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Experimental study on horizontal gas temperature distribution of two propane diffusion flames impinging on an unconfined ceiling
International Journal of Thermal Sciences 136 (2019) 1–8
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Experimental study on horizontal gas temperature distribution of two propane diffusion flames impinging on an unconfined ceiling
T
Huaxian Wana, Zihe Gaoa, Jie Jia,b,∗, Jun Fanga,∗∗, Yongming Zhanga a b
State Key Laboratory of Fire Science, University of Science and Technology of China, JinZhai Road 96, Hefei, Anhui, 230026, China Institute of Advanced Technology, University of Science and Technology of China, Hefei, Anhui, 230088, China
A R T I C LE I N FO
A B S T R A C T
Keywords: Unconfined ceiling Multiple flames Flame tilt Maximum temperature Temperature distribution
Ceiling gas temperature is one of the most important factors for heat detection and alarm once an undesirable fire along with releasing hot and toxic smoke is erupted in a building. The impinging flame characterized by the unburnt fuel burning along the ceiling has received much attention in recent years as it poses a greater threat to the ceiling structure, devices and trapped people than the non-impinging flame. Many studies have been focused on the ceiling gas temperature induced by a single flame, while little effort has been put with respect to the multiple flames. The interaction between multiple flames might lead to flames tilt to each other and even merge together with small spacings, resulting in different ceiling gas temperature distribution from the single flame. The aim of this experimental work is to investigate the ceiling gas temperature decay profile induced by two impinging flames. Propane was used as the fuel. The heat release rate (HRR), burner edge spacing and ceiling height above the fuel were overall changed. The ceiling gas temperatures along the direction of changing spacing were measured to determine the impingement point position and temperature decay profile. The results showed that the impingement point position is dependent on the HRR and the spacing as well as the ceiling height, while the maximum gas temperature is weakly affected by the spacing. The established correlation reveals that the maximum excess temperature increases first and then maintains unchanged with increasing the HRR normalized by the ceiling height. The plume radius proposed for the single impinging flame is not enough to characterize the ceiling gas temperature of two impinging flames. A new correlation for temperature decay profile induced by two impinging flames is therefore proposed and validated using the experimental results.
1. Introduction Diffusion flame is one of the most commonly used flames in fire research field. When a buoyant turbulent diffusion flame burns under a ceiling, the induced fire plume will impinge on and spread horizontally to form a ceiling jet [1]. Statistics have shown that about 85% of the deaths in building fire accidents were caused by the hot and toxic smoke [2–4]. When an undesirable fire is erupted in a building, the ceiling-mounted thermal and smoke actuated detectors are required to be activated timely to achieve quick heat detection and alarm. When the flame height is smaller than the ceiling height above the fuel, the ceiling jet is driven by a weak plume [5]. Conversely, a strong plume driven flow is formed when the flame height is comparable to the ceiling height [5]. For a strong plume impingement, the ceiling gas temperature and ceiling heat flux will be dramatically increased [6–8], which has a greater threat to the ceiling structures, devices and trapped
∗
people than the weak plume. To calculate the heat flux from both vertical and ceiling flames to surroundings and to improve the efficiency of heat detection at the early burning stage, the information of ceiling gas temperature is necessary [9]. There have been numerous studies on ceiling jet flow induced by single flame in the past. And different empirical correlations were proposed to estimate the ceiling gas temperatures [5,9–15]. Alpert [9] proposed a widely used model for predicting the ceiling gas temperature distribution of a weak plume impingement. By introducing the parameter of plume radius, Heskestad and Hamada [5] proposed a feasible model for the temperature decay profile of strong plume. Kurioka et al. [10] and Li et al. [11] respectively proposed empirical equations of maximum excess gas temperature under a ventilated confined ceiling. Gong et al. [12] proposed semi-empirical equation of longitudinal ceiling gas temperature of ventilated tunnel based on heat balance analysis. Correlations for predicting the transverse and
Corresponding author. State Key Laboratory of Fire Science, University of Science and Technology of China, JinZhai Road 96, Hefei, Anhui, 230026, China. Corresponding author. E-mail addresses: [email protected] (J. Ji), [email protected] (J. Fang).
∗∗
https://doi.org/10.1016/j.ijthermalsci.2018.10.010 Received 28 February 2018; Received in revised form 5 October 2018; Accepted 7 October 2018 1290-0729/ © 2018 Published by Elsevier Masson SAS.
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∗ Q˙ Hc r
Nomenclature b b′ cp D g Hc Hf LB
Q˙ Q˙ c Q˙ c′
plume radius at the ceiling level (m) modified plume radius in Eq. (6) (m) specific heat of air (kJ/(kg·K)) burner diameter/length (m) gravitational acceleration (m/s2) ceiling height above the burner surface (m) free flame height without ceiling (m) distance from impingement point induced by burner B to the center of burner B (m) heat release rate of each burner (kW) convective heat release rate (kW) modified convective heat release rate in Eq. (5) (kW)
rA S T∞ ΔT ΔTmax
dimensionless heat release rate for group flames radial distance from the flame axis and/or impingement point (m) horizontal distance from the center of burner A (m) burner edge spacing (m) ambient temperature (K) temperature rise (K) maximum temperature rise at impingement zone (K)
Greek symbols ρ∞
ambient density (kg/m3)
efficiency, steady and adjustable heat release rate, and lower smoke [31–33]. To avoid the impact of heat feedback, the porous gas burners are therefore adopted as the fire sources in this work. Following our recent experimental study on the merging criterion and ceiling flame length [34], this work aims to establish a global model for predicting the temperature decay profile induced by two impinging flames of propane. The heat release rate, burner edge spacing and ceiling height above the fuel were overall changed. A new model for ceiling gas temperature decay profile of two flames was proposed and validated by the experimental results. The present study can improve the understanding of multiple impinging flames. The established model for ceiling gas temperature of multiple impinging flames can provide a guidance of arrangement of detectors so as to raise the efficiency of heat detection and alarm. A further contribution of this work is to enrich the experimental results of multiple impinging flames which can be used for validation of simulated results.
