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An experimental study on fire behavior of an inclined ceiling jet in a low-pressure environment
International Journal of Thermal Sciences 138 (2019) 487–495
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International Journal of Thermal Sciences journal homepage: www.elsevier.com/locate/ijts
An experimental study on fire behavior of an inclined ceiling jet in a lowpressure environment
T
Zhenxiang Tao, Rui Yang∗, Cong Li, Yina Yao, Ping Zhang, Hui Zhang Department of Engineering Physics, Tsinghua University, Beijing, 100084, China
A R T I C LE I N FO
A B S T R A C T
Keywords: Inclined ceiling Low pressure Ceiling jet fire Aircraft cargo compartment
Inclined ceiling jet fire may occur in a low-pressure aircraft cargo, which poses a great threat to airplane safety. To simulate an inaccessible area in cargo compartment, investigate the effects of pressure on the combustion characteristics of inclined ceiling jet fire, a series of fire experiments under an inclined ceiling (0°, 15°, 30°, 45°) in different pressure environments (50 kPa, 76 kPa, 101 kPa) were carried out in a full-size simulated cargo compartment. N-heptane square pool fires (20 × 20 × 5 cm), as radiation-controlled oil pool fires, were used as fire sources. The burning rate, heat radiation feedback, flame temperature, and ceiling temperature were measured and analyzed. The experiments showed that the heat radiation to pool surface had a significantly positive correlation with ambient pressure, and the penetration of thermal radiation made up a large proportion of heat radiation feedback, which should not be neglected for thin-layer oil burning. When the inclination angle was θ = 0° or θ = 15°, owing to the effects of ceiling, no significant differences existed on the rate of the axial flame temperature decrease in different pressure environments. Moreover, there were some fluctuations when flame was close to the ceiling. Based on previous models, new correlations to predict ceiling temperature in the upward direction and downward direction in different pressure environments were proposed, respectively.
1. Introduction Cargo fire is one of the most dangerous threats to aircraft in operation, which contain heavy bulk loads filled with various combustibles [1–3]. When a fire occurs in the cargo compartment, it may cause an inclined ceiling jet fire due to the different flight attitudes or the curved sidewall of the cargo compartment [4,5]. On the other hand, the internal pressure of the cargo compartment for many commercial airplanes in flight is approximately 76 kpa, while for regional airliner it is 50 kPa [6]. To understand the combustion characteristics of inclined ceiling jet in a low-pressure environment will improve our understanding of the mechanism of the aircraft cargo fire. To design a more scientific and reasonable smoke alarm, or water mist system in building and tunnel fires, many scholars have discussed the combustion characteristics of ceiling jet [7–16]. In early years, according to theoretical analysis and experimental verification, Alpert [7], and Heskestad [8] proposed classical models on the gas temperature for unconfined ceiling and confined ceiling, respectively. You & Faeth [9] performed a series of experiments on liquid pool fires and pointed out that the flame length tended to increase in confinement. By introducing flame radius b , Heskestad & Hamada [10] developed a model for temperature distribution in ceiling jets generated by strong ∗
plume when the ratio of flame height to ceiling clearance ranged from 0.3 to 3. In recent years, based on a series of gas fire tests, Zhang [11] developed models on flame extension length and temperature profile for a thermal impinging flow. Gao et al. [12] studied the characteristics of burner with different vertical heights and heat releases. They claimed that ceiling temperature at the impingement point could be well fitted with three zones. Meng et al. [13] developed models for the maximum temperature beneath the tunnel ceiling related to the vehicular blockage ratio, and the longitudinal ventilation velocity. Zhou et al. [14] also studied the changes of transverse fire locations and the sidewall constraint on the temperature distribution, and concluded that the temperature under the arced ceiling were higher than those under the flat ceiling. Wang [15] conducted experiments to study the natural ventilations on pool fire characteristics and concluded that some smoke may backflow, and despite smoke temperature decreasing in tunnel fire with roof opening. Tang et al. [16] investigated the effect of point extraction system in a reduced scale model, showing that the air entrainment coefficient increases with the HRRs when the ceiling extraction velocity was set to a fixed value. In addition, some studies were focused on the characteristics of ceiling jet under an inclined ceiling [17–23]. Oka [17–19] systematically performed pool fire experiments under a ceiling inclined at
Corresponding author. E-mail address: [email protected] (R. Yang).
https://doi.org/10.1016/j.ijthermalsci.2019.01.023 Received 5 September 2018; Received in revised form 11 December 2018; Accepted 17 January 2019 1290-0729/ © 2019 Published by Elsevier Masson SAS.
International Journal of Thermal Sciences 138 (2019) 487–495
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Nomenclature
τ q˙ ″ (0) q˙ ″ (θ) q˙ ″con q″conv q″rad q″b, p Tf Tl Tb L ΔHg p cP Xsf D H HT m˙ m˙ ″ m˙ u m˙ up
m˙ down Q˙ b ΔTa ΔT0 ΔTr
Transmissivity coefficient of Quartz glass Heat radiation feedback in the case ofθ = 0° (kW/m2) Average heat radiation feedback to pool surface in steady stage (kW/m2) Heat conduction (kW/m2) Heat convention (kW/m2) Heat radiation (kW/m2) Thermal radiative penetration (kW/m2) Flame temperature (K) Fuel surface temperature (K) Boiling point of liquid fuel (K) Effective heat gasification (kJ/kg) Evaporation heat (kJ/kg) Internal pressure of cargo compartment (kPa) Heat capacity (kJ/kg·K) Fuel surface reflectivity Length of container (m) Ceiling clearance (m) Axial height of thermocouple (m) Burning rate (g/s) Mass burning rate (g/s·m2) Unburned mass flow Mass flow in the upward direction
Q˙ c ΔTup ΔTdown
Mass flow in the upward direction Heat release rate (kW/s) Characteristic radius length (m) Axial temperature of flame (K) Ceiling temperature rise at flame impingement point (K) Ceiling temperature rise of r horizontally away from the impingement point (K) Convective heat release rate (kW/m2) Ceiling temperature rise in the upward direction (K) Ceiling temperature rise in the downward direction (K)
Subscripts
0 r
∞ l f con conv rad up down
Flame impingement point Horizontal distance between the specific point and the impingement point Ambient Liquid Flame
Heat conduction Heat convention Heat radiation Upward Downward
attention has to be paid to the combustion characteristics of ceiling jet, especially those of inclined ceiling jet in a low-pressure environment. In this paper, the effects of pressure (50 kPa, 76 kPa, 101 kPa) on nheptane pool fires under a ceiling at different inclination angles (0°, 15°, 30°, 45°) with the same ceiling clearance (0.6 m) were studied in a full-size simulated cargo compartment. The burning rate, heat radiation feedback to the pool surface, vertical temperature, and ceiling temperature were measured and analyzed comprehensively.
