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Research Cite this article: Yang H, Zhou Y, So RMC, Liu Y. 2016 Turbulent jet manipulation using two unsteady azimuthally separated radial minijets. Proc. R. Soc. A 472: 20160417. http://dx.doi.org/10.1098/rspa.2016.0417 Received: 5 June 2016 Accepted: 23 June 2016

Subject Areas: fluid mechanics, mechanical engineering, energy Keywords: active jet control, unsteady minijet, flapping jet, asymmetric excitation Author for correspondence: Y. Zhou e-mail: [email protected]

Turbulent jet manipulation using two unsteady azimuthally separated radial minijets H. Yang1,3 , Y. Zhou1,2 , R. M. C. So3 and Y. Liu3 1 Institute for Turbulence-Noise-Vibration Interactions and Control,

Shenzhen Graduate School, Harbin Institute of Technology, Shenzhen, People’s Republic of China 2 Digital Engineering Laboratory of Offshore Equipment, Shenzhen, People’s Republic of China 3 Department of Mechanical Engineering, The Hong Kong Polytechnic University, Kowloon, Hong Kong HY, 0000-0002-1540-1793 The active manipulation of a turbulent round jet is experimentally investigated based on the injection of two radial unsteady minijets, prior to the issue of the main jet. The parametric study is conducted for the mass flow ratio Cm of the minijets to the main jet, and the ratio fe /f0 of the minijet frequency to the preferred-mode frequency of the main jet. It is found that the decay rate of the jet centreline mean velocity could be greatly increased if the two minijets are separated azimuthally by an angle θ = 60◦ , instead of by θ = 180◦ . This increase is a consequence of the flapping motion of the jet column, and the formation process and generation mechanism of this flapping motion are unveiled by careful analysis of the experimental data.

1. Introduction The study of jet control has been of great interest over the past few decades due to a wide range of industrial applications and global environmental problems such as mixing enhancement, noise suppression, chemical reactions, heating or combustion chambers, pollutant dispersal, spraying, and electronic equipment cooling and drying. The rate of jet mixing plays a crucial role in most of these applications. Clearly, this rate is strongly influenced by the coherent structures and

2016 The Author(s) Published by the Royal Society. All rights reserved.

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can be manipulated either passively or actively. Passive control techniques include noncircular nozzles [1,2] or tabs [3], while active control strategies comprise acoustic excitation [4], piezoelectric actuators [5,6], plasma actuators [7], synthetic jets [8] or steady/unsteady jets [9]. Considerable interest has been given to the fluidic means for jet mixing control (e.g. [10,11]). The injection of the steady control jets produces a significant reduction in the potential core and greatly increases entrainment and mixing in a low-speed jet. New & Tay [12] demonstrated that the counter-rotating vortex pairs, generated by the penetration of continuous control jets, contributed to jet mixing enhancement. The steady minijets also have a great effect on the high-speed jet, producing mixing enhancement and noise suppression due to the presence of streamwise vortices, which disrupt the generation of azimuthally large-scale coherent structures [13]. Recently, unsteady injections are becoming popular because they can be more efficient for the manipulation of jet mixing compared with steady injection [14]. The pulsed jets seek to manage not only the large-scale changes via penetration but also the generation and interactions of primary vortex rings via periodic excitation. Given a proper excitation frequency, unsteady perturbations may maximize their effect on the entrainment characteristics of jets [15]. For a low-speed jet, Raman [16] investigated the mixing characteristics of a rectangular jet with the excitation of two unsteady fluidic injections and achieved a 35% reduction in the potential core length and about a 60% increase in the normalized mass flux with respect to the unexcited jet. Zhang [17] studied in detail the active control of a turbulent round jet using two symmetrically arranged radial unsteady minijets, and found a much more efficient control than using steady minijets. Three types of coherent structures were identified, i.e. the distorted vortex ring, two pairs of azimuthally fixed streamwise vortices and sequentially ejected mushroom-like counterrotating structures, and jet entrainment was found to be dictated by the interactions of the three distinct coherent structures. For compressible jets, Ibrahim et al. [18] experimentally manipulated compressible round jets using 12 microjets equally separated along the circumference of the nozzle exit and found a higher spreading rate, in terms of the decay of jet centreline velocity, than steady injection. Asymmetric disturbances are less stable than symmetric ones, due to more complex vortex topologies [1,18], and hence may achieve better jet mixing enhancement. Longmire & Duong [19] introduced the combination of both asymmetric passive technique and axial periodic excitation to manipulate a round jet by attaching a stepped trailing edge and a speaker upstream of the jet plenum. The vortex ring in the jet developed an inclined component and became asymmetrical, resulting in significant enhancement of entrainment and spreading. Pothos & Longmire [20] investigated a turbulent rectangular jet under the asymmetric forcing of a piezoelectric actuator. They found that the periodic forcing at low frequencies developed asymmetric vortical structures, causing a fast decay of the centreline velocity and a high spreading rate. Tamburello & Amitay [21] investigated a turbulent round jet under the asymmetric excitation of a steady minijet, pointing perpendicularly to the main jet, thus effectively accelerating the decay of the centreline streamwise mean velocity, and enhancing spreading and increasing jet width. It is well known that the excitation could be made unsteady to optimize the actuator efficiency (e.g. [22]). Unsteady excitation allows jet penetration and spread to be enhanced under specific conditions [14] and may capitalize not only on large-scale changes through penetration but also on the excitation frequency to manipulate the inherent instabilities of the main jet. Thus, one naturally wonders how jet mixing is enhanced under the asymmetric excitation of unsteady minijets that can provide both asymmetric and periodic excitations. Following the manipulation of a turbulent round jet using two opposing radial minijets by Zhang et al. [23], we have manipulated the same jet using two asymmetrically arranged radial minijets, separated by an angle of θ = 60◦ and 120◦ , respectively. We found that the excitation for the case of θ = 60◦ is more efficient than that for the case of θ = 120◦ and the physical mechanisms behind them are essentially the same. Therefore, this work is focused on the case of θ = 60◦ . One objective is to understand the dependence of the jet decay rate on control parameters, i.e. the mass flow ratio (Cm ) of the minijets to the main jet and the frequency ratio fe /f0 , where fe is the

