Radiant Heat Flux Profile of Horizontally Oriented Rectangular Source

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Radiant heat flux profile of horizontally oriented rectangular source fuel jet fires Youbo Huang, Yanfeng Li, and Bingyan Dong Ind. Eng. Chem. Res., Just Accepted Manuscript • DOI: 10.1021/acs.iecr.7b03977 • Publication Date (Web): 27 Dec 2017 Downloaded from http://pubs.acs.org on January 3, 2018

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Industrial & Engineering Chemistry Research

Radiant heat flux profile of horizontally oriented rectangular source fuel jet fires Youbo Huang*,†, Yanfeng Li*,†, Bingyan Dong‡ † ‡

College of Architecture and Civil Engineering, Beijing University of Technology, Beijing, 100124, China

School of Energy and Environmental Engineering, Hebei University of Technology, Tianjin, 300401, China

ABSTRACT A series of numerical simulations were performed to investigate the flame radiant heat flux of horizontally oriented jet fires by rectangular source fuel with same orifice area (400mm2) but different aspect ratios (1, 2, 4). The natural gas was carried out as fuel which jet velocity varied from 27.5m/s to 205.8m/s. The non-dimensional radiant heat flux were defined to reveal the effect of fuel jet velocity and orifice aspect ratio on radiant heat flux. Results show that the flame size increases with the increasing of fuel jet velocity and the larger orifice aspect ratio results in shorter flame length. The radiant heat flux is affected by orifice aspect ratio as the different soot particle distribution. The predicted model to characterize the radiant heat flux is proposed by taking the orifice aspect ratio into account. The prediction results of proposed model agree well with the simulated data and previous experimental results. Keywords: Horizontal jet fire, Radiant heat flux, Natural gas, Rectangular source fuel, Aspect ratio

1 INTRODUCTION Loss of hydrocarbon containment can lead to different types of leaks occurring in process and storage plants and during the transportation. On the basis of API5811, the probability of safe dispersion, making jet fire, flash fire and vapor cloud explosion after gas fuel pipeline and storage tank broken is in the vicinity of 0.8, 0.1, 0.06 and 0.04, respectively. From this information, the jet fire accident is major damage for hydrocarbon gas fuel or two-phase flow in case of pipeline, storage tank and valve broken, or some other similar accident scenarios. A 1

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historical survey shows that 50% of jet fire accidents would lead to at least one additional event with more severe effects and consequences.2 Jet fires often producing very high heat fluxes, which are usually occurred due to high pressure gas or two-phase flow leaks with ignition or heater source, have the tendency to reach full intensity instantaneously and similarly be shut down very quickly.3 The jet fire hazards personnel and buildings due to a high thermal radiation4-6 and temperature which depends on flame shape, and may result in weakening or melting of surrounding equipment and mechanical failure. In order to design possible mitigation measures to prevent and reduce jet fire accident, it is required to research jet fire behavior and mechanism. Several experiments and simulations of horizontal7-9 and vertical10-16 jet fires ranging from small to large sizes and mathematical correlations have been developed with various variable parameters in industrial groups and academia. Various authors have investigated the flame shape and size.3, 7, 9-22 Moreover, the research into jet fire axial temperature profile and thermal characteristics have been performed based on the flame geometry.16, 17, 19, 20

The predicted function for axial temperature has been proposed by authors. Zhang et al.23 and Hu et al.24

conducted a series of vertical jet fire experiments with rectangular source fuel in normal and reduced pressure atmosphere to investigate the axial temperature profile. They found the Quintiere’s function cannot apply to subatmosphere pressure and modified it. Gómez-Mares et al.25 performed large vertical sonic jet fire experiments with propane as fuel to measure axial temperatures along the jet fire centerline and the flame contour was determined from infrared (IR) images. From the literatures, the temperature researches of jet fire are mainly on vertically oriented fire. And most predictions have been derived from flares or vertical jet flames, 6 however less on horizontal jet fire. But the knowledge of the temperature variation of horizontal jet fires was useful for a better prediction of the thermal radiation intensity and hazard. Flame radiant heat flux of jet fire is a serious hazard to personal and equipment.26 It is essential ability for oil 2


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and gas industry to determine incident radiation from jet fires in order to safety. A series of large scale vertical jet fire experiments with natural gas as fuel and heat release rate varied from 135MW to 210MW have been carried out by Gore to investigate flame configuration and radiation properties. It has been reported that the prediction of radiant heat flux was 15% lower than measurement.26 Hu et al.27 has conducted vertical jet fire experiments in reduced and normal pressure atmosphere to study the flame radiation fraction. A global correlation of the flame radiation fraction with Reynolds numbers has been proposed for both reduced- and normal pressures. They found that the flame radiation fraction changed little with atmospheric pressure. Li et al.28 revealed that the radiation heat flux at the higher altitude was lower experimentally. Zhou et al.29,30 proposed thermal radiation predicted model and found the line source model describing the heat flux radiated from a horizontal propane jet fire was more similar with experimental data than point source model and multipoint source model. They suggested the line source could be used to predict flame radiation after compared with previous reports.31-34 Hankinson et al.35 proposed a weighted multipoint source model both considering nearfield and far-field behavior to predict incident radiation in terms of the fraction of heat radiated. Smith et al.36 has carried out horizontally oriented jet fire experiments with circular and elliptic burners to investigate the flame temperature and radiant heat flux. The effect of burner shape and orientation of elliptic burner on flame characteristics were analyzed. The most previous researches set fuel orifice as circle or ellipse, and the flame characteristic is different between those two burners shape.37-41 Papanikolaou et al.38 suggested the fuel exit shape holds an important effect on flame characteristics including flame size and radiation. Akbarzadeh and Birouk 42 conducted experiments to study the effect of fuel nozzle orifice geometry including circular and rectangular on liftoff of co-flowing non-premixed turbulent methane flame. They obtained that the level of turbulence in the jet near-field is higher for rectangular nozzle than that for circular nozzle. Akbarzadeh and 3



Birouk

43

also investigated the effect of nozzle outlet geometry (orifice diameter and lip thickness) on flame

liftoff height and flow characteristics, the correlation of flame liftoff height in the hysteresis region were developed. For rectangular orifice jet flame, Akbarzadeh and Birouk

44-46

conducted some experiments and

numerical simulations to reveal the jets and flame characteristics of co-flowing turbulent flame and free jet issuing from the rectangular nozzle. From above, much work has been conducted to investigate the effect of orifice shape on jets and flame characteristics. However, the research of free jet fire with rectangular source fuel is still limited. In the above discussed studies, the radiant heat fluxes of vertical jet fires have been widely investigated.29, 32 However, in horizontally oriented jet fires the heat fluxes have less been studied, especially for rectangular burners. This present paper is focused on the heat characteristics of horizontally oriented jet fires issued from rectangular source fuel with same orifice area but different aspect ratios (L/W=1, 2, 4). A series of numerical simulations were conducted with different fuel exit velocity varied from 27.5m/s to 205.8m/s, and the effects of orifice aspect ratio and fuel jet velocity on heat flux were analyzed. Further, the radiant heat flux predicted model for horizontally oriented rectangular source fuel jet fires has been proposed.

2 THEORETICAL MODEL Four kinds of semi-empirical model including single point source model, multipoint model, solid flame model and line source model have been proposed to predict the thermal radiation from jet fire.29 The single point source model can predict the incident radiation in far field (distance to flame center is greater than two flame lengths) but which is clearly invalid in near field.35 However, in the near field (within 1.5 flame lengths of a fire) the multipoint and solid flame model47 can predict radiation successfully, but not satisfactory in far field. The line source model is developed to predict the radiant heat flux of small and large scale jet fires, which agrees better 4


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with experimental data than point and solid model. Zhou et al.29, 48 suggested that the line source model could predict radiant heat flux well. Above predicted models for radiant heat flux are always used for vertical jet fire.13, 26, 26, 35

For horizontally oriented jet fire, Zhang et al.32 used solid model to predict vapor propane jet fire thermal

radiation. Zhou et al. proposed the line source model to predict radiant heat flux for horizontal29 and vertical48 jet fires and the predictions agreed well with experimental data. Thus, the radiant heat flux predicted model is proposed based on line source model. The line source model assumes that all the thermal energy radiates from the centerline inside the jet flame volume with the length equaling the flame length. The jet flame shape assumed as kite could calculate the flame surface area better. And the liftoff distance holds a significant effect on radiant heat flux.7, 29 Therefore, line source model with the kite considering liftoff distance is used to calculate the radiant heat flux. Figure 1 shows the schematic of radiant heat transfer from horizontal jet fire. The line source model29 for horizontal jet fire is expressed as following: .

S L

q'' 

 S

 E' cos  dx 4 R 2

(1)

The atmospheric transmissivity τ is influenced by relative humidity, and can be determined using following equation which takes relative humidity into account. 1 16

 100    h 

 =0.79 

1 16

 30.5     x 

(2)

The length R can be expressed as

R= ( x  x0 )2  ( y  y0 )2  ( z  z0 )2

(3)

Where (x, y, z) is flame centerline coordinate position in m, (x0, y0, z0) is target coordinate position. The angle θ can be determined by following equation. 5



cos 

 x  x0  nx  ( y  y0 )ny   z  z0  nz

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(4)

R

Where (nx, ny, nz) is target surface normal orientation. The flame emissive power per line length connected with maximum flame emissive power per line length48 can be expressed as ’ 2 E’ =E（ 0 b / b0）  (  r Q /

S L



2 (b / b0 ) 2 dx（ ) b / b0）

(5)

S

Where χr is the radiative fraction formulated35 as

r  0.21e

0.00323u j

 0.11

(6)

The integral of flame surface area of kite considering liftoff distance is formulated as eq 7. The expression b/b0 can be calculated by eq 8. S +L

 S

(b / b0 )2 dx 

SL ( S )3  3 3( S   L) 2

(7)

x / ( S   L), S  x  S   L  b / b0   ( S  L  x) / (1   ) L, S   L  x  S +L

(8)

The non-dimensional flame length and liftoff distance of horizontally oriented jet fires can be expressed29 as eq 9 and eq 10, respectively. Akbarzadeh 42,43,45 and Kalghatgi 49 have investigated the liftoff height of co-flowing and still air turbulent jet flame, they revealed that the liftoff height was nearly independent of the orifice diameter. The flame length of horizontally released jet fire is related to Froude numeber. The left hand side and right hand side of eq 10 are normolazed by orifice diameter d. In fact, the liftoff distance is independent of the orifice diameter which conforms to Akbarzadeh and Kalghatgi. 45,49

(S  L) / d  22Fr1 5

(9)

6


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S / d  9.55 103 u j / d

(10)

The equations 3-5, 7 and 8 can be inserted to eq 1. This presented paper analyses the radiant heat flux at the horizontal plane with exit orifice height. The radiant heat flux to the horizontal target along flame axial direction (x direction) which is at the same height with exit orifice can be written as 

q'' 

S  L S L   3 r Qy0 1 x2 1 ( S  L  x) 2 dx  dx  3 2  2  2 2 32 2  2 2 32 4 ( S  L  S / ( S   L) )  ( S   L) S ( y0  ( x  x0 ) ) (1   L) S  L ( y0  ( x  x0 ) ) 

(11)

and the radaint heat flux loads to the horizontal target along transverse axial direction (y direction) which is at same height with exit orifice can be expressed as S  L  3 r Q 1 x3 1 q''  dx  3 2  2  2 2 32 4 ( S  L  S / ( S   L) )  ( S   L) S ( y0  ( x  x0 ) ) (1   L) 2 

 x( S  L  x) 2 dx 2 2 3 2  ( y0  ( x  x0 ) )  S  L S L

(12)

Z

αL

S

(1-α)L X

(nx, ny, nz) b0

R θ Y

. q” Target (x0, y0, z0)

Figure 1. Schematic of radiant heat transfer from horizontal jet fire.

3 NUMERICAL SETUP 3.1 FDS governing equation for analysis of gas combustion FDS (fire dynamics simulator) commercial CFD software which contains LES (Large Eddy Simulation) and DNS (Direct Numerical Simulation) developed by NIST (National Institute of Standards and Technology) is employed to simulate jet fires. LES simulator, which disposes turbulence and buoyancy well, is selected in this study. The grid size in the simulation field must allow the sub grid-scale (SGS) stress model of LES to precisely calculate the flow field viscous stress, and the Smagorinsky model is adopted to deal the turbulence. 7



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The physical equations of FDS solver including Navier-Stokes equations for flow analysis and other scalar conservation equations is shown in technical reference guide.50 3.2 Numerical tests The simulation area was 8m length and high, 7m width (8m×7m×8m). There 13 kinds of fuel jet velocity varied from 27.5m/s to 205.8m/s were simulated based on previous experiments, 3 shown in Table 1. The fuel orifice with long side setting along the horizontal direction was established to discharge natural gas. The ignition source was below the orifice to supply low ignition energy which was turned off after ignition. Three rectangular orifices with same area (400mm2) but different aspect ratio were carried out. The variable aspect ratio n (the ratio of long side over short side) were 1, 2 and 4, shown in Figure 2. It should be noted that the orifice area with aspect ratio 2 was not 400mm2 precisely. For all the cases, the rectangular orifice and ignition source were along Y-Z plane with maximum X. The long side of the orifice was parallel to the ground and located centerline of Y axis (Y=3.5m), as shown in Figure 3. Table 1. Summary of simulated cases

Flow

Exit

Release

Fuel exit area

rate(kg/s)

velocity(m/s)

temperature(K)

(mm2)

1

0.015

27.5

304

2

0.016

30.5

303

3

0.025

46.5

303

4

0.04

74.2

303

5

0.042

78.2

295

Serial no

8


400

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6

0.047

87.4

293

7

0.054

101

303

8

0.067

125

303

9

0.092

171.2

305

10

0.093

173.1

304

11

0.101

188.1

307

12

0.109

203.4

307

13

0.11

205.8

303

20mm 28mm

40mm

20mm

(a) Aspect ratio 1

14mm

10mm

(b) Aspect ratio 2

(c) Aspect ratio 4

Figure 2. Cross-section geometry of rectangular orifice with same area but different aspect ratios.

