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Effects of blade shape on convective heat transfer induced by a piezoelectrically actuated vibrating fan
International Journal of Thermal Sciences 132 (2018) 597–609
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International Journal of Thermal Sciences journal homepage: www.elsevier.com/locate/ijts
Effects of blade shape on convective heat transfer induced by a piezoelectrically actuated vibrating fan
T
Xin-Jun Lia, Jing-zhou Zhanga,b,∗, Xiao-ming Tana a
College of Energy and Power Engineering, Jiangsu Province Key Laboratory of Aerospace Power System, Nanjing University of Aeronautics and Astronautics, Nanjing, 210016, China b Collaborative Innovation Center of Advanced Aero-Engine, Beijing, 100191, China
A R T I C LE I N FO
A B S T R A C T
Keywords: Piezoelectric fan Blade shape Vibration dynamics Instantaneous flow field Convective heat transfer
An experimental and numerical investigation is performed to explore the effects of blade shape on the convective heat transfer performance induced by piezoelectric fans. Five blade types are taken into consideration corresponding to the ones presented by Lin et al. [28], including one baseline type with a rectangular shape (Type-A), two rectangular shapes with wider widths (Type-B and Type-C), and two trapezoidal shapes in divergent (TypeD) and convergent (Type-E). All the blades are attached to the same piezoelectric patch and have the same exposed length. The vibration tests show that the blade shape has a significant influence on the vibrating characteristics of piezoelectric fan. Related to the baseline Type-A, Type-B and Type-C make the first-order resonance frequency a little descent. Type-D makes its first-order resonance frequency far less than the baseline type but Type-E is opposite. From the numerical simulations, the vortical structures induced by different blades vibrating at their respective resonance frequencies are illustrated. It is found that Type-B and Type-C produce stronger vortical flow although they have a little less vibrating frequency than the baseline Type-A. For Type-E, as its vibration frequency is obviously larger than Type-A, the scale of vortex shedding from the vibrating fan seems much stronger. In comparison with baseline type of piezoelectric fan, the location of highly local heat transfer zone moves from the center to both edges of fan-tip vibration envelope of fan-tip vibration envelope with the increase of blade width. In general, the blade types like Type-C and Type-E are suggested to be the favorable shapes for achieving better convective heat transfer performance. However, a little larger power consumption for actuating the piezoelectric fan is paid in relative to the baseline blade shape.
1. Introduction Efficient heat removal of electronics systems is a critical issue for avoiding poor efficiency or damage. Although the air-based cooling technique is generally not capable of providing the same powerful cooling capability as the liquid-based cooling, it is still an important concern in the thermal management of electronics systems on account of its native advantages, such as high reliability, low cost and simplicity. In order to improve the thermal dissipation capability of an airbased heat sink, considerable efforts have been devoted in the past decades. Among the heat transfer enhancement techniques, an advanced active means by using the piezoelectric fans attracts much attention recently. It is a smart solid-state device which generally consists of a patch of piezoelectric material and a flexible blade. Relying on the reversed piezoelectric effect, the piezoelectric patch expands and contracts in the lengthwise direction, driving the attached blade to oscillate
at the same frequency. Consequently, this oscillatory motion of flexible blade produces a pseudo-jet flow and results in highly local convective heat transfer. Toda and Osaka [1,2] promoted the exploratory research dealing with the use of a piezoelectric fan as an air flow generator in the rear of 19th century. Excited by its potential applications in the active flow control and heat transfer enhancement, considerable efforts had been paid for revealing the streaming flow features induced by a resonating piezoelectric fan and optimizing the actuated parameters. For instances, Ihara and Watanabe [3] performed a study on the flow around the ends of oscillating flexible cantilevers. Kim et al. [4] investigated the flow field generated by a vibrating cantilever by using the phase-resolved particle image velocimetry and smoke visualization technique. It was revealed that a pair of counter-rotating vortices was generated during each vibration cycle and a high velocity region was formed between these two counter-rotating vortices, making the flow field of two-
∗ Corresponding author. 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.ijthermalsci.2018.06.036 Received 13 March 2018; Received in revised form 11 May 2018; Accepted 29 June 2018
1290-0729/ © 2018 Elsevier Masson SAS. All rights reserved.
International Journal of Thermal Sciences 132 (2018) 597–609
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transfer for the vertical piezoelectric fan showed a symmetrical distribution whereas the horizontal piezoelectric fan possessed an asymmetric distribution. The heat transfer augmentation of the piezoelectric fans came from the entrained airflow during each oscillation cycle and the jet-like air stream at the fan tip. Both the vertical and horizontal piezoelectric fan arrangements produced the same order of heat transfer enhancement magnitude. Abdullah et al. [18,19] performed experimental investigations concerning on the effects of tip gap and amplitude of piezoelectric fan vibration 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. Tan et al. [20] and Fairuz et al. [21] performed numerical investigations to illustrate the effect of piezoelectric fan mode shape on the heat transfer characteristics. Their results suggested that the fundamental resonance mode was favorable for the practical piezoelectric fan application. Sufian et al. [22] studied the influence of dual vibrating fans on flow and thermal fields through numerical analyses and experimental measurements. Ma et al. [23] as well as Li and Wu [24] investigated experimentally the heat transfer of pin-fin heat sinks cooled by dual piezoelectric fans. It was found that the vibration phase difference between the fans had a great influence on the thermal and flow performance of double fans. Yeom et al. [25] and Li et al. [26] proposed a concept of active heat sink system that combined micro pin-fin surfaces and translational agitators. By using high-frequency translational agitation to aid existing channel flow generated by an external blower, the heat transfer coefficients were confirmed to be 250% of those on smooth surfaces without agitation. To our knowledge, a lot of efforts have been paid to reveal the influence of geometric and operational parameters on the heat transfer performance of piezoelectric fan, such as fan tip-to-target distance, vibration amplitude, operating frequency and mode shape, etc. However, little attention was focused on the effect of fan-blade shape. Recently, Shyu et al. [27] presented a novel finger-like piezoelectric fan comprising four flexible rectangular blades. This design enhanced the fin array heat transfer and reduced cooler volume by embedding multiple vibrating beams into the fin array. Lin et al. [28] performed an experimental and numerical investigation on the flow fields induced by variously shaped piezoelectric fans. Five blade types were examined in their work, including three rectangular with different widths and two trapezoidal blades with divergent and convergent shapes. These piezoelectric fans were actuated at their respectively first resonant frequencies for ensuring the same vibration amplitude. It was demonstrated that a blade with a larger width had a larger velocity in general. The blade with a convergent shape was suggested to be better for hot spot heat sources than those with divergent and rectangular shapes. Excited by the work of Lin et al. [28] in the exploration of an effective heat-dissipating piezoelectric fan for high heat density devices, an experimental and numerical investigation is performed in the current study to further illustrate the influencing mechanism of fan-blade shape on the flow field in the presence of a target surface as well as the convective heat transfer performance. Totally three aspects of research contents are involved in the current study, including the vibration test, three-dimensional flow simulation and convective heat transfer analysis.
dimensional nature near the cantilever tip but more complex and threedimensional further downstream. Wait et al. [5] studied the influence of resonance mode on the performances of piezoelectric fans. It was illustrated that the electro-mechanical energy conversion in higher resonance modes could be greater than in the first bending mode. However, losses in the piezoceramic were also shown to be higher at those modes. Therefore, the first resonance mode was suggested to be more favorable due to its minimum overall power consumption. Kimber et al. [6] made an experimental study on the pressure and flow rate performance of piezoelectric fans. Their results showed that the attainable flow rate exhibited a nearly quadratic dependence on the tip velocity and the vibration frequency was more influential in determining the attainable pressure compared to the vibration amplitude. Kim et al. [7] and Choi et al. [8] made further investigations on the flow field generated by a vibrating cantilever using phase-locked particle image velocimetry. The vortical structures generated by a vibrating cantilever were identified and characterized by using the continuous wavelet transform. It was found that the static pressure difference across the tip played an important role in the formation and development of each individual vortex. Jeffers et al. [9] and Agarwal et al. [10] presented phase locked PIV results of an unconfined piezoelectric fan operating in its first vibration frequency mode. A three-dimensional λ2 criterion isosurfaces were constructed from interpolated PIV measurements to identify the vortex core in the vicinity of the fan. These results clearly identified the formation of a horse shoe vortex that turned into a hairpin vortex before it broke up due to a combination of vortex shedding and flow along the fan blade. It was also clearly identified that a horse shoe type vortex was initially formed around the fan blade as it accelerated from zero velocity at maximum deflection. As the fan blade advanced beyond a certain phase angle, the horse shoe vortex begun to separate from the fan tip and a hairpin vortex was formed. Lin [11] performed a numerical simulation of three-dimensional heat and fluid flow induced by piezoelectric fans in the presence of an impinging target plate. Of particular was the illustration of interaction between the pseudo-jet flow and the target surface. Due to the presence of impinging target plate, the vibrating fan produced two air streams, namely a stream in the longitudinal direction and a stream in the transverse direction. The longitudinal stream was generated by the impingement jet effect at the fan tip, while the transverse stream was produced by the normal force exerted on the air by the vibrating fan. These two streams interacted to form two counter-rotating screw-type flow structures on either side of the blade adjacent to the heated surface. By using the pulsating feature of a pseudo-jet flow produced by the piezoelectric fan, the local convective heat transfer enhancement was achieved [12]. Acikalin et al. [13] demonstrated the feasibility of using piezoelectric fans in small scale electronic cooling applications. In a commercially available laptop computer, a 6–8 K temperature drop was observed in the electronic components within the laptop. Acikalin et al. [14] also performed a parametric study to illustrate the influence of governing parameters including fan tip-to-target distance, vibration amplitude, and operating frequency on the heat transfer of miniature piezoelectric fans. It was revealed that the fan frequency offset from resonance and the fan amplitude were the critical parameters. For the best case, an enhancement in convective heat transfer coefficient exceeding 375% related to natural convection was observed. Kimber and Garimella [15,16] experimentally investigated the local heat transfer performance of piezoelectric fan. 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 distribution became elliptical in shape. Their work quantified the influence of each operational parameter and its relative impact on the thermal performance. Of particular importance were the vibration frequency and amplitude of the vibrating cantilever beam. Liu et al. [17] made an experimental study concerning the influence of piezoelectric fan orientation on the thermal performance over a flat surface. It was illustrated that the heat
2. Piezoelectric fans and vibration tests 2.1. Brief description of piezoelectric fans Totally five piezoelectric fans are designed in the current study. They have the same piezoelectric patch size but different blade shapes. As seen in Fig. 1(a), the piezoelectric patch is rectangular with a fixed width (W0) of 12.7 mm, length (L0) of 29 mm and thickness (tp) of 1 mm, which is made of piezoelectric ceramic packaged with electric cords. The blade attached to the piezoelectric patch is made of stainless steel with a thickness (tb) of 0.1 mm. Its length is 51 mm and the 598
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Fig. 1. Schematic diagram of piezoelectric fans.
