Operation analysis of a spiral ground heat exchanger functioning as a lower heat source in a pressurizing heat pump

The main aim of the study is to identify functioning of a ground, spiral heat exchanger co-functioning with a pressurizing heat pump. The heat pump is connected with a heat battery and works periodically during the heating period. The analysis was made by means of numerical modelling and using the finite element method.


Introduction
A common solution for lower heat source in low-power, pressurizing heat pump installations are horizontal, ground heat exchangers. Horizontal exchangers are usually installed at the depth of 1.5-1.6 metre in relation to the ground level. The main limitations connected with using such solutions are:  the efficiency is strongly dependant on the degree of base ground moisture;  there is strong influence of atmospheric air temperature on the efficiency of a ground heat exchanger;  large ground area is required in order to provide appropriate efficiency of the exchanger;  there is a possibility of freezing the ground surface layers, which leads to hindering plant vegetation;  high investment costs connected with laying pipes of the exchanger in the ground.
The so-called spiral ground heat exchangers are free from these disadvantages.  Figure 1 shows temperature distribution in ground for particular months. The closer to the surface the higher amplitudes of temperature changes in the ground can be observed. It is the effect of temperature wave penetrating the ground, which results from seasonal changes of atmospheric temperature. In the case of a spiral exchanger, which is installed at the depth of 1.8-5.5 m beneath the ground level, one can observe a significantly lower amplitude of temperature change than in the case of a horizontal exchanger. This enables to provide much more stable working conditions of a spiral exchanger during whole year and its smaller influence on temperature in the area just below the ground surface. It has significant influence on plant vegetation. Apart from that, in deeper parts grounds have lower moisture, which has positive impact on heat transfer from the ground to the working medium in the ground heat exchanger [6,8].

Model
In order to conduct the analysis of a ground heat exchanger in the conditions of nondetermined heat exchange, the measurement data were approximated to average monthly temperature of atmospheric air on the basis of many-year meteorological research of Rzeszów [10], Table 1, by using Hillel's model, fig. 2: where: x-depth, m The amplitude of atmospheric air was determined on the basis of meteorological data [10]. Constant values of specific heat, density and ground conductance coefficients were assumed for the analysis of lower heat source operation. Boundary conditions at the ground surface were also determined on the basis with Hillel's model, assuming the coefficient of atmospheric air transfer of 16 W/m 2 K.  The data for December were assumed as an initial condition for numerical calculations. On this basis, as well as by using Hillel's model, the initial profile of temperature in ground was determined, fig. 3.

Numerical model
The computational domain was divided into: 148774 3D prismatic elements, 6296 triangular elements of 2D surface and 940 boundary elements. The numerical calculations encompassed the analysis of the unsteady temperature area in the ground, the temperature of the working medium flowing in coils of ground heat exchangers. The flow of the medium and the unsteady heat exchange in coils were analysed by using 1 D-time models, and in the ground by means of the 3D-time method. Comsol Multiphysics software was used for calculations [1,7].   9. Isotherms around the ground heat exchanger on the 5th day of operation from its start. Figures 8 and 9 show the temperature field in the ground around coil-spiral heat exchangers. As one can notice, the area of the influence of heat exchanger on the temperature field encompasses a small area around the exchanger. Additionally, heat is transported to the medium from deeper parts of the ground [3]. It provides the possibility to increase condensation of coils in the given area. It enables to increase unit heat power when comparing to horizontal ground heat exchangers. Additionally, absorption of heat from   Cold working medium flows in at the lowest point of the coil and then is transported upwards. As one can notice the medium gradually heats up, but in the upper part of the coil that is placed below the ground surface it is cooled down. It is due to lower ground temperature than the temperature of the medium. It causes deterioration of the efficiency of heat exchanger performance [2,5]. Therefore, in order to improve the efficiency of operation one should apply an exchanger with variable scale so that it is smaller in the lower part and bigger in the upper part. It enables to increase the efficiency of heat exchangers as the difference between the ground and the medium becomes bigger.  Figure 11 presents temperature of the medium in the inlet and outlet of the coil heat exchanger. As it can be seen, after some time the waveform of temperature is stabilised and almost reaches a quasi-stastic state. One can notice a small amplitude of the working medium changes, about 2 o C, as well as that temperatures above 0 o C that are maintained at the outlet of the exchanger. It has positive influence on the conditions of heat exchanger operation as it improves the thermal coefficient of performance.

Conclusion
Final effects of the R&D studies in the context of the research results will allow for quantitative and qualitative analysis of the influence of coupling photo-thermal collectors with a heat pump in the lower part of the heat pump on the energy output, as well as productivity and general efficiency of the installation [4,9]. The economic analysis together with the what-if analysis will enable to consider the influence of control algorithms and characteristics of energy receivers, which should allow to optimize the choice of technological installation scheme selection to the building where it is to be installed.
The result of the R&D research in the implementation aspect will be preparation of the offer for energy system working on the basis of photo-thermal collectors with a heat pump that uses the effect of synergy of their coupling in the lower part of the pump and component elements of such a system.