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In G. Pernigotti, F. Patuzzi, A. Prada, V. Corrado & A. Gasparella (Eds.), Building Simulation Applications BSA 2022 (pp. 299–304).

The present Ph.D. dissertation deals with the finite element analysis of the heat transfer processes in double U-tube Borehole Heat Exchangers, called BHEs. In the evaluation of thermal response tests (TRTs), in the design of the BHE fields, and in the dynamic simulation of ground-coupled heat pumps (GCHPs), the mean temperature Tm of the working fluid in a BHE, is usually approximated by the arithmetic mean of inlet and outlet temperatures. In TRTs, this approximation causes an overestimation of the thermal resistance of the heat exchanger. In the dynamic simulation of GCHPs, this approximation introduces an error in the evaluation of the outlet temperature from the ground heat exchangers. In the present thesis, by means of 3D finite element simulations, firstly, the analysis of the fluid temperature distribution is carried out, then, correlations are proposed to determine the mean fluid temperature, for double U-tube BHEs. Tables of a dimensionless coefficient are provided that allows an immediate evaluation of Tm in any working condition, with reference to double U-BHEs with a typical geometry. In addition, the effects of the surface temperature distribution on the thermal resistance of a double U-tube BHE are investigated. It is shown that the thermal resistance of a BHE cross section (2D) is not influenced by the bulk-temperature difference between pairs of tubes, but is influenced by the thermal conductivity of the ground when the shank spacing is high. Then it is shown that, if the real mean values of the bulk fluid temperature and of the BHE external surface are considered, the 3D thermal resistance of the BHE coincides with the thermal resistance of a BHE cross section, provided that the latter is invariant along the BHE., La presente Tesi di Dottorato tratta dell’analisi agli elementi finite dei processi di trasmissione del calore in scambiatori verticali con il terreno detti “Borehole Heat Exchangers”, BHEs, con riferimento a BHEs a doppio tubo a U. Nella valutazione di Test di Risposta Termica (TRTs), per il progetto di campi di BHEs, e nella simulazione dinamica di pompe di calore accoppiate al terreno (Ground-Coupled Heat Pumps, GCHPs), la temperatura media Tm del fluido operatore in un BHE è abitualmente approssimata dalla media aritmetica della temperatura in ingresso e di quella in uscita del fluido. Nei TRT, questa approssimazione causa una sovrastima della resistenza termica dello scambiatore. Nella simulazione dinamica delle GCHPs, questa approssimazione introduce un errore nel calcolo della temperatura in uscita dallo scambiatore di calore. In questa Tesi, la distribuzione di temperatura del fluido nello scambiatore viene studiata mediante accurate simulazioni 3D agli elementi finiti, quindi vengono proposte semplici correlazioni adimensionali che consentono di determinare la temperatura media Tm del fluido in qualsiasi condizione operativa, date le temperature in entrata e in uscita e la portata in volume del fluido e la conducibilità termica della malta sigillante. Vengono inoltre analizzati gli effetti della distribuzione di temperatura superficiale dello scambiatore sulla resistenza termica dello stesso. Si mostra che la resistenza termica 2D di una sezione trasversale non è influenzata dalla differenza della temperatura di bulk fra coppie di tubi, ma è influenzata dalla conducibilità termica del terreno circostante se l’interasse fra i tubi è elevato. Si mostra anche che, se vengono considerati i veri valori della temperatura media di bulk del fluido e della temperatura alla superficie esterna dello scambiatore, la resistenza termica 3D dello scambiatore coincide con quella 2D di una sezione trasversale, a condizione che questa possa essere considerata invariante lungo lo scambiatore.

The design of ground-coupled heat pump systems requires the knowledge of the mean temperature Tfm of the working fluid in borehole heat exchangers. This quantity is usually approximated by the arithmetic mean of inlet and outlet temperature. The approximation yields an overestimation of the thermal resistance of the heat exchanger in thermal response tests, as well as errors in the estimation of the outlet fluid temperature in the dynamic simulation of ground-coupled heat pumps. Recently (Applied Energy 206, 2017, 1406–1415), Zanchini and Jahanbin determined, by finite element simulations, correlations that allow an immediate evaluation of Tfm in any working condition, with reference to double U-tube boreholes with length 100 m and shank spacing 85 mm. In this paper, the analysis presented there is extended to double U-tube boreholes with any length, between 50 and 200 m, and any shank spacing, between 65 and 105 mm. The results hold for every thermal conductivity of the sealing grout between 0.9 and 1.6 W/(m K), every volume flow rate between 12 and 24 L per minute, every diameter of the BHE and every working condition (heating, cooling, thermal response test), both in quasi-stationary and in transient regime.

