ground source heat pump air conditioning system of vertical geothermal heat exchangers heat transfer...
TRANSCRIPT
Ground source heat pump air conditioning system of vertical geothermal heat exchangers heat transfer process and design
calculation method
Shaoqing Liang
Zhongda Hospital Affiliated to Southeast University, Nanjing, Jiangsu, 210037, China
Keywords: Vertical tube ; Geothermal heat exchanger ; Heat transfer; Design calculation
Abstract: Geothermal heat exchanger is an important part of the GSHP air-conditioning system
and different from other traditional air-conditioning systems. This article through to the geothermal
heat exchanger heat transfer performance analysis and the design, derived from the geothermal heat
exchanger length calculation formula, for actual engineering construction to provide a scientific
basis.
Introduction
Geothermal heat exchanger is an important part of the GSHP air-conditioning system and different
from other traditional air-conditioning systems. It is also the embodiment of ground-source heat
pump air conditioning system superiority is the key part of one. Air conditioning system design
although have a variety of types, is using the traditional boiler and refrigeration machine or the use
of ground source heat pump as the cold and heat source, air conditioning system design for the
interior of the building is not affected, the new system with a conventional difference lies in the
increase of soil heat exchanger. Application of ground source heat pump technology is the difficulty
and key of geothermal heat exchanger heat transfer performance analysis and puts forward the
corresponding methods of design calculation. Through the geothermal heat exchanger heat transfer
performance analysis, design and calculation of the geothermal heat exchanger optimization
research, to find more suitable for practical engineering and operable to the geothermal heat
exchanger design, construction scheme, at present, it is necessary and realistic significance.
Geothermal heat exchanger performance analysis
Geothermal heat exchanger is the particularity of this kind of heat exchanger and engineering
usually encountered in different heat exchanger, it is not a two fluid between the heat, but buried
pipe in fluid and solid (strata) heat exchanger. The heat transfer process is very special. It is
unsteady, covering a time span is very long, conditions are very complex; the traditional heat
exchanger study no experience can learn from. While geothermal heat exchanger design is
reasonable or not is decide buried tube ground-source heat pump system operation reliability and
economy of the key. Therefore, To adopt and promote ground-source heat pump we must bury the
fluid in the tubing and the land between the heat transfer processes were studied in detail, including
the horizontal and vertical buried tube and land in short - and long-term condition of heat transfer
law, the mutual influence between multiple groups of tubes, soil freezing and thawing effect,
geological structure (around layer material, water content and groundwater movement) influence.
Applied Mechanics and Materials Vols. 291-294 (2013) pp 1728-1734Online available since 2013/Feb/13 at www.scientific.net© (2013) Trans Tech Publications, Switzerlanddoi:10.4028/www.scientific.net/AMM.291-294.1728
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2.1 Geothermal heat exchanger heat transfer mathematical model
Analysis of the geothermal heat performance, first we should establish the heat transfer model, heat
transfer model is established the main purpose is to establish the heat pump operation earth
temperature field distribution, based on the basic theories can be divided into [1]：
(1)1948. In 1948, Ingersoll and Plass proposed line source theory, most of the current
ground-source heat pump design is the use of the theoretical basis;
(2)1983. BNL modified line source theory, it is the buried pipe surrounding rock is divided into two
districts, namely, strict zones and free zones, in the ground source heat pump operation, different
interval by heat conduction on regional temperature change;
(3) In 1986 V.C.Mei presented 3D transient far boundary heat transfer model, the theory is built on
the basis of energy balance, is different from the line source theory.
The broader application of the model of heat transfer is mainly:
(1) V.C.Mei heat transfer model, the model based on energy balance based on [2]；
(2)IGSHPA model (International Ground-source Heat Pump Association) is North America
determine the underground heat exchanger size standard method. The model provides the
calculation of single vertical buried pipe, a plurality of vertical pipe and a horizontal buried tube
heat exchanger soil thermal resistance method, to solve the vertical buried pipe of the thermal
interference problem between provides a basis 3]；
(3NWWA (National Water-Well Association) model is a kind of common underground heat
exchanger numerical method, the method is in the Kelvin line source closed analytical solution of
equation is established on the basis of the soil temperature field, and the use of superposition
simulation pump intermittent operation, can be directly given within the heat exchanger average
fluid temperature [4].
The common three kinds of vertical buried tube heat exchanger heat transfer model：
(1) Line source heat transfer model [5]. The line source model the vertical buried tube as a uniform
line heat source, and assuming that the heat source along the depth direction per unit length of the
heat dissipating capacity is constant, with constant heat flux. The tube around the earth together
with backfill section as an infinite solid.Line source model of drilling and soil as a whole, ignoring
the backfill material and soil physical property differences of borehole. If the buried pipe in
borehole depth within the soil physical properties of longitudinal distribution is uniform, the
backfill material is drilled out of soil, and in the backfill, ensure adequate compaction backfill soil
contact, and drilling well. In such conditions, can think of drilling and soil with the same thermal
properties, choose a simple line source model error is small, it is practical.
(2) Cylindrical bore heat transfer model [6]. A cylindrical bore in the heat transfer model of drill
hole, outside the soil as an infinite solid, set the wall of the hole with a constant heat flux will be
bored as a uniform cylindrical heat source, and the heat exchanger, the heat transfer process simple
as heat conduction.
Applied Mechanics and Materials Vols. 291-294 1729
(3) Three dimensional transient far boundary heat transfer model [7]. Three dimensional transient
heat transfer model was established far boundary on the basis of energy balance, the model
describes the borehole within each segment of the heat transfer process, and considering the fluid
along the depth direction of the temperature gradient. With the line source model and the cylindrical
hole model is compared, although the line source and cylindrical hole model is established and
solved more easily, in engineering practice and practical. However, when the needs of buried tube
heat transfer process of in-depth and accurate research, using the two models are required to
achieve a condition is very harsh, usually do not use these two kinds of models instead of using the
transient model. Three dimensional transient heat transfer model and remote boundary and explain
the geometry complexity advantage, when the actual problem to seek short-term effect of borehole,
must be on the hole geometry layout were analyzed, also should take the three-dimensional heat
transfer model.
2.2 Vertical ground heat exchangers performance analysis
For engineering project, to get a detailed simulation and analysis, all the necessary data is almost
impossible. Now, the United States of America Swedish scholar heating refrigeration and Air
Conditioning Engineers Association (ASHRAE), the United States and Canada some university and
company are respectively put forward their own design calculation method. Due to the heat transfer
processes involving physical model is very complex, involving a lot of factors, the existing design
calculation method is based on a simplified model, which assumes the character of stratum is
uniform (the thermal property is best at the scene with special instrument and determination) [8]。
A design calculation method the results usually vary greatly, but in a short period of time it is
difficult to reach a consensus. According to the engineering practice in recent years, it is
recommended that are employed in IGSHPA model simplification for heat transfer analysis
method, this method satisfies the general ground source heat pump air conditioning engineering
land heat exchanger design calculations, and more effective.
Vertical geothermal heat exchangers is calculated from a single drill hole (U type) tube heat transfer
analysis. In the multiple drill holes in the circumstances, can be in single hole based on the
superposition principle to be expanded [9]. In the cooling mode, the fluid in the tube the heat is
transferred to the ground; in the heating conditions, the fluid in the tube from the stratigraphic
absorption heat. Both heat flow in opposite directions, but the heat transfer model is the same. Heat
flow from the fluid in the tube to away from the borehole temperature formation needed to
overcome the resistance is composed of four parts [10]：
1. The fluid to the inner wall of the pipe convective heat transfer resistance;
2. Plastic tube wall heat conduction thermal resistance;
3. Within the borehole thermal conductivity, whereby the pipe into the drill hole wall thermal
resistance;
4. Stratum thermal resistance, namely by the walls of the borehole to formation of distant thermal
resistance.The following are the four thermal resistance calculation method.
The fluid to the inner wall of the pipe convective heat transfer coefficienth(W/m2·℃) According to
the traditional convection heat transfer correlation calculation, then the fluid to the inner wall of the
pipe convective heat transfer resistance is:
1730 Advances in Energy Science and Technology
hd
Ri
f π=
1
（1）
Because the diameter of the borehole is relatively small, so the fluid within the borehole sealing
materials, plastic pipe and the heat capacity and the borehole outside the formation heat capacity is
a small. On the time scale is larger (more than a few hours) conditions, drilling hole inside material
endothermic or exothermic negligible, according to heat conduction can be considered.In addition,
due to the hole set is U type pipe in borehole, the cross section shape is complex, often used in
engineering calculation simplified model, namely two plastic tube is simplified into a larger pipe, so
that the problem is changed into radial One-dimensional heat conduction. Usually assumes the U
shape buried pipe of equivalent diameter 02dd e = . Thus, the thermal resistance of plastic pipe
wall and drilling well sealing material heat resistance respectively:
the thermal resistance of U shape buried pipe wall:
( )
−−π=
iooe
oe
p
peddd
d
kR ln
2
1
（2）
Drilling well sealing material thermal resistance :
π=
e
b
b
bd
d
kR ln
2
1
（3）
Formation of the resistance is the four resistance in the main, is also more difficult to
calculate.Geothermal heat exchanger in continuous operation, fluid continuously to the formation
around the borehole heat flux, formation temperature will rise. Therefore the stratum thermal
resistance changes with time.Calculation of the thermal resistance of many models, they are applied
to different situations. The simplest model is linear heat source model, which is based on the
infinite medium with constant heat flux line heat source generated by the temperature field solution.
For the practical engineering problems, the line source approximation for hours to months time
range. In the following the recommended formula we used by line source is assumed by the
formula, it is clear in physical concept, can also meet the general requirements of engineering
design [11].