0.5m

0.5m

Fuel orifice

0.5m

0.5m

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


Z

Z

1.3m

Y 3.5m

1.3m 3.5m

(a) Fuel source

3.5m

X

1.3m 8m

3.5m

(b) Thermocouples at Y-Z plane

(c) Thermocouples at X-Z plane

Figure 3. A schematic layout of the simulation cases and detector.

In order to make simulation cases being same with practical fire, the bottom ground and fuel inlet surface 9



(Y-Z plane) of simulation area were closed boundaries, the other boundaries were set as open boundaries (unbounded) and connected with atmospheric condition. The relative humidity was 40%. The ambient pressure was one standard atmospheric pressure. The initial temperatures were not same for every case, the detail boundaries and initial conditions data were shown in Table 1. 3.3 Measurement system The slices and detectors were used to measure flame parameter in all cases. The temperature slices were made at X-Z plane (Y=4) and X-Y plane (Z=1.3) to obtain temperature of plane, respectively. The radiative heat flux detectors were used to detect radiant heat flux. A sketch of the arrangement of radiative heat flux detector was shown in Figure 3. The radiative heat flux detectors were made at 105 points in two stations at different distances from the fuel orifice, including horizontal and vertical station. Horizontal station had 60 detectors (15 longitudinal, 4 transverse) distributed along the X-axis and Y-axis which were fixed 0.5m front of the fuel orifice. The longitudinal and transverse interval of every detectors was 0.5m. All the detectors of horizontal were on the right of fuel orifice. The vertical station had 45 radiative heat flux detectors (15 longitudinal, 3 vertical) where the interval of every one was 0.5m. All the vertical detectors were made along the orifice centerline. The thermocouples with a diameter of 1.0 mm were distributed at same place with radiative heat flux detectors, in other words every radiative heat flux detecting station had a thermocouple. The flame shape, length and liftoff length are important to determine the flame radiant flux received by external targets.32 To obtain the flame shape, the temperature slice, iso-surface and visible coordinates were set up. The simulated flame length and liftoff length were determined by ‘fire line function’ combined with ‘grid line’ and ‘user ticks’.

10


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3.4 Grid sensitivity analyses The result is more accurate with refining grid size, but that would increase mesh quantity and consume more computation time. The grid dimension is always determined by the characteristic fire diameter D* correlation with heat release rate shown in eq 13. It is suggested that the ratio of fire characteristic diameter D* to grid size ranges from 4 to 16, 50 that means the grid size should be 0.0625 D* - 0.25D*. When grid size is less than this value the effect of grid size on simulated result can be ignored. The minimum heat release rate of jet fire with fuel exit velocity 27.5m/s is 835kW in presented paper. The corresponding characteristic fire diameter D* is 0.892, and the grid size is 56mm when it is 0.0625 D*. The heat release rate increases with fuel exit velocity increasing, and the grid size can be increased. In order to guarantee fuel exit orifice not being ignored, the grid size cannot larger than the fuel exit orifice size. The near fire source field needs the smallest grid size which is the orifice size. Therefore, different grid sizes are conducted for different orifice aspect ratios. The grid size in far field is larger but all the grid size is less than critical value 56mm. In order to save time and guarantee accuracy of result, the grids in X axis are of uniform size 0.2m, but grids in orifice width (Y axis) and height (Z axis) directions are of non-uniform. The computation zones with different grid sizes are listed in Table 2. Every case of same orifice aspect ratio had same grid size arrangement, but different orifice aspect ratio had different grid layout.

  Q  D*     c pT g   0 0 

25

(13)

Table 2. Computation domains and the grid layout

x

y

z

Aspect ratio

Grid number Grid size

Coordinate

Grid size

Coordinate

11


Grid size


(m)

1:1

1:2

1:4

0.2

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value(m)

(mm)

value(m)

(mm)

0-2

40

0-1

40

2-5

20

1-7

20

5-7

40

7-8

40

0-2.1

42

0-1.05

42

2.1-4.9

14

1.05-6.93

14

4.9-7

42

6.93-67.98

42

0-2

40

0-1

40

2-5

20

1-7

10

5-7

40

7-8

40

40×250×350

40×300×475

40×250×650

3.5 Model validation The numerical prediction was compared with the experimental data to validate the accuracy of the numerical simulation. The simulated flame length and flame width were compared with data from a full scale test by Gopalaswami3, 7 shown in Figure 4. The experimental flame lengths were obtained by CCD camera and 600K IR camera contour, respectively. When exit velocity is less than 171.2m/s, the numerical predicted flame length is close to the experimental data obtained by CCD camera and when exit velocity is equal to or more than 171.2m/s the numerical predicted flame length is in good agreement with the experimental data obtained by IR camera. Some simulation flame lengths are higher than the experimental data, the reason may be that sometimes 600K is low and 700K or even 800K fits the best. The other one reason is that the wind is not considered by simulation which in the experiment blow away fuel and the flame length are decreased. The experimental flame widths were obtained by 700K IR camera contour. The results show that the flame width calculated by numerical 12


