Elsevier

Combustion and Flame

Volume 205, July 2019, Pages 422-433
Combustion and Flame

Experimental study and physical analysis of flame geometry in pool fires under relatively strong cross flows

https://doi.org/10.1016/j.combustflame.2019.04.025Get rights and content

Abstract

This paper investigated the influence of horizontal cross flows on the flame geometry in pool fires. Four square gaseous burners with dimensions of 8 cm, 10 cm, 15 cm, and 20 cm were used employing propane as fuel with various heat release rates. The cross flows were provided by a wind tunnel with air speed ranging from 0 m/s to 6.0 m/s in 0.5 m/s intervals. Five basic quantities of the flame geometry were measured comprehensively, namely, the horizontal flame length Lx, the vertical flame height H and the flame base drag Ldrag as well as two definitions of the flame tilt angle θ1 (originating from pool center) and θ2 (originating from flame base center). The horizontal flame length Lx and the flame base drag Ldrag are found to firstly increase then decrease, while the vertical flame height H decreases and the flame tilt angles θ1, θ2 increase monotonically, with increasing of cross flow air speed. The flame is characterized into two regions, i.e., one similar to boundary layer near the pool surface followed by the other similar to free flow rising above ground. This explains the aforementioned different behaviors of horizontal flame length Lx and vertical flame height H under different cross flow air speeds. In addition, none of correlations previously proposed describes all the flame geometry parameters comprehensively in both horizontal- and vertical directions under relatively strong cross flows. A physical model is developed based on the characteristic length scale derived by combining cross flow air speed, the characteristic volumetric air entrainment, the turbulent flame buoyancy and the air required for stoichiometric combustion. The basic new element is the flame buoyancy (ΔTfTag=g)in combination with the cross flow air speed, which determines a characteristic length scale, Uw2/g. The proposed model correlates well the above five basic quantities of flame geometry in pool fires under cross flows. This approach allows us predicting the flame geometry in both horizontal- and vertical directions of pool fires for relatively high cross flow air speeds having cross flow (wind) Froude number Uw2gD>0.13.

Introduction

Subjected to a horizontal cross flow, the buoyancy of the flame and the inertia of the cross flow interact to affect and change the flame geometry [1]. Extensive works have been done on the vertical flame height of pool fires in still air, revealing the controlling physical mechanisms (buoyancy induced air entrainment and mixing, as well as its characteristic length scales of different source dimensions) and proposing well established correlations [2], [3], [4], [5], [6]. However, in real cases, most pool fires happen in open space where there can be wind (cross flow). The cross flow not only changes the heat transfer mechanism and mass burning rate [7], [8] but also influences the flame shape by changing the convection, counteracting the plume buoyancy and affecting the entrainment and mixing of air with fuel [1]. Cross flow imposed on the pool fire pushes the flame downstream leading to modifications of flame geometry. Researches have been done on flame geometry parameters in this situation including horizontal flame length (Lx) [9], vertical flame height (H) [10], [11], flame base drag (Ldrag) [12], [13], [14], [15], [16], [17], [18], [19], [20], [21], [22], flame tilt (θ) [23], [24], [25], [26], [27], [28], [29], [30], [31] and flame length [23], [25], [32], respectively. A detailed review of previous works on vertical flame height, flame tilt angle and flame base drag can be found in [1]. Comparisons of previous correlations on various flame geometry parameters of pool fires in cross flows have been recently reported in [9].

In summary, the various correlations predicting horizontal flame length, vertical flame height, flame tilt angle and flame base drag use similar dimensionless factors. The dimensionless factors being used are the wind Froude number Frw(Frw=Uw2gD) relative to source diameter and the non-dimensional heat release rate at the end of combustion Q˙*(Q˙ρacpTagDD2). These dimensionless parameters are used in various power law correlations empirically determined often different with each other [1], [21], [33]. One reason for the differences may be that researchers used liquid or gaseous pool fires, in natural wind poorly controlled or in wind tunnels, with different situations or boundary conditions. One more note is that there is still not a model to describe all these flame geometry basic parameters comprehensively.

