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1

Study of temperature distribution in the ground

Larwa Barbara, Kupiec Krzysztof

Chemical and Process Engineering

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2019

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Vol. 40, nr 1

123–-137

EN

Knowledge of the temperature distribution in subsurface layers of the ground is important in thedesign, modelling and exploitation of ground heat exchangers. In this work a mathematical model ofheat transfer in the ground is presented. The model is based on the solution of the equation of transientheat transfer in a semi-infinite medium. In the boundary condition on the surface of the groundradiation fluxes (short- and long-wave), convective heat flux and evaporative heat flux are taken intoaccount. Based on the developed model, calculations were carried out to determine the impact ofclimatic conditions and the physical properties of the ground on the parameters of the Carslaw-Jeagerequation. Example results of calculated yearly courses of the daily average temperature of the surfaceof the ground and the amount of particular heat fluxes on the ground surface are presented. Thecompatibility of ground temperature measurements at different depths with the results obtained fromthe Carslaw–Jaeger equation is evaluated. It was found thatthe temperature distribution in the groundand its variability in time can be calculated with good accuracy.

2

Parameters of the Carslaw-Jaeger equation describing the temperature distribution in the ground

Larwa B., Gwadera M., Kicińska I., Kupiec K.

Technical Transactions

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2018

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Vol. 115, iss. 9

67--78

EN

The ground temperature changes with depth and time. Time variability is considered as a harmonic function. The equation describing changes of the ground temperature contains four parameters: the average annual temperature of the surface of the ground, the annual amplitude of the temperature of the ground surface as well as the phase angle of the temperature and thermal diffusivity of the ground. Based on the results of the measurements presented in the literature, the parameters of the equation using the combined method on the basis of linear regression, described in the literature, were determined. This method, however, leads to an ambiguous value of the thermal diffusivity. It was found that the nonlinear regression method gives much better results, leading to obtaining precise and unambiguous values of all parameters of the equation.

PL

Temperatura gruntu zmienia się z głębokością oraz w czasie. Zmienność czasowa ma charakter harmoniczny. Równanie opisujące zmiany temperatury gruntu zawiera cztery parametry: średnioroczną temperaturę powierzchni gruntu, roczną amplitudę temperatury powierzchni gruntu, kąt fazowy oraz dyfuzyjność cieplną gruntu. Na podstawie wyników pomiarów przedstawionych w literaturze wyznaczono parametry równania kombinowaną metodą opierającą się na regresji liniowej, opisaną w literaturze. Metoda ta prowadzi jednak do otrzymania niejednoznacznej wartości współczynnika dyfuzyjności cieplnej. Stwierdzono, że znacznie lepsze wyniki daje metoda regresji nieliniowej, prowadząc do otrzymania dokładnych i jednoznacznych wartości wszystkich parametrów równania.

3

Pomiary temperatury w gruncie oraz w gruntowym wymienniku ciepła (GWC) w rocznym cyklu eksploatacyjnym

Sikora K.

Pomiary Automatyka Kontrola

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2010

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R. 56, nr 3

265-267

PL

W artykule przedstawiono układ do pomiaru i rejestracji temperatury w wybranych punktach w obszarze gruntu, oraz w obszarze powietrznym gruntowego wymiennika ciepła (GWC), oraz przedstawiono i omówiono wyniki pomiarów dla rocznego cyklu eksploatacyjnego GWC. Celem pomiarów było wyznaczenie efektywności wymiennika oraz pozyskanie danych do weryfikacji numerycznego modelu wymiennika gruntowego. Na podstawie pomiarów określono kryteria efektywnej pracy wymiennika.

EN

Experimental investigations of the ground tube heat exchanger were performed. An automatic measurement system for data acquisition was constructed. The system consists of six RTD temperature sensors, one thermoanemometric sensor, a multichannel power supply and a PC with the Advantech USB 4711 acquisition module (see Fig. 1). All the sensors were calibrated and the profile of the velocity distribution along the tube was determined for the thermoanemometric sensor. The measurement data were written to .xls files (three days in one file). For this purpose the own data acquisition program in VBA was developed. The measurement period began in January 2006 and ended in April 2007. The experimental data were averaged to one hour and extended with those taken at the IMGW meteorological station in Bielsko-Biala Aleksandrowice (relative humidity and absolute pressure of the ambient air). On the basis of these data, the heat fluxes were calculated (heat transfer from the ground to the air). The ground tube heat exchanger efficiency was also calculated. The thermal ground diffusivity value necessary for numerical analysis was determined from the experimental data in the form of the ground temperature distributions (Fig. 2).