Numerical Investigation of Single and Multiple Impinging Synthetic Jets on the Flow Field and Heat Transfer at Low Orifice-to-Plate Distances

In the present numerical study, the thermal performance and fluid flow properties have been investigated to show the effect of single-orifice and multiple-orifice impingement of synthetic jets for dimensionless orifice-to-plate distance (H/D) of lower than one. Investigations have been done for an actuation frequency of f=500 Hz, 0.10 ≤ H/D ≤ 0.75, and dimensionless pitch ratio of 1.25 ≤ D o /D ≤ 1.75. The results were validated with experimental results from the literature, and a fair agreement was obtained. The results showed that at low nozzle-to-plate spacing, lower target plate temperatures could be obtained. It was observed that with the use of multiple orifices at especially higher D o /D higher heat transfer values are present. The study was performed to add knowledge to the electronics and aviation industries where high temperatures in small cavities occur.


INTRODUCTION
Synthetic impinging jets are considered an attractive heat removal technique, which has gradually attracted attention due to some advantages like higher heat transfer in comparison to natural convection, no rotating and moving parts, and no need for complicated piping and pumping [1]. Synthetic jets are called zero-massflux systems due to no mass injection. On the other hand, linear momentum is transferred to the fluid [2]. Synthetic jets have been utilized in various applications such as active flow control applications including control of boundary layer transformation/detachment, lift enhancement and drag reduction, underwater vehicle propulsion, heat transfer enhancement by cooling of microprocessors in electronics industry, and mixing augmentation [3,4]. Especially the development in electronics has led to an increase in heat loads in compact volumes. Cooling of the electronic components used in aircraft, unmanned air vehicles, spacecraft, and satellites is vital to maintain efficient use [5]. Within these applications, the cooling of electronic elements in small volumes with less use of components is desired. Hence, synthetic jets are a promising method for the cooling of electronic components in small spaces.
In synthetic jets, a membrane placed on a cavity oscillates which generates flow by causing volume change in the cavity (Fig. 1) [1,6]. Throughout the oscillating movement of the membrane, the air is ejected and sucked through a nozzle placed at the other end of the cavity [7,8]. The Reynolds number in synthetic jets is defined as follows.
where ρ shows the fluid density, D is the center nozzle diameter, μ shows the dynamic viscosity, and U 0 shows the jet characteristic velocity, which is defined as where u 0 (t) shows the velocity at the exit plane of the orifice, and τ is the actuation period of jet generation [2]. There exist many studies in the literature considering the heat transfer applications and performance of single and multiple impinging synthetic jets.
Singh et al. [4] investigated the circular synthetic jet impingement heat transfer under different waveforms experimentally. Investigations were performed for different Re numbers, dimensionless nozzle-to-plate spacing of 1-25, and frequencies. The effect of stroke length and jet-to-target surface distance (H/D = 2-10) on synthetic jet impingement cooling performance was investigated experimentally by Greco et al. [6]. Chaudhari et al. [7] examined the heat transfer of a single circular synthetic jet impingement experimentally to obtain the heat transfer performance for various Re numbers, the distance between the jet and impingement surface, and the orifice plate length. The impingement of synthetic jet under various orifice geometries was studied by Singh  Slupski et al. [15] investigated the effect of oscillation frequency on the sweeping jet experimentally and numerically. They observed that there is a relationship between the inlet mass flow rate and oscillating frequency. In addition, they concluded that the 2D URANS model is a