Proper Orthogonal Decomposition for Reduced Order Thermal Modeling of Air Cooled Data Centers

2010 ◽  
Vol 132 (7) ◽  
Author(s):  
Emad Samadiani ◽  
Yogendra Joshi
Keyword(s):  
Proper Orthogonal Decomposition ◽  
Thermal Modeling ◽  
Orthogonal Decomposition ◽  
Total Power ◽  
Algebraic Equations ◽  
Computationally Efficient ◽  
Reduced Order ◽  
Convective Systems ◽  
Design Variables ◽  
Proper Orthogonal

Computational fluid dynamics/heat transfer (CFD/HT) methods are too time consuming and costly to examine the effect of multiple design variables on the system thermal performance, especially for systems with multiple components and interacting physical phenomena. In this paper, a proper orthogonal decomposition (POD) based reduced order thermal modeling approach is presented for complex convective systems. The basic POD technique is used with energy balance equations, and heat flux and/or surface temperature matching to generate a computationally efficient thermal model in terms of the system design variables. The effectiveness of the presented approach is studied through application to an air-cooled data center cell with a floor area of 23.2 m2 and a total power dissipation of 240 kW, with multiple turbulent convective components and five design variables. The method results in average temperature rise prediction error of 1.24°C (4.9%) for different sets of design variables, while it is ∼150 times faster than CFD/HT simulation. Also, the effects of the number of available algebraic equations and retained POD modes on the accuracy of the obtained thermal field are studied.

Reduction of Multibody Dynamic Models in Automotive Systems Using the Proper Orthogonal Decomposition

2015 ◽  
Vol 10 (3) ◽  
Author(s):  
Ramin Masoudi ◽  
Thomas Uchida ◽  
John McPhee
Keyword(s):  
Proper Orthogonal Decomposition ◽  
Dynamic Models ◽  
Kinematic Model ◽  
Differential Algebraic Equations ◽  
Orthogonal Decomposition ◽  
Small Scale ◽  
Algebraic Equations ◽  
Vehicle Model ◽  
Reduced Order ◽  
Proper Orthogonal

The proper orthogonal decomposition (POD) is employed to reduce the order of small-scale automotive multibody systems. The reduction procedure is demonstrated using three models of increasing complexity: a simplified dynamic vehicle model with a fully independent suspension, a kinematic model of a single double-wishbone suspension, and a high-fidelity dynamic vehicle model with double-wishbone and trailing-arm suspensions. These three models were chosen to evaluate the effectiveness of the POD given systems of ordinary differential equations (ODEs), algebraic equations (AEs), and differential-algebraic equations (DAEs), respectively. These models are also components of more complicated full vehicle models used for design, control, and optimization purposes, which often involve real-time simulation. The governing kinematic and dynamic equations are generated symbolically and solved numerically. Snapshot data to construct the reduced subspace are obtained from simulations of the original nonlinear systems. The performance of the reduction scheme is evaluated based on both accuracy and computational efficiency. Good agreement is observed between the simulation results from the original models and reduced-order models, but the latter simulate substantially faster. Finally, a robustness study is conducted to explore the behavior of a reduced-order system as its input signal deviates from the reference input that was used to construct the reduced subspace.

Modeling the Turbulent Wake Behind a Wall-Mounted Square Cylinder

2020 ◽  
Author(s):  
Christian Amor ◽  
José M Pérez ◽  
Philipp Schlatter ◽  
Ricardo Vinuesa ◽  
Soledad Le Clainche
Keyword(s):  
Proper Orthogonal Decomposition ◽  
Turbulent Wake ◽  
Orthogonal Decomposition ◽  
Dynamic Mode Decomposition ◽  
Dynamic Mode ◽  
Square Cylinder ◽  
Complex Flow ◽  
Reduced Order ◽  
Mode Decomposition ◽  
Proper Orthogonal

Abstract This article introduces some soft computing methods generally used for data analysis and flow pattern detection in fluid dynamics. These techniques decompose the original flow field as an expansion of modes, which can be either orthogonal in time (variants of dynamic mode decomposition), or in space (variants of proper orthogonal decomposition) or in time and space (spectral proper orthogonal decomposition), or they can simply be selected using some sophisticated statistical techniques (empirical mode decomposition). The performance of these methods is tested in the turbulent wake of a wall-mounted square cylinder. This highly complex flow is suitable to show the ability of the aforementioned methods to reduce the degrees of freedom of the original data by only retaining the large scales in the flow. The main result is a reduced-order model of the original flow case, based on a low number of modes. A deep discussion is carried out about how to choose the most computationally efficient method to obtain suitable reduced-order models of the flow. The techniques introduced in this article are data-driven methods that could be applied to model any type of non-linear dynamical system, including numerical and experimental databases.

Reduced-Order Model of a Bladed Rotor With Geometric Mistuning

2007 ◽  
Author(s):  
Alok Sinha
Keyword(s):  
Proper Orthogonal Decomposition ◽  
Orthogonal Decomposition ◽  
Reduced Order Model ◽  
Order Model ◽  
Reduced Order ◽  
Coordinate Measurement ◽  
Coordinate Measurement Machine ◽  
Bladed Disk ◽  
Bladed Rotor ◽  
Proper Orthogonal

This paper deals with the development of an accurate reduced-order model of a bladed disk with geometric mistuning. The method is based on vibratory modes of various tuned systems and proper orthogonal decomposition of coordinate measurement machine (CMM) data on blade geometries. Results for an academic rotor are presented to establish the validity of the technique.

scholarly journals Local improvements to reduced-order models using sensitivity analysis of the proper orthogonal decomposition

2009 ◽  
Vol 629 ◽  
pp. 41-72 ◽  
Author(s):  
ALEXANDER HAY ◽  
JEFFREY T. BORGGAARD ◽  
DOMINIQUE PELLETIER
Keyword(s):  
Sensitivity Analysis ◽  
Proper Orthogonal Decomposition ◽  
Stokes Equations ◽  
Orthogonal Decomposition ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Reduced Order ◽  
Selection Step ◽  
Low Dimensional ◽  
Proper Orthogonal

The proper orthogonal decomposition (POD) is the prevailing method for basis generation in the model reduction of fluids. A serious limitation of this method, however, is that it is empirical. In other words, this basis accurately represents the flow data used to generate it, but may not be accurate when applied ‘off-design’. Thus, the reduced-order model may lose accuracy for flow parameters (e.g. Reynolds number, initial or boundary conditions and forcing parameters) different from those used to generate the POD basis and generally does. This paper investigates the use of sensitivity analysis in the basis selection step to partially address this limitation. We examine two strategies that use the sensitivity of the POD modes with respect to the problem parameters. Numerical experiments performed on the flow past a square cylinder over a range of Reynolds numbers demonstrate the effectiveness of these strategies. The newly derived bases allow for a more accurate representation of the flows when exploring the parameter space. Expanding the POD basis built at one state with its sensitivity leads to low-dimensional dynamical systems having attractors that approximate fairly well the attractor of the full-order Navier–Stokes equations for large parameter changes.

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