PSI - Issue 72

Emre Kara / Procedia Structural Integrity 72 (2025) 77–84

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Figure 1 is generated for the current problem in ANSYS Fluent (2022), representing the transient solution. The jet has 'zero mass' in terms of the time average, as no external air source is used. Figure 1 shows the operating principle of an SJA with the flow trajectories in four steps: start of suction stage (1a), end of suction and start of blowing stage (1b), end of blowing and start of suction stage (1c), and end of suction and start of blowing stage (1d). Figure 1 displays the cavity below the nozzle, which is bounded by the loudspeaker diaphragm, the nozzle itself, and its outlet. The jet is drawn into the low momentum region of the driver cavity during the suction stages. The vibrating diaphragm allows the jet to pass through the actuator cavity and exit the orifice in the blowing stage, creating a positive impulse. The principal objective of this study is to establish the correlation between input geometrical parameters, i.e. cavity inner diameter, d c , orifice exit diameter, d 0 , cavity height, h c , orifice height, h 0 (Kara, 2025) and a range of output parameters, i.e. Reynolds number, Re (Jankee, 2020), Strouhal number, St (Persoons et al., 2018), Stokes number, S (Kordik and Travni cek, 2019), orifice utilization factor, β 0 (Jain et al., 2011), characteristic velocity, V 0 (Jankee, 2020), full stroke length, L 0 (Uruba, 2005), dimensionless stroke length, L (Girfoglio, 2015), Thrust, T (Seifert, 2006), peak velocity, U p (Jain et al., 2011), frictional velocity, U τ (Jankee, 2020), frictional Reynolds number, Re τ (Jankee, 2020), mechanical efficiency, η mech (Seifert, 2015), Overall Figure of Merit, OFM (Seifert, 2015), Synthetic Jet Actuator Efficiency η SJA (Gil and Smyk, 2019). These variables are considered for a loudspeaker-driven SJA depicted in Fig. 2 that shows the geometric input parameters of a loudspeaker driven SJA and main members of the SJA (cavity, orifice, vibrating diaphragm). It is assumed that the diaphragm and surround move together as a single unit for the purpose of simplified vibration simulation and the unit is called vibrating diaphragm. The cavity inner diameter, d c , and the cavity height, h c , form the cavity that is in direct contact with the vibrating diaphragm. Pale green region states the loudspeaker with gasket height. Height of the orifice channel, h 0 , is the length of orifice through which the synthesized air inside the cavity discharged into still air. In order to establish a correlation between the input and output parameters, the input-output relations are revealed through the application of alternative numerical methods, such as the Buckingham- Π theorem and correlation matrices. 1.1. Input and output parameters of the loudspeaker-driven SJA simulation

Fig. 2. Nomenclature of a loudspeaker driven SJA.

2. Material and methods 2.1. Buckingham- Π theorem

Buckingham- Π theorem is a classical method to determine the independent nondimensional parameters that will govern the synthetic jet flow. Characteristic velocity, V 0 , of the SJA is a function of seven parameters that are geometric parameters d 0 , d c , h 0 , h c , the actuation frequency f and the fluidic parameters air density, ρ, kinematic viscosity, ν. If one can apply Buckingham - Π theorem on the parameters indicated in the introduction, one obtains: