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 Simulation Tool ...... 137 6.2 Parametric Study ...... 138 6.3 Conclusions ...... 142
VII. CONCLUSIONS AND RECOMMENDATIONS ...... 143
REFERENCES ...... 147
APPENDICES ...... 152
vi
LIST OF TABLES
Table Page
2.1: Validation of the simple harmonic model ------15
2.2: Chronological list of the developed models and their features ------22
3.1: Soil Climate Analysis Network (SCAN) measurement sites ------56
3.2: Two-harmonic model parameters for WTARS, Alabama ------59
3.3: RMSEs of the harmonic models for WTARS, Alabama------59
3.4: Two-harmonic model parameters for Nenana, Alaska ------61
3.5: RMSEs of the harmonic models for Nenana, Alaska ------62
3.6: RMSEs of the numerical model at 5, 20, 50 and 100 cm (2, 8, 20 and 40”) depths -----65
3.7: RMSEs of the two-harmonic model ------66
3.8: RMSEs of the one-harmonic model------67
4.1: Köppen - Geiger climate groups and type ------84
4.2: Description of Köppen - Geiger climate subtypes ------85
4.3: Vegetation density value in different Köppen-Geiger climates ------86
4.4: 19 Soil Climate Analysis Network sites------87
4.5: Snow depth calculation in different Köppen-Geiger climates ------91
4.6: SCAN measurement sites and typical meteorological year weather sites ------95
4.7: Estimated constant values used in the simplified design model, fixed soil diffusivity --97
4.8: RMSEs of the simplified design model, fixed soil diffusivity, in °C ------98
4.9: Estimated constant values used in the simplified design method - site specified soil
diffusivity ------100
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Table Page
4.10: RMSEs of the simplified design model – fixed soil diffusivity and site specified soil
diffusivity, in °C ------101
4.11: Simplified design model RMSEs - with and without vegetation density estimation
procedure, arid or dry summer climates, in °C ------102
4.12: RMSEs of the simplified design model - with and without snow model, snow climates, in
°C ------105
4.13: RMSEs of estimated typical year ground temperature from measured results ------107
4.14: RMSEs of estimated maximum and minimum ground temperature of multiple years from
measured results ------108
5.1: Nineteen SCAN sites and TMY3 weather stations ------115
5.2: Constant values used in Equation 5-1, simplified design model – 19 SCAN sites ----117
5.3: Constant values used in Equation 5-2, ASHRAE Handbook – 19 SCAN sites------119
5.4: Constant values used in Equation 5-3, ASHRAE District Heating Manual - 19 SCAN
sites ------120
5.5: Constant values used in Equation 5-1, tuned from measured results - 19 SCAN sites -121
5.6 Annual average near-surface ground temperature Ts,avg - 19 SCAN sites ------129 5.7: Twelve Oklahoma Mesonet sites and TMY3 weather stations ------131
5.8: Constant values used in the Equation 5-1, simplified design model - 12 Oklahoma
Mesonet sites ------132
5.9: RMSEs of simplified design model, simplified design model - 12 Oklahoma Mesonet
sites ------133
5.10: Simplified design model correction factors used for estimations of peak ground
temperature of multiple years ------135
6.1: Required lengths of the HGHX tubing------140
6.2: Percentage error of estimated HGHX pipe lengths using simplified design method,
ASHRAE Handbook method and ASHRAE district heating manual method ------141
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Table Page
A-1: Country names ------153
A-2: Region names ------156
A-3: Constant values for short grass ------157
A-4: Constant values for tall grass ------263
ix
LIST OF FIGURES
Figure Page
2.1: Approximate groundwater temperatures (°F) in the continental US------30
2.2: 1925 map of annual average air temperature------30
2.3: IP and SI versions of the ground temperature amplitude------31
2.4: Range (i.e. twice the amplitude) at 10 cm (4”) depth from Chang (1958)------32
3.1: Non-uniform grid detailed plot for grass covered sites ------37
3.2: Soil enthalpy vs. soil temperature ------39
3.3: Major heat flux components for the plant canopy model------41
3.4: Time step independency study------51
3.5: Grid size independency study------52
3.6: Domain depth independency study------53
