Barbara Larwa

The results of calculations of the heat transfer in a horizontal ground heat exchanger are presented. The applied model is based on a one-dimensional equation of the transient heat conduction with an internal heat source. The model was correctly verified by comparison of computational results and experimental measurements presented in literature. Thermal calculations concerning heat transfer in the ground under natural conditions are also presented.

This paper concerns the basics of modelling ground heat exchangers. Several specific cases were described, for which computational dependencies and calculation results were presented. Models based on analytical solutions were considered as well as models that use computer applications based on numerical calculations.

Artykuł dotyczy analizy teoretyczno-doświadczalnej przenoszenia ciepła w gruncie. Przedstawiono wyniki
obliczeń przenoszenia ciepła w warunkach naturalnych. Wyznaczono profile temperatur w gruncie w zależności od czasu dla cyklicznego stanu ustalonego. W części eksperymentalnej przedstawiono wyniki badań prowadzonych w instalacji laboratoryjnej. Badania dotyczyły wyznaczenia temperatur w ogrzewanym złożu ziarnistym. Przedstawione wyniki badań i obliczeń zostały wykorzystane do opracowania modelu matematycznego gruntowego wymiennika ciepła.

The results of the numerical simulation of heat conduction in ground with a horizontal, tubular (parallel pipes) heat exchanger installed are presented in this paper. On the basis of analysis of courses of temperature isolines in the ground, a simplified mathematical heat transfer model in a horizontal ground exchanger was developed. The ground thermal diffusivity was assumed to be a variable of location. On the basis of the model, the temperature profiles in the ground with a heat exchanger installed were determined.

Simple cases of heat conduction in the ground are presented. Systems without interaction with the ground surface are considered. For heating or cooling of the ground by a flat slab, an analytical solution was used. Heat transfer between the ground and a single pipe and several parallel pipes is also considered. In these cases, a numerical solution was used. The analysed problems are of practical importance for modelling and simulation of ground heat exchangers cooperating with heat pumps.

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. 

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.

A mathematical model of a ground heat exchanger cooperating with a heat pump was presented. The model is based on a one-dimensional heat conduction equation with an internal heat source. On the basis of the solutions to the model equations, both the temperature distribution of different types of ground at different times of year as well as the time courses of temperature at different depths are shown. Calculations based on the presented model can be useful for the simulation and design of this apparatus.