from 0° to 40°, and established a more effective model to predict the temperature and velocity of ceiling jet. Based on a series of reducedscale inclined tunnel fire experiments, Hu et al. [20] modified the classical exponential decay model on temperature profiles of buoyant gas. More recently, Zhang et al. [21] analyzed the flame extensions at different inclination angles with various ceiling clearances. They found that the flame extension in the upward direction larger than in the downward direction, and this difference was enlarged as the ceiling's inclination angle increased. Zhang [22] studied the smoke temperature distribution on rectangle propane gas fires at different ceiling angles, and developed a unified correlation for the prediction of maximum temperature. Based on these previous studies and analysis for gas fuel ceiling jet fire, Zhang [23] also proposed a unified correlation for the temperature attenuation along the slopped ceiling. Although experimental evidences have shown that fire behaviors are inherently different in a low-pressure environment: reduction in burning rate, prolonged flame shape, up-shift of flame's high-temperature zone [24–33], there are only a few studies on the effects of pressure on ceiling jet fires. Wang [5] used a simulated cargo compartment to test four pool fires of different sizes in different low-pressure environments. By introducing air entrainment ratio, they proposed the correlations for maximum ceiling temperature and ceiling temperature decay profile in different pressure environments. Considering the multi-sensor (such as the smoke density, ceiling temperature, air humidity in a fire) detectors could improve the accuracy of aircraft fire detection, our
2. Experimental apparatus and measurements The experiments were carried out in a heat-resistant rig that was placed at the center of a full-size simulated cargo compartment, as shown in Fig. 1. The whole rig was made of 4040 standard industrial aluminum alloys with the dimensions of 0.78 × 0.78 × 1.52 m. Two adjustable angle brackets were equipped in the middle of the frame to adjust the ceiling's inclination angle, and the maximum value was 45°. In order to meet different ceiling sizes, six heat-resistant clips, which could be adjusted in four directions, were fixed on the frames. The cargo compartment was made of high-grade stainless steel with the dimensions of 8.11 × 4.16 × 1.67 m. During the test, the pressure inside the compartment was controlled firstly by letting airflow in and out through a vacuum pump to maintain at the target value, and then the fuel was ignited by an electrifying looped nickel-cadmium resistance wire, which was placed at the surface of the liquid fuel.
Fig. 1. Full-scale simulated cargo compartment and heat-resistant rig. 488
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Fire experiment layout and instrumentation in our study were illustrated in Fig. 2. Above the oil pool, a 120 * 50 * 2 cm fireproof board with a low thermal conductivity of 0.03 W/(m*K) was used as the ceiling. 19 K-type thermocouples whose diameter was 0.5 mm were located 10 mm below the ceiling to measure the gas temperature. The interval between X-axis thermocouples was 0.1 m and the interval between Y-axis thermocouples was 0.05 m, as shown in Fig. 2 (b). The flame temperature was measured by an array of 1 mm K-type thermocouples, arranged in the centerline of the oil pan. The distance from the lowest thermocouple to the oil pool surface was 0.02 m, and the interval between other thermocouples was 0.05 m. Previous researches [34,35] revealed that the radiation heat from thermocouples to the exterior would result in the deviation between the measured and true flame temperature. In this research, the maximum radiation error of the axial flame temperature is less than 17 K, which the relative error is in the range of 2.1%; the maximum radiation error of ceiling temperature is less than 2 K, which the relative error is in the range of 0.4%. A square glass container (20 × 20 × 5 cm) with a quartz glass cover (4.5 × 5 cm), where a water cooled radiometer was arranged into, was used as a special fuel container; the radiometer was paralleled to the fuel surface before the burning in each test, as shown in Fig. 2 (c). This method was in accordance with Hu's design to measure the heat feedback to the pool surface [36]. As shown in Fig. 2 (c), the transmissivity coefficient (τ ) of quartz glass was calculated by the average ratio of qwithout to qwith , these two values were measured by the water-cooled radiometers in a comparative experiment of oil pool fire during the steady burning stage: one with the quartz glass cover and the other without. Two water-cooled radiometers were placed at the 1.0 m horizontal distance from the oil pool center, and nearly at same height with the oil pool surface, as shown in Fig. 2 (a). In order to improve the measurement accuracy, the quartz glass cover was cleaned up with alcohol after each test and the calibration needs to be made in every test. The field of view of the radiometer to be 180°, whose absorptivity is 0.95. And the range of the radiometer is 0.3–50.000 μm, which covers the dominant radiation spectrum of the n-heptane fire [37]. During all the experiments, the calibration of transmissivity coefficient of quartz
Table 1 The configure of experiment cases. Case groups
Environment pressure (kPa)
Ceiling inclined angel (°)
Measured parameters
A B C
50 76 101
0,15,30,45
Mass loss, Flame temperature, ceiling temperature, heat radiation feedback
glass, i.e. the value of τ varied from 0.659 to 0.723. 200 g of n-heptane (industrial purity above 99% and density being 0.684 g/ml) went into the glass pool, and it was the test fuel in each test. A highly accurate electronic scale (AMPT 418) was placed beneath the pan to measure the mass loss of the fuel during the tests; the burning rate was calculated based on these data. The data from the electronic scale, thermocouples and radiometers were recorded by the data acquisition system of National Instruments, whose sampling rates were 1 Hz. Table 1 shows the experimental configurations of oil pool fire tests, and each test was repeated three times. The repeatability error of liquid mass was less than 6%. This is can be explained by the liquid vaporization when the cabin pressure was adjusted to the working pressure. In this research, the influence of environment pressure on the boiling point, vapor pressure was neglected because the discussion of the fire behavior, ceiling temperature were focused on the stable stage of fire burning.
3. Results and discussion 3.1. Heat radiation feedback The real value of heat radiation feedback was calculated by q″m / τ , where q″m was measured by the radiometers. It is worth noticing that although the fuel vapor, soot particles and combustion products may block much heat from the heated ceiling [38,39], the calculated value of q″m / τ represents the real value received by the container surface. Fig. 3 shows the flame radiation feedback to pool surface versus
Fig. 2. Fire experiment layout and instrumentation. (a) Experimental layout, (b) Fireproof board, (c) Glass container. 489
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Fig. 3. Heat radiation feedback at different ceiling inclined angle under: (a) 50 k Pa, (b) 76 kPa, (c) 101 kPa.
burning time at different angles under 50 kPa, 76 kPa and 101 kPa. The curves are divided into three stages, and each curve rises at the beginning of the first stage (i) and the end of third stage (iii). This because there is a smaller amount of oil vapor at the pool surface owing to the smaller heat release rate at the initial burning stage and the descending mass of liquid fuel at the end of third stage, resulting into a relatively low flame height, and a closer distance from flame to the measured quartz glass cover, which is in line with the Zhao's thin-layer pool fires research [40]. It also can be found that there are apparent fluctuations in curves even at the steady stage, which is caused by the flame pulsation; and turning to be more vigorous when the flame extension length difference in the upward direction and in the downward direction of ceiling is more remarkable (θ = 45°) [21]. After the comparison of those curves at the same inclination angle under different ambient pressures, it also can be seen that the incident radiation feedback increases considerably with ambient pressure. This can be explained by Tu et al. [41]: they pointed out that for the middle-sized oil pool fires, the radiation fraction (q˙ ″rad / q˙ ″) nearly remained unchanged under different pressures, so the discrepancy between heat radiation feedback curves can be attributed to different burning rates. In addition, there is no doubt that under a higher-pressure environment, burning rate tends to be larger. Note that in this figure the stage of the heat radiation feedback takes up a large amount of time of burning, however, it will be observed that in burning rate curves (Fig. 5) the time of steady burning is a very short process, these two stages not corresponding to each other on time. This also can be evidenced by the work of Zhao et al. [40], they concluded that when the flame height is high enough, the heat radiation feedback can be assumed as a constant in burning, and they also pointed out that the heat feedback is not the main factor influencing thin-layer oil pool fire. Fig. 4 shows the relationship between dimensionless average heat radiation feedback and inclined ceiling angle in the steady stage, which can be well fitted by a second-order equation, the correlation coefficient is 0.9285: q˙ ″ (θ)/ q˙ ″ (0) = 0.0004746θ 2 − 0.01787θ + 0.9981. In it q˙ ″ (θ)
represents the average heat radiation feedback during the steady stage, and q˙ ″ (0) as the reference value represents the heat radiation feedback value in the case of θ = 0°. In this study, it can be seen that the maximum value of each radiation curve appears in the case of θ = 45°; the minimum value in the case of θ = 15°. The value is not a monotone changing trend as the inclined ceiling angle increases. This is because the differences in burning rate and geometric radiation coefficients are caused by different inclination angles. It is worthy of noticing that geometric radiation coefficients also are affected by the flame shape, because Zhang's research showed the flame extension lengths in the upward and the downward directions were changed by the inclination angle [21].
Fig. 4. Dimensionless average heat radiation feedback with different slopped angle ceiling at the steady stage. 490
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Fig. 5. Burning rates versus time of different ceiling angles under 50 kPa.
Fig. 6. Mass burning rate with the flame radiation feedback at the steady stage.
3.2. Burning rate
m″ ∝ q˙ ″θ /(cP ΔT + ΔHg )
Fig. 5 displays the burning rates of oil pool fires under 50 kPa. In the case of θ = 0°, it can be seen that the burning rate can be divided into pre-burning stage, steady burning stage (the axial temperature maintains relatively stable), and decay stage. During the first stage, the burning rate increases at a fast speed; after almost 200s, the curve reaches its maximum and keeps the value for a period; then during the third stage, owing to the increase of fuel consumption, the burning rate decreases rapidly. It can be found that the maximum burning rate in the steady burning stage appears in the case of θ = 0°. The smaller burning rate tends to be in the case of θ = 45°and in this case, the process of steady burning lasts almost for the completely burning time. It also can be found that there are significant differences in the curve slopes of the first stage and the third stage under different pressures. Two reasons are for the differences: on the one hand, Kuang [43] revealed that as the angle increased, the air entrainment increased in the upward direction, while the decreasing buoyancy force of the vertical flame could restrict the air entrainment. On the other hand, as shown in Fig. 3, the heat radiation feedback continues to change as the inclination angle increases. The burning of an oil pool fire is generally considered to be the combustion of the liquid vapor. In the process of combustion, the oil is heated to be the liquid vapor, and then mixed with air for burning. Previous studies [27,41] indicated that burning rate was determined by the heat conduction (q¨con ), heat convection (q¨conv ), and heat radiation (q¨rad ), as shown in the following correlation:
(3)
Without the consideration of the effects of pressure on the boiling point of the liquid fuel, the mass burning rate with flame radiation feedback in the steady stage is illustrated in Fig. 6, where the fitting line is m″ = 0.6491q″θ + 5.243. Apparently, the prediction of the correlation is not ideal, with correlation coefficient being 0.7332. This is because in this study, the initial fuel thickness was relatively thin (less than 8 mm), and there was no water layer between the fuel and the container bottom, which was different from the previous studies on oil fire. Zhao et al. [43] conducted a series of experiments on thin oil pool fire with the fuel thickness ranging from 2 mm to 11.5 mm, and pointed out that a large part of heat radiation feedback was not absorbed by the oil but directly penetrated through the bottom of the fuel container. They also revealed that the amount of the unabsorbed part increased as the thickness of the oil layer decreased, expressed asq″b, p = (0.26q″θ + 0.74q″θ × e−0.5h ) × (1 − Xsf ), where q″b, P was the thermal radiative penetration, and Xsf was fuel surface reflectivity. Therefore, the part of thermal radiative penetration should be not neglected. By substituting q″b, P into Equation (2), the model of mass burning rate can be rewritten as
m″ ∝ (q″θ − q″b, P )/ L ∝ (0.74q″θ + 0.26q″θ Xsf + 0.74q″θ × e−0.5h)/ L
(4)
In Equation (4), the q″θ is a relative constant during the burning, as a result: as the burning time goes on, the decreasing fuel thickness will weaken the heat absorbability of unburned oil fuel, influencing the burning intensity of pool fire.
m˙ ″ ∝ (q˙ ″con + q˙ ″conv + q˙ ″rad )/ L k
∝ [4 D (Tf − Tl ) + h (Tf − Tl ) + σ (T f4 − Tl4 )(1 − exp (−κs lm))/ L
(1) 3.3. Axial temperature distribution
WhereTf , Tl is flame temperature, fuel surface temperature respectively. k , h andσ represents heat conduction coefficient, the convective heat transfer coefficient, and Stefan–Boltzmann constant, respectively. κs is the emissivity coefficient, lm is the mean beam length, L is effective heat gasification. For an oil pool with the diameter of more than 20 cm, the fire is dominated by radiation [41]. In this study, the container is a 20 × 20 × 5 cm square oil pan, whose equivalent diameter is greater than 20 cm. During the steady stage of oil pool burning, q˙ ″rad can be represented by the heat radiation feedback q˙ ″θ , thus, the correlation (1) can be rewritten as:
m″ ∝ q˙ ″θ / L
The flame temperature in the steady stage recorded by thermocouples at different axial heights are presented in Fig. 7. It can be seen that, along with the centerline axis, flame temperature increases first, then decreases, and finally rises when flame is closed to the ceiling. At the first measurement point (HT = 0.02m ), the temperature in the highpressure environment is larger than that in the low-pressure environment. In addition, heat radiation feedback to the pool surface is larger in the high-pressure environment, and the burning rate of the oil pool tends to be violent, which is corresponding with the previous studies [31]. In this study, owing to the effects of ceiling, under the inclined ceiling at 0° and 15°, the rate of flame temperature decrease along the axial height was not much influenced by the pressure change; And when the ceiling inclination angle was relatively small, the effects on flame temperature near the ceiling were more significant.
(2)
Based on the fact that the evaporation rate of the liquid is basically equal to the heating rate, L = ΔHg + cP (Tb − Tl ) . Thus, the mass burning rate in the steady stage can be calculated: 491
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Fig. 7. Steady stage flame temperature recorded by thermocouples at different axial height.
