An experimental investigation on comparison of synthetic and continuous jets impingement heat transfer

International Journal of Heat and Mass Transfer 90 (2015) 227–238

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An experimental investigation on comparison of synthetic and continuous jets impingement heat transfer Xiao-ming Tan a, Jing-zhou Zhang a,b,⇑, Shan Yong a, Gong-nan Xie c a

College of Energy and Power Engineering, Jiangsu Province Key Laboratory of Aerospace Power System, Nanjing University of Aeronautics and Astronautics, Nanjing 210016, China Collaborative Innovation Center of Advanced Aero-Engine, Beijing 100191, China c School of Mechanical Engineering, Northwestern Polytechnical University, Xi’an 710072, China b

a r t i c l e

i n f o

Article history: Received 21 February 2015 Received in revised form 23 June 2015 Accepted 23 June 2015

Keywords: Synthetic jet Jet impingement Piston actuator Convective heat transfer Orifice shape

a b s t r a c t The convective heat transfer characteristics under a normally synthetic jet impingement driven by a piston actuator are investigated experimentally in the present study. Particular attentions are paid to present the detailed local and laterally-averaged heat transfer comparison between synthetic jet and continuous jet, as well as the effect of orifice shape on the synthetic jet impingement. Three jet orifices including single-round, single-square, and single-rectangular are designed to have the approximately same exit area. In additional, heat transfer regimes for the synthetic jet impingement in the situation of large stroke length to jet-to-surface spacing are further identified. In the present, the equivalent convective heat transfer coefficient is defined in terms of the difference between target temperature and ambient temperature. The results show that continuous jet exhibits stronger local heat transfer than the synthetic jet in the vicinity of stagnation point. However, the synthetic jet produces much flatter and more uniform local heat transfer coefficient distributions over the surface, showing its advantage over the continuous jet on laterally-averaged convective heat transfer enhancement at a larger jet-to-surface spacing. For the piston-driven synthetic jet featured by low excitation frequency and large stroke length, there is evidence for a power law relationship between stagnation Nusselt number and jet Reynolds number with an exponent of approximately 0.32. Two kinds of heat transfer regimes are observed and a critical ratio of stroke length to jet-to-surface spacing is identified as 18 approximately regardless of orifice shape. The orifice shape has a moderate effect on the convective heat transfer. The single-rectangular synthetic jet produces a slightly better stagnation point heat transfer than the other orifices. The synthetic jet originated from the round-hole orifice seems to introduce favorable overall convective heat transfer achievement. The advantage of synthetic jet impingement in comparison to the corresponding continuous jet is relatively degraded for the square-hole orifice. Ó 2015 Elsevier Ltd. All rights reserved.

1. Introduction A synthetic jet is a quasi-steady jet with zero-net-mass flux generated by the periodic motion of a membrane in a cavity with orifices on one or more walls. As the membrane oscillates, fluid is periodically entrained into and expelled out from the orifice. During the expulsion portion of the cycle, the fluid inside the cavity is expelled through the orifice, inducing a vortex ring that moves outwards under its own momentum. During the suction portion of the cycle, the vortex ring is sufficiently distant from the orifice

⇑ Corresponding author at: College of Energy and Power Engineering, Jiangsu Province Key Laboratory of Aerospace Power System, Nanjing University of Aeronautics and Astronautics, Nanjing 210016, China. E-mail addresses: [email protected] (J.-z. Zhang), [email protected] (G.-n. Xie). http://dx.doi.org/10.1016/j.ijheatmasstransfer.2015.06.065 0017-9310/Ó 2015 Elsevier Ltd. All rights reserved.

that it is virtually unaffected by the entrainment of the fluid into the cavity. In this fashion, a train of vortex rings moving away from the orifice occurs, whereupon the coherent structures then interact, coalesce, and break down in a transition towards a quasi-steady jet [1–3]. The periodic vortical structures introduced into the flow exhibit a potential ability of synthetic jet for active flow control [4–6]. Synthetic jets have been studied extensively for flow control applications. They are also draw attention in the heat transfer enhancement due to their highly pulsating nature as well as their self-synthesis directly from the working fluid. The first literature work using synthetic jets as heat sinks or cooling devices was published by Mahalingam et al. [7]. Later, Mahalingam and Glezer [8] discussed the design and thermal performance of a synthetic air-jet based heat sink for high power dissipation electronics. The jets were created by electromagnetic actuators. The results

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Nomenclature A a b Bi c de D f H h L L0 Ly l Nu Pr Rej s Sr T t U0 Um

area (m2) constant in Eq. (15) constant in Eq. (15) Biot number constant in Eq. (15) hydraulic diameter of orifice (m) cavity inner diameter (m) excitation frequency (Hz) cavity height (m) heat transfer coefficient (W/(m2 K)) stroke length of piston (m) synthetic jet stroke length (m) Laterally-averaged length in y-direction (m) slot width (m) Nusselt number Prandtl number jet Reynolds number jet-to-orifice spacing (m) Strouhal number temperature (K), time period (s) 1/f time (s), thickness of orifice plate (mm) characteristic synthetic jet velocity (m/s) characteristic continuous jet velocity (m/s)

revealed that the synthetic-jet heat sink dissipated approximately 40% more heat compared to steady flow from a ducted fan blowing air through the heat sink. Jagannatha et al. [9] reported a detailed numerical study on a synthetic jet-based electronic cooling module. It was indicated that the thermal performance of the synthetic jet is highly dependent on its oscillating diaphragm amplitude and frequency. The overall heat transfer rate of the synthetic jet module was about 30% better than an equivalent continuous jet. Recently, Yu et al. [10] proposed an integrated air-cooled heat sink by using piezoelectric-driven agitators and synthetic jets. The proposed integration was investigated experimentally and computationally in a single-channel heat sink with one agitator and two synthetic jet arrays. It was shown that the combination of the agitator and synthetic jets raises the heat transfer coefficient of the channel by 82.4%, compared with a same channel having channel flow only. A lot of studies have been made covering the general flow behavior and heat transfer performance of the synthetic jet impingement during the last decade. Major factors that influence the local and average heat transfer characteristics including excitation frequency (f), orifice shape and cavity geometry, Reynolds number (Rej), Strouhal number (Sr) or dimensionless stroke length (L0/de), and jet-to-surface spacing (s/de) were investigated. Garg et al. [11] made an experimental investigation on the synthetic jet impingement heat transfer over a small heater surface area. They reported a maximum heat transfer enhancement of approximately 10 times over natural convection was measured from a vertical surface. It was also reported that the heat transfer augmentation caused by the jets depends on several parameters, such as, driving frequency, driving voltage, jet axial distance, heater size, and heat flux. Pavlova and Amitay [12] experimentally investigated the cooling efficiency and mechanism of a piezoelectric-driven synthetic jet impingement on the constant heat flux surface. The jet parameters that were varied in the experiments include 140 < Rej < 740, 1.9 < s/de < 38.1, and 0.18 < Sr < 2.17. In their measurements, high frequency (f = 1200 Hz) synthetic jets were found to remove heat better than

