An integrated numerical simulation tool that couples the Reynolds averaged Navier-Stokes (RANS) or the large eddy simulation (LES) solver for incompressible flows with the dielectric barrier discharge (DBD) electro-hydrodynamic (EHD) body force model has been developed. 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 the charge density on the dielectric surface is obtained from a Space-Time Lumped-Element (STLE) circuit model that accounts for the time and space dependence of air ionization on the input voltage amplitude, frequency, electrode geometry, and dielectric properties. The development of the numerical simulation tool is based on the framework of NavyFOAM using a multi-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 the 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.
This paper focuses on its application to numerical simulation of flow separation and control over a high-lift flapped airfoil at a Reynolds number of 240,000. The 2-D unsteady RANS simulation utilized the Wilcox k-ω, the SST k-ω, and the k-kl-ω turbulence models. For the baseline case, in comparison with the measurement, the k-kl-ω model captures the feature of the unsteadiness of flow field associated with flow separation and shedding of vortices, better than the Wilcox k-ω and SST k-ω models. In the RANS simulations for flow separation control with DBD plasma actuation, the actuator is driven by voltage signals of a continuous or an amplitude-modulated sine waveform with a range of voltage amplitudes. The numerical results indicate that the modulated forcing is more effective than the continuous forcing for a certain range of applied voltages. The electrical power consumption calculated by the plasma model fits to a parabolic curve as a function of the root-mean-square of applied voltage.