1、Michel Bernier is a professor, Vivien Godefroy and Corentin Lecomte are graduate students in the Department of Mechanical Engineering, Polytechnique Montral, Montral, Qubec. Mark Douglas is R Tg1 and Tg2 are the temperatures of pipes 1 and 2, respectively. The grout region is sub-divided into three
2、volumes, two half circles each with a volume Vg and a quasi-rectangular volume between the pipes, Vgg .The corresponding temperatures are Tg3, Tg4 and Tg5, respectively. Finally, the borehole wall temperature is Tb. T1 T2Vg VgVggTg1 Tg2Tg3 Tg4Tb Tg5Governing Equations Based on the nomenclature prese
3、nted in Figure 1, the governing equations for the nodal temperatures can be derived based on simple energy balances: , , +, , +, , =0 (1), , +, , +, , =0 (2), , +, , = , , (3) , , +, , = , , (4) , , +, , = , , (5) In these equations, Rfp is the combined thermal resistance of the fluid and of the pip
4、e wall; Rg and Rgg follow the model of the delta-circuit presented by Eskilson and Claesson (1988) with Rg = R1/2 and Rgg = R12/2. The thermal capacitance terms are Cgg = Vgg(Cp)g , Cg = Vg(Cp)g where (Cp)g is the product of the density times the specific heat of the grout. Finally, superscript “0”
5、refers to the value at the previous time step and t is the simulation time step. An energy balance on the fluid segments in each pipe for each vertical region i leads to: Pipe 1: !, #$ !, % otherwise it is off. A 50% propylene-glycol mixture is used as the heat transfer fluid. Balancing valves are i
6、nstalled in the circuit such that the total flow rate is divided equally in each heat pump and in each borehole. The volumetric flow rates, ! and ; * ,using the appropriate fluid density. Fluid temperatures in and out of the two boreholes, Tin and Tout, are measured with type-T thermocouples with an
7、 uncertainty of 0.5 C. These thermocouples are installed inside the house about 5 m (16 ft.) from the borehole inlets. Whenever the heat pumps are not in operation Tin and Tout will tend to reach the house temperature. The system shown on Figure 2 supplied the space heating needs for 47 consecutive
8、days from November 4th to December 20th, 2006. During that period, parameters related to the system energy performance and characteristics were measured and recorded by a data acquisition system. Measurements were scanned every ten seconds and averaged over 5 minute periods. Based on these measureme
9、nts and on the knowledge of the specific heat of the propylene glycol (Cppg), the rate of energy extraction from the ground for each 5 minute time period, Qground, is calculated with Equation 10. !+; *) =. ( #$ ) (10)Thermal Response Test A thermal response test (TRT) was conducted on a third boreho
10、le, 76 m deep, located in-between the two boreholes shown on Figure 2. The TRT was conducted over a 48 hour period about a month prior to the 47 day test. A study of the TRT results by Yang et al. (2007) establishes that the ground thermal conductivity is equal to 2.5 W/m-K (1.45 BTU/hr.ft.F). The T
11、RT was also used to calibrate the ground portion of the TRC model to obtain the ground thermal diffusivity. For this purpose, the TRT was simulated using the TRC model with various ground thermal diffusivities. A thermal diffusivity of 0.086 m2/day yielded the best fit with a corresponding ground th
12、ermal capacitance of 2510 kJ/m3-K (37.4 BTU/ft3-F). As shown in Figure 3 the agreement between the TRT test results and the proposed TRC model are excellent with this value of ground thermal diffusivity. Figure 3 Results of the TRT and of the simulation with the proposed TRC model Validation The pro
13、posed TRC model had previously been validated using the numerical results of He et al. (2012) and the sand box experimental data of Beier et al. (2011). The validation exercise presented here consists of comparing the outlet temperature predicted by the TRC model with the ones obtained during the op
14、eration of a real system. In addition, a qualitative comparison is made between grout temperature measurements inside the borehole and model predictions at a particular borehole depth. Table 1 lists the borehole and ground characteristics used as inputs in the TRC model. Furthermore, the measurement
15、s of Qground (Equation 10) and total mass flow rates, taken every five minutes, are used as inlet conditions to the proposed model. The undisturbed ground temperature used in the model is the average of 8 temperature measurements taken at depth of 5, 10, 25, and 50 m in boreholes #1 and #2 prior to
16、the start of the test. A one-minute time step is used in the simulations and the number of vertical segments, nh, is set to 20. Two single boreholes are simulated with the assumption that there is no thermal interference between them. Hellstrm (1991) established that borehole thermal interference co
17、uld be neglected provided that the distance B between boreholes is greater than 3?8 9. In the present case, 3?8 9=6.5 ; which is less than the distance of 9.2 m betweenthe two boreholes. The full set of data over 47 days is presented in Figure 4. The bottom portion of the figure presents the value o
