Numerical Study of Propane-Air Mixture Combustion in a Burner Element

C.E.L. Pinho1,a, J.M.P.Q. Delgado2,b, R. Pilão3,c, J. Conde1,d and C. Pinho2,e

1INEGI − Rua do Barroco, nº 174; 4465-591 Leça do Balio, Portugal 2CEFT − DEMEGI, Faculdade de Engenharia da Universidade do Porto

Rua Dr. Roberto Frias, s/n; 4200-465 Porto, Portugal 3CIEA − Instituto Superior de Engenharia do Porto, Rua Dr. António Bernardino de Almeida

nº 341, 4200-072 Porto, Portugal

acpinho@inegi.up.pt, bjdelgado@fe.up.pt, crmp@isep.ipp.pt, djsantos@inegi.up.pt, ectp@fe.up.pt

Keywords: Heat transfer, Combustion, Turbulence, Computer Fluid Dynamics.

Abstract. This study considers numerical simulations of the combustion of propane with air, in a

burner element due to high temperature and velocity gradients in the combustion chamber. The

effects of equivalence ratio (φ) and oxygen percentage (γ) in the combustion air are investigated for

different values of φ between 0.5 and 1.0 and γ between 10 and 30%. In each case, combustion is

simulated for the fuel mass flow rate resulting in the same heat transfer rate (Q) to the combustion

chamber.

Numerical calculations are performed individually for all cases with the use of the Fluent CFD

code. The results shown that the increase of equivalence ratio corresponds to a significantly

decrease in the maximum reaction rates and the maximum temperature increase with the increases

of oxygen percentage. Mixing hydrogen with propane causes considerable reduction in temperature

levels and a consequent reduction of CO emissions.

Introduction

When early commercial CFD packages became available more than 20 years ago, simulating the

complex physics inside combustion chambers was already one of the target applications. Of course,

projects were often limited by computer resources these days [1,2]. Therefore in most cases reaction

was taken into account using relatively simple approaches such as the Eddy Dissipation Model.

Today, with increasing maturity of CFD technique and computing power, one focus in numerical

simulation of combustion is in the area of non-equilibrium chemistry and multiphase flow. New

fields of application, such as the formation of pollutants in technical flames or the optimization of

combustion processes, can be tackled that way. Some of the elements contend by fuel form

dangerous combustion products. The amount of these products is related with their percentage in

the fuel. The complete combustion of the main elements of fuel increases the efficiency of the

boiler. The construction of burner defines the combustion efficiency.

Turbulent combustion of hydrocarbon fuels is an integral part of many segments of the chemical

and power industries, and also in hot water boilers usually used as heating source for residences.

Combustion phenomenon is a complex mixture of fluid dynamics and chemistry.

The primary objectives in burner design are to increase combustion efficiency and to minimize

the formation of environmentally hazardous emissions, such as CO, unburned hydrocarbons (HC)

and NOx. Critical design factors that impact combustion include: the temperature and residence time

in the combustion zone, the initial temperature of the combustion air, the amount of excess air and

turbulence in the burner and the way in which the air and fuel streams are delivered and mixed.

Therefore, CFD codes can serve as a powerful tool used to perform low cost parametric studies.

The CDF codes solve the governing mass, momentum and energy equations in order to calculate the

pressure, concentrations, velocities and temperatures fields.

This work considers the combustion of propane with air due to the high temperature and velocity

gradients in combustion chamber using a single burner element. In order to investigate the effect of

Defect and Diffusion Forum Vols. 273-276 (2008) pp 144-149online at http://www.scientific.net© (2008) Trans Tech Publications, SwitzerlandOnline available since 2008/Feb/11

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oxygen percentage on the combustion, the combustion of fuel with air is examined at various

oxygen percentages in the air by using Fluent CFD code [3].

Mathematical Model

In this work we used the following models for the numerical calculations: (a) turbulent flow, with

turbulent model of RNG k–ε applied [4] with a standard wall functions for near wall treatment; (b)

for the chemical species transport and reacting flow, the eddy-dissipation model with the diffusion

energy source option. The following assumptions are made: (a) the flow is steady, turbulent and

compressible; (b) the mixture (propane-air) is assumed as an ideal gas; (c) no-slip condition is

assumed at the burner element walls.

