew = 2780 based on the outer diameter of tube) was not low enough to allow the jet to soot up periodically to high altitude, the puff flow mode therefore was not observed. The frequencies of the puff and the up–down oscillation flow modes were estimated by counting the number of puffs passing through a fixed position downstream the tube exit or the number of up–down oscillations within a period. An average value exceeding 100 excitation cycles was taken from video images. The frequencies of puffs and up–down oscillations in the deflected jet are the same as the acoustic excitation frequency. The Strouhal number (St = f × d/uj ) based on the frequencies (f ) of puffs and up–down oscillations was calculated to represent the frequency characteristic of the periodical oscillation flow behaviour in the deflected jet. Because the frequency of the puffs and the up–down oscillations in the deflected jet is kept constant (f = 275 Hz), the Strouhal number decreases with increasing jet velocity. In
C.M. Hsu, R.F. Huang / European Journal of Mechanics B/Fluids 31 (2012) 140–148
145
Fig. 8. Variations of Strouhal numbers with crossflow Reynolds number. fexc = 275 Hz.
Fig. 6. Instantaneous flow patterns in the median plane of pulsed elevated transverse jet. R = 0.25, Rew = 2100. Exposure time: 1/10 000 s. Excitation frequency out of near-resonance range 265–285 Hz. (a) fexc = 100 Hz (Stexc = 0.19 and Ipul = 29%), (b) fexc = 500 Hz (Stexc = 0.98 and Ipul = 3%).
Fig. 9. Long-exposure flow patterns of pulsed elevated transverse jet excited at fexc = 275 Hz. (a) Puff flow mode, Rew = 2100 (Stexc = 0.54 and Ipul = 82%), (b) oscillation flow mode, Rew = 3000 (Stexc = 0.37 and Ipul = 81%). R = 0.25. Exposure time: 2 s. Fig. 7. Characteristic flow modes of pulsed elevated transverse jet at fexc = 275 Hz. Symbols (empty and filled circles) denote the conditions based on which the experimental observations were performed.
this study, the increase in the jet velocity was produced by two situations: (1) increasing R at a fixed Rew , (2) increasing Rew at a fixed R. Fig. 8 shows the variations of the Strouhal number with the crossflow Reynolds number at various jet-to-crossflow momentum flux ratios. At a fixed Rew , larger R induces smaller St. The Strouhal number decreases with increasing crossflow Reynolds number. The Strouhal numbers in the puff flow mode are higher than those in the oscillation flow mode.
3.3. Jet penetration and spread Fig. 9 shows long-exposure images of the acoustically excited elevated transverse jet at puff and oscillation flow modes. The white colour in the images indicates the mixing area of the jet and the crossflow. The puff mode (Fig. 9(a)) has a significantly larger penetration and spread than the up–down oscillation mode (Fig. 9(b)). To quantify the penetration and spread characteristics, an image processing method, the edge detection technique [19], was utilized to identify the upper and lower boundaries of the deflected
146
C.M. Hsu, R.F. Huang / European Journal of Mechanics B/Fluids 31 (2012) 140–148
jet. The vertical distance measured from the level z = 0 to the upper boundary of the deflected jet was defined as the penetration height H, and the vertical distance between the upper and lower boundaries was called the spread width W . The variations of the penetration height H and spread width W normalized by the inner diameter d of the elevated tube with crossflow Reynolds numbers are shown in Fig. 10 for various jet-to-crossflow momentum flux ratios R. At the same Rew , larger R values induce larger H /d and spread width W /d. Both the normalized penetration height H /d and the spread width W /d decrease with increasing the crossflow Reynolds number Rew . As the flow mode changes from ‘‘puff’’ to ‘‘oscillation’’, both H /d and W /d decrease abruptly. The puff flow mode has a higher penetration and a wider spread than oscillation flow mode. For example, for the puff flow mode characterized at R = 0.25 and Rew = 2100, the normalized penetration height H /d and spread width W /d are 6.2 and 7.2, respectively. For the oscillation flow mode characterized at R = 0.25 and Rew = 3000, the normalized penetration height H /d and spread width W /d are 3 and 4.5, respectively. The decrease of the penetration height and spread width are about 52% and 38%, respectively, when the crossflow Reynolds number Rew increases from 2100 to 3000 while the jet-to-crossflow momentum flux ratio R remains at 0.25. For the case of the non-excited jet the H /d and W /d values are marked with filled circles. The acoustic excitation has a higher penetration than without excitation. The puff flow mode has a wider spread width than the non-excited transverse jet, while the oscillation flow mode has a smaller spread width than the nonexcited transverse jet. 3.4. Dispersion The dispersion characteristics were examined by performing tracer-gas concentration measurements. Since the mixture ejected from the tube tip contains 10% carbon monoxide and 90% nitrogen gases, the carbon monoxide concentration (CCO ) at the tube exit should be 10%. Fig. 11 shows typical distribution profiles of the measured carbon monoxide concentration (CCO ) measured in the median planes of the non-excited and excited transverse jets at the streamwise stage of x/d = 2. The non-excited transverse jet has a much steeper CO concentration distribution profile than the excited transverse jet. By forcing the jet at fexc = 275 Hz, the maximum CO concentration (Cmax ) marked by the arrow decreases from 2.82% to 1.06%, and the altitude of Cmax rises from z /d = 0.66 to z /d = 2.0. Thus, acoustic excitation enhances the jet spread and penetration. Carbon monoxide in the non-excited transverse jet was detected behind the elevated tube, because the jet ejected from the tube tip was entrained into the wake near the tube tip by the downwash effect, as previously mentioned for the discussion of Fig. 3. However, the carbon monoxide concentration measured in the wake near the tube tip of the acoustically excited case in Fig. 11 exhibits small values. This is because acoustic excitation increases the jet momentum, and therefore the puff flow structure evolved from the elevated tube is strong enough to sustain the shear effect of the transverse stream. This phenomenon can also be observed in the flow visualization pictures of Figs. 4 and 9. Fig. 12 shows the variations of carbon monoxide concentration distribution profiles with different flow modes at the streamwise stage of x/d = 15. The oscillation flow mode has much higher gradient of CO concentration distribution profiles when compared with the puff flow mode. As the crossflow Reynolds number Rew increases from 1800 to 3500, the normalized altitude (z /d), where Cmax appears, reduces from 4.0 to 0.66. Typically, the location of Cmax depicts the locus of the jet trajectory. The measurement results demonstrate that the jet trajectory in the puff flow mode penetrates more deeply into the crossflow than that in the oscillation flow mode, and the spread width of the
Fig. 10. Normalized penetration height (a) and spread width (b) of pulsed elevated transverse jet at x/d = 15. fexc = 275 Hz.
