PSI - Issue 72

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

80

( 0 , 0 , ,ℎ 0 ,ℎ , , , ) = 0

(1) Since there have eight dimensional parameters, a group of five independent dimensionless parameters can be formed using Buckingham- Π theorem with repeating variables selected as d 0 , f and ρ: 1 = 0 0 (2) 2 = 0 (3) 3 = ℎ 0 0 (4) 4 = ℎ 0 (5) 5 =√ 0 2 (6) The above dimensionless parameters can be divided into two groups: The boundary conditions group: Π 2 , Π 3 , Π 4 and the excitation parameters group: Π 1 , Π 5 . Additionally, Π 5 can be converted to Stokes number (S) by multiplying it with the square root of 2π as shown: 2 ( 5 ) 2 = 2 = 2 0 2 (7) They can also be related with Re as in Eq. (8). Π 1 can be defined as the dimensionless stroke length (L) or the reciprocal of the Strouhal number (St). 2 = 2 0 2 =2 1 =2 = 2 (8) Therefore, according to the Buckingham- Π theorem, the geometric and fluidic parameters of the synthetic jet can be made non-dimensional and mathematically modelled by using Re, St and S in Eq. (9). They are the main non dimensional parameters to focus on in a mathematical model of a loudspeaker-driven SJA. = √2 (9) 2.2. Correlations between input and output parameters The correlations between input and output parameters of loudspeaker-driven SJA are generated using ANSYS DesignXplorer (2022). Correlation matrices are given in Figure 3 for each frequency tested to easily evaluate the quality of the response surface, with a relevance threshold of 0.5 and a correlation value threshold of 1.0. The corresponding input and output parameters of Figure 3 are given in Table 1 and Table 2, respectively.

Table 1. Parameter numbering given in Figure 3 versus the input parameter expression. Input parameter numbering Parameter expression (unit) Parameter name P1 d 0 (m) Orifice inner diameter P2 d c (m) Cavity inner diameter P3 h 0 (m) Orifice height P4 h c (m) Cavity height