- Email: [email protected]
Experimental study of upward flame spread over discrete thin fuels
Fire Safety Journal 110 (2019) 102907
Contents lists available at ScienceDirect
Fire Safety Journal journal homepage: http://www.elsevier.com/locate/firesaf
Experimental study of upward flame spread over discrete thin fuels Wohan Cui, Ya-Ting T. Liao * Department of Mechanical and Aerospace Engineering, Case Western Reserve University, 10900, Euclid Ave, Cleveland, OH, USA
A R T I C L E I N F O
A B S T R A C T
Keywords: Upward flame spread Discrete fuels Burning rate
Experiments are performed to study upward flame propagation over discrete combustibles separated by air gaps. An array of ten 1 cm-long 5 cm-wide filter papers is uniformly distributed on a vertical sample holder subjected to double-sided burn. The distance between the samples was varied from 0 to 4 cm. After being ignited from the bottom end, the flame spread process is recorded by front and side video cameras. A precision balance with 0.01g resolution is used to monitor the mass loss and deduce the solid burning rate. The results show that both flame spread rate and solid burning rate have a non-monotonic relationship with the gap size. The presence of gaps decreases the fuel load (fuel mass per unit length), which results in an increasing apparent flame spread rate as the gap size increases. The gaps also allow the lateral entrained air to push the flame closer to the sample surface, enhancing the conductive heat input to the samples. This results in an increased solid burning rate and flame spread rate. However, when the gap size is large, the effective heating length of the sample and hence the total burning rate decrease as the gap size increases. Eventually, the flame fails to spread.
1. Introduction
variables. For example, Vogel and Williams [12], one of the first groups to study flame spread over discrete fuels, used a horizontal array of vertically oriented matchsticks (with the heads removed). Matchstick height and inter-stick separation distance were varied. The critical separation distance (beyond which the flames fail to spread) was found to increase with increasing matchstick height. Vogel and Williams also performed thermal analysis and provided a theoretical thermal model that yielded good agreement with their experiment data, suggesting that convective heat transfer is of primary importance in flame propagation at matchstick size scales. Many studies using similar experimental setups followed, investigating a wide range of parameters including imposed ambient wind speed [11,13], wood type [11], fuel element height [11], fuel-bed inclination angle [15], and moisture content of the fuel [11]. In general, flames are more likely to spread in deeper fuel beds [11,12], with higher imposed wind speed [13], and with a steeper fuel bed slope [15]. The flame spread rate was also observed to have a positive cor relation with imposed wind velocity [11,13] and a negative correlation with fuel mass load [11]. At a slightly larger scale, Finney et al. [17] studied fuel elements consisting of excelsior spun around vertical metal rods, using them to simulate vegetation canopies encountered in forest fires. They studied how fire spread thresholds varied with vertical fuel-bed depth, inter-rod spacing, and slope of the fuel bed arrays, and concluded that fires spread only after ignition by direct flame contact. Fires were also more likely to spread in deeper fuel beds and with steeper
Discrete fuels refer to scenarios where multiple solid combustibles are in close proximity but are separated by air gaps or inert materials. Compared to homogeneous (or continuous) fuel arrangements, discrete fuels better represent some realistic fire scenarios (e.g., wildland fires, urban fires, commodities stored in warehouses). While fire behavior and flame spread over continuous fuels have been extensively studied with various configurations [1–3] and over a wide range of ambient condi tions [3–6], a comprehensive understanding of the fire behaviors of discrete fuels has not yet been achieved. Flame spread over discrete fuels can be very different from spread over continuous fuels. Intuitively, gaps between combustibles act as barriers, preventing or slowing down flame propagation. However, when the flame does spread, the presence of gaps can increase the flame spread rate [7–11] and the solid burning rate [7,9,10]. In other words, discrete fuel can be more hazardous than continuous fuel in terms of fire safety. Previous studies of flame spread over discrete fuels include experi ments and theories involving horizontal [8,11–14], inclined [15–17], and vertical [7,9,10] fuel beds. For many of these studies, the fuel ele ments were arrays of matchstick-like materials oriented perpendicularly to the flame spread direction. These studies investigated the relationship between separation distance and flame spread rate, among other * Corresponding author. E-mail address: [email protected] (Y.-T.T. Liao).
https://doi.org/10.1016/j.firesaf.2019.102907 Received 11 May 2019; Received in revised form 6 September 2019; Accepted 4 November 2019 Available online 5 November 2019 0379-7112/© 2019 Elsevier Ltd. All rights reserved.
W. Cui and Y.-T.T. Liao
Fire Safety Journal 110 (2019) 102907
slopes. For upward flame spread, Gollner et al. [7] studied horizontally oriented matchsticks held on a vertical steel wall, and showed that flame spread rates and sample mass loss rates increase with matchstick spacing. Flat discrete samples have also been studied [8–10,14]. The critical mechanism of flame spread over a flat continuous fuel is heat transfer from the flame to the solid fuel in the preheat and pyrolysis regions [2,6, 18]. A similar phenomenon has been observed for discrete fuels. How ever, in flat discrete samples, the flame spread rate exhibits a non-monotonic trend with respect to fuel load. This has been demon strated in experiments involving paper samples with randomly distrib uted pores [8] where there is an optimal porosity (total pore area over paper area) for flame spread rate. Gollner and Miller [9] conducted experiments using a vertical array of PMMA blocks separated by insu lated materials, and identified an optimal fuel coverage (total fuel length over total length) that maximizes flame spread rate. Gollner and Miller [9] also found that the fuel spread rate (distance of fuel traversed by the pyrolysis front over time) decreases but the average mass flux on the sample surface increases when fuel coverage decreases. The authors hypothesized that this latter relationship is due to delayed thickening of the boundary layer and/or increased air entrainment at the gaps. Park et al. [10] focused on thin samples where solid burnout occurs. They conducted numerical simulation of concurrent flame spread over discrete thin fuels separated by air gaps. Two scenarios were considered: upward flame spread in normal gravity and purely concurrent flame spread in a low-speed forced flow in zero gravity. Their modeling sug gested that the effects of the air gaps on the sample burning rate are two-fold. On one hand, the gaps break the aerodynamic boundary layer and reduce the flame standoff distance. This increases the conductive heat flux from the flame to the sample surface, thus enhancing the solid burning rate. On the other hand, the presence of gaps reduces the effective preheat length and pyrolysis length of the samples (when the flame does not cover the entire fuel span). This reduces the solid burning rate. The two effects result in a non-monotonic trend of the solid burning rate when the gap size increases. To validate their numerical simula tions, Park et al. [10] performed experiments of upward flame spread over an array of filter papers with inter-sample separation distance being the main variable. The average flame spread rate and total burning duration were deduced through visual inspection of videos recorded during the experiments. While the experimental data correlated reasonably well with their modeling results, Park et al. focused on the numerical study and did not provide an in-depth analysis of the exper imental data. The goal of this work is to critically examine the hypotheses posed by Park et al. [10] and to achieve as complete as possible an understanding of the underlying physics of flame spread processes for discrete thin fuels in concurrent flow. We extend the experimental work of Park et al. [10] and conduct a series of experiments using a separate enhanced experi mental setup. A precision balance is added to collect mass loss data and to provide information on the solid burning rate. Instead of visually inspecting of the experimental videos, we develop methodologies to attain information regarding global and local burning processes via image analysis. Flame shapes and transient flame development pro cesses for continuous and discrete fuel configurations are also compared in detail. The major difference between this work and previous upward flame spread experiments is that this work concerns thin flat samples. In previous work where horizontally oriented matchsticks were used [7], flames spread along the fuel depth horizontally (a scenario closer to thick samples) in addition to spreading across fuel elements vertically. Furthermore, solid pyrolysis occurs on both tip and side surfaces of the matchsticks. In this work, thin flat paper samples are used and flame spread is approximated to occur only along the sample surface and across the gaps. The simple configuration also facilitates the comparison of burning characteristics between discrete and continuous samples. In Miller and Gollner’s work [9], thick PMMA blocks were separated by
inert materials. While delayed thickening of the boundary layer and/or increased air entrainment were hypothesized to occur near inert mate rials, flame shapes were not compared directly. These effects are ex pected to be even more significant when samples are separated by air gaps in this work. The thin short (1 cm) samples used in this work also yield a more regular laminar flame base at the upstream region, facili tating the extraction of flame shapes to test the hypothesis. 2. Experiment setup The experimental apparatus is shown in Fig. 1. An array of fuel sample elements is arranged uniformly on a vertical sample holder. The sample material is CFP40 quantitative cellulose filter paper (manufac tured by I⋅W.Tremont) with area density of 85 g=m2 . Sample material is cut into 1 cm-long 8 cm-wide segments and stored in a sealed jar with desiccant Drierite (98% CaSO4 and 2% CoCl2, manufactured by W.A. Hammond Drierite Company) for at least 24 h before each test. The sample holder consists of four 3-mm-thick aluminum plates, two on each side, sandwiching the samples. The sample holder can support a maximum fuel span of 50 cm. The exposed width of the samples is adjustable and set at 5 cm for all tests in this work. The sample and the sample holder are placed on top of a precision balance (A&D Fx-5000i) to monitor the mass loss of the sample during each test. The resolution and frequency of the balance are 0.01 g and 20 Hz respectively. An ignition paper strip, wrapped by a saw-tooth shaped Kanthal 27 GA resistant wire (with DC power 13.5A and 3.46V for 5.5s) is placed 3 cm beneath the first fuel sample. The ignition wire and the ignition paper strip are held by a separate mounting rack so that the mass loss of the ignition strip is not reflected in the mass loss data obtained by the precision balance. The dimensions of the ignition paper is 0.7 cm long by 4.5 cm wide. The dimension and the location of the ignition paper strip were defined after a series of tests to ensure ignition and to minimize the effects of ignition on the flame spread over the sample array. Two video cameras (Canon Rebel T3i 1080P) are used to record front and side images during the experiment at 30 frames per second with a spatial resolution of 0.47 mm/pixel. Experiments are conducted in a dark room with green LEDs illuminating the sample surface. All tests are performed underneath a ventilation hood and inside a hazard screen so that exhaust gasses and smoke are collected, debris is confined, and the effect of surrounding airflow on the apparatus is mitigated. Ambient temperature and moisture are recorded before each test and ranged from 68 to 70 � F and 31–39% respectively. The test matrix of this study is summarized in Table 1. For discrete fuel arrangements, ten fuel elements are used in each test so that the total mass of the sample is constant in all tests. The separation distance (or the gap size) between samples varies in each test, ranging from 1 to 4 cm. In addition, a 10 cm-long continuous sample is tested. For each fuel configuration, experiments are repeated three times to ensure reproducibility. Also listed in Table 1 is the total sample span, defined as the distance between the bottom edge of the first fuel segment and the top edge of the last fuel segment. While the total available sample length is fixed to 10 cm in all tests, the sample span increases as the gap size increases. Also listed in Table 1 is the total burning duration, averaged between three repetitive tests for each fuel configuration. This will be discussed further in section 4.1. 3. Experimental results 3.1. Transient flame spread over continuous sample The transient process of flame spread over the continuous sample is demonstrated using the front and side-view images at selected instances in Fig. 2. In Fig. 2a, the tip of the flame from the ignition strip has ignited the bottom end of the first sample strip, and laminar diffusion flames are present on both sides of the samples (see side-view image in Fig. 2a). Shortly after ignition, the flame grows in length and covers the entire 2
W. Cui and Y.-T.T. Liao
Fire Safety Journal 110 (2019) 102907
Sample Holder
Sample Array Ignition Strip
Ignitor Mounting Rack
Precision Balance Fig. 1. Experimental apparatus. Left: front-view image. Right: side-view schematics.
