A Simple Explicit Formula for Evaluating the Total Capacity of Chilled-Water Cooling Coils under Wet Conditions
Abstract
:1. Introduction
2. Proposed Calculation Formula
2.1. Mathematical Formulation
- (1)
- The energy flow due to the condensate draining from the coil is small compared to the other energy terms and is neglected.
- (2)
- The coil surface is assumed to be totally and evenly wet. It has been proven that the error caused by approximating a partially wet coil as totally wet is generally less than 5% [2].
- (3)
- The temperature gradients along the thickness of the coil surface and condensate film are neglected since they are thin. Thus, the surface and the film have an identical temperature.
2.2. Parameter Identification
3. Validation of the Formula
3.1. Data Source and Evaluation Indicators
3.2. FCU Cooling Coils
3.3. AHU Cooling Coils
4. Discussion
5. Conclusions
Author Contributions
Funding
Data Availability Statement
Conflicts of Interest
Nomenclature
total cooling capacity, in W; | sensible cooling capacity, in W; | ||
air flow rate, in kg/s; | water flow rate, in kg/s; | ||
moist air-specific heat, in J/kg-K; | water-specific heat, in J/kg-K; | ||
air inlet dry-bulb temperature, in °C; | water inlet temperature, in °C; | ||
air outlet dry-bulb temperature, in °C; | water outlet temperature, in °C; | ||
air inlet enthalpy, in J/kg; | saturated air enthalpy at the water inlet temperature, in J/kg; | ||
air outlet enthalpy, in J/kg; | |||
air inlet humidity, in g/kg; | saturated air enthalpy at the water outlet temperature, in J/kg; | ||
effective coil surface temperature, in °C; | |||
saturated air enthalpy at the coil surface temperature, in J/kg; | overall fin surface efficiency; | ||
air-side thermal conductance, in W/(K·m2); | water-side thermal conductance, in W/(K·m2); | ||
air-side heat transfer area, in m2; | water-side heat transfer area, in m2; | ||
overall effectiveness of the coil; | air-side effectiveness of the coil; | ||
enthalpy-based overall thermal conductance, in W/(J/kg); | temperature-based overall thermal conductance, in W/K; | ||
log mean enthalpy difference, in J/kg; | log mean temperature difference, in K; | ||
fictitious specific heat; | moisture separation coefficient | ||
coefficient of variation; | root mean squared error; | ||
relative prediction error proportion of the number of points to all operating points smaller than 5%; | relative prediction error proportion of the number of points to all operating points smaller than 10%. |
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Equation Type | Enthalpy-Based ε-NTU Method | Temperature-Based ε-NTU Method |
---|---|---|
Total capacity | ||
Sensible capacity | ||
Overall effectiveness | ||
For wet conditions, . | ||
(e.g., for counterflow cooling coils) | ||
Air-side effectiveness (or contact effectiveness [32,43,44]) |
Parameter | All Operation Conditions | Training Set |
---|---|---|
Inlet water temperature (°C) | Five levels: 5, 6, 7, 8, 9 | Two levels: 6, 8 |
Water flow rate (L/min) | Four levels that differ with model number, i.e., 2.4, 4.8, 6, 7.2 for model no. 200; 3.6, 4.8, 7.2, 9.6 for model no. 300; 4.8, 7.2, 9.6, 12 for model no. 400; 6.0, 9.6, 13.2, 15.6 for model no. 500; 7.2, 12, 15, 18 for model no. 600; 12, 15.6, 19.2, 24 for model no. 800; 14.4, 18, 24, 30 for model no. 1000; 18, 24, 30, 33 for model no. 1200; 18, 24, 30, 39 for model no. 1400. | All four levels |
Inlet air dry and wet bulb temperature (°C) | Four levels: (24, 17), (25, 17.8), (26, 18.7), (27, 19.5) | Two levels: (24, 17), (26, 18.7) |
Air flow rate (m3/h) | Three levels that differ with model number, i.e., 195, 280, 360 for model no. 200; 290, 415, 550 for model no. 300; 380, 560, 720 for model no. 400; 450, 675, 900 for model no. 500; 545, 765, 1040 for model no. 600; 755, 1090, 1450 for model no. 800; 910, 1355, 1800 for model no. 1000; 1095, 1650, 2180 for model no. 1200; 1550, 2050, 2600 for model no. 1400. | All three levels |