Fig. 11. Carbon monoxide concentration distributions of non-excited and pulsed transverse jets measured at x/d = 2. R = 0.25, Rew = 2100.
CO concentration in the puff flow mode is wider than that in the oscillation mode. Fig. 13 shows the normalized maximum carbon monoxide concentration Cmax /Co , where Co is the CO concentration at the
C.M. Hsu, R.F. Huang / European Journal of Mechanics B/Fluids 31 (2012) 140–148
147
Fig. 12. Carbon monoxide concentration distributions of pulsed transverse jet measured at x/d = 15. R = 0.25, fexc = 275 Hz.
dominates the change in flow mode from puff to oscillation. A series of puffs travelling in the shear layer of the transverse jet are observed when the crossflow Reynolds number is less than 2300. As the crossflow Reynolds number is increased over 2300, large up–down oscillations exist in the deflected jet. The puffs and oscillations appear in the deflected jet synchronized with the acoustic excitation frequency. The puff flow mode was induced due to the strong instantaneous jet momentum penetrating into the weak crossflow momentum. The oscillation flow mode was induced by the swinging motion of the jet column near the tube exit. The measured penetration height and spread width revealed that the puff flow mode has significantly higher penetration and wider spread than the oscillation flow mode. The acoustic excitation also deactivated the downwash effect induced by the shear of the transverse stream. The tracer-gas concentration distributions revealed that exciting the transverse jet at the puff flow mode would induce better mixing and dispersion characteristics than the oscillation flow mode. Fig. 13. Variation of maximum carbon monoxide concentration at x/d = 15 with crossflow Reynolds number. R = 0.25, fexc = 275 Hz.
tube exit. The normalized maximum CO concentration increases slowly with increasing crossflow Reynolds number Rew in the puff flow mode. As the flow mode becomes oscillatory, Cmax /Co increases abruptly with increasing crossflow Reynolds number Rew . The puff flow mode has a significantly lower normalized maximum CO concentration than that in the oscillation flow mode, because the penetration and spread of the puff flow mode are much larger than those of the oscillation flow mode. 4. Conclusions The effects of crossflow on the flow behaviour (penetration, spread, and dispersion) of an elevated-jet in crossflow subject to acoustic excitation around the resonance frequency were investigated experimentally in a wind tunnel. A jet velocity with sinusoidal oscillation was generated by a loudspeaker driven around the resonance frequency. Forcing the transverse jet at fexc = 275 Hz, the flow can be classified as puff and oscillation flow modes in the domain of the jet-to-crossflow momentum flux ratio and crossflow Reynolds number. The crossflow Reynolds number
Acknowledgement This research was supported by the National Science Council of the Republic of China, under Grant No. NSC 97-2221-E-011-133. 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. [3] T.F. Fric, A. Roshko, Vortical structure in the wake of a transverse jet, Journal of Fluid Mechanics 279 (1994) 1–47. [4] S.H. Smith, M.G. Mungal, Mixing, structure and scaling of the jet in crossflow, Journal of Fluid Mechanics 357 (1998) 83–122. [5] O.S. Eiff, J.F. Keffer, On the structures in the near-wake region of an elevated turbulent jet in a crossflow, Journal of Fluid Mechanics 333 (1997) 161–195. [6] R.F. Huang, R.H. Hsieh, An experimental study of elevated round jets deflected in crosswind, Experimental Thermal and Fluid Science 27 (3) (2002) 77–86. [7] R.F. Huang, J. Lan, Characteristic modes and evolution processes of shear-layer vortices in an elevated transverse jet, Physics of Fluids 17 (3) (2005) 1–13. [8] P.J. Vermeulen, C.-F. Chin, W.K. Yu, Mixing of an acoustically pulsed air jet with a confined crossflow, Journal of Propulsion and Power 6 (6) (1990) 777–783. [9] S. Gogineni, L. Goss, M. Roquemore, Manipulation of a jet in crossflow, Experimental Thermal and Fluid Science 16 (1998) 209–219. [10] H. Johari, M. Pacheco-Tougas, J.C. Hermanson, Penetration and mixing of fully modulated turbulent jets in crossflow, AIAA Journal 37 (7) (1999) 842–850. [11] A. Eroglu, R.E. Breidenthal, Structure, penetration, and mixing of pulsed jets in crossflow, AIAA Journal 39 (3) (2001) 417–423.
148
C.M. Hsu, R.F. Huang / European Journal of Mechanics B/Fluids 31 (2012) 140–148
[12] H. Johari, Scaling of fully pulsed jets in crossflow, AIAA Journal 44 (11) (2006) 2719–2725. [13] R.T. M’Closkey, J.M. King, L. Cortelezzi, A.R. Karagozian, The actively controlled jet in crossflow, Journal of Fluid Mechanics 452 (2002) 325–335. [14] S.R. Shapiro, J.M. King, R.T. M’Closkey, A.R. Karagozian, Optimization of controlled jets in crossflow, AIAA Journal 44 (6) (2006) 1292–1298. [15] J. Davitian, C. Hendrickson, D. Getsinger, R.T. M’Closkey, A.R. Karagozian, Strategic control of transverse jet shear layer instabilities, AIAA Journal 48 (9) (2010) 2145–2156.
