# New Calculation Technique for Assessment of Smoke Layer Interface in Large Buildings in Connection with the Design of Buildings in the Czech Republic

^{1}

^{2}

^{3}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Materials and Methods

#### 2.1. Dynamics of Fire in Relation to the Matter in Question

_{g}and fire growth rate α can be described using the following equation [37]:

#### 2.2. Spread of Smoke in an Area without Discharge into an External Environment

#### 2.3. Selected Techniques for Evaluating the Smoke Layer Interface

^{−3}for the attainment of conservative results. The calculation technique was derived from the Zukoski equation [32,42], which can be used for the fire plume [33,41]. The usual rule for the application of Equation (7) is the limit criterion of the mean flame height L

_{f}. The height of the smoke-free layer must be greater or equal to the mean flame height, i.e., ${L}_{f}\le z$. The fire growth phase is described by a so-called t-quadratic fire with value n = 2 [41]. Under these assumptions, it is possible to correct Equation (7) to the following form [43]:

#### 2.4. Existing Technique for Evaluating the Smoke Layer Interface in the Czech Republic

_{g}.

#### 2.5. Relationship of Foreign Characteristics for Evaluation of fire Dynamism and Characteristics in the Czech Republic

_{g}can be designated using the following equations [47]:

_{g}, fire growth rate α, and aforementioned basic quantities for evaluating the dynamism of fire in the Czech Republic constituted the basis for drafting a new technique for evaluating the level of the smoke layer interface without its release into an external environment.

#### 2.6. New Technique for Evaluating the Smoke Layer Interface in the Czech Republic

#### 2.7. Evaluation of Designated Deviations

## 3. Results

#### 3.1. Input Values

#### 3.2. Output Values

^{2}(A/H

^{2}). The specified dependency was selected on the basis of limitations of the NFPA calculation technique, and the floor area of the evaluated area of space was chosen so that the ratio A/H

^{2}is 1 (900 m

^{2}), 5 (4500 m

^{2}), 10 (9000 m

^{2}), and 20 (18,000 m

^{2}). The output values are presented as the ratio of the smoke free layer in the area of space z to the clear height of space H (z/H).

^{2}= 1 is described in Figure 2, the ratio of the geometry of space A/H

^{2}= 5 is described in Figure 3, the ratio of the geometry of space A/H

^{2}= 10 is described in Figure 4, the ratio of the geometry of space A/H

^{2}= 20 is described in Figure 5.

_{f}was always lower than the level of the smoke-free layer z. The results obtained through the ASET and ISO techniques agree with each other quite well. The deviations increase with increasing fire growth time. The results obtained using the ISO and CSN techniques are virtually identical.

^{2}= 1 and for ultra-fast fire growth, when Equation (11) achieves approximately identical results. Equation (11) is therefore more conservative than other calculation techniques. Due to the fact that Equation (11) does not take into account the effect of the floor area, it can be concluded that Equation (11) has been derived for a smaller floor area than the floor areas being compared. The constraints of Equation (11) are not currently presented anywhere. The fact that the results of Equation (11) can be misleading for the objects with a larger area is evidenced by the relatively small deviations between the values provided by all other equations, including the newly derived CSN calculation technique.

#### 3.3. Evaluation of Designated Deviations

## 4. Discussion

_{f}is less than or equal to the smoke interface above the base of fire source z. Therefore, this limit also applies to the CSN calculation technique.

_{g}).

_{g}from fire loading for non-production buildings (15) and average fire loading for buildings intended for production and storage (16). Thus, the Czech national standard for evaluating fire dynamism can be linked to the characteristic types of fires, and also to the NFPA, ASET, and ISO techniques. By substitution of the specified equations in the ISO calculation, the equations for designating the smoke layer interface descent were designated in the Czech Republic. The ISO calculation was selected as the “representative” technique, primarily due to its long-term, extensive use.

^{2}. The ratio of the area to the height of space in the given form is usual in the case of the application of one of the calculation techniques (such as the limits of the NFPA technique).

## 5. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Conflicts of Interest

## Nomenclature

A | floor area of enclosure (m^{2}) |

ASET | available Safe Egress Time (min) |

E | etalon value (-) |

$\overline{E}$ | average of etalon values (-) |

H | height of enclosure (m) |

L_{f} | mean flame height (m) |

MBE | mean bias error (-) |

P | value of assessed model (-) |

PBIAS | percent bias (%) |

RHR_{f} | maximum heat release (kW.m^{−2}) |

RMSE | root mean square error (-) |

RSET | required Safe Egress Time (min) |

Q | heat flux (kW) |

a | coefficient expressing combustion rate from aspect of character of flammable materials (-) |

k_{v} | air intake constant (0.064 m^{4/3}.s^{−1}.kW^{−1/3}) |

m | number of samples (-) |

n | n-th power (-), n = 2 for quadratic fire |

p | fire loading (kg.m^{−2}) |

$\overline{p}$ | average fire loading (kg.m^{−2}) |

p_{1} | probability of the occurrence and the spread of the fire (-) |

t | fire growth time (s) |

t_{g} | time needed to reach reference rate (the reference flow is understood to be the value of thermal 1055 kW) (s) |

t_{(z)} | time until attainment of smoke layer 2.5 m above floor (s) |

z | interface height above the base of fire source (m) |

α | fire growth rate (kW.s^{−2}) |

χ | fraction of heat released that is emitted as thermal radiation (-) |

ρ_{s} | smoke density (kg.m^{−3}) |

## References

- A Shared Vision, a Common Approach: A Stronger Europe. Global Strategy of Foreign and Safety Policy of the European Union; European Union: Brussels, Belgium, 2016; Available online: https://eeas.europa.eu/archives/docs/top_stories/pdf/eugs_review_web.pdf (accessed on 10 February 2022).
- Directive of the European Parliament and Council. Directive of the European Parliament and Council (EU) No. 305/2011 of 9 March 2011 Laying down Harmonised Conditions for the Marketing of Construction Products and Repealing Council Directive 89/106/EEC; EUR-Lex, 2011; Available online: https://eur-lex.europa.eu/legal-content/EN/TXT/?uri=celex%3A32011R0305 (accessed on 29 March 2022).
- Zehfuss, J. Guide to Engineering Methods of Fire Protection. Braunschweig: Association for the Promotion of German Fire Protection e. V. (vfdb), Technical and Scientific Advisory Board (TWB), Technical Report TB 04/01, 4th Revised and Expanded Edition. 2020, p. 494. Available online: https://www.vfdb.de/fileadmin/download/vfdb-Leitfaden_IngMethoden_4Auflage_2020-03-26.pdf (accessed on 10 February 2022).
- Hurley, M. SFPE Handbook of Fire Protection Engineering; Springer Science+Business Media: New York, NY, USA, 2015; ISBN 978-1-4939-2564-3. [Google Scholar]
- Islam, M.R.; Amiruzzaman, M.; Nasim, S.; Shin, J. Smoke Object Segmentation and the Dynamic Growth Feature Model for Video-Based Smoke Detection Systems. Symmetry
**2020**, 12, 1075. [Google Scholar] [CrossRef] - Folwarczny, L.; Pokorny, J. Evacuation of People; Association of Fire and Safety Engineering: Ostrava, Czech Republic, 2006; ISBN 978-80-86634-92-0. [Google Scholar]
- ISO/TR 16738; Fire Safety Engineering—Technical Information on Methods for Evaluating Behaviour and Movement of People. International Organization for Standardization: Genava, Switzerland, 2009; p. 61.
- Karlsson, B.; Quintiere, J.G. Enclosure Fire Dynamics; Environmental and Energy Engineering Series; CRC Press: Boca Raton, FL, USA, 2000; p. 315. ISBN 978-0-8493-1300-4. [Google Scholar]
- Orlikova, K.; Stroch, P. Chemistry of Combustion Processes; Association of Fire and Safety Engineering: Ostrava, Switzerland, 1999; ISBN 978-80-86111-39-1. [Google Scholar]
- Klote, H.J. Method of Prediction Smoke Movement in Atria with Apllication to Smoke Management; NISTIR 5516; Building and Fire Reserch Laboratory, National Institute of Standards and Technology: Gaithersburg, MD, USA, 1994; p. 98. [Google Scholar]
- Gomez, R.S.; Porto, T.R.N.; Magalhães, H.L.F.; Santos, A.C.Q.; Viana, V.H.V.; Gomes, K.C.; Lima, A.G.B. Thermo-Fluid Dynamics Analysis of Fire Smoke Dispersion and Control Strategy in Buildings. Energies
