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Transcript of TRANSIENT REDUCED-ORDER CONVECTIVE HEAT TRANSFER MODELING FOR A DATA CENTER Rajat Ghosh G.W....
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
Ph.D. Proposal Presentation
Ph.D. Proposal Presentation
OUTLINE
• Introduction• Problem Statement• Representative Case Studies
– Case study-1– Case Study-2– Case Study-3
• Remaining Deliverable• Dissertation Timeline• ClosureIntroduction 2/35
Ph.D. Proposal Presentation
INCREASING ENERGY CONSUMPTION
• Need to improve energy efficiency in data centers (DCs).Introduction 3/35
(Based on data reported by J. Koomey in the New York Times, July 31, 2012.)
Ph.D. Proposal Presentation
INCREASING POWER DENSITY
• Need of high-resolution monitoring and feedback control– Both in temporal and spatial dimensions.
Introduction 4/35
Datacom Equipment Power Trends and Cooling Applications (2005), ASHARE TC 9.9
http://download.intel.com/technology/eep/data-center-efficiency/state-of-date-center-cooling.pdf
Ph.D. Proposal Presentation
DYNAMIC DATA CENTERS
Introduction 5/35
(Liu, J.,Terzis, A., "Sensing data centers for energy efficiency,“Phil. Trans. R. Soc. A (2012))
(CRAC supply temperature data from CEETHERM: Sept. 9-10, 2012, 11 pm -11pm )
• 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
DATA CENTER COOLING
Introduction 6/35
• 1/3 of energy spent in a DC is dedicated to its cooling systems.
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.
• Forced convective air cooling:
- Heat generated at chips dissipates via cooling airflow propelled by fans in the computer room air conditioning (CRAC) units.
Ph.D. Proposal Presentation
MULTISCALE THERMAL SYSTEM
Introduction 7/35
• Involvement of several decades of length and time scales- Spatial: 5 decades (mm to Dm).- Temporal: 4 decades (10-2 s to 10 s).
Turbulent Convection
Turbulent Convection Turbulent Convection + Conduction
Conduction
Ph.D. Proposal Presentation
CURRENT APPROACHES FOR TRANSIENT THERMAL MODELING
Introduction 8/35
Computational Time
Mo
del
Acc
ura
cy
Lumped System Modeling
Computational fluid dynamics/ Heat Transfer (CFD/ HT) Modeling
Reduced-order Modeling
Involves iterative solution of non-
linear conservation equations.
Involves posing zero
local gradient
condition.
Optimal and controllable
Trade-off.
Ph.D. Proposal Presentation
TYPES OF REDUCED-ORDER MODEL (ROM)
Introduction 9/35
ROM
Statistical Response Surface Model
Simplified Physics-based Model
Proper Orthogonal Decomposition
(POD/ PCA)
Nonlinear Volterra Theory
Modal Reduction-based Low- Dimensional Model
Harmonic Balance Approximation
Laplacian Model
Thermal Zone Model
Ph.D. Proposal Presentation
COMPUTATION FOR A TRANSIENT CFD SIMULATION
• DC Modeling Requirement– m spatial nodes and n 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 machineIntroduction 10/35
CFL
./scale
tU x
Ph.D. Proposal Presentation
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.Introduction 11/35
Ph.D. Proposal Presentation
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. Problem Statement 12/35
Ph.D. Proposal Presentation
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.
Problem Statement 13/35
Ph.D. Proposal Presentation
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.
Representative Case Study
14/35
Ph.D. Proposal Presentation
CASE STUDY FOR SINGLE PARAMETER (TIME) POD MODEL
• After remaining shut down for 2 minutes, the CRAC unit is turned on at t=0.
Representative Case Study
15/35
Ph.D. Proposal Presentation
OPTIMALITY OF POD MODES
• First 10 POD modes capture more than 90% characteristics of the temperature field.
Representative Case Study
16/35
Ph.D. Proposal Presentation
PRINCIPAL COMPONENT NUMBER
• As captured energy percentage increases, the corresponding principal component number increases.
Representative Case Study
17/35
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Ph.D. Proposal Presentation
ERROR FORMULATION
Representative Case Study
18/35
Prediction Experiment POD .E T T MeasurementPrediction Scale ,E f T
Analytical Exact POD .E T T POD/InterpolationAnalytical 0
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Prediction Analytical
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Ph.D. Proposal Presentation
TEMPERATURE MEASUREMENT
Representative Case Study
19/35
• Grid: 21 T-type copper-constantan thermocouples made 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
POD/ INTERPOLATION FRAMEWORK• Temperature map at the rack inlet at t=92 s.
Representative Case Study
20/35
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
CALIBRATION OF ANALYTICAL ERROR
Representative Case Study
21/35
0 20 40 60 80 100 120 140 160 180 200-0.25
-0.2
-0.15
-0.1
-0.05
0
0.05
0.1
0.15
0.2
Time (s)
Err
or
(0 C)
Prediction Error
Analytical Error
• Calibrated analytical error obviates the necessity of determining a posteriori prediction error .
Ph.D. Proposal Presentation
POD/ EXTRAPOLATION FRAMEWORK• Temperature map at the rack inlet at t=207 s.