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Figure 1. Schematic of minijet assembly. excitation frequency of minijets and f0 is the preferred-mode frequency of the main jet. Another objective is to gain insight into the physical mechanism behind possible effective control of the main jet under asymmetric manipulation. The experimental set-up is described in §2. Section 3 presents the dependence of jet decay rate on Cm and fe /f0 , and a comparison of the performance of the asymmetric and symmetric controls. The minijet actuator performance and its effect on the initial condition of the main jet are discussed in §4. The effect of Cm and fe /f0 on the flow structure is investigated in §5, while the evolution of the flow structure is examined in §6, along with a discussion of the physical mechanism behind the effective jet manipulation. The conclusions drawn are presented in §7.

2. Experimental details Experiments on an axisymmetric air jet were performed. The jet facility consists of a main jet with different minijet assemblies, as described by Zhang et al. [23]. The flow rates of the main jet and minijets are adjusted via two separate control valves and measured using two separate flow meters. The air supplied for the main jet passes through a mixing vessel, mixed with seeding particles in the case of flow visualization or particle image velocimetry (PIV) measurements, and a plenum box before entering the main jet chamber. The chamber includes a 300 mm long diffusing section, a cylindrical part of 400 mm in length and a smooth contraction nozzle. The inlet diameter of the contraction section is 114 mm and the exit diameter D is 20 mm, while the profile of the nozzle contraction is given by R = 57 − 47 sin1.5 (90 − 9x /8) following closely the design of Mi et al.’s nozzle [24]. The contraction was extended with a 47 mm long smooth tube of diameter D. The jet Reynolds number ReD based on D is fixed at 8000. The main jet is issued with a ‘top-hat’ mean velocity distribution and a low turbulence intensity of 0.25%. The minijet assembly includes a stationary and a rotating disc (figure 1). The stationary disc is made with two orifices of 0.9 mm in diameter, separated azimuthally by 60◦ degrees, located at 17 mm upstream of the main jet exit. The rotating disc has 12 orifices of 1 mm in diameter and is driven by a servomotor; the orifices are equally separated azimuthally. Once the orifices on both discs are aligned during rotation, two pulsed minijets are injected into the main jet. Two control parameters are examined, i.e. the ratio fe /f0 of the minijet excitation frequency fe to the main jet preferred-mode frequency f0 , and the mass flow ratio Cm of the minijets to the main jet, over a range of fe /f0 = 0.31–1.24 with Cm varying from 1.1% to 10.9%. The origin of the coordinate system is chosen at the centre of the main jet exit, with the x-axis positioned along the streamwise direction. The corresponding cylindrical coordinate system (x, ϕ, r) is defined in figure 1. Measurements were conducted in the symmetry plane, i.e. the (x, y) plane, of the two minijets, the orthogonal plane through the jet geometric centreline, i.e. the (x, z)

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The control performance depends on the mass flow ratio, excitation frequency ratio, number, shapes and geometric arrangement of unsteady minijets [6,9]. In this work, the effect of Cm and fe /f0 on jet entrainment was investigated. The main jet velocity is 6 m s−1 and the preferred-mode frequency is 128 Hz, corresponding to a Strouhal number of StD = f0 D/Ue = 0.43, which falls in the range (0.24–0.64) reported by Gutmark & Ho [25]. Figure 2 presents the dependence of the jet centreline mean velocity decay rate (K) on Cm and fe /f0 , along with that under symmetric control when θ is 180◦ and the injections of two minijets are in-phased, which serves as a reference for comparison. The K variation for these two cases is qualitatively similar. However, the asymmetric control case is significantly more effective in enhancing jet entrainment than the symmetric case; for example, K is increased by 30% at fe /f0 = 1.0 for Cm = 1.6% when compared with the symmetric case (figure 2a). A local K maximum occurs at fe /f0 = 1.0, as noted by others (e.g. [7]). The dependence of K on Cm at fe /f0 = 1.0 (figure 2b) is characterized by a rapid rise in K with initial increase in Cm , reaching a maximum K (0.284) at Cm = 2.0% and then dropping to 0.186 at Cm = 4.2%. A further increase in Cm leads to K rising asymptotically to a constant. This constant is apparently substantially larger for the asymmetric case compared with the symmetric case. The case of Cm = 2.0% and fe /f0 = 1.0 only gives rise to a local maximum K. From the practical application point of view, a manipulation should ideally require the minimum energy consumption [9,26]; in other words, the mass flow of the minijets is required to be as small as possible. With this consideration, a minijet excitation with Cm = 2.0% and fe /f0 = 1 gives the optimal condition. Note that the injection time of the minijets (or disc rotation frequency) is one of the factors that affect the character of the jet in crossflow [27]. For a fixed minijet mass flow rate, the rotation frequency may have an effect on the minijet velocity. As fe /f0 → 0, the injected flow may exhibit a behaviour similar to that of the steady injection. On the other hand, as fe /f0 → ∞, the injection time of each pulse approaches 0 and accordingly the injected mass goes to zero, that is its velocity approaches zero. As such, the minijet velocity depends on how fast the openings in the rotor pass those in the stationary disc, i.e. the opening time of the orifice issuing the minijet. The main jet exit velocity is 6 m s−1 if unexcited; as Cm increases, the main jet exit velocity changes little in the range of Cm tested (not shown). Two factors may contribute to this observation. First, the actual

