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«A Dissertation Presented to The Academic Faculty by Ethan E. Cruz In Partial Fulfillment of the Requirements for the Degree Doctor of Philosophy in ...»

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COUPLED INVISCID-VISCOUS SOLUTION METHODOLOGY

FOR BOUNDED DOMAINS: APPLICATION TO DATA CENTER

THERMAL MANAGEMENT

A Dissertation

Presented to

The Academic Faculty

by

Ethan E. Cruz

In Partial Fulfillment

of the Requirements for the Degree

Doctor of Philosophy in the

School of Mechanical Engineering

Georgia Institute of Technology

December 2015

Copyright © 2015 by Ethan E. Cruz

COUPLED INVISCID-VISCOUS SOLUTION METHODOLOGY

FOR BOUNDED DOMAINS: APPLICATION TO DATA CENTER

THERMAL MANAGEMENT

Approved by:

Dr. Yogendra K. Joshi, Advisor Dr. Lakshmi N. Sankar School of Mechanical Engineering School of Aerospace Engineering Georgia Institute of Technology Georgia Institute of Technology Dr. G. Paul Neitzel Dr. Paul S. Krueger School of Mechanical Engineering Department of Mechanical Engineering Georgia Institute of Technology Southern Methodist University Dr. Satish Kumar Dr. Roger R. Schmidt School of Mechanical Engineering Systems and Technology Group Georgia Institute of Technology International Business Machines Date Approved: August 19, 2015 Although to penetrate into the intimate mysteries of nature and thence to learn the true causes of phenomena is not allowed to us, nevertheless it can happen that a certain fictive hypothesis may suffice for explaining many phenomena.

-Leonard Euler (1707-1783) To my wife, Ryan.

Without her love, patience, and understanding, I would be lost forever.

ACKNOWLEDGEMENTS

I wish to thank my advisor, Professor Joshi, for his patience, encouragement, and guidance throughout the entire process. I am especially grateful for his permission to complete the work in absentia. I express my sincere gratitude to my PhD reading committee, Professors Neitzel, Kumar, Sankar, and Krueger, and Dr. Schmidt, for their time spent reviewing the dissertation, their support, and their helpful comments.

I would also like to thank my manager at IBM, Peter W. Kelly, for his support in pursuing my graduate education, and for his vital role in gaining the funding that allowed me to return to school full time. I also appreciate all of the encouragement of the late IBM Fellow, Dr. Dick Chu, who exhorted me to not just pursue this degree, but to “create something they will name after you.” I wish to thank all of my colleagues at IBM for their patience and understanding. I would like to especially thank Dr. Vic Mahaney for picking up the slack that I invariably left as I finished the dissertation.

Although my residency at Georgia Tech was relatively short, I would like to acknowledge all of my professors and fellow students with whom I had the privilege of working. I would also like to thank the Woodruff School of Mechanical Engineering administrative staff, especially Glenda Johnson, who helped me with numerous issues that arose throughout my studies.

Finally, I would like to thank my wife, Ryan, my two children, Tino and Taryn, my parents, Eddie and Jean, my in-laws, Russ and Deb Miller, and my dear friends, Peter and Paulette Bonk, Jon and Lisa Ellingworth, and Dr. Gregory Durgin for all of their

–  –  –

ACKNOWLEDGEMENTS

LIST OF TABLES

LIST OF FIGURES

LIST OF SYMBOLS

LIST OF ABBREVIATIONS

SUMMARY

CHAPTER 1 INTRODUCTION

1.1 Design of Data Centers

1.1.1 Air-Cooling Configurations

1.1.2 Air-Flow Velocities and Reynolds Numbers

1.1.3 Air Temperatures

1.1.4 Cooling Energy Efficiency

1.2 Data Center Numerical Modeling

1.2.1 Reynolds-Averaged Navier-Stokes

1.2.2 Reduced Order Modeling

1.2.3 Inviscid Methods

1.2.4 Hybrid Methods

1.3 Preview of the Present Work

2 MODELING OF A SINGLE-RACK DATA CENTER TEST CELL................10

2.1 Experimental Setup of the Single-Rack Data Center Test Cell..............10 2.1.1 Experimental Uncertainty

–  –  –

2.2.1 Flow Models

2.2.2 Grid Studies

2.3 Computational Effort

2.3.1 Convergence Criteria

2.3.2 Results

2.4 Experimental Data and Model Comparison

2.4.1 Overall Comparison

2.4.2 Localized Comparison

2.5 Conclusions

3 COUPLED INVISCID-VISCOUS SOLUTION METHOD

3.1 Overall Solution Method

3.2 Governing Equations

3.2.1 Viscous Domains

3.2.2 Inviscid Domains

3.2.3 Grid Sizing

3.3 Partitioning Algorithm

3.4 Boundary Conditions and Coupling Procedure

3.5 Mass and Energy Balance Algorithm

3.6 Pressure-Velocity Coupling Method

3.7 Convergence Criteria

3.8 Results and Discussion

3.8.1 Parameter Definition

3.8.2 Grid Study

3.8.3 Mass Balance Algorithm

–  –  –

3.8.5 Temperature Difference Contours

3.9 Summary

4 TEMPERATURE VERIFICATION OF THE CIVSM IN A MULTIRACK DATA CENTER





4.1 Experimental Setup of the Data Center Laboratory

4.2 Numerical Models

4.2.1 Flow Modeling

4.2.2 Tile Modeling

4.2.3 Grid Studies

4.3 CIVSM Refinements

4.3.1 Boundary Condition Under-Relaxation

4.3.2 Partitioning Algorithm and Thin Flow Blockages

4.4 Results and Discussion

4.4.1 CIVSM Parameter Definition

4.4.2 Partitioning Algorithm

4.4.3 Convergence Criteria

4.4.4 RMS Difference vs. Solution Time

4.5 Summary

5 FLOW VERIFICATION OF THE CIVSM IN A MULTI-RACK DATA

CENTER

5.1 Experimental Setup of the Data Center Laboratory

5.2 Numerical Models

5.2.1 Flow Modeling

5.2.2 Tile Modeling

5.2.3 Grid Studies

–  –  –

5.3.1 CIVSM Parameter Definition

5.3.2 Partitioning Algorithm

5.3.3 Convergence Criteria

5.3.4 Flow Results

5.3.5 Solution Time

5.4 Summary

6 FUTURE WORK, RECOMMENDATIONS, AND CONCLUSIONS............107

6.1 CIVSM Partitioning Algorithm

6.1.1 Non-Uniform Grid

6.1.2 Viscous Region Smoothing

6.1.3 Partitioning Algorithm Parameters

6.1.4 Relatively Small Viscous Regions

6.2 Mass Balance Algorithm

6.3 Under-Relaxation Parameters

6.4 Non-Solving Operations

6.5 Conclusions

APPENDIX A: TURBULENCE MODELING

APPENDIX B: NUMERICAL ERROR ANALYSIS

APPENDIX C: VELOCITY PROFILE PLOTS

REFERENCES

VITA

–  –  –

Conditions necessary to change a cell to =1

Table 1 Table 2 List of parameters used in the CIVSM

Table 3 Details of the Various Grids Used in the Grid Study

Table 4 Convergence Criteria Used for the CIVSM Models

Table 5 Single-Rack Data Center Test Cell Discretization Error Calculations for Traditional CFD Flow Models

Table 6 Single-Rack Data Center Test Cell Discretization Error Calculations for the CIVSM Models

Table 7 Multi-Rack Data Center Discretization Error Calculations

–  –  –

Figure 1 Hot and Cold Aisle Raised Floor Data Center Layout

Figure 2 Photograph of the Region of Interest in the Single-Rack Data Center Test Cell

Figure 3 Plan View of the Single-Rack Data Center Test Cell

Figure 4 Isometric View of the Single-Rack Data Center Test Cell

Figure 5 RMS Temperature Difference vs. Solution Time for the 23 kW Cases

Figure 6 RMS Temperature Difference vs. Solution Time for the 11 kW Cases

Figure 7 RMS Temperature Difference vs. Solution Time for the Inviscid Cases

Figure 8 Temperature and Absolute Temperature Difference Contours within the Region of Interest of the Single-Rack Data Center Test Cell for the 1 Tile, 23 kW Case

Figure 9 Absolute Temperature Difference Contours within the Region of Interest of the Single-Rack Data Center Test Cell for the 1 Tile, 23 kW Case

Figure 10 Overall Coupled Inviscid-Viscous Solution Method (CIVSM) Flow Chart

Figure 11 Viscous Regions of the Single-Rack Data Center Test Cell

Partitioning Algorithm -values and Region and Domain Definition Figure 12 for the Single-Rack Data Center Test Cell

Figure 13 Partitioning Algorithm Flow Chart

Figure 14 Mass Balance Algorithm Flow Chart

Figure 15 RMS Temperature Difference vs. Solution Time for the CIVSM and CFD/HT Cases

–  –  –

Figure 17 Absolute Temperature Difference Contours within the Region of Interest of the Single-Rack Data Center Test Cell for the 3 Tile, 23 kW Case

