# Helmholtz Resonance Frequency of the Synthetic Jet Actuator
## 5 Conclusions  
Loudspeaker synthetic jet actuators were tested using 108 various geometrical configurations. The experiment was performed to determine the impact of SJ geometry on the Helmholtz resonance frequency. Geometrical parameters of the SJ actuator--orifice diameter, orifice length, and cavity volume--were changed within a wide range. An additional geometric dimensionless parameter representing a ratio of the orifice cross-section area to the cross-section area of the cavity was introduced. The investigated cases of the SJ actuator were characterized by a high \(CR\) parameter.  
The dependences of electrical and flow parameters that characterize the considered synthetic jet actuators, as a function of the excitation frequency, were also identified.  
Based on the obtained experimental results, an improved version of the classical model of the Helmholtz resonance frequency was derived. The model provides valuable insights into the behavior of SJ actuators.  
Based on the research conducted and the obtained findings, some conclusions can be formulated:  
* The Helmholtz resonance frequency can be determined from measurements of electrical parameters or measurements of the air velocity. However, due to the higher precision and greater repeatability of electrical measurements in relation to air velocity measurements with the use of constant temperature anemometry, the first method appears to be more appropriate.
* The resonance frequencies do not depend on the actuator supply voltage in the considered range of effective voltages.
* There is a decrease in \(f_{H}\) with an increase in \(V\), in the cases of constant \(d\) or \(l\) values. In addition, the Helmholtz resonance frequency increases as the orifice diameter increases at a constant value of the cavity volume and decreases as the orifice length increases.
* The additive length \(\Delta l\) in the effective orifice length \(l_{e}\) is a function not only of the orifice diameter, but also of the orifice length \(l\) and the surface ratio \(\sigma\).
* The obtained investigation results enabled the determination of an improved model for the Helmholtz resonance frequency of a synthetic jet actuator.
* The model obtained is valid in the case of SJ actuators characterized by large values of the coupling ratio.  
The results of the conducted research represent a step towards the development of practical applications of loudspeaker-driven SJ actuators. The obtained knowledge about the Helmholtz resonance frequency can be of significance in SJ applications in cooling systems due to its impact on SJ actuator energetic efficiency and, consequently, heat transfer intensity.  
Conceptualization, P.G. and J.W.; methodology, P.G., J.W. and M.K.; software, validation, formal analysis, P.G., J.W. and M.K.; investigation, P.G.; resources, J.W. and P.G.; writing--original draft preparation, J.W.; writing--review and editing, J.W., P.G. and M.K.; visualization, P.G. and M.K.; supervision, J.W.; project administration, funding acquisition, P.G. All authors have read and agreed to the published version of the manuscript.  
This work was supported by the National Center for Research and Development, Poland Grant No.: LIDER/6/0024/L-10/18/NCBR/2019.