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Measurement of temperature distribution in ground


Experimental Thermal and Fluid Science 25 (2001) 301±309

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Measurements of temperature distribution in ground
C.O. Popiel
a

/>a,*

, J. Wojtkowiak a, B. Biernacka

b

Fluid and Heat Flow Research Group, Institute of Environmental Engineering, Poznan University of Technology, Piotrowo 3A, 60965 Poznan, Poland b Institute of Environmental Engineering, Bialystok University of Technology, Bialystok, ul. Wiejska 45a, Poland Received 14 September 2000; received in revised form 15 April 2001; accepted 15 June 2001

Abstract Temperature distributions in ground are important, for example, for calculations of heat losses of buildings to the ground, for design of thermal energy storage equipment and ground heat exchangers, and for analysis of biodegradation processes of organic substances and processes of nitri?cation. In this communication, the temperature distributions measured in ground since the summer of 1999 to the spring 2001 are presented. The investigation has been done in Poznan for two di?erent ground surface covered locations (car park and lawn). Temperatures were measured with thermocouples distributed in ground at a depth from 0 to 7 m (car park) and from 0 to 17 m (lawn). It was found that the short-period temperature variations reached a depth of approximately 1 m. From July to the end of September from the surface region at ground depth (below about 1.5 m) a heat ?ux of density q ? 3:6 W=m2 was transferred. The measurements show also that during the summer period the temperature of ground under the bare surface (car park) below 1 m was about 4° higher in comparison with the temperature of ground covered with short grass (lawn). However, in winter, the temperature distributions were almost the same. A comparison of the Buggs's formula for the ground temperature distribution adopted to the European region of the Poznan city shows a good agreement with the experimental data. ? 2001 Elsevier Science Inc. All rights reserved. Keywords: Ground; Temperature distribution

1. Introduction For determination of the thermal interaction of engineering systems such as buildings, pipelines, ground heat storage, and heat pump ground heat exchangers with the ground, precise knowledge of the natural ground temperature distributions are required. Besides, the knowledge of the ground temperature is important for the estimation of nitri?cation processes and of the biodegradation of organic substances. The ground temperature distribution is a?ected by the following factors: (a) structure and physical properties of the ground, (b) ground surface cover (e.g. bare ground, lawn, snow),

* Corresponding author. Tel.: +48-061-8782-537; fax: +48-061-8782-439. E-mail address: popiel@sol.put.poznan.pl (C.O. Popiel).

(c) climate interaction (i.e. boundary conditions) determined by air temperature, wind, solar radiation, air humidity and rainfall. From the point of view of the temperature distribution, we can distinguish the following ground zones: 1. Surface zone reaching a depth of about 1m, in which the ground temperature is very sensitive to short time changes of weather conditions. 2. Shallow zone extending from the depth of about 1±8 m (for dry light soils) or 20 m (for moist heavy sandy soils) where the ground temperature is almost constant and close to the average annual air temperature [1]; in this zone the ground temperature distributions depend mainly on the seasonal cycle weather conditions. 3. Deep zone (below about 8±20 m), where the ground temperature is practically constant (and very slowly rising with depth according to the geothermal gradient). The results of the numerical simulation of the ground temperature distributions are not reliable, because of di?culties of the precise determination of the physical properties of ground and surface bound-

0894-1777/01/$ - see front matter ? 2001 Elsevier Science Inc. All rights reserved. PII: S 0 8 9 4 - 1 7 7 7 ( 0 1 ) 0 0 0 7 8 - 4

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Nomenclature a average annual (apparent) thermal di?usivity of undisturbed ground, m2 =s amplitude of annual average air temperature As wave (based on mean average yearly maximum and minimum on a monthly basis), °C k heat conductivity of ground, W/(mK) vegetation coe?cient kv

q t to T Tm DTm x

heat ?ux density, W=m time, day phase of air temperature wave, day temperature, °C average annual air temperature, °C ground temperature di?erential, °C depth below the ground surface, m

2

ary conditions (i.e. climate interaction). Therefore the simple semi-empirical formulas, such as for example, the formula proposed by Baggs [1,2] for Australian climate conditions are more accurate and easy to use. In this communication, an attempt of use of his formula for the European climate conditions is shown and compared with the experimental data. The results of measurements of the temperature distributions in ground collected in Poznan (Poland) since the summer of 1999 to the spring of 2001 are presented.

2. Experimental stations As the type of a ground cover may a?ect the ground temperature [3] it was decided to set up two experimental stations. One station having ``bare ground surface'', i.e. having surface clear of vegetation which can produce some kind of a solar radiation screen. In our case, it was a ``car park'' paved with bricks. The second one was a ``lawn'' having short grass cover. Both stations were located in the city of Poznan at a distance 30 and 50 m, respectively, from low buildings. For temperature measurements Cu±Konstantan thermocouple wires of 0.5 mm in diameter and thermocouple meter type SR60 (Stanford Research System, USA) having resolution ?0.1 K were used. The temperature readings were taken every 7 or 14 days at 13±15 h. The structure and moisture content of the ground for both stations are shown in Fig. 1.

Fig. 1. Structure and moisture content of soil.

3. Results Ground temperature histories from mid summer of 1999 to February of 2001 at the station having a bare surface (car park) and at the station covered with grass (lawn) for various depths are shown in Fig. 2. Short term strong and irregular ?uctuations of temperature gradually cease at larger depths. Below the depth of about 1.5 m the temperature ?uctuations were hardly discernible. These ?uctuations are the result of a short time erratic changes of weather conditions and are imposed on a long time (seasonal) temperature variations. At a depth below about 1 m the shift of the phase and strong damping of amplitude of the ground

temperature wave with the depth are clearly visible. It is interesting to notice that generally the ground temperature distributions under the lawn are lower than these ones under a bare ground surface. From the temperature history at the depth of x ? 6:9 m, we can infer that that below the shallow zone the ground temperature is constant and under bare surface equal to Tm ? 11:5 °C and under grass surface equal to Tm ? 10:25 °C. In Fig. 3 an evolution of the ground temperature distributions at the station having bare ground (car park) for intervals of 4 weeks from July to November is shown. Initially, the ground temperature in the region of ground close to the surface was higher then in the deeper

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Fig. 2. History of the ground temperature at various depths for bare ground (car park) and for ground covered with grass (lawn) in Poznan since summer of 1999 to February of 2001.

region of the ground. This means that the heat was transferred down from the surface. At the end of September the situation reversed and the heat began to be transferred up to the ground surface. A comparison of ground temperature distributions under bare surface (car park) and under short grass surface (lawn) is given in Fig. 4. In summer, in the temperature distributions directly under the ground surface a typical saddle having minimum at about 25 cm from the surface is seen. This is the result of the night chilling. It is interesting that in summer at the depth below 1 m the ground temperature under grass surface is lower by about 4° then the ground temperature under bare surface. Presumably, the grass played a role of a screen decreasing the e?ect of solar radiation during summer period, whereas, in winter and in early spring the temperature distributions under bare and

lawn surfaces are almost the same as the solar radiation is weak (Figs. 4(j)±(s)). The e?ect of solar radiation during calm sunny hours in summer causes that temperature of the bare ground surface to be considerably higher than the temperature of air, e.g. at noon April of 2000 an excess of the air temperature was 7° (see Fig. 4(s)). From July to the end of September the uniform negative temperature gradient in the temperature distributions below a depth of about 1 m from ground surface is seen. It means that almost constant heat ?ux is transferred from the ground surface to the shallow zone of the ground, e.g. below 2 m depth we have q ? ?k oT 2 ? 1:8 ? 2:0 ? 3:6 W=m ; ox ?1?

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Fig. 2. (Continued).

where: oT =ox ?$ ?2:0 K=m ± average temperature gradient below 2 m depth, k ? 1:8 W/(mK) ± average heat conductivity of ground (e.g. [4]).

4. Comparison of the experimental data with the Baggs's formula The Baggs's formula is based on the solution for a transient heat conduction in a semi-in?nite solid (e.g. 5, p. 210) where the temperature of the exposed surface (x ? 0) is varying periodically with time Tx?0;t ? As cos ?2p?t ? to ?=365?. This formula adopted for the northern hemisphere has a form

Fig. 3. Ground temperature distributions for bare ground in summer and autumn of 1999.

C.O. Popiel et al. / Experimental Thermal and Fluid Science 25 (2001) 301±309

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Fig. 4. Comparison of the ground temperature distributions for bare and grass surfaces.

T ?x; t? ? ?Tm ? DTm ? ? 1:07kv As exp??0:00031552xa?0:5 ?   2p ?0 : 5 ?t ? to ? 0:018335xa ? : ? 2? ? cos 365 The vegetation coe?cient kv used in the above formula depends on the ``proportion of vegetation projective shade cover''. According to Baggs for a ``bare ground in full sun'' the vegetation coe?cient is equal to unity (kv ? 1), and for the proportion of vegetation projec-

tive shade cover equal 100% the vegetation coe?cient is about kv ? 0:22 [2]. In Figs. 5 and 6, a comparison of the results of measurements and prediction with the Eq. (2) of the ground temperature distributions show a very good agreement. From Figs. 6 and 7, we can see that under the lawn at the depth below x ? 10 m the ground temperature is constant and equal to Tm ? 10:25 °C. The calculations were performed with the Eq. (2) using Tm ? 9:4 °C and As ? 11:6K ± data based on the last

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Fig. 4. (Continued).

5 years on-site meteorological records, DTm ? 10:25±9:4 ? 0:85 K, kv ? 0:9, a ? 5:5 ? 10?7 m2 /s [2]. 5. Concluding remarks 1. Short-period strong ?uctuations of the ground temperature reach a depth of about 1 m. 2. During summer time, the heat ?ux density transferred from the ground surface zone to the deeper 2 part of ground is about q ? 3:6 W=m . At the end

of September at the depth of about 1 m the ground temperature gradient reaches zero and the situation reversed, the heat began to be transferred up to the ground surface. 3. In summer at a depth below 1 m the temperature of ground under the lawn surface is about 4° lower. Therefore for the ground ``cold'' source, e.g. for the air conditioning application the lawn surface is recommended. 4. Usually the recommended depth for horizontal ground heat exchangers is from 1.5 to 2 m. At these

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Fig. 4. (Continued).

depths the natural ground temperatures for bare surface in Poznan for 1999/2000 season reach the following values: · summer maximum (in August): from 15 to 17 °C · winter minimum (in February): $5 °C. 5. For the investigated stations the boundary between the shallow zone and the deep zone of constant ground temperature is at a depth of about 10 m and the corresponding constant ground temperature is equal

· for a ground under bare surface (car park): Tm ? DTm ? 11:5 °C, · for a ground under short grass surface (lawn): Tm ? DTm ? 10:25 °C at the average annual air temperature equal to Tm ? 9:4 °C. 6. A comparison of the Buggs's formula for the ground temperature distribution adopted to the European climate conditions (Poznan, Poland) shows a good agreement with the experimental data.

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C.O. Popiel et al. / Experimental Thermal and Fluid Science 25 (2001) 301±309

Fig. 5. Comparison of measured and predicted ground temperature history for ground under a lawn at a depth of 1, 2 and 4 m for: Tm ? 9:4 °C, DTm ? 0:85 K, kv ? 0:9, As ? 11:6 K, a ? 5:5 ? 10?7 m2 /s, to ?21 days.

Fig. 6. Comparison of measured and predicted ground temperature distributions for ground under a lawn for: Tm ? 9:4 °C, DTm ? 0:85 K, kv ? 0:9, As ? 11:6 K, a ? 5:5 ? 10?7 m2 /s, to ? 21 days.

Fig. 7. Ground temperature history for ground under a lawn at a depth of 6, 8, 10, 12.5, 15 and 17.3 m.

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References
[1] S.A. Baggs, Remote prediction of ground temperature in Australian soils and mapping its distribution, Solar Energy 30 (1983) 351± 366. [2] S.A. Baggs, in: Australian Earth-Covered Building, New South Wales University Press, New South Wales, 1991, pp. 154±173 (Appendices).

[3] G. Mihalakakou, M. Santamouris, J.O. Lewis, D.N. Asimakopoulos, On the application of the energy equation to predict ground temperature pro?les, Solar Energy 60 (1997) 181±190. [4] V.R. Tarnawski, B. Wagner, A new computerised approach to estimating the thermal properties of unfrozen soils, Canadian Geotech. J. 29 (1992) 714±720. [5] E.R.G. Eckert, R.M. Drake, Analysis of Heat and Mass Transfer, McGraw-Hill Book, New York, 1972.


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