Turbulence Control Based on Reduced-Order Models and Nonlinear Control Design

Reduced-Order Modelling for Flow Control

“…ROM offer an ideal plant for these investigations (Luchtenburg et al, 2010). Current turbulence control applications indicate a pressing need for understanding the nonlinearities of the turbulence cascade and actuation effects -transcending the current possibilities of available knowledge.…”

“…One example is high-frequency forcing to mitigate von Kármán vortex shedding (Thiria et al, 2006;. Corresponding 4-dimensional models for flows with two dominant frequencies have been used for open-and closed-loop control of wakes (Luchtenburg et al, 2010) and flow around airfoils (Luchtenburg et al, 2009a). Numerous straight-forward techniques are available.…”

“…In the sequel, we outline a simple identification technique which has been employed in a number of turbulence control studies with periodic forcing (Luchtenburg et al, 2009a(Luchtenburg et al, , 2010John et al, 2010). Let f i be the propagator of the natural dynamics and b be the amplitude of a local actuator.…”

Optimal Boundary Control Problems Related to High-Lift Configurations

“…The filter modes contain significant information gained from the URANS solution by the k-ω-model. Following [20,29], the main idea of the ROM is to set up a small size system of ODEs for (a 1 (t), · · · , a 4 (t)) T that rebuilds the computed fluid flow best under the operating conditions. Similarly to the work of Luchtenburg et al [20], the dynamical system consists of the uniformly oscillating of the unactuated and the actuated coefficient pairs (a 1 , a 2 ) respectively (a 3 , a 4 ), which are coupled through the equations for amplified saturation.…”

“…The ansatz (13) is motivated by a global momentum balance equation and the constant and linear term in (13) are related to this equation. The lift effect of base-flow variation can be lumped in c 5 (A n ) 2 + c 6 (A n ) 4 assuming slow transients, see [29] in this volume. The parameters c i j and c k are obtained by a least-squares fit of C L ((a n i )) and C L ((a a i )) to the original lift values of the URANS simulation.…”