Numerical Simulations of Plasma Based Flow Control Applications

A mathematical model was developed to simulate flow control applications using plasma actuators. The effects of the plasma actuators on the external flow are incorporated into Navier Stokes computations as a body force vector. In order to compute this body force vector, the model solves two additional equations: one for the electric field due to the applied AC voltage at the electrodes and the other for the charge density representing the ionized air. The model is calibrated against an experiment having plasma-driven flow in a quiescent environment and is then applied to simulate a low pressure turbine flow with large flow separation. The effects of the plasma actuator on control of flow separation are demonstrated numerically. Cp = pressure coefficient Cx = axial chord for Pak-B blade e E = elementary charge, C � = electric field, N/C ε = permittivity, ε = ε rε o ε r = relative permittivity Nomenclature ε o = permittivity of free space, 8.854x10-12 C 2 /Nm 2 fB � = body force vector, N/m 3 FSTI = freestream turbulence intensity, % Φ = total electric potential, Volt, Φ = φ + ϕ φ = electric potential due to external electric field, Volt ϕ = electric potential due to net charge density, Volt k = Boltzmann’s constant Le = length of the electrode λ d = Debye length, m µ = location parameter for Gaussian distribution n i = ion density in the plasma