w x y z

slot width (m) x-direction y-direction z-direction

Greek letters d foil thickness (m) k thermal conductivity (W/(m K)) m kinematic viscosity (m2/s) Subscripts 0 stagnation point a ambient av laterally-averaged CJ continuous jet j jet SJ synthetic jet w wall Superscripts n exponent of Rej

low frequency (f = 420 Hz) jets for smaller axial distances while low frequency jets were more effective at larger s/de. Moreover, synthetic jets were about three times more effective in cooling than continuous jets at the same Reynolds number. Gillespie et al. [13] studied the influence of jet-to-surface spacing on the heat transfer to a rectangular electromagnetic-driven impinging synthetic jet experimentally. In the near-field the synthetic jet had a tendency to ingest heated air from the thermal boundary layer and the jet velocity was relatively low, causing relatively low heat transfer rates. In the far-field the diminished jet velocity at the surface was unable to effectively penetrate the boundary layer which also leads to low heat transfer rates. Average Nusselt numbers were maximized when the dimensionless plate spacing was between 14 and 18. Zhang and Tan [14] investigated experimentally the flow and heat transfer characteristics of a rectangular synthetic jet driven by piezoelectric actuator. Two resonance frequencies of 540 Hz and 1140 Hz were identified. They found that synthetic jet introduces stronger entrainment and penetration, and that the cooling region under synthetic jet impingement is greater than that of a continuous jet. Some attractive findings of using impinging synthetic jets formed from a single cavity but with different orifices, such as single-slot, single-hole, three-slots and three-holes, were fatherly explored by the authors [15]. Chaudhari et al. [16] performed a detailed study of the average heat transfer characteristics of round synthetic jet impingement using an electromagnetic actuator and compared it with continuous jet. A strong effect of enclosure was noted that the average Nusselt number increases by 108% with decreasing the jet-to-surface spacing by 42%. In other studies, Chaudhari et al. [17,18] experimentally investigated different shapes of a cavity in an effort to maximize the synthetic jet from the orifice and explored the effect of square, circular and rectangular shape of orifice on synthetic jet impingement cooling of heated surface. The heat transfer enhancement with a square orifice was found to be larger than that with rectangular and circular shapes at larger axial distances, for the same set of boundary conditions. It was also found that rectangular orifice with aspect ratio between 3 and 5

X.-m. Tan et al. / International Journal of Heat and Mass Transfer 90 (2015) 227–238

gives best performance at smaller axial distances. They also made an investigation for improving the impingement heat transfer by using multiple orifice synthetic jet [19]. Bhapkar et al. [20] experimentally investigated acoustic aspects and average heat transfer characteristics of an elliptic synthetic jet impinging on a heated flat plate. A comparison with circular, rectangular and square orifices having same equivalent diameter was also made. The maximum heat transfer enhancement was obtained at the resonance frequency for elliptical orifice of aspect ratio 1.4 at the non-dimensional jet-to-surface spacing (s/de) of 3. For low jet-to-surface spacing ratios (s/de < 6), elliptical orifice performed better as compared to other shapes of the orifice. However, for higher jet-to-surface spacings, circular and square orifices outperformed elliptic and rectangular orifices. Valiorgue et al. [21] investigated the relation between the convective heat transfer characteristics and the impinging synthetic jet flow structure, for a small jet-to-surface spacing (s/de = 2), dimensionless stroke length 1 < L0/de < 22, and jet Reynolds number 1000 < Rej < 4300. The synthetic jet flow was produced by a cavity enclosed on one side by an acoustic speaker. The heat transfer measurements showed two different flow regimes depending on stroke length. A critical stroke length L0/s = 2.5 had been identified. Persoons et al. [22] provided an objective comparison of the stagnation point heat transfer performance of axisymmetric impinging synthetic jets versus established steady jet correlations. Furthermore, a general correlation for the stagnation point Nusselt number was proposed including the effect of all appropriate scaling parameters: Reynolds number (500 6 Rej 6 1500), jet-to-surface spacing (2 6 s/de 6 16) and stroke length (2 6 L0/de 6 40). Based on the ratio of stroke length to jet-to-surface spacing L0/s, four heat transfer regimes were identified. McGuinn et al. [23] also made an investigation on flow regime characterization of an impinging axisymmetric synthetic jet to identify the various flow regimes as a function of stroke length. Most of the presented results were for a single Reynolds number of 1500. Four free synthetic jet flow morphology regimes were identified. He et al. [24] experimentally compared heat transfer characteristics of single-slot impinging steady and synthetic jets on a 25.4 mm  25.4 mm vertical surface. For the steady jet study, the parameters varied in the testing were nozzle length (4 mm, 8 mm, 12 mm, 15 mm) with a fixed nozzle width of 1 mm and Reynolds number (100–2500). An 8 mm  1 mm synthetic jet was studied by varying the applied voltage (20–100 V) and frequency (200–600 Hz). Both jets impingement were conducted at several dimensionless jet-to-surface spacings (s/de = 5, 10, 15, 20). For the synthetic jet, the best heat transfer was observed at s/de = 10. The synthetic jet exhibited better heat transfer performance than the steady jet with up to a 40% enhancement in area-averaged Nusselt number. As mentioned in the above, a lot of studies have been conducted to demonstrate the synthetic jet impingement heat transfer behaviors. However, limited results are presented for the detailed local heat transfer comparison between synthetic jet and continuous jet. Compared with continuous jet, synthetic jet generates wider and slower flows in the near field due to its pulsating flow feature [25]. The difference between two jets impingement will be tightly associated with the jet-to-surface spacing. As such, one of the objectives of this work is to provide an objective quantitative comparison of the stagnation, local and laterally-averaged heat transfer characteristics of synthetic jets versus continuous jets for a wider range of jet-to-surface spacings. It is also noted that in the previous works, most of the synthetic jets is driven by acoustic speaker or piezoelectric diaphragm with high frequency but little stroke length. These synthetic jets generally have low Reynolds numbers. For the synthetic jet driven by piston actuator, the excitation frequency is extremely lower while the stroke length is extremely bigger in relative to acoustic or