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3. Dependence of jet decay rate on Cm and fe /f0

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plane, and a number of cross-sectional (y, z) planes using flow visualization, PIV and hotwire techniques. Following Zhou et al. [11], the decay rate K of the jet centreline mean velocity is used to evaluate jet mixing, given by K = (Ue − U5D )/Ue , where Ue and U5D denote the jet centreline time-averaged velocities at x∗ = x/D = 0 and 5, respectively. The streamwise velocity was measured using a single calibrated hotwire probe, operated on a constant temperature circuit (Dantec Streamline) with an overheat ratio of 1.8. The tungsten wire was 5 µm in diameter and approximately 1.5 mm in length. The bridge output voltage signal was offset, amplified and low-pass filtered at a cut-off frequency of 3 kHz before being digitized at a sampling frequency of 6 kHz with a 12-bit A/D converter. The duration for each record was 80 s. The hotwire signal was calibrated based on the streamwise mean velocity measured with a standard static Pitot tube, connected to an electronic micromanometer (Furness FCO510) and placed side by side with the hotwire near the centre of the nozzle exit. Flow visualization and PIV measurements were carried out using a Dantec standard PIV 2100 system. A seeding particle generator (TSI 9307-6) was used to generate smoke, which was mixed with air in the mixing vessel. Smoke-seeded flow was illuminated by a laser sheet generated from two New Wave standard pulsed laser sources of 532 nm in wavelength with a maximum energy output of 120 mJ per pulse. Each laser pulse lasted for 0.01 µs. Instantaneous images were obtained at a sampling rate of 4 Hz using a CCD camera (HiSense MkII, double frames, 2048 × 2048 pixels). A Dantec Flow Map Processor (PIV 2001 type) was used to synchronize illumination and image capturing. The settings of the PIV system are chosen to be the same for both flow visualization and PIV measurements.

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mass flow rate of the minijets injected into the main jet is less than the measured mass flow rate due to a clearance, necessary to allow the rotor to rotate, between the stationary and rotating discs, which implies a flow leakage. This leakage is worse at a large Cm . Second, there is an appreciable increase in the jet width measured at x∗ = 0.05 (not shown) for large Cm .

4. Performance and role of the minijet actuator The minijet actuators can increase the jet decay rate substantially (figure 2). Therefore, it is very important to carefully examine the flow physics in order to explore the minijet actuator performance and its effect, especially at the optimal excitation condition (Cm = 2.0%, fe /f0 = 1.0). In order to study actuator performance, an experiment was carried out by operating one minijet at a mass flow rate and a frequency corresponding to Cm = 0.99% and fe /f0 = 1.0 in the absence of the main jet. A single calibrated hot wire was deployed at x∗ = −0.85 (ϕ = 120◦ and r∗ = r/D = 0.35), where the minijet was injected. The wire is oriented normally to the axis of the minijet orifice. The time history of the radial fluctuating velocity −vr signal (figure 3) shows periodically uniform peaks, thus suggesting the actuator can produce the observed uniform minijet flow. Furthermore, to explore the effect of the minijets on the initial condition of the main jet, two minijets are operated at Cm = 2.0% and fe /f0 = 1.0 in the presence of the main jet. Following Zhou et al. [11], a hotwire probe is placed at x∗ = −0.7 (ϕ = 120◦ and r∗ = 0.35), almost immediately downstream of one of the minijets. Compared with the natural jet (Cm = 0 and fe /f0 = 0), the normalized streamwise velocity u/Ue signal (figure 4a) exhibits significant fluctuations in the excited jet, thus indicating the minijet actuators can produce large amplitude perturbations. This is consistent with the result obtained by Choi et al. [28] in their investigation of a supersonic jet excited with 16 unsteady microjets. The presence of two concave peaks apparently reflects the interaction between two approaching minijets. At θ = 120◦ –180◦ , only one concave peak is observed for each pulse, indicating that the two minijets do not interact appreciably with each other. As θ decreases to 60◦ , the two minijets are more close to each other and more mutually aligned, hence potentially interacting with each other. As a result, the flow structure of the first minijet (located just upstream of the hotwire) may be affected by the presence of the second, thus leading to the appearance of two concave peaks in the hotwire signal. At the extreme case θ = 0◦ , the two minijets merge into one, forming a single high-momentum jet. The corresponding spectrum Eu is shown in figure 4b. There is no obvious peak in the natural jet except that at f ∗ = fD/Ue = 0.17 (f = 50 Hz), which is associated with the noise linked to the power supply. Once excited, Eu exhibits a number of pronounced peaks at f ∗ = 0.43 (fe = 128 Hz) and higher harmonics due to periodic excitation (figure 4b), as previously reported by Raman & Cornelius [26]. Evidently, the unsteady minijet injections can produce velocity fluctuations with large enough amplitude around the required

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Figure 4. (a) Time histories and (b) power spectral density function Eu of u obtained at x ∗ = −0.7 (ϕ = 120◦ and r∗ = 0.35), downstream of one of the minijets.