Figure 18 Isometric View of the Data Center Lab at Georgia Tech

Figure 19 Viscous Regions of the Data Center Lab at Georgia Tech for the 1 CRAC, MBF Case

Figure 20 RMS Temperature Difference vs. Solution Time for the DCL at Georgia Tech

Figure 21 Isometric View of the Data Center Lab at Georgia Tech

Figure 22 Region Locations for the Flow Verification Models

Figure 23 Measured and Predicted Streamtraces for the Full Tile (Case 1) Using the Modified Body Force Model

Figure 24 Measured and Predicted Streamtraces for the Full Tile (Case 1) Using the Porous Jump Model

Figure 25 Measured and Predicted Streamtraces for the Framed Tile (Case 2) Using the Modified Body Force Model

Figure 26 Measured and Predicted Streamtraces for the Framed Tile (Case 2) Using the Porous Jump Model

Figure 27 Measured and Predicted Streamtraces for the Blocked Tile (Case 3) Using the Modified Body Force Model

Figure 28 Measured and Predicted Streamtraces for the Blocked Tile (Case 3) Using the Porous Jump Model

Figure 29 Velocity Plots for Case 1, Modified Body Force Model @ 0.15 m (0.5 ft)

Figure 30 Velocity Plots for Case 1, Porous Jump Model @ 0.15 m (0.5 ft)...........101 Figure 31 Velocity Plots for Case 1, Modified Body Force Model @ 1.68 m (5.5 ft)

Figure 32 Velocity Plots for Case 1, Porous Jump Model @ 1.68 m (5.5 ft)...........103

–  –  –

Figure 34 Seed Cell and Viscous Region Locations for 1 CRAC, Modified Body Force Model when Using Vorticity Magnitude

Figure 35 Seed Cell and Viscous Region Locations for 1 CRAC, Modified Body Force Model when Using Turbulent Kinetic Energy

Figure 36 Seed Cell and Viscous Region Locations for 1 CRAC, Modified Body Force Model when Using Turbulent Dissipation

Figure 37 Seed Cell and Viscous Region Locations for 1 CRAC, Modified Body Force Model when Using Turbulent Viscosity

Figure 38 RMS Temperature Difference vs. Solution Time for the 1 CRAC Case

Figure 39 Rack Inlet Air Temperature Predictions for the CIVSM Using the Standard k- Turbulence Model

Figure 40 Rack Inlet Air Temperature Predictions for the CIVSM Using the Standard k- Turbulence Model and Measured Data

Figure 41 Velocity Plots for Case 1, Modified Body Force Model @ 0.91 m (3.0 ft)

Figure 42 Velocity Plots for Case 1, Porous Jump Model @ 0.91 m (3.0 ft)...........134 Figure 43 Velocity Plots for Case 2, Modified Body Force Model @ 0.15 m (0.5 ft)

Figure 44 Velocity Plots for Case 2, Modified Body Force Model @ 0.91 m (3.0 ft)

Figure 45 Velocity Plots for Case 2, Modified Body Force Model @ 1.68 m (5.5 ft)

Figure 46 Velocity Plots for Case 2, Porous Jump Model @ 0.15 m (0.5 ft)...........138 Figure 47 Velocity Plots for Case 2, Porous Jump Model @ 0.91 m (3.0 ft)...........139 Figure 48 Velocity Plots for Case 2, Porous Jump Model @ 1.68 m (5.5 ft)...........140 Figure 49 Velocity Plots for Case 3, Modified Body Force Model @ 0.15 m (0.5 ft)

Figure 50 Velocity Plots for Case 3, Modified Body Force Model @ 0.91 m (3.0 ft)

–  –  –

Figure 52 Velocity Plots for Case 3, Porous Jump Model @ 0.15 m (0.5 ft)...........144 Figure 53 Velocity Plots for Case 3, Porous Jump Model @ 0.91 m (3.0 ft)...........145 Figure 54 Velocity Plots for Case 3, Porous Jump Model @ 1.68 m (5.5 ft)...........146

–  –  –

A

c p

C 

dcell

ddistance

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g

h

i, j

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k

K

L

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p

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r21

–  –  –

Ri

S

S MBF

t

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x

 max

 t

–  –  –

ASHRAE... American Society of Heating, Refrigerating and Air Conditioning Engineers CDU

CFD

CFD/HT

CIVSM

CRAC

DCL

GCI

IT

MBF

PDU

PIV

PJ

POD

RANS

RMS

RSS

SIMPLE

VSD

–  –  –



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