An investigation on convective heat transfer performance around piezoelectric fan vibration envelope in a forced channel flow

International Journal of Heat and Mass Transfer 126 (2018) 48–65

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An investigation on convective heat transfer performance around piezoelectric fan vibration envelope in a forced channel flow Xin-Jun Li a, Jing-zhou Zhang a,b,⇑, Xiao-ming Tan a a b

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

a r t i c l e

i n f o

Article history: Received 11 July 2017 Accepted 3 June 2018

Keywords: Piezoelectric fan Channel flow Combined flows Instantaneous flow field Time-averaged convective heat transfer

a b s t r a c t An experimental and numerical investigation is performed in the current study to further explore the convective heat transfer performance by a vertically-oriented piezoelectric fan in the presence of channel flow. The effects of velocity ratio and fan tip-to-heated surface clearance are taken into considerations. It is illustrated that the presence of channel flow has an innegligible influence on the vibration amplitudes of the piezoelectric fan under large channel flow velocities. In the presence of channel flow, the vortical structures at the edges of vibrating fan are certainly suppressed, especially under large velocity ratios. On the other hand, the vortical streaming flow mixes with the channel flow to form a long stripe of vortical structure downstream of the fan vibration envelope. Under small velocity ratios, the impingement role of streaming flow along fan tip is still dominated and simultaneously the channel flow passing through the vibration envelope is effectively pulsated. Therefore, combined flows generally produce heat transfer enhancement around the fan vibration envelope related to the pure vibrating fan, especially at a small non-dimensional tip-to-surface gap. While under large velocity ratios, the impingement role of streaming flow induced by a vibrating fan is seriously weakened by the strong channel flow. The convective heat transfer produced by combined flows in the fan vibration envelope is generally reduced in comparison with pure piezoelectric fan. Related to the pure channel flow, the combined flows effectively improve the convective heat transfer, especially downstream of the fan vibration envelope. Ó 2018 Elsevier Ltd. All rights reserved.

1. Introduction Piezoelectric fan is a solid-state device which employs the reversed piezoelectric effect to make the piezoelectric patch expand and contract periodically, driving the attached flexible blade to oscillate at the same frequency [1]. Due to the oscillatory motion of flexible blade, the neighboring fluid is periodically excited and thus a pseudo-jet or streaming flow is produced shedding along the fan tip. Previous investigations illustrated that the streaming flow induced by a piezoelectric fan is of vortical feature and the attainable flow rate is tightly dependent on the vibration parameters (such as vibration frequency, amplitude and mode shape) and geometric parameters of the piezoelectric fan [2–5]. Recently, the piezoelectric fan has gained much attention in the electronic cooling applications on account of its pseudo-jet impingement role [6]. ⇑ 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 address: [email protected] (J.-z. Zhang). https://doi.org/10.1016/j.ijheatmasstransfer.2018.06.021 0017-9310/Ó 2018 Elsevier Ltd. All rights reserved.

Toda and Osaka [7] were the pioneers who promoted the exploratory research dealing with heat transfer enhancements by piezoelectric fans. Since the work of Toda and Osaka [7], considerable efforts had been paid to reveal the convective heat transfer performances induced by piezoelectric fans. Schmidt [8] experimentally investigated the local and average heat transfer coefficients on a vertical surface cooled by two piezoelectric fans. It was found that varying the distance between the fan and the surface noticeably changed the heat transfer coefficients for the system. Acikalin et al. [9–11] performed a series of studies on the thermal performance of piezoelectric fans. Their results demonstrated that an enhancement in convective heat transfer coefficient of more than 100% related to natural convection was achieved. The influence of main governing parameters such as fan tip-to-target distance, vibration amplitude and operating frequency on the heat transfer were also illustrated. Kimber and Garimella [12,13] experimentally investigated the local heat transfer performance of vibrating cantilevers. The local heat transfer coefficient distribution for a single fan was found to change from a lobed shape at small fan tip-to-surface gaps to an almost circular shape at intermediate gaps. At larger gaps, the heat transfer coefficient

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49

Nomenclature Ap App D f G h H Lb Lp Ly Nu q Re t T U u UR W

vibration amplitude of fan-tip (m) peak to peak amplitude of fan-tip (m) hydraulic diameter (m) frequency (Hz) fan tip-to-surface distance (m) convective heat transfer coefficient (W/(m2
K)) inner height of channel (m) exposed length of fan (m) PZT length (m) lateral distance for average use (m) Nusselt number heat flux (W/m2) Reynolds number time (s) temperature (K) operation voltage (V) velocity (m/s) velocity ratio width of fan (m)

distribution became elliptical in shape. Wait et al. [14] investigated the performance of piezoelectric fans operating at higher resonance modes. Both finite element analysis and experimental test demonstrated that the electromechanical coupling factor (EMCF) of a piezoelectric fan can be greater at higher resonance modes. However, this certain advantage of piezoelectric fan operating at higher resonance modes were offset by some serious disadvantages, such as increased power consumption and losses, as well as decreased bulk fluid flow. Liu et al. [15] made an experimental study concerning the influence of piezoelectric fan orientation on the thermal performance over a flat surface. It was illustrated that both vertical and horizontal arrangements have the same order of heat transfer enhancement magnitude. The heat transfer for the vertical arrangement showed a symmetrical distribution whereas the horizontal arrangement possessed an asymmetric distribution. Abdullah et al. and Fairuz et al. [16–18] performed a set of investigations concerning the effects of fan height, tip gap, vibrating amplitude and mode shape on the heat transfer characteristics of finned heat sinks. Among the tested ranges, the case with least tip gap and highest amplitude was confirmed to be the best. Their results also showed that the increase of vibrating mode number decreases the attainable air flow velocity approaching to the target surface, thus impeding the cooling capabilities. Lin [19] performed a numerical simulation on three-dimensional flow induced by piezoelectric fans in the presence of an impinging target plate. Of particular was that the vibrating fan produced two air streams due to the presence of impinging target plate, namely a stream in the longitudinal direction and a stream in the transverse direction. The two streams interacted to form two counter-rotating screw-type flow structures on either side of the blade adjacent to the heated surface. Huang et al. [20] made an inverse problem investigation on determining the optimal position for piezoelectric fan. Experimental verifications were also made to justify the validity of the presented estimation of the optimal fan position. Tan et al. [21] performed a numerical investigation on the flow and heat transfer performances induced by vertically-oriented vibrating cantilevers in a confined space. It was found that the interaction of vortex induced by the vibrating beam and wall jet formed by the pseudo-jet impingement makes the intensity of vortices strong and pushes the vortex core upwards or downwards, contributing for higher heat transfer.

x y z

x-direction y-direction z-direction

Greek letters surface emissivity k2 criterion for vortex structure identification m kinematic viscosity (m2/s) r Stefan-Boltzmann constant

e

Subscripts 0 Stagnation point a relative to ambient avx laterally-averaged b relative to back surface of wall c relative to working fluid CF cross flow PF piezoelectric fan w relative to wall