229

piezoelectric actuators [26–29]. Therefore, the other objectives of this work are to present the effect of orifice shape (single-round, single-square, and single-rectangular orifices having the same jet exit area) on the synthetic jet impingement driven by piston actuator, and to further identify heat transfer regimes of the synthetic jet with big ratio of stroke length to jet-to-surface spacing (10 < L0/s). 2. Experimental approach 2.1. Synthetic jet facility The piston-driven synthetic jet actuator is schematically shown in Fig. 1, which is a slightly modified figure from Crittenden and Glezer [27]. It was composed of a cylindrical cavity (inner diameter D = 23.6 mm, height H = 30.6 mm), a piston and an orifice plate. In the present experiments, the synthetic jet was formed by the sinusoidal, time harmonic motion of a 23.6 mm diameter piston within a matching cylinder with a stroke length (from bottom dead center (BDC) to top dead center (TDC)) of L = 22.6 mm. The piston was linked to an AC/DC universal electric motor. The motor rated speed (or the resulting actuation frequency, f) is controlled using a stepping adjustor which holds the frequency constant to within ±1.0 Hz of the nominal level. In the present study, the actuation frequency was adjusted below 24 Hz for eliminating the self-vibration of the piston actuator. The top surface of the cylinder was covered by an interchangeable orifice plate with thickness (t) of 1 mm, with sharp-edged orifices of varying shape. Four orifices were designed in the current study, including single-round orifice, single-square orifice, and single-rectangular orifice with aspect ratio of 7. All the orifices were designed to have approximately the same exit area, as listed in Table 1. Fig. 2 shows the schematic diagram of the synthetic jet experimental setup. The velocity of the synthetic jet downstream the orifice was measured a constant temperature hot-wire anemometry (TSI model 1201-20) without considering the jet impingement

Fig. 1. Schematic of synthetic jet actuator driven by piston.

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X.-m. Tan et al. / International Journal of Heat and Mass Transfer 90 (2015) 227–238 Table 1 Synthetic jet orifice parameters. Orifice shape

Width (w) (mm)

Length (l) (mm)

Hydraulic diameter (de) (mm)

Exit area (Aj) (mm2)

Single-round-hole Single-square-hole Single-rectangular-hole

5.3 2

5.3 14

6 5.3 3.5

28.3 28.1 28.0

thermocouples placed on the black painted test surface to act as the benchmark [30]. These thermocouples were used to estimate the emissivity of the test surface. The emissivity of the black painted test when viewed directly was about 0.96. To make the thermal object image to be detected by an infrared camera, a viewing window with a width of 60 mm and a length of 120 mm is made in the nylon plate, corresponding to the constantan sheet heater. Three thermocouples were fixed on the heater sheet to check the surface temperature and to help determine steady-state conditions. To enable the heater foil be viewed directly by the infrared camera, a viewing window was made on the impinging target plate. When the thin constantan sheet was being heated, this viewing window was covered with an asbestos plate. Once the temperature field on the impinging target reached steady, the asbestos plate was taken out, and then the thermal image was quickly recorded by the infrared camera within approximately 5 s. By monitoring the temperature variations of there thermo-couples during the procedure in that taking out the asbestos plate, it was confirmed that the adopted procedure has little influence the temperature field of interest, within 1.5% of the nominal local temperature in the present experiments. The detective distance was set as 100 mm so that the transmissivity for the infrared camera was approximately regarded as 1. 2.2. Continuous jet facility

Fig. 2. Schematic diagram of the experimental setup.

action, as seen in Fig. 2(a). A tungsten–platinum coated single wire probe with temperature coefficient of resistance of 0.0042/°C, wire diameter of 5 lm, sensing element length of 1 mm was positioned close to the synthetic jet orifice within approximately 1 mm. The sampling rate was set at 100 kHz, which is adequate to capture the dynamic nature of the synthetic jet gas flow. The experimental apparatus for the synthetic jet impingement is sketched in Fig. 2(b). The impinging target plate was rectangular and made of nylon plate with a thickness of 20 mm, which is fixed at a traverse mechanism. This plate had a spanwise width (y-direction) of 150 mm and streamwise length (x-direction) of 200 mm. A thin constantan sheet (150 mm in long, 100 mm in wide, and 0.01 mm in thick) was mounted on the surface of nylon plate substrate, subjected to the jet impingement. During the experiment, this sheet was heated by DC current with two-side edges connecting to the copper bus bars by using a silver-filled epoxy adhesive to ensure uniform heat flux. These two bus bars were embedded into the nylon plate substrate so that the heater foil could be tensely mounted on the surface of substrate. The voltage (V) and the current (I) were recorded to determine the electric heat flux. The temperature distribution on the rear face of the foil (the opposite side of jet impingement) were measured by an infrared camera (TVS-2000MK) which works at speed of 30 frames per second, and the revolution of the temperature is 20 °C to 200 °C. The infrared camera calibration was conducted using a series of

The continuous jet impingement heat transfer was conducted in the same experimental apparatus for the synthetic jet impingement, where the piston-driven synthetic jet actuator was substituted by an impinging plenum cavity. This plenum cavity was connected to a coolant air supply passage. The coolant air from the compressor was firstly drawn through a standard flow meter and forced to enter into the test section. Then the coolant air was discharged through the orifice plate to impinge at the target plate. By using a flow controlling value, the needed air mass flow rate was adjusted in the experiment. 2.3. Data treatment and parameter definition Based on the work of Smith and Glezer [1], the Reynolds number charactering the synthetic jet was defined as

Rej ¼ U 0 de =v

ð1Þ

where de is the hydraulic diameter of orifice, m is the kinematic viscosity of the synthetic jet, and U0 is the time-averaged orifice velocity during the ejection part of the cycle at the exit and centerline of the orifice. This last parameter is calculated as

U 0 ¼ L0 f

ð2Þ

where f is the excitation frequency and L0 is the stroke length calculated over the ejection part of the total cycle as

L0 ¼

Z

T=2

UðtÞdt

ð3Þ

0

where U(t) is the instantaneous velocity during the ejection part of the cycle, T is the time period of the cycle.