Number of operation states | (20%) |
FCU No. | Training Set | Test Set | |||||||||
CV | CV | ||||||||||
200 | 0.499 | −0.502 | 1.152 | 27.766 | 0.032 | 2.7% | 91% | 100% | 3.2% | 85% | 100% |
300 | 0.606 | −0.707 | 1.157 | 28.510 | 0.098 | 2.5% | 95% | 100% | 3.1% | 92% | 100% |
400 | 1.294 | −0.551 | 0.967 | 36.633 | 0.031 | 2.2% | 100% | 100% | 2.8% | 95% | 100% |
500 | 1.061 | −0.529 | 0.981 | 38.931 | 0.044 | 2.2% | 100% | 100% | 2.9% | 95% | 100% |
600 | 1.552 | −0.490 | 0.911 | 49.894 | −0.026 | 2.5% | 98% | 100% | 2.8% | 96% | 100% |
800 | 2.335 | −0.602 | 0.892 | 41.253 | 0.122 | 2.1% | 98% | 100% | 2.6% | 97% | 100% |
1000 | 2.138 | −0.527 | 0.887 | 47.094 | 0.046 | 1.7% | 100% | 100% | 3.0% | 92% | 100% |
1200 | 3.088 | −0.507 | 0.825 | 53.254 | 0.028 | 2.3% | 100% | 100% | 3.3% | 92% | 100% |
1400 | 0.166 | −0.492 | 1.200 | 54.231 | 0.018 | 3.1% | 93% | 100% | 2.3% | 98% | 100% |
Information | Value |
---|---|
Tube-fin surface area of each row (m2) | 24.05 |
Airflow windward area (m2) | 1.87 |
Waterflow crossing area (m2) | 0.00407 |
Overall thermal conductance (W/m2-K) | |
Air-side effectiveness |
Parameter | Training Dataset | Test Dataset | ||
---|---|---|---|---|
Number of Levels | Values | Number of Levels | Values | |
Inlet water temperature (°C) | 3 | 5, 7, 9 | 5 | 5, 6, 7, 8, 9 |
Water velocity (m/s) | 3 | 0.6, 1.2, 1.8 | 7 | 0.6, 0.8, 1, 1.2, 1.4, 1.6, 1.8 |
Air velocity (m/s) | 4 | 1.5, 2, 2.5, 3 | 4 | 1.8, 2.1, 2.4, 2.7 |
Inlet air dry-bulb temperature (°C) | 3 | 28, 30, 32 | 815 | Beijing TMY weather data in summer [54] (>26 °C, >40%) |
Inlet air relative humidity (%) | 2 | 40, 80 | ||
Number of operation states | 216 (<0.2%) | 114,100 |
AHU No. | Training Set | Test Set | |||||||||
CV | CV | ||||||||||
JW10_4R | 0.615 | 0.172 | 0.718 | 2.323 | −0.304 | 2.1% | 99.5% | 100.0% | 2.4% | 99.9% | 100.0% |
JW10_6R | 0.965 | 0.047 | 0.806 | 2.993 | −0.237 | 2.0% | 99.1% | 100.0% | 1.8% | 100.0% | 100.0% |
JW10_8R | 0.967 | 0.042 | 0.849 | 4.085 | −0.248 | 2.1% | 98.6% | 100.0% | 1.8% | 99.9% | 100.0% |
JW20_4R | 0.841 | 0.148 | 0.727 | 2.832 | −0.240 | 2.5% | 97.5% | 100.0% | 2.7% | 99.5% | 100.0% |
JW20_6R | 1.416 | −0.014 | 0.812 | 3.331 | −0.184 | 3.0% | 93.8% | 100.0% | 2.6% | 99.4% | 100.0% |
JW20_8R | 1.422 | −0.027 | 0.857 | 3.945 | −0.178 | 3.6% | 90.6% | 98.6% | 2.8% | 98.9% | 99.9% |
JW30_4R | 0.948 | 0.136 | 0.732 | 3.021 | −0.235 | 2.5% | 97.5% | 100.0% | 2.6% | 99.7% | 100.0% |
JW30_6R | 1.539 | −0.022 | 0.816 | 3.552 | −0.181 | 3.1% | 92.9% | 100.0% | 2.6% | 99.4% | 100.0% |
JW30_8R | 1.519 | −0.034 | 0.860 | 4.194 | −0.175 | 3.6% | 89.7% | 98.6% | 2.8% | 98.8% | 99.9% |
JW40_4R | 1.145 | 0.112 | 0.740 | 3.113 | −0.212 | 2.8% | 95.9% | 100.0% | 2.9% | 98.3% | 100.0% |
JW40_6R | 2.097 | −0.090 | 0.826 | 3.493 | −0.164 | 3.8% | 86.4% | 99.0% | 3.2% | 98.0% | 99.9% |
JW40_8R | 2.126 | −0.116 | 0.876 | 3.920 | −0.158 | 4.6% | 78.1% | 96.7% | 3.6% | 95.4% | 99.7% |
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Wang, C.; Wang, S.; Ding, X.; An, J.; Fu, X. A Simple Explicit Formula for Evaluating the Total Capacity of Chilled-Water Cooling Coils under Wet Conditions. Buildings 2024, 14, 2630. https://doi.org/10.3390/buildings14092630
Wang C, Wang S, Ding X, An J, Fu X. A Simple Explicit Formula for Evaluating the Total Capacity of Chilled-Water Cooling Coils under Wet Conditions. Buildings. 2024; 14(9):2630. https://doi.org/10.3390/buildings14092630
Chicago/Turabian StyleWang, Chuang, Shan Wang, Xiaoxiao Ding, Jingjing An, and Xiao Fu. 2024. "A Simple Explicit Formula for Evaluating the Total Capacity of Chilled-Water Cooling Coils under Wet Conditions" Buildings 14, no. 9: 2630. https://doi.org/10.3390/buildings14092630