ACTIVE FLOW CONTROL

✍ Scribed by J.E. FFOWCS WILLIAMS

• Publisher: Elsevier Science
• Year: 2001
• Tongue: English
• Weight: 122 KB
• Volume: 239
• Category: Article
• ISSN: 0022-460X
• DOI: 10.1006/jsvi.2000.3225

✦ Synopsis

This paper considers the two-dimensional problem of a plane vortex sheet disturbed by an impulsive line source. A previous incorrect treatment of this problem is examined in detail. Instabilities of the vortex sheet are triggered by the source and grow exponentially in space and time. The Green function is constructed for the problem and it is shown that a point source properly positioned and delayed will induce a "eld that cancels the unstable growing modes. The resulting displacement of the vortex sheet is expressed in simple terms. The instabilities are checked by the anti-source which combines with the "eld of the primary source into a vortex sheet response which decays with time at large time. This paper is a contribution to the study of active control of shear layer instabilities, the main contribution being to clear up a previous paper with peculiar results that are, in fact, wrong.

2001 Academic Press

because

At y"0, >"!> and the symmetry of about y"0 equates equations ( 6) and ( 8). The second vortex sheet boundary condition, that the two sides of the sheet move together requires that D Dt *> *y " * *t *\ *y at y"0. (10)

This is also the case for these "elds, as can be shown as: