Reduced-order description of fluid flow with moving boundaries by proper orthogonal decomposition

Utturkar, Yogen; Zhang, Baoning; Shyy, Wei

doi:10.1016/j.ijheatfluidflow.2004.08.008

Cited by 40 publications

(11 citation statements)

References 29 publications

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“…The first interpretation regards the POD as the Karhunen-Loeve decomposition (KLD), and the second one considers that the POD consists of three methods: the KLD, the principal component analysis (PCA), and the singular value decomposition (SVD). In recent years, there have been many reported applications of the POD methods in engineering fields such as in studies of turbulence [9][10][11][12][13], vibration analysis [14][15][16][17][18], process identification [19][20][21][22], and control in chemical engineering [23][24][25][26][27][28][29][30][31][32]. In general, POD is a methodology that first identifies the most energetic modes in a time-dependent system and subsequently provides a means of obtaining a low-dimensional description of the system's dynamics where the low-dimensional system is obtained directly from the Galerkin projection of the governing equations on the empirical basis set (the POD modes).…”

Section: Proper Orthogonal Decomposition (Pod) and Galerkin Projectionmentioning

confidence: 99%

Model Reduction Using Proper Orthogonal Decomposition and Predictive Control of Distributed Reactor System

Márquez

Jos^eacute

Oviedo

et al. 2013

Journal of Control Science and Engineering

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This paper studies the application of proper orthogonal decomposition (POD) to reduce the order of distributed reactor models with axial and radial diffusion and the implementation of model predictive control (MPC) based on discrete-time linear time invariant (LTI) reduced-order models. In this paper, the control objective is to keep the operation of the reactor at a desired operating condition in spite of the disturbances in the feed flow. This operating condition is determined by means of an optimization algorithm that provides the optimal temperature and concentration profiles for the system. Around these optimal profiles, the nonlinear partial differential equations (PDEs), that model the reactor are linearized, and afterwards the linear PDEs are discretized in space giving as a result a high-order linear model. POD and Galerkin projection are used to derive the low-order linear model that captures the dominant dynamics of the PDEs, which are subsequently used for controller design. An MPC formulation is constructed on the basis of the low-order linear model. The proposed approach is tested through simulation, and it is shown that the results are good with regard to keep the operation of the reactor.

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Section: Proper Orthogonal Decomposition (Pod) and Galerkin Projectionmentioning

confidence: 99%

Model Reduction Using Proper Orthogonal Decomposition and Predictive Control of Distributed Reactor System

Márquez

Jos^eacute

Oviedo

et al. 2013

Journal of Control Science and Engineering

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“…The essential idea of the POD is finding among a set of realizations of the flow fields the one that maximizes the mean square energy. The method has been intensively investigated for real-time flow control and physical process simulation because of its ability to yield a basis for low-order dynamic systems (Berkooz 1991;Ly and Tran 2001;Utturkar et al 2005;Rowley et al 2004;Ravindran 2002;Epureanu 2003;Perret et al 2006), and especially for the cyclic variability evaluation via statistical properties of the POD temporal coefficients (Druault et al 2005;Druault and Chaillou 2007;Roudnitzky et al 2006;Cosadia et al 2006;Bizon et al 2010;Fogleman et al 2004;Graftieaux et al 2001). The paper is organized as follows.…”

Section: Abbreviationsmentioning

confidence: 99%

Proper orthogonal decomposition analysis for cycle-to-cycle variations of engine flow. Effect of a control device in an inlet pipe

Guibert

2012

Exp Fluids

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This paper aims to investigate cycle-to-cycle variations of non-reacting flow inside a motored singlecylinder transparent engine in order to judge the insertion amplitude of a control device able to displace linearly inside the inlet pipe. Three positions corresponding to three insertion amplitudes are implemented to modify the main aerodynamic properties from one cycle to the next. Numerous particle image velocimetry (PIV) two-dimensional velocity fields following cycle database are posttreated to discriminate specific contributions of the fluctuating flow. We performed a multiple snapshot proper orthogonal decomposition (POD) in the tumble plane of a pent roof SI engine. The analytical process consists of a triple decomposition for each instantaneous velocity field into three distinctive parts named mean part, coherent part and turbulent part. The 3rd-and 4th-centered statistical moments of the proper orthogonal decomposition (POD)-filtered velocity field as well as the probability density function of the PIV realizations proved that the POD extracts different behaviors of the flow. Especially, the cyclic variability is assumed to be contained essentially in the coherent part. Thus, the cycle-to-cycle variations of the engine flows might be provided from the corresponding POD temporal coefficients. It has been shown that the in-cylinder aerodynamic dispersions can be adapted and monitored by controlling the insertion depth of the control instrument inside the inlet pipe.

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“…hÁi denotes an ensemble average over the number of observations hf i ¼ P M i¼1 f ðx; t i Þ=M. The optimum condition specified by (12) is equivalent to finding functions u that maximize the normalized averaged projection of u onto u, that is, max u2L 2 ðDÞ hjðu; uÞj 2 i=kuk 2 , where j Á j denotes the modulus. This maximization problem reduces to [19, p. 89] Z D huðxÞu Ã ðyÞiuðyÞ dy ¼ kuðxÞ:…”

Section: Reduced-order Model Based On Proper Orthogonal Decompositionmentioning

confidence: 99%

“…As a result, these models were limited in their applicability. Reduced-order models were also developed for flows with large perturbations using the method of proper orthogonal decomposition (POD) [9][10][11]1,2,12,13]. Recent reviews of ROMs based on POD are presented in [14,15].…”

Section: Introductionmentioning

confidence: 99%

Acceleration techniques for reduced-order models based on proper orthogonal decomposition

Cizmas

Richardson

Brenner

et al. 2008

Journal of Computational Physics

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Reduced-order description of fluid flow with moving boundaries by proper orthogonal decomposition

Cited by 40 publications

References 29 publications

Model Reduction Using Proper Orthogonal Decomposition and Predictive Control of Distributed Reactor System

Model Reduction Using Proper Orthogonal Decomposition and Predictive Control of Distributed Reactor System

Proper orthogonal decomposition analysis for cycle-to-cycle variations of engine flow. Effect of a control device in an inlet pipe

Acceleration techniques for reduced-order models based on proper orthogonal decomposition

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