A reduced-order model for a bubbling fluidized bed based on proper orthogonal decomposition

Yuan, Tianyu; Cizmas, Paul G. A.; O’Brien, Thomas J.

doi:10.1016/j.compchemeng.2005.09.001

Cited by 43 publications

(24 citation statements)

References 18 publications

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“…The projection of the discretized differential equation onto the basis functions takes most of the computational time of a subiteration. For a minimum fluidization case (Yuan, 2003) numerical tests showed that the components of the projectedÃ matrix do not vary significantly past the transient period. To quantify the variation of theÃ matrix, the eigenvalues ofÃ(t) −1Ã…”

Section: Acceleration Methods For the Rommentioning

confidence: 99%

“…The method takes advantage of the fact that the A s matrix is constant and only the right-hand-side vector b (i) changes. The method proposed herein replaced the LU decomposition (Press et al, 1992, p. 34) that was previously used to solve the linear algebraic systems for the field variables (Yuan et al, 2005). For a system with m equations, the number of operations for the LU decomposition is m 3 /3 while the number of operations for the Cholesky decomposition is m 3 /6.…”

Section: Acceleration Methods For the Rommentioning

confidence: 99%

“…The increase in the speed-up factor was the result of using fewer modes in the post transient period. The error of the reduced-order model with respect to the full-order model was defined as (Yuan et al, 2005) …”

Section: Acceleration Methods For the Rommentioning

confidence: 99%

“…Previous work has explored the problem of interpolation and extrapolation of solids-phase particle diameters and fluid viscosity (Yuan et al, 2005). Additionally the extrapolation of the field variables in time has been studied (Richardson, 2007).…”

Section: Interpolation and Extrapolationmentioning

confidence: 99%

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A Reduced-Order Model of Transport Phenomena for Power Plant Simulation

Cizmas¹,

Richardson²,

Brenner³

et al. 2009

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This report summarizes the objectives and tasks of this project, and describes how they were achieved. The report presents the progress made towards the program milestones and deliverables and summarizes the additional work done in the pursuit of these goals.A reduced-order model based on proper orthogonal decomposition (POD) has been developed to simulate transient two-and three-dimensional isothermal and non-isothermal flows in a fluidized bed. Reduced-order models of void fraction, gas and solids temperatures, granular energy, and z-direction gas and solids velocity have been added to the previous version of the code. These algorithms are presented and their implementation is discussed. Verification studies are presented for each algorithm.A number of methods to accelerate the computations performed by the reduced-order model are presented. The errors associated with each acceleration method are computed and discussed. Using a combination of acceleration methods, a two-dimensional isothermal simulation using the reduced-order model is shown to be 114 times faster than using the full-order model.In the pursue of achieving the objectives of the project and completing the tasks planned for this program, several unplanned and unforeseen results, methods and studies have been generated. These additional accomplishments are also presented and they include: (1) a study of the effect of snapshot sampling time on the computation of the POD basis functions, (2) an investigation of different strategies for generating the autocorrelation matrix used to find the POD basis functions, (3) the development and implementation of a bubble detection and tracking algorithm based on mathematical morphology, (4) a method for augmenting the proper orthogonal decomposition to better capture flows with discontinuities, such as bubbles, and (5) a mixed reduced-order/full-order model, called point-mode proper orthogonal decomposition, designed to avoid unphysical due to approximation errors.The limitations of the proper orthogonal decomposition method in simulating transient flows with moving discontinuities, such as bubbling flows, are discussed and several methods are proposed to adapt the method for future use.

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Section: Acceleration Methods For the Rommentioning

confidence: 99%

Section: Acceleration Methods For the Rommentioning

confidence: 99%

Section: Acceleration Methods For the Rommentioning

confidence: 99%

Section: Interpolation and Extrapolationmentioning

confidence: 99%

See 2 more Smart Citations

A Reduced-Order Model of Transport Phenomena for Power Plant Simulation

Cizmas¹,

Richardson²,

Brenner³

et al. 2009

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show abstract

“…It is also difficult to assess how the process variables influence each other. To address these problems, reduced-order models of fluidized bed have been recently developed [1,2].…”

Section: Introductionmentioning

confidence: 99%