# Multi-Objective Optimization of a Multilayer Wire-on-Tube Condenser: Case Study R134a, R600a, and R513A

^{1}

^{2}

^{3}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. General Aspects and Optimization

#### 2.1. Multilayer Wire-on-Tube Condenser

^{2}and a mass of 1.216 kg. The range selection in the variation of the eight geometric parameters was defined taking into consideration the commercial dimensions of both the tube and the wire, as well as the limitations in the space where the multilayer wire-on-tube condenser is located, and the typical values found in the literature.

#### 2.2. Operating Conditions

#### 2.3. Proposed Objective Functions

_{T}, is provided by the wire area and the tube area:

#### 2.4. Algorithms

#### 2.5. Case Study

_{c}, and the number of rows, N

_{f}, were kept fixed, and the other geometric parameters were varied considering the two objective functions, the minimization of the area and the maximization of the heat transfer. These three cases were defined as follows: case 1: N

_{c}= N

_{f}= 6; case 2: N

_{c}= N

_{f}= 7; and case 3: N

_{c}= N

_{f}= 8. Notice that a square (N

_{c}= N

_{f}) condenser section (exchanger side) was maintained, mainly considering the limitations in the space of the refrigerator where the multilayer wire-on-tube condenser was installed.

## 3. Results and Discussion

#### 3.1. Analysis of the Optimization Algorithm

#### 3.2. Optimization Results

^{2}) of the condenser. This was also reflected in a decrease in the mass of the heat exchanger, where the reference mass was 1.216 kg.

_{c}= N

_{f}), there was a decrease in the length of the tube without a wire, a, as well as a decrease in the tube with a wire, L

_{tp}. While in the case of R513A a different situation was presented, for the three study cases the length without a wire was kept constant and practically the length with a wire remained unchanged. In fact, for this refrigerant, the largest designs of the condenser were presented, being reflected in a greater surface and a greater mass of the heat exchanger. Finally, it was noted that the results returned a wires number, N

_{w}, that did not correspond to integer values, so rounding to the nearest value could be assumed.

^{2}, which was considered 100%. In each case, the condenser optimization was conducted using each of the refrigerants and starting from the current surface. Thus, in Figure 7, it can be seen that for the geometric arrangement of case 1, there was practically no reduction of the area in the heat exchange equipment for any refrigerant. However, for cases 2 and 3, a reduction in area can be seen, thus showing a more compact wire-on-tube condenser. In fact, the use of R134 showed the greatest area reduction, in the order of 15% compared to the current heat exchanger design.

## 4. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## Nomenclature

a | length without wires (mm) |

A | area (m^{2}) |

CFD | computational fluid dynamics |

D | diameter (mm) |

FOA | Falcon Optimization Algorithm |

GWP | Global Warming Potential |

L | length (mm) |

L_{tp} | length with wire (mm) |

$\dot{m}$ | mass flow rate (kg/s) |

MOEAD | Multi-objective Evolutionary Algorithm based on Decomposition |

MOGA | Multi-objective Genetic Algorithm |

MOHTS | Multi-objective Heat Transfer Search |

MOWO | Multi-objective Wale Optimization |

N_{c} | layers number (-) |

N_{f} | rows number (-) |

N_{w} | wires number (-) |

NSGAII | Non-dominated Sorting Genetic Algorithm-II |

NTU | number of transfer units (-) |

OMOPSO | Optimized Multi-objective Particle Swarm Optimization |

P | pressure (bar) |

$\dot{Q}$ | heat transfer rate (W) |

S | pitch (mm) |

T | temperature (K) |

Subscripts | |

amb | ambient |

air | air |

cond | Condensation and condenser |

dsh | desuperheating |

in | inlet |

out | outlet |

r | refrigerant |

sub | subcooling |

T | total |

t | tube |

w | wire |

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**Figure 3.**Statistical comparison between NSGAII, OMOPSO, and MOEAD algorithms. (

**a**,

**c**,

**e**) heat transfer area; (

**b**,

**d**,

**f**) heat transfer.

Variable | Nomenclature | Type of Variable | Reference | Lower Limit | Upper Limit |
---|---|---|---|---|---|

