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Use of the ground for heat dissipation
Enqy
Pergamon
Vol. 19, No. I. pp. 17-25, 1994
Copyright @ 19Y4 Elscvier Scicncc Ltd Printed in Great Britain. All rights reserved 03ho-5442/94 $6.00 + 0.00
USE
OF THE
G.
GROUND
model
numerical
air heat exchangers through
temperature
of the natural
thermal
experimental
while
model multi-year investigation
which
process. data.
investigated
to calculate
is described.
the ground, the
DISSIPATION ASIMAKOPOULOS
of Meteorology, Applied Physics Department, University Ippokratous 33, 106 80 Athens. Greece (Received
Abstract-A
HEAT
M. SANTAMOuRIs,t and D.
MIHALAKAKOU,
Laboratory
FOR
ground.
The
operational
of multiple,
air is propelled
The technique model
potential limits
soil and ambient
has been performed
the cooling potential
the performance
or indoor
proposed
The cooling
I.5 March 1993)
The system consists of N parallel
ambient
of Athens,
been
of the system were
air-temperature
in
by the bulk
validated
real climatic
analyzed
measurements.
to analyse the impact
earth-toburied
was used for analysis of
successfully
of the system under
tubes,
and cooled
of superposition
has
parallel,
earth
against
conditions
using as inputs An extensive
was
to the
sensitivity
of the main design parameters
on
of the system.
INTRODUCTION
Earth-to-air heat exchangers consist of pipes buried in the ground, together with the circulation system which forces air through pipes and eventually mixes it with indoor air of a building or a greenhouse. exchangers under
Detailed are based
simulation models of the thermal on algorithms describing simultaneous
a temperature
symmetric
heat
gradient.]-’
flow into
the ground
performance of earth-to-air heat transfer of heat and mass in soils
However, most of the earlier models involve which does not take into account the natural
axially thermal
stratification of the soil. An accurate and validated model of heat transfer and moisture migration, taking into account thermal stratification in the soil, is given in Refs. 8 and 9. Cleasson”’ and Nissan” provide a complete mathematical analysis of the basic principle of superposition for the heat-transfer process. The
main
objective
of this paper
model
based
on coupled
is to develop
and simultaneous
transfer
an accurate, of heat
transient,
implicit
and mass into the soil and pipes.
The cooling potential of the system has been investigated under real climatic system sensitivity to different design parameters such as pipe lengths, depths below the surface, distances between The model incorporates a complete the soil under moisture depends
a thermal
gradient on the
stratification
gradient
conditions. of buried
The pipes
adjacent pipes, and the pipe radius has been evaluated. mathematical description of moisture migration through
from the higher
to the lower temperature
regions,
while the
redistributes moisture. The net result of the two interrelated phenomena magnitude of the temperature and moisture gradients. Natural thermal
in the
soil
is also
considered
while
appropriate
soil-boundary
applied at the ground surface. Heat transfer from several pipes was obtained principle of superposition and the analysis for a single pipe. MODELLING
OF
EARTH-TO-AIR
HEAT
Modelling of a single earth-to-air heat exchanger The thermal model is first developed for a single pipe.
+To whom
numerical
all correspondence
should
be addressed. 17
conditions
EXCHANGERS
The energy
balance
are
by using the basic
in the soil is
G. MIHALAKAKOU
18
the mass-transfer
et al
equation is
(2)
is the component
is the component
of moisture flux due to the temperature
of moisture
flux due to the moisture
gradient, and
gradient.
The initial conditions
are
T(r, y, t = 0) = ‘I;,(r), h(r, y, t = 0) = ho(r). The boundary conditions at r = R, are: T(R,,
y, t) = T(R,), h(R,, y, t) = h(R,), where R, is a large radial distance in the soil, which has been taken equal to 59 m. At this distance (R,), the temperature and moisture distributions are not influenced by the coupled and simultaneous transfers of heat and mass into the soil caused by the presence of the earth-to-air heat-exchanger system. This far-field boundary for temperature and moisture profiles in the soil and the same distance R, have been used by Schiller,4 Puri,” and Ahmed.‘* At r = R,, the heat-transfer in the soil is equal to the heat losses caused by air Aow through the pipe, i.e.
G,[%(Y) - @,,y,
t)l
= %(=,[dW)l,
(3)
where Gl= 2~~/{(l/~,h,)
+ [ln(R,lri,)/k,]}.
(4)
Here, T.(O) is the ambient air temperature. At r = R,, moisture transfer is only caused by the temperature gradient because the pipe is impervious. Therefore, the component of moisture flux due to the moisture gradient is equal to zero, i.e. 8h(R,, y, t)l& = 0; also, at y =yA, T(r, yA, t)= z(r), h(r, YA? t)=hs(r); at Y =YB, T(r7 yB7 t) = &tr)? h(r, YB, t) =h&). The soil temperature at a point in the pipe vicinity is estimated by superposition of the temperature field due to the pipe system T(r, y, t) and the undisturbed temperature field TU(z, t) due to the ground-surface temperature. Assuming a homogeneous soil of constant thermal diffusivity, the undisturbed temperature T’,(z, t) at any depth z and time t is T,(z, t) = T, -A,
exp[-z(n/365a)“*]
cos{2n/365[t
- to - z/2(365/na)“*]}.
(5)
This expression’3 can be regarded as an analytical solution of the one-dimensional, transient heat-conduction equation. The method of control-volume formulation is used to discretise Eqs. (1) and (2). Details of the numerical method can be found in Ref. 9. The time dependence was best handled by using implicit integration techniques. The basic algorithm used for the evaluation has been developed for TRNSYS, which is a transient system simulation program with a modular structure that facilitates addition to the programs of other mathematical models which are not included in the standard TRNSYS Modelling
library.
of N earth-to-air
heat exchangers
The formulas for N parallel pipes buried in the ground are obtained by superposition from the thermal analysis for a single pipe. Let Qi denote the heat transferred through pipe i, Qj the heat transferred through pipe j and Gj the single-pipe thermal conductance. Qi and Qj are equal to the rhs of Eq. (3) because both are equal to the heat losses from the air flowing through the pipe. The quantity Gij represents the coupling thermal conductance between two of the parallel pipes i and j, where i,j = 1, 2, . . . , N pipes and i #j. Theoretical results on thermal conductance theory have been taken from Claesson.“’ The temperatures of the air which flows
Use of the ground for heat dissipation
along pipe i and of pipe i are Taj(y) and T(R,, is obtained
by superposition
air temperature
dl
equation
system
I
p>,
between
fluctuation
single
pipe
thermal
due to the influence
coupling thermal conductance. while the coupling conductance
As an example, buried
we solved
at the same
the temperature while
K,(y)
and the heat fluxes Q;. The
the second
of the air along term
pipes on pipe i. The coefficients
the particular
are the single-pipe
for pipe i is equal
and
to G, [Eq. (4)],
+ 4z,z,]“*/Bj,}.
case of four parallel
z in the ground
pipes with the same length
and with equal
spacing
between
pipes and the first (or last) pipe,
and G, is the single-pipe
which
conductance,
the pipe i
is the air-temperature
pipes. The heat fluxes are Q, and Q2 for the internal thermal
the
(6)
variation
The single-pipe conductance between pipes i and j is
depth
region
between
,=, G,i’ ,#i
G;
G;, = 2n1nlk,lln{[(B,i)2
radius,
influence
the difference
t,=O’++
y
conductances, of other
The thermal
Therefore,
the air temperature
first term of the rhs of Eq. (6) expresses due to the
results.
for pipe i is
and the pipe temperature
This is a linear
y, t), respectively.
of the single-pipe
T.-T(R
19
is the same
respectively,
for the four pipes
they have the same length and radius. The equations for the difference pipe temperatures for the internal pipes 2 and 3 are, respectively,
between
and
adjacent
because
the air and the
T,~(Y) - ~W,,Y,
t) =
Q,/G
+ Q,/G
+ QJG
+ QJG,,
(7)
MY)
t) =
Q,/G
+ Q,/Gx + QJG,
+ QJGw
(8)
- W&Y,
For the first pipe 1, the temperature T,,(Y) - T,(R,,y,
difference
between
air and pipe is
t) =
QJG
+ QJG,
+ Q,/G,
+ Q,/h.
t) =
QJG, + QJG,
+ Q,lG
+ Q,/Ge
(9)
For the last pipe 4, K,,,(Y) - W,,Y,
(W
Equations (7)-(10) represent relations between the temperature of the air which flows along the pipe and the heat transferred from the pipe to the ground and to neighbouring pipes. For the same example, the air temperature at the internal pipe outlet was compared with the temperature
at an independent
pipe outlet.
For this purpose,
our thermal
model
was used to
simulate the performance of a single earth-to-air heat exchanger. The thermal performance of a plastic pipe, 0.125 m in radius and 30 m in length, buried in the ground at a depth of 1.5 m and with a spacing of 1.5 m while guiding air at a speed of 10 m/set, was simulated. The thermal model for N earth-to-air heat exchangers was used to simulate the performance of these four parallel pipes. Calculations covered the time period 1981-1990 for July and August using hourly values of the air and ground temperatures from 9 a.m. to 7 p.m. The calculated cumulative frequency distributions of the air temperatures at the single-pipe outlet and at the outlet of an internal pipe for July and August are given in Fig. 1.
MODEL
VALIDATION
An extensive set of experiments was performed to measure the temperatures of the air passing through underground pipes. Four plastic pipes of 0.125 m radius and 30 m length were buried in the ground at a depth of 1.5 m. The distance between adjacent pipes was equal to 4 m, while the air velocity in the pipes was equal to 9 m/set. The air temperatures at different points along the pipe were measured using iron-constantan thermocouples. The experiments
20
G.
MIHALAKAKOU et al
60
4
23.0
23.5
24.0
24.5
25.0
25.5
26.0
26.5
27.0
27.5
28.0
28.0
28.5
29.0
28.5
29.0
Temperature
August
0
24.0
24.5
25.0
25.5
26.0
26.5
27.0
27.5
29.5
30.0
Temperature
Fig. 1. Cumulative frequency distribution of the exit-air temperature from an independent earth-toair heat exchanger and from an internal earth-to-air heat exchanger.
44 t
Observed
temperatures
Fig. 2. Measured and predicted values of the air temperature at the outlet of an internal pipe.
Use of the ground for heat dissipation
were carried out during the summer and lasted from were recorded at lo-min intervals. The results were Fig. 2). It is seen that there is very good agreement for the air temperature at the internal pipe outlet. exceeded 0.5 “C.
ASSESSMENT
OF
THE
ENERGY
21
17 to 30 June. Data of the air temperature compared with theoretical predictions (see between the observed and predicted values The maximum observed differences rarely
POTENTIAL
OF
THE
SYSTEM
To prove that the use of earth-to-air heat exchangers can provide an effective means for cooling a number of basic parametric studies were performed. The thermal model was used to simulate the performance and assess the feasibility of using four plastic pipes of 0.125 m radius and 30 m length buried at a depth of 1.5 m. The air velocity in the pipes was again 10 m/set while the distance between adjacent pipes remained at 1.5 m. The calculations cover 1981-1990 for July and August using hourly values of air and ground temperatures from 0900 to 1900 LST. July 100
d ._ ‘c) 5‘
60
5 s e
40
23
25
27
29
31
33
35
37
39
41
Temperature
Temperature Fig. 3. Cumulative frequency distribution of the exit-air temperature heat exchanger for July and August.
from an internal earth-to-air
G.
22
M~HALAKAKOU et al
The air and ground temperatures were collected by the National Observatory of Athens network and includes ground-temperatures (available from 1917) at the ground surface over bare and short-grass-covered soils at 0.3, 0.6, 0.9, and 1.2m depths under the short-grasscovered soil. Based on these measurements, an accurate model to predict annual and daily variations of the ground temperature was developed. I7 Cumulative frequency distributions of air temperatures at the second pipe outlet for July and August are given in Fig. 3, which shows that the outlet-air temperature fluctuated between 24.1 and 28.2”C and 25.4 and 29.7”C for July and August, respectively, while the inlet-air temperatures varied between 23.2 and 40 and 25.3 and 39.3”C. The use of earth-to-air heat exchangers is an important method for space cooling.
SENSITIVITY
To determine the impact analysis was performed for lengths, soil depth, distance again to four pipes buried at 10 m/set.
ANALYSIS
of parameter variations on system performance, a sensitivity 1981-1990 for July and August. The system variables are pipe between adjacent pipes, and pipe radius. The simulations refer 1.5 m and with equal spacing of 1.5 m; the air velocity remained at
Influence of pipe length
The pipe length is a crucial variable in the design of the earth-tubes system. A sensitivity analysis has been carried out for three different values of pipe lengths (20, 30 and 40 m). Figure 4 shows the inlet-and outlet-temperature variations of the air of an internal earth-to-air heat exchanger for three pipe lengths. As can be seen, an increase of the buried pipe length results in a reduction of the exit-air temperature which, in turn, represents an increase of the potential cooling capacity of the system. Influence of pipe radius
Simulations have been performed for three different pipe radii (0.125, 0.180 and 0.250 m) while the other parameters remained unchanged. Figure 5 shows the air-temperature variation at the exit of an internal pipe for the three pipe radius and for the time period l-3 July. This figure indicates that an increase of the buried pipe radius results in a reduction in its convective heat-transfer coefficient which, in turn, increases the outlet-air temperature, thus reducing the system-cooling capacity.
0
Inlet
temperature
.L=20m
n
28.0 -
. r = 0.125 m * I = 0.250 m
32
26
-- 9
14 19 24 29 34 39 44 Time
Fig.
4. Variation
of the inlet-
tures from an internal
49 54 59 64
69
24.5
14 19 24
III1
29 34 39 44
I
49 54 59 64 69
Time (h)
(h) and exit-air
earth-to-air
III1
III 9
tempera-
heat exchanger
for
three days of July and for 20, 30 and 40 m long pipes.
Fig. 5. Variation internal
earth-to-air
of the exit-air
temperature
heat exchanger
days of July and for 0.125, radii.
0.180
from an
for the three first and 0.250m
pipe
Use of the ground
?h
0
B=Sm
.
B = 0 5
--
Fig. 6. Variation internal
heat
oB=.sm
?5
,I,
temperature
exchanger
from an at 2.5 m
buried
Fig. 7. Variation internal
IJ
IY
2-i
?Y
34
39
44
Time Fig. 8. Variation
of the exit-air
54
59
64
of soil
tram
buried
an
at 4 m
09
Time
temperature
from the
pipe buried at I.5 m
for spacing between
temperature
exchanger
depth for three days of July.
adjacent
pipes equal
Fig. 9. Variation
of the exit-air
(h) temperature
first (or last) and from an internal soil depth,
to 0.5 m. for three days of July.
Influence
heat
(h)
first (or last) and from an internal soil depth,
49
of the exit-air
earth-to-air
depth for three days of July.
Y
. B = 0.5 m
I--
of the exit-air
earth-to-air
for heat dissipation
from the
pipe buried at
for spacing between
adjacent
I .5 m
pipes equal
to l.S m, for three days of July.
depth
The soil depth is another purpose, simulations temperature variation
parameter
which has to be considered
in the system
design.
For this
were performed for 2.5 and 4 m depths. Figure 6 shows the airat the exit of an internal pipe for a soil depth equal to 2.5 m, for
distances between adjacent pipes equal to 0.5, 1.S, 2.5, and 5 m, and for the same time period (1-3 July). Figure 7 shows the air-temperature variation at the pipe outlet for 4 m depth. An
27 5
27.5
27 0 2h S I6
Zh.S
0
?6.0
?S S
25.5
25 0
?S.O
1-I 5 24 0
Z4.S
11) 0
I4
I,, I’)
21
i 10
31
39
Time Fig.
B = 1.5 m
r
27.0
IO. Variation
of the
1
I
44
49
1, 54
IJ 59
64
I
24.0 69
1)
14
1, 19
I 24
7Y
(h)
exit-air
I 34
39
Time temperature
from
the first (or last) and from an internal
pipe buried
2.5 m soil depth.
adjacent
for spacing between
equal to 0.5 m, for three days of July.
at
pipes
Fig.
11. Variation
of the
I
I
I
1,
44
49
S4
.io
64 69
(h)
exit-air
temperature
from
the first (or last) and from an internal
pipe buried
2.S m soil depth.
adjaccnr
for spacing between
cqual to 1.5 m, for three days of July.
at
pipes
G.
24 increase
of soil depth
capacity.
However,
leaves the system
again
provides
at depths
greater
performance
et al
MIHALAKAKOU
a considerable than
increase
4 m, the ground
in the potential temperature
system
cooling
stops decreasing
and
unaffected.
Influence of distance between adjacent pipes Four different
spacings
of adjacent
0.5, 1.5, 2.5, and 5 m. The depth the air-temperature respectively, distances
at the outlet
July. The overall
of 2.5 and 5 m, indicated
a reduction
of the air temperature
the air-temperature exit buried be seen,
fluctuation
and for l-3
variations
at a depth
equal
the air-temperature
at the internal
pipes were used for the simulations.
of the buried
pipes was equal of an internal
analysis,
at the internal
pipe
for distance
which was completed
that an increase
in spacing
The distances
to 1.5 m. Figures
between
or first pipe outlet.
were
8 and 9 show 0.5 and
1.5 m,
using the other
adjacent Figures
equal
at the first pipe outlet
to 0.5 and 1.5 m, respectively.
was slightly
in
10 and 11 show
at the exit of the first and last pipes and also at the internal to 2.5 m, for a spacing
two
pipes results
pipe As can
lower than the air temperature
pipe outlet.
REFERENCES
1. M. Santamouris and C. C. Lefas, Energy in Agric. 5, 161 (1986). E. A. Rondriguez, J. M. Cjudo, and S. Alvarez, Proc. CIB Meeting, Paris, France (1988). 3. A. L. T. Seroa da Motta and A. N. Younf, Proc. INTERSOL’8.5, pp. 759-770, E. Bilgen and K. G. T. Holland (1985). 4. G. Schiller, “Earth Tubes for Passive Cooling,” M.Sc. Report, L.B.L. (June 1982). 5. H. J. Levit, R. Gaspar, and R. D. Piacentini, Agric. Forest. Meteor. 47, 31 (1989). 6. V. M. Puri, ASAE Paper No 84-4537, 526, The Pennsylvania State University, University Park, PA (1986). 7. A. M. Amhmed, M. Y. Hamdy, W. L. Roller, and D. L. Elwell, Trans. ASAE 26, 200 (1983). 8. G. Mihalakakou, M. Santamouris, and D. Asimakopoulos, Clima ZOOO,ht. Conf., London (1993). 9. G. Mihalakakou, M. Santamouris, and D. Asimakopoulos, submitted to Sol. Energy (1993). 10. J. Cleasson and A. Dunand, “Heat Extraction from the Ground by Horizontal Pipes,” ISBN 91-540-3851-0, University of Lund, Sweden (1983). 11. C. Nilsson, “Preheating of Ambient Air by a System of Earth Tubes as a Heat Source for Buildings,” Research Project, Chalmers University of Technology, GGteborg, Sweden (1991). 12. A. Ahmed, “Simulation of Simultaneous Heat and Moisture Transfer in Soils Heated by Buried Pipes”, Ph.D. Dissert., The Ohio State University, Columbus (1980). 13. H. S. Carslaw and J. C. Jeager, Conduction of Heat in Solids, Oxford Science Publishers, Oxford, U.K. (1959). 14. G. Agas, T. Matsagos, M. Santamouris, and A. Argiriou, Energy Bldgs 17, 321 (1991). 15. A. Tombazis, A. Argiriou, and M. Santamouris, ht. J. Sol. Energy 9, 1 (1990). 16. M. S. Sodha, D. Buddhi, and R. L. Sawhney, Energy Cowers. Mgmt 31, 95 (1991). 17. G. Mihalakakou, M. Santamouris, and D. Asimakopoulos, Energy Bldgs 19, 1 (1992). 18. T. Tzaferis, D. Liparakis, M. Santamouris, and A. Argiriou, Energy Bldgs 18, 35 (1992). 19. H. N. Shapiro, “Simultaneous Heat and Mass Transfer in Porous Media With Application to Soil Warming With Power Plant Waste Heat,” Ph. D. Dissert, The Ohio State University, Columbus, OH (1975). 2.
NOMENCLATURE
A, = Amplitude of the surfacetemperature variation (“C) a = Thermal diffusivity of the ground (m’/sec)
B,, = Distance between pipes i and j (m) B = Distance between adjacent pipes (m) C, = Specific heat of air (J/kg”(Z)
Use of the ground for heat dissipation C, = Specific heat capacity (J/kg”(Z) Du,_, = Isothermal diffusivity of moisture in vapour form (m’/sec) D., = Thermal moisture diffusivity (m’/sec”C) D, = Isothermal moisture diffusivity (m’/sec) G, = Thermal conductance for a single pipe (W/m) G, = Thermal conductance G,, = h = h, = h,(r) = k =
(W/m’C) k, = Thermal conductivity I = I, = ti,, = Q, = r = R, =
for pipe i
(W/m) Coupling thermal conductance tween pipes i and j (W/M) Moisture content (kg of moisture/kg of moist soil) Heat-transfer coefficient (W/m%) Soil moisture at a large radial distance Soil thermal conductivity
be-
of the pipe
(W/m’C) Pipe length (m) Heat of vaporisation (J/kg) Mass-flow rate of ambient air through the pipe (kg/set) Heat transferred from pipe i to the soil (W) Radial polar coordinate (m) An arbitrarily large radial distance from the pipe axis (m)
r,, R, T T,(y)
= = = =
T(R,, y, t) 7;,(y) T,(R,, y, t) T,
= = = =
2s
Inner pipe radius (m) Outer pipe radius (m) Soil temperature (“C) Temperature of air which flows along a single pipe (“C) Temperature of the pipe (“C) Air temperature of pipe i (“C) Temperature of pipe i (“C) Mean annual ground temperature
(“C) T,(r) = Undisturbed soil temperature which is not influenced by the earth-tube system (“C) T,(z, t) = Ground-temperature at time t and depth i’ (“C) t = Time (set) f,, = Phase constant y = Axial polar coordinate (m) y, = An arbitrarily large axial distance from the pipe inlet (m) y, = An arbitrarily large axial distance from the pipe outlet (m) z = Depth below the ground surface (m) z, = Depth of the buried pipe i below the earth surface (m)
Greek characters p = Soil density (kg/m’) pm = Density of moisture
(kg/m.‘)
Pergamon
Vol. 19, No. I. pp. 17-25, 1994
Copyright @ 19Y4 Elscvier Scicncc Ltd Printed in Great Britain. All rights reserved 03ho-5442/94 $6.00 + 0.00
USE
OF THE
G.
GROUND
model
numerical
air heat exchangers through
temperature
of the natural
thermal
experimental
while
model multi-year investigation
which
process. data.
investigated
to calculate
is described.
the ground, the
DISSIPATION ASIMAKOPOULOS
of Meteorology, Applied Physics Department, University Ippokratous 33, 106 80 Athens. Greece (Received
Abstract-A
HEAT
M. SANTAMOuRIs,t and D.
MIHALAKAKOU,
Laboratory
FOR
ground.
The
operational
of multiple,
air is propelled
The technique model
potential limits
soil and ambient
has been performed
the cooling potential
the performance
or indoor
proposed
The cooling
I.5 March 1993)
The system consists of N parallel
ambient
of Athens,
been
of the system were
air-temperature
in
by the bulk
validated
real climatic
analyzed
measurements.
to analyse the impact
earth-toburied
was used for analysis of
successfully
of the system under
tubes,
and cooled
of superposition
has
parallel,
earth
against
conditions
using as inputs An extensive
was
to the
sensitivity
of the main design parameters
on
of the system.
INTRODUCTION
Earth-to-air heat exchangers consist of pipes buried in the ground, together with the circulation system which forces air through pipes and eventually mixes it with indoor air of a building or a greenhouse. exchangers under
Detailed are based
simulation models of the thermal on algorithms describing simultaneous
a temperature
symmetric
heat
gradient.]-’
flow into
the ground
performance of earth-to-air heat transfer of heat and mass in soils
However, most of the earlier models involve which does not take into account the natural
axially thermal
stratification of the soil. An accurate and validated model of heat transfer and moisture migration, taking into account thermal stratification in the soil, is given in Refs. 8 and 9. Cleasson”’ and Nissan” provide a complete mathematical analysis of the basic principle of superposition for the heat-transfer process. The
main
objective
of this paper
model
based
on coupled
is to develop
and simultaneous
transfer
an accurate, of heat
transient,
implicit
and mass into the soil and pipes.
The cooling potential of the system has been investigated under real climatic system sensitivity to different design parameters such as pipe lengths, depths below the surface, distances between The model incorporates a complete the soil under moisture depends
a thermal
gradient on the
stratification
gradient
conditions. of buried
The pipes
adjacent pipes, and the pipe radius has been evaluated. mathematical description of moisture migration through
from the higher
to the lower temperature
regions,
while the
redistributes moisture. The net result of the two interrelated phenomena magnitude of the temperature and moisture gradients. Natural thermal
in the
soil
is also
considered
while
appropriate
soil-boundary
applied at the ground surface. Heat transfer from several pipes was obtained principle of superposition and the analysis for a single pipe. MODELLING
OF
EARTH-TO-AIR
HEAT
Modelling of a single earth-to-air heat exchanger The thermal model is first developed for a single pipe.
+To whom
numerical
all correspondence
should
be addressed. 17
conditions
EXCHANGERS
The energy
balance
are
by using the basic
in the soil is
G. MIHALAKAKOU
18
the mass-transfer
et al
equation is
(2)
is the component
is the component
of moisture flux due to the temperature
of moisture
flux due to the moisture
gradient, and
gradient.
The initial conditions
are
T(r, y, t = 0) = ‘I;,(r), h(r, y, t = 0) = ho(r). The boundary conditions at r = R, are: T(R,,
y, t) = T(R,), h(R,, y, t) = h(R,), where R, is a large radial distance in the soil, which has been taken equal to 59 m. At this distance (R,), the temperature and moisture distributions are not influenced by the coupled and simultaneous transfers of heat and mass into the soil caused by the presence of the earth-to-air heat-exchanger system. This far-field boundary for temperature and moisture profiles in the soil and the same distance R, have been used by Schiller,4 Puri,” and Ahmed.‘* At r = R,, the heat-transfer in the soil is equal to the heat losses caused by air Aow through the pipe, i.e.
G,[%(Y) - @,,y,
t)l
= %(=,[dW)l,
(3)
where Gl= 2~~/{(l/~,h,)
+ [ln(R,lri,)/k,]}.
(4)
Here, T.(O) is the ambient air temperature. At r = R,, moisture transfer is only caused by the temperature gradient because the pipe is impervious. Therefore, the component of moisture flux due to the moisture gradient is equal to zero, i.e. 8h(R,, y, t)l& = 0; also, at y =yA, T(r, yA, t)= z(r), h(r, YA? t)=hs(r); at Y =YB, T(r7 yB7 t) = &tr)? h(r, YB, t) =h&). The soil temperature at a point in the pipe vicinity is estimated by superposition of the temperature field due to the pipe system T(r, y, t) and the undisturbed temperature field TU(z, t) due to the ground-surface temperature. Assuming a homogeneous soil of constant thermal diffusivity, the undisturbed temperature T’,(z, t) at any depth z and time t is T,(z, t) = T, -A,
exp[-z(n/365a)“*]
cos{2n/365[t
- to - z/2(365/na)“*]}.