3.7: Comparison of estimated soil temperature at 50cm (20”) depth using numerical model and
analytical solutions------54
3.8: Map of United States with SCAN sites located (Wikipedia 2013)------57
3.9: Soil temperature at 5cm (2") depth at WTARS, Alabama (SCAN site)------60
3.10: Soil temperature at 50cm (20") depth at WTARS, Alabama (SCAN site)------60
3.11: Soil temperature at 5cm (2") depth at Nenana, Alaska (SCAN site)------63
3.12: Soil temperature at 50cm (20") depth at Nenana, Alaska (SCAN site) ------63
3.13: Mean RMSEs of the simulation results at four depths, in all three climates – arid or dry
summer climates, warm temperate climates and snow climates ------69
3.14: Mean RMSEs of the simulation results at four depths, in arid or dry summer climates -----
------70
3.15: Mean RMSEs of the simulation results at four depths, in warm temperate climates --70 x
Figure Page
3.16: Mean RMSEs of the simulation results at four depths, in snow climates ------71
3.17: Soil temperature at 5cm (2”) depth, at Los Lunas PMC SCAN site, New Mexico ------72
3.18: Soil temperature at 100cm (40”) depth, at Los Lunas PMC SCAN site, New Mexico -73
3.19: Soil temperature at 5cm (2”) depth, at Fort Reno SCAN site, Oklahoma ------74
3.20: Soil temperature at 100cm (40”) depth, at Fort Reno SCAN site, Oklahoma ------74
3.21: Soil temperature at 5cm (2”) depth, at Aniak SCAN site, Alaska ------75
3.22: Soil temperature at 50cm (20”) depth, at Aniak SCAN site, Alaska ------76
4.1: Vegetation density VS. simplified design model RMSEs, arid or dry summer climates ------89
4.2: Vegetation density vs. simplified design model RMSEs, other climates------89
4.3: Estimated snow depth vs. air temperature at SCAN site – Aniak, Alaska ------93
4.4: Snow depth coefficient β vs. model RMSEs, snow or polar climates ------94
4.5: Mean RMSEs of the simplified design model w/ and w/o vegetation density estimation
procedure, arid or dry summer climates, in °C ------103
4.6: Mean RMSEs of the simplified design model of the four depths w/ and w/o vegetation
density estimation procedure, arid or dry summer climates, in °C ------104
4.7: Mean RMSEs of the simplified design model with and without snow model, snow
climates, in °C ------106
4.8: Mean RMSEs of the simplified design model of the four depths with and without snow
model, snow climates, in °C ------106
4.9: RMSEs of estimated typical year ground temperature for measured results ------108
4.10: RMSEs of estimated maximum ground temperatures of multiple years from measured
results at four depths ------109
4.11: RMSEs of estimated minimum ground temperatures of multiple years from measured
results at four depths ------109
5.1: Mean RMSEs of model results for nineteen SCAN sites located in all three climates –
arid or dry summer climates, warm temperate climates and snow climates ------122
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Figure Page
5.2: Mean model RMSEs of all sites in arid or dry summer climates ------124
5.3: Mean model RMSEs of all sites in warm temperate climates ------125
5.4: Mean model RMSEs of all sites in snow climates ------125
5.5: Model RMSEs for nineteen SCAN sites at 50cm (20") depth ------128
5.6: Model RMSEs for nineteen SCAN sites at 100cm (40") depth ------128
6.1: Estimated HGHX pipe lengths using simplified design method, ASHRAE Handbook
method and ASHRAE district heating manual method ------142
B-1: Annual average ground temperature for Continental US, short grass covered sites -----369
B-2: Annual amplitude of surface temperature variation for Continental US, short grass
covered sites ------370
B-3: Annual average ground temperature for Asia, short grass covered sites ------371
B-4: Annual amplitude of surface temperature variation for Asia, short grass covered sites -----
------372
B-5: Annual average ground temperature for Australia, short grass covered sites ------373
B-6: Annual amplitude of surface temperature variation for Australia, short grass covered sites
------374
B-7: Annual average ground temperature for Europe, short grass covered sites ------375
B-8: Annual amplitude of surface temperature variation for Europe, short grass covered sites –
------376
B-9: Annual average ground temperature for North America, short grass covered sites -----377