Tube diameter (mm) | D_{t} | Continuous | 4.76 | 4 | 6 |

Wire diameter (mm) | D_{w} | Continuous | 1.30 | 1 | 2 |

Tube pitch (mm) | S_{t} | Continuous | 25.4 | 20 | 30 |

Wire pitch (mm) | S_{w} | Continuous | 4.06 | 4 | 5 |

Length with a wire (mm) | L_{tp} | Continuous | 101.6 | 80 | 120 |

Length without a wire (mm) | a | Continuous | 16.72 | 12 | 18 |

Number of layers | N_{c} | Discrete | 7 | 6 | 8 |

Number of rows | N_{f} | Discrete | 7 | 6 | 8 |

R134a | R600a | R513A | |
---|---|---|---|

P_{cond} (bar) | 9.2 | 5.3 | 11.4 |

T_{in,r} (°C) | 44.5 | 45.1 | 50.2 |

T_{amb} (°C) | 30 | 30 | 30 |

${\dot{\mathrm{m}}}_{r}$ (kg/s) | 0.0013 | 0.0006 | 0.0013 |

Refrigerant | Algorithm | Diff | lwr | upr | p adj |
---|---|---|---|---|---|

R134a | NSGAII-MOEAD | 0.000000466 | −0.000000902 | 0.000001833 | 0.6976122 |

OMOPSO-MOEAD | −0.000001939 | −0.000003307 | −0.000000572 | 0.0029952 | |

OMOPSO-NSGAII | −0.000002405 | −0.000003773 | −0.000001038 | 0.0001789 | |

R600a | NSGAII-MOEAD | 0.001188397 | 0.000970156 | 0.001406639 | 0.0000000 |

OMOPSO-MOEAD | 0.000159179 | −0.000059061 | 0.000377421 | 0.1973007 | |

OMOPSO-NSGAII | −0.001029218 | −0.001247459 | −0.000810977 | 0.0000000 | |

R513A | NSGAII-MOEAD | −0.006567517 | −0.007110653 | −0.006024381 | 0.0000000 |

OMOPSO-MOEAD | 0.000395047 | −0.000148089 | 0.000938183 | 0.1990515 | |

OMOPSO-NSGAII | 0.006962564 | 0.006419428 | 0.007505700 | 0.0000000 |

Refrigerant | R134a | R600a | R513A | ||||||
---|---|---|---|---|---|---|---|---|---|

Case 1 | Case 2 | Case 3 | Case 1 | Case 2 | Case 3 | Case 1 | Case 2 | Case 3 | |

$\dot{Q}$ (W) | 240.53 | 240.72 | 240.72 | 218.80 | 221.10 | 222.25 | 238.58 | 242.92 | 243.14 |

A (m^{2}) | 0.36723 | 0.31415 | 0.31268 | 0.36570 | 0.32961 | 0.36189 | 0.36512 | 0.36334 | 0.35886 |

D_{w} (mm) | 1.3 | 1.0 | 1.0 | 1.3 | 1.0 | 1.0 | 1.2 | 1.0 | 1.0 |

S_{w} (mm) | 4.0 | 5.0 | 5.0 | 4.0 | 5.0 | 5.0 | 4.0 | 5.0 | 5.0 |

D_{t} (mm) | 6.0 | 6.0 | 6.0 | 6.0 | 6.0 | 6.0 | 6.0 | 6.0 | 4.8 |

S_{t} (mm) | 21.5 | 20.0 | 20.0 | 21.7 | 20.0 | 20.0 | 27.1 | 22.2 | 20.0 |

L_{tp} (mm) | 120.0 | 105.1 | 80.0 | 120.0 | 111.3 | 80.0 | 120.0 | 120.0 | 116.0 |

N_{c} (-) | 6 | 7 | 8 | 6 | 7 | 8 | 6 | 7 | 8 |

N_{f} (-) | 6 | 7 | 8 | 6 | 7 | 8 | 6 | 7 | 8 |

a (mm) | 18.0 | 15.4 | 10.0 | 18.0 | 16.0 | 14.1 | 18.0 | 18.0 | 18.0 |

L_{t} (mm) | 6716.0 | 8070.0 | 8269.0 | 6721.0 | 8437.0 | 8787.0 | 6998.0 | 9211.0 | 11,597.0 |

N_{w} (-) | 361.0 | 295.2 | 257.0 | 361.0 | 312.6 | 257.0 | 361.0 | 338.7 | 372.2 |

L_{w} (mm) | 118.5 | 130.0 | 150.0 | 119.1 | 130.0 | 150.0 | 148.9 | 144.1 | 150.0 |

Volume (m^{3}) | 0.000144 | 0.000130 | 0.000132 | 0.000142 | 0.000136 | 0.000139 | 0.000146 | 0.000152 | 0.000154 |

Mass (kg) | 1.1205 | 1.0202 | 1.0376 | 1.1184 | 1.0698 | 1.0910 | 1.1449 | 1.1951 | 1.2094 |

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**MDPI and ACS Style**

Heredia-Aricapa, Y.; Belman-Flores, J.M.; Soria-Alcaraz, J.A.; Pérez-García, V.; Elizalde-Blancas, F.; Alfaro-Ayala, J.A.; Ramírez-Minguela, J.
Multi-Objective Optimization of a Multilayer Wire-on-Tube Condenser: Case Study R134a, R600a, and R513A. *Energies* **2022**, *15*, 6101.
https://doi.org/10.3390/en15176101

**AMA Style**

Heredia-Aricapa Y, Belman-Flores JM, Soria-Alcaraz JA, Pérez-García V, Elizalde-Blancas F, Alfaro-Ayala JA, Ramírez-Minguela J.
Multi-Objective Optimization of a Multilayer Wire-on-Tube Condenser: Case Study R134a, R600a, and R513A. *Energies*. 2022; 15(17):6101.
https://doi.org/10.3390/en15176101

**Chicago/Turabian Style**

Heredia-Aricapa, Yonathan, Juan M. Belman-Flores, Jorge A. Soria-Alcaraz, Vicente Pérez-García, Francisco Elizalde-Blancas, Jorge A. Alfaro-Ayala, and José Ramírez-Minguela.
2022. "Multi-Objective Optimization of a Multilayer Wire-on-Tube Condenser: Case Study R134a, R600a, and R513A" *Energies* 15, no. 17: 6101.
https://doi.org/10.3390/en15176101