International Journal of Heat and Mass Transfer 73 (2014) 776–788

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International Journal of Heat and Mass Transfer

journal homepage: www.elsevier .com/locate / i jhmt

Time and phase average heat transfer in single and twin circularsynthetic impinging air jets

http://dx.doi.org/10.1016/j.ijheatmasstransfer.2014.02.0300017-9310/� 2014 Elsevier Ltd. All rights reserved.

⇑ Corresponding author. Tel.: +39 081 7683405/389; fax: +39 081 7683389.E-mail address: carlosalvatore.greco@unina.it (C.S. Greco).

Carlo Salvatore Greco a,⇑, Andrea Ianiro b, Gennaro Cardone a

a Dipartimento di Ingegneria Industriale – Sezione Aerospaziale, Università di Napoli Federico II, 80125 via Claudio 21, Napoli, Italyb Aerospace Engineering Group, Universidad Carlos III de Madrid, 28911 Av. de la Universidad 30, Laganés, Spain

a r t i c l e i n f o

Article history:Received 24 July 2013Received in revised form 19 December 2013Accepted 12 February 2014Available online 19 March 2014

Keywords:Synthetic jetsImpingement heat transferIR thermography

a b s t r a c t

This work presents an experimental investigation of impingement heat transfer in single circular syn-thetic jets and twin circular synthetic jets in phase opposition. All experiments have been performedat Reynolds number equal to 5100 and Strouhal number equal to 0.024 varying the jet axes distanceand nozzle to plate distance. An IR camera is used as temperature transducer for both time averageand phase average heat transfer measurements. Time average heat transfer maps show that singlesynthetic impinging jets have a behavior similar to that of continuous jets: at low nozzle to plate distance(up to 4 diameters) the heat transfer distribution shows an inner and an outer ring shaped region ofmaximum while for higher nozzle to plate distance such a feature disappears.

While obviously the twin configurations produce an heat transfer enhancement due to the fact that twojets instead of one are impinging, the interaction is found in general to have a beneficial effect. The phys-ical behavior is in common between single synthetic jets and twin configurations at jet axes distanceequal to 3 and 5 diameters. The twin circular synthetic air jets, with jet axes distance equal to 1.1 diam-eter, shows a different behavior with respect to single synthetic jet for H/D equal to 2 but for values ofH/D higher than 4 it starts acting like a single synthetic jet differently from the other twin configurationswhich behave as two separated synthetic jets. Phase averaged measurements allow for an accuratedescription of the heat transfer mechanism: at low nozzle to plate distances (2 and 4 diameters) the heattransfer is dominated by the unsteady impinging flow produced by the ring vortex that sweeps the walland causes the formation of the inner and outer ring shaped regions. At higher nozzle to plate distancethe heat transfer is due also to a steady and less coherent turbulent flow since the impingement occursafter the potential core and the saddle point.

� 2014 Elsevier Ltd. All rights reserved.

1. Introduction

The high heat transfer rate obtainable with impinging jets iswidely recognized and explained in scientific literature [1,2] andthe use of jets is very popular in many industrial applications suchas paper drying, glass tempering and turbine blades cooling. Ahuge quantity of data is available for single, rows and multiple jetswith also correlations for heat and mass transfer [3,4]. The averageand instantaneous flow topology of circular impinging jets is wellknown as well as its effect on heat transfer [5,6].

Recent literature is focusing on the design and optimization ofadvanced impinging jets devices in order to apply them inparticular fields such as electronic cooling. In particular several

recent literature works (see for instance [7–9]) focus on the studyof synthetic impinging jets. Synthetic jets are jets with zero-net-mass flux synthesized directly from the fluid in the system inwhich the jet device is embedded [10]. Such a feature obviatesthe need for an external input piping, making them ideal for lowcost and low space applications. A synthetic jet is generated by amembrane oscillation in a cavity which produces a periodicvolume change and thus pressure variation. As the membraneoscillates, fluid is periodically entrained into and expelled out fromthe orifice. During the injection portion of the cycle the flow fieldcould be considered as one inducted by a sink, which coincideswith the orifice, while during the expulsion portion of the cycle,a vortex ring can form near the orifice and, under certain operatingconditions [11], convects away to form a time averaged jet [10]. Insynthetic jets literature the stroke length L0 is the integral of theaverage velocity at the nozzle exit during the ejection part of thecycle:

Nomenclature

Bi Biot numbercp stainless steel specific heat (J/(kg K))D nozzle diameter (m)dTw/dt time derivative of wall temperature (K/s)f phenomenon frequency (Hz)f1 actuation frequency (Hz)Fof1 modified Fourier numberH nozzle to plate distance (m)H/D dimensionless nozzle to plate distanceh convective heat transfer coefficient (W/(m2 K))h time average convective heat transfer coefficient

(W/(m2 K))k air thermal conductivity (W/(m K))kloss head lossl jet-to-jet spacing (m)L nozzle length (m)L0 stroke length (m)Nu time average Nusselt numberNuu phase average Nusselt numberNu0 standard deviation of Nusselt number phase averagepc cavity pressure (Pa)pamb ambient pressure (Pa)q00j Joule heat flux (W/m2)q00r radiation heat flux (W/m2)q00r time average radiation heat flux (W/m2)q00n natural convection heat flux (W/m2)q00k tangential conduction heat flux (W/m2)q00k time average tangential conduction heat flux (W/m2)Re Reynolds numbers foil thickness (m)

