Keywords

1 Introduction

Technological innovation in electronics is leading to smaller components with better performance and higher heat fluxes than ever before. As far as the reliability and optimum performance of these devices are concerned, the conventional cooling techniques are becoming inadequate for handling these intense heat fluxes. As a result, there is a need for compact and high-efficiency cooling devices. Impingement jets have attracted great interest recently for heat removal [1]. Impingement cooling at maximum flow speed is known to offer heat transfer coefficients up to three times that of conventional convective cooling [2]. Among impingement jet cooling methods, synthetic jet cooling has received significant attention because of the enhanced mixing due to its transient nature. SJs are found to be superior to continuous jets in terms of entrainment rate due to the rapid formation of periodic vertical structures in SJ [3]. Especially among SJs, the enhanced entrainment and mixing properties of Non-circular SJs are better than those of axisymmetric jets [4]. Synthetic Jet Actuators are novel active flow control zero-net-mass-flux (ZNMF) devices [1], i.e., the mass ejected by the actuator cavity during ejection is equal to the mass sucked during the suction stroke. SJs have significant momentum flux, i.e., there is a net-momentum addition due to the movement of the diaphragm. When an SJ is ejected through a non-axisymmetric orifice, the shape of the jet fluctuates as it flows downstream due to self-induced deformations of the vortex rings [5]. This phenomenon of the rotation of the jet shape in symmetric vortex rings is called axis switching. This change in cross-section shape increases downstream, away from the jet origin. The shape change is such that the forms remain almost similar to the jet opening, with its major and minor axis rotated at angles concerning the jet origin. Axis switching is of great significance for heat transfer applications and has been observed in rectangular jets [6], elliptic jets [4, 7], and other more complicated non-circular jets [8, 9]. Depending on initial conditions at the jet inlet, the cross-section of non-circular jets can evolve in the expansion region of the jet between the orifice exit and the impingement plate [5, 6]. It takes place through shapes similar to that at the jet inlet, with its major and minor axis rotated at angles depending on the jet geometry.

2 Literature Review and Objective

Synthetic Jets (SJ) have a vast potential to meet the cooling demand for future electronic applications. The main advantages of SJ cooling are its simple structure, low weight, low power consumption, and its high reliability in operations without the need for a dedicated plumbing system, since SJs are generated directly from the ambient fluid [5]. Axis switching is a phenomenon that is extensively studied in the case of non-axisymmetric impingement jets. Reodikar et al. [10] considered compressible impingement jets from different orifice geometries to study the mechanism of axis switching and its influence on heat transfer characteristics. They found that the phenomenon of axis switching is prevalent in elliptic jets at low orifice-to-plate ratios (z/D ≈ 2), and elliptic jets mostly undergo an axis switch of 90 degrees. At larger z/D values, they reported that the jet section becomes axisymmetric regardless of the initial shape or aspect ratio at the orifice exit. They attributed this phenomenon to differential velocity gradients and jet spreading. It is seen that most of the work on elliptic impingement jet cooling focuses on lower aspect ratios. Gutmark and Grinstein [10] reported that the evolution of the jets strongly depends on multiple initial conditions at the elliptic nozzle exit, such as thickness distribution at the nozzle lip, non-uniformity of shear-layer thickness, the eccentricity measured by the nozzle geometrical aspect ratio, and Reynolds and Mach numbers. Shi et al. [7] studied the influence of various initial conditions on the behavior of elliptic jets experimentally. With a laser-induced fluorescence and 2D stereoscopic particle image velocimetry, they concluded that the entrainment ability of the elliptical synthetic jet is greater than that of the circular synthetic jet and increases with the orifice aspect ratio (AR ≤ 4) and Reynolds number. On the other hand, Reodikar et al. [9] reported that the heat transfer characteristics of circular and non-circular jets are comparable and observed a better performance for the case of circular jets in all conditions. In addition to this, Lee and Lee’s [11] experimental study of local heat transfer distribution of elliptic impinging jet found that for higher orifice-to plate distance (z/D > 6), the heat transfer rates of the elliptic impinging jet are lower than those for the circular jet in the stagnation region. They argued that the cause of this phenomenon is that, in the central area, most of the momentum of the elliptic jet is lost before arriving at the impingement plate due to significant entrainment and substantial mixing with the ambient fluid. Additionally, they correlated the Nusselt number for the nozzle aspect ratio and the nozzle-to-plate spacing as Nu ∝ AR−0.082 z/D−0.077. Straccia and Farnsworth [6] studied the axis switching phenomenon for moderate orifice aspect ratios (AR = 13,19) of a jet expelled from a synthetic jet actuator with a rectangular orifice. They used stereoscopic particle image velocimetry in addition to a Biot-Savart velocity induction solver to study the effect of orifice shape on vortex dynamics and axis switching. They reported that for AR > 6, the jet axis switched once and did not complete the axis switching cycle as opposed to jets with lower AR, which switched axis 2–3 times before the vortices lost coherence. They found a double peak in the mean jet centerline velocity profile, which became more prominent with increasing AR. A literature survey suggests a significant amount of studies on elliptic jet impingement. However, most studies consider only a lower aspect ratio (AR < 4) of an elliptic orifice. On the other hand, the effects of higher aspect ratios in rectangular orifices on impinging jets’ dynamics and heat transfer characteristics have been studied in great detail. The objective of the present study is to investigate the influence of higher orifice aspect ratios (AR = 10,14) on the axis switching behavior and the heat transfer characteristics of the elliptic jet. The present study experimentally analyzes the local and average Nu over the impingement plate and studies the temperature variation on the impingement plate (Fig. 1).

Fig. 1
A diagram presents the axis-switching behavior and heat transfer characteristics of the elliptic jet. It labels the nozzle.

Axis switching (Reodikar et al. [9])

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3 Materials and Methods

The experimental setup comprises a Synthetic Jet Actuator (SJA) assembly, hot-wire anemometry, an IR thermal imaging setup along with a heated foil, as shown in Fig. 2. The SJ actuator assembly uses a loudspeaker of 133 mm diaphragm size and a 15 mm diameter orifice plate (t/d = 0.33). A power oscillator (SI-28DR) supplies the input sinusoidal signal to the SJ actuator. The amplitude of the input signal is maintained constant (= 4.5Vrms). The frequency of SJ actuation is fixed as 40 Hz (i.e., its resonance frequency). A constant temperature hot-wire anemometer (Mini CTA 54 T42) with a single wire probe is employed to measure the flow velocity at the orifice exit. A 120  × 120 mm size matte finish test foil (SS material, AISI-304) is heated by a direct current power source for a constant heat flux of 2.5 kW/m2. The back side of the test surface is painted with flat black paint to achieve uniform emissivity (ϵ = 0.95). The thermal imaging technique with an IR camera (FLIR: A655sc) is used to study the heat transfer characteristics by gauging the temperature of the test surface. The IR camera measures temperatures from 0 to 2000 °C with an uncertainty of 1.5%. A calibration technique elaborated in [12] is employed to obtain the emissivity of 0.95 from the IR camera setup.

Fig. 2
A diagram presents the experimental setup. It labels the components via numbers from 1 to 10. 1. S J actuator. 2. Heating plate. 3. Traversing stand. 4. I R camera. 5. H W A probe. 6. Oscilloscope. 7. Power oscillator. 8. D C power supply. 9. Computer. 10. Cubical enclosure.

Schematic of the experimental setup used in present investigation

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Apart from this, a stepper motor-controlled traversing stand is used to maintain the surface distance between the orifice plate and heated foil. All the experiments are conducted in an enclosed environment to abstain from surrounding effects. The ambient temperature (Ta) during the experimental investigation is measured with a pre-calibrated K-type thermocouple by placing it in the enclosed chamber of the experimental setup.

3.1 Data Reduction

The centerline mean velocity is measured by the instantaneous velocity during the ejection stroke (half cycle) calculated as follows

$$U_{0} = \frac{1}{T}\int\limits_{0}^{T/2} {u(t)\,{\text{d}}t}$$
(1)

The Reynolds number (Re) based on mean centerline velocity can be calculated as

$${\text{Re}} = \frac{{U_{0} \times d}}{\nu }$$
(2)

where d is the orifice diameter and ν is the kinematic viscosity of the fluid.