longitudinal ceiling gas temperatures of sidewall confined ceiling jet plume were proposed by Gao et al. [13]. Fan et al. [14] proposed a correlation to determine the transverse smoke temperature distribution in a tunnel with different fire locations. Tang et al. [15] established empirical equation of the ceiling maximum plume temperature by taking the ceiling smoke extraction into account. However, in real disastrous fire accidents, there are usually more than one fire source as the adjacent combustibles would be ignited. Unlike the considerable research on single flame, very limited study has been focused on the multiple flames in confined spaces. Tsai et al. [16] performed experiments and simulations to study the effects of heat release rate and spacing on critical ventilation velocity for two fires below a confined ceiling. Ingason and Li [17] studied the impact of ventilation on maximum ceiling gas temperature induced by 1–3 fires. Hansen and Ingason [18] found that the ignition time of the adjacent wooden pallet decreases with increasing the ventilation of a confined ceiling. Li et al. [19] studied the convective heat transfer from a flat ceiling impinged by multiple jets. It can be summarized that the key factors influencing the burning behaviors of multiple fires have not been well characterized. One of the most important parameters for multiple fires is the spacing since it determines whether the flames are merging, tilting or develop independently [20–25]. As a result, extensive studies have been done on multiple fires in free space. For example, in years of 2011 and 2014, Finney and McAllister [20] and Vasanth et al. [21] respectively conducted reviews of multiple fires in free space, in which the spacing effect was discussed elaborately. Afterwards, Liu et al. [22] studied the effect of spacing on burning rate of multiple pool fires. Wan et al. [23,24] studied the flame height and overall flame outward radiation from two propane fires at varying spacing and heat release rate. Zhang et al. [25] studied the effect of spacing on flame characteristics of propane fire array with N by N fires (N = 2, 4, 6). For confined spaces, Ji et al. [26] and Wan et al. [27] studied the effect of spacing on the burning behaviors of two fires including the mass loss rate, flame length, gas temperature distribution and heat flux under confined ceilings. However, the effect of the ceiling height above the fuel, which is concerned as the other key parameter influencing the ceiling jet flow [8,28–30], is not well presented for multiple flames in literature. This work aims to bridge the knowledge gap. And in order to study the effect of ceiling height on ceiling flame shape and resulting ceiling gas temperature, the ceiling height of this work will be considered small enough so that the ceiling flames can be formed. Ji et al. [26] found that the mass loss rate induced by two impinging flames of liquid n-heptane increases first and then decreases with decreasing the spacing. They explained this non-monotonous trend as a result of the competition mechanism of the air entrainment restriction and the heat feedback enhancement. The porous burner is wildly used as an alternative fire source to produce both premixed and diffusion flames as it offers attractive features such as enhanced combustion
2. Experiments The experiments were conducted under a horizontal and unconfined ceiling with the dimension of 3 m × 3 m and a thickness of 20 mm. As shown in Fig. 1, two identical square burners with side length of D = 15 cm, denoted as burner A and B, were placed side by side and at a same height below the ceiling. In the experiments, the position of burner A was fixed under the ceiling center, seven burner edge spacings of S = 0, 5, 10, 15, 20, 30 and 45 cm were set by moving burner B along the longitudinal direction. Propane gas was used as the fuel and the heat release rate (HRR) of each burner (Q˙ ) was assumed identical. It was found from preliminary tests that at the ceiling height above the burner surface (Hc) of 64 cm, the flame will impinge on the ceiling and spread horizontally when Q˙ ≥21.6 kW. In order to produce the ceiling flames, five different Q˙ of 21.6, 32.4, 43.2, 54.0 and 64.8 kW and three Hc of 64, 54, and 45 cm were changed in the experiments. Based on the present burner size and HRR, the gas outflow velocity was calculated
Fig. 1. Experimental setup [34]. 2
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within 0.14–0.42 m/s, indicating that the flame is a subsonic jet. As shown in Fig. 1, the horizontal heat fluxes facing the ceiling and the flame shape were also measured, as they are out of the scope of this work, the description of them is not presented here. While the arrangement of thermocouples below the ceiling is presented in detail. As illustrated in Fig. 1, the ceiling gas temperatures along the longitudinal centerline were measured by a total of 16 thermocouples with an equal interval of 10 cm. The first thermocouple is located right above the center of burner A. Due to the heat loss from the fire plume to the ceiling, the thermocouples were positioned 10 mm below the ceiling to measure the vertical maximum temperature based on the study of Ji et al. [35]. The thermocouples were K-type with 1 mm in diameter and the response time less than 1 s. The uncertainty of temperature measurement was mainly attributed to the radiation error of thermocouple and the error related to the measurement repeatability [13]. Using the same type and diameter of thermocouples of this work, Gao et al. [13] measured the ceiling gas temperatures under a confined ceiling and reported that the maximum radiation error was less than 6%. This value of radiation error is deemed acceptable in industry since comparable errors were reported in literature with different combustion scenarios [36–38]. Therefore, the radiation error of the present measured temperatures seems to be small. Typical tests were repeated presently, the repeatability error of measured temperatures was found to be less than 5%. During the experiments, the ambient temperature was about 30 °C.
shape formed below the ceiling. Our previous work found that [34] the vertical flames would tilt to each other obviously for Hc = 64 cm, while the flame tilt of the two vertical flames is insignificant when Hc = 54 and 45 cm. As a result, LB < 0 for Hc = 64 cm, and most LB are ranged within −7.5 cm and 7.5 cm for Hc = 54 and 45 cm. Fig. 4 shows the two typical flame images at the steady state respectively for S = 15 and 20 cm under Q˙ = 64.8 kW and Hc = 54 cm. When S = 15 cm, as shown in Fig. 4a, the ceiling flames in the inner zone of two burners are merged together and flowed downward to form a vortex. Due to the anti-buoyant flow of the vortex, the air entrainment at this zone is prevented, resulting in LB < 0. While for S = 20 cm, as shown in Fig. 4b, the intensity of the anti-buoyant flow is weakened, it is obvious that the impingement point position shifts from the inner zone to the outer free zone, i.e. LB > 0. Fig. 5 shows the maximum gas temperature (Tmax) against Q˙ . It can be seen that at given S and Hc, the Tmax increases first and then maintains unchanged with increasing Q˙ . As Hc decreases, the influence of S on Tmax is weak. For a weak plume impingement, Alpert [9] proposed a widely used equation to predict the Tmax under an unconfined ceiling:
ΔTmax = Tmax − T∞ = 16.9
2/3 Q˙ , r / Hc < 0.18 Hc5/3
(1)
where ΔTmax is the maximum temperature rise, T∞ is the ambient temperature, r is the horizontal distance from the flame axis. Similar equations while larger constants of 17.5 and 17.9 have been respectively reported by Li et al. [11] and Ji et al. [35] for weak plumes impinging on confined ceilings. For a strong plume impingement, Ji et al. [8] established a simple equation to predict the Tmax under a confined ceiling:
3. Results and discussion 3.1. Longitudinal maximum temperature and its position under the ceiling Fig. 2 shows the time-averaged temperature distribution along the longitudinal centerline of ceiling at the steady state under the condition of Q˙ = 54.0 kW and Hc = 54 cm, where rA is the horizontal distance from the center of burner A. It is observed that there is only one peak temperature with small spacings of S ≤ 5 cm, while two peak temperatures are presented when S = 10–45 cm. Kurioka et al. [10] reported that the maximum gas temperature below the ceiling is consistent with the position that flame and/or hot current impinges on the ceiling. Under no ventilation, the impingement point induced by a single ignition source is presented at the flame center below the ceiling. While for the present two burners, the impingement point position is changed due to the flame interaction. It should be noted that the maximum temperature (Tmax) along the longitudinal direction and 10 mm below the ceiling is studied in this work. The position of occurring Tmax is regarded as the impingement point. Based on the symmetrical assumption, the Tmax induced by burner B and its position are studied presently. The impingement point position is quantified as the horizontal distance from the center of burner B and denoted as LB, as shown in Fig. 3a. Considering the intervals of thermocouples, rather than using only the measured maximum temperature, Oka et al. [39] determined the maximum temperature and its position based on a quadratic fit to the measured data of three points including the measured maximum temperature and the two adjacent temperatures. Applying Oka's method to our work, the experimental Tmax and LB can be determined. Fig. 3 shows the dependence of LB on Q˙ under varying S and Hc, where the positive LB represents the impingement point being located at the downstream of burner B, and vice versa. It is seen from Fig. 3a that for a large Hc of 64 cm, LB < 0 for most cases and LB from various Q˙ are nearly identical for a given S, indicating that the impingement points are presented in the inner zone between two burners and the impact of Q˙ is weak. As Hc decreases to 54 and 45 cm, as shown in Fig. 3b and c, LB ≤ 0 when S ≤ 15 cm. As S increases to 20–30 cm, LB increases with increasing Q˙ and changes to LB > 0 for large Q˙ . Further increasing S to 45 cm, the weak interaction effect causes the impingement point position presented near the burner surface area. Note that the above trend of LB is consistent with the flame
2/5
⎧ 0.267 Q˙ , ⎪ ΔTmax Hc = ⎨ T∞ ⎪ 2.9, ⎩
Q˙ 2/5 Hc
< 10.9
2/5 Q˙ Hc
≥ 10.9
(2)
The two parts in Eq. (2) are consistent with the intermittent and continuous impinging flames, respectively. It can be summarized from Eqs. (1) and (2) that the normalized maximum temperature rise ΔTmax / T∞ can be expressed as a function of the HRR normalized by the ceiling height above the fuel ∗ ∗ Q˙ Q˙ H = . Fig. 6 shows the ΔTmax / T∞ against Q˙ H for all the c
ρ∞ cp T∞ g1/2Hc5/2
c
present cases. It is observed that ΔTmax / T∞ increases first and then maintains un∗ changed with increasing Q˙ Hc . Ignoring the effect of spacing and fitting
Fig. 2. Longitudinal temperature distribution against horizontal distance from the center of burner A under Q˙ = 54.0 kW and Hc = 54 cm. 3
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Fig. 3. Position of the impingement point from the center of burner B (LB) against Q˙ .
