Application of symbolic mathematics in modelling fire for providing a safe environment

Chow, Wan Ki; Meng, Linlin

doi:10.1016/j.buildenv.2006.04.009

Cited by 3 publications

(4 citation statements)

References 15 publications

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“…The two‐layer zone for studying compartment fire is schematically shown in Figure 1 25 . Here the compartment has a height H and a square cross section of area A , with a fire at the centre of the floor.…”

Section: The Two‐layer Zone Modelmentioning

confidence: 99%

A simplified analytical approach for the clear height in compartment fire based on a two‐layer zone model

Cheng

Chow

2022

Fire and Materials

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Compartment fire is an important research area in fire science and fire safety. Owing to its simplicity, the zone model remains attractive in studying compartment fire.Although computer software packages for the two-layer zone are in popular use, a basic understanding of the physical phenomena involved and the mathematical formulation thereon would benefit users of the zone model in terms of critical judgement of software outputs, which could be unreasonable, and insight of the general trends of important variables. In general, the differential equations based on a twolayer zone model have no analytical solutions and numerical methods are required. However, stiffness is present in using numerical methods to solve these differential equations, and reliable results are obtained only when very small time steps are used in computation. Nevertheless, in some special cases, analytical solution for the clear height in the zone model exists, as demonstrated in the present study. Predicted values of smoke layer height in the present approach are shown to be in good agreement with experimental results reported in the literature. The present work would provide insight into the tenability condition of a compartment on fire and is an important issue in fire safety management.

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Section: The Two‐layer Zone Modelmentioning

confidence: 99%

A simplified analytical approach for the clear height in compartment fire based on a two‐layer zone model

Cheng

Chow

2022

Fire and Materials

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“…According to Chow and Meng, 10,20 the combustion products of the whirling flame will flow outward through the vent of the space, as shown in Figure 2. Different velocity gradients are formed when the velocity of gas flowing into the space and the velocity of gas flowing out are superposed.…”

Section: Mass Transport Modelmentioning

confidence: 99%

“…Based on dimensional analysis, the main parameters controlling the flame structure and the relationship between these parameters were studied, the theoretical model describing the interaction among diffusion, momentum, and buoyancy was established, and an analytical relationship between flame height and vortex core radius was obtained. Based on the theoretical research and numerical simulation results, Quintiere 9 and Chow 10 summarized the formulas of mass inflow and outflow caused by flame in a confined space with a vent. In the field of numerical simulation, computational fluid dynamics plays an important role.…”

Section: Introductionmentioning

confidence: 99%

Flame whirling characteristics of fire in a room with vent

Fan

Wang

et al. 2021

Fire and Materials

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Summary Velocity distribution and motion of a whirling flame in a room fire with vent were studied analytically in this article. Using Rankine vortex model, whirling flame models with and without decay of the rotation velocity were established. The whirling flame model and the cross‐wind velocity boundary conditions were used to study the velocity distribution of the rotating flame under the action of side wind. When there is a linear velocity gradient in the lateral wind, the whirling flame still revolves around the same axis at different heights in the model without attenuation of rotation velocity, but the axis becomes tilted. In the rotation velocity attenuation model, the axis of the whirling flame changes from a straight line to a curve, and the change of the shape of the whirling flame is related to the flame height, the rotation angular velocity, and the maximum wind velocity. Under the assumption of Rankine vortex model with the same rotation angular velocity, the uniform lateral wind and lateral wind with linear velocity gradient can only affect the position and shape of the whirling flame axis but not change the rotation angular velocity.

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“…Studies of whirling flame in confined space is limited [1], with few experimental works [2]. For the whirling flame in a confined space, the air inflow and outflow through vents will have a significant impact on the formation and development of the flame due to shear force and suction resulting from swirling flow of flame [3]. At present, the behavior of whirling flame under the influence of cross wind has not received adequate attention.…”

Section: Introductionmentioning

confidence: 99%

Wind action on whirling flame characteristics

Wang¹,

Fan

et al. 2023

THERM SCI

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The behavior of whirling flame above a pool fire under cross wind was studied using a small wind tunnel. Whirling flames with different heat release rates were generated by an experimental rig. Effect of different wind speeds on the whirling flame was studied by an oil pool of two different diameters. Lateral images of the whirling flame collected were analyzed. Results show that under cross flow, the whirling flame was deflected along the direction of incoming flow. With the increase in wind speed, the deflection angle increased gradually. The angle also increased with the increase in pool diameter. When the cross flow increased to a certain value, the flame stopped swirling, and changed to an irregular shape. The maximum cross wind speed of the flame that did not stop flame rotation decreased with diameter. Crosswind with lower speed would raise the temperature of the whirling flame. When the wind speed was higher than a critical value, the temperature was reduced because burning rate decreased.

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Application of symbolic mathematics in modelling fire for providing a safe environment

Cited by 3 publications

References 15 publications

A simplified analytical approach for the clear height in compartment fire based on a two‐layer zone model

A simplified analytical approach for the clear height in compartment fire based on a two‐layer zone model

Flame whirling characteristics of fire in a room with vent

Wind action on whirling flame characteristics

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