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Revue des Energies Renouvelables CISM’08 Oum El Bouaghi (2008) 227 - 237

227

TFC modeling of hydrogenated methane premixed combustion

A. Mameri1*, A. Kaabi2 and I. Gökalp3

1 Institut des Sciences Technologiques, Centre Universitaire Larbi Ben M’Hidi, Oum El Bouaghi, Algérie

2 Département du Génie Climatique, Université des Frères Mentouri, Constantine, Algérie

3 Institut de Combustion, Aérothermique, Réactivité et Environnement, ‘ICARE’, CNRS, Orléans, France

Abstract - The use of hydrogenated fuels shows considerable promise for applications in

gas turbines and internal combustion engines. Hydrogen addition to methane will have an

important role to reach a fully developed hydrogen economy. The effects of this addition

on the flame structure is evaluated in three fuels with the following compositions at

constant global equivalent ratio: 100 % CH4, 10 % H2 + 90 % CH4, 20 % H2 + 80 %

CH4. The turbulence is modeled by the standard k -

ε

model which is improved by the

Pope correction in order to better predict round jet spreading. Combustion is modeled by

the turbulent flame closure (TFC) model which is used with flamelet to give detailed

chemistry. Computations were achieved by the ANSYS CFX code. A good agreement with

experiments was found, it was noted that one can replace a significant fraction of basic

fuel by hydrogen without making recourse to major modifications on the installations.

Résumé - L’utilisation de combustibles hydrogénés est très prometteuse pour des

applications dans les turbines à gaz et les moteurs à combustion interne. L’hydrogène en

addition avec le méthane aura un rôle important pour arriver à une économie en

hydrogène pleinement développé. Les effets de cet ajout sur la structure de la flamme est

évalué à trois carburants à la suite de compositions à taux constant global équivalent:

100 % CH4, 10 % H2 + 90 % CH4, 20 % H2 + 80 % CH4. La turbulence est modélisé par

le modèle standard k -

ε

, qui est inspiré par la correction de Pope, afin de mieux prédire

la propagation du jet. La combustion est modélisée par le modèle de la fermeture de la

flamme turbulente (TFC), qui est utilisé avec des flamelets de façon détaillée en chimie.

Les calculs ont été réalisés par le code ANSYS CFX. Un bon accord a été trouvé avec les

expériences. Il est à noter que l’on peut remplacer une fraction importante du carburant

de base par de l’hydrogène sans recourir à des modifications importantes sur les

installations.

Keywords: Premixed flames - Hydrogenated fuels - Burning velocity - Turbulent flame

speed.

1. INTRODUCTION

Internal combustion engine and gas turbine manufacturers are faced with stricter

anti-pollution regulations. Lean premixed combustion is a well established technique to

achieve low emissions while maintaining high efficiency. According to the thermal

x

NO generation mechanism; low flame temperatures given by lean conditions, results

in low x

NO emissions. However, close to lean flammability limits, the stability of the

flame decreases and flame extinction phenomena may occur.

Since further reduction of x

NO will require even leaner mixtures, schemes for lean

stability extension must be considered. A solution to increase the flame stability at lean

condition is to add small amounts of hydrogen into the mixtures [1-4]. Several studies

* mameriabdelbaki@yahoo.fr

A. Mameri et al.

228

have been performed to estimate the impact of 2

H addition on the stability, on the

reactivity and on the pollutant emissions of the methane-air flames.

It has been shown that hydrogen addition, at constant global equivalence ratio,

extends the lean operating limit of natural gas engines, leading to a potential decrease in

pollutant formation. The origin of this effect is that the stretch resistance of these flames

is considerably increased by hydrogen blending, while other properties are

comparatively little modified.

In spark ignited engine [5], the authors show that mixture of natural gas blended

with hydrogen improves thermal efficiency, specific fuel consumption, reduces CO

and x

NO emissions, extend lean operating limit to lower equivalence ratios and finally

allows stable engine operation with lower pollutant emissions.

Hydrogen addition was experimentally tested in several atmospheric flame burners’

configurations. It was observed a decreasing in the height of the blue cone with

hydrogen addition. The increase in laminar burning velocity was identified as the main

effect of the behavior of this parameter. Also a significant reduction in CO emission

was obtained [6].

Experimental investigation on the flame stability of hydrogenated mixtures was also

performed for swirl stabilized flame configuration [7].

We perform a numerical study to understand and to complete F. Halter et al. [8]

measured data. The authors conducted experiments on a lean methane combustor at

several pressures with hydrogen enrichment.

