# Operation Optimization of Thermal Management System of Deep Metal Mine Based on Heat Current Method and Prediction Model

^{1}

^{2}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Introduction of the Refrigeration and Ventilation System Experimental Platform

#### 2.1. System Description and Thermal Analysis

^{3}. The refrigerator uses R134 as refrigerant, with a pressure of 0.47 Mpa, a constant pressure specific heat capacity of 1304 J/(kg K), and a density of 1100 kg/m

^{3}when saturated with liquid (300 K ± 10 K). The medium of the air cooling pipeline is air, the constant pressure-specific heat capacity of air is 1005 J/(kg K) and the density is 1.293 kg/m

^{3}[26].

_{awj}and Q

_{aaj}, respectively, represent the heat transfer rate on the cold and hot sides of the air cooler. m

_{aaj}and m

_{awj}represent the mass flow rate of the airflow and water flow of the j-th air cooler, c

_{p,a}and c

_{p,w}represent the specific heat capacity of air and water, and T

_{aaj,i}and T

_{aaj,o}are the inlet and outlet temperatures of hot air. T

_{awj,i}and T

_{awj,o}are the inlet and outlet temperatures of chilled water. According to the law of conservation of energy, Q

_{aaj}shouldequal to Q

_{awj}.

_{ch}is the refrigerating capacity of the refrigerator, Q

_{c}is the heat transfer rate of the water side of condenser, m

_{ch}is the mass flow rate of the chilled water, m

_{cw}is the mass flow rate of cooling water of condenser, T

_{chws}and T

_{chwr}are the supply and return temperatures of chilled water, and T

_{cw,i}and T

_{cw,o}are the inlet and outlet temperatures of cooling water of the condenser. Q

_{ch}equals the total heat transfer rate of the air coolers, Q

_{c}is equal to the sum of Q

_{ch}and the power consumption of the refrigerator (P

_{re}), and also the total heat transfer rate of the system, which can be expressed as

_{aj}is the heat transfer rate of the j-th air cooler.

_{mh}and Q

_{mc}are the heat transfer rate of the cold water side and hot water side of the intermediate heat exchanger, m

_{m}is the mass flow rate of ICC, T

_{mh,i}and T

_{mh,o}are the inlet and outlet temperatures of the hot side. m

_{ct}is the mass flow rate of ACTC, T

_{mc,i}and T

_{mc,o}are the inlet and outlet temperatures of the cold side. The heat transfer rate of the intermediate heat exchanger is equal to Q

_{c}, which is

#### 2.2. Uncertainty Analysis

_{1}, x

_{2}, …, x

_{n}, Wx

_{1}, Wx

_{2}, …, Wx

_{n}is the uncertainty corresponding to each variable. So, the uncertainty of function R can be determined by

## 3. Theoretical Analysis and Constraints

#### 3.1. Heat Current Model of System

_{h,i}and T

_{h,o}are the inlet and outlet temperatures of the hot side fluid, T

_{c,i}and T

_{c,o}are the inlet and outlet temperatures of the cold side fluid, respectively, and G represents the thermal capacity flow of the fluid, and its expression is

_{p}is the specific heat capacity of the fluid at constant pressure.

_{c}and G

_{h}, respectively, represent the thermal capacity flow of cold and hot fluids, while a

_{c}and a

_{h}, respectively, represent the ratio of the thermal conductivity (kA) of the heat exchanger to the thermal capacity flow of cold and hot fluids. The combination of heat current models for different heat exchangers can establish a heat current network model.

