Control of Mixing in Aeroengines Using Modern Dynamical Systems Methods

Abstract

Abstract : In this project we have sought to understand and locate coherent material structures that govern turbulent fluid mixing. As we have showed, these structures coincide with invariant manifolds of the fluid particle dynamics. We have developed several numerically assisted analytic criteria to extract invariant manifolds from simulated and measured flow data. Our criteria have been applied by others in analyzing controlled shear flows I, vortex merger problems 2, geophysical data 3, and geological phenomena 4. As an example, Fig. 1 shows coherent structures rendered by our criteria in a two-dimensional turbulence simulation.. Unexpectedly, we have also managed to extend Prandtl's classic steady flow separation criterion to unsteady flows. Remarkably, we also obtained explicit asymptotic formulae for unsteady separation profiles near a general no-slip boundary. As an example, Figure 2. compares a separation prediction from the widely used zero-skin friction principle (Fig. 2a), and from our unsteady separation criterion (Fig. 2b). Figure 3. (a) Instantaneous streamlines, separation points predicted the classical theory (zero skin friction), and actual unsteady flow separation. Separation is visualized by plotting the current position of an initially horizontal layer of fluid particles in the oscillating separation bubble model of S. Ghosh (UTRC). (b)Same as (a), with our analytically predicted unsteady separation profile superimposed. In a new approach to flow control, we have explored the use invariant manifolds to shape global coherent structures via local feedback control. We have applied these ideas in the control of advective mixing behind the flameholder of a combustor and the control of unsteady separation in bluff body shear flows (see Fig. 3).