To our knowledge, relatively little efforts had been devoted to reveal the flow and thermal performance of piezoelectric fans in the presence of a cross flow. For the conventionally continuous jet impingement, vast investigations had revealed that the initial cross flow has a significant influence on the convective heat transfer [22–25]. Lin [26] performed a numerical investigation on the heat transfer performance of cylindrical surface by the piezoelectric fan under forced convection conditions with an inlet velocity in the range of 0.46–2.30 m/s. It was found that the streaming jet induced by the vibrating fan mixes the free stream in the wake region and prompts an improved heat transfer performance. However, it was also noted that streaming jet induced by the vibrating fan can increase the wake region and reduce the local heat transfer from the cylindrical surface over the baseline case if the operational criteria beyond certain limits, such as under some specific situations with a large fan tip amplitude, a large fan tip-toheated surface clearance and a high free flow velocity. Jeng and Liu [27] experimentally investigated the heat transfer and fluid flow behaviors of the heat sink partially filled in a rectangular channel with the axial mainstream interacted by the oscillating movement of the upstream piezoelectric fan. It was illustrated that the oscillating movement of piezoelectric fan strengthen the turbulent intensity of the mainstream at low Reynolds number, giving the additional disturbance momentum to the mainstream and making the fluid flow through the heat sink with turbulent flow characteristic. In a common sense, due to the fluid-structure coupling nature, the presence of a cross flow will affect the fluid-structure interaction of piezoelectric fans and consequently the flow and thermal performance. For addressing further insights on convective heat transfer performance around piezoelectric fan vibration envelope in a forced channel flow, a series of experimental tests are made by varying the excitation voltage of piezoelectric fan and channel flow inlet velocity. The influences of the channel flow on the vibration amplitude of piezoelectric fan and convective heat transfer around the fan vibration envelope are illustrated. Besides, threedimensional numerical simulations are also performed by using the dynamic meshing technique and sophisticated user defined functions describing the time-varying displacements of a vibrating fan. The instantaneous vortical structures and temperature contours on the heated surface are captured for illustrating the

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affecting mechanism of channel flow on the convective heat transfer performance by a vertically-oriented piezoelectric fan. 2. Experimental procedures 2.1. Experimental setup The experimental setup used in the current investigation is schematically shown in Fig. 1. It consists basically of three main components: the forced channel flow supply passage, the piezoelectric-fan actuation system, and the test section. The forced channel flow is supplied by a screw air compressor with a nominal pressure of 0.8 MPa. It is firstly drawn through a standard flow meter. A control valve is set in the flow metering supply passage for adjusting the flow mass rate. The rectangular channel is 600 mm in length with a sectional size of 80 mm (inner height)  140 mm (inner width). To ensure a uniformly-distributed channel flow at the inlet of tested section, a flow straightening net with a length of 250 mm is placed in the front of tested section. The temperature of channel flow is measured by a thermocouple probe located inside the tested channel immediately close to the straightening net outlet. The forced channel flow Reynolds number (ReCF) is defined as

ReCF ¼

uCF DCF

m

ð1Þ

where uCF is the channel flow velocity, DCF is the hydraulic diameter of channel, m is the kinematic viscosity of the air. In the current study, the channel flow velocity is varied between 0.94 m/s and 8.0 m/s. Accordingly, the channel flow Reynolds number is varied between 6000 and 51250. The piezoelectric fan is located at the bottom side and a heater foil is adhered tightly on the top side of the tested section. The piezoelectric fan is arranged normally to the heated surface with a fan tip-to-heated surface gap (G) and its vibrating direction is perpendicular to the channel flow direction. A specific piezoelectric fan designed for the current experiment is schematically shown in Fig. 2. The piezoelectric bimorph used in the present study is PZT with length (Lp) of 28 mm, width (W) of 25 mm, and thickness of 0.5 mm. The blade attached to PZT patch is made of stainless steel with a thickness of 0.1 mm. Its exposed length (Lb) is 38 mm. Therefore, the total length of stainless steel sheet (Lp + Lb) is 66

(a) x-z plane

(b) y-z plane

Fig. 2. Schematic geometry of piezoelectric fan.

mm. An additional bracket is affixed to the end of piezoelectric fan for facilitating it to a rigid surface via two bolt holes. By adjusting the bracket, a series of fan tip-to-heated surface gaps or nondimensional distances (G/H, here H is inner height of cross flow channel) are obtained. The peak-to-peak amplitude of fan-tip is denoted as App. The vibration amplitude of fan-tip (Ap) is a half of peak-to-peak amplitude of fan-tip. To drive the piezoelectric fan, a function generator and a voltage amplifier are needed. The sinusoidal voltage provided by a function generator is fed to the piezoelectric fan through the voltage amplifier. By pre-calibrated tests, it is determined that the first-mode resonant frequency of this piezoelectric fan is 51 Hz. According to the previous studies (Kimber et al. [4], Wait et al. [14], Fairuz et al. [18], etc.), the operating frequency (f) of the piezoelectric fan is therefore fixed at 51 Hz. Details of this specific piezoelectric fan are summarized in Table 1. 2.2. Vibration test and characterization of vibrating fan The vibrating characteristics of piezoelectric fan are tested by a Laser Doppler Vibrometer (OptoMET Vector-Master) with a resolution of 2.5 nm/s. By adjusting the forced channel flow velocity and operating voltages, the displacements of this specific piezoelectric fan under different conditions are determined.

Fig. 1. Schematic diagram of experimental setup.

X.-J. Li et al. / International Journal of Heat and Mass Transfer 126 (2018) 48–65

the front surface exposed to internal forced convective heat trans-

Table 1 Details of the piezoelectric fan.

fer, that is T front ¼ T rear ¼ Tw. w w

Specification

Value

Blade material Exposed blade size (Lb  W  tp) PZT patch length (Lp) Input waveform Operating voltage (U) First-mode resonant frequency (f) Power consumption

Stainless steel 38 mm  25 mm  0.1 mm 28 mm Sinusoidal wave 50–250 V 51 Hz 15–40 mW

The Reynolds number of streaming jet induced by a vibrating cantilever was characterized by using the maximum fan-tip displacement velocity (uPF) as a characteristic velocity and the hydraulic diameter (DPF) of the fan-tip vibration envelope as a characteristic length [12].

RePF ¼

uPF DPF

m

ð2Þ

The characteristic velocity and hydraulic diameter are defined as

uPF ¼ 2pfAp DPF

4Ap W ¼ 2Ap þ W

uCF uPF

front qfront ¼ qjoule  qrear c loss  qr

ð6Þ

where qjoule is the constant electric heat-flux on the heater foil, qrear loss is the heat loss from the rear surface of the heater foil, qfront is the r radiative heat flux from the front surface to surrounding walls. The heat loss from the rear side of the heater foil to the ambient though the solid wall is estimated by the following formula

qrear loss ¼ heff ;b ðT b  T a Þ

ð7Þ

where Ta and Tb are the ambient temperature and the averaged wall temperature on the back or outer side of top wall exposed to the ambient surrounding, respectively. heff,b is effective heat transfer coefficient which taking both the natural convective heat transfer and the radiative heat transfer into consideration. By a series of pre-calibrated tests, a linear fitted formula for predicting the effective heat transfer coefficient is deduced in a temperature difference ranging from 10 °C to 70 °C.

ð3Þ

heff ;b ¼ 0:11ðT b  T a Þ þ 12:5 W=ðm2
KÞ

ð4Þ

The radiative heat transfer from the front surface of heater foil to surrounding walls is approximately estimated by adopting a simple radiative heat transfer formula

where Ap is the vibration amplitude of fan-tip. W is the width of piezoelectric fan. f is the operating frequency. Viewing from Eq. (3), the characteristic velocity of the piezoelectric fan is tightly associated with the operating frequency and vibrating amplitude of fan-tip. For the specific piezoelectric fan designed in the current study, as the operating frequency is fixed at the first resonant frequency, thus the varying of characteristic velocity is realized by changing the operating voltage or vibrating amplitude of the piezoelectric fan. The velocity ratio is defined as the ratio of channel flow velocity to characteristic velocity of the fan.