Sr Strouhal numberTa ambient temperature (K)Tw wall temperature (K)Tw time average wall temperature (K)Taw adiabatic wall temperature (K)Taw time average adiabatic wall temperature (K)U axial velocity (m/s)Ua exit velocity on the jet axis (m/s)U0 reference velocityV sub-cavity volume (m3)x abscissa in the foil plane (m)y ordinate in the foil plane (m)

Greek symbolsa thermal diffusivity (m2/s)e total hemispherical emissivity coefficientu phase (�)kf foil thermal conductivity (W/(m K))l air dynamic viscosity (kg/(m s))q air density (kg/m3)qfoil stainless steel density (kg/m3)P

dimensionless jet-to-jet spacingr Stefan Boltzmann’s constant (W/(m2 K4))s actuation period (s)

AcronymNETD Noise equivalent temperature differenceSSJ Single synthetic jetTSJ Twin synthetic jet

C.S. Greco et al. / International Journal of Heat and Mass Transfer 73 (2014) 776–788 777

L0 ¼Z s=2

0UaðtÞdt ð1Þ

and the reference velocity is defined as:

U0 ¼ L0=s ð2Þ

where s is the actuation period and Ua is the exit velocity on the jetaxis.

Following Smith and Glezer [10] synthetic jets are characterizedby Reynolds number and dimensionless stoke length, which essen-tially is the inverse of the Strouhal number [11]:

Re ¼ q � U0 � D=l ð3Þ

1Sr¼ L0

Dð4Þ

where q is air density, l is air dynamic viscosity and D is the nozzlediameter.

The first literature work on synthetic jets used as cooling de-vices was published in 1982 by Gutmark et al. [12] that presentedheat transfer data on synthetic jet used to enhance both naturaland forced convection. The results revealed that the acousticallyexcited airflow can increase the overall heat-transfer coefficientby a factor of four. Later [13] studied the design and thermal per-formance of a heat sink for high power dissipation in electronicsenhanced with synthetic jet impingement. The results revealed acase temperature decrease from 71.5 to 36 �C with synthetic jetsoperation and a power dissipation of 20–40% higher with respectto the same heat sink with a fan in the flow rate range of 3–5 cubicfeet per minute.

Chaudhari et al. [7] carried out experiments on the cooling of aflat plate by using a synthetic jet generated through a circular

orifice. Such experiments for Reynolds number in the range1500–4200 and nozzle to plate distance in the range 0–25 D showthat the Nusselt number is comparable with that of continuous axi-symmetric jets at low Reynolds number (up to 4000), expecting itto be higher at greater values of Reynolds number.

Valiorgue et al. [8] identified two different flow regimesthrough defining a critical stoke length versus nozzle to plate dis-tance L0/H equal to 2.5. The heat transfer rate (that obviously in-creases with Reynolds number increasing) is found to be linearlyproportional with L0/H up to L0/H = 2.5 than constant for increasingL0/H values.

As for steady jets, heat transfer correlations have been devel-oped also for synthetic jets [14,15]. Arik and Icoz [14] establisheda closed form empirical correlation to predict the heat transfercoefficient as a function of Reynolds number, axial distance, orificesize and jet driving frequency. They observed that the heat transfercoefficient on a vertical surface increases with the driving voltage;it has a peak at the resonance frequency and the effect of the axialdistance on the heat transfer becomes stronger as the jet drivingfrequency increases. The empirical correlation proposed by Arikand Icoz [14] is valid for Re < 2900, 5 < H/D < 20 and actuation fre-quency between 0.16 times the resonance frequency and the reso-nance frequency. Persoons et al. [15] compared the stagnationpoint heat transfer performance of an axisymmetric synthetic jetversus established steady jet correlations. Such a research led toa general correlation for the stagnation point Nusselt numberincluding the effect of all appropriate scaling parameters: Reynoldsnumber (500 < Re < 1500), jet to surface spacing (2 < H/D < 16) andstroke length (2 < L0/D < 40). Based on such correlation, Persoonset al. [15] defined four heat transfer regimes, each one identifiedby a different range of values acquired by the ratio L0/H. The fourthregime, which is attained for a value of L0/H greater than 2.5, shows

Fig. 1. Sketch of experimental apparatus.

778 C.S. Greco et al. / International Journal of Heat and Mass Transfer 73 (2014) 776–788

an asymptotical behavior achieving the highest stagnation Nusseltnumber values with respect to the other regimes. The flow fieldfeatures of such four heat transfer regimes were reported byMcGuinn et al. [16] that carried out high speed PIV and single pointhot wire anemometry experiments in order to highlight thedependence of the impinging synthetic jet flow field (and of thecorresponding surface heat transfer distribution) on the dimen-sionless stroke length for a wide range of nozzle-to-surface spacing(2 < H/D < 16) and a single Reynolds number (1500).