[16] A.S. Ginevsky, Y.V. Vlasov, R.K. Karavosov, Acoustic Control of Turbulent Jets, Springer-Verlag, Berlin, 2004. [17] 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 Journal 31 (10) (1993) 1891–1896. [18] R. Mei, Velocity fidelity of flow tracer particles, Experiments in Fluids 22 (1996) 1–13. [19] L.G. Shapiro, G.C. Stockman, Computer Vision, Prentice Hall, Upper Saddle River, New Jersey, 2001.
Contents lists available at SciVerse ScienceDirect
European Journal of Mechanics B/Fluids journal homepage: www.elsevier.com/locate/ejmflu
Effects of crossflow on puff and oscillation modes of a pulsed elevated transverse jet Ching Min Hsu, Rong Fung Huang ∗ Department of Mechanical Engineering, National Taiwan University of Science and Technology, Taipei 10672, Taiwan, ROC
article
info
Article history: Received 11 November 2010 Received in revised form 30 August 2011 Accepted 1 September 2011 Available online 13 September 2011 Keywords: Jets in crossflow Acoustic excitation Flow structure
abstract The effects of crossflow on the flow behaviour and mixing characteristics of an acoustically excited elevated transverse jet were investigated experimentally in a wind tunnel. The jet was excited at a frequency around the resonance condition by using a loudspeaker. The temporally varying flow structures of the excited elevated transverse jet in the median plane were captured by a high-speed digital camera. Visual penetration height and spread width were obtained by using an image processing method. The measured tracer-gas concentration revealed the dispersion characteristics. Forcing the transverse jet around the resonance frequency induced two distinct characteristic flow modes, puff and up–down oscillation of the deflected jet. A series of puffs travelling in the shear layer of the deflected jet were formed as the crossflow Reynolds number was lower than about 2300. For crossflow Reynolds numbers larger than 2300, large up–down oscillations of the deflected jet were observed. Acoustic excitation also eliminated the downwash effect induced by the shear of the transverse stream. The deflected transverse jet excited in the puff flow mode generated a significantly larger penetration height and spread width when compared with those in the oscillation flow mode and with the un-excited transverse jet. The measured tracer-gas concentration distributions demonstrated that the excited transverse jet has much better mixing and dispersion characteristics than the un-excited transverse jet. Besides, the puff flow mode has better mixing and dispersion characteristics than those in the oscillation flow mode. © 2011 Elsevier Masson SAS. All rights reserved.
1. Introduction A jet deflected in a crossflow, which is commonly referred to as a ‘‘transverse jet’’, has been studied for many years, and is important in various practical engineering applications such as combustion, industrial mixing, injection cooling, and pollution transport. According to the jet configurations, jet-in-crossflow studies were conventionally classified into two categories, wallissued [1–4] and stack-issued [5–7] transverse jets. A wall-issued transverse jet is characterized by three-dimensional flows, which are subject to interactions among the jet, the jet wake, and the wall boundary layer. Flow structures in the stack-issued transverse jet result from interactions among the jet, the jet wake, and the stack wake. A common feature of the time-averaged flow structure of wall-issued and stack-issued transverse jets is a counter-rotating vortex pair appearing in the far field. However, the characteristics of the flow field, the coherent structure along the upwind shear layer of the deflected jet, the trajectory of the deflected jet,
∗ Correspondence to: 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). 0997-7546/$ – see front matter © 2011 Elsevier Masson SAS. All rights reserved. doi:10.1016/j.euromechflu.2011.09.003
and the wake properties of these two cases represent prominent differences. The mixing process of the wall-issued transverse jet can be improved by pulsating the jet flow. Investigators have employed several methods, for instance, a loudspeaker, a piezoelectric actuator, and a solenoid valve, to generate jet velocity oscillation. Recent investigations [8–15] have revealed that the jet oscillation increased the jet penetration and spread when a transverse jet is subjected to some specific excitation conditions of acoustic waves. Vermeulen et al. [8] indicated that acoustic forcing of a jet in crossflow significantly increases the jet spread, penetration, and mixing and decreases the mixing length. The turbulence and penetration data showed that these responses were optimized at a Strouhal number of about 0.22. Gogineni et al. [9] utilized the piezoelectric actuators mounted on the interior walls of a square jet to modulate an air jet in the crossflow. They found that manipulating the upstream and downstream segments of the jet shear layer increased the jet penetration and mixing. A solenoid valve operated by a square wave signal of variable frequency, injection time, and duty cycle was used to pulse the transverse jet in a water tunnel [10–12]. Johari et al. [10] demonstrated that the penetration of a fully modulated jet in the crossflow can be characterized by injection time and duty cycle. A long injection time yielded a moderate increase in the mixing of a fully pulsed jet.
