# Selection of Appropriate Criteria for Optimization of Ventilation Element for Protective Clothing Using a Numerical Approach

^{*}

## Abstract

**:**

## 1. Introduction

**The Continuity Equation:**

**Navier–Stokes Equations (Momentum Equation):**

**The Energy Equation:**

## 2. Model Components and Boundary Conditions

- The jacket is closed at the top and bottom to prevent air from passing through, allowing for an investigation into the efficiency of ventilation.
- The study does not take radiation into consideration, as the heat loss due to radiation is assumed to be the same across all scenarios.
- The process of heat transmission occurs through conduction and convection from the body to the jacket and, subsequently, to the outer environment.

## 3. Results and Discussion

_{i,}when the i-th experiment point is not used in the approximation, and n—refers to the total number of experiment points. A more meaningful measure for assessing the accuracy of the approximation is the relative cross-validation error (Sigma Cross%), expressed as a percentage of the Standard Deviation (STD).

## 4. Conclusions

## Author Contributions

## Funding

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## Nomenclature:

NURBS | Non-Uniform Rational B-Splines |

MSDLH | Mean Square Distance Latin Hypercube |

DOE | Design of Experiments |

HTR | Heat Transfer Rate [W] |

H (avg.) | Absolute Total Enthalpy (average) [J/kg] |

ΔH | Absolute Total Enthalpy Rate [W] |

HF (avg.) | Surface Heat Flux (average) [W/m^{2}] |

dP | Pressure Difference (from flow trajectories) [Pa] |

dT | Surface Temperature Difference (body) [°C] |

Sigma Cross% | Relative Cross-validation error |

Max Rel Error | Maximum Relative Error |

## References

- Sacks, J.; Welch, W.J.; Mitchell, T.J.; Wynn, H.P. Design and analysis of computer experiments. Stat. Sci.
**1989**, 4, 409–423. [Google Scholar] [CrossRef] - Jones, D.R.; Schonlau, M.; Welch, W.J. Efficient global optimization of expensive black-box functions. J. Glob. Optim.
**1998**, 13, 455–492. [Google Scholar] [CrossRef] - Jones, D.R. A taxonomy of global optimization methods based on response surfaces. J. Glob. Optim.
**2001**, 21, 345–383. [Google Scholar] [CrossRef] - Sasena, M.J. Flexibility and Efficiency Enhancements for Constrained Global Design Optimization with Kriging Approximations. Ph.D. Thesis, Michigan Publishing, University of Michigan Library, Ann Arbor, MI, USA, 2002. Available online: https://deepblue.lib.umich.edu/handle/2027.42/132844 (accessed on 18 April 2024).
- Janusevskis, J.; Le Riche, R. Simultaneous Kriging-Based Sampling for Optimization and Uncertainty Propagation. Technical Report, Equipe: Calcul de Risque, Optimisation et Calage par Utilisation de Simulateurs—CROCUS-ENSMSE—UR LSTI—Ecole Nationale Superieure des Mines de Saint-Etienne, 29 July 2010. Deliverable no. 2.2.2-A of the ANR/OMD2 Project. Available online: http://hal.archives-ouvertes.fr/hal-00506957 (accessed on 18 April 2024).
- Rasmussen, C.E.; Williams, C.K.I. Gaussian Processes for Machine Learning (Adaptive Computation and Machine Learning); The MIT Press: Cambridge, MA, USA, 2005. [Google Scholar]
- Sajjad, U.; Hamid, K.; Rehman, T.-U.; Sultan, M.; Abbas, N.; Ali, H.M.; Imran, M.; Muneeshwaran, M.; Chang, J.-Y.; Wang, C.-C. Personal thermal management—A review on strategies, progress, and prospects. Int. Commun. Heat Mass Transf.
**2022**, 130, 105739. [Google Scholar] [CrossRef] - Ebi, K.L.; Capon, A.; Berry, P.; Broderick, C.; de Dear, R.; Havenith, G.; Honda, Y.; Kovats, R.S.; Ma, W.; Malik, A.; et al. Hot weather and heat extremes: Health risks. Lancet
**2021**, 398, 698–708. [Google Scholar] [CrossRef] [PubMed] - Ren, S.; Han, M.; Fang, J. Personal Cooling Garments: A Review. Polymers
**2022**, 14, 5522. [Google Scholar] [CrossRef] [PubMed] - Janushevskis, A.; Vejanand, S.R.; Gulevskis, A. Analysis of Different Shape Ventilation Elements for Protective Clothing. WSEAS Trans. Fluid Mech.
**2022**, 17, 140–146. [Google Scholar] [CrossRef] - Janushevskis, A.; Vejanand, S.R.; Gulevskis, A. Shape optimization of ventilation elements for protective clothing by using Metamodeling approach. In Proceedings of the Engineering for Rural Development, Jelgava, Latvia, 25–27 May 2022; pp. 164–172. [Google Scholar] [CrossRef]
- Auzins, J.; Janushevskis, A. KEDRO User Manual v.1.01, 2023; 50p. Scientific Laboratory for Machine and Mechanism Dynamics. Riga Technical University, Riga, RTU. 2023. Available online: http://www.mmd.rtu.lv/ProgramsA.htm (accessed on 18 April 2024).
- Hasse, C.; Debiagi, P.; Wen, X.; Hildebrandt, K.; Vascellari, M.; Faravelli, T. Advanced modeling approaches for CFD simulations of coal combustion and gasification. Prog. Energy Combust. Sci.
**2021**, 86, 100938. [Google Scholar] [CrossRef] - Ji, G.; Zhang, M.; Lu, Y.; Dong, J. The Basic Theory of CFD Governing Equations and the Numerical Solution Methods for Reactive Flows. In Computational Fluid Dynamics—Recent Advances, New Perspectives and Applications; IntechOpen: London, UK, 2023. [Google Scholar] [CrossRef]
- Chris Chikadibia Esionwu. CFD Methodology and Governing Equations. Kingston University, London. Available online: https://www.academia.edu/6690577/CFD_Methodology_and_Governing_Equations (accessed on 11 March 2014).
- Anderson, J.D. Fundamentals of Aerodynamics, 2nd ed.; McGraw-Hill: New York, NY, USA, 1991. [Google Scholar]
- Saxena, A.; Sahay, B. Computer Aided Engineering Design; Springer: New York, NY, USA; Anamaya Publishers: New Delhi, India, 2005; 410p. [Google Scholar]
- Janushevskis, A.; Vejanand, S.R.; Gulevskis, A. Comparative Analysis of Different Shape Ventilation Elements for Protective Clothing. In Proceedings of the Engineering for Rural Development, Jelgava, Latvia, 25–27 May 2022. [Google Scholar] [CrossRef]
- Rajesh Kumar, R.K.; Aggarwal, J.D. Sharma and Sunil Pathania. Predicting Energy Requirement for Cooling the Building Using Artificial Network. J. Technol. Innov. Renew. Energy
**2012**, 1, 113–121. [Google Scholar] - Giering, K.; Lamprecht, I.; Minet, O. Specific heat capacities of human and animal tissues. Proc. SPIE—Int. Soc. Opt. Eng.
**1996**, 2624, 188–197. [Google Scholar] - Rugh, J.P.; Bharathan, D. Predicting Human Thermal Comfort in Automobiles. In Proceedings of the Vehicle Thermal Management Systems Conference and Exhibition, Toronto, ON, Canada, 10 May 2005. [Google Scholar]

**Figure 1.**CAD model of a ventilation element with lower bounds on design variables [11].

**Figure 2.**CAD model of a ventilation element with upper bounds for design variables [11].

**Figure 3.**MSDLH DOE: (a) DOE with 12 trials for 2 factors generated by KEDRO; (b) 12 geometrical models of elements constructed using this DOE.

**Figure 4.**Model design of the body and jacket [18].

**Figure 6.**Flow pressure plot in the air gap between the body and jacket for element 1: (

**a**) Flow trajectories over the entire model; (

**b**) Enlarged view near inlet ventilation.

**Figure 7.**Surface temperature plot of the body for element 1: (

**a**) Surface temperature of the body over the entire model; (

**b**) Enlarged view near inlet ventilation.

**Figure 8.**Response surface dT = f (R60, R90) using 12 DOE for Kriging approximation: (

**a**) Cross-section plane of the response surface; (

**b**) Indications of approximation quality.

**Figure 9.**Optimization result (red point indicates global minimum of criteria -dT): (

**a**) Cross-section plane of the criterion surface; (

**b**) Optimum values.

**Figure 10.**Pressure plots for optimum element design: (

**a**) Flow pressure over the entire model; (

**b**) Zoomed view near the ventilation hole.

**Figure 11.**Surface temperature of the body: (

**a**) Surface temperature plot of the whole model; (

**b**) Zoomed view near the ventilation hole.

Material Property | Human Body | Jacket |
---|---|---|

Average density [kg.m^{−3}] | 985 | 1420 |

Specific heat [J.kg^{−1}.K^{−1}] | 3500 | 1140 |

Thermal conductivity [W.m^{−1}.K^{−1}] | 0.21 | 0.261 |

Element | HTR [W] | H (Avg.) [J/kg] | ΔH [W] | HF (Avg.) [W/m^{2}] | dP [Pa] | dT [°C] |
---|---|---|---|---|---|---|

1 | 17.655 | 312,509.94 | −0.997 | 29.682 | 5.55 | 7.5 |

2 | 17.644 | 312,509.58 | −1.00 | 29.663 | 6.17 | 6.2 |

3 | 17.622 | 312,509.25 | −0.997 | 29.693 | 6.06 | 7.7 |

4 | 17.693 | 312,509.84 | −0.997 | 29.746 | 8.49 | 7.24 |

5 | 17.650 | 312,509.43 | −0.997 | 29.674 | 5.89 | 7.38 |

6 | 17.599 | 312,509.65 | −1.00 | 29.587 | 5.74 | 6.91 |

7 | 17.617 | 312,510.01 | −0.997 | 29.617 | 8.25 | 7.04 |

8 | 17.612 | 312,510.09 | −0.997 | 29.584 | 34.4 | 6.64 |

9 | 17.692 | 312,510.21 | −0.997 | 29.744 | 18.83 | 6.91 |

10 | 17.689 | 312,509.84 | −0.997 | 29.739 | 13.92 | 7.27 |

11 | 17.687 | 312,509.94 | −0.997 | 29.725 | 5.7 | 6.76 |

12 | 17.632 | 312,509.62 | −0.997 | 29.643 | 5.44 | 6.68 |

X1 | X2 | Y1 | Y2 | |
---|---|---|---|---|

Mnemonic | R60 | R90 | dP | dT |

1 | 1.2545 | 1.8209 | 5.55 | 7.5 |

2 | 1.5527 | 0.01 | 6.17 | 6.2 |

3 | 0.6581 | 0.2363 | 6.06 | 7.7 |

4 | 1.8509 | 0.6890 | 8.49 | 7.24 |

5 | 0.36 | 0.9154 | 5.89 | 7.38 |

6 | 1.1054 | 0.4627 | 5.74 | 6.91 |

7 | 0.5090 | 2.0472 | 8.25 | 7.04 |

8 | 0.9563 | 2.5 | 34.4 | 6.64 |

9 | 1.7018 | 2.2736 | 18.83 | 6.91 |

10 | 2 | 1.5945 | 13.92 | 7.27 |

11 | 1.4036 | 1.1418 | 5.7 | 6.76 |

12 | 0.8072 | 1.3681 | 5.44 | 6.68 |

Indices | dP [Pa] | dT [°C] |
---|---|---|

Optimum shape of element | R60 = 0.50; | R60 = 0.50; |

R90 = 0.01 | R90 = 0.01 | |

Sigma Cross% | 50.09 | 44.62 |

Optimum values from KEDRO | 6.63 (Min) | 8.35 (Max) |

Value from flow simulation results | 6.75 | 8.55 |

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**MDPI and ACS Style**

Vejanand, S.R.; Janushevskis, A.; Vaicis, I.
Selection of Appropriate Criteria for Optimization of Ventilation Element for Protective Clothing Using a Numerical Approach. *Computation* **2024**, *12*, 90.
https://doi.org/10.3390/computation12050090

**AMA Style**

Vejanand SR, Janushevskis A, Vaicis I.
Selection of Appropriate Criteria for Optimization of Ventilation Element for Protective Clothing Using a Numerical Approach. *Computation*. 2024; 12(5):90.
https://doi.org/10.3390/computation12050090

**Chicago/Turabian Style**

Vejanand, Sanjay Rajni, Alexander Janushevskis, and Ivo Vaicis.
2024. "Selection of Appropriate Criteria for Optimization of Ventilation Element for Protective Clothing Using a Numerical Approach" *Computation* 12, no. 5: 90.
https://doi.org/10.3390/computation12050090