Analysis of a Ground Coupled Heat Exchanger
by
Brett Vincent Walsh
An Engineering Project Submitted to the Graduate
Faculty of Rensselaer Polytechnic Institute
in Partial Fulfillment of the
Requirements for the degree of
MASTER OF ENGINEERING IN MECHANICAL ENGINEERING
Approved:
_______________________________________________________
Professor Ernesto Gutierrez-Miravete, Project Adviser
Rensselaer Polytechnic Institute
Hartford, Connecticut
December, 2011
i
© Copyright 2011
by
Brett Walsh
All Rights Reserved
ii
CONTENTS
List of Tables ..................................................................................................................... v
List of Figures ................................................................................................................... vi
List of Symbols ................................................................................................................ vii
Acknowledgement .......................................................................................................... viii
Abstract ............................................................................................................................. ix
1. Introduction .................................................................................................................. 1
1.1
Background ........................................................................................................ 1
1.2
Project Scope ...................................................................................................... 3
2. Theory/Methodology ................................................................................................... 5
2.1
Elementary Heat Exchanger Analysis ................................................................ 7
2.2
Finite Element Modeling .................................................................................. 10
3. Results ........................................................................................................................ 11
3.1
Assumptions ..................................................................................................... 11
3.2
Elementary Heat Exchanger Analysis .............................................................. 11
3.3
3.2.1
Open and Closed Loop – Air................................................................ 15
3.2.2
Open and Closed Loop – Ethylene Glycol ........................................... 17
Finite Element Modeling .................................................................................. 21
3.3.1
Open and Closed Loop – Air................................................................ 21
3.3.2
Open and Closed Loop – Ethylene Glycol and Air .............................. 23
3.3.3
Open and Closed Loop – Ethylene Glycol ........................................... 25
4. Conclusion ................................................................................................................. 29
References ........................................................................................................................ 31
Bibliography .............................................................................................................. 31
Appendices ....................................................................................................................... 32
Appendix 1: Open Loop Elementary Heat Exchanger Analysis for Air ................... 32
Appendix 2: Closed Loop Elementary Heat Exchanger Analysis for Air ................. 32
iii
Appendix 3: Open Loop Elementary Heat Exchanger Analysis for Air & Ethylene Glycol
.......................................................................................................................... 32
Appendix 4: Closed Loop Elementary Heat Exchanger Analysis for Air & Ethylene Glycol
.......................................................................................................................... 32
Appendix 5: Open Loop Elementary Heat Exchanger Analysis for Ethylene Glycol32
Appendix 6: Closed Loop Elementary Heat Exchanger Analysis for Ethylene Glycol32
Appendix 7: Validation Calculation for Ethylene Glycol .......................................... 32
iv
List of Tables
Table 1: Summary of Cases Analyzed ............................................................................................ 5
Table 2: Input Parameters ............................................................................................................. 11
Table 3: Mean Temperature Data of Groton, CT ......................................................................... 12
Table 4: Material Properties for Air.............................................................................................. 13
Table 5: Material Properties for Ethylene Glycol ......................................................................... 14
Table 6: Maximum Pipe Length Required (m) ............................................................................. 29
v
List of Figures
Figure 1: Ground Coupled Heat Exchanger Loops [1] ................................................................... 2
Figure 2: Sketch of Open Loop for Air ........................................................................................... 6
Figure 3: Sketch of Closed Loop for Air ........................................................................................ 6
Figure 4: Sketch of Open Loop for Air and Closed Loop for Ethylene Glycol.............................. 6
Figure 5 Sketch of Closed Loop for both Air and Ethylene Glycol ............................................... 6
Figure 6: COMSOL 2-Dimensional Model with Fine Mesh ........................................................ 10
Figure 7: Daily Surface Temperature (°C) for Groton, CT .......................................................... 13
Figure 8: Open Loop – Air; Maximum Required Pipe Length (m): 13.098 ................................. 15
Figure 9: Closed Loop – Air; Maximum Required Pipe Length (m): 10.80 ................................ 16
Figure 10: Open Loop – Air in Secondary Heat Exchanger; Maximum Required Pipe Length
(m): 14.621 .................................................................................................................................... 17
Figure 11: Open Loop – Ethylene Glycol; Maximum Required Pipe Length (m): 54.374 .......... 18
Figure 12: Closed Loop – Air in Secondary Heat Exchanger; Maximum Required Pipe Length
(m): 12.167 .................................................................................................................................... 19
Figure 13: Closed Loop – Ethylene Glycol; Maximum Required Pipe Length (m): 51.009........ 20
Figure 14: 13.098m Pipe; Air Inlet -3.145°C, Air Outlet 12.7671°C ........................................... 21
Figure 15: 10.80m Pipe; Air Inlet 21.869°C, Air Outlet 12.7909°C ............................................ 22
Figure 16: 14.621m Pipe; Air Inlet -3.145°C, Air Outlet 12.7755°C ........................................... 23
Figure 17: 12.034m Pipe; Air Inlet 21.869°C, Air Outlet 12.7812°C .......................................... 24
Figure 18: 10.0m Pipe; Ethylene Glycol Inlet 12.008°C, Ethylene Glycol Outlet 12.6815°C..... 26
Figure 19: Ethylene Glycol Calculation Validation: 10m pipe, 12.008°C ................................... 27
Figure 20: Ethylene Glycol Calculation Validation: 54.374m pipe, 12.008°C ............................ 28
vi
List of Symbols
𝐴𝑖
D
∆𝑇𝑙𝑚,𝑐𝑓
f
F
Area, 𝑚2
Diameter of Pipe, 𝑚
Log Mean Temperature Difference, °C
Friction Factor
Correction Factor
ℎ𝑎
Convective Heat Transfer Coefficient, Air,
ℎ𝑐
Convective Heat Transfer Coefficient, Inner Tube Surface,
ℎ𝑒𝑔
Convective Heat Transfer Coefficient, Ethylene Glycol,
𝑊
𝑚2 ∙𝐾
𝑊
𝑊
𝑚2 ∙𝐾
𝑊
𝑚2 ∙𝐾
𝑘𝑎
Thermal Conductivity, Fluid,
𝑘𝑝
Thermal Conductivity, Pipe,
𝑘𝑠
Thermal Conductivity, Soil,
L
Length of Pipe, 𝑚
𝑚̇
Mass Flow Rate of Fluid,
𝑁𝑢
𝑃𝑟
Nusselt Number
Prandtl Number
𝜇
Dynamic Viscosity,
ν
Kinematic Viscosity,
𝑄̇
Heat Transfer Rate, W
𝑅𝐶𝑜𝑛𝑣
Convective Resistance For Fluid,
𝑅𝐶𝑜𝑛𝑣𝑒𝑔
Convective Resistance For Fluid,
𝑅𝐶𝑜𝑛𝑣𝑇𝑢𝑏𝑒
Convective Resistance Between Fluid and Pipe,
𝑅𝐶𝑜𝑛𝑣𝑇𝑢𝑏𝑒
Convective Resistance Between Pipe and Soil,
𝑅𝑇𝑢𝑏𝑒
Total Thermal Resistance,
𝑟1
𝑟2
𝑟3
Re
Inner radius of the tube, 𝑚
Thickness of the tube, 𝑚
Distance between the tube external surface and the undisturbed soil, 𝑚
Reynolds Number
𝜌
Density,
T
𝑇𝑐,𝑖
𝑇𝑐,𝑜
𝑇ℎ,𝑖
𝑇ℎ,𝑜
𝑇𝑒
𝑇𝑖
𝑇𝑤
Surface Temperature, °C
Inlet Temperature, Cold Fluid, °C
Outlet Temperature, Cold Fluid, °C
Inlet Temperature, Hot Fluid, °C
Outlet Temperature, Hot Fluid, °C
Exit Temperature , °C
Inlet Temperature, °C
Wall Temperature, °C
U
Overall Heat Transfer Coefficient,
V
Velocity of the Fluid,
⁄𝑆𝑜𝑖𝑙
𝑚∙𝐾
𝑊
𝑚∙𝐾
𝑊
𝑚∙𝐾
𝑘𝑔
𝑠
𝑘𝑔
𝑚∙𝑠
𝑚2
𝑠
𝑊
𝐾
𝑊
𝐾
𝑊
𝐾
𝑊
𝐾
𝑊
𝐾
𝑘𝑔
𝑚3
𝑚
𝑠
vii
𝑊
𝑚2 ∙𝐾
Acknowledgement
I would like to thank my family for their continuous support throughout my entire education. I
would also like to thank Dr. Gutierrez-Miravete and all my other professors at Rensselaer for
their help and guidance.
viii
Abstract
This study performs an analysis of ground coupled heat exchangers used to improve the
efficiency of heating, ventilation, and air conditioning (HVAC) systems. A ground coupled heat
exchanger can be used in either a heating or cooling mode by taking advantage of a “near
constant” ground temperature. The “near constant” ground temperature can be used as either a
heat sink to remove heat to cool a building, or as a heat source to heat a building.
Heat transfer analysis was performed for a single pass ground coupled heat exchanger that
utilizes an open and/or closed loop. The open and/or closed loop can use different fluids in the
system to optimize the ground coupled heat exchanger. Heat transfer analysis involved the use of
conservation of energy, the heat transfer rate equation, and the evaluation of the total thermal
resistance between the two fluids. Finite element modeling was also performed in COMSOL
Multiphysics to verify the results calculated based on the heat transfer analysis. Analysis of both
elementary heat exchanger analysis and finite element modeling were used to determine the
optimal ground coupled heat exchanger design.
ix
1. Introduction
1.1 Background
Through the use of a ground coupled heat exchanger (GCHE), the efficiency of heating,
ventilation, and air conditioning (HVAC) systems can be improved. A ground coupled heat
exchanger uses the “near constant” 12.77°C ground temperature of the Earth to heat/cool air or
other fluids. A ground coupled heat exchanger can be used in either a heating or cooling mode,
depending on the climate and season.
The ground temperature can vary significantly, depending on depth, geographical region, and
season. However, at approximately 5 m deep, the ground temperature is a “near constant”
12.77°C. Temperature variations at different depths depend on several variables such as soil
composition and water content, distance to the surface, depth and duration of snow cover, etc.
The main cause of variations at different depths close to the surface is the variation of heat
transfer to and from the surface by radiation, convection, conduction, etc; therefore, seasonal
ground temperature variations are expected. However, ground temperature becomes more
stabilized with depth. For the purpose of this analysis, the soil temperature at a depth of
approximately 5 m is assumed to be a constant 12.77°C and the soil temperature near the pipe is
not influenced by the pipe. The soil around the pipe is homogeneous and it has a constant
thermal conductivity.
The construction and operation of a ground coupled heat exchanger system can widely vary
depending on the use and system design. There are many different configurations that can be
used to make a ground coupled heat exchanger system. These systems can use open and closed
loops, different fluids, or any combination in the system all to optimize ground coupled heat
exchangers. The ground loops can be arranged in a vertical, horizontal, slinky ground loop, or
pond loop, as shown in Figure (1).
1
Figure 1: Ground Coupled Heat Exchanger Loops [1]
A vertical ground loop is used where there is little yard space, when surface rocks make digging
impractical, or when you want to disrupt the landscape as little as possible. Vertical holes are
bored in the ground, 150 to 450 feet deep, and a single loop of pipe with a U-bend at the bottom
is inserted before the hole is backfilled. Each vertical pipe is then connected to a horizontal
underground pipe that carries the air or fluid inside.
A horizontal ground loop is usually the most cost effective when trenches are easy to dig and the
size of the yard is adequate. Trenches are dug below the ground in which a series of pipes are
laid. Then, the air or fluid runs through the pipe to be heated or cooled.
A slinky ground loop is a variation on the horizontal loop. The horizontal slinky layout consists
of piping unrolled in overlapping circular loops that are laid flat in trenches of approximately the
same width as the coil diameters. In the vertical slinky layout, coils stand upright in narrow
trenches that are deep enough to accommodate the coil diameter and a sufficient overburden so
that the tops of the coils do not experience large seasonal temperature swings. Overall, slinky
systems require three to five times less land area than straight horizontal-loop systems.