applied to the last 50% of the averaged mass loss data and an averaged mass loss rate (MLR) is deduced using the slope of the trend line (the black dash line on Fig. 4).
Table 1 Test matrix. Sample Length (cm)
Gap Size (cm)
Number of Samples
Total Sample Span (cm)
Average Total Burning Duration (s)
10 1 1 1 1 1
– 1 1.5 2 3 4
1 10 10 10 10 10
10 19 23.5 28 37 46
6.93 4.48 4.29 4.33 5.36 7.70
3.2. Transient flame spread over discrete samples Fig. 5 through 7 show the flame spread process for the discrete fuel arrangement with 1 cm gaps. Compared to the continuous fuel, the process was similar except that the flame exhibited a wavy pattern in the side view images. This is because, as predicted by Park et al. [10], the gaps between the samples broke the no slip boundary condition and the local flame standoff distance was reduced at the gaps (see the right-hand-side flame in the side-view image in Fig. 5c). The funda mentally different flame shapes of the continuous and discrete fuels have significant impact on heat feedback to the sample and therefore affects the sample burning rate. This will be discussed further in Section 4. The flame base location versus time in Fig. 6 shows a staircase-like curve, corresponding to how the flame jumps across gaps. Note that the flame base can jump multiple gaps if multiple fuel elements are consumed simultaneously. The data shown in Figs. 6 and 7 suggest reasonable consistency between the repetitive tests.
sample array (Fig. 2b and c). In the meantime, the flame base (the bottom of the flame) moves upward slowly as the sample is consumed (Fig. 2b–g). Eventually, the sample fuel is fully consumed and the flame is extinguished (Fig. 2h). Note that in Fig. 2, the rear aluminum sample holder plates were removed and the samples were attached to the front plates using Kapton tape. This allowed examination of the flame shape close to the sample surface in the side-view images, which would otherwise be partially blocked by the 3 mm-thick sample holder. As will be shown later, removing the rear sample holder plate has negligible effects on the flame spread process. The flame on the rear side of the sample (the right-sided flame in the side-view images) shows that the flame shape ensembles the flow boundary layer and the local flame standoff distance grows monotonically along the sample surface. This is because for a concurrent diffusion flame, the gaseous pyrolysate needs to travel across the flow boundary layer to meet with the oxidizer. This typical flame shape has been observed in many studies of concurrent flame spread [3,5,6,10,18, 19]. The flame in front of the sample (left flame in the side-view images) was partially blocked from view by the aluminum sample holder plate. Therefore, the front flame base was seemingly farther from the sample surface and more downstream than the rear flame in the side-view im ages. Note that this alteration of the sample setup was only used for generating Figs. 2, 5 and 12. All other data reported was obtained using the original sample setup from Section 2. A MATLAB code was developed to analyze the front-view images and to track the flame location in each frame. In this work, flame base is defined as the uppermost point of the lowest boundary of the flame, and flame tip is defined as the uppermost point of the flame (see Fig. 2e). The results for the three repetitive tests for the continuous sample are shown in Fig. 3, which suggests reasonable reproducibility of the tests. The mass loss data recorded by the precision balance is shown in Fig. 4, and also demonstrates reasonable reproducibility. Linear fitting is
4. Analysis and discussion 4.1. Total burning duration and average mass loss rate The total burning durations (averaged between three repeated tests) for all fuel arrangements are compared in Table 1 and in Fig. 8. In this work, the total burning duration is defined as the time from the onset of preheating of the first fuel segment (start time) to the extinction of the flame (end time). The start and end times are deduced from video image analysis (see section 4.2) and deliberately exclude the residual flamelets or smoldering near the sample holders on two sides (see Fig. 5g and f) after majority of the samples was consumed. The uncertainty of the total burning duration for each test is 0.033 s (based on video camera frame rate at 30 Hz). The measurement deviations between the repeated tests are marked by the error bars on Fig. 8. The data obtained using the previous experimental setup in Park et al. [10] for the same sample materials is also included. Compared to our setup, the experimental setup of Park et al. [10] is slightly larger and hence can accommodate fuel configurations with larger gaps. Note that the data for 0 cm gap in Fig. 8 is for the continuous sample. While the total burning duration in this study is slightly lower than in the previous larger setup of Park et al., the trend is the same. The total burning 3
W. Cui and Y.-T.T. Liao
Fire Safety Journal 110 (2019) 102907
Fig. 2. Front and side-view images of flame spread over a 10 cm-continuous fuel at select instances. The rear sample holders were removed in these images.
Fig. 4. Mass loss data for the continuous sample. The result of the additional test with one-sided sample holder is also shown.
Fig. 3. Locations of flame base and flame tip versus time for the continuous sample. The result of the additional test with one-sided sample holder is also shown.
4
W. Cui and Y.-T.T. Liao
Fire Safety Journal 110 (2019) 102907
Fig. 5. Front and side-view images of flame spread over discrete fuels with 1 cm gap size at select time instances.
Fig. 7. Mass loss data for discrete fuels with 1 cm gap size. The result of the additional test with one-sided sample holder is also shown.
Fig. 6. Locations of flame base and flame tip versus time for discrete fuels with 1 cm gap size. The result of the additional test with one-sided sample holder is also shown.
5
W. Cui and Y.-T.T. Liao
Fire Safety Journal 110 (2019) 102907
distribution of the solid burning rate on the sample surface. Park et al. [10] showed that the solid burning rate has local maximum near the upstream leading edge of each fuel segment. Therefore, before the up stream sample was fully consumed, the leading edge of the next sample (located directly above it, “downstream”) had already burned out. When the upstream fuel segment was fully consumed, the flame base needed to jump not only across the inter-sample gap but also across the length of next fuel sample that had already burned out, resulting in the steps in the adjusted flame base location in Fig. 9. Linear fitting was applied to the last 50% (5–10 cm) of the curves in Fig. 9. The slope of the fitted line defined the burning speed of the flame base (or the spread rate of the flame base along the fuel surface). The burning speed is then used to estimate the MLR: �cm� �g� ¼ Burning Speed � Sample Width ðcmÞ Mass Loss Rate s s � g � � Area Density : cm2 The averaged MLR is also calculated based on the linear fit of the mass loss data from the precision balance. The mass loss data for various fuel configurations is shown in Fig. 10. Linear fitting is applied to the last 50% of the averaged mass loss data and an averaged mass loss rate (MLR) is deduced using the slope of the trend line for each of the fuel configuration. Results of the two methods are compared in Fig. 11. Quantitatively, the MLR deduced based on the flame base spread rate is around twice as large as that deduced from the precision balance reading. This indicates that the steady state is not fully reached. Nevertheless, two curves correlate with each other well qualitatively and both show that the MLR first increases and then decreases with increasing gap size, consistent with the trend of the total burning duration in Fig. 8. The maximum MLR occurs at gap size of 2 cm.
