Numerical analysis of synthetic jet flows using a diagonally implicit harmonic balance method with preconditioning

Synthetic jet flow is one of the active flow control mechanisms used to suppress flow instabilities including separation and wake vortices. It induces turbulent flows by ejecting or suctioning periodic jet streams into freestream air. A single piezoelectric actuator is often used to generate a periodic synthetic jet flow into quiescent air. The main purpose of the current study is to develop an efficient diagonally implicit harmonic balance method based on the nonlinear frequency domain method. This method is implemented in a compressible RANS flow solver with a preconditioning treatment to improve the performance of the numerical analysis. The transpiration wall boundary condition for periodic velocity of jet flows is used to avoid mesh deformation associated with the movement of the jet actuator diaphragm, where the periodic velocity profile is modeled from existing experimental data. With varying numbers of harmonics of up to fifteen the results are compared with the experimental data as well as those of the time-accurate computations. Reasonable agreement with the experimental data is obtained at reduced computational costs.