Determination of laminar burning velocities for natural gas

S.Y. Liaoa,*, D.M. Jianga, Q. Chengb

aSchool of Energy and Power Engineering, Xi’an Jiaotong University, Xi’an 710049, ChinabChongqing Communication Institute, Chongqing 40035, China

Received 9 June 2003; accepted 2 December 2003; available online 4 January 2004

Abstract

Spherically expanding flames of natural gas–air mixtures have been employed to measure the laminar flame speeds, at the equivalence

ratios from 0.6 to 1.4, initial pressures of 0.05, 0.1 and 0.15 MPa, and preheat temperatures from 300 to 400 K. Following Markstein theory,

one then obtains the corresponding unstretched laminar burning velocity after omitting the effect of stretch imposed at the flame front. Over

the ranges studied, the burning velocities are fit by a functional form ul ¼ ul0ðTu=Tu0ÞaT ðPu=Pu0Þ

bP ; and the dependencies of aT and bP upon

the equivalence ratio of mixture are also given. The effects of dilute gas on burning velocities have been studied at the equivalence ratios from

0.7 to 1.2, and the explicit formula of laminar burning velocities for dilute mixtures is achieved.

q 2004 Elsevier Ltd. All rights reserved.

Keywords: Natural gas; Laminar burning velocity; Premixed laminar flame

1. Introduction

The laminar combustion properties are of fundamental

importance for analyzing and predicting the performance of

combustion engines, which can be extremely useful in the

analysis of fundamental processes and serve as a design aid.

There are several techniques for measuring the laminar

burning velocity of combustible gas, such as counterflow

double flames [1], flat flame burner [2,3], and spherically

expanding flames [4–9]. For spherically expanding flames,

the stretch rate of flame front is well defined and the

asymptotic theories and experimental measurements have

suggested a linear relationship between flame speed and

flame stretch, which result in an extensive use of spherically

expanding flames to determine unstretched laminar burning

velocities.

With the growing crisis of energy resources and the

strengthening of automotive pollutant legislations, the use

of natural gas (NG) as an alternative fuel has been

promoted, and natural gas is being regarded as one of the

most promising alternative fuels for combustion engines.

Although there are so many literatures on laminar burning

velocities of pure methane–air mixtures, and it is believed

that the main chemical component of natural gas is methane,

it is not justified that the methane burning velocity data can

be available for natural gas. In this work, the natural gas

selected for the present study is from the north of Shannxi

province, which consists of 96.160% volume fraction

methane, 1.096% ethane, approximate 0.189% hydrocarbon

components higher than C3, and the remains including

carbon dioxide, nitrogen, sulfurated hydrogen and water are

only about 2.555%. The measurements for spherical laminar

premixed flames, freely propagating from spark ignition

source in an initially quiescent natural gas–air mixture, are

made at the equivalence ratios from 0.6 to 1.4, initial

pressures of 0.05, 0.1 and 0.15 MPa, and preheat tempera-

tures from 300 to 400 K. The unstretched laminar velocity

then yields from these stretched flames. The objective of the

measurements is to provide an explicit expression of the

laminar burning velocities for the natural gas, and their

dependencies with the equivalence ratio, unburned gas

temperature, initial pressure and dilute ratio, etc.

2. Experimental measurement of laminar burning

velocity

Quiescent natural gas–air mixtures and natural gas–air

dilute mixtures are ignited in a constant combustion bomb.

The detailed description of experimental setup is in

0016-2361/$ - see front matter q 2004 Elsevier Ltd. All rights reserved.

doi:10.1016/j.fuel.2003.12.001

Fuel 83 (2004) 1247–1250

www.fuelfirst.com

* Corresponding author. Tel.: þ86-29-2663421; fax: þ86-29-2668789.

E-mail address: shyliao@mailst.xjtu.edu.cn (S.Y. Liao).

Ref. [10]. The combustion bomb has an inside size of

108 £ 108 £ 135 mm. Two sides of this bomb are transpar-

ent to make the inside observable, which are to provide the

optical access, and the other four sides are enclosed with

resistance coils to heat the bomb to the desired preheat

temperature. The combustible mixture is prepared within

the chamber by adding gases needed to appropriate partial

pressures. The gases are then mixed through the motion of a

perforated plate across the cubic chamber. The normal

function of the perforated plate is to provide a turbulent

combustion environment if needed, where it is only used to

ensure the reactants are well mixed. At least 10 min wait is

then allowed from the stop of the perforated plate to

ignition, for letting the mixture quiescent. Two extended

stainless steel electrodes are used to form the spark gap at

the center of this bomb. A standard capacitive discharge

ignition system is used for producing the spark. In this

study, the ignition energy is 45 mJ. The history of the shape

and size of the developing flame kernel is recorded by a

high-speed camera operating at 5000 pictures/s with

schlieren method. The camera is NEC E-10. Dynamic

pressure is measured since spark ignition with a piezo-

electric Kistler absolute pressure transducer, model 4075A,

with a calibrating element Kistler 4618A.

The laminar burning velocity can be deduced from

schlieren photographs as described in Refs. [7,9]. From the

definition, the stretched flame velocity, Sn; is derived from

the flame radius versus time data as

Sn ¼dru

dtð1Þ

where the flame size ru is defined as the isotherm that is

5 K above the temperature of the reactants. It has been

suggested that this radius is related to the flame front size,

rsch; defined in the schlieren photography, and is modified

by [7]:

ru ¼ rsch þ 1:95dl

ru

rb

� �0:5

ð2Þ

Here ru is the density of the unburned and rb that of the

burned gas and laminar flame thickness dl given by dl ¼

n=ul; in which n is the kinematic viscosity of the

unburned mixture and ul is the unstretched laminar

burning velocity. The evaluation of ru requires that ul be

known. Hence ul is first estimated using rsch and then

Eq. (2) is adopted to give ru. From the definition of the

flame stretch, a of a flame front in a quiescent mixture is

given by

a ¼1

A

dA

dtð3Þ

However, as to a spherically outwardly expanding flame

front, the flame stretch is well defined as

a ¼1

A

dA

dt¼

2

ru

dru

dt¼

2

ru

Sn ð4Þ

From the linear relationship between flame speed and the

total stretch rate, as Eq. (5)

Sl 2 Sn ¼ Lba ð5Þ

the unstretched flame speed, Sl; can be obtained as the

intercept value at a ¼ 0; in the plot of Sn against a:

When the observation is limited to the initial part of the

flame expansion, where the pressure does not vary

significantly yet, a simple relationship links the spatial

flame velocity, Sl; to the fundamental one, i.e. the

unstretched laminar burning velocity, ul; as

ul ¼ rbSl=ru ð6Þ

3. Results and discussions

Shown in Fig. 1 is the variation of flame speed with the

total stretch rate, a: One can see that at higher stretch (small

flame size), the flame speed is lower. As the flame expands,

the flame speed slowly increases due to the reduced flame

stretch. In the present experiment, the linear relationship

between flame stretches and flame burning velocities exists

for flame size from 5 mm to about 15 mm, marked by points

A and B in Fig. 1. The values of Sl; and ul can be obtained in

turn using Eqs. (5) and (6).

Fig. 2 shows the experimental laminar burning velocities

for natural gas–air mixtures with the preheat temperature of

300 K, at 0.05, 0.1 and 0.15 MPa. The experimental results

for methane–air mixtures are shown as well. Generally, the

present experimental results of methane are in good

agreement with the previous experiments [11], which is

indicative of that this experimental uncertainty is reasonable.

In order to study the effects of preheat temperature and

the unburned gas pressure on laminar burning velocity, the

systematic measurements of laminar burning velocities for

natural gas–air mixtures are made at equivalence ratios of

0.8, 1.0 and 1.2. At each equivalence ratio, initial pressures

of 0.05, 0.1 and 0.15 MPa and temperature of 300 K are

chosen. And then the measurements are extended to

Fig. 1. A typical measurement of flame speeds against different flame

stretch rates.

S.Y. Liao et al. / Fuel 83 (2004) 1247–12501248

the higher temperatures keeping the same pressure con-

ditions. The results are shown in Fig. 3. To obtain an

explicit expression about laminar burning velocities depen-

dent on pressure and temperature, the measured laminar

burning velocities have been fit to a simple power law

relation at the datum temperature Tu 300 K, and the datum

pressure Pu 0.1 MPa, as

ul

ul0

¼Tu

Tu0

� �aT Pu

Pu0

� �bP

ð7Þ

where coefficients aT is 1.94, 1.58, 1.68 and bP is 20.465,

20.398, 20.405 for equivalence ratios 0.8, 1.0, 1.2,

respectively. And over the ranges studied, they can be fit

as functions about the equivalence ratio, given as following

aT ¼ 5:75f2 2 12:15fþ 7:98 ð8Þ

and

bP ¼ 20:925f2 þ 2f2 1:473 ð9Þ

The power law fit curves are shown graphically by the

dashed curves in Fig. 3, and ^5% standard deviation of

experiment is also shown in this figure. Over the ranges

studied, the fit curves agree with the experimental very well,

particularly for high-pressure flames (Pu ¼ 0:1; 0.15 MPa).

There is less point falling out ^5% standard deviation of

measurements, however, there appear to be some small

systematic deviations for pressure 0.05 MPa.

The datum laminar burning velocities ul0 can be fit best

with third-order polynomial as Eq. (10), as shown in Fig. 2

with a solid line

ul0 ¼ 2177:43f3 þ 340:77f2 2 123:66f2 0:2297 ð10Þ

The maximum burning velocity in Eq. (10) is 40.1 cm/s

at about the equivalence ratio of 1.05, corresponding to

39.1 cm/s of experiment. The fit burning velocities show

good agreements with the results of experiment. Especially,

the best consistent estimations are within the lean flames.

Based on the concept of exhaust gas recirculation, which

is regarded as an effective way to decrease NOx emissions in

combustion engines, measurements of the burning vel-

ocities are then made, for dilute natural gas–air mixtures.

Here the simulated combustion products with dilute volume

fractions up to 0.3 are considered. Since there is above 96%

volume fraction methane in natural gas, the dilution used to

simulate combustion products consists of 88% N2 and 12%

CO2 by volume in this work, which is in reasonable

agreement with the practical products for natural gas

stoichiometric combustion at ambient temperature. The

experiment is conducted at an initial temperature of 300 K

and pressure of 0.1 MPa, and the results are shown in Fig. 4,

Fig. 2. Experimental laminar burning velocities for natural gas.

Fig. 3. Laminar burning velocity on temperatures at different pressures.

Fig. 4. Non-dimensional laminar burning velocity on dilution rate at

different equivalence ratios.

S.Y. Liao et al. / Fuel 83 (2004) 1247–1250 1249

where the ratios of the burning velocities with and without

dilution are plotted as a function of the equivalence ratio for

dilute volume fractions from 0 to 0.30. It can be seen that the

decrease in burning velocity is dependent on the equival-

ence ratio of combustible mixture. Over the equivalence

ratios from 0.7 to 1.2, the laminar burning velocity ulðfrÞ

can be expressed by a second-order polynomial for dilute

mixture with dilute fraction of fr; as

ulðfrÞ

ulð0Þ¼ Af2

r þ Bfr þ C ð11Þ

where ulð0Þ represents the reference burning velocities

without dilution, and constants A ¼ 5:4825; B ¼ 24:1988;

C ¼ 0:9952:

4. Conclusion

The experimental study on the burning velocities of

natural gas has been conducted using spherical expanding

flames. The correlation formula of laminar burning velocities

dependent on the pressure, temperature and equivalence ratio

is obtained. The simulated combustion products (88%

N2 þ 12% CO2) are used as dilute gas to study the effects

on burning velocities at 0.1 MPa, 300 K, and non-dimen-

sional burning velocities of dilute natural gas are fit well

by a polynomial about the equivalence ratio of the

combustible gas.

Acknowledgements

This work is supported by the state key project of

fundamental research plan titled as ‘New Generation of

Engine of Alternative Fuels’ Grant No. 2001CB209208, and

supported in part by the Doctorate Foundation of Xi’an

Jiaotong University.

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