Fig. 8. Total burning durations versus gap sizes. The error bars denote the maximum and minimum values in the repetitive tests.
duration first decreases when the gap size increases. After it reaches a minimum value, the total burning duration has a reverse dependence on the gap size. The data from the large setup also indicates that the flame eventually fails to spread at a critical gap size between 6.5 and 6.6 cm. In Park et al.’s work [10], the total burning durations were deduced based on visual inspection of the video images and included the side residual burning (which can last as long as 2–3s). The elimination of the residual burning from the burning duration in this work is considered the major reason for the discrepancy of the total burning durations using the two experimental setups. The average MLR are also compared. In this work, the average MLR are deduced using two different methods. The first method is based on the spread rate of the flame base. In this work, we define an adjusted flame base location as the original flame base location (as shown in Figs. 3 and 6) minus the total gap sizes upstream to the flame base. The results for various fuel configurations are shown in Fig. 9. Note that even after the gaps are removed, flame base locations versus time still exhibit “jumping” (or steps) for discrete fuel configurations. The same trend was reported in Park et al. [10] and was attributed to the non-monotonic
4.2. Local burning duration and solid burning rate Burning duration for individual fuel elements are also examined. To achieve this, non-dimensionalized overall flame intensity (or flame coverage) over each fuel segment is tracked using MATLAB. The flame intensity over the k-th fuel segment is defined as PI PJ i j Rði; jÞ I *k ¼ (1) 255 � I � J Here, k ranges from 1 to 10 with 1 denoting the bottommost fuel
Fig. 9. Adjusted flame base location (flame base location minus the distance of the gaps traversed by the flame base) versus time for different gap sizes.
Fig. 10. Mass loss (averaged between three repetitive tests) versus time for all fuel configurations. 6
W. Cui and Y.-T.T. Liao
Fire Safety Journal 110 (2019) 102907
local burning duration is determined using the average burning duration of the last five fuel segments (i.e., the 6th to 10th segments). The local burning duration for all cases are compared in Fig. 13. The total burning duration (discussed in section 4.1) is also plotted. Notice that while the total burning duration displays an obvious nonmonotonic dependency on the gap size, the local average burning du rations are less sensitive to the gap size for discrete fuel cases. Never theless, all discrete cases have a smaller average local burning duration compared to the continuous case. This implies that the local burning rate (mass loss rate per unit area or the mass flux of each solid sample) is significantly enhanced when gaps are present. This is consistent with Miller and Gollner’s experiments [9] and Park et al.’s prediction [10]. In Fig. 13, compared to 1 cm gap size, the configuration with 4 cm gap size has a slightly lower average local burning duration but signif icantly higher total burning duration. To understand this, the start and end times and the local burning durations for the two cases are examined in Fig. 14. For the case of 1 cm gap size, samples are close to each other and their burning times overlap. On the other hand, for the case of 4 cm gap size, samples tend to burn sequentially, resulting in a larger total burning duration.
Fig. 11. Average mass loss rate versus gap size. Error bars denote maximum and minimum values from the repetitive tests.
segment and 10 denoting the uppermost fuel segment. R (i, j) is the red value of a RGB image at a pixel located at (i, j). R ranges from 0 to 255. I and J are the total pixels in the width and length of each fuel segment. To demonstrate the concept, Fig. 11a shows the evolution of the flame intensity over every other fuel segment for discrete fuel configu ration with 1-cm gap size. Once the flame reaches the k-th fuel segment, I*k increases and then reaches a plateau of a value approximated at 1 (i.e., most of the pixels on the sample surface reaches maximum red value). After the fuel segment is fully consumed, the flame is no longer present above the fuel segment and I*k decreases to zero. The burning durations of each fuel segment are determined using a constant threshold value of I*k ¼ 0.1 (red dashed line in Fig. 12a). The non-zero value was chosen to eliminate flamelets and smoldering of the sample residual near the sample holders on two sides (see Fig. 5g and f). Fig. 12 shows that the burning of the residual near the side sample holders can last 2–3 s. Also, note that the local burning duration defined in this work includes both the preheat time and the pyrolysis time of each sample segment. Fig. 12b shows the flame intensity over the last five fuel segments. In this plot, time is adjusted so that the start times (i.e., the onset of pre heating) of all fuel segments are aligned. The curves have a similar shape, implying a quasi-steady flame spreading process. In this work,
(a)
4.3. Flame shape and preheat length Flame shape and flame standoff distance (distance of flame from sample surface) have direct influence on heat feedback from the flame to the fuel surface, which in turns dictates the solid burning rate. To better capture the flame shapes near the sample surface, two sets of extra ex periments were performed with the rear aluminum sample holder plates removed for continuous and 1-cm gap discrete fuel configurations. The purpose of these additional tests was to facilitate the comparisons of the edge view flame profiles (shown in Figs. 2 and 5). The flame location analysis (Figs. 3 and 6) and the mass loss data (Figs. 4 and 7) show that such modification of the experimental setup has minimal effects on the burning event. Nevertheless, all the data reported in this work are with the original setup with double-sided sample holder plates. Fig. 15 shows the original RGB (Fig. 15a), and post-processed black and white binary (Fig. 15b) side-images of the flame (on the rear where there were no sample holders) for continuous fuel and for discrete fuels with 1 cm gap. These images were taken at t ¼ 1.83s after ignition in both tests. For continuous fuel, the flame shape resembles the flow boundary layer. The flame standoff distance increases along the direction of flame propaga tion. In the discrete case, the flame shows a zigzag-shaped contour as described earlier. The binary images are further transformed into edge
(b)
Start Time End Time
Start Time
Fig. 12. Non-dimensionalized flame intensity of each fuel segment for discrete fuels with 1 cm gap size. 7
End Time
W. Cui and Y.-T.T. Liao
Fire Safety Journal 110 (2019) 102907
length thus started to decrease. Fig. 15a shows that the maximum flame length first increases and then decreases when the gap size increases. The case with 2 cm gap has the largest flame length among all discrete cases. In this case, the flame reached the maximum length of 40 cm and the flame was able to cover its total fuel span of 28 cm. For 4 cm gap size, the maximum flame length is ~22 cm, which is much shorter than the total fuel span of 46 cm. The flame only covered the first five fuel segments. Fig. 16b further compares the non-dimensionalized flame lengths versus time in each case. The non-dimensionalized flame length is defined as flame length divided by corresponding fuel span in each case. Fig. 16b shows that the non-dimensionalized flame height decreases monotonically as gap size increases. After gap size exceeds 2 cm, the non-dimensionalized flame length drops below one, indicating that the flame is no longer able to cover all available fuel samples, resulting in a reduction of the effective sample heating length (as predicted by Park et al. [10]). This results in the decrease of the MLR at large gaps as shown in Fig. 11, despite the fact that the local solid burning rate may be similar or larger at larger gap sizes. It will eventually cause the flame cease to spread as the gap size increases. Fig. 13. Local and total burning durations versus gap size. The error bars denote the maximum and minimum values in the repetitive tests.
4.4. Flame spread rate and fuel spread rate Fig. 17a shows the start time for each fuel segment at different gap sizes. The curves are fairly linear after the 5th fuel segments in all cases. The flame spread rate for each fuel arrangement was deduced using the slope of the linear fit of the last five fuel segments: � 1 � � dðstart timeÞ Vflame ¼ Lgap þ Lfuel (2) dðnumber of fuelÞ
images (using the built-in Robert edge detection function of Matlab) and overlaid in Fig. 15c. This confirms the predictions of Park et al. [10]: the flame standoff distance drops at the gaps, resulting in a smaller overall flame distance from the sample surface for discrete fuels compared with a continuous fuel. This implies greater conductive heat transfer from the flame to the solid sample, contributing to the larger local burning rate for discrete fuel configurations compared to the continuous configuration. Flame lengths (averaged between three repetitive tests) deduced from flame base and flame tip location (see Figs. 3 and 6) for all fuel arrangements are compared in Fig. 16. Fig. 16a shows the 9th-order polynomial fitting lines (solid line) along with the original data (dotted line). For the continuous case, the flame covered the entire sample span (10 cm) and reached maximum length at ~23 cm shortly after ignition (see Fig. 2c). For discrete fuels, the maximum flame length occurred at ~2s in all cases. At this instance, the flame base was still anchored at the first fuel segment (see Fig. 9). Shortly after that, the first fuel segment was consumed and the flame base jumped across the gap. The flame
(a)
Lgap and Lfuel are the gap size (or the separation distance between sam ples) and the length of each fuel sample respectively. The deduced flame spread rates are plotted against the fuel per centages in Fig. 17b. The fuel percentage is defined as: f¼
Lfuel Lgap þ Lfuel
(3)
The flame spread rate exhibits a non-monotonic trend with respect to fuel percentage. It first increases and then decreases as the fuel per centage decreases. For thermally thin continuous samples, theory pre dicts that the surface flame spread rate follows the equation below [20]:
(b)
Fig. 14. Start time, end time, and burning duration of each fuel segment for discrete fuel configurations with gap sizes at (a) 1 cm and (b) 4 cm. The error bars denote the maximum and minimum values in the repetitive tests. 8
W. Cui and Y.-T.T. Liao
(a)
Fire Safety Journal 110 (2019) 102907
(b)
length. Note that gaps can affect flame spread rate through multiple terms in Eq. (5). First, as samples completely burn out from the upstream direction, the flame base moves along the sample surface. The flame base is forced to jump when a gap is encountered. This effect can be interpreted as a reduction of the fuel load and is reflected by the apparent sample area density term f ρd in Eq. (5). Second, as discussed in Section 4.3, flame standoff distance reduces when gaps are present. It is expected that when the gap size increases, the flame standoff distance decreases and the incident heat flux from the flame increases. If the flame standoff profile can be approximated by the boundary layer thickness [19], the convective heat flux from the flame is expected to have the following negative correlation with f: q_f ’’ ðfÞe f n where n~0.5. Third, the presence of gaps reduces the sample pyrolysis length (assuming that pyrolysis length is greater than individual sample strip lengths). Since the flame extension length δf is proportional to the fuel pyrolysis length [21], δf is expected to decrease with f. Therefore, fδf ef n where ne2. In this work, when the gaps are small (Lgap <2 cm or f >33%), the flame spans the entire set of fuel samples. In this situation, the pyrolysis and sample preheat lengths are limited by the available downstream fuel. The third effect (reduction of effective preheat length) is nullified and the first two effects (the decrease of the apparent sample area density and the increase of the heat flux from the flame) dominate. This explains the negative correlation between flame spread rate and fuel percentage. When the gaps are large (Lgap >2 cm or f <33%), the flame does not span the entire set of fuel samples. The third effect (the reduction of preheat length) dominates and the flame spread rate posi tively correlates with fuel percentage. Note that with this analysis, the optimal fuel percentage obtained is specific to the experimental setup and depends on the length of each fuel element (relative to the pyrolysis length) and the total fuel span (relative to the flame length). Also note that in a previous study by Miller and Gollner [9], a similar trend for flame spread rate with respect to fuel percentage was reported, except that the peak spread rate occurred at ~67% fuel percentage. It should be noted that there are several key differences between the previous and the current studies. One key difference is that in the previous study, thick (~1.27 cm) PMMA blocks were burned and there was no indication that the material burned out completely during tests. Without complete burnout, the first effect above (reduction of the apparent area density) is less significant because the flame base does not move. Another key difference between
(c)
Fig. 15. Side-view flame shape profiles for the continuous sample and the discrete samples with 1 cm gaps. (a) RGB images. (b) Binary images. (c) Overlaid edge image.
