Numerical Analysis of the Factors Influencing a Vertical U-Tube Ground Heat Exchanger
Abstract
:1. Introduction
2. Methods
2.1. Model Description
2.2. The Governing Equations
2.3 Data Processing
- (1)
- The initial temperature is a constant of 290.6 K.
- (2)
- The far-field and bottom surfaces are set as undisturbed boundaries.
- (3)
- The top ground surface is set as a convective boundary with an air temperature of 289.0 K and a heat transfer coefficient of 10 W/(m2·K).
- (4)
- The inlet is set as a velocity-inlet boundary, and the outlet is set as a pressure-outlet boundary.
- (5)
- The reference parameters for simulation are listed in Table 2.
3. Analysis of Influencing Factors of Heat Transfer
3.1. Influence of Grout Materials
3.2. Influence of Soil
3.3. Influence of Inlet Water Temperature
3.4 Influence of Inlet Water Velocity
3.5. Influence of Groundwater Flow
4. Conclusions
- (1)
- Before the heat in the borehole is saturated, the heat flux in the GHE is directly proportional to the thermal conductivity coefficient of the grout materials.
- (2)
- The greater the thermal diffusion coefficient of the soil materials, the larger the radius of the thermal effect of the GHE and the faster the recovery rate of the temperature in the soil.
- (3)
- Increasing the inlet water temperature strengthens the heat transfer in the GHE, but it can cause heat buildup problems.
- (4)
- Increasing the inlet water velocity can enlarge the heat convection in the tube; when the inlet water velocity values are 0.2 m/s, 0.3 m/s, and 0.6 m/s, the computed average surface heat transfer coefficients are 17.97 W/(m2·K), 21.06 W/(m2·K), and 25.95 W/(m2·K), respectively.
- (5)
- The thermal-seepage coupling effect in groundwater can remove the accumulated heat, and therefore, can effectively enhance the heat transfer in the GHE.
Acknowledgments
Author Contributions
Conflicts of Interest
Nomenclature
Main symbols | |
H | borehole depth (m) |
heat flux per unit borehole depth (W/m) | |
S | source term |
T | temperature (K) |
velocity vector | |
velocity components in directions | |
Cartesian coordinates | |
Greek symbols | |
soil permeability (m2) | |
turbulent dissipation rate (m2/s3) | |
turbulent kinematic energy (m2/s2) | |
thermal conductivity (W/m·K) | |
dynamic viscosity (N·s/m2) | |
turbulent viscosity (N·s/m2) | |
inlet flow (m3/h) | |
temperature recovery rate | |
density (kg/m3) | |
volumetric heat capacity (kJ/(m3·K)) | |
time (h) | |
soil porosity | |
generalized variable | |
Subscripts | |
f | underground water |
inlet and outlet | |
s | soil |
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Coarse Mesh | Medium Mesh | Finer Mesh | Experiment | |
---|---|---|---|---|
Mesh number | 353,127 | 485,227 | 692,570 | - |
Heat flux (W/(m·K)) | 51.81 | 52.77 | 53.62 | 53.31 |
Difference (%) | 2.81 | 1.01 | 0.6 |
Parameters | Units | Values |
---|---|---|
Soil thermal conductivity | W/(m·K) | 2 |
Soil density | kg/m3 | 2183 |
Soil heat capacity | J/(kg·K) | 996 |
Soil porosity | % | 39 |
Soil permeability | m2 | 2.3 × 10−10 |
Grout thermal conductivity | W/(m·K) | 2 |
Grout density | kg/m3 | 2500 |
Grout heat capacity | J/(kg·K) | 1110 |
Inlet temperature | K | 303 |
Inlet velocity | m/s | 0.3 |
Groundwater seepage | m/s | 0 |
Grout | Density | Specific Heat | Thermal Conductivity Coefficient | Thermal Diffusion Coefficient |
---|---|---|---|---|
kg/m3 | J/(kg·K) | W/(m·K) | m2/s | |
Bentonite | 2600 | 720 | 1.6 | 8.5 × 10−7 |
Sand | 2500 | 1110 | 2.0 | 7.2 × 10−7 |
Cement | 1631 | 900 | 2.8 | 1.9 × 10−6 |
Soils | Density | Specific Heat | Thermal Conductivity Coefficient | Thermal Diffusion Coefficient |
---|---|---|---|---|
kg/m3 | J/(kg·K) | W/(m·K) | m2/s | |
Silt | 1760 | 1510 | 1.6 | 6.0 × 10−7 |
Sand | 2500 | 1110 | 2.0 | 7.2 × 10−7 |
Granite | 2500 | 840 | 2.4 | 1.14 × 10−6 |
Inlet Velocity | Reynolds Numbers | Nusselt Numbers | Heat Transfer Coefficient |
---|---|---|---|
m/s | - | - | W/(m2·K) |
0.2 | 6568 | 29.95 | 17.97 |
0.3 | 9852 | 35.09 | 21.06 |
0.6 | 19,705 | 43.25 | 25.95 |
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Chen, S.; Mao, J.; Han, X.; Li, C.; Liu, L. Numerical Analysis of the Factors Influencing a Vertical U-Tube Ground Heat Exchanger. Sustainability 2016, 8, 882. https://doi.org/10.3390/su8090882
Chen S, Mao J, Han X, Li C, Liu L. Numerical Analysis of the Factors Influencing a Vertical U-Tube Ground Heat Exchanger. Sustainability. 2016; 8(9):882. https://doi.org/10.3390/su8090882
Chicago/Turabian StyleChen, Shangyuan, Jinfeng Mao, Xu Han, Chaofeng Li, and Liyao Liu. 2016. "Numerical Analysis of the Factors Influencing a Vertical U-Tube Ground Heat Exchanger" Sustainability 8, no. 9: 882. https://doi.org/10.3390/su8090882
APA StyleChen, S., Mao, J., Han, X., Li, C., & Liu, L. (2016). Numerical Analysis of the Factors Influencing a Vertical U-Tube Ground Heat Exchanger. Sustainability, 8(9), 882. https://doi.org/10.3390/su8090882