At the same time, in order to improve synthetic jet heat transferperformances in practical applications, some recent studies are fo-cused on the design of special configurations. Rylatt et al. [17]decided to confine the impinging synthetic air jet asserting that,with such a configuration, cold air is drawn from a remote locationinto the jet flow. The experiments show that the ducted configura-tion, achieve a heat transfer enhancement of up to 36% in the stag-nation region. Chaudhari et al. [18] realized a particular syntheticjet device by means of a center orifice surrounded by multiple sa-tellite orifices. All the experiments were carried out varying boththe Reynolds number (1000 < Re < 2600) and the normalized axialdistance (1 < H/D < 30). Such an innovative configuration shows amaximum heat transfer coefficient which is approximately 30%more than the one of the conventional single orifice jet. Luo et al.[19] proposed a new generation of synthetic jet actuators consist-ing in two cavities sharing the same wall equipped with a singlepiezoelectric diaphragm and a slide block separating the two exitslots at an appropriate distance. Their numerical simulation re-sulted in a device which not only doubles the function of the exist-ing synthetic jet with a single diaphragm but also resolves theproblems of pressure loading and energy inefficiency of the exist-ing synthetic jet. Luo et al. [20] carried out PIV measurements ofsuch a dual synthetic jets actuator at Reynolds number and Strou-hal number equal to 2500 and 0.17. In the near field, they found amore complex flow field characterized by a ‘‘self-support’’ phe-nomenon between the two synthetic jets while in the far fieldthe two jets merge a single and more stable synthetic jet. Persoonset al. [21] studied two adjacent synthetic jets, with slot orifice,which allows to direct the flow by changing the phase betweenthe jets. Both PIV and IR thermography heat transfer measure-ments were carried out, at a fixed Reynolds number, equal to600, and dimensionless stroke length L0/D = 29 in order to quantifythe local convective heat transfer and flow field for different valuesof phase and jet-to-surface spacing H/D (6, 12 and 24). This workreports a 90% enhancement of the maximum and overall coolingrate, compared to a single jet, for a phase equal to 120� and ajet-to-surface spacing H/D equal to 12. Lasance et al. [22] replacedthe classical circular single jet configuration with a double circularconfiguration. The double configuration is found to be advanta-geous because of noise reduction [23] and improvement of heattransfer performances [24].

The flow field of a twin circular configuration was investigatedby Greco et al. [25]. Their PIV experiments [25], carried out using adevice composed by two adjacent synthetic jets, result in higherstreamwise velocity component, lower jet width and different vor-tex behavior for the configuration whose jet-axes-distance is equalto 1.1 D.

The aim of the present work is the investigation of circular sin-gle synthetic jets (SSJ) and twin synthetic jets (TSJ) impingementheat transfer. An acoustic resonator is designed as a cavity splitin two equal sub-cavities with the same resonance frequency bythe membrane of a loudspeaker therefore the synthetic jets issuedby the two sub-cavities are in phase opposition and this allows toreduce synthetic jet noise [23]. Experiments are carried out varyingthe jet axes distance between 1.1 and 5 nozzle diameters and thenozzle to plate distance between 2 and 10 nozzle diameters. Theinvestigation is performed for a fixed value of the Reynolds number

Re = 5100 and fixed value of Strouhal number Sr = 0.024 thusfalling in the fourth impinging synthetic jet regime defined byMcGuinn et al. [16], in order to achieve the maximum value ofthe stagnation Nusselt number. The impinging wall heat transferis measured by using IR thermography as temperature transducercoupled with the steady [26] and unsteady [27] heated thin foilheat transfer sensor. Data is reduced in non-dimensional form asNusselt number.

2. Experimental setup and data reduction

The experimental apparatus, sketched in Fig. 1, includes a stain-less steel foil (243 mm wide, 715 mm long and 40 lm thick). Thefoil, constituting the target plate, is steadily and uniformly heatedby Joule effect by passing an electric current through it and iscooled by the synthetic air jets impinging on it. Two couples ofbus bars, made of copper, clamped at the shortest sides of the foilare maintained at constant potential difference by using a stabi-lized DC power supply. The electrical contact between bus barsand foil is enhanced by putting there an indium wire (about1 mm in diameter). Furthermore, the foil thermal expansion is bal-anced by the spring-loaded bolts linked to the bus bars and by twospring-loaded insulators [28]. The target plate is positioned hori-zontally with the synthetic jets impinging vertically above in orderto minimize the effects of the natural convection on the foil. Thetwin circular synthetic air jets are generated by means of the de-vice shown in Fig. 1 that substantially coincides with the deviceused by the authors in [25]. The loudspeaker, whose diameter is270 mm, splits the cavity in two sub-cavities with a volume Vequal to 2 dm3. The two pipes, attached to both the sub-cavities,have a length L of 210 mm, a thickness of 1 mm and an inner diam-eter D of 21 mm. The jet axes distance l can be varied so that the

C.S. Greco et al. / International Journal of Heat and Mass Transfer 73 (2014) 776–788 779

non-dimensional distance R (defined as l/D) is varied between 1.1and 5 nozzle diameters; R equal to 1.1 corresponds to the condi-tion for which the two pipes are adjacent. The two sub-cavitiesare designed in order to have the same resonance frequency. In-deed the pipe length and diameter are equal for both the syntheticjets and the same cavity volume is achieved by filling the upperand the bottom sub-cavity using particular geometrical items.The single jet configuration is obtained deflecting one of the twosynthetic jets by using a bended tube at the exit of the orifice.

