# Design and Optimization of the Inlet Header Structure in Microchannel Heat Exchanger Based on Flow Distribution Uniformity

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## Abstract

**:**

_{2}flows in the PCHE, the structural types and working parameters of the inlet header and diversion zone may lead to differences in the flow distribution in each channel of the PCHE. This flow distribution difference affects the thermal hydraulic characteristics of the PCHE. A numerical simulation method was applied to explore the flow uniformity of the PCHE and the overall performance and analyze the influence of the type of straight barrel inlet header PCHE. Within each layer, the flow showed an uneven flow distribution, and the optimized inlet header was the tapered type. The results showed that when the taper angle varies from 6° to 9°, the flow distribution in each layer is relatively uniform. The comprehensive heat transfer performance of the straight-channel PCHE can be improved by 17.3–19.7%. Finally, the response surface and a genetic algorithm were combined to optimize the inlet header. The heat transfer performance of the optimized PCHE was improved by 19.7%.

## 1. Introduction

_{2}) Brayton cycle system, instead of the traditional steam Rankine cycle system, shows great potential in improving the photoelectric conversion efficiency of the system and reducing the power generation cost. S-CO

_{2}Brayton cycle power generation technology, with its significant technological and performance advantages, has considerable application potential in the utilization of ship flue gas waste heat, which is a critical way to improve the green level of ships and realize energy conservation and emission reduction in the shipping industry [1,2,3]. As one of the core components of the system, the S-CO

_{2}heat exchange precooler influences the system circulation efficiency. The printed circuit heat exchanger (PCHE) is considered the ideal S-CO

_{2}high-efficiency heat exchanger in the system due to its advantages of pressure reduction, large heat exchange area, good compactness, high heat exchange efficiency, and proper operation under high-intensity conditions [4].

_{2}(density, specific heat, viscosity, thermal conductivity, etc.) change with temperature, the flow state of S-CO

_{2}in the flow channel will also be affected [5,6]. Therefore, the study of flow allocation in microchannels of the PCHE is of great significance.

_{2}Brayton cycle power generation is still in the development stage. Studies on flow and heat transfer in PCHE belong to the field of applied research, and most of them focus on the establishment of the heat transfer correlation and the design of PCHEs [26,27,28,29]. Nevertheless, most studies are based on the assumption that the flow in the PCHE channel is evenly distributed, and few studies consider the uniformity of the flow distribution in each channel of the PCHE, PCHE pressure drops, and heat transfer efficiency, mainly because the flow channel is small. The internal flow parameters are difficult to measure. Thus, there are still problems in the study of PCHE heat transfer characteristics. For the straight barrel inlet header PCHE channel, the non-uniform flow distribution phenomenon is caused by the structure itself. If a guide plate is set up in the diversion area, then a higher flow can be obtained in the middle of the channel. Nevertheless, the additional guide plate structure is bound to cause a diversion area with increased pressure drop, leading to deterioration of the PCHE hydraulic characteristics on the whole, thus affecting the turbine inlet pressure in the Brayton cycle, which is a pyrrhic gain. In addition, due to the high operating pressure of the system, the setting of the guide plate may cause local stress concentration, which is not conducive to safe and stable operation of the system. Therefore, the design of the existing straight barrel inlet header PCHE must be optimized to improve the non-uniformity of the flow distribution in each layer of the PCHE so that the flow in the straight barrel inlet header PCHE can be generally evenly distributed.

_{2}flows in the PCHE, the structural types and working parameters of the inlet header and diversion zone may lead to differences in the flow distribution in each channel of the PCHE, and the uniformity of the flow distribution increases with increasing PCHE scale. This difference in flow distribution affects the thermal hydraulic characteristics of the PCHE and further reduces the comprehensive performance of the Brayton cycle power generation system. Therefore, a numerical simulation method is proposed to explore the influence of flow uniformity on the overall performance of the PCHE and improve the structure of the straight barrel inlet header PCHE to optimize the S-CO

_{2}distribution in the PCHE flow channel.

## 2. Flow Distribution Characteristics of the Straight Barrel Inlet Header PCHE

#### 2.1. Physical and Numerical Models

_{2}–water heat transfer is on the S-CO

_{2}side, so only the S-CO

_{2}side flow channel needs to be calculated, and a constant wall temperature is given on the S-CO

_{2}side.

_{2}in the PCHE. This model can consider the influence of temperature and pressure changes on the physical properties of S-CO

_{2}. The SST k-ω model is used for the turbulence model. SIMPLE is used for the discrete algorithm. The second-order discrete scheme is used for the pressure, the second-order upwind method is used for the momentum and density, and the second-order upwind scheme is used for the turbulent kinetic energy and turbulent dissipation rate. The convergence criterion is 10

^{−3}.

_{ij}. Then, the average flow rate of the flow channels is

_{ave}is the average flow rate of the flow channels, kg/s.

_{ij}is the non-uniformity of each flow channel. The plate non-uniformity of each layer is defined as

_{i}is the non-uniformity of layer i. The overall non-uniformity of the straight barrel inlet header PCHE is defined as

_{o}is the standard deviation of the overall non-uniformity. The standard deviation of the non-uniformity of each layer is

_{i,c}is the standard deviation of the non-uniformity of each flow channel of the layer i heat exchanger plate.

#### 2.2. Flow Distribution Characteristics of the Straight Barrel Inlet Header PCHE

_{i,c}) is shown in Table 2. σ

_{i,c}and ${\sigma}_{p}$ are equivalent in order of magnitude. The flow distribution in the straight barrel inlet header PCHE is uneven between each heat exchanger plate layer and between the flow channels of a single-layer heat exchanger plate.

## 3. Flow Distribution Characteristics of the Tapered Header

_{2}flows downward in the tapered area, the pressure energy and velocity energy at the entrance of the heat exchanger plate in each layer from top to bottom remain unchanged. The backflow dead zone at the bottom of the header is eliminated to realize uniform distribution of the flow of the heat exchanger plate in each layer. Figure 8 shows the structure diagram of the tapered header. The magnitude of different taper angles θ represents the rate at which pressure energy is converted into velocity energy along the flow direction of the tapered area. Limited by the structural characteristics of the model, the diameter of the top circle is constant at d

_{1}= 10 mm, and the distance between the first heat exchanger plate and the tenth heat exchanger plate is 29.8 mm. Assuming that the bottom circle diameter d

_{2}is 0, the maximum value of the angle θ is 18.55°; that is, angle θ ranges from 0° to 18.55°. In this paper, 3° to 15° models which inlet mass flow is 0.05 kg/s are selected for numerical simulation to explore the influence of different structural parameters on the non-uniformity of the flow distribution in each layer. The d

_{2}corresponding to specific angles is listed in the following Table 3.

_{2}of the bottom circle of the header slowly decreases, and the inclination degree of the tapered header slowly increases, leading to a more significant proportion of pressure energy being converted to velocity energy along the flow direction of the header. The larger the velocity energy is, the less flow is distributed to the layer. Therefore, as the taper angle θ increases, the average slope of the flow distribution ratio curve of each layer of the straight barrel inlet header PCHE gradually decreases from positive to 0 and then negative. On the whole, when θ = 6° and θ = 9°, the flow distribution in each layer is approximately 10%. Uniform flow distribution in each layer of the PCHE can be considered to be realized under these structural parameters.

## 4. Influence of Non-Uniformity on Thermal Hydraulic Characteristics

#### 4.1. Thermal Hydraulic Characteristics of Tapered Header PCHE

#### 4.2. Optimization of the Tapered Inlet Header

#### 4.2.1. Sensitivity Analysis

#### 4.2.2. Optimization Results

^{2}= 0.9924, indicating that the model can explain up to 99% of the changes, that the regression model can run in the design space, and that it is meaningful to optimize CP.

^{−3}. After 200 iterations, 10 Pareto optimal solution sets are obtained (Table 5). As seen from the table, the effect on the heat transfer performance is optimal when the taper angle is approximately 7.2°, and the Reynolds number influence on the heat transfer performance is not as strong as that of the taper angle, which is consistent with the ranges determined by numerical simulation. In addition, CP increases with increasing Reynolds number.

## 5. Conclusions

## Author Contributions

## Funding

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

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**Figure 2.**Single-side flow channel model and grid block division strategy of the straight-channel PCHE.

**Figure 3.**Numerical model validation (Experimental Results [10]).

**Figure 11.**Mass flow rate cloud diagram and flow diagram of the headers with different angles. (

**a**) θ = 0°; (

**b**) θ = 3°; (

**c**) θ = 6°; (

**d**) θ = 9°; (

**e**) θ = 12°; (

**f**) θ = 15°.

Number | Pressure/MPa | Flow Rate/(kg·s^{−1}) | Inlet Temperature/K | Wall Temperature/K | Re |
---|---|---|---|---|---|

1 | 9.5 | 0.01 | 305 | 333 | 1275.8 |

2 | 0.02 | 2551.6 | |||

3 | 0.03 | 3827.4 | |||

4 | 0.04 | 5103.2 | |||

5 | 0.05 | 6379.0 |

**Table 2.**Statistics of the standard deviation of the non-uniformity of each flow channel of each heat exchanger plate layer.

i | C 1 | C 2 | C 3 | C 4 | C 5 | C 6 | C 7 | C 8 | C 9 | C 10 |

σ_{i,c} | 0.116 | 0.125 | 0.144 | 0.152 | 0.099 | 0.096 | 0.153 | 0.209 | 0.23 | 0.214 |

Taper Angle θ/° | 3 | 6 | 9 | 12 | 15 |

d_{2}/mm | 8.4 | 7.0 | 5.0 | 3.6 | 2.0 |

Source | Sum of Square | Degree of Freedom | Mean Square | F-Value | p-Value | |
---|---|---|---|---|---|---|

Model | 0.4431 | 14 | 0.0317 | 140.75 | <0.0001 | significant |

A-Tapered Angle | 0.0001 | 1 | 0.0001 | 0.402 | 0.5356 | |

B-Re | 0.0104 | 1 | 0.0104 | 46.03 | <0.0001 | |

AB | 0.0002 | 1 | 0.0002 | 0.8928 | 0.3597 | |

A² | 0.0561 | 1 | 0.0561 | 249.29 | <0.0001 | |

B² | 0.0001 | 1 | 0.0001 | 0.3598 | 0.5576 | |

A²B | 0.0003 | 1 | 0.0003 | 1.37 | 0.2601 | |

AB² | 0.0006 | 1 | 0.0006 | 2.58 | 0.129 | |

A³ | 0.0003 | 1 | 0.0003 | 1.16 | 0.298 | |

B³ | 0.0054 | 1 | 0.0054 | 23.87 | 0.0002 | |

A²B² | 0.0002 | 1 | 0.0002 | 0.961 | 0.3425 | |

A³B | 0.0002 | 1 | 0.0002 | 1.06 | 0.3193 | |

AB³ | 0.0001 | 1 | 0.0001 | 0.2986 | 0.5928 | |

A⁴ | 0.0322 | 1 | 0.0322 | 143.05 | <0.0001 | |

B⁴ | 0.0002 | 1 | 0.0002 | 1.04 | 0.3231 | |

Residual | 0.0034 | 15 | 0.0002 | |||

Lack of fit | 0.0028 | 1 | <0.0001 | 0.27 | 0.187 | |

Cor total | 0.4465 | 29 |

Number | Angle | Re | CP | Desirability | |
---|---|---|---|---|---|

1 | 7.271 | 6200 | 1.187 | 0.98 | Selected |

2 | 7.209 | 6199.993 | 1.187 | 0.979 | |

3 | 7.152 | 6199.987 | 1.187 | 0.979 | |

4 | 7.456 | 6199.999 | 1.187 | 0.979 | |

5 | 7.047 | 6199.998 | 1.186 | 0.979 | |

6 | 6.938 | 6199.991 | 1.186 | 0.977 | |

7 | 6.374 | 6199.995 | 1.179 | 0.964 | |

8 | 6.228 | 6200.000 | 1.176 | 0.959 | |

9 | 0.000 | 6199.997 | 0.983 | 0.577 | |

10 | 15.000 | 6199.998 | 0.979 | 0.570 |

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**MDPI and ACS Style**

Zhang, K.; Wei, W.; Sun, Y.; Wu, Q.; Tang, M.; Lu, M.
Design and Optimization of the Inlet Header Structure in Microchannel Heat Exchanger Based on Flow Distribution Uniformity. *Appl. Sci.* **2022**, *12*, 6604.
https://doi.org/10.3390/app12136604

**AMA Style**

Zhang K, Wei W, Sun Y, Wu Q, Tang M, Lu M.
Design and Optimization of the Inlet Header Structure in Microchannel Heat Exchanger Based on Flow Distribution Uniformity. *Applied Sciences*. 2022; 12(13):6604.
https://doi.org/10.3390/app12136604

**Chicago/Turabian Style**

Zhang, Kaidi, Wei Wei, Yuwei Sun, Qiang Wu, Min Tang, and Mingjian Lu.
2022. "Design and Optimization of the Inlet Header Structure in Microchannel Heat Exchanger Based on Flow Distribution Uniformity" *Applied Sciences* 12, no. 13: 6604.
https://doi.org/10.3390/app12136604