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Acoustic extinction of laminar line-flames
Fire Safety Journal 93 (2017) 102–113
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Fire Safety Journal j o u r n a l h o m e p a g e : w w w . e l s e v i e r . c o m / l o c a t e / fi r e s a f
Acoustic extinction of laminar line-flames Adam N. Friedman a, b, Stanislav I. Stoliarov b, * a b
Jensen Hughes, Baltimore, MD, 21227, USA Department of Fire Protection Engineering, University of Maryland, College Park, MD, 20742, USA
A R T I C L E I N F O
A B S T R A C T
Keywords: Flame suppression Sound waves Burning rate Spalding B number
A systematic study was conducted to elucidate the effects of acoustic perturbations on laminar diffusion lineflames burning in air, and to determine the conditions required to cause acoustically-driven extinction. Lineflames were produced from the fuels n-pentane, n-hexane, n-heptane, and n-octane using fuel-laden wicks. The wicks were housed inside a burner whose geometry produced line-flames that approximated a two-dimensional flame sheet. The acoustics utilized ranged in frequency from 30 to 50 Hz, and acoustic pressures from 5 to 50 Pa. Prior to acoustic testing, the unperturbed mass loss rates and flame heights were measured. These quantities were found to scale linearly, which is consistent with the Burke-Schumann theory. The mass loss rates associated with hexane-fueled flames experiencing acoustic perturbations were then studied. It was found that the strongest influence on the mass loss rate was the speed of oscillatory air movement experienced by the flame. It was also found that the average mass loss rate increased linearly with the increasing air movement speed. Finally, acoustic perturbations were imposed on the flames from all fuels to determine acoustic extinction criterion. To ascertain if the observed phenomenon was unique to the alkanes tested, flames fueled by JP-8 (a kerosene-based fuel) were also examined. Using the data collected, a model was developed which characterized the acoustic conditions required to cause flame extinction. The model was based on the ratio of a modified Nusselt number to the Spalding B number of the fuel. It was found that at the minimum speaker power required to cause extinction, this ratio was a constant (independent of the chemical nature of the fuel).
1. Introduction Halon 1301 has been the primary non-aqueous fire suppression agent since the 1960's. However, concerns about the environmental impact of this chemical led to a ban on its production. Consequently, the development of Halon replacement technologies has become an active area of research [1]. One of the technologies considered has been the use of acoustics. Early research into the interaction of acoustic waves and flames was focused on droplet burning in turbine engines and combustion chambers; this area continues to be an active field of inquiry [2–5]. Of particular interest are hydrodynamic instabilities created by the acoustics. The physics of these instabilities have been reviewed in detail by O'Connor et al. [6]. Acoustics have also been shown to affect combustion chemistry. Specifically, Sevilla-Esparaza et al. [5] showed that there was a coupling between acoustic pressure and relative concentration of hydroxyl radicals in the flame region surrounding a droplet of liquid fuel. The magnitude of this coupling was found to depend on the frequency of the acoustics, with lower frequencies exhibiting a stronger response.
There has also been a growing body of research on the interaction of acoustics with both premixed and diffusion flames using gaseous fuel sources [7–14]. Generally speaking, the response of these flames to acoustic excitation can be classified as either linear or non-linear with respect to the excitation frequency [13]. Kim and Williams [8] studied the linear responses of a counter-flow diffusion flame to acoustic excitation through a theoretical analysis. They showed that linear responses in the heat release rates, flame chemistry, and mass fluxes were caused by oscillations in the position of the reaction sheet and the magnitude of field variables in the transport zone. Wang et al. [11] studied the non-linear response of puffing frequency to acoustic excitation in buoyant diffusion methane flames. At low acoustic frequencies, they found that the puffing frequency was half the excitation frequency, while at higher acoustic frequencies, the puffing frequency was double the excitation frequency. In both cases, the observed responses were attributed to the acoustic disruption of the natural periodic buoyancy-induced flame instabilities. Along with basic research into the interaction of acoustics and flames, there have also been investigations into practical applications. For
* Corresponding author. E-mail address: [email protected] (S.I. Stoliarov). http://dx.doi.org/10.1016/j.firesaf.2017.09.002 Received 22 December 2016; Received in revised form 14 September 2017; Accepted 15 September 2017 Available online 22 September 2017 0379-7112/© 2017 Elsevier Ltd. All rights reserved.
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Fire Safety Journal 93 (2017) 102–113
fully understood. An investigation into acoustically-driven flame extinction, especially for flames from a stagnant liquid fuel sources, is therefore ripe for inquiry. An apparatus was constructed that produced collimated acoustic waves which could interact with a laminar diffusion line-flame. Fuel to the flame was supplied by a wick, which limited the mechanical interaction between the sound and condensed phase. The fuels chosen for testing were n-pentane, n-hexane, n-heptane and n-octane. By modulating the frequency and amplitude of the acoustics produced, the conditions required to cause extinction of flames from each fuel could be determined. The frequencies tested ranged from 30 to 50 Hz, and the acoustic pressures ranged from 5 to 50 Pa. To confirm that the extinction results were not unique to the alkanes, flames fueled by JP-8 (a kerosenebased fuel used in aviation) were also subjected to the same testing regime.
example, it has been shown that, under certain conditions, acoustics can be used to stabilize combustion of fuel droplets [15] and reduce the production of pollutants in laminar flames [16]. Another potential application that has been studied is use of acoustics to suppress flames [7, 8,12,17,18]. It had been shown as early as 1857 that vocally produced acoustics could cause the extinction of a gas-fueled flame [18]. More recently, Whiteside studied the acoustically driven extinction of gas burner flames [7]. In his study, acoustics in the frequency range of 35–150 Hz and pressure range of 0.2–112 Pa were used to extinguish flames fueled by methane, ethanol, hexane and heptane. Analysis of Whiteside's data showed that as the molar mass and molar heat of combustion of the fuels increased, so too did the acoustic pressure required to cause flame extinction. In addition, the extinction pressure for each fuel was independent of the burner size. Whiteside concluded that the most likely cause of flame extinction was blow-off. The author noted, though, that this mechanism didn't fully explain his results since the flames could exist in a lifted state for short periods. Whiteside further concluded that there was a minimum acoustic velocity required to cause extinction for each fuel, and that acoustic extinction could be achieved at any frequency provided the acoustic pressure was high enough to achieve that velocity. Although not explicitly discussed by the author, Whiteside's data and conclusions are generally consistent with extinction strain-rate theory [2,19–24]. Edmonson and Heap [24] showed that the phenomenon of blow-off was caused by the quenching effect of increased mixing. The magnitude of this effect scaled with the strain rate in the flow of the unburned gases near the burner. If it is assumed that a diffusion flame subjected to an acoustic flow experiences increased strain as the acoustic pressure and velocity increases, then it supports Whiteside's supposition that there exists a threshold acoustic extinction velocity. In addition, Won et al. showed that the extinction strain rate for heavy hydrocarbon fuels scales with the molar heat of combustion [19]. When these results are extrapolated to the lighter hydrocarbons used by Whiteside, it correctly predicts the trend observed between the acoustic extinction velocity and molar heats of combustion for the fuels tested. Underlying extinction strain-rate theory is the understanding that flame stretch enhances transport processes, which in turn compete with combustion reactions [2,25]. Since the effects of transport processes and chemical kinetics are so closely coupled, it is often desirable to represent them in relationship to each other. Such a comparison is often done with a Damk€ ohler number (Da), which is defined as the ratio of a characteristic transport time to a characteristic chemistry time [2,22,23,25,26]. For large values of Da, it is expected that the effects of slow transport processes will dominate, and flame chemistry will occur at a faster rate. As values of Da become smaller, the slower chemical kinetics begins to dominate until the system becomes non-reactive [25]. Therefore, for every flame there is a critical value of Da, below which flame extinction will occur [2,8,26]. A somewhat different extinction mechanism was described by McKinney and Dunn-Rankin [4], who studied the acoustically driven-extinction of methanol droplets. In their study, droplets of various sizes were injected into a resonating tube and exposed to acoustic waves at various frequencies and pressures to identify extinction criteria. They found that at the same frequency, the acoustic pressure required to cause extinction increased with droplet size. They also found that for droplets of the same size, the acoustic pressure required to cause extinction increased with frequency. The authors determined that extinction occurred when the flame was displaced far enough from the droplet that evaporation of the fuel was shut down. The critical magnitude of displacement was determined to be at least the radius of the droplet. While other authors have explored acoustic extinction criterion for gaseous flames from a burner [7,12] and droplet flames [4], there has been no work in this context on flames fueled by a stagnant liquid. The flame from a stagnant liquid represents the most relevant scenario from a fire safety perspective. In addition, the governing phenomena of the observed extinctions, especially in the case of Whiteside's work, are not
2. Experimental setup and results 2.1. Experimental setup overview The primary objective of the experimental design was to create a lineflame that could simultaneously interact with a planar acoustic wave across the entire flame surface. Additional design considerations included the ability to measure the fuel's mass loss rate and observe the effects of a forced flow on the flame. A detailed description of the experimental setup and its components is given by Friedman [27]. As shown in Fig. 1, the setup was composed of four main components: (1) perturbation source, (2) collimator, (3) screened enclosure and (4) burner. Depending on the type of experiment being conducted, the perturbation source was either a speaker or fan mounted at a fixed position inside the collimator. The collimator was a 0.25 m diameter, 3.05 m long PVC tube which was supported by wooden blocks. At the opposite end from the perturbation source, the collimator protruded through an opening into the screened enclosure. Within the screened enclosure, the burner was placed adjacent to the tube opening. Depending on the experiment type, the burner was supported by either metal stands or a mass balance, both of which are shown in the inset of Fig. 1. The burner was designed to produce a laminar diffusion flame of a near planar geometry. To produce this flame, rectangular wicks made from Kaowool PM ceramic fiber were placed inside aluminum-foil-lined insulation panels. For each test, 3.5 mL of fuel was poured along the center line of the wick. Two pieces of 3.2 mm thick borosilicate glass were then placed over the panels, leaving a 5 mm gap through which the
Fig. 1. Schematic of the experimental setup. 103
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conducted to serve as a point of reference for other experiments. Three burns were conducted for each alkane tested, during which time mass readings and videography were obtained simultaneously. Using the mass _ were data collected, discrete values of the mass loss rate (mlr or m) calculated as:
fuel could emanate. Depending on the type of fuel being tested and the time since ignition, the burner produced line-flames that ranged from 0.02 to 0.12 m in width, and 0.02–0.05 m in height. Abbreviated schematics of the burner assembly process are shown in Fig. 2(a) and (b). Front and side images of a representative line-flame are shown in Fig. 2(c) and (d), respectively. A detailed characterization of the experimental setup was conducted, the results of which are described elsewhere [27]. The objectives were to understand the system's harmonics, the acoustic pressures generated, and nature of the acoustically induced air movements. Acoustic pressures were measured using an integrated constant current power microphone. Air speeds were measured using a hot-wire anemometer. Air movements were visualized with clouds of atomized glycerol droplets. Videography of the visualizations was captured with a high speed camera at 400 frames per second. Results of this characterization showed that: (1) the collimator exhibited acoustic resonance at frequencies consistent with those predicted by sound theory; (2) acoustic pressures inside the enclosure showed a steady decay proportional to the distance from the collimator opening; (3) acoustic pressures at the flame position were approximately 1:2 times greater with the burner assembly in place, and this was most likely due to acoustic waves reflecting off the top surface of the burner; (4) anemometer measurements of acoustically induced air movements were indicative of a root mean square (rms) air speed; and (5) there was a positive correlation between acoustic pressure and rms air speed.