UR ¼

51

ð5Þ

2.3. Heat transfer test and validation As schematically shown in Fig. 3(a), a stainless steel sheet (200 mm in length and 90 mm in width) with a thickness of 0.05 mm is acted as a target surface. The foil is heated by DC current with twoend edges connecting to the copper bars to ensure a uniform heat flux. The electrical power is fed to the heater foil through a transformer and the heating flux is evaluated on the basis of electric voltage and current measurements. The temperature distribution on the back surface of heater foil is measured by an infrared camera which operates in the long infrared band (8–14 lm). A ZincSelenide glass (45 mm wide, 105 mm long and 5 mm thick) with a high transmissivity of nearly 0.97 in the long IR band (8–14 lm) of the infrared spectrum is located on the test section to act as an infrared transparent window. To make the measurement more accurately, the test surface is sprayed with a uniform thin black paint which has a high emissivity. The emissivity of 0.96 is identified for the black painted test surface from a calibration test similar to that adopted by Zhang et al. [28]. In the determination of local convective heat transfer coefficient, the really convective heat flux (qfront ) is derived from the heat c flux balance on the heater foil, as schematically shown in Fig. 3(b). Since the heater foil thickness is very thin, the temperature on the rear surface of the foil is practically regarded the same as that on

qfront ¼ rew ðT 4w  T 4surrounding Þ r

ð8Þ

ð9Þ

where Tsurrounding is the surrounding temperature to the heated surface, which is practically regarded as the working fluid temperature Tc. Tw and ew are the temperature and emissivity of the heated surface, respectively. r is the Stefan-Boltzmann constant. According to the above treatment, the local convective heat transfer coefficient is finally determined.

h¼

front qjoule  qrear qfront c loss  qr ¼ Tw  Tc Tw  Tc

ð10Þ

The laterally-averaged convective heat transfer coefficient (havs) along streamwise direction is determined in a certain lateral distance for average use.

hav x ¼

1 Ly

Z

Ly =2

hðx; yÞdy Ly =2

ð11Þ

here Ly is the lateral distance for average use. As the magnitude of the selected lateral distance for average affects significantly the assessment of heat transfer performance due to the localized cooling feature of piezoelectric fans, therefore several distances are adopted in the current study, such as 1–3 times of peak-to-peak amplitudes at fan tip in the lateral direction. Strictly, the temperature distribution on the heated surface is varied in time due to the periodic movement of vibrating fan. However, a quasi-steady state where the variation of temperature distribution on the heated surface is very little is reached after certain cycles. In the experimental test, quasi-steady state condition is demonstrated to be reached after 10 min once the piezoelectric fan is turned on. To examine the current heat transfer test, a comparison of stagnation Nusselt number (Nu0,PF) versus non-dimensional gap G/Ap with the experimental data presented by Kimber et al. [12] under the sole role of piezoelectric fan is demonstrated in Fig. 4. Here the Nusselt number (Nu0,PF) is defined by using the hydraulic diameter (DPF) of the fan vibration envelope as the characteristic length. It is seen that the present experimental results are very coincident with the corresponding data of Kimber et al. [12].

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(a) Schematic diagram of heater foil

(b) Schematic diagram of heat balance on heater foil Fig. 3. Schematic heat transfer measurement.

2.4. Uncertainty estimation

Fig. 4. Stagnation Nusselt number versus non-dimensional gap G/Ap under piezoelectric fan.

The experimental uncertainties for the main parameters are summarized in Table 2. According to the pre-calibrated data, the standard flow meter for channel flow measurement has an accuracy of ±1%. Assuming the measurement uncertainty of the channel flow inlet area is about ±2%, the maximum uncertainty of the channel flow velocity is approximately ±5%. The function generator for controlling the excitation frequency has an accuracy of ±1%. The measured resolution of vibrating displacement is assumed as 0.05 mm. Therefore, the maximum uncertainty of the characteristic velocity of piezoelectric fan is approximately 3%. The uncertainty of the heat flux for determining local convective heat transfer coefficient is approximately estimated to be ±5%. The measured temperature difference between the surface and channel flow is suggested with an uncertainty of ±2%. The uncertainty in the measurement of convective heat transfer coefficient is estimated to be within ±8%.

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X.-J. Li et al. / International Journal of Heat and Mass Transfer 126 (2018) 48–65 Table 2 Summarization of test uncertainties. Parameter

Error source

Maximum uncertainty

Channel velocity uCF (m/s)

Mass flow rate (kg/s), ±1% Inlet area (m2), ±2% Excitation frequency (Hz), ±1% Vibrating amplitude (m), ±2% Heat flux (W/m2), ±5% Temperature (°C), ±2%

±5%

Characteristic velocity uPF (m/s) Convective heat transfer coefficient (W/(m2
K))

±3%

Table 3 Influence of operating voltage on characteristic parameters of piezoelectric fan without channel flow. Operating voltage (V)

UPF (m/s)

RePF

50 150 220 250

0.83 1.67 2.15 2.34

450 1540 2360 2710

±8%

3. Experimental results and analysis 3.1. Vibration amplitude and displacement Fig. 5(a) shows the effect of operating voltage on the piezoelectric fan vibration displacements in the situations without the presence of channel flow. It is seen that the operating voltage has a significant influence on the deformation of piezoelectric fan. Approximately 200% relative increase of the fan-peak amplitude is demonstrated when the operating voltage is increased from 50 V to 250 V. According to Eqs. (2) and (3), the characteristic

velocities (uPF) and Reynolds numbers of the piezoelectric fan under different operating voltages are illustrated in Table 3. Fig. 5(b) shows the effect of channel flow on the piezoelectric fan vibration displacements under the excitation voltage (U) of 220 V. It is seen that the fan-tip amplitude is decreased with the increase of channel flow velocity. The channel flow with a velocity less than 1.56 m/s has a very weak influence on the piezoelectric fan vibration. In the presence of a channel flow with uCF = 3.75 m/s, the fan-tip amplitude is decreased within 10% related to that of no cross flow case. Once the channel flow velocity is increased up to 8 m/s, the relative decrease of fan-tip amplitude reaches to 56%. The presence of channel flow has an innegligible influence on the vibration amplitudes of the piezoelectric fan under high channel flow velocities. The aerodynamic loading on the vibrating cantilever due to fluid-structure interaction is suggested to be significantly enhanced due to the presence of strong channel flow, resulting the damping of vibration amplitude. The characteristic velocities (uPF) and Reynolds numbers of the piezoelectric fan under different channel flow velocities are illustrated in Table 4. With regard to the influence of fan tip-to surface gap, it is confirmed that the fan tip-to surface gaps in range between 3 mm and 7 mm has nearly no impaction on the vibration amplitudes of the piezoelectric fan, either under different operating voltages or under different channel flow velocities. The displacement of the PZT patched portion (Lp) is really regarded as zero. The displacement function of the vibrating cantilever beam Y(z) is deduced by using a polynomial fitting.

YðzÞ ¼ p1 z4 þ p2 z3 þ p3 z2 þ p4 z þ p5

ðLp 6 z 6 ðLp þ Lb ÞÞ

ð12Þ

Here the unit of z and Y(z) is mm. The relevant coefficients in Eq. (11) under different operating voltages and channel flow situations are shown in Tables 5 and 6 respectively. The maximum displacement deviation of the fitting correlations is limited within 5%.

(a) without channel flow 3.2. Heat transfer coefficients without channel flow Fig. 6 presents the tested heat transfer coefficient maps on the heated surface under individual piezoelectric fan operating at 220 V. The fan vibration envelope is illustrated by the dotted lines on each image. It is found from Fig. 6(a) and (b) that convective heat transfer coefficient maps take on dumbbell-shaped contour around the fan vibration envelope under a small or moderate fan tip-to-surface gap. While under a larger fan tip-to-surface gap, as seen in Fig. 6(c), the heat transfer coefficient distribution takes on almost circular shape at the center of fan vibration envelope. As the increase of fan tip-to-surface, the peak heat transfer is found

Table 4 Influence of channel flow velocity on characteristic parameters of piezoelectric fan operating at 220 V.

(b) operating voltage of 220V Fig. 5. Tested deformations of vibrating fan.