Experiments are performed for five values of the nozzle-to-plate distance (namely 2, 4, 6, 8 and 10 D) and 3 values of jet tojet spacing R (namely 1.1, 3 and 5). All the experiments are per-formed at the same value of the Reynolds number (5100) andStrouhal number (0.024). Such values of Reynolds number andStrouhal number are evaluated according to [29] from the mea-sured cavity pressure (pc) with respect to ambient pressure (pamb)by integrating the unsteady Bernoulli equation for an incompress-ible flow between a location inside the cavity and a location out-side the pipe:

dU ¼ pc � pamb

qþ klossUjUj

2

� �� 1

Lð5Þ

where the head losses kloss are estimated with PIV measurements[25]. The transducers used to measure the cavity pressure are twoHoneywell HSCDRRN002NDAA5 with a response time of 0.46 msand an accuracy of ±1.5% of the full scale (2 inches of water).

The complete synthetic jet device behaves like a mass–spring–damper system with two degrees of freedom [30]. The loudspeakerused in the present experiments (CIARE� HS250) has a measuredfree-space resonance frequency of 25 Hz, a nominal diameter of208 mm and an equivalent oscillating mass of 56 g. The resonancefrequency of the system was experimentally evaluated by measur-ing the loudspeaker impedance and the two resonance frequenciesof the complete system are found to be equal to about 4 and210 Hz, respectively, as shown in Fig. 2. At the higher resonancefrequency of the system the synthetic jet formation criterion [11]is not satisfied. The loudspeaker is thus supplied with a sinusoidalinput signal with a frequency f1 of 4 Hz by an Hi-Fi amplifier(CIARE� YSA 300) driven with a signal generator (DIGILENT AnalogDiscovery™). In order to perform phase averaged heat transfermeasurements, the same signal generator is used as external trig-ger with frequency equal to 120 Hz for the infrared camera (whoseintegration time is 590 ls), thus sampling the investigated phe-nomenon each 12�. For each sampled phase, 200 thermal imagesare acquired.

An infrared camera (CEPID JADE III 320 � 240 InSb focal planearray) measures the foil surface temperature with a spatial resolu-tion of 1.17 pixels/mm (24.5 pixels/D). The IR camera is accuratelycalibrated with a blackbody [26] for the whole measurement range

Fig. 2. Impedance versus the input frequency.

taking also in account the mirror presence in the optical path; thenoise equivalent temperature level (NETD) of the camera is about25 mK and the rms error from the blackbody calibration is lessthan 0.1 K. The foil surface is coated with high emissivity paint(e = 0.95) in order to increase accuracy of temperature measure-ments. In the present case, the IR camera is used in conjunctionwith the unsteady [27] and steady [26] heated thin foil heat trans-fer sensor. According to the application of the local unsteady en-ergy balance to the foil, the convective heat transfer coefficient hcan be evaluated as:

h ¼q00j � q00r � q00k � q00n � qfoil � cp � s � dTw=dt

Tw � Tawð6Þ

with q00j the Joule heat flux, q00r the radiation heat flux, q00k the tangen-tial conduction heat flux, q00n the natural convection heat flux, qfoil

the stainless steel density, cp the stainless steel specific heat, s thefoil thickness, dTw/dt the time derivative of wall temperature, Tw

the wall temperature and Taw the adiabatic wall temperature.On the other hand, by applying a steady state energy balance to

a foil [26] the relationship obtained is:

h ¼q00j � q00r � q00k � q00n

Tw � Tawð7Þ

where the upper bar indicates the time averaged quantities in stea-dy conditions (evaluated as the average of the whole 6000 acquiredIR images).

The surface temperature distribution is measured by viewingthe rear face of the foil (i.e., the side opposite to jet impingement)through a mirror, as shown in Fig. 1. In fact, since the Biot number(Bi ¼ �hs=kf where kf is the thermal conductivity of the foil) and theinverse of the modified Fourier number (Fof1 ¼ a=pf1s2 where a isthe thermal diffusivity) are small with respect to unity, the timeaverage and phase average temperature can be considered as uni-form across the foil thickness [31]. The unsteady heat transfermeasurements can be performed not only if the inverse of themodified Fourier number is small but also if the IR camera has en-ough sensitivity to detect the temperature oscillation. Such a con-dition is satisfied only if:

q00j � q00r � q00k � q00nqfoil � cp � s � f � NETD

� 1 ð8Þ

where f is the phenomenon frequency.For the present experiments, considering a loudspeaker fre-

quency equal to 4 Hz, the condition in (8) is verified since the typ-ical value of the ratio is equal to 25. Such a value was achieved witha typical Joule heating of about 830 W/m2 which was limited bythe temperature increase above the adiabatic wall temperature(i.e., Tw � Taw equal to about 14 K in the stagnation point) chosenin order to afford to perform such measurements without affectingflow quality and system operability.

Each test run consists of two parts: first, with electric currentoff, Taw is measured and the so-called ‘‘cold images’’ are recorded;then, electric current on, Tw is measured and the ‘‘hot images’’ arerecorded.

The net rate of radiation heat loss is estimated as:

q00r ¼ er T4w � T4

a

� �ð9Þ

where, r is the Stefan Boltzmann’s constant, Ta is the ambient tem-perature and e is the total hemispherical emissivity coefficient ofthe surface (it is found being at worst 45% of q00j at distances fromthe center of impingement higher than 4 diameters).