A pond loop design may be the most economical when a home is near a body of water such as a
shallow pond or lake. The air or fluid circulates underwater through piping, just as it does
through ground loops. The pipes may be coiled in a slinky shape to fit more of it into a given
amount of space. Since the air or fluid does not directly interact with the pond, it results in no
adverse impacts on the aquatic system.
2
A closed loop ground coupled heat exchanger draws the already heated/cooled air from inside
the building and through a series of underground pipes to be heated/cooled before re-entering the
building.
An open loop ground coupled heat exchanger draws outside air, through a series of underground
pipes, into the building trying to be heated/cooled. An open loop system uses the “near constant”
temperature of the earth to heat/cool the outside air prior to it being admitted into the building.
An open loop system is naturally less efficient, in extreme climates, than a closed loop system
due to the need to heat/cool the air further before it reaches the required temperature.
A combination of both open and closed loop ground coupled heat exchangers can be utilized to
optimize a heating and cooling system and circulate more air.
Typically, a ground coupled heat exchanger system is constructed with smooth-walled pipe. It is
assumed that the pipe has a uniform internal and external diameter in the axial direction. The
diameter and material will vary depending on the designed heat transfer properties and
efficiency. Large diameter pipes allow for high flow with less energy. Small diameter pipes will
require more energy to move the same amount of fluid as the large pipe. A larger quantity of
small diameter pipes will be needed; therefore, they will provide more heat transfer due to the
increased pipe surface area.
Generally, air is not circulated through the underground pipes in a ground coupled heat
exchanger. This is due to the potential for mold and bacteria growth caused by condensate
formation in the pipes as a result of the heat transfer process. Typically, ethylene glycol (or other
similar fluid) is used in the underground portion of a ground coupled heat exchanger and it is
then passed through a secondary heat exchanger where air is drawn in to be heated or cooled to
the desired temperature by ethylene glycol.
1.2 Project Scope
The objective of this study is to analyze a ground coupled heat exchanger in a horizontal loop in
an effort to optimize an already efficient design. Analysis was performed for a single pass
ground coupled heat exchanger that utilizes an open and/or closed loop, and that uses different
fluids in the system all to optimize ground coupled heat exchangers. Calculations were
3
performed to determine the length of pipe required to achieve a specific outlet temperature based
on varying inlet and exterior temperatures. The pipe was located in a horizontal loop to take
advantage of the constant ground temperature. The ground coupled heat exchanger was
approximately 100% efficient for the purpose of this analysis. This is due to the fluid (air or
ethylene glycol) entering the pipe with a varying inlet temperature and exiting the pipe at the
temperature of the ethylene glycol or soil on the outside of the pipe, which is 12.77°C.
4
2. Theory/Methodology
This study used both an elementary heat exchanger analysis and finite element modeling to
determine the length of pipe required to achieve a specific outlet temperature based on varying
inlet and exterior temperatures. This analysis is based on a single pass heat exchanger with
approximately 100% efficiency.
The exterior temperature for this study varied, from approximately -3.145°C to 21.869°C, based
on a wide range of heating/cooling seasons. The inlet temperature to the heat exchanger also
varied depending on the type of heat exchanger being analyzed. For an open loop heat
exchanger, the inlet temperature varied as a function of the exterior temperature. For a closed
loop heat exchanger, the air was drawn into the heat exchanger from inside the building;
therefore, the inlet temperature only varied from approximately 9.93°C to 21.869°C.
For an open loop ground coupled heat exchanger, analysis was performed initially for air in a
single pass heat exchanger. Then, calculations were performed again for air but using a closed
loop ground coupled heat exchanger.
The analysis was then repeated for both an open loop and a closed loop heat exchanger through
the use of a different fluid (Ethylene Glycol). Ethylene glycol was used in a closed loop and then
circulated between the building and the ground through piping and then to the secondary heat
exchanger. Air was either drawn in from outside (open loop) or inside (closed loop) the building
and then was passed through a secondary heat exchanger to be heated/cooled by the Ethylene
Glycol. Table (1) below summarizes each case that will be looked at in this study.
Table 1: Summary of Cases Analyzed
Case
Case 1
Case 2
Case 3
Case 4
Case 5
Case 6
Study
Open Loop - Air
Closed Loop - Air
Open Loop - Air and Ethylene Glycol through a Secondary Heat Exchanger
Closed Loop - Air and Ethylene Glycol through a Secondary Heat Exchanger
Open Loop - Ethylene Glycol
Closed Loop - Ethylene Glycol
5
Figure
2
3
4
5
4
5
Figure 2: Sketch of Open Loop for Air
Figure 3: Sketch of Closed Loop for Air
Figure 4: Sketch of Open Loop for Air and Closed Loop for Ethylene Glycol
Figure 5 Sketch of Closed Loop for both Air and Ethylene Glycol
Heat transfer analysis involved the use of conservation of energy, the heat transfer rate equation,
and the evaluation of the total thermal resistance between either air and soil, ethylene glycol and
soil, or air and ethylene glycol. It is assumed that the convective flow inside the pipe is thermally
and hydro-dynamically developed.
The two more commonly used approaches to analyze heat transfer in a heat exchanger are the log
mean temperature difference (LMTD) method and the effectiveness-NTU (ε-NTU) method [2].
The LMTD method is typically used for design problems and ε-NTU method is typically used
6
for rating; however, either method can used to look at heat exchanger design or rating. In
analysis methods, LMTD and ε-NTU, the overall heat transfer coefficient is needed. For this
study, the LMTD method was used to determine the highest possible efficiency that the system
could provide and the necessary pipe length was determined to achieve the optimum output
temperature.
2.1 Elementary Heat Exchanger Analysis
The LMTD method was used to determine the highest possible efficiency that the system could
provide and the necessary pipe length was determined to achieve the optimum output
temperature [2].
For each specific case examined, for either air, ethylene glycol or both, the velocity, inlet
temperature, and heat source (i.e. soil or ethylene glycol) temperature are known. The mass flow
rate of a fluid flowing inside a pipe was calculated using Equation [1], based on the pipe size,
fluid properties, and fluid velocity.
𝒎̇ = 𝝆 ∙ 𝑽 ∙ 𝑨𝒊
[1]
Likewise, the Reynolds Number was calculated to determine if the flow in the pipe was laminar
or turbulent. Equation [2] was used to calculate the Reynolds Number.
𝟒∙𝒎̇
𝑹𝒆 = 𝝅∙𝝁∙𝑫
[2]
The friction factor, Nusselt Number, and the heat transfer coefficient were calculated using
Equation [3], Equation [4], and Equation [5], respectively.
𝒇 = √(𝟎. 𝟕𝟗 ∙ 𝒍𝒏(𝑹𝒆) − 𝟏. 𝟔𝟒)
7
[3]
𝑫
𝑳
𝟎.𝟖
(𝟎.𝟎𝟏𝟗∙(𝑹𝒆∙𝑷𝒓∙( ))
𝑵𝒖 = (𝟑. 𝟔𝟓𝟕 +
𝑫
𝑳
)
(𝟏+𝟎.𝟏𝟏𝟕∙(𝑹𝒆∙𝑷𝒓∙( ))
𝒉𝒄 = 𝒌𝒂 ∙
𝝁
𝟎.𝟒𝟔𝟕
)
𝟎.𝟏𝟒
) ∙ (𝝁 )
[4]
𝒘
𝑵𝒖
[5]
𝑫
Using the conservation of energy equation, the heat transfer rate was calculated using Equation
[6]. 𝑇𝑐,𝑖 is the inlet temperature of the fluid, which varies with the ground surface temperature.
𝑇𝑐,𝑜 is the outlet temperature of the fluid which is a constant 12.77°C.
𝑸̇ = 𝒎̇ ∙ 𝑪𝒑 ∙ (𝑻𝒄,𝒐 − 𝑻𝒄,𝒊 )
[6]
The overall heat transfer coefficient (U) was calculated using Equation [7] by dividing 1 by the
total thermal resistance.
𝟏
𝑼
= 𝑹𝑻𝒐𝒕𝒂𝒍
[7]
The analysis of the total thermal resistance for the ground coupled heat exchanger is as follows.
The total thermal resistance is the summation of the convective resistance in the fluid, Equation
[8], the conductive resistance of the pipe wall, Equation [9], and between the pipe and soil,
Equation [10].
𝟏
𝑹𝑪𝒐𝒏𝒗 = (𝟐∙𝝅∙𝒓
[8]
𝟏 ∙𝑳∙𝒉𝒄 )
𝟏
𝒓𝟏 +𝒓𝟐
𝑹𝑪𝒐𝒏𝒗𝑻𝒖𝒃𝒆 = (𝟐∙𝝅∙𝑳∙𝒌 ) ∙ 𝒍𝒏 (
𝑷
𝑹𝑪𝒐𝒏𝒗𝑻𝒖𝒃𝒆
⁄𝑺𝒐𝒊𝒍
𝟏
𝒓𝟏
= (𝟐∙𝝅∙𝑳∙𝒌 ) ∙ 𝒍𝒏 (
𝒔
)
𝒓𝟏 +𝒓𝟐 +𝒓𝟑
𝒓𝟏 +𝒓𝟐
[9]
)
[10]
The analysis of the total thermal resistance for the secondary heat exchanger is as follows. The
total thermal resistance is the summation of the convective resistance for air, Equation [11],
between the air and pipe, Equation [12], and between the pipe and ethylene glycol, Equation
[13].
8
𝟏
𝑹𝑪𝒐𝒏𝒗 = (𝟐∙𝝅∙𝒓
[11]
𝟏 ∙𝑳∙𝒉𝒂 )
𝟏
𝒓𝟏 +𝒓𝟐
𝑹𝑪𝒐𝒏𝒗𝑻𝒖𝒃𝒆 = (𝟐∙𝝅∙𝑳∙𝒌 ) ∙ 𝒍𝒏 (
𝑷
𝑹𝑪𝒐𝒏𝒗𝑬𝑮 = (𝟐∙𝝅∙𝒓
𝒓𝟏
)
𝟏
𝟏 ∙𝑳∙𝒉𝒆𝒈 )
[12]
[13]
The log mean temperature difference is calculated using Equation [14].
(∆𝑻𝟐 −∆𝑻𝟏 )
∆𝑻𝒍𝒎,𝒄𝒇 =
𝒍𝒏
∆𝑻𝟐
∆𝑻𝟏
[14]
where;
∆𝑻𝟏 = 𝑻𝒉,𝒊 − 𝑻𝒄,𝒊
[15]
∆𝑻𝟐 = 𝑻𝒉,𝒐 − 𝑻𝒄,𝒐
[16]
Based on the governing rate equation, Equation [17], the area pipe and therefore the length need
to achieve an outlet temperature of 12.77°C can be calculated using Equation [18] and Equation
[19].
𝑸̇ = 𝑼 ∙ 𝑨 ∙ 𝑭 ∙ ∆𝑻𝒍𝒎,𝒄𝒇
𝑸̇
𝑨 = (𝑼∙𝑭∙∆𝑻
𝒍𝒎,𝒄𝒇 )
𝐴
𝑳𝒑 = (𝟐∙𝝅∙𝑟)
9
[17]
[18]
[19]
2.2 Finite Element Modeling
The finite element modeling was performed using COMSOL Multiphysics. Laminar NonIsothermal Fluid Flow physics was chosen to best represent the ground coupled heat exchanger
being analyzed. The ground coupled heat exchanger was modeled as a fluid (air or ethylene
glycol) in a pipe surrounded by soil. The secondary heat exchanger was modeled as air in a pipe
surrounded by ethylene glycol. The cases were modeled as a 2-Dimensional axisymmetric
model, as shown below in Figure (6), with varying length based on the results of the elementary
heat exchanger analysis performed. As shown in Figure (6), a fine mesh consisting of 71,967
elements was used to obtain an accurate heat transfer representation.
