# The PIV Measurements of Time-Averaged Parameters of the Synthetic Jet for Different Orifice Shapes
## 3 Results and Discussion
### The Turbulent Kinetic Energy of the Synthetic Jet
#### 3.2.1 Impact of the Orifice Shape on the Turbulent Kinetic Energy  
The dimensionless TKE at \(L_{0}=2\) had the highest value near the orifice, and at the distance \(2<x/d<6\), it had the highest value around the centerline. This shape of the TKE field can be compared to the shape of rabbit ears. The highest values of dimensionless TKE were observed in the case of the slot orifice (Figure 11c) and then in the case of the square orifice (Figure 11b), and the lowest in the case of the circle orifice (Figure 11a). The TKE field decreased with the increased the distance, \(x/d\); the fastest decreasing rate was for the slot orifice, and the lowest decreasing rate is for square orifice. Similar dependence can be observed in Figure 12 at \(L_{0}=10\). The dimensionless TKE centerline distributions (Figures 13 and 14) showed that the TKE for the square orifice was higher than for the circle orifice at the distance \(x/d<4\). The TKE for the slot orifice was higher than for the square at a distance of \(0.5<x/d<3\) at \(L_{0}=2\) (Figure 13) and at a distance of \(2.4<x/d<3.4\) at \(L_{0}=10\) (Figure 14). The initial decline and subsequent increase in TKE in the case of the circle and square orifice at \(L_{0}=2\) visible in Figure 13 were also observed by [PERSON] et al. [17] for the SJA with the chevron and circle nozzle and was named a calming effect by [PERSON] et al. [40], who observed this effect for the continuous jet. This effect was not observed in the case of the slot SJ and at \(L_{0}=10\).  
Figure 11: Synthetic jet dimensionless turbulent kinetic energy field at \(Re=5000\), \(St=0.5\), and \(L_{0}=2\): (**a**) circle orifice, (**b**) square orifice, (**c**) slot-long side, and (**d**) slot-short side.  
Figure 12: Synthetic jet dimensionless turbulent kinetic energy field at \(Re=5000\), \(St=0.1\), and \(L_{0}=10\): (**a**) circle orifice, (**b**) square orifice, (**c**) slot-long side, and (**d**) slot-short side.  
Figure 14: Centerline dimensionless turbulent kinetic energy axial distribution at \(L_{0}=10\).  
Figure 13: Centerline dimensionless turbulent kinetic energy axial distribution at \(L_{0}=2\).  
Figure 15: Dimensionless turbulent kinetic energy radial distribution at \(L_{0}=2\).  
As mentioned, the TKE field width for the slot SJ contract for the slot-long side and expand for the slot-short side. This behavior complies with the flow structure of the slot SJ [14]. The higher SJ TKE level in the case of the slot orifice concerning the circle orifice was demonstrated by [PERSON] et al. [20]. They observed that the slot SJ lost its coherent structure and thus produced a higher level of TKE. Therefore, the square and slot SJ enhanced the heat transfer better than the circle SJ [21, 22], and this can be related to the higher TKE. The highest Nusselt number for the impingement SJ was achieved for a distance of \(x/d<5\) for slot orifice and \(x/d>5\). Moreover, it should be remembered that the efficiency of the SJ in cooling applications depends also on the dimensionless stroke length [2]. This is in line with the presented results.