Fig. 4. Typical flame images at steady state under Q˙ = 64.8 kW and Hc = 54 cm.
Fig. 5. Temperature at the impingement point (Tmax) against Q˙ .
ΔTmax / T∞ maintains at 2.77. Taking the 95% of this value as the upper ∗ limit, it gives ΔTmax / T∞ = 2.63 when Q˙ Hc ≥ 0.2 , suggesting that the maximum temperature rise at the impingement zone is a constant of ∗ 797 K when Q˙ Hc ≥ 0.2 . 3.2. Temperature distribution in the downstream of burner B For a strong plume impingement, Heskestad and Hamada [5] proposed the following correlation for predicting the temperature decay below the ceiling:
ΔT r −1 r r = 1.92 ⎛ ⎞ −exp ⎡1.61 ⎛1 − ⎞ ⎤, 1 ≤ ≤ 40 ΔTmax b b ⎝b⎠ ⎝ ⎠ ⎣ ⎦ 1/2 −1/2 Tmax
3/5 2/5 b = 0.42[(cp ρ∞) 4/5T∞ g ]
2/5 Q˙ c
3/5 ΔTmax
(4b)
where cp, ρ∞ are ambient parameters, g is the gravitational acceleration, b is the plume radius where the mean velocity is one-half the centerline value, Q˙ c is the convective heat release rate, which can be calculated as Q˙ c = 0.8Q˙ for propane [27]. Note that Eq. (4) is proposed for the single circular ignition source and the plume radius in Eq. (4b) is proposed for the undeflected flame at the level of the ceiling [5]. As a first attempt, the model proposed by Heskestad and Hamada [5] is adopted here to predict the temperature decay profile of two impinging flames. Fig. 7 shows the dependence of the normalized temperature rise (ΔT /ΔTmax ) on the normalized horizontal distance from the impingement point (r/b) for two burners with
Fig. 6. Relationship between normalized maximum temperature rise and normalized HRR.
the data points gives
ΔTmax ∗ = 2.77 − 4.0 exp (−17.5Q˙ Hc ) T∞
(4a)
(3)
∗ It can be calculated from Eq. (3) that when Q˙ Hc is large enough,
4
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Fig. 7. Temperature distribution against horizontal distance from the impingement point normalized by the plume radius r/b under Hc = 54 cm.
Q˙ c′ = (Hf − Hc )/ Hf ⋅Q˙ c
various S under Hc = 54 cm. It can be seen from Fig. 7a that when S = 0, the data points are converged regardless of Q˙ . While for the other S, the data points from various Q˙ are scattered, as shown in Fig. 7b–g, suggesting that the plume radius proposed for the undeflected flame is not enough to characterize the temperature decay profile induced by two impinging flames. As the ΔT /ΔTmax decays slower with increasing Q˙ as in Fig. 7, which makes it possible to introduce the free flame height without ceiling to modify the term of Q˙ c in Eq. (4b) as follows.
(5)
where Hf is the free flame height, which can be determined as 2/5 Hf = 0.235Q˙ − 1.02D [1]. The physical meaning of introducing Q˙ c′ in Eq. (5) is that only the flame part that impinges on and spreads along the ceiling determines the ceiling flame extension and thus the plume radius for the strong plume impingement. Substituting Eq. (5) into Eq. (4b) gives
b′ = [(Hf − Hc )/ Hf ]2/5 ⋅b 5
(6)
International Journal of Thermal Sciences 136 (2019) 1–8
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where b′ is the modified plume radius using the free flame height. Fig. 8 shows the relationship between ΔT /ΔTmax and r / b′ for two burners with various S under Hc = 54 cm. It can be seen that the data points become more converged by taking b′ as the characteristic length when compared to the results shown in Fig. 7. Similar trends can be found for the cases of Hc = 64 and 45 cm. Fig. 9 shows the correlation of ΔT /ΔTmax against r / b′ in a double logarithm coordinate system. It should be noted that for the cases of Q˙ = 21.6 kW and Hc = 64 cm, the calculated free flame height of 65 cm
is slightly larger than 64 cm, leading to large values of r / b′. Therefore, the cases of Q˙ = 21.6 kW and Hc = 64 cm are not included in the figure. It is observed from Fig. 9 that the data points at a given Hc are converged, showing that the effect of spacing is weak. Fitting the dense data points from all the present Hc using the piecewise function, the final formula for the temperature decay profile of two impinging flames is given as
Fig. 8. Temperature distribution against horizontal distance from the impingement point normalized by the modified plume radius r / b′ under Hc = 54 cm. 6
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while two peak temperatures are presented with large spacings. This observation implies that as the fire spacing increases, the interaction of flames changes from both vertical and ceiling flames merging to the vertical flames separated. This finding may be useful for practical storage and arrangement of flammable combustibles in buildings, i.e., the fire load of combustibles should be small enough and its spacing should be large enough so as to avoid ignition and possible merging of flames. (2) The ceiling gas temperature decays slower with increasing the heat release rate. And the established correlation shows that the maximum gas temperature increases first and then maintains at 797 K with increasing the heat release rate normalized by the ceiling height. Therefore, it is suggested to limit the height and number of combustibles to a minimum in actual industrial production. (3) The conventional plume radius proposed by Heskestad and Hamada for the single impinging flame is not enough to characterize the temperature decay profile induced by two impinging flames. A new model by modifying the plume radius based on the free flame height is therefore proposed and validated using the experimental results. The proposed model provide a viable method to determine the temperature decay profile of two impinging flames, which can be used to estimate the overall outward heat flux from the ceiling and flame and to calculate the safety distance between combustibles as well. A further application of the model is to provide reliable data of ceiling gas temperatures for fire safety professionals to better design the arrangement of heat detectors and sprinklers below the ceiling.
Fig. 9. Correlation of ΔT /ΔTmax against r / b′.
⎧1, ΔT = ⎨ 0.88 + 0.12 r ΔTmax b′ ⎩
(
−1.94
)
,
r b′
≤1
r b′
>1
(7) ∗ Q˙ Hc ,
as Note that ΔTmax has been expressed as a function of the shown in Eq. (3). Thus the impact of ceiling height on temperature decay profile is implicitly embodied in Eq. (7). Fig. 10 shows the comparison of the calculated ceiling gas temperatures using Eq. (7) and the experimental results of two flames, where the error lines of ± 32% are determined using the method proposed by Moffat [40] as shown in Appendix and Table 1. It should be noted that the uncertainty value of 32% is the maximum uncertainty for T, which is determined by assuming that the uncertainty of each component related to T is the maximum. In this work, the overall uncertainty of T is consisted of two parts, one is the model uncertainty, the other is the parameter uncertainty. Therefore, the overall relative high uncertainty of T does not mean that the proposed model is unreliable. And the parameter uncertainty is the principal factor leading to the high overall uncertainty of T in this work. Based on Eq. (7), the uncertainty of T is dependent on the uncertainty of ΔTmax (calculated as 21%, as listed in Table 1), which is one of the main sources for the large maximum uncertainty of T. In addition, the maximum uncertainty of Q˙ c listed in Table 1 for determining b′ in Eq. (7) is assumed as large as 20%, this would be the other source for the high uncertainty. In spite of this, the model is deemed reliable based on the following reasons. As shown in Fig. 9, the fitting coefficient is as large as 0.94, indicating that the model uncertainty is small. By taking all impact factors into account, it can be seen in Fig. 10 that all data points are located within the maximum error lines of ± 32% and most of the data points are distributed close to the equivalent line, which not only validates that the calculation of the maximum uncertainty is correct, but also justify the prediction accuracy of the proposed model for the temperature decay profile under the condition of two interacting flames below the ceiling.
As two identical burners with the same burner size, shape and heat release rate are used in this work, the present results may be unsuitable for the two burners with different geometries and heat release rates. Hence, more burner sizes and shapes will be considered in the future.
Acknowledgements This work was supported by National Natural Science Foundation of China under Grant No. 51722605, the National Post-doctoral Program for Innovative Talents under Grant No. BX20180288 and the Fundamental Research Funds for the Central Universities under Grant No. WK2320000038. Jie Ji was supported by the National Program for Support of Top-Notch Young Professionals and the Youth Innovation Promotion Association of CAS (2015386).
4. Conclusions An experimental study on the temperature decay profile of ceiling jet induced by two propane flames burning under an unconfined ceiling is performed. The motivation behind this study is the lack of experimental data of the ceiling gas temperatures induced by multiple fires. This work contributes to establish feasible model for predicting the ceiling gas temperature of multiple impinging flames by taking the heat release rate, spacing and ceiling height into account. The main conclusions are: Fig. 10. Comparison of calculated and experimental ceiling gas temperatures of two impinging flames.
(1) There is only one peak ceiling gas temperature with small spacings, 7
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Table 1 Maximum uncertainty of parameters. Parameters
Sources of uncertainty
Uncertainty value
Final uncertainty value
ΔT-exp
Exp. Radiation error Exp. Radiation error Exp.
± 5.0% ± 6.0% ± 5.0% ± 6.0% ± 5.0%
± 7.8%
ΔTmax-exp
± 7.8% ± 5.0%
Q˙ Q˙ c in Eq. (4b) ΔTmax calculated using Eq. (3)
Assumed error
± 20.0%
± 20.0%
ΔTmax-exp Q˙
± 7.8% ± 5.0%
± 21.1%
b calculated using Eq. (4b)
Fitting error ΔTmax-exp Q˙ c
± 19.0% ± 7.8% ± 20.0%
± 21.5%
Calculated error Q˙ c Hf Hf b ΔT-exp b′ Fitting error
± 10.0% ± 20.0%
± 10.0% ± 22.4%
Hf in Eq. (5) Q˙ c′ calculated using Eq. (5) b′ calculated using Eq. (6) ΔT calculated using Eq. (7)
± 10.0% ± 10.0% ± 21.5% ± 5.0% ± 23.7% ± 6.0%
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Energy 185 (2017) 573–581. [28] M.F. Koseoglu, S. Baskaya, The effect of flow field and turbulence on heat transfer characteristics of confined circular and elliptic impinging jets, Int. J. Therm. Sci. 47 (10) (2008) 1332–1346. [29] Q. Liu, A.K. Sleiti, J.S. Kapat, Application of pressure and temperature sensitive paints for study of heat transfer to a circular impinging air jet, Int. J. Therm. Sci. 47 (6) (2008) 749–757. [30] M.R. Morad, A. Momeni, E. Ebrahimi Fordoei, M. Ashjaee, Experimental and numerical study on heat transfer characteristics for methane/air flame impinging on a flat surface, Int. J. Therm. Sci. 110 (2016) 229–240. [31] M.H. Akbari, P. Riahi, R. Roohi, Lean flammability limits for stable performance with a porous burner, Appl. Energy 86 (12) (2009) 2635–2643. [32] S. Chen, J. Marx, A. Rabiei, Experimental and computational studies on the thermal behavior and fire retardant properties of composite metal foams, Int. J. Therm. Sci. 106 (2016) 70–79. [33] B.H. Bang, C.S. Ahn, J.G. Lee, Y.T. Kim, M.H. Lee, B. Horn, D. Malik, K. Thomas, S.C. James, A.L. Yarin, S.S. Yoon, Theoretical, numerical, and experimental investigation of pressure rise due to deflagration in confined spaces, Int. J. Therm. Sci. 120 (2017) 469–480. [34] H. Wan, Z. Gao, J. Ji, L. Wang, Y. Zhang, Experimental Study on Merging Behaviors of Two Identical Buoyant Diffusion Flames Under an Unconfined Ceiling with Varying Heights, Proc. Combust. Inst, Available online https://doi.org/10.1016/j. proci.2018.05.154. [35] J. Ji, C.G. Fan, W. Zhong, X.B. Shen, J.H. Sun, Experimental investigation on influence of different transverse fire locations on maximum smoke temperature under the tunnel ceiling, Int. J. Heat Mass Tran. 55 (17–18) (2012) 4817–4826. [36] W.M. Pitts, E. Braun, R.D. Peacock, H.E. Mitler, E. Johnson, P.A. Reneke, L.G. Blevins, Temperature Uncertainties for Bare-bead and Aspirated Thermocouple Measurements in Fire Environments 1427 ASTM Special Technical Publication, 2003, pp. 3–15. [37] D. Yang, R. Huo, X.L. Zhang, S. Zhu, X.Y. Zhao, Comparative study on carbon monoxide stratification and thermal stratification in a horizontal channel fire, Build. Environ. 49 (2012) 1–8. [38] R. Lemaire, S. Menanteau, Assessment of radiation correction methods for bare bead thermocouples in a combustion environment, Int. J. Therm. Sci. 122 (2017) 186–200. [39] Y. Oka, O. Imazeki, Temperature and velocity distributions of a ceiling jet along an inclined ceiling – Part 1: approximation with exponential function, Fire Saf. J. 65 (2014) 41–52. [40] R.J. Moffat, Describing the uncertainties in experimental results, Exp. Therm. Fluid Sci. 1 (1) (1988) 3–17.
± 23.7% ± 32.3%
Appendix. for uncertainty analysis The uncertainty analysis is conducted based on the method reported by Moffat [40]. When using Moffat's method, it is crucial to identify the key error sources in the first. Then the overall uncertainty can be determined as the root sum square combination of all the error components [40], i.e., Xtotal =(X12+X22 + … +Xn2)1/2, where n is the total number of error sources. The uncertainties of primary and derived parameters in this work are listed in Table 1. In the Table, the uncertainties of the first 4 parameters including ΔT-exp, ΔTmax-exp, Q˙ and Q˙ c are determined based on the experimental results, while the uncertainties of rest parameters are calculated based on the relevant sources. For example, the sources of uncertainty of ΔT calculated using Eq. (7) are from the ΔT-exp, b′ and fitting error (R2 = 0.94), the uncertainty values of the three terms are 5.0%, 23.7%, 6.0%, respectively. Then based on the method of Moffat, the final uncertainty of ΔT can be determined as 0.0782 + 0.2372 + 0.062 = 32.3%, which is consistent with the maximum uncertainty of calculated ΔT and resulting T as in Fig. 10. References [1] B. Karlsson, J. Quintiere, Fire plumes and flame heights, Enclosure Fire Dynamics, CRC press, New York, Washington, D.C., 1999, pp. 60–93. [2] J. Ji, M. Li, Y. Li, J. Zhu, J. Sun, Transport characteristics of thermal plume driven by turbulent mixing in stairwell, Int. J. Therm. Sci. 89 (0) (2015) 264–271. [3] J. Ji, H. Wan, Y. Li, K. Li, J. Sun, Influence of relative location of two openings on fire and smoke behaviors in stairwell with a compartment, Int. J. Therm. Sci. 89 (2015) 23–33. [4] J. Ji, F. Guo, Z. Gao, J. Zhu, Effects of ambient pressure on transport characteristics of thermal-driven smoke flow in a tunnel, Int. J. Therm. Sci. 125 (2018) 210–217. [5] G. Heskestad, T. Hamada, Ceiling jets of strong fire plumes, Fire Saf. J. 21 (1) (1993) 69–82. [6] H. You, G. Faeth, Ceiling heat transfer during fire plume and fire impingement, Fire Mater. 3 (3) (1979) 140–147. [7] Z. Gao, J. Ji, H. Wan, K. Li, J. Sun, An investigation of the detailed flame shape and flame length under the ceiling of a channel, Proc. Combust. Inst. 35 (3) (2015) 2657–2664. [8] J. Ji, Y. Fu, K. Li, J. Sun, C. Fan, W. Shi, Experimental study on behavior of sidewall fires at varying height in a corridor-like structure, Proc. Combust. Inst. 35 (3) (2015) 2639–2646. [9] R.L. Alpert, Calculation of response time of ceiling-mounted fire detectors, Fire Technol. 8 (3) (1972) 181–195. [10] H. Kurioka, Y. Oka, H. Satoh, O. Sugawa, Fire properties in near field of square fire source with longitudinal ventilation in tunnels, Fire Saf. J. 38 (4) (2003) 319–340. [11] Y.Z. Li, B. Lei, H. Ingason, The maximum temperature of buoyancy-driven smoke flow beneath the ceiling in tunnel fires, Fire Saf. J. 46 (4) (2011) 204–210.