A little more complex is the procedure to compute thermallosses for tangential conduction (that are found to be at worst

780 C.S. Greco et al. / International Journal of Heat and Mass Transfer 73 (2014) 776–788

equal to 2% of q00j ). In particular, considering the foil plane corre-sponding with axes x and y, thermal losses for tangential conduc-tion for a metallic foil sensor can be expressed following [32]:

q00k ¼ kf ðx; yÞs@2T@x2 ðx; yÞ þ

@2T@y2 ðx; yÞ

!¼ kf s � r2T ð10Þ

Losses due to natural convection are mostly related to those of aheated plate facing downward [33]. To calculate exactly theselosses in our experimental facility, ad hoc experiments were per-formed to get an empirical correlation. By applying this correlationthermal losses were evaluated with an accuracy of ±10% of the totalvalue of said losses. The natural convection losses are, at worst,equal to 7% of q00j .

The unsteady term dTw/dt was evaluated over phase averaged andfiltered time sequences. The signal measured by the IR camera, infact, is affected by measurement noise (noise equivalent tempera-ture difference equal to 25 mK); the effect of noise is reduced byaveraging data over the 200 samples for each phase. In order to im-prove the accuracy of derivatives, a more smooth data is attainedwith a 7 points second order polynomial filter both in time and space.

The experimental data are reduced in dimensionless form interms of time average Nusselt number Nu ¼ hD=k (k is the thermalconductivity of air at film temperature defined as (Tw + Taw)/2),phase average Nusselt number Nuu = h(u)D/k and standard devia-tion of Nusselt number phase averaged fields Nu

0.

2.1. Error analysis

The present experimental methodology is well assessed in pre-vious works on circular impinging jets [5] for time averaged mea-surements. For the present experiments the control parametersand their uncertainty for time and phase average measurementsare reported in Table 1. With uncertainty analysis based on themethod of [34], the error in Re, considering Eqs. (3) and (5) and Ta-ble 1, is less than ±4%, the error for the Nu, considering Eq. (7)andTable 1, is less than ±3.5%, the error of Nuu, considering Eq. (6)andTable 1, is less than ±12.5% and the error of Nu

0is less than ±7.4%.

3. Results

3.1. Time average heat transfer measurements

Nu and Nu0maps for single and twin circular impinging synthetic

air jets with R equal to 1.1, 3 and 5 are shown in Figs. 3–7. Since thetime averaged flow field of all tested configurations is symmetricwith respect to x and y axes, Nu and Nu

0maps are obtained by

Table 1Control parameters and their uncertainty.

Parameter Typical value Typical error

Taw 293 K 0.25 KTw 305–323 K 0.25 KTa 293 K 0.1 KV 3 V 0.03 VI 46 A 0.46 Ae 0.95 0.01q00n 51 W/m2 5.1 W/m2

qfoil 79500 kg/m3 79.5 kg/m3

cp 502 J/Kgk 20 J/KgKs 40 � 10�6 m 8 � 10�7 mdTw/dt �3.9–2.5 K/s 0.21 K/sq 1.225 kg/m3 1.225 � 10�2 kg/m3

pc-pamb �100–100 Pa 7.5 PaD 0.021 m 0.1 � 10�3 ml 1.8 � 10�5 Pa s 1.8 � 10�7 Pa skloss 0.47 0.047L 0.21 m 0.1 � 10�3 m

Fig. 3. Nu (left) and Nu0

(right) maps for single synthetic jet, at Re = 5100 andSr = 0.024.

averaging the four quadrants in order to reduce the noise of themeasurements. For the sake of brevity, owing to the symmetry withrespect to y axis, only half map of Nu (on the left) and Nu

0(on the

right) are presented.

3.1.1. Single synthetic jet (SSJ)At short distance from the nozzle, as in continuous jets, a poten-

tial core exists also in synthetic jets as shown by Greco et al. [25],

Fig. 5. Nu (left) and Nu0(right) maps for twin synthetic jet (R = 3), at Re = 5100 and

Sr = 0.024.

Fig. 4. Nu (left) and Nu0

(right) maps for twin synthetic jet (R = 1.1), at Re = 5100and Sr = 0.024.

C.S. Greco et al. / International Journal of Heat and Mass Transfer 73 (2014) 776–788 781

thus many physical features can be considered as in analogy withcontinuous jets [2] impinging within the length of their potentialcore (i.e., H/D = 2 and 4). At H/D = 2 an inner ring shaped regionwith local Nu maximum appears at x/D � 0.5 and an outer regionwith local Nu maximum appears at x/D � 1.9 (see Fig. 3). Such aphenomenon is even more evident in Fig. 7 where the Nu andNu

0profiles at y/D = 0 are presented for H/D = 2, 4, 6 and 10.

Maximum values of Nu0

are also obtained approximately in thesame regions where inner and outer ring shaped structures are lo-cated as easily detectable in Nu

0map. The Nu values, measured in

the first ring shaped region, are slightly higher than the values ob-tained in the stagnation region. These first ring shaped regions arenot present for nozzle to plate distances higher than 4 (after theend of the potential core), as detectable from Nu and Nu

0profiles

Fig. 7. Nu (left) and Nu0

(right) profile for y/D = 0, at Re = 5100 and Sr = 0.024.Fig. 6. Nu (left) and Nu

0(right) maps for twin synthetic jet (R = 5), at Re = 5100 and

Sr = 0.024.

782 C.S. Greco et al. / International Journal of Heat and Mass Transfer 73 (2014) 776–788

in Fig. 7. It has to be remarked that a further increase of nozzle toplate distance up to 6 diameters increases the maximum Nu, inagreement with what happens for continuous jets. For all thetested values of H/D, the Nu

0profile reflects exactly the behavior

of the Nu profile. Moreover the value of Nu0

map becomes moreuniform and its maximum value decreases at high H/D because,as the distance from the nozzle increases [35], synthetic jets actlike turbulent continuous jets.

3.1.2. Twin synthetic jet (TSJ)The Nu maps for twin synthetic jets with R = 1.1 (Fig. 4) show

two distinct stagnation points only for H/D = 2. As a matter offact, considering Fig. 7, the relative Nu profile shows a first peakat x/D = 0 and a symmetric second peak at approximately x/D � 1.05. The first and the second peak are probably related tothe existence of the inner ring shaped region. Such a ring occursaround the two stagnation points, located at x/D � 0.55, andshows a diameter equal to 1 D. The superimposition of the twoinner ring shaped regions at x/D = 0 is the reason why the first

Fig. 8. Phase average Nusselt number maps for single synthetic jet at H/D = 2, at Re = 5100 and Sr = 0.024.

Fig. 9. Phase average Nusselt number maps for single synthetic jet at H/D = 6, at Re = 5100 and Sr = 0.024.

C.S. Greco et al. / International Journal of Heat and Mass Transfer 73 (2014) 776–788 783

Fig. 10. Phase average Nusselt number maps twin synthetic jet (R = 1.1) at H/D = 2, at Re = 5100 and Sr = 0.024.

784 C.S. Greco et al. / International Journal of Heat and Mass Transfer 73 (2014) 776–788

peak is higher than the second one. Moreover for this value of H/D also the outer ring shaped region can be detected at about x/D � 2.5 (see Fig. 7). Such considerations can be supported observ-ing the Nu

0maps and profile which clearly show the effect of the

unsteady passage of the ring vortex. Due to the superimpositionof the two inner ring shaped regions, the value of Nu

0acquired

at x/D = 0 is not equal to the one attained at x/D � 1.05, as canbe also inferred by Nu

0maps (Fig. 4). As H/D increases the strong

interaction between the two adjacent jets produces a differentheat transfer behavior characterized by a maximum Nu value atH/D = 4 as visibile in Fig. 7. For R = 1.1 and 4 6 H/D 6 8 Nu

0pre-

sents a different behavior from the Nu profile. In fact at H/D equalto 4 the Nu

0profile shows the peak relative to the inner ring

shaped region but the second peak is strongly reduced. Such asecond peak disappears for H/D higher than 4 differently fromthe first one. The first peak shifts toward the center as H/D in-creases because the jet, as previously explained, starts acting asa turbulent continuous jet. At H/D equal to 10 the Nu

0profile is

very similar to the one of a single synthetic jet. At all the nozzleto plate distances the values of Nu measured are higher. More-over it is worth to note that the values attained by Nu

0for such

a twin synthetic jets configuration are lower than the one ac-quired by the single synthetic jet (Figs. 3, 4 and 7).

Regarding the twin synthetic jets with R = 3 (Fig. 5) the Nus-selt number maps show two clearly distinct stagnation regions,approximately at x/D � 1.5 with its inner and outer ring shapedregions. In this configuration, for H/D = 2, the peak locatedapproximately at x/D � 1 (i.e., the outer peak of the consideredjet) is higher than the peak at x/D � 2 (i.e., the inner peak of theconsidered jet). This effect is related to the fact that the peak

which is closer to the center is more affected by the presence ofthe other jet and a beneficial effect is attained. Such a phenome-non decreases with H/D increase, disappearing already for H/D = 4.Also in this case the Nu

0and Nu maps and profiles present a sim-

ilar behavior. As matter of fact at H/D = 2 the Nu0

profile showstwo peaks at approximately x/D � 2.1 and x/D � 3.5 showing thepresence of the inner and outer shaped regions. The inflectionpoint at about x/D � 1.1, which attains a lower value of Nu

0with

respect to Nu0

at x/D � 3.5, can be ascribed to the interaction be-tween the outer ring of one jets with the other impinging jet.As H/D increases, the inner and outer structures disappear as vis-ible in Figs. 5 and 7. Moreover the maxima in Nu

0profile merge in

a unique maximum located at approximately x/D � 1.5, where thesynthetic jet impinges. The behavior of twin synthetic circular airjets with R = 5 (Fig. 6) is very similar to the one shown for R = 3.Nusselt number maps show two distinct stagnation regions,approximately at x/D equal to 2.5, which are present for all H/Ds. Also in this case, as for the single synthetic jet, for H/D = 2 aring-shaped region is visible around each stagnation region, asshown in Fig. 7. Indeed the Nu

0profile shows two peaks at about

x/D � 2.2 and x/D � 3.2. The inner peak is lower because is moreaffected by the other impinging synthetic jet, as occurs for thetwin configuration at R = 3. In this figure a mild plateau at x/D � 0 is detectable for values of H/D equal to 2, 4 and, barely, 6.Such a plateau decreases with increasing the nozzle to platedistance disappearing already for H/D = 8. This phenomenon isascribed to the interaction of the two outer ring shaped regionsrelated to the two existing stagnation regions. The behavior ofNu and Nu

0profile at higher H/D is similar to one of twin synthetic

jets with R = 3.