18、f Qground. When no heat pump is operating, Qground = 0, while values of Qground 1700 and 3400 W indicate the operation of one and two heat pumps, respectively. The figure shows that the rate of energy extraction varies frequently, between 0 and the full-load of the two heat pumps. 0 5 10 15 20 25 30
19、 35 40 45102030HourBorehole fluid temperature(C)00.51Differencebetween model and TRT(C)Proposed TRC ModelTRTDifferenceTable 1. Borehole and ground characteristics Parameter Value Unit Buried depth Borehole #1 depth Borehole #2 depth Borehole spacing Borehole diameter Shank spacing 1.5 (5) 51.8 (170)
20、 50.3 (165) 9.2 (30) 150 (6) 50.8 (2) m (ft) m (ft) m (ft) m (ft) mm (in.) mm (in.) Pipe outer diameter 25.4 (1) mm (in.) Pipe inner diameter 20.4 (0.8) mm (in.) Pipe conductivity 0.4 (0.23) W/mK (BTU/hr.ft.F) Grout conductivity 0.8 (0.46) W/mK (BTU/hr.ft.F) Ground conductivity 2.5 (1.45) W/mK (BTU/
21、hr.ft.F) Grout capacitance 3900 (58.1) kJ/m3.K(BTU/ft3.F)Ground capacitance 2510 (37.4) kJ/m3.K(BTU/ft3.F)Fluid composition 50% Propylene-Glycol - Fluid density 1050 (65.5) kg/m3 (lbm/ft3) Fluid mass capacitance 3470 (0.83) kJ/kg.K (BTU/lbm.F) Ground temperature 10.95 (51.7) C (F) Number sections nh
22、 20 - The middle portion of Figure 4 shows the experimental outlet temperature as well as the one predicted by the model. It should be noted that this middle graph only shows data points when at least one heat pump is operating as the experimental measurements of Tin and Tout, taken inside the house
23、 away from the boreholes, are meaningless when both heat pumps are inactive. Finally, the top portion of Figure 4 compares the values of Tg3 and Tg4 obtained by the model with grout temperature measurements in borehole #2 at a distance of 10 m below the ground surface. The results show an excellent
24、agreement between the model predictions and the experimental data. The Root Mean Square Error (RMSE) on the value of Tout is 0.28C (0.5F) over the test period when at least one heat pump is operating, whereas it is 0.63C(1.1F) when borehole thermal capacity is neglected. A zoomed portion of Figure 4
25、 (represented by the dotted rectangle) is presented in Figure 5. It represents the behavior of the system over an 18 hour period starting at 3pm on day 19. During that period, the system experiences different levels of operation: a long off period starting at 15:00 and lasting about an hour; frequen
26、t heat pump cycling from 19:00 to 21:00; a four-hour long period of continuous operation starting at 0:00. During this first period, there is excellent agreement between the values of Tout predicted with and without thermal capacity. This is to be expected as conditions do not change (Qground = 0 fo
27、r a long period) and both values of Tout will tend to reach the same value, i.e, the neighboring ground temperature. The results that starts at 19:00 show that there is better agreement between the model and the experiments when borehole thermal capacity is accounted for. For the third period starti
28、ng at 0:00, the model predictions without thermal capacity underestimate the value of Tout by 1K. Then, as the conditions remain stable (Qground constant) both values tend towards the same value. However, both values differ by about 0.3 K with the experimental results at the end of this continuous h
29、eat pump operation at 4:00. As shown in the top portion of Figure 5, the fluctuations of the grout temperatures are less pronounced than the ones observed for Tout. This was to be expected as fluid and grout capacities tend to dampen rapid fluctuations in operating conditions. The agreement between
30、the predicted and measured grout temperatures is good considering that the final position of the thermocouple measuring the grout temperature is unknown and that Tg3 and Tg4 are average temperatures of a relatively large volume of grout as shown in Figure 1b. Figure 4 Comparison between the model an
31、d CCHT data Figure 5 Evaluation of the model on a 18-hour time period. CONCLUSION The objective of this study is to validate a borehole model, based on the thermal resistance and capacity (TRC) approach, with experimental data obtained at the Canadian Center for Housing Technology (CCHT) in Ottawa,
32、Canada. Experimental data from two sets of tests are used. The first data set is taken from a thermal response test (TRT) and is used to obtain the ground thermal conductivity and calibrate the ground model against the TRT results to obtain the ground thermal diffusivity. The second data set is take
33、n from the actual operation, over 47 days, of two parallel boreholes linked to two 3.52 kW (1 ton) heat pumps used to heat a house. Results show that there is excellent agreement between the outlet temperatures predicted by the TRC model and the corresponding experimental temperatures with a RMSE 81
34、0T grout,10m(C) 46810Outlet temperature(C) 15:00 18:00 21:00 00:00 03:00 06:00 09:00012Time Q ground(kW)Tout expTout modelTout w/o capacityTg3Tg4Tgrout exp4550T grout,10m(F)404550Outlet temperature(F)048Q ground(kBTU/hr)Borehole #2difference of 0.28C (0.5F). Results also show that the prediction of
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