Cross-flow

UPF (m/s)

RePF

UCF = 0.94 m/s or ReCF = 6000 UCF = 1.56 m/s or ReCF = 10000 UCF = 3.75 m/s or ReCF = 24020 UCF = 8.0 m/s or ReCF = 51250

2.15 2.08 1.95 0.98

2360 2240 2020 600

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Table 5 Coefficients of Eq. (12) under different operating voltages without channel flow. Voltage (V) 50 150 250

p1

p2 7

6.38  10 1.214  106 2.004  106

p3 5

8.699  10 1.683  104 2.615  104

p4 3

2.794  10 5.363  103 7.839  103

p5 2

2.608  10 4.945  102 6.548  102

3.028  102 5.605  102 5.569  102

Table 6 Coefficients of Eq. (12) under operating voltage of 220 V in presence of channel flow. uCF (m/s)

p1

p2

p3

p4

p5

0.00 1.56 3.75 8.00

1.886  106 2.028  106 1.603  106 8.22  107

2.447  104 2.628  104 2.159  104 1.133  104

7.31  103 8.095  103 6.764  103 3.714  103

6.078  102 7.162  102 6.077  102 3.572  102

5.092  102 7.407  102 6.426  102 4.428  102

to decrease gradually because the fan-excited streaming flow approaching the target surface is decayed. The above features are in good agreements with the findings of Kimber et al. [12]. Also,

(a) G/H=0.0375

as illustrated early in Fig. 4, the present experimental results coincide well with the corresponding data of Kimber et al. [12] in quantity. Fig. 7 shows the local convective heat transfer coefficient distributions in the center line of z = 0 mm. In this figure, the dotted lines represent the bounders of fan vibration envelope in xdirection. Two peaks of local convective heat transfer coefficient distribution are demonstrated in the situations where the piezoelectric fan is excited with a large operating voltage and the fan tip is close to the heated surface. When the piezoelectric fan is excited with a little operating voltage, only one peak heat transfer coefficient is appeared at the center of fan vibration envelope even the fan tip is located close to heated surface. It is also noted that when the piezoelectric fan is excited with a large fan-tip amplitude, the convective heat transfer enhancement in the fan vibration envelope is quantified to exceed 375% related to natural convection, showing a good agreement with the finding of Acikalin et al. [10]. 3.3. Heat transfer coefficients in presence of channel flow The convective heat transfer performance around piezoelectric fan vibration envelope in a forced channel flow is tightly dependant on the mutual interaction of both flows. To illustrate clearly the influence of channel flow on the convective heat transfer around fan vibration envelope, two typical situations are discussed respectively. (1) Under small velocity ratios

(b) G/H=0.0625

(c) G/H=0.0875 Fig. 6. Tested heat transfer coefficient maps under individual piezoelectric fan operating at 220 V.

Fig. 8 presents the local convective heat transfer coefficient maps produced by a piezoelectric fan operating at 250 V in the presence of a weak channel flow. It is seen that the distribution of local convective heat transfer coefficients surrounding the fan vibration envelope behaves very intricately. Under a small nondimensional gap (G/H) of 0.0375, as seen in Fig. 8(a) and (b), the local convective heat transfer around the fan vibration envelope is mostly improved by the combined action of vibrating fanexcited streaming flow and channel flow. Approximately 50% increase of peak heat transfer coefficient is achieved by comparison with the pure piezoelectric fan condition. Under larger nondimensional gaps (G/H) of 0.0625 and 0.0875, as seen in Fig. 8(c) and (d), the peak heat transfer coefficient is decreased obviously related to that of G/H = 0.0375. But about 30% increase of peak heat transfer coefficient is still achieved in comparison with the pure piezoelectric fan condition. Two main causes are suggested to be associated with the local convective heat transfer enhancement under combined-flow condition where the channel flow velocity is relatively less than the characteristic velocity of the fan. Firstly,

X.-J. Li et al. / International Journal of Heat and Mass Transfer 126 (2018) 48–65

55

70 PF(U=50V) PF(U=150V) PF(U=220V) PF(U=250V)

60

2 h (W/m K)

G/H=0.0375 50 40 30 20 10

(a) G/H=0.0375, uCF=0.94m/s (UR=0.4) -2

-1

0

1

2

x/W

(a) G/H=0.0375 70 PF(U=50V) PF(U=150V) PF(U=220V) PF(U=250V)

60

h (W/m2 K)

G/H=0.0625 50

(b) G/H=0.0375, uCF=1.56m/s (UR=0.67)

40 30 20 10

-2

-1

0

1

2

(c) G/H=0.0625, uCF=0.94m/s (UR=0.4)

x/W

(b) G/H=0.0625 70 PF(U=50V) PF(U=150V) PF(U=220V) PF(U=250V)

60

h (W/m2 K)

G/H=0.0875 50

(d) G/H=0.0875, uCF=0.94m/s (UR=0.4) 40

Fig. 8. Tested heat transfer coefficient maps under small velocity ratios (U = 250 V).

30 20 10

-2

-1

0

1

2

x/W

(c) G/H=0.0875 Fig. 7. Tested convective heat transfer coefficient in center line of z = 0 mm under individual piezoelectric fan.

the channel flow velocity is low enough to weakening the impingement role of streaming jet produced by the vibrating fan. Secondly, the vibrating fan plays a disturbance role on disturbing the channel flow and thus improves the channel-flow convective heat transfer.

The laterally-averaged convective heat transfer coefficients under small velocity ratios are presented in Fig. 9. Here three times of fan-tip peak-to-peak amplitudes is adopted as the lateral distance for average use. Viewing from Fig. 9, the role of streaming jet impingement induced by piezoelectric fan is confirmed to be dominated on convective heat transfer around the fan vibration envelope. Due to the influence of cross flow, the streamwise location corresponding to the peak laterally-averaged convective heat transfer coefficient is moved downward, especially under a large fan tip-to-surface gap. Under a small non-dimensional gap, the convective heat transfer around fan vibration envelope is increased about 40% in comparison with the pure piezoelectric fan case, as seen Fig. 9(a). Under a moderated or large nondimensional gap, the laterally-averaged convective heat transfer coefficient in the front of fan vibration envelope is found to be less than that produced by the pure piezoelectric fan, as seen in

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Generally, in the situations where the velocity ratio is small, the impingement role of streaming jet induced by a vibrating fan is dominated around the fan vibration envelope and simultaneously the channel flow passing through the vibration envelope is effectively pulsated. Therefore, combined flows produce significant heat transfer enhancement around the fan vibration envelope, in comparison with the pure piezoelectric fan. (2) Under large velocity ratios

(a) G/H=0.0375

(b) G/H=0.0625

(c) G/H=0.0875 Fig. 9. Tested laterally-averaged convective heat transfer coefficient under small velocity ratios (U = 250 V, average in 3App).

Fig. 9(b) and (c). However, in the downstream zone of fan vibration envelope, the convective heat transfer is significantly improved in the presence of channel flow related to the pure piezoelectric fan action.