(5)
This expression’3 can be regarded as an analytical solution of the one-dimensional, transient heat-conduction equation. The method of control-volume formulation is used to discretise Eqs. (1) and (2). Details of the numerical method can be found in Ref. 9. The time dependence was best handled by using implicit integration techniques. The basic algorithm used for the evaluation has been developed for TRNSYS, which is a transient system simulation program with a modular structure that facilitates addition to the programs of other mathematical models which are not included in the standard TRNSYS Modelling
library.
of N earth-to-air
heat exchangers
The formulas for N parallel pipes buried in the ground are obtained by superposition from the thermal analysis for a single pipe. Let Qi denote the heat transferred through pipe i, Qj the heat transferred through pipe j and Gj the single-pipe thermal conductance. Qi and Qj are equal to the rhs of Eq. (3) because both are equal to the heat losses from the air flowing through the pipe. The quantity Gij represents the coupling thermal conductance between two of the parallel pipes i and j, where i,j = 1, 2, . . . , N pipes and i #j. Theoretical results on thermal conductance theory have been taken from Claesson.“’ The temperatures of the air which flows
Use of the ground for heat dissipation
along pipe i and of pipe i are Taj(y) and T(R,, is obtained
by superposition
air temperature
dl
equation
system
I
p>,
between
fluctuation
single
pipe
thermal
due to the influence
coupling thermal conductance. while the coupling conductance
As an example, buried
we solved
at the same
the temperature while
K,(y)
and the heat fluxes Q;. The
the second
of the air along term
pipes on pipe i. The coefficients
the particular
are the single-pipe
for pipe i is equal
and
to G, [Eq. (4)],
+ 4z,z,]“*/Bj,}.
case of four parallel
z in the ground
pipes with the same length
and with equal
spacing
between
pipes and the first (or last) pipe,
and G, is the single-pipe
which
conductance,
the pipe i
is the air-temperature
pipes. The heat fluxes are Q, and Q2 for the internal thermal
the
(6)
variation
The single-pipe conductance between pipes i and j is
depth
region
between
,=, G,i’ ,#i
G;
G;, = 2n1nlk,lln{[(B,i)2
radius,
influence
the difference
t,=O’++
y
conductances, of other
The thermal
Therefore,
the air temperature
first term of the rhs of Eq. (6) expresses due to the
results.
for pipe i is
and the pipe temperature
This is a linear
y, t), respectively.
of the single-pipe
T.-T(R
19
is the same
respectively,
for the four pipes
they have the same length and radius. The equations for the difference pipe temperatures for the internal pipes 2 and 3 are, respectively,
between
and
adjacent
because
the air and the
T,~(Y) - ~W,,Y,
t) =
Q,/G
+ Q,/G
+ QJG
+ QJG,,
(7)
MY)
t) =
Q,/G
+ Q,/Gx + QJG,
+ QJGw
(8)
- W&Y,
For the first pipe 1, the temperature T,,(Y) - T,(R,,y,
difference
between
air and pipe is
t) =
QJG
+ QJG,
+ Q,/G,
+ Q,/h.
t) =
QJG, + QJG,
+ Q,lG
+ Q,/Ge
(9)
For the last pipe 4, K,,,(Y) - W,,Y,
(W
Equations (7)-(10) represent relations between the temperature of the air which flows along the pipe and the heat transferred from the pipe to the ground and to neighbouring pipes. For the same example, the air temperature at the internal pipe outlet was compared with the temperature
at an independent
pipe outlet.
For this purpose,
our thermal
model
was used to
simulate the performance of a single earth-to-air heat exchanger. The thermal performance of a plastic pipe, 0.125 m in radius and 30 m in length, buried in the ground at a depth of 1.5 m and with a spacing of 1.5 m while guiding air at a speed of 10 m/set, was simulated. The thermal model for N earth-to-air heat exchangers was used to simulate the performance of these four parallel pipes. Calculations covered the time period 1981-1990 for July and August using hourly values of the air and ground temperatures from 9 a.m. to 7 p.m. The calculated cumulative frequency distributions of the air temperatures at the single-pipe outlet and at the outlet of an internal pipe for July and August are given in Fig. 1.
MODEL
VALIDATION
An extensive set of experiments was performed to measure the temperatures of the air passing through underground pipes. Four plastic pipes of 0.125 m radius and 30 m length were buried in the ground at a depth of 1.5 m. The distance between adjacent pipes was equal to 4 m, while the air velocity in the pipes was equal to 9 m/set. The air temperatures at different points along the pipe were measured using iron-constantan thermocouples. The experiments
20
G.
MIHALAKAKOU et al
60
4
23.0
23.5
24.0
24.5
25.0
25.5
26.0
26.5
27.0
27.5
28.0
28.0
28.5
29.0
28.5
29.0
Temperature
August
0
24.0
24.5
25.0
25.5
26.0
26.5
27.0
27.5
29.5
30.0
Temperature
Fig. 1. Cumulative frequency distribution of the exit-air temperature from an independent earth-toair heat exchanger and from an internal earth-to-air heat exchanger.
44 t
Observed
temperatures
Fig. 2. Measured and predicted values of the air temperature at the outlet of an internal pipe.
Use of the ground for heat dissipation
were carried out during the summer and lasted from were recorded at lo-min intervals. The results were Fig. 2). It is seen that there is very good agreement for the air temperature at the internal pipe outlet. exceeded 0.5 “C.
ASSESSMENT
OF
THE
ENERGY
21
17 to 30 June. Data of the air temperature compared with theoretical predictions (see between the observed and predicted values The maximum observed differences rarely
POTENTIAL
OF
THE
SYSTEM
To prove that the use of earth-to-air heat exchangers can provide an effective means for cooling a number of basic parametric studies were performed. The thermal model was used to simulate the performance and assess the feasibility of using four plastic pipes of 0.125 m radius and 30 m length buried at a depth of 1.5 m. The air velocity in the pipes was again 10 m/set while the distance between adjacent pipes remained at 1.5 m. The calculations cover 1981-1990 for July and August using hourly values of air and ground temperatures from 0900 to 1900 LST. July 100
d ._ ‘c) 5‘
60
5 s e
40
23
25
27
29
31
33
35
37
39
41
Temperature
Temperature Fig. 3. Cumulative frequency distribution of the exit-air temperature heat exchanger for July and August.
from an internal earth-to-air
G.
