Stability and Transition in Shear Flows. Applied Mathematical Sciences, Vol. 142

Using Stability Theory to Analyse Configurations of Pulsed Jets for Flow Control

“…3b. The obtained spectrum is similar to the one usually obtained for laminar flows (see [14]). A continuous and a discrete part of the spectrum can be identified.…”

“…The work on laminar flow stability was mainly focused on the growth or not of random infinitesimal velocity fluctuations in time (amplification or damping), which was closely associated with the appearance of turbulence and used for the prediction of the onset of transition. In the frame of the present work, use of this simple linear stability theory will suffices for our purpose and more D. Skamnakis (B) · K. Papailiou Laboratory of Thermal Turbomachines, National Technical University of Athens, Athens, Greece e-mail: d.skamnakis@ltt.ntua.gr accurate stability analysis approaches [14] will not be considered. This linear stability analysis, developed for laminar flows will be extended, under certain assumptions which will be discussed, to turbulent flows, in order to analyze the unsteady active flow control influence to turbulent separated flows for internal configurations (ducts or compressor cascades) which will be the exclusive object of the present work.…”

Fluid flow control applications of &#x210B;<inf>2</inf> optimal actuator and sensor placement

“…With 125 nodes, the leading eigenvalues of A match Fig. 3.1 of [17], and the optimal placements are well-converged. We consider three sets of parameters in this section.…”

“…First, eigenmodes of nonnormal operators tend to be nearly parallel. As a result, they generally fail to reveal the transient behavior of the operator [17]. Thus, even if control at the eigenmode-based actuator and sensor placements is able to stabilize the dynamics for large times, they may not be able to suppress transient growths to any significant degree.…”

“…At the endpoints of the domain, v = v ′ = ω = 0. For more information about the equations and their stability analyses, consult [17]. In this example, our base flow of interest is the "plane Poiseuille" flow through a channel bounded by y = ±1, but is infinite in the streamwise and spanwise directions.…”