divided into two parts: upward direction temperature (Tup ), downward direction temperature (Tdown ). For the first part, new correlations are proposed for the prediction of ceiling temperature distribution in the upward direction (r > 0 ). By introducing the flame characteristic radius length (b ), Heskestad and Hamada [10] obtained a model for ceiling temperature distribution of strong plume impingement flow:
3.4. Temperature decay distribution of ceiling According to the work on flame extension of strong plume impingement flow by Zhang et al. [21], owing to the unequal distribution of unburned mass flow, they divided the ceiling into upward direction part and downward direction part by the flame impingement point. They pointed out that the mass flow in the upward direction wasm˙ up = m˙ u (1 + sinθ)/2 , and that in the downward direction wasm˙ down = m˙ u (1 − sinθ)/2 , and the difference continued to increase as the ceiling inclination angle increased. As shown in Fig. 2 (b), the right and left parts of the ceiling are defined as the upward direction and downward direction respectively in this paper. In the cases of 50 kPa, it can be seen in Fig. 8 that owing to the unequal distribution of the unburned mass flow, the ceiling temperature contour profiles also show asymmetry. Therefore, in the follow-up study, ceiling temperature is
ΔTr r −1 r = 1.92 ⎛ ⎞ − exp ⎛1.61 ⎛1 − ⎞ ⎞, 1 < r / b < 40 ΔT0 b ⎠⎠ ⎝b⎠ ⎝ ⎝
(5)
Where ΔT0 is the ceiling temperature rise at the flame impingement point, and ΔTr is the ceiling temperature rise of r horizontally away from the impingement point. Flame characteristic radius length b can be 2/5 −1/2 T0 H1/2Q˙ c
3/5 2/5 g ] calculated through b = [5.67(cp ρ∞) 4/5T∞
Fig. 8. Ceiling temperature contour profiles under 50 kPa. 492
ΔT03/5
, calculated
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by Q˙ c = Sm˙ ″ΔHc . In the previous studies on the temperature distribution and velocity of gas flow under an inclined ceiling, owing to the effects of ceiling inclination angle, Oka [18] suggested that Q˙ c should be replaced byQ˙ c (1 + sinθ) , and r should be replaced by projector distance rcosθ . Considering the parameters above, we re-fit them in Equation (5) for the cases with different angles under the same pressure, as shown in Fig. 9. −1 ⎧ ΔTr /ΔT0 = 2.0571(rcosθ /b) ∗ exp [1.2927(1 − rcosθ /b)], ΔTr /ΔT0 = 1.9256(rcosθ / b)−1 ∗ exp [1.5657(1 − rcosθ / b)], ⎨ −1 ⎩ ΔTr /ΔT0 = 1.8767(rcosθ /b) ∗ exp [1.5464(1 − rcosθ /b)],
strong plumes ceiling jets, the prediction model for ceiling temperature in the downward direction was established by Kung [42], where ΔTdown/ ΔT0 was the function ofr / b .
ΔTdown = (0.15sinθ + 0.11) r / b + 0.97 − 0.06sinθ ΔT0
Fig. 10 shows the dimensionless temperature distribution ΔTdown/ ΔT0 versus dimensionless distancer / b at different angles.
P = 50kPa P = 76kPa P = 101kPa
⎧ ΔTdown/ΔT0 = 0.0763 ∗ (r / b) + 0.7881, ⎪ ΔTdown/ΔT0 = 0.0613 ∗ (r / b) + 0.6175,
(6)
⎨ ΔTdown/ΔT0 = 0.0737 ∗ (r / b) + 0.5766, ⎪ ΔT /ΔT = 0.1090 ∗ (r / b) + 0.8166, 0 ⎩ down
It can be seen that the rate of ceiling temperature decay with the radius turns to slow as the ceiling inclination angle increases, which is in accordance with the conclusion that unburned mass flow increases significantly in the upward direction as the angle increases. After the comparison of the model coefficients in the cases under different pressures, it can be found that as the pressure inside the compartment decreases, the rate of temperature decline turns to be faster, which can be explained by the flame extension elongation and the upper-shift of high-temperature zone. As shown in Fig. 9, the current experimental data can be well correlated by the model of Heskestad & Hamada [10], which can be concluded that compared to the ceiling inclined angle, the environment pressure was the key factor influencing the ceiling temperature distribution of the strong plume impingement. By fitting the equation coefficient under different pressures, we can establish a unified correlation for ceiling temperature distribution in the upward direction: −1 ⎧ ΔTup/ ΔT0 = αup ∗ (r cos θ) − exp [βup (1 − r cos θ) b] ⎪ − 5 2 αup = 6e ∗ p − 0.0127 ∗ p + 2.5411 , ⎨ ⎪ βup = 0.0002 ∗ p2 + 0.0383 ∗ p + 0.0722 ⎩
(8)
θ = 0° θ = 15° θ = 30° θ = 45°
(9)
It can be found that at the same ceiling inclination angle, there is a good linear relationship between the dimensionless temperature distribution ΔTdown/ ΔT0 and dimensionless distancer / b , revealing that the low-pressure environment almost had no influence on downward distribution. When the angle increases from θ = 0° to θ = 45°, the dimensionless distance between the impinging point and the specific point, where the measured value is equal to environment temperature, decreases from 10.3 to 7.5. Therefore, it can be concluded that as the inclination angle increases, the rate of temperature decline in the downward direction also increases significantly. This corresponds to previous studies [42] and can be attributed to the decrease of unburned mass flow at the ceiling inclination angle. As shown in Fig. 10, it is obvious that the predicted value of inclined ceiling temperature model obtained by Kung [42] cannot be well correlated to our measured value, because in our experiments the ceiling inclined angle, the dimensionless distance was larger than those in the previous model. In addition, Zhang et al. [11] pointed out that the dimensionless ceiling clearance H / D played a dominant role to influence the ceiling temperature. In the downward direction, a unified model for gas ceiling temperature can be expressed as:
r>0
(7) Whereαup , βup are calculated by fitting the equation coefficient in Equation (6) to the value of ambient pressure p . The second part is for the study of the ceiling temperature distribution in the downward direction (r < 0 ). In fire experiments on
Fig. 9. Dimensionless temperature decay profiles in the upward direction ΔTupwrad/ ΔT0 against dimensionless distance rcosθ / b under (a) 50 kPa, (b) 76 kPa, and (c) 101 kPa. 493
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Fig. 10. Dimensionless temperature decay profiles in the downward direction ΔTdownward/ ΔT0 against dimensionless distance r / b for the cases of (a) θ = 0°, (b)θ = 15°, (c)θ = 30° , and (d) θ = 45°.
ΔTdown/ ΔT0 = αdown ∗ (r / b) + βdown ⎧ ⎪ αdown = −0.0239 ∗ sin2 (θ) + 0.1235 ∗ sin (θ) − 0.0765 , ⎨ ⎪ βdown = 1.8378 ∗ sin2 (θ) − 1.2914 ∗ sin (θ) + 0.7976 ⎩
jet in the low-pressure environment, which is meaningful for fire protection in aircraft safety. The penetration heat loss in low-pressure environment for the thin-layer pool fires needs more investigation, and our future work will also focus on the flame extension on the inclined ceiling in an airplane compartment.
r<0 (10)
Whereαdown , βdown are calculated by fitting the equation coefficient in Equation (9) to the value of ceiling inclined angleθ .
Acknowledgement This work is supported by National Key R&D Program of China (No. 2018YFC0809500), National Natural Science Foundation of China (Grant No: U1633203) and the R&D project of Civil Aviation Administration of China (Grant No: 20160103).
