Flame Extensions Under a Curved Ceiling

Fire Safety Engineering is an essential component in the design, construction and overall functioning of buildings, means of transportation and many other aspects of life. Flame extensions under ceilings are a particularly important aspect in Fire Safety Engineering since they have a direct impact on the fire spread and growth inside a compartment and to other parts of a building or environment. The extension of flames are affected by different factors including compartment geometry [1, 2], ventilation [3], fuel type and fire size [4]. Advances in architectural and building design see continuous innovation which also includes the utilization of curved structures. Additionally, the increasing worldwide population has promoted the development of urban underground space resulting in structures such as underground utility and vehicle tunnels [5, 6]. For this reason investigation of fire and flame behaviour in such geometries needs to be conducted. Extensive literature is present regarding tunnels [4, 7, 8], but not much focus is put into the flame extension aspect. Most of the flame length models produced for curved ceiling geometries have been developed from well established flame length models created for horizontal and inclined flat ceilings. The first equation created to describe the flame length under a horizontal ceiling after impingement was proposed by You and Faeth [4] and is presented in Eq. 1.Their correlation determines the flame length \(L_f\) from the pool fire flame height in free condition (\(H_f\)), the effective ceiling height of the compartment (\(H_{ef}\)) and the fire’s diameter (D). The multiplication coefficients a, b in Eq. 1 vary depending on the ceiling characteristics: Table 1 summarizes the different coefficients that have been utilized in conjunction with Eq. 1 for different ceiling configurations. Further studies presented by Zhang et al. [9] take into account the air entrainment contribution to the flame extension of flame produced by linear fire sources under horizontal and inclined ceiling geometries. In their work they find that the flame extension is composed of two components: the first is the non-combusted fuel that is present at the impingement point and the second is made up by the air that is entrained during the combustion of unburnt fuel after the impingement point. By taking into consideration the work performed on flame extensions under horizontal ceilings, Pan et al. [10] develop an adaptation of You and Faeth’s empirical correlation, Eq. 1, to characterize flame extensions under curved ceiling geometries. An experimental campaign was carried out using oil pool fires in a scaled concrete setup. While the equation form is the same as You and Faeth’s one [4], due to the application to a curved ceiling geometry, new coefficients are found compared to the flat ceiling geometry and are shown in Table 1. Their model does not offer a complete characterization of the flame extension since the buoyancy component (the vertical component of the fire’s flow) along the curved ceiling and momentum conservation equations are not accounted for [11].

When the ceiling is flat and horizontal, after impinging the momentum of the fire’s plume shifts from vertical to horizontal [12]. The flames can also impinge on the ceiling and spread radially with this ceiling configuration. If the ceiling is curved instead, after impinging the momentum of the fire plume is not purely horizontal anymore. The curved geometry induces both a horizontal and vertical component to the flow after impingement. In particular, when the flow is buoyancy dominated (heptane pool fire), buoyancy controls the flame extension until all the fuel is combusted. On the other hand, when the flow is momentum dominated both momentum and buoyancy components contribute to the flame development. This combined effect can result in even longer extensions since fuel needs to travel longer beneath the ceiling to undergo complete combustion.

Further theoretical and experimental developments were performed by Pan et al.: in their work they investigated how the residual unburnt mass flow after impingement and the varying buoyancy component influence the flame extensions under the curved ceiling [11]. By assuming that the relationship between the ceiling jet velocity and the entrained air is linear, a momentum balance equation was put in place to correlate the two quantities. The study of these additional parameters by Pan et al. resulted in the development of Eq. 2 that describes the flame extensions beneath a curved ceiling in terms of fire source size, heat release rate and tunnel geometry characteristics.where:These flame models have only been developed from buoyancy-dominated flows, and it has not been assessed whether these correlations can also represent flames of momentum dominated flow fires. In this paper, thanks to additional experimental work, new adaptations of the existing correlations have been created.

The flame length or height is the level at which the combustion process is complete [13]. Due to the intermittent nature of flames, the mean flame height is used in engineering equations to calculate flame height: the mean flame height is the area where the flame appears 50% of the time [12]. When the fuel is not supplied at high velocities, buoyancy will dictate the upward velocity of the gaseous flow. Examples of buoyancy dominated flows are those resulting from pool fires. On the other hand, if the fuel is injected at high velocities, the flow becomes momentum dominated and the buoyancy effect becomes negligible [12]. Jet flames are an example of momentum dominated flows.