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Table 2 Time-averaged velocities and Reynolds numbers of synthetic jet under different excitation frequencies (single-round orifice). Frequency (Hz)

8

12

16

20

24

U0 (m/s) L0 (m) Rej

4.1 0.51 1550

6.2 0.52 2345

8.7 0.54 3320

11.2 0.56 4275

13.8 0.58 5265

Table 3 Time-averaged velocities and Reynolds numbers of synthetic jet under different orifice shapes (f = 24 Hz).

Fig. 3. Absolute velocities near synthetic jet orifice in a time period of the cycle.

By using the hot-wire anemometry, the absolute velocities near the orifice were measured for different orifice shapes and excitation frequencies. In these tests, the synthetic jets are free without the presence of impingement target. Fig. 3 shows the absolute velocity distributions in a time period of the cycle. The curves in this figure are modified by smoothing the pulsed features in the original hot-wire data and approximately 100 samples are used to calculate the absolute velocity of each data point. It is noticed that the suction and ejection parts of the cycle can be distinguished from the time series in accordance with the synthetic jet mechanism. As the hot-wire probe suffers adverse affection in reversible flow when it is located closely to the centre of orifice, the velocity data maybe somewhat differ from the real velocity during the suction, and the data corresponding to the suction stroke should be accordingly reverted in this figure due to the hot-wire probe is insensitive to the direction of the flow. However, the measured data are guaranteed for charactering the time-averaged orifice velocity during the ejection part of the cycle. As seen in Fig. 3(a), the excitation frequency of the piston operating at low frequencies has an important effect on the exit velocity of synthetic jet. Whereas the orifice shape shows very weaker effect on the exit velocity of synthetic jet, given the same orifice exit area, as seen in Fig. 3(b). As the excitation frequency is limited within 30 Hz in the present study, the peak jet speeds do not exceed 30 m/s, indicating that the compressibility effect is very weak within the cylinder. According to the work of Crittenden and Glezer [27] where the maximum piston-driven frequency was 200 Hz, the normalized cylinder pressure ratio (defined as the pressure ratio between the cylinder and ambient level) over the cycle are comparatively small and the system is nominally incompressible for sufficiently low combinations of L0/de and f. Also, as the excitation frequency is increased, the maximum normalized cylinder pressure ratio increases, thus resulting

Orifice shape

Round

Square

Rectangular

U0 (m/s) L0 (m) Rej

13.8 0.58 5265

13.7 0.57 4630

13.2 0.55 2930

more intensive synthetic jet. The present results are in accordance with the finding presented by Crittenden and Glezer [27]. Tables 2 and 3 present the effects of the excitation frequency and the orifice shape on the time-averaged orifice velocity and the stroke length during the ejection part of the cycle. It is evident that the piston-driven actuator produces fairly big velocity at higher operating frequency and the time-averaged orifice velocity is nearly proportional to the frequency when the piston reciprocates at relatively low frequency (from 8 Hz to 24 Hz). The stroke length changes a little over the range of 8 Hz 6 f 6 24 Hz. Although the volume displaced per oscillation of a reciprocating piston is constant, the ejection and suction phases of the cycle will undergo a change in shape as the excitation frequency is increased. It is also found that the orifice shape has nearly no influence on the time-averaged orifice velocity and stroke length during the ejection part of the cycle under sufficiently low excitation frequency, given the same orifice exit area in the present study. The ratio of stroke length to hydraulic diameter of orifice (L0/de) is nearly 100 for the round-hole orifice and beyond 200 for the rectangular-hole orifice. Compared with the synthetic jets driven by the acoustic speaker or piezoelectric diaphragm [13–20], the synthetic jet driven by piston actuator has extremely bigger stroke length. According to the work of McGuinn et al. [23], the flow for the big stroke length induced by a piston-driven actuator is mainly dominated by the trailing jet which overtakes the vortex, resulting in a highly turbulent intermittent jet flow. In the present study, a comparison was performed between the synthetic jet and continual jet. For the continual jet, the jet Reynolds number is defined as

Rej ¼ U m de =v

ð4Þ

where de is the hydraulic diameter of orifice, m is the kinematic viscosity of the jet, and Um is the mean jet velocity at the nozzle exit. Both for the synthetic jet and for the continual jet, the jet Reynolds numbers are all characterized as Rej. The basic difference between Eqs. (1) and (4) is behaved in the evaluation of the characteristic velocity. The local time-averaged jet velocity during the ejection part of the cycle is used for the synthetic jet and the mean jet velocity is used for the continual jet. According to the thermal images, heat transfer coefficients were determined. Since the foil sheet is thin enough that the Biot number (Bi ¼ hd=k where k is the thermal conductivity and d is the thickness of the foil) is much less than unity, the temperature is reasonable to be considered practically as uniform across the foil thickness [31]. The local convective heat transfer coefficient on the target surface was evaluated as

232

h¼

X.-m. Tan et al. / International Journal of Heat and Mass Transfer 90 (2015) 227–238

Q  Qs AðT w  T j Þ

ð5Þ

where Tw is the target wall temperature, Tj is the jet temperature which is selected as ambient temperature Ta, A is the effective area of heater sheet, Q is the input power imposing on heating sheet, Qs is the heat loss from heater insulation. It should be noticed that the practical jet temperature will be affected by the restriction of heated impingement target due to entrainment and recirculation of hot air. Therefore it may be more appropriate to define the heat transfer coefficient in terms of the difference between Tw and practical Tj rather than (Tw–Ta) [13]. However, as the overall heat transfer or cooling efficiency is tightly associated with the nature feature of synthetic jet formation process, the definition of the heat transfer coefficient in terms of (Tw–Ta) is more relevant from practical viewpoint [18]. So that the convective heat transfer coefficient defined in Eq. (5)should be regarded as equivalent convective heat transfer coefficient which considering the variation of jet temperature on the practical heat transfer. This definition of convective heat transfer coefficient is relatively simple to apply and was adopted by almost previous researchers, including Gillespie et al. [13]. Heat loss form the back of the insulation was estimated according to the average temperature measured by five thermocouples fixed on the outer surface of the nylon plate. Since the experiment was done in an isolation enclosed room, the heat loss from the back of the nylon plate included mainly the natural convection and radiation heat transfer to the ambient. This heat loss was calculated as following