m_ i ¼
miþ1 mi ti tiþ1
(1)
The three mlr data sets for each fuel tested were then averaged together and smoothed using a running average with a kernel of ±15 s. This kernel accounted for no more than 15% of the data points from a composite data set. Estimates of the flame's height (Lf ) and width (Wf ) were obtained from analysis of the video recorded during each burn using the process described in detail by Friedman [27]. Mean mlr and Lf are shown as a function of time for each fuel tested in Figs. 3 and 4, respectively. All uncertainties were computed from the scatter of the data as two standard deviations of the mean. 2.2.2. Burning rate during acoustic excitation A study of the flame's burning rate, characterized by wick's mass loss rate, while experiencing acoustic perturbations was conducted. The flames in this study were fueled using hexane, which acted as a surrogate for the other alkanes. As shown in the inset of Fig. 1, the burner was placed on the balance in front of the collimator. The fuel-laden wicks were then ignited and allowed to burn freely until the flame stabilized. After the free-burn period, the speaker was activated and the flame was allowed to burn under acoustic excitation at a constant frequency and acoustic pressure until it self-extinguished. Measurements of the acoustic pressure and rms air speed were then taken at the flame position approximately 0.02 m above the burner. The ranges of acoustic pressures
2.2. Experimental results 2.2.1. Alkane free-burn A study of the line-flame without acoustic perturbations was
Fig. 2. (a) and (b) – assembly process of burner used in this study. (c) and (d) – views of the line-flame from the frontal and medial planes. 104
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Fire Safety Journal 93 (2017) 102–113
and rms air speeds that could be tested were limited by the operational characteristics of the speaker and by the occurrence of acoustic extinction. For each combination of acoustic frequency and pressure, three tests were performed. The results were averaged together using the process previously described to generate mean mlr histories. Representative histories obtained at 30 and 40 Hz and a range of acoustic pressures are shown in Fig. 5. The histories presented begin at speaker activation, which was approximately 20 s after ignition. For reference, the free-burn profile for hexane is shown from ignition. A complete set of these histories, including those at obtained 35 and 45 Hz, can be found elsewhere [27]. To serve as a basis for comparison, an attempt was also made to study the burning rate under various fan-driven flows. During these experiments, the balance acted as a bluff-body obstruction in the flow as it exited the collimator. As a result, large-scale, unsteady, turbulent structures developed around the flame, and precise flow measurements were difficult to obtain. In addition, re-circulation currents often formed too, causing the flame to be drawn toward the collimator in the windward direction. Given the lack of uniformity and unsteady nature of these flows, coupled with the difficulty in obtaining precise measurements, the results of these experiments lacked probative value and have been omitted here.
Fig. 3. Free-burn mean mlr histories for each alkane tested shown as splines of individual data points. The error bars are two standard deviations of the mean.
2.2.3. Acoustically driven extinction Flames produced using the fuels n-pentane, n-hexane, n-heptane and n-octane were subjected to acoustic perturbations at varying frequencies and acoustic pressures to determine extinction conditions. For comparison, the speaker was then replaced with a fan, and the speed of fan-driven flows required to cause extinction of each fuel was also measured. To determine if the results were unique to alkanes, flames fueled by JP-8 were subjected to the same testing procedure. The conditions required to cause acoustic extinction of a particular fuel at a particular frequency (ω) were determined by finding the lowest speaker power that could cause three consecutive extinction events within 10 s of speaker activation. For each test, the flame was allowed to burn unperturbed until it reached a height of approximately 0.02 m. The speaker was then activated and the experimental outcome was noted. Measurements of the acoustic pressure (PA ) and rms acoustic air speed (UA ) were made after every trial at the flame position, approximately 0.02 m above the burner. For those trials where acoustic extinction was achieved, the acoustic pressure ðPA;ext Þ and rms air speed ðUA;ext Þ were calculated as the mean from the three individual trials. The results, including uncertainties, are summarized in Table 1. Graphs of PA;ext and UA;ext are shown in Figs. 6 and 7, respectively. The error bars were omitted from these figures because their values were comparable to the
Fig. 4. Free-burn mean flame height histories for the alkanes tested shown as splines of individual data points. The error bars are two standard deviations of the mean.
Fig. 5. Mean Hexane mlr histories at (a) 30 and (b) 40 Hz and various acoustic pressures and corresponding rms air speeds shown as splines of individual data points. The error bars are two standard deviations of the mean. 105
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size of the data markers used. Included in the legend of each graph are the mean (μ), standard deviation (σ) and coefficient of variation (σ=μ) for the aggregate data set. Along with measurements of acoustic pressure and rms air speed, high speed video of several acoustic extinction events was also captured. A sample sequence of frames from a hexane fueled flame experiment, just prior to total flame extinction, is shown in Fig. 8. The flame shown is being perturbed by 35 Hz acoustic waves, traveling right-to-left, at an acoustic pressure of 19.4 Pa and rms air speed of 0.76 m s1. The sequence shows the flame through approximately one acoustic cycle. The flame begins over the wick, the center of which is indicated by the red marker. As the acoustic wave passes, the flame is displaced from the wick. Near the end of the acoustic cycle, a new flamelet is seen emerging through the gap between the glass panes. The air speed of the fan-driven flow required to cause extinction (UF;ext ) for each fuel was determined by finding the lowest fan power that could cause three consecutive extinction events within 10 s of fan activation. The air speed was measured using an anemometer at the same position as that used in the acoustic extinction experiments. Values of UF;ext were then calculated as the mean of the three individual trials. The results, including uncertainties, are summarized in Table 2. Values of UF;ext are shown graphically in Fig. 9, where they are plotted against the fuel's molar mass for visual clarity. During the fan-driven extinction experiments, the flame lost its normal incandescent coloring and took on a faint blue hue. As a result, the flames were difficult to see and could not be captured easily using high speed videography. It was still desirable, though, to visualize the fan-driven flow over the burner. This was done with a cloud of atomized glycerol droplets, using the methodology described in detail elsewhere [27]. Visualizations of the fan flow at 400 and 600 ms after fan activation are show in Fig. 10. The faint outline of a boundary layer forming over the burner can be seen at 400 ms. By 600 ms, a clearly defined boundary layer has fully formed over the burner.
Fig. 6. Acoustic pressure at extinction measured for each fuel at different sound frequencies. The reported mean (μ), standard deviation (σ) and coefficient of variation (σ/μ) are for the aggregate data set.
3. Analysis and discussion 3.1. Alkane free-burn Reexamining Figs. 3 and 4, there is an obvious qualitative relationship between the profiles of mlr and Lf for each fuel. Specifically, each profile shows peak values and points of inflection at approximately the same times. Since the burner used in this study was sui generis, existing flame height correlations are likely to be inadequate. Therefore, an Fig. 7. rms air speed at extinction for each fuel at different sound frequencies. The reported mean (μ), standard deviation (σ) and coefficient of variation (σ/μ) are for the aggregate data set.
Table 1 Acoustic flame extinction results. The uncertainties are two standard deviations of the mean. Fuel
ω (Hz)
PA;ext (Pa)
Pentane
30 35 40 30 35 40 45 30 35 40 45 50 30 35 40 45 30 35 40 45
16.2 22.2 35.5 14.6 19.5 27.0 28.4 13.7 15.9 26.6 25.5 29.9 14.7 16.6 25.3 29.9 16.1 24.3 23.2 20.6
Hexane
Heptane
Octane
JP-8
± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ±
0.1 0.2 0.2 0.1 0.1 0.2 0.2 0.1 0.1 0.2 0.2 0.2 0.1 0.1 0.2 0.2 0.1 0.1 0.2 0.1
analysis of a relationship between mlr and Lf was conducted. Since these quantities were measured in time, a direct comparison on a temporal _ basis was made. The mass loss rate normalized by the flame width (m') was calculated as:
U A;ext (m s1) 0.71 0.86 0.95 0.65 0.75 0.68 0.86 0.58 0.60 0.72 0.72 0.74 0.60 0.58 0.60 0.64 0.57 0.55 0.59 0.66
± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ±
0.02 0.03 0.03 0.02 0.02 0.02 0.03 0.02 0.02 0.02 0.02 0.02 0.02 0.02 0.02 0.02 0.02 0.02 0.02 0.03
_ ¼ m_ Wf m'
(2)
where Wf is the width of the line-flame. A heat release rate per unit flame _ was then calculated as: width (Q')
_ ¼ Δhc m' _ Q'
(3)
where values for the heat of combustion per unit mass, Δhc , were obtained from the literature and are presented in Table 4, which is introduced in a subsequent section of the manuscript. Values of Lf were then _ as shown in Fig. 11. plotted against corresponding values of Q', Close examination of Fig. 11 showed that values of Lf < 0:01 m were _ This value appeared to constitute a clustered about a constant value of Q'. 106
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Fig. 8. High speed video frames of hexane fueled flame, just prior to extinction at (a) þ4 ms, (b) þ12 ms, (c) þ20 ms, and (d) þ28 ms from the start of an acoustic cycle. The flame is experiencing perturbations at 35 Hz, 19.4 Pa of acoustic pressure, and an rms air speed of 0.76 m s1. The sequence shows the flame through approximately one acoustic cycle. The red marker indicates the center of the wick. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)
minimum heat release rate, below which a flame could not exist. On average, this value was found to be 3.7 kW/m. For values of Lf 0:01 m, there appeared to be an approximately linear relationship between Lf and _ This relationship was fitted as: Q'.
Table 2 Fan-driven flame extinction test results. The uncertainties are two standard deviations of the mean. Fuel
U F;ext (m s1)
Pentane Hexane Heptane Octane JP-8
1.55 1.58 1.89 1.96 2.03
± ± ± ± ±
0.03 0.03 0.04 0.04 0.08
Lf ¼
3:9 103
m2 _ ' Q 4:5 103 m kW
(4)
The results of this fitting exercise are shown in Fig. 11. Since the lineflames produced by all fuels were in the laminar regime during free-burn, _ is consistent with the Burkethe linear relationship between Lf and Q' Schumann theory [28]. 3.2. Mass loss rate during acoustic excitation Reexamining the hexane mlr profiles presented in Fig. 5, certain qualitative trends are apparent. As the acoustic pressure and rms air speed increased, flame growth was accelerated. After peak mlr was achieved, though, most profiles converged towards the free-burn profile. For a more quantitative analysis, the average mass loss rate (mlr) was used to characterize each mass loss rate time dependence. Values of mlr were calculated as the ratio of the total mass lost by the wick to the total burn time. These values were then plotted against PA and UA for comparison; the results are shown in Fig. 12 and Fig. 13, respectively. These figures demonstrate near linear relationships that were captured by the following expressions:
Fig. 9. Fan-driven air speeds required to cause extinction. The error bars are two standard deviations of the mean. The reported mean (μ), standard deviation (σ) and coefficient of variation (σ/μ) are for the aggregate data set.
mg mg PA þ 7:2 mlr ¼ 0:31 s⋅Pa s
(5)
mg mg UA þ 8:2 mlr ¼ 10:4 m s
(6)
The coefficient of determination (R2 ) is notably higher for the linear 107
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Fig. 10. Visualization of fan-driven flow over the burner at the air speed of 1.6 m s1 at (a) 400 ms and (b) 600 ms after the fan activation.
