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Applied Thermal Engineering 31 (2011) 1347e1351

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Applied Thermal Engineering

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Numerical modeling of fires on gas pipelines

Yang Zhao*, Lai Jianbo, Liu LuThermal Energy Research Institute, Tianjin University, Tianjin 300072, PR China

a r t i c l e i n f o

Article history:Received 12 November 2009Accepted 5 January 2011Available online 22 January 2011

Keywords:CFDLifted jet firesFlame lengthNatural gas

* Corresponding author. Tel.: þ86 (0) 22 2789 0627E-mail address: zhaoyang@tju.edu.cn (Y. Zhao).

1359-4311/$ e see front matter Crown Copyright � 2doi:10.1016/j.applthermaleng.2011.01.006

a b s t r a c t

When natural gas is released through a hole on a high-pressure pipeline, it disperses in the atmosphereas a jet. A jet fire will occur when the leaked gas meets an ignition source. To estimate the dangerousarea, the shape and size of the fire must be known. The evolution of the jet fire in air is predicted by usinga finite-volume procedure to solve the flow equations. The model is three-dimensional, elliptic andcalculated by using a compressibility corrected version of the k - x turbulence model, and also includesa probability density function/laminar flamelet model of turbulent non-premixed combustion process.Radiation heat transfer is described using an adaptive version of the discrete transfer method. The modelis compared with the experiments about a horizontal jet fire in a wind tunnel in the literature withsuccess. The influence of wind and jet velocity on the fire shape has been investigated. And a correlationbased on numerical results for predicting the stoichiometric flame length is proposed.

Crown Copyright � 2011 Published by Elsevier Ltd. All rights reserved.

1. Introduction

Natural gas is one of the most widely used domestic fuels in theindustrialized countries with the growing of annual consumption.The transportation system for natural gas consists of a complexnetwork of pipelines, designed to transport natural gas from itsorigin to areas of high natural gas demand quickly and efficiently.Transportation of natural gas is closely linked to highly populatedzones. Gas leaking from a high-pressure natural gas pipeline is anundesirable event. It means wasting energy and losing income forthe natural gas industry. Furthermore, a potential safety hazardwillbe introduced. If leaking gas comes in contact with a lit match ora spark from a vehicle, an explosion or fire could result [1].

Gas pipelines leak or fail mainly because of damage fromexcavation operations. Other causes are corrosion, constructiondefects, material defects or outside forces. A jet firewill occur whenleaking gas encounters an ignition source. Jet fire is of particularconcern as it represents a hazard. To assess the hazard presented bya jet fire, safety engineers are interested in evaluating flametrajectory, flame length and heat transfer to the surroundingbuildings and personnel. The flame length is of particular interestbecause the appropriate separation distances between gas pipe-lines and the surrounding buildings can be specified by it.

A number of flame length correlations have been derived usingdimensionless groups or some measure of combustion. Kim et al.[2] proposed a modified flame length correlation between dimen-sionless flame lengths and a fire Froude number on the basis of the

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measured oxy-fuel flame lengths. Becker and Liang [3] useda Richardson number and a parameter to correlate their flamelength measurements. Kalghatgi [4] used a film speed of 1/30 s andaveraged three images to calculate the mean flame length.

Flame length correlations derived from laboratory-scale jet firesare not applicable to large fires in the open air, as the atmosphericboundarylayerevenat lowwindspeedscanaffect theflame length.Toovercome the limitations of the flame length alternative approachesbased onmore objective criteria have been derived. Hawthorne et al.[5] proposed the term the chemicalflame length and defined it as theaxial location of 99% complete combustion. Hottel [6] defined thechemical flame length as the axial location where the ratio of CO toCO2 was 0.15. Cumber and Spearpoint [7] proposed a flame lengthmethodology that mimics the human eye or camera using a compu-tational fluid dynamics (CFD) framework to calculate the flamestructure.