Vflame ¼
q_f ’’ δf � ρdcp Tp T∞
(4)
Here q_f ’’ is the incident heat flux from the flame unto the sample surface, δf is the flame extension length over the new sample material (i.e., sample preheat length), ρd is the sample area density (i.e., density times thickness), and Tp and T∞ are the pyrolysis and ambient temperatures respectively. For the discrete fuel configuration, this equation can be rewritten as: Vflame ¼
q_f ’’ ðf Þf δf � f ρdcp Tp T∞
(5)
Here f ρd is the apparent area density, q_f ’’ ðfÞ is the incident heat flux as a function of fuel percentage, and fδf is the effective sample preheat
(b)
(a)
Fig. 16. (a) Flame length (b) Non-dimensionalized flame length (flame length divided by the total fuel span) for different gap sizes. Dotted lines are for the original data. Solid lines are for the 9th-order polynomial fitting of the original data. 9
W. Cui and Y.-T.T. Liao
Fire Safety Journal 110 (2019) 102907
(b)
(a)
Fig. 17. (a) Start time (defined as onset of preheating) for different fuel samples at different gap sizes. (b) Flame spread rate at different gap sizes. The error bars in (a) denote the maximum and minimum values in the repetitive tests.
and warrant a separate study.
the two studies is that combustible materials were separated by inert blocks in the previous study and by air gaps in this current study. The boundary layer is expected to behave differently in these situations. Therefore, the second effect above (convective heat flux from the flame) differs between these studies. The final key difference is that in the current study, the total fuel length (the sum of the individual segment lengths) is fixed, but the total fuel span (fuel length þ total gap length) varies. When the flame spans the entire fuel span, the available-fuel and preheat lengths are not affected when fuel percentage is reduced. Miller and Gollner fixed the total fuel span. When the flame extends to the entire fuel span, the available-fuel and preheat lengths decrease when fuel percentage is reduced. These differences contribute to the different optimal fuel percentages for flame spread observed in the previous and the current work.
Declaration of competing interest None. Acknowledgement The authors would like to acknowledge support from Underwriters Laboratories. This work was also partially supported by NASA Glenn Research Center under Grant # NNX16AL61A. References [1] M.J. Gollner, X. Huang, J. Cobian, A.S. Rangwala, F.A. Williams, Experimental study of upward flame spread of an inclined fuel surface, Proc. Combust. Inst. 34 (2) (2013) 2531–2538. [2] G.H. Markstein, J. de Ris, Upward fire spread over textiles, Proc. Combust. Inst. 14 (1) (1973) 1085–1097. [3] S.L. Olson, F.J. Miller, Experimental comparison of opposed and concurrent flame spread in a forced convective microgravity environment, Proc. Combust. Inst. 32 (2) (2009) 2445–2452. [4] X. Zhao, Y.-T.T. Liao, M.C. Johnston, J.S. T’ien, P.V. Ferkul, S.L. Olson, Concurrent flame growth, spread, and quenching over composite fabric samples in low speed purely forced flow in microgravity, Proc. Combust. Inst. 36 (2) (2017) 2971–2978. [5] D.L. Urban, P. Ferkul, S. Olson, G.A. Ruff, J. Easton, J.S. T’ien, Y.-T.T. Liao, C. Li, C. Fernandez-Pello, J.L. Torero, G. Legros, C. Eigenbrod, N. Smirnov, O. Fujita, S. Rouvreau, B. Toth, G. Jomaas, Flame spread: effects of microgravity and scale, Combust. Flame 199 (2019) 168–182. [6] H.T. Loh, A.C. Fernandez-Pello, Flow assisted flame spread over thermally thin fuels, Fire Saf. Sci. 1 (1986) 65–74. [7] M.J. Gollner, Y. Xie, M. Lee, Y. Nakamura, A.S. Rangwala, Burning behavior of vertical matchstick arrays, Combust. Sci. Technol. 184 (5) (2012) 585–607. [8] Y. Watanabe, H. Torikai, A. Ito, Flame spread along a thin solid randonly distributed combustible and noncombustible areas, Proc. Combust. Inst. 33 (2011) 2449–2455. [9] C.H. Miller, M.J. Gollner, Upward flame spread over discrete fuels, Fire Saf. J. 77 (2015) 36–45. [10] J. Park, J. Brucker, R. Seballos, B. Kwon, Y.-T.T. Liao, Concurrent flame spread over discrete thin fuels, Combust. Flame 191 (2018) 116–125. [11] M.F. Wolff, G.F. Carrier, F.E. Fendell, Wind-aided firespread across arrays of discrete fuel elements. II. Experiment, Combust. Sci. Technol. 77 (1991) 261–289. [12] M. Vogel, F.A. Williams, Flame propagation along matchstick arrays, Combust. Sci. Technol. 1 (6) (1970) 429–436. [13] J.M. Prahl, J.S. Tien, Preliminary investigations of forced convection on flame propagation along paper and matchstick arrays, Combust. Sci. Technol. 7 (6) (1973) 271–282. [14] S. Abe, A. Ito, H. Torikai, Flame spread along a thin combustible solid with randomly distributed square pores of two differnet sizes, Mod. Appl. Sci. 6 (9) (2012). [15] C.C. Hwang, Y. Xie, Flame propagation along matchstick arrays on inclined base boards, Combust. Sci. Technol. 42 (1984) 1–12.
5. Conclusion Upward flame spread experiments are conducted using an array of discrete thin filter papers separated by air gaps. The size of the air gap is the variable in this study. The experimental results show that the flame spread rate and the mass loss rate (or the total burning rate) first in crease and then decrease when the gap size increases. There is an optimal gap size (or fuel load) for the flame spread. Analysis of the experimental images suggest that the local burning rate (or the mass flux on the sample surface) is significantly enhanced by the presence of the gaps. However, the local burning rate is less sensitive to gap size than the total burning rate. It is concluded that the presence of the gaps has three major effects on fire behavior. First, the flame jumps at each gap, thereby increasing the apparent flame spread rate. Second, gaps alter the flame shape by breaking the flow boundary layer. The flame exhibits a wavy pattern and has a smaller overall standoff distance from the sample surface compared to a continuous sample. This implies a larger conductive heat flux onto the sample surface, and a larger local solid burning rate of the solid fuel. Third, the presence of gaps reduces the effective sample heating length (when the flame does not cover the entire fuel span). This would lead to a smaller total heat input to the solid and a smaller total burning rate. These findings support the theory provided by an earlier numerical study of Park et al. [10]. For downward or opposed-flow flame spread, configuration and coupling between the gaseous flame, pyrolysis zone, and preheat zone are different from the upward flame spread. Hence, the effects of the fuel arrangement (or gap size) on flame spread are anticipated to be different 10
W. Cui and Y.-T.T. Liao
Fire Safety Journal 110 (2019) 102907
[16] R.O. Weber, A model for fire propagation in arrays, Math. Comput. Model. 13 (12) (1990) 95–102. [17] M.A. Finney, J.D. Cohen, I.C. Grenfell, K.M. Yedinak, An examinatiion of fire spread thresholds in discontinuous fuel beds, Int. J. Wildland Fire 19 (2010) 163–170. [18] A.C. Fernandez-Pello, Flame spread in a forward forced flow, Combust. Flame 36 (1979) 63–78.
[19] A. Vetturini, W. Cui, Y.-T.T. Liao, S. Olson, P. Ferkul, Flame spread over ultra-thin solids: effect of area density and concurrent-opposed spread reversal phenomenon, Fire Technology, 2019 submitted for publication, https://doi.org/10.1007/s1 0694-019-00878-w. [20] J.G. Quintiere, Fundamental of Fire Phenomena, John Wiley & Sons Ltd, West Sussex, England, 2006. [21] J.L. Torero, Scaling-up fire, Proc. Combust. Inst. 34 (1) (2013) 99–124.
