The Optimization of the Thermal Performances of an Earth to Air Heat Exchanger for an Air Conditioning System: A Numerical Study
Abstract
:1. Introduction
1.1. General Concepts and Context
1.2. State of the Art
1.3. Aim of the Paper
2. Methods
2.1. The Design and the Assumptions Made
- the computational domain has two-dimensional geometry (formed by the ground and the duct) modelled in a longitudinal section for symmetry;
- the thermal resistance of the pipe is not considered (the reason for this is explained in the following subsection);
- a time-dependent analysis is conducted on the model until the stationarity is observed;
- 20 m is the depth where temperature of the ground is considered undisturbed;
- the properties of the soil in the whole domain are assumed to be constant;
- the soil is considered as an isotropic medium.
2.2. The Thermal Resistance Approach in the EAHX System
2.3. The Mathematical System
- the mass conservation of the humid air:
- the conservation momentum is guaranteed by the Navier-Stokes equations for turbulent air flow:
- the energy equation for the air flow:
- Using the K- model for turbulent flow, the turbulence kinetic energy equation is:
- to the lateral sides of the ground domain there is symmetry with the behavior of the ground beyond the sides; thus, adiabatic (2nd type) conditions are imposed;
- the sun-air temperature model is a 1st type boundary condition imposed at the top of the ground domain, as visible in Figure 1. This temperature takes into account the influence of both the incident solar radiation on the ground surface and the convective heat exchange with the external air, according to the following equation:
- at the inlet of the pipe, the temperature and relative humidity of the external air are imposed, whereas the inlet velocity of the air is a variable to be optimized through the investigation introduced in this paper (Figure 1).
2.4. Parameters of the Optimization and Operative Conditions
- the temperature of the outlet air;
- absolute value of the temperature difference between the inlet and outlet sections of the tube;
- efficiency of the EAHX, that is the ratio between the EAHX temperature span and the ideal temperature difference and it is defined as:
- (D = 0.1 m, v = 0.5 m s−1), where the fluid motion is associated to Re = 3312;
- (D = 0.1 m, v = 1.0 m s−1) and (D = 0.2 m, v = 0.5 m s−1) where Re = 6624;
3. Results
3.1. Effect of the Burial Depth
3.2. Effect of the Pipe Diameter
3.3. Effect of the Pipe Length
3.4. Effect of the Air Flow Velocity
3.5. Effect of the Air Temperature
4. Discussion and Conclusions
- the burial depth does not affect the thermal performances from 1.5 m onwards because of the typology of the study conducted (forcing design conditions to observe the steady-state answer of the EAHX).
- The thermal performances increase with the length of the pipe up to a certain limit, called saturation length over which no longer enhancements are registered. The smaller the diameter, the lower the saturation length;
- with the same length, the smaller the diameter the closer the outlet temperature to the ground temperature both for cooling and heating operation modes;
- a form factor greater than 500 is recommended with a Reynolds number that follows in the turbulent regime in order to optimize the thermal performances of the EAHX.
- Supposing that the fluid motion is fully turbulent, the slower the air flow, the closer the outlet temperature is to the ground temperature.
- The combination that optimizes the performances of the EAHX system that works under the design conditions for cooling and heating is D = 0.1 m s−1; v = 1.5 m s−1; L = 50 m.
- The effect of the inlet temperature of the air, if D = 0.1 m and v = 1.5 m s−1, reveals that the heat transfer is more pronounced at the beginning of the tube and that the temperature gradients along the pipe are greater for greater values of ∆T between the inlet air and the ground. Nevertheless, if the tube length exceeds the saturation value, the influence of this parameter is negligible.
- If the EAHX works in cooling mode, the air entering at higher temperatures could during the flowing process, generate water condensation along the tube. For fixed length and relative humidity, the entity of such a phenomenon grows with the inlet temperature.
Author Contributions
Funding
Conflicts of Interest
Nomenclature
Roman symbols | |
A | amplitude of the temperature variation, °C |
C | constant of K- model |
c | specific heat, J kg−1 K−1 |
D | diameter of the pipe, m |
E | energy, J |
EAHX | Earth-to-Air-Heat-eXchanger |
G | incident radiation, W m−2 |
h | specific enthalpy, kJ kg−1 |
HVAC | Heating, Ventilation & Air Conditioning |
identity vector, - | |
component of diffusion flux, kg m−3 s−1 | |
K | turbulent kinetic energy, J |
k | thermal conductivity, W m−1 K−1 |
L | length of the pipe, m |
flow rate, kg s−1 | |
power, kW | |
p | pressure, Pa |
R | thermal resistance, W m−1 K−1 |
Re | Reynolds number, - |
source term, kg m−3 s−1 | |
T | temperature, °C |
t | time, s |
U | convective heat transfer coefficient, W m−2 K−1 |
fluid velocity vector, m s−1 | |
z | generic property, m |
Greek symbols | |
α | absorbance of the surface |
Δ | finite difference |
partial derivative | |
efficiency, % | |
turbulent cinematic viscosity, m2 s−1 | |
μ | dynamic viscosity, Pa s−1 |
ν | cinematic viscosity, m2 s−1 |
ρ | density, kg m−3 |
σ | constant of K- model |
τ | tangential stress, Pa m−1 |
Φ | relative humidity, % |
ψ | porosity, % |
ω | humidity ratio, gv kga−1 |
Subscripts | |
0 | phase constant of the lowest average/mean soil surface temperature since the beginning of the year |
air | air |
c | convective |
cond | condensed |
eff | effective |
eq | equivalent |
ext | external |
related to turbulent cinematic viscosity | |
f | fluid |
ground | ground |
h | heating |
in | inlet of the EAHX |
int | internal |
j | species |
liquid | liquid |
m | annual mean soil |
mass | mass |
min | minimum |
out | outlet of the EAHX |
μ | related to the evaluation of turbulent dynamic viscosity |
sa | sun-air |
soil | soil |
solid | solid |
T | turbulent |
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Constant | Value |
---|---|
Cµ | 0.09 |
Cε1 | 1.44 |
Cε2 | 1.92 |
1.0 | |
1.3 |
Climatic Zone—Locality | Geographic Coordinates | Winter Design Parameters | Summer Design Parameters | ||||
---|---|---|---|---|---|---|---|
T [°C] | Φ [%] | G [Wm−2] | T [°C] | Φ [%] | G [Wm−2] | ||
Csa—Naples | Lat. 40°51′22″ N Long. 14°14′47″ W | 1.90 | 52.00 | 808 | 31.90 | 48.60 | 825 |
D [m] | u [m s−1] | Re [104] |
---|---|---|
0.1 | 0.5 | 3312 |
0.1 | 1 | 6624 |
0.1 | 1.5 | 9936 |
0.1 | 2 | 13,248 |
0.1 | 2.5 | 16,560 |
0.2 | 0.5 | 6624 |
0.2 | 1 | 13,248 |
0.2 | 1.5 | 19,873 |
0.2 | 2 | 26,497 |
0.2 | 2.5 | 33,121 |
0.3 | 0.5 | 9936 |
0.3 | 1 | 19,873 |
0.3 | 1.5 | 29,809 |
0.3 | 2 | 39,745 |
0.3 | 2.5 | 49,681 |
0.4 | 0.5 | 13,248 |
0.4 | 1 | 26,497 |
0.4 | 1.5 | 39,745 |
0.4 | 2 | 52,993 |
0.4 | 2.5 | 66,242 |
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Greco, A.; Masselli, C. The Optimization of the Thermal Performances of an Earth to Air Heat Exchanger for an Air Conditioning System: A Numerical Study. Energies 2020, 13, 6414. https://0-doi-org.brum.beds.ac.uk/10.3390/en13236414
Greco A, Masselli C. The Optimization of the Thermal Performances of an Earth to Air Heat Exchanger for an Air Conditioning System: A Numerical Study. Energies. 2020; 13(23):6414. https://0-doi-org.brum.beds.ac.uk/10.3390/en13236414
Chicago/Turabian StyleGreco, Adriana, and Claudia Masselli. 2020. "The Optimization of the Thermal Performances of an Earth to Air Heat Exchanger for an Air Conditioning System: A Numerical Study" Energies 13, no. 23: 6414. https://0-doi-org.brum.beds.ac.uk/10.3390/en13236414