_{a}represents the equivalent thermal potential difference, and its expression is

_{ch}is the heat capacity flow of chilled water, there is

_{aj}is the equivalent thermal resistance of the j-th air cooler. Since the air cooler is a cross-flow heat exchanger, its expression is:

_{aaj}represents the heat capacity flow of the airflow of the j-th air cooler. G

_{awj}is the heat capacity flow of the water flow of the j-th air cooler. NTU

_{aaj}and NTU

_{awj}are dimensionless parameters. Their expressions are:

_{aj}is the thermal conductance of the j-th air cooler. φ

_{aj}is the correction factor of the thermal conductivity of the cross-flow heat exchanger. The calculation of φ

_{aj}requires the introduction of two dimensionless coefficients P

_{aj}and U

_{aj}[29]. The expressions are as follows:

_{ct,i}is the inlet air temperature of the air-cooling tower, i.e., the atmospheric temperature. ε

_{m}and ε

_{ct}represent the equivalent thermal potential difference, which can be expressed as

_{m}represents the heat capacity flow of the water flow of ICC. G

_{ct}represents the heat capacity flow of the water flow of ACTC. They can be represented as:

_{m}is the equivalent thermal resistance of the intermediate heat exchanger. R

_{ct}is the equivalent thermal resistance of the air-cooling tower. The cold side of the air-cooling tower is assumed to have infinite heat capacity. After the simplification and derivation of the thermal resistance, their expressions are

_{mc}, a

_{mh}, and a

_{ct}are dimensionless parameters, which are determined by the following relations:

_{m}is the thermal conductance of the intermediate heat exchanger. (kA)

_{ct}is the thermal conductance of the air-cooling tower.

#### 3.2. Flow Resistance Constraint Model

_{0}, a

_{1}, and a

_{2}are the characteristic parameters, which can be obtained through fitting and regression of experimental data. m is the mass flow rate. Table 3 shows the characteristic parameters and maximum deviation of the power components obtained through experiments. The maximum error is within the allowable range.

_{0}is the dynamic head coefficient of the pipe network. For a fixed pipe network, it is the property parameter of the pipe network.

^{2}.

- (1)
- Keeping the circuit fully open, adjusting the valve to parallel the six heat exchangers, and measuring the flow rate of each branch and the two ends of the pump under the condition of 100% frequency operation of the pump. The constraint relationships are as follows:

- (2)
- Operating the three heat exchangers in parallel in the first branch and closing the valves in the second branch, there are the following constraints:

- (3)
- Similarly, closing the first branch, and the constraint for the third branch is

- (4)
- Finally, only one branch is opened at a time, and its constraint can be written as

_{0}, d

_{01}, d

_{02}, d

_{03}, d

_{04}, d

_{05}, d

_{06}, d

_{1}, d

_{2}, d

_{3}, d

_{4}, d

_{5}, and d

_{6}are pipe network characteristic parameters. H

_{c}, H

_{c1}, H

_{c3}, H

_{1}, H

_{2}, H

_{3}, H

_{4}, H

_{5}, and H

_{6}are the pressure heads of each branch. M

_{0}, m

_{01}, m

_{02}, m

_{03}, m

_{04}, m

_{05}, and m

_{06}are mass flow rates of each branch, which is

_{0,aj}, a

_{1,aj}, and a

_{2,aj}are characteristic parameters of the j-th ACL fan, ω

_{aaj}is the frequency of the j-th ACL fan, d

_{aj}is the characteristic parameter of the j-th ACL. a

_{0,ch1}, a

_{1,ch1}, and a

_{2,ch1}are characteristic parameters of the No. 1 CHWC pump, ω

_{ch1}is the frequency of No.1 CHWC pump. a

_{0,ch3}, a

_{1,ch3}, and a

_{2,ch3}are characteristic parameters of No. 3 CHWC pump, ω

_{ch3}is the frequency of No. 3 CHWC pump. a

_{0,ct}, a

_{1,ct}, and a

_{2,ct}are characteristic parameters of the ACTC pump, ω

_{ct}is the frequency of the ACTC pump, and d

_{ct}is the characteristic parameter of the ACTC pump. a

_{0,m}, a

_{1,m}and a

_{2,m}are characteristic parameters of the ICC pump, ω

_{m}is the frequency of the ICC pump, and d

_{ct}is the characteristic parameter of the ICC pump. At this point, the flow resistance model of the system has been derived.

#### 3.3. Energy Consumption Model of the Refrigerator

_{0}–a

_{5}represents the undetermined characteristic coefficient, which can be obtained through fitting and regression of the operation data.