exposed length (L1) is 47 mm by using a length of 4 mm overlapping the piezoelectric patch. Therefore, the total length of piezoelectric fan (L) is 76 mm. Fig. 1(b) shows the manufactured piezoelectric fans. Among these fan-blade shapes, type-A is a common shape which is rectangular with the same width as the piezoelectric patch, defined as a baseline type. By varying the root width (W1) and tip width (W2) of the blade, the blade shape is changed in relative to the baseline type. Type-B and Type-C are also rectangular but have wider fan-blade widths than the Type-A. The former type has a fan-blade width of 19.1 mm and the latter type has a fan-blade width of 25.4 mm. Type-D has the same root width but wider tip width related to the baseline type, taking on divergent shape with a diffused ratio (W2/W1) of 2. Type-E has the same tip width but wider root width related to the baseline type, taking on convergent shape with a contracted ratio (W2/W1) of 0.5. The main geometric parameters of the blade are summarized in Table 1. To drive the piezoelectric fan, a function generator and a voltage amplifier are used. The sinusoidal voltage provided by function generator is fed to the piezoelectric fan through the voltage amplifier, forcing an excitation voltage (U). When the piezoelectric patch is excited by an alternating voltage, it expands and contracts in the lengthwise direction, driving the attached blade to oscillate at the same frequency. The peak-to-peak amplitude of fan-tip maximum
Fig. 2. Influence of blade shape on frequency response function of piezoelectric fan.
displacement is denoted as App. And the vibration amplitude of the fantip (Ap) is a half of App. 2.2. Vibration tests and results The vibrating characteristics of a piezoelectric fan are tested by a Laser Doppler Vibrometer (OptoMET Vector-Master) with a resolution of 2.5 nm/s. Two sets of experimental test are performed to determine the resonant frequencies of the specific piezoelectric fan as well as the influence of blade shape on the deformation of the vibrating fan. The test procedure is described in detail in our previous work [29]. The first test is made under clamped boundary condition, as seen in Fig. 2(a). The end of piezoelectric fan is fixed rigidly on the vibration test frame. Totally 7 test points are arranged uniformly in the centerline of piezoelectric fan. By forcing the external actuation, the frequency
Table 1 Main parameters of piezoelectric fans. Specification
L (mm)
L0 (mm)
W0 (mm)
L1 (mm)
W1 (mm)
W2 (mm)
W2/W1
Type-A Type-B Type-C Type-D Type-E
76 76 76 76 76
29 29 29 29 29
12.7 12.7 12.7 12.7 12.7
47 47 47 47 47
12.7 19.1 25.4 12.7 25.4
12.7 19.1 25.4 25.4 12.7
1 1 1 2 0.5
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Table 2 First-order resonant frequencies for the piezoelectric fans.
f (Hz)
Type-A
Type-B
Type-C
Type-D
Type-E
42.5
40.2
39.9
34.8
50.5
response functions (FRF) of these piezoelectric fans are obtained. Referring the previous studies (such as Wait et al. [5], Kimber et al. [6], Acikalin et al. [14], etc.), the operating frequency (f) of a piezoelectric fan is generally fixed at its first-order resonance frequency, therefore, only the first-order resonance frequency is discussed here, as displayed in Fig. 2(b) and Table 2. It is seen that the blade shape has a significant influence on the vibrating characteristics of piezoelectric fan. Related to the baseline type, the Type-B and Type-C both having the rectangular shape but wider blade width make the first-order resonance frequency a little descent. While trapezoidal shapes, either in divergent or in convergent, make the first-order resonance frequency far offset from the baseline type. The former produces less but the latter produces higher first-order resonance frequency related to the baseline case. It is also confirmed that the blade size is not the dominant factor affecting the vibration characteristics. For instance, both the Type-D and Type-E have the same blade size, but their first-order resonance frequencies are distinctly different. The fluid-structure coupling should be the main due for the above differences. The deformation of piezoelectric fan is measured under the situation where the piezoelectric fan is actuated at its first-order resonance frequency, as seen in Fig. 3(a). Totally 15 test points are arranged uniformly in the centerline of piezoelectric fan and the top point keeps its distance of d = 2 mm away from the fan-tip. To ensure that the piezoelectric fan with different blade shape has the same peak-to-peak amplitude of fan-tip (App) as the baseline case for providing direct comparison of convective heat transfer performance among these different blades, the excitation voltage is accordingly adjusted by the voltage amplifier. As displayed in Table 3, it is found that the excitation voltage is not associated with the first-order resonance frequency. For achieving the same amplitude of fan-tip with the baseline case, a larger excitation voltage is needed for the other piezoelectric fans, especially for Type-C which has a biggest blade size. Then a little bigger power consumption is resulted for the operation of piezoelectric fans related to the baseline case. Fig. 3(b) shows the vibration displacements of the piezoelectric fans under respective first-order frequency and excitation voltage. It is seen that each piezoelectric fan has nearly the same vibration displacement regardless of blade shape. Also, the normalized displacement of piezopatch is practically negligible. According to displacement measurement, a polynomial fitting is built up for describing the maximum deformation of vibrating fan.
Fig. 3. Measured vibration displacements. Table 3 Excitation voltages and power consumption of piezoelectric fans.
U (V) Wc (mW)
Type-A
Type-B
Type-C
Type-D
Type-E
220 31.5
232 34.1
238 36.5
230 33.2
234 34.4
3. Three-dimensional flow simulations 3.1. Computational model
⎧ Y (x ) = 0 2 3 4 ⎨ ⎩Y (x ) = Ap (c0 + c1 x + c2 x + c3 x + c4 x )
(0 ≤ x ≤ L0) (L0 ≤ x ≤ L)
In order to clarify the flow and heat transfer performance induced by the vibrating piezoelectric fans with different shapes, two kinds of computational models are taken into consideration. One computational model is used for simulating the flow fields around the vibrating piezoelectric fan without the targeting confinement, which is based on the experiment. As illustrated in Fig. 4(a), the dimensions of computational domain are chosen as 114 mm (in x-direction) × 100 mm (in y-direction) × 100 mm (in z-direction). The corresponding boundary conditions in accordance to this model are specified as the followings. 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. The other computational model is adopted for simulating the
(1)
where x is the distance along the fan and Y(x) is the maximum displacement corresponding to the location of x. In this formulation, the unit of x and Y(x) is mm. The coefficients are determined as c0 = −6.259×10−1, × 10−3 mm−2
c1 = 2.124 × 10−2mm−1,
c2 = −1.232
c3 = 5.764 × 10−5 mm−3, c4 = −3.741 × 10−7 mm−4 600
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Fig. 5. Grid independence test.
the displacement function of vibrating cantilever beam. According to the vibration test results, the trajectory of the cantilever beam in time is set as
Fig. 4. Schematic there-dimensional computational models.
y (x , t ) = Y (x )sin(2πft ) convective heat transfer on a targeting surface due to the piezoelectric fan, as shown in Fig. 4(b). The piezoelectric fan is arranged vertically to the targeting surface with a fixed tip-to-surface distance (G) of 3 mm. A uniform heat flux of q = 1700 W/m2 is applied on the heated surface. No-slip condition is applied to the solid wall and the other surfaces are treated in the same manner as that in the above computational model.
(2)
During computation, each vibration period is partitioned into 100 time steps. According to displacement function, dynamic meshes are used to model the deformation of vibrating piezoelectric fan in time. 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 (Choi et al. [8], Tan et al. [20]). In the spring-based smoothing method, all edges between two nodes are treated as interconnected springs. The local re-meshing occurs in a mesh cell when its skewness is higher than a critical value, improving the mesh quality during an unsteady calculation. 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
3.2. Computational procedure Considering a compromise between accuracy and computational cost, three-dimensional unsteady Reynolds-averaged Navier-Stokes (RANS) simulation is employed in the current study. The computation is performed using FLUENT code. According to the previous works performed by Lin [11] and Fairuz et al. [21], the SST k-ω two-equation model is selected for modeling the turbulence viscosity. In the simulation, the piezoelectric fan is modeled as a cantilever beam without thickness. A user defined function (UDF) is implemented for describing 601
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Fig. 6. Instantaneous iso-surfaces of λ2 = −4 × 104 for different fiezoelectric fans without confinement.