Fig. 11. Relation between flame height and heat release rate (HRR) per unit flame width observed for unperturbed flames.
Fig. 13. Relation between rms air speed and average mass loss rate.
Although not perfectly analogous, the link between the speed of oscillatory air movement and burning rate is consistent with the observations of other authors. In studies of flame spread in opposed flows, both Fernandez-Pello et al. [29] and De Ris [30] showed that increased flow speed enhanced burning rate. This behavior was due to the flames being forced closer to the fuel surface, which enhanced heat transfer into the fuel bed. By studying the burning rate of gasoline pool fires in cross-flows, Hu et al. [31] showed that this same mechanism leads to a linear correlation between the flow speed and burning rate. It is reasonable to conclude that a similar phenomenon was occurring due to the oscillatory air movement over the fuel: as the rms air speed increased, the flame was forced closer to the wick which increased heat transfer to the liquid fuel. This mechanism would then explain both the positive correlation and linearity of the relationship between mlr and UA . 3.3. Acoustic and fan-driven flame extinction 3.3.1. Comparison of results Reexamining the extinction pressures in Fig. 6, and rms air speeds in Fig. 7, each curve can be thought of as delineating condition between where the flame could and could not exist. For conditions where values of PA < PA;ext and UA < UA;ext , the flame could continue to burn; for conditions where values of PA PA;ext and UA UA;ext , total flame extinction occurred. The amount of scatter in the values of PA;ext (σ=μ ¼ 0:27) obtained for different fuels and at different frequencies was found to be significantly greater than the amount of scatter observed in the values of UA;ext (σ=μ ¼ 0:16). This finding indicated that the mean value of UA;ext
Fig. 12. Relation between acoustic pressure and average mass loss rate.
fit of mlr versus UA (R2 ¼ 0.91) than for the mlr versus PA (R2 ¼ 0.83). This finding indicates that the rms air speed had a stronger influence on the average mass loss rate, and further suggests that the acoustic pressure only influenced mlr values insofar as it affected the rms air speed.
108
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was a more universal predictor of flame extinction than the corresponding acoustic pressure. To give further insight into the values of UA;ext , they were compared to the values UF;ext for the corresponding fuels. On average, the values of UF;ext were found to be 2:5 times greater than the values of UA;ext . More significantly, there was reversal in the “ordering” of the fuels between the two data sets. As indicated in Fig. 14, the values of UF;ext were observed to increase as the molar mass and the molar heat of combustion (ΔHc ) of the fuel increased, while values of UA;ext were observed to decrease. The data are plotted against the molar heat of combustion, which is proportional to the fuel's molar mass.
3.3.3. Proposed acoustic extinction mechanism To understand how an acoustic extinction mechanism would work, a simplified model of the flame is utilized: fuel enters the flame region and reacts with the oxidizer; heat is released, a portion of which is fed back into the fuel source; this drives more fuel into the flame region. In this model the propensity of the fuel to maintain this cycle is best described by the Spalding mass transfer number (B), and a large disruption to this cycle would cause flame extinction. Reexamining the image sequence presented in Fig. 8, it can be seen that as the acoustic wave propagates over the burner, it temporarily displaces the flame from the region above the wick. In contrast to the fandriven flows, the flame is not confined to a boundary layer, and the fuel bed is periodically exposed directly to cool air. During the displacement period, it is assumed that the fuel bed experiences convective cooling from the acoustic flow passing over it. The magnitude of this cooling can be characterized by a local Nusselt number (Nuξ ). The combination of forced flow over the flame and displacement of the flame creates two competing processes. At acoustic pressures and rms air speeds below PA;ext and UA;ext , heat transfer to the fuel bed is enhanced in a mechanism similar to that in traditional forced flows. This additional heating compensates for the cooling that occurs during the flame's displacement. At a critical point, though, convective losses during the flame's displacement begin to overwhelm the effects of enhanced heat transfer. From the stagnant layer theory, it is known that as the heat flux from the flame into the fuel bed decreases, so too will the burning rate [22]. Furthermore, according to the fire point theory described by Rashbash [34,35], there is a critical mass flux for any given fuel, below which total flame extinction will occur. It would be reasonable to conclude that at the point acoustic extinction was achieved, convective cooling of the fuel bed during the flame's displacement had created conditions for such extinction conditions. In the model proposed, the B number characterizes a fuel's ability to maintain the flame-fuel-supply cycle, and a Nusselt number characterizes the amount of disruption to this cycle. A ratio of these two nondimensional numbers might then constitute a criterion by which acoustic extinctions can be predicted. For consistency with Figs. 6 and 7, it would be useful to structure this ratio so that larger values correspond with flame extinction, while smaller values correspond with continued burning. It is, therefore, proposed that the ratio of Nuξ to B at the point where acoustic extinction was achieved is a constant, and that this value forms a boundary delineating conditions where the flame can and cannot exist. As shown in Equation (8), this ratio shall be called ΘA ; the terms of this equation will be further developed in the following sections.
3.3.2. Discussion of observations As previously noted, the fan-driven flows produced a boundary layer over the burner, which is shown in Fig. 10. The flames in these experiments were, therefore, similar to the flames in a forced flow over a stagnant fuel film studied by Emmons [32]. In his analysis of such flames, he showed that the flame existed in the boundary layer of the flow, and that it separated the region of cooler air above the flame from the fuel below it. As the free-stream velocity of the flow increased, the boundary layer thickness decreased and strain rate increased. Extinction occurred when the free-stream velocity and corresponding strain rate became so great that chemical reactions driving combustion could not compete with the mixing rate of the reactants, and the value of Da dropped below a critical value [32,33]. Won et al. [19] showed that the extinction strain rate (aE ) for diffusion flames fueled by hydrocarbons scales as:
aE ∝½DF YF;∞ ΔHc ½kinetic term
(7)
where DF is the diffusivity of the fuel into oxidizer, and YF;∞ is the fuelmass fraction on the fuel side of the reaction zone, which is close to unity for the conditions used in this study. Provided that the diffusivities of the fuels are similar, the extinction strain rate should, therefore, scale with the fuels' molar heats of combustion. Using the results from Emmons and Won, it can be concluded that for the fan-driven extinctions, values of UF;ext and ΔHc should show a positive correlation. Reexamining the plot in Fig. 14, this was precisely the trend that was observed. In contrast, the values of UA;ext were observed to decrease with increasing ΔHc . Furthermore, values of UF;ext were significantly greater than UA;ext . These observations suggest that flame stretch was not the extinction mechanism in the acoustic experiments, and that an alternative mechanism must be found.
ΘA ¼
Nuξ B
(8)
3.3.4. Spalding B number In a study of ethanol and heptane pool fires of various areas with varying crosswinds, Hu et al. [36] found that the radiative portion of the heat flux from flame to liquid fuel decreased significantly as the fuel area decreased and the crosswind increased. For their smallest heptane pool fire, which had an area of 10 cm2, at crosswind air speed of 0.7 m s1, the radiative portion was 10%. In the experiments of the present study, the exposed wick area was only 2.5 cm2 while air speeds were comparable. Thus, the gasification of the fuel can be considered to be driven exclusively by convective heat transfer. With this assumption, Quintiere [22] gives the B number as:
B¼
YO2 ;∞ ðΔhc =rÞ cp;air ðTb T∞ Þ L
(9)
where YO2 ;∞ ¼ 0:233 is the mass fraction of oxygen in ambient air; T∞ ¼ 298 K is the ambient temperature; and cp;air is the air heat capacity evaluated at 12 ðT∞ þ Tb Þ. The stoichiometric fuel oxidizer mass ratio, r, boiling point, Tb , and heat of gasification, L, are fuel properties. The air
Fig. 14. Comparison of UF;ext and UA;ext at 35 Hz for the different fuels studied. 109
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and fuel properties are summarized in Tables 3 and 4, respectively. The fuel properties were amalgamated from a range of sources discussed in detail by Friedman [27]. Some of the air properties reported in Table 3 were used in the evaluation of the Nusselt number and are discussed in a subsequent section.
Table 3 Properties of air used for different fuels [37].
3.3.5. Nusselt number correlation Nusselt number correlations are based on the assumption that convective heat transfer scales with momentum transfer [37,38]. Therefore, a Reynolds Number (Re) was needed, which in turn required a characteristic length (ℓ) to be defined. For a sound-driven flow, this length can be specified as the rms displacement of a particle in an acoustic cycle, and calculated as:
ℓ¼
UA ω
cp;air (J kg1 K1)
νair (m2 s1)
Pentane Hexane Heptane Octane JP-8
309 342 372 399 456
1007 1008 1008 1009 1012
1.68 2.01 2.33 2.63 3.16
r
Fuel Pentane Hexane Heptane Octane JP-8
(10)
UA ℓ U2 ¼ A νair νair ω
T b (K)
105 105 105 105 105
Pr 0.706 0.701 0.696 0.690 0.686
Table 4 Calculated fuel properties [27].
Using Equation (10), the Reynolds number for the acoustic flow was defined as:
ReA ¼
Fuel
3.55 3.53 3.51 3.50 3.40
L (J kg1) 3.93 4.59 5.24 5.84 6.21
Δhc (J kg1) 5
10 105 105 105 105
45.4 45.1 44.9 44.8 42.8
6
10 106 106 106 106
B 7.54 6.39 5.54 4.93 4.49
(11)
where νair is the kinematic viscosity of air taken at Tb . These viscosity values are given in Table 3. Unfortunately, Nusselt number correlations are not well studied for oscillating flows [39]. Here, it was assumed that a functional correlation between a local Nusselt number at the flame position and the Reynolds and Prandtl (Pr) numbers is analogous to that for a non-oscillating flow over a flat plate [37,38]:
Nuξ ¼ cReγA Prδ
(12)
where the values of c; γ and δ are empirical constants. Examining Table 3, it can be seen that the values of Pr are practically constant for all fuels used. Since the value of c in Equation (12) is also a constant, the substitution C ¼ cPrδ was made, which yielded:
Nuξ ¼ CReγA
(13)
A modified Nusselt number (Nuξ ') was then defined as Nuξ ' ¼ Nuξ =C. Substituting this expression into Equation (13) yielded:
Nuξ ' ¼ ReγA
Fig. 15. Calculated values of Θ'A at the lowest speaker power that could consistently cause total flame extinction. The reported mean (μ), standard deviation (σ) and coefficient of variation (σ=μ) are for the aggregate data set.
(14)
Finally, replacement of Nuξ with Nuξ ' in Equation (8) yielded:
Θ'A ¼
ReγA B
verify this model, additional experiments were conducted under the conditions other than those corresponding to the minimum speaker power required for extinction. The results of these experiments are summarized in Table 5 together with the corresponding values of Θ'A .