2. EXPERIMENTAL SETUP

The ICARE (Institut de Combustion, Aérothermique, Réactivité et Environnement)

high pressure turbulent flame facility is composed from stainless steel cylindrical

combustion chamber (Fig. 1). The inner chamber diameter is 300 mm. The chamber is

composed of two superposed vertical portion each of 600 mm height, and each equipped

with four windows of 100 mm diameter for optical diagnostics.

Fig. 1: ICARE combustion installation Fig. 2: Bunsen burner

An axisymmetric bunsen type turbulent burner (Fig. 2) is located inside the

chamber. The burner internal diameter is 25 mm. It is fed by methane/hydrogen/air

mixtures.

CISM’2008: TFC modeling of hydrogenated methane premixed combustion

229

The global equivalence ratio is 0.6, the bulk mean flow velocity of the reactants, at

the exit is 2 m/s. The reactants flow exhibits a turbulence level about 10 %. The integral

length scale is about 3 mm.

3. COMPUTATIONAL MODEL

To gain a more complete understanding of the impact of 2

H addition to lean 4

CH

flames, the Ansys CFX 11 code is used to compute the multi component turbulent

reacting flow. The Reynolds averaged equations are given by:

Continuity

0)U(

t=ρ•∇+

∂

ρ∂ (1)

Momentum

{}

M

'' S)uu()UU(

t

U+⊗ρ−τ•∇=⊗ρ•∇+

∂

ρ∂ (2)

Energy

h

''

tot

tot S)huT()hU(

t

p

t

h+ρ−∇λ•∇=ρ•∇+

∂

∂

−

∂

ρ∂ (3)

Where kU

2

1

hh 2

tot ++=

The other equations are similar and they can be cast in the following general form:

φφ +φρ−φ∇Γ•∇=φρ•∇+

∂

φρ∂ S)u()U(

t

'' (4)

Where φ is a general scalar.

The perfect gas state equation is given by:

∑

ρ=

jj

j

W

Y

TRp (5)

The Reynolds stresses '' uu ⊗ρ and fluxes ''

uφρ represent the convective effect

of turbulent velocity fluctuations. These terms need to be modelled.

3.1 ε−k turbulence model

Today, even with the successful development of DNS and LES for turbulent flows,

the most popular models for industrial modeling are the two-equation Reynolds

averaged Navier-Stokes (RANS) models. Of these, the

ε

−

k two equations model

accounts for 95 % or more of the industrial use at the present [9]. This form of model is

easy to solve, converges relatively quickly, is numerically robust and stable, is able to

solve large domains and high Reynolds numbers and requires minimal computational

expense, which is important for industrial models. The standard

ε

−

k model with the

standard constants predicts the velocity field of a two dimensional plane jet quite

accurately, but results in large errors for axisymmetric round jets. Although the standard

ε−k model matches the spreading rate of the round jet more accurately than other two

equations models, it still overestimates it by 15 % [10]. In this model, the Reynolds

stresses are given by a Newtonian type closure which looks like:

A. Mameri et al.

230

)U.k(

3

2

))U.(U.(uu t

T

t

'' ∇µ+ρδ−∇+∇µ=⊗ρ− (6)

Where t

µis the turbulence ‘viscosity’ (also called the eddy viscosity). By analogy with

the turbulence viscosity, the turbulence diffusivity is defined, and the Reynolds fluxes

are given by:

φ∇Γ=φρ− ..u t

'' (7)

Where t

Γ is the turbulence ‘diffusivity’, it is related to the turbulence viscosity by:

t

t

tPr

µ

=Γ (8)

Where t

Pr is the turbulent Prandtl number.

In the

ε

−k model, the turbulent viscosity is computed by the relation:

ε

ρ=µ µ

2

t

k

..C (9)

The

k

and

ε

equations are given by:

ερ−+

∇

σ

µ

+µ•∇=ρ•∇+

∂

ρ∂

k

k

tPk.)kU(

t

k (10)

()

ερ−

ε

+

ε∇

σ

µ

+µ•∇=ερ•∇+

∂

ερ∂ εε

ε2k1

tCPC.

k

.)U(

t (11)

To tailor the ε−k model for solving round jet flows, McGuirk and Rodi [11],

Morse [12], Launder et al. [13], and Pope [10] suggested modified turbulence model

constants. The best correction in our case is the Pope’s one; it is a new source term

added to the ε equation. It is given by the following relation:

p

2

3pope .

k

..CS χ

ε

ρ= ε (12)

With

∂

∂

−

∂

∂

∂

∂

−

∂

∂

ε

=χ y

v

x

u

.

x

v

y

u

.

k

4

12

3

p (13)

for two dimensional axisymmetric geometry.

In this work, a limited version of the Pope correction introduced by Davidenko [14]

is adopted and incorporated in the CFX code. Its expression is:

()

)(sign,min.

k

..CS plimp

2

3pope χχχ

ε

ρ= ε (14)

With lim

χ, a limiting value of p

χ

.

3.2 Combustion model

The model for premixed or partially premixed combustion can be split into two

independent parts:

• Model for the progress of the global reaction: Burning Velocity Model (BVM),

also called Turbulent Flame Closure (TFC);

CISM’2008: TFC modeling of hydrogenated methane premixed combustion

231

• Model for the composition of the reacted and non-reacted fractions of the fluid:

Laminar Flamelet with PDF.

Reaction Progress

A single progress variable c

~

is used to describe the progress of the global reaction:

iburndifreshi Y

~

.c

~

Y

~

.)c

~

1(Y

~

+−= (15)

The reaction progress variable is computed by solving a transport equation:

c

jc

t

jj

i

x

c

~

.D.

xx

)c

~

u

~

(

t

c

~ω+

∂

∂

σ

µ

+ρ

∂

∂

=

∂

ρ∂

+

∂

ρ∂ (16)

The burning velocity model (BVM), also known as turbulent flame closure (TFC), is

used to close the combustion source term for reaction progress.

∂

∂

ρ

∂

∂

−∇ρ=ω

jj

Tuc x

c

~

.D.

x

c

~

..S. (17)

Where the turbulent flame velocity is given by:

4/l

t

4/1

u

2/1

L

4/3'

Tl..S.u.G.AS

−

λ= (18)

And the stretch factor:

σ

+

ε

ε

σ

−= 2

ln.

2

1

erfc

2

1

Gcr

(19)

The integral and Kolmogorov length scales are given by:

ε

=2/3

t

k

l and 4/1

4/3

v

ε

=η

Flamelet libraries

Under flamelet regime hypothesis [15], the species transport equations are

simplified to:

k

2

k

2

k

lk

Z

Y

Le2t

Yω=

∂

∂χρ

−

∂

∂

ρ (20)

A detailed chemical mechanism of 64 species and 752 equations was adopted.

The simplified energy equation is:

k

N

1k

k

p

2

2

l.h.

C

1

Z

T

2t

Tω=

∂

∂χρ

−

∂

∂

ρ∑

=

(21)

With the laminar scalar dissipation:

2

l)Z(.D2 ∇=χ (22)

An external program CFXRIF solves these equations to obtain a laminar flamelet

table, which is integrated using a beta PDF to have the turbulent flamelet library.

This library provides the mean species mass fractions as functions of mean mixture

fraction Z

~

, variance of mixture fraction 2''

Z

~ and turbulent scalar dissipation rate χ

~

:

(

)

st

2''

ii ~

,Z

~

,Z

~

Y

~

Y

~

χ= (23)

A. Mameri et al.

232

On the other hand two transport equations are solved in the CFD code, the first gives

mixture fraction:

∂

∂

σ

µ

+µ

∂

∂

=

∂

ρ∂

+

∂

ρ∂

jz

t

jj

j

x

Z

~

xx

)Z

~

u

~

(

t

Z

~

(24)

And the second gives the mixture fraction variance:

χρ−

∂

∂

σ

µ

+

∂

∂

σ

µ

+µ

∂

∂

=

∂

ρ∂

+

∂

ρ∂ ~

x

Z

~

2

x

Z

~

xx

)Z

~

u

~

(

t

Z

~2

jz

t

j

2''

z

t

jj

j

2''

(25)

The turbulent dissipation scalar is modelled by:

2''

Z

~

.

k

~

~

.C

~ε

=χ χ (26)

To interpolate species mass fractions from the turbulent flamelet table, the CFD

program use the mixture fraction, mixture fraction variance and the turbulent scalar

dissipation computed above.

4. FLAME GEOMETRY AND NUMERICAL PROCEDURE

The computational domain is the half of the chamber with 3 degrees thick (Fig. 3).

200 × 300 × 1 grid nodes are taken inside the domain. The grid is refined near walls and

in the high gradients regions (Fig. 4). Boundary conditions for the main flame, pilot

flame, at wall, exit and symmetry axis are taken from experiments; the most important

are shown for the flame in figure 5.

Fig. 3: Combustion chamber geometry

Fig. 4: Near burner meshing

CISM’2008: TFC modeling of hydrogenated methane premixed combustion

233

Fig. 5: Inlet velocity and turbulence kinetic energy

A double precision computation is done with the CFX code. The high resolution

scheme with an automatic time scale control was used. To reach the target maximum

residual of 10-7 for all equations, the computation takes about 3000 to 5000 iterations to

converge.