^{2}, and the deviation between experimental data and fitting data. The fitting similarity R

^{2}is 0.984, and the maximum deviation is 2.7%. Therefore, the prediction model can reflect the operating characteristics of the refrigerator commendably.

#### 3.4. Artificial Neural Network Model for Predicting Thermal Conductivity of Heat Exchangers

^{2}of heat exchangers.

#### 3.5. Objective Function and Optimization Model

_{pump}is the total pump power of all power components, P

_{aj}(j = 1, 2, …, 10) is the power of the j-th ACL fan. P

_{ch1}is the power of the No.1 CHWC pump, P

_{ch3}is the power of the No.3 CHWC pump, P

_{m}is the power of the ICC pump, and P

_{ct}is the power of the ACTC pump, their expressions are

_{aj}is the pressure head of the j-th ACL fan. H

_{ch1}is the pressure head of the No. 1 CHWC pump, H

_{ch3}is the pressure head of the No. 3 CHWC pump, H

_{m}is the pressure head of the ICC pump, and H

_{ct}is the pressure head of the ACTC pump.

_{k}(k = 1, 2, …, 10) are Lagrange multipliers.

_{aaj}, ω

_{m}, ω

_{ct}, m

_{awj}, and lamda

_{k}equal to zero, the following optimization equations can be obtained:

## 4. Results and Discussion

#### 4.1. Optimization Results and Experimental Verification

_{pump}) decreases by 39.1%, the energy consumption of the refrigerator saves by 11.4%, and the total power consumption of the system (P

_{t}) drops by 16.5%. Due to the decrease in power consumption of the refrigerator, according to Formula (6), the total heat transfer rate of the system decreases by 3.35%, which slows down the cooling pressure of the intermediate heat exchanger and air-cooling tower. The COP of the refrigerator increases by 11.6%.

#### 4.2. The Variation Law of Optimal Operating Parameters under Variable Heat Load

## 5. Conclusions

## Author Contributions

## Funding

## Data Availability Statement

## Conflicts of Interest

## Nomenclature

a | Performance characteristic parameters of power components (variable frequency pump or variable frequency fan) |

A | Heat transfer area, m^{2} |

ACTC | Air-cooling tower circuit |

CHWC | Chilled water circuit |

CAL | Cooling airline |

COP | The coefficient of performance of the refrigerator |

c_{p} | Constant pressure specific heat, (J/(kg·K)) |

H | Pressure head, m |

ICC | intermediate cooling circuit |

g | Acceleration of gravity, m/s^{2} |

G | Entransy, J·K; Heat capacity flow, W/K |

k | Heat transfer coefficient, W/(K·m^{2}) |

kA | Thermal conductance, W/K |

KCL | Kirchhoff’s circuit law |

KVL | Kirchhoff’s voltage law |

lamda | Lagrange multiplier |

m | Mass flow rate, kg/s |

NTU | Number of heat transfer units |

ρ | Density, kg/m^{3} |

p | Pressure, Pa |

P | Power, W |

Q | Heat transfer rate, W |

Q_{a} | Heat transfer rate of air coolers, W |

Q_{ch} | Total refrigeration capacity of the refrigerator, W |

Q_{ct} | Heat transfer rate of air-cooling tower, W |

Q_{m} | Heat transfer rate of the intermediate heat exchanger/total heat transfer rate of system, W |

R | Equivalent thermal resistance, K/W |

R_{g} | Entransy dissipation-based thermal resistance, K/W |

T | Temperature, K or °C |

ΔT_{m} | Logarithm mean temperature difference, K |

U | Uncertainty |

ω | Operating frequency of power components, Hz |

W | Power consumption, W |

δ | Deviation |

ε | Equivalent thermal potential difference |

Subscripts | |

a | Air |

c | Condensation process; condenser |

cal | Calculated value |

cr | Refrigerant |

ch, chw | Chilled water |

chws | Chilled water supply |

chwr | Chilled water return |

ct | Air-cooling tower cooling circuit/air-cooling tower |

cw | Cooling water |

cws | Cooling water supply |

cwr | Cooling water return |

e | Evaporation process/evaporator |

exp | Experimental value |

fit | Fitting value |

h | Hot side; hot fluid |

i | Inlet |

m | Intermediate cooling circuit/intermediate heat exchanger |

o | Outlet |

re | Refrigerator |

w | Water |

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**Figure 10.**Optimal frequency of system power components under different heat loads. (