frequency at the upstream of the main jet exit and the subsequent shear layer issuing from the nozzle. Such periodic velocity fluctuations may accelerate the growth of the shear layer, forming large-scale coherent structures [29]. Therefore, the unsteady minijet excitation may cause the shear layer at the actuator side to roll up into vortices earlier than that in the opposite side of the actuators. To understand the effect of Cm on the initial state of the main jet exit, u∗rms = urms /Ue was measured at x∗ = 0.05 in the natural jet case as well as in the manipulated jet case for various Cm (figure 5). In the natural jet case, the small humps of u∗rms occur at y∗ = y/D ≈ ±0.46, resulting from the instability wave in the initial shear layer. Once the natural jet is manipulated, u∗rms changes substantially. At small Cm (=2.0%), u∗rms does not show any appreciable increase for y∗ < 0 but does for y∗ ≥ 0, apparently as a result of minijet injections. The major characteristics of the jet remain unchanged except for the flow near the actuator side. The hump at y∗ ≈ 0.46 grows, suggesting the fluctuation in the shear layer is amplified, which may account for the rapid growth of the shear layer. Considerable increase in u∗rms along the y-axis with a maximum occurring around the centre is observed once Cm is increased to 4.2%. It could be inferred that the two minijets may have penetrated the jet centre, clashing with each other at the jet exit. The turbulence produced by the collision of two minijets may also account for the increase in u∗rms along the z-axis, especially around the centre (figure 5b). As Cm is increased to 9.3%, u∗rms increases throughout y∗ and z∗ (= z/D), especially for y∗ < 0 (figure 5a) and even z∗ < −0.2 (figure 5b), suggesting that the two minijets may collide with each other even before reaching the nozzle exit. The resultant mixed fluid travels along the negative y-axis, producing a highly turbulent jet right from the beginning.

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Figure 5. Radial distribution of turbulent intensity urms /Ue at x ∗ = 0.05 of the manipulated jet in (a) x–y plane and (b) x–z plane. Another consideration of the minijet actuator is the effect of the rotating disc; it might produce azimuthal velocity to the main jet. Firstly, the rotating disc may have an effect on f0 . Consider the optimal excitation condition ( fe /f0 = 1.0, Cm = 2.0%). Attention is focused on the jet with and without the inner disc rotating at the speed corresponding to fe /f0 = 1.0 and Cm = 0. According to Hussain [30], f0 is defined by the predominant vortex passage frequency near the end of the potential core. It is found that f0 decreases from 143 Hz (StD = 0.48) without the disc rotating to 128 Hz (StD = 0.43) with the disc rotating (not shown). The reason for the frequency decrease could be attributed to the fact that the rotating jet may result in a slight growth of the axial shear layer thickness [31], and the preferred-mode frequency is inversely proportional to the initial shear layer momentum thickness (e.g. [32]). For clarity, f0 is equal to 128 Hz in the natural jet setup, unless otherwise stated. Furthermore, the K value increases from 2.4% to 5.4%. Finally, it is necessary to examine whether centrifugal instability due to swirling effect occurs in the present natural jet/minijet set-up. The PIV-measured azimuthal mean velocity at x∗ = 0.1 is very small, only discernible at r∗ ≈ 0.5 with a maximum value of about 0.06Ue (not shown). This suggests, following the criterion of Oberleithner et al. [31], that the rotation of the inner disc is not strong enough to excite the centrifugal instability that occurs in a swirling jet. In summary, the major characteristics of the natural jet remain largely unchanged with the disc rotating.

5. Effect of Cm and fe /f0 on flow structure From the current experiments on perturbed jets, it can be seen that Cm and fe /f0 have a great effect on the jet decay rate (figure 2). This could be explained from the jet flow structures under the effect of different Cm and fe /f0 . Thus, in this section, the flow structures under typical excitation conditions are examined through the velocity signals and photographs of flow visualization. The evolutions of the hotwire-measured streamwise velocity u signals are shown in figure 6, with and without manipulation. In the natural jet (Cm = 0 and fe /f0 = 0), the signal shows a quasiperiodically sinusoidal wave at x∗ = 2.0, indicating the shear layer rolls up, forming vortices due to Kelvin–Helmholtz instability [32]. Then, the frequency of large events appears to be halved at x∗ = 3.0, probably resulting from vortex pairing [29,33]. Once manipulated, the signals exhibit a dramatic change in characteristics, depending on Cm . A number of observations can be made from the u-signals at three representative Cm in figure 6. Firstly, at Cm = 2.0%, u signals exhibit early sign of periodic fluctuations at given y∗ and z∗ , suggesting an early roll-up of the shear layer. The signals remain smooth or laminar even at x∗ = 2.0, especially along y∗ = −0.3 or z∗ = 0.3. Secondly, given Cm = 9.3%, all the signals, be they from the x–y or x–z plane, appear fluctuating randomly even at x∗ = 0.5, suggesting a turbulent state from the very beginning. This observation is further supported by flow visualization data (figure 7a). Note that larger spreading can be observed in the x–y plane than in the x–z plane, resulting from the more effective entrainment by