(15)
3.3.6. Model optimization and validation The value of γ in Equation (15) was optimized to reduce the scatter in Θ'A values computed for the acoustic extinction events achieved using the minimum speaker power; details of this optimization process can be found elsewhere [27]. From this process, it was determined that γ ¼ 1=3 was the optimal value. It is worth noting that most Nusselt number correlations for flows over a flat plate scale as Re1=2 ½37; 38. In its final form, Equation (15) became:
'
When these results are plotted with respect to ΘA ¼ 1:4, as shown in Fig. 16, it becomes apparent that this parameter clearly delineates between conditions where flame can and cannot exist. 3.3.7. Model application to fan driven extinction To determine whether the proposed acoustic extinction mechanism was also consistent with the fan-driven extinction, the acoustic extinction model was applied to the fan-driven extinction results. In this case, the characteristic length ℓ was taken to be the distance from windward edge of the burner to the center of the fuel wick, which was 0.067 m. The Reynolds number was calculated as:
2=3
Θ'A ¼
UA
(16)
ðνωÞ1=3 B
As shown in Fig. 15, application of this expression to the acoustic extinction data yields highly consistent results. The mean value of Θ'A for
ReF ¼
'
the aggregate data set, μ ¼ ΘA ¼ 1:4, is within 4% of all individual values of this parameter. This means that Θ'A is a much more consistent descriptor of conditions at extinction than the mean values of PA;ext or UA;ext . For values of Θ'A < 1:4, a flame was expected to continue burning; for values of Θ'A 1:4, total flame extinction was expected. To further
UF ℓ νair
(17)
where UF was the air speed measured at the flame position, approximately 0.02 m above the burner. Substituting this Reynolds number into Equation (15) yielded:
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Table 5 Summary of acoustic perturbation experiments where the speaker power setting was other than the minimum required to consistently cause flame extinction. Fuel
ω (Hz)
U A (m s1)
Extinction
Θ'A
Pentane Pentane Hexane Hexane Heptane Heptane Heptane Heptane Heptane Octane JP-8
30 30 30 35 30 35 45 45 50 30 40
0.61 0.77 0.52 0.69 0.48 0.53 0.69 0.86 0.78 0.50 0.61
No Yes No No No No No Yes Yes No Yes
1.20 1.41 1.20 1.38 1.25 1.26 1.38 1.41 1.45 1.38 1.51
Fig. 17. Calculated values of Θ'F for the fan-driven extinctions at the lowest fan power required to consistently cause flame extinction. The error bars are uncertainties propagated from the UF;ext data (shown in Table 2). The reported mean (μ), standard deviation (σ) and coefficient of variation (σ=μ) are for the aggregate data set.
Fig. 16. Values of Θ'A calculated for the acoustic perturbation experiments where the speaker power setting was other than the minimum required to consistently cause flame extinction.
Θ'F ¼
ðUF ℓÞ1=3 1=3
νair B
(18)
The values of Θ'F computed for the fan driven extinctions achieved at the minimum fan power are shown in Fig. 17. In contrast to the acoustic results, the values of Θ'F showed an increased scatter when compared to UF;ext values shown in Fig. 9. This calculation further confirmed that the acoustic and fan-driven extinctions occur through different mechanisms.
Fig. 18. Minimum speaker power required to achieve consistent acoustic extinction. Each point is the average power used by the speaker for the extinction events summarized in Table 1. The dashed black line indicates the maximum operating power of the speaker used.
3.3.8. Potential application of acoustic extinction The speaker used in this study had a maximum operating power of 250 W. This power limit placed significant constraints on the range of acoustic frequencies and pressures that could be tested. As shown in Fig. 18, the minimum speaker power required to cause flame extinction increased dramatically with increasing frequency. It stands to reason, though, that if the speaker had been rated for a higher power, acoustic extinction could have been achieved at higher frequencies. This supposition is consistent with the findings of Whiteside [7], who concluded that acoustic extinctions occur at any frequency, provided that a critical acoustic air speed is also achieved. When compared to other flame suppression techniques, the concept of acoustic flame suppression has several unique advantages. Chief among these advantages is that there is no flame suppressing agent that needs to be applied. It would therefore be beneficial to consider whether acoustics could be used to suppress a relatively large fire. To do so, a 1 m diameter, heptane pool fire was considered, and the sound parameters
required to extinguish this fire at ω ¼ 30 Hz were estimated. According to the model developed, acoustic flame extinction requires the oscillatory movement of air to be sufficiently fast and high in amplitude to convectively cool the fuel bed. An implicit assumption within this statement is that, to achieve extinction, not only must the proposed extinction criterion Θ'A be greater than 1.4, but the rms displacement distance (ℓ) defined by Equation (10) must also be at least as large as the fuel bed size. This additional condition for extinction is consistent with the observations of McKinney and Dunn-Rankin [4]. In all experiments where extinction was attempted, including those where it was not achieved, this condition was satisfied. For the experiments the results of which are listed in Table 1, the average value of ℓ was 1.8 cm, which is almost 4 times greater than the width of the exposed fuel bed. While the current data indicate that this condition is necessary but not sufficient to achieve extinction, it can still be used to estimate the minimum sound pressure required to extinguish substantially larger fires. To achieve ℓ ¼ 1 m (equal to that of the pool diameter), the rms air 111
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speed produced by 30 Hz acoustics needs to reach 30 m s1, in accordance with Equation (10). Using the characteristic impedance of air ðZw Þ at 20 C, which is given as 412 Pa s m1 [40], the acoustic pressure can be calculated as:
PA ¼ UA Zw
mlr dropped below the critical value needed to sustain a flame. To explore this hypothesis, a simple model was proposed. In this model, the Spalding B number was used to characterize the fuel's propensity to sustain combustion, and a local Nusselt number was used to characterize the convective cooling of the fuel bed. Mathematical expressions were developed for each term, and they were evaluated using values reported in the literature, and conditions measured during the experiments. It was found that at the minimum speaker power required to cause extinction, the ratio of a modified Nusselt number to the fuel's B number was a constant. Application of the model to additional data sets showed that when this ratio was below this constant, the flame continued to burn. When this ratio was greater than or equal to this constant, flame extinction occurred. It was therefore asserted that this constant constituted a boundary between regions of flammability and flame extinction, and served as a reliable predictor of the acoustically-driven extinction events for small fire sizes explored in this study.
(19)
The results from Equation (19) show that an acoustic pressure of 12.4 kPa or 176 dB would be required to suppress the flame. Typical commercial sub-woofers produce acoustics no louder than 110 dB at 1 m distance [41]. Taking into account that dB is a logarithmic unit, it would therefore be extremely difficult to engineer a practical device for acoustic suppression of a fire of this size. 4. Conclusions An experimental setup was constructed to study the interaction of acoustic waves with laminar, near-planar, diffusion flames burning in air. The acoustics utilized ranged in frequency from 30 to 50 Hz and acoustic pressures from 5 to 50 Pa. To produce these flames, fuel-laden wicks were placed under panes of borosilicate glass, leaving a small gap through which the fuel vapor emanated. The fuels used in the study were the alkanes, n-pentane through n-octane. To confirm that the acoustic extinction experiments were not unique to the alkanes, flames fueled by JP-8 were also tested. Prior to acoustic testing, studies of the alkane flames' unperturbed burning rate, height and width were conducted. Flames from each alkane were produced on a mass balance and allowed to evolve without acoustic excitation. During the evolution, mass readings were obtained while simultaneously obtaining videography. Mass loss rates were evaluated from the temporally indexed mass readings of the balance. Estimates of the flame height and flame width were made from analysis of the videos. Using each fuel's heat of combustion, a direct comparison was made between each flame's height and heat release rate per unit flame width. An approximately linear relationship was observed between these quantities, which is consistent with the Burke-Schumann theory [28]. To more thoroughly understand the effects of the acoustics on the flame, a study of the flame's burning rate under acoustic excitation was carried out. Hexane fueled flames were generated on a mass balance, and allowed to evolve under various combinations of acoustic frequency and pressure. It was observed that the introduction of acoustics enhanced mass loss rate from the wick. Once peak mlr was achieved, most mass loss rate histories converged towards the free burn profile. Analysis showed that there was a linear correlation between the average mlr and the rms air speed of the acoustics. This observed relationship is consistent with the results from studies where flames were subjected to forced flows [29,30]. Finally, a study of acoustically-driven extinction was performed using the alkanes and JP-8. Samples were ignited and subjected to acoustic perturbations at various frequencies and speaker powers until the minimum speaker power was found that could cause three consecutive flame extinctions. After flame extinction, the acoustic pressure and rms air speeds were measured. As a basis for comparison, the minimum fandriven flows required to cause flame extinction for each fuel were also evaluated. Analysis of the data showed that the fan-driven air speeds required to cause extinction increased with the fuel's molar heat of combustion. This trend is consistent with the extinction strain rate theory [19,32]. For acoustically-driven extinctions, though, the rms air speed at extinction was seen to decrease with the fuel's molar heat of combustion. It was therefore concluded that flame stretch was not the cause of these extinctions and that an alternate explanation was needed. Analysis of high speed video recorded during acoustic extinction revealed that the flame was periodically displaced from the region over the fuel bed. It was theorized that, as the acoustic flow passed over, the fuel bed experienced convective cooling. At the point acoustic extinction was achieved, the cooling effect had become so great that the fuel's
Acknowledgements Initial funding for this research was provided by the Federal Aviation Administration grant #12-G-011. Subsequently, Adam Friedman was supported by an appointment to the Student Research Participation Program at the U.S. Army Research Laboratory, administered by the Oak Ridge Institute for Science and Education, through an inter-agency agreement between the U.S. Department of Energy and USARL. The authors are grateful to Dr. Ed Habtour, Dr. Asha Hall , Mr. Brent Mills and Dr. Nancy Vyas for providing equipment, resources and facilities that made this project possible. References [1] J. McDougal, D. Dodd, Air Force approach to risk assessment for Halon replacements, Toxicol. Lett. 68 (no. 1) (1993) 31–35. [2] F. Williams, Combustion Theory, second ed., Benjamin Cummings Publishing Company, Melon Park, California, 1985. [3] W. Strahle, A Theoretical Study of Droplet Burning: Transient and Periodic Solutions, 1963. [4] D. McKinney, D. Dunn-Rankin, Acoustically driven extinction in a droplet stream flame, Combust. Sci. Technol. 161 (no. 1) (2000) 27–48. [5] C. Sevilla-Esparza, J. Wegener, S. Teshome, J. Rodriguez, O. Smith, A. Karagozian, Droplet combustion in the presence of acoustic excitation, Combust. Flame 161 (no. 6) (June 2014) 1604–1619. [6] J. O'Connor, V. Acharya, T. Lieuwen, Transverse combustion instabilities: acoustic, fluid mechanic, and flame processes, Prog. Energy Combust. Sci. 49 (August 2015) 1–39. [7] G. Whiteside, Instant Flame Suppresion; Phase II - Final Report, U.S. Department of Defense, 2013. [8] J. Kim, F. Williams, Contribution of strained diffusion flames to acoustic pressure response, Combust. Flame 98 (no. 3) (1994) 279–299. [9] H. Wang, J. Bechtold, C. Law, Forced oscillation in diffusion flames near diffusive–thermal resonance, Int. J. Heat Mass Transf. 51 (no. 3–4) (February 2008) 630–639. [10] S. Kartheekeyan, S. Chakravarthy, An experimental investigation of an acoustically excited laminar premixed flame, Combust. Flame 146 (no. 3) (August 2006) 513–529. [11] Q. Wang, H.W. Huang, H.J. Tang, M. Zhu, Y. Zhang, Nonlinear response of buoyant diffusion flame under acoustic excitation, Fuel 103 (January 2013) 364–372. [12] Y. Hardalupas, A. Selbach, Imposed oscillations and non-premixed flames, Prog. Energy Combust. Sci. 28 (no. 1) (2002) 75–104. [13] L. Chen, Q. Wang, Y. Zhang, Flow characterisation of diffusion flame under nonresonant acoustic excitation, Exp. Therm. Fluid Sci. 45 (2013) 227–233. [14] L. Chen, Application of {PIV} measurement techniques to study the characteristics of flame–acoustic wave interactions, Flow Meas. Instrum. 45 (2015) 308–317. [15] A. Miglani, S. Basu, R. Kumar, Suppression of instabilities in burning droplets using preferential acoustic perturbations, Combust. Flame 161 (no. 12) (December 2014) 3181–3190. [16] K. Deng, Z. Shen, M. Wang, Y. Hu, Y. Zhong, Acoustic excitation effect on {no} reduction in a laminar methane-air flame, Energy Procedia 61 (2014) 2890–2893. [17] S. Nair, Acoustic Characterization of Flame Blowout Phenomenon, Georgia Institute of Technology, 2006. [18] J. Tyndall, Sound: a Course of Eight Lectures Delivered at the Royal Institution of Great Briton, Longmans, Green, and Co, , London, 1867, p. 227. [19] S. Won, S. Dooley, F. Dryer, Y. Ju, A radical index for the determination of the chemical kinetic contribution to diffusion flame extinction of large hydrocarbon fuels, Combust. Flame 159 (no. 2) (2012) 541–551.