602
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Fig. 7. Instantaneous temperature maps and iso-surfaces of λ2 = −4 × 104 for different fiezoelectric fans with target surface confinement.
h=
∫0
t
1 h (t ) dt Δt
3.3. Instantaneous flow fields without targeting confinement
(3)
To reveal the instantaneous flow features around a vibrating piezoelectric fan, the vortical structure visualization by using λ2 criterion (Jeong and Hussain [31]) is adopted in the current study. In this technique for vortex structure identification, the velocity gradient tensor (∇u) is split into symmetric and anti-symmetric parts corresponding to the strain rate tensor (S) and the rotation tensor (Ω), which could be calculated by
where Δt is the product of periodic cycle numbers and the time of each period, dt is the time step. The computational meshes are generated using the grid-generation software ANSYS ICEMCFD 14.5. As the largest distortion of the mesh elements appears in the vicinity of the cantilever beam tip during the periodic vibration, the unstructured tetrahedral mesh elements between the cantilever beam tip and the targeting wall as well as the mesh near the cantilever are particularly refined. Taking the convective heat transfer subjected to a baseline piezoelectric fan (Type-A) as an example, to evaluate the systematic mesh sensitivity, a mesh sensitivity analysis based on the Grid Convergence Index (GCI) (Celik et al. [30]) is carried out in advance. For this purpose, three different tetrahedron meshes, with 802,231 elements (coarse grid), 1,087,201 elements (intermediate grid), and 1,373,045 elements (fine grid) respectively, are constructed. Fig. 5 shows the influence of grid number on the local convective heat transfer coefficient at the centerline (y = 0) of the target surface. It is illustrated that the overall maximum difference is mainly below 4.1% when the total grid number increased up to 1087201. Accordingly, approximately 1.1 million computational grids are finally selected in the presented computations.
S = 0.5(∇u + ∇uT )
Ω = 0.5(∇u − ∇uT )
(4)
Consequently, the λ2 is the second eigenvalue of S 2 + Ω2 . Fig. 6 presents the instantaneous vortical structures visualized by λ2 = −40000 around the vibrating piezoelectric fan in the free space under two typical phases (the neutral position from right to left and the maximum displacement position at left) for the five different piezoelectric fan types respectively. The corresponding excited frequency for each piezoelectric fan is determined according to Table 2. As revealed by previous investigations on the flow fields (Kim et al. [7], Choi et al. [8] and Jeffers et al. [9], etc.), the vibrating fan produces complex vortical structures. When the fan is moved from its maximum deflection position to zero deflection or neutral position, as
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Fig. 8. Instantaneous velocity vectors at y-z plane tightly close to target surface for Type-A.
the same vibration amplitude, the scale of vortex shedding from the vibrating fan is much weaker than that from Type-A. While for Type-E, as its vibration frequency is obviously larger than that of Type-A, the scale of vortex shedding from the vibrating fan seems much stronger than that from Type-A. Fig. 7 presents the instantaneous vortical structures visualized by λ2 = −40000 inside the confined cavity and the instantaneous temperature contours on the heated surface under two typical phases (the neutral position from right to left and the maximum displacement position at left) for the five different piezoelectric fan types respectively. Once the targeting surface is presented in front of the piezoelectric fan, the interaction between the streaming flow induced by the vibrating fan and the confined target will affect the vortex development in comparison with the situation without the targeting surface. The streaming flow induced by the vibrating fan plays an impingement role on the target surface. After impingement, the wall jet flow is formed and thus interacts with the vortical flow induced by the vibrating fan, introducing more complicated vortical structures. For example, as seen in Fig. 7(b), (c) and (e), where the vortical flow intensity induced by the piezoelectric is strong, the additional vortical structures near the target surface are distinctly observed. The generation of these additional vortical structures is certainly due to the interaction between the vortical flow induced by the vibrating fan and the confined surface. As the iso-surface of vortex structure is identified by λ2 = −40000, the
seen in Figs. 6(a-1), 6(b-1), 6(c-1) 6(d-1) and 6 (e−1), the horse shoe type vortex structures around both edges of vibrating fan seem more stable and strong, moving towards the fan tip and rolling up over the fan tip. During this vibrating process, the vibrating fan is accelerated to its maximum displacement velocity, producing the most significant pressure differential and the shear role with the surrounding air, thus forming the strongest vortical structures during a cycle. When the vibrating fan reaches to its maximum deflection position, due to the deceleration of displacement velocity, the shear action of vibrating fan on the surrounding air is drastically decayed. Therefore, at this instant, the induced horse shoe type vortex structures around both edges of vibrating fan is very weak and unstable, as seen in Figs. 6(a-2), 6(b-2), 6(c-2), 6(d-2) and 6 (e−2). It is also noted that at this instant, the vortex structure formed at the early stage (such as neutral position) remains its role. However, due to the attenuation of the vortical intensity during its development and the entrainment of the surrounding air, the vortex structure appears to be reduced in its scale and even be split. In comparison with the common shape of fan (Type-A), it is confirmed that the Type-B and Type-C produce larger scale of the shedding vortex, especially at the maximum deflection position. According to the vibration test, both Type-B and Type-C have nearly the same vibration frequency, a little less than that of Type-A. With regard to Type-D, as its vibration frequency is obviously less than that of Type-A for achieving 604
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This heater foil has a length of 140 mm and width of 120 mm, which is stretched tightly by two copper connectors. The heater foil is heated by DC current with two-end edges connecting to the copper connector to ensure a uniform heat flux. In the current experiment, the constant electric heat-flux on the heater foil is set as 1700 W/m2. The temperature distribution on the back surface of heat foil is measured by an infrared camera which operates in the long infrared band (8–14 μm). A zinc-selenide glass (100 mm wide, 100 mm long and 5 mm thick) with a high transmissivity nearly 0.97 is embedded in the bakelite to act as an infrared transparent window. To make the measurement more accurately, the test surface is sprayed with a uniform thin black paint in advance which has a high emissivity. The infrared measurement calibration is conducted in advance by using five thermocouples which are embedded on the black painted test surface. The temperature measured by the thermocouples is used as the benchmark to estimate the emissivity of the test surface. The calibrated results show that the emissivity of black painted test surface is about 0.96. 4.2. Data treatment and uncertainty analysis 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 the front surface exposed to internal forced convective heat transfer. That is, Twfront = Twrear = Tw . The local convective heat transfer coefficient on the heated surface is evaluated as
h=
rear qjoule − qloss − qrfront
Tw − Tc
(5)
where qjoule is heat flux density due to the electric heating, which is directly determined from the input power imposing on heater foil and the heater foil area. Tw is the temperature on the heater surface and Tc rear is the working fluid temperature. qloss and qrfront are heat losses from the rear and front surfaces of the heater foil respectively, as illustrated in Fig. 9(a). The main heat losses from the rear side of the heater foil are due to the radiative and convective heat transfer to the ambient.
Fig. 9. Convective heat transfer experiment setup.
vortical structures with low intensity can not be visualized, thus in Fig. 7(a) and (e), the additional vortical structures due to the interaction between the vortical flow and the confined surface are not clearly appeared. It is also found that the heated surface directly impinged by the vortical flow shows relative low temperature, producing strong convective heat transfer in the vicinity of fan vibration envelope. Around the fan vibration envelope, the temperature distribution takes on dumbbell-shaped feature in general. This is due to the wall jet flow after the impingement of steaming flow induced by the vibrating fan. As seen in Fig. 8 which presents the instantaneous velocity vectors at y-z plane tightly close to the impinging target (0.5 mm away from the heated wall), the wall jet originating from the fan-tip vibration envelope flows in all outward directions firstly but then the surrounding flow is suctioned toward the fan vibration envelope from the central zones at both sides of fan. This flow feature is obviously due to the interaction between the vortical flow and the targeting surface, which is responsible for producing a dumbbell-shaped temperature distribution around fan vibration envelope observed in Fig. 7.
rear qloss = heff , b (Tb − Ta)
(6)
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. According to the our previous study [29], heff,b is estimated by the following formula
heff , b = 0.11(Tb − Ta) + 12.5
(7)
The main heat loss from the front side of the heater foil is due to the radiative heat transfer to the channel. It is approximately estimated as the following.
qrfront = σεw (Tw4 − Ta4 )
(8)
where εw and σ are the emissivity of the heated surface and the StefanBoltzmann constant, respectively. According to the heat flux balance on the heated foil, the real heat flux (qcfront ) adopted for determining local convective heat transfer coefficient is deduced. Also, the laterally-averaged convective heat transfer coefficient is determined as the following
4. Convective heat transfer analysis
L ∫0 y h (y, z ) dy
4.1. Experimental setup
havz =
The experimental setup for heat transfer measurement is schematically shown in Fig. 9. A stainless steel sheet with a thickness of 0.05 mm is acted as a heater foil or heated surface, which is adhered tightly on a 10 mm thick bakelite. The piezoelectric fan is arranged normally to the heated surface with a fan tip-to-surface clearance (G).
where Ly is the laterally-averaged distance, which is selected as 1App and 3App respectively in the current study. In all the experiments, the measured temperature difference between the surface and ambient air temperature is at least 25 °C with an uncertainty of ± 2%. The uncertainty of the heat flux for determining 605
Ly
(9)
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Fig. 10. Time-averaged heat transfer coefficient maps for different fans.
maximum local convective heat transfer coefficient is nearly the same as the baseline case, but the location of highly local heat transfer zone moves from the center to both edges of fan-tip vibration envelope of fan-tip vibration envelope, as distinctly observed in numerical simulation (Figs. 10(c-1)) and experimental tests (Figs. 10(b-2) and Figure 10(c-2)). With regard to Type-D, as its vibration frequency is much less than that of Type-A, the convective heat transfer produced by the vibrating fan is obviously deteriorated, as seen in Fig. 10(d). By comparing Fig. 10(c) and (d), it is demonstrated that Type-C is more superior to Type-D although both types have the same vibration envelope of fan-tip, suggesting that the divergent shape is not appropriate for the blade design. For Type-E, as its vibration frequency is much higher than Type-A for a given vibration amplitude, thus the convective heat transfer is stronger due to the more intensively vortical flow, as seen in Fig. 10(e). Viewing from Fig. 10, it is also noticed that the experiment results show good agreement with numerical results in the affecting roles of blade shape on the convective heat transfer performance, although there are certain deviation between them in the time-averaged heat transfer coefficient maps. Fig. 11 and Fig. 12 present the computed and tested laterallyaveraged convective heat transfer coefficient distributions for different fans at their corresponding frequencies, averaged within two different lateral distances (1App and 3App), respectively. The vertical solid line
local convective heat transfer coefficient is approximately ± 5%. According to the methodology of Moffat [32], the uncertainty in the measurement of convective heat transfer coefficient is within ± 7%. 4.3. Time-averaged convective heat transfer Fig. 10 presents the time-averaged heat transfer coefficient maps on the heated surface by simulation and experiment for the five different piezoelectric fan types. The corresponding excited frequency for each piezoelectric fan is determined according to Table 2. The dash rectangular box and the solid line superimposed on each image represent the vibration envelope and fan tip at neutral position, respectively. It is clearly seen that the maximum local convective heat transfer appears in the vicinity of the vibration envelope of fan-tip, either from numerical simulations or experimental tests, which is consequent result of direct impingement of steaming flow. Around the fan vibration envelope, the local heat transfer coefficient distribution takes on dumbbell-shaped feature. This is due to the wall jet flow after the impingement of steaming flow induced by the vibrating fan. In comparison with baseline type of piezoelectric fan (as illustrated in Fig. 10(a)), Type-B and Type-C have wider vibration envelope of fan-tip and produce wider affecting zone, as seen in Fig. 10 (b) and Fig. 10(c). For these two cases, as the vibration frequency is nearly closer to that of baseline type, the 606
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Fig. 11. Computed laterally-averaged convective heat transfer coefficients for different fans.
Fig. 12. Tested laterally-averaged convective heat transfer coefficients for different fans.
and dash line drawn in this figure represent the fan centerline and two edges of the fan beam, respectively. Both the numerical simulation and experimental test results show the same affecting roles of blade shape on the laterally-averaged convective heat transfer coefficient distributions. As shown in Fig. 11 (a) and Fig. 12(a), when the laterally-averaged distance is selected as one vibration amplitude (1App), it is clearly seen that the peak laterally-averaged convective heat transfer coefficient appears at the center of the fan vibration envelope when the fantip width is relatively small (such as Type-A, Type-B and Type-E). For the piezoelectric fans with big fan-tip width (such as Type-C and TypeD), two peaks of laterally-averaged convective heat transfer coefficient appear in the vicinity of the both edges of the fan-tip vibration envelope. In general, the Type-B, Type-C and Type-E are capable of producing higher peak convective heat transfer and wider affecting zone than the common fan-shape of Type-A. With regard to Type-D, it produces smaller peak convective heat transfer but wider affecting zone than the common fan-shape of Type-A. Viewing from Figs. 11(b) and Figure 12(b) where the lateral distance for average use is three times of vibration amplitude (3App), the difference of laterally-averaged convective heat transfer coefficient distributions between piezoelectric fans remains. For the five types of blade shapes concerned in the current
study, Type-C and Type-E seem to be the more favorable blade shapes. By selecting a specified zone, the area-averaged convective heat transfer coefficient (hav) is determined. Here six specified zones are chosen for the comparison purpose of different blade shapes, they are W0 × App (1 S), 2W0 × 2App (4 S), 3W0 × 3App (9 S), 4W0 × 4App (16 S), 5W0 × 5App (25 S) and 6W0 × 6App (36 S), respectively. Fig. 13 presents the area-averaged convective heat transfer coefficients. Evaluated on the localized zone with W0 × App (1 S), Type-B produces the highest area-averaged convective heat transfer coefficient, with approximately 15% increase related to Type-A. Type-E is the next. These two blade types have relatively small fan width so that they produce concentrated steaming flow impinging onto the target surface. Evaluated on the specified zone with 2W0 × 2App (4 S), Type-C is the best, producing about 25% increase of area-averaged convective heat transfer coefficient related to Type-A. Evaluated on larger specified zones, both the Type-C and Type-E are demonstrated advantageously. Of particular is that these two blade types also introduce relatively larger excitation voltage and power consumption of piezoelectric fan, as illustrated in Table 3. As the steaming flow is stronger for achieving higher convective heat transfer, a larger driving power of piezoelectric fan is needed for oscillating the surrounding fluid. In general, the blade 607
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piezoelectric fans and consequently results in larger power consumption, especially for Type-C which has a biggest blade size. (2) The vortical structures induced by piezoelectric fans are changed correspondingly to the blade shapes. In comparison with Type-A, the Type-B and Type-C produce larger scale of the shedding vortex, especially at the maximum deflection position. With regard to TypeD, as its vibration frequency is obviously less than that of Type-A for achieving the same vibration amplitude, the scale of vortex shedding from the vibrating fan is much weaker than that from Type-A. While for Type-E, the scale of vortex shedding from the vibrating fan seems much stronger due to its obviously larger vibration frequency. (3) In comparison with baseline type of piezoelectric fan, the location of highly local heat transfer zone moves from the center to both edges of fan-tip vibration envelope with the increase of blade width. In general, the blade types like Type-C and Type-E are suggested to be the favorable shapes for achieving better convective heat transfer performance. The divergent shape (Type-D) is confirmed to be not appropriate for the blade design. Acknowledgements The authors gratefully acknowledge the financial support for this project from the National Key Basic Research Program of China (grant No: 2014CB239603) and NUAA Research Funding (NS2014018). Appendix A. Supplementary data Supplementary data related to this article can be found at http://dx. doi.org/10.1016/j.ijthermalsci.2018.06.036. Nomenclature Ap vibration amplitude of fan-tip (mm) App peak to peak amplitude of fan-tip (mm) ci coefficients in Eq. (1) f frequency (Hz) G fan tip-to-surface distance (mm) h heat transfer coefficient (W/m2K) L total length of piezoelectric fan (mm) L0 piezoelectric ceramics length (mm) L1 exposed length of blade (mm) Ly lateral distance for average use (mm) q heat flux (W/m2) S strain rate tensor t time (s) tb blade thickness (mm) tp piezoelectric patch thickness (mm) T temperature (K) u velocity (m/s) W0 piezoelectric ceramics width (mm) W1 blade root width (mm) W2 blade tip width (mm) Wc power consumption (mW) Y(x) maximum displacement corresponding to x x,y,z x-, y-, z-directions Greek letters
Fig. 13. Area-averaged convective heat transfer coefficients for different fans.
