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###### 日期：2019-07-28 11:01

Assignment #2

(Individual submission, world limit: 2000 words)

1. Results from Thermal Response Testing (TRT) of a single U-loop, 30m long ground heat exchanger

is presented in the attached excel file. For an estimated thermal diffusivity of 9.5e-7 (m2

/s), constant

thermal load (Q) of 1400W, borehole diameter of 140 mm and undisturbed ground temperature of

18°C, calculate the ground thermal conductivity and ground heat exchanger thermal resistance.

2. A residential building with peak heating and cooling demand of 1kW has considered the installation

of vertical ground source heat pump systems.

a. Assuming the ground source heat pump and the ground properties shown in tables below

and estimated ground thermal conductivity from the TRT results, calculate the required

total ground heat exchanger (GHE) length for the system (equations and plots required to

be shown).

b. Accounting for the maximum length of 5m/GHE and the minimum required distance

between the GHE (2m) in a GHE-field, calculate the ground thermal load distribution (by

time) for each GHE (remember heating load is positive and cooling load is negative in

COMSOL).

c. Simulate the transient thermal interaction between the GHEs and the ground by coupling

and solving heat transfer and fluid flow equations using COMSOL with a coarse – physics

controlled – mesh and present a plot of the 3D temperature field of the model for time=60

days.

d. Estimate the maximum radius of thermal disturbance in the ground by plotting the

temperature increase/decrease in the ground and investigate the effect of farfield boundary

on carrier fluid average temperature.

e. Plot the average carrier fluid temperature variations by time. Conduct a parametric analysis

on carrier fluid velocity, varying between Re of 1,000, 4,000 and 10,000 and discuss the

changes in the carrier fluid average temperature variations by time for each Re number.

f. Discuss how groundwater flow might impact the efficiency of the GHE field (if the ground

has a hydraulic conductivity of 1e-4 m/s and porosity of 0.3).

Material Thermal

conductivity

Ground From TRT

results 1100 1900 18 18 10 NA NA

Grout 1.5 890 2250 NA 18 0.114 NA NA

Pipe 0.45 NA NA NA 18 0.025 (outer) 2.27 NA

Carrier fluid 0.58 4180 1000 NA 18 NA NA 0.3

COP Heating=3.9

Cooling=2.5

Qpeak 1kW (heating, cooling)

Tbalance 18°C

EWT min 7°C

LWT min 4°C

EWT max 32°C

LWT max 35°C

Rborehole 0.19 mK/W

FH 0.6