good approximation for the design of sweeping jet actuators. Also, many studies are present in the literature representing multiple impinging synthetic jets. Ahmad and Qayoum [3] investigated the heat transfer of synthetic jets under different excitation voltages and frequencies by using one and two orifices. Singh et al. [16] showed the results of a single-orifice and multiple-orifice impingement of a synthetic jet for several orifice geometries. They experimentally compared the thermal performance of single and multiple-orifice synthetic jet impingement under various Re numbers and H/D = 1-25. A comparison study was performed for single-ori-fice and multiple-orifice synthetic impinging jet heat transfer and fluid flow by Gil [17]. Experimental mea-surements were carried out by Xiao-Ming and Jing-Zhou [18] to show the synthetic jet impingement cooling performance and flow characteristics from a single cavity with various orifice arrangements. Chaudhari et al. [19] explored the effects of various Re numbers and jet-to-plate gaps (H/D=1-30) by utilizing multiple orifice synthetic jet impingement. The thermal performance of various orifice geometries of the synthetic impinging jet was examined by Mangate et al. [20]. Different Stokes numbers, pitch ratios, and orificeto-plate distances were taken into account by the researchers. Mangate and Chaudhari [21] investigated the multiple-orifice synthetic jet impingement on a heat sink experimentally. They considered frequency, the distance between orifices, and nozzle-to-plate distance. Particle image velocimetry experiments were performed by Yadav et al. [22] to show the flow of synthetic jets formed from a different number of orifices. Ye et al [23] presented the velocities in the turbulent boundary layer of a synthetic jet array at different locations in the streamwise and spanwise directions.
Fanning et al. [24] experimentally showed the effects of jet-to-plate gap and the distance between orifices for two rectangular synthetic jets. The heat transfer and particle image velocimetry measurement results were presented in the study for H/D = 6 -24. Paolillo et al. [25] experimentally examined the thermal performance of quadruple-impinging synthetic jets. The effect of various Re and Strouhal numbers was examined by the authors. Kim et al. [26] showed the effect of interaction between two synthetic jets on the flow field. They investigated the effect of the distance between the orifices and stroke length for a fixed Re number. Talapati and Katti [27] experimentally investigated the effect of the temperature of the jet on the heat transfer distribution. Investigations were performed for different frequencies and nozzle-to-surface spacing (H/D=1-8).
The effect of waveform shape on the heat transfer and flow characteristics of a single-orifice and multipleorifice synthetic jet impingements was numerically investigated by Singh et al. [28].
The literature review represents that there have been many experimental as well as numerical studies performed employing single and multiple synthetic impinging jets. Investigations for different orifice-to-plate distances, frequencies, geometries, etc. have been done. However, the investigations are limited to the dimensionless orifice-to-plate distance above 1, where the majority of the range is H/D>2. Hence, there is a lack of information on synthetic jet impingement flow and heat transfer at low orifice-to-plate distances. This knowledge is important due to the continual development in the electronics industry, which has led to higher heat loads in smaller volumes. The less need for piping and pumps, and the absence of any rotating part are advantages for synthetic impinging jets in small spaces. Hence, it was aimed to numerically investigate the synthetic jet impingement on a flat plate from a single orifice and multiple circular orifices for H/d ≤ 1. The findings could give guidance in the cooling of electronic components used in aviation and space applications, where it is important to maintain less weight with high thermal cooling efficiency.