Initial temperature ∞t Infinite medium from the moment 0=τ There is strength Iq (w/m) of
constant heat flux line heat source, the temperature of the solution is the coordinate and time
function:
( )
τπ+=τ ∞
a
rI
k
qt,rt I
42
2
（4）
Applied Mechanics and Materials Vols. 291-294 1731
In which k(w/m·℃) and a(m2/s) Is the heat transfer coefficient and the thermal diffusivity, I is
a form of exponential integral:
ds2
1
t∫∞ −
=s
eI
s
（5）
Therefore, the line source model of single pipe stratum thermal resistance, namely from the
wall of the bore to infinity resistance is:
τπ=
a
rI
kR b
s
ss42
12
（6）
br (m) which is the radius of borehole, sk and a is average coefficient of thermal conductivity
and thermal diffusivity of stratum， τ is running time. When the heat exchanger is composed of N
parallel holes (U tube) consisting of clusters, A drill hole temperature rise is not only due to the
hole in the pipe cooling, Also by other boreholes radiating effect. Assumes that the U type tube heat
dissipating capacity of the same, By that time the principle of linear superposition of strata
resistance should be
τ+
τπ= ∑
=
N
i
ib
s
sa
xI
a
rI
kR
2
22
442
1
（7）
In which ix (m) is the ith borehole and the borehole distance between.
Because the heat pump load is usually change over time, but often is not continuous, so the
heat exchanger is exothermic (heat) is also changing with time. After a period of time after the
operation of geothermal heat exchanger fluid to the maximum temperature rise depend on both the
time average heat load size, also depends on the single pulse load intensity and duration.
Geothermal heat exchanger for long-term balanced load ability, short time of strong load may also
make the fluid within the heat exchanger temperature exceeds the heat pump rated inlet
temperature, this point should be pay attention to in design. In the design calculation of the
maximum temperature rise value or the calculation of the required geothermal heat exchanger
length can be approximated by the intermittent pulse heat flux is simplified as a continuous mean
heat load and a pulse load. It can give attention to two different functions, while the calculation is
relatively simple. Approximation of a line heat source is assumed [12]，short-term continuous
pulse load caused by the additional thermal resistance is:
π=
p
b
s
spa τ
rI
kR
42
12
（8）
In which pτ (s) short pulse load continuous running time of 8 hours, for example. For a long
time, must consider the direction of the depth of heat transfer. Analysis shows that, When
2H/aτ >1，The time scale for decades or longer, in the constant heat flow under the action of the
system will reach stable state. Buried in the ground and a cylindrical heat source of steady
analytical solution of temperature field are given by Carslaw and Jeager [5]。Thus we get steady
state conditions stratum thermal resistance is
1732 Advances in Energy Science and Technology
=∗
bs r
H
πkR
2ln
2
1
( )Hrb ⟨⟨ （9）
But for one year in geothermal heat exchangers cooling and heating load in roughly the same
situation, the average heat load is close to zero, or steady state thermal resistance of thermal effects
can be neglected [13].
Vertical buried pipe geothermal heat exchanger design calculation
Geothermal heat exchanger design calculation, the pipeline length calculation is the key and
core. According to the above the geothermal heat exchanger heat resistance analysis, it can be used
to determine the vertical U-tube geothermal heat exchanger length calculation formula of the
engineering design:
Cooling condition：
( )[ ]( )
+
−
−×+×+++=
∞ c
c
max
cspcsbpefc
cCOP
COP
tt
FRFRRRRQL
111000
（10）
Heating condition：
( )[ ]( )
−
−
−×+×+++=
∞ h
h
min
hsphsbpefh
hCOP
COP
tt
FRFRRRRQL
111000
（11）
Where the subscript c, H said refrigeration and heating condition, L is a geothermal heat
exchanger required drilling total length (m), cQ ， hQ ,respectively is the heat pump rated load
(kW),COP Is the performance coefficient of the heat pump, By the heat pump manufacturers, run
the share is considered the influence of heat pump
Heating operation share hF
= A heating season heat pump running hours /( A heating quarter days×24)
Refrigeration operation share cF
=A heat pump refrigeration season running hours /( A cooling season days×24)
Or when the run time taken for one month
Heating operation share hF = The coldest month run hours /( The coldest month days×24)
Refrigeration operation share cF = The hottest month run hours /( The hottest month days×24)
Geothermal heat exchanger circulating fluid design options for the mean temperature
tmax=37℃，tmin=-2~5℃[14]. The two temperature selection will affect the geothermal heat
exchanger design length, while the impact of ground source heat pump system in runtime
performance coefficient.
Applied Mechanics and Materials Vols. 291-294 1733
If the requirements of the geothermal heat exchanger at the same time to meet the heating and
cooling conditions, the geothermal heat exchanger length should be Lc, Lh the larger of two. If the
building's cooling and heating load vary greatly, so that the calculated Lc and Lh have great
differences, the savings from the initial investment and the geothermal heat exchanger heat balance
consideration, can adopt the mixed system, namely the geothermal heat exchanger length according
to the lesser of two selection, While geothermal heat exchanger can not meet the part cold (or hot)
load by auxiliary heating or cooling equipment to complete. For example, if the geothermal heat
exchanger cooling load is greater than that in the heating load, can be considered according to the
heating requirements, Lh to the design of geothermal heat exchanger, cooling can not meet the part
heat load can be additionally provided with a smaller cooling tower to finish.
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1734 Advances in Energy Science and Technology
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