Figure 6: COMSOL 2-Dimensional Model with Fine Mesh
10
3. Results
3.1 Assumptions
The models investigated in this study involved the following assumptions.

Steady state conditions.

The pipe has a uniform internal/external diameter in the axial direction.

The soil around the pipe is homogeneous and its thermal conductivity has a constant
value.

The soil temperature near the pipe is not influenced by the pipe; therefore the surface
temperature of the pipe is uniform in the axial direction.

The soil temperature is a constant 12.77°C.

The convective flow inside the pipe is thermally and hydro-dynamically developed.

The ground coupled heat exchanger is 100% efficient.
3.2 Elementary Heat Exchanger Analysis
The results of the elementary heat exchanger analysis performed used the highest possible
efficiency that the system could provide and the necessary pipe length was determined to achieve
the optimum output temperature. The input parameters for the elementary heat exchanger
analysis performed are shown below in Table (2).
Table 2: Input Parameters
𝑇ℎ,𝑖
𝑇𝑐,𝑖
𝑇𝑐,𝑜
d
D
Thickness (𝑟1.5)
𝑟𝑖 (𝑟1)
𝑟𝑜 (𝑟2 )
𝑟3
V_Air
V_EG
𝑘𝑝𝑖𝑝𝑒
𝑘𝑠𝑜𝑖𝑙
12.77
Various
12.77
25.4
0.0254
0.005
0.0127
0.0177
0.0381
1.0
0.01
44
1.65
11
°C
°C
°C
mm
m
m
m
m
m
m/s
m/s
W/(m K)
W/(m K)
The length of pipe required to achieve a preferred outlet temperature varied as a function of
the inlet temperate. Table (3), as shown below, contains the monthly mean surface
temperatures reported for Groton Connecticut [3].
Table 3: Mean Temperature Data of Groton, CT
Month
Mean
Temperature
°F
°C
26.5 -3.06
29.7 -1.28
36.6 2.56
47.3 8.50
57.4 14.11
66.5 19.17
71.9 22.17
70 21.11
62.4 16.89
51.1 10.61
42 5.56
31.8 -0.11
January
February
March
April
May
June
July
August
September
October
November
December
Mean Year
49.43
Temperature
9.69
After plotting Table (3) in Microsoft Excel, a 7th order polynomial was obtained based on
the LINEST function in Microsoft Excel. The 7th order polynomial, Equation [20], was used
to extrapolate the daily surface temperature for Groton, CT. The daily surface temperature
was used as a basis for the air inlet temperature, as shown below in Figure (7).
𝒚 = (−𝟏. 𝟒𝟐𝟒𝐄 − 𝟏𝟓 ∙ 𝒙𝟕 ) + (𝟏. 𝟒𝟕𝟕𝐄 − 𝟏𝟐 ∙ 𝒙𝟔 ) + (−𝟒. 𝟖𝟕𝟖𝐄 − 𝟏𝟎 ∙ 𝒙𝟓 ) + (𝟓. 𝟎𝟑𝟑𝐄 − 𝟎𝟖 ∙ 𝒙𝟒 ) +
(−𝟑. 𝟔𝟒𝟕𝐄 − 𝟎𝟔 ∙ 𝒙𝟑 ) + (𝟏. 𝟒𝟐𝟑𝐄 − 𝟎𝟑 ∙ 𝒙𝟐 ) + (−𝟏. 𝟕𝟖𝟗𝐄 − 𝟎𝟐 ∙ 𝒙𝟏 ) + (−𝟑. 𝟎𝟖𝟖 ∙ 𝒙𝟎 ) [20]
12
25.00
Temperature (°C)
20.00
15.00
10.00
5.00
0.00
-5.00
0
50
100
150
200
250
300
350
400
Day of the Year
Figure 7: Daily Surface Temperature (°C) for Groton, CT
Based on the input parameters provided in Table (2) and Table (3), and as shown below in
Table (4) and Table (5), the material properties of air and ethylene glycol vary with
temperature. Due to the density of the air and ethylene glycol varying with temperature, the
mass flow rate will also vary with temperature, see Equation [1]. However, the material
property variation for ethylene glycol is less than air due to a smaller temperature variation.
Table 4: Material Properties for Air
m_dot
Material Property
kg/s
Maximum
6.437E-04
Minimum
6.159E-04
Cp,air
J/(kg K)
1004.94
1005.32
ρ_air
kg/m^3
1.22
1.27
μ_air
kg/(m s)
1.738E-05
1.801E-05
ν_air
m^2/s
1.368E-05
1.482E-05
5.599E-01
5.828E-01
2.456E-02
2.556E-02
Pr_air
k_air
W/(m K)
13
Table 5: Material Properties for Ethylene Glycol
Material Property
m_dot
kg/s
Maximum
5.685E-03
Cp,fluid
J/(kg K)
2351.73
2349.07
ρ,fluid
kg/m^3
1121.87
1121.45
μ,fluid
kg/(m s)
2.256E-02
2.217E-02
ν,fluid
m^2/s
2.011E-05
1.977E-05
214.68
211.04
2.471E-01
2.468E-01
Pr,fluid
k,fluid
W/(m K)
Minimum
5.682E-03
Elementary heat exchanger analysis was performed for a single pass ground coupled heat
exchanger that utilizes an open and/or closed loop. Analysis was performed initially for air
in an open loop single pass heat exchanger. Then, calculations were performed again for air
but using a closed loop single pass heat exchanger. The analysis was then repeated for both
an open loop and a closed loop heat exchanger through the use of a different fluid (Ethylene
Glycol). Ethylene glycol was used in a closed loop and then circulated between the building
and the ground through piping and then to the secondary heat exchanger. Air was either
drawn in from outside (open loop) or inside (closed loop) the building and then was passed
through a secondary heat exchanger to be heated/cooled by the Ethylene Glycol.