4. Conclusion In this study, the square liquid pool fires under an inclined ceiling with the same ceiling clearance were studied in a full-size cargo compartment in different pressure environments. Some major conclusions are summarized as follows:
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1. For oil pool fire on the assumption of heat radiation domination, heat feedback radiation to the pool was discussed, which not accord with the trend of burning rates. This is because for the thin-layer burning, the penetration heat loss makes up a large proportion of heat radiation feedback; the burning rate model is suggested to be written as: m″ ∝ (0.74q″θ + 0.26q″θ Xsf + 0.74q″θ × e−0.5h)/ L 2. Owing to the effects of ceiling, the rate of flame temperature decrease is not much affected by the pressure change inside the cargo when the ceiling inclination angles are θ = 0° and θ = 15° 3. According to the flame impingement point, the ceiling is divided into upward direction part and downward direction part. Owing to the inhomogeneous distribution of unburned fuel flow, gas temperature distribution also shows asymmetry on these two parts. 4. Based on the previous model, the correlations of ceiling temperature distribution in the upward direction and downward direction are established, respectively. This study provides an understanding of fires with inclined ceiling 494
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International Journal of Thermal Sciences journal homepage: www.elsevier.com/locate/ijts
An experimental study on fire behavior of an inclined ceiling jet in a lowpressure environment
T
Zhenxiang Tao, Rui Yang∗, Cong Li, Yina Yao, Ping Zhang, Hui Zhang Department of Engineering Physics, Tsinghua University, Beijing, 100084, China
A R T I C LE I N FO
A B S T R A C T
Keywords: Inclined ceiling Low pressure Ceiling jet fire Aircraft cargo compartment
Inclined ceiling jet fire may occur in a low-pressure aircraft cargo, which poses a great threat to airplane safety. To simulate an inaccessible area in cargo compartment, investigate the effects of pressure on the combustion characteristics of inclined ceiling jet fire, a series of fire experiments under an inclined ceiling (0°, 15°, 30°, 45°) in different pressure environments (50 kPa, 76 kPa, 101 kPa) were carried out in a full-size simulated cargo compartment. N-heptane square pool fires (20 × 20 × 5 cm), as radiation-controlled oil pool fires, were used as fire sources. The burning rate, heat radiation feedback, flame temperature, and ceiling temperature were measured and analyzed. The experiments showed that the heat radiation to pool surface had a significantly positive correlation with ambient pressure, and the penetration of thermal radiation made up a large proportion of heat radiation feedback, which should not be neglected for thin-layer oil burning. When the inclination angle was θ = 0° or θ = 15°, owing to the effects of ceiling, no significant differences existed on the rate of the axial flame temperature decrease in different pressure environments. Moreover, there were some fluctuations when flame was close to the ceiling. Based on previous models, new correlations to predict ceiling temperature in the upward direction and downward direction in different pressure environments were proposed, respectively.
1. Introduction Cargo fire is one of the most dangerous threats to aircraft in operation, which contain heavy bulk loads filled with various combustibles [1–3]. When a fire occurs in the cargo compartment, it may cause an inclined ceiling jet fire due to the different flight attitudes or the curved sidewall of the cargo compartment [4,5]. On the other hand, the internal pressure of the cargo compartment for many commercial airplanes in flight is approximately 76 kpa, while for regional airliner it is 50 kPa [6]. To understand the combustion characteristics of inclined ceiling jet in a low-pressure environment will improve our understanding of the mechanism of the aircraft cargo fire. To design a more scientific and reasonable smoke alarm, or water mist system in building and tunnel fires, many scholars have discussed the combustion characteristics of ceiling jet [7–16]. In early years, according to theoretical analysis and experimental verification, Alpert [7], and Heskestad [8] proposed classical models on the gas temperature for unconfined ceiling and confined ceiling, respectively. You & Faeth [9] performed a series of experiments on liquid pool fires and pointed out that the flame length tended to increase in confinement. By introducing flame radius b , Heskestad & Hamada [10] developed a model for temperature distribution in ceiling jets generated by strong ∗
plume when the ratio of flame height to ceiling clearance ranged from 0.3 to 3. In recent years, based on a series of gas fire tests, Zhang [11] developed models on flame extension length and temperature profile for a thermal impinging flow. Gao et al. [12] studied the characteristics of burner with different vertical heights and heat releases. They claimed that ceiling temperature at the impingement point could be well fitted with three zones. Meng et al. [13] developed models for the maximum temperature beneath the tunnel ceiling related to the vehicular blockage ratio, and the longitudinal ventilation velocity. Zhou et al. [14] also studied the changes of transverse fire locations and the sidewall constraint on the temperature distribution, and concluded that the temperature under the arced ceiling were higher than those under the flat ceiling. Wang [15] conducted experiments to study the natural ventilations on pool fire characteristics and concluded that some smoke may backflow, and despite smoke temperature decreasing in tunnel fire with roof opening. Tang et al. [16] investigated the effect of point extraction system in a reduced scale model, showing that the air entrainment coefficient increases with the HRRs when the ceiling extraction velocity was set to a fixed value. In addition, some studies were focused on the characteristics of ceiling jet under an inclined ceiling [17–23]. Oka [17–19] systematically performed pool fire experiments under a ceiling inclined at
Corresponding author. E-mail address: [email protected] (R. Yang).
https://doi.org/10.1016/j.ijthermalsci.2019.01.023 Received 5 September 2018; Received in revised form 11 December 2018; Accepted 17 January 2019 1290-0729/ © 2019 Published by Elsevier Masson SAS.
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Nomenclature
τ q˙ ″ (0) q˙ ″ (θ) q˙ ″con q″conv q″rad q″b, p Tf Tl Tb L ΔHg p cP Xsf D H HT m˙ m˙ ″ m˙ u m˙ up
m˙ down Q˙ b ΔTa ΔT0 ΔTr
Transmissivity coefficient of Quartz glass Heat radiation feedback in the case ofθ = 0° (kW/m2) Average heat radiation feedback to pool surface in steady stage (kW/m2) Heat conduction (kW/m2) Heat convention (kW/m2) Heat radiation (kW/m2) Thermal radiative penetration (kW/m2) Flame temperature (K) Fuel surface temperature (K) Boiling point of liquid fuel (K) Effective heat gasification (kJ/kg) Evaporation heat (kJ/kg) Internal pressure of cargo compartment (kPa) Heat capacity (kJ/kg·K) Fuel surface reflectivity Length of container (m) Ceiling clearance (m) Axial height of thermocouple (m) Burning rate (g/s) Mass burning rate (g/s·m2) Unburned mass flow Mass flow in the upward direction
Q˙ c ΔTup ΔTdown
Mass flow in the upward direction Heat release rate (kW/s) Characteristic radius length (m) Axial temperature of flame (K) Ceiling temperature rise at flame impingement point (K) Ceiling temperature rise of r horizontally away from the impingement point (K) Convective heat release rate (kW/m2) Ceiling temperature rise in the upward direction (K) Ceiling temperature rise in the downward direction (K)
Subscripts
0 r
∞ l f con conv rad up down
Flame impingement point Horizontal distance between the specific point and the impingement point Ambient Liquid Flame
Heat conduction Heat convention Heat radiation Upward Downward
attention has to be paid to the combustion characteristics of ceiling jet, especially those of inclined ceiling jet in a low-pressure environment. In this paper, the effects of pressure (50 kPa, 76 kPa, 101 kPa) on nheptane pool fires under a ceiling at different inclination angles (0°, 15°, 30°, 45°) with the same ceiling clearance (0.6 m) were studied in a full-size simulated cargo compartment. The burning rate, heat radiation feedback to the pool surface, vertical temperature, and ceiling temperature were measured and analyzed comprehensively.
from 0° to 40°, and established a more effective model to predict the temperature and velocity of ceiling jet. Based on a series of reducedscale inclined tunnel fire experiments, Hu et al. [20] modified the classical exponential decay model on temperature profiles of buoyant gas. More recently, Zhang et al. [21] analyzed the flame extensions at different inclination angles with various ceiling clearances. They found that the flame extension in the upward direction larger than in the downward direction, and this difference was enlarged as the ceiling's inclination angle increased. Zhang [22] studied the smoke temperature distribution on rectangle propane gas fires at different ceiling angles, and developed a unified correlation for the prediction of maximum temperature. Based on these previous studies and analysis for gas fuel ceiling jet fire, Zhang [23] also proposed a unified correlation for the temperature attenuation along the slopped ceiling. Although experimental evidences have shown that fire behaviors are inherently different in a low-pressure environment: reduction in burning rate, prolonged flame shape, up-shift of flame's high-temperature zone [24–33], there are only a few studies on the effects of pressure on ceiling jet fires. Wang [5] used a simulated cargo compartment to test four pool fires of different sizes in different low-pressure environments. By introducing air entrainment ratio, they proposed the correlations for maximum ceiling temperature and ceiling temperature decay profile in different pressure environments. Considering the multi-sensor (such as the smoke density, ceiling temperature, air humidity in a fire) detectors could improve the accuracy of aircraft fire detection, our
2. Experimental apparatus and measurements The experiments were carried out in a heat-resistant rig that was placed at the center of a full-size simulated cargo compartment, as shown in Fig. 1. The whole rig was made of 4040 standard industrial aluminum alloys with the dimensions of 0.78 × 0.78 × 1.52 m. Two adjustable angle brackets were equipped in the middle of the frame to adjust the ceiling's inclination angle, and the maximum value was 45°. In order to meet different ceiling sizes, six heat-resistant clips, which could be adjusted in four directions, were fixed on the frames. The cargo compartment was made of high-grade stainless steel with the dimensions of 8.11 × 4.16 × 1.67 m. During the test, the pressure inside the compartment was controlled firstly by letting airflow in and out through a vacuum pump to maintain at the target value, and then the fuel was ignited by an electrifying looped nickel-cadmium resistance wire, which was placed at the surface of the liquid fuel.
Fig. 1. Full-scale simulated cargo compartment and heat-resistant rig. 488
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Fire experiment layout and instrumentation in our study were illustrated in Fig. 2. Above the oil pool, a 120 * 50 * 2 cm fireproof board with a low thermal conductivity of 0.03 W/(m*K) was used as the ceiling. 19 K-type thermocouples whose diameter was 0.5 mm were located 10 mm below the ceiling to measure the gas temperature. The interval between X-axis thermocouples was 0.1 m and the interval between Y-axis thermocouples was 0.05 m, as shown in Fig. 2 (b). The flame temperature was measured by an array of 1 mm K-type thermocouples, arranged in the centerline of the oil pan. The distance from the lowest thermocouple to the oil pool surface was 0.02 m, and the interval between other thermocouples was 0.05 m. Previous researches [34,35] revealed that the radiation heat from thermocouples to the exterior would result in the deviation between the measured and true flame temperature. In this research, the maximum radiation error of the axial flame temperature is less than 17 K, which the relative error is in the range of 2.1%; the maximum radiation error of ceiling temperature is less than 2 K, which the relative error is in the range of 0.4%. A square glass container (20 × 20 × 5 cm) with a quartz glass cover (4.5 × 5 cm), where a water cooled radiometer was arranged into, was used as a special fuel container; the radiometer was paralleled to the fuel surface before the burning in each test, as shown in Fig. 2 (c). This method was in accordance with Hu's design to measure the heat feedback to the pool surface [36]. As shown in Fig. 2 (c), the transmissivity coefficient (τ ) of quartz glass was calculated by the average ratio of qwithout to qwith , these two values were measured by the water-cooled radiometers in a comparative experiment of oil pool fire during the steady burning stage: one with the quartz glass cover and the other without. Two water-cooled radiometers were placed at the 1.0 m horizontal distance from the oil pool center, and nearly at same height with the oil pool surface, as shown in Fig. 2 (a). In order to improve the measurement accuracy, the quartz glass cover was cleaned up with alcohol after each test and the calibration needs to be made in every test. The field of view of the radiometer to be 180°, whose absorptivity is 0.95. And the range of the radiometer is 0.3–50.000 μm, which covers the dominant radiation spectrum of the n-heptane fire [37]. During all the experiments, the calibration of transmissivity coefficient of quartz
Table 1 The configure of experiment cases. Case groups
Environment pressure (kPa)
Ceiling inclined angel (°)
Measured parameters
A B C
50 76 101
0,15,30,45
Mass loss, Flame temperature, ceiling temperature, heat radiation feedback
glass, i.e. the value of τ varied from 0.659 to 0.723. 200 g of n-heptane (industrial purity above 99% and density being 0.684 g/ml) went into the glass pool, and it was the test fuel in each test. A highly accurate electronic scale (AMPT 418) was placed beneath the pan to measure the mass loss of the fuel during the tests; the burning rate was calculated based on these data. The data from the electronic scale, thermocouples and radiometers were recorded by the data acquisition system of National Instruments, whose sampling rates were 1 Hz. Table 1 shows the experimental configurations of oil pool fire tests, and each test was repeated three times. The repeatability error of liquid mass was less than 6%. This is can be explained by the liquid vaporization when the cabin pressure was adjusted to the working pressure. In this research, the influence of environment pressure on the boiling point, vapor pressure was neglected because the discussion of the fire behavior, ceiling temperature were focused on the stable stage of fire burning.
3. Results and discussion 3.1. Heat radiation feedback The real value of heat radiation feedback was calculated by q″m / τ , where q″m was measured by the radiometers. It is worth noticing that although the fuel vapor, soot particles and combustion products may block much heat from the heated ceiling [38,39], the calculated value of q″m / τ represents the real value received by the container surface. Fig. 3 shows the flame radiation feedback to pool surface versus
Fig. 2. Fire experiment layout and instrumentation. (a) Experimental layout, (b) Fireproof board, (c) Glass container. 489
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Fig. 3. Heat radiation feedback at different ceiling inclined angle under: (a) 50 k Pa, (b) 76 kPa, (c) 101 kPa.
burning time at different angles under 50 kPa, 76 kPa and 101 kPa. The curves are divided into three stages, and each curve rises at the beginning of the first stage (i) and the end of third stage (iii). This because there is a smaller amount of oil vapor at the pool surface owing to the smaller heat release rate at the initial burning stage and the descending mass of liquid fuel at the end of third stage, resulting into a relatively low flame height, and a closer distance from flame to the measured quartz glass cover, which is in line with the Zhao's thin-layer pool fires research [40]. It also can be found that there are apparent fluctuations in curves even at the steady stage, which is caused by the flame pulsation; and turning to be more vigorous when the flame extension length difference in the upward direction and in the downward direction of ceiling is more remarkable (θ = 45°) [21]. After the comparison of those curves at the same inclination angle under different ambient pressures, it also can be seen that the incident radiation feedback increases considerably with ambient pressure. This can be explained by Tu et al. [41]: they pointed out that for the middle-sized oil pool fires, the radiation fraction (q˙ ″rad / q˙ ″) nearly remained unchanged under different pressures, so the discrepancy between heat radiation feedback curves can be attributed to different burning rates. In addition, there is no doubt that under a higher-pressure environment, burning rate tends to be larger. Note that in this figure the stage of the heat radiation feedback takes up a large amount of time of burning, however, it will be observed that in burning rate curves (Fig. 5) the time of steady burning is a very short process, these two stages not corresponding to each other on time. This also can be evidenced by the work of Zhao et al. [40], they concluded that when the flame height is high enough, the heat radiation feedback can be assumed as a constant in burning, and they also pointed out that the heat feedback is not the main factor influencing thin-layer oil pool fire. Fig. 4 shows the relationship between dimensionless average heat radiation feedback and inclined ceiling angle in the steady stage, which can be well fitted by a second-order equation, the correlation coefficient is 0.9285: q˙ ″ (θ)/ q˙ ″ (0) = 0.0004746θ 2 − 0.01787θ + 0.9981. In it q˙ ″ (θ)
represents the average heat radiation feedback during the steady stage, and q˙ ″ (0) as the reference value represents the heat radiation feedback value in the case of θ = 0°. In this study, it can be seen that the maximum value of each radiation curve appears in the case of θ = 45°; the minimum value in the case of θ = 15°. The value is not a monotone changing trend as the inclined ceiling angle increases. This is because the differences in burning rate and geometric radiation coefficients are caused by different inclination angles. It is worthy of noticing that geometric radiation coefficients also are affected by the flame shape, because Zhang's research showed the flame extension lengths in the upward and the downward directions were changed by the inclination angle [21].
Fig. 4. Dimensionless average heat radiation feedback with different slopped angle ceiling at the steady stage. 490
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Fig. 5. Burning rates versus time of different ceiling angles under 50 kPa.
Fig. 6. Mass burning rate with the flame radiation feedback at the steady stage.
3.2. Burning rate
m″ ∝ q˙ ″θ /(cP ΔT + ΔHg )
Fig. 5 displays the burning rates of oil pool fires under 50 kPa. In the case of θ = 0°, it can be seen that the burning rate can be divided into pre-burning stage, steady burning stage (the axial temperature maintains relatively stable), and decay stage. During the first stage, the burning rate increases at a fast speed; after almost 200s, the curve reaches its maximum and keeps the value for a period; then during the third stage, owing to the increase of fuel consumption, the burning rate decreases rapidly. It can be found that the maximum burning rate in the steady burning stage appears in the case of θ = 0°. The smaller burning rate tends to be in the case of θ = 45°and in this case, the process of steady burning lasts almost for the completely burning time. It also can be found that there are significant differences in the curve slopes of the first stage and the third stage under different pressures. Two reasons are for the differences: on the one hand, Kuang [43] revealed that as the angle increased, the air entrainment increased in the upward direction, while the decreasing buoyancy force of the vertical flame could restrict the air entrainment. On the other hand, as shown in Fig. 3, the heat radiation feedback continues to change as the inclination angle increases. The burning of an oil pool fire is generally considered to be the combustion of the liquid vapor. In the process of combustion, the oil is heated to be the liquid vapor, and then mixed with air for burning. Previous studies [27,41] indicated that burning rate was determined by the heat conduction (q¨con ), heat convection (q¨conv ), and heat radiation (q¨rad ), as shown in the following correlation:
(3)
Without the consideration of the effects of pressure on the boiling point of the liquid fuel, the mass burning rate with flame radiation feedback in the steady stage is illustrated in Fig. 6, where the fitting line is m″ = 0.6491q″θ + 5.243. Apparently, the prediction of the correlation is not ideal, with correlation coefficient being 0.7332. This is because in this study, the initial fuel thickness was relatively thin (less than 8 mm), and there was no water layer between the fuel and the container bottom, which was different from the previous studies on oil fire. Zhao et al. [43] conducted a series of experiments on thin oil pool fire with the fuel thickness ranging from 2 mm to 11.5 mm, and pointed out that a large part of heat radiation feedback was not absorbed by the oil but directly penetrated through the bottom of the fuel container. They also revealed that the amount of the unabsorbed part increased as the thickness of the oil layer decreased, expressed asq″b, p = (0.26q″θ + 0.74q″θ × e−0.5h ) × (1 − Xsf ), where q″b, P was the thermal radiative penetration, and Xsf was fuel surface reflectivity. Therefore, the part of thermal radiative penetration should be not neglected. By substituting q″b, P into Equation (2), the model of mass burning rate can be rewritten as
m″ ∝ (q″θ − q″b, P )/ L ∝ (0.74q″θ + 0.26q″θ Xsf + 0.74q″θ × e−0.5h)/ L
(4)
In Equation (4), the q″θ is a relative constant during the burning, as a result: as the burning time goes on, the decreasing fuel thickness will weaken the heat absorbability of unburned oil fuel, influencing the burning intensity of pool fire.
m˙ ″ ∝ (q˙ ″con + q˙ ″conv + q˙ ″rad )/ L k
∝ [4 D (Tf − Tl ) + h (Tf − Tl ) + σ (T f4 − Tl4 )(1 − exp (−κs lm))/ L
(1) 3.3. Axial temperature distribution
WhereTf , Tl is flame temperature, fuel surface temperature respectively. k , h andσ represents heat conduction coefficient, the convective heat transfer coefficient, and Stefan–Boltzmann constant, respectively. κs is the emissivity coefficient, lm is the mean beam length, L is effective heat gasification. For an oil pool with the diameter of more than 20 cm, the fire is dominated by radiation [41]. In this study, the container is a 20 × 20 × 5 cm square oil pan, whose equivalent diameter is greater than 20 cm. During the steady stage of oil pool burning, q˙ ″rad can be represented by the heat radiation feedback q˙ ″θ , thus, the correlation (1) can be rewritten as:
m″ ∝ q˙ ″θ / L
The flame temperature in the steady stage recorded by thermocouples at different axial heights are presented in Fig. 7. It can be seen that, along with the centerline axis, flame temperature increases first, then decreases, and finally rises when flame is closed to the ceiling. At the first measurement point (HT = 0.02m ), the temperature in the highpressure environment is larger than that in the low-pressure environment. In addition, heat radiation feedback to the pool surface is larger in the high-pressure environment, and the burning rate of the oil pool tends to be violent, which is corresponding with the previous studies [31]. In this study, owing to the effects of ceiling, under the inclined ceiling at 0° and 15°, the rate of flame temperature decrease along the axial height was not much influenced by the pressure change; And when the ceiling inclination angle was relatively small, the effects on flame temperature near the ceiling were more significant.
(2)
Based on the fact that the evaporation rate of the liquid is basically equal to the heating rate, L = ΔHg + cP (Tb − Tl ) . Thus, the mass burning rate in the steady stage can be calculated: 491
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Fig. 7. Steady stage flame temperature recorded by thermocouples at different axial height.
divided into two parts: upward direction temperature (Tup ), downward direction temperature (Tdown ). For the first part, new correlations are proposed for the prediction of ceiling temperature distribution in the upward direction (r > 0 ). By introducing the flame characteristic radius length (b ), Heskestad and Hamada [10] obtained a model for ceiling temperature distribution of strong plume impingement flow:
3.4. Temperature decay distribution of ceiling According to the work on flame extension of strong plume impingement flow by Zhang et al. [21], owing to the unequal distribution of unburned mass flow, they divided the ceiling into upward direction part and downward direction part by the flame impingement point. They pointed out that the mass flow in the upward direction wasm˙ up = m˙ u (1 + sinθ)/2 , and that in the downward direction wasm˙ down = m˙ u (1 − sinθ)/2 , and the difference continued to increase as the ceiling inclination angle increased. As shown in Fig. 2 (b), the right and left parts of the ceiling are defined as the upward direction and downward direction respectively in this paper. In the cases of 50 kPa, it can be seen in Fig. 8 that owing to the unequal distribution of the unburned mass flow, the ceiling temperature contour profiles also show asymmetry. Therefore, in the follow-up study, ceiling temperature is
ΔTr r −1 r = 1.92 ⎛ ⎞ − exp ⎛1.61 ⎛1 − ⎞ ⎞, 1 < r / b < 40 ΔT0 b ⎠⎠ ⎝b⎠ ⎝ ⎝
(5)
Where ΔT0 is the ceiling temperature rise at the flame impingement point, and ΔTr is the ceiling temperature rise of r horizontally away from the impingement point. Flame characteristic radius length b can be 2/5 −1/2 T0 H1/2Q˙ c
3/5 2/5 g ] calculated through b = [5.67(cp ρ∞) 4/5T∞
Fig. 8. Ceiling temperature contour profiles under 50 kPa. 492
ΔT03/5
, calculated
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by Q˙ c = Sm˙ ″ΔHc . In the previous studies on the temperature distribution and velocity of gas flow under an inclined ceiling, owing to the effects of ceiling inclination angle, Oka [18] suggested that Q˙ c should be replaced byQ˙ c (1 + sinθ) , and r should be replaced by projector distance rcosθ . Considering the parameters above, we re-fit them in Equation (5) for the cases with different angles under the same pressure, as shown in Fig. 9. −1 ⎧ ΔTr /ΔT0 = 2.0571(rcosθ /b) ∗ exp [1.2927(1 − rcosθ /b)], ΔTr /ΔT0 = 1.9256(rcosθ / b)−1 ∗ exp [1.5657(1 − rcosθ / b)], ⎨ −1 ⎩ ΔTr /ΔT0 = 1.8767(rcosθ /b) ∗ exp [1.5464(1 − rcosθ /b)],
strong plumes ceiling jets, the prediction model for ceiling temperature in the downward direction was established by Kung [42], where ΔTdown/ ΔT0 was the function ofr / b .
ΔTdown = (0.15sinθ + 0.11) r / b + 0.97 − 0.06sinθ ΔT0
Fig. 10 shows the dimensionless temperature distribution ΔTdown/ ΔT0 versus dimensionless distancer / b at different angles.
P = 50kPa P = 76kPa P = 101kPa
⎧ ΔTdown/ΔT0 = 0.0763 ∗ (r / b) + 0.7881, ⎪ ΔTdown/ΔT0 = 0.0613 ∗ (r / b) + 0.6175,
(6)
⎨ ΔTdown/ΔT0 = 0.0737 ∗ (r / b) + 0.5766, ⎪ ΔT /ΔT = 0.1090 ∗ (r / b) + 0.8166, 0 ⎩ down
It can be seen that the rate of ceiling temperature decay with the radius turns to slow as the ceiling inclination angle increases, which is in accordance with the conclusion that unburned mass flow increases significantly in the upward direction as the angle increases. After the comparison of the model coefficients in the cases under different pressures, it can be found that as the pressure inside the compartment decreases, the rate of temperature decline turns to be faster, which can be explained by the flame extension elongation and the upper-shift of high-temperature zone. As shown in Fig. 9, the current experimental data can be well correlated by the model of Heskestad & Hamada [10], which can be concluded that compared to the ceiling inclined angle, the environment pressure was the key factor influencing the ceiling temperature distribution of the strong plume impingement. By fitting the equation coefficient under different pressures, we can establish a unified correlation for ceiling temperature distribution in the upward direction: −1 ⎧ ΔTup/ ΔT0 = αup ∗ (r cos θ) − exp [βup (1 − r cos θ) b] ⎪ − 5 2 αup = 6e ∗ p − 0.0127 ∗ p + 2.5411 , ⎨ ⎪ βup = 0.0002 ∗ p2 + 0.0383 ∗ p + 0.0722 ⎩
(8)
θ = 0° θ = 15° θ = 30° θ = 45°
(9)
It can be found that at the same ceiling inclination angle, there is a good linear relationship between the dimensionless temperature distribution ΔTdown/ ΔT0 and dimensionless distancer / b , revealing that the low-pressure environment almost had no influence on downward distribution. When the angle increases from θ = 0° to θ = 45°, the dimensionless distance between the impinging point and the specific point, where the measured value is equal to environment temperature, decreases from 10.3 to 7.5. Therefore, it can be concluded that as the inclination angle increases, the rate of temperature decline in the downward direction also increases significantly. This corresponds to previous studies [42] and can be attributed to the decrease of unburned mass flow at the ceiling inclination angle. As shown in Fig. 10, it is obvious that the predicted value of inclined ceiling temperature model obtained by Kung [42] cannot be well correlated to our measured value, because in our experiments the ceiling inclined angle, the dimensionless distance was larger than those in the previous model. In addition, Zhang et al. [11] pointed out that the dimensionless ceiling clearance H / D played a dominant role to influence the ceiling temperature. In the downward direction, a unified model for gas ceiling temperature can be expressed as:
r>0
(7) Whereαup , βup are calculated by fitting the equation coefficient in Equation (6) to the value of ambient pressure p . The second part is for the study of the ceiling temperature distribution in the downward direction (r < 0 ). In fire experiments on
Fig. 9. Dimensionless temperature decay profiles in the upward direction ΔTupwrad/ ΔT0 against dimensionless distance rcosθ / b under (a) 50 kPa, (b) 76 kPa, and (c) 101 kPa. 493
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Fig. 10. Dimensionless temperature decay profiles in the downward direction ΔTdownward/ ΔT0 against dimensionless distance r / b for the cases of (a) θ = 0°, (b)θ = 15°, (c)θ = 30° , and (d) θ = 45°.
ΔTdown/ ΔT0 = αdown ∗ (r / b) + βdown ⎧ ⎪ αdown = −0.0239 ∗ sin2 (θ) + 0.1235 ∗ sin (θ) − 0.0765 , ⎨ ⎪ βdown = 1.8378 ∗ sin2 (θ) − 1.2914 ∗ sin (θ) + 0.7976 ⎩
jet in the low-pressure environment, which is meaningful for fire protection in aircraft safety. The penetration heat loss in low-pressure environment for the thin-layer pool fires needs more investigation, and our future work will also focus on the flame extension on the inclined ceiling in an airplane compartment.
r<0 (10)
Whereαdown , βdown are calculated by fitting the equation coefficient in Equation (9) to the value of ceiling inclined angleθ .
Acknowledgement This work is supported by National Key R&D Program of China (No. 2018YFC0809500), National Natural Science Foundation of China (Grant No: U1633203) and the R&D project of Civil Aviation Administration of China (Grant No: 20160103).
4. Conclusion In this study, the square liquid pool fires under an inclined ceiling with the same ceiling clearance were studied in a full-size cargo compartment in different pressure environments. Some major conclusions are summarized as follows:
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