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code is in good agreement with experimental data when exit velocity is less than 140m/s. The experimental data is smaller and turbulent when exit velocity is more 140m/s, the reason is that the flame width strongly influenced by the experimental background noise and can lead to a larger uncertainty. In general, based on the comparison of the numerical prediction with the experimental data, the accuracy of the numerical scheme is indeed credible. 7.0

2.2 Flame length Simulation results Experiments by N. Gopalaswami (CCD) Experiments by N. Gopalaswami (IR)

6.0 5.5

2.0 1.8

5.0

1.6

4.5

1.4

4.0

1.2

3.5 1.0

3.0

0.8

2.5 2.0

0.6 Flame width Simulation results Experimentsby D.W.Laboureur (IR)

1.5 1.0

0.4 0.2

0.5 0.0

Flame width (m)

6.5

Flame length (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


20

40

60

80

100

120

140

160

180

200

220

0.0

Exit velocity (m/s) Figure 4. Parameter validation with the experimental data.

4 RESULTS AND DISCUSSION 4.1 Flame shape At first, the flame envelope spread horizontally and arrived farthest edge, then flame length decreased and spread vertically, as shown in Figure 5. That is because the flame is mainly driven by momentum firstly. Then the flame oppose with force and buoyance that results in flame spread vertically. The flame envelope which including both stability and intermittence flame was violently turbulence, and this phenomenon was more obvious with higher exit velocity. Figure 6 shows the flame boundary with different exit velocity and orifice aspect ratio during the quasi-steady 13



conditions of fire, four exit velocity are selected which are 27.5m/s, 87.4m/s, 173.1m/s and 205.8m/s, respectively. The main geometrical features of horizontally oriented jet fires, especially the flame length and vertical thickness, increased with exit velocity. All flames exhibited some amount of bending upwards. Moreover, with the increasing of fuel exit velocity, the amount of bending decreased which indicated the transition from buoyancy-driven to momentum-driven condition. When exit velocity was small that the flame spread mainly in vertical direction and with the exit velocity increasing the flame spread mainly in horizontal direction. This is because when exit velocity is small the flame is dominated by buoyance and spreading vertically, when exit velocity increases the momentum is predominant and conducts flame spreading horizontally. The amount of bending upwards increased with orifice aspect ratio36 except 27.5m/s. The flame length for each orifice aspect ratio is shown in Figure 7. For a given fuel exit velocity, the flame length is larger with the increasing of orifice aspect ratio. When the fuel orifice aspect ratio increased the flame spread from horizontal to vertical, which resulted in shorter flame projection distance in horizontal direction and larger flame height in vertical direction. This phenomenon was more obvious with larger exit velocity. Because increasing the orifice aspect ratio (same area), induces greater mixing between fuel and air in the near-field due to the occurrence of axis-switching closer to the orifice and reducing the length of fuel jet potential core. This consequently leads to a short and thick flame. The axis-switching is an important physical phenomenon that governs the behavior and characteristics of jet flows and flame from rectangular nozzles with considerable aspect ratio, which conforms to Akbarzadeh 42,44.

14


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(a) t=1s

(b) t=2.5s

(c) t=13.5s

Figure 5. Flame shape with burning time (Exit velocity 171.2m/s).

27.5m/s

Aspect ratio 1

Aspect ratio 2

Aspect ratio 4

Aspect ratio 1

Aspect ratio 2

Aspect ratio 4

87.4m/s

173.1m/s

Aspect ratio 1

Aspect ratio 2

Aspect ratio 4

Aspect ratio 1

Aspect ratio 2

Aspect ratio 4

205.8m/s

Figure 6. Flame boundary with different exit velocity.

15



7.0 6.5

Flame length Aspect ratio 1 Aspect ratio 2 Aspect ratio 4

6.0 5.5 5.0

Flame length (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

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4.5 4.0 3.5 3.0 2.5 2.0 1.5 1.0 0.5 0.0

0

20

40

60

80

100

120

140

160

180

200

220

Eixt velocity (m/s) Figure 7. Flame length versus exit velocity.

4.2 Heat release rate The heat release rate (HRR) was same with different orifice aspect rate under same exit velocity due to same fuel mass and sufficient air to support complete combustion in open space. That can be assumed the total heat of jet fire with same exit velocity but different orifice aspect ratio is same. The heat release rate increases with exit velocity linearly shown in Figure 8. The correlation between the heat release rate and fuel exit velocity can be expressed as eq 14.