From [14], it was determined that small scale test results fit full scale test results accurately: to relate quantities from large to small scale, Froude scaling is applied. The Froude number derives from hydraulics but can be applied to the hot gases produced during combustion. It represents a relationship between the flow velocity (v) and buoyancy and is shown in the first term of Eq. 4: g is the gravitational acceleration constant.The Froude number can also be related to the heat release rate (\(\dot{\textrm{Q}}\)), yielding the expression in the second term of Eq. 4: D is the fuel source’s characteristic diameter. Through experimental procedures, it was determined that the variation in flame geometry can be represented with the square root of the Froude number through Eq. 5.Extensive experimental campaigns relating flame height to heat release rate and characteristic diameter have shown that expressing data in terms of nondimensional heat release rate is more convenient [12]. This new expression is represented in Eq. 6, where \(\dot{Q^*}\) is the non dimensional HRR, \(\dot{Q}\) is the fire’s HRR, \(\rho _{\infty }\) is the density of ambient air, \(c_p\) is the specific heat capacity of air and \(T_{\infty }\) is the ambient air temperature. Heskestad’s work [12] resulted in the definition in an expression for a fire’s flame length, \(H_f\), and is shown in Eq. 7.This correlation is used to estimate the flame length of buoyant fires in free burning conditions and was developed from experimental data mostly using pool fires. It assumes a stable axisymmetric plume with no influence from external wind or turbulence. Heskestad determined that the flame height is proportional to the square root of the heat release rate [12]: for this reason, its application is not fully intended for fires with flame heights that are significantly larger than the fuel diameter [13]. Furthermore, while this equation is not intended for momentum dominated flow fires, it is believed that it can still provide an estimation of the flame length [13]. Heskestad’s equation is not applicable for fires bounded by a wall or placed in a corner: in these cases, the geometry affects the combustion process, extending the flame length and providing additional heat feedback to the fire source resulting in higher HRR values[12]. During the experimental campaign carried out in this work, the flame extension resulting from free burning conditions (\(H_f\)) was not measured. For this reason, in order to obtain this quantity, Eq. 7 was utilized for both fuels and burners in the centre position of the curved ceiling setup. Furthermore, to determine the flame length in cases where the fire is placed flush to a sidewall or in a corner, Eq. 8 was applied. Wang et al. [15] adapted Heskestad’s original equation by performing experiments in wall and corner bounded conditions at different pressures.\(H_f\) is the total flame height of the wall bounded fire, \(\beta\) is the mirror coefficient that is a correction coefficient that accounts for the wall or corner bounding (\(\beta\) = 1.6 for wall fires, \(\beta\) = 2.4 for corner fires), P is the pressure of the testing environment in kPa. This equation is an adaptation of Heskestad’s correlation and has been extended to cases where the fire is bounded. For this reason, the correlation put forwards by Heskestad and its adaptation for the wall bounded case have been used to determine the flame length in free burning conditions (\(H_f\)) for the different burner positions and fuel types. While for the propane tests the empirically calculated flame length may present some discrepancy with the free burning condition flame length, they are less than 5% [12, 13, 16]. Furthermore, while equations that describe flame lengths of momentum dominated flows can be found in literature for free burning fires, correlations that account for the wall bounding effects have not been identified. Finally, in order to further characterize the differences in the flame extensions produced by the two different fuel types, heat release rate per unit area (HRRPUA) [7] has been utilized. Heat release rate per unit area (\(\dot{Q"}\)) is used to determine the intensity of a fire: in particular, the higher the \(\dot{Q"}\) value, the more intense the fire. It is defined as the ratio between the heat release rate resulting from combustion and the area of the fuel source (\(A_f\)). Larger HRRs and smaller \(A_f\) values cause the heat release rate per unit area (HRRPUA) to increase. Based on this, a larger burner area does not necessarily result in a more intense fire. This is important to consider when testing different fuel types and flows that have different characteristics. Higher HRRPUA values are characteristic of momentum dominated fires and fires that produce jet flames; lower HRRPUA values instead are attributed to buoyancy dominated flows [13].

Experiments presented in this work were carried out using a concrete tunnel like structure. This was chosen based on previous work carried out for similar studies [11]. Figure 1 illustrates a schematic of the setup including its dimensions. On the left is a top view, highlighting where the burners were placed during the different tests in the centre and flush to the side wall of the setup. On the right, the front view of the setup shows its shape and its internal geometry.

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The structure had an internal diameter of 900 mm, was 1200 mm long and 75 mm thick. Since this work focused solely on flame extension in the direction perpendicular to the tunnel’s length, the effect of a longer tunnel on the flame extensions was not investigated. While the study of the effect of longer structures on flame extensions is undoubtedly relevant to tunnel fires, it would add different layers of complexity to this research, while the primary focus remains on the flame extensions. For these reasons, the length of the setup was determined by the size of the precast concrete pipes utilized to obtain the curved ceiling geometry. The bare concrete was left untreated for the tests in a similar fashion as the experimental studies of other work presented in literature [10, 11]. In the literature, curved ceiling tunnel dimensions vary: in [17] two real life tunnel dimensions were studied. Comparing the setup used in this work with the dimensions found in literature [17], the setup’s scaling ratio is between 1:11 and 1:15 depending on which tunnel dimensions are taken as reference. Furthermore, HRR values from the different tests presented in Sect. 4 also correspond to full scale HRR data resulting from fires of vehicles that are typically found in tunnels [18, 19]. More in depth discussion regarding the HRR scaling is presented in Sect. 4. Promatect H.ETA 06/0206 boards [20] were used to create the structure inside the curved ceiling setup: Fig. 2 shows the experimental setup. The addition of the boards made it possible to have a flat horizontal base for the burners to rest on. Furthermore, the placement of the boards on each side of the setup introduced two vertical walls which were not present in similar studies from literature [10, 11]: the boards were introduced to remove the effect of the concave part of the curved setup on the flame extensions. The Promatect H.ETA 06/0206 boards are high-performance boards used for passive fire protection applications. They are made of calcium silicate and is reinforced with selected cellulose fibers and fillers.

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In this work, a gas burner and a pool fire were utilized as fire sources in the experiments. Propane was burned through a square sandbox burner with the base measuring 74 × 74 mm and 70 mm thick: the burner was connected to the gas supply line through a steel tubing system and the gas flow rate could be managed with the use of an electronic flow controller [21]. The pool fire was fueled with heptane: a square metal vessel measuring 180 × 180 × 50 mm in width, height and thickness was used in this case. For each test 5 dl of heptane were utilized: a 10 mm thick layer of water was placed in the bottom of the vessel before pouring the heptane in order to have a flat base for combustion. Since heptane’s density is less than water’s, the heptane can float above it. As the HRR of a pool fire depends on its diamter [12] only one HRR was obtained when using this fuel source. The HRR could not be varied like in the case of propane, where the flow could be increased or decreased. Since from initial tests it was determined that the flame extension resulting from the heptane pool was not long enough to extend beneath the ceiling, the fuel source was placed on a set of 6 cm bricks in order for the flames to reach the curved ceiling and extend beneath them. The bricks can be seen in Fig. 3.

The tests were performed under an extraction hood installed in the fire lab. The hood is equipped with various equipment and in intervals of 1 s, the gases are extracted and analyzed: \(O_2\), \(CO_2\) and CO concentrations are measured in addition to other quantities. The HRR resulting from each test was determined utilizing the oxygen depletion method presented in [22]. Only one heptane pool fire size was used, while different HRRs were tested by changing the propane burner’s gas flow rates. The locations of the burners inside the curved ceiling setup were also varied between a central (600 mm length, 342.5 mm width) and a flush to the sidewall (600 mm length, 685 mm width) positions as shown in Fig. 1. Finally, each test was repeated three times in order to reduce the measurement errors through averaging. Table 2 outlines the tests that were performed. The HRR values are the average of the three repetitions of the tests performed in each position.

The differences in flame length extensions under the curved ceiling were analyzed in this work. Due to the setup’s geometry, the flame extensions could be seen from a transverse direction only at a distance of 930 mm and height of 525 mm; the longitudinal flame extensions could not be captured due to the impossibility to perform recordings from the side of the setup. To capture the flame extensions, a 12 Megapixels camera was utilized: both normal speed videos (1080p definition, 30 frames per second (FPS)) and slow-motion videos (1080p definition, 240 FPS) were recorded for each test. The slow motion videos yield higher quality and more detailed videos, especially with regards to the pixel colours: this is due to the lower exposures that result when using this video recording mode.

Figure 3 shows the flame extensions beneath the curved ceiling setup for the two tested fuel types.

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In order to evaluate the flame lengths, an image analysis Python script [23] was created using the Open CV (Open Source Computer Vision) library. Open CV was preferred due to its advanced computer vision library. The videos were taken for each test when the flame was stable: this stable condition was determined by looking at real time HRR data and by visual inspection of the flame extensions in the different tests. Each video was approximately 30 s long. Table 3 shows the standard deviation of the HRR during the period in which the flame extension videos were recorded. The standard deviations of the HRR values are all less than 5%, which the authors considered to be an acceptable variation. As can be seen from the Table, heptane overall presents a larger variation than propane. For heptane, changes in vaporization rates of its phase change during combustion and potential incomplete mixing with air, introduce larger HRR fluctuations compared to propane’s more uniform combustion process [24, 25].

Further discussion on the HRR values is presented in Sect. 4. The basic principle behind the functioning of the code and its ability to detect fire is pixel identification. The fire identification was performed by executing the following process:

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In this study, an experimental campaign was performed in order to evaluate the flame extension of buoyancy and momentum dominated flows beneath a curved ceiling. Based on literature findings, adaptations of existing flame length models were proposed to extend their application to different fire behaviors. The comparison of experimental data with models developed utilizing solely pool fires [4, 10] resulted in a failure to represent the flame extensions beneath the curved ceiling. In particular, lack of characterization of momentum dominated flows was observed. Logarithmic adaptations of these models presented in this paper through Eqs. 10, 11 and 12 extend the domain of application of the existing models to include flame extensions produced by momentum dominated flows. The new correlations yield an \(R^2\) value of 0.8552, 0.7851 and 0.8358 respectively. Subsequently, extension of the improved model based on work by Pan et al. [11] to momentum dominated flows resulted in the formulation of Equation 13, obtained by fitting the experimental data. The \(R^2\) value of 0.8902 associated to Eq. 13 highlights how flame extensions under curved ceiling geometries resulting form both momentum and buoyancy dominated flows can be represented in more effective and precise manner.