C.M. Hsu, R.F. Huang / European Journal of Mechanics B/Fluids 31 (2012) 140–148
141
Nomenclature Cco Cmax Co D d Eexc f fexc fres H Ipul R Rej Rew St Stexc Stres uj uw uj0 u′j0 W x, y , z
ρj ρw νj νw
carbon monoxide concentration maximum carbon monoxide concentration carbon monoxide concentration at the jet exit outer diameter of the tube, 0.0064 m inner diameter of the tube, 0.005 m root-mean-square value of excitation voltage supplied to the loudspeaker frequency of vortical flow structure (puff or oscillation) acoustic excitation frequency resonance frequency of nozzle/tube/loudspeaker assembly visual penetration height of jet in the z direction jet pulsation intensity (= u′j0 /uj )
jet-to-crossflow momentum flux ratio (= ρj u2j /ρw u2w ) exit Reynolds number of jet (= uj d/νj ) free-stream Reynolds number of crossflow (= uw D/νw ) Strouhal number of vortical flow structure in upper shear layer of bent jet (St = fd/uj ) Strouhal number of acoustic excitation (= fexc d/uj ) Strouhal number based on fres (= fres d/uj ) average exit velocity of the jet free-stream velocity of crossflow velocity at the jet exit under zero-crossflow condition root-mean-square of jet pulsation velocity visual spread width of jet in the z direction cartesian coordinates with origin at the centre of the jet exit plane density of jet fluid density of crossflow viscosity of jet fluid viscosity of crossflow
Eroglu and Breidenthal [11] observed that the pulsed jet consists of a sequence of vortex rings that penetrate deeply into the crossflow. A classification scheme proposed by Johari [12] demarcated the various flow regimes of a pulsed jet depending on the stroke ratio and duty cycle. M’Closkey et al. [13], and Shapiro et al. [14] demonstrated that in some cases, applying forcing frequencies corresponding to sub-harmonics of the upstream shear layer mode for the unforced transverse jet increases the jet penetration. In other scenarios, merely exciting at the optimal pulse width and low excitation frequency yielded the best jet penetration and spread. At jet-to-crossflow velocity ratios smaller than 4, largeamplitude excitation did not produce a significant jet response when compared to that of the unforced jet in crossflow. Davitian et al. [15] forced a transverse jet at an excitation frequency of ten percent of the natural frequency of the unforced transverse jet. They found that the effect of acoustic excitation 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. Although the pulsed wall-issued transverse jet at various pulsating configurations has been studied extensively, investigations of flow behaviour and mixing for the pulsed stack-issued transverse jet are rare. In this study, a flow visualization technique was applied to characterize the effect of crossflow on the vortical flow behaviour of a pulsed stack-issued transverse jet. Penetration height and spread width were measured by an image processing method. Dispersion of the transverse jet was measured by detecting the tracer-gas concentration. The aim of this study was to identify the characteristic flow modes of a transverse jet subjected to
Fig. 1. Experimental setup.
excitation by acoustic waves, and the effects of flow modes on jet mixing and dispersion. 2. Experiments The experiments were conducted in an open-circuit wind tunnel. The test section was 30 × 30 × 110 cm. In order to visualize the flow behaviour in the test section, the lateral walls and ceiling were constructed of glass plates that transmit the laser lights. The crossflow was conditioned using honeycombs and screens mounted in the upstream chamber of the wind tunnel. The turbulence intensity of the crossflow in the test section for Rew from 1800 to 3500 was less than 0.25%. A nozzle with a contraction ratio of 9:1 was utilized to accelerate the flow and to further reduce the turbulence intensity. The turbulence intensity of the jet flow in the experimental range Rej = 800–2000 continuously increases from 0.2% to 2% and no abrupt change was observed. An acoustic excitation device, as shown in Fig. 1, was used to pulse the jet. A stainless steel tube with an inner diameter d = 5 mm, outer diameter D = 6.4 mm, and length L = 510 mm was protruded normally from the nozzle assembly into the test section. The protruding tube height measured from the test-section floor was 160 mm. A loudspeaker installed in the nozzle assembly excited the jet flow. The method for installing the loudspeaker in the nozzle assembly was called ‘‘downstream longitudinal irradiation’’ by Ginevsky et al. [16]. The jet velocity pulsation conditions were controlled by a loudspeaker driven with a function generator and power amplifier. According to the investigations of M’Closkey et al. [13] and Shapiro et al. [14], the square-wave excitation had a better effect on the jet penetration and spread than a sinusoidal excitation. Therefore, the square wave forcing was used in this study to force the transverse jet. The square waves created from the function generator with a duty cycle of 50% was first amplified by a power amplifier, and then transmitted to the loudspeaker.
142
C.M. Hsu, R.F. Huang / European Journal of Mechanics B/Fluids 31 (2012) 140–148
provided as the jet flow. Properties, such as molecular weight, density, viscosity, and diffusivity, of this carbon monoxide/nitrogen mixture at 1 atm and 20 °C were Mmix = 28.01, ρmix = 1.164 kg/m3 , µmix = 1.747 × 10−5 kg/s-m, and Dmix-air = 1.982 × 10−5 m2 /s, respectively; these values were close to those of air (Mair = 28.97, ρair = 1.205 kg/m3 , µair = 1.801 × 10−5 kg/sm, and Dair −air = 1.981 × 10−5 m2 /s). By considering the response to acoustic excitation, the carbon monoxide/nitrogen mixture jet flow was similar to air. The carbon monoxide gas was detected by a non-dispersive infrared analyser (Model 880A, Rosemount Inc.) with a detectable range 0%–4.74% and an uncertainty within 1% of the full-scale reading. An L-shaped stainless steel probe with an outer diameter of 3 mm and inner diameter of 2.6 mm detected the tracer gas. Before concentration detection, the isokinetic status of the flowfield was confirmed by using the flow visualization method for inserting the probe with a suction flow rate of 500 cm3 /min into the test section. The CO concentration values presented in this paper were the mean values of concentration measurement recorded within 2 min. Fig. 2. Velocity histories of jet at the tube exit. fexc = 275 Hz, Rew = 0.