Fig. 10 presents the local convective heat transfer coefficient maps produced by a piezoelectric fan operating at 220 V in the presence of a strong channel flow. It is seen that the convective heat transfer under combined flows with large velocity ratio is contrary to that with small velocity ratio. As illustrated previously in Fig. 5(b), the fan-tip amplitude is seriously reduced by a strong cross flow. Due to the reduction of fan-tip amplitude, the streaming flow induced by the vibrating fan is certainly weakened. Besides, the fan-excited streaming jet approaching the heated surface will also be supposed to be deflected by the strong cross flow. Consequently, the potential benefit of a piezoelectric fan for localized convective heat transfer enhancement in the fan vibration envelope is affected by the presence of a strong channel flow. However, downstream of the fan vibration envelope, the local convective heat transfer is effectively enhanced, as seen in Fig. 10(a)–(c). Of particular is that a branchingshaped distribution of local heat transfer coefficients is clearly observed under UR = 1.92 and G/H = 0.0875, as seen in Fig. 10 (c). Under UR = 8.2, the effect of piezoelectric fan on the local convective heat transfer coefficient maps is limited in a narrow strip downstream of the fan vibration envelope, as seen in Fig. 10(d). Fig. 11 presents the tested laterally-averaged convective heat transfer coefficient distributions under the individual piezoelectric fan, individual channel flow and combined flows under large velocity ratios. Here the piezoelectric fan is actuated at 220 V. It is conformed that the combined action of channel flow and fan-excited streaming flow improves the laterally-averaged convective heat transfer coefficient related to the pure channel flow, especially in the downstream zone of the fan vibration envelope. However, it is also found that the laterally-averaged convective heat transfer coefficient produced by combined flows is generally less than that by pure piezoelectric fan in the fan vibration envelope. This suggests that the impingement role of the fan-excited streaming flow is seriously weakened by the strong channel flow. On the other hand, as the convective heat transfer due to the channel flow is enhanced with the increase of the channel flow velocity, the combined flows with a velocity ratio of 8.2 produce higher convective heat transfer around the fan vibration envelope than that with a velocity ratio of 1.92. Generally, in the situation where the velocity ratio is large, the impingement role of streaming jet induced by a vibrating fan is seriously weakened by the channel flow. On the other hand, the convective heat transfer due to the channel flow is enhanced with the increase of the channel flow velocity. Therefore, the convective heat transfer around the fan vibration envelope maybe less than that under pure piezoelectric fan case. However, the combined action effectively improves the convective heat transfer coefficient in comparison with pure channel flow around the fan vibration envelope, especially at the downstream of fan vibration envelope. In the region between x/W = 1 and x/W = 3, the laterally-averaged convective heat transfer coefficient under combined action is increased approximately by 50% at the downstream of fan vibration envelope related to the pure channel flow.

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70

G/H=0.0375

CF(uCF=8.00m/s) PF+CF(UR=1.92) PF+CF(UR=8.20)

50

2

havz (W/m K)

60

PF(U=220V) CF(uCF=3.75m/s)

40 30 20 10

(a) G/H=0.0375, u CF=3.75m/s (UR=1.92)

-2

-1

0

1

2

3

4

x/W

(a) average in 1 App 70

(b) G/H=0.0625, uCF=3.75m/s (UR=1.92)

havz (W/m2 K)

60

PF(U=220V) CF(uCF=3.75m/s)

G/H=0.0375

CF(uCF=8.00m/s) PF+CF(UR=1.92) PF+CF(UR=8.20)

50 40 30 20 10

-2

-1

1

0

2

3

4

x/W

(b) average in 2 App 70

(c) G/H=0.0875, uCF=3.75m/s (UR=1.92) havz (W/m2 K)

60

PF(U=220V) CF(uCF=3.75m/s)

G/H=0.0375

CF(uCF=8.00m/s) PF+CF(UR=1.92) PF+CF(UR=8.20)

50 40 30 20

(d) G/H=0.0375, uCF=8m/s (UR=8.2) Fig. 10. Tested heat transfer coefficient maps under large velocity ratios (U = 220 V).

4. Three-dimensional flow field simulations

10

-2

-1

0

1

2

3

4

x/W

(c) average in 3 App Fig. 11. Tested laterally-averaged convective heat transfer coefficient under large velocity ratios (U = 220 V, G/H = 0.0375).

4.1. Brief description of computational scheme The numerical simulation models are built up according to the experimental tested model. In order to reveal the difference of flow fields around the vibrating piezoelectric fan with and without the

targeting surface, as well as the effect of channel flow on the flow and heat transfer behaviors of a piezoelectric fan, three computational models are taken into considerations as schematically shown in Fig. 12.

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(a) no targeting surface

corresponding to the channel flow inlet is replaced by a velocityinlet boundary, while the other boundary conditions are kept the same as the corresponding ones in Fig. 12(b). Considering a compromise between accuracy and computational cost, three-dimensional unsteady Reynolds-averaged Navier–Stokes (RANS) simulation is employed in the current study. As the governing equations for describing the three-dimensional unsteady flow and heat transfer are common [19,21], for simplicity, only some important issues are outlined as the follows. In performing the simulation of convective heat transfer, the density of air is assumed to vary with the temperature in accordance with the general properties of an incompressible ideal gas. The other thermal proprieties are treated as constants with values determined in accordance with the ambient air temperature. In the simulation, the piezoelectric fan is modeled as a cantilever beam without thickness. The trajectory of the cantilever beam in time is given as the following.

yðz; tÞ ¼ YðzÞ sinð2pftÞ

(b) no channel flow

here Y(z) is the displacement of the vibrating cantilever beam, f is the operating frequency. z is the distance from the fixed end of the vibrating cantilever beam. The displacement functions for the vibrating piezoelectric fan under different situations are taken from Table 6. That is, in the current computations, only the operating voltage of 220 V is taken into consideration. According to displacement function, dynamic meshes are used to model the deformation of a vibrating piezoelectric fan in time. In order to avoid negative cell volume, a very small time step is required. At every time step, the computational domain is then re-meshed according to the trajectory of the piezoelectric fan. The dynamic mesh is implemented by using the spring-based smoothing method combined with the local re-meshing method [5,21]. The computational meshes are generated using the gridgeneration software ANSYS ICEMCFD 14.5. The mesh between the cantilever beam tip and the targeting wall as well as the mesh near the cantilever beam are particularly refined. To evaluate the systematic mesh sensitivity, a mesh sensitivity analysis based on the Grid Convergence Index (GCI) [29] is carried out. For the purpose of GCI estimation, three different tetrahedron meshes, with 417,363 elements (coarse grid), 916,948 elements (intermediate grid), and 1,514,550 elements (fine grid), are constructed. The computational domain is chosen as Fig. 12(b) with a channel inletvelocity (uCF) of 3.75 m/s under G/H = 0.0375. Fig. 13 presents the grid independence tested results. It is illustrated that the overall

(c) with channel flow Fig. 12. Schematic there-dimensional simulation models.

For the situation without targeting surface, as seen in Fig. 12(a), the dimensions of computational domain are chosen as 100 mm (length)  140 mm (width)  140 mm (height). The boundary conditions are specified as follows. The surrounding air temperature is set as 300 K and the surrounding boundary is treated as pressure boundary, permitting the flow of air in the inward or outward direction. While for the situations with targeting surface, the dimensions of computational domain are chosen as 145 mm (length)  140 mm (width)  80 mm (height). In Fig. 12(b), no channel flow is presented. While in Fig. 12(c), the cross flow is presented. A uniform heat flux of q = 1700 W/m2 is applied on the heated surface while other surfaces are treated as thermally adiabatic. No-slip condition is applied to the solid wall. For the computational domain shown in Fig. 12(c), the flow boundary

ð13Þ

Fig. 13. GCI plotted on local convective heat transfer coefficient.

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discretization errors are mainly blow 10%. Accordingly, approximately 1  106 computational grids are finally selected in the presented computations. Another important issue in the computation is the selection of turbulence model. According to the previous numerical investigation on the piezoelectric fan [18,26] as well as steady jet and unsteady jet impingement [30,31], the SST k-x two-equation model is selected for modeling the turbulence viscosity. The computation is performed using FLUENT code. A user defined function (UDF) is implemented for describing the displacement function of vibrating cantilever beam. Each vibration period is partitioned into 100 time steps, giving a temporal resolution of 0.0002 s. The simulation is selected such that the temperature reached a steady value during this period. Approximately 5000 iterations are at least required for the run of each simulation. During a period, the time-averaged local convective heat transfer coefficient is calculated by

Z hðx; yÞ ¼ 0

t

1 hðt; x; yÞdt Dt

ð14Þ

(a) maximum displacement position at left

(c) quadric position from right to left

59

where Dt is the product of periodic cycle numbers and the time of each period, dt is the time step. 4.2. Computed instantaneous flow and temperature fields To reveal the effect of targeting surface on the flow fields induced by a piezoelectric fan, the computed instantaneous vortical structures under some typical phases (such maximum displacement position at left, neutral position from left to right, quadric position from right to left, neutral position from right to left) without and with the targeting surface are presented in Figs. 14 and 15, respectively. Here the vortical structures are visualized by the use of k2 criterion [32,33]. In this technique for vortex structure identification, the velocity gradient tensor ru is split into symmetric and anti-symmetric parts corresponding to the strain rate tensor S ¼ 0:5ðru þ ruT Þ and the rotation tensor X ¼ 0:5ðru  ruT Þ and the k2 is the second eigenvalue of S2 þ X2 . The instantaneous temperature contours on the heated surface are also illustrated in Fig. 15 where the targeting surface is presented. In order to

(b) neutral position from left to right

(d) neutral position from right to left

Fig. 14. Isosurfaces of k2 identified by a value of 6  104 at different phases without targeting surface.