In the evaluation of thermal response tests and in the dynamic simulation of ground-coupled heat pumps, the mean temperature Tm of the working fluid in a borehole heat exchanger is usually approximated by the arithmetic mean of inlet and outlet temperature. In thermal response tests, this approximation causes an overestimation of the thermal resistance of the heat exchanger. In the dynamic simulation of ground-coupled heat pumps, this approximation introduces an error in the evaluation of the outlet temperature from the ground heat exchangers. In this paper, by means of 3D finite element simulations, we provide tables of a dimensionless coefficient that allows an immediate evaluation of Tm in any working condition, with reference to double U-tube borehole heat exchangers with a typical geometry. These tables allow a more accurate estimation of the borehole thermal resistance by thermal response tests and a more accurate evaluation of the outlet temperature in dynamic simulations of ground-coupled heat pump systems. Criteria for the extension of the results to other geometries are also provided.

An accurate assessment of thermal comfort inside a building is essential since it is associated to the human’s perception of well-being and comfort. In the present study, a 3D computational fluid dynamic (CFD) code is employed to evaluate the indoor comfort indexes for a university office located in a historical building, built of thick masonry walls and of large single-glass windows, using fan coil as an air conditioning system. The experimental measurement has been carried out to validate the numerical model and to obtain the required initial and boundary conditions. The experimental set-up employs an innovative system for the sensor localization, based on acoustic sources, signal processing and trilateration algorithms. By means of finite volume method, the turbulent air flow, the local heat transfer characteristics and the operative temperature inside the room are obtained for a typical winter day. The results yielded by numerical simulations allow to evaluate thermal comfort condition at working places inside the office and to identify the best comfort areas. The results show that even when the air temperature is quite uniform inside the room, the operative temperature at the positions where occupants are placed is significantly affected by surface temperature of the windows, due to the large window to wall surface ratio and also by the position and operational condition of fan coil. It is concluded that 3D comfort map allows to optimize internal layout of the office room; furthermore, the possibility of thermal comfort optimization in specific workstation together with local control of heating system lead to gain remarkable energy saving results.

Forced convective heat transfer and wall characteristics of nanofluid flow containing Al2O3 nanoparticles and water inside a miniature tube is studied numerically by means of computational fluid dynamic (CFD) code. Problem is solved by employing finite volume approach using both single-phase (homogeneous) and dispersion models. In both models, constant and temperature-dependent thermophysical properties are used and results are compared to available experimental and theoretical literatures. It can be seen as the Reynolds number increases, the Nusselt number improves, too. However, it is accompanied by higher wall shear stress. Moreover, in the case of temperature-dependent properties, lower values for shear stress were obtained. In comparison with experimental data and available theoretical correlations, dispersion model in both temperature-dependent and constant properties shows a desirable compatibility. On the other hand, single-phase model in constant thermophysical properties underestimates the amount of convective heat transfer. Furthermore, it can be observed at wall, by increasing the particles volume concentration, not only wall temperature decreases also, rate of thermal enhancement decreases slightly.

The effects of the surface temperature distribution on the thermal resistance of a double U-tube Borehole Heat Exchanger (BHE) are studied by finite element simulations. It is shown that the thermal resistance of a BHE cross section is not influenced by the bulk-temperature difference between pairs of tubes, but is influenced by the thermal conductivity of the ground when the shank spacing is high. Then it is shown that, if the real mean values of the fluid bulk temperature and of the BHE external surface are considered, the 3D thermal resistance of the BHE coincides with the thermal resistance of a BHE cross section, provided that the latter is invariant along the BHE. Finally the difference between the BHE thermal resistance and the effective BHE thermal resistance, defined by replacing the real mean temperature of the fluid with the average of inlet and outlet temperature, is evaluated in some relevant cases.

This paper proceeds numerical investigation on forced convective heat transfer of nanofluids in laminar flow inside a mini-channel with circular cross-section under constant heat flux boundary condition at walls. Nanofluid contains CuO nanoparticles with diameter of 50 nanometer in water base fluid. At the entrance of channel, profiles of uniform velocity & temperature prevail. In order to obtain fully developed profiles, geometry of problem considers as L/D = 100. Problem is solved by means of 4 different models, including Homogeneous and Dispersion models in both of constant and variable thermophysical properties through the finite-volume method. The temperature-dependent properties was used for the first time in nanofluids dispersion model. It was regarded in the presence of nanoparticles the heat transfer coefficient will be increased to some considerable extent and the heat transfer enhancement strongly depends on the volume concentration of nanoparticles and Peclet number. Also, comparison with experimental data and literatures' correlations is carried out which indicates the Dispersion model in both cases is more precise and Homogeneous model (single phase) underestimates the Nusselt number in constant thermo physical properties.