Model reduction of turbulent fluid flows using the supply rate
Model reduction of turbulent fluid flows using the supply rate
A method for finding reduced-order approximations of turbulent flow models is presented. The method preserves bounds on the production of turbulent energy in the sense of the L2 norm of perturbations from a notional laminar profile. This is achieved by decomposing the Navier–Stokes system into a feedback arrangement between the linearized system and the remaining, normally neglected, nonlinear part. The linear system is reduced using a method similar to balanced truncation, but preserving bounds on the supply rate. The method involves balancing two algebraic Riccati equations. The bounds are then used to derive bounds on the turbulent energy production. An example of the application of the procedure to flow through a long straight pipe is presented. Comparison shows that the new method approximates the supply rate at least as well as, or better than, canonical balanced truncation.
model reduction, proper orthogonal decomposition, sector bounding, supply rate, passivity, flow control, hagen–poiseuille flow, pipe flow, turbulence, fluids, robust control
1267-1278
Sharma, A.S.
cdd9deae-6f3a-40d9-864c-76baf85d8718
2009
Sharma, A.S.
cdd9deae-6f3a-40d9-864c-76baf85d8718
Sharma, A.S.
(2009)
Model reduction of turbulent fluid flows using the supply rate.
International Journal of Bifurcation and Chaos, 19 (4), .
(doi:10.1142/S0218127409023615).
Abstract
A method for finding reduced-order approximations of turbulent flow models is presented. The method preserves bounds on the production of turbulent energy in the sense of the L2 norm of perturbations from a notional laminar profile. This is achieved by decomposing the Navier–Stokes system into a feedback arrangement between the linearized system and the remaining, normally neglected, nonlinear part. The linear system is reduced using a method similar to balanced truncation, but preserving bounds on the supply rate. The method involves balancing two algebraic Riccati equations. The bounds are then used to derive bounds on the turbulent energy production. An example of the application of the procedure to flow through a long straight pipe is presented. Comparison shows that the new method approximates the supply rate at least as well as, or better than, canonical balanced truncation.
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Published date: 2009
Keywords:
model reduction, proper orthogonal decomposition, sector bounding, supply rate, passivity, flow control, hagen–poiseuille flow, pipe flow, turbulence, fluids, robust control
Organisations:
Aerodynamics & Flight Mechanics Group
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Local EPrints ID: 350134
URI: http://eprints.soton.ac.uk/id/eprint/350134
ISSN: 0218-1274
PURE UUID: b1b78e62-bde1-4395-af5c-993a2b911be1
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Date deposited: 25 Mar 2013 10:28
Last modified: 15 Mar 2024 03:46
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Author:
A.S. Sharma
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