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[20] K. Kuo, R. Acharya, Fundamentals of Turbulent and Multiphase Combustion, John Wiley & Sons, Hoboken, New Jersey, 2012. [21] B. Karlovitz, D. Denniston, D. Knapschaefer, F. Wells, Studies on Turbulent Flames: a. flame propagation across velocity gradients B. turbulence measurement in flames, Symp. Int. Combust. 4 (no. 1) (1953) 613–620. [22] J. Quintiere, Fundamentals of Fire Phenomena, West Sussex, John Wiley & Sons, 2006. [23] S. Turns, An Introduction to Combustion, 3 ed., McGraw-Hill, New York, New York, 2007. [24] H. Edmondson, M. Heap, A precise test of the flame-stretch theory of blow-off, Symp. Int. Combust. 12 (no. 1) (1969) 1007–1014. [25] S. McAllister, J. Chen, A. Fernandez-Pello, Fundamentals of Combustion Processes, Springer, New York, NY, 2011. [26] V. Lecoustre, P. Narayanan, H. Baum, A. Trouve, Local extinction of diffusion flames in fires, Fire Saf. Sci. 10 (2011) 583–595. [27] A. Friedman, Interaction of Acoustic Waves with a Laminar Line-flame, University of Maryland, College Park, 2016. [28] C. Law, Combustion Physics, Cambridge University Press, New York, NY, 2006. [29] A. Fernandez-Pello, S. Ray, I. Glassman, Flame spread in an opposed forced flow: the effect of ambient oxygen concentration, Symp. Int. Combust. 18 (no. 1) (1981) 579–589. [30] J. De Ris, Spread of a laminar diffusion flame, Symp. Int. Combust. 12 (no. 1) (1969) 241–252.
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Contents lists available at ScienceDirect
Fire Safety Journal j o u r n a l h o m e p a g e : w w w . e l s e v i e r . c o m / l o c a t e / fi r e s a f
Acoustic extinction of laminar line-flames Adam N. Friedman a, b, Stanislav I. Stoliarov b, * a b
Jensen Hughes, Baltimore, MD, 21227, USA Department of Fire Protection Engineering, University of Maryland, College Park, MD, 20742, USA
A R T I C L E I N F O
A B S T R A C T
Keywords: Flame suppression Sound waves Burning rate Spalding B number
A systematic study was conducted to elucidate the effects of acoustic perturbations on laminar diffusion lineflames burning in air, and to determine the conditions required to cause acoustically-driven extinction. Lineflames were produced from the fuels n-pentane, n-hexane, n-heptane, and n-octane using fuel-laden wicks. The wicks were housed inside a burner whose geometry produced line-flames that approximated a two-dimensional flame sheet. The acoustics utilized ranged in frequency from 30 to 50 Hz, and acoustic pressures from 5 to 50 Pa. Prior to acoustic testing, the unperturbed mass loss rates and flame heights were measured. These quantities were found to scale linearly, which is consistent with the Burke-Schumann theory. The mass loss rates associated with hexane-fueled flames experiencing acoustic perturbations were then studied. It was found that the strongest influence on the mass loss rate was the speed of oscillatory air movement experienced by the flame. It was also found that the average mass loss rate increased linearly with the increasing air movement speed. Finally, acoustic perturbations were imposed on the flames from all fuels to determine acoustic extinction criterion. To ascertain if the observed phenomenon was unique to the alkanes tested, flames fueled by JP-8 (a kerosene-based fuel) were also examined. Using the data collected, a model was developed which characterized the acoustic conditions required to cause flame extinction. The model was based on the ratio of a modified Nusselt number to the Spalding B number of the fuel. It was found that at the minimum speaker power required to cause extinction, this ratio was a constant (independent of the chemical nature of the fuel).
1. Introduction Halon 1301 has been the primary non-aqueous fire suppression agent since the 1960's. However, concerns about the environmental impact of this chemical led to a ban on its production. Consequently, the development of Halon replacement technologies has become an active area of research [1]. One of the technologies considered has been the use of acoustics. Early research into the interaction of acoustic waves and flames was focused on droplet burning in turbine engines and combustion chambers; this area continues to be an active field of inquiry [2–5]. Of particular interest are hydrodynamic instabilities created by the acoustics. The physics of these instabilities have been reviewed in detail by O'Connor et al. [6]. Acoustics have also been shown to affect combustion chemistry. Specifically, Sevilla-Esparaza et al. [5] showed that there was a coupling between acoustic pressure and relative concentration of hydroxyl radicals in the flame region surrounding a droplet of liquid fuel. The magnitude of this coupling was found to depend on the frequency of the acoustics, with lower frequencies exhibiting a stronger response.
There has also been a growing body of research on the interaction of acoustics with both premixed and diffusion flames using gaseous fuel sources [7–14]. Generally speaking, the response of these flames to acoustic excitation can be classified as either linear or non-linear with respect to the excitation frequency [13]. Kim and Williams [8] studied the linear responses of a counter-flow diffusion flame to acoustic excitation through a theoretical analysis. They showed that linear responses in the heat release rates, flame chemistry, and mass fluxes were caused by oscillations in the position of the reaction sheet and the magnitude of field variables in the transport zone. Wang et al. [11] studied the non-linear response of puffing frequency to acoustic excitation in buoyant diffusion methane flames. At low acoustic frequencies, they found that the puffing frequency was half the excitation frequency, while at higher acoustic frequencies, the puffing frequency was double the excitation frequency. In both cases, the observed responses were attributed to the acoustic disruption of the natural periodic buoyancy-induced flame instabilities. Along with basic research into the interaction of acoustics and flames, there have also been investigations into practical applications. For
* Corresponding author. E-mail address: [email protected] (S.I. Stoliarov). http://dx.doi.org/10.1016/j.firesaf.2017.09.002 Received 22 December 2016; Received in revised form 14 September 2017; Accepted 15 September 2017 Available online 22 September 2017 0379-7112/© 2017 Elsevier Ltd. All rights reserved.
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fully understood. An investigation into acoustically-driven flame extinction, especially for flames from a stagnant liquid fuel sources, is therefore ripe for inquiry. An apparatus was constructed that produced collimated acoustic waves which could interact with a laminar diffusion line-flame. Fuel to the flame was supplied by a wick, which limited the mechanical interaction between the sound and condensed phase. The fuels chosen for testing were n-pentane, n-hexane, n-heptane and n-octane. By modulating the frequency and amplitude of the acoustics produced, the conditions required to cause extinction of flames from each fuel could be determined. The frequencies tested ranged from 30 to 50 Hz, and the acoustic pressures ranged from 5 to 50 Pa. To confirm that the extinction results were not unique to the alkanes, flames fueled by JP-8 (a kerosenebased fuel used in aviation) were also subjected to the same testing regime.
example, it has been shown that, under certain conditions, acoustics can be used to stabilize combustion of fuel droplets [15] and reduce the production of pollutants in laminar flames [16]. Another potential application that has been studied is use of acoustics to suppress flames [7, 8,12,17,18]. It had been shown as early as 1857 that vocally produced acoustics could cause the extinction of a gas-fueled flame [18]. More recently, Whiteside studied the acoustically driven extinction of gas burner flames [7]. In his study, acoustics in the frequency range of 35–150 Hz and pressure range of 0.2–112 Pa were used to extinguish flames fueled by methane, ethanol, hexane and heptane. Analysis of Whiteside's data showed that as the molar mass and molar heat of combustion of the fuels increased, so too did the acoustic pressure required to cause flame extinction. In addition, the extinction pressure for each fuel was independent of the burner size. Whiteside concluded that the most likely cause of flame extinction was blow-off. The author noted, though, that this mechanism didn't fully explain his results since the flames could exist in a lifted state for short periods. Whiteside further concluded that there was a minimum acoustic velocity required to cause extinction for each fuel, and that acoustic extinction could be achieved at any frequency provided the acoustic pressure was high enough to achieve that velocity. Although not explicitly discussed by the author, Whiteside's data and conclusions are generally consistent with extinction strain-rate theory [2,19–24]. Edmonson and Heap [24] showed that the phenomenon of blow-off was caused by the quenching effect of increased mixing. The magnitude of this effect scaled with the strain rate in the flow of the unburned gases near the burner. If it is assumed that a diffusion flame subjected to an acoustic flow experiences increased strain as the acoustic pressure and velocity increases, then it supports Whiteside's supposition that there exists a threshold acoustic extinction velocity. In addition, Won et al. showed that the extinction strain rate for heavy hydrocarbon fuels scales with the molar heat of combustion [19]. When these results are extrapolated to the lighter hydrocarbons used by Whiteside, it correctly predicts the trend observed between the acoustic extinction velocity and molar heats of combustion for the fuels tested. Underlying extinction strain-rate theory is the understanding that flame stretch enhances transport processes, which in turn compete with combustion reactions [2,25]. Since the effects of transport processes and chemical kinetics are so closely coupled, it is often desirable to represent them in relationship to each other. Such a comparison is often done with a Damk€ ohler number (Da), which is defined as the ratio of a characteristic transport time to a characteristic chemistry time [2,22,23,25,26]. For large values of Da, it is expected that the effects of slow transport processes will dominate, and flame chemistry will occur at a faster rate. As values of Da become smaller, the slower chemical kinetics begins to dominate until the system becomes non-reactive [25]. Therefore, for every flame there is a critical value of Da, below which flame extinction will occur [2,8,26]. A somewhat different extinction mechanism was described by McKinney and Dunn-Rankin [4], who studied the acoustically driven-extinction of methanol droplets. In their study, droplets of various sizes were injected into a resonating tube and exposed to acoustic waves at various frequencies and pressures to identify extinction criteria. They found that at the same frequency, the acoustic pressure required to cause extinction increased with droplet size. They also found that for droplets of the same size, the acoustic pressure required to cause extinction increased with frequency. The authors determined that extinction occurred when the flame was displaced far enough from the droplet that evaporation of the fuel was shut down. The critical magnitude of displacement was determined to be at least the radius of the droplet. While other authors have explored acoustic extinction criterion for gaseous flames from a burner [7,12] and droplet flames [4], there has been no work in this context on flames fueled by a stagnant liquid. The flame from a stagnant liquid represents the most relevant scenario from a fire safety perspective. In addition, the governing phenomena of the observed extinctions, especially in the case of Whiteside's work, are not
2. Experimental setup and results 2.1. Experimental setup overview The primary objective of the experimental design was to create a lineflame that could simultaneously interact with a planar acoustic wave across the entire flame surface. Additional design considerations included the ability to measure the fuel's mass loss rate and observe the effects of a forced flow on the flame. A detailed description of the experimental setup and its components is given by Friedman [27]. As shown in Fig. 1, the setup was composed of four main components: (1) perturbation source, (2) collimator, (3) screened enclosure and (4) burner. Depending on the type of experiment being conducted, the perturbation source was either a speaker or fan mounted at a fixed position inside the collimator. The collimator was a 0.25 m diameter, 3.05 m long PVC tube which was supported by wooden blocks. At the opposite end from the perturbation source, the collimator protruded through an opening into the screened enclosure. Within the screened enclosure, the burner was placed adjacent to the tube opening. Depending on the experiment type, the burner was supported by either metal stands or a mass balance, both of which are shown in the inset of Fig. 1. The burner was designed to produce a laminar diffusion flame of a near planar geometry. To produce this flame, rectangular wicks made from Kaowool PM ceramic fiber were placed inside aluminum-foil-lined insulation panels. For each test, 3.5 mL of fuel was poured along the center line of the wick. Two pieces of 3.2 mm thick borosilicate glass were then placed over the panels, leaving a 5 mm gap through which the
Fig. 1. Schematic of the experimental setup. 103
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conducted to serve as a point of reference for other experiments. Three burns were conducted for each alkane tested, during which time mass readings and videography were obtained simultaneously. Using the mass _ were data collected, discrete values of the mass loss rate (mlr or m) calculated as:
fuel could emanate. Depending on the type of fuel being tested and the time since ignition, the burner produced line-flames that ranged from 0.02 to 0.12 m in width, and 0.02–0.05 m in height. Abbreviated schematics of the burner assembly process are shown in Fig. 2(a) and (b). Front and side images of a representative line-flame are shown in Fig. 2(c) and (d), respectively. A detailed characterization of the experimental setup was conducted, the results of which are described elsewhere [27]. The objectives were to understand the system's harmonics, the acoustic pressures generated, and nature of the acoustically induced air movements. Acoustic pressures were measured using an integrated constant current power microphone. Air speeds were measured using a hot-wire anemometer. Air movements were visualized with clouds of atomized glycerol droplets. Videography of the visualizations was captured with a high speed camera at 400 frames per second. Results of this characterization showed that: (1) the collimator exhibited acoustic resonance at frequencies consistent with those predicted by sound theory; (2) acoustic pressures inside the enclosure showed a steady decay proportional to the distance from the collimator opening; (3) acoustic pressures at the flame position were approximately 1:2 times greater with the burner assembly in place, and this was most likely due to acoustic waves reflecting off the top surface of the burner; (4) anemometer measurements of acoustically induced air movements were indicative of a root mean square (rms) air speed; and (5) there was a positive correlation between acoustic pressure and rms air speed.
