Theor. Comput. Fluid Dyn.
DOI 10.1007/s00162-013-0302-5
ORIGINAL ARTICLE
Mark Riherd · Subrata Roy · S. Balachandar
Local stability effects of plasma actuation on a zero pressure
gradient boundary layer
Received: 10 October 2012 / Accepted: 29 March 2013
© Springer-Verlag Berlin Heidelberg 2013
Abstract The effects of plasma actuation in a flat plate boundary layer with zero pressure gradient have been
simulated. Based on these simulations, non-dimensional parameters and a combined wall jet/boundary layer
model of the velocity profile have been developed. A parametric study using local linear stability analysis has
been performed to examine the hydrodynamic stability of the velocity profiles created through this model.
Convective and absolute instability mechanisms are found to be important, some of which have not been
previously documented. Neutral stability curves have been computed for the different instabilities, and when
put in terms of the shape factor, they still compare favorably with reported canonical results, indicating that
the critical Reynolds number is primarily a function of the shape factor. These results are also discussed in
relation to existing experimental results as well as with respect to their implementation.
Keywords Hydrodynamic stability · Plasma actuators · Boundary layer control
1 Introduction
The process of a flow’s transition to turbulence has long been a topic of study in fluid mechanics. Specifically,
flows over flat plates with or without a pressure gradient are particularly important, as they share many
characteristics with more complex flows. These flows can be described by the Falkner–Skan similarity solution,
where the Blasius boundary layer is the special case of a zero pressure gradient (ZPG). Boundary layer flows
such as these are prevalent on many types of air, ground, and marine vehicles, such as the flow over and around
airfoils for fixed and rotating wing aircraft, the flat surfaces of automobiles and cargo trucks, and the sides and
bottoms of ships. Reduction in the overall levels of drag on these different types of vehicles can lead to energy
savings, allowing for more efficient and less costly operation, along with the associated benefits of reduced
fuel consumption.
Stabilization or destabilization of a boundary layer flow can have a significant impact on the level of drag
experienced by the body. Stabilizing the boundary layer decelerates the laminar to turbulent transition process.
When attempting to reduce the level of friction drag experienced by a body, this is a beneficial course of action,
as the drag associated with a laminar boundary layer is less than the drag associated with a turbulent boundary
layer. However, when aiming to reduce the drag created by flow separation downstream, it is sometimes
beneficial to accelerate the laminar to turbulent transition, as a turbulent boundary layer is more likely to
remain attached than a laminar boundary layer. Additional flow control applications may exist with regard to
heat transfer, chemical mixing, noise control, etc. where it may be prudent to stabilize or to destabilize the
boundary layer, based on the problems specifications.
Communicated by O. Zikanov.
M. Riherd · S. Roy (B ) · S. Balachandar
Mechanical and Aerospace Engineering, University of Florida, Gainesville, FL 32611, USA
E-mail: roy@ufl.edu
Tel.: +352-392-9823