11
Contents lists available at ScienceDirect
Fire Safety Journal journal homepage: http://www.elsevier.com/locate/firesaf
Experimental study of upward flame spread over discrete thin fuels Wohan Cui, Ya-Ting T. Liao * Department of Mechanical and Aerospace Engineering, Case Western Reserve University, 10900, Euclid Ave, Cleveland, OH, USA
A R T I C L E I N F O
A B S T R A C T
Keywords: Upward flame spread Discrete fuels Burning rate
Experiments are performed to study upward flame propagation over discrete combustibles separated by air gaps. An array of ten 1 cm-long 5 cm-wide filter papers is uniformly distributed on a vertical sample holder subjected to double-sided burn. The distance between the samples was varied from 0 to 4 cm. After being ignited from the bottom end, the flame spread process is recorded by front and side video cameras. A precision balance with 0.01g resolution is used to monitor the mass loss and deduce the solid burning rate. The results show that both flame spread rate and solid burning rate have a non-monotonic relationship with the gap size. The presence of gaps decreases the fuel load (fuel mass per unit length), which results in an increasing apparent flame spread rate as the gap size increases. The gaps also allow the lateral entrained air to push the flame closer to the sample surface, enhancing the conductive heat input to the samples. This results in an increased solid burning rate and flame spread rate. However, when the gap size is large, the effective heating length of the sample and hence the total burning rate decrease as the gap size increases. Eventually, the flame fails to spread.
1. Introduction
variables. For example, Vogel and Williams [12], one of the first groups to study flame spread over discrete fuels, used a horizontal array of vertically oriented matchsticks (with the heads removed). Matchstick height and inter-stick separation distance were varied. The critical separation distance (beyond which the flames fail to spread) was found to increase with increasing matchstick height. Vogel and Williams also performed thermal analysis and provided a theoretical thermal model that yielded good agreement with their experiment data, suggesting that convective heat transfer is of primary importance in flame propagation at matchstick size scales. Many studies using similar experimental setups followed, investigating a wide range of parameters including imposed ambient wind speed [11,13], wood type [11], fuel element height [11], fuel-bed inclination angle [15], and moisture content of the fuel [11]. In general, flames are more likely to spread in deeper fuel beds [11,12], with higher imposed wind speed [13], and with a steeper fuel bed slope [15]. The flame spread rate was also observed to have a positive cor relation with imposed wind velocity [11,13] and a negative correlation with fuel mass load [11]. At a slightly larger scale, Finney et al. [17] studied fuel elements consisting of excelsior spun around vertical metal rods, using them to simulate vegetation canopies encountered in forest fires. They studied how fire spread thresholds varied with vertical fuel-bed depth, inter-rod spacing, and slope of the fuel bed arrays, and concluded that fires spread only after ignition by direct flame contact. Fires were also more likely to spread in deeper fuel beds and with steeper
Discrete fuels refer to scenarios where multiple solid combustibles are in close proximity but are separated by air gaps or inert materials. Compared to homogeneous (or continuous) fuel arrangements, discrete fuels better represent some realistic fire scenarios (e.g., wildland fires, urban fires, commodities stored in warehouses). While fire behavior and flame spread over continuous fuels have been extensively studied with various configurations [1–3] and over a wide range of ambient condi tions [3–6], a comprehensive understanding of the fire behaviors of discrete fuels has not yet been achieved. Flame spread over discrete fuels can be very different from spread over continuous fuels. Intuitively, gaps between combustibles act as barriers, preventing or slowing down flame propagation. However, when the flame does spread, the presence of gaps can increase the flame spread rate [7–11] and the solid burning rate [7,9,10]. In other words, discrete fuel can be more hazardous than continuous fuel in terms of fire safety. Previous studies of flame spread over discrete fuels include experi ments and theories involving horizontal [8,11–14], inclined [15–17], and vertical [7,9,10] fuel beds. For many of these studies, the fuel ele ments were arrays of matchstick-like materials oriented perpendicularly to the flame spread direction. These studies investigated the relationship between separation distance and flame spread rate, among other * Corresponding author. E-mail address: [email protected] (Y.-T.T. Liao).
https://doi.org/10.1016/j.firesaf.2019.102907 Received 11 May 2019; Received in revised form 6 September 2019; Accepted 4 November 2019 Available online 5 November 2019 0379-7112/© 2019 Elsevier Ltd. All rights reserved.
W. Cui and Y.-T.T. Liao
Fire Safety Journal 110 (2019) 102907
slopes. For upward flame spread, Gollner et al. [7] studied horizontally oriented matchsticks held on a vertical steel wall, and showed that flame spread rates and sample mass loss rates increase with matchstick spacing. Flat discrete samples have also been studied [8–10,14]. The critical mechanism of flame spread over a flat continuous fuel is heat transfer from the flame to the solid fuel in the preheat and pyrolysis regions [2,6, 18]. A similar phenomenon has been observed for discrete fuels. How ever, in flat discrete samples, the flame spread rate exhibits a non-monotonic trend with respect to fuel load. This has been demon strated in experiments involving paper samples with randomly distrib uted pores [8] where there is an optimal porosity (total pore area over paper area) for flame spread rate. Gollner and Miller [9] conducted experiments using a vertical array of PMMA blocks separated by insu lated materials, and identified an optimal fuel coverage (total fuel length over total length) that maximizes flame spread rate. Gollner and Miller [9] also found that the fuel spread rate (distance of fuel traversed by the pyrolysis front over time) decreases but the average mass flux on the sample surface increases when fuel coverage decreases. The authors hypothesized that this latter relationship is due to delayed thickening of the boundary layer and/or increased air entrainment at the gaps. Park et al. [10] focused on thin samples where solid burnout occurs. They conducted numerical simulation of concurrent flame spread over discrete thin fuels separated by air gaps. Two scenarios were considered: upward flame spread in normal gravity and purely concurrent flame spread in a low-speed forced flow in zero gravity. Their modeling sug gested that the effects of the air gaps on the sample burning rate are two-fold. On one hand, the gaps break the aerodynamic boundary layer and reduce the flame standoff distance. This increases the conductive heat flux from the flame to the sample surface, thus enhancing the solid burning rate. On the other hand, the presence of gaps reduces the effective preheat length and pyrolysis length of the samples (when the flame does not cover the entire fuel span). This reduces the solid burning rate. The two effects result in a non-monotonic trend of the solid burning rate when the gap size increases. To validate their numerical simula tions, Park et al. [10] performed experiments of upward flame spread over an array of filter papers with inter-sample separation distance being the main variable. The average flame spread rate and total burning duration were deduced through visual inspection of videos recorded during the experiments. While the experimental data correlated reasonably well with their modeling results, Park et al. focused on the numerical study and did not provide an in-depth analysis of the exper imental data. The goal of this work is to critically examine the hypotheses posed by Park et al. [10] and to achieve as complete as possible an understanding of the underlying physics of flame spread processes for discrete thin fuels in concurrent flow. We extend the experimental work of Park et al. [10] and conduct a series of experiments using a separate enhanced experi mental setup. A precision balance is added to collect mass loss data and to provide information on the solid burning rate. Instead of visually inspecting of the experimental videos, we develop methodologies to attain information regarding global and local burning processes via image analysis. Flame shapes and transient flame development pro cesses for continuous and discrete fuel configurations are also compared in detail. The major difference between this work and previous upward flame spread experiments is that this work concerns thin flat samples. In previous work where horizontally oriented matchsticks were used [7], flames spread along the fuel depth horizontally (a scenario closer to thick samples) in addition to spreading across fuel elements vertically. Furthermore, solid pyrolysis occurs on both tip and side surfaces of the matchsticks. In this work, thin flat paper samples are used and flame spread is approximated to occur only along the sample surface and across the gaps. The simple configuration also facilitates the comparison of burning characteristics between discrete and continuous samples. In Miller and Gollner’s work [9], thick PMMA blocks were separated by
inert materials. While delayed thickening of the boundary layer and/or increased air entrainment were hypothesized to occur near inert mate rials, flame shapes were not compared directly. These effects are ex pected to be even more significant when samples are separated by air gaps in this work. The thin short (1 cm) samples used in this work also yield a more regular laminar flame base at the upstream region, facili tating the extraction of flame shapes to test the hypothesis. 2. Experiment setup The experimental apparatus is shown in Fig. 1. An array of fuel sample elements is arranged uniformly on a vertical sample holder. The sample material is CFP40 quantitative cellulose filter paper (manufac tured by I⋅W.Tremont) with area density of 85 g=m2 . Sample material is cut into 1 cm-long 8 cm-wide segments and stored in a sealed jar with desiccant Drierite (98% CaSO4 and 2% CoCl2, manufactured by W.A. Hammond Drierite Company) for at least 24 h before each test. The sample holder consists of four 3-mm-thick aluminum plates, two on each side, sandwiching the samples. The sample holder can support a maximum fuel span of 50 cm. The exposed width of the samples is adjustable and set at 5 cm for all tests in this work. The sample and the sample holder are placed on top of a precision balance (A&D Fx-5000i) to monitor the mass loss of the sample during each test. The resolution and frequency of the balance are 0.01 g and 20 Hz respectively. An ignition paper strip, wrapped by a saw-tooth shaped Kanthal 27 GA resistant wire (with DC power 13.5A and 3.46V for 5.5s) is placed 3 cm beneath the first fuel sample. The ignition wire and the ignition paper strip are held by a separate mounting rack so that the mass loss of the ignition strip is not reflected in the mass loss data obtained by the precision balance. The dimensions of the ignition paper is 0.7 cm long by 4.5 cm wide. The dimension and the location of the ignition paper strip were defined after a series of tests to ensure ignition and to minimize the effects of ignition on the flame spread over the sample array. Two video cameras (Canon Rebel T3i 1080P) are used to record front and side images during the experiment at 30 frames per second with a spatial resolution of 0.47 mm/pixel. Experiments are conducted in a dark room with green LEDs illuminating the sample surface. All tests are performed underneath a ventilation hood and inside a hazard screen so that exhaust gasses and smoke are collected, debris is confined, and the effect of surrounding airflow on the apparatus is mitigated. Ambient temperature and moisture are recorded before each test and ranged from 68 to 70 � F and 31–39% respectively. The test matrix of this study is summarized in Table 1. For discrete fuel arrangements, ten fuel elements are used in each test so that the total mass of the sample is constant in all tests. The separation distance (or the gap size) between samples varies in each test, ranging from 1 to 4 cm. In addition, a 10 cm-long continuous sample is tested. For each fuel configuration, experiments are repeated three times to ensure reproducibility. Also listed in Table 1 is the total sample span, defined as the distance between the bottom edge of the first fuel segment and the top edge of the last fuel segment. While the total available sample length is fixed to 10 cm in all tests, the sample span increases as the gap size increases. Also listed in Table 1 is the total burning duration, averaged between three repetitive tests for each fuel configuration. This will be discussed further in section 4.1. 3. Experimental results 3.1. Transient flame spread over continuous sample The transient process of flame spread over the continuous sample is demonstrated using the front and side-view images at selected instances in Fig. 2. In Fig. 2a, the tip of the flame from the ignition strip has ignited the bottom end of the first sample strip, and laminar diffusion flames are present on both sides of the samples (see side-view image in Fig. 2a). Shortly after ignition, the flame grows in length and covers the entire 2
W. Cui and Y.-T.T. Liao
Fire Safety Journal 110 (2019) 102907
Sample Holder
Sample Array Ignition Strip
Ignitor Mounting Rack
Precision Balance Fig. 1. Experimental apparatus. Left: front-view image. Right: side-view schematics.