Q s ¼ hback Aback ðT w;back  T surrounding Þ þ Aback eback rðT 4w;back  T 4surrounding Þ

ð6Þ

where hback is the convection heat transfer coefficient over the back of the nylon plate, which was determined according to the empirical relation for natural convection from vertical flat plate [32]. Aback is the heat transfer area over the back of nylon plate; Tw,back is the averaged temperature on the back of nylon plate; Tsurrounding is the surrounding ambient temperature; eback is the emissivity of nylon plate; r is the Stefan–Boltzmann constant. In this manner, the heat loss was found to be about 5% of the power input. The local Nusselt number (Nu) on the target surface is defined as

hde Nu ¼ k

ð7Þ

In the present, the laterally-averaged convective heat transfer coefficient and Nusselt number (Nuav,x) on the target surface are defined according to the viewable thermal image visualization region of 120 mm  60 mm surrounding the jet orifice, as shown in Fig. 4.

R Ly hav x ¼

0

Nuav ;x ¼

hdy Ly

ð8Þ

hav ;x de k

ð9Þ

where Ly is set as 60 mm in the present investigation. In all the experiments, the measured temperature difference between the surface and ambient is at least 25 °C with an uncertainty of ±1.5%. The uncertainty of the power supplied to the heater, assumed to be the same as the uncertainty of the heat flux out of the heater, is approximately ±5%. The uncertainty in the thermal conductivity of air, given the small temperature fluctuations, is estimated to be less than ±2%. According to the methodology of Moffat [33], the maximum uncertainty in the measurement of the average convective heat transfer is ±8%. 3. Results and analysis 3.1. Stagnation convective heat transfer For a simple continuous impinging jet, the heat transfer characteristics depend strongly on the boundary conditions (e.g. the velocity profile in the orifice, turbulence intensity, and geometric confinement). This explains the wide range of correlations reported in the literature. Viskanta [34] presented a comprehensive literature review for steady jet heat transfer, showing that the values for the Reynolds exponent vary between 0.23 and 0.67 depending on factors such as the nozzle exit velocity profile. Persoons et al. [22] summarized some typical correlations of stagnation Nusselt for a continuous jet impinging perpendicularly onto a flat surface. For the purpose of comparison between the present work and former works, the following analytical and experimental results are cited as the following (Eqs. (10) and (11)). The analytical solution for an incompressible laminar jet with a uniform velocity profile: 0:4 NuCJ;0 ¼ 0:5856Re0:5 j Pr

NuCJ;0 ¼

0:4 0:5051Re0:5 j Pr

ðfor an axisymmetric jetÞ ðfor a two-dimensional jetÞ

ð10Þ

The experimental correction for an axisymmetric sharp orifice: 0:024

NuCJ;0 ¼ 0:462Re0:585 Pr0:4 ðs=de Þ j ðfor 1 6 s=de 6 5; NuCJ;0 ¼

4000 6 Rej 6 23; 000Þ

0:56 0:499Re0:694 Pr0:4 ðs=de Þ j

ðfor 6 6 s=de 6 14;

ð11Þ

4000 6 Rej 6 23; 000Þ

where the subscript CJ denotes continuous jet. Fig. 5 presents the current experimental results of stagnation Nusselt numbers for continuous impinging jets, which is plotted 0.4 as Nu0/(Re0:5 ) versus s/de, with the exponents m = 0.5 and j Pr n = 0.4 determined from laminar flow theory. It is seen that the presented experimental data are located in the zone bounded by Eqs. 0.4 (10) and (11). For a round-hole orifice, the value of Nu0/(Re0:5 ) j Pr is higher than that described by Eq. (10)and less than that described by Eq. (11). It remains the same (approximately 0.8) when the jet-to-surface spacing is less than 5. Beyond the jet-to-surface spac0.4 ing of 5, the value of Nu0/(Re0:5 ) decays as the increase of j Pr jet-to-surface spacing. This variation trend is in accordance with 0.4 that described by Eq. (11). At s/de = 8, the value of Nu0/(Re0:5 ) j Pr equals to that obtained from Eq. (10). For the rectangular-hole orifice, the jet-to-surface spacing has relatively less influence on the 0.4 value of Nu0/(Re0:5 ) in comparison with the round-hole orifice. j Pr

Fig. 4. Schematic diagram of average heat transfer coefficient definition.

0.4 Under the condition of s/de 6 8, the value of Nu0/(Re0:5 ) is about j Pr

X.-m. Tan et al. / International Journal of Heat and Mass Transfer 90 (2015) 227–238

233

Fig. 6. Dependence of stagnation Nusselt number NuSJ,0 on jet Reynolds number.

Fig. 5. Stagnation Nusselt numbers for continuous impinging jets.

0.61. Under the condition of 10 6 s/de 6 14, this value is about 0.51 which is the same with that obtained from Eq. (10). For the synthetic jet, the affecting factors on the heat transfer are more complicated as the synthetic jet is synthesized directly from the working fluid. It is known from available literature that the stagnation Nusselt number (NuSJ,0) impingement depends on the jet Reynolds number (Rej) and the ratio of stroke length to impinging distance (L0/s). Valiorgue et al. [21] performed isoflux and isothermal experiments at s/de = 2 and proposed scaling of the vertical axis as NuSJ,0/Renj .

NuSJ;0 ¼c Renj

ðL0 =s P 2:5Þ

NuSJ;0 L0 =s ¼ a þ ðc  aÞ 2:5 Renj

ð10=12Þ ðL0 =s < 2:5Þ

where the exponent was found to be n = 0.32 ± 0.06, the saturation value c = 1.52 ± 0.04 and the intercept a = 0.19 ± 0.07. The subscript SJ denotes synthetic jet. Persoons et al. [22] gave a re-treated relationship according to the experimental data obtained by Valiorgue et al. [21], as seen in Eq. (13).

NuSJ;0 ¼ 2:182Re0:32 Pr0:4 j

for ð2:5 6 L0 =s; 500 6 Rej 6 2150Þ ð13Þ

Persoons et al. [22] also proposed a general correlation for the stagnation point Nusselt number as seen in Eq. (14). This correlation includes the effect of all appropriate scaling parameters: Reynolds number (500 6 Rej 6 1500), jet-to-surface spacing (2 6 s/de 6 16) and stroke length (2 6 L0/de 6 40).

