There has been an increasing interest in dielectric barrier discharge (DBD) plasma actuation for flow control in the past decade. Compared to other means of active flow controls, the DBD plasma actuations have several advantages, including absence of moving parts, a fast time response for unsteady applications, a very low mass of the device, no cavities or holes on control surfaces, and possibly low energy consumption. These features are especially important for applications with high g-loads, such as turbomachinery blades rotating at high speed.

A computational method has been developed to couple a DBD electro-hydrodynamic (EHD) body force model with the Reynolds averaged Navier-Stokes (RANS) model for incompressible flows. The EHD body force model is based on solving the electrostatic equations for the electric potential due to applied voltage and the net charge density due to ionized air. The boundary condition for charge density on the dielectric surface is obtained from a Space-Time Lumped-Element (STLE) circuit model that accounts for time and space dependence of the air ionization on the input voltage amplitude, frequency, electrode geometry, and dielectric properties. Alternatively, an empirical formulation representing a Gaussian distribution of charge density on the dielectric surface can also be used. The EHD body force is calculated using the solutions obtained from solving the electric potential and the net charge density equations. As a comparison, a much simpler Linearized Electric Body Force (LEBF) model is also used to directly specify the spatial distribution of the averaged EHD body force. The coupled computational models have been implemented using a multiple-domain approach. The electric potential equation, the net charge density equation, and the flow equations are solved in separate computational domains. All equations are discretized in space using a cell-centered finite volume method. Parallel computation is implemented using domain-decomposition and message passing interface (MPI). Due to a large disparity in time scales between the electric discharge and the flow, a multiple sub-cycle technique is used in coupling the plasma solver and the flow solver.

The DBD plasma induced flow in quiescent air is used as a test case and the computational results are validated against experimental measurement. A comparison between different EHD body force models is also presented. Then, the effect of driving duty-cycles with different waveforms and input voltage amplitudes is investigated in terms of electrical power, EHD thrust, and kinetic energy of induced flow.

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