Title :
Transient energy analysis of a spatially interconnected model for 3D Poiseuille flow
Author :
Chughtai, S.S. ; Werner, H.
Author_Institution :
Inst. of Control Syst., Hamburg Univ. of Technol., Hamburg, Germany
fDate :
June 30 2010-July 2 2010
Abstract :
In this paper a new model for 3D Poiseuille flow is presented. The model is based on applying a combined spectral-finite difference approach on the velocity-vorticity formulation of the Navier-Stokes equations. In 3D the dominating feature of the problem is non-normality of the eigenvectors. One measure to assess the non-normality is the transient energy response. The model is validated by comparing the maximum transient energy for two different cases; for both cases the Reynolds number is fixed at 5000, in the first case the span-wise spatial frequency is set to zero and the stream-wise spatial frequency is varied from 0.1 to 2, while for the second case the streamwise frequency is set to zero and the span-wise frequency is varied from 0.1 to 3. It is known that for the first case the system is stable, while the second case is highly non-normal with maximum transient energy reaching 4500. It is observed that the model predicts both of these characteristics. Next, as a first step towards controller synthesis, a stabilizing state feedback controller is designed to minimize the transient energy response, by minimizing the induced ℒ2-norm. The closed loop response shows that the energy is reduced by the factor of 30.
Keywords :
Navier-Stokes equations; Poiseuille flow; closed loop systems; control system synthesis; eigenvalues and eigenfunctions; finite difference methods; flow control; state feedback; transient response; turbulence; vortices; 3D Poiseuille flow; Navier-Stokes equations; Reynolds number; closed loop response; eigenvectors; span-wise spatial frequency; spatially interconnected model; spectral-finite difference approach; stabilizing state feedback controller; stream-wise spatial frequency; transient energy response; velocity-vorticity formulation; Control system synthesis; Energy measurement; Frequency; Navier-Stokes equations; Neutron spin echo; Open loop systems; Partial differential equations; Predictive models; State feedback; Transient analysis;
Conference_Titel :
American Control Conference (ACC), 2010
Conference_Location :
Baltimore, MD
Print_ISBN :
978-1-4244-7426-4
DOI :
10.1109/ACC.2010.5530564