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(a) maximum displacement position at left

(c) quadric position from right to left

(a) neutral position from left to right

(d) neutral position from right to left

Fig. 15. Instantaneous temperature maps and iso-surface of k2 = 6  104 at different phase without channel flow (G/H = 0.0375).

visualize the temperature contours more clearly, Fig. 15 is displayed in reverse related to Fig. 14. In Fig. 14, the velocity vector distributions at the x-y plane in the vicinity of fan tip are also displayed. When the fan is moved from its maximum deflection position to zero deflection or neutral position, as seen in Fig. 14(b) and (d), it is clearly seen that two sets of horse shoe type vortex are formed from both edges of vibrating fan, moving towards the fan tip and rolling up over the fan tip. In this process, the displacement velocity of fan tip varies from zero to its peak value. During the acceleration of vibrating fan from its maximum deflection position to neutral position, a pair of counter-rotating vortices (one in the clockwise direction and the other in the counter-clockwise direction) is also observed to be initiated around the horse shoe type vortex. Due to the difference of vibrating direction between Fig. 14(b) and (d), the counter-rotating vortices displayed in Fig. 14(d) are is in the opposite directions to Fig. 14(b). As previously revealed by Choi et al. [5], the formation of these vortices is caused by the pressure differential and the shear with the surrounding air because the fan generates positive pressure on its leading surface and a negative pressure on its trailing surface. When the vibrating fan reaches its maximum deflection position, as seen in Fig. 14(a), the vortex core increasingly lags behind the fan towards the fan tip throughout its motion. The vortex structure indicated by the k2 = 60,000 iso-surface appears to be split from the half position of the vibrating fan, which is in accordance with the tested results presented by Jeffers et al. [32]. Due to the entrainment, the surrounding air travels into the low pressure zone, thus developing and separating the vortex in the vicinity of fan tip. When the vibrating fan approaches a

quadric position from its maximum deflection position to neutral position, as seen in Fig. 14(c), the branch of horse shoe type vortex behind the fan is weakened (corresponding to the left branch in Fig. 14(a)) and the other branch in the front of fan is enhanced (corresponding to the right branch in Fig. 14(a)). Beyond the tip of the fan, the vortex develops freely downwards. It is also found that the ejection of fluid downstream the fan tip is stronger in the situation of zero deflection position. As illustrated by Jeffers et al. [32], the inertial resistance to entrainment behind the retreating fan appears more apparent as the vibrating fan decelerates to its position of maximum deflection. Once the targeting surface is presented, the interaction between the streaming flow induced by the vibrating fan and the impingement target will affect the vortex development in comparison with the situation without the targeting surface. After impingement of the vertical flow induced by the vibrating fan, the wall jet flow is formed in the outward direction and thus interacts with the vertical flow induced by the vibrating fan. As the vortex at the fan tip is certainly affected by the wall jet flow, it is easier to be destroyed, as seen in Fig. 15. It is also found that the heated surface directly impinged by the vertical flow has a relative low temperature, producing a convective heat transfer enhancement in the vicinity of fan vibration envelope. Fig. 16 presents the instantaneous velocity vectors at x-y plane tightly close to the impinging target under G/H = 0.0375. It is seen that the wall jet flow is originated from the center of the fan vibration envelope in the outward direction and the surrounding flow is suctioned toward the fan vibration envelope from the central zones at both sides of fan, thus producing a dumbbell-shaped

X.-J. Li et al. / International Journal of Heat and Mass Transfer 126 (2018) 48–65

(a) maximum displacement position at left

0

(b) neutral position from left to right

61

distribution of transient surface temperature map around the fan vibration envelope as seen in Fig. 15. Fig. 17 show the vortical structures visualized by k2 = 60,000 and the temperature contours on the heated surface in the presence of channel flow under G/H = 0.0375, at two topical vibrating phases respectively. By comparing with Fig. 15, it is certainly that the channel flow has a great influence on the vertical structure around piezoelectric fan under high velocity ratios. Under a small velocity ratio of 0.72, the vibration amplitude of the piezoelectric fan is nearly the same as that without channel flow. Therefore, the horse shoe type vortex structures visualized by k2 = 60,000 at the edges of vibrating fan are weakly affected by the channel flow at neutral position, as seen in Fig. 17(a1). However, at maximum displacement position, as seen in Fig. 17(a2), the horse shoe type vortex structure at the front edge of vibrating fan is destroyed by the channel flow. During the sweep of vibrating fan, the local heat transfer improvement in the vicinity of fan vibration envelope is obviously demonstrated. Downstream of the fan vibration envelope, the heat transfer improvement is also behaved obviously. Under a large velocity ratio of 1.92, as seen in Fig. 17(b1) and Fig. 17(b2), the horse shoe type vortex structures visualized by k2 = 60,000 at the edges of vibrating fan are obviously suppressed. Due to the weakness of vortical structure induced by the piezoelectric fan, the local heat transfer improvement in the vicinity of fan vibration envelope is certainly reduced in the presence of channel flow. On the other hand, when the channel flow passes the vibrating fan, the vortical flow near the fan tip mixes with the channel flow to produce a long stripe of vortical structure downstream of the fan vibration envelope, resulting in two stripes with relatively low temperature in the rear zone downstream of the fan vibration envelope. When the velocity ratio in increased further up to 8.2, as seen in Fig. 17(c1) and (c2), the horse shoe type vortex structures visualized by k2 = 60,000 at the edges of vibrating fan are strongly suppressed. Even at the neutral position where the displacement velocity of fan tip reaches its peak value, the horse shoe type vortex structures are only observed at the frond edge of the fan. The local heat transfer improvement in the vicinity of fan vibration envelope is extremely reduced and limited in a narrow stripe. Besides, in this situation, as the vibration amplitude is very small, the shedding vortices during different vibration phases are merged together, forming a long stripe of vortical structure downstream of the fan vibration envelope, but with a little different deflection at each phase. 4.3. Computed time-averaged convective heat transfer

(c) maximum displacement position at right Fig. 16. Instantaneous velocity vectors at x-y plane tightly close to the impinging target without channel flow (G/H = 0.0375).

