# Air Duct Optimization Design Based on Local Turbulence Loss Analysis and IMOCS Algorithm

^{1}

^{2}

^{*}

## Abstract

**:**

^{3}/min and reduced the noise by 2.3 dB.

## 1. Introduction

^{3}/min under the same noise conditions. Wang [5] simulated and analyzed the sound field intensity of the air duct system of the range hood. According to the simulation analysis results, the noise reduction of the air duct system was carried out. The experimental results showed that the noise of the optimized range hood decreased by 3.1 dBA compared with the original value, and the air performance remained basically unchanged.

## 2. Local Loss Analysis of Air Duct System

^{2}.

## 3. Feasibility Verification of Design Methods

#### 3.1. Validation Object

#### 3.2. Computational Modeling and Validation

#### 3.3. Boundary Conditions and Calculation Methods

_{i}denotes the velocity component averaged over the x

_{i}direction, and ρ, t, μ, and p are the air density, time, dynamic viscosity, and average fluid pressure, respectively.

^{−5}.

## 4. Multiobjective Optimization Design of Air Duct Guide Vane

#### 4.1. Head Duct Flow Field Analysis

#### 4.2. Head Air Duct Optimization Design

#### 4.3. Parametric Design of Guide Vane

_{1}, S

_{2}, and S

_{3}, where S

_{1}is the profile shape of the guide lobe at the inlet of the head duct, S

_{2}is the profile shape of the middle section of the head duct, and S

_{3}is the profile shape at the outlet of the head duct. The shape of S

_{2}is a vertical straight line, and its position is controlled by the depth L

_{1}of the cavity formed by the guide lobe and the front baffle, and the length L

_{2}of the air direct current in the head duct controls its length. The parameterized guide lobe has fixed endpoints M

_{1}and M

_{6}, and the ray from point M

_{1}is made to intersect with the S

_{2}extension line at point M

_{2}. The ray from point M

_{6}is made to intersect with the S

_{2}extension line at point M

_{5}, and M

_{1}, M

_{2}, and M

_{3}are set as control points to establish B-sample curve S

_{1}. Then M

_{4}, M

_{5}, and M

_{6}are set as control points to establish the B-sample curve S

_{3}. Finally, the specific size of line segment S

_{2}can be determined, and the specific size and position of line S

_{2}can be determined. These three B-line segments can express the overall characteristics of the guide leaf profile.

#### 4.4. Approximate Model

_{i}(x) denotes the basis function, b

_{i}denotes the coefficient corresponding to the basis function, $\sum _{\mathrm{i}=1}^{\mathrm{k}}{b}_{i}{f}_{i}(x)},$ denotes the mathematical expectation of f(x), and z(x) denotes the variance ${\sigma}_{s}^{2}$.

^{2}. The closer R

^{2}is to 1, the more accurate the prediction results of the approximation model. The following equation can calculate it as

^{2}denotes the regression coefficient, y

_{i}denotes the actual response value obtained from the simulation, $\overline{y}$ denotes the sample mean, and ${\widehat{y}}_{i}$ denotes the predicted value of the test sample.

^{2}values of the outlet air volume Q and the sound pressure level SPL of the whole machine calculated by the above equation are all between 0.9 and 1, which proves the usability of the Kriging approximation model and provides reliable data support for the multi-objective optimization search below.

#### 4.5. Improved MOCS Algorithm

_{a}, resulting in the loss of better solutions, which severely impacts the final optimization results [19]. In order to solve the problems of the above MOCS algorithm, it will be improved.

_{c}, variance probability P

_{m}, crossover distribution index eta_c, and variance distribution index eta_m need to be adjusted. The data in the figure shows that the Pareto solution set obtained by the IMOCS algorithm is closer to the natural Pareto frontier, and the optimization results of the IMOCS algorithm are more accurate compared with the NSGA-II algorithm and the MOCS algorithm. Due to the limited number of iterations, the optimization effect of the MOCS algorithm is not shown, which also shows the limitation of the MOCS algorithm.

## 5. Experimental Verification

## 6. Conclusions

^{3}/min, and the noise is reduced by 2.3 dB under the design working conditions.

## Author Contributions

## Funding

## Conflicts of Interest

## References

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**Figure 1.**Diagram of local loss of bent pipes [12].

**Figure 6.**Position calibration of the X-directional section within the prototype head duct of the integrated stove.

**Figure 7.**Cross-sectional flow diagram in the X-direction within the prototype head duct of the integrated stove.

**Figure 8.**Turbulent kinetic energy cloud map of X-direction cross-section in the head duct of integrated stove prototype.

**Figure 11.**Flow diagram of the X-directional cross-section within the initial optimized head duct of the integrated stove.

**Figure 12.**Turbulent energy cloud of X-directional cross-section in the preliminary optimized head duct of the integrated stove in head air duct of integrated stove.

**Figure 19.**Flow diagram of different X-directional cross-sections in the optimized head duct of the integrated stove.

**Figure 20.**Turbulent energy clouds for different X-directional cross-sections in the optimized head duct of the integrated stove.

Part Name | Geometric Parameters | Numerical Value |
---|---|---|

Air inlet | length A_{1} (mm) | 900 |

width A_{2} (mm) | 170 | |

Head | length B_{1} (mm) | 900 |

width B_{2} (mm) | 80 | |

height B_{2} (mm) | 505 | |

Intake box | length C_{1} (mm) | 600 |

width C_{2} (mm) | 200 | |

height C_{3} (mm) | 460 | |

Guided air box | length D_{1} (mm) | 760 |

width D_{1} (mm) | 166 | |

width D_{1} (mm) | 166 | |

Air outlet | diameter R (mm) | 166 |

Domains | Number of Grids |
---|---|

import | 860,778 |

head | 1,721,557 |

inlet box | 891,927 |

fans | 5,611,692 |

guided airbox | 55,962 |

export | 123,545 |

Samples | Air Volume Q | Sound Pressure Level SPL | ||||
---|---|---|---|---|---|---|

Projections | Simulations | Experiments | Projections | Simulations | Experiments | |

A | 16.57 | 16.82 | 16.65 | 55.71 | 56.23 | 55.85 |

B | 17.12 | 18.65 | 17.02 | 53.90 | 55.98 | 54.82 |

C | 16.28 | 17.39 | 16.36 | 55.89 | 56.73 | 55.97 |

D | 15.95 | 16.36 | 16.05 | 56.85 | 57.04 | 56.14 |

E | 16.55 | 17.33 | 16.02 | 55.67 | 56.72 | 56.25 |

Guide Vane | L_{1} (mm) | L_{2} (mm) | A (°) | Β (°) |
---|---|---|---|---|

Original | 27.05 | 0 | 156.13 | 155.87 |

Optimized | 32.06 | 162.96 | 105.71 | 118.55 |

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**MDPI and ACS Style**

Wu, Z.; Zhou, S.; Li, Y.; Jin, W.; Luo, Y.
Air Duct Optimization Design Based on Local Turbulence Loss Analysis and IMOCS Algorithm. *Machines* **2023**, *11*, 129.
https://doi.org/10.3390/machines11020129

**AMA Style**

Wu Z, Zhou S, Li Y, Jin W, Luo Y.
Air Duct Optimization Design Based on Local Turbulence Loss Analysis and IMOCS Algorithm. *Machines*. 2023; 11(2):129.
https://doi.org/10.3390/machines11020129

**Chicago/Turabian Style**

Wu, Zhenghui, Shuiqing Zhou, Yuebing Li, Weiya Jin, and Yu Luo.
2023. "Air Duct Optimization Design Based on Local Turbulence Loss Analysis and IMOCS Algorithm" *Machines* 11, no. 2: 129.
https://doi.org/10.3390/machines11020129