8
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International Journal of Thermal Sciences journal homepage: www.elsevier.com/locate/ijts
Experimental study on horizontal gas temperature distribution of two propane diffusion flames impinging on an unconfined ceiling
T
Huaxian Wana, Zihe Gaoa, Jie Jia,b,∗, Jun Fanga,∗∗, Yongming Zhanga a b
State Key Laboratory of Fire Science, University of Science and Technology of China, JinZhai Road 96, Hefei, Anhui, 230026, China Institute of Advanced Technology, University of Science and Technology of China, Hefei, Anhui, 230088, China
A R T I C LE I N FO
A B S T R A C T
Keywords: Unconfined ceiling Multiple flames Flame tilt Maximum temperature Temperature distribution
Ceiling gas temperature is one of the most important factors for heat detection and alarm once an undesirable fire along with releasing hot and toxic smoke is erupted in a building. The impinging flame characterized by the unburnt fuel burning along the ceiling has received much attention in recent years as it poses a greater threat to the ceiling structure, devices and trapped people than the non-impinging flame. Many studies have been focused on the ceiling gas temperature induced by a single flame, while little effort has been put with respect to the multiple flames. The interaction between multiple flames might lead to flames tilt to each other and even merge together with small spacings, resulting in different ceiling gas temperature distribution from the single flame. The aim of this experimental work is to investigate the ceiling gas temperature decay profile induced by two impinging flames. Propane was used as the fuel. The heat release rate (HRR), burner edge spacing and ceiling height above the fuel were overall changed. The ceiling gas temperatures along the direction of changing spacing were measured to determine the impingement point position and temperature decay profile. The results showed that the impingement point position is dependent on the HRR and the spacing as well as the ceiling height, while the maximum gas temperature is weakly affected by the spacing. The established correlation reveals that the maximum excess temperature increases first and then maintains unchanged with increasing the HRR normalized by the ceiling height. The plume radius proposed for the single impinging flame is not enough to characterize the ceiling gas temperature of two impinging flames. A new correlation for temperature decay profile induced by two impinging flames is therefore proposed and validated using the experimental results.
1. Introduction Diffusion flame is one of the most commonly used flames in fire research field. When a buoyant turbulent diffusion flame burns under a ceiling, the induced fire plume will impinge on and spread horizontally to form a ceiling jet [1]. Statistics have shown that about 85% of the deaths in building fire accidents were caused by the hot and toxic smoke [2–4]. When an undesirable fire is erupted in a building, the ceiling-mounted thermal and smoke actuated detectors are required to be activated timely to achieve quick heat detection and alarm. When the flame height is smaller than the ceiling height above the fuel, the ceiling jet is driven by a weak plume [5]. Conversely, a strong plume driven flow is formed when the flame height is comparable to the ceiling height [5]. For a strong plume impingement, the ceiling gas temperature and ceiling heat flux will be dramatically increased [6–8], which has a greater threat to the ceiling structures, devices and trapped
∗
people than the weak plume. To calculate the heat flux from both vertical and ceiling flames to surroundings and to improve the efficiency of heat detection at the early burning stage, the information of ceiling gas temperature is necessary [9]. There have been numerous studies on ceiling jet flow induced by single flame in the past. And different empirical correlations were proposed to estimate the ceiling gas temperatures [5,9–15]. Alpert [9] proposed a widely used model for predicting the ceiling gas temperature distribution of a weak plume impingement. By introducing the parameter of plume radius, Heskestad and Hamada [5] proposed a feasible model for the temperature decay profile of strong plume. Kurioka et al. [10] and Li et al. [11] respectively proposed empirical equations of maximum excess gas temperature under a ventilated confined ceiling. Gong et al. [12] proposed semi-empirical equation of longitudinal ceiling gas temperature of ventilated tunnel based on heat balance analysis. Correlations for predicting the transverse and
Corresponding author. State Key Laboratory of Fire Science, University of Science and Technology of China, JinZhai Road 96, Hefei, Anhui, 230026, China. Corresponding author. E-mail addresses: [email protected] (J. Ji), [email protected] (J. Fang).
∗∗
https://doi.org/10.1016/j.ijthermalsci.2018.10.010 Received 28 February 2018; Received in revised form 5 October 2018; Accepted 7 October 2018 1290-0729/ © 2018 Published by Elsevier Masson SAS.
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∗ Q˙ Hc r
Nomenclature b b′ cp D g Hc Hf LB
Q˙ Q˙ c Q˙ c′
plume radius at the ceiling level (m) modified plume radius in Eq. (6) (m) specific heat of air (kJ/(kg·K)) burner diameter/length (m) gravitational acceleration (m/s2) ceiling height above the burner surface (m) free flame height without ceiling (m) distance from impingement point induced by burner B to the center of burner B (m) heat release rate of each burner (kW) convective heat release rate (kW) modified convective heat release rate in Eq. (5) (kW)
rA S T∞ ΔT ΔTmax
dimensionless heat release rate for group flames radial distance from the flame axis and/or impingement point (m) horizontal distance from the center of burner A (m) burner edge spacing (m) ambient temperature (K) temperature rise (K) maximum temperature rise at impingement zone (K)
Greek symbols ρ∞
ambient density (kg/m3)
efficiency, steady and adjustable heat release rate, and lower smoke [31–33]. To avoid the impact of heat feedback, the porous gas burners are therefore adopted as the fire sources in this work. Following our recent experimental study on the merging criterion and ceiling flame length [34], this work aims to establish a global model for predicting the temperature decay profile induced by two impinging flames of propane. The heat release rate, burner edge spacing and ceiling height above the fuel were overall changed. A new model for ceiling gas temperature decay profile of two flames was proposed and validated by the experimental results. The present study can improve the understanding of multiple impinging flames. The established model for ceiling gas temperature of multiple impinging flames can provide a guidance of arrangement of detectors so as to raise the efficiency of heat detection and alarm. A further contribution of this work is to enrich the experimental results of multiple impinging flames which can be used for validation of simulated results.
longitudinal ceiling gas temperatures of sidewall confined ceiling jet plume were proposed by Gao et al. [13]. Fan et al. [14] proposed a correlation to determine the transverse smoke temperature distribution in a tunnel with different fire locations. Tang et al. [15] established empirical equation of the ceiling maximum plume temperature by taking the ceiling smoke extraction into account. However, in real disastrous fire accidents, there are usually more than one fire source as the adjacent combustibles would be ignited. Unlike the considerable research on single flame, very limited study has been focused on the multiple flames in confined spaces. Tsai et al. [16] performed experiments and simulations to study the effects of heat release rate and spacing on critical ventilation velocity for two fires below a confined ceiling. Ingason and Li [17] studied the impact of ventilation on maximum ceiling gas temperature induced by 1–3 fires. Hansen and Ingason [18] found that the ignition time of the adjacent wooden pallet decreases with increasing the ventilation of a confined ceiling. Li et al. [19] studied the convective heat transfer from a flat ceiling impinged by multiple jets. It can be summarized that the key factors influencing the burning behaviors of multiple fires have not been well characterized. One of the most important parameters for multiple fires is the spacing since it determines whether the flames are merging, tilting or develop independently [20–25]. As a result, extensive studies have been done on multiple fires in free space. For example, in years of 2011 and 2014, Finney and McAllister [20] and Vasanth et al. [21] respectively conducted reviews of multiple fires in free space, in which the spacing effect was discussed elaborately. Afterwards, Liu et al. [22] studied the effect of spacing on burning rate of multiple pool fires. Wan et al. [23,24] studied the flame height and overall flame outward radiation from two propane fires at varying spacing and heat release rate. Zhang et al. [25] studied the effect of spacing on flame characteristics of propane fire array with N by N fires (N = 2, 4, 6). For confined spaces, Ji et al. [26] and Wan et al. [27] studied the effect of spacing on the burning behaviors of two fires including the mass loss rate, flame length, gas temperature distribution and heat flux under confined ceilings. However, the effect of the ceiling height above the fuel, which is concerned as the other key parameter influencing the ceiling jet flow [8,28–30], is not well presented for multiple flames in literature. This work aims to bridge the knowledge gap. And in order to study the effect of ceiling height on ceiling flame shape and resulting ceiling gas temperature, the ceiling height of this work will be considered small enough so that the ceiling flames can be formed. Ji et al. [26] found that the mass loss rate induced by two impinging flames of liquid n-heptane increases first and then decreases with decreasing the spacing. They explained this non-monotonous trend as a result of the competition mechanism of the air entrainment restriction and the heat feedback enhancement. The porous burner is wildly used as an alternative fire source to produce both premixed and diffusion flames as it offers attractive features such as enhanced combustion
2. Experiments The experiments were conducted under a horizontal and unconfined ceiling with the dimension of 3 m × 3 m and a thickness of 20 mm. As shown in Fig. 1, two identical square burners with side length of D = 15 cm, denoted as burner A and B, were placed side by side and at a same height below the ceiling. In the experiments, the position of burner A was fixed under the ceiling center, seven burner edge spacings of S = 0, 5, 10, 15, 20, 30 and 45 cm were set by moving burner B along the longitudinal direction. Propane gas was used as the fuel and the heat release rate (HRR) of each burner (Q˙ ) was assumed identical. It was found from preliminary tests that at the ceiling height above the burner surface (Hc) of 64 cm, the flame will impinge on the ceiling and spread horizontally when Q˙ ≥21.6 kW. In order to produce the ceiling flames, five different Q˙ of 21.6, 32.4, 43.2, 54.0 and 64.8 kW and three Hc of 64, 54, and 45 cm were changed in the experiments. Based on the present burner size and HRR, the gas outflow velocity was calculated
Fig. 1. Experimental setup [34]. 2
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within 0.14–0.42 m/s, indicating that the flame is a subsonic jet. As shown in Fig. 1, the horizontal heat fluxes facing the ceiling and the flame shape were also measured, as they are out of the scope of this work, the description of them is not presented here. While the arrangement of thermocouples below the ceiling is presented in detail. As illustrated in Fig. 1, the ceiling gas temperatures along the longitudinal centerline were measured by a total of 16 thermocouples with an equal interval of 10 cm. The first thermocouple is located right above the center of burner A. Due to the heat loss from the fire plume to the ceiling, the thermocouples were positioned 10 mm below the ceiling to measure the vertical maximum temperature based on the study of Ji et al. [35]. The thermocouples were K-type with 1 mm in diameter and the response time less than 1 s. The uncertainty of temperature measurement was mainly attributed to the radiation error of thermocouple and the error related to the measurement repeatability [13]. Using the same type and diameter of thermocouples of this work, Gao et al. [13] measured the ceiling gas temperatures under a confined ceiling and reported that the maximum radiation error was less than 6%. This value of radiation error is deemed acceptable in industry since comparable errors were reported in literature with different combustion scenarios [36–38]. Therefore, the radiation error of the present measured temperatures seems to be small. Typical tests were repeated presently, the repeatability error of measured temperatures was found to be less than 5%. During the experiments, the ambient temperature was about 30 °C.
shape formed below the ceiling. Our previous work found that [34] the vertical flames would tilt to each other obviously for Hc = 64 cm, while the flame tilt of the two vertical flames is insignificant when Hc = 54 and 45 cm. As a result, LB < 0 for Hc = 64 cm, and most LB are ranged within −7.5 cm and 7.5 cm for Hc = 54 and 45 cm. Fig. 4 shows the two typical flame images at the steady state respectively for S = 15 and 20 cm under Q˙ = 64.8 kW and Hc = 54 cm. When S = 15 cm, as shown in Fig. 4a, the ceiling flames in the inner zone of two burners are merged together and flowed downward to form a vortex. Due to the anti-buoyant flow of the vortex, the air entrainment at this zone is prevented, resulting in LB < 0. While for S = 20 cm, as shown in Fig. 4b, the intensity of the anti-buoyant flow is weakened, it is obvious that the impingement point position shifts from the inner zone to the outer free zone, i.e. LB > 0. Fig. 5 shows the maximum gas temperature (Tmax) against Q˙ . It can be seen that at given S and Hc, the Tmax increases first and then maintains unchanged with increasing Q˙ . As Hc decreases, the influence of S on Tmax is weak. For a weak plume impingement, Alpert [9] proposed a widely used equation to predict the Tmax under an unconfined ceiling:
ΔTmax = Tmax − T∞ = 16.9
2/3 Q˙ , r / Hc < 0.18 Hc5/3
(1)
where ΔTmax is the maximum temperature rise, T∞ is the ambient temperature, r is the horizontal distance from the flame axis. Similar equations while larger constants of 17.5 and 17.9 have been respectively reported by Li et al. [11] and Ji et al. [35] for weak plumes impinging on confined ceilings. For a strong plume impingement, Ji et al. [8] established a simple equation to predict the Tmax under a confined ceiling:
3. Results and discussion 3.1. Longitudinal maximum temperature and its position under the ceiling Fig. 2 shows the time-averaged temperature distribution along the longitudinal centerline of ceiling at the steady state under the condition of Q˙ = 54.0 kW and Hc = 54 cm, where rA is the horizontal distance from the center of burner A. It is observed that there is only one peak temperature with small spacings of S ≤ 5 cm, while two peak temperatures are presented when S = 10–45 cm. Kurioka et al. [10] reported that the maximum gas temperature below the ceiling is consistent with the position that flame and/or hot current impinges on the ceiling. Under no ventilation, the impingement point induced by a single ignition source is presented at the flame center below the ceiling. While for the present two burners, the impingement point position is changed due to the flame interaction. It should be noted that the maximum temperature (Tmax) along the longitudinal direction and 10 mm below the ceiling is studied in this work. The position of occurring Tmax is regarded as the impingement point. Based on the symmetrical assumption, the Tmax induced by burner B and its position are studied presently. The impingement point position is quantified as the horizontal distance from the center of burner B and denoted as LB, as shown in Fig. 3a. Considering the intervals of thermocouples, rather than using only the measured maximum temperature, Oka et al. [39] determined the maximum temperature and its position based on a quadratic fit to the measured data of three points including the measured maximum temperature and the two adjacent temperatures. Applying Oka's method to our work, the experimental Tmax and LB can be determined. Fig. 3 shows the dependence of LB on Q˙ under varying S and Hc, where the positive LB represents the impingement point being located at the downstream of burner B, and vice versa. It is seen from Fig. 3a that for a large Hc of 64 cm, LB < 0 for most cases and LB from various Q˙ are nearly identical for a given S, indicating that the impingement points are presented in the inner zone between two burners and the impact of Q˙ is weak. As Hc decreases to 54 and 45 cm, as shown in Fig. 3b and c, LB ≤ 0 when S ≤ 15 cm. As S increases to 20–30 cm, LB increases with increasing Q˙ and changes to LB > 0 for large Q˙ . Further increasing S to 45 cm, the weak interaction effect causes the impingement point position presented near the burner surface area. Note that the above trend of LB is consistent with the flame
2/5
⎧ 0.267 Q˙ , ⎪ ΔTmax Hc = ⎨ T∞ ⎪ 2.9, ⎩
Q˙ 2/5 Hc
< 10.9
2/5 Q˙ Hc
≥ 10.9
(2)
The two parts in Eq. (2) are consistent with the intermittent and continuous impinging flames, respectively. It can be summarized from Eqs. (1) and (2) that the normalized maximum temperature rise ΔTmax / T∞ can be expressed as a function of the HRR normalized by the ceiling height above the fuel ∗ ∗ Q˙ Q˙ H = . Fig. 6 shows the ΔTmax / T∞ against Q˙ H for all the c
ρ∞ cp T∞ g1/2Hc5/2
c
present cases. It is observed that ΔTmax / T∞ increases first and then maintains un∗ changed with increasing Q˙ Hc . Ignoring the effect of spacing and fitting
Fig. 2. Longitudinal temperature distribution against horizontal distance from the center of burner A under Q˙ = 54.0 kW and Hc = 54 cm. 3
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Fig. 3. Position of the impingement point from the center of burner B (LB) against Q˙ .