The excitation voltage, Eexc , defined by measuring the root-meansquare value of excitation signals across the loudspeaker terminals, was fixed at 10 V. The excitation frequency, fexc , driving the loudspeaker was 275 Hz. The crossflow velocity (uw ) was measured by a Pitot tube associated with a high-precision electronic pressure transducer. The accuracy of the freestream velocity measurement was affected primarily by the alignment of the Pitot tube and the calibration of the pressure transducer. With the help of an on-line micropressure calibration system and the aforementioned careful alignment of the Pitot tube, the uncertainty in the crossflow velocity was estimated [17] to be as large as 3% of reading. A rotameter calibrated by a micro-pressure calibration system was used to monitor the jet velocity (uj ) with an accuracy of about 1% of the full-scale reading. The crossflow Reynolds number is defined as Rew = uw D/νw , where D is the outer diameter of the tube and νw denotes the kinematic viscosity of the crossflow. The jet Reynolds number is defined as Rej = uj d/νj , where d is the inner diameter of the tube and νj is the kinematic viscosity of the jet fluid. The jet-to-crossflow momentum flux ratio is defined as R = ρj u2j /ρw u2w , where ρj and ρw are the densities of the jet and the crossflow, respectively, which were in the range of 0.1–1.4. The subset in Fig. 1 shows the coordinate system. As no crossflow was applied, the velocity (uj0 ) of the jet flow at the tube exit was measured by using a one-component hot-wire anemometer. Output signals of the hot-wire anemometer were transferred to a high-speed PC-based data acquisition system to analyse the feature of jet velocity pulsation. Flow patterns were visualized using the Mie scattering technique [18]. Air seeded with mineral-oil 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 oilmist particles on the median plane of the flow field. Streak images of the smoke-traced flow patterns on the median plane y = 0 were captured by a high-speed digital CCD camera. The camera had an array of CMOS monochrome sensor with 512 × 512 active pixels. The camera frame rate at full resolution was 5145 fps. The dispersion and mixing of the elevated pulsed transverse jet was characterized using the tracer-gas concentration detection technique. Carbon monoxide gas was used as the tracer gas. A gas mixture containing 10% carbon monoxide and 90% nitrogen was
3. Results and discussion 3.1. Pulsation of the jet velocity A one-component hotwire anemometer placed near the tube exit at (x/d, y/d, z /d) = (0, 0, 0.6) measured the temporal variation of the pulsating jet velocity under the zero-crossflow condition. Measurements were made over a range of 800–2000 of jet Reynolds numbers (Rej ). The resonance frequency of the tube/nozzle/loudspeaker assembly (hereafter simply termed ‘‘resonance frequency’’), which produced the highest jet velocity pulsation amplitude, was observed at 270 Hz. Forcing the jet in the frequency range 265–285 Hz around the resonance frequency fres = 270 Hz, the jet pulsating velocities near the tube exit present drastically large values. A specific acoustic excitation frequency, fexe = 275 Hz, was used in this study. Fig. 2 shows velocity histories of the pulsed jet induced by acoustic excitation at fexc = 275 Hz. Acoustic excitation produces periodic oscillations of the jet velocity uj0 at the tube exit. The maximum and time-averaged jet pulsating velocities increased as the jet Reynolds number Rej increased. For instance, the maximal jet pulsating velocities increase from 10.6 m/s to 13 m/s, the time-averaged jet velocities increase from 4.81 m/s to 5.94 m/s, and the root-mean-square values of the jet pulsation velocities u′j0 increases from 3.93 m/s to 4.81 m/s when Rej increases from 820 to 1200. The jet pulsation intensities Ipul are therefore 82% and 81% for Rej = 820 and 1200, respectively. The frequency of the jet pulsation was 275 Hz which was the same as the excitation frequency. The Strouhal number values of the acoustic excitation Stexc measured 0.54 and 0.37 for Rej = 820 and 1200, respectively. 3.2. Characteristic flow modes Fig. 3 shows the typical instantaneous flow pattern in the median plane of the non-excited transverse jet at R = 0.25, Rew = 2100, Rej = 820. The jet issued from the tube tip is deflected by the crossflow. A vortex ring evolved from the tube tip rotates clockwise. As the vortex travelled downstream, the head of the vortex turns up-right and the outline of the coherent structure looks like an asymmetric ‘‘mushroom’’. The right hand side of the mushroom vortex rotates clockwise, while the left hand side of it rotates counterclockwise. When the mushroom structure is turned over towards the right, only the vortices rotating counterclockwise appear in the shear layer in the downstream area. Additionally, some smoke particles emitted from the tube tip are entrained into the tube wake because of the downwash effect. The flow behaviour
C.M. Hsu, R.F. Huang / European Journal of Mechanics B/Fluids 31 (2012) 140–148
Fig. 3. Instantaneous flow pattern in the median plane of non-excited transverse jet. R = 0.25, Rew = 2100. Exposure time: 1/10 000 s.
of shear-layer vortices is consistent with observations obtained by Huang and Lan [7]. They referred this type of shear-layer vortices as ‘‘backward-rolling vortices’’. The backward-rolling vortices appear in the shear layer as the jet-to-crossflow momentum flux ratio R is 0.15–0.34. Fig. 4 shows the typical instantaneous flow patterns in the median plane of the transverse jet in the crossflow at R = 0.25, Rew = 2100, Rej = 820, and fexc = 275 Hz (Stexc = 0.54, Ipul = 82%). The dimensionless time in the evolution is defined as t ∗ = t /T , where t is the evolving time starting from the beginning of an excitation cycle and T is the period of the acoustic excitation cycle. At the beginning of the jet velocity pulsation (t ∗ = 0), as shown in Fig. 4(a), the exit jet column bends towards the right at a large angle deviating from the tube centreline. The smoke flow near the tube tip is nearly invisible because the instantaneous jet-to-crossflow momentum flux ratio R near the tube exit at the beginning of the cycle is not large [6]. At t ∗ = 0.28, as shown in Fig. 4(b), the jet column issued from the tube tip tilts up because the instantaneous jet velocity is increased by the positive pulsation phase of the acoustic excitation. A leading vortex ring is formed in the upwind shear layer of the tilting exit jet column. At t ∗ = 0.55, as seen in Fig. 4(c), the leading vortex ring enlarges and deforms. At t ∗ = 0.83, as shown in Fig. 4(d), the leading vortex ring travels farther downstream and becomes a ‘‘puff’’ due to entrainment and turbulent diffusion effects. The exit jet column tilts downstream because the instantaneous jet-to-crossflow momentum flux ratio reduces in the negative pulsation phase of the acoustic excitation. This process continues for each excitation cycle and thus a series of puffs appears in the upper part of the deflected jet in the pictures of Fig. 4. As the pulsating jet is deflected in the crossflow, no images of smoke particles emitted from the tube tip are observed near the tube wake. Comparisons between the flow patterns of the acoustically excited case (Fig. 4) with those of the non-excited case (Fig. 3) yield that the acoustic excitation eliminates the downwash effect induced by the shear effect of the transverse stream. This flow behaviour is termed the ‘‘puff mode’’.
