Numerical Research on the Resonance Frequency Characteristics of the SparkJet Actuator using Modal Analysis

In this study, the resonance frequency characteristics of the SparkJet actuator are examined through numerical investigation using modal analysis. First, an eigenvalue problem is established to compute the resonance frequencies of the SparkJet actuator, considering its configuration, boundary conditions and internal physical phenomena. To validate the eigenvalue problem, computational fluid dynamics (CFD) simulation is conducted utilizing unsteady three-dimensional Navier-Stokes equations with plasma energy source term, assuming local thermal equilibrium (LTE). Subsequently, the resonance frequencies are obtained by performing fast Fourier transform (FFT) on the thrust and average pressure data obtained from the CFD. In our investigation of the resonance frequency characteristics, eigenmode decomposition on the pressure contour obtained from the CFD is conducted utilizing the eigenfunctions obtained from the eigenvalue problem and their orthogonality. The eigenmode decomposition enables us to quantitatively evaluate the contribution of each eigenfunction to the thrust. Comparisons between the frequencies corresponding to the eigenfunctions significantly influencing on the thrust and the resonance frequencies obtained by FFT reveal a maximum error of 5.29 % and an average error of 2.35 %. Moreover, when the taper angle is relatively large (approximately 45∘ or more), eigenfunctions significantly influencing on the thrust can be categorized into two distinct geometric patterns. These physically represent the waves that propagate and reflect in the streamwise or radial direction within the SparkJet actuator. This observation implies that the complex interactions of shock waves within the SparkJet actuator can be reduced to a few waves with simple physical interpretations. This may potentially aid in analyzing the physical phenomena within the SparkJet actuator.