NuSJ;0

 2 s=de 1 þ 1:108 5:21 0:686 0:4 ¼ 0:1676Rej Pr f ðsÞ with f ðsÞ ¼  2:487 s=de 1 þ 5:21 ð14Þ

Fig. 6 shows the stagnation point Nusselt number varying with the Reynolds number for a round-hole synthetic jet impingement actuated by piston actuator. Also, some of experimental data and correlations for the synthetic jet are presented for comparison. It is found that the value of Reynolds exponent for the synthetic jet impingement actuated by piston actuator is about 0.32, as the same as that proposed by Valiorgue et al. [21]. However, the

obtained exponent for the synthetic jet impingement actuated by piston actuator is smaller than those reported for continuous impinging jets and synthetic jets proposed by Persoons et al. [22]. As the synthetic jets are characterized by Reynolds number and Strouhal number (Sr = fde/U0) or dimensionless stroke length (1/Sr = L0/de) [3,23], the effect of jet Reynolds number on the heat transfer will undergo a change as the dimensionless stroke length is increased. Comparing the experimental results presented by Valiorgue et al. [21] and Persoons et al. [22], although the synthetic jets were excited by the same acoustic actuator which has relatively higher frequency and lower stroke length, the jet-to-surface spacing was different for both studies. In the works of Valiorgue et al. [21], jet-to-surface spacing was maintained as 2. In the works of Persoons et al. [22], jet-to-surface spacing was varied between 2 and 16. Thus it is supposed that the ratio of stroke length to jet-to-surface spacing used by Valiorgue et al. [21] will be larger than that used by Persoons et al. [22]. As regards as the presented experimental results are concerned, the piston-driven synthetic jet has relatively lower frequency and higher stroke length. The ratio of stroke length to jet-to-surface spacing was considerably larger than those reported by Persoons et al. [22]. By comparing the presented results with the previous works, it is found the variation slope of NuSJ,0 vs Rej of the present is the same as that proposed by Valiorgue et al. [21]. This variation slope is less than that presented by Persoons et al. [22]. Therefore, it is suggested that the effect of jet Reynolds number on the heat transfer will be relatively weaker under larger dimensionless stroke length. In the work of Persoons et al. [22], four heat transfer regimes were identified. They also pointed out that the relative difference in terms of stagnation Nusselt number between the different regimes is about 30–40% for the same Reynolds number. Peak heat transfer performance at a given Reynolds number is obtained for a high ratio of stroke length to jet-to-surface (i.e. low frequency and low s/de). By comparing the present study with Valiorgue et al. [21], it is also found that the stagnation point Nusselt number of the piston-driven synthetic jet is relatively higher than the corresponding value presented by Valiorgue et al. [21] at the same Reynolds number, due to that the piston-driven synthetic jet is excited at low frequency but big stroke length. Fig. 7 presents a comparison of stagnation Nusselt number correlations and data reported for continuous impinging jets and synthetic impinging jets. It is seen that continuous jets exhibit stronger stagnation heat transfer than the synthetic jets, especially at low jet-to-surface spacing. By comparing the value of 0.4 Nu0/(Re0:5 ) varied from s/de for the synthetic jet from j Pr round-hole orifice, it is found that there is a significant deviation between Rej = 1550 and Rej = 5265. Under low Reynolds number, 0.4 ) varied from s/de for the synthetic the behavior of Nu0/(Re0:5 j Pr

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Fig. 7. Comparison of stagnation Nusselt number for continuous jet and synthetic jet.

jet is closed to the continuous jet impingement. As the time-averaged orifice velocity (U0) during the ejection part of the cycle is nearly proportional to the actuated frequency for the piston-driven synthetic jet, the influence of the confinement of impinging target on the synthetic jet away from the orifice could be relaxed under low Reynolds number. 0.4 Fig. 8 shows the dependence of NuSJ,0/(Re0:5 ) on j Pr jet-to-surface spacing. It is seen that there is an optimum jet-to-surface spacing for each synthetic jet at which the stagnation heat transfer reaches its peak value. The peak stagnation Nusselt numbers by synthetic jet impingement occur at jet-to-surface spacing of approximately 5 for the round-hole orifice, 5.5 for the square-hole orifice and 8 for the rectangular-hole orifice, respectively. As revealed by Gillespie et al. [13], if the impingement target is placed in the near-field with respect to the synthetic jet, the jet centerline velocity is low in the near-field and the ability of the synthetic jet to ingest cooler ambient fluid is restricted by the presence of heated target. Furthermore, the practical jet temperature is more significantly affected by the heated target. The lack of a fresh supply of cooling air in the confined synthetic jet case is also contributed to low heat transfer capacity. When the impingement target is placed in the far-field, the strength of the synthetic jet will diminish lowering the heat transfer capacity. It is also found that all the orifices have nearly the same optimum impinging distance (s) which is approximately 30 mm

Fig. 8. Dependence of NuSJ,0/(Re0:32 Pr0.4) on jet-to-surface spacing. j

in the present study. At this impinging distance, the stagnation point heat transfer coefficients are 167 W/(m2 K), 159 W/(m2 K) and 181 W/(m2 K) for the, round-hole orifice, square-hole orifice and rectangular-hole orifice, respectively. The synthetic jet heat transfer at stagnation point for the rectangular-hole orifice is slightly better than the other orifices. For the rectangular-hole orifice, one of the remarkable features is that the synthetic jet spreads rapidly along the minor axis direction of the orifice, while along the major axis the synthetic jet initially contracts and then spreads slowly [14]. When the impingement target is placed at intermediate or optimum impinging distance, the jet column along the spanwise edges of the jet is primarily confined to finite sectors around the major axis plane and a secondary counter rotating vortex pair is formed in the minor axis plane just below the impingement surface [13], providing enhanced heat transfer removed from the stagnation zone. Similar to Persoons et al. [22], a general correction function for taking consideration of jet-to-surface spacing on stagnation Nusselt number is recommended for the synthetic jet driven by a piston actuator.