In this paper, a fire model including flow model, flamelet modeland thermal radiation model is presented. Based on the fire model,the structure of turbulent jet diffusion flames of natural gas in theatmosphere surface layer is predicted using CFD framework. Thenumerical results are compared with the available experimentaldata and flame length correlations proposed in the literature.

2. General description of the model

2.1. Flow model

The basis of the flow model used in this study is the Favreaveraged NaviereStokes equations in an axi-symmetric co-ordinatesystem, which is closed through using the standard k - e turbulence

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Fig. 1. Laminar flamelet prescription for temperature.

Y. Zhao et al. / Applied Thermal Engineering 31 (2011) 1347e13511348

model and can be found in Ref. [8]. The system is based on generalassumption similar to those employed by Fairweather et al. [9], andhas been solved by the control volume numerical approach tocalculate the evolution of the horizontal turbulent jet diffusionflame in the surface layer of the atmospheric boundary layer.

Fig. 2. Computational flow chart.

2.2. Flamelet model

The turbulent diffusion flame is viewed as an ensemble offluctuating, contorted, stretched diffusion flamelets in laminardiffusion flamelet models. The stretching of a flamelet is due to thestrain rates in the turbulent flow, which produce steep concentra-tion gradients and increase the rate at which reactants diffusetoward the reaction zone. Under the assumptions of fast chemistry,a mixture fraction approach is provided to describe the combustionprocess. The obvious advantage of the mixture fraction approach isthat all of the species transport equations are combined into one,reducing the computation cost. Themixture fraction, x, is a constantrepresenting the mass fraction of gas at a given point. By definition,it varies from x¼ 1 in the fuel stream to x¼ 0 in the oxidizer stream.The mixture fraction x satisfies the conservation equation

rDxDt

¼ V$rDVx (1)

In laminar famelets, all scalars are unique functions in themixture fraction/scalar dissipation rate space. Consequently, theirbalance equations are written as follows:

rvYivt

¼ rc

2v2Yivx2

þ Si (2)

rvTvt

¼ rc

2v2T

vx2�

Xni¼1

hiCp

Si þ1Cp

vpvt

(3)

where the scalar dissipation rate c is defined by

c ¼ 2DðVxÞ2 (4)

Yi ¼ Yiðx;cÞ (5)

T ¼ Tðx;cÞ (6)

An important quantity in non-premixed combustion is theinstantaneous scalar dissipation rate defined by Eq. (4), and espe-cially the scalar dissipation rate at stoichiometric conditions denotedby cst.

c

f ðxÞ ¼ cstf ðxstÞ

(7)

where the scalar dissipation rate c as a function of the mixturefraction x,

c ¼ f ðxÞ ¼ aspexp

n� 2

herfc�1ð2xÞ2

io(8)

where erfc�1 is the inverse of the complementary error function.Using this expression in the flamelet equations, the flamelet data-base is built with only two input parameters: x and cst. Typicalscalars of the flame, such as density, temperature and species massfractions, can be obtained by integration over the probability densityfunction (pdf). Here, a two-parameter, b - pdf was used. The flameletdatabase is derived froma global chemical kinetic scheme formethane-air combustion [9], with laminar flame calculations performed fora strain rate of 110s - 1. The resulting T(x) is represented in Fig. 1.

2.3. Thermal radiation model

The discrete transfer method (DTRM) [10] has been used tocalculate the thermal radiation of flame in this paper. Given theorientation and location of the receiver and the orientation ofeach characteristic ray, its path through computational spacecan be traced, to the edge of the domain. The radiationintensity is calculated by back tracking along the ray to thereceiver. The differential radiative transport equation is shownas follows:

dIds

þ aI ¼ asT4

p(9)

where I is the radiation intensity and s is the distance in thedirection; a is the radiation absorption coefficient, and s is theStefaneBoltzmann constant. In the DTRM, the computationaldomain is divided into a number of control volumes (or cells)defined by computational grids. The flame temperature and radi-ation absorption coefficient of the medium within each cell aretaken as constant. The intensity distribution for a ray along its pathcan be calculated from the following recurrence formula which isobtained by integration of Eq. (9):

Iðnþ 1Þ ¼ sT4

p

�1� e�a$ds

�þ IðnÞe�a$ds (10)

where I(n) and I(n þ 1) are the intensity of the ray at the entranceand exit of a cell, respectively, and ds is the distance traveled by theray within the cell. The net gain or loss of energy in a cell byradiation is the source term, which is given by

q ¼X

all rays

½Iðnþ 1Þ � IðnÞ�U$dAdU (11)

where A is the area of the cell surface from which the radiationbeam emerges.