**2020**, 13, 6000. [Google Scholar] [CrossRef] - Klote, J.H.; Milke, J.A. Principles of Smoke Management; American Society of Heating, Refrigerating and Air-Conditioning Engineers: Atlanta, GA, USA, 2002; p. 377. ISBN 978-1-883413-99-6. [Google Scholar]
- Brändli, O.; Will, R.; Winkler, T.; Konrath, B.; Lucka, F.; White, P.; Sypek, G.; Khoshchevnikov, V.; Samoshin, D. Fire Protection in Buildings; REHVA Association of European Heating, Ventilation and Air Conditioning Engineers: Dusseldorf, German, 2018; ISBN 978-3-931384-92-0. [Google Scholar]
- CSN P CEN/TR 12101-5; Smoke and Heat Control Systems—Part 5: Guidelines on Functional Recommendations and Calculation Methods for Smoke and Heat Exhaust Ventilation Systems. Office for Technical Standardisation, Metrology and State Testing: Prague, Czech Republic, 2008.
- BS 7974:2019; Application of Fire Safety Engineering Principles to the Design of Buildings. Code of Practice. British Standards Institution: London, UK, 2019.
- Haouari-HarrakK, S.; Mehaddi, R.; Boulet, P.; Koutaiba, E.M. Evaluation of the room smoke filling time for fire plumes: Influence of the room geometry. Fire Mater.
**2020**, 44, 793–803. [Google Scholar] [CrossRef] - Qin, Y.; Huang, W.; Xiang, Y.; Yhang, R.; Lu, P.; Tan, X. Feasibility Analysis on Natural Smoke Extraction for Large Space Warehouse Buildings. Procedia Eng.
**2016**, 135, 495–500. [Google Scholar] [CrossRef] [Green Version] - Tang, F.; Zhao, Z.; Zhao, K. Experimental investigation on carriage fires hazards in the longitudinal ventilated tunnels: Assessment of the smoke stratification features. Saf. Sci.
**2020**, 130, 104901. [Google Scholar] [CrossRef] - Hu, P.; Zhang, Z.; Zhang, X.; Tang, F. An experimental study on the transition velocity and smoke back-layering length induced by carriage fire in a ventilated tunnel. Tunn. Undergr. Space Technol.
**2020**, 106, 103609. [Google Scholar] [CrossRef] - Morgan, H.P.; Hansell, G.O. Atrium buildings: Calculating smoke flows in atria for smoke-control. Fire Saf. J.
**1987**, 12, 9–35. [Google Scholar] [CrossRef] - Wegrzynski, W.; Konecki, M. Influence of the Fire Location and the Size of a Compartment on the Heat and Smoke Flow Out of the Compartment. AIP Conf. Proc.
**2018**, 1922, 110007. [Google Scholar] [CrossRef] - Gao, Z.H.; Ji, J.; Fan, C.G.; Li, L.J.; Sun, J.H. Determination of smoke interface height of medium scale tunnel fire scenarios. Tunn. Undergr. Space Technol.
**2016**, 56, 118–124. [Google Scholar] [CrossRef] - Zhu, Y.; Tang, F.; Chen, L.; Wang, Q.; Xu, X. Effect of lateral concentrated smoke extraction on the smoke back-layering length and critical velocity in longitudinal ventilation tunnel. J. Wind. Eng. Ind. Aerodyn.
**2020**. [Google Scholar] [CrossRef] - Vigne, G.; Wegrzinsky, W.; Cantizano, A.; Ayala, P.; Rein, G.; Gutiérrez-Montes, C. Experimental and computational study of smoke dynamics from multiple fire sources inside a large-volume building. Build. Simul.
**2021**, 14, 1147–1161. [Google Scholar] [CrossRef] - Sun, N.; Wang, L.; Xu, H. Study on Mutual Influence of Water Spray and Natural Smoke Exhaust System in Single Chamber Fire Based on FDS Simulation. AIP Conf. Proc.
**2018**, 2036, 020002. [Google Scholar] [CrossRef] - Li, K.Y.; Spearpoint, M.J. Simplified Calculation Method for Determining Smoke Downdrag Due to a Sprinkler Spray. Fire Technol.
**2011**, 47, 781–800. [Google Scholar] [CrossRef] - Kavan, S.; Brehovska, L. Cross-border cooperation on the example of international exercises between the Czech Republic, Austria and Germany. In XXI. International Colloquium on Regional Sciences, Kurdejov; Masaryk University: Brno, Czech Republic, 2018; pp. 404–409. ISBN 978-80-210-8970-9. [Google Scholar] [CrossRef]
- Fire Model Survey of Computer Models for Fire and Smoke; Combustion Science & Engineering, Inc.: Columbia, MD, USA; Available online: http://www.firemodelsurvey.com (accessed on 10 March 2022).