14
3.2.1 Open and Closed Loop – Air
3.2.1.1 Open Loop – Air
The Open Loop Ground Coupled Heat Exchanger draws outside air underground to be heated or
cooled, depending on the surface temperature, to a temperature of 12.77°C. Figure (8) below
shows the length of pipe required to achieve an outlet temperature of 12.77°C for varying inlet
temperatures from -3.145°C to 21.869°C. Based on the inlet temperature variation of Groton
Connecticut, the longest length of pipe required to achieve an air outlet temperature of 12.77°C
is approximately 13.098 meters.
14.000
Pipe Length (m)
12.000
10.000
8.000
6.000
4.000
2.000
0.000
-5.00
0.00
5.00
10.00
15.00
20.00
25.00
Temperature (°C)
Figure 8: Open Loop – Air; Maximum Required Pipe Length (m): 13.098
15
3.2.1.2 Closed Loop – Air
The Closed Loop Ground Coupled Heat Exchanger draws air from inside the house through
underground pipes to be heated/cooled, depending on the surface temperature, to a temperature
of 12.77°C. Figure (9) below shows the length of pipe required to achieve an outlet temperature
of 12.77°C for varying inlet temperatures. The interior temperature of a building changes
depending on personal preference; however, based on temperatures seen in my home, the inlet
air temperature for a closed loop system will vary from approximately 9.93°C to 21.869°C.
Based on the inlet temperature variation from 9.93°C to 21.869°C, the longest length of pipe
required achieve an air outlet temperature of 12.77°C is approximately 10.80 meters.
12.000
Pipe Length (m)
10.000
8.000
6.000
4.000
2.000
0.000
0.00
5.00
10.00
15.00
20.00
25.00
Temperature (°C)
Figure 9: Closed Loop – Air; Maximum Required Pipe Length (m): 10.80
16
3.2.2 Open and Closed Loop – Ethylene Glycol
3.2.2.1 Open Loop – Ethylene Glycol
The Open Loop Ground Coupled Heat Exchanger circulates Ethylene Glycol through
underground pipes to be heated/cooled to a temperature of 12.77°C. The ethylene glycol then
enters a secondary heat exchanger to heat/cool air. The heat transfer in the secondary heat
exchanger is now investigated as the air is drawn in to be heated or cooled by ethylene glycol,
depending on surface temperature, to a temperature of 12.77°C. Figure (10) below shows the
length of pipe required to achieve an air outlet temperature of 12.77°C for varying inlet
temperatures. Based on the air inlet temperature variation of Groton, Connecticut ranging from
-3.145°C to 21.869°C and an inlet temperature of 12.77°C for Ethylene Glycol, the longest
length of pipe required to achieve an air outlet temperature of 12.77°C is approximately 14.621
meters.
16.000
14.000
Pipe Length (m)
12.000
10.000
8.000
6.000
4.000
2.000
0.000
-5.00
0.00
5.00
10.00
15.00
20.00
25.00
Temperature (°C)
Figure 10: Open Loop – Air in Secondary Heat Exchanger; Maximum Required Pipe Length (m): 14.621
17
Due to the heat transfer process of the air acting on Ethylene Glycol in the secondary heat
exchanger and the thermal properties of Ethylene Glycol, the outlet temperature for Ethylene
Glycol will vary from 12.008°C to 13.197°C. This is based on air entering the secondary heat
exchanger with a temperature variation from -3.145°C to 21.869°C. After the Ethylene Glycol
exits the secondary heat exchanger, the fluid will then be circulated through underground pipes,
at which time it will either be heated or cooled back to 12.77°C. The heat transfer analysis for the
ethylene glycol is now analyzed as the Ethylene Glycol will need to travel through an
underground pipe that is approximately 54.374 meters long to achieve an outlet temperature of
12.77°C, as shown in Figure (11).
60.000
Pipe Length (m)
50.000
40.000
30.000
20.000
10.000
0.000
11.80
12.00
12.20
12.40
12.60
12.80
13.00
13.20
13.40
Temperature (°C)
Figure 11: Open Loop – Ethylene Glycol; Maximum Required Pipe Length (m): 54.374
18
3.2.2.2 Closed Loop – Ethylene Glycol
The Closed Loop Ground Coupled Heat Exchanger circulates Ethylene Glycol through
underground pipes to be heated/cooled and then into a secondary heat exchanger to heat/cool the
air. The heat transfer in the secondary heat exchanger is now investigated as the air is drawn in to
be heated or cooled by ethylene glycol, depending on temperature, to a temperature of 12.77°C.
Figure (12) below shows the length of pipe required to achieve an air outlet temperature of
12.77°C for varying inlet temperatures. The interior temperature of homes changes depending on
personal preference; however, based on temperatures seen in my home, the inlet air temperature
for a closed loop system will vary from approximately 9.93°C to 21.869°C. Based on the inlet
temperature variation from 9.93°C to 21.869°C and an inlet temperature of 12.77°C for Ethylene
Glycol, the longest length of pipe required to achieve an air outlet temperature of 12.77°C is
approximately 12.034 meters.
14.000
Pipe Length (m)
12.000
10.000
8.000
6.000
4.000
2.000
0.000
0.00
5.00
10.00
15.00
20.00
25.00
Temperature (°C)
Figure 12: Closed Loop – Air in Secondary Heat Exchanger; Maximum Required Pipe Length (m): 12.167
19
Due to the heat transfer process of the air acting on Ethylene Glycol in the secondary heat
exchanger, and the thermal properties of Ethylene Glycol, the outlet temperature for Ethylene
Glycol will vary from 12.645°C to 13.197°C. This is based on air entering the secondary heat
exchanger, which is drawn in from inside the building, with a temperature variation from 9.93°C
to 21.869°C. After the Ethylene Glycol exits the secondary heat exchanger, the fluid will then be
circulated through underground pipes, at which time it will either be heated or cooled back to
12.77°C. The heat transfer analysis for the ethylene glycol is now analyzed as the Ethylene
Glycol will need to travel through an underground pipe that is approximately 51.009 meters long
to achieve an outlet temperature of 12.77°C, as shown in Figure (13).