applied to the last 50% of the averaged mass loss data and an averaged mass loss rate (MLR) is deduced using the slope of the trend line (the black dash line on Fig. 4).
Table 1 Test matrix. Sample Length (cm)
Gap Size (cm)
Number of Samples
Total Sample Span (cm)
Average Total Burning Duration (s)
10 1 1 1 1 1
– 1 1.5 2 3 4
1 10 10 10 10 10
10 19 23.5 28 37 46
6.93 4.48 4.29 4.33 5.36 7.70
3.2. Transient flame spread over discrete samples Fig. 5 through 7 show the flame spread process for the discrete fuel arrangement with 1 cm gaps. Compared to the continuous fuel, the process was similar except that the flame exhibited a wavy pattern in the side view images. This is because, as predicted by Park et al. [10], the gaps between the samples broke the no slip boundary condition and the local flame standoff distance was reduced at the gaps (see the right-hand-side flame in the side-view image in Fig. 5c). The funda mentally different flame shapes of the continuous and discrete fuels have significant impact on heat feedback to the sample and therefore affects the sample burning rate. This will be discussed further in Section 4. The flame base location versus time in Fig. 6 shows a staircase-like curve, corresponding to how the flame jumps across gaps. Note that the flame base can jump multiple gaps if multiple fuel elements are consumed simultaneously. The data shown in Figs. 6 and 7 suggest reasonable consistency between the repetitive tests.
sample array (Fig. 2b and c). In the meantime, the flame base (the bottom of the flame) moves upward slowly as the sample is consumed (Fig. 2b–g). Eventually, the sample fuel is fully consumed and the flame is extinguished (Fig. 2h). Note that in Fig. 2, the rear aluminum sample holder plates were removed and the samples were attached to the front plates using Kapton tape. This allowed examination of the flame shape close to the sample surface in the side-view images, which would otherwise be partially blocked by the 3 mm-thick sample holder. As will be shown later, removing the rear sample holder plate has negligible effects on the flame spread process. The flame on the rear side of the sample (the right-sided flame in the side-view images) shows that the flame shape ensembles the flow boundary layer and the local flame standoff distance grows monotonically along the sample surface. This is because for a concurrent diffusion flame, the gaseous pyrolysate needs to travel across the flow boundary layer to meet with the oxidizer. This typical flame shape has been observed in many studies of concurrent flame spread [3,5,6,10,18, 19]. The flame in front of the sample (left flame in the side-view images) was partially blocked from view by the aluminum sample holder plate. Therefore, the front flame base was seemingly farther from the sample surface and more downstream than the rear flame in the side-view im ages. Note that this alteration of the sample setup was only used for generating Figs. 2, 5 and 12. All other data reported was obtained using the original sample setup from Section 2. A MATLAB code was developed to analyze the front-view images and to track the flame location in each frame. In this work, flame base is defined as the uppermost point of the lowest boundary of the flame, and flame tip is defined as the uppermost point of the flame (see Fig. 2e). The results for the three repetitive tests for the continuous sample are shown in Fig. 3, which suggests reasonable reproducibility of the tests. The mass loss data recorded by the precision balance is shown in Fig. 4, and also demonstrates reasonable reproducibility. Linear fitting is
4. Analysis and discussion 4.1. Total burning duration and average mass loss rate The total burning durations (averaged between three repeated tests) for all fuel arrangements are compared in Table 1 and in Fig. 8. In this work, the total burning duration is defined as the time from the onset of preheating of the first fuel segment (start time) to the extinction of the flame (end time). The start and end times are deduced from video image analysis (see section 4.2) and deliberately exclude the residual flamelets or smoldering near the sample holders on two sides (see Fig. 5g and f) after majority of the samples was consumed. The uncertainty of the total burning duration for each test is 0.033 s (based on video camera frame rate at 30 Hz). The measurement deviations between the repeated tests are marked by the error bars on Fig. 8. The data obtained using the previous experimental setup in Park et al. [10] for the same sample materials is also included. Compared to our setup, the experimental setup of Park et al. [10] is slightly larger and hence can accommodate fuel configurations with larger gaps. Note that the data for 0 cm gap in Fig. 8 is for the continuous sample. While the total burning duration in this study is slightly lower than in the previous larger setup of Park et al., the trend is the same. The total burning 3
W. Cui and Y.-T.T. Liao
Fire Safety Journal 110 (2019) 102907
Fig. 2. Front and side-view images of flame spread over a 10 cm-continuous fuel at select instances. The rear sample holders were removed in these images.
Fig. 4. Mass loss data for the continuous sample. The result of the additional test with one-sided sample holder is also shown.
Fig. 3. Locations of flame base and flame tip versus time for the continuous sample. The result of the additional test with one-sided sample holder is also shown.
4
W. Cui and Y.-T.T. Liao
Fire Safety Journal 110 (2019) 102907
Fig. 5. Front and side-view images of flame spread over discrete fuels with 1 cm gap size at select time instances.
Fig. 7. Mass loss data for discrete fuels with 1 cm gap size. The result of the additional test with one-sided sample holder is also shown.
Fig. 6. Locations of flame base and flame tip versus time for discrete fuels with 1 cm gap size. The result of the additional test with one-sided sample holder is also shown.
5
W. Cui and Y.-T.T. Liao
Fire Safety Journal 110 (2019) 102907
distribution of the solid burning rate on the sample surface. Park et al. [10] showed that the solid burning rate has local maximum near the upstream leading edge of each fuel segment. Therefore, before the up stream sample was fully consumed, the leading edge of the next sample (located directly above it, “downstream”) had already burned out. When the upstream fuel segment was fully consumed, the flame base needed to jump not only across the inter-sample gap but also across the length of next fuel sample that had already burned out, resulting in the steps in the adjusted flame base location in Fig. 9. Linear fitting was applied to the last 50% (5–10 cm) of the curves in Fig. 9. The slope of the fitted line defined the burning speed of the flame base (or the spread rate of the flame base along the fuel surface). The burning speed is then used to estimate the MLR: �cm� �g� ¼ Burning Speed � Sample Width ðcmÞ Mass Loss Rate s s � g � � Area Density : cm2 The averaged MLR is also calculated based on the linear fit of the mass loss data from the precision balance. The mass loss data for various fuel configurations is shown in Fig. 10. Linear fitting is applied to the last 50% of the averaged mass loss data and an averaged mass loss rate (MLR) is deduced using the slope of the trend line for each of the fuel configuration. Results of the two methods are compared in Fig. 11. Quantitatively, the MLR deduced based on the flame base spread rate is around twice as large as that deduced from the precision balance reading. This indicates that the steady state is not fully reached. Nevertheless, two curves correlate with each other well qualitatively and both show that the MLR first increases and then decreases with increasing gap size, consistent with the trend of the total burning duration in Fig. 8. The maximum MLR occurs at gap size of 2 cm.