22
M~HALAKAKOU et al
The air and ground temperatures were collected by the National Observatory of Athens network and includes ground-temperatures (available from 1917) at the ground surface over bare and short-grass-covered soils at 0.3, 0.6, 0.9, and 1.2m depths under the short-grasscovered soil. Based on these measurements, an accurate model to predict annual and daily variations of the ground temperature was developed. I7 Cumulative frequency distributions of air temperatures at the second pipe outlet for July and August are given in Fig. 3, which shows that the outlet-air temperature fluctuated between 24.1 and 28.2”C and 25.4 and 29.7”C for July and August, respectively, while the inlet-air temperatures varied between 23.2 and 40 and 25.3 and 39.3”C. The use of earth-to-air heat exchangers is an important method for space cooling.
SENSITIVITY
To determine the impact analysis was performed for lengths, soil depth, distance again to four pipes buried at 10 m/set.
ANALYSIS
of parameter variations on system performance, a sensitivity 1981-1990 for July and August. The system variables are pipe between adjacent pipes, and pipe radius. The simulations refer 1.5 m and with equal spacing of 1.5 m; the air velocity remained at
Influence of pipe length
The pipe length is a crucial variable in the design of the earth-tubes system. A sensitivity analysis has been carried out for three different values of pipe lengths (20, 30 and 40 m). Figure 4 shows the inlet-and outlet-temperature variations of the air of an internal earth-to-air heat exchanger for three pipe lengths. As can be seen, an increase of the buried pipe length results in a reduction of the exit-air temperature which, in turn, represents an increase of the potential cooling capacity of the system. Influence of pipe radius
Simulations have been performed for three different pipe radii (0.125, 0.180 and 0.250 m) while the other parameters remained unchanged. Figure 5 shows the air-temperature variation at the exit of an internal pipe for the three pipe radius and for the time period l-3 July. This figure indicates that an increase of the buried pipe radius results in a reduction in its convective heat-transfer coefficient which, in turn, increases the outlet-air temperature, thus reducing the system-cooling capacity.
0
Inlet
temperature
.L=20m
n
28.0 -
. r = 0.125 m * I = 0.250 m
32
26
-- 9
14 19 24 29 34 39 44 Time
Fig.
4. Variation
of the inlet-
tures from an internal
49 54 59 64
69
24.5
14 19 24
III1
29 34 39 44
I
49 54 59 64 69
Time (h)
(h) and exit-air
earth-to-air
III1
III 9
tempera-
heat exchanger
for
three days of July and for 20, 30 and 40 m long pipes.
Fig. 5. Variation internal
earth-to-air
of the exit-air
temperature
heat exchanger
days of July and for 0.125, radii.
0.180
from an
for the three first and 0.250m
pipe
Use of the ground
?h
0
B=Sm
.
B = 0 5
--
Fig. 6. Variation internal
heat
oB=.sm
?5
,I,
temperature
exchanger
from an at 2.5 m
buried
Fig. 7. Variation internal
IJ
IY
2-i
?Y
34
39
44
Time Fig. 8. Variation
of the exit-air
54
59
64
of soil
tram
buried
an
at 4 m
09
Time
temperature
from the
pipe buried at I.5 m
for spacing between
temperature
exchanger
depth for three days of July.
adjacent
pipes equal
Fig. 9. Variation
of the exit-air
(h) temperature
first (or last) and from an internal soil depth,
to 0.5 m. for three days of July.
Influence
heat
(h)
first (or last) and from an internal soil depth,
49
of the exit-air
earth-to-air
depth for three days of July.
Y
. B = 0.5 m
I--
of the exit-air
earth-to-air
for heat dissipation
from the
pipe buried at
for spacing between
adjacent
I .5 m
pipes equal
to l.S m, for three days of July.
depth
The soil depth is another purpose, simulations temperature variation
parameter
which has to be considered
in the system
design.
For this
were performed for 2.5 and 4 m depths. Figure 6 shows the airat the exit of an internal pipe for a soil depth equal to 2.5 m, for
distances between adjacent pipes equal to 0.5, 1.S, 2.5, and 5 m, and for the same time period (1-3 July). Figure 7 shows the air-temperature variation at the pipe outlet for 4 m depth. An
27 5
27.5
27 0 2h S I6
Zh.S
0
?6.0
?S S
25.5
25 0
?S.O
1-I 5 24 0
Z4.S
11) 0
I4
I,, I’)
21
i 10
31
39
Time Fig.
B = 1.5 m
r
27.0
IO. Variation
of the
1
I
44
49
1, 54
IJ 59
64
I
24.0 69
1)
14
1, 19
I 24
7Y
(h)
exit-air
I 34
39
Time temperature
from
the first (or last) and from an internal
pipe buried
2.5 m soil depth.
adjacent
for spacing between
equal to 0.5 m, for three days of July.
at
pipes
Fig.
11. Variation
of the
I
I
I
1,
44
49
S4
.io
64 69
(h)
exit-air
temperature
from
the first (or last) and from an internal
pipe buried
2.S m soil depth.
adjaccnr
for spacing between
cqual to 1.5 m, for three days of July.
at
pipes
G.
24 increase
of soil depth
capacity.
However,
leaves the system
again
provides
at depths
greater
performance
et al
MIHALAKAKOU
a considerable than
increase
4 m, the ground
in the potential temperature
system
cooling
stops decreasing
and
unaffected.