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turbulent vortical structures [11]. Thus, this turbulence, boosted by increasing Cm , is responsible for the increasing K with Cm > 4.2% (figure 2b). This mechanism is apparently different from that observed when the jet is excited by a Cm in the range 0 < Cm < 3.5%, which will be discussed in detail later. Finally, at Cm = 4.2%, the signals obtained at y∗ = 0.3 and −0.3 both exhibit the transitional characteristics, though that at z∗ = 0.3 remains smooth or laminar until x∗ = 1.5. This is confirmed by flow visualization data (figure 7b). The laminar vortices can only be seen at x∗ ≈ 1.2 in the x–z plane, while a turbulent state occurs in the x–y plane. The observations are consistent with the distribution of urms at the jet exit (figure 5). The observations at Cm = 2.0% are particularly interesting because of the impressive enhancement of the jet entrainment rate with such a small Cm . One naturally wonders what physical mechanism is responsible for this behaviour. Understanding of this physical behaviour can be gleaned from the flow visualization data presented in figure 7c,d. The shear layer in the natural jet starts to roll up at x∗ ≈ 2 and the vortices formed display symmetry about the centreline (figure 7d) due to the occurrence of the well-known ring vortices. Under the manipulation of Cm = 2.0%, there is a great change in the flow structure (figure 7c(i)(ii)). Firstly, the occurrence of shear layer roll-up moves upstream at x∗ ≈ 1. Secondly, the large-scale vortices appear very different between the x–y and the x–z plane. While the vortices in the x–z plane remain almost symmetrical about the centreline, those in the x–y plane do not. This observation is derived from the visualization result showing that two minijets excitation is symmetrical about the x–y

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Figure 7. Photographs of typical flow structures from flow visualization. (a) Manipulated jet (Cm = 9.3%, fe /f0 = 1), (b) Cm = 4.2%, fe /f0 = 1, (c) Cm = 2.0%, fe /f0 = 1 and (d) natural jet (Cm = 0, fe /f0 = 0). plane, but not the x–z plane. This is in agreement with previous investigations on asymmetric manipulation of the jet, where asymmetric excitation may lead to asymmetrically arranged vortices [19,20]. Finally, the jet column in the x–y plane wobbles rightwards at x∗ ≈ 2 and then leftwards at x∗ ≈ 2.7 and rightwards again further downstream, along with a significant spread compared with that at x∗ ≈ 2. Such an oscillation of the jet column is similar to observation in a round jet excited by two anti-phased slot jets at a Reynolds number of 3600 (see Figs 6 and 7 in [22]), which was referred to as the flapping jet column. As a matter of fact, the phase spectrum Φu1u2 between u1 and u2 measured at y∗ = −0.3 and 0.3 (x∗ = 2), respectively, shows a jump from 0 in the natural jet to near π or −π over a broad range of frequencies about the preferred-mode frequency StD = 0.43 (figure 8). Note that both Φu1u2 = −π and π correspond to anti-phase. It may be inferred that, unlike the natural jet, the flow is oscillating while moving downstream. Goldschmidt & Bradshaw [34] proposed the flapping of the jet based on the negative correlation between two fluctuating streamwise velocities obtained on opposite sides of the jet. Figure 9a presents two snapshots of typical instantaneous lateral velocity vectors captured at x∗ = 2.0 using PIV, which are selected to present the highly repeatable velocity vectors, showing the predominantly upward and downward motions, respectively, and the unequivocal evidence for the flapping motion of the jet column (figure 7c(i)). Note that the jet spreads along the flapping direction. Thus, it may be inferred that the flapping motion is responsible for the increased spreading and the rapid decay of the jet. Considering the presence of an initially tilting vortex ring and the absence of an axisymmetric counterpart, jet flapping may be due to the excitation of the m = ±1 mode, where m denotes the azimuthal mode [6,7]. The momentum thickness of the natural jet is θm = 0.17 mm, thus giving θm /D = 0.0085. Previous investigations [35–37] have confirmed that the initial region of an axisymmetric jet surrounded by a thin initial shear layer (θm /D 1) is equally unstable to an axisymmetric (m = 0) as well as to the first helical modes (m = + or −1). Samimy et al. [7] achieved a higher enhancement of jet mixing and a faster decay rate of jet centreline velocity by exciting a round jet with the m = ±1 mode at the jet preferredmode frequency than that excited with the m = 0 mode at the same frequency, where the m = 0, ±1 modes are forced by changing the way actuators are operated. They observed that the structures

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(ii) 3 m s–1

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0 0.5 1.0 –1.0

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Figure 9. (a) Two typical PIV snapshots of instantaneous velocity vectors in a cross-sectional plane of the manipulated jet (Cm = 2.0%, fe /f0 = 1) at x ∗ = 2.0. (b) Schematic of the jet flapping motion. The a(i) and a(ii) in panel (b), corresponding to (a(i)) and (a(ii)), respectively, represent two typical phases in the process of the jet flapping motion. are symmetric in the m = 0 mode excitation, but staggered in the m = ±1 mode excitation. Parekh et al. [6] employed two anti-phase slot jets to excite the m = ±1 mode of a round jet, thus producing a flapping jet that enhanced jet mixing effectively. Although the excitation techniques

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natural jet manipulated jet (Cm = 2.0%, fe /f0 = 1)

4

(a)

(b)

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Figure 10. Photographs of typical flow structures from flow visualization in the x–y plane of the manipulated jet (Cm = 1.6%): (a) fe /f0 = 0.85, (b) 1.0, (c) 1.24.

are different, the present excitation (Cm = 2.0%, fe /f0 = 1) also introduces an asymmetric excitation at the preferred-mode frequency, which probably excites the unstable m = ±1 mode, producing the staggered vortices and eventually a flapping jet. The K value experiences an obvious sharp rise as fe /f0 approaches 1 (figure 2a). On the other hand, the drop in K is not so sharp beyond fe /f0 = 1. The distinct behaviours suggest a difference in the flow physics involved. Figure 10 presents the typical flow visualization photographs taken in the x–y plane of the excited jet at fe /f0 = 0.85, 1.0 and 1.24 for a fixed Cm = 1.6%, respectively. The case of fe /f0 = 1.0 serves as a reference. The excited jet reveals staggered vortices and a vigorous flapping motion. By contrast, if forced at fe /f0 = 0.85, the vortices appear approximately symmetric about the centreline, and the flapping motion is not readily visible (figure 10a). The absence of jet flapping may lead to weak spreading, and hence a relatively small K. At fe /f0 = 1.24, the flow structure is quite similar to that at fe /f0 = 1.0. However, with increasing excitation frequency, the time interval between two adjacent vortices is reduced; thus, relatively small vortices emerge with reduced spatial separation [20,33,38], which may weaken the induced lateral velocity due to vortex pairing. As a result, jet flapping is less pronounced and the flow spreads less (figure 10c) than that at fe /f0 = 1.0 (figure 10b), leading to a drop in K. Iio et al. [39] also confirmed that excitation at fe /f0 > 1 can produce a weak flapping motion of the jet column. We may conclude that fe /f0 ≥ 1 could create the right condition to generate flapping motion in a round jet, though this motion is most pronounced at fe /f0 = 1.

6. Flow structure development A flapping jet is generated under the excitation of Cm = 2.0% and fe /f0 = 1, which may account largely for the increased jet decay rate and is of great interest. To further understand the flow structure development under this excitation, flow visualization and PIV measurements were conducted in the cross-sectional planes and the streamwise planes, with and without manipulation (figures 11–15). The initial formation of vortex ring in the manipulated jet may be investigated from flow photographs, taken in cross-sectional planes from x∗ = 0.7–1.3, along with their counterparts without manipulation (figure 11). The flow images of the natural jet look like a full moon (figure 11a(i)(iii)), which is the potential core of the jet. Apparently, there is no roll-up of shear layers. Once perturbed, the shear layer on the upper side always rolls up first at x∗ = 0.7 to form a vortical structure (figure 11b(i)). This is due to the unsteady minijet injections placed on the upper side. The periodic excitation may accelerate shear layer growth [19]. At x∗ = 1.0, the shear layer

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4

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part of the ring structure

(a(ii))

(b(ii))

x* = 1.3 vortex ring

vortex ring

streamwise structures

y (a(iii))

(b(iii))

(b(iv))

(b(v))

z

Figure 11. Typical photographs of flow visualization in the cross-sectional planes. (a) Natural jet, (b) manipulated jet (Cm = 2.0%, fe /f0 = 1). Flow is outward from the paper.

on the lower side also starts to roll up (figure 11b(ii)). The black curve between the vortex and the potential core is the ambient fluid entrained during vortex formation. Both upper and lower vortical structures are part of slightly tilting vortex rings, which will be elaborated later. At x∗ = 1.3, complete ring vortices are captured, though with small distortions (figure 11b(iii)(v)). Also, the braid region between ring vortices is shown in figure 11b(iv), two streamwise vortices are discernible in this image, most probably generated under the high strain rate of the braid region. In order to explore the downstream evolution of vortex rings, four images in the x–y plane are selected to present typical phases of the vortex evolution (figure 12a). We wish to point out that the flow behaviour observed is highly repeatable. For ease of discussion on the two oppositely orientated ring vortices, the vortices are designated as ring vortex A and ring vortex B as shown in figure 12a. The structure B0+ moves inwards to B1+ as a consequence of induction of the downstream vortex. Consequently, vortex ring B0 rotates clockwise to B1 around an axis parallel to the z-axis. On the other side, vortex ring A0 grows to a larger size A1. As such, the adjacent vortex rings A1 and B1 are oppositely tilted (figure 12a(ii)(iv)), as indicated by the upper and lower ends (A1+ and A1−) and (B1+ and B1−), respectively (figure 12a(ii)(iv)). Such a process is sketched in figure 12b(i)(ii). Recall the vortex rings captured in the cross-sectional plane of x∗ = 1.3 shown in figure 11b(iii)(v); these could be interpreted as corresponding to B1 and A1, respectively, and the incomplete rings, i.e. the upper turbulent segments, should be the consequence of tilting. Further downstream, the vortex rings are more stretched and tilted. The ring vortex B rotates clockwise from B1 to B6, while A turns anti-clockwise from A1 to A6 (figure 12a). As a result, two adjacent rings approach each other at one end (e.g. B2+ and A4+ on the upper side, A4− and B6− on the lower side as shown in figure 12a(i)), forming zigzag-arranged vortex structures. This evolution of vortex tilting is sketched in figure 12b and represented by sketches in figure 12b(ii)– b(iii). Note that two interacting vortices on either the upper or the lower side undergo localized pairing. Specifically, on the upper side, the vortex B1+ evolves downstream to B2+, approaching to and then pairing with A4+, thus forming AB+. On the lower side, the vortex A1− moves upwards to A3−, catching up with B5−. The two vortices undergo pairing, forming AB−. It should be noted that the pairing process is not symmetrical about the jet centreline, a behaviour that is different from that observed in a natural jet. This asymmetric arrangement of the pairing

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A0+ B2+

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Figure 12. (a) Photographs of typical flow structures from flow visualization in the x–y plane of the manipulated jet (Cm = 2.0%, fe /f0 = 1). (b) Sketch to illustrate the evolution of vortex tilting. The sequence is from (b(i)) to (b(iii)).

(a)

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Figure 13. Typical v ∗ -contours in the x–y plane: (a) natural jet, (b) manipulated jet (Cm = 2.0%, fe /f0 = 1). Contour interval = 0.05. Continuous and dashed lines represent the positive v ∗ (upward motion) and the negative (downward motion), respectively. Symbols ‘+’ and ‘×’ denote anti-clockwise and clockwise vortices, respectively.

x* = 2.0

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(b)

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Figure 14. Typical photographs of flow visualization in the cross-sectional planes. (a) Natural jet, (b) manipulated jet (Cm = 2.0%, fe /f0 = 1). Flow is outward from the paper. (a)

natural jet

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Figure 15. The contours of time-averaged (a) streamwise velocity and (b) lateral velocity, the contour increments being 0.1 and 0.02, respectively.

