Reduced order model for a forced convection case: application to a heating circular cylinder in a cross-flow at turbulent Reynolds numbers

Abstract Vortex shedding around circular cylinders is a well known and studied phenomenon that appears in many engineering fields. A Reduced Order Model (ROM) of the incompressible ow around a circular cylinder is presented in this work. The ROM is built performing a Galerkin projection of the governing equations onto a lower dimensional space. The reduced basis space is generated using a Proper Orthogonal Decomposition (POD) approach. In particular the focus is into (i) the correct reproduction of the pres- sure field, that in case of the vortex shedding phenomenon, is of primary importance for the calculation of the drag and lift coefficients; (ii) the projection of the Governing equations (momentum equation and Poisson equation for pressure) performed onto different reduced basis space for velocity and pressure, respectively; (iii) all the relevant modifications necessary to adapt standard finite element POD-Galerkin methods to a finite volume framework. The accuracy of the reduced order model is assessed against full order results.

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Developing a Reduced-Order Model of Nonsynchronous Vibration in Turbomachinery Using Proper-Orthogonal Decomposition Methods

Journal of Engineering for Gas Turbines and Power ◽

10.1115/1.4028675 ◽

2015 ◽

Vol 137 (5) ◽

Cited By ~ 4

Author(s):

Stephen T. Clark ◽

Fanny M. Besem ◽

Robert E. Kielb ◽

Jeffrey P. Thomas

Keyword(s):

Proper Orthogonal Decomposition ◽

Cross Flow ◽

Decomposition Methods ◽

Initial Study ◽

Orthogonal Decomposition ◽

Reduced Order Model ◽

Two Dimensional ◽

Order Model ◽

Reduced Order ◽

Proper Orthogonal

The paper develops a reduced-order model of nonsynchronous vibration (NSV) using proper orthogonal decomposition (POD) methods. The approach was successfully developed and implemented, requiring between two and six POD modes to accurately predict computational fluid dynamics (CFD) solutions that are experiencing NSV. This POD method was first developed and demonstrated for a transversely moving, two-dimensional cylinder in cross-flow. Later, the method was used for the prediction of CFD solutions for a two-dimensional compressor blade. This research is the first to offer a POD approach to the reduced-order modeling of NSV in turbomachinery. Modeling NSV is especially challenging because NSV is caused by complicated, unsteady flow dynamics; this initial study helps researchers understand the causes of NSV, and aids in the future development of predictive tools for aeromechanical design engineers.

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Developing a Reduced-Order Model of Non-Synchronous Vibration in Turbomachinery Using Proper Orthogonal Decomposition Methods

Volume 7B: Structures and Dynamics ◽

10.1115/gt2014-25547 ◽

2014 ◽

Author(s):

Stephen T. Clark ◽

Fanny M. Besem ◽

Robert E. Kielb ◽

Jeffrey P. Thomas

Keyword(s):

Proper Orthogonal Decomposition ◽

Cross Flow ◽

Initial Study ◽

Orthogonal Decomposition ◽

Reduced Order Model ◽

Two Dimensional ◽

Order Model ◽

Decomposition Approach ◽

Reduced Order ◽

Proper Orthogonal

The paper develops a reduced-order model of non-synchronous vibration (NSV) using proper orthogonal decomposition (POD) methods. The approach was successfully developed and implemented, requiring between two and six POD modes to accurately predict CFD solutions that are experiencing non-synchronous vibration. This POD method was first developed and demonstrated for a transversely-moving, two-dimensional cylinder in cross-flow. Later, the method was used for the prediction of CFD solutions for a two-dimensional compressor blade. This research is the first to offer a proper orthogonal decomposition approach to the reduced-order modeling of non-synchronous vibration in turbomachinery. Modeling non-synchronous vibration is especially challenging because NSV is caused by complicated, unsteady flow dynamics; this initial study helps researchers understand the causes of NSV, and aids in the future development of predictive tools for aeromechanical design engineers.

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