Boundary Optimal Control of Natural Convection by Means of Mode Reduction

Park, H. M.; Lee, W. J.

doi:10.1115/1.1435646

Cited by 12 publications

(4 citation statements)

References 11 publications

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“…The basis functions, or 'POD modes', (ϕ i ) are commonly homogeneous and the u 0 source function takes the inhomogeneous boundary conditions, akin to traditional spectral methods. This technique has been very successful in constructing low-dimensional dynamical models in fluid mechanics [15] and developing control schemes for distributed parameter systems (e.g., [24,25,33]) by projecting the governing equations onto the m-dimensional POD subspace, producing m coupled ordinary differential equations in time describing the weight coefficient (a i ) evolution. The POD has been previously limited to prototypical systems with simple geometries because inhomogeneous boundary conditions present difficulties.…”

Section: Reduced-order Modeling Frameworkmentioning

confidence: 99%

Optimizing thermal design of data center cabinets with a new multi-objective genetic algorithm

Azarm

et al. 2007

Distrib Parallel Databases

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There is an ever increasing need to use optimization methods for thermal design of data centers and the hardware populating them. Airflow simulations of cabinets and data centers are computationally intensive and this problem is exacerbated when the simulation model is integrated with a design optimization method. Generally speaking, thermal design of data center hardware can be posed as a constrained multiobjective optimization problem. A popular approach for solving this kind of problem is to use Multi-Objective Genetic Algorithms (MOGAs). However, the large number of simulation evaluations needed for MOGAs has been preventing their applications to realistic engineering design problems. In this paper, details of a substantially more efficient MOGA are formulated and demonstrated through a thermal analysis simulation model of a data center cabinet. First, a reduced-order model of the cabinet problem is constructed using the Proper Orthogonal Decomposition (POD). The POD model Springer 168 Distrib Parallel Databases (2007) 21: is then used to form the objective and constraint functions of an optimization model. Next, this optimization model is integrated with the new MOGA. The new MOGA uses a "kriging" guided operation in addition to conventional genetic algorithm operations to search the design space for global optimal design solutions. This approach for optimal design is essential to handle complex multi-objective situations, where the optimal solutions may be non-obvious from simple analyses or intuition. It is shown that in optimizing the data center cabinet problem, the new MOGA outperforms a conventional MOGA by estimating the Pareto front using 50% fewer simulation calls, which makes its use very promising for complex thermal design problems.

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Section: Reduced-order Modeling Frameworkmentioning

confidence: 99%

Optimizing thermal design of data center cabinets with a new multi-objective genetic algorithm

Azarm

et al. 2007

Distrib Parallel Databases

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show abstract

“…The POD has already been used to create reduced order models of transient temperature fields using Galerkin Projection of the system POD modes onto the governing equations, resulting in a set of coupled non-linear Ordinary Differential Equations (ODEs) in time to be solved to find the POD coefficients, b i in Eq. (1), in terms of mostly one parameter such as Reynolds/Raleigh number [10][11][12][13][14][15][16][17].…”

Section: Proper Orthogonal Decompositionmentioning

confidence: 99%

Multi-parameter model reduction in multi-scale convective systems

Samadiani¹,

Joshi²

2010

International Journal of Heat and Mass Transfer

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“…This results in a set of coupled non‐linear ordinary differential equations in time for transient systems, or a set of algebraic equations for steady state systems, to be solved for the POD coefficients. This method has been used to create reduced order models of transient temperature fields in terms of mostly one parameter, such as Reynolds/Raleigh number (Ravindran, 2002; Park and Cho, 1996a, b; Sirovich and Park, 1990a, b; Tarman and Sirovich, 1998; Park and Li, 2002; Ding et al , 2008). The previous investigations have been either for prototypical flows (such as flow around a cylinder), or for simple geometries such as channel flow where inhomogeneous boundary conditions are easily homogenized by the inclusion of a source function in the decomposition.…”

Section: Low‐dimensional Modeling Approachesmentioning

confidence: 99%

Reduced order thermal modeling of data centers via proper orthogonal decomposition: a review

Samadiani

Joshi

2010

International Journal of Numerical Methods for Heat &Amp; Fluid Flow

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PurposeThe purpose of this paper is to review the available reduced order modeling approaches in the literature for predicting the flow and specially temperature fields inside data centers in terms of the involved design parameters.Design/methodology/approachThis paper begins with a motivation for flow/thermal modeling needs for designing an energy‐efficient thermal management system in data centers. Recent studies on air velocity and temperature field simulations in data centers through computational fluid dynamics/heat transfer (CFD/HT) are reviewed. Meta‐modeling and reduced order modeling are tools to generate accurate and rapid surrogate models for a complex system. These tools, with a focus on low‐dimensional models of turbulent flows are reviewed. Reduced order modeling techniques based on turbulent coherent structures identification, in particular the proper orthogonal decomposition (POD) are explained and reviewed in more details. Then, the available approaches for rapid thermal modeling of data centers are reviewed. Finally, recent studies on generating POD‐based reduced order thermal models of data centers are reviewed and representative results are presented and compared for a case study.FindingsIt is concluded that low‐dimensional models are needed in order to predict the multi‐parameter dependent thermal behavior of data centers accurately and rapidly for design and control purposes. POD‐based techniques have shown great approximation for multi‐parameter thermal modeling of data centers. It is believed that wavelet‐based techniques due to the their ability to separate between coherent and incoherent structures – something that POD cannot do – can be considered as new promising tools for reduced order thermal modeling of complex electronic systems such as data centersOriginality/valueThe paper reviews different numerical methods and provides the reader with some insight for reduced order thermal modeling of complex convective systems such as data centers.

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Boundary Optimal Control of Natural Convection by Means of Mode Reduction

Cited by 12 publications

References 11 publications

Optimizing thermal design of data center cabinets with a new multi-objective genetic algorithm

Optimizing thermal design of data center cabinets with a new multi-objective genetic algorithm

Multi-parameter model reduction in multi-scale convective systems

Reduced order thermal modeling of data centers via proper orthogonal decomposition: a review

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