0
TECHNICAL PAPERS

Development and Implementation of an Experimental-Based Reduced-Order Model for Feedback Control of Subsonic Cavity Flows

[+] Author and Article Information
E. Caraballo, J. Little, M. Debiasi

Gas Dynamics and Turbulent Laboratory, Collaborative Center for Control Science, Department of Mechanical Engineering, GDTL/AARL, 2300 West Case Road, The Ohio State University, Columbus, OH 43235-7531

M. Samimy1

Gas Dynamics and Turbulent Laboratory, Collaborative Center for Control Science, Department of Mechanical Engineering, GDTL/AARL, 2300 West Case Road, The Ohio State University, Columbus, OH 43235-7531samimy.1@osu.edu

1

Corresponding author.

J. Fluids Eng 129(7), 813-824 (Jan 22, 2007) (12 pages) doi:10.1115/1.2742724 History: Received August 16, 2006; Revised January 22, 2007

This work is focused on the development of a reduced-order model based on experimental data for the design of feedback control for subsonic cavity flows. The model is derived by applying the proper orthogonal decomposition (POD) in conjunction with the Galerkin projection of the Navier-Stokes equations onto the resulting spatial eigenfunctions. The experimental data consist of sets of 1000 simultaneous particle image velocimetry (PIV) images and surface pressure measurements taken in the Gas Dynamics and Turbulent Laboratory (GDTL) subsonic cavity flow facility at the Ohio State University. Models are derived for various individual flow conditions as well as for their combinations. The POD modes of the combined cases show some of the characteristics of the sets used. Flow reconstructions with 30 modes show good agreement with experimental PIV data. For control design, four modes capture the main features of the flow. The reduced-order model consists of a system of nonlinear ordinary differential equations for the modal amplitudes where the control input appears explicitly. Linear and quadratic stochastic estimation methods are used for real-time estimation of the modal amplitudes from real-time surface pressure measurements.

Copyright © 2007 by American Society of Mechanical Engineers
Your Session has timed out. Please sign back in to continue.

References

Figures

Grahic Jump Location
Figure 1

Schematic of the experimental setup showing the incoming flow, the actuation location, and other geometrical details

Grahic Jump Location
Figure 2

Phase-averaged PIV images of the Mach 0.30 flow over the cavity; vector field superimposed on an absolute velocity contour

Grahic Jump Location
Figure 3

Location and numbering of Kulite pressure transducers in the cavity geometry

Grahic Jump Location
Figure 4

Total energy recovered by the POD modes for increasing number of snapshots

Grahic Jump Location
Figure 5

Mean turbulent kinetic energy of the cavity flow at different locations in the shear layer

Grahic Jump Location
Figure 6

First POD mode of the normal fluctuating velocity (v′) for the cavity flow: Top 500 snapshots, bottom 1000 snapshots

Grahic Jump Location
Figure 7

Comparison of the normal velocity fluctuation from the PIV measurements with reconstruction using 130, 30, and 4 POD modes

Grahic Jump Location
Figure 8

First four POD modes of the normal velocity fluctuations (v′) for different flow conditions

Grahic Jump Location
Figure 9

Energy recovered by the POD modes: (a) total energy and (b) individual mode energy

Grahic Jump Location
Figure 10

First four POD modes of the normal velocity fluctuations (v′) for different combinations of the experimental flow conditions

Grahic Jump Location
Figure 11

Schematic of the cavity showing two subdomains s1 and s2

Grahic Jump Location
Figure 12

Effect of the additional viscous term in the solution of the Galerkin system, baseline flow model four modes

Grahic Jump Location
Figure 13

Solution of the Galerkin system for two different models: (a) MF4 and (b) MBF4

Grahic Jump Location
Figure 14

Linear stochastic estimation of the modal amplitude using zero to three time steps back (s=0–3), from experimental data in comparison to two standard deviation (2 stdv) of the modal coefficient from PIV data

Grahic Jump Location
Figure 15

Quadratic stochastic estimation of the modal amplitude using zero to three time steps back (s=0–3), from experimental data in comparison to two standard deviation (2 stdv) of the modal coefficient from PIV data

Grahic Jump Location
Figure 16

SPL spectra obtained from sensor 5 (Fig. 3) in closed-loop experiments with LQ design based on baseline flow model, MB (a), and combined flow model, MBF4 (b)

Tables

Errata

Discussions

Some tools below are only available to our subscribers or users with an online account.

Related Content

Customize your page view by dragging and repositioning the boxes below.

Related Journal Articles
Related eBook Content
Topic Collections

Sorry! You do not have access to this content. For assistance or to subscribe, please contact us:

  • TELEPHONE: 1-800-843-2763 (Toll-free in the USA)
  • EMAIL: asmedigitalcollection@asme.org
Sign In