60.000
Pipe Length (m)
50.000
40.000
30.000
20.000
10.000
0.000
12.60
12.70
12.80
12.90
13.00
13.10
13.20
13.30
Temperature (°C)
Figure 13: Closed Loop – Ethylene Glycol; Maximum Required Pipe Length (m): 51.009
20
3.3 Finite Element Modeling
Finite element modeling was performed at two different temperatures for air and at the most
extreme case for ethylene glycol. Analysis was performed at -3.145 and 21.869°C for air. The
specific temperatures above were used since they are the largest value that was seen for the open
and closed loops, respectively. Similar analysis was performed for the most extreme case of
ethylene glycol at 12.008°C.
3.3.1 Open and Closed Loop – Air
For the first case examined, the inlet temperature for air was specified to be -3.145°C. Figure
(14) below is a plot of temperature vs. distance for air at -3.145°C in an open loop. Figure (14)
shows the effect of the constant soil temperature on the cooler air temperature along the length of
pipe. As the temperature of the air approaches the constant soil temperature, the heat transfer
starts to slow down. At the outlet of the 13.098 meter pipe, the temperature of the air is
12.7671°C.
Figure 14: 13.098m Pipe; Air Inlet -3.145°C, Air Outlet 12.7671°C
21
The second case had an air inlet temperature of 21.869°C. Figure (15) below is a plot of
temperature vs. distance for air at 21.869°C in a closed loop. Figure (15) shows the effect of the
constant soil temperature on the hotter air temperature along the length of pipe. As the
temperature of the air approaches the constant soil temperature, the heat transfer starts to slow
down. At the outlet of the 10.80 meter pipe, the temperature of the air is 12.7909°C.
Figure 15: 10.80m Pipe; Air Inlet 21.869°C, Air Outlet 12.7909°C
22
3.3.2
Open and Closed Loop – Ethylene Glycol and Air
The secondary heat exchanger was examined to determine the length of pipe required to achieve
an outlet temperature for air of 12.77°C, based on the heat transfer between air and ethylene
glycol. The first case looked at; the inlet temperature for air was specified to be -3.145°C. Figure
(16) below is a plot of temperature vs. distance for air at -3.145°C in an open loop through the
secondary heat exchanger. Figure (16) shows the effect of ethylene glycol on the cooler air
temperature along the length of pipe in the secondary heat exchanger. As the temperature of the
air approaches the temperature of ethylene glycol, which is initially 12.77°C the heat transfer
starts to slow down. At the outlet of the 14.621 meter pipe, the temperature of the air is
12.7755°C.
Figure 16: 14.621m Pipe; Air Inlet -3.145°C, Air Outlet 12.7755°C
23
The second case had an air inlet temperature of 21.869°C. Figure (17) below is a plot of
temperature vs. distance for air at 21.869°C in a closed loop through the secondary heat
exchanger. Figure (17) shows the effect of ethylene glycol on the hotter air temperature along the
length of pipe in the secondary heat exchanger. As the temperature of the air approaches the
temperature of ethylene glycol, which is initially 12.77°C, the heat transfer starts to slow down.
At the outlet of the 12.034 meter pipe, the temperature of the air is 12.7812°C.
Figure 17: 12.034m Pipe; Air Inlet 21.869°C, Air Outlet 12.7812°C
24
3.3.3 Open and Closed Loop – Ethylene Glycol
Based on the temperature of ethylene glycol changing after passing through the secondary heat
exchanger, the temperature of ethylene glycol needed to be returned to 12.77°C. This is
accomplished by passing the ethylene glycol through underground pipes. From the elementary
heat exchanger analysis performed above, for air in an open loop passing through the secondary
heat exchanger, the outlet temperature for ethylene glycol was 12.008°C. Therefore, the
underground pipe inlet temperature for ethylene glycol was specified to be 12.008°C. Also,
based on the elementary heat exchanger analysis, 54.374 meters of underground pipe is required
to heat ethylene glycol from 12.008°C to 12.77°C.
Due to the large amount of computing power required to perform a simulation in COMSOL
Multiphysics for a 54.347 meter pipe, the length of pipe analyzed needed to be made shorter. The
pipe was shortened to 10 meters.
Figure (18) below is a plot of temperature vs. distance for ethylene glycol at 12.008°C in a 10
meter pipe. Figure (18) shows the effect of the constant soil temperature on the cooler ethylene
glycol temperature along the length of pipe. As the temperature of the air approaches the
constant soil temperature, the heat transfer starts to slow down significantly. At the outlet of the
10 meter pipe, the temperature of the ethylene glycol is 12.6815°C.
25
Figure 18: 10.0m Pipe; Ethylene Glycol Inlet 12.008°C, Ethylene Glycol Outlet 12.6815°C
A calculation was performed, independent from the elementary heat exchanger analysis
performed above, to verify the results of the COMSOL Multiphysics model for ethylene glycol
at 12.008°C in a 10 meter pipe. In the calculation, it was assumed that there was no thermal
resistance from the pipe wall or the soil, as well as a constant heat transfer coefficient for the
inner wall of the pipe.
𝑇𝑒 = 𝑇𝑖 +
(ℎ𝑒𝑔 ∙(𝑇𝑤 −𝑇𝑖 ))∙2∙∆𝑥
𝜌∙𝑟1 ∙𝑉∙𝐶𝑝
26
[21]
The calculation uses Equation [21] and values obtained from the COMSOL Multiphysics model
for ethylene glycol at 12.008°C in a 10 meter pipe to obtain a temperature at a distance along the
pipe. At 10 meters, the temperature of ethylene glycol is 12.7067°C, as shown below in Figure
(19). A significant portion of the heat transfer process takes place in the first 10 meters of the
pipe. As shown below in Figure (20), after the first 10 meters, the change in temperature starts to
slow down significantly. This is due to the difference between 𝑇𝑤 and 𝑇𝑖 Equation [21]. As
𝑇𝑖 starts to approach 𝑇𝑤 , each temperature increase becomes smaller. At 54.347 meters, the
temperature is 12.7777°C. The results from this calculation are slightly different than the results
obtained from both the elementary heat exchanger analysis and finite element modeling due to
the initial assumptions that there was no thermal resistance from the pipe wall or the soil, as well
as a constant heat transfer coefficient for the inner wall of the pipe. Based on the temperature vs.
pipe length trend, shown in Figure (19), this calculation validates both the elementary heat
exchanger analysis and the finite element modeling performed for ethylene glycol.