m_ i ¼
miþ1 mi ti tiþ1
(1)
The three mlr data sets for each fuel tested were then averaged together and smoothed using a running average with a kernel of ±15 s. This kernel accounted for no more than 15% of the data points from a composite data set. Estimates of the flame's height (Lf ) and width (Wf ) were obtained from analysis of the video recorded during each burn using the process described in detail by Friedman [27]. Mean mlr and Lf are shown as a function of time for each fuel tested in Figs. 3 and 4, respectively. All uncertainties were computed from the scatter of the data as two standard deviations of the mean. 2.2.2. Burning rate during acoustic excitation A study of the flame's burning rate, characterized by wick's mass loss rate, while experiencing acoustic perturbations was conducted. The flames in this study were fueled using hexane, which acted as a surrogate for the other alkanes. As shown in the inset of Fig. 1, the burner was placed on the balance in front of the collimator. The fuel-laden wicks were then ignited and allowed to burn freely until the flame stabilized. After the free-burn period, the speaker was activated and the flame was allowed to burn under acoustic excitation at a constant frequency and acoustic pressure until it self-extinguished. Measurements of the acoustic pressure and rms air speed were then taken at the flame position approximately 0.02 m above the burner. The ranges of acoustic pressures
2.2. Experimental results 2.2.1. Alkane free-burn A study of the line-flame without acoustic perturbations was
Fig. 2. (a) and (b) – assembly process of burner used in this study. (c) and (d) – views of the line-flame from the frontal and medial planes. 104
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and rms air speeds that could be tested were limited by the operational characteristics of the speaker and by the occurrence of acoustic extinction. For each combination of acoustic frequency and pressure, three tests were performed. The results were averaged together using the process previously described to generate mean mlr histories. Representative histories obtained at 30 and 40 Hz and a range of acoustic pressures are shown in Fig. 5. The histories presented begin at speaker activation, which was approximately 20 s after ignition. For reference, the free-burn profile for hexane is shown from ignition. A complete set of these histories, including those at obtained 35 and 45 Hz, can be found elsewhere [27]. To serve as a basis for comparison, an attempt was also made to study the burning rate under various fan-driven flows. During these experiments, the balance acted as a bluff-body obstruction in the flow as it exited the collimator. As a result, large-scale, unsteady, turbulent structures developed around the flame, and precise flow measurements were difficult to obtain. In addition, re-circulation currents often formed too, causing the flame to be drawn toward the collimator in the windward direction. Given the lack of uniformity and unsteady nature of these flows, coupled with the difficulty in obtaining precise measurements, the results of these experiments lacked probative value and have been omitted here.
Fig. 3. Free-burn mean mlr histories for each alkane tested shown as splines of individual data points. The error bars are two standard deviations of the mean.
2.2.3. Acoustically driven extinction Flames produced using the fuels n-pentane, n-hexane, n-heptane and n-octane were subjected to acoustic perturbations at varying frequencies and acoustic pressures to determine extinction conditions. For comparison, the speaker was then replaced with a fan, and the speed of fan-driven flows required to cause extinction of each fuel was also measured. To determine if the results were unique to alkanes, flames fueled by JP-8 were subjected to the same testing procedure. The conditions required to cause acoustic extinction of a particular fuel at a particular frequency (ω) were determined by finding the lowest speaker power that could cause three consecutive extinction events within 10 s of speaker activation. For each test, the flame was allowed to burn unperturbed until it reached a height of approximately 0.02 m. The speaker was then activated and the experimental outcome was noted. Measurements of the acoustic pressure (PA ) and rms acoustic air speed (UA ) were made after every trial at the flame position, approximately 0.02 m above the burner. For those trials where acoustic extinction was achieved, the acoustic pressure ðPA;ext Þ and rms air speed ðUA;ext Þ were calculated as the mean from the three individual trials. The results, including uncertainties, are summarized in Table 1. Graphs of PA;ext and UA;ext are shown in Figs. 6 and 7, respectively. The error bars were omitted from these figures because their values were comparable to the
Fig. 4. Free-burn mean flame height histories for the alkanes tested shown as splines of individual data points. The error bars are two standard deviations of the mean.
Fig. 5. Mean Hexane mlr histories at (a) 30 and (b) 40 Hz and various acoustic pressures and corresponding rms air speeds shown as splines of individual data points. The error bars are two standard deviations of the mean. 105
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size of the data markers used. Included in the legend of each graph are the mean (μ), standard deviation (σ) and coefficient of variation (σ=μ) for the aggregate data set. Along with measurements of acoustic pressure and rms air speed, high speed video of several acoustic extinction events was also captured. A sample sequence of frames from a hexane fueled flame experiment, just prior to total flame extinction, is shown in Fig. 8. The flame shown is being perturbed by 35 Hz acoustic waves, traveling right-to-left, at an acoustic pressure of 19.4 Pa and rms air speed of 0.76 m s1. The sequence shows the flame through approximately one acoustic cycle. The flame begins over the wick, the center of which is indicated by the red marker. As the acoustic wave passes, the flame is displaced from the wick. Near the end of the acoustic cycle, a new flamelet is seen emerging through the gap between the glass panes. The air speed of the fan-driven flow required to cause extinction (UF;ext ) for each fuel was determined by finding the lowest fan power that could cause three consecutive extinction events within 10 s of fan activation. The air speed was measured using an anemometer at the same position as that used in the acoustic extinction experiments. Values of UF;ext were then calculated as the mean of the three individual trials. The results, including uncertainties, are summarized in Table 2. Values of UF;ext are shown graphically in Fig. 9, where they are plotted against the fuel's molar mass for visual clarity. During the fan-driven extinction experiments, the flame lost its normal incandescent coloring and took on a faint blue hue. As a result, the flames were difficult to see and could not be captured easily using high speed videography. It was still desirable, though, to visualize the fan-driven flow over the burner. This was done with a cloud of atomized glycerol droplets, using the methodology described in detail elsewhere [27]. Visualizations of the fan flow at 400 and 600 ms after fan activation are show in Fig. 10. The faint outline of a boundary layer forming over the burner can be seen at 400 ms. By 600 ms, a clearly defined boundary layer has fully formed over the burner.
Fig. 6. Acoustic pressure at extinction measured for each fuel at different sound frequencies. The reported mean (μ), standard deviation (σ) and coefficient of variation (σ/μ) are for the aggregate data set.
3. Analysis and discussion 3.1. Alkane free-burn Reexamining Figs. 3 and 4, there is an obvious qualitative relationship between the profiles of mlr and Lf for each fuel. Specifically, each profile shows peak values and points of inflection at approximately the same times. Since the burner used in this study was sui generis, existing flame height correlations are likely to be inadequate. Therefore, an Fig. 7. rms air speed at extinction for each fuel at different sound frequencies. The reported mean (μ), standard deviation (σ) and coefficient of variation (σ/μ) are for the aggregate data set.
Table 1 Acoustic flame extinction results. The uncertainties are two standard deviations of the mean. Fuel
ω (Hz)
PA;ext (Pa)
Pentane
30 35 40 30 35 40 45 30 35 40 45 50 30 35 40 45 30 35 40 45
16.2 22.2 35.5 14.6 19.5 27.0 28.4 13.7 15.9 26.6 25.5 29.9 14.7 16.6 25.3 29.9 16.1 24.3 23.2 20.6
Hexane
Heptane
Octane
JP-8
± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ±
0.1 0.2 0.2 0.1 0.1 0.2 0.2 0.1 0.1 0.2 0.2 0.2 0.1 0.1 0.2 0.2 0.1 0.1 0.2 0.1
analysis of a relationship between mlr and Lf was conducted. Since these quantities were measured in time, a direct comparison on a temporal _ basis was made. The mass loss rate normalized by the flame width (m') was calculated as:
U A;ext (m s1) 0.71 0.86 0.95 0.65 0.75 0.68 0.86 0.58 0.60 0.72 0.72 0.74 0.60 0.58 0.60 0.64 0.57 0.55 0.59 0.66
± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ±
0.02 0.03 0.03 0.02 0.02 0.02 0.03 0.02 0.02 0.02 0.02 0.02 0.02 0.02 0.02 0.02 0.02 0.02 0.02 0.03
_ ¼ m_ Wf m'
(2)
where Wf is the width of the line-flame. A heat release rate per unit flame _ was then calculated as: width (Q')
_ ¼ Δhc m' _ Q'
(3)
where values for the heat of combustion per unit mass, Δhc , were obtained from the literature and are presented in Table 4, which is introduced in a subsequent section of the manuscript. Values of Lf were then _ as shown in Fig. 11. plotted against corresponding values of Q', Close examination of Fig. 11 showed that values of Lf < 0:01 m were _ This value appeared to constitute a clustered about a constant value of Q'. 106
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Fig. 8. High speed video frames of hexane fueled flame, just prior to extinction at (a) þ4 ms, (b) þ12 ms, (c) þ20 ms, and (d) þ28 ms from the start of an acoustic cycle. The flame is experiencing perturbations at 35 Hz, 19.4 Pa of acoustic pressure, and an rms air speed of 0.76 m s1. The sequence shows the flame through approximately one acoustic cycle. The red marker indicates the center of the wick. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)
minimum heat release rate, below which a flame could not exist. On average, this value was found to be 3.7 kW/m. For values of Lf 0:01 m, there appeared to be an approximately linear relationship between Lf and _ This relationship was fitted as: Q'.