**a**) Frequency variation of 6 air coolers. (

**b**) Frequency variation of each circulating water pump.

**Figure 11.**Optimal frequency of system power components under different heat loads. (

**a**) Frequency variation of 6 air coolers. (

**b**) Frequency variation of each circulating water pump.

Measuring Instrument | Type | Range | Accuracy |
---|---|---|---|

Thermocouple | TT-T-24-SLE-1000 | −267–150 °C | 0.4% |

Flowmeter | AXF050G | 0.3–10 m/s | 0.5% |

Differential pressure gauge | EJA110E | 0–500 kPa | 0.055% |

Anemometer | WD-400 | 0–20 m/s | 3% |

Heat Transfer Rate (W) | Uncertainty (P = 68.3%) |
---|---|

Hot side of the air cooler | 6.7% |

Cold side of the air cooler | 5.6% |

Refrigerating capacity | 5.8% |

Cooling water side of condenser | 9.7% |

Hot side of intermediate heat exchanger | 5.7% |

Cold side of intermediate heat exchanger | 9.7% |

Power Components | a_{0} | a_{1} | a_{2} | R^{2} | Maximum Deviation |
---|---|---|---|---|---|

No. 1 fan | 0.00993 | −0.14186 | −186.506 | 0.965 | 6.6% |

No. 2 fan | 0.00705 | 1.26833 | −508.908 | 0.999 | 5.0% |

No. 3 fan | 0.01541 | 1.27508 | −421.1733 | 0.997 | 4.3% |

No. 4 fan | 0.01616 | −2.62011 | 247.85273 | 0.993 | 2.7% |

No. 5 fan | 0.00986 | 0.19266 | −178.1779 | 0.984 | 3.1% |

No. 6 fan | 0.00896 | 1.64393 | −589.0558 | 0.929 | 3.5% |

No. 1 CHWC pump | 0.0118 | 0.09784 | −16.27054 | 0.991 | 6.1% |

No. 3 CHWC pump | 0.01243 | 0.02437 | −12.02754 | 0.992 | 5.1% |

ICC pump | 0.01074 | 0.02506 | −2.40889 | 0.995 | 4.7% |

ACTC pump | 0.00657 | 0.26856 | −5.6721 | 0.992 | 5.4% |

Parameters | d_{0} (m·s^{2}/kg^{2}) | R^{2} |
---|---|---|

No. 1 airline | 482.8 | 0.952 |

No. 2 airline | 437.1 | 0.995 |

No. 3 airline | 1054.8 | 0.998 |

No. 4 airline | 727.8 | 0.994 |

No. 5 airline | 500.9 | 0.967 |

No. 6 airline | 1210.6 | 0.956 |

ICC | 10.1 | 0.999 |

ACTC | 10.5 | 0.997 |

Item | d_{0} | d_{01} | d_{02} | d_{03} | d_{04} | d_{05} | d_{06} |

value | 84.62 | 94.1 | 41.02 | −1.994 | 78.2 | −0.8533 | 41.27 |

Item | d_{1} | d_{2} | d_{3} | d_{4} | d_{5} | d_{6} | |

value | 91.38 | 47.5 | −4.038 | 58.45 | 5.695 | 72.43 |

a_{0} | a_{1} | a_{2} | a_{3} | a_{4} | a_{5} | R^{2} | δ_{max} |
---|---|---|---|---|---|---|---|

2986.3 | 53.9 | 1.14 | −0.132 | 7.588 × 10^{−6} | −0.00248 | 0.984 | 2.7% |

Parameters | (kA)_{a}_{1} | (kA)_{a}_{2} | (kA)_{a}_{3} | (kA)_{a}_{4} | (kA)_{a}_{5} | (kA)_{a}_{6} | (kA)_{m} | (kA)_{ct} |
---|---|---|---|---|---|---|---|---|