Fig. 8. Total burning durations versus gap sizes. The error bars denote the maximum and minimum values in the repetitive tests.
duration first decreases when the gap size increases. After it reaches a minimum value, the total burning duration has a reverse dependence on the gap size. The data from the large setup also indicates that the flame eventually fails to spread at a critical gap size between 6.5 and 6.6 cm. In Park et al.’s work [10], the total burning durations were deduced based on visual inspection of the video images and included the side residual burning (which can last as long as 2–3s). The elimination of the residual burning from the burning duration in this work is considered the major reason for the discrepancy of the total burning durations using the two experimental setups. The average MLR are also compared. In this work, the average MLR are deduced using two different methods. The first method is based on the spread rate of the flame base. In this work, we define an adjusted flame base location as the original flame base location (as shown in Figs. 3 and 6) minus the total gap sizes upstream to the flame base. The results for various fuel configurations are shown in Fig. 9. Note that even after the gaps are removed, flame base locations versus time still exhibit “jumping” (or steps) for discrete fuel configurations. The same trend was reported in Park et al. [10] and was attributed to the non-monotonic
4.2. Local burning duration and solid burning rate Burning duration for individual fuel elements are also examined. To achieve this, non-dimensionalized overall flame intensity (or flame coverage) over each fuel segment is tracked using MATLAB. The flame intensity over the k-th fuel segment is defined as PI PJ i j Rði; jÞ I *k ¼ (1) 255 � I � J Here, k ranges from 1 to 10 with 1 denoting the bottommost fuel
Fig. 9. Adjusted flame base location (flame base location minus the distance of the gaps traversed by the flame base) versus time for different gap sizes.
Fig. 10. Mass loss (averaged between three repetitive tests) versus time for all fuel configurations. 6
W. Cui and Y.-T.T. Liao
Fire Safety Journal 110 (2019) 102907
local burning duration is determined using the average burning duration of the last five fuel segments (i.e., the 6th to 10th segments). The local burning duration for all cases are compared in Fig. 13. The total burning duration (discussed in section 4.1) is also plotted. Notice that while the total burning duration displays an obvious nonmonotonic dependency on the gap size, the local average burning du rations are less sensitive to the gap size for discrete fuel cases. Never theless, all discrete cases have a smaller average local burning duration compared to the continuous case. This implies that the local burning rate (mass loss rate per unit area or the mass flux of each solid sample) is significantly enhanced when gaps are present. This is consistent with Miller and Gollner’s experiments [9] and Park et al.’s prediction [10]. In Fig. 13, compared to 1 cm gap size, the configuration with 4 cm gap size has a slightly lower average local burning duration but signif icantly higher total burning duration. To understand this, the start and end times and the local burning durations for the two cases are examined in Fig. 14. For the case of 1 cm gap size, samples are close to each other and their burning times overlap. On the other hand, for the case of 4 cm gap size, samples tend to burn sequentially, resulting in a larger total burning duration.
Fig. 11. Average mass loss rate versus gap size. Error bars denote maximum and minimum values from the repetitive tests.
segment and 10 denoting the uppermost fuel segment. R (i, j) is the red value of a RGB image at a pixel located at (i, j). R ranges from 0 to 255. I and J are the total pixels in the width and length of each fuel segment. To demonstrate the concept, Fig. 11a shows the evolution of the flame intensity over every other fuel segment for discrete fuel configu ration with 1-cm gap size. Once the flame reaches the k-th fuel segment, I*k increases and then reaches a plateau of a value approximated at 1 (i.e., most of the pixels on the sample surface reaches maximum red value). After the fuel segment is fully consumed, the flame is no longer present above the fuel segment and I*k decreases to zero. The burning durations of each fuel segment are determined using a constant threshold value of I*k ¼ 0.1 (red dashed line in Fig. 12a). The non-zero value was chosen to eliminate flamelets and smoldering of the sample residual near the sample holders on two sides (see Fig. 5g and f). Fig. 12 shows that the burning of the residual near the side sample holders can last 2–3 s. Also, note that the local burning duration defined in this work includes both the preheat time and the pyrolysis time of each sample segment. Fig. 12b shows the flame intensity over the last five fuel segments. In this plot, time is adjusted so that the start times (i.e., the onset of pre heating) of all fuel segments are aligned. The curves have a similar shape, implying a quasi-steady flame spreading process. In this work,
(a)
4.3. Flame shape and preheat length Flame shape and flame standoff distance (distance of flame from sample surface) have direct influence on heat feedback from the flame to the fuel surface, which in turns dictates the solid burning rate. To better capture the flame shapes near the sample surface, two sets of extra ex periments were performed with the rear aluminum sample holder plates removed for continuous and 1-cm gap discrete fuel configurations. The purpose of these additional tests was to facilitate the comparisons of the edge view flame profiles (shown in Figs. 2 and 5). The flame location analysis (Figs. 3 and 6) and the mass loss data (Figs. 4 and 7) show that such modification of the experimental setup has minimal effects on the burning event. Nevertheless, all the data reported in this work are with the original setup with double-sided sample holder plates. Fig. 15 shows the original RGB (Fig. 15a), and post-processed black and white binary (Fig. 15b) side-images of the flame (on the rear where there were no sample holders) for continuous fuel and for discrete fuels with 1 cm gap. These images were taken at t ¼ 1.83s after ignition in both tests. For continuous fuel, the flame shape resembles the flow boundary layer. The flame standoff distance increases along the direction of flame propaga tion. In the discrete case, the flame shows a zigzag-shaped contour as described earlier. The binary images are further transformed into edge
(b)
Start Time End Time
Start Time
Fig. 12. Non-dimensionalized flame intensity of each fuel segment for discrete fuels with 1 cm gap size. 7
End Time
W. Cui and Y.-T.T. Liao
Fire Safety Journal 110 (2019) 102907
length thus started to decrease. Fig. 15a shows that the maximum flame length first increases and then decreases when the gap size increases. The case with 2 cm gap has the largest flame length among all discrete cases. In this case, the flame reached the maximum length of 40 cm and the flame was able to cover its total fuel span of 28 cm. For 4 cm gap size, the maximum flame length is ~22 cm, which is much shorter than the total fuel span of 46 cm. The flame only covered the first five fuel segments. Fig. 16b further compares the non-dimensionalized flame lengths versus time in each case. The non-dimensionalized flame length is defined as flame length divided by corresponding fuel span in each case. Fig. 16b shows that the non-dimensionalized flame height decreases monotonically as gap size increases. After gap size exceeds 2 cm, the non-dimensionalized flame length drops below one, indicating that the flame is no longer able to cover all available fuel samples, resulting in a reduction of the effective sample heating length (as predicted by Park et al. [10]). This results in the decrease of the MLR at large gaps as shown in Fig. 11, despite the fact that the local solid burning rate may be similar or larger at larger gap sizes. It will eventually cause the flame cease to spread as the gap size increases. Fig. 13. Local and total burning durations versus gap size. The error bars denote the maximum and minimum values in the repetitive tests.
4.4. Flame spread rate and fuel spread rate Fig. 17a shows the start time for each fuel segment at different gap sizes. The curves are fairly linear after the 5th fuel segments in all cases. The flame spread rate for each fuel arrangement was deduced using the slope of the linear fit of the last five fuel segments: � 1 � � dðstart timeÞ Vflame ¼ Lgap þ Lfuel (2) dðnumber of fuelÞ
images (using the built-in Robert edge detection function of Matlab) and overlaid in Fig. 15c. This confirms the predictions of Park et al. [10]: the flame standoff distance drops at the gaps, resulting in a smaller overall flame distance from the sample surface for discrete fuels compared with a continuous fuel. This implies greater conductive heat transfer from the flame to the solid sample, contributing to the larger local burning rate for discrete fuel configurations compared to the continuous configuration. Flame lengths (averaged between three repetitive tests) deduced from flame base and flame tip location (see Figs. 3 and 6) for all fuel arrangements are compared in Fig. 16. Fig. 16a shows the 9th-order polynomial fitting lines (solid line) along with the original data (dotted line). For the continuous case, the flame covered the entire sample span (10 cm) and reached maximum length at ~23 cm shortly after ignition (see Fig. 2c). For discrete fuels, the maximum flame length occurred at ~2s in all cases. At this instance, the flame base was still anchored at the first fuel segment (see Fig. 9). Shortly after that, the first fuel segment was consumed and the flame base jumped across the gap. The flame
(a)
Lgap and Lfuel are the gap size (or the separation distance between sam ples) and the length of each fuel sample respectively. The deduced flame spread rates are plotted against the fuel per centages in Fig. 17b. The fuel percentage is defined as: f¼
Lfuel Lgap þ Lfuel
(3)
The flame spread rate exhibits a non-monotonic trend with respect to fuel percentage. It first increases and then decreases as the fuel per centage decreases. For thermally thin continuous samples, theory pre dicts that the surface flame spread rate follows the equation below [20]:
(b)
Fig. 14. Start time, end time, and burning duration of each fuel segment for discrete fuel configurations with gap sizes at (a) 1 cm and (b) 4 cm. The error bars denote the maximum and minimum values in the repetitive tests. 8
W. Cui and Y.-T.T. Liao
(a)
Fire Safety Journal 110 (2019) 102907
(b)
length. Note that gaps can affect flame spread rate through multiple terms in Eq. (5). First, as samples completely burn out from the upstream direction, the flame base moves along the sample surface. The flame base is forced to jump when a gap is encountered. This effect can be interpreted as a reduction of the fuel load and is reflected by the apparent sample area density term f ρd in Eq. (5). Second, as discussed in Section 4.3, flame standoff distance reduces when gaps are present. It is expected that when the gap size increases, the flame standoff distance decreases and the incident heat flux from the flame increases. If the flame standoff profile can be approximated by the boundary layer thickness [19], the convective heat flux from the flame is expected to have the following negative correlation with f: q_f ’’ ðfÞe f n where n~0.5. Third, the presence of gaps reduces the sample pyrolysis length (assuming that pyrolysis length is greater than individual sample strip lengths). Since the flame extension length δf is proportional to the fuel pyrolysis length [21], δf is expected to decrease with f. Therefore, fδf ef n where ne2. In this work, when the gaps are small (Lgap <2 cm or f >33%), the flame spans the entire set of fuel samples. In this situation, the pyrolysis and sample preheat lengths are limited by the available downstream fuel. The third effect (reduction of effective preheat length) is nullified and the first two effects (the decrease of the apparent sample area density and the increase of the heat flux from the flame) dominate. This explains the negative correlation between flame spread rate and fuel percentage. When the gaps are large (Lgap >2 cm or f <33%), the flame does not span the entire set of fuel samples. The third effect (the reduction of preheat length) dominates and the flame spread rate posi tively correlates with fuel percentage. Note that with this analysis, the optimal fuel percentage obtained is specific to the experimental setup and depends on the length of each fuel element (relative to the pyrolysis length) and the total fuel span (relative to the flame length). Also note that in a previous study by Miller and Gollner [9], a similar trend for flame spread rate with respect to fuel percentage was reported, except that the peak spread rate occurred at ~67% fuel percentage. It should be noted that there are several key differences between the previous and the current studies. One key difference is that in the previous study, thick (~1.27 cm) PMMA blocks were burned and there was no indication that the material burned out completely during tests. Without complete burnout, the first effect above (reduction of the apparent area density) is less significant because the flame base does not move. Another key difference between
(c)
Fig. 15. Side-view flame shape profiles for the continuous sample and the discrete samples with 1 cm gaps. (a) RGB images. (b) Binary images. (c) Overlaid edge image.
