Mathematical modeling of the output parameters for a loudspeaker-driven synthetic jet actuator

Abstract

The principal objective of this study is to establish the correlation between input geometrical parameters (cavity inner diameter, dc, orifice exit diameter, d₀, cavity height, h_c, orifice height, h₀) and a range of output parameters, i.e. Reynolds number, Re, Strouhal number, St, Stokes number, S, orifice utilization factor, β₀, characteristic velocity, V₀, full stroke length, L₀, dimensionless stroke length, L, Thrust, T, peak velocity, U_p, frictional velocity, U_τ, frictional Reynolds number, Re_τ, mechanical efficiency, η_mech, Overall Figure of Merit, OFM, Synthetic Jet Actuator Efficiency η_SJA. These variables are considered for a loudspeaker-driven synthetic jet actuator (SJA). 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.