types like Type-C and Type-E are suggested to be the favorable shapes in the blade design. 5. Conclusions This paper summarizes an experimental and numerical investigation to further illustrate the effects of fan-blade shape on the convective heat transfer performance of piezoelectric fans. Totally five fan-blade shapes are taken into consideration and three aspects of research contents are involved in the current study. From the results, the following conclusions are drawn:
criterion for vortex structure identification λ2 Ω rotation tensor Subscripts
(1) The blade shape has a significant influence on the vibrating characteristics of piezoelectric fan. Related to the baseline Type-A, the Type-B and Type-C both having the rectangular shape but wider blade width make the first-order resonance frequency a little descent. While trapezoidal shapes, either in divergent or in convergent, make the first-order resonance frequency far offset from the baseline type. For achieving the same amplitude of fan-tip with the baseline case, a larger excitation voltage is needed for the other
av avz c w 608
area-averaged laterally-averaged along z-direction working fluid wall
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[1] M. Toda, S. Osaka, Vibrational fan using the piezoelectric polymer PVF2, Proc. IEEE 67 (1979) 1171–1173. [2] M. Toda, Theory of air flow generation by a resonant type PVF2 bimorph cantilever vibrator, Ferroelectrics 22 (1979) 911–918. [3] A. Ihara, H. Watanabe, On the flow around flexible plates oscillating with large amplitude, J. Fluid Struct. 8 (1994) 601–619. [4] 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. [5] S.M. Wait, S. Basak, S.V. Garimella, A. Raman, Piezoelectric fans using higher flexural models for electronics cooling applications, IEEE Trans. Compon. Packag. Technol. 30 (2007) 119–128. [6] M. Kimber, K. Suzuki, N. Kitsunai, K. Seki, S.V. Garimella, Pressure and flow rate performance of piezoelectric fans, IEEE Trans. Compon. Packag. Technol. 32 (2009) 766–775. [7] Y.H. Kim, C. Cierpka, S.T. Wereley, Flow field around a vibrating cantilever: coherent structure eduction by continuous wavelet transform and proper orthogonal decomposition, J. Fluid Mech. 669 (2011) 584–606. [8] M. Choi, C. Cierpka, Y.H. Kim, Vortex formation by a vibrating cantilever, J. Fluid Struct. 31 (2012) 67–78. [9] N. Jeffers, K. Nolan, J. Stafford, B. Donnelly, High fidelity phase locked PIV measurements analysing the flow fields surrounding an oscillating piezoelectric fan, J. Physics Conf. Series 525 (2014) 012013. [10] A. Agarwal, K.P. Nolan, J. Stafford, N. Jeffers, Visualization of three-dimensional structures shed by an oscillating beam, J. Fluid Struct. 70 (2017) 450–463. [11] C.N. Lin, Analysis of three-dimensional heat and flow induced by piezoelectric fan, Int. J. Heat Mass Tran. 55 (2012) 3043–3053. [12] J.H. Yoo, J.I. Hong, W. Cao, Piezoelectric ceramic bimorph coupled to thin metal plate as cooling fan for electronic devices, Sens. Actuators, a 79 (2000) 8–12. [13] T. Acikalin, S.M. Wait, S.V. Garimella, A. Raman, Experimental investigation of the thermal performance of piezoelectric fans, Heat Tran. Eng. 25 (2004) 4–14. [14] 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. [15] 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. [16] M. Kimbe, S.V. Garimella, Measurement and prediction of the cooling characteristics of a generalized vibrating piezoelectric fan, Int. J. Heat Mass Tran. 52 (2009) 4470–4478. [17] S.F. Liu, R.T. Huang, W.J. Sheu, C.C. Wang, Heat transfer by a piezoelectric fan on a
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Contents lists available at ScienceDirect
International Journal of Thermal Sciences journal homepage: www.elsevier.com/locate/ijts
Effects of blade shape on convective heat transfer induced by a piezoelectrically actuated vibrating fan
T
Xin-Jun Lia, Jing-zhou Zhanga,b,∗, Xiao-ming Tana a
College of Energy and Power Engineering, Jiangsu Province Key Laboratory of Aerospace Power System, Nanjing University of Aeronautics and Astronautics, Nanjing, 210016, China b Collaborative Innovation Center of Advanced Aero-Engine, Beijing, 100191, China
A R T I C LE I N FO
A B S T R A C T
Keywords: Piezoelectric fan Blade shape Vibration dynamics Instantaneous flow field Convective heat transfer
An experimental and numerical investigation is performed to explore the effects of blade shape on the convective heat transfer performance induced by piezoelectric fans. Five blade types are taken into consideration corresponding to the ones presented by Lin et al. [28], including one baseline type with a rectangular shape (Type-A), two rectangular shapes with wider widths (Type-B and Type-C), and two trapezoidal shapes in divergent (TypeD) and convergent (Type-E). All the blades are attached to the same piezoelectric patch and have the same exposed length. The vibration tests show that the blade shape has a significant influence on the vibrating characteristics of piezoelectric fan. Related to the baseline Type-A, Type-B and Type-C make the first-order resonance frequency a little descent. Type-D makes its first-order resonance frequency far less than the baseline type but Type-E is opposite. From the numerical simulations, the vortical structures induced by different blades vibrating at their respective resonance frequencies are illustrated. It is found that Type-B and Type-C produce stronger vortical flow although they have a little less vibrating frequency than the baseline Type-A. For Type-E, as its vibration frequency is obviously larger than Type-A, the scale of vortex shedding from the vibrating fan seems much stronger. In comparison with baseline type of piezoelectric fan, the location of highly local heat transfer zone moves from the center to both edges of fan-tip vibration envelope of fan-tip vibration envelope with the increase of blade width. In general, the blade types like Type-C and Type-E are suggested to be the favorable shapes for achieving better convective heat transfer performance. However, a little larger power consumption for actuating the piezoelectric fan is paid in relative to the baseline blade shape.
1. Introduction Efficient heat removal of electronics systems is a critical issue for avoiding poor efficiency or damage. Although the air-based cooling technique is generally not capable of providing the same powerful cooling capability as the liquid-based cooling, it is still an important concern in the thermal management of electronics systems on account of its native advantages, such as high reliability, low cost and simplicity. In order to improve the thermal dissipation capability of an airbased heat sink, considerable efforts have been devoted in the past decades. Among the heat transfer enhancement techniques, an advanced active means by using the piezoelectric fans attracts much attention recently. It is a smart solid-state device which generally consists of a patch of piezoelectric material and a flexible blade. Relying on the reversed piezoelectric effect, the piezoelectric patch expands and contracts in the lengthwise direction, driving the attached blade to oscillate
at the same frequency. Consequently, this oscillatory motion of flexible blade produces a pseudo-jet flow and results in highly local convective heat transfer. Toda and Osaka [1,2] promoted the exploratory research dealing with the use of a piezoelectric fan as an air flow generator in the rear of 19th century. Excited by its potential applications in the active flow control and heat transfer enhancement, considerable efforts had been paid for revealing the streaming flow features induced by a resonating piezoelectric fan and optimizing the actuated parameters. For instances, Ihara and Watanabe [3] performed a study on the flow around the ends of oscillating flexible cantilevers. Kim et al. [4] investigated the flow field generated by a vibrating cantilever by using the phase-resolved particle image velocimetry and smoke visualization technique. It was revealed that a pair of counter-rotating vortices was generated during each vibration cycle and a high velocity region was formed between these two counter-rotating vortices, making the flow field of two-
∗ Corresponding author. 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.ijthermalsci.2018.06.036 Received 13 March 2018; Received in revised form 11 May 2018; Accepted 29 June 2018
1290-0729/ © 2018 Elsevier Masson SAS. All rights reserved.
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transfer for the vertical piezoelectric fan showed a symmetrical distribution whereas the horizontal piezoelectric fan possessed an asymmetric distribution. The heat transfer augmentation of the piezoelectric fans came from the entrained airflow during each oscillation cycle and the jet-like air stream at the fan tip. Both the vertical and horizontal piezoelectric fan arrangements produced the same order of heat transfer enhancement magnitude. Abdullah et al. [18,19] performed experimental investigations concerning on the effects of tip gap and amplitude of piezoelectric fan vibration 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. Tan et al. [20] and Fairuz et al. [21] performed numerical investigations to illustrate the effect of piezoelectric fan mode shape on the heat transfer characteristics. Their results suggested that the fundamental resonance mode was favorable for the practical piezoelectric fan application. Sufian et al. [22] studied the influence of dual vibrating fans on flow and thermal fields through numerical analyses and experimental measurements. Ma et al. [23] as well as Li and Wu [24] investigated experimentally the heat transfer of pin-fin heat sinks cooled by dual piezoelectric fans. It was found that the vibration phase difference between the fans had a great influence on the thermal and flow performance of double fans. Yeom et al. [25] and Li et al. [26] proposed a concept of active heat sink system that combined micro pin-fin surfaces and translational agitators. By using high-frequency translational agitation to aid existing channel flow generated by an external blower, the heat transfer coefficients were confirmed to be 250% of those on smooth surfaces without agitation. To our knowledge, a lot of efforts have been paid to reveal the influence of geometric and operational parameters on the heat transfer performance of piezoelectric fan, such as fan tip-to-target distance, vibration amplitude, operating frequency and mode shape, etc. However, little attention was focused on the effect of fan-blade shape. Recently, Shyu et al. [27] presented a novel finger-like piezoelectric fan comprising four flexible rectangular blades. This design enhanced the fin array heat transfer and reduced cooler volume by embedding multiple vibrating beams into the fin array. Lin et al. [28] performed an experimental and numerical investigation on the flow fields induced by variously shaped piezoelectric fans. Five blade types were examined in their work, including three rectangular with different widths and two trapezoidal blades with divergent and convergent shapes. These piezoelectric fans were actuated at their respectively first resonant frequencies for ensuring the same vibration amplitude. It was demonstrated that a blade with a larger width had a larger velocity in general. The blade with a convergent shape was suggested to be better for hot spot heat sources than those with divergent and rectangular shapes. Excited by the work of Lin et al. [28] in the exploration of an effective heat-dissipating piezoelectric fan for high heat density devices, an experimental and numerical investigation is performed in the current study to further illustrate the influencing mechanism of fan-blade shape on the flow field in the presence of a target surface as well as the convective heat transfer performance. Totally three aspects of research contents are involved in the current study, including the vibration test, three-dimensional flow simulation and convective heat transfer analysis.
dimensional nature near the cantilever tip but more complex and threedimensional further downstream. Wait et al. [5] studied the influence of resonance mode on the performances of piezoelectric fans. It was illustrated that the electro-mechanical energy conversion in higher resonance modes could be greater than in the first bending mode. However, losses in the piezoceramic were also shown to be higher at those modes. Therefore, the first resonance mode was suggested to be more favorable due to its minimum overall power consumption. Kimber et al. [6] made an experimental study on the pressure and flow rate performance of piezoelectric fans. Their results showed that the attainable flow rate exhibited a nearly quadratic dependence on the tip velocity and the vibration frequency was more influential in determining the attainable pressure compared to the vibration amplitude. Kim et al. [7] and Choi et al. [8] made further investigations on the flow field generated by a vibrating cantilever using phase-locked particle image velocimetry. The vortical structures generated by a vibrating cantilever were identified and characterized by using the continuous wavelet transform. It was found that the static pressure difference across the tip played an important role in the formation and development of each individual vortex. Jeffers et al. [9] and Agarwal et al. [10] presented phase locked PIV results of an unconfined piezoelectric fan operating in its first vibration frequency mode. A three-dimensional λ2 criterion isosurfaces were constructed from interpolated PIV measurements to identify the vortex core in the vicinity of the fan. These results clearly identified the formation of a horse shoe vortex that turned into a hairpin vortex before it broke up due to a combination of vortex shedding and flow along the fan blade. It was also clearly identified that a horse shoe type vortex was initially formed around the fan blade as it accelerated from zero velocity at maximum deflection. As the fan blade advanced beyond a certain phase angle, the horse shoe vortex begun to separate from the fan tip and a hairpin vortex was formed. Lin [11] performed a numerical simulation of three-dimensional heat and fluid flow induced by piezoelectric fans in the presence of an impinging target plate. Of particular was the illustration of interaction between the pseudo-jet flow and the target surface. Due to the presence of impinging target plate, the vibrating fan produced two air streams, namely a stream in the longitudinal direction and a stream in the transverse direction. The longitudinal stream was generated by the impingement jet effect at the fan tip, while the transverse stream was produced by the normal force exerted on the air by the vibrating fan. These two streams interacted to form two counter-rotating screw-type flow structures on either side of the blade adjacent to the heated surface. By using the pulsating feature of a pseudo-jet flow produced by the piezoelectric fan, the local convective heat transfer enhancement was achieved [12]. Acikalin et al. [13] demonstrated the feasibility of using piezoelectric fans in small scale electronic cooling applications. In a commercially available laptop computer, a 6–8 K temperature drop was observed in the electronic components within the laptop. Acikalin et al. [14] also performed a parametric study to illustrate the influence of governing parameters including fan tip-to-target distance, vibration amplitude, and operating frequency on the heat transfer of miniature piezoelectric fans. It was revealed that the fan frequency offset from resonance and the fan amplitude were the critical parameters. For the best case, an enhancement in convective heat transfer coefficient exceeding 375% related to natural convection was observed. Kimber and Garimella [15,16] experimentally investigated the local heat transfer performance of piezoelectric fan. 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 distribution became elliptical in shape. Their work quantified the influence of each operational parameter and its relative impact on the thermal performance. Of particular importance were the vibration frequency and amplitude of the vibrating cantilever beam. Liu et al. [17] made an experimental study concerning the influence of piezoelectric fan orientation on the thermal performance over a flat surface. It was illustrated that the heat
2. Piezoelectric fans and vibration tests 2.1. Brief description of piezoelectric fans Totally five piezoelectric fans are designed in the current study. They have the same piezoelectric patch size but different blade shapes. As seen in Fig. 1(a), the piezoelectric patch is rectangular with a fixed width (W0) of 12.7 mm, length (L0) of 29 mm and thickness (tp) of 1 mm, which is made of piezoelectric ceramic packaged with electric cords. The blade attached to the piezoelectric patch is made of stainless steel with a thickness (tb) of 0.1 mm. Its length is 51 mm and the 598
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Fig. 1. Schematic diagram of piezoelectric fans.
exposed length (L1) is 47 mm by using a length of 4 mm overlapping the piezoelectric patch. Therefore, the total length of piezoelectric fan (L) is 76 mm. Fig. 1(b) shows the manufactured piezoelectric fans. Among these fan-blade shapes, type-A is a common shape which is rectangular with the same width as the piezoelectric patch, defined as a baseline type. By varying the root width (W1) and tip width (W2) of the blade, the blade shape is changed in relative to the baseline type. Type-B and Type-C are also rectangular but have wider fan-blade widths than the Type-A. The former type has a fan-blade width of 19.1 mm and the latter type has a fan-blade width of 25.4 mm. Type-D has the same root width but wider tip width related to the baseline type, taking on divergent shape with a diffused ratio (W2/W1) of 2. Type-E has the same tip width but wider root width related to the baseline type, taking on convergent shape with a contracted ratio (W2/W1) of 0.5. The main geometric parameters of the blade are summarized in Table 1. To drive the piezoelectric fan, a function generator and a voltage amplifier are used. The sinusoidal voltage provided by function generator is fed to the piezoelectric fan through the voltage amplifier, forcing an excitation voltage (U). When the piezoelectric patch is excited by an alternating voltage, it expands and contracts in the lengthwise direction, driving the attached blade to oscillate at the same frequency. The peak-to-peak amplitude of fan-tip maximum
Fig. 2. Influence of blade shape on frequency response function of piezoelectric fan.
displacement is denoted as App. And the vibration amplitude of the fantip (Ap) is a half of App. 2.2. Vibration tests and results The vibrating characteristics of a piezoelectric fan are tested by a Laser Doppler Vibrometer (OptoMET Vector-Master) with a resolution of 2.5 nm/s. Two sets of experimental test are performed to determine the resonant frequencies of the specific piezoelectric fan as well as the influence of blade shape on the deformation of the vibrating fan. The test procedure is described in detail in our previous work [29]. The first test is made under clamped boundary condition, as seen in Fig. 2(a). The end of piezoelectric fan is fixed rigidly on the vibration test frame. Totally 7 test points are arranged uniformly in the centerline of piezoelectric fan. By forcing the external actuation, the frequency
Table 1 Main parameters of piezoelectric fans. Specification
L (mm)
L0 (mm)
W0 (mm)
L1 (mm)
W1 (mm)
W2 (mm)
W2/W1
Type-A Type-B Type-C Type-D Type-E
76 76 76 76 76
29 29 29 29 29
12.7 12.7 12.7 12.7 12.7
47 47 47 47 47
12.7 19.1 25.4 12.7 25.4
12.7 19.1 25.4 25.4 12.7
1 1 1 2 0.5
599
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Table 2 First-order resonant frequencies for the piezoelectric fans.
f (Hz)
Type-A
Type-B
Type-C
Type-D
Type-E
42.5
40.2
39.9
34.8
50.5
response functions (FRF) of these piezoelectric fans are obtained. Referring the previous studies (such as Wait et al. [5], Kimber et al. [6], Acikalin et al. [14], etc.), the operating frequency (f) of a piezoelectric fan is generally fixed at its first-order resonance frequency, therefore, only the first-order resonance frequency is discussed here, as displayed in Fig. 2(b) and Table 2. It is seen that the blade shape has a significant influence on the vibrating characteristics of piezoelectric fan. Related to the baseline type, the Type-B and Type-C both having the rectangular shape but wider blade width make the first-order resonance frequency a little descent. While trapezoidal shapes, either in divergent or in convergent, make the first-order resonance frequency far offset from the baseline type. The former produces less but the latter produces higher first-order resonance frequency related to the baseline case. It is also confirmed that the blade size is not the dominant factor affecting the vibration characteristics. For instance, both the Type-D and Type-E have the same blade size, but their first-order resonance frequencies are distinctly different. The fluid-structure coupling should be the main due for the above differences. The deformation of piezoelectric fan is measured under the situation where the piezoelectric fan is actuated at its first-order resonance frequency, as seen in Fig. 3(a). Totally 15 test points are arranged uniformly in the centerline of piezoelectric fan and the top point keeps its distance of d = 2 mm away from the fan-tip. To ensure that the piezoelectric fan with different blade shape has the same peak-to-peak amplitude of fan-tip (App) as the baseline case for providing direct comparison of convective heat transfer performance among these different blades, the excitation voltage is accordingly adjusted by the voltage amplifier. As displayed in Table 3, it is found that the excitation voltage is not associated with the first-order resonance frequency. For achieving the same amplitude of fan-tip with the baseline case, a larger excitation voltage is needed for the other piezoelectric fans, especially for Type-C which has a biggest blade size. Then a little bigger power consumption is resulted for the operation of piezoelectric fans related to the baseline case. Fig. 3(b) shows the vibration displacements of the piezoelectric fans under respective first-order frequency and excitation voltage. It is seen that each piezoelectric fan has nearly the same vibration displacement regardless of blade shape. Also, the normalized displacement of piezopatch is practically negligible. According to displacement measurement, a polynomial fitting is built up for describing the maximum deformation of vibrating fan.
Fig. 3. Measured vibration displacements. Table 3 Excitation voltages and power consumption of piezoelectric fans.
U (V) Wc (mW)
Type-A
Type-B
Type-C
Type-D
Type-E
220 31.5
232 34.1
238 36.5
230 33.2
234 34.4
3. Three-dimensional flow simulations 3.1. Computational model
⎧ Y (x ) = 0 2 3 4 ⎨ ⎩Y (x ) = Ap (c0 + c1 x + c2 x + c3 x + c4 x )
(0 ≤ x ≤ L0) (L0 ≤ x ≤ L)
In order to clarify the flow and heat transfer performance induced by the vibrating piezoelectric fans with different shapes, two kinds of computational models are taken into consideration. One computational model is used for simulating the flow fields around the vibrating piezoelectric fan without the targeting confinement, which is based on the experiment. As illustrated in Fig. 4(a), the dimensions of computational domain are chosen as 114 mm (in x-direction) × 100 mm (in y-direction) × 100 mm (in z-direction). The corresponding boundary conditions in accordance to this model are specified as the followings. 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. The other computational model is adopted for simulating the
(1)
where x is the distance along the fan and Y(x) is the maximum displacement corresponding to the location of x. In this formulation, the unit of x and Y(x) is mm. The coefficients are determined as c0 = −6.259×10−1, × 10−3 mm−2
c1 = 2.124 × 10−2mm−1,
c2 = −1.232
c3 = 5.764 × 10−5 mm−3, c4 = −3.741 × 10−7 mm−4 600
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Fig. 5. Grid independence test.
the displacement function of vibrating cantilever beam. According to the vibration test results, the trajectory of the cantilever beam in time is set as
Fig. 4. Schematic there-dimensional computational models.
y (x , t ) = Y (x )sin(2πft ) convective heat transfer on a targeting surface due to the piezoelectric fan, as shown in Fig. 4(b). The piezoelectric fan is arranged vertically to the targeting surface with a fixed tip-to-surface distance (G) of 3 mm. A uniform heat flux of q = 1700 W/m2 is applied on the heated surface. No-slip condition is applied to the solid wall and the other surfaces are treated in the same manner as that in the above computational model.
(2)
During computation, each vibration period is partitioned into 100 time steps. According to displacement function, dynamic meshes are used to model the deformation of vibrating piezoelectric fan in time. 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 (Choi et al. [8], Tan et al. [20]). In the spring-based smoothing method, all edges between two nodes are treated as interconnected springs. The local re-meshing occurs in a mesh cell when its skewness is higher than a critical value, improving the mesh quality during an unsteady calculation. 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
3.2. Computational procedure Considering a compromise between accuracy and computational cost, three-dimensional unsteady Reynolds-averaged Navier-Stokes (RANS) simulation is employed in the current study. The computation is performed using FLUENT code. According to the previous works performed by Lin [11] and Fairuz et al. [21], the SST k-ω two-equation model is selected for modeling the turbulence viscosity. In the simulation, the piezoelectric fan is modeled as a cantilever beam without thickness. A user defined function (UDF) is implemented for describing 601
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Fig. 6. Instantaneous iso-surfaces of λ2 = −4 × 104 for different fiezoelectric fans without confinement.
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Fig. 7. Instantaneous temperature maps and iso-surfaces of λ2 = −4 × 104 for different fiezoelectric fans with target surface confinement.
h=
∫0
t
1 h (t ) dt Δt
3.3. Instantaneous flow fields without targeting confinement
(3)
To reveal the instantaneous flow features around a vibrating piezoelectric fan, the vortical structure visualization by using λ2 criterion (Jeong and Hussain [31]) is adopted in the current study. In this technique for vortex structure identification, the velocity gradient tensor (∇u) is split into symmetric and anti-symmetric parts corresponding to the strain rate tensor (S) and the rotation tensor (Ω), which could be calculated by
where Δt is the product of periodic cycle numbers and the time of each period, dt is the time step. The computational meshes are generated using the grid-generation software ANSYS ICEMCFD 14.5. As the largest distortion of the mesh elements appears in the vicinity of the cantilever beam tip during the periodic vibration, the unstructured tetrahedral mesh elements between the cantilever beam tip and the targeting wall as well as the mesh near the cantilever are particularly refined. Taking the convective heat transfer subjected to a baseline piezoelectric fan (Type-A) as an example, to evaluate the systematic mesh sensitivity, a mesh sensitivity analysis based on the Grid Convergence Index (GCI) (Celik et al. [30]) is carried out in advance. For this purpose, three different tetrahedron meshes, with 802,231 elements (coarse grid), 1,087,201 elements (intermediate grid), and 1,373,045 elements (fine grid) respectively, are constructed. Fig. 5 shows the influence of grid number on the local convective heat transfer coefficient at the centerline (y = 0) of the target surface. It is illustrated that the overall maximum difference is mainly below 4.1% when the total grid number increased up to 1087201. Accordingly, approximately 1.1 million computational grids are finally selected in the presented computations.
S = 0.5(∇u + ∇uT )
Ω = 0.5(∇u − ∇uT )
(4)
Consequently, the λ2 is the second eigenvalue of S 2 + Ω2 . Fig. 6 presents the instantaneous vortical structures visualized by λ2 = −40000 around the vibrating piezoelectric fan in the free space under two typical phases (the neutral position from right to left and the maximum displacement position at left) for the five different piezoelectric fan types respectively. The corresponding excited frequency for each piezoelectric fan is determined according to Table 2. As revealed by previous investigations on the flow fields (Kim et al. [7], Choi et al. [8] and Jeffers et al. [9], etc.), the vibrating fan produces complex vortical structures. When the fan is moved from its maximum deflection position to zero deflection or neutral position, as
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Fig. 8. Instantaneous velocity vectors at y-z plane tightly close to target surface for Type-A.
the same vibration amplitude, the scale of vortex shedding from the vibrating fan is much weaker than that from Type-A. While for Type-E, as its vibration frequency is obviously larger than that of Type-A, the scale of vortex shedding from the vibrating fan seems much stronger than that from Type-A. Fig. 7 presents the instantaneous vortical structures visualized by λ2 = −40000 inside the confined cavity and the instantaneous temperature contours on the heated surface under two typical phases (the neutral position from right to left and the maximum displacement position at left) for the five different piezoelectric fan types respectively. Once the targeting surface is presented in front of the piezoelectric fan, the interaction between the streaming flow induced by the vibrating fan and the confined target will affect the vortex development in comparison with the situation without the targeting surface. The streaming flow induced by the vibrating fan plays an impingement role on the target surface. After impingement, the wall jet flow is formed and thus interacts with the vortical flow induced by the vibrating fan, introducing more complicated vortical structures. For example, as seen in Fig. 7(b), (c) and (e), where the vortical flow intensity induced by the piezoelectric is strong, the additional vortical structures near the target surface are distinctly observed. The generation of these additional vortical structures is certainly due to the interaction between the vortical flow induced by the vibrating fan and the confined surface. As the iso-surface of vortex structure is identified by λ2 = −40000, the
seen in Figs. 6(a-1), 6(b-1), 6(c-1) 6(d-1) and 6 (e−1), the horse shoe type vortex structures around both edges of vibrating fan seem more stable and strong, moving towards the fan tip and rolling up over the fan tip. During this vibrating process, the vibrating fan is accelerated to its maximum displacement velocity, producing the most significant pressure differential and the shear role with the surrounding air, thus forming the strongest vortical structures during a cycle. When the vibrating fan reaches to its maximum deflection position, due to the deceleration of displacement velocity, the shear action of vibrating fan on the surrounding air is drastically decayed. Therefore, at this instant, the induced horse shoe type vortex structures around both edges of vibrating fan is very weak and unstable, as seen in Figs. 6(a-2), 6(b-2), 6(c-2), 6(d-2) and 6 (e−2). It is also noted that at this instant, the vortex structure formed at the early stage (such as neutral position) remains its role. However, due to the attenuation of the vortical intensity during its development and the entrainment of the surrounding air, the vortex structure appears to be reduced in its scale and even be split. In comparison with the common shape of fan (Type-A), it is confirmed that the Type-B and Type-C produce larger scale of the shedding vortex, especially at the maximum deflection position. According to the vibration test, both Type-B and Type-C have nearly the same vibration frequency, a little less than that of Type-A. With regard to Type-D, as its vibration frequency is obviously less than that of Type-A for achieving 604
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This heater foil has a length of 140 mm and width of 120 mm, which is stretched tightly by two copper connectors. The heater foil is heated by DC current with two-end edges connecting to the copper connector to ensure a uniform heat flux. In the current experiment, the constant electric heat-flux on the heater foil is set as 1700 W/m2. The temperature distribution on the back surface of heat foil is measured by an infrared camera which operates in the long infrared band (8–14 μm). A zinc-selenide glass (100 mm wide, 100 mm long and 5 mm thick) with a high transmissivity nearly 0.97 is embedded in the bakelite to act as an infrared transparent window. To make the measurement more accurately, the test surface is sprayed with a uniform thin black paint in advance which has a high emissivity. The infrared measurement calibration is conducted in advance by using five thermocouples which are embedded on the black painted test surface. The temperature measured by the thermocouples is used as the benchmark to estimate the emissivity of the test surface. The calibrated results show that the emissivity of black painted test surface is about 0.96. 4.2. Data treatment and uncertainty analysis 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 the front surface exposed to internal forced convective heat transfer. That is, Twfront = Twrear = Tw . The local convective heat transfer coefficient on the heated surface is evaluated as
h=
rear qjoule − qloss − qrfront
Tw − Tc
(5)
where qjoule is heat flux density due to the electric heating, which is directly determined from the input power imposing on heater foil and the heater foil area. Tw is the temperature on the heater surface and Tc rear is the working fluid temperature. qloss and qrfront are heat losses from the rear and front surfaces of the heater foil respectively, as illustrated in Fig. 9(a). The main heat losses from the rear side of the heater foil are due to the radiative and convective heat transfer to the ambient.
Fig. 9. Convective heat transfer experiment setup.
vortical structures with low intensity can not be visualized, thus in Fig. 7(a) and (e), the additional vortical structures due to the interaction between the vortical flow and the confined surface are not clearly appeared. It is also found that the heated surface directly impinged by the vortical flow shows relative low temperature, producing strong convective heat transfer in the vicinity of fan vibration envelope. Around the fan vibration envelope, the temperature distribution takes on dumbbell-shaped feature in general. This is due to the wall jet flow after the impingement of steaming flow induced by the vibrating fan. As seen in Fig. 8 which presents the instantaneous velocity vectors at y-z plane tightly close to the impinging target (0.5 mm away from the heated wall), the wall jet originating from the fan-tip vibration envelope flows in all outward directions firstly but then the surrounding flow is suctioned toward the fan vibration envelope from the central zones at both sides of fan. This flow feature is obviously due to the interaction between the vortical flow and the targeting surface, which is responsible for producing a dumbbell-shaped temperature distribution around fan vibration envelope observed in Fig. 7.
rear qloss = heff , b (Tb − Ta)
(6)
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. According to the our previous study [29], heff,b is estimated by the following formula
heff , b = 0.11(Tb − Ta) + 12.5
(7)
The main heat loss from the front side of the heater foil is due to the radiative heat transfer to the channel. It is approximately estimated as the following.
qrfront = σεw (Tw4 − Ta4 )
(8)
where εw and σ are the emissivity of the heated surface and the StefanBoltzmann constant, respectively. According to the heat flux balance on the heated foil, the real heat flux (qcfront ) adopted for determining local convective heat transfer coefficient is deduced. Also, the laterally-averaged convective heat transfer coefficient is determined as the following
4. Convective heat transfer analysis
L ∫0 y h (y, z ) dy
4.1. Experimental setup
havz =
The experimental setup for heat transfer measurement is schematically shown in Fig. 9. A stainless steel sheet with a thickness of 0.05 mm is acted as a heater foil or heated surface, which is adhered tightly on a 10 mm thick bakelite. The piezoelectric fan is arranged normally to the heated surface with a fan tip-to-surface clearance (G).
where Ly is the laterally-averaged distance, which is selected as 1App and 3App respectively in the current study. In all the experiments, the measured temperature difference between the surface and ambient air temperature is at least 25 °C with an uncertainty of ± 2%. The uncertainty of the heat flux for determining 605
Ly
(9)
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Fig. 10. Time-averaged heat transfer coefficient maps for different fans.
maximum local convective heat transfer coefficient is nearly the same as the baseline case, but the location of highly local heat transfer zone moves from the center to both edges of fan-tip vibration envelope of fan-tip vibration envelope, as distinctly observed in numerical simulation (Figs. 10(c-1)) and experimental tests (Figs. 10(b-2) and Figure 10(c-2)). With regard to Type-D, as its vibration frequency is much less than that of Type-A, the convective heat transfer produced by the vibrating fan is obviously deteriorated, as seen in Fig. 10(d). By comparing Fig. 10(c) and (d), it is demonstrated that Type-C is more superior to Type-D although both types have the same vibration envelope of fan-tip, suggesting that the divergent shape is not appropriate for the blade design. For Type-E, as its vibration frequency is much higher than Type-A for a given vibration amplitude, thus the convective heat transfer is stronger due to the more intensively vortical flow, as seen in Fig. 10(e). Viewing from Fig. 10, it is also noticed that the experiment results show good agreement with numerical results in the affecting roles of blade shape on the convective heat transfer performance, although there are certain deviation between them in the time-averaged heat transfer coefficient maps. Fig. 11 and Fig. 12 present the computed and tested laterallyaveraged convective heat transfer coefficient distributions for different fans at their corresponding frequencies, averaged within two different lateral distances (1App and 3App), respectively. The vertical solid line
local convective heat transfer coefficient is approximately ± 5%. According to the methodology of Moffat [32], the uncertainty in the measurement of convective heat transfer coefficient is within ± 7%. 4.3. Time-averaged convective heat transfer Fig. 10 presents the time-averaged heat transfer coefficient maps on the heated surface by simulation and experiment for the five different piezoelectric fan types. The corresponding excited frequency for each piezoelectric fan is determined according to Table 2. The dash rectangular box and the solid line superimposed on each image represent the vibration envelope and fan tip at neutral position, respectively. It is clearly seen that the maximum local convective heat transfer appears in the vicinity of the vibration envelope of fan-tip, either from numerical simulations or experimental tests, which is consequent result of direct impingement of steaming flow. Around the fan vibration envelope, the local heat transfer coefficient distribution takes on dumbbell-shaped feature. This is due to the wall jet flow after the impingement of steaming flow induced by the vibrating fan. In comparison with baseline type of piezoelectric fan (as illustrated in Fig. 10(a)), Type-B and Type-C have wider vibration envelope of fan-tip and produce wider affecting zone, as seen in Fig. 10 (b) and Fig. 10(c). For these two cases, as the vibration frequency is nearly closer to that of baseline type, the 606
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Fig. 11. Computed laterally-averaged convective heat transfer coefficients for different fans.
Fig. 12. Tested laterally-averaged convective heat transfer coefficients for different fans.
and dash line drawn in this figure represent the fan centerline and two edges of the fan beam, respectively. Both the numerical simulation and experimental test results show the same affecting roles of blade shape on the laterally-averaged convective heat transfer coefficient distributions. As shown in Fig. 11 (a) and Fig. 12(a), when the laterally-averaged distance is selected as one vibration amplitude (1App), it is clearly seen that the peak laterally-averaged convective heat transfer coefficient appears at the center of the fan vibration envelope when the fantip width is relatively small (such as Type-A, Type-B and Type-E). For the piezoelectric fans with big fan-tip width (such as Type-C and TypeD), two peaks of laterally-averaged convective heat transfer coefficient appear in the vicinity of the both edges of the fan-tip vibration envelope. In general, the Type-B, Type-C and Type-E are capable of producing higher peak convective heat transfer and wider affecting zone than the common fan-shape of Type-A. With regard to Type-D, it produces smaller peak convective heat transfer but wider affecting zone than the common fan-shape of Type-A. Viewing from Figs. 11(b) and Figure 12(b) where the lateral distance for average use is three times of vibration amplitude (3App), the difference of laterally-averaged convective heat transfer coefficient distributions between piezoelectric fans remains. For the five types of blade shapes concerned in the current
study, Type-C and Type-E seem to be the more favorable blade shapes. By selecting a specified zone, the area-averaged convective heat transfer coefficient (hav) is determined. Here six specified zones are chosen for the comparison purpose of different blade shapes, they are W0 × App (1 S), 2W0 × 2App (4 S), 3W0 × 3App (9 S), 4W0 × 4App (16 S), 5W0 × 5App (25 S) and 6W0 × 6App (36 S), respectively. Fig. 13 presents the area-averaged convective heat transfer coefficients. Evaluated on the localized zone with W0 × App (1 S), Type-B produces the highest area-averaged convective heat transfer coefficient, with approximately 15% increase related to Type-A. Type-E is the next. These two blade types have relatively small fan width so that they produce concentrated steaming flow impinging onto the target surface. Evaluated on the specified zone with 2W0 × 2App (4 S), Type-C is the best, producing about 25% increase of area-averaged convective heat transfer coefficient related to Type-A. Evaluated on larger specified zones, both the Type-C and Type-E are demonstrated advantageously. Of particular is that these two blade types also introduce relatively larger excitation voltage and power consumption of piezoelectric fan, as illustrated in Table 3. As the steaming flow is stronger for achieving higher convective heat transfer, a larger driving power of piezoelectric fan is needed for oscillating the surrounding fluid. In general, the blade 607
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piezoelectric fans and consequently results in larger power consumption, especially for Type-C which has a biggest blade size. (2) The vortical structures induced by piezoelectric fans are changed correspondingly to the blade shapes. In comparison with Type-A, the Type-B and Type-C produce larger scale of the shedding vortex, especially at the maximum deflection position. With regard to TypeD, as its vibration frequency is obviously less than that of Type-A for achieving the same vibration amplitude, the scale of vortex shedding from the vibrating fan is much weaker than that from Type-A. While for Type-E, the scale of vortex shedding from the vibrating fan seems much stronger due to its obviously larger vibration frequency. (3) In comparison with baseline type of piezoelectric fan, the location of highly local heat transfer zone moves from the center to both edges of fan-tip vibration envelope with the increase of blade width. In general, the blade types like Type-C and Type-E are suggested to be the favorable shapes for achieving better convective heat transfer performance. The divergent shape (Type-D) is confirmed to be not appropriate for the blade design. Acknowledgements The authors gratefully acknowledge the financial support for this project from the National Key Basic Research Program of China (grant No: 2014CB239603) and NUAA Research Funding (NS2014018). Appendix A. Supplementary data Supplementary data related to this article can be found at http://dx. doi.org/10.1016/j.ijthermalsci.2018.06.036. Nomenclature Ap vibration amplitude of fan-tip (mm) App peak to peak amplitude of fan-tip (mm) ci coefficients in Eq. (1) f frequency (Hz) G fan tip-to-surface distance (mm) h heat transfer coefficient (W/m2K) L total length of piezoelectric fan (mm) L0 piezoelectric ceramics length (mm) L1 exposed length of blade (mm) Ly lateral distance for average use (mm) q heat flux (W/m2) S strain rate tensor t time (s) tb blade thickness (mm) tp piezoelectric patch thickness (mm) T temperature (K) u velocity (m/s) W0 piezoelectric ceramics width (mm) W1 blade root width (mm) W2 blade tip width (mm) Wc power consumption (mW) Y(x) maximum displacement corresponding to x x,y,z x-, y-, z-directions Greek letters
Fig. 13. Area-averaged convective heat transfer coefficients for different fans.
types like Type-C and Type-E are suggested to be the favorable shapes in the blade design. 5. Conclusions This paper summarizes an experimental and numerical investigation to further illustrate the effects of fan-blade shape on the convective heat transfer performance of piezoelectric fans. Totally five fan-blade shapes are taken into consideration and three aspects of research contents are involved in the current study. From the results, the following conclusions are drawn:
criterion for vortex structure identification λ2 Ω rotation tensor Subscripts
(1) The blade shape has a significant influence on the vibrating characteristics of piezoelectric fan. Related to the baseline Type-A, the Type-B and Type-C both having the rectangular shape but wider blade width make the first-order resonance frequency a little descent. While trapezoidal shapes, either in divergent or in convergent, make the first-order resonance frequency far offset from the baseline type. For achieving the same amplitude of fan-tip with the baseline case, a larger excitation voltage is needed for the other
av avz c w 608
area-averaged laterally-averaged along z-direction working fluid wall
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