Influence of distance between adjacent pipes Four different
spacings
of adjacent
0.5, 1.5, 2.5, and 5 m. The depth the air-temperature respectively, distances
at the outlet
July. The overall
of 2.5 and 5 m, indicated
a reduction
of the air temperature
the air-temperature exit buried be seen,
fluctuation
and for l-3
variations
at a depth
equal
the air-temperature
at the internal
pipes were used for the simulations.
of the buried
pipes was equal of an internal
analysis,
at the internal
pipe
for distance
which was completed
that an increase
in spacing
The distances
to 1.5 m. Figures
between
or first pipe outlet.
were
8 and 9 show 0.5 and
1.5 m,
using the other
adjacent Figures
equal
at the first pipe outlet
to 0.5 and 1.5 m, respectively.
was slightly
in
10 and 11 show
at the exit of the first and last pipes and also at the internal to 2.5 m, for a spacing
two
pipes results
pipe As can
lower than the air temperature
pipe outlet.
REFERENCES
1. M. Santamouris and C. C. Lefas, Energy in Agric. 5, 161 (1986). E. A. Rondriguez, J. M. Cjudo, and S. Alvarez, Proc. CIB Meeting, Paris, France (1988). 3. A. L. T. Seroa da Motta and A. N. Younf, Proc. INTERSOL’8.5, pp. 759-770, E. Bilgen and K. G. T. Holland (1985). 4. G. Schiller, “Earth Tubes for Passive Cooling,” M.Sc. Report, L.B.L. (June 1982). 5. H. J. Levit, R. Gaspar, and R. D. Piacentini, Agric. Forest. Meteor. 47, 31 (1989). 6. V. M. Puri, ASAE Paper No 84-4537, 526, The Pennsylvania State University, University Park, PA (1986). 7. A. M. Amhmed, M. Y. Hamdy, W. L. Roller, and D. L. Elwell, Trans. ASAE 26, 200 (1983). 8. G. Mihalakakou, M. Santamouris, and D. Asimakopoulos, Clima ZOOO,ht. Conf., London (1993). 9. G. Mihalakakou, M. Santamouris, and D. Asimakopoulos, submitted to Sol. Energy (1993). 10. J. Cleasson and A. Dunand, “Heat Extraction from the Ground by Horizontal Pipes,” ISBN 91-540-3851-0, University of Lund, Sweden (1983). 11. C. Nilsson, “Preheating of Ambient Air by a System of Earth Tubes as a Heat Source for Buildings,” Research Project, Chalmers University of Technology, GGteborg, Sweden (1991). 12. A. Ahmed, “Simulation of Simultaneous Heat and Moisture Transfer in Soils Heated by Buried Pipes”, Ph.D. Dissert., The Ohio State University, Columbus (1980). 13. H. S. Carslaw and J. C. Jeager, Conduction of Heat in Solids, Oxford Science Publishers, Oxford, U.K. (1959). 14. G. Agas, T. Matsagos, M. Santamouris, and A. Argiriou, Energy Bldgs 17, 321 (1991). 15. A. Tombazis, A. Argiriou, and M. Santamouris, ht. J. Sol. Energy 9, 1 (1990). 16. M. S. Sodha, D. Buddhi, and R. L. Sawhney, Energy Cowers. Mgmt 31, 95 (1991). 17. G. Mihalakakou, M. Santamouris, and D. Asimakopoulos, Energy Bldgs 19, 1 (1992). 18. T. Tzaferis, D. Liparakis, M. Santamouris, and A. Argiriou, Energy Bldgs 18, 35 (1992). 19. H. N. Shapiro, “Simultaneous Heat and Mass Transfer in Porous Media With Application to Soil Warming With Power Plant Waste Heat,” Ph. D. Dissert, The Ohio State University, Columbus, OH (1975). 2.
NOMENCLATURE
A, = Amplitude of the surfacetemperature variation (“C) a = Thermal diffusivity of the ground (m’/sec)
B,, = Distance between pipes i and j (m) B = Distance between adjacent pipes (m) C, = Specific heat of air (J/kg”(Z)
Use of the ground for heat dissipation C, = Specific heat capacity (J/kg”(Z) Du,_, = Isothermal diffusivity of moisture in vapour form (m’/sec) D., = Thermal moisture diffusivity (m’/sec”C) D, = Isothermal moisture diffusivity (m’/sec) G, = Thermal conductance for a single pipe (W/m) G, = Thermal conductance G,, = h = h, = h,(r) = k =
(W/m’C) k, = Thermal conductivity I = I, = ti,, = Q, = r = R, =
for pipe i
(W/m) Coupling thermal conductance tween pipes i and j (W/M) Moisture content (kg of moisture/kg of moist soil) Heat-transfer coefficient (W/m%) Soil moisture at a large radial distance Soil thermal conductivity
be-
of the pipe
(W/m’C) Pipe length (m) Heat of vaporisation (J/kg) Mass-flow rate of ambient air through the pipe (kg/set) Heat transferred from pipe i to the soil (W) Radial polar coordinate (m) An arbitrarily large radial distance from the pipe axis (m)
r,, R, T T,(y)
= = = =
T(R,, y, t) 7;,(y) T,(R,, y, t) T,
= = = =
2s
Inner pipe radius (m) Outer pipe radius (m) Soil temperature (“C) Temperature of air which flows along a single pipe (“C) Temperature of the pipe (“C) Air temperature of pipe i (“C) Temperature of pipe i (“C) Mean annual ground temperature
(“C) T,(r) = Undisturbed soil temperature which is not influenced by the earth-tube system (“C) T,(z, t) = Ground-temperature at time t and depth i’ (“C) t = Time (set) f,, = Phase constant y = Axial polar coordinate (m) y, = An arbitrarily large axial distance from the pipe inlet (m) y, = An arbitrarily large axial distance from the pipe outlet (m) z = Depth below the ground surface (m) z, = Depth of the buried pipe i below the earth surface (m)
Greek characters p = Soil density (kg/m’) pm = Density of moisture
(kg/m.‘)