Numerical investigation of plasma-actuator force-term estimations from flow experiments

The accuracy of the experimental force-term estimation for cold, dielectric barrier discharge (DBD) plasma actuators based on fluid-velocity information is investigated by means of numerical simulations for cases without and with a laminar base flow. First, a wall jet induced by a steady planar body force similar to that induced by a plasma actuator under quiescent-air conditions is simulated. Second, the same steady force is applied to stabilise a laminar two-dimensional zero-pressure-gradient boundary-layer flow under the usual assumption of force independence. For both cases the force distribution is reconstructed applying two different methods to eliminate the pressure gradients unknown from experiments. The method based on the vorticity transport equation requires the force to be dominated by one component only. It is found that its accuracy is unaffected by a base flow but strongly dependent on the characteristics of the force distribution. The other method is based on the primitive-variable formulation of the Navier-Stokes equations, and the force components are assumed to dominate the pressure gradients, which are neglected. It is shown that this assumption is valid for the wall-parallel force component only, and in the case of a base flow the pressure gradients must not be neglected. The clarification of the accuracy of the different methods enables to evaluate the force-independence assumption in detail. For the case with base flow, the effect of force unsteadiness is investigated.