- ISO 16730-1; Fire Safety Engineering—Procedures and Requirements for Verification and Validation of Calculation Methods—Part 1: General. International Organization for Standardization: Genava, Switzerland, 2015; p. 42.
- Yamana, T.; Tanaka, T. Smoke Control in Large Scale Spaces. Fire Sci. Technol.
**1985**, 5, 41–54. [Google Scholar] [CrossRef] [Green Version] - Yamaguchi, J.; Tanaka, T. Simple Equations for Predicting Smoke Filling Time in Fire Rooms with Irregular Ceilings. Fire Sci. Technol.
**2005**, 24, 165–177. [Google Scholar] [CrossRef] [Green Version] - Zukoski, E.E.; Kubota, T.; Cetegen, B. Entrainment in Fire Plumes. Fire Saf. J.
**1981**, 3, 107–121. [Google Scholar] [CrossRef] - Brein, D. Areas of Application and Limits for Practice-Relevant Model Approaches for Evaluating the Spread of Smoke in Buildings (Plume Formulas); Version 1.2; Research Center for Fire Protection Technology at the University of Karlsruhe: Karlsruhe, Germany, 2001; p. 59. [Google Scholar]
- CSN 73 0802 ed. 2; Fire Protection of Buildings—Non-Industrial Buildings. Office for Technical Standardization, Metrology and State Testing: Prague, Czech Republic, 2020.
- CSN 73 0804 ed. 2; Fire Protection of Buildings—Industrial Buildings. Office for Technical Standardization, Metrology and State Testing: Prague, Czech Republic, 2020.
- Quintiere, J.G. Fundamentals of Fire Phenomena; John Wiley: Chichester, UK, 2006; p. 439. ISBN 978-0-470-09113-5. [Google Scholar]
- Pokorny, J.; Pavlik, T. Evaluation of Fire Development in Assessing the Fire Safety of Buildings in the Czech Republic; Association of Fire and Safety Engineering: Ostrava, Czech Republic, 2018; p. 100. ISBN 978-80-7385-208-5. [Google Scholar]
- Cote, A.E. Fire Protection Handbook, 19th ed.; National Fire Protection Association: Quincy, MA, USA, 2003; ISBN 978-0-87765-474-2. [Google Scholar]
- CSN EN 1991-1-2; Eurocode. Czech Standardisation Institute: Prague, Czech Republic, 2004; p. 56.
- Mozer, V.; Pokorny, J.; Kucera., P.; Vrablova, L.; Wilkinson, P. Utility of computer modelling in determination of safe available evacuation time. Komunikacie
**2015**, 17, 67–72. [Google Scholar] [CrossRef] - ISO 16735; Fire Safety Engineering—Requirements Governing Algebraic Equations—Smoke Layers. International Organization for Standardization: Geneva, Switzerland, 2006; p. 55.
- ISO 16734; Fire Safety Engineering—Requirements Governing Algebraic Equations—Fire Plumes. International Organization for Standardization: Geneva, Switzerland, 2006; p. 17.
- Wu, G.Y.; Chen, R.C. The Analysis of the Natural Smoke Filling Times in an Atrium. J. Combust.
**2010**, 2010, 687039. [Google Scholar] [CrossRef] [Green Version] - NFPA 92; Standard for Smoke Control Systems. National Fire Protection Association: Quincy, MA, USA, 2021.
- Computer Models for Fire and Smoke, Available Safe Egress Time (ASET). Available online: http://www.firemodelsurvey.com/pdf/ASET_2001.pdf (accessed on 2 April 2021).
- National Institute of Standards and Technology. Available online: https://www.nist.gov/ (accessed on 5 April 2022).
- Pokorny, J.; Malerova, L.; Gondek, H. Determination of local fire characteristics in connection with standards for fire safety assessment of buildings in the Czech Republic. The Science for Population Protection. Lazne Bohdanec Minist. Inter. Gen. Dir. Fire Rescue Serv. Popul. Prot. Inst.
**2017**, 9, 10. [Google Scholar] - Warner, M.R. Applied Statistics II. Multivariable and Multivariate Techniques, 3rd ed.; University of New Hampshire: Durham, NH, USA; Sage Publications: Southend Oaks, CA, USA, 2020; ISBN 978-1-07-181337-9. [Google Scholar]
- Pokorny, J. Characteristics of the Local Fire Column in the Context of National Standards for Assessing the Fire Safety of Buildings in the Czech Republic. Habilitation Work; VSB—Technical University of Ostrava, Faculty of Safety Engineering: Ostrava, Czech Republic, 2017. [Google Scholar]

**Figure 2.**Comparison of the simple calculation techniques for the ratio of the geometry of space A/H

^{2}= 1, where (

**a**) is slow fire growth, (

**b**) is medium fire growth, (

**c**) is fast fire growth, and (

**d**) is ultra-fast fire growth.

**Figure 3.**Comparison of the simple calculation techniques and the CFAST model for the ratio of the geometry of space A/H

^{2}= 5, where (

**a**) is slow fire growth, (

**b**) is medium fire growth, (

**c**) is fast fire growth, and (

**d**) is ultra-fast fire growth.

**Figure 4.**Comparison of the simple calculation techniques and the CFAST model for the ratio of the geometry of space A/H

^{2}= 10, where (

**a**) is slow fire growth, (

**b**) is medium fire growth, (

**c**) is fast fire growth, and (

**d**) is ultra-fast fire growth.

**Figure 5.**Comparison of the simple calculation techniques for the ratio of the geometry of space A/H

^{2}= 20, where (

**a**) is slow fire growth, (

**b**) is medium fire growth, (

**c**) is fast fire growth, and (

**d**) is ultra-fast fire growth.

**Figure 6.**Deviations between the etalon equation and other equations designated by the PBIAS, where there is (

**a**) slow fire growth, (

**b**) medium fire growth, (

**c**) fast fire growth, and (

**d**) ultra-fast fire growth.

**Figure 7.**Deviations between the etalon equation and other equations designated by the RMSE, where there is (

**a**) slow fire growth, (

**b**) medium fire growth, (

**c**) fast fire growth, and (

**d**) ultra-fast fire growth.

Designation of Input Values | Symbol | Value | Physical Unit |
---|---|---|---|

fire loading | p | 6, 24, 96, 383 | kg.m^{−2} |

combustion rate coefficient | a | 1.09 | - |

maximum heat release rate | RHR_{f} | 300 | kW.m^{−2} |

intake constant | k_{v} | 0.064 | m^{4/3}.s^{−1}.kW^{−1/3} |

height of space | H | 30 | m |

fire growth time | t | 900 | s |

time needed to reach reference rate | t_{g} | 600, 300, 150 and 75 | s |

time interval of calculations | 30 | s | |

smoke density | ρ_{s} | 1 | kg.m^{−3} |

radiation fraction of heat flux | χ | 0.2 | - |

fire growth rate | α | 0.003, 0.012, 0.047, 0.19 | kW.s^{−2} |

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**MDPI and ACS Style**

Podkul, M.; Pokorny, J.; Brumarova, L.; Dlouha, D.; Heinzova, Z.; Kubricka, K.; Szurgacz, D.; Fanta, M.
New Calculation Technique for Assessment of Smoke Layer Interface in Large Buildings in Connection with the Design of Buildings in the Czech Republic. *Sustainability* **2022**, *14*, 6445.
https://doi.org/10.3390/su14116445

**AMA Style**

Podkul M, Pokorny J, Brumarova L, Dlouha D, Heinzova Z, Kubricka K, Szurgacz D, Fanta M.
New Calculation Technique for Assessment of Smoke Layer Interface in Large Buildings in Connection with the Design of Buildings in the Czech Republic. *Sustainability*. 2022; 14(11):6445.
https://doi.org/10.3390/su14116445

**Chicago/Turabian Style**

Podkul, Marek, Jiri Pokorny, Lenka Brumarova, Dagmar Dlouha, Zuzana Heinzova, Katerina Kubricka, Dawid Szurgacz, and Miroslav Fanta.
2022. "New Calculation Technique for Assessment of Smoke Layer Interface in Large Buildings in Connection with the Design of Buildings in the Czech Republic" *Sustainability* 14, no. 11: 6445.
https://doi.org/10.3390/su14116445