In this work, we report systematically on basic parameters of flame geometry (horizontal flame length and flame base drag, vertical flame height and two flame tilt angles) in pool fires under cross flow (wind) conditions for four square gaseous pool fires, employing propane as fuel of various heat release rates with controlled cross flow air speeds up to 6 m/s provided by a wind tunnel. The novelty of the present study lies in the following aspects:

  • (1)

    We note that the cross flow air speed studied by previous researchers with controlled cross flows is relatively small (i.e., less than 3 m/s), meanwhile considering the flame as one whole region. But under relatively strong cross flow, the flame is partially pushed to the ground, leading to a different flame behavior which is initially similar to a boundary layer flow followed by the flame raised above the ground. Therefore, in the present study, the flame is characterized by these two regions to more clearly reflect the physics.

  • (2)

    We propose that the scaling depends on the cross flow air speed Uw and a length scale relating the competition of the cross flow and flame boundary. The flame buoyancy defined as ΔTfTag=g is practically constant along the flame so that the cross flow-buoyancy interaction length scale can be defined simply as Uw2g. Note also that the air entrainment contributed by the forced cross flow influences the flame geometry as well, which is more prominent in relatively strong cross flows, however, not included in the previous models. The proposed non-dimensional model takes this air entrainment into consideration and explains the different flame behaviors under relative weak and strong cross flows. The correlation of experimental results supports this approach.

The structure of the paper is the following. In Section 2, the experimental setup is described together with the definition of flame geometry parameters and an uncertainty analysis. Section 3 presents the experimental results. Then in Section 4, a physical model is proposed and discussed regarding the non-dimensional analysis, and correlations of the experimental data of the flame geometry parameters are shown. Section 4 includes also some comparison with previous work [24] and discussions on the limitations of the present model. Conclusions follow in Section 5.

Section snippets

Experimental setup

Figure 1 illustrates the experimental setup. To generate the cross flow, a wind tunnel was used having dimensions of 72 m (length) × 1.5 m (width) × 1.3 m (height). More details of this wind tunnel were presented in [34]. The experimental cross flow air speed was set between 0 and 6 m/s, at intervals of 0.5 m/s (no velocities below 0.5 m/s could be tested in the present set up because these small flows were not steady). The local turbulence velocity fluctuation urms/umean was measured to be

Experimental results

Figures 3–7 show the experimental data for the horizontal flame length (Lx, Fig. 3), vertical flame height (H, Fig. 4), flame tilt angles (θ1, Fig. 5; θ2, Fig. 6) and flame base drag (D+Ldrag, Fig. 7). The following observations are made:

  • (1)

    With increasing of pool diameter, Lx, H, θ1, θ2, and D+Ldrag decrease.

  • (2)

    Lx, H and D+Ldrag increase with the increasing of heat release rate. In addition, θ1 and θ2, decrease with increasing of heat release rate.

  • (3)

    Lx and D+Ldrag increase then decrease with

A physical model

A sketch of the physical model is shown in Fig. 8 essentially illustrating the features in pictures of Fig. 2. The physical model is developed based on the following considerations and mechanisms:

  • (1)

    The source momentum is negligible compared to the cross flow inertial force, as discussed in the description of the experiments.

  • (2)

    The cross flow (wind) Froude number of the source (Uw2gD>0.13) is high enough so that the pool size effect is not important as it will be verified by the correlations. Note

Conclusions

This paper investigated the flame geometry of pool fires under relatively strong cross flows (namely cross flow (wind) Froude number Uw2gD>0.13). Three flame lengths, namely horizontal flame length, vertical flame height and flame base drag, as well as two flame tilt angles were measured experimentally to describe systematically the flame geometry. A physical model was proposed to interpret the mechanism and to represent these flame geometry basic parameters comprehensively. Major findings are:

  • (1)

Acknowledgment

This work was supported jointly by Key Project of National Natural Science Foundation of China (NSFC) under Grant No. 51636008, the Newton Advanced Fellowship (RS: NA140102), NSFC-STINT joint project (51811530015), Key Research Program of Frontier Sciences, Chinese Academy of Sciences (CAS) under Grant No. QYZDB-SSW-JSC029, Fok Ying Tong Education Foundation under Grant No. 151056 and Fundamental Research Funds for the Central Universities under Grant Nos. WK2320000035 and WK2320000038.

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