# Synthetic Jet Actuators with the Same Cross-Sectional Area Orifices-Flow and Acoustic Aspects
## 3 Results and Discussion  
### Time-Mean Reaction Force Measurements  
In Figure 3a, the Reynolds number for different orifice types as a function of frequency are shown. The course of the charts is very similar and it is only for \(f>50\) Hz that the value of the Reynolds number begins to differ significantly. The Reynolds numbers of SJAs with circular and square orifices are the same. Based on Reynolds numbers, the characteristic frequency of SJs can be designed as \(f=44\) Hz for the circular and the square orifice at Reynolds numbers equal to 13,174 and 13,219 respectively, and \(f=54\) Hz at Reynolds number 13213 for the slot orifice. It can be assumed that the Reynolds number calculated for the equivalent diameter is independent of the orifice shape at the resonant frequency. This is confirmed by the dependence presented in Figure 3b.  
In Figure 4 the dimensionless stroke length was presented. This parameter is used as a formation criterion of SJ. It must be noted, that in this case the equivalent diameter was used [40], the hydraulic diameter [41], or another parameter e.g., slot width [5; 42]. The formation criterion was fulfilled in the whole measuring range. This issue is described in more detail in [34]. [PERSON] and [PERSON] [43] defined the formation criterion as \(L/d>0.4\). In this case, the diameter \(d\) can be understood as hydraulic diameter \(d_{h}\). Because \(d^{\prime}\geq d_{h}\) then \(L/d\geq L/d^{\prime}\geq 0.4\). Thus, the criterion is fulfilled. The dimensionless stroke length for the slot orifice is smaller than for other orifices. Generally, the higher the power, the higher the difference, and at the \(P=5\) W the dimensionless stroke length for the slot orifice is about 18% smaller than for the circular or rectangular orifice.  
Figure 4: Dimensionless stroke length of SJ as a function of frequency at real power \(P=3\) W (**a**) and as a function of real power at a resonant frequency (**b**).  
Figure 3: Reynolds number of SJ as a function of frequency at real power \(P=3\) W (**a**) and as a function of real power at a resonant frequency (**b**).  
In Figure 5 the energetic efficiency of an SJA as a function of frequency at real power \(P=3\) W (Figure 5a) and as a function of real power at a resonant frequency (Figure 5b) were presented. The resonant frequency of the SJA designated based on efficiency is the same as in the case of the Reynolds number. The maximum efficiency was the same for each orifice and was equal to 5.3%. The increase of real power does not increase the energetic efficiency of the SJA (Figure 5b). That this course of efficiency charts as a function of real power is typical and it can be observed in many papers for different actuator types [8; 26; 29; 34]. The electrical efficiency function of the SJA was independent of the orifice shape.  
The Reynolds number (Figure 3), the dimensionless stroke length (Figure 4), and the efficiency (Figure 5) are similar and independent of the orifice shape for frequency \(f<60\). The dimensionless stroke length as a function of real power (Figure 4b) for the slot orifice also differs from other cases. This may be due to a fact that the Equations (1)-(3) have been checked and confirmed only for axisymmetric, circular orifices. However, these differences are not particularly significant because the SJA operates mainly at resonant frequencies. However, this is an area that should be additionally investigated with the use of velocity measurement.