NUMERICAL METHODOLOGY
The problem under investigation has been introduced in this part of the study. In addition, the computation domain, governing equations, and boundary conditions have been described in detail.

Computational Domain and Governing Equations
In the present study, the problem under investigation has been built three dimensionally to simulate the impingement of synthetic jets impingement arising from a circular single orifice and multiple orifices as shown in Fig. 2. The cavity is formed with the orifices and an oscillating diaphragm. The height of the cavity is modelled as h c =6.3 mm. The cavity is formed with a square cross-section with extensions (d c ) of 48 mm x 48 mm.

Figure 2. Computational Domain and Boundary Conditions
The diaphragm oscillation creates the synthetic impinging jet which hits a flat target plate that is modelled with a length of L=58 mm and width of W = 53 mm (Fig. 2).
The orifice-to-surface gap (H) is defined as the space among the nozzle exit and the impingement plate. Table 1   Simulations were performed with different nozzle configurations: single circular, and a center orifice with four satellite orifices (see Table 2). The center nozzle was modelled with a diameter of D = 8 mm, and the satellite orifices were modelled with a diameter of 4 mm. The orifice plate has a thickness of t d = 2.4 mm (Fig. 2). On the impingement plate, a constant heat flux (q" = 1000 W/m 2 ) was applied, and adiabatic boundary conditions were set on all other walls. The boundary conditions applied on the walls were the no-slip boundary condition. Air at 20°C was used as the fluid. Also, the environmental air temperature was used as 20°C. The pressure boundary condition at the atmospheric pressure was applied at the outlet section. Therefore, an inflow and outflow at the outlet section could occur. The boundary condition applied to the diaphragm has a sinusoidal movement profile and is assumed as a reciprocating piston [9]. The displacement of the diaphragm was modelled time-dependently as follows [1,14]; where A (A=200 μm) shows the Amplitude, t is Time, and f is the Frequency, which was applied as f=500 Hz in the present study. By taking the derivative of Eq. (3), the boundary condition applied to the diaphragm could be obtained [1,14].
This equation is used to calculate the speed of the movement of the diaphragm, which forms the velocity inlet boundary condition [1].
The problem under investigation was modelled as time-dependent as a three-dimensional case. The flow was assumed incompressible and turbulent. Viscous dissipation and buoyancy forces were not taken into account. The thermal properties of air like conductivity, viscosity, and density were assumed to be constant. The target surface was heated with a constant heat flux (q"), and investigations of the cooling of the surface by using synthetic impinging jets at low nozzle-to-plate spacing were performed.
Based on these assumptions and simplifications, the mass conservation, momentum, and energy equations are solved in terms of RANS as follows [13,29,30,31]; represents the Reynolds stresses.
To enclose the above equations, the Boussinesq assumptions are accepted which are given as follows; where μ t , shows the eddy viscosity, k is representing turbulent kinetic energy [28].
In the present study, the FloEFD CFD software was employed to numerically investigate synthetic jet impingement heat transfer and fluid flow.
To determine the turbulent quantities, the Lam-Bremhorst k-ε turbulence model was utilised in the study. In the k-ε model, empirical additions were employed [33]. In this turbulence model, damping functions were used to obtain a better boundary profile [33]. The equations representing the model are presented.
where μ t shows the turbulent kinetic energy, C µ , C 1, and C 2 are constant coefficients in the model. The turbulent Prandtl numbers have been represented with σ k and σ ε . The damping functions used in the model are determined by [32]; where Re t and Re z show the turbulent Reynolds numbers.

Data Reduction
In the present study, the synthetic jet impingement of single and multiple orifices on a flat target surface under constant heat flux has been investigated, and the results have been presented in the form of timeaveraged local heat transfer coefficient (h) and Nusselt number (Nu), which are evaluated as follows; where T p and T o show the time-averaged local surface temperature and air temperature, respectively. The time and area-averaged Nusselt number (Nu avg ) and heat transfer coefficient (h avg ) could be calculated by replacing T p in Eq. (14) and Eq. (15) with the time and area-averaged temperature on the impingement surface.

Mesh and Time Step Independency Study
Reliable results of the parametric study could be obtained by independency studies for mesh and time step by taking f=500 Hz and H/D = 1.00 as an example case. As shown in Table 3, five different mesh numbers are used to acquire mesh independency. A systematic increase was applied in x × y × z directions to show the change in heat transfer with mesh number. Table 3 summarizes the time and area-averaged heat transfer coefficient on the target plate. The mesh values represent the grid numbers in the x × y × z directions. It is obvious that the highest deviation was around 3% between Case 1 and Case 2. Afterwards, the relative deviation between the cases was around 1%, which is enough to justify when the mesh number is higher than 80 × 80 × 80. In addition, it was observed that the computational time and computational sources increased by almost 30% and 21%, respectively, with the increase in mesh number from 80 × 80 × 80 to 88 × 88 × 88. Hence, by taking computational accuracy and sources into account, the grid with the 80 × 80 × 80 mesh number was selected to carry out further solutions. The mesh structure used within the study has been presented in Fig. 3. To capture the impingement heat transfer and flow structure in the vicinity of the target surface, a more dense mesh was applied above the surface. Hence, the requirement of y+ < 1 was satisfied.
In addition, a time-step independency study has been performed by using the mesh number of 80 × 80 × 80, and the results are listed in Table 4. The time steps have been chosen to satisfy the Courant-Friedrichs-Lewy (CFL) number below 1. The CFL was obtained by using the average jet exit velocity and the mesh number of 80 × 80 × 80. It was observed that the time step should be less than 5.7 × 10 -5 (i.e. τ/35). Four kinds of time steps such as τ/100, τ/250, τ/400, and τ/800 were employed to define the suitable time step. Table 4 represents that there is a small change in the heat transfer coefficient, where τ/250 was selected for all simulations in the parametric study. As can be seen from the results, the deviation between τ/250 and τ/400 is small enough, and hence the time step of τ/250 is regarded as adequate for all simulations.   Fig. 5 represents that a fair agreement with the experimental results has been obtained.
It could be mentioned that the results obtained for the single-orifice as well as the multiple-orifices are valid.