143
Fig. 5 shows the typical instantaneous flow patterns in the median plane of the elevated transverse jet at R = 0.25, Rew = 3000, and fexc = 275 Hz (Stexc = 0.37, Ipul = 81%). To keep R constant, the jet Reynolds number is changed with the change of the crossflow Reynolds number. In this situation, Rej is varied to 1200. The jet-to-crossflow momentum flux ratio R and the acoustic excitation frequency fexe are the same as those used in Fig. 4. The only difference is the crossflow Reynolds number Rew . At the beginning of the jet velocity pulsation (t ∗ = 0), as shown in Fig. 5(a), the jet smoke near the tube is nearly invisible. At t ∗ = 0.28, as seen in Fig. 5(b), a vortex ring appears in the upwind shear-layer of the jet column emitted from the elevated tube as the exit jet column tilts up towards the upstream direction. The behaviour of the jet column illustrated in Fig. 5(a) and (b) is similar to that shown in Fig. 4(a) and (b). At t ∗ = 0.55, as shown in Fig. 5(c), the initial vortex enlarges and deforms. This vortex is bent over in the downstream direction. At t ∗ = 0.83, as shown in Fig. 5(d), the exit jet column tilts downstream due to the reduction in the instantaneous jet momentum. The shearlayer vortex travels farther downstream and follows an up/down wavy path. The up/down wavy appearance of the deflected jet can be attributed to the periodical swinging motion of the jet column near the tube exit. The crossflow Reynolds number in the case of Fig. 5 is 3000, which is greater than 2100 of Fig. 4. A large crossflow momentum may have the effect of suppressing the ‘‘over-shoot’’ of the jet. The puff mode appearing in Fig. 4 therefore is hardly observed in Fig. 5. The flow structure like the flow pattern shown in Fig. 5 is termed the ‘‘oscillation mode’’. Fig. 6 shows the flow patterns at excitation conditions out of the range fexc = 265 − 285 Hz. The oscillation mode appears in Fig. 6(a) and shear-layer organized vortices can be observed in Fig. 6(b). The puff flow structure is not observed in the experimental range R = 0.1 − 1.4 because the excitation frequency is not within the range around the resonance frequency. Fig. 7 shows the effect of the crossflow Reynolds number Rew on the characteristic jet flow modes. The symbols, empty and filled circles, in the domain of the jet-to-crossflow momentum flux ratio R vs. the crossflow Reynolds number Rew denote the conditions for the experimental observations (assisted by video recordings). All flows with conditions located in the regime to the left of the narrow band marked by the short slashed lines represent the puff flow pattern, which is similar to those shown in Fig. 4. All flows with conditions located in the regime to the right of the narrow band marked by short slashed lines represent the oscillation flow pattern, which was similar to those shown in Fig. 5. The width of the band indicates the uncertainty in the flow mode identification. The critical crossflow Reynolds number Rew,cri is about 2300. As the crossflow Reynolds number is lower than 2300, the flow structure of the elevated pulsating transverse jet represents the puff mode. As the crossflow Reynolds number is higher than 2300, the flow structure of the elevated pulsating transverse jet shows an up–down oscillation mode. According to the results of the wide-range search conducted in this study, the mode-bifurcation phenomenon occurs only within the range of excitation frequency fexe = 265 − 285 Hz, which is around the resonance frequency of 270 Hz. As discussed in above paragraphs, when the jet is excited around the resonance frequency at crossflow Reynolds number lower than about 2300, the velocity pulsation significantly produces a series of puff flow structures evolving in the upwind shear layer of the deflected jet. As the crossflow Reynolds number is increased to exceed the critical crossflow Reynolds number, the flow behaviour changes from puff flow structures to up–down oscillation in the downstream direction of the deflected jet. The above discussed phenomenon of the puff flow mode appears as two conditions coexist: (1) the excitation frequency must
144
C.M. Hsu, R.F. Huang / European Journal of Mechanics B/Fluids 31 (2012) 140–148
Fig. 4. Temporal evolution of flow patterns (puff mode) in the median plane of pulsed elevated transverse jet. fexc = 275 Hz (Stexc = 0.54 and Ipul = 82%), R = 0.25, Rew = 2100. Exposure time: 1/10 000 s.
Fig. 5. Temporal evolution of flow patterns (oscillation mode) in the median plane of pulsed elevated transverse jet. fexc = 275 Hz (Stexc = 0.37 and Ipul = 81%), R = 0.25, Rew = 3000. Exposure time: 1/10 000 s.
be around the resonance frequency so that the jet pulsation velocity is large and (2) the crossflow Reynolds number must be low enough (Rew < 2300 in this study). Under these two conditions, the pulsating jet can shoot up periodically to a high altitude before it is deflected by the crossflow. If the crossflow Reynolds number is larger than 2300, the pulsating jet cannot attain a high altitude periodically because it is deflected earlier by large crossflow momentum. However, the up-shooting pulsating jet near the jet exit swings back and forth (because the jet-tocrossflow momentum flux ratio varies periodically) and induces an up–down oscillation of the bent jet. The oscillation mode therefore appears. Davitian et al. [15] found that forcing a transverse jet at an acoustic excitation frequency fexc = 88 Hz and for a low jetto-crossflow momentum flux ratio (R = 1.44) would induce little effect on the jet structure, penetration, and spread. The excitation frequency fexc = 88 Hz used in their study was not near the resonance frequency to induce a large enough jet pulsation velocity
and the crossflow Reynolds number (Rew = 2780 based on the outer diameter of tube) was not low enough to allow the jet to soot up periodically to high altitude, the puff flow mode therefore was not observed. The frequencies of the puff and the up–down oscillation flow modes were estimated by counting the number of puffs passing through a fixed position downstream the tube exit or the number of up–down oscillations within a period. An average value exceeding 100 excitation cycles was taken from video images. The frequencies of puffs and up–down oscillations in the deflected jet are the same as the acoustic excitation frequency. The Strouhal number (St = f × d/uj ) based on the frequencies (f ) of puffs and up–down oscillations was calculated to represent the frequency characteristic of the periodical oscillation flow behaviour in the deflected jet. Because the frequency of the puffs and the up–down oscillations in the deflected jet is kept constant (f = 275 Hz), the Strouhal number decreases with increasing jet velocity. In
C.M. Hsu, R.F. Huang / European Journal of Mechanics B/Fluids 31 (2012) 140–148
145
Fig. 8. Variations of Strouhal numbers with crossflow Reynolds number. fexc = 275 Hz.