The Average Nusselt (Nuavg) number is computed as follows:

$$Nu_{{{\text{avg}}}} = \frac{{h_{{{\text{avg}}}} \times d}}{{k_{f} }}$$
(3)

where, kf is the thermal conductivity of fluid.

The average heat transfer coefficient (havg) can be calculated as

$$h_{{{\text{avg}}}} = \frac{{q_{{{\text{conv}}}} }}{{\left( {T_{{\text{s}}} - T_{{\text{a}}} } \right)}}$$
(4)

Here, Ts and Ta are the temperature of test foil and its ambience, respectively, while qconv is the net heat supplied to the test specimen.

$$q_{{{\text{conv}}}} = q_{{\text{j}}} - q_{{{\text{loss}}}} \,;\,\,q_{{\text{j}}} = \frac{V \times I}{A}$$
(5)

qj, while qloss denotes the total heat loss from the target surface. The net supplied heat flux (qj) is calculated by the supplied voltage (V) and current (I) across the test foil.

The heat loss from the target surface is obtained by no-flow experiment [13] and the corresponding equation for heat loss w.r.t (Ts-Ta) is stated as below for Ta = 32 \(^\circ{\rm C}\).

$$Q_{{{\text{loss}}}} = 0.23143 \times (T_{s} - T_{a} ) - 0.31364$$
(6)

A maximum of 21.1% heat loss is computed, which combines the heat loss due to natural convection and radiation from the foil surface (from both top and rear surface). The maximum uncertainty associated with qconv and Nu0 is found to be \(\pm 3.95\) and \(\pm 4.53\mathrm{\%},\) respectively as calculated based on Coleman and Steel [14].

4 Results and Discussion

In this section, heat transfer characteristics of the circular orifice (AR = 1) are compared to elliptical orifices (AR = 10,14). All the orifices have the same effective orifice area among the studied orifices. The effective orifice diameter D is taken to be 15 mm based on our previous study [12], and the Reynolds number (Re) for the present investigation is calculated to be 8986.

4.1 Validation Study

The results of heat transfer characteristics in the case of synthetic jet impingement cooling are compared to available literature data to evaluate the correctness of the experimental method. The reduced stagnation point Nusselt number (Nu0,r) is considered for comparison to different experimental conditions. A 150 mm size diaphragm synthetic jet actuator with Vrms = 1 to 6 V, Re = 3600 to 22,950, and L0 = 0.84 to 170.5 were used by Gil and Wilk [15]. In another study, Greco et al. [16] used an SJ actuator with a diaphragm size of 208 mm operating at Re = 5250 and L0/d = 5 to 20. The current validation study employs a 133 mm diaphragm size actuator operating at Vrms = 4. The comparative heat transfer results are shown in Fig. 3 and the results closely match with the heat transfer results obtained by Gil and Wilk [15] and Greco et al. [16] (Fig. 4).

Fig. 3
A scatter plot plotted against z over d. It presents the data points for the present experiment, P. Gill and J. Wilk, and Greco et al between 0.3 and 1.3 on the vertical axis and 0 and 16 on the horizontal axis. P. Gill and J. Wilk has the highest peak among other data points.

Results of reduced stagnation point Nusselt number as compared to the literature data

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Fig. 4
4 graphs of nu versus r over d present 3 lines each, for circular orifice of A R = 1, elliptic of A R = 10, and elliptic of A R = 14. They present Z over d = 1, 3, 6, and 10. In all graphs, the lines have an ascending trend in the minor axis and a descending trend in the major axis.

Distribution of local Nusselt Number for various r/d and z/d values

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4.2 Effect of AR on Local and Average Nu