RESULTS AND DISCUSSION
In this part of the study, the numerical results were shown for single-orifice and multiple-orifice synthetic impinging jets under H/D=0.10 -1.00, D o /D = 1.25 -1.75, and f = 500 Hz. The overall aim was to present and add knowledge in the field of synthetic impinging jets at low nozzle-to-plate distances for single-and multiple-orifice impinging synthetic jets. Hence, the flow characteristics and the heat transfer performance were shown for impinging synthetic jets at H/D≤1.00.
To understand the flow behaviour and to interpret the thermal results of multiple-orifice synthetic impinging jets at low nozzle-to-plate distances, streamlines and velocity contours at f=500 Hz actuation frequency and various D o /D values for orifice-to-plate distances of 0.15 and 0.75 are shown for different time intervals in Fig. 6 and Fig. 7, respectively. Due to symmetry, only the right half of the domain is shown in the Figures 6-7. At time t=0, the fluid ejected from the cavity at maximum velocity, and the velocity decreased until t=0.4τ when the suction phase began. Fig. 6 shows that in the discharge phase, two clockwise vortexes occurred in the cavity due to the cavity geometry. It was noted that especially the vortex above the center orifice deflected the flow; hence, higher velocities were observed close to the side surfaces of the orifices. Thus, lower velocities were seen at the x=0 location during the ejection phase. Therefore, lower heat transfer was expected around the stagnation point. The impingement under the satellite orifices occurred at higher velocities due to the smaller diameter of the satellites, where during the ejection phase (t=0 -0.2τ), a clockwise vortex was formed along the height of the channel at the near side of the center orifice. It could be observed that this vortex blocks the wall jet flowing from the center orifice. This will have a decreasing effect on heat transfer at this region for all investigated D o /D values. The suction phase begins at the time t=0.4τ and continues until t=0.8τ. As one can see, with the start of the suction phase, vortexes occur in the cavity region, and at t=0.6τ, two vortexes are present in the cavity. Also, when t=0.6τ during the suction phase near the stagnation region of the center as well as satellite orifices anticlockwise vortexes occur. These vortexes have a blocking effect on the fresh air (cold air) coming from the outlet section into the cavity. This could have a decreasing influence on heat transfer due to the decrease in cold air entering the cavity. When t=0.8τ, the flow is sucked into the cavity within the center orifice, which creates a major clockwise vortex in the cavity. This vortex leads the air to satellite orifices where ejection occurs. Hence, the air is sucked through the center orifice and ejected through the satellite orifices and impinges on the target surface. After the impingement through the satellite orifices when t=0.8τ, the air is directed towards the outlet, as well as to the center orifice although a moderate increase in heat transfer could occur due to the impingement through the satellite orifice. At this time step, heated air is circulated through the cavity, which could result in a decreased heat transfer.
The time-dependent velocity distribution for H/D=0.75 is shown in Fig. 7. At time t=0, air impinges on the target surface at the highest velocity, and a decrease in velocity occurs at t=0.2τ. At that moment, vortexes occur near the outlet region of the channel. These vortexes have a blocking effect on the wall jets, especially for D o /D=1.25. However, at t=0.4τ the suction of fresh air to the cavity starts, and for D o /D>1.25, a large anticlockwise vortex occurs, which has a blocking effect on the fresh air (cold air). In addition, the heated air is mixed with the fresh air; hence, the temperature increases in the cavity, which has a degrading effect on heat transfer. This large vortex is present at t=0.6τ -0.8τ for D o /D=1.75. On the other hand, at t=0.8τ, a large anticlockwise vortex is found below the center orifice for all D o /D. The vortex around the impingement region causes mixing with the cold fluid which enters from the outlet. Hence, an increase in the temperature inside the cavity occurs.
Afterwards, the heat transfer performance of the single-orifice and multiple-orifice impinging synthetic jet has been shown. Fig. 8 -Fig. 10 shows the timeaveraged local Nu number distributions for nozzle-toorifice distances of 0.15, 0.50, and 0.75, respectively. The results were shown for various D o /D values.