Q=18.61+29.1uj

(14)

16


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6500 6000 5500 5000

Heat release rate (kW)

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


4500 4000 3500 3000 2500 2000 1500 1000 500 0 20

40

60

80

100

120

140

160

180

200

220

Exit velocity (m/s)

Figure 8. Heat release rate of horizontal jet fire at varying exit velocity.

4.3 Effect of exit velocity on radiant heat flux Flame radiation arises from molecular emissions (from hot H20 and C2O) and from soot. Molecular radiation dominates in small flames whereas in these of interest here, soot radiation may be significant or even dominant. The soot radiation intensity depends on soot concentration. Two factors which are production rate of soot (streamline of soot particle) and residence time impact the soot concentration. When the distance to fuel orifice was less than 1m, the radiant heat flux closed to constant for relatively large fuel exit velocity, shown in Figure 9. That is because the jet flame produced less soot particle in this region and the soot concentration is very low. Therefore the radiant heat flux is low and steady. With the increasing of fuel exit velocity, the radiant heat flux increased in horizontal direction. Because larger fuel exit velocity results in larger fuel mass flow rate, the air entrainment of jet flame is corresponding more strongly. That results in the larger soot concentration and larger soot surface rising rate. With the fuel exit velocity growth also makes soot particle arriving farther region. That means the residence time of soot particle in farther region for relatively large fuel exit velocity is longer than that for relatively small fuel exit velocity, and the streamline of soot particle can arriving further region. So, the radiant heat flux increased with the increasing of fuel exit velocity for a given point, and the influence distance 17



by radiant heat flux is larger. When exit velocity was higher than 46.5m/s, the radiant heat flux increased firstly and reached peak value, then decreased along the axial direction. Finally the radiant heat flux for all case tended to be constant and the variation was very small at positions where the distance to the fuel orifice was larger than 7m. That means the radiation is less affected by the fuel exit velocity in the far field. This tendency is same with previous experimental results.13, 21 Therefore, those data was not presented in this paper. When exit velocity was less than 46.5m/s, the peak value of radiant heat flux was near the exit orifice. But when exit velocity was larger the peak value of radiant heat flux was away from exit position. This is because as the exit velocity relative small, the flame is closer to the exit and the soot concentration increased. But when exit velocity is relatively larger, the fuel cannot ignite immediately and the flame envelope axially spread some distance then diffusing due to momentum and air entrainment. There is not soot particle produced near orifice. The radiant heat flux increased with the heat release rate, as shown in Figure 10. The radiant heat flux approached a constant away from exit 1m, and the distance from exit port rim larger than 1m the radiant heat flux increased with heat release rate obviously. The same correlation has been found using actual experiment jet fires both for horizontal and vertical jet fires.21, 26, 27

18


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100 Exit velocity 27.5m/s 30.5m/s 46.5m/s 74.2m/s 78.2m/s 87.4m/s 101m/s 125m/s 171.2m/s 173.1m/s 188.1m/s 203.4m/s 205.8m/s

90

Radiant heat flux (kW/m2)

80 70 60 50 40 30 20 10

0 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0 5.5 6.0 6.5 7.0 7.5

Axial distance from exit (m)

Figure 9. Radiant heat flux at exit centerline. 100

Axial distance 0.5m 1.0m 1.5m 2.0m 2.5m 7.0m

80


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


60

40

20

0 0

500 1000 1500 2000 2500 3000 3500 4000 4500 5000 5500 6000 6500

Heat release rate (kW)

Figure 10. Correlation of the radiant heat flux with the heat release rate.

From the theoretical analysis that the radiant heat flux is the function of the heat release rate, flame length, liftoff distance and position. Since at centerline of exit, the non-dimensional radiant heat flux is defined based on eq 12 written as following. 

 = q''/

3 r Q  f ( L, S , x) 4 ( S  L  S 3 / ( S   L)2 )

(15)

The non-dimensional radiant heat flux distributions are fitted by Gauss function, as shown in Figure 11. The reasonable flame length ratio  is selected as 0.5.29, 48 The function for radiant heat flux distribution can be 19



expressed as eq 16. The degree of fitting (R-squared) is more than 0.98. The coefficients for eq 16 are correlated with exit velocity linearly, shown in Figure 12.

  a  be

1 x c 2  ( ) 2 w

(16)

a  0.01481  (3.38777 10-5 )u j   b  0.50812  0.00228u j   c  0.32012  0.00994u j  w  0.29002  0.00355u j 

(17)

Where a, b, c and w are coefficients. The predictions of radiant heat flux calculated by proposed model are compared with simulated results and experimental data, as shown in Figure 13. The predictions are in good agreement with simulated and previous experiment measured data. However, more actual experimental data is needed to validate the application near the fuel exit port rim field. The difference between the predictions and experimental data is mainly because the fuel species is different and the wind exists in some experiments. 1.1

27.5m/s 30.5m/s 46.5m/s 74.2m/s 78.2m/s 87.4m/s 101m/s 125m/s 171.2m/s 173.2m/s 188.1m/s 203.4m/s 205.8m/s Fitting

1.0

Non-dimensional radiant heat flux 

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 20 of 33

0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1

0.0 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0 5.5 6.0 6.5 7.0 7.5

Axial distance from exit x (m)

Figure 11. Non-dimensional radiant heat flux distribution in horizontal direction.

20


Page 21 of 33

2.50

a b c w Fitting

2.25 2.00 1.75

Coefficients

1.50 1.25 1.00 0.75 0.50 0.25 0.00 -0.25 20

40

60

80

100

120

140

160

180

200

220

Exit velocity (m) Figure 12. Coefficients in eq 16.

Predicted radiant heat fluxs by eq 16 (kW/m )

98 2

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


95 90 80 70 60 50 40 30

27.5m/s 30.5m/s 46.5m/s 74.2m/s 78.2m/s 87.4m/s 101m/s 125m/s 171.2m/s 173.1m/s 188.1m/s 203.4m/s 205.8m/s Zhou et al [31] Zhang et al [32]

20

In the orifice near field

10 5 2 1 0.5 0.1 0.1

0.5 1

2

5

10

20

30 40 50 60 70

80

90

Simulated and experimental radiant heat flux (kW/m2)

95

98

Figure 13. Comparison of predicted radiant heat fluxes with simulated and experimental data.

4.4 Effect of aspect ratio on radiant heat flux The flame projection distances are influenced by rectangular burning nozzle aspect ratio obviously.9 The flame

21



radiation distribution depends on the flame geometry due to the flame geometry have effects upon residence time and streamline of soot particle. Therefore, the burning nozzle geometry may affect the flame radiation. Smith et al. 36 found that the flame radiation of horizontally oriented propane jet flames has been influenced by burning cross-section geometry. The radiant heat flux with different orifice aspect ratio along exit centerline is shown in Figure 14. Six kinds of fuel exit velocity ranging from small to large velocity are selected to display. It can be observed that the radiant heat flux is affected by orifice aspect ratio. Because the source perimeter multiplying length reflects the entrainment area of a fire plume. Actually, it is the ambient cold air that entrained into the fire plume through this surrounding surface area and changes the soot particle distribution, which dominates the radiant heat flux profile. When the exit velocity was relatively small (uj≤46.5m/s), the peak value of radiant heat flux was largest with aspect ratio 1. But when uj>46.5m/s, the largest peak value of radiant heat flux was appeared with aspect ratio 2. That is because when exit velocity is relatively small the flame is dominated by buoyance, the soot concentration is greater. But when exit velocity increases the flame is dominated from buoyancy to momentum. The peak radiant heat fluxes located at same position for different orifice aspect ratios when exit velocity was more than 46.5m/s. The radiant heat flux decreased fastest with the orifice aspect ratio 4. From Figure 14, the radiant heat flux of horizontally oriented rectangular source fuel jet fire with bigger orifice aspect ratio was less than that with smaller orifice aspect ratio near the exit port field. However, the radiant heat flux with bigger orifice aspect ratio was more than that with smaller orifice aspect ratio near the position where peak value appeared. Moreover, away from exit port the radiant heat flux with bigger orifice aspect ratio was less than that with smaller orifice aspect ratio again. That is because the orifice aspect ratio affects the jet flame surface which emits power and influences soot particle concentration. The increasing of fuel orifice aspect ratio 22


Page 22 of 33

Page 23 of 33

results in the shorter flame length and larger flame width, therefore the radiant heat flux with bigger aspect ratio is less away from flame axis due to the residence time and the concentration of soot particle are shorter and lower. The maximum flame cross-section increases with orifice aspect ratio that results in larger radiant heat flux at the position where peak value appears. The detail information about the effect of orifice aspect ratio on flame geometry is shown in previous work.51 27.5

22.5

17.5

Aspect ratio 1 Aspect ratio 2 Aspect ratio 4

22.5



25.0


20.0

15.0 12.5 10.0 7.5 5.0

20.0 17.5 15.0 12.5 10.0 7.5 5.0

2.5

2.5 0.0 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0 5.5 6.0 6.5 7.0 7.5

0.0 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0 5.5 6.0 6.5 7.0 7.5

Axial diatance from exit (m)


(a) 27.5m/s

(b) 46.5m/s 110

40

100


30


90


35


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


25 20 15 10

80 70 60 50 40 30 20

5

10

0 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0 5.5 6.0 6.5 7.0 7.5

0 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0 5.5 6.0 6.5 7.0 7.5



(c) 87.4m/s

(d) 173.1m/s

23



120

120 110

110


90


100


100


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 33

80 70 60 50 40 30

90 80 70 60 50 40 30

20

20

10

10

0 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0 5.5 6.0 6.5 7.0 7.5

0 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0 5.5 6.0 6.5 7.0 7.5



(e) 203.4m/s

(f) 205.8m/s

Figure 14. Radiant heat flux with exit velocity for different orifice aspect ratio.

For such a rectangular fuel source horizontally oriented discharged flame, the hydraulic diameter d=[4(LW)]/[2(L+W)] are used. The new non-dimensional radiant heat flux can be redefined as

n = n

14 

q''/

3 r Q  f ( L, S , x) 4 ( S  L  S 3 / (S   L)2 )

(18)

Where n is aspect ratio. So the radiant heat flux for rectangular source fire are presented as 

q''=

1 n

14

1 x (0.32012  0.00994 u j ) 2 ) 0.29002  0.00355u j

 ( 3 r Q 2 5 [(0.01481  (3.38777  10 ) u )  (0.50812  0.00228 u ) e j j 4 ( S  L  S 3 / (S   L)2 )

]

(19)

Figure 15 shows the comparison of the simulated radiant heat fluxes with the predictions by eq 19. It is shown that when the radiant heat flux is more than 80kW/m2, some predictions are less than the simulated data. But in general, the predictions by the proposed equations agree well with the simulated data. Therefore, the radiant heat flux of horizontally oriented rectangular source fire with any nozzle aspect ratio can be predicted by eq 19.

24


Page 25 of 33

99 98

Predicted radiant heat fluxs (kw/m2)

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



95 90 80 70 60 50 40 30 20 10 5 2 1 0.5 0.1 0.1

0.5 1

2

5

10

20 30 40 50 60 70 80

90

95

98 99

Simulated radiant heat fluxs (kw/m2)

Figure 15. Comparison of predictions of proposed model with simulated data on radiant heat fluxes.

5 CONCLUSIONS This paper reveals the effect of fuel exit velocity and orifice dimension aspect ratio on flame shape and radiant heat flux distribution of horizontally oriented rectangular source jet fire. The main conclusions of the present study can be summarized as: 1 The flame length in horizontal direction is larger with fuel exit velocity growth due to more fuel mass and momentum. Moreover, the flame length decreases with the increasing of orifice aspect ratio because of the occurrence of axis-switching is closer to the nozzle exit and reducing the length of the jet potential core. 2 The radiant heat flux are influenced by fuel exit velocity and orifice dimension aspect ratio. The radiant heat flux along centerline increases with fuel exit velocity except near orifice 1m field. That is, the residence time and concentration of soot particle induced by jet flame are longer and greater with larger fuel exit velocity, and near orifice 1m field has less soot particle produced. Far from the fuel orifice, the radiant heat flux stabilizes in a constant along orifice centerline due to no streamline of soot particle. 3 The empirical model to predict the radiant heat flux along the orifice centerline is put forward based on line 25



source model with kite by taking the effect of fuel orifice aspect ratio into consideration. The prediction results of the proposed model are in good agreement with the simulated data and previous experimental results.

AUTHOR INFORMATION Corresponding Author *Tel: +86 010 67391147. E-mail addresses: [email protected] (Y.B.Huang), [email protected] (Y.F.Li).

ORCID Youbo Huang: 0000-0002-5197-4812 Notes The authors declare no competing financial interest.

ACKNOWLEDGMENTS The authors wish to acknowledge the financial support from the National key research and development plan [grant number 2017YFC0805008], Beijing Natural Science Foundation [grant number 8172006].

NOMENCLATURE Nomenclature b

flame radius (m)

R

length of the connecting line (m)

b0

maximum flame radius (m)

S

liftoff distance (m)

cp

specific heat of air (kJ kg-1 K-1)

T0

ambient temperature (K)

d

orifice diameter (m)

uj

exit velocity (m s-1)

E’

flame emissive power per length (kW m-1)

x

distance (m)

E’0

maximum flame emissive power per length

26


Page 26 of 33

Page 27 of 33 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


(kW m-1)

Greek symbols

Fr

Fronde number

α

g

gravitational acceleration (m s-2)

h

relative humidity

ρ0

ambient density (kg m-3)

L

flame length (m)

θ

angle between connecting line and

Q

heat release rate (kW)

whole flame

target surface normal orientation.

.

q ''

radiant heat flux (kW

flame length ratio of lower flame to

τ

atmospheric transmissivity

χr

radiative fraction

m-2)

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For Table of Contents Only

2.50

a b c w Fitting

2.25 2.00 1.75 1.50

Coefficients

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


1.25 1.00 0.75 0.50 0.25 0.00

-0.25 20

40

60

80

100

120

140

160

Exit velocity (m)

33


180

200

220

Radiant Heat Flux Profile of Horizontally Oriented Rectangular Source

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