The governing equations for mass, momentum and energy conservation, respectively, for the

two-dimensional steady flow of an incompressible Newtonian fluid are:

Mass conservation equation

iiii .).( SJYu +−∇=∇ ρ (1)

with

( ) ittmi,i Sc/ YDJ ∇+−= µρ (2a)

and

∑=

ji,j

imi,

/

-1

DY

YD (2b)

where ρ is the density, iu is the fluid velocity, iY is the local mass fraction, iJ is the diffusion flux,

iS is the rate of creation by chemical reaction, mi,D is the diffusion coefficient, tµ and tSc are the

turbulent viscosity and Schmidt number, respectively.

Momentum conservation equation

effji ..).( τρ ∇+−∇=∇ Puu (3)

with

( ) δµτ uuu .2/3Teff ∇−∇+∇= (4)

where effτ is the stress tensor, µ is the molecular viscosity and δ is the unit tensor.

Energy conservation equation

[ ] heffeffi ..)(. SuJhTkPEuj

jjj +

+−∇∇=+∇ ∑ τρ (5)

with

2

2iuP

hE +−=ρ

(6)

where E is the energy, P is the pressure, effk is the effective conductivity, hS is the source of

energy and h is the sensible enthalpy.

In this work, the combustion of propane with air is modelled with one-step reaction mechanism.

The reaction mechanism takes place according to the constraints of chemistry and it is defined by

Defect and Diffusion Forum Vols. 273-276 145

22222283 O1

5N0015

OH4CO3N0015

O5

HCφφ

γγ

φγγ

φφ−

+−

++→−

++ (7)

where φ ( [ ] )/( /)100(5 airfuelfuelN2O2 mMmMM &&γγ−+= ) is the equivalence ratio and fuelm& and airm&

are fuel and air mass flow rates, respectively and γ is the oxygen percentage in air.

Computational Model

A two-dimensional burner element (see Figure 1) was designed using Gambit package (v2.2.30,

Fluent Inc). The skewness of the cells was improved in Gambit and using the grid

refinement/adaptation procedure of the Fluent code it was refined.

In the numerical calculation, two

calculation models, a laminar flow

model and a turbulent flow model, were

used because the Reynolds numbers

based on the hydraulic diameter and the

flow velocity vary from 500 to 3000.

For flows of Reynolds number below

1000, a steady laminar flow model was

used. For Reynolds numbers over 1000,

a turbulent model of RNG k–ε was

applied with a standard wall function

rout= 0.01 m

L= 0.5 m

rair= 0.01 m

rfuel= 0.004m rwall= 0.006 m

Air

Propane

Figure 1 – Scheme of the burner analysed.

for near wall treatment.

Geometry and Mesh Generation

Grid generation represents a major challenge for CFD analysis. It is a time-consuming task and, in

spite of steady advances in automatic mesh generation, it still requires the skill of a CFD

practitioner to yield a suitable mesh. The choice of the type of grid depends on geometrical

complexity and on physics. The skewness of the cells was improved in Gambit package and using

the grid refinement/ /adaptation procedure of the Fluent code it was refined. The grid was smoothed

using the swap/smooth options in both codes. Grid refinement was performed until further

refinement showed no noticeable effects. The final unstructured grid that had 50000 cells was used

in the simulation.

Gas Flow Simulation

For gas simulation a propane-air mixture was used with the following physical values:

K W/m20 2

amb =h , K 300refambin === TTT , Pa 101325=P and 3

air kg/m 225.1=ρ and

3 8

3

C H 1.91 kg/mρ = at the air and fuel inlet, respectively. The thermal properties ( pc ,µ and λ) of the

propane and species are function of temperature. The propane density at the fuel inlet and the

molecular weights, enthalpies and lower heating values of reactant and product species are taken

from the material property database given by Fluent Inc. [3]. The ranges of the simulation values

are: 10000WQ =& , 1.0 0.7, ,5.0=φ and 30% 20%, %,10=γ .

Fluent Modelling

The Fluent modelling is based on the two-dimensional conservation equations for mass and

momentum. The differential equations are discretised by the Finite Volume Method and are solved

by the SIMPLE algorithm. As a turbulence model, the k–ε was employed [4]. The Fluent code uses

an unstructured non-uniform mesh, on which the conservation equations for mass, momentum and

energy are discretised. The k–ε model describes the turbulent kinetic energy and its dissipation rate

and thus compromises between resolution of turbulent quantities and computational time. No-slip

146 Diffusion in Solids and Liquids III

condition is assumed at the burner walls. The model constants for the RNG k–ε model are

0845.0µ =C , 42.1ε 1 =C , 68.1ε 2 =C , and wall Prandtl number of 0.85.

Grid independence/solution adaptive refinement

While finer meshes would yield more accurate results, we were limited to this number of elements

because of the computer speed and memory. However, doubling the total number of elements

yielded less than 2% change in overall pressure drop and the solutions were considered basically

grid-independent. The standard k–ε model was used with non-equilibrium wall functions. Non-

equilibrium wall functions were preferred to the standard wall functions because non-equilibrium

wall functions are better to deal with complex flows involving separation, reattachment, other non-

equilibrium effects and strong pressure gradients (see Fluent User’s Guide [3]).

Results and Discussion

Numerical modelling of the burner element was performed at different stoichiometric mixture ratios

and oxygen percentage in the air. Table 1 shows the inlet velocities of air and stoichiometric air/fuel

ratios for W10000=Q and m/s 247.2fuel =u , with stoR and airu given by:

2 2

3 8

O N

sto

C H

(100 ) / 5M M

RM

γ γ+ −= (8)

fuel

airair

fuelfuelsto

air uA

ARu

ρρ

φ= (9)

Table 1 – Inlet velocities of air and stoichiometric air/fuel ratios, for W10000=Q .

uair (m/s)

γγγγ (%) Rsto φφφφ = 0.5 φφφφ = 0.7 φφφφ = 1.0

10 32.22 56.436 40.312 28.218

20 16.34 28.614 20.439 14.307

30 11.04 19.340 13.814 9.670

0.0050.010.05

0.010.005

0.10.20.4

x (m)

r(m

)

0 0.05 0.1 0.15 0.20

0.01

0.02

0.03

0.04

0.05

( 5.0=φ and %10=γ )

0.010.05

0.20.2

0.005

x (m)

r(m

)

0 0.05 0.1 0.15 0.20

0.01

0.02

0.03

0.04

0.05

( 0.1=φ and %10=γ )

0.005

0.01

0.050.1

0.2

x (m)

r(m

)

0 0.05 0.1 0.15 0.20

0.01

0.02

0.03

0.04

0.05

( 0.1=φ and %30=γ )

Figure 2 – Reaction rates contours for different equivalence ratios and oxygen percentage.

Figure 2 presents the distributions of reaction rates in the burner element for %10=γ to 30% in

the case of 0.1=φ . The numerical results showed that the maximum reaction rates decrease

significantly with the increase of equivalence ratios and with the increase of oxygen percentage in

air, these regions contract in the axial direction whereas they expand in the radial direction. The

maximum reaction rate profiles obtained were 31.14, 0.55 and 0.41 kmol/m sR = in the cases of

%10/5.0 == γφ , %10/0.1 == γφ and %30/0.1 == γφ , respectively.

Figure 3 shows the temperature distribution in the burner element for the cases of

30% 20%, %,10=γ and 1.0 ,5.0=φ . The numerical results illustrates an increase of temperature

Defect and Diffusion Forum Vols. 273-276 147

with both increases of γ and φ . The maximum temperature level was about 2701 K ( 5.0=φ and

30% =γ ). The average temperatures of the burner element increased from 1322 to 2701 K and

from 1251 to 2652 K in the cases of 5.0=φ and 0.1=φ , respectively, with the increase of γ from

10 to 30, i.e., the results shows that γ has more effect in temperature than φ . Temperature level is

decreasing considerably from the maximum zone trough the burner exit.

13001200

1100

1000

900

800700

600

500

x (m)

r(m

)

0 0.1 0.2 0.3 0.4 0.50

0.01

0.02

0.03

0.04

0.05

( 5.0=φ and %10=γ )

1100

1300

1500

17001900

700 900500

2100

x (m)

r(m

)

0 0.1 0.2 0.3 0.4 0.50

0.01

0.02

0.03

0.04

0.05

( 5.0=φ and %20=γ )

2500

2100

1900

1700

1500

1300700

900

1100500

2700

x (m)

r(m

)

0 0.1 0.2 0.3 0.4 0.50

0.01

0.02

0.03

0.04

0.05

( 5.0=φ and %30=γ )

1200

1100

1000900

600 700

800 9

00

500

1240

x (m)

r(m

)

0 0.1 0.2 0.3 0.4 0.50

0.01

0.02

0.03

0.04

0.05

( 0.1=φ and %10=γ )

500

700

900

13001100

1500

1700

1900

1950

1990

x (m)

r(m

)

0 0.1 0.2 0.3 0.4 0.50

0.01

0.02

0.03

0.04

0.05

( 0.1=φ and %20=γ )

500

1700

19002100

2300

2500

2300

1300

1700900

700

1300

11002100 1900

2600

2650

x (m)

r(m

)

0 0.1 0.2 0.3 0.4 0.50

0.01

0.02

0.03

0.04

0.05

( 0.1=φ and %30=γ )

Figure 3 – Temperature distribution for 5.0=φ and 0.1=φ at different values of γ .

300

600

900

1200

1500

1800

2100

0 0.1 0.2 0.3 0.4 0.5x (m)

T (K

)

Series1

Series2

Series3

Series4

γ = 20%

φ = 0.5φ = 0.7φ = 1.0φ = 1.0 (50%H2+50%C3H8)

300

700

1100

1500

1900

2300

2700

0 0.1 0.2 0.3 0.4 0.5x (m)

T (K

)

Series1

Series2

Series3

φ = 0.5

γ = 10%γ = 20%γ = 30%

Figure 4 – Axial temperature variation at different (a)-equivalence ratio and (b)-oxygen percentage.

Figure 4 illustrates the axial temperature, along the axis of the burner, for different equivalence

ratios and oxygen percentage in air, on propane combustion. In general, increasing the oxygen

percentage increases the temperature. This trend is as expected and similar to the works developed

by other authors [5,6].

Moreover, this computational fluid dynamics study also considered the combustion of hydrogen–

propane mixture fuel with 50%H2+50%C3H8. It is known [2] that hydrogen reduces the emission of

some pollutants, pure hydrogen fuel combustion does not give CO or unburned HC emissions.

Figure 4(a) shows that mixing hydrogen with propane causes considerable increase in

temperature levels. The predicted maximum temperature level, for pure propane combustion with

an equivalence ratio of 1.0 and an oxygen percentage in air of 20%, was about 1992 K, whereas the

148 Diffusion in Solids and Liquids III

predicted temperature distributions for hydrogen–propane (50%H2+50%C3H8) mixture combustion,

at the same conditions, showed a predicted high temperature of 2195 K.

The overall flame temperature increases as hydrogen is added to the fuel due to the higher

energy input and lower flame radiation. It must be stressed that although a higher combustors

temperature will reduce CO and unburned HC emissions it will, on the other end, raise NO

emissions through the thermal or Zeldovich mechanisms [7].

Conclusions

The combustion of propane with air was analyzed in a burner element and the effect of the

equivalence ratio and oxygen percentage in air investigated, for different numerical values.

Combustion was simulated for the fuel mass flow rate resulting in the same heat transfer rate to the

combustion chamber in each case.

The results shown that the increase of equivalence ratio corresponds to a significantly decrease

in the maximum reaction rates and the maximum temperature increase with the increases of oxygen

percentage. Mixing hydrogen with propane causes considerable reduction in temperature levels and

a consequent, expected, reduction of CO and unburned HC but higher NOx emissions are expected.

Acknowledgment

J.M.P.Q. Delgado wishes to thank FCT for the grant Nº SFRH/BPD/11639/2002.

Notation

A Area Rsto Stoichiometric air/fuel ratio

cp Constant-pressure specific heat Sct Turbulent Schmidt number

µC Coefficient in k-ε turbulence model Sh Source of energy

ε 1C Coefficient in k-ε turbulence model Si Rate of creation by chemical reaction

ε 2C Coefficient in k-ε turbulence model T Temperature

Di,m Molecular diffusion coefficient u Velocity

E Energy Yi Local mass fraction of each specie

h Sensible enthalpy γ Oxygen percentage in air

Ji Diffusion flux of species δ Unit tensor

keff Effective conductivity φ Equivalence ratio

m& Mass flow rate λ Thermal conductivity

M Molecular weight of species µ Molecular viscosity

P Pressure µ t Turbulent viscosity

Q& Heat transfer rate ρ Density

R Reaction rate effτ Stress tensor

References

[1] G. Wecel and R.A. Białecki: Combust. Sci. and Tech. Vol. 178 (2006), p. 1413

[2] M. Ilbas, I. Yılmaz and Y. Kaplan: Int. J. Hydrogen Energ. Vol. 30 (2005), p. 1139

[3] Fluent Incorporated: FLUENT User’s guide version 6.2 (2005).

[4] V. Yakhot and S.A. Orszag: J. Sci. Comput. Vol. 1 (1986), p. 151

[5] M. Ilbas: Int. J. Hydrogen Energ. Vol. 30 (2005), p. 1113

[6] M. Ilbas: Studies of ultra low NOx burner (PhD thesis, Cardiff, University of Wales, 1997).

[7] S.R. Turns: An introduction to combustion - Concepts and application (McGraw Hill, Inc.,

New York, 1996).

Defect and Diffusion Forum Vols. 273-276 149