September 2018, 8(3): 277-286. doi: 10.3934/naco.2018016

Application of box-behnken design with response surface for optimizing ventilation system of underground shelter

Center for Fluid Dynamics, College of Engineering, Universiti Tenaga Nasional (UNITEN), 43000 Kajang, Selangor, Malaysia

* Corresponding author: azfarizal.mukhtar@gmail.com

Received  February 2017 Revised  June 2017 Published  June 2018

Fund Project: The first author is supported by YTN scholarship

Ventilation shaft is one of the effective elements in natural ventilation for ensuring acceptable Indoor Air Quality (IAQ) and thermal comfort. It has been found that the opening of ventilation shaft plays a significant role in the ventilation efficiency of an underground shelter. In this study, we aim to develop a predictive ventilation rate model for a naturally-ventilated underground shelter. Computational Fluid Dynamics (CFD) was employed as a simulation tool, where the result was validated with experimental data obtained from the previous literature. Goal Driven Optimization (GDO) was used for the optimization process by considering three geometrical factors and their effects on the objective function. From this study, it is found that the predicted response surface values agree well with the CFD values and hence the predictive model is reliable.

Citation: Azfarizal Mukhtar, Ng Khai Ching, Mohd Zamri Yusoff. Application of box-behnken design with response surface for optimizing ventilation system of underground shelter. Numerical Algebra, Control & Optimization, 2018, 8 (3) : 277-286. doi: 10.3934/naco.2018016
References:
[1]

E. M. Barber, T. Kusuda, P. J. Reynolds and F. J. Powell, A Study of Air Distribution in Survival Shelters Using a Small-Scale Modeling Technique, Technical Report, Washington D. C., 1972. doi: 10.6028/NBS.RPT.10689.

[2]

C. V. Chestert, Preparing underground structures for Civil Defense, Undergr. Sp., 6 (1981), 160-165.

[3]

R. Daghigh, Assessing the thermal comfort and ventilation in Malaysia and the surrounding regions, Renew. Sustain. Energy, 48 (2015), 682-691. doi: 10.1016/j.rser.2015.04.017.

[4]

U. M. Diwekar and J. R. Kalagnanam, Efficient sampling technique for optimization under uncertainty, AIChE J., 43 (1997), 440-447. doi: 10.1002/aic.690430217.

[5]

E. J. Edward and W. C. Randall, The neutral zone in ventilation, Trans. Am. Soc. Heat. Vent. Eng, 32 (1926), 59-74.

[6]

J. C. King, Gravity Ventilation of Underground Shelters, Technical Report, Port Hueneme, California, 1965. doi: 10.21236/AD0613550.

[7]

Y. Li and P. Heiselberg, Analysis methods for natural and hybrid ventilation - a critical literature review and recent developments, Int. J. Vent, 1 (2003), 3-20. doi: 10.1080/14733315.2003.11683640.

[8]

R. H. Myers, D. C. Montgomery and C. M. Anderson-cook, Response Surface Methodology: Process and Product Optimization Using Designed Experiments, 3$^{rd}$ edition, John Wiley and Sons Ltd, 2009.

[9]

W. YuB. LiH. JiaM. Zhang and D. Wang, Application of multi-objective genetic algorithm to optimize energy efficiency and thermal comfort in building design, Energy Build, 88 (2015), 3-20. doi: 10.1016/j.enbuild.2014.11.063.

show all references

References:
[1]

E. M. Barber, T. Kusuda, P. J. Reynolds and F. J. Powell, A Study of Air Distribution in Survival Shelters Using a Small-Scale Modeling Technique, Technical Report, Washington D. C., 1972. doi: 10.6028/NBS.RPT.10689.

[2]

C. V. Chestert, Preparing underground structures for Civil Defense, Undergr. Sp., 6 (1981), 160-165.

[3]

R. Daghigh, Assessing the thermal comfort and ventilation in Malaysia and the surrounding regions, Renew. Sustain. Energy, 48 (2015), 682-691. doi: 10.1016/j.rser.2015.04.017.

