Dynamic Reduced-order Model for the Air Temperature Field Inside a Data Center G.W. Woodruff School of Mechanical Engineering Georgia Institute of Technology Atlanta, GA Rajat Ghosh and Yogendra Joshi

Project Objective Development of experimentally validated reduced order modeling framework for dynamic energy usage optimization of data centers and telecoms  Dynamic reduced order modeling framework development  Experimental validation of dynamic reduced order modeling framework Implementation and generalization of modeling approach in data centers and telecom test sites  Assessment and refinement of approach at a selected facility  Development of data center thermal design software 2

Accomplishments Developed a CFD/HT model for predicting transient temperature field Developed an experimental setup for measuring transient temperature field Utilizing a reduced-order model to generate new temperature data from an existing temperature ensemble obtained from CFD/HT simulations or experiments 3

Modeling Algorithm 4 POD coefficient calculation Interpolation Ensemble generation POD mode calculation Number of principal components determination CFD/HT simulation Reduced-order temperature computation Error estimation

Case Study for CFD/HT Simulation CRAC A1 A2 A3 A4 B4B3B2B1 Cold aisle Hot aisle Row X Y X Z Row B Row A 1218 Plenum CRAC Adiabatic Symmetry plane Insulated room wall Initial condition -T(x, y, z; t=0)=15 0 C - V(x, y, z; t=0)=0 Heat load/ rack = 5 KW Air flow rate from CRAC= 5500 CFM Grid Size - 182,000 - Adaptive meshing With hexagonal grid-cells

Row Inlet at a Known Time (t=30s) 6 X Z  POD model can reproduce CFD/HT data accurately Row A inlet Error~1% POD temp. FieldCFD temp. fieldDeviation~1 % Velocity field Row B inlet

Temperature at an Intermediate Instant (t=15 s) 7 POD based model can efficiently generate temperature data at t=15 s from existing CFD/HT temperature ensemble, obviating need for independent simulation X Z POD temp. field ~4 s CFD temp. field ~8 min Deviation~1 % Row A inlet Row B inlet

Experimental Validation CFM CRAC unit 14 kW racks Parameters -Eight 14 kW racks arranged symmetrically about cold aisle -CFM from CRAC unit=12700 Transient Condition Sudden shutdown of CRAC unit for 2 min -Observe following transient temperature field at cold aisle for 200 s at 10 s interval

Temperature Measurement at Rack A Inlet 9 t=0 st=30 s t=60 st=90 s X Z

Validation of POD based Interpolation 10 POD temperature field ~4sExperimental temperature field ~ 3 min Error between POD and Experimental temperature field~1% Temperature data at t=45 s are not included in original temperature ensemble generated by experiments POD based model can generate temperature data at t=45 s from existing temperature ensemble generated by experiments,, obviating need for independent experiment POD based model is significantly faster than experiments without compromising accuracy X Z

Validation of POD-based Extrapolation X Z POD temperature field ~4s Experimental temperature field ~ 6 min Error between POD and Experimental temperature field~1% Temperature data at t=205 s are outside the temperature range t=0-200 s POD based model can generate temperature data at t=205 s from existing experimental observations, obviating need for independent experiment POD based model is significantly faster than experiments without compromising accuracy

Publication/ Presentation Conference Proceedings Ghosh, R., and Joshi, Y., 2011,”Dynamic Reduced Order Thermal Modeling of Data Center Air Temperature”, ASME InterPack 2011 Conference Poster Presentation Ghosh, R., and Joshi, Y., 2010 " Dynamic Reduced Order Modeling of Convective transports in Data Centers" at NSF I/UCRC meeting 12

Plan for Next Quarter Refining POD based model – Designing more representative experiments with distributed temperature measuring facility Capable of measuring instantaneous room level temperature field Developing thermal design software for data centers 13

Acknowledgement We acknowledge support for this work from IBM Corporation as a sub-contract on Department of Energy funds 14