# Synthetic Jet Actuators with the Same Cross-Sectional Area Orifices-Flow and Acoustic Aspects
## 3 Results and Discussion
### Impact of the Hydraulic Diameter on Results  
The choosing of equivalent diameter as a characteristic dimension had an impact on the presented results. The Reynolds number is directly proportional to the characteristic dimensions and a dimensionless stroke length is inversely proportional to the square of the characteristic diameter. The time-mean reaction force method of the energetic efficiency calculation is independent of the characteristic diameter. The percentage changes of Reynolds number and dimensionless stroke length when considering the hydraulic diameter are shown in Table 3.  
The choice of the equivalent diameter instead of the hydraulic diameter causes an increase of Reynolds number in the case of the square and slot orifice and a decrease of dimensionless stroke length. The dimensionless stroke length is used generally only for the formation criterion validation. However, [PERSON] [25] showed that the formation criterion is met if the SJA generates the time-mean reaction force higher than zero and this criterion  
Figure 5: The energetic efficiency of SJA as a function of frequency at real power \(P=3\) W (**a**) and as a function of real power at a resonant frequency (**b**).  
\begin{table}
\begin{tabular}{c c c} \hline \hline
**Office Type** & **Reynolds Number** & **Dimensionless Stroke Length** \\ \hline circular & 0\% & 0\% \\ square & \(-\)11.39\% & +25.44\% \\ slot & \(-\)29.11\% & +96\% \\ \hline \hline \end{tabular}
\end{table}
Table 3: Change of parameters for the hydraulic diameter.  
can be used by the reaction force measurement. In the case of the calculation of stroke length based on the velocity measurements, the difference between dimensionless stroke length calculated for the hydraulic diameter and for the equivalent diameter will be not so large as values presented in Table 3 (the stroke length will be independent of the chosen characteristic diameter), and the formation criterion formed by [PERSON] et al. [44] or [PERSON] and [PERSON] [43] can be easily modified to account for the equivalent diameter.  
The changes in the values of the Reynolds number may seem more controversial. The Reynolds number is the ratio between the internal and viscous force and is used for the flow classification and in the scaling of different-sized flows. This dimensionless number was used initially only for flows in pipes and for this reason, it is customary to use the hydraulic diameter for its calculation. However, it is not the rule and, for example, [PERSON] and [PERSON] [45] applied the width of the slot orifice. Additionally, in the case of SJ, the diameter of the orifice (hydraulic or equivalent) is equal to or higher than the orifice height. For this reason, the viscous forces between the orifice walls and the fluid are less important than the shape of the orifice (viscous forces in the fluid). For example, [PERSON] et al. [17] showed that the SJ generated by an actuator with a circular orifice is less turbulent than the SJ generated by an actuator with a slot orifice. There are more differences in the topology of the SJ generated by different orifice shapes [5].  
The SJA had a similar energetic efficiency at the resonant frequency and the real power (Figure 5b) and it can suggest that the flow conditions were also similar. It must be noted that the calculations of SJ and SJA parameters based on the time-mean force reaction measurements are independent of the orifice shape [26], in contrast to the velocity calculation method.  
Taking all the above facts into account, one would expect the Reynolds number for all orifice types to be similar as well. For the hydraulic diameter, that is not true. However, in the case of the equivalent diameter, this is. For this reason, we believe that the equivalent diameter is better suited to calculate parameters when comparing actuators with orifices of different shapes than the hydraulic diameter.