12.8
Temperature (°C)
12.7
12.6
12.5
12.4
12.3
12.2
12.1
12
0
2
4
6
8
Pipe Length (m)
Figure 19: Ethylene Glycol Calculation Validation: 10m pipe, 12.008°C
27
10
12.80000
Temperature (°C)
12.70000
12.60000
12.50000
12.40000
12.30000
12.20000
12.10000
12.00000
0
5
10
15
20
25
30
35
40
45
50
55
Pipe Length (m)
Figure 20: Ethylene Glycol Calculation Validation: 54.374m pipe, 12.008°C
28
4. Conclusion
The goal of this project was to perform an analysis of ground coupled heat exchangers used to
improve the efficiency of HVAC systems. This study used both an elementary heat exchanger
analysis and finite element modeling to determine the length of pipe required to achieve a
specific outlet temperature based on varying inlet and exterior temperatures. This analysis was
based on a single pass heat exchanger with approximately 100% efficiency.
The elementary heat exchanger analysis was performed using the log mean temperature
difference (LMTD) method. The finite element modeling was performed using COMSOL
Multiphysics. For both the elementary heat exchanger analysis and finite element modeling, a
complete analysis of a single pass ground coupled heat exchanger with an open and/or closed
loop which utilizes different fluids in the system. Analysis was performed to determine the
optimal ground coupled heat exchanger design.
Table 6: Maximum Pipe Length Required (m)
Loop
Open
Closed
Air
13.098
10.800
Ethylene Glycol/Air
14.621
12.034
Ethylene Glycol
54.374
51.009
Table (6) shows the summary of the results obtained from the elementary heat exchanger
analysis. Based on the results of the elementary heat exchanger analysis and validated by the
finite element modeling performed, a closed loop ground coupled heat exchanger with air is the
optimum ground coupled heat exchanger design. A closed loop ground coupled heat exchanger is
the simplest design analyzed in this study. A closed loop ground coupled heat exchanger draws
already heated/cooled air from inside the building and through underground pipes to be
heated/cooled. Using air, the closed ground coupled heat exchanger will achieved the required
outlet temperature of 12.77°C by utilizing only 10.80 meters of underground pipe.
However, due to the potential for mold and bacteria growth when air is circulated through
underground pipes in a ground coupled heat exchanger. The more realistic option for a ground
coupled heat exchanger is a closed loop ground coupled heat exchanger with ethylene glycol in
the underground pipes and air in the secondary heat exchanger.
29
The closed ground coupled heat exchanger circulates ethylene glycol through underground pipes
to be heated/cooled and then into a secondary heat exchanger to heat/cool the air. The air was
drawn into the secondary heat exchanger from inside the building has a temperature variation
from 9.93°C to 21.869°C. The ethylene glycol enters the secondary heat exchanger at a
temperature of 12.77°C. Based on inlet temperature of air and ethylene glycol, the air will
achieved the required air outlet temperature of 12.77°C in 12.034 meters of pipe. The ethylene
glycol will exit the secondary heat exchanger at a temperature ranging from 12.645°C to
13.197°C. The Ethylene Glycol will need to travel through an underground pipe that is
approximately 51.009 meters long to achieve an outlet temperature of 12.77°C. A 51.009 meter
pipe may be the ideal pipe length to achieve an outlet temperature of 12.77°C; however, it may
be excessive to increase the pipe to such an extreme just to get a slight increase in temperature.
30
References
1. http://greeningthemachine.blogspot.com/ (09/20/11)
2. Deborah A. Kaminski, Michael K. Jensen, Introduction to Thermodynamic and Fluids
Engineering, Wiley, 2005
3. http://www.usa.com/groton-ct-weather.htm#HistoricalTemperature (09/20/2011)
Bibliography
A. Benazza, E. Blanco, M. Aichouba, José Luis Río, S. Laouedj, “Numerical Investigation of
Horizontal Ground Coupled Heat Exchanger”, Energy Procedia, Volume 6, 2011, Pages 29-35
Angelo Zarrella, Massimiliano Scarpa, Michele De Carli, “Short time step analysis of vertical
ground-coupled heat exchangers: The approach of CaRM”, Renewable Energy, Volume 36,
Issue 9, September 2011, Pages 2357-2367
Fabrizio Ascione, Laura Bellia, Francesco Minichiello, “Earth-to-air heat exchangers for Italian
climates”, Renewable Energy, Volume 36, Issue 8, August 2011, Pages 2177-2188
James R. Cullin, Jeffrey D. Spitler, “A computationally efficient hybrid time step methodology
for simulation of ground heat exchangers”, Geothermics, Volume 40, Issue 2, June 2011, Pages
144-156
Michael J. Moran, Howard N. Shapiro, Fundamentals of Engineering Thermodynamics, Wiley,
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Ping Cui, Xin Li, Yi Man, Zhaohong Fang, “Heat transfer analysis of pile geothermal heat
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31
Appendices
Appendix 1: Open Loop Elementary Heat Exchanger Analysis for Air
See Excel Document “Final Project Calculation"
Appendix 2: Closed Loop Elementary Heat Exchanger Analysis for Air
See Excel Document “Final Project Calculation"
Appendix 3: Open Loop Elementary Heat Exchanger Analysis for Air &
Ethylene Glycol
See Excel Document “Final Project Calculation"
Appendix 4: Closed Loop Elementary Heat Exchanger Analysis for Air &
Ethylene Glycol
See Excel Document “Final Project Calculation"
Appendix 5: Open Loop Elementary Heat Exchanger Analysis for Ethylene
Glycol
See Excel Document “Final Project Calculation"
Appendix 6: Closed Loop Elementary Heat Exchanger Analysis for Ethylene
Glycol
See Excel Document “Final Project Calculation"
Appendix 7: Validation Calculation for Ethylene Glycol
See Excel Document “Final Project Calculation"
32