Fig. 4. Typical flame images at steady state under Q˙ = 64.8 kW and Hc = 54 cm.
Fig. 5. Temperature at the impingement point (Tmax) against Q˙ .
ΔTmax / T∞ maintains at 2.77. Taking the 95% of this value as the upper ∗ limit, it gives ΔTmax / T∞ = 2.63 when Q˙ Hc ≥ 0.2 , suggesting that the maximum temperature rise at the impingement zone is a constant of ∗ 797 K when Q˙ Hc ≥ 0.2 . 3.2. Temperature distribution in the downstream of burner B For a strong plume impingement, Heskestad and Hamada [5] proposed the following correlation for predicting the temperature decay below the ceiling:
ΔT r −1 r r = 1.92 ⎛ ⎞ −exp ⎡1.61 ⎛1 − ⎞ ⎤, 1 ≤ ≤ 40 ΔTmax b b ⎝b⎠ ⎝ ⎠ ⎣ ⎦ 1/2 −1/2 Tmax
3/5 2/5 b = 0.42[(cp ρ∞) 4/5T∞ g ]
2/5 Q˙ c
3/5 ΔTmax
(4b)
where cp, ρ∞ are ambient parameters, g is the gravitational acceleration, b is the plume radius where the mean velocity is one-half the centerline value, Q˙ c is the convective heat release rate, which can be calculated as Q˙ c = 0.8Q˙ for propane [27]. Note that Eq. (4) is proposed for the single circular ignition source and the plume radius in Eq. (4b) is proposed for the undeflected flame at the level of the ceiling [5]. As a first attempt, the model proposed by Heskestad and Hamada [5] is adopted here to predict the temperature decay profile of two impinging flames. Fig. 7 shows the dependence of the normalized temperature rise (ΔT /ΔTmax ) on the normalized horizontal distance from the impingement point (r/b) for two burners with
Fig. 6. Relationship between normalized maximum temperature rise and normalized HRR.
the data points gives
ΔTmax ∗ = 2.77 − 4.0 exp (−17.5Q˙ Hc ) T∞
(4a)
(3)
∗ It can be calculated from Eq. (3) that when Q˙ Hc is large enough,
4
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Fig. 7. Temperature distribution against horizontal distance from the impingement point normalized by the plume radius r/b under Hc = 54 cm.
Q˙ c′ = (Hf − Hc )/ Hf ⋅Q˙ c
various S under Hc = 54 cm. It can be seen from Fig. 7a that when S = 0, the data points are converged regardless of Q˙ . While for the other S, the data points from various Q˙ are scattered, as shown in Fig. 7b–g, suggesting that the plume radius proposed for the undeflected flame is not enough to characterize the temperature decay profile induced by two impinging flames. As the ΔT /ΔTmax decays slower with increasing Q˙ as in Fig. 7, which makes it possible to introduce the free flame height without ceiling to modify the term of Q˙ c in Eq. (4b) as follows.
(5)
where Hf is the free flame height, which can be determined as 2/5 Hf = 0.235Q˙ − 1.02D [1]. The physical meaning of introducing Q˙ c′ in Eq. (5) is that only the flame part that impinges on and spreads along the ceiling determines the ceiling flame extension and thus the plume radius for the strong plume impingement. Substituting Eq. (5) into Eq. (4b) gives
b′ = [(Hf − Hc )/ Hf ]2/5 ⋅b 5
(6)
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where b′ is the modified plume radius using the free flame height. Fig. 8 shows the relationship between ΔT /ΔTmax and r / b′ for two burners with various S under Hc = 54 cm. It can be seen that the data points become more converged by taking b′ as the characteristic length when compared to the results shown in Fig. 7. Similar trends can be found for the cases of Hc = 64 and 45 cm. Fig. 9 shows the correlation of ΔT /ΔTmax against r / b′ in a double logarithm coordinate system. It should be noted that for the cases of Q˙ = 21.6 kW and Hc = 64 cm, the calculated free flame height of 65 cm
is slightly larger than 64 cm, leading to large values of r / b′. Therefore, the cases of Q˙ = 21.6 kW and Hc = 64 cm are not included in the figure. It is observed from Fig. 9 that the data points at a given Hc are converged, showing that the effect of spacing is weak. Fitting the dense data points from all the present Hc using the piecewise function, the final formula for the temperature decay profile of two impinging flames is given as
Fig. 8. Temperature distribution against horizontal distance from the impingement point normalized by the modified plume radius r / b′ under Hc = 54 cm. 6
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while two peak temperatures are presented with large spacings. This observation implies that as the fire spacing increases, the interaction of flames changes from both vertical and ceiling flames merging to the vertical flames separated. This finding may be useful for practical storage and arrangement of flammable combustibles in buildings, i.e., the fire load of combustibles should be small enough and its spacing should be large enough so as to avoid ignition and possible merging of flames. (2) The ceiling gas temperature decays slower with increasing the heat release rate. And the established correlation shows that the maximum gas temperature increases first and then maintains at 797 K with increasing the heat release rate normalized by the ceiling height. Therefore, it is suggested to limit the height and number of combustibles to a minimum in actual industrial production. (3) The conventional plume radius proposed by Heskestad and Hamada for the single impinging flame is not enough to characterize the temperature decay profile induced by two impinging flames. A new model by modifying the plume radius based on the free flame height is therefore proposed and validated using the experimental results. The proposed model provide a viable method to determine the temperature decay profile of two impinging flames, which can be used to estimate the overall outward heat flux from the ceiling and flame and to calculate the safety distance between combustibles as well. A further application of the model is to provide reliable data of ceiling gas temperatures for fire safety professionals to better design the arrangement of heat detectors and sprinklers below the ceiling.