Fig. 6. Instantaneous flow patterns in the median plane of pulsed elevated transverse jet. R = 0.25, Rew = 2100. Exposure time: 1/10 000 s. Excitation frequency out of near-resonance range 265–285 Hz. (a) fexc = 100 Hz (Stexc = 0.19 and Ipul = 29%), (b) fexc = 500 Hz (Stexc = 0.98 and Ipul = 3%).
Fig. 9. Long-exposure flow patterns of pulsed elevated transverse jet excited at fexc = 275 Hz. (a) Puff flow mode, Rew = 2100 (Stexc = 0.54 and Ipul = 82%), (b) oscillation flow mode, Rew = 3000 (Stexc = 0.37 and Ipul = 81%). R = 0.25. Exposure time: 2 s. Fig. 7. Characteristic flow modes of pulsed elevated transverse jet at fexc = 275 Hz. Symbols (empty and filled circles) denote the conditions based on which the experimental observations were performed.
this study, the increase in the jet velocity was produced by two situations: (1) increasing R at a fixed Rew , (2) increasing Rew at a fixed R. Fig. 8 shows the variations of the Strouhal number with the crossflow Reynolds number at various jet-to-crossflow momentum flux ratios. At a fixed Rew , larger R induces smaller St. The Strouhal number decreases with increasing crossflow Reynolds number. The Strouhal numbers in the puff flow mode are higher than those in the oscillation flow mode.
3.3. Jet penetration and spread Fig. 9 shows long-exposure images of the acoustically excited elevated transverse jet at puff and oscillation flow modes. The white colour in the images indicates the mixing area of the jet and the crossflow. The puff mode (Fig. 9(a)) has a significantly larger penetration and spread than the up–down oscillation mode (Fig. 9(b)). To quantify the penetration and spread characteristics, an image processing method, the edge detection technique [19], was utilized to identify the upper and lower boundaries of the deflected
146
C.M. Hsu, R.F. Huang / European Journal of Mechanics B/Fluids 31 (2012) 140–148
jet. The vertical distance measured from the level z = 0 to the upper boundary of the deflected jet was defined as the penetration height H, and the vertical distance between the upper and lower boundaries was called the spread width W . The variations of the penetration height H and spread width W normalized by the inner diameter d of the elevated tube with crossflow Reynolds numbers are shown in Fig. 10 for various jet-to-crossflow momentum flux ratios R. At the same Rew , larger R values induce larger H /d and spread width W /d. Both the normalized penetration height H /d and the spread width W /d decrease with increasing the crossflow Reynolds number Rew . As the flow mode changes from ‘‘puff’’ to ‘‘oscillation’’, both H /d and W /d decrease abruptly. The puff flow mode has a higher penetration and a wider spread than oscillation flow mode. For example, for the puff flow mode characterized at R = 0.25 and Rew = 2100, the normalized penetration height H /d and spread width W /d are 6.2 and 7.2, respectively. For the oscillation flow mode characterized at R = 0.25 and Rew = 3000, the normalized penetration height H /d and spread width W /d are 3 and 4.5, respectively. The decrease of the penetration height and spread width are about 52% and 38%, respectively, when the crossflow Reynolds number Rew increases from 2100 to 3000 while the jet-to-crossflow momentum flux ratio R remains at 0.25. For the case of the non-excited jet the H /d and W /d values are marked with filled circles. The acoustic excitation has a higher penetration than without excitation. The puff flow mode has a wider spread width than the non-excited transverse jet, while the oscillation flow mode has a smaller spread width than the nonexcited transverse jet. 3.4. Dispersion The dispersion characteristics were examined by performing tracer-gas concentration measurements. Since the mixture ejected from the tube tip contains 10% carbon monoxide and 90% nitrogen gases, the carbon monoxide concentration (CCO ) at the tube exit should be 10%. Fig. 11 shows typical distribution profiles of the measured carbon monoxide concentration (CCO ) measured in the median planes of the non-excited and excited transverse jets at the streamwise stage of x/d = 2. The non-excited transverse jet has a much steeper CO concentration distribution profile than the excited transverse jet. By forcing the jet at fexc = 275 Hz, the maximum CO concentration (Cmax ) marked by the arrow decreases from 2.82% to 1.06%, and the altitude of Cmax rises from z /d = 0.66 to z /d = 2.0. Thus, acoustic excitation enhances the jet spread and penetration. Carbon monoxide in the non-excited transverse jet was detected behind the elevated tube, because the jet ejected from the tube tip was entrained into the wake near the tube tip by the downwash effect, as previously mentioned for the discussion of Fig. 3. However, the carbon monoxide concentration measured in the wake near the tube tip of the acoustically excited case in Fig. 11 exhibits small values. This is because acoustic excitation increases the jet momentum, and therefore the puff flow structure evolved from the elevated tube is strong enough to sustain the shear effect of the transverse stream. This phenomenon can also be observed in the flow visualization pictures of Figs. 4 and 9. Fig. 12 shows the variations of carbon monoxide concentration distribution profiles with different flow modes at the streamwise stage of x/d = 15. The oscillation flow mode has much higher gradient of CO concentration distribution profiles when compared with the puff flow mode. As the crossflow Reynolds number Rew increases from 1800 to 3500, the normalized altitude (z /d), where Cmax appears, reduces from 4.0 to 0.66. Typically, the location of Cmax depicts the locus of the jet trajectory. The measurement results demonstrate that the jet trajectory in the puff flow mode penetrates more deeply into the crossflow than that in the oscillation flow mode, and the spread width of the
Fig. 10. Normalized penetration height (a) and spread width (b) of pulsed elevated transverse jet at x/d = 15. fexc = 275 Hz.