Fig. 11. Phase average Nusselt number maps twin synthetic jet (R = 1.1) at H/D = 6, at Re = 5100 and Sr = 0.024.

C.S. Greco et al. / International Journal of Heat and Mass Transfer 73 (2014) 776–788 785

3.2. Phase average heat transfer measurements

In order to reduce the measurement noise, owing to the factthat phase average flow field is symmetric with respect to the xaxis, Nuu maps are obtained averaging the positive y region withnegative one. With the objective to compare heat transfer distribu-tion at different phases and different value of H/D, it is necessary toset a reference phase zero. The reference phase zero is set to corre-spond with the phase in which the heat transfer time derivative inthe stagnation point changes its sign and becomes positive (for theTSJ the reference stagnation point is the right one). For sake ofbrevity, only the impingement half cycle is presented with 8 heattransfer phase maps with a step of 24�, for both single and twinsynthetic jet configurations.

Fig. 8 shows Nusselt number maps for the SSJ at H/D = 2, start-ing from u = 0� up to u = 168� (for all the phases see movie 1). Aspreviously assumed, at u = 0� the jet reaches the target plate andstarts spreading over the foil, as visible at u = 24�. At u = 48� thejet is sweeping the surface and the inner ring shaped region arisesat radial distance from the center of impingement r/D � 0.5. Thisresult is in agreement with DNS simulation of a continuous circularimpinging jet by Rohlfs et al. [36]. This inner ring shaped region iscaused by the radial wall acceleration [36,37]. At u = 72� the Nuuvalue at inner ring location increases its value, likely because syn-thetic jet continues impinging over the foil causing an increase ofthe wall radial acceleration, and an outer ring shaped region canbe detected at r/D � 1.9. Also in this case the outer ring shaped re-gion can been ascribed to unsteady separation and later reattach-ment as shown by Hadziabdic and Hanjalic [38] and Rohlfs et al.[36]. According to Rohlfs et al. [36] the unsteady separation isdue to the formation of the secondary vortex on the wall which

is generated by the passage of the ring vortex. Hence the delay be-tween the appearances of the two ring shaped regions can be as-cribed to the traveling time necessary to the vortex ring toassume the requested vorticity in order to generate the secondaryvortex. Such ring structures can be clearly seen at u = 96�; at thisphase the Nusselt number acquires its maximum value. Further-more the outer ring shaped region moves from r/D equal to about1.8 to r/D equal to approximately 2. Such a motion is caused by thetraveling secondary vortex which, according to Rohlfs et al. [36],separates from the wall at r/D equal to 2.1. After u = 96�, phaseaverage Nusselt number values in this region decrease and thetwo ring shaped regions weaken probably because the biggest partof the incoming flow (for the cycle) has already impinged. The mapfor H/D equal to 4 (not shown herein but present in the Supple-mentary material as movie 1) presents result similar to those atH/D = 2. The case of H/D equal to 6 is presented in Fig. 9. In agree-ment with what seen in the Nu map at H/D = 6, the two ring shapedregions are not present. The absence of the inner ring shapedregion is likely ascribed to the value of H/D which is greater thanthe synthetic jet potential core [25]. Moreover the absence of theouter ring shaped region is probably related to the fact that,according to [16], for L0/D > 16 the ring vortex rapidly loses coher-ence (at about H/D � 5). Probably in this condition the vortex ringdoes not have the possibility of impinge as a coherent structure onthe wall and generate the secondary vortex. It is possible also tonote that the maximum value of Nuu is attained around u = 72�

for H/D equal to 6 while it is attained at around u = 96� for H/Dequal to 2. Moreover the heat transfer rate is more spatially con-centrated near the stagnation point for H/D = 6 with respect tothe case with H/D = 2 where such cooling occurs inside the area en-closed by the outer ring shaped region.

Fig. 12. Phase average Nusselt number maps twin synthetic jet (R = 5) at H/D = 2, at Re = 5100 and Sr = 0.024.

786 C.S. Greco et al. / International Journal of Heat and Mass Transfer 73 (2014) 776–788

For all the H/D values, the phase average Nusselt number mapsfor u > 168� (not shown herein but present in the movie 1) presenta decreasing value of the heat transfer, with respect to the map atu = 168� and have all a similar spatial distribution.