Fig. 9. Correlation of ΔT /ΔTmax against r / b′.
⎧1, ΔT = ⎨ 0.88 + 0.12 r ΔTmax b′ ⎩
(
−1.94
)
,
r b′
≤1
r b′
>1
(7) ∗ Q˙ Hc ,
as Note that ΔTmax has been expressed as a function of the shown in Eq. (3). Thus the impact of ceiling height on temperature decay profile is implicitly embodied in Eq. (7). Fig. 10 shows the comparison of the calculated ceiling gas temperatures using Eq. (7) and the experimental results of two flames, where the error lines of ± 32% are determined using the method proposed by Moffat [40] as shown in Appendix and Table 1. It should be noted that the uncertainty value of 32% is the maximum uncertainty for T, which is determined by assuming that the uncertainty of each component related to T is the maximum. In this work, the overall uncertainty of T is consisted of two parts, one is the model uncertainty, the other is the parameter uncertainty. Therefore, the overall relative high uncertainty of T does not mean that the proposed model is unreliable. And the parameter uncertainty is the principal factor leading to the high overall uncertainty of T in this work. Based on Eq. (7), the uncertainty of T is dependent on the uncertainty of ΔTmax (calculated as 21%, as listed in Table 1), which is one of the main sources for the large maximum uncertainty of T. In addition, the maximum uncertainty of Q˙ c listed in Table 1 for determining b′ in Eq. (7) is assumed as large as 20%, this would be the other source for the high uncertainty. In spite of this, the model is deemed reliable based on the following reasons. As shown in Fig. 9, the fitting coefficient is as large as 0.94, indicating that the model uncertainty is small. By taking all impact factors into account, it can be seen in Fig. 10 that all data points are located within the maximum error lines of ± 32% and most of the data points are distributed close to the equivalent line, which not only validates that the calculation of the maximum uncertainty is correct, but also justify the prediction accuracy of the proposed model for the temperature decay profile under the condition of two interacting flames below the ceiling.
As two identical burners with the same burner size, shape and heat release rate are used in this work, the present results may be unsuitable for the two burners with different geometries and heat release rates. Hence, more burner sizes and shapes will be considered in the future.
Acknowledgements This work was supported by National Natural Science Foundation of China under Grant No. 51722605, the National Post-doctoral Program for Innovative Talents under Grant No. BX20180288 and the Fundamental Research Funds for the Central Universities under Grant No. WK2320000038. Jie Ji was supported by the National Program for Support of Top-Notch Young Professionals and the Youth Innovation Promotion Association of CAS (2015386).
4. Conclusions An experimental study on the temperature decay profile of ceiling jet induced by two propane flames burning under an unconfined ceiling is performed. The motivation behind this study is the lack of experimental data of the ceiling gas temperatures induced by multiple fires. This work contributes to establish feasible model for predicting the ceiling gas temperature of multiple impinging flames by taking the heat release rate, spacing and ceiling height into account. The main conclusions are: Fig. 10. Comparison of calculated and experimental ceiling gas temperatures of two impinging flames.
(1) There is only one peak ceiling gas temperature with small spacings, 7
International Journal of Thermal Sciences 136 (2019) 1–8
H. Wan et al.
Table 1 Maximum uncertainty of parameters. Parameters
Sources of uncertainty
Uncertainty value
Final uncertainty value
ΔT-exp
Exp. Radiation error Exp. Radiation error Exp.
± 5.0% ± 6.0% ± 5.0% ± 6.0% ± 5.0%
± 7.8%
ΔTmax-exp
± 7.8% ± 5.0%
Q˙ Q˙ c in Eq. (4b) ΔTmax calculated using Eq. (3)
Assumed error
± 20.0%
± 20.0%
ΔTmax-exp Q˙
± 7.8% ± 5.0%
± 21.1%
b calculated using Eq. (4b)
Fitting error ΔTmax-exp Q˙ c
± 19.0% ± 7.8% ± 20.0%
± 21.5%
Calculated error Q˙ c Hf Hf b ΔT-exp b′ Fitting error
± 10.0% ± 20.0%
± 10.0% ± 22.4%
Hf in Eq. (5) Q˙ c′ calculated using Eq. (5) b′ calculated using Eq. (6) ΔT calculated using Eq. (7)
± 10.0% ± 10.0% ± 21.5% ± 5.0% ± 23.7% ± 6.0%
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± 23.7% ± 32.3%
Appendix. for uncertainty analysis The uncertainty analysis is conducted based on the method reported by Moffat [40]. When using Moffat's method, it is crucial to identify the key error sources in the first. Then the overall uncertainty can be determined as the root sum square combination of all the error components [40], i.e., Xtotal =(X12+X22 + … +Xn2)1/2, where n is the total number of error sources. The uncertainties of primary and derived parameters in this work are listed in Table 1. In the Table, the uncertainties of the first 4 parameters including ΔT-exp, ΔTmax-exp, Q˙ and Q˙ c are determined based on the experimental results, while the uncertainties of rest parameters are calculated based on the relevant sources. For example, the sources of uncertainty of ΔT calculated using Eq. (7) are from the ΔT-exp, b′ and fitting error (R2 = 0.94), the uncertainty values of the three terms are 5.0%, 23.7%, 6.0%, respectively. Then based on the method of Moffat, the final uncertainty of ΔT can be determined as 0.0782 + 0.2372 + 0.062 = 32.3%, which is consistent with the maximum uncertainty of calculated ΔT and resulting T as in Fig. 10. References [1] B. Karlsson, J. Quintiere, Fire plumes and flame heights, Enclosure Fire Dynamics, CRC press, New York, Washington, D.C., 1999, pp. 60–93. [2] J. Ji, M. Li, Y. Li, J. Zhu, J. Sun, Transport characteristics of thermal plume driven by turbulent mixing in stairwell, Int. J. Therm. Sci. 89 (0) (2015) 264–271. [3] J. Ji, H. Wan, Y. Li, K. Li, J. Sun, Influence of relative location of two openings on fire and smoke behaviors in stairwell with a compartment, Int. J. Therm. Sci. 89 (2015) 23–33. [4] J. Ji, F. Guo, Z. Gao, J. Zhu, Effects of ambient pressure on transport characteristics of thermal-driven smoke flow in a tunnel, Int. J. Therm. Sci. 125 (2018) 210–217. [5] G. Heskestad, T. Hamada, Ceiling jets of strong fire plumes, Fire Saf. J. 21 (1) (1993) 69–82. [6] H. You, G. Faeth, Ceiling heat transfer during fire plume and fire impingement, Fire Mater. 3 (3) (1979) 140–147. [7] Z. Gao, J. Ji, H. Wan, K. Li, J. Sun, An investigation of the detailed flame shape and flame length under the ceiling of a channel, Proc. Combust. Inst. 35 (3) (2015) 2657–2664. [8] J. Ji, Y. Fu, K. Li, J. Sun, C. Fan, W. Shi, Experimental study on behavior of sidewall fires at varying height in a corridor-like structure, Proc. Combust. Inst. 35 (3) (2015) 2639–2646. [9] R.L. Alpert, Calculation of response time of ceiling-mounted fire detectors, Fire Technol. 8 (3) (1972) 181–195. [10] H. Kurioka, Y. Oka, H. Satoh, O. Sugawa, Fire properties in near field of square fire source with longitudinal ventilation in tunnels, Fire Saf. J. 38 (4) (2003) 319–340. [11] Y.Z. Li, B. Lei, H. Ingason, The maximum temperature of buoyancy-driven smoke flow beneath the ceiling in tunnel fires, Fire Saf. J. 46 (4) (2011) 204–210.
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