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TRANSIENT REDUCED-ORDER CONVECTIVE HEAT TRANSFER MODELING FOR A DATA CENTER

This Ph.D. proposal presentation discusses the need for improved energy efficiency and high-resolution monitoring in data centers. It explores the limitations of existing computational fluid dynamics/heat transfer modeling and proposes a measurement-based parametric modeling framework for transient convective heat transfer. The goal is to develop a fast surrogate modeling algorithm that can provide near-real-time analysis of the dynamic thermal environment in data centers.

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TRANSIENT REDUCED-ORDER CONVECTIVE HEAT TRANSFER MODELING FOR A DATA CENTER

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  1. Ph.D. Proposal Presentation TRANSIENT REDUCED-ORDER CONVECTIVE HEAT TRANSFER MODELING FOR A DATA CENTER Rajat Ghosh G.W. Woodruff School of Mechanical Engineering Georgia Institute of Technology Atlanta, GA 30332-0405 September 25, 2012

  2. Outline • Introduction • Problem Statement • Representative Case Studies • Case study-1 • Case Study-2 • Case Study-3 • Remaining Deliverable • Dissertation Timeline • Closure Ph.D. Proposal Presentation

  3. Increasing energy consumption • Need to improve energy efficiency in data centers (DCs). (Based on data reported by J. Koomey in the New York Times, July 31, 2012.) Ph.D. Proposal Presentation

  4. Increasing power density • Need of high-resolution monitoring and feedback control • Both in temporal and spatial dimensions. http://download.intel.com/technology/eep/data-center-efficiency/state-of-date-center-cooling.pdf Datacom Equipment Power Trends and Cooling Applications (2005), ASHARE TC 9.9 Ph.D. Proposal Presentation

  5. Dynamic data centers (CRAC supply temperature data from CEETHERM: Sept. 9-10, 2012, 11 pm -11pm ) (Liu, J.,Terzis, A., "Sensing data centers for energy efficiency,“Phil. Trans. R. Soc. A (2012)) • Rapidly changing server load leads to dynamic thermal environment • -Dynamic thermal analysis requires fast (near-real-time) modeling algorithm. • -State-of-the-art CFD/HT frameworks are too sluggish. • Need of fast surrogate modeling algorithm Ph.D. Proposal Presentation

  6. Data center cooling • 1/3 of energy spent in a DC is dedicated to its cooling systems. • Forced convective air cooling: • - Heat generated at chips dissipates via cooling airflow propelled by fans in the computer room air conditioning (CRAC) units. http://www.cisco.com/en/US/solutions/collateral/ns340/ns517/ns224/ns944/white_paper_c11-627731_ps10280_Products_White_Paper.html • Various airflow schemes exist: • - Underfloor plenum supply and ceiling return airflow scheme. Ph.D. Proposal Presentation

  7. Multiscale thermal system Turbulent Convection Turbulent Convection Turbulent Convection + Conduction Conduction • Involvement of several decades of length and time scales • Spatial: 5 decades (mm to Dm). • Temporal: 4 decades (10-2 s to 10 s). Ph.D. Proposal Presentation

  8. Current Approaches for transient thermal modeling Computational fluid dynamics/ Heat Transfer (CFD/ HT) Modeling Involves iterative solution of non-linear conservation equations. Model Accuracy Involves posing zero local gradient condition. Reduced-order Modeling Optimal and controllable Trade-off. Lumped System Modeling Computational Time Ph.D. Proposal Presentation

  9. Types of Reduced-order Model (ROM) ROM Statistical Response Surface Model ModalReduction-based Low- Dimensional Model Simplified Physics-based Model Proper Orthogonal Decomposition (POD/ PCA) Nonlinear Volterra Theory Laplacian Model Thermal Zone Model Harmonic Balance Approximation Ph.D. Proposal Presentation

  10. computation for a Transient CFD Simulation • DC Modeling Requirement • m spatial nodes andn time steps. • Restriction on temporal discretization: • The dependent variables for the turbulent convective temperature field: u, v, w, T, ε, k. • Computational step~ O(n(m3+ 4m)) • m3: For solving momentum equations together. • 4m: For solving pressure correction (continuity)+Temperature + Turbulence • n: Number of time steps • For a rack-level simulation: • m~ 1.4 millions, n~1 • t~2 hours in a 5.6 GHz machine Ph.D. Proposal Presentation

  11. Computation for a Reduced order modeling • DC Modeling Requirement: m dimensional temperature field with n transient observations. • Initial data is collected via measurements or CFD. • POD/Interpolation-based reduced-order modeling • Computational step~ O(3mn+log(n)+kn+n2+k2)) • 3mn: Row-wise average + Generation of parameter-dependent component+ Generation of covariance matrix • log(n): Proper orthogonal decomposition of covariance matrix (Power algorithm). • kn: Finding POD coefficients for the input parameter space • n2: Interpolation • k2:Computation of new data (k=principal component number). • No higher power of m. Ph.D. Proposal Presentation

