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

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 m 2 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.

[1]  I. E. Idelchik,et al.  Flow Resistance : A Design Guide for Engineers , 1989 .

[2]  Lawrence Sirovich,et al.  Turbulent thermal convection in a finite domain: Part II. Numerical results , 1990 .

[3]  Lawrence Sirovich,et al.  Turbulent thermal convection in a finite domain: Part I. Theory , 1990 .

[4]  H. Park,et al.  The use of the Karhunen-Loève decomposition for the modeling of distributed parameter systems , 1996 .

[5]  H. M. Park,et al.  Low dimensional modeling of flow reactors , 1996 .

[6]  Viswanath R. Katta,et al.  A Numerical Study of Droplet-Vortex Interactions in an Evaporating Spray, , 1996 .

[7]  P. Holmes,et al.  Turbulence, Coherent Structures, Dynamical Systems and Symmetry , 1996 .

[8]  Lawrence Sirovich,et al.  Extensions to Karhunen-Loève based approximation of complicated phenomena , 1998 .

[9]  H. Tran,et al.  Modeling and control of physical processes using proper orthogonal decomposition , 2001 .

[10]  S. S. Ravindran,et al.  Adaptive Reduced-Order Controllers for a Thermal Flow System Using Proper Orthogonal Decomposition , 2001, SIAM J. Sci. Comput..

[11]  H. Park,et al.  Boundary Optimal Control of Natural Convection by Means of Mode Reduction , 2002 .

[12]  Jeffrey S. Chase,et al.  Making Scheduling "Cool": Temperature-Aware Workload Placement in Data Centers , 2005, USENIX Annual Technical Conference, General Track.

[13]  Farrokh Mistree,et al.  Robust Design of Air-Cooled Server Cabinets for Thermal Efficiency , 2005 .

[14]  Jeffrey S. Chase,et al.  Balance of power: dynamic thermal management for Internet data centers , 2005, IEEE Internet Computing.

[15]  J. Rambo,et al.  Reduced-Order Modeling of Multiscale Turbulent Convection: Application to Data Center Thermal Management , 2006 .

[16]  Jeffrey S. Chase,et al.  Weatherman: Automated, Online and Predictive Thermal Mapping and Management for Data Centers , 2006, 2006 IEEE International Conference on Autonomic Computing.

[17]  Farrokh Mistree,et al.  An Approach to Robust Design of Turbulent Convective Systems , 2006 .

[18]  Yogendra Joshi,et al.  Reduced-order modeling of turbulent forced convection with parametric conditions , 2007 .

[19]  Yogendra Joshi,et al.  Multiscale Thermal Modeling Methodology for Thermoelectrically Cooled Electronic Cabinets , 2007 .

[20]  S. Sanghi,et al.  Proper orthogonal decomposition and low-dimensional modelling of thermally driven two-dimensional flow in a horizontal rotating cylinder , 2007, Journal of Fluid Mechanics.

[21]  C. Rowley,et al.  Modeling of transitional channel flow using balanced proper orthogonal decomposition , 2007, 0707.4112.

[22]  W. Tao,et al.  A Fast and Efficient Method for Predicting Fluid Flow and Heat Transfer Problems , 2008 .

[23]  Sandeep K. S. Gupta,et al.  Energy-Efficient Thermal-Aware Task Scheduling for Homogeneous High-Performance Computing Data Centers: A Cyber-Physical Approach , 2008, IEEE Transactions on Parallel and Distributed Systems.

[24]  Yogendra Joshi,et al.  Reduced order modeling and experimental validation of steady turbulent convection in connected domains , 2008 .

[25]  Thorsten Bogner General variational model reduction applied to incompressible viscous flows , 2008, Journal of Fluid Mechanics.

[26]  Christian Inard,et al.  Fast simulation of temperature distribution in air conditioned rooms by using proper orthogonal decomposition , 2009 .

[27]  A. Velazquez,et al.  Robust reduced order modeling of heat transfer in a back step flow , 2009 .