Table 2 Fan-driven flame extinction test results. The uncertainties are two standard deviations of the mean. Fuel
U F;ext (m s1)
Pentane Hexane Heptane Octane JP-8
1.55 1.58 1.89 1.96 2.03
± ± ± ± ±
0.03 0.03 0.04 0.04 0.08
Lf ¼
3:9 103
m2 _ ' Q 4:5 103 m kW
(4)
The results of this fitting exercise are shown in Fig. 11. Since the lineflames produced by all fuels were in the laminar regime during free-burn, _ is consistent with the Burkethe linear relationship between Lf and Q' Schumann theory [28]. 3.2. Mass loss rate during acoustic excitation Reexamining the hexane mlr profiles presented in Fig. 5, certain qualitative trends are apparent. As the acoustic pressure and rms air speed increased, flame growth was accelerated. After peak mlr was achieved, though, most profiles converged towards the free-burn profile. For a more quantitative analysis, the average mass loss rate (mlr) was used to characterize each mass loss rate time dependence. Values of mlr were calculated as the ratio of the total mass lost by the wick to the total burn time. These values were then plotted against PA and UA for comparison; the results are shown in Fig. 12 and Fig. 13, respectively. These figures demonstrate near linear relationships that were captured by the following expressions:
Fig. 9. Fan-driven air speeds required to cause extinction. The error bars are two standard deviations of the mean. The reported mean (μ), standard deviation (σ) and coefficient of variation (σ/μ) are for the aggregate data set.
mg mg PA þ 7:2 mlr ¼ 0:31 s⋅Pa s
(5)
mg mg UA þ 8:2 mlr ¼ 10:4 m s
(6)
The coefficient of determination (R2 ) is notably higher for the linear 107
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Fig. 10. Visualization of fan-driven flow over the burner at the air speed of 1.6 m s1 at (a) 400 ms and (b) 600 ms after the fan activation.
Fig. 11. Relation between flame height and heat release rate (HRR) per unit flame width observed for unperturbed flames.
Fig. 13. Relation between rms air speed and average mass loss rate.
Although not perfectly analogous, the link between the speed of oscillatory air movement and burning rate is consistent with the observations of other authors. In studies of flame spread in opposed flows, both Fernandez-Pello et al. [29] and De Ris [30] showed that increased flow speed enhanced burning rate. This behavior was due to the flames being forced closer to the fuel surface, which enhanced heat transfer into the fuel bed. By studying the burning rate of gasoline pool fires in cross-flows, Hu et al. [31] showed that this same mechanism leads to a linear correlation between the flow speed and burning rate. It is reasonable to conclude that a similar phenomenon was occurring due to the oscillatory air movement over the fuel: as the rms air speed increased, the flame was forced closer to the wick which increased heat transfer to the liquid fuel. This mechanism would then explain both the positive correlation and linearity of the relationship between mlr and UA . 3.3. Acoustic and fan-driven flame extinction 3.3.1. Comparison of results Reexamining the extinction pressures in Fig. 6, and rms air speeds in Fig. 7, each curve can be thought of as delineating condition between where the flame could and could not exist. For conditions where values of PA < PA;ext and UA < UA;ext , the flame could continue to burn; for conditions where values of PA PA;ext and UA UA;ext , total flame extinction occurred. The amount of scatter in the values of PA;ext (σ=μ ¼ 0:27) obtained for different fuels and at different frequencies was found to be significantly greater than the amount of scatter observed in the values of UA;ext (σ=μ ¼ 0:16). This finding indicated that the mean value of UA;ext
Fig. 12. Relation between acoustic pressure and average mass loss rate.
fit of mlr versus UA (R2 ¼ 0.91) than for the mlr versus PA (R2 ¼ 0.83). This finding indicates that the rms air speed had a stronger influence on the average mass loss rate, and further suggests that the acoustic pressure only influenced mlr values insofar as it affected the rms air speed.
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was a more universal predictor of flame extinction than the corresponding acoustic pressure. To give further insight into the values of UA;ext , they were compared to the values UF;ext for the corresponding fuels. On average, the values of UF;ext were found to be 2:5 times greater than the values of UA;ext . More significantly, there was reversal in the “ordering” of the fuels between the two data sets. As indicated in Fig. 14, the values of UF;ext were observed to increase as the molar mass and the molar heat of combustion (ΔHc ) of the fuel increased, while values of UA;ext were observed to decrease. The data are plotted against the molar heat of combustion, which is proportional to the fuel's molar mass.
3.3.3. Proposed acoustic extinction mechanism To understand how an acoustic extinction mechanism would work, a simplified model of the flame is utilized: fuel enters the flame region and reacts with the oxidizer; heat is released, a portion of which is fed back into the fuel source; this drives more fuel into the flame region. In this model the propensity of the fuel to maintain this cycle is best described by the Spalding mass transfer number (B), and a large disruption to this cycle would cause flame extinction. Reexamining the image sequence presented in Fig. 8, it can be seen that as the acoustic wave propagates over the burner, it temporarily displaces the flame from the region above the wick. In contrast to the fandriven flows, the flame is not confined to a boundary layer, and the fuel bed is periodically exposed directly to cool air. During the displacement period, it is assumed that the fuel bed experiences convective cooling from the acoustic flow passing over it. The magnitude of this cooling can be characterized by a local Nusselt number (Nuξ ). The combination of forced flow over the flame and displacement of the flame creates two competing processes. At acoustic pressures and rms air speeds below PA;ext and UA;ext , heat transfer to the fuel bed is enhanced in a mechanism similar to that in traditional forced flows. This additional heating compensates for the cooling that occurs during the flame's displacement. At a critical point, though, convective losses during the flame's displacement begin to overwhelm the effects of enhanced heat transfer. From the stagnant layer theory, it is known that as the heat flux from the flame into the fuel bed decreases, so too will the burning rate [22]. Furthermore, according to the fire point theory described by Rashbash [34,35], there is a critical mass flux for any given fuel, below which total flame extinction will occur. It would be reasonable to conclude that at the point acoustic extinction was achieved, convective cooling of the fuel bed during the flame's displacement had created conditions for such extinction conditions. In the model proposed, the B number characterizes a fuel's ability to maintain the flame-fuel-supply cycle, and a Nusselt number characterizes the amount of disruption to this cycle. A ratio of these two nondimensional numbers might then constitute a criterion by which acoustic extinctions can be predicted. For consistency with Figs. 6 and 7, it would be useful to structure this ratio so that larger values correspond with flame extinction, while smaller values correspond with continued burning. It is, therefore, proposed that the ratio of Nuξ to B at the point where acoustic extinction was achieved is a constant, and that this value forms a boundary delineating conditions where the flame can and cannot exist. As shown in Equation (8), this ratio shall be called ΘA ; the terms of this equation will be further developed in the following sections.
3.3.2. Discussion of observations As previously noted, the fan-driven flows produced a boundary layer over the burner, which is shown in Fig. 10. The flames in these experiments were, therefore, similar to the flames in a forced flow over a stagnant fuel film studied by Emmons [32]. In his analysis of such flames, he showed that the flame existed in the boundary layer of the flow, and that it separated the region of cooler air above the flame from the fuel below it. As the free-stream velocity of the flow increased, the boundary layer thickness decreased and strain rate increased. Extinction occurred when the free-stream velocity and corresponding strain rate became so great that chemical reactions driving combustion could not compete with the mixing rate of the reactants, and the value of Da dropped below a critical value [32,33]. Won et al. [19] showed that the extinction strain rate (aE ) for diffusion flames fueled by hydrocarbons scales as:
aE ∝½DF YF;∞ ΔHc ½kinetic term
(7)
where DF is the diffusivity of the fuel into oxidizer, and YF;∞ is the fuelmass fraction on the fuel side of the reaction zone, which is close to unity for the conditions used in this study. Provided that the diffusivities of the fuels are similar, the extinction strain rate should, therefore, scale with the fuels' molar heats of combustion. Using the results from Emmons and Won, it can be concluded that for the fan-driven extinctions, values of UF;ext and ΔHc should show a positive correlation. Reexamining the plot in Fig. 14, this was precisely the trend that was observed. In contrast, the values of UA;ext were observed to decrease with increasing ΔHc . Furthermore, values of UF;ext were significantly greater than UA;ext . These observations suggest that flame stretch was not the extinction mechanism in the acoustic experiments, and that an alternative mechanism must be found.
ΘA ¼
Nuξ B
(8)
3.3.4. Spalding B number In a study of ethanol and heptane pool fires of various areas with varying crosswinds, Hu et al. [36] found that the radiative portion of the heat flux from flame to liquid fuel decreased significantly as the fuel area decreased and the crosswind increased. For their smallest heptane pool fire, which had an area of 10 cm2, at crosswind air speed of 0.7 m s1, the radiative portion was 10%. In the experiments of the present study, the exposed wick area was only 2.5 cm2 while air speeds were comparable. Thus, the gasification of the fuel can be considered to be driven exclusively by convective heat transfer. With this assumption, Quintiere [22] gives the B number as:
B¼
YO2 ;∞ ðΔhc =rÞ cp;air ðTb T∞ Þ L
(9)
where YO2 ;∞ ¼ 0:233 is the mass fraction of oxygen in ambient air; T∞ ¼ 298 K is the ambient temperature; and cp;air is the air heat capacity evaluated at 12 ðT∞ þ Tb Þ. The stoichiometric fuel oxidizer mass ratio, r, boiling point, Tb , and heat of gasification, L, are fuel properties. The air
Fig. 14. Comparison of UF;ext and UA;ext at 35 Hz for the different fuels studied. 109
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and fuel properties are summarized in Tables 3 and 4, respectively. The fuel properties were amalgamated from a range of sources discussed in detail by Friedman [27]. Some of the air properties reported in Table 3 were used in the evaluation of the Nusselt number and are discussed in a subsequent section.
Table 3 Properties of air used for different fuels [37].
3.3.5. Nusselt number correlation Nusselt number correlations are based on the assumption that convective heat transfer scales with momentum transfer [37,38]. Therefore, a Reynolds Number (Re) was needed, which in turn required a characteristic length (ℓ) to be defined. For a sound-driven flow, this length can be specified as the rms displacement of a particle in an acoustic cycle, and calculated as:
ℓ¼
UA ω
cp;air (J kg1 K1)
νair (m2 s1)
Pentane Hexane Heptane Octane JP-8
309 342 372 399 456
1007 1008 1008 1009 1012
1.68 2.01 2.33 2.63 3.16
r
Fuel Pentane Hexane Heptane Octane JP-8
(10)
UA ℓ U2 ¼ A νair νair ω
T b (K)
105 105 105 105 105
Pr 0.706 0.701 0.696 0.690 0.686
Table 4 Calculated fuel properties [27].