[4]

U. M. Diwekar and J. R. Kalagnanam, Efficient sampling technique for optimization under uncertainty, AIChE J., 43 (1997), 440-447. doi: 10.1002/aic.690430217.

[5]

E. J. Edward and W. C. Randall, The neutral zone in ventilation, Trans. Am. Soc. Heat. Vent. Eng, 32 (1926), 59-74.

[6]

J. C. King, Gravity Ventilation of Underground Shelters, Technical Report, Port Hueneme, California, 1965. doi: 10.21236/AD0613550.

[7]

Y. Li and P. Heiselberg, Analysis methods for natural and hybrid ventilation - a critical literature review and recent developments, Int. J. Vent, 1 (2003), 3-20. doi: 10.1080/14733315.2003.11683640.

[8]

R. H. Myers, D. C. Montgomery and C. M. Anderson-cook, Response Surface Methodology: Process and Product Optimization Using Designed Experiments, 3$^{rd}$ edition, John Wiley and Sons Ltd, 2009.

[9]

W. YuB. LiH. JiaM. Zhang and D. Wang, Application of multi-objective genetic algorithm to optimize energy efficiency and thermal comfort in building design, Energy Build, 88 (2015), 3-20. doi: 10.1016/j.enbuild.2014.11.063.

Figure 1.  Boundary conditions
Figure 2.  Optimization parameters
Figure 3.  Grid independence test
Figure 4.  Validation of CFD model
Figure 5.  Correlation matrix
Figure 6.  Coefficient of determination
Figure 7.  Scatter plot
Figure 8.  Comparison between CFD and RSM
Figure 9.  Quality of fit between predicted and observed point
Figure 10.  Sensitivities of the three parameters for optimization
Figure 11.  Response of two major inputs on ventilation rate
Table 1.  Boundary conditions for the simulation
Domain Inlet constant velocity, 2.68 m/s at a constant temperature, 23$^0$C
Domain Outlet zero pressure
Domain Wall free slip wall at a constant temperature, 23$^0$C
Supply Duct adiabatic, no-slip wall
Exhaust Duct adiabatic, no-slip wall
Heating Cable 70 $W/m^2$
Underground Shelter adiabatic, no-slip wall
Domain Inlet constant velocity, 2.68 m/s at a constant temperature, 23$^0$C
Domain Outlet zero pressure
Domain Wall free slip wall at a constant temperature, 23$^0$C
Supply Duct adiabatic, no-slip wall
Exhaust Duct adiabatic, no-slip wall
Heating Cable 70 $W/m^2$
Underground Shelter adiabatic, no-slip wall
Table 2.  Quantification of factor and response parameters
Parameter Name Max $(m)$ Min $(m)$ Constraints
P1 Factor Inlet Opening (D1) 0.1524 0.1016 -
P2 Factor Ratio of Elbow Shaft (R/H) 2.5 0.75 R/H $\geq 0.75$
P3 Factor Outlet Opening (D1) 0.1524 0.1016 -
P4 Response Ventilation Rate $(m^3/s)$ -
Parameter Name Max $(m)$ Min $(m)$ Constraints
P1 Factor Inlet Opening (D1) 0.1524 0.1016 -
P2 Factor Ratio of Elbow Shaft (R/H) 2.5 0.75 R/H $\geq 0.75$
P3 Factor Outlet Opening (D1) 0.1524 0.1016 -
P4 Response Ventilation Rate $(m^3/s)$ -
Table 3.  Candidate points generated from the screening algorithm
Candidate Point P1 $(m)$ P2 $(m)$ P3 $(m)$ P4 $(m^3/s)$ Deviation $(\%)$
CP 1 0.1524 0.833 0.1524 0.0445 2.24
CP 2 0.1509 1.538 0.1522 0.0441 3.11
CP 3 0.1522 1.172 0.1506 0.0439 3.53
Candidate Point P1 $(m)$ P2 $(m)$ P3 $(m)$ P4 $(m^3/s)$ Deviation $(\%)$
CP 1 0.1524 0.833 0.1524 0.0445 2.24
CP 2 0.1509 1.538 0.1522 0.0441 3.11
CP 3 0.1522 1.172 0.1506 0.0439 3.53
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