Numerical Study on Control of Tollmien-Schlichting Waves Using Plasma Actuators Marios Kotsonis * Rogier Giepman † and Leo Veldhuis ‡ Delft University of Technology, Delft, 2629HS, The Netherlands A numerical investigation on the use of plasma actuators for transition control is pre- sented. The numerical framework involves the solution of the full unsteady 2D incom- pressible Navier Stokes equations using a finite volume formulation. The set of equations is formulated by solving for the perturbations in the flow while a mean laminar bound- ary layer flow is considered fixed and superimposed. The effect of the plasma actuator is represented as an imposed unsteady body force distribution derived from experimen- tal measurements. Furthermore, an adaptive control system based on the filtered-x LMS algorithm is implemented directly into the flow solver. The control system uses pressure signals at the wall in order to compute the frequency, phase and amplitude of the plasma body force which minimizes the intensity of the propagating TS waves. Results show large reductions in wave amplitude for both single and multi frequency cases. I. Introduction Plasma actuators have been studied extensively in recent years, as flow control devises. Their low power consumption, lack of moving parts and robustness render them ideal for flow manipulation. There are several implementations of the actuators the most popular being the Dielectric Barrier Discharge (DBD) kind. It is commonly accepted that some sort of collisional processes between the heavy plasma species (mostly ions) and neutral air is responsible for the momentum transfer. In a macroscopic scale, which is usually the scale of the flow to be controlled, the model of an exerted body force on the fluid seems to describe the effect reasonably. Plasma actuators have been used in several studies aiming at separation control, 1 turbulent drag reduc- tion, 2 boundary layer control 3–5 and transition delay. 6 Excellent reviews on plasma actuators for aerody- namic flow control have been published recently. 7, 8 The capabilities of the actuators suggest the feasibility of their implementation in several flow control scenarios. It is therefore desirable to have an efficient and accurate model of the effect of the actuator on a given flow. A large amount of simulation studies has been conducted in order to simulate and capture the underlying physics of the ionization process. 9, 10 These vary in model complexity, from simple phenomeno- logical models to first principles fluid models. 11 Extended simulations for multi-species fluids have also been investigated. 12 In the majority of these modeling approaches the final goal is to determine the exerted body force on the fluid. A number of studies on flow solvers implementing plasma actuators have used this approach successfully to couple the effect of the actuator with the flow dynamics. ?, 13 More recently, the authors, 14 have developed a technique which enables the measurement of the two-dimensional body force field experimentally for a selected applied voltages and carrier frequencies. One of the promising concepts for the utilization of plasma actuators is the cancellation of Tollmien- Schlichting waves in a transitional boundary layer. This technique aims at tackling the instability waves while still in linear amplification stage. At this stage the waves have little energy content with typical amplitudes of 0.01 % of the freestream velocity. 15 This technique has been investigated experimentally 16, 17 as well as numerically. 18, 19 In recent studies 6 artificially introduced TS waves were successfully canceled using plasma actuators. * PhD researcher, Faculty of Aerospace Engineering, Kluyverweg 1. † MSc candidate, Faculty of Aerospace Engineering, Kluyverweg 1. ‡ Associate Professor, Faculty of Aerospace Engineering, Kluyverweg 1, AIAA Member. 1 of 15 American Institute of Aeronautics and Astronautics 29th AIAA Applied Aerodynamics Conference 27 - 30 June 2011, Honolulu, Hawaii AIAA 2011-3175 Copyright © 2011 by the American Institute of Aeronautics and Astronautics, Inc. All rights reserved. Downloaded by TECHNISCHE UNIVERSITEIT DELFT on February 28, 2013 | http://arc.aiaa.org | DOI: 10.2514/6.2011-3175