R^{2} | 0.964 | 0.946 | 0.971 | 0.938 | 0.985 | 0.967 | 0.953 | 0.943 |

T_{aa1,i} | T_{aa2,i} | T_{aa3,i} | T_{aa4,i} | T_{aa5,i} | T_{aa6,i} | T_{chws} | T_{cw,o} | T_{ct,i} |
---|---|---|---|---|---|---|---|---|

298.4 | 301 | 301.7 | 303.3 | 305 | 305 | 280.0 | 295.8 | 284.6 |

ω_{a1} | ω_{a2} | ω_{a3} | ω_{a4} | ω_{a5} | ω_{a6} | ω_{c1} | ω_{c3} | ω_{m} | ω_{ct} | |
---|---|---|---|---|---|---|---|---|---|---|

Opt. | 36.9 | 25.0 | 26.0 | 44.2 | 26.8 | 36.2 | 27.4 | 30.2 | 45.9 | 27.9 |

P_{pump} (W) | P_{re} (W) | P_{t} (W) | COP | Q_{c} (W) | |
---|---|---|---|---|---|

Pre. | 816.5 | 3600 | 4416.5 | 2.52 | 12,700 |

Opt. | 497.3 | 3193.1 | 3690.4 | 2.85 | 12,293.1 |

Deviation | −39.1% | −11.4% | −16.5% | 11.6% | −3.3% |

(kA)_{a1} | (kA)_{a2} | (kA)_{a3} | (kA)_{a4} | (kA)_{a5} | (kA)_{a6} | (kA)_{m} | (kA)_{ct} | |
---|---|---|---|---|---|---|---|---|

Opt. | 88.8 | 89.2 | 98.0 | 108.8 | 99.5 | 158.1 | 1667.9 | 5612.9 |

Exp. | 82.6 | 93.8 | 95.4 | 102.4 | 91.9 | 149.5 | 1731.4 | 5294.4 |

Deviation | 7.5% | 5.2% | 2.7% | 5.9% | 7.7% | 5.5% | 3.7% | 5.7% |

Q_{a1} | Q_{a2} | Q_{a3} | Q_{a4} | Q_{a5} | Q_{a6} | Q_{ch} | P_{re} | Q_{c} | |
---|---|---|---|---|---|---|---|---|---|

Opt. | 1200 | 1200 | 1400 | 1600 | 1400 | 2300 | 9100 | 3193.1 | 12,293.1 |

Exp. | 1095 | 1240 | 1278 | 1625 | 1312 | 2464 | 8820 | 3285.0 | 13,393.0 |

Deviation | 8.8% | 3.4% | 8.8% | 1.6% | 6.3% | 7.2% | 3.1% | 2.8% | 8.3% |

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## Share and Cite

**MDPI and ACS Style**

Wang, W.; Shao, W.; Wang, S.; Liu, J.; Shao, K.; Cao, Z.; Liu, Y.; Cui, Z.
Operation Optimization of Thermal Management System of Deep Metal Mine Based on Heat Current Method and Prediction Model. *Energies* **2023**, *16*, 6626.
https://doi.org/10.3390/en16186626

**AMA Style**

Wang W, Shao W, Wang S, Liu J, Shao K, Cao Z, Liu Y, Cui Z.
Operation Optimization of Thermal Management System of Deep Metal Mine Based on Heat Current Method and Prediction Model. *Energies*. 2023; 16(18):6626.
https://doi.org/10.3390/en16186626

**Chicago/Turabian Style**

Wang, Wenpu, Wei Shao, Shuo Wang, Junling Liu, Kun Shao, Zhuoqun Cao, Yu Liu, and Zheng Cui.
2023. "Operation Optimization of Thermal Management System of Deep Metal Mine Based on Heat Current Method and Prediction Model" *Energies* 16, no. 18: 6626.
https://doi.org/10.3390/en16186626