The phase average Nusselt number maps for the TSJ with Requal to 1.1 and 5 at H/D equal to 2 and 6 are reported in Figs. 10–13. The phase average Nusselt number maps for the configurationwith R = 3 have not been reported because their behavior is verysimilar to that of the twin synthetic jets with R = 5. All phase aver-age Nusselt number maps are reported as video sequences in mo-vie 2, 3 and 4 for R = 1.1, 3 and 5, respectively. The phase averageNuu maps (Fig. 10) of TSJ for R = 1.1 at H/D equal to 2 show a dif-ferent behavior with respect to SSJ (Fig. 8). During the ejectionphase, at u = 0�, a higher heat transfer (Nuu in the stagnation pointis about double with respect to the single synthetic jet), is shownmainly due to the strong jet interaction [25]. At u = 24� the phaseaverage Nuu map of TSJ already shows, with respect to SSJ, theinner ring shaped region; at u = 48� such a map shows an highervalue of Nuu at the inner ring shaped region and the presence ofthe outer ring shaped region differently from SSJ. These phenom-ena are caused by the higher centerline velocity of the TSJ withrespect to SSJ [25]. In fact such a higher velocity generates a fasterspreading of the impinging synthetic jet over the foil, hence agreater wall radial acceleration, and a quicker traveling of the ringvortex. Furthermore at u = 72� the TSJ Nuu map shows a highervalue at inner and outer ring regions with respect to SSJ. The great-er value of Nuu at the outer ring shaped region is due to the exist-ing strong interaction between the two jets [25] which causes anincrease in vortex ring strength [25]. In the following phases thevalue acquired by the phase average Nusselt number for TSJ arecomparable (at u = 96�) or slightly lower (at u = 120�) than the

those of SSJ in the same phase. Finally the inner and outer ringshaped regions disappear approximately at the same phase forboth configurations. For H/D equal to 6 the outer and inner ringshaped regions for both configurations (Figs. 9 and 11) are notdetected because, as in the case of the single synthetic jet, thenozzle-to-plate distance is much higher than the potential coreof the synthetic jet. Moreover it is possible to highlight that alsofor this value of H/D the phase averaged Nusselt number map ofTSJ, for the first four phases, attain a higher value with respect tothe SSJ due to the higher jet centerline velocity [25]. On the otherhand, the behavior, in the last four phases, is the same for bothconfigurations.

TSJ for R = 3 and R = 5, differently to the SSJ and to R = 1.1 pres-ent at phase zero two heat transfer maxima in the stagnationpoints (see Figs. 12 and 13). One maximum is due to the right jetgenerated from the right TSJ that is reaching the target plate (inthe right part of map), while on the left the maximum is due tothe extinguishing left TSJ. All these TSJ configurations show abehavior close to SSJ one during the ejection phase but with a dif-ferent position of stagnation point. For all the H/D values, in eachtwin synthetic jet configuration, the phase average Nusselt numbermaps for u > 168� (not shown herein) present a symmetric distri-bution respect 180� phase delay and the y axis (as visible in movie2, 3 and 4).

4. Conclusions

In this work impinging single and twin synthetic jets are experi-mentally studied at Reynolds number equal to 5100 and Strouhalnumber equal to 0.024. The heat transfer on the impinged plate is

Fig. 13. Phase average Nusselt number maps twin synthetic jet (R = 5) at H/D = 6, at Re = 5,100 and Sr = 0.024.

C.S. Greco et al. / International Journal of Heat and Mass Transfer 73 (2014) 776–788 787

measured with the steady and unsteady heated thin foil heat fluxsensors using IR thermography as temperature transducer. The anal-ysis is conducted for nozzle to plate distances ranging between 2 and10 diameters and for jet to jet spacing between 1.1 and 5 diameters.

Synthetic impinging jets behave in a similar way to that of cir-cular continuous jets: when impingement occurs within thelength of the jet potential core (i.e., at nozzle to plate distanceequal to 2 and 4 diameters) the heat transfer distribution showsan inner and an outer ring-shaped region of maximum. For highervalues of nozzle to plate distance the double ring shaped maximadisappear and the stagnation heat transfer reaches a maximumfor H/D equal to 6. This behavior is in common between singlesynthetic jets and twin configurations at R equal to 3 and 5.The twin circular synthetic air jet, with R equal to 1.1, shows adifferent behavior with respect to single synthetic jet for H/Dequal to 2 but for values of H/D higher than 4 it starts acting likea single synthetic jet differently from the other twin configura-tions which behave as two separated synthetic jets. Indeed atH/D equal to 10 such a twin configuration shows Nu and Nu

0

profiles very similar to the single synthetic jet one.Phase average measurements show as the heat transfer mecha-

nisms at low nozzle to plate distance is achieved through the ringvortex that sweeps the wall and causes the formation of the innerand outer ring shaped region in analogy with what found in contin-uous circular impinging jet. In particular, immediately after the ar-rival of the air issued by the nozzle, a first ring-shaped region ofheat transfer maximum forms; as the ring vortex sweeps the wallthe outer heat transfer ring maximum appears. At higher nozzle toplate distance the heat transfer is due to also to a steady turbulentflow since the impingement occurs after the potential core and thesaddle point.

The results presented in this paper show a general heat transfergain achieved with the twin synthetic jets, especially at lower jet-to-jet spacing. Future research is required to analyze this gain witha look at the power input into the device, which was not possiblewith current experimental setup since both devices have practi-cally the same power input (the single jet configuration is obtaineddeflecting one of the two synthetic jets by using a bended tube atthe exit of the orifice). Furthermore, to exploit the advantageouseffect of the jet-to-jet interactions, systems of jets arrays shouldbe designed for intensive surface cooling and for the study of theeffect of different phase shifts.

Appendix A. Supplementary data

Supplementary data associated with this article can be found, inthe online version, at http://dx.doi.org/10.1016/j.ijheatmasstrans-fer. 2014.02.030.

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