Vflame ¼
q_f ’’ δf � ρdcp Tp T∞
(4)
Here q_f ’’ is the incident heat flux from the flame unto the sample surface, δf is the flame extension length over the new sample material (i.e., sample preheat length), ρd is the sample area density (i.e., density times thickness), and Tp and T∞ are the pyrolysis and ambient temperatures respectively. For the discrete fuel configuration, this equation can be rewritten as: Vflame ¼
q_f ’’ ðf Þf δf � f ρdcp Tp T∞
(5)
Here f ρd is the apparent area density, q_f ’’ ðfÞ is the incident heat flux as a function of fuel percentage, and fδf is the effective sample preheat
(b)
(a)
Fig. 16. (a) Flame length (b) Non-dimensionalized flame length (flame length divided by the total fuel span) for different gap sizes. Dotted lines are for the original data. Solid lines are for the 9th-order polynomial fitting of the original data. 9
W. Cui and Y.-T.T. Liao
Fire Safety Journal 110 (2019) 102907
(b)
(a)
Fig. 17. (a) Start time (defined as onset of preheating) for different fuel samples at different gap sizes. (b) Flame spread rate at different gap sizes. The error bars in (a) denote the maximum and minimum values in the repetitive tests.
and warrant a separate study.
the two studies is that combustible materials were separated by inert blocks in the previous study and by air gaps in this current study. The boundary layer is expected to behave differently in these situations. Therefore, the second effect above (convective heat flux from the flame) differs between these studies. The final key difference is that in the current study, the total fuel length (the sum of the individual segment lengths) is fixed, but the total fuel span (fuel length þ total gap length) varies. When the flame spans the entire fuel span, the available-fuel and preheat lengths are not affected when fuel percentage is reduced. Miller and Gollner fixed the total fuel span. When the flame extends to the entire fuel span, the available-fuel and preheat lengths decrease when fuel percentage is reduced. These differences contribute to the different optimal fuel percentages for flame spread observed in the previous and the current work.
Declaration of competing interest None. Acknowledgement The authors would like to acknowledge support from Underwriters Laboratories. This work was also partially supported by NASA Glenn Research Center under Grant # NNX16AL61A. References [1] M.J. Gollner, X. Huang, J. Cobian, A.S. Rangwala, F.A. Williams, Experimental study of upward flame spread of an inclined fuel surface, Proc. Combust. Inst. 34 (2) (2013) 2531–2538. [2] G.H. Markstein, J. de Ris, Upward fire spread over textiles, Proc. Combust. Inst. 14 (1) (1973) 1085–1097. [3] S.L. Olson, F.J. Miller, Experimental comparison of opposed and concurrent flame spread in a forced convective microgravity environment, Proc. Combust. Inst. 32 (2) (2009) 2445–2452. [4] X. Zhao, Y.-T.T. Liao, M.C. Johnston, J.S. T’ien, P.V. Ferkul, S.L. Olson, Concurrent flame growth, spread, and quenching over composite fabric samples in low speed purely forced flow in microgravity, Proc. Combust. Inst. 36 (2) (2017) 2971–2978. [5] D.L. Urban, P. Ferkul, S. Olson, G.A. Ruff, J. Easton, J.S. T’ien, Y.-T.T. Liao, C. Li, C. Fernandez-Pello, J.L. Torero, G. Legros, C. Eigenbrod, N. Smirnov, O. Fujita, S. Rouvreau, B. Toth, G. Jomaas, Flame spread: effects of microgravity and scale, Combust. Flame 199 (2019) 168–182. [6] H.T. Loh, A.C. Fernandez-Pello, Flow assisted flame spread over thermally thin fuels, Fire Saf. Sci. 1 (1986) 65–74. [7] M.J. Gollner, Y. Xie, M. Lee, Y. Nakamura, A.S. Rangwala, Burning behavior of vertical matchstick arrays, Combust. Sci. Technol. 184 (5) (2012) 585–607. [8] Y. Watanabe, H. Torikai, A. Ito, Flame spread along a thin solid randonly distributed combustible and noncombustible areas, Proc. Combust. Inst. 33 (2011) 2449–2455. [9] C.H. Miller, M.J. Gollner, Upward flame spread over discrete fuels, Fire Saf. J. 77 (2015) 36–45. [10] J. Park, J. Brucker, R. Seballos, B. Kwon, Y.-T.T. Liao, Concurrent flame spread over discrete thin fuels, Combust. Flame 191 (2018) 116–125. [11] M.F. Wolff, G.F. Carrier, F.E. Fendell, Wind-aided firespread across arrays of discrete fuel elements. II. Experiment, Combust. Sci. Technol. 77 (1991) 261–289. [12] M. Vogel, F.A. Williams, Flame propagation along matchstick arrays, Combust. Sci. Technol. 1 (6) (1970) 429–436. [13] J.M. Prahl, J.S. Tien, Preliminary investigations of forced convection on flame propagation along paper and matchstick arrays, Combust. Sci. Technol. 7 (6) (1973) 271–282. [14] S. Abe, A. Ito, H. Torikai, Flame spread along a thin combustible solid with randomly distributed square pores of two differnet sizes, Mod. Appl. Sci. 6 (9) (2012). [15] C.C. Hwang, Y. Xie, Flame propagation along matchstick arrays on inclined base boards, Combust. Sci. Technol. 42 (1984) 1–12.
5. Conclusion Upward flame spread experiments are conducted using an array of discrete thin filter papers separated by air gaps. The size of the air gap is the variable in this study. The experimental results show that the flame spread rate and the mass loss rate (or the total burning rate) first in crease and then decrease when the gap size increases. There is an optimal gap size (or fuel load) for the flame spread. Analysis of the experimental images suggest that the local burning rate (or the mass flux on the sample surface) is significantly enhanced by the presence of the gaps. However, the local burning rate is less sensitive to gap size than the total burning rate. It is concluded that the presence of the gaps has three major effects on fire behavior. First, the flame jumps at each gap, thereby increasing the apparent flame spread rate. Second, gaps alter the flame shape by breaking the flow boundary layer. The flame exhibits a wavy pattern and has a smaller overall standoff distance from the sample surface compared to a continuous sample. This implies a larger conductive heat flux onto the sample surface, and a larger local solid burning rate of the solid fuel. Third, the presence of gaps reduces the effective sample heating length (when the flame does not cover the entire fuel span). This would lead to a smaller total heat input to the solid and a smaller total burning rate. These findings support the theory provided by an earlier numerical study of Park et al. [10]. For downward or opposed-flow flame spread, configuration and coupling between the gaseous flame, pyrolysis zone, and preheat zone are different from the upward flame spread. Hence, the effects of the fuel arrangement (or gap size) on flame spread are anticipated to be different 10
W. Cui and Y.-T.T. Liao
Fire Safety Journal 110 (2019) 102907
[16] R.O. Weber, A model for fire propagation in arrays, Math. Comput. Model. 13 (12) (1990) 95–102. [17] M.A. Finney, J.D. Cohen, I.C. Grenfell, K.M. Yedinak, An examinatiion of fire spread thresholds in discontinuous fuel beds, Int. J. Wildland Fire 19 (2010) 163–170. [18] A.C. Fernandez-Pello, Flame spread in a forward forced flow, Combust. Flame 36 (1979) 63–78.
[19] A. Vetturini, W. Cui, Y.-T.T. Liao, S. Olson, P. Ferkul, Flame spread over ultra-thin solids: effect of area density and concurrent-opposed spread reversal phenomenon, Fire Technology, 2019 submitted for publication, https://doi.org/10.1007/s1 0694-019-00878-w. [20] J.G. Quintiere, Fundamental of Fire Phenomena, John Wiley & Sons Ltd, West Sussex, England, 2006. [21] J.L. Torero, Scaling-up fire, Proc. Combust. Inst. 34 (1) (2013) 99–124.
11