 2 s=de  b 0:4 NuSJ;0 ¼ cRe0:32 Pr f ðsÞ with f ðsÞ ¼ 1  a j b

ð15Þ

where a, b and c are the constants. These constants for different orifices are listed in Table 4. The above correction matches more than 90% of the experimental data in the entire parameter range to within ±10%, as shown in Fig. 9. It is noted that this correlation is obtained in the following range of parameters. For the single-round orifice: 1550 6 Rej 6 5265, 2 6 s/de 6 8, L0/de P 100. For the single-square orifice: 1500 6 Rej 6 4630, 2 6 s/de 6 9, L0/de P 100. For the single-rectangular orifice: 950 6 Rej 6 2930, 2 6 s/de 6 14, L0/de > 100.

Table 4 Constants in Eq. (15). Orifice shape

Round 2 6 s/ de 6 8

Square 2 6 s/ de 6 9

Rectangular 2 6 s/ de 6 14

a b c

0.5 5 2.94

0.2 5.5 2.48

0.3 8 2.24

Fig. 9. Agreement of NuSJ,0 between experimental data and correlation in Eq. (15).

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3.2. Local convective heat transfer Fig. 10 presents local heat transfer coefficient distributions along x direction at y = 0. It is seen that continuous jets exhibit stronger local heat transfer than the synthetic jets in the vicinity of stagnation point, especially at low jet-to-surface spacing. For the continuous jet, the local heat transfer decreases rapidly from its peak value at the stagnation point. This local heat transfer coefficient distribution along x direction coincides with the flow patterns of a continuous jet, such as the stagnation region and the wall jet region. In comparison to the continuous jet, the synthetic jet produces much flatter and more uniform local heat transfer coefficient distributions over the surface. It is also seen from Fig. 10(a) that the effect of geometric confinement on the continuous jet is significantly less than the synthetic jet at low jet-to-surface spacing. As discussed in the above, both the low jet centerline velocity and lack of a fresh supply of cooling air are contributed to low heat transfer when the impingement target is placed in the near-field with respect to the synthetic jet. Although the continuous jet yields higher local heat transfer coefficients in the vicinity of stagnation point, the stronger entrainment of surrounding fluid and the vigorous mixing near the impingement surface featured by the synthetic jet are beneficial to produce more satisfactory heat transfer over the impinging target surface, especially at large jet-to-surface spacing. As seen in

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Fig. 10(b), the synthetic jet results in higher local heat transfer than the continuous jet in the far streamwise zone beyond x P 20 mm. When the jet-to-surface spacing is increased, the effect of geometric confinement on the evolution of vortical structures of synthetic jet will be weakened allowing the jet to propagate more fully. In additionally, the lack of a fresh supply of cooling air in the confined synthetic jet will also be weakened. Therefore, it is suggested that the synthetic jet behaves its superiority to the continuous jet on the overall heat transfer at large jet-to-surface spacing. With regards to the effect of orifice shape on local heat transfer, it is seen that the profile of local heat transfer coefficient distributions along x direction at y = 0 for the single-rectangular orifice is similar to that for the single-round orifice. The reason is associated with the advection dynamics of the high aspect ratio vortex loops that are formed around the circumference of the rectangular jet orifice during each actuation cycle [13]. In the near field of rectangular jet the crossstream major and minor axes switch or alternate with streamwise distance such that the jet ultimately becomes round in the far field. It is also found that the single-rectangular orifice produces a little higher local convective heat transfer than the other orifices in the vicinity of stagnation point. However the single-round orifice produces a little higher local convective heat transfer than the other orifices in the far streamwise zone beyond x P 20 mm. 3.3. Laterally-averaged convective heat transfer

Fig. 10. Local heat transfer coefficients along x direction at y = 0.

Fig. 11 present the variations of laterally-averaged Nusselt number with jet-to-surface spacing for single-round-hole, single-square-hole and single-rectangular-hole synthetic jets. Here the synthetic jets are all operated at the frequency of 24 Hz. It is seen that the laterally-averaged convective heat transfer at the target surface impinged by the synthetic jet varies with the jet-to-surface spacing increment. The optimum jet-to-surface distances for these orifices are nearly same, about 30 mm. When the jet-to-surface distance is small, the vortex ring generated in the vicinity of the orifice is not sufficiently distant from the orifice that it is virtually affected by the entrainment of the fluid into the cavity. On the other hand, if the jet-to-surface distance is beyond the optimum impinging distance, the intensity of the synthetic jet near the target will be decayed due to its large normal penetration, resulting in a degradation of the convective heat transfer on the impinging target. The orifice shape has slightly little influence on the optimum jet-to-surface spacing for the synthetic jet impingement driven by the piston actuator. It is however noticed that the orifice shape has a moderate effect on the convective heat transfer. For the single-round orifice, the peak laterally-averaged Nusselt number under the optimum jet-to-surface spacing is approximately 33, which is about 30% higher as compared to that under jet-to-surface spacing of 10 mm, as seen in Fig. 11(a). For the single-square orifice, the peak laterally-averaged Nusselt number under the optimum jet-to-surface spacing is approximately 25, which is about 10% as compared to that under jet-to-surface spacing of 10 mm, as seen in Fig. 11(b). For the single-rectangular orifice, the peak laterally-averaged Nusselt numbers under the optimum jet-to-surface spacing is approximately 18, which is about 25% higher as compared to that under jet-to-surface spacing of 10 mm, as seen in Fig. 11(c). Because the hydraulic diameter of orifice (de) is tightly associated with the orifice shape, one could not compare directly the convective heat transfer for different orifice shapes only on dependence of Nusselt number. Fig. 12 presents the laterally-averaged convective heat transfer coefficients for these three orifice shapes under the optimum jet-to-surface spacing. At this impinging distance, the peak laterally-averaged heat transfer coefficients are

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Fig. 11. Laterally-averaged Nusselt numbers for synthetic jets.

Fig. 12. Laterally-averaged heat transfer coefficients for synthetic jets at optimum jet-to-surface spacing.

143 W/(m2 K), 126 W/(m2 K) and 139 W/(m2 K) for the round-hole orifice, square-hole orifice and rectangular-hole orifice, respectively. It seems that the round-hole orifice is slightly better for a stronger overall heat transfer achievement than the other orifices.

