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Numerical Modeling of Compartment Fires: Ventilation Characteristics and Limitation of Kawagoe’s Law

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Abstract

Kawagoe’s Law is an essential correlation in compartment fire research, which defines the relationship between the ventilation factor and maximum fuel burning of the compartment. Although this law has been widely used, there is still a lack of numerical validation and knowledge on the limiting conditions of its application. In this paper, a numerical study is conducted under full-scale compartment fire with different opening sizes and gas fuel supply rates using the LES model for validating Kawagoe’s Law. The mass flow rate of inflow through the opening and the indoor heat release rate is focused during the numerical validation. Numerical results show that the inflow rate and indoor heat release rate comply well with Kawagoe’s Law under ordinary openings with a small aspect ratio. However, Kawagoe’s Law becomes less valid for openings with large aspect ratios and small-gap openings. The jet flame was observed in the case of openings with large aspect ratios under a high fuel supply rate. For compartment fires with small gaps, a breathing process, i.e., the periodical suppression and revitalization of the fire, is modeled. This work provides practical guidance for modeling compartment fires and paving the way for constructing a numerical compartment fire database.

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Abbreviations

CFD:

Computational fluid dynamics

FDS:

Fire dynamics simulator

HRR:

Heat release rate

HRRPUV:

Heat release rate per unit volume

A :

Area of the opening (m2)

c p :

Specific heat (kJ/(kg K))

C :

Fitting coefficient (-)

D*:

Characteristic diameter

g :

Acceleration of gravity (m/s2)

H :

Height of the opening (m)

\(\dot{m}\) :

Mass flow rate (kg/s)

\(\dot{Q}\) :

Heat release rate of fire (kW)

T:

Temperature (K)

W:

Width of the opening (m)

\(\rho\) :

Density (kg m3)

\(\delta _{x}\) :

Nominal grid size

K:

Kawagoe’s Law

a:

Air

F:

Fuel

g:

Gas

in:

Inside the compartment

jet:

Jet flame

\(\infty\) :

Ambient

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Acknowledgements

This work is funded by the Hong Kong Research Grants Council Theme-based Research Scheme (T22-505/19-N) and the PolyU Emerging Frontier Area (EFA) Scheme of RISUD (P0013879). TZ thanks the support from the Hong Kong PhD Fellowship Scheme.

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Correspondence to Xinyan Huang.

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Appendices

Appendix A Summary of Kawagoe’ pioneering work in 1950s

Report No. 27, “Fire Behavior in Rooms” [5] is a summary of Kawagoe’s ten years of work from 1948 to 1958. In his report, different scales of compartment fire tests were conducted with compartment models and full-scale rooms, and the test list is summarized in Table A1.

Table A1 Kawagoe’s compartment fire experiments in report No. 27, where fire duration is the time from the beginning of the room temperature rise to its maximum, and (× n) means n openings

According to his experiment results, Kawagoe’s Law can be obtained using linear regression, which is consistent with his theoretical derivation [6]. All fuel burning rate data of Kawagoe’s pioneering experiment are replotted in Figure 

Figure 12
figure 12

Comparison of fuel burning rate measured in Kawagoe’s early experiments and the uncertainty of the Kawagoe’s Law

12 to illustrate the accuracy and uncertainty of Kawagoe’s law in the form of Eq. (1), \({\dot{m}}_{F}^{K}=5.5A{H}^{1/2}\)(kg/min). The upper and lower limits of the original test data are \({\dot{m}}_{F}=7.3A{H}^{1/2}\) and \({\dot{m}}_{F}=3.9A{H}^{1/2}\), respectively. Therefore, based on the experimental data, the uncertainty of applying Kawagoe’s law is about 30%.

Appendix B The temporal evolutions of temperature and air inflow rate

The temporal evolutions of temperature and air flow rate in the compartment fire with a 2.4 m (W) × 0.5 m (H) opening (\(A\sqrt{H}=0.85\)) is taken as an example to clarify the semi-steady state from 600 to 1200 s. The ceiling temperature (TC1 and TC2) as well as the opening flow characteristics during the compartment fire can be seen in Figure 

Figure 13
figure 13

Temporal evolution of a temperatures at 0.1 m under the ceiling, b mass flow rate through the opening (2.4 m × 0.5 m and \(A\sqrt{H}=0.85\)), where the HRR of the over-ventilated fire is 500 kW

13, which shows that the fire has reached a semi-steady state between 600 and 1200 s.

Appendix C Impact of spilled flame on air inflow rate

The compartment with a 0.6 m (W) × 0.8 m (H) opening (\(A\sqrt{H}=0.43\)) is taken as an example to show the impact of spilled flame on the air inflow rate. Compared with the over-ventilated fire scenario (\({\dot{m}}_{F}/{\dot{m}}_{F}^{K}\)=0.8), the air inflow rate under the under-ventilated fire scenario at the initial stage of the fire conforms to the description of Kawagoe’s Law. However, as the spilled flame heats the air outside the compartment, the air inflow rate begins to decrease and then reaches a semi-steady state (Figure 

Figure 14
figure 14

The temporal evolutions of air inflow rate with and without spilled flame under the compartment fire scenario with a 0.6 m (W) × 0.8 m (H) opening (\(A\sqrt{H}=0.43\))

14).

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Wang, Z., Zhang, T. & Huang, X. Numerical Modeling of Compartment Fires: Ventilation Characteristics and Limitation of Kawagoe’s Law. Fire Technol 60, 1245–1268 (2024). https://doi.org/10.1007/s10694-022-01218-1

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