  12. Limitation of Existing Modeling Algorithm • Computational fluid dynamic and heat transfer (CFD/HT) modeling • Too sluggish to be fit for a near-real-time modeling algorithm. • Stochastic nature does not warrant expensive CFD simulations. • Reduced-order modeling • A few studies exist with time as the parameter. • No study exists with spatial location as the parameter. • No multi-parameter model exists. • Few studies use experimental data as model input: use of CFD defeats the purpose of using ROM. • Need an alternative to Galerkine projection-based POD coefficient determination. Ph.D. Proposal Presentation

  13. Scope of dissertation • Development of measurement-based parametric modeling framework • One parameter model • For improving temporal resolution. • For improving spatial resolution. • Multi-parameter model • For improving resolution in an additional dimension like rack heat load. • Development of interconnected multiscale model - Hybrid reduced-order modeling approach. Ph.D. Proposal Presentation

  14. single parameter (Time)Reduced-order Algorithm • Proper Orthogonal Decomposition (POD)-based modal reduction. • Time is the modeling parameter. • Reduces the sampling rate • Use interpolation/ extrapolation to determine POD coefficients • Avoid computationally-prohibitive Galerkin projection. Ph.D. Proposal Presentation

  15. Case study for single parameter (TIME) POD Model • After remaining shut down for 2 minutes, the CRAC unit is turned on at t=0. Ph.D. Proposal Presentation

  16. Optimality of POD Modes • First 10 POD modes capture more than 90% characteristics of the temperature field. Ph.D. Proposal Presentation

  17. Principal Component Number • As captured energy percentage increases, the corresponding principal component number increases. Ph.D. Proposal Presentation

  18. Error Formulation Ph.D. Proposal Presentation

  19. Temperature measurement • Grid: 21 T-type copper-constantan thermocouplesmade from 28 gauge (0.9 mm diameter) wire. • Response time • 20 ms. • Measurement Frequency: • 1 Hz. • x-axis: Parallel to rack width. • y-axis: Parallel to tiles. • z-axis: parallel to rack height. S. Ravindran, Error Estimates for Reduced Order POD Models of Navier-Stokes Equations, ASME IMECE, 2008, pp. 652-657. Ph.D. Proposal Presentation

  20. POD/ Interpolation framework • Temperature map at the rack inlet at t=92 s. A posterior measurement, t~100 s An extra step of interpolation, t~10 s Deviation~ O(1%) POD model is efficient in improving parametric resolution of transient temperature data Accuracy of POD model prediction is identical to experimental data. Ph.D. Proposal Presentation

  21. Calibration of analytical error • Calibrated analytical error obviates the necessity of determining a posteriori prediction error . Ph.D. Proposal Presentation

  22. POD/ Extrapolation framework • Temperature map at the rack inlet at t=207 s. A posterior measurement, t~207 s An extra step of interpolation, t~10 s Deviation~ O(5%) POD model is efficient in improving parametric resolution of transient temperature data Accuracy of POD model prediction is identical to experimental data. Ph.D. Proposal Presentation

  23. Calibration of analytical Error • Calibrated analytical error obviates the necessity of determining a posteriori prediction error . Ph.D. Proposal Presentation

  24. single parameter (SPACE)Reduced-order Algorithm • Proper Orthogonal Decomposition (POD)-based modal reduction. • Coordinates of spatial location are the modeling parameters. • Improves the granularity of experimental data. • Reduction in sensor density. Ph.D. Proposal Presentation

  25. Case study for single parameter (Space) POD Model • Sudden shut down of the CRAC unit and power back after 100 s. (Photo courtesy to IBM) Ph.D. Proposal Presentation

  26. Prediction for DOF-1 Points • Improves spatial resolution between (70, 51, -1) and (70, 50, -1). Ph.D. Proposal Presentation

  27. Prediction for Dof-2 points • Improves spatial resolution between (56, 31, 2.5) and (56,30,5.5). Ph.D. Proposal Presentation

  28. TWO parameter Reduced-order Algorithm • POD-based modal decomposition. • Time and rack heat load as the modeling parameters. Ph.D. Proposal Presentation

  29. Case study for multi-parameter (Time, rack heat load) POD Model • Sudden shut down of the CRAC unit and power back after 100 s (t=0 in the plot). Ph.D. Proposal Presentation

  30. Comparison for Extrapolation at Q=1500 W • Extrapolation in time and interpolation in heat load. Ph.D. Proposal Presentation

  31. Interconnected Multiscale modeling • Experimentally validated CFD/HT modeling for a selected part of the CEETHERM data center laboratory. • Development of the hybrid modeling framework combining finite network modeling (FNM) and POD for simulating a selected part of the CEETHERM data center laboratory. • Comparison and validation. Ph.D. Proposal Presentation