Fig. 3. Schematic of jet fire. Fig. 4. Effect of grid on numerical results (Case 2).

Fig. 5. Comparison between numerical and experimental results in the symmetryplane (Case 1).

Y. Zhao et al. / Applied Thermal Engineering 31 (2011) 1347e1351 1349

3. Computational procedure and boundary conditions

The governing equations have been solved numerically by usingCFD code. The equations are discretized on a staggered, non-uniformCartesian grid using a finite-volume procedure with a hybrid differ-encing scheme for the convective terms. The SIMPLEST algorithm[11] is used to solve the coupling between continuity andmomentumequations through pressure. Specific subroutines have been written,including initializations, turbulent combustion model, source termsof the partial differential equations and some specific boundaryconditions. The detailed computation scheme is outlined in Fig. 2.

In Fig. 3, the release source is located at a height H over theground surface, horizontal and parallel to the air stream. Torepresent the release, an exit area and a uniform velocity have beenchosen. At the upstream boundary, the incoming air flow is taken asthat corresponding to the atmospheric surface layer with uniform.At the downstream boundary, far enough from the pipe exit, thepressure is fixed to the external ambient pressure and normalderivatives of all dependent variables are equally set to zero. At therest of the boundaries, far enough from the flame, the pressure isfixed to the external ambient pressure.

4. Wind-tunnel modeling

The experiments have been performed in a wind tunnel withsome barriers on the floor to get a similar surface roughness to theatmospheric boundary layer. The supply-pipe has an exit diameterwith 5 mm and is located at a height with 300 mm above the floor.Among the supplied fuel, the methane, ethane, nitrogen, carbon-dioxide, other hydrocarbons accounted for 69.97%, 4.63%, 21.52%,2.10%, 1.78% of mass, respectively [12].

The velocity of the air and the fuel will be adjusted automaticallythrough the transducer. For flame temperature measurement,a coated Pt/Pt-10% Rh thermocouple has been used, with a spatial

Table 1Wind-tunnel experiments.

Experiment number 1 2 3 4 5

Wind velocity,ua (m/s)

0.82 1.23 1.52 0.79 1.64

Fuel velocity,uv (m/s)

26.2 26.2 26.2 12.3 12.6

Froude number, Fr 14,009 14,009 14,009 3088 3240ua/uv 0.029 0.044 0.053 0.060 0.121

and temporal resolution adequate to the temperature gradients andfluctuations observed in the flame. The experimental conditions ofdifferent cases are given in Table 1.

5. Numerical results compared with experimental results

Different grids were tested to ensure that the numerical resultswere independent of the grid density for the physical domain. In

Fig. 6. Comparison between numerical and experimental results in the symmetryplane (Case 2).

Fig. 7. Comparison between numerical and experimental results in the symmetryplane (Case 3).

Fig. 9. Comparison between numerical and experimental results in the symmetryplane (Case 5).

Y. Zhao et al. / Applied Thermal Engineering 31 (2011) 1347e13511350

Fig. 4 stoichiometric contours and temperature contours (373 K) arepresented for the flame of case 2 in Table 1, calculated using 25,000nodes, 40,000 nodes, 70,000 nodes and 120,000 nodes.

Fig. 4 shows numerical results on different nodes. The curves of70,000 (50 � 20 � 70) and 120,000 (60 � 20 � 100) nodes arenearly coincide with each other which means 70,000 nodes isenough to calculate overall flame characteristics.