Using Equation (10), the Reynolds number for the acoustic flow was defined as:
ReA ¼
Fuel
3.55 3.53 3.51 3.50 3.40
L (J kg1) 3.93 4.59 5.24 5.84 6.21
Δhc (J kg1) 5
10 105 105 105 105
45.4 45.1 44.9 44.8 42.8
6
10 106 106 106 106
B 7.54 6.39 5.54 4.93 4.49
(11)
where νair is the kinematic viscosity of air taken at Tb . These viscosity values are given in Table 3. Unfortunately, Nusselt number correlations are not well studied for oscillating flows [39]. Here, it was assumed that a functional correlation between a local Nusselt number at the flame position and the Reynolds and Prandtl (Pr) numbers is analogous to that for a non-oscillating flow over a flat plate [37,38]:
Nuξ ¼ cReγA Prδ
(12)
where the values of c; γ and δ are empirical constants. Examining Table 3, it can be seen that the values of Pr are practically constant for all fuels used. Since the value of c in Equation (12) is also a constant, the substitution C ¼ cPrδ was made, which yielded:
Nuξ ¼ CReγA
(13)
A modified Nusselt number (Nuξ ') was then defined as Nuξ ' ¼ Nuξ =C. Substituting this expression into Equation (13) yielded:
Nuξ ' ¼ ReγA
Fig. 15. Calculated values of Θ'A at the lowest speaker power that could consistently cause total flame extinction. The reported mean (μ), standard deviation (σ) and coefficient of variation (σ=μ) are for the aggregate data set.
(14)
Finally, replacement of Nuξ with Nuξ ' in Equation (8) yielded:
Θ'A ¼
ReγA B
verify this model, additional experiments were conducted under the conditions other than those corresponding to the minimum speaker power required for extinction. The results of these experiments are summarized in Table 5 together with the corresponding values of Θ'A .
(15)
3.3.6. Model optimization and validation The value of γ in Equation (15) was optimized to reduce the scatter in Θ'A values computed for the acoustic extinction events achieved using the minimum speaker power; details of this optimization process can be found elsewhere [27]. From this process, it was determined that γ ¼ 1=3 was the optimal value. It is worth noting that most Nusselt number correlations for flows over a flat plate scale as Re1=2 ½37; 38. In its final form, Equation (15) became:
'
When these results are plotted with respect to ΘA ¼ 1:4, as shown in Fig. 16, it becomes apparent that this parameter clearly delineates between conditions where flame can and cannot exist. 3.3.7. Model application to fan driven extinction To determine whether the proposed acoustic extinction mechanism was also consistent with the fan-driven extinction, the acoustic extinction model was applied to the fan-driven extinction results. In this case, the characteristic length ℓ was taken to be the distance from windward edge of the burner to the center of the fuel wick, which was 0.067 m. The Reynolds number was calculated as:
2=3
Θ'A ¼
UA
(16)
ðνωÞ1=3 B
As shown in Fig. 15, application of this expression to the acoustic extinction data yields highly consistent results. The mean value of Θ'A for
ReF ¼
'
the aggregate data set, μ ¼ ΘA ¼ 1:4, is within 4% of all individual values of this parameter. This means that Θ'A is a much more consistent descriptor of conditions at extinction than the mean values of PA;ext or UA;ext . For values of Θ'A < 1:4, a flame was expected to continue burning; for values of Θ'A 1:4, total flame extinction was expected. To further
UF ℓ νair
(17)
where UF was the air speed measured at the flame position, approximately 0.02 m above the burner. Substituting this Reynolds number into Equation (15) yielded:
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Table 5 Summary of acoustic perturbation experiments where the speaker power setting was other than the minimum required to consistently cause flame extinction. Fuel
ω (Hz)
U A (m s1)
Extinction
Θ'A
Pentane Pentane Hexane Hexane Heptane Heptane Heptane Heptane Heptane Octane JP-8
30 30 30 35 30 35 45 45 50 30 40
0.61 0.77 0.52 0.69 0.48 0.53 0.69 0.86 0.78 0.50 0.61
No Yes No No No No No Yes Yes No Yes
1.20 1.41 1.20 1.38 1.25 1.26 1.38 1.41 1.45 1.38 1.51
Fig. 17. Calculated values of Θ'F for the fan-driven extinctions at the lowest fan power required to consistently cause flame extinction. The error bars are uncertainties propagated from the UF;ext data (shown in Table 2). The reported mean (μ), standard deviation (σ) and coefficient of variation (σ=μ) are for the aggregate data set.
Fig. 16. Values of Θ'A calculated for the acoustic perturbation experiments where the speaker power setting was other than the minimum required to consistently cause flame extinction.
Θ'F ¼
ðUF ℓÞ1=3 1=3
νair B
(18)
The values of Θ'F computed for the fan driven extinctions achieved at the minimum fan power are shown in Fig. 17. In contrast to the acoustic results, the values of Θ'F showed an increased scatter when compared to UF;ext values shown in Fig. 9. This calculation further confirmed that the acoustic and fan-driven extinctions occur through different mechanisms.
Fig. 18. Minimum speaker power required to achieve consistent acoustic extinction. Each point is the average power used by the speaker for the extinction events summarized in Table 1. The dashed black line indicates the maximum operating power of the speaker used.
3.3.8. Potential application of acoustic extinction The speaker used in this study had a maximum operating power of 250 W. This power limit placed significant constraints on the range of acoustic frequencies and pressures that could be tested. As shown in Fig. 18, the minimum speaker power required to cause flame extinction increased dramatically with increasing frequency. It stands to reason, though, that if the speaker had been rated for a higher power, acoustic extinction could have been achieved at higher frequencies. This supposition is consistent with the findings of Whiteside [7], who concluded that acoustic extinctions occur at any frequency, provided that a critical acoustic air speed is also achieved. When compared to other flame suppression techniques, the concept of acoustic flame suppression has several unique advantages. Chief among these advantages is that there is no flame suppressing agent that needs to be applied. It would therefore be beneficial to consider whether acoustics could be used to suppress a relatively large fire. To do so, a 1 m diameter, heptane pool fire was considered, and the sound parameters
required to extinguish this fire at ω ¼ 30 Hz were estimated. According to the model developed, acoustic flame extinction requires the oscillatory movement of air to be sufficiently fast and high in amplitude to convectively cool the fuel bed. An implicit assumption within this statement is that, to achieve extinction, not only must the proposed extinction criterion Θ'A be greater than 1.4, but the rms displacement distance (ℓ) defined by Equation (10) must also be at least as large as the fuel bed size. This additional condition for extinction is consistent with the observations of McKinney and Dunn-Rankin [4]. In all experiments where extinction was attempted, including those where it was not achieved, this condition was satisfied. For the experiments the results of which are listed in Table 1, the average value of ℓ was 1.8 cm, which is almost 4 times greater than the width of the exposed fuel bed. While the current data indicate that this condition is necessary but not sufficient to achieve extinction, it can still be used to estimate the minimum sound pressure required to extinguish substantially larger fires. To achieve ℓ ¼ 1 m (equal to that of the pool diameter), the rms air 111
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speed produced by 30 Hz acoustics needs to reach 30 m s1, in accordance with Equation (10). Using the characteristic impedance of air ðZw Þ at 20 C, which is given as 412 Pa s m1 [40], the acoustic pressure can be calculated as:
PA ¼ UA Zw
mlr dropped below the critical value needed to sustain a flame. To explore this hypothesis, a simple model was proposed. In this model, the Spalding B number was used to characterize the fuel's propensity to sustain combustion, and a local Nusselt number was used to characterize the convective cooling of the fuel bed. Mathematical expressions were developed for each term, and they were evaluated using values reported in the literature, and conditions measured during the experiments. It was found that at the minimum speaker power required to cause extinction, the ratio of a modified Nusselt number to the fuel's B number was a constant. Application of the model to additional data sets showed that when this ratio was below this constant, the flame continued to burn. When this ratio was greater than or equal to this constant, flame extinction occurred. It was therefore asserted that this constant constituted a boundary between regions of flammability and flame extinction, and served as a reliable predictor of the acoustically-driven extinction events for small fire sizes explored in this study.
(19)
The results from Equation (19) show that an acoustic pressure of 12.4 kPa or 176 dB would be required to suppress the flame. Typical commercial sub-woofers produce acoustics no louder than 110 dB at 1 m distance [41]. Taking into account that dB is a logarithmic unit, it would therefore be extremely difficult to engineer a practical device for acoustic suppression of a fire of this size. 4. Conclusions An experimental setup was constructed to study the interaction of acoustic waves with laminar, near-planar, diffusion flames burning in air. The acoustics utilized ranged in frequency from 30 to 50 Hz and acoustic pressures from 5 to 50 Pa. To produce these flames, fuel-laden wicks were placed under panes of borosilicate glass, leaving a small gap through which the fuel vapor emanated. The fuels used in the study were the alkanes, n-pentane through n-octane. To confirm that the acoustic extinction experiments were not unique to the alkanes, flames fueled by JP-8 were also tested. Prior to acoustic testing, studies of the alkane flames' unperturbed burning rate, height and width were conducted. Flames from each alkane were produced on a mass balance and allowed to evolve without acoustic excitation. During the evolution, mass readings were obtained while simultaneously obtaining videography. Mass loss rates were evaluated from the temporally indexed mass readings of the balance. Estimates of the flame height and flame width were made from analysis of the videos. Using each fuel's heat of combustion, a direct comparison was made between each flame's height and heat release rate per unit flame width. An approximately linear relationship was observed between these quantities, which is consistent with the Burke-Schumann theory [28]. To more thoroughly understand the effects of the acoustics on the flame, a study of the flame's burning rate under acoustic excitation was carried out. Hexane fueled flames were generated on a mass balance, and allowed to evolve under various combinations of acoustic frequency and pressure. It was observed that the introduction of acoustics enhanced mass loss rate from the wick. Once peak mlr was achieved, most mass loss rate histories converged towards the free burn profile. Analysis showed that there was a linear correlation between the average mlr and the rms air speed of the acoustics. This observed relationship is consistent with the results from studies where flames were subjected to forced flows [29,30]. Finally, a study of acoustically-driven extinction was performed using the alkanes and JP-8. Samples were ignited and subjected to acoustic perturbations at various frequencies and speaker powers until the minimum speaker power was found that could cause three consecutive flame extinctions. After flame extinction, the acoustic pressure and rms air speeds were measured. As a basis for comparison, the minimum fandriven flows required to cause flame extinction for each fuel were also evaluated. Analysis of the data showed that the fan-driven air speeds required to cause extinction increased with the fuel's molar heat of combustion. This trend is consistent with the extinction strain rate theory [19,32]. For acoustically-driven extinctions, though, the rms air speed at extinction was seen to decrease with the fuel's molar heat of combustion. It was therefore concluded that flame stretch was not the cause of these extinctions and that an alternate explanation was needed. Analysis of high speed video recorded during acoustic extinction revealed that the flame was periodically displaced from the region over the fuel bed. It was theorized that, as the acoustic flow passed over, the fuel bed experienced convective cooling. At the point acoustic extinction was achieved, the cooling effect had become so great that the fuel's
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