Either from the viewing of stagnation point heat transfer or overall heat transfer, only two kinds of heat transfer regimes is observed in the present study. A critical ratio of stroke length to jet-to-surface spacing (L0/s) for achieving maximum heat transfer is identified as 18 approximately for the piston actuator regardless of orifice shape. It is found that this critical ratio for identifying the flow or heat transfer regimes of a synthetic jet driven by piston is far bigger than the corresponding value for the synthetic jet excited with high frequency [22,22]. For the synthetic jet excited with high frequency, the synthetic jet stroke length is far less than that of a piston-driven synthetic jet with low excitation frequency. As smaller stokes lengths impact less momentum to the vortex ring, thus the synthetic jet with bigger stroke length has stronger penetration capacity. For small distances (s < 20 mm), the impingement surface will play a restriction role on the formation and development of the vortex, as illustrated by Valiorgue et al. [21], resulting in a gradual increase of heat transfer as the jet-to-surface spacing is increased from 10 mm to about 30 mm. When the jet-to-surface spacing is increased beyond 30 mm, the jet average velocity upon impingement is like to be decayed, resulting in heat transfer decrease. It is also concluded that the synthetic jet originated from the single-square orifice introduces a weaker heat transfer achievement than the single-rectangular orifice or single-round orifice

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Fig. 13. Comparison of laterally-averaged Nusselt numbers between synthetic jets and continuous jets.

under the same jet-to-surface spacing. This finding is not fit well with the conclusion of Chaudhari et al. [18]. However, it is noticed that the orifice exit area was varied with the changed orifice and the synthetic jets issued form different orifices were all excited at a fixed frequency (200 Hz) in the experiment of Chaudhari et al. [18]. Thus the time-averaged orifice velocity and stroke length during the ejection part of the cycle at the exit was varied for the different orifice in the experiment of Chaudhari et al. [18]. While in the present experiment, the comparison for the orifice shapes (round, square and rectangular with aspect ratio of 7) was done under the condition where all the orifices were designed to have the approximately same exit area. The time-averaged orifice velocity and stroke length during the ejection part of the cycle at the exit maintains nearly the same for the different orifices. Fig. 13 presents a comparison of the laterally-averaged heat transfer coefficient ratios between the synthetic jet and the continuous jet impingement. Under jet-to-surface spacing of 10 mm, the laterally-averaged heat transfer coefficient ratios are below one, especially at x = 0 mm. The laterally-averaged Nusselt number for the synthetic jet at x = 0 mm is only 0.8 times that of continuous jet for the round-hole or square-hole orifice, as seen in Fig. 13(a) and (b). This ration is 0.74 for the rectangular-hole orifice, as seen in Fig. 13(c). When the impingement target is positioned close tightly to the orifice, the suction of surrounding fluid into the actuator cavity is affected seriously and the synthetic jet is not fully developed as it would in a free jet flow. As the

jet-to-surface spacing is increased to 30 mm, the advantage of synthetic jet takes on more obviously for stronger and wider impinging heat transfer in relative to the continuous jet. The heat transfer coefficient of synthetic jet is approximately 1.05–1.15 times that of the corresponding continuous jet at x = 0 mm. In addition, the relative heat transfer enhancement is more significant in the regions away from x = 0 mm. From Fig. 13, it is also shown that the advantage of synthetic jet in relative to the corresponding continuous jet impingement is more significant for the rectangular-hole orifice under larger jet-to-surface spacing. This advantage of synthetic jet impingement is relatively degraded for the square-hole orifice.

4. Conclusions This paper conducted an experimental research on the convective heat transfer characteristics under a normally synthetic jet driven by piston actuator. Particular attentions are paid to present the detailed local and laterally-averaged heat transfer comparison between synthetic jet and continuous jet, as well as to present the effect of orifice shape (single-round orifice, single-square orifice, and single-rectangular orifice) on the synthetic jet impingement driven by piston actuator. In additional, heat transfer regimes for the synthetic jet impingement in the situation of large stroke length to jet-to-surface spacing are further identified. The main conclusions are summarized as follows:

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(1) Continuous jets exhibit stronger local heat transfer than the synthetic jets in the vicinity of stagnation point. At lower jet-to-surface spacing, the laterally-averaged heat transfer coefficient ratios between synthetic jets and continuous jets are below one. However, the advantage of synthetic jets take on more obviously for stronger and wider impinging heat transfer in relative to the continuous jets at larger jet-to-surface spacing. (2) Either from the viewing of stagnation point heat transfer or overall heat transfer by synthetic jet impingement, only two kinds of heat transfer regimes is observed in the present study. A critical ratio of stroke length to jet-to-surface spacing (L0/s) is identified as 18 approximately regardless of orifice shape. (3) For the piston-driven synthetic jet with low frequency and larger stroke length, there is evidence for a power law relationship between stagnation Nusselt number and jet Reynolds number, as NuSJ;0 ¼ cRe0:32 Pr 0:4 f ðsÞ with f ðsÞ ¼ j  2 1  a s=dbe b . The constants (a, b and c) in this correction function are also determined for three different orifice shapes. (4) The orifice shape has a moderate effect on the convective heat transfer. The synthetic jet stagnation point heat transfer of a rectangular-hole orifice is slightly better than the other orifices. The synthetic jet originated from the round-hole orifice seems to introduce favorable overall convective heat transfer achievement. The advantage of synthetic jet in relative to the corresponding continuous jet impingement is more significant for the rectangular-hole orifice under larger jet-to-surface spacing. Conflict of interest None declared. Acknowledgements The authors gratefully acknowledge the financial support for this project from the National Natural Science Foundation of China (Grant No: 51306088) and the Fundamental Research Funds for the Central Universities (Grant No: NS2014018). References [1] B.L. Smith, A. Glezer, The formation and evolution of synthetic jets, Phys. Fluids 10 (1998) 2281–2297. [2] A. Glezer, M. Amitay, Synthetic jets, Annu. Rev. Fluid Mech. 34 (2002) 503–529. [3] J.E. Cater, J. Soria, The evolution of round zero-net-mass-flux jets, J. Fluid Mech. 472 (2002) 167–200. [4] B.L. Smith, A. Glezer, Jet vectoring using synthetic jets, J. Fluid Mech. 458 (2002) 1–34. [5] C. Lee, G. Hong, Q.P. Ha, A piezoelectrically actuated micro synthetic jet for active flow control, Sens. Actuators A 108 (2003) 168–174. [6] Q.F. Xia, S. Zhong, Enhancement of laminar flow mixing using a pair of staggered lateral synthetic jets, Sens. Actuators A 207 (2014) 75–83. [7] R. Mahalingam, N. Rumigny, A. Glezer, Thermal management with synthetic jet ejectors, IEEE Trans. Compon. Packag. Technol. 27 (2004) 439–444.

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