Ground Coupled Heat Exchanger Design and Analysis for a
Connecticut Residential Home
by
Mark Scarzella
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, 2012
i
© Copyright 2012
by
Mark Scarzella
All Rights Reserved
ii
CONTENTS
List of Tables ..................................................................................................................... v
List of Figures ................................................................................................................... vi
List of Symbols ................................................................................................................ vii
List of Keywords ............................................................................................................... x
Acknowledgement ............................................................................................................ xi
Abstract ............................................................................................................................ xii
1. Introduction.................................................................................................................. 1
1.1
Background ........................................................................................................ 1
1.2
Project Scope...................................................................................................... 3
2. Theory/Methodology ................................................................................................... 4
2.1
Design Parameters .............................................................................................. 4
2.2
ASHRAE Space Cooling and Heating Load Analysis ....................................... 8
2.3
2.2.1
Sensible Heating and Cooling Space Loads .......................................... 8
2.2.2
Loads Associated with Infiltration and Ventilation Losses ................. 10
2.2.3
Latent Cooling Loads ........................................................................... 12
2.2.4
Total Heating and Cooling Loads ........................................................ 12
GCHX Analysis ............................................................................................... 12
2.3.1
Ground Temperature Calculation ......................................................... 12
2.3.2
Heat Transfer of the GCHX ................................................................. 13
3. Results........................................................................................................................ 16
3.1
Space Cooling and Heating Load Results ........................................................ 16
3.1.1
Assumptions and Input Parameters ...................................................... 16
3.1.2
Opaque Surface Loads ......................................................................... 18
3.1.3
Window Loads ..................................................................................... 18
3.1.4
Infiltration and Ventilation Loads ........................................................ 20
3.1.5
Latent Loads ......................................................................................... 21
iii
3.1.6
3.2
Load Summary ..................................................................................... 21
GCHX Results.................................................................................................. 22
4. Conclusions................................................................................................................ 33
5. References.................................................................................................................. 35
6. Appendices ................................................................................................................ 37
iv
List of Tables
Table 1: Conceptual Home Construction Assumptions..................................................... 6
Table 2: Indoor and Outdoor Design Conditions .............................................................. 7
Table 3: Polyethylene Pipe Dimensions ............................................................................ 7
Table 4: House Component Quantity Dimensions and Total Area ................................. 16
Table 5: Design Temperatures, ºF ................................................................................... 16
Table 6: Thermal Resistance Values for Construction Components, (hr·ft2·ºF/Btu) ...... 17
Table 7: Overall Component Heat Transfer Coefficients, (Btu/hr·ft2·ºF)....................... 18
Table 8: Dimensionless Opaque Surface Factors for Cooling......................................... 18
Table 9: Opaque surface HFs, CFs and Associated Sensible Loads ............................... 18
Table 10: Window Cooling Factor Input Parameters ...................................................... 19
Table 11: Calculated Window Cooling Factor Parameters ............................................. 19
Table 12: Window HFs, CFs and Associated Sensible Loads ......................................... 20
Table 13: Infiltration and Ventilation Input Parameters and Calculated Flow Rates ...... 20
Table 14: Infiltration, Ventilation and Distribution Loss Sensible Loads, Btu/hr........... 21
Table 15: Humidity Ratios and Latent Loads .................................................................. 21
Table 16: Summary of Total Loads, Btu/hr ..................................................................... 21
Table 17: Propylene Glycol, DOWFROST HD .............................................................. 24
Table 18: GCHX Volumetric Flow Rates, gpm .............................................................. 25
Table 19: Summary of Pipe Lengths at 10ft Soil Depth ................................................. 32
v
List of Figures
Figure 1: Horizontal Closed Loop Configuration [1] ........................................................ 2
Figure 2: GHP Components and Operation [2] ................................................................. 3
Figure 3: Conceptual Home Schematic [4] ....................................................................... 5
Figure 4: Monthly Average Temperatures and Mean Surface Temperature ................... 23
Figure 5: Maximum and Minimum Soil Temperature at Various Depths ....................... 23
Figure 6: Reynolds Numbers for Cooling Inlet Fluid Temperatures ............................... 26
Figure 7: Reynolds Numbers for Heating Inlet Fluid Temperatures .............................. 26
Figure 8: Total Thermal Resistance of 0.75NPS and 1NPS for Cooling ........................ 27
Figure 9: Total Thermal Resistance of 0.75NPS and 1NPS for Heating......................... 27
Figure 10: GCHX Outlet Fluid Temperatures for Cooling Conditions ........................... 28
Figure 11: GCHX Outlet Fluid Temperatures for Heating Conditions ........................... 28
Figure 12: Heat Exchange Rate at Various Depths ......................................................... 29
Figure 13: GCHX Pipe Length at Various Depths (Tw,c,i @ 90ºF) ................................. 30
Figure 14: GCHX Pipe Length at Various Depths (Tw,h,i @ 30ºF) ................................. 30
vi
List of Symbols
Aes
Total Exposed Surface Area of Home (ft2)
Aul
Unit Leakage Rate (in2/ft2)
As,tot
Total Square Area of Home (ft2)
Ac
Area of Component (ft2)
CF
Cooling Factor (Btu/hr·ft2)
Cp,w
Specific Heat of Fluid (Btu/lb·ºF)
Doh
Depth of Roof Overhang (ft)
Di
Inner Diameter of Pipe (ft)
Do
Outer Diameter of Pipe (ft)
Ed
Diffuse Rate (Btu/hr·ft2)
ED
Direct Irradiance Diffuse Rate (Btu/hr·ft2)
Fo
Fourier Number
Fshd
Shading Factor
HF
Heating Factor (Btu/hr·ft2)
h
Window Height (ft)
ℎ̅𝑖
Average Internal Fluid Convective Heat Transfer Coefficient (Btu/hr·ft2·ºF)
IAC
Interior Attenuation Coefficient
kw
Thermal Conductivity of Fluid (Btu/hr·ft2·ºF)
kp
Thermal Conductivity of Piping (Btu/hr·ft2·ºF)
ks
Thermal Conductivity of Soil (Btu/hr·ft2·ºF)
Lc
Length of Piping, Cooling (ft)
Lh
Length of Piping, Heating (ft)
𝑚̇𝑐
Mass Flow Rate of Fluid, Cooling (lbm/hr)
𝑚̇ℎ
Mass Flow Rate of Fluid, Heating (lbm/hr)
Nbr
Total Number of Bedrooms in Home
PXI
Peak Exterior Irradiance
Qi,h
Air Infiltration Flow Rate, heating (cfm)
Qi,c
Air Infiltration Flow Rate, Cooling (cfm)
vii
Qv
Required Fresh Air Ventilation Flow Rate (cfm)
Qw,c
Flow Rate of Fluid, Cooling (gpm)
Qw,h
Flow Rate of Fluid, Heating (gpm)
ql,tot
Total Latent Cooling Load (Btu/hr)
ql,iv
Infiltration Ventilation Latent Load (Btu/hr)
ql,tot
Total Latent Cooling Load (Btu/hr)
qs,h
Sensible Heat Load (Btu/hr)
qs,iv,h
Sensible Infiltration Ventilation Heat Load (Btu/hr)
qs,iv,c
Sensible Infiltration Ventilation Cooling Load (Btu/hr)
qs,dl,h
Sensible Distribution Loss Heating Load (Btu/hr)
qs,dl,c
Sensible Distribution Loss Cooling Load (Btu/hr)
qs,g
Sensible Heat Gain (Btu/hr)
ql,g
Latent Heat Gain (Btu/hr)
qh,tot
Total Heating Space Load (Btu/hr)
qc,tot
Total Cooling Space Load (Btu/hr)
qʹgchx,c
GCHX Heat Exchange Rate, Cooling (Btu/hr·ft)
qʹgchx,h
GCHX Heat Exchange Rate, Heating (Btu/hr·ft)
Re
Reynolds Number
Rside
Thermal Resistance of House Exterior Siding (hr·ft2·ºF/Btu)
Rw,ply
Thermal Resistance of Wall Plywood (hr·ft2·ºF/Btu)
Rgb
Thermal Resistance of Gypsum Board/Sheetrock (hr·ft2·ºF/Btu)
Rw,ins
Thermal Resistance of Wall Insulation (hr·ft2·ºF/Btu)
Rwind
Thermal Resistance of Glazed Window (hr·ft2·ºF/Btu)
Rw,stud
Thermal Resistance of Wall Stud (hr·ft2·ºF/Btu)
Rr,ply
Thermal Resistance of Roof Plywood (hr·ft2·ºF/Btu)
Rr,ins
Thermal Resistance of Roof Insulation (hr·ft2·ºF/Btu)
Rr,shing
Thermal Resistance of Roof Shingles (hr·ft2·ºF/Btu)
Rcarp
Thermal Resistance of Carpet (hr·ft2·ºF/Btu)
Rdoor
Thermal Resistance of House Exterior Door (hr·ft2·ºF/Btu)
Rʹconv
Thermal Convective Resistance of Fluid (hr·ft·ºF/Btu)
viii
Rʹcond
Thermal Conductive Resistance of Pipe (hr·ft·ºF/Btu)
Rʹsoil
Thermal Resistance of Soil (hr·ft·ºF/Btu)
Rʹtot
Total Thermal Resistance of GCHX (hr·ft·ºF/Btu)
SHGC
Solar Heat Gain Coefficient
SLF
Shade Line Factor
Tc,id
Dry Bulb Cooling Indoor Temperature (ºF)
Tc,od
Dry Bulb Cooling Outdoor Temperature (ºF)
Th,id
Dry Bulb Heating Indoor Temperature (ºF)
Th,od
Dry Bulb Heating Outdoor Temperature (ºF)
Tw,c,o
Fluid GCHX Outlet Temperature, Cooling (ºF)
Tw,c,i
Fluid GCHX Inlet Temperature, Cooling (ºF)
Tw,h,o
Fluid GCHX Outlet Temperature, Heating (ºF)
Tw,h,i
Fluid GCHX Inlet Temperature, Heating (ºF)
Ts,min
Minimum (winter) Soil Temperature (ºF)
Ts,max
Maximum (summer) Soil Temperature (ºF)
Tmean
Air Average Surface Temperature (ºF)
Tamp
Amplitude of Air Average Surface Temperature
Tx
Exterior Screen Window Attachment Transmission Factor
U
Overall Heat Transfer Coefficient (Btu/hr·ft2·ºF)
αs
Thermal Diffusivity of Soil (ft2/day)
μw
Dynamic Viscosity of Fluid (lb/ft·hr)
ρw
Density of Fluid (lb/gal)
τ
Total Operation Time of GHP (days)
φc,od
Outdoor Humidity Ratio, Cooling (lb/lb)
φh,id
Indoor Humidity Ratio, Cooling (lb/lb)
ix
List of Keywords
DB
Dry Bulb
DR
Daily Range
GCHX
Ground Coupled Heat Exchanger
GHP
Geothermal Heat Pump
MCWB
Mean Coincident Wet Bulb
x
Acknowledgement
I would like to thank all of my family and friends for their support throughout my entire
education. I would also like to thank Professor Ernesto Gutierrez for his guidance and
support throughout the project.
xi
Abstract
The design of a ground coupled heat exchanger for a geothermal heat pump system is
fairly complex as it must take into account the thermal properties and temperatures of
the soil as well as the thermal loads of the conditioned space for which it is being
implemented. This study executed a comprehensive analysis to design a horizontal
ground coupled heat exchanger based on calculated heating and cooling loads for
conceptual residential home in Oxford, Connecticut.
More specifically, this study
examined the effects pipe installation depth and geothermal heat pump inlet water
temperature variations on heat exchanger piping length and heat transfer rate. The
analysis assumed the home utilizes a water-to-air geothermal heat pump system.
The results of the study showed the loads which are required for the ground coupled heat
exchanger in the winter are significantly higher than those of the summer. It was
observed that the assumptions associated with the construction of the house as well as
the mean seasonal temperatures for the area played a major role in the calculation of the
overall loads. Through the GCHX heat transfer calculations it was shown horizontal
pipe configurations have a significant disadvantage in heating dominated environments.
It was determined large pipe lengths would be needed to accommodate the large winter
heating loads for the home.
xii
1. Introduction
1.1 Background
A geothermal heat pump (GHP) utilizes the earth as a heat exchanging medium for both
residential and commercial heating and cooling applications. Water or an antifreeze
solution is typically pumped through a series of pipes to exchange or absorb heat from
the ground. Compared to traditional HVAC heat pumps, geothermal heat pumps achieve
a higher operational efficiency, as they are less susceptible to the extreme temperature
fluctuations in the heat exchanging environment throughout the year. According to the
American Society of Heating, Refrigerating and Air Conditioning Engineers (ASHRAE)
Handbook of Fundamentals 2007 [1] at depths between 30 and 40ft the ground is
relatively insensitive to the sun thermal fluxes, temperature changes of the air and
rainfalls.
As a result, the soil yearly mean temperature is relatively constant or
experiences only small temperature fluctuations at these depths.
A typical GHP uses a ground coupled heat exchanger (GCHX) to exchange heat between
the ground and a refrigerant within the heat pump unit. The GCHX is a closed network
of pipes which can be looped either vertically or horizontally in the ground. Spiral or
slinky type pipe configurations are also used when space is limited and installation of
vertical loops is not practical.
Vertical loop configurations are preferred in applications where there is very limited
yard space or where the terrain is rather rocky making wide spread ground excavation
difficult.
According to ASHRAE [1] installation involves drilling bore holes 100-
450feet in depth and inserting pipe with U-tube bends at the ends. The vertical pipe
loops are connected to horizontal pipe headers leading into the GHP unit. A grouting
material is then used to backfill the bore holes. This ensures sufficient sealing and
allows more efficient heat transfer between the piping, bore hole and the soil.
Horizontal loop configurations consist of a single or series of closed loop U-tube pipes.
They are placed in trenches at depths between 3 and 10ft and commonly take the
1
configurations shown in Figure 1. Horizontal ground loops have several advantages
over vertical loops, for instance, they are usually less expensive to install as they do not
require special drilling rigs. A simple backhoe or construction vehicles can perform the
excavation.
There is also no potential for aquifer contamination because of the
shallower depth of the trench. However, there are some limitations. Horizontal ground
loops usually require sufficient land for installation, usually for an average house it’s
about 0.5acre. This makes theses systems less feasible in urban areas. In addition,
because of the shallower depth, they are more susceptible to ground soil temperature
fluctuations, which is highly dependent on the soil type and moisture content.
Figure 1: Horizontal Closed Loop Configuration [1]
The GHP unit itself runs on a vapor-compression refrigerant cycle and is merely an air
conditioner with a reversing valve. The reversing valve changes the direction of flow of
the refrigerant allowing the condenser and evaporator to reverse roles in the winter. For
water-to-air GHP systems the ventilation air coil acts as the evaporator in cooling modes
of operation and as the condenser in heating modes of operation. A coaxial fined tube
heat exchanger is typically used to exchange heat between the refrigerant and the GCHX
water/coolant. In cooling modes of operation the coaxial heat exchanger acts as the
condenser and in heating modes of operation it acts as the evaporator. Figure 2 provides
a detailed schematic of a water-air-geothermal heat pump system with the previously
described components.
2
Figure 2: GHP Components and Operation [2]
1.2 Project Scope
The objective of this study was to execute a comprehensive analysis to aid in the design
of a GCHX for a conceptual residential home in Oxford, Connecticut utilizing water-toair GHP. Although there are several GCHX pipe configurations, this study focused
solely on the analysis of a horizontal pipe configuration. Initially, this study performed a
series of heat transfer calculations to determine necessary heating (winter) and cooling
(summer) loads for the conceptual residence. These calculations considered the yearly
environment temperature conditions at Oxford, CT. The heating and cooling loads were
then used to calculate required flow rates and water/coolant temperatures for the GHP.
More specifically, a heat transfer analysis was performed on the ground loop piping to
estimate the required piping length and size for winter and summer conditions. These
calculations involved estimating the soil thermal properties and yearly mean soil
temperatures of Oxford, CT. Overall, the analysis of the GCHX determined how piping
length and heat transfer rate vary with installation depth and GHP inlet water
temperatures.
3
2. Theory/Methodology
2.1 Design Parameters
The heating and cooling load calculations were performed in accordance with the
ASHRAE Handbook of Fundamentals 2009 [3]. These procedures were chosen because
they are considered the industry standard and apply a simplified analysis method to
estimate residential heating and cooling loads. The ASHRAE methods also consider
both sensible and latent loads for cooling. Latent cooling loads ultimately govern the
wet bulb temperature and relative humidity within the conditioned space. ASHRAE
recommends relative humidity levels between 40 and 60% in the conditioned space to
ensure a comfortable environment for the occupants.
Oxford, Connecticut was chosen as the location of the conceptual home since it is more
closely related to a rural area. Rural areas are typically more favorable for geothermal
heat pump and horizontal GCHX installations due to the larger plots of land on which
the homes are built. The conceptual home was chosen to be a single-family detached
residence with a total square footage of 1280 ft2. The layout and dimensions of the
home are shown in Figure 3.
4
Figure 3: Conceptual Home Schematic [4]
Assumptions were made for the construction of all the major components in the house
such as the walls, windows, doors, roofing and flooring.
These assumptions are
summarized in Table 1 and include the overall dimensions of the components and the
insulation thickness and type if applicable. The construction assumptions were used in
conjunction with the schematic to calculate total heat transfer coefficients or U-factors
for each major component of the home, which is discussed in detail in a later section of
this report.
5
Table 1: Conceptual Home Construction Assumptions
Construction Assumptions
Total Floor and Ceiling Area = 32’*40’=1280
Walls
16 O.C. - inches from the center of one stud the center of the next
2x4 Pine studs (actual 1.5” x 3.5”)
½ sheetrock (gypsum board)
Vinyl siding
0.5" Plywood
Insulation: R13 - 3.5” fiberglass batts
Ceiling/Roofing
Ceiling Height: 9ft
Insulation: R30 – 9” fiberglass insulation
Asphalt shingles (medium color) on 7/16" OSB (oriented strand board)
½" sheetrock (gypsum board) ceiling
Windows
Double Pane, vinyl frame, ½” air space, 4’.0” x 4’.0” everywhere but living room
Double Pane, vinyl frame, ½” air space, 4’.0” x 7’.0” in living room.
All windows have insect screens
Doors
1.75” Solid wood core 3x7 (only included the doors facing outside in calculation)
Flooring
Concrete slab with carpet and rubber pad
Chapter 14 of the ASHRAE Handbook of Fundamentals 2009 [5] was used to obtain the
outdoor climate, summer and winter, conditions of Oxford, CT. The elevation and
latitude of Oxford was estimated at 720ft and 41ºN respectively.
The outdoor
temperature conditions utilized for this analysis were a heating dry bulb (DB)
temperature of 9ºF corresponding to 99.0% of the cumulative frequency of occurrence
(winter conditions) and a cooling DB temperature of 84ºF with a mean coincident wet
bulb (MCWB) temperature of 71ºF at 1.0% of the cumulative frequency of occurrence
(summer conditions). The summer (cooling) daily temperature range (DR) is calculated
as the difference between the outdoor summer DB and MCWB temperatures and was
determined to be 13ºF.
The indoor conditions for the home were assumed based on ASHRAE rules of thumb.
The indoor cooling wet bulb temperature was determined from a psychometric chart
using the estimated dry bulb temperature and inferring a corresponding wet bulb
6
temperature for 50% humidity. All of these temperatures, along with other relevant
outdoor and indoor data, are summarized in Table 2.
Table 2: Indoor and Outdoor Design Conditions
Indoor (Tid)
Outdoor (Tod )
Daily Range (DR)
Temperature Difference (ΔT)
Cooling
(Summer Conditions)
DB
MCWB
(ºF)
(ºF)
75
63
84
71
13
9
-
Heating
(Winter Conditions)
DB
MCWB
(ºF)
(ºF)
70
9
61
-
For the GCHX calculations a horizontal pipe configuration was utilized. The calculation
considered only Polyethylene piping with dimensions in accordance with Table 3.
Applications in a heating dominated environment typically require an antifreeze solution
to avoid freezing.
Therefore, this analysis considered an industrial grade water-
antifreeze solution, DOWFROST HD, containing 20% Propylene Glycol. This set the
freezing temperate to about 18 ºF without significantly increasing the viscosity. The soil
properties of Oxford, CT were estimated and the soil grade was assumed to be
representative of red sandstone at depths below 5ft.
Table 3: Polyethylene Pipe Dimensions
Nominal Pipe Size
(NPS)
(in)
0.75
1
1.25
1.5
2
OD
(in)
Min
Wall thickness
(in)
1.05
1.315
1.66
1.9
2.375
0.095
0.12
0.151
0.173
0.216
7
2.2 ASHRAE Space Cooling and Heating Load Analysis
2.2.1
Sensible Heating and Cooling Space Loads
The calculation of the residential heat loads involves estimating the heat flow for a
conditioned space while maintaining the required indoor air temperature during the
specified outdoor weather conditions. The heating calculations use simple worst-case
scenario assumptions: no internal or solar gains and no heat storage with all heat losses
to be evaluated simultaneously. These simplifications allow the problem to be reduced
to a simple heat transfer problem. Only the above grade components and surfaces
exposed to outside conditions are considered in the analysis and are treated identically as
follows:
qs ,h  Ac  HF
[1]
HF  U  Th
[2]
where qs,h is the sensible heat load in Btu/hr, HF is regarded as the Heat Factor in
Btu/hr·ft2 and Th is the difference between the dry bulb heating indoor temperature
( Th ,id ) and the heating outdoor temperature ( Th ,od ) in ºF. Ac is defined as the square area
in ft2 of the component. The heat transfer coefficient U in Btu/hr·ft2·ºF is calculated for
each individual component (wall, windows, exterior doors, roofing and flooring) and
each can be expressed as:
 1
 1
1
1
1 
1
1
1 
U wall  0.8  



 0.2  



R

R

 side Rw, ply Rw,ins R gb 
 w, side Rw, ply Rw, stud R gb 
U wind 
U door 
1
Rwind
1
Rdoor
[3]
[4]
[5]
 1
1
1
1 
U roof  



R

 r ,shing Rr , ply Rr ,ins Rgb 
[6]
 1
1 
U floor  

R

 pad Rcarp 
[7]
8
For Equations [3]-[7] R is the thermal resistance in hr·ft2/Btu. Equation [3] includes the
heat transfer of the wall studs, which comprise 20% of the total wall area. It should be
noted these overall heat transfer coefficients are utilized for both heating and cooling
calculations. However, ASHRAE [3] states that for a concrete slab floor, the heat loss is
proportional to the slab perimeter. As a result, Ufloor is usually adjusted to describe the
heat transfer in terms of Btu/hr·ft·ºF. Thus for heating only:
U floor  Fp
[7b]
where Fp is the heat transfer coefficient for concrete slab floor for heating only and is
obtained from ASHRAE [3] based on floor construction.
Cooling loads are calculated in similar manner to heating loads but include the additional
internal and solar heat gains. The sensible cooling load calculations not only determine
the heat gains from opaque surfaces as in the heat load calculations, but also solar heat
grain from transparent fenestration surfaces (windows), the effects from air infiltration,
ventilation fresh air requirements and occupancy heat loads. The sensible cooling loads
resulting from heat gains from the walls, exterior doors, roofing and flooring can be
calculated as follows:
q s ,c  Ac  CF
[8]
CF  U  (OFt  Tc  OFb  OFr  DR )
[9]
where qs,c is the sensible cooling load in Btu/hr and OFt , OFb and OFr are opaque
surface cooling factors which are listed in Table 7 of the ASHRAE Handbook [3]. To
determine solar heat gain from transparent fenestration surfaces such as the windows, the
cooling factor (CF) of Equation [8] is adjusted to calculate the solar fenestration heat
gain. The fenestration CF is highly dependent on cardinal direction (east, west, north or
south) because of the variability of the suns exterior irradiance on the windows.
Therefore, CFfen is calculated for each window in its installed direction. For this study
Figure 3 implies the northern direction in relation to the house. The CF for fenestration
for each window in its oriented direction (north, south, east and west) can be expressed
as follows:
CF fen  U wind (Tc  0.46  DR )  PXI  SHGC  IAC  FFs
9
[10]
where Tc is the difference between the dry bulb cooling outdoor temperature ( Tc ,od )
and the cooling indoor temperature ( Tc ,id ) in ºF. The fenestration load factor (FFs) is
the fraction of transmitted solar heat gain. These values are listed in Table 13 of the
ASHRAE Handbook [3] for all cardinal directions. The peak exterior irradiance (PXI) is
expressed as follows:
PXI  Tx  Ed  1  Fshd   ED 
[11]
where Table 10 of the ASHRAE Handbook [3] provides the diffuse rate (Ed) and direct
irradiance diffuse rate (ED) in Btu/hr·ft2 for all cardinal directions based on geographical
latitude. Tx is the exterior attachment Transmission due to window screens. A value of
0.64 is typically used for insect screens and a value of 1 is used if there are no screens.
The shading factor (Fshd) provides an estimate solar heat gain reduced by the overhang of
the house and is described by:
Fshd 
SLF  Doh
h
[12]
where Doh is the depth of overhang from the plane of fenestration in feet, h is the height
of the window and SLF is the shade line factor obtained from Table 12 of the ASHRAE
Handbook [1]. The solar heat gain coefficient (SHGC) acts as a solar radiation heat
transfer coefficient and is obtained from Table 2 of the ASHRAE Handbook [3] for
various window constructions. The interior attenuation coefficient (IAC) represents the
rate of solar radiation heat gain blocked by shades or blinds on the windows and is
expressed as:
IAC  1  Fcl  IACcl  1
[13]
Where Fcl is the fraction of the shade closed and IACcl is the interior attenuation
coefficient of a fully closed shade which can be obtained from Table 14 of the ASHRAE
Handbook [3].
2.2.2
Loads Associated with Infiltration and Ventilation Losses
The effects from air infiltration, ventilation fresh air requirements, ventilation
distribution losses and occupancy heat loads increase the total sensible heating and
10
cooling loads. The loads associated strictly with air infiltration and ventilation in Btu/hr
are expressed as:
q s ,iv,h  C s  Qi ,h  Qv   Th
[14]
q s ,iv,c  C s  Qi ,c  Qv   Tc
[15]
where Qi,h and Qi,c are the infiltration flow rates in cfm for heating and cooling
respectively and Qvent is the required fresh air ventilation flow rate in cfm. Cs is the air
sensible heat factor and is taken to be 1.1 Btu/hr·ºF·cfm at sea level. The severity of air
infiltration depends on the construction characteristics of the home. The air infiltration
flow rates in cfm are calculated as follows:
 698  8.1 Th  
Qi ,h  Aes  Aul  

1000


[16]
 343  8.8  Tc  
Qi ,c  Aes  Aul  

1000


[17]
Aes is the total exposed surface area of the residential home (gross area of the walls plus
the ceiling) in ft2. Aul is the unit leakage rate in in2/ft2 and can be obtained from Table 3
of the AHSRAE Handbook [3] based on the construction integrity of the home. The
minimum ventilation fresh air requirement in cfm which must enter the home for
suitable air quality as specified by the AHSRAE Handbook [3] is calculated as follows:
Qv  0.01 As ,tot  7.5  N br  1
[18]
where As,tot is the total square footage of the home and Nbr is the total number of
bedrooms.
According to ASHRAE [3] Equation [14] can be multiplied by 16% and Equation [15]
by 27% to obtain conservative heating and cooling loads associated with ventilation
losses if the ducting is well insulated. These loads are summarized as follows
q s ,dl ,h  0.16  q s ,vi ,h 
[19]
q s ,dl ,c  0.27  q s ,vi ,c 
[20]
11
2.2.3
Latent Cooling Loads
As previously stated, the latent cooling loads govern the wet bulb temperature and
relative humidity within the conditioned space. The total latent heat load in Btu/hr is
expressed as:
ql ,tot  ql ,vi  ql , g
[21]
Where ql,vi and ql,g are the latent cooling loads associated with infiltration/ventilation
and internal heat gain respectively. These loads are calculated as follows:
ql ,iv  Cl  Qi ,c  Qv    c ,od   c ,id 
[22]
ql , g  68  0.07  As ,tot   N b  1
[23]
For Equation [22] φc,od and φc,id are the humidity ratios in lb/lb for the outdoor and
indoor conditions respectively. These values are determined by utilizing a psychometric
chart given the outdoor and indoor DB and MCWB temperatures. The latent cooling
load factor (Cl) is taken to be 4840 Btu/hr·cfm at sea level.
2.2.4
Total Heating and Cooling Loads
With all individual heat loads defined the total combined heating (winter) and cooling
(summer) loads in Btu/hr are calculated as:
qh,tot   qs ,h  qs ,iv,h  qs,dl ,h
[24]
qc,tot   qs,c  qs,iv,c  qs ,dl ,c  ql ,tot  qs , g
[25]
The total cooling load also includes the sensible heat gain due to occupancy for
conservatism and is expressed as:
q s , g  464  0.7  As ,tot   N b  1
[26]
2.3 GCHX Analysis
2.3.1
Ground Temperature Calculation
The minimum (winter) and maximum (summer) soil temperatures are defined as a
function of depth below the surface (Z) and soil thermal diffusivity (αs).
relationship is described by Florides and Kalogirou [6] as the Kasuda correlation:
12
This


Ts ,min  Tmean  Tamp  exp   Z 
365   s





[27]


Ts , max  Tmean  Tamp  exp   Z 
365   s





[28]
Tmean and Tamp are the air average surface temperature and amplitude of the average air
temperature. This data is usually determined from yearly temperature data for the
geographical location of interest. As depth increases the soil temperature begins to
stabilize and approaches Tmean.
2.3.2
Heat Transfer of the GCHX
The heat transfer of the GCHX can be approximated as a steady state one dimensional
process. This implies the calculations can be performed assuming the pipe surface
temperature is constant and equal to that of the soil for a given depth. This was assumed
a reasonable approximation by References [7] and [8]. Equations [29] and [30] were
utilized to determine the required length of the GCHX given inlet and outlet propylene
glycol fluid temperatures for cooling and heating conditions respectively.
These
equations were specified by Incropera and Dewitt [9] for a pipe of constant surface
temperature.
Ts  Tw , c , o
Ts  Tw , c , i
T s  Tw , h , o
Ts  Tw , h , i

 Lc
 exp 
 m  c  R '
tot
 c p,w




[29]

 Lh
 exp 
 m  c  R'
tot
 h p,w




[30]
The total thermal resistance R’tot in hr-ft-ºF/Btu can be expressed as follows:
R'tot  R'conv  R'cond  R'soil
[31]
The thermal convective resistance of the flowing fluid R’cov and thermal resistance due
to conduction in the pipe R’cond and are calculated as follows:
1
  Di  hi
[32]
1nDo / Di 
2   k p
[33]
R 'conv 
R'cond 
13
Although thermal resistance of the soil (R’soil) is highly dependent on moisture content, a
reasonable approximation can be made utilizing cylindrical source theory as stated by
Sanaye and Niroomand [8]. Cylindrical source theory provides a solution for a buried
cylinder pipe with infinite length under the boundary condition of a constant pipe surface
temperature. The model also assumes the pipe is surrounded by a homogenous medium
with constant properties.
R ' soil 
G Fo ,1
s
[34]
The G function is the analytical solution of the cylindrical source theory and is a
function of the dimensionless Fourier number (Fo).
Fo 
4   s 
Do
2
[35]
The variable τ is characterized as the time of operation of the GHP and can be
approximated as 3680.25days. This was specified by the 2007 ASHRAE Handbook [1]
which models the GHP system total run time as 10 years, 30 days and 6 hours. Figure
15 of the 2007 ASHRAE Handbook [1] is used to determine the G function in Equation
[34] given the calculated Fourier number.
The average convective heat transfer coefficient (hi) was determined by the DittusBoelter correlation which is expressed as follows:
hi 
0.023  Re 0.8  Pr n  k w
Di
[36]
In order to ensure sufficient heat transfer, the fluid within the pipe must remain fully
turbulent. This implies the Reynolds number (Re) for the fluid flowing through a
specific pipe size must be greater than 4,000. The Reynolds number for the fluid was
calculated as follows:
Re 
4  m
  Di   w
[37]
The mass flow rates for cooling and heating modes of operation were determined by
Equations [38] and [39].
14
m c   w  Qw,c  60
[38]
m h   w  Q w, h  60
[39]
For this study the density (ρw) and viscosity (μw) of the fluid corresponds to that of the
water-antifreeze solution containing 20% Propylene Glycol. The volumetric flow rates
for cooling (Qw,c) and heating (Qw,h) modes are calculated assuming a GHP requires
3gpm for every 12,000 Btu/hr, where 12,000 Btu/hr is equivalent to one refrigerant ton.
This is stated as a rule of thumb in GCHX design by the 2007 ASHRAE Handbook [1].
The GCHX will be designed to the total loads within the GHP compressor and
evaporator. The total loads for the condenser and evaporator are defined as the total
heating and cooling loads expressed in Equations [24] and [25]. This study did not
account the additional heat load imparted on the refrigerant within the GHP as a result of
the compressor. The outlet temperature for the GCHX was calculated utilizing the basic
convective heat transfer equation for a flowing fluid:
qGCHX ,c  qconden  qc ,tot  m  c p  (Tw,c ,o  Tw,c ,i )
[40]
qGCHX ,h  qevap  qh ,tot  m  c p  (Tw,h ,o  Tw,h ,i )
[41]
For this study, the inlet temperatures for the cooling (Tw,c,i) and heating (Tw,c,i) modes of
operation were varied to determine the impact on overall length and heat transfer rate per
unit length. The heat transfer rate per length of the GCHX (qʹgchx,c and qʹgchx,h) was
determined by dividing Equations [40] and [41] by the total length calculated from
Equations [29] and [30].
15
3. Results
3.1 Space Cooling and Heating Load Results
3.1.1
Assumptions and Input Parameters
The plan layout and construction assumptions of the Oxford, CT home, Figure 3 and
Table 1 of Section 2.1 of this report, were used extensively to define the input
parameters for the heating and cooling space load analysis. Table 4 summarizes the total
areas required for the load calculations from the dimensions specified in Figure 3.
Table 4: House Component Quantity Dimensions and Total Area
Component
Total Area
(ft2)
Ceiling - 32'x40'
Walls - (9'x32') and (9'x40')
Doors - 3'x7'
Floor - 32'x40'
West Windows - 4'x4'
1280
1011
42
1280
32
West Windows - 4'x7'
East Windows - 4'x4'
East Windows - 4'x7'
North Windows - 4'x4'
North Windows - 4'x7'
South Windows - 4'x4'
Notes
Wall area subtracts total area of windows
Floor perimeter = 144ft
42
32
42
16
21
16
The home is subject to the design temperature parameters listed in Table 2 of section 2.1.
These are reiterated in Table 5 for completeness and to comply with the notation.
Table 5: Design Temperatures, ºF
Tc,od
Tc,id
Tc,od,WB
Tc,id,WB
Th,od
Th,od
DR
ΔTc
ΔTh
84
75
63
71
70
9
13
9
61
16
ºF
ºF
ºF
ºF
ºF
ºF
ºF
ºF
ºF
In addition to the layout of the home, construction characteristics/assumptions and
design temperature conditions, the following assumptions were also applied:

The home is treated as a single conditioned space and the effects of interior
doors, walls or unventilated rooms are not considered.

The home was assumed to have “good” construction characteristics according to
Reference [3] implying it was carefully sealed by knowledgeable builder and air
infiltration rates will be relatively low.

Cs and Cl are equal to values found at sea level.

Assumed a total of 4 occupants within the home to calculate internal heat gain.
The R values for the construction items of the home are summarized in Table 6 and were
taken from McQuiston, Parker and Spitler [10].
Utilizing these values the total heat
transfer coefficients (U-factors) of the walls, doors, roofing and flooring were calculated
using Equations [3]-[7]. These values are listed in Table 7.
Table 6: Thermal Resistance Values for Construction Components, (hr·ft2·ºF/Btu)
Vinyl Siding
Rside
0.61
0.5" Plywood
Rw,ply
0.63
R13 -3.5" Insulation
Rw,ins
13
0.5" Gypsum Board
Rgb
0.45
2x4 Frame Studs
Rw,stud
4.31
Shingles Asphalt Medium Color
Rr,shing
0.44
0.75" Plywood
Rr,ply
0.93
R30- 9" Insulation
Rr,ins
30
Rdoor
1.75" solid core flush door
Double Pane window vinyl frame 1/2" air
Rwind
space
Rpad
3/8" Rubber Pad
Rcarp
3/8" Carpet
2.5
17
1.96
0.32
1.05
Table 7: Overall Component Heat Transfer Coefficients, (Btu/hr·ft2·ºF)
UWall
UDoor
URoof
UWind
UFloor
3.1.2
0.088
0.400
0.031
0.510
0.730
Opaque Surface Loads
The heating factors for the opaque surfaces were calculated by applying the calculated
heat transfer coefficients in Table 7 to Equation [2]. Equation [9] was used to calculate
the cooling factors for the opaque surfaces. The dimensionless opaque surface factors
for Equation [9] are listed and Table 8 and were determined from the previously defined
design and construction assumptions.
Table 8: Dimensionless Opaque Surface Factors for Cooling
OFt
OFb
OFr
0.64
0.35
2
The sensible heating and cooling loads for each opaque surface were calculated using
Equations [1] and [8]. These results are summarized in Table 9.
Table 9: Opaque surface HFs, CFs and Associated Sensible Loads
Component
Ceiling
Walls
Doors
Floor
3.1.3
HF
CF
(Btu/hr·ft2) (Btu/hr·ft2)
1.90
5.36
24.40
43.92
0.52
1.68
7.65
-0.63
Area
(ft2)
1280
1011
42
1280
Perimeter
qs,h
qs,c
(ft)
Btu/hr Btu/hr
144
2430
5417
1025
6324
672
1698
321
-806
Window Loads
The cooling factors for the windows associated with solar fenestration were derived by
considering their glazing configurations, their overall construction, as well as their
installed direction in the house. All windows were defined as double pane with a vinyl
18
frame and ½” air space. Variations in the window cooling factor are a result of the input
values within Equation [10]. These values are listed below in Table 10 and take into
account window sun exposure, height, shading, overhang, and frame type.
Table 10: Window Cooling Factor Input Parameters
ED - North
Ed - North
ED - South
Ed - South
ED - East/West
Ed - East/West
SLF
IACcl
Fcl
Doh
SHGC
Tx
26
26
94
65
178
60
1.1
0.64
0.35
2
0.57
0.64
Btu/hr·ft2
Btu/hr·ft2
Btu/hr·ft2
Btu/hr·ft2
Btu/hr·ft2
Btu/hr·ft2
ft
-
To fully determine the cooling factors associated with each window the input parameters
defined in Table 10 were used to evaluate Equations [11]-[13]. Table 11 summarizes the
calculated shading factors, peak solar irradiance, interior attenuation, and solar
fenestration factors for each window size at their respective exposure direction.
Table 11: Calculated Window Cooling Factor Parameters
Window Exposure
Direction
West
East
North
South
Window
Height
(ft)
Fshd
PXI
(Btu/hr·ft2)
IAC
FFs
4
7
4
7
4
7
4
0.55
0.31
0.55
0.31
0
0
0
93.867
121.978
93.867
121.978
34.840
34.840
106.530
0.874
0.874
0.874
0.874
0.874
0.874
0.874
0.56
0.56
0.31
0.31
0.44
0.44
0.47
19
The sensible heating and cooling loads for each window configuration were calculated
using Equations [1] and [8] for the given the calculated heating and cooling factors.
These results are summarized in Table 12.
Table 12: Window HFs, CFs and Associated Sensible Loads
Component
HF
CF
Area Perimeter
qs,h
qs,c
(Btu/hr·ft2) (Btu/hr·ft2) (ft2)
(ft)
Btu/hr Btu/hr
West Windows - 4'x4'
West Windows - 4'x7'
East Windows - 4'x4'
East Windows - 4'x7'
North Windows - 4'x4'
North Windows - 4'x7'
South Windows - 4'x4'
3.1.4
31.11
31.11
31.11
31.11
31.11
31.11
31.11
27.73
35.57
16.04
20.38
9.18
9.18
26.48
32
42
32
42
16
21
16
-
996
1307
996
1307
498
653
498
887
1494
513
856
147
193
424
Infiltration and Ventilation Loads
The input parameters for these for infiltration and ventilation are listed in Table 13 and
are based on the construction assumptions of the home. The “good” home construction
assumption defined the average leakage per unit (Aul). The infiltration and ventilation
flow rates were determined utilizing the parameters in Table 13 and applying them to
Equations [16],[17] and [18]. The calculated flow rates are also summarized in Table
13.
Table 13: Infiltration and Ventilation Input Parameters and Calculated Flow Rates
Aes
As,tot
Aul
Nbr
Qi,h
Qi,c
Qv
2576
1280
0.02
3
61
22
43
ft2
ft2
in2/ft2
cfm
cfm
cfm
Applying Equations [14] and [15] the heating and cooling loads associated with the
infiltration and ventilation flow rates were determined.
20
Equations [19] and [20]
determined the distribution losses and Equation [26] determined cooling sensible heat
gain. These loads are summarized in Table 14.
Table 14: Infiltration, Ventilation and Distribution Loss Sensible Loads, Btu/hr
qs,iv,h
qs,iv,c
qs,dl,h
qs,dl,c
qs,g
3.1.5
6993
639
4551
2348
1660
Latent Loads
Latent heating and cooling loads associated with infiltration and ventilation and internal
heat were determined from Equations [22] and [23]. These results along with the
relative outdoor and indoor humidity ratios, φc,od and φc,id respectively, are documented
in Table 15.
Table 15: Humidity Ratios and Latent Loads
φc,od
φc,id
ql,iv
ql,g
3.1.6
0.0133
0.0095
1187
322
lb/lb
lb/lb
Btu/hr
Btu/hr
Load Summary
Table 16 provides a summary of all calculated heating and cooling loads. The total
cooling and heating loads are taken to be the total loads to be removed by the GCHX.
Table 16: Summary of Total Loads, Btu/hr
Heating
Loads
(Winter)
Cooling
Loads
(Summer)
Σqs,h
qs,iv,h
qs,dl,h
qh,tot
Σqs,c
qs,iv,c
qs,dl,c
qs,g
ql,tot
qc,tot
21
21450
6993
4551
32994
6398
639
2348
1660
1509
12555
3.2 GCHX Results
The following assumptions were applied to the analysis of the GCHX:

Steady state conditions

Heat transfer along the pipe is one dimensional

Soil temperature remains unaffected by the pipe temperature fluctuations.
As a result, the pipe has a constant surface temperature along the axis of the
pipe and is equal to that of the soil at a specified depth.

Convective flow inside the pipe is thermally and hydro-dynamically fully
developed.

The additional heat load imparted on the refrigerant within the GHP as a
result of the compressor is to be neglected. Thus the thermal loads to be
handled by the GCHX are equal to that of the space heating and cooling
loads.

The GCHX is taken to be 100% efficient and does not account for losses.

Soil properties in Oxford, CT are representative of red sandstone at depths
greater than 5ft.

Soil is assumed to be homogenous throughout.
Therefore, thermal
properties of the soil remain constant.

Fluid circulating through GCHX is a water-antifreeze solution containing
20% Propylene Glycol.
All properties were for DOWFROST HD an
industrial grade propylene glycol solution commonly used for GHP systems.

Pipe is of a polyethylene material with a thermal conductivity (kp) of 0.24
Btu/hr·ft2·ºF. Dimensions of the piping were specified in Table 3.
The mean surface temperature or infinite depth soil temperature (Ts,mean) was calculated
by obtaining average monthly temperature from Reference [11]. Figure 4 plots the
average temperatures for Oxford with the calculated mean surface temperature of 52ºF.
22
Monthly Average Temperatures for Oxford, CT
80
Temperature (ºF)
70
60
50
40
30
20
Monthly Average Temperatures
Mean Temp 52ºF
10
0
Jan
Feb
Mar
Apr
May
Jun
July
Aug
Sept
Oct
Nov
Dec
Month
Figure 4: Monthly Average Temperatures and Mean Surface Temperature
Utilizing reference [12] the thermal diffusivity (αs) and conductivity (ks) for the soil were
taken to be 0.939 ft2/day and 1.61 Btu/hr·ft2·ºF respectively. Using sandstone as the soil
composition for the location was merely an estimate as actual soil properties would be
determined by inspection before installation. The minimum and maximum seasonal soil
temperatures for Oxford, CT were determined at various depths using Equations [27]
and [28]. These results are displayed in Figure 5.
Ts max and min at various depths (z)
80.0
70.0
Temperature (F)
60.0
50.0
Max
Min
40.0
30.0
20.0
10.0
0.0
0
10
20
30
40
50
60
Depth (Ft)
Figure 5: Maximum and Minimum Soil Temperature at Various Depths
23
It can be seen that as depth increases the max and min soil temperatures begin to
converge to the mean soil temperature of 52 ºF. However, at depths closer to the surface
the soil temperature difference between seasons can be enough to impact the
performance of the GCHX. This is a result of the thermal properties of the soil or in this
case the diffusivity of sandstone. Soils with high thermal diffusivities can dissipate the
effects from the surface environment at a faster rate allowing them to reach thermal
equilibrium at shorter depths than soils with low thermal diffusivities. While sandstone
is not a poor soil for heat dissipation, there are compositions which are more effective
such as dense sand. Thermal diffusivities for this composition can range from 1.042 to
1.265ft2/day depending on moisture content.
The properties of Dowfrost HD Propylene Glycol fluid were estimated at various
temperatures from Dow Chemical [13]. A summary of these properties used are listed in
Table 17.
Table 17: Propylene Glycol, DOWFROST HD
Tw
(ºF)
ρw
(lb/ft3)
μw
(lb/ft·hr)
kw
(Btu/hr·ft·F)
Cp
(Btu/lb·F)
20
30
40
50
60
70
80
90
100
64.65
64.56
64.46
64.34
64.22
64.09
63.95
63.8
63.64
12.97
10.24
8.25
6.75
5.61
4.72
4.02
3.46
3.03
0.261
0.263
0.267
0.272
0.276
0.28
0.284
0.287
0.291
0.929
0.932
0.935
0.937
0.94
0.943
0.945
0.948
0.951
The heating and cooling volumetric flow rates for the Propylene Glycol fluid were
calculated by the ASHRAE rule of thumb, (3gpm/12,000Btu/hr), based on qh,tot and qc,tot.
These results are displayed in Table 18.
24
Table 18: GCHX Volumetric Flow Rates, gpm
Qw,h
3
Qw,c
8
The fluid Reynolds numbers for each pipe size were calculated from Equations [37] with
GCHX inlet temperatures ranging from 80-100ºF for cooling and 20-40ºF for heating.
These results are shown in Figure 6 and Figure 7. The mass flow rates used to calculate
the Reynolds number compensated for the change in fluid density based on the inlet
GCHX fluid temperatures. For cooling conditions, pipe 1.25” NPS and greater, the
Reynolds number falls below or approaches 4,000 for various inlet fluid temperatures.
This will result in laminar fluid flow which is not desirable. For heating conditions the
GCHX inlet fluid temperatures are much lower resulting in a higher viscosity. This
causes the Reynolds number to fall below or approach 4,000 for pipe sizes greater than
1” NPS. Therefore, for the given flow conditions, 0.75” and 1” pipe is the best size to
use as they ensure a turbulent flow for a wide range for fluid temperatures.
However, by examining the thermal resistance of both pipe sizes, it can be seen for the
1” pipe, the increased surface area provides only a marginal benefit to the overall heat
transfer performance. Figure 8 and Figure 9 compare the thermal resistances for 0.75”
and 1” pipe for cooling and heating conditions. The plots show that the decrease in
thermal resistance for 1” pipe is insignificant. Therefore, for this application, utilizing a
0.75” pipe size is the most beneficial and cost efficient choice. The cost of installing the
1” pipe would be greater than 0.75” due to the increase in material and would only
slightly increase the overall heat transfer performance.
25
Figure 6: Reynolds Numbers for Cooling Inlet Fluid Temperatures
Figure 7: Reynolds Numbers for Heating Inlet Fluid Temperatures
26
Figure 8: Total Thermal Resistance of 0.75NPS and 1NPS for Cooling
Figure 9: Total Thermal Resistance of 0.75NPS and 1NPS for Heating
27
The length of required 0.75” piping for the GCHX was determined along with its heat
exchange rate characteristics by utilizing inlet temperature ranges of 80-100ºF for
cooling and 20-40ºF for heating. The respective outlet temperatures are displayed in
Figure 10 and Figure 11.
Figure 10: GCHX Outlet Fluid Temperatures for Cooling Conditions
Figure 11: GCHX Outlet Fluid Temperatures for Heating Conditions
28
To examine the effects of soil depth on GCHX heat exchange rate and piping length the
summer and winter inlet fluid temperatures were taken to be 90ºF and 30ºF respectively.
These values were chosen since they are the considered, by most literature, the normal
inlet working temperatures for a fluid in a GCHX. Using Equations [40] and [41] the
outlet fluid temperatures, Tw,c,o and Tw,h,o, were calculated to be 82ºF and 38 ºF
respectively. Figure 12 displays the results of heat exchange rate per foot of pipe at
various depths below the surface. Referring to back to Figure 5, it is valid to assume as
the depth of the GCHX increases, the surface temperature of the pipe approaches the
equilibrium soil temperature of 52ºF.
This creates a larger temperature difference
between the inlet fluid temperature and the ground. The increase in heat exchange rate
results in shorter pipe runs, as displayed in Figure 13 and Figure 14. At soil depths less
than 5ft under heating (winter) conditions, with an inlet fluid temperature of 30ºF, the
ground temperature is not low enough to achieve the desired outlet temperature of 38ºF.
At these depths Ts,min is below 38ºF. Therefore, the equations used to determine pipe
length are not valid for this condition.
Figure 12: Heat Exchange Rate at Various Depths
29
Figure 13: GCHX Pipe Length at Various Depths (Tw,c,i @ 90ºF)
Figure 14: GCHX Pipe Length at Various Depths (Tw,h,i @ 30ºF)
The results show the optimal performance of the heat exchanger is essentially reached at
a depth of 40ft for inlet fluid temperatures of 90 ºF and 30 ºF.
Under these condtions
the cooling heat exchange rate, qʹgchx,c, is approximately 43.00Btu/hr·ft and the
corresponding pipe length Lc is 292ft.
The heating heat exchange rate qʹgchx,h, is
approximately 22.88 Btu/hr·ft and the corresponding pipe length Lh is 1442ft.
However, a depth of 40ft is not conducive to a horizontal pipe arrangement. If this depth
30
were desired it would more than likely require a vertical pipe configuration in order to
avoid excessive installation cost.
As previously stated a GCHX depth between 3 and 10ft is more favorable for a
horizontal pipe configuration. A depth of 10ft would be the more desirable choice. It
would provide a more stable heat transfer medium given the ground temperature
locations for the given location. At a depth of 10ft and fluid temperatures of 90ºF and
30ºF the cooling heat exchange rate, qʹgchx,c, is approximately 32.00Btu/hr·ft and the
corresponding pipe length Lc is 392ft.
The heating heat exchange rate qʹgchx,h, is
approximately 11.36 Btu/hr·ft and the corresponding pipe length Lh is 2905ft. The heat
exchange rate and the associated pipe length can be optimized further if the temperature
difference between the inlet fluid temperature and soil is increased.
If the inlet cooling fluid temperature is increased to 100ºF and heating fluid temperature
decreased to 20ºF the GCHX performance is significantly increased. The outlet fluid
temperatures, Tw,c,o and Tw,h,o, were calculated to be 82ºF and 38 ºF respectively and are
shown in Figure 10 and Figure 11. The increased heat exchange rate not only decreases
the required pipe length at the shallower installation depth of 10ft.
For instance, the
heat exchange rate for cooling is increased by 50% and is almost doubled for heating,
45.29 Btu/hr·ft and 24.98 Btu/hr·ft. This increase in performance occurs even though
at 10ft Ts,max and Ts,min are 61º and 43ºF respectively. With the increased performance
the respective pipe lengths (Lc and Lh) are approximately 277ft and 1321ft.
It is not possible to decrease the lengths of the pipe further by altering the inlet fluid
temperatures.
Lowering the heating inlet temperature below 20ºF is will result in
freezing of the water-20%Propylene Glycol antifreeze solution. If the Propylene Glycol
concentration is increased above 20% the freezing temperature of the antifreeze will
drop.
However, this will increase the fluid viscosity increases which will result in a
greater compressor energy consumption to overcome the pressure drop. In addition, the
increase in fluid viscosity is compounded as a result of decreased in temperature.
Therefore, to avoid degradation of the GHP efficiency, it is not advantageous to pursue
31
inlet temperatures lower than 20ºF. For this reason this study did not consider inlet
temperatures below 20ºF. Table 19 summarizes the total calculated pipe lengths for soil
depths of 10ft under the given inlet fluid temperatures.
Table 19: Summary of Pipe Lengths at 10ft Soil Depth
Tw,c,i=90F and Tw,h,i=30F
L,c
(ft)
392
Tw,c,i=100F and Tw,h,i=20F
L,h
(ft)
2905
L,c
(ft)
277
L,h
(ft)
1321
Since there are two distinct pipe lengths, the home will require an installed length
between that of calculated cooling and heating lengths. ASHRAE typically recommends
sizing more in favor of the cooling loads to avoid excessive pipe material cost.
However, for a heating dominated environment such as this, this is proven to be an
invalid assumption. Many of the ASHRAE recommendations for GHP are for cooling
dominated environments. The calculations have shown there is a significant difference
between the pipe length for cooling and heating. Therefore, the designer of the GCHX
must provide adequate piping to accommodate the large heating loads. Since the pipe
length for heating is so long it may require the GHP electric heating elements in order to
supply the desired heat load. This would ultimately impact the efficiency of the GHP in
the winter but would still allow for sufficient operation in the summer.
32
4. Conclusions
For the conceptual home in Oxford Connecticut the total space heating (winter) and
cooling (summer) loads were calculated to be 32,994 Btu/hr and 12,555 Btu/hr
respectively. The assumptions associated with the construction of the house as well as
the mean seasonal temperatures for the area played a major role in the calculation of the
overall loads. The insulation type was identified as one major contributing factor.
Using insulation with a greater thermal resistance for the walls and attic/roofing would
significantly decrease the heat transfer rate. This study assumed R13 insulation for the
walls and R30 for the roofing. However, newly constructed homes in New England
have been known to have insulations as highs R21 for walls and R60 for the
attic/roofing. Utilizing these insulation types can cut the heating and cooling space loads
by approximately 10%. The assumed orientation of the home also played a major factor
in resulting space cooling loads. The cardinal directions of the windows essentially
governed the overall solar heat gain throughout the home. If the windows were in a
different orientation or if northern direction of the home were different, the peak exterior
irradiance (PXI) would be altered, thus significantly altering the window loads.
It was determined a total pipe length of 292ft required for the GCHX for the space
cooling load of 12,555 Btu/hr when operating with an inlet temperature of 90ºF. A total
pipe length of 1442ft is required for the space heating load of 32,994 Btu/hr when
operating with an inlet temperature 30ºF. However, these results can only be obtained at
a near optimal depth of 40ft, which is not conducive to a horizontal pipe configuration.
In order to increase the heat transfer performance and decreases the total required pipe
length at an acceptable depth of 10ft, the temperature difference between the inlet fluid
temperature and soil must be increased.
This can only be accomplished by
implementing a GHP unit which operates with GCHX fluid temperatures as high 100ºF
and as low as 20ºF. It was determined this would allowed the most cost efficient
performance. The pipe lengths under these conditions were determined to be 277ft for
cooling and 1321ft for heating. Because of the large difference in cooling and heating
piping lengths the home will likely require an installed length between that of calculated
33
cooling and heating lengths to remain cost efficient. Installing only the calculated
cooling length would not adequately handle the heating loads of the home. Providing an
even greater temperature difference between the soil and fluid was deemed not possible,
as lowering the heating inlet temperature below 20ºF would result in freezing of the
water-20%Propylene Glycol antifreeze solution.
Overall, the results of this study demonstrated horizontal pipe configurations have a
significant disadvantage in heating dominated environments. In particular, as a result of
the large pipe length required for heating; the GHP may require electrical heating
elements, such as those seen in traditional HVAC heat pumps, in order to adequately
handle the heat load demand. Even if the home were better insulated it is expected the
GCHX pipe lengths would remain quite large. In general, the installation area need for a
GCHX sized to accommodate the full heating load would be quite large, even if the
house was well insulated.
34
5. References
[1] American Society of Heating, Refrigerating and Air Conditioning Engineers,
"Chapter 34 - Geothermal Energy," in ASHRAE Handbook of Fundamentals 2007,
ANSI/ASHRAE, 2007.
[2] Roth, "RXT Series Packaged Water-to-Air Multi-Positional Heat Pumps
Engineering
Data
and
Installation
Manual,"
2011.
[Online].
Available:
http://www.rothusa.com/PDF_Download_Files/Roth%20RXT%20Series%20EDIM.pdf. [Accessed
27 9 2012].
[3] American Society of Heating, Refrigerating and Air Conditioning Engineers,
"Chapter 17 - Residential Cooling and Heating Load Calculations," in ASHRAE
Handbook of Fundamentals 2009, ANSI/ASHRAE, 2009.
[4] "Architectural Designs," Architectural Designs, 57 Danbury Road, Wilton, CT
06897, 2012. [Online]. Available: http://www.architecturaldesigns.com/house-plan26136SD.asp. [Accessed 17 September 2012].
[5] American Society of Heating, Refrigerating and Air Conditioning Engineers,
"Chapter 14 - Climate Design Information," in ASHRAE Handbook of
Fundamentals 2009, ANSI/ASHRAE, 2009.
[6] G. Florides and S. Kalogirou, Measurements of Gournd Temperature at Various
Depths, Higher Technical Institute, 2005.
[7] H. Yang, P. Cui and Z. Fang, "Vertical-borehole ground-coupled heat pumps: A
review of models and systems," Applied Energy, vol. 87, no. 1, pp. 16-27, 2010.
[8] S. Sanaye and B. Niroomand, "Horizontal ground coupled heat pump: Thermaleconomic modeling and optimization," Energy Conversion and Management, vol.
51, no. 12, pp. 2600-2612, 2010.
[9] F. P. Incropera, D. P. Dewitt, T. L. Bergman and A. S. Lavine, Fundamentals of
Heat and Mass Transfer, 6th ed., Hobooken: John Wiley & Sons, 2007.
[10] F. C. McQuiston, J. D. Parker and J. D. Spitler, Heating, Ventilating, And Air
35
Conditioning Analysis and Design, Sixth ed., Hoboken: John Wiley & Sons, Inc.,
2005.
[11] Weather.com, " Monthly Averages for Oxford, CT," The Weather Channel,
[Online].
Available:
http://www.weather.com/weather/wxclimatology/monthly/graph/06478. [Accessed
12 November 2011].
[12] L. Jun, Z. Xu, G. Jun and Y. Jie, "Evaluation of heat exchange rate of GHE in
geothermal heat pump systems," Renewable Energy, vol. 34, no. 12, pp. 2898-2904,
2009.
[13] The Dow Chemical Company, DOWFROST and DOWFROST HD INhibited
Propylene Glycol-based Heat Transfer Fluids, Midland, Michigan: The Dow
Chemical Company, 2008.
36
6. Appendices
Appendix A: Component Thermal Resistance Values and U-Factor Calculations
See Excel document: Space Heating and Cooling Load Calculations
Appendix B: Space Heating and Cooling Load Calculations
See Excel document: Space Heating and Cooling Load Calculations
Appendix C: Ground Soil Temperature Calculations
See Excel document: Soil Temperature Calculations
Appendix D: Calculated Properties of DOWFROST HD
See Excel document: GCHX Calculations
Appendix E: GCHX Length and Heat Exchange Rate Calculations
See Excel document: GCHX Calculations
37