Comparisons between numerical andwind-tunnel experimentalresults for temperature contours in the symmetry plane are pre-sented in Figs. 5e9. It obviously shows a good match betweennumerical and experimental results. With higher ua/uv (where ua isthe wind velocity at the supply-pipe height and uv is fuel velocity atthe supply-pipe exit), the consistency becomes better. Maindiscrepancies are in the lowerpart of theflame,where thenumericalcontours of temperature are above the experimental ones. Ingeneral, buoyancy effects are higher in the numerical results forthe use of laminar flamelet combustion model. The maximummean temperature in the experiments was about 1500 K,whereas in the numerical results was higher than 1600 K. Thereason is that the thermal radiation model ignores the scatteringcombustion products. The discrepancy would be reduced byintroducing corrections to the measured temperatures due toradiation.

Under constant Froude numbers (Fr ¼ uv2/(gD)), the higher the

value of ua/uv, the lower the deviation between the numericalresults and the experimental ones, which can be seen from Figs.5e7. Along the downstream, the deviation increases. For the low

Fig. 8. Comparison between numerical and experimental results in the symmetryplane (Case 4).

values of ua/uv, buoyancy effects in the numerical results are higherthan that in the experimental. In Figs. 8 and 9, the Reynoldsnumbers at the supply-pipe exit (of the order of 3000) are transi-tional, and the flow is not fully turbulent. The higher the value of ua/uv, the smaller the width of temperature contour. On the otherhand, the higher the Froude number, the longer the length oftemperature contour.

6. Flame length correlation

The geometry of a jet fire is important in predicting radiationfrom the flame and the possibility of flame impingement on nearbyfacilities. There is a considerable body of literature on the geometryof jet flames [4e7]. The most important geometric parameter is theflame length. In this article, a correlation for predicting the flamelength based on a computational fluid dynamics (CFD) represen-tation of the flame structure is proposed. The details of the meth-odology are presented in the literature [7]. According to thenumerical results, a correlation for the stoichiometric flame lengthas a function of the Froude number and the velocity ratio ua/uv canbe written as follows:

LstD

¼ 4:8� ½1:8� 7:2ðua=uvÞ�Frð0:25þua=uvÞ (12)

where 3000 < Fr < 14,000 and 0 < ua/uv < 0.1 with an error lowerthan 2%.

1 2 3 4 5

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

Flam

e le

ngth

/ (m

)

Experimental case

Ott Model Proposed Model

Fig. 10. Flame length of horizontal jet fire.

Y. Zhao et al. / Applied Thermal Engineering 31 (2011) 1347e1351 1351

Otthasobtainedacorrelation forL/Dbasedonexperimental resultsforhorizontalnatural-gas/airflames in the range2000< Fr<300,000.The correlation can be written as follows:

LD

¼ 18:8Fr0:218�uauv

�0:085(13)

Based on the experimental conditions given in Table 1, flamelength calculated by Eq. (12) is about 1.4 times greater than that byEq. (13), which can be seen in Fig.10. The reason is that the radiativeheat loss in the experimental is more than that in the numericalresults.

7. Conclusions

A numerical model based on the conserved scalar approachand the laminar flamelet concept have been developed topredict the evolution of turbulent jet diffusion flames from theleaked gas of high-pressure natural gas pipes. Experimentshave been carried out for horizontal flames in a wind tunnelwith simulated atmospheric boundary layer, and a good matchof measurements of temperature distributions compared withthe numerical predictions, particularly in cases with higher ua/uv. A correlation based on the numerical results has beenproposed to predict the stoichiometric flame length by fittedformulas with the Froude number and the velocity ratio asparameters. This correlation has been compared with the Ottmodel based on the experimental results in the literature. It canbe concluded that buoyancy effects are higher in the numericalresults whereas the radiative heat loss is bigger in the experi-mental results.

Acknowledgements

Supported by the Hi-tech Research and Development Programof China (2007AA05Z223), and by National Education Departmentfor Doctor Center Foundation (200800560041), National NaturalScience Foundation of China (Grant No. 51076112).

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