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Estimations of Undisturbed Ground Temperatures Using Numerical and Analytical Modeling ESTIMATIONS OF UNDISTURBED GROUND TEMPERATURES USING NUMERICAL AND ANALYTICAL MODELING By LU XING Bachelor of Arts/Science in Mechanical Engineering Huazhong University of Science & Technology Wuhan, China 2008 Master of Arts/Science in Mechanical Engineering Oklahoma State University Stillwater, OK, US 2010 Submitted to the Faculty of the Graduate College of the Oklahoma State University in partial fulfillment of the requirements for the Degree of DOCTOR OF PHILOSOPHY December, 2014 ESTIMATIONS OF UNDISTURBED GROUND TEMPERATURES USING NUMERICAL AND ANALYTICAL MODELING Dissertation Approved: Dr. Jeffrey D. Spitler Dissertation Adviser Dr. Daniel E. Fisher Dr. Afshin J. Ghajar Dr. Richard A. Beier ii ACKNOWLEDGEMENTS I would like to thank my advisor, Dr. Jeffrey D. Spitler, who patiently guided me through the hard times and encouraged me to continue in every stage of this study until it was completed. I greatly appreciate all his efforts in making me a more qualified PhD, an independent researcher, a stronger and better person. Also, I would like to devote my sincere thanks to my parents, Hongda Xing and Chune Mei, who have been with me all the time. Their endless support, unconditional love and patience are the biggest reason for all the successes in my life. To all my good friends, colleagues in the US and in China, who talked to me and were with me during the difficult times. I would like to give many thanks to my committee members, Dr. Daniel E. Fisher, Dr. Afshin J. Ghajar and Dr. Richard A. Beier for their suggestions which helped me to improve my research and dissertation. This thesis is based on measured results provided by the Soil Climate Analysis Network, United States Department of Agriculture and Oklahoma Mesonet. Their support is gratefully acknowledged. I would like to thank Arkasama Bandyopadhyay for processing the Mesonet raw data. iii Acknowledgements reflect the views of the author and are not endorsed by committee members or Oklahoma State University. Name: LU XING Date of Degree: DECEMBER, 2014 Title of Study: ESTIMATIONS OF UNDISTURBED GROUND TEMPERATURES USING NUMERICAL AND ANALYTICAL MODELING Major Field: MECHANICAL ENGINEERING Abstract: The interaction of buildings and ground source heat pump systems with the surrounding ground is quite important for design and energy calculation procedures. Building design load calculations, building energy calculations, ground heat exchangers design and design and energy analyses of district heating and cooling systems often require as inputs the undisturbed ground temperatures. Currently, the available undisturbed ground temperatures are rather limited. In the U.S., the ground temperatures are usually represented with a three-parameter one-harmonic model. The model parameters for the continental US or North America are presented in maps in the ASHRAE handbooks. The results presentation in small maps can be quite difficult to read for a specific location. Furthermore, the sources of some results are unknown, and where the source is known, the results were published more than half a century ago. ASHRAE district heating manual also published a world-wide data set presented in one-harmonic model with model parameters presented in tables. However, the data are computed based on a simplified approximation that the ground surface temperature is equal to the air temperature; this approximation can lead to significant error in the cold climates and arid climates. Therefore, the main objective of this research is to provide a new set of ground temperature estimates for use by engineers. A numerical model and a simplified design model have been developed for the estimations of the typical year ground temperature and maximum/minimum ground temperatures of multiple years. Both models have been validated against the experimental results. The validated numerical model will be run with 1020 TMY3 weather files in the U.S., 80 CWEC weather files in Canada and 3012 IWEC-2 weather files around the world. The simplified design model relies on empirical parameters to estimate the ground temperatures. Therefore, the numerical model results will be used to generate parameters for the design model. Two sets of ground temperature estimates approximated for with two different earth surface conditions will be developed; these two earth surface conditions are short grass, tall grass. These ground temperatures are presented in a two-harmonic form using parameters estimated from the numerical model results. iv TABLE OF CONTENTS Chapter Page I. INTRODUCTION ......................................................................................................1 II. LITERATURE REVIEW ..........................................................................................9 2.1 Experimental Measurements ............................................................................10 2.1.1 Ground Temperature Data ......................................................................10 2.1.2 Factors Affecting Ground Temperatures ................................................12 2.1.3 Summary .................................................................................................12 2.2 Modeling of Ground Temperatures .................................................................12 2.2.1 Analytical Model ....................................................................................13 2.2.2 Numerical Model ....................................................................................19 2.3 Common Procedures for Estimating Ground Temperatures ............................27 2.3.1 Average Annual Ground Temperature....................................................29 2.3.2 Annual Amplitude at the Ground Surface ..............................................31 2.3.3 Phase Lag ................................................................................................32 2.3.4 Summary .................................................................................................33 2.4 Summary of the Literature Review ..................................................................33 III. NUMERICAL MODEL AND SIMPLIFIED DESIGN MODEL DEVELOPEMENTAND EXPERIMENTAL VALIDATION .............................36 3.1 Numerical Model .............................................................................................36 3.1.1 Ground Domain ......................................................................................38 3.1.2 Surface Heat Balance ..............................................................................39 3.2 Two-harmonic Model ......................................................................................49 3.3 Model Verification ...........................................................................................50 3.3.1 Independency Study ................................................................................51 3.3.2 Comparison with Analytical Solution .....................................................53 3.4 Experimental Validation ..................................................................................55 3.4.1 Model Input .............................................................................................57 3.4.2 Sample Results ........................................................................................58 3.4.3 Validation of All Sites ............................................................................64 3.4.4 Case Study in Arid Climates, Warm Climates and Snow Climates .......71 3.5 Conclusions ......................................................................................................76 v Chapter Page IV. METHODOLOGY FOR DEVELOPING A WORLD-WIDE DATASET...........79 4.1 Methodology ....................................................................................................81 4.1.1 Köppen - Geiger Climate Classification .................................................84 4.1.2 Vegetation Density..................................................................................85 4.1.3 Snow Depth .............................................................................................90 4.2 Experimental Validations.................................................................................94 4.2.1 Soil diffusivity ........................................................................................99 4.2.2 Vegetation Density................................................................................101 4.2.3 Snow Depth ...........................................................................................104 4.3 Experimental Data Uncertainty......................................................................107 4.4 Conclusions ....................................................................................................110 V. EXPERIMENTAL VALIDATION OF A WORLD-WIDE DATASET .............112 5.1 Simplified Design Model ...............................................................................113 5.2 Experimental Validation ................................................................................114 5.2.1 Typical Year - Ground Temperature.....................................................116 5.2.2 Extreme Hot/Cold Year - Ground Temperature ...................................130 5.3 Conclusions ....................................................................................................135 VI. IMPACT OF SIMPLIFIED DESIGN MODEL DEVELOPMENT ON HORIZONTAL GROUND HEAT EXCHANGER DESIGN .............................137 6.1 HGHX
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