15064 gas turbine combustor - eddy characteristics

8/9/2019 15064 Gas Turbine Combustor - Eddy Characteristics

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AN EDDY CHARACTERI ST I C T IME MODELI NG IN LES FOR GAS TURBI NE COMB USTOR

Mitsuru Yaga

Tohoku U niversity

Department of Chem ical Engineering

07, Aoba , Aramaki, Aoba-ku

Sendai 980-8579

Japan

TEL:+81-22-217-7252, FAX:+81-22-217-6165

Tsuyoshi Yamamoto

Tohoku University

Department of Chemical

Engineering

07, Aoba, Aram aki, Aoba-ku

Sendai 980-8579

Japan

TEL:+81-22-217-7252,

FAX:+81-22-217-6165

Hideyuki Aoki

Tohoku University


Engineering

07, Aoba, Aramaki, Aoba-ku

Sendai 980-8579

Japan

TEL: +81-22-217-7251,

FAX:+81-22-217-6165

Kousuke Sasada

Tohoku University

Department of C hemical Engineering


Sendai 980 8579

Japan

TEL: +81-22-217-7252, FAX:+81-22-217-6165

Takatoshi Miura

Tohoku U niversity


Engineering


Sendai 980 8579

Japan

TEL:+81-22-217-7250,

FAX:+81-22-217-6165

ABSTRACT

For calculating turbulent flame characteristics such as

temperature and chem ical species in the gas turbine combustor,

an effort applying Large Eddy Simulation (LES) to a

combustion simulation has been made in recent years.

However, there is n o established method of estimating reaction

rate on LES comb ustion simulation. In this paper, we construct

an eddy characteristic tim e derived from large-scale motio n to

calculate the combustion reaction rate using an eddy

dissipation concept model (EDC) and estimate combustion

characteristics (temperature and chemical species distribution)

in the combustor for the purpose of solving fundamental

problems of gas turbine combustor such as swirling effect or

formation of pollutant products. As a result, it is shown that

the combustion simulation using LES with EDC model is

effective method to calculate the characteristics of turbulent

diffusion flame su ch as g as turbine combustor.

KEYWORDS

Large Eddy Simulation, Combustion, Eddy Dissipation

Concept Model, Eddy Characteristic Time, Three Step Global

Reaction Mechanisms

INTRODUCTION

In order to construct a new combustor, scaling up of the

furnace usually advances in order o f laboratory-, batch-, pilot-

and commercial-scale. Since this met hod needs much cost and

time, a method o f using sim ulations adjusted on the

commercial furnace is recommended to predict the

characteristics of combustion. On the other hand, it is usually

said that experiments are better than th e simulations to predict

characteristics of combustion. However, it is difficult to

measure the characteristics o f combustion such as temperature

and chemical compounds even in the case of experiment and

the data include unavoidable errors, because the characteristics

of combustion are complicated in high temperature condition.

So the need of established combustion simulation model is

earnest ly desired. The simulatio n mod el is available for 1)

scaling up of the furnace, 2) development of new com bustor

purposing reduction of pollutant formation and adjustment on

various fuels and 3) s earch o f reasonable operation condition.

The sim ulation model is, furthermore, expected as an effective

technology to adjust various needs in future. Nowadays, from

the view of saving energy and reducing amount of discharged

environmental pollution substances, the importance of

controlling combustion phenom ena hasincreased. We may not

Copyright © 2000 by ASM E

Proceedings of2000 International Joint Power Generation Conference

Miami Beach, Florida, July 23-26, 2000

IJPGC2000-15064



¢~ : genera lized variable

or equivalence ratio [-]

<subscripts>

A r t : Arrhenius

e f f : effective

e d d y : eddy mixing

f u : fuel

i n : inlet

o x

: oxidant

<superscripts>

: spatial average

S I M U L A T I O N M E T H O D

G o v e r n i n o E a u a t i o n

All transport equations in this study can be expressed for

cylindrical three-dimensional geometry as:

( , o : ) + O --- / ; : l + ± l + ' - ±

O x - - r o t r O 0 ~

: o +

(')

oxk o~) fo rk or) ro ok ~oo)

where ff represents the dep endent variables which denote the

mass (1), momentum (u, v, w), enthalpy (h) and mass fraction

(m~; i=CI-h, O~, CO~, 1-120, N~, C O a nd 1-12). F + is th e

exchange coefficient, S# is the source term in the gas phase, p

is density, x, r and 0 are axial, radial and tangential coordinate,

respectively. Over bar means a spatial average. The source

terms and exchange coefficients are shown in Table 1. The

wall function model (Gosman and Pun, 1974) is applied to

calculate the flow near the wall. Radiative heat transfer is

calculated by 6-flux model (Gosman and Lockwood, 1972).

Mathemat i ca l Mode l ino

Large eddy simulation (LES) is a method of solving

spatial-averaged Navier-Stokes equation. In this method,

dependent variables are divided into resolved scale and

subgrid-scale (SGS) by a fil tering procedure. This procedure

is shown by following equation as:

f f f o , (2)

~ t J i = l

Table 1 Source terms and diffusion coefficients for

govcrining Equations.

Mass 1 0 0

Axial

u /teff

momentum

m

Radial v /~eff

momentum

m

Tangential w tt¢ff

momentum

o f d ; ) l o 0 ; 3 i o o g ) o-~

o f o : ] l o ( o ;3 l o f o ¢= ,3 1

7 t,'~'~

7 j , or

o ( o ; )

s < . n f

o(~,)

l o ; /

, ~ , { t , o : , J J , o : { - : , f

~w OP

r rO

Ma ss m / t~eff ~/

fraction am

Enthalpy ~ , u e f f 2 a R ( F x+ F r

F o -

3 E )

oh

/ 5 f 1 o ;

o;)]' f,(o= oZ312 h ( o ; o=

= , ~ ? l \

\ + fo ;q :+ V ;Lf o= +=)2

/

\ t~-J t T t ,~ ; j /

#eft --- # + /2t

O ' m O h

0.4 0.4

where G i ( x i , x ' i ) is a fil tering function and dash means a

fluctuation. In this study, the Gaus sian filter is used.

G(x,,x,0__ f-g7_ x p( - 6(x - x' ,Y )

V W --~ C T ~ 7 ) , (3)

where A is grid length. The dependent variable can be

decompose d as following equation:

= 7 + ¢ ' , 4 )

After the filtering procedure operated on Navier-Stokes

equations, the Reynolds term R O. is appear. The Reynolds term

is modeled as follows (written in Cartesian geometry):

l r r

Ru = - ~ u , u : oS:- , (5)

1 (0~ ag)

Copyright © 2000 by ASME



where o~0 s K ronecker's delta, vt is turbulent viscosity and S O.

is strain rate. V iscosity v t is further mode led as follows:

where Cs represents the Smagorinsky constant and w e assume

it as 0.2 (Smagorinsky, 1963).

React ion Model ino

We use three step global reaction mechanisms to express

methane-air com bustion reaction as:

C H 4 + 0 . 5 0 2