  32. Dissertation TimeLine Ph.D. Proposal Presentation

  33. publications REFEREED JOURNAL PUBLICATION • Rajat Ghosh, and Yogendra Joshi, “Error Estimate in POD-based Dynamic Reduced-order Thermal Modeling of Data Centers,” International Journal of Heat and Mass Transfer (Revised version submitted). REFEREED CONFERENCE PUBLICATIONS • Rajat Ghosh, Levente Klein, Yogendra Joshi, and Hendrik Hamann, “Reduced-order Modeling Framework for Improving Spatial Resolution of the Temperature Data Measured in an Air-cool Data Center,” Semi-Therm, San Jose, California, March 17-21, 2013. • Rajat Ghosh, Vikneshan Sundaralingam, and Yogendra Joshi, “Effect of Rack Server Population on Temperatures in Data Centers,” Intersociety Thermal Conference (ITherm), San Diego, California, May 30-June 1, 2012. • Rajat Ghosh, Vikneshan Sundaralingam, Steven Isaacs, Pramod Kumar and Yogendra Joshi, “Transient Air Temperature Measurements in a Data Center,” Indian Society of Heat and Mass Transfer Conference, Chennai, India, Dec. 27-30, 2011. • Rajat Ghosh, Pramod Kumar, Vikneshan Sundaralingam, and Yogendra Joshi, “Experimental Characterization of Transient Temperature Evolution in a Data Center Facility,” International Symposium on Transport Phenomena, Delft, the Netherlands, Nov. 8-11, 2011. • Rajat Ghosh and Yogendra Joshi, “Dynamic Reduced-order Thermal Modeling of Data Center Air Temperatures,” InterPACK, Portland, Oregon, July 6-8, 2011. Planned PUBLICATIONS • Rajat Ghosh, and Yogendra Joshi, “Error Estimate in POD-based Dynamic Reduced-order Thermal Modeling of Data Centers,” International Journal of Heat and Mass Transfer (Revised version submitted). • Rajat Ghosh, and Yogendra Joshi, “Error Estimate in POD-based Dynamic Reduced-order Thermal Modeling of Data Centers,” International Journal of Heat and Mass Transfer (Revised version submitted). Ph.D. Proposal Presentation

  34. Acknowledgement The support for this work from IBM Corporation, with Dr. Hendrik Hamann as the Technical Monitor, is acknowledged . Acknowledgements are also due to the United States Department of Energy as the source of primary funds. Additional support from the National Science Foundation award CRI 0958514 enabled the acquisition of some of the test equipment utilized. The support from the G.W. Woodruff School of Mechanical Engineering as a Graduate Teaching Assistant is acknowledged. The collaboration, goodwill, and help received from all CEETHERM and METTL members (particularly Vikneshan Sundaralingam, Vaibhav Arghode, Pramod Kumar, Steven Isaacs) are highly appreciated. Ph.D. Proposal Presentation

  35. Thank YOU! Ph.D. Proposal Presentation

  36. Appendix Ph.D. Proposal Presentation

  37. Ph.D. Proposal Presentation

  38. Ph.D. Proposal Presentation

  39. Introduction • Impact of proliferated cloud computing-based e-commerce services on data Centers: • Increasing dynamic characteristics. • Increasing energy consumption. • Increasing power densities of racks. • Effect on cooling • 30%-40% energy consumed by cooling systems. • Importance of local thermal characteristics. • Need • High resolution (space/time) temperature monitoring. • Near-real-time feedback control for temperature. Ph.D. Proposal Presentation

  40. Temperature measurement • Grid: 21 T-type copper-constantan thermocouplesmade from 28 gauge (0.9 mm diameter) wire. • Response time • 20 ms. • Measurement Frequency: • 1 Hz. • x-axis: Parallel to rack width. • y-axis: Parallel to tiles. • z-axis: parallel to rack height. Ph.D. Proposal Presentation

  41. Dissertation time line • Development of a single-parameter POD-based framework for transient convective heat transfer modeling for an air-cool data center (May 2010-Dec. 2011). • Development of a grid-based thermocouple network for transient air temperature measurements (Nov. 2010-Nov. 2011). • Development of design protocol for filling out an empty rack (Nov. 2011-Dec. 2012). • Development of a single-parameter POD-based framework capable of improving spatial resolution of transient temperature data (Mar. 2012-June 2012). • Development of a two-parameter POD-based framework for transient convective heat transfer modeling for an air-cool data center (May 2012-Dec. 2012). • Development of a scale-linking across various length-scales in a data center (Oct. 2012-Mar. 2013). • Ph.D. dissertation defense (Mar. 2013). Ph.D. Proposal Presentation

  42. Ph.D. Proposal Presentation

  43. Literature REVIEW Ph.D. Proposal Presentation

  44. Literature REVIEW Contd. Ph.D. Proposal Presentation

  45. Literature REVIEW Contd. Ph.D. Proposal Presentation

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