Fig. 11. Carbon monoxide concentration distributions of non-excited and pulsed transverse jets measured at x/d = 2. R = 0.25, Rew = 2100.
CO concentration in the puff flow mode is wider than that in the oscillation mode. Fig. 13 shows the normalized maximum carbon monoxide concentration Cmax /Co , where Co is the CO concentration at the
C.M. Hsu, R.F. Huang / European Journal of Mechanics B/Fluids 31 (2012) 140–148
147
Fig. 12. Carbon monoxide concentration distributions of pulsed transverse jet measured at x/d = 15. R = 0.25, fexc = 275 Hz.
dominates the change in flow mode from puff to oscillation. A series of puffs travelling in the shear layer of the transverse jet are observed when the crossflow Reynolds number is less than 2300. As the crossflow Reynolds number is increased over 2300, large up–down oscillations exist in the deflected jet. The puffs and oscillations appear in the deflected jet synchronized with the acoustic excitation frequency. The puff flow mode was induced due to the strong instantaneous jet momentum penetrating into the weak crossflow momentum. The oscillation flow mode was induced by the swinging motion of the jet column near the tube exit. The measured penetration height and spread width revealed that the puff flow mode has significantly higher penetration and wider spread than the oscillation flow mode. The acoustic excitation also deactivated the downwash effect induced by the shear of the transverse stream. The tracer-gas concentration distributions revealed that exciting the transverse jet at the puff flow mode would induce better mixing and dispersion characteristics than the oscillation flow mode. Fig. 13. Variation of maximum carbon monoxide concentration at x/d = 15 with crossflow Reynolds number. R = 0.25, fexc = 275 Hz.
tube exit. The normalized maximum CO concentration increases slowly with increasing crossflow Reynolds number Rew in the puff flow mode. As the flow mode becomes oscillatory, Cmax /Co increases abruptly with increasing crossflow Reynolds number Rew . The puff flow mode has a significantly lower normalized maximum CO concentration than that in the oscillation flow mode, because the penetration and spread of the puff flow mode are much larger than those of the oscillation flow mode. 4. Conclusions The effects of crossflow on the flow behaviour (penetration, spread, and dispersion) of an elevated-jet in crossflow subject to acoustic excitation around the resonance frequency were investigated experimentally in a wind tunnel. A jet velocity with sinusoidal oscillation was generated by a loudspeaker driven around the resonance frequency. Forcing the transverse jet at fexc = 275 Hz, the flow can be classified as puff and oscillation flow modes in the domain of the jet-to-crossflow momentum flux ratio and crossflow Reynolds number. The crossflow Reynolds number
Acknowledgement This research was supported by the National Science Council of the Republic of China, under Grant No. NSC 97-2221-E-011-133. 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. [3] T.F. Fric, A. Roshko, Vortical structure in the wake of a transverse jet, Journal of Fluid Mechanics 279 (1994) 1–47. [4] S.H. Smith, M.G. Mungal, Mixing, structure and scaling of the jet in crossflow, Journal of Fluid Mechanics 357 (1998) 83–122. [5] O.S. Eiff, J.F. Keffer, On the structures in the near-wake region of an elevated turbulent jet in a crossflow, Journal of Fluid Mechanics 333 (1997) 161–195. [6] R.F. Huang, R.H. Hsieh, An experimental study of elevated round jets deflected in crosswind, Experimental Thermal and Fluid Science 27 (3) (2002) 77–86. [7] R.F. Huang, J. Lan, Characteristic modes and evolution processes of shear-layer vortices in an elevated transverse jet, Physics of Fluids 17 (3) (2005) 1–13. [8] P.J. Vermeulen, C.-F. Chin, W.K. Yu, Mixing of an acoustically pulsed air jet with a confined crossflow, Journal of Propulsion and Power 6 (6) (1990) 777–783. [9] S. Gogineni, L. Goss, M. Roquemore, Manipulation of a jet in crossflow, Experimental Thermal and Fluid Science 16 (1998) 209–219. [10] H. Johari, M. Pacheco-Tougas, J.C. Hermanson, Penetration and mixing of fully modulated turbulent jets in crossflow, AIAA Journal 37 (7) (1999) 842–850. [11] A. Eroglu, R.E. Breidenthal, Structure, penetration, and mixing of pulsed jets in crossflow, AIAA Journal 39 (3) (2001) 417–423.
148
C.M. Hsu, R.F. Huang / European Journal of Mechanics B/Fluids 31 (2012) 140–148
[12] H. Johari, Scaling of fully pulsed jets in crossflow, AIAA Journal 44 (11) (2006) 2719–2725. [13] R.T. M’Closkey, J.M. King, L. Cortelezzi, A.R. Karagozian, The actively controlled jet in crossflow, Journal of Fluid Mechanics 452 (2002) 325–335. [14] S.R. Shapiro, J.M. King, R.T. M’Closkey, A.R. Karagozian, Optimization of controlled jets in crossflow, AIAA Journal 44 (6) (2006) 1292–1298. [15] J. Davitian, C. Hendrickson, D. Getsinger, R.T. M’Closkey, A.R. Karagozian, Strategic control of transverse jet shear layer instabilities, AIAA Journal 48 (9) (2010) 2145–2156.
[16] A.S. Ginevsky, Y.V. Vlasov, R.K. Karavosov, Acoustic Control of Turbulent Jets, Springer-Verlag, Berlin, 2004. [17] 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 Journal 31 (10) (1993) 1891–1896. [18] R. Mei, Velocity fidelity of flow tracer particles, Experiments in Fluids 22 (1996) 1–13. [19] L.G. Shapiro, G.C. Stockman, Computer Vision, Prentice Hall, Upper Saddle River, New Jersey, 2001.