Fig. 18 presents the computed time-averaged heat transfer coefficient maps on the heated surface under individual piezoelectric fan action. Compared with Fig. 6, it is seen that both the computed and the tested results illustrate the same convective heat transfer distribution feature of the piezoelectric fan. Fig. 19 presents some computed time-averaged heat transfer coefficient maps on the heated surface respectively in the presence of channel flow. Under a small velocity ratio of UR = 0.72, it is found that the local convective heat transfer in the regions both surrounding and downstream of the fan vibration envelope is mostly improved by the combined action of vibrating fan-excited streaming flow and channel flow related to the pure piezoelectric fan condition, as seen in Fig. 19(a). Under a large velocity ratio of UR = 1.92, the local time-averaged convective heat transfer enhancement by the vibrating fan is behaved obviously downstream of the fan vibration envelope. Form the computed results, as seen in Fig. 19(b) and (c), two stripes with relatively high convective heat transfer coefficient are observed downstream of the

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a1. neutral position

a2. maximum displacement position

(a) uCF=1.56m/s (UR=0.72)

b1. neutral position

b2. maximum displacement position

(b) uCF=3.75m/s (UR=1.92)

c1. neutral position

c2. maximum displacement position

(c) uCF=8.00m/s (UR=8.2) Fig. 17. Instantaneous temperature maps and iso-surface of k2 = 6  104 in presence of channel flow (G/H = 0.0375).

fan vibration envelope. This feature is also clearly observed in the tested time-averaged heat transfer coefficient maps under G/H = 0.0875, as seen in Fig. 10(c). But under G/H = 0.0625, this feature is not well demonstrated by the experimental test. Compared with the pure piezoelectric fan, it is sure that the local convective heat transfer in the fan vibration envelope is weakened due to the presence of channel flow. Two reasons are also suggested to be associated with this phenomenon. As displayed in Fig. 6, the fan vibration amplitude is affected significantly by the strong cross flow. The reduction of fan vibration amplitude makes the vortical streaming flow induced by a vibrating fan to be weakened. Under a velocity ratio of UR = 8.2, the effect of piezoelectric fan on the local convective heat transfer coefficient maps under combined action of channel flow and piezoelectric-fan flow is limited in a narrow strip downstream of the fan vibration envelope, as seen in Fig. 19(d). Fig. 20 presents the computed laterally-averaged convective heat transfer coefficient distributions under the individual piezoelectric fan, individual cross flow and combined flows under a small velocity ratio of 0.72 and G/H = 0.0375. It is seen that the combined action of vibrating fan-excited streaming flow and

channel flow produces higher laterally-averaged convective heat transfer coefficient from the beginning of fan leading edge. Viewing from Fig. 20(a), the peak laterally-averaged convective heat transfer coefficient under combined flows is increased approximately 70% in comparison with the individual piezoelectric fan. Viewing from the average in 2App, as seen in Fig. 20(b), the peak laterally-averaged convective heat transfer coefficient under combined flows is increased approximately 40%. Viewing from the average in 3App, as seen in Fig. 20(c), the peak laterally-averaged convective heat transfer coefficient under combined flows is increased approximately 25%. Fig. 21 presents the computed laterally-averaged convective heat transfer coefficient distributions under the individual piezoelectric fan, individual cross flow and combined flows under large velocity ratios. Here the fan-tip to heated surface is fixed as G/H = 0.0375. By comparison with pure channel flow, the combined action of channel flow and streaming flow significantly improves the laterally-averaged convective heat transfer coefficient, especially downstream of the fan vibration envelope. However, by comparison with pure piezoelectric fan, it is found

X.-J. Li et al. / International Journal of Heat and Mass Transfer 126 (2018) 48–65

that the laterally-averaged convective heat transfer coefficient produced by combined flows is generally reduced in the fan vibration envelope. This suggests that the impingement role of the streaming flow induced by vibrating fan is seriously weakened by the strong channel flow. On the other hand, as the convective heat transfer due to the channel flow is enhanced with the increase of the channel flow velocity, the combined action with a velocity ratio of 8.2 produces higher convective heat transfer around the fan vibration envelope than combined action with a velocity ratio of 1.92. The above tendencies are also demonstrated by the tested results, although there are some differences between the computational and experimental results. In general, the effect of piezoelectric fan on local heat transfer enhancement in the presence of channel flow is tightly dependant on the mutual interaction between both flows. In the situation where the channel flow velocity is small, the impingement role of vortical streaming flow along fan tip is dominated and simultaneously the channel flow passing through the vibration envelope is effectively pulsated. Therefore, combined flows produce significant heat transfer enhancement surrounding and downstream of the fan vibration envelope, in comparison with either pure piezoelectric fan or pure channel flow. Under large velocity ratios, the impingement role of streaming flow induced by a vibrating fan is

63

seriously weakened by the strong channel flow. But the convective heat transfer due to the channel flow is enhanced with the increase

(a) G/H=0.0375, UR=0.72

(b) G/H=0.0625, UR=1.92

(a) G/H=0.0375

(c) G/H=0.0875, UR=1.92

(b) G/H=0.0625

(c) G/H=0.0875 Fig. 18. Computed time-averaged heat transfer coefficient maps under individual piezoelectric fan action.

(d) G/H=0.0375, UR=8.2 Fig. 19. Computed time-averaged heat transfer coefficient maps in the presence of channel flow.

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70

90 80

PF+CF(UR=0.72)

60

2 havz (W/m K)

havx (W/m2 K)

60

PF(U=220V)

70

G/H=0.0375

50 40

PF(U=220V) CF(uCF=3.75m/s)

G/H=0.0375

CF(uCF=8.00m/s) PF+CF(UR=1.92) PF+CF(UR=8.20)

50 40 30

30

20

20 10

-2

-1

0

1

2

3

10

4

x/W

-2

70

80

PF(U=220V)

60

PF+CF(UR=0.72)

60

G/H=0.0375

2 havz (W/m K)

havx (W/m2 K)

70

50 40 30 20

G/H=0.0375

3

4

CF(uCF=8.00m/s) PF+CF(UR=1.92) PF+CF(UR=8.20)

40 30 20

-2

-1

0

1

3

2

10

4

-2

-1

0

1

70 PF(U=220V)

70

3

4

(b) average in 2 App

90 80

2

x/W

(b) average in 2 App

60

PF+CF(UR=0.72)

havz (W/m K)

G/H=0.0375

2

havx (W/m2 K)

2

PF(U=220V) CF(uCF=3.75m/s)

50

x/W

50 40 30 20 10

1

(a) average in 1 App

90

60

0

x/W

(a) average in 1 App

10

-1

PF(U=220V) CF(uCF=3.75m/s)

G/H=0.0375

CF(uCF=8.00m/s) PF+CF(UR=1.92) PF+CF(UR=8.20)

50 40 30 20

-2

-1

0

1

2

3

4

x/W

10

-2

Fig. 20. Computed laterally-averaged convective heat transfer coefficient under small velocity ratio.

of the channel flow velocity. In these situations, the combined action with a bigger velocity ratio produces higher convective heat transfer around the fan vibration envelope, mainly due to the increase of convective heat transfer by the channel flow. In addition, the combined action effectively improves the convective heat transfer coefficient in comparison with pure channel flow, especially downstream of the fan vibration envelope.

-1

0

1

2

3

4

x/W

(c) average in 3 App

(c) average in 3 App Fig. 21. Computed laterally-averaged convective heat transfer coefficient under large velocity ratios.

5. Conclusions This paper summarizes an experimental and numerical research on the convective heat transfer performance by a vertically-oriented piezoelectric fan in the presence of channel flow. The effects of channel flow velocity and fan tip-to-heated

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surface clearance are taken into considerations. The following conclusions are made from this study: (1) The presence of channel flow has an innegligible influence on the vibration amplitudes of the piezoelectric fan under large channel flow velocities. In the presence of channel flow with a velocity ratio of 1.92, the amplitude of fan-tip is decreased approximately 10% related to that of no channel flow case. Once the velocity ratio reaches to 8.2, the amplitude of fan-tip is decreased by 56%. (2) The interaction between the streaming flow induced by the vibrating fan and the impinging target affects the vortical structure development in comparison with the situation without the targeting surface. In the presence of channel flow, the vortical structures at the edges of vibrating fan are certainly suppressed, especially under large velocity ratios. On the other hand, the vortical streaming flow mixes with the channel flow to form a long stripe of vortical structure downstream of the fan vibration envelope. The interaction between the vortical streaming flow and channel flow is tightly dependent on the velocity ratio. (3) Under small velocity ratios, the impingement role of streaming flow along fan tip is dominated and simultaneously the channel flow passing through the vibration envelope is effectively pulsated. Therefore, combined flows generally produce heat transfer enhancement around the fan vibration envelope related to the pure vibrating fan, especially at a small non-dimensional tip-to-surface gap. At a large tip-tosurface gap, the peak local convection coefficient is moved a little downwards by the presence of channel flow. (4) Under large velocity ratios, the impingement role of streaming flow induced by a vibrating fan is seriously weakened by the strong channel flow. The convective heat transfer produced by combined flows in the fan vibration envelope is generally reduced in comparison with pure piezoelectric fan. On the other hand, the combined flows effectively improve the convective heat transfer related to the pure channel flow, especially downstream of the fan vibration envelope.