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process is also observed in the numerical study of a bifurcating jet [40]. In that study, it was reported that the jet splits into two separate jets. As the asymmetrically arranged vortex pairing only occurs in the x–y plane rather than in the x–z plane, as is evident in figure 7c(i)(ii), this event could be directly responsible for the flapping observed in the x–y plane. To further explore the connection between the flapping motion and the asymmetrically arranged vortex pairing, the typical instantaneous contours of the lateral velocity v ∗ = v/Ue in the x–y plane are shown in figure 13. Symbols ‘+’ and ‘×’ denote vortex centres above and below the centreline, respectively. Solid and broken contours represent the positive v ∗ or upward motion and the negative or downward motion, respectively. In the natural jet, the velocity contours are nearly symmetric about the jet centreline, ambient fluid is induced either outward or inward and the potential core fluid does not move laterally until x∗ ≈ 4.5. Once manipulated, the jet exhibits alternate upward and downward motions from x∗ ≈ 1.4 onwards. Ambient fluid is entrained upstream of two interacting vortices, evident in the vorticity contours (not shown), while the core fluid is tossed out downstream of the two vortices. Asymmetrically arranged, vortex interactions entrain ambient fluid on the lower side and push the core fluid out on the upper side at the same streamwise position (e.g. x∗ ≈ 1.6 in figure 13b), thus producing a strong upward motion. Similarly, a strong downward motion occurs at x∗ ≈ 2.2 in figure 13b. As a result, a flapping motion of the jet column is generated. The mechanism for generating the flapping motion proposed here is distinct from those previously reported by Reynolds et al. [41]. No pairing was observed in their investigation. In their review of a round bifurcating jet, obtained by combining the axial and circumferential excitations with a ratio of axial to transverse excitation frequency equal to two, Reynolds et al. [41] proposed that the opposite tilting of adjacent vortex rings tends to tilt toward each other due to their mutual induction. Consequently, vortex rings move away from the jet centreline and stretch the jet core fluid between them, producing a flapping jet (refer to fig. 2 in [41] for details). To gain better understanding of the remarkable spread (e.g. figure 12), we explore the flow structure based on the photographs captured in a series of cross-sectional planes at x∗ = 2.0, 2.4, 3.0 and 5.0 (figure 14). The natural jet, also shown for reference, is approximately axisymmetric. At x∗ = 2.0, the shear layer rolls up to form an axisymmetric vortex ring (figure 14a(i)). This ring starts to become unstable at x∗ = 2.4 (figure 14a(ii)), though the jet remains essentially axisymmetric. At x∗ = 3.0, small mushroom-like structures emerge around the vortex ring (figure 14a(iii)). These are generated in the braid region between two consecutive vortex rings due to azimuthal instabilities and stretching around the following vortex ring [42]. At x∗ = 5.0, the flow becomes fully turbulent and the jet is still roughly axisymmetric (figure 14a(iv)). Once excited, transition to fully turbulent flow occurs early, at x∗ ≈ 2.0, in the manipulated jet, along with a significant spread along the y direction. It should be noted that, comparing with a natural jet, early formation and subsequent pairing of the vortices occur in a manipulated jet. During vortex pairing, a large strain rate is generated [32], causing the braid region to deform [43] and thus producing counter-rotating streamwise vortex pairs, which stretch upstream and superimpose on the following primary vortex [42,44]. Hence, at x∗ = 2.0–2.4, the mushroomlike structures can be observed at the edge of the jet (figure 14b(i)(ii)). Note that such streamwise vortices and the azimuthal vortices appear to be pushed out by the flapping motion. Owing to the presence of jet flapping, the lateral velocity is dramatically increased in the flapping plane [45], and thus the jet fluid is transported outwards approximately vertically. Further downstream at x∗ = 3.0 (figure 14b(iii)), the vortices break down, and the manipulated jet looks less ordered and becomes turbulent. The jet fluid is pushed outwards approximately along the y-axis. Terashima et al. [46] proposed that flapping motion could increase turbulent diffusion to the outer region of the jet. Finally, a state of fully turbulent flow occurs at x∗ = 5.0, along with a significant spread along the y-axis (figure 14b(iv)). Note that the manipulated jet spreads only along the flapping direction (y−axis). It may be inferred that it is the jet flapping motion that contributes to the significantly increased spreading and hence rapid jet decay. This finding is consistent with previous reports (e.g. [6,7,47]), where the flapping motion was found to be effective in increasing jet spreading and large-scale mixing. The flapping jet in this study is realized with two in-phase

Investigations have been conducted on the active manipulation of a turbulent round jet (ReD = 8000) using two unsteady radial minijets separated azimuthally by θ = 60◦ . Two control parameters are examined, i.e. Cm (1.1%–10.9%) and fe /f0 (0.3–1.24). Measurements were performed in the (x, y) plane, i.e. the symmetry plane of the two minijets, the (x, z) plane, and a number of cross-sectional (y, z) planes over x∗ = 0.45–5 using PIV, flow visualization and hotwire techniques. A comparison is also made with the jet excited by two radial unsteady minijets placed at θ = 180◦ apart. The following conclusions could be drawn from this work. 1. The jet decay rate K exhibits a strong dependence on Cm and fe /f0 (figure 2). This behaviour is qualitatively the same as that of a jet under symmetric control (θ = 180◦ ). However, asymmetric excitation increases K by 30%, suggesting a considerably more effective control strategy. A flapping jet is generated. This flapping behaviour is responsible for a substantial increase in jet spread, thus giving rise to rapid jet decay.