Representative Case Study
22/35
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
CALIBRATION OF ANALYTICAL ERROR
Representative Case Study
23/35
200 205 210 215 220 225-3.5
-3
-2.5
-2
-1.5
-1
-0.5
0
0.5
Time (s)
Err
or
(0 C)
Prediction Error
Analytical Error
• Calibrated analytical error obviates the necessity of determining a posteriori prediction error .
Ph.D. Proposal Presentation
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.
Representative Case Study
24/35
Ph.D. Proposal Presentation
CASE STUDY FOR SINGLE PARAMETER (SPACE) POD MODEL
Representative Case Study
25/35
• Sudden shut down of the CRAC unit and power back after 100 s.
(Photo courtesy to IBM)
Ph.D. Proposal Presentation
PREDICTION FOR DOF-1 POINTS
Representative Case Study
26/35
• Improves spatial resolution between (70, 51, -1) and (70, 50, -1).
Ph.D. Proposal Presentation
PREDICTION FOR DOF-2 POINTS
Representative Case Study
27/35
• Improves spatial resolution between (56, 31, 2.5) and (56,30,5.5).
Ph.D. Proposal Presentation
TWO PARAMETER REDUCED-ORDER ALGORITHM
• POD-based modal decomposition.• Time and rack heat load as the modeling parameters.Representative Case Study
28/35
Ph.D. Proposal Presentation
CASE STUDY FOR MULTI-PARAMETER (TIME, RACK HEAT LOAD) POD MODEL
Representative Case Study
29/35
• Sudden shut down of the CRAC unit and power back after 100 s (t=0 in the plot).
Ph.D. Proposal Presentation
COMPARISON FOR EXTRAPOLATION AT Q=1500 W
Representative Case Study
30/35
Extrapolation in time and interpolation in heat load.
Ph.D. Proposal Presentation
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. Deliverable 31/35
Ph.D. Proposal Presentation
DISSERTATION TIMELINE
May 2010
-Dec. 2011
• Single-parameter POD framework development with time as the parameter.
Jan. 2012
-June 2012
• Single-parameter POD framework development with spatial location(s) as the parameter(s).
June 2012-Oct. 2012
• Multi-parameter POD framework development with spatial location and time as the parameters.
Nov. 2012
- April 2013
• Interconnected multi-scale modeling.
Planning 32/35
Ph.D. Proposal Presentation
PUBLICATIONSREFEREED 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).
Closure 33/35
Ph.D. Proposal Presentation 34/35
ACKNOWLEDGEMENT
Closure
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 37/35Introduction
10
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Ph.D. Proposal Presentation 38Introduction
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Ph.D. Proposal Presentation 39/35
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.
Introduction
Ph.D. Proposal Presentation 40/35
TEMPERATURE MEASUREMENT
Introduction
• Grid: 21 T-type copper-constantan thermocouples made 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 41/35
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).Introduction
Ph.D. Proposal Presentation 42/35Introduction
May 2010-Dec. 2010
Jan. 2011-June 2011
July 2011-Dec. 2011
Jan. 2012-June 2012
June 2012-Dec. 2012
Jan. 2013-May 2013
Single-parameter POD Framework Development
Ph.D. Proposal Presentation 43/35
LITERATURE REVIEW
Introduction
Paper/ Thesis Comments
S. V. Patankar, Airflow and Cooling in a Data Center, Journal of Heat Transfer 132 (2010)
73001-1-73001-17.
CFD/HT simulation for a steady data center.
A.H. Beitelmal, C.D. Patel, Thermo-Fluids Provisioning of a High Performance High Density Data Center, Distributed and Parallel Databases,
21, 227–238, 2007.
CFD/HT simulation for a transient data center.
Shawn Shields, Dynamic Thermal Response of the Data Center to Cooling Loss during Facility Power Failure, Masters Thesis, Georgia Tech,
2009.
Measurement-based transient characterization of a data center.
J. D. Rambo, Reduced-order Modeling of Multiscale Turbulent Convection: Application to
Data Center Thermal Management, Ph.D. Dissertation, Georgia Tech, 2007.
Reduced-order modeling of data center and a posterior error
analysis.
Ph.D. Proposal Presentation 44/35
LITERATURE REVIEW CONTD.
Introduction
Paper/ Thesis Comments
Q. Nie, Experimentally Validated Multiscale Thermal Modeling of Electronic Cabinets , Ph.D.
Dissertation, Georgia Tech, 2008.
Interconnected multiscale modeling for a rack.
Graham Nelson, Development of an Experimentally-Validated Compact Model of a Server Rack, Masters Thesis, Georgia Tech,
2009.
Development of grid-based temperature measurement
system and compact modeling of a server.
E. Samadiani, Energy Efficient Thermal Management of Data Centers via Open Multi-
scale Design, Ph.D. Dissertation, Georgia Tech, 2009.
Reduced-order open design for a multi-scale data center.
V. López and H. F. Hamann, Heat transfer modeling in data centers, International journal of
heat and mass transfer 54 (2011) 5306-5318.
Simplified Physics-based Laplacian Model for a data
center.
Ph.D. Proposal Presentation 45/35
LITERATURE REVIEW CONTD.
Introduction
Paper/ Thesis Comments
S. Ravindran, Error Estimates for Reduced Order POD Models of Navier-Stokes Equations, ASME
IMECE, 2008, pp. 652-657.
A priori error estimate for a proper orthogonal
decomposition (POD)-based reduced order model for the
Navier-Stokes equations