Acknowledgements The authors gratefully acknowledge the financial support for this project from the National Natural Science Foundation of China (Grant No: 51106073) and NUAA Research Funding (NS2014018). Conflict of interest There is no conflict of interest. References [1] M. Toda, Theory of air flow generation by a resonant type PVF2 bimorph cantilever vibrator, Ferroelectrics 22 (1979) 911–918. [2] A. Ihara, H. Watanabe, On the flow around flexible plates oscillating with large amplitude, J. Fluids Struct. 8 (1994) 601–619. [3] Y.H. Kim, S.T. Wereley, C.H. Chun, Phase-resolved flow field produced by a vibrating cantilever plate between two endplates, Phys. Fluids 16 (2004) 145–162. [4] M. Kimber, K. Suzuki, N. Kitsunai, K. Seki, S.V. Garimella, Pressure and flow rate performance of piezoelectric fans, IEEE Trans. Compon. Pack. Technol. 32 (2009) 766–775. [5] M. Choi, C. Cierpka, Y.H. Kim, Vortex formation by a vibrating cantilever, J. Fluids Struct. 31 (2012) 67–78.

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[6] J.H. Yoo, J.I. Hong, W. Cao, Piezoelectric ceramic bimorph coupled to thin metal plate as cooling fan for electronic devices, Sensor Actuat. A Phys. 79 (2000) 8–12. [7] M. Toda, S. Osaka, Vibrational fan using the piezoelectric polymer PVF2, Proc. IEEE 67 (1979) 1171–1173. [8] R.R. Schmidt, Local and average transfer coefficients on a vertical surface due to convection from a piezoelectric fan, in: Proc. Inter Soc. Conf. Therm. Phenom, 1994, 41–49, Washington DC. [9] T. Acikalin, S.M. Wait, S.V. Garimella, A. Raman, Experimental investigation of the thermal performance of piezoelectric fans, Heat Transfer Eng. 25 (2004) 4–14. [10] T. Acikalin, S.V. Garimella, A. Raman, J. Petroski, Characterization and optimization of the thermal performance of miniature piezoelectric fans, Int. J. Heat Fluid Flow 28 (2007) 806–820. [11] T. Acikalin, S.V. Garimella, Analysis and prediction of the thermal performance of piezoelectrically actuated fans, Heat Transfer Eng. 30 (2009) 487–498. [12] M. Kimber, S.V. Garimella, A. Raman, Local heat transfer coefficients induced by piezoelectrically actuated vibrating cantilevers, ASME J. Heat Transfer 129 (2007) 1168–1176. [13] M. Kimber, S.V. Garimella, Measurement and prediction of the cooling characteristics of a generalized vibrating piezoelectric fan, Int. J. Heat Mass Transfer 52 (2009) 4470–4478. [14] S.M. Wait, S. Basak, S.V. Garimella, A. Ramam, Piezoelectric fans using higher flexural modes for electronics cooling applications, IEEE Trans. Compon. Pack. Technol. 30 (2005) 119–128. [15] S.F. Liu, R.T. Huang, W.J. Sheu, C.C. Wang, Heat transfer by a piezoelectric fan on a flat surface subject to the influence of horizontal/vertical arrangement, Int. J. Heat Mass Transfer 52 (2009) 2565–2570. [16] M.K. Abdullah, M.Z. Abdullah, M.V. Ramana, C.Y. Khor, K.A. Ahmad, M.A. Mujeebu, et al., Numerical and experimental investigations on effect of fan height on the performance of piezoelectric fan in microelectronic cooling, Int. Commun. Heat Mass Transfer 36 (2009) 51–58. [17] M.K. Abdullah, N.C. Ismail, M.Z. Abdullah, M.A. Mujeebu, K.A. Ahmad, Z.M. Ripin, Effects of tip gap and amplitude of piezoelectric fans on the performance of heat sinks in microelectronic cooling, Heat Mass Transfer 48 (2012) 893–901. [18] Z.M. Fairuz, S.F. Sufian, M.Z. Abdullah, M.Z. Zubair, M.S. Abdul, Aziz, Effect of piezoelectric fan mode shape on the heat transfer characteristics, Int. Commun. Heat Mass Transfer 52 (2014) 140–151. [19] C.N. Lin, Analysis of three-dimensional heat and flow induced by piezoelectric fan, Int. J. Heat Mass Transfer 55 (2012) 3043–3053. [20] C.H. Huang, Y.F. Chen, H. Ay, An inverse problem in determining the optimal position for piezoelectric fan with experimental verification, Int. J. Heat Mass Transfer 55 (2012) 5289–5301. [21] L. Tan, J.Z. Zhang, X.M. Tan, Numerical investigation of convective heat transfer on a vertical surface due to resonating cantilever beam, Int. J. Therm. Sci. 80 (2014) 93–107. [22] R.J. Goldstein, A.I. Behbahani, Impingement of a circular jet with and without cross flow, Int. J. Heat Mass Transfer 25 (1982) 1377–1382. [23] L.W. Florschuetz, D.E. Metzger, C.C. Su, Heat transfer characteristics for jet array impingement with initial crossflow, ASME J. Heat Transfer 106 (1984) 34–41. [24] M. Popovac, K. Hanjalic, Vortices and heat flux around a wall-mounted cube cooled simultaneously by a jet and a crossflow, Int. J. Heat Mass Transfer 52 (2009) 4047–4062. [25] Y.Z. Yu, J.Z. Zhang, Y. Shan, Convective heat transfer of a row of air jets impingement excited by triangular tabs in a confined crossflow channel, Int. J. Heat Mass Transfer 80 (2015) 126–138. [26] C.N. Lin, Enhanced heat transfer performance of cylindrical surface by piezoelectric fan under forced convection conditions, Int. J. Heat Mass Transfer 60 (2013) 296–308. [27] T.M. Jeng, C.H. Liu, Moving-orientation and position effects of the piezoelectric fan on thermal characteristics of the heat sink partially filled in a channel with axial flow, Int. J. Heat Mass Transfer 85 (2015) 950–964. [28] J.Z. Zhang, S. Gao, X.M. Tan, Convective heat transfer on a flat plate subjected to normally synthetic jet and horizontal forced flow, Int. J. Heat Mass Transfer 57 (2013) 321–330. [29] I.B. Celik, U. Ghia, P.J. Roache, et al., Procedure for estimation and reporting of uncertainty due to discretization in CFD applications, J. Fluids Eng. 130 (2008) 078001. [30] N. Zuckerman, N. Lior, Impingement heat transfer: correlations and numerical modeling, J. Heat Transfer 127 (2005) 544–552. [31] O. Caggese, G. Gnaegi, G. Hannema, et al., Experimental and numerical investigation of a fully confined impingement round jet, Int. J. Heat Mass Transfer 65 (2013) 873–882. [32] N. Jeffers, K. Nolan, J. Stafford, et al., High fidelity phase locked PIV measurements analysing the flow fields surrounding an oscillating piezoelectric fan, J. Physics Conf. Series 525 (2014) 012013. [33] J. Jeong, F. Hussain, On the definition of a vortex, J. Fluid Mechan. 285 (1995) 69–94.