5. COMPUTATION RESULTS

5.1 Cold jet test

Before computing the reacting flow, a cold jet test case is performed with the same

boundary conditions. The Pope correction constants 3

Cε and lim

χ

were adjusted to

have the best agreement with the experimental axial turbulent kinetic energy variation

and mean velocity decay.

The potential core length is well reproduced, the figures 6 and 7 show this

agreement. We note that the core length is 75 mm or three times the jet diameter

(3D/X =).

5.2 Reacting flow computations

Three cases are taken into consideration; the first is the methane-air combustion

using TFC with a detailed chemical mechanism. The second and third cases are the

blended hydrogen-methane combustion using the same model with a chemical

A. Mameri et al.

234

mechanism of 64 species and 752 reactions. The fuel compositions, for the second and

third cases, are: 10 % H2 + 90 % CH4 and 20 % H2 + 80 % CH4.

The following figures showing general field are taken for the case of 10 % H2. The

other cases are similar, and the difference resides in the flame length and maximum

variables values. Figure 8 shows the flow structure near the burner. Streamlines are

parallel in the potential core, and they are deviated in the preheat zone and the velocity

increases under the gas expansion effect.

Fig. 6: Axial velocity

Fig. 7: Axial turbulent kinetic energy

Fig. 8: Near burner flow field

CISM’2008: TFC modeling of hydrogenated methane premixed combustion

235

Fig. 9: Near burner temperature field

In figure 9, we have the temperature distribution for the fuel with 10 % H2. In this

case, the maximum temperature is about 1668 K (the adiabatic one is 1674 K). For the

case of the pure methane, we obtain 1664 K which is the same as the adiabatic one. The

last fuel (20 % H2) has an adiabatic temperature of 1680 K.

Fig. 10: Top- Turbulent flame velocity; Bottom- Laminar flame velocity

The figure 10 shows the difference between laminar and turbulent flame velocity.

The laminar flame velocity is a fuel property; it depends only on the chemical

composition. The turbulent flame velocity depends also on the flow conditions. It

represents the interaction of the flame with the turbulence. In this case, it is nearly thirty

times the laminar one.

Fig. 11: Axial reaction progress

A. Mameri et al.

236

We can see the good agreement between measured and computed axial reaction

progress variable c for all fuels (Fig. 11). We note that maximum reaction depends on

fuel composition, it becomes close to the burner when we add more hydrogen to the

fuel. This means that flame velocity becomes more important.

6. CONCLUSION

In this study turbulent premixed combustion of pure methane and hydrogenated

methane is computed. We have used a detailed chemistry with a turbulent flame closure

model. The most important result found is that hydrogen enrichment with small

amounts doesn’t increase significantly combustion temperature. On the other hand it

increases flame velocity and stabilises combustion process. Also hydrogen doesn’t

contain carbon, it is a clean fuel. The replacement of a fraction of the methane by

hydrogen results in lower pollutant emissions. Turbine gas and IC engines can be fed

with hydrogenated fuels without recourse to major modification in installations.

NOMENCLATURE

A: Zimont model constant 2

Cε:

ε

−

k model coefficient (= 1.92)

1

Cε: ε−k model coefficient (= 1.44) µ

C:

ε

−

k model coefficient (= 0.09)

3

Cε: POPE correction coefficient (= 0.79) I: Chemical species I

h, tot

h: Static and total enthalpy k

N: Number of species in the mixture

k

: Turbulence kinetic energy k

R: Production rate of species

k

t

Pr :Turbulent Prandtl number I

S: Source term of the I species equation

M

S, E

S: Source terms of the momentum and energy equations

R

: Universal gas constant t: Time

U: Velocity vector U(u, v, w) T: Static temperature

u: Axial velocity component v: Radial velocity component

I

W: Species I molar weight i

Y: Species I mass fraction

Greek symbols

α: Hydrogen mass fraction t

Γ

: Turbulent diffusivity coefficient

δ: Kronecker delta c

σ

: Transport coefficient for c (=0.9)

σ: Standard deviation – Distribution of

ε

µ

: Dynamic viscosity

k

σ, ε

σ: Transport coefficient for

k

and

ε

(= 1.0 and 1.3)

z

σ, ''z

σ: Transport coefficient for Z

~

and 2''

Z

~

(= 0.9 and 0.9)

t

µ: Turbulent viscosity c

ω

: Rate of production of c

k

ω: Rate of production of species

k

p

χ, lim

χ: Vortex stretching rate invariant and limited invariant (Pope correction)

CISM’2008: TFC modeling of hydrogenated methane premixed combustion

237

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