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Research Papers: Electronic Cooling

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

[+] Author and Article Information

G.W. Woodruff School of Mechanical Engineering, Georgia Institute of Technology, Atlanta, GA 30332samadiani@gatech.edu

Yogendra Joshi

G.W. Woodruff School of Mechanical Engineering, Georgia Institute of Technology, Atlanta, GA 30332yogendra.joshi@me.gatech.edu

J. Heat Transfer 132(7), 071402 (Apr 29, 2010) (14 pages) doi:10.1115/1.4000978 History: Received July 28, 2009; Revised December 01, 2009; Published April 29, 2010; Online April 29, 2010

## Abstract

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.

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## Figures

Figure 1

Data center and its multiscale nature

Figure 2

Typical air-cooling system in data centers

Figure 3

General algorithm for POD temperature field generation

Figure 4

Convective components in a complex system

Figure 5

Data center cell in the case study. (a) Top view: Dimensions are in m. (b) 3D model.

Figure 6

Reference air temperature contours (°C) at the racks inlets: (a) racks A1–A4 and (b) racks B1–B4

Figure 7

Energy percentage (%) captured by each POD mode for the case study

Figure 8

Structures of the first and last POD mode at the inlets: (a) mode 1 and (b) mode 20

Figure 9

POD coefficients of the associated modes for four test cases when all 20 modes are used in the POD reconstruction

Figure 10

Effect of the number of retained POD modes on the error (°C) in the energy conservation in the component boundaries of the data center cell for four test cases

Figure 11

Effect of the number of retained POD modes on the mean POD temperature error (°C) for the entire data center for four test cases

Figure 12

Contours of CFD/HT temperature, POD temperature, and relative error (°C) at the inlets of racks A1–A4 for two test cases: (a) [2.31 m/s, 5 kW, 5 kW, 20 kW, 30 kW] and (b) [5.5 m/s, 14 kW, 23 kW, 3 kW, 19 kW]

Figure 13

Mean POD temperature error (°C) versus used mode number for scenarios 1–4: (a) test case of [3 m/s, 27 kW, 7 kW, 13 kW, 24 kW] and (b) test case of [5.5 m/s, 14 kW, 23 kW, 3 kW, 19 kW]

Figure 14

Contours of POD temperature error (°C) at the inlets of racks A1–A4 for scenarios 1–4 for test case of [3 m/s, 27 kW, 7 kW, 13 kW, 24 kW]. The results have been obtained using all possible modes. (a) Scenario 1: thermal information for six servers per rack, a total of 50 equations and 20 modes. (b) Scenario 2: thermal information for four servers per rack, a total of 34 equations and 20 modes. (c) Scenario 3: thermal information for three servers per rack, a total of 26 equations and 20 modes. (d) Scenario 4: thermal information for two servers per rack, a total of 18 equations and 18 modes.

Figure 15

Contours of POD temperature error (°C) at the inlets of racks A1–A4 for scenarios 1–4 for test case of [3 m/s, 27 kW, 7 kW, 13 kW, 24 kW]. The results have been obtained using only ten modes. (a) Scenario 1: thermal information for six servers per rack, a total of 50 equations and ten modes. (b) Scenario 2: thermal information for four servers per rack, a total of 34 equations and ten modes. (c) Scenario 3: thermal information for three servers per rack, a total of 26 equations and ten modes. (d) Scenario 4: thermal information for two servers per rack, a total of 18 equations and ten modes.

Figure 16

POD mean temperature error (°C) versus used mode number for scenarios 5–8 for four test cases. Relevant test case is mentioned at the top of each plot.

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