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minijets separated by an angle of 60◦ , distinctly different from two anti-phase actuators deployed at the opposite sides used by previous researchers, e.g. piezoelectric actuators [6], slot jets [6], electromagnetic flap actuators [48], acoustic actuators [39,49] and synthetic jets [47]. The time-averaged flow field obtained from PIV measurements provide a quantitative measurement of jet entrainment and spreading. The streamwise and lateral mean velocities are derived from 1500 pairs of PIV images. Figure 15a presents the contours of time-averaged streamwise velocity U∗ = U/Ue of the jet, with and without manipulation. Two observations can be made. Firstly, under the excitation of minijets, the location, where the contour of U∗ = 0.9 intersects the jet axis, has moved from x∗ ≈ 6.1 to 3.4, implying that the excitation gives rise to a reduced potential core length by almost one half. Secondly, the edge of the jet splits into a larger angle than the unexcited jet in the x–y plane, as indicated by a comparison between the two contours of U∗ = 0.1 for the manipulated and natural jets. Note that the outer boundary of the jet (e.g. the U∗ = 0.1 contour) is pushed outward only for x∗ < 3 in the x–z plane, which may be due to early roll-up in this plane (figure 7c(ii)). The widening of the jet is much more pronounced in the x–y plane than in the x–z plane, indicating greater spreading in the x–y plane. The slight narrowing of the jet occurs in the x–z plane, which is orthogonal to the flapping plane (figure 15a(i)(iii)). This phenomenon is also observed by other researchers, e.g. Parekh et al. [6] and Samimy et al. [7]. Parekh et al. [6] attributed this behaviour to an enhanced entrainment in this plane, thus inducing more ambient fluid to move towards the jet centre. It is worth pointing out that the streamwise mean velocity profile is different from that in the bifurcating jet, where two distinct peaks occur in the lateral distribution of the flapping plane (e.g. [48]), that is the present manipulated jet is different from the bifurcating jet. Figure 15b presents the contours of time-averaged lateral velocity V ∗ = V/Ue and W ∗ = W/Ue of the excited jet, compared with unexcited jet. The same lowest contour level is chosen for these plots to facilitate comparison. Without excitation, the lateral velocity is quite small. Once excited, the V ∗ and W ∗ distributions change greatly. The contours of V ∗ are positive on the upper side and negative on the lower side from x∗ ≈ 2.0 onward, suggesting strong spreading occurs in the x–y plane. This is consistent with the location where the flapping motion occurs, reconfirming that the flapping of the jet causes spreading. On the other hand, the negative V ∗ on the upper side and the positive on the lower side ahead of x∗ ≈ 2.0 suggest an entrainment of ambient fluid due to the formation and pairing of the vortex rings. Similarly, the negative W ∗ on the upper side (z∗ > 0.5) and the positive on the lower side (z∗ < −0.5) also indicate that ambient fluid is entrained toward the jet. This also validates the reason why the narrowing stream occurs in the x–z plane, as discussed above. The maximum level of V ∗ is increased by 600% and that of W ∗ by 300%. In summary, two mechanisms may contribute to rapid decay of the jet centreline mean velocity. One is due to the enhanced entrainment of the ambient fluid during early formation and pairing of the vortex rings. The other is the remarkable spreading associated with the flapping motion in the x–y plane.

idea of the study, funded and supervised the project. Y.Z. and R.M.C.S. revised the draft. Y.L. supervised partially H.Y.’s experimental work at PolyU. All authors regularly discussed the progress during the entire work. Competing interests. We declare we have no competing interests. Funding. Y.Z. wishes to acknowledge support given to him from NSFC through grant 51421063 and from Scientific Research Fund of Shenzhen Government through grants, JCYJ20130329154125496, KQCX2014052114430139 and KQCX20130627094615415.

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Data accessibility. This work has no accompanying data. Authors’ contributions. H.Y. performed the experimental measurements and drafted the paper. Y.Z. proposed the

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A combination of three factors may have contributed to this observation. Firstly, two minijets, separated by θ = 60◦ , provide an asymmetric excitation, thus generating an asymmetric flow structure that is more unstable (e.g. [1,18]). Secondly, at a critical Cm such as Cm = 2.0%, vortex rings interact vigorously (e.g. Figure 7c(i)(ii)). Finally, an excitation at fe /f0 = 1 triggers the formation and alternated pairing of vortex rings. Henderson [9] suggested that the most essential requirement for mixing enhancement is to excite a jet-flapping mode. This work provides a new strategy to create a flapping jet, thus enhancing jet mixing effectively. The excitation may be less effective for higher ReD , as reported by e.g. Suzuki et al. [48] and Benard et al. [50]. 2. In order to understand the generation of the flapping motion, flow structure under optimal excitation (Cm = 2.0%, fe /f0 = 1) is analysed in detail. Minijet perturbation gives rise to early roll-up on the ‘upper’ side because of direct minijet impingement. This then leads the vortex on the upper side to move inwards to catch up with the adjacent downstream vortex due to their mutual induction. As a result, the vortex rings are tilted alternately to the opposite directions, creating a ‘zigzag’ structure and the localized pairing between the ends of two adjacent rings (figure 12). The vigorous interactions of these vortical structures entrain ambient fluid into the jet core alternatively from the upper and the lower side, thus producing a flapping motion.

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