As one can see from the figures, the highest stagnation point Nu number under the center orifice is obtained for the single nozzle. This is attributed to the fact that the vortexes at that region below the center orifice increase the air temperature; thus, a decrease in heat transfer in the region of 0.0 ≤ x/D ≤ 0.5 occurs. On the other hand, for the multiple-orifice case at H/D=0.15 (Fig. 8), a sudden increase in Nu number occurs, and the highest Nu number values are obtained below the center of the satellite orifices. Also, the maximum Nu number values are moving towards the outlet with the increase in D o /D.
In addition, a considerable augmentation in heat transfer is observed with the increase in D o /D, which is attributed to the interaction of the jets with the decrease in D o /D with a degrading effect on heat transfer (Fig. 6). Although a small maximum region occurs when H/D=0.15 (Fig. 8), a wider maximum region has been observed with the increase in H/D. This is attributed to the widening and development of the jet with the increase in H/D. As can be seen for H/D=0.50 and H/D=0.75, a minimum heat transfer region occurs around x/D=0.75 for D o /D=1.75. This shows that the vortexes in the mid-region of the orifices have a degrading effect on heat transfer (Fig. 7).
The heated air recirculates at this region, and prevents fresh air (cold air) to enter the cavity. Hence, a decrease occurs.
The temperature distribution occurring on the target plate for single-orifice and multiple-orifice has been presented for various H/D values in Fig. 11. As one can see, the lowest temperatures occur at low orifice-toplate distances, which is because of the high momentum of the jet. This causes high momentum in the wall jet region, which has an increasing effect on heat transfer. Conversely, the impingement regions of the satellite nozzles could be observed distinctly, whereas the impingement region of the center jet could be hardly observed. This is not the case for the single orifice, where the impingement region becomes wider by growing the gap between the nozzle and plate. In addition, at higher orifice-to-surface distances, the impingement regions under satellite orifices widen, which is in agreement with Fig. 9 and Fig. 10. Besides, at high nozzle-to-plate distances and low D o /D values, due to the lowering in jet momentum, higher temperature values are observed at the corner of the target plate. In general, it could be concluded that lower temperature values have been observed for multiplenozzle, especially at higher D o /D. The variation in time and area-averaged Nu number (Nu avg ) with respect to H/D for several dimensionless pitch diameters (D o /D) is shown in Fig. 12. The findings are compatible with Fig. 11. It is observed that the least heat transfer has been seen for the single-orifice within the limits of 0.10 ≤ H/D ≤ 0.50.
On the other hand, within the limits of 0.10 ≤ H/D < 0.50, the average heat transfer results for multiple orifices are close for all D o /D. This is due to the high momentum of the jets at low nozzle-to-plate spacing, which provides high heat transfer rates. In addition, the flow field at low nozzle-to-plate spacing is less affected by the dimensionless pitch diameter (D o /D). However, for H/D > 0.50, the heat transfer for D o /D=1.25 and 1.50 remains almost constant, whereas a high increase rate has been observed by using a single orifice in a similar range of nozzle-to-plate spacing.
In the range of 0.75 ≤ H/D ≤ 1.00, an increase of around 23% has been obtained in heat transfer for the single-orifice case. This is attributed to the widening of the jet with an increase in nozzle-to-plate spacing, where it is possible to cool a larger area (Fig. 11). On the other hand, with the increase in nozzle-to-plate spacing and at low pitch diameters, the heat transfer drops due to the jet interaction, which is also observed in Fig. 11.

CONCLUSIONS
Synthetic jet impingement flow and heat transfer have been investigated numerically to show the effect of a single-orifice and multiple-orifices at low nozzle-to-plate spacing and dimensionless pitch ratios. Simulations were done for f=500 Hz, H/D = 0.10 -1.00, and D o /D=1. 25 -1.75. In this direction, the problem under investigation has been first validated with experimental studies from the literature, and a good agreement has been obtained. Afterwards, a parametric study has been done.  The overall aim was to present and add knowledge in the field of synthetic impinging jets at low nozzle-to-plate distances for single-and multiple-orifice-impinging synthetic jets. The findings could be concluded as follows:  The flow field was affected by the number of orifices, and with the increase in nozzle-to-plate spacing and decrease in dimensionless pitch  Experimental investigation of the thermal behaviour a single-cavity and multiple-orifice synthetic jet impingement driven by electromagnetic actuator for electronics cooling,