Study of a pseudo-empirical model approach to characterize plasma actuators

Abstract

The use of plasma actuators is a recent technology that imposes a localized electric force that is used to control air flows. A suitable representation of actuation enables to undertake plasma actuators optimization, to design flow-control strategies, or to analyse the flow stabilization that can be attained by plasma forcing. The problem description may be clearly separated in two regions. An outer region, where the fluid is electrically neutral, in which the flow is described by the Navier-Stokes equation without any forcing term. An inner region, that forms a thin boundary layer, where the fluid is ionized and electric forces are predominant. The outer limit of the inner solution becomes the boundary condition for the outer problem. The outer problem can then be solved with a slip velocity that is issued from the inner solution. Although the solution for the inner problem is quite complex it can be contoured proposing pseudo-empirical models where the slip velocity of the outer problem is determined indirectly from experiments. This pseudo-empirical model approach has been recently tested in different cylinder flows and revealed quite adapted to describe actuated flow behaviour. In this work we determine experimentally the influence of the duty cycle on the slip velocity distribution. The velocity was measured by means of a pitot tube and flow visualizations of the starting vortex (i.e. the induced flow when actuation is activated in a quiescent air) have been done by means of the Schlieren technique. We also performed numerical experiments to simulate the outer region problem when actuation is activated in a quiescent air using a slip velocity distribution as a boundary condition. The experimental and numerical results are in good agreement showing the potential of this pseudo-empirical model approach to characterize the plasma actuation.