B-10: Annual amplitude of surface temperature variation for North America, short grass
covered sites ------378
B-11: Annual average ground temperature for South America, short grass covered sites ----379
B-12: Annual amplitude of surface temperature variation for South America, short grass
covered sites ------380
B-13: Annual average ground temperature for Continental US, tall grass covered sites -----381
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Figure Page
B-14: Annual amplitude of surface temperature variation for Continental US, tall grass covered
sites ------382
B-15: Annual average ground temperature for Asia, tall grass covered sites ------383
B-16: Annual amplitude of surface temperature variation for Asia, tall grass covered sites ------
------384
B-17: Annual average ground temperature for Australia, tall grass covered sites ------385
B-18: Annual amplitude of surface temperature variation for Australia, tall grass covered sites –
------386
B-19: Annual average ground temperature for Europe, tall grass covered sites ------387
B-20: Annual amplitude of surface temperature variation for Europe, tall grass covered sites ---
------388
B-21: Annual average ground temperature for North America, tall grass covered sites ---389
B-22: Annual amplitude of surface temperature variation for North America, tall grass covered
sites ------390
B-23: Annual average ground temperature for South America, tall grass covered sites --391
B-24: Annual amplitude of surface temperature variation for South America, tall grass covered
sites------392
xiii
CHAPTER I
INTRODUCTION
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.
These include:
• Design load calculations for both residential and non-residential cooling and heating load
calculations. For design purposes, the basement wall and floor heat loss is estimated
using an estimate of the minimum ground surface temperature, which could be
determined from:
o the annual average ground temperature
o the ground temperature amplitude
• Building energy calculation procedures. The annual-mean slab foundation and basement
heat loss/gain is currently estimated using an annual average ambient temperature and an
annual amplitude.
• Design of vertical ground heat exchangers used in the ground source heat pump systems.
Vertical ground heat exchangers are deep enough that annual transients in the undisturbed
1
ground temperature are relatively unimportant, so a single value - annual average undisturbed
ground temperature may be used as a design condition. This value can be measured if a test
borehole is drilled.
• Design of horizontal ground heat exchangers used in the ground source heat pump systems.
Horizontal ground heat exchangers are relatively shallow so that annual transients in the
undisturbed ground temperature are very important. A single temperature profile would not
be adequate for this. A more accurate procedure - simple harmonic model for predicting
undisturbed ground temperatures as a function of depth and time of year is usually used. This
procedure mainly relies on three parameters: annual average ground temperature, annual
amplitude of ground temperature at the surface and phase angle. More details about this
procedure will be introduced in the following part and in Section 2.2.1.
• Design and energy analysis of district heating and cooling systems. Estimates of ground
temperature are needed for calculation of heat loss and gain through the pipes which
distribute thermal energy from a central source to buildings. The district heating pipes are
usually buried at relatively shallow depths so that annual transients in the undisturbed ground
temperature are very important. So a similar procedure as used for design of horizontal
ground heat exchanger is commonly used.
The simple design and analysis procedures mentioned above rely on ground temperatures as inputs.
Likewise, more sophisticated analyses like numerical simulations still rely on undisturbed ground temperatures for initial conditions and boundary conditions.
Lord Kelvin presented a higher order harmonic model (Thomson 1862) to estimate the ground temperatures, as shown in Equation 1-1: