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Experimental investigation on the effect of reduced pressure on the combustion characteristics and flame height of gaseous fuel jets in parallel sidewalls Qiang Wang, Fei Tang, Huan Liu, Zheng Zhou, and Adriana Palacios Energy Fuels, Just Accepted Manuscript • DOI: 10.1021/acs.energyfuels.7b03871 • Publication Date (Web): 26 Dec 2017 Downloaded from http://pubs.acs.org on January 7, 2018

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Energy & Fuels

Experimental investigation on the effect of reduced pressure on the combustion characteristics and flame height of gaseous fuel jets in parallel sidewalls

Qiang Wanga, Fei Tanga*, Huan Liua, Zheng Zhoua, Adriana Palaciosb

a

School of Automotive and Transportation Engineering, Hefei University of Technology Hefei, Anhui 230009, China

b

Department of Chemical, Food and Environmental Engineering, Fundacion Universidad de las Americas, Puebla 72810, Mexico

*Corresponding author: Tel: (86) 551 62901960; Fax: (86) 551 62901960; Email address: [email protected]; Postal address: School of Automotive and Transportation Engineering, Hefei University of Technology, Hefei, Anhui, 230009, China.

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Nomenclature Cp

Specific heat at constant pressure [kJ kg-1K-1]

T0

Ambient temperature [K]

D

Source diameter [m]

S

Sidewall separation distance [m]

g

Gravitational acceleration [m/s2]

Scri

Critical sidewall separation distance [m]

Lf

Maximum flame height [m]

Q&

Heat release rate [kW]

δ 99% ( L f )

Jet width at the flame tip [m]

Q& D*

Dimensionless heat release rate, based on source diameter D,

ρ0

Ambient air density [kg/m3]

Q& S*

Dimensionless heat release rate, based on sidewall separations distance S,

Greek symbols

Q& Q& D* = ρ 0 c pT0 g1/2 D 5/ 2

Q& S* =

Q& ρ 0 c pT0 g1/2 S 5/2

1


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Abstract The increasing energy demand stimulates the increase of natural gas transmitting pipeline all around China and provoke serious fire risks due to accidental pipeline breaks and gas leakage, especially in cities at different altitudes. This work concerns the pressure effect on the flame height of buoyant jet diffusion flames restricted by parallel sidewalls in reduced pressure, which does exist in natural gas leakage fire accident in high plateau areas. Experiments were conducted in Lhasa, Tibet (Altitude: 3650m, Pressure: 0.64 atm), and the corresponding comparison results conducted in normal pressure are referred from our previous work obtained in Hefei, Anhui (Altitude: 50m, Pressure: 1.0 atm). The evolution of the flame heights of a buoyant jet diffusion flame restricted by parallel sidewalls in a reduced pressure are examined, and the major new findings are that the evolution of a parabolic uprising buoyant vortex at the flame boundary and the flame height vary much like that in normal pressure as the sidewall separation distance increases from the minimum value. Moreover, the flame height in a reduced pressure is found to be slightly higher than that in normal pressure, implying that a wider range of areas will be dangerous, due to larger flames and exposure distances to radiation fluxes. The critical sidewall separation distance ( Scri ) in reduced pressure is figured out and correlated with the model obtained from our previous scaling analysis. Besides, it is found that, in reduced pressure, the critical separation distance in reduced pressure is slightly wider than that in normal pressure, indicating that the surroundings should be located further to reduce fire risk. Finally, a global correlation accounting the pressure effect based on the proposed model to characterize the variation of flame height is obtained, correlating the experimental results in both reduced and normal pressures with good agreement. The current work can not only provide some supplemental knowledge on gas leakage flames restricted by surroundings in both reduced and 2


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normal pressures, but also serve as a scientific basis to the management on the gas fuel energy storage and transportation systems in the cities at different altitudes to reduce possible fire thread.

Keywords Reduced pressure; Gas pipeline leakage flames; Parallel sidewalls; Flame height.

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1. Introduction In recent 20 years, three West-East gas transmission pipeline has been built to transport natural gas from west to east to meet the increasing energy demand, just as seen in Fig. 1. This tremendous fuel supply system covers most of the big cities with altitude ranging from 0 to 3650 m, all around China, brings much convenience to the public and alleviates serious air pollution conditions resulted from combustion production emissions due to coal combustion. However, it can also provoke serious fire risks due to accidental pipeline breaks and gas leakages, especially in the city with many clusters of buildings. Just as exemplified in our previous work [1] and in Fig. 1, it has been repeatedly reported that gas leakages caused large scale jet flames and seriously damages the surrounding buildings [2, 3]. Nevertheless, there is still few scientific reports on buoyant turbulent jets restricted by surroundings, especially for the condition that the flame is restricted by parallel sidewalls. We noticed this problem and conducted a primary work with buoyant turbulent jets in normal altitude (Hefei City, altitude: 50 m) [1]. Recently, a following work was conducted in a reduced pressure at high altitude (Lhasa, altitude: 3650 m) to investigate the pressure effect on the flame restricted by surroundings. This is a supplement of our previous work that can provide a supplemental scientific basis for the management of the gas fuel energy storage and transportation systems in reduced pressure at high plateau cities to reduce the possible fire thread. The flame length scale is a crucial parameter that determine the impinging area [4]. Previous works have extensively focused on this issue [3-14] due to its practical significance to fire safety. Among them, several models, relating the dimensionless flame heights to some particular scaling parameters, proposed by Becker and Liang [12], Delichatsios et al. [13] and Heskestad [15] are the most widely accepted. These models has been extensively proved to be valid for buoyancy controlled 4


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gaseous fuel jets without restriction. With regards to the restriction effect, some researchers [16-20] have paid attention to the flame adjacent to single walls. As the flame approaches a lateral wall on one side, the evolution characteristics of flame height and the buoyant vortex are investigated by Chao et al. [16], and Zukoski et al. [14]. Poreh et al. [18] experimentally clarified the reduction on the entrainment and enlargement of the mean and peak flame heights as the flame approaches the walls. Jiang et al. [19] and Gövert et al. [20] numerically investigated half-confined sidewall effects on flame. These works referred above have implied that the restriction effects will inevitably restrict the air entrainment and change the evolution of the flame length [14, 16-21]. Moreover, our recent work [1] and Hu’s paper [21] have clarified the fundamental differences in the air entraining physics of flame in free condition and restricted by parallel sidewalls. The results has indicated that the flame length will be enlarged due to sidewall blocks air entrainment at a critical condition. However, it should be noted that, until now, most of the previous works and suggested correlations have been carried out in a standard pressure atmosphere (1 atm). There is still no work on clarifying the flame height variation characteristics of buoyant turbulent gaseous diffusion jets, restricted by sidewalls at various separation distances at sub-pressure atmospheric conditions, which does exist in leakage accidents at high altitude as seen from Fig. 1. One should notice that in a sub-pressure atmosphere, the density of the ambient air changes proportionally with the ambient pressure. It has been reported by Most et al. [22] that the flame height of a pool-type diffusion flame, produced by a 0.3 m porous gas burner with a low Froude number of 6·10-5 in a 1 m height pressure vessel, changes proportional with the ambient pressures (0.3-3 atm). Moreover, some recent works conducted in Lhasa City (altitude: 3650 m; ambient pressure: 0.64 atm) and reduced pressures revealed that the ambient 5


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Energy & Fuels

pressure leads to significant changes into the jet flame geometrical characteristics, boundary instability, buoyancy force and air entrainment [10, 23-26]. However, there is still a lack of thorough understanding on the influence of a sub-atmospheric pressure on the flame height of buoyant gaseous jet diffusion flames restricted by parallel sidewalls, a task undertaken in the present work. In this work, we endeavor to clarify the differences in the flame height of buoyant turbulent jets restricted by parallel sidewalls in both reduced (Lhasa: 0.64 atm) and normal (Hefei: 1.0 atm) pressures, which has not been revealed ever before. A new global model was obtained to characterize flame height variation of buoyant turbulent jets restricted by parallel sidewalls for various nozzles and fuel flow rates in both reduced and normal pressures. The current study can provide some supplemental knowledge on buoyant turbulent jets, relevant for the management on the gas fuel energy storage and transportation systems in high plateau cities to reduce possible fire thread.

2. Experiment A set of identical experimental systems was built in Lhasa, Tibet (Altitude: 3650, Ambient pressure: 0.64 atm), just as presented in Fig. 2. As the same in [1], the experimental system consist a flow supply system, a 2 m long pipe, a stainless nozzle, two parallel sidewalls and a CCD digital camera. The fuel was propone with purity of 99%. Three nozzles with diameters of 3, 6 and 10 mm were used in the experiments. The sidewall was made of mica plate with a dimension of 1.5 m in width, 3 m in height. A mass flow controller was employed to regulate the fuel flow rate with an accuracy of 0.01 SLPM. More details of the experimental system can be referred from [1].The experimental conditions are listed in Table 1. The experimental system was placed in the center of a prototype of a GB 4715—2005 standard combustion room built in Lhasa with size of with 10 m 6


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long, 7 m wide and 4 m high. All the experimental procedures, environmental conditions, and the identification method of flame height can be referred from [1].

3. Results and Discussion 3.1 Flame evolution and flame height Figure 3 compared the evolution characteristics of flame visual characteristics of axisymmetric gaseous diffusion jets in reduced pressure (0.64 atm) and in normal pressure (1.0 atm), restricted by parallel sidewalls at various separation distances, obtained from a nozzle with diameter of 6 mm and heat release rate of 8.25 kW and 8.78kW. From the flame images in Fig. 3, the dynamic interaction process of the flame with the sidewalls, in both pressures at the various separation distances, can be clearly observed to be basically the same. Initially, as the sidewall separation distance decreases from a totally free condition to a critical distance (around 30 cm in the presented conditions), the flame almost keeps the same as an unrestricted flame. The flame height and the buoyant vortex at the flame boundary in both pressure did not present obvious changes. After then, just as it has been observed in [1] and in Fig. 3a, in a reduced pressure for Fig. 3b, further reduction on the sidewall separation distances will disturb the evolution process of the buoyant vortex and result into the enlargement of the flame height. Besides, in general view, the flame in reduced pressure is slightly higher than that in normal pressure. As we can observed from Fig. 3a, the flame boundary instability phenomena for the flame in a reduced pressure propagate much like that in normal pressure [1]. And these parabolic processes provide the oxidant to support combustion along the flame surface downstream until the fuel is burnt out at the flame tip. However, in a reduced pressure, the air/oxygen density is lower. This implies that the flame cannot obtain the same amount of oxygen in the same space in a reduced pressure. 7


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Thus, the unburnt fuel can be survived downstream to a higher height. Namely, the flame will get higher and the flame envelop will become bigger to entrain enough volumetric air/oxygen flow into the flame to consume the fuel. When the conditions involved restrictions from the parallel sidewalls in reduced pressure, these processes gets much more complicated due to the blockage of sidewalls. Thus, in the following section, the flame height variation characteristics restricted by sidewalls in reduced pressure will be examined along with comparison with the results in normal pressure. Figure 4 displays the jet flame height with increasing the sidewall distances in both reduced pressure (0.64 atm) and normal pressure (1.0 atm). As revealed in Fig. 4, the flame heights in reduced pressure present a similar variation trend with that observed in normal pressure. Initially, the flame height significantly decreases with increasing the sidewall separation distance within the range that closer than a certain separation distance. The decreasing process will end at a critical condition where the sidewall separation distance is close to the entraining radius, just as we depicted in [1]. Beyond this critical distance, a further increase of the sidewall separation distance has no effect on the variation of the jet flame height. Besides, as we can observed from the Fig. 4, the flame height in reduced pressure is significantly higher than that in normal pressure, which is consistent with the observations in Fig. 3. This indicates that the gas leakage fires at sub-atmospheric pressures can reach to a higher height or larger region, implying

that a wider range of areas will get seriously

damaged due to radiation fluxes exposed to areas reached by larger flames

3.2 Comparison of critical sidewall separation distances and flame height in reduced and normal pressures Just as depicted in our previous work [1], the critical sidewall separation distances start to have a pronounced impact on the flame height by hindering the air entrainment at the condition of 8


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Scri ≤ δ99%(Lf ) . And the solution for the flow field can be solved out by accounting for the turbulent characteristics into the conservation governing equations of mass, momentum and species. Furthermore, we have deduced [1] that the flame radius in a turbulent jet flow has a linear relationship with the flame height:

δ 99% ( L f ) Lf

∝ const

(1)

Thus, the critical sidewall separation distance is also proportional to the flame height by a linear relationship:

Scri = δ99% ( Lf ) ∝ Lf ,cri

(2)

The experimental results of the critical transition points in reduced pressure are marked out according to the increasing rate ( ∂Lf ∂S ≥ 2% ) with red stars in Fig. 4. The data are summarized in Fig. 5 to have a more clearly comparison with the data in normal pressure [1]. As observed in Fig. 5, the data shows a relatively good agreement with Eq. (2) as the critical sidewall separation distances increase linearly with the flame height in both reduced and normal pressures. From Fig. 5, it also indicates that, in reduced pressure, the critical sidewall separation distance is slightly wider than that in normal pressure. This means that in reduced pressure, the surroundings should be located at a further distance to reduce fire risk. In a buoyant turbulent jet flame without restriction, the flame height has a 2/5 power dependence on the dimensionless heat release rate ( Q& * ) [14, 15, 27], thus the critical sidewall D

separation distance also has the similar power dependence due to its linear relation with flame height at critical condition: *2/5

S cri ∝ L f ,cri ∝ Q& D

(3a)

Then, a model can be obtained by correlating the critical sidewall separation distance ( Scri ) and the 9


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dimensionless heat release rate ( Q& * ), just as presented in Fig. 6. The model can be specified as: D

0.98Q& D* 2/5 + 20.68 0.64atm S cri / D =  & * 2/5  0.93Q D + 10.07 1.0atm

(3b)

The correlations in both pressures show good agreement with the data. The normalized critical sidewall separation distance in reduced pressure is also found to be higher than that in normal pressure. With regards to the variation of the jet flame height, in conditions where the sidewall separation distance is larger than the critical value ( S > δ 9 9 % ( L f ) ), the entrainment is not hindered by the sidewalls as depicted in [1]. Thus, the flame height in both reduced and normal pressure can be correlated with a classical model [14, 15, 27] for free condition, just as shown in Fig. 7:

28.33 + 3.63QD* = D  −1.16 + 4.3QD*2/5

2/5

Lf

0.64atm

(4)

1.0atm

As observed in Fig. 7, both correlations agree quite well with the experimental data, indicating that, in reduced pressure, the flame height of unrestricted flame can also be figured out by the proposed model in Eq. (3). When the sidewall separation distances are closer to the maximum jet width ( S ≤ δ99%(Lf ) ), the air can only be entrained from the two free sides as shown in [1]. Based on this assumption, in our previous work [1], we have deduced that the flame height normalized by sidewall distance has a 2/3 power dependence on the dimensionless heat release rate ( Q& S* ):

Lf S

2/3 ∝ Q& S*

(5a)

where Q& S* =

Q& ρ 0 c pT0 g1/2 S 5/2 10


(5b)

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Figure 8 present the correlation results of the flame height normalized by the sidewall separation distance ( L f S ) with the dimensionless heat release rate ( Q& S* ), showing good agreement with Eq. (5), for all the data in both reduced and normal pressures. Thus, the overall model for predicting the buoyant jet flame height restricted by the sidewalls in reduced and normal pressures can be concluded as:

Lf , pred

0.64 atm

( ( ( −1.16 + 4.3Q  =  ( 0.97 + 3.55Q 

*2/5 D

Lf , pred

1.0 atm

) ) )*D )* S

 28.83 + 3.63Q*2/5 * D S > S D cri  = 2/3  2.01 + 2.93QS* * S S ≤ Scri 

*2/3 S

(6a)

S > Scri S ≤ Scri

(6b)

In Fig. 9, the prediction results from Eq. (6) are compared with the experimental results, showing quite good agreement. This implies that the suggested model is suitable for the prediction of the flame height for a buoyant jet flame restricted by sidewalls in both reduced and normal pressures.

4. Conclusions This work concerns the pressure effect on the flame height of buoyant jet diffusion flames restricted by parallel sidewalls in reduced pressure, which does exist in natural gas leakage fire accidents in high plateau areas. Experiments were conducted in Lhasa, Tibet (Altitude: 3650m, Pressure: 0.64 atm), and the corresponding comparison results conducted in normal pressure are referred from our previous work [1], obtained in Hefei, Anhui (Altitude: 50m, Pressure: 1.0 atm). The evolution of the jet flame heights in reduced pressure, restricted bysidewalls are examined, and the major new findings can be concluded as: 1. The evolution of the parabolic uprising buoyant vortex at the flame boundary and the flame height for sub-atmospheric pressures varied much like that in normal pressure, as the sidewall 11


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separation distance increases from the minimum value. In the initial stage, the vortex was observed to be severely blocked by the sidewalls and the flame height was significantly enlarged until the sidewall separation distance was increased to a critical value ( Scri ). As the sidewalls distance was further increased beyond that critical sidewall, the flame visual characteristics almost kept the same. Moreover, the flame height in a reduced pressure was found to be slightly higher than that in normal pressure, implying that a wider range of areas will be dangerous, due to larger flames reaching larger distances with radiation fluxes. 2. The critical sidewall separation distance in a reduced pressure was figured out and a correlation model was obtained, based on our previous scaling analysis [1]. Besides, it was found that the critical separation distance in a reduced pressure was slightly wider than that in normal pressure, indicating that the surroundings should be located further to reduce fire risk. 3. A global correlation accounting for the pressure effects, based on the proposed model to characterize the variation of flame height [1] was obtained. The experimental results in both reduced and normal pressures were found to correlate with good agreement. The results in the present work could provide some supplemental knowledge on axisymmetric jets restricted by surroundings in both reduced and normal pressures. They also serve as a scientific basis relevant to the management on the gaseous fuel energy storage and transportation systems in the cities at different altitudes, to reduce the possible thread of fire.

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Acknowledgements This work was supported by The National Nature Foundation of China (Grant No. 51606057 and No. 51776060). A.P. gratefully acknowledges the financial support of the Royal Society in the form of a Postdoctoral Newton International Fellowship.

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Sci. Tech. 2000, 158, 93-113. [17] Hasemi, Y.; Tokunaga, T. Some experimental aspects of turbulent diffusion flames and buoyant plumes from fire sources against a wall and in a corner of walls. Combust. Sci. Technol. 1984, 40, 1–18. [18] Poreh, M.; Garrad, G. A study of wall and corner fire plumes. Fire Saf. J. 2000, 34, 81–98. [19] Jiang, X.; Luo, K.H. Dynamics and structure of transitional buoyant jet diffusion flames with side-wall effects. Combust. Flame 2003, 133, 29–45. [20] Gövert, S.; Mira, D.; Kok, J.B.W.; Vázquez, M.; Houzeaux, G. Turbulent combustion modelling of a confined premixed jet flame including heat loss effects using tabulated chemistry. Appl.

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Figure Captions Figure 1. a) Natural Gas pipeline leakage accidents occurred along the West-East gas transmission pipeline in recent years at different altitudes in China; b) A case of natural gas pipeline leakage fire accident surrounded by buildings in the city [Cited from www.hebnews.cn 2017/12]

Figure 2. Schematic of the experimental facility. Figure 3. Variation of the jet flame shape with the increase of the sidewall separation distance. Nozzle diameter of 6 mm, heat release rate of a) 8.78kW in reduced pressure (0.64 atm) and b) 8.25 kW in normal pressure (1.0 atm). Separation distances range from 10 to +∞ cm.

Figure 4. Variation of the flame height in both reduced and normal pressures with the sidewall separation distance for different nozzle diameters ((a) 3 mm; (b) 6 mm and (c) 10 mm) and heat release rates. The stars show the critical transition point.

Figure 5. Variation of the critical sidewall separation distance, S cri , with the flame height,

L f ,cri ,in both reduced and normal pressures. Figure 6. Variation of the dimensionless critical sidewall separation distances in reduced and normal pressures with the dimensionless heat release rate, Q& D* .

Figure 7. Variation of the normalized flame height in both reduced and normal pressures with the dimensionless heat release rate Q& D* at free (+∞) or S > S cri conditions.

Figure 8. Variation of the normalized flame height with the dimensionless heat release rate Q& S* in a

S ≤ S cri condition, in both reduced and normal pressures. Figure 9. Comparison of experimental and calculated flame heights.

17


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Page 19 of 30 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Energy & Fuels

Table caption Table 1. Summary of experimental conditions.

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Energy & Fuels 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Figure 1. a) Natural Gas pipeline leakage accidents occurred along the West-East gas transmission pipeline in recent years at different altitudes in China; b) A case of natural gas pipeline leakage fire accident surrounded by buildings in the city [Cited from www.hebnews.cn 2017/12]

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Page 21 of 30 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Energy & Fuels

Figure 2. Schematic of the experimental facility.

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Energy & Fuels 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Figure 3. Variation of the jet flame shape with the increase of the sidewall separation distance. Nozzle diameter of 6 mm, heat release rate of a) 8.78kW in reduced pressure (0.64 atm) and b) 8.25 kW in normal pressure (1.0 atm). Separation distances range from 10 to +∞ cm.

21


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Page 23 of 30

1.2

(a) D=3mm

Flame height Lf(m)

1.0

0.8

0.6

0.4

0.2 0.0

0.2

0.4

0.6

0.8

HRR 0.64 atm (kW) 4.39 8.78 13.17 17.56 21.95 HRR 1.0 atm (kW) 1.65 4.93 8.25 11.55 14.85

+∞ 1.2

Sidewalls Separation Distance S (m)

1.2

(b) D=6mm 1.0

Flame height Lf(m)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Energy & Fuels

0.8

0.6

0.4

0.2 0.0

0.2

0.4

0.6

0.8

+∞ 1.2


22



Energy & Fuels

1.2

(c) D=10 mm 1.0

Flame height Lf(m)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 24 of 30

0.8

0.6

0.4

0.2 0.0

0.2

0.4

0.6

0.8


+∞ 1.2


Figure 4. Variation of the flame height in both reduced and normal pressures with the sidewall separation distance for different nozzle diameters ((a) 3 mm; (b) 6 mm and (c) 10 mm) and heat release rates. The stars show the critical transition point.

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0.4

0.3

Scri (m)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Energy & Fuels

1.0 atm 3 mm 6 mm 10 mm

0.2

0.64 atm 3 mm 6 mm 10 mm

0.1

0.0 0.0

0.2

0.4

0.6

0.8

1.0

1.2

Lf, cri (m)

Figure 5. Variation of the critical sidewall separation distance, Scri , with the flame height, L f ,cri in both reduced and normal pressures.

24


Energy & Fuels

100

80

60

Scri/D

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 26 of 30

2

Scri / D = 0.98Q& D* 2/5 + 20.68 0.64 atm 3 mm 6 mm 10 mm

R =0.97

1.0 atm

3 mm 6 mm 10 mm

40 2

R =0.93

20

0 -10000

Scri / D = 0.93Q& D* 2/5 + 10.07 0

10000

20000

30000

40000

Q& D*

Figure 6. Variation of the dimensionless critical sidewall separation distances in * reduced and normal pressures with the dimensionless heat release rate, Q&D.

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S > Scri

2/5

300

L f / D = 28.33 + 3.63QD*

D

2

R =0.96 S

200

Lf/D

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Energy & Fuels

Heskestad Model [27]

D

2/5

100

L f / D = −1.16 + 4.3QD*

S

2

R =0.97 0

0

10000

20000

30000

0.64 atm 3 mm 6 mm 10 mm 30cm 40cm 50cm 60cm

30cm 40cm 50cm 60cm

30cm 40cm 50cm 60cm

+∞ +∞ +∞ 1.0 atm 3 mm 6 mm 10 mm 30cm 40cm 50cm

30cm 40cm 50cm

30cm 40cm 50cm

+∞

+∞

+∞

40000

*

QD

Figure 7. Variation of the normalized flame height in both reduced and normal * pressures with the dimensionless heat release rate Q&D at free (+∞) or S > Scri

conditions.

26


Energy & Fuels

20

15

0.6 atm S ≤ Scri 2 3 mm R =0.93 2/3 6 mm L f / S = 2.01 + 2.93QS* 10mm

10

Lf/S

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 28 of 30

5

0

2

R =0.99 2/3

L f / S = 0.97 + 3.55QS* 0

1

2

  Q& Q& s*2/3 =  1/ 2 5/2  ρ c T g S   0 p 0 

1.0atm 3 mm 6 mm 10 mm 3

4

2/3

Figure 8. Variation of the normalized flame height with the dimensionless heat release rate Q&S* in a S ≤ Scri condition, in both reduced and normal pressures.

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2.5 2.0

L f , pred

1.0 atm

( (

) )

 −1.16 + 4.3Q*2/5 * D D  = 2/3  0.97 + 3.55QS* * S 

S > Scri

0.64 atm S > Scri S S ≤ Scri

S ≤ Scri

1.5

Lf, pred (m)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Energy & Fuels

D

3 mm 6 mm 10 mm

3 mm 6 mm 10mm

1.0 0.5 0.0 -0.5 -0.5

L f , pred 0.0

0.64 atm

0.5

( (

) )

 28.83 + 3.63Q *2/5 * D D  = 2/3  2.01 + 2.93QS* * S  1.0

1.5

S > Scri S ≤ Scri

2.0

1.0 atm S > Scri S S ≤ Scri 3 mm 3 mm 6 mm 6 mm D 10 mm 10 mm

2.5

Lf, exp (m) Figure 9. Comparison of experimental and calculated flame heights.

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Page 30 of 30

Table 1. Summary of experimental conditions. Ambient pressure

0.64 atm

1.0 atm

Sidewall distances S (cm) 10 20 30 40 50 60 +∞* 10 15 20 30 40 50 +∞*

Heat release rate（kW） Nozzle diameter: 3/6/10 mm 4.39 4.39 4.39 4.39 4.39 4.39 4.39 1.65 1.65 1.65 1.65 1.65 1.65 1.65

8.78 8.78 8.78 8.78 8.78 8.78 8.78 4.95 4.95 4.95 4.95 4.95 4.95 4.95

13.17 13.17 13.17 13.17 13.17 13.17 13.17 8.25 8.25 8.25 8.25 8.25 8.25 8.25

*+∞ denotes free conditions.

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17.56 17.56 17.56 17.56 17.56 17.56 17.56 11.55 11.55 11.55 11.55 11.55 11.55 11.55

21.95 21.95 21.95 21.95 21.95 21.95 21.95 14.85 14.85 14.85 14.85 14.85 14.85 14.85

Experimental investigation on the effect of reduced ... - ACS Publications

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