The distribution of local Nu on the heated surface is shown in Fig. 5a–d for different orifice-to-surface spacings (z/d = 1,3,6,10). In Fig. 5a–d, local Nu is shown for orifices of different aspect Ratios (AR): AR = 1 (circular orifice) and AR = 10,14 (elliptic orifice). The local Nu along the major and minor axis is plotted on the right and left side of the stagnation point, respectively, in each of the plots Fig. 5a–d. For all the orifices, the local Nu is observed to be largest at the stagnation point (r/d = 0), and then it decreases away from the stagnation point and reaches a local minimum at r/d = 2.67. For z/D = 1, a bell-shaped curve is observed for the case of AR = 10 on both the major and the minor axis. But such a shape of Nu is observed only on the major axis in the case of AR = 14. The Nu of AR = 10 and AR = 14 is higher than the Nu for circular orifice near the stagnation region, but the Nu for AR = 10,14 is lower otherwise. High AR elliptic jets perform 28% better cooling in the near-field (z/D = 1). The Nu of AR = 10 and 14 has similar values closer to the stagnation region. For all the cases z/D = 3, 6, 10, the circular orifice performs better local cooling, as evident by a higher local Nu. In the case of far-field, The AR = 10 elliptic jet has higher Nu values than the jet with AR = 14 and thus, performs cooling better.

Fig. 5
2 graphs plotted against Z over d present 3 lines each, for circular orifice of A R = 1, elliptic of A R = 10, and elliptic of A R = 14. A and B present the major and minor axes where the lines have an ascending to descending trend between 55 and 83 on the y-axis and 0 and 15 on the x-axis. B.

Line average Nusselt number of studied orifices along a major axis, b minor axis

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Figure 6 shows the line average Nusselt number (Nul-avg) variation on the Major (X) axis and Minor (Y) axis for the different aspect ratios (AR = 1,10,14) with the z/D values. The Nul-avg for the circular orifice (AR = 1) gradually increases and decreases after a certain point, whereas for elliptic orifices, a double peak is observed. Both plots show that, at low z/D values, Nul-avg is minimum. This is a consequence of low entrainment of surrounding air due to walling of the orifice and the heated surface. Additionally, at the near-field, the formed vortices fail to escape, and the recirculation decreases the heat transfer rate. However, for higher surface spacing (z/D = 12 to 14), Nu starts to decrease again due to a decrease in the kinetic energy and jet turbulence in the far-field region. So, the maximum heat transfer is obtained in the intermediate field (z/d = 6 to 10). The higher aspect ratio elliptic jets offer a higher Nu at lower z/D distances than circular orifices, similar to the findings of Bhapkar et al. [4]. This is due to the high spreading rate of elliptical orifices as compared to circular orifices. Among AR = 10 and 14, the elliptic jet with AR = 10 performs better cooling than AR = 14, evident for the Nul-avg plots.

Fig. 6
12 contour maps in 4 columns, present orifices of circular of A R = 1, elliptic of A R = 10, and elliptic of A R = 14. From left to right, the columns present z over D = 1, 3, 6, and 10. In all contour maps, the temperature is minimum in the center and is progressively increasing toward the sides.

Local temperature contour maps for different aspect ratios and orifice to surface distances

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4.3 Axis Switching

In Fig. 5a,b, at the near-field (z/D = 1,3), the local Nu values for the major axis of the AR = 14 jet are higher than the minor axis Nu measurements. This suggests that the cooling is highly localized and similar to the shape of the orifice. This is also clearly apparent from the Fig. 6 showing IR thermography plots for z/D = 1,3 with AR = 14. As the jet progresses downstream, for values of z/D = 6 and 10, the minor axis Nu values are slightly higher than the major axis plots. The IR thermography contour plots also depict a similar behavior. The heat transfer characteristics of the elliptic jets change with the axial distances. This suggests that axis switching is observed even in the case of higher AR elliptic jets.

5 Conclusion

This experimental study investigates the influence of the elliptic orifice aspect ratio on local heat transfer between a smooth flat plate and the impinging jet of air at different nozzle-to-plate distances. The following conclusions are drawn from this study:

  1. 1.

    Higher aspect ratio jets offer higher Nu values at low z/D values than axisymmetric orifices. For z/D = 1, elliptic jets offered 28% higher heat transfer rate in the stagnation region than the circular jet. Thus, high aspect ratio elliptic jets perform better cooling in the near-field region of the jet.

  2. 2.

    Circular jets produce a single peak in the Nuavg vs. z/D plot, which lies in the mid-field region (z/D = 6 to 10). Contrary to this, elliptic jets (AR = 10,14) produce double peaks lying in near-field (z/D = 1 to 3) and mid-field regions (z/D = 6 to 10).

  3. 3.

    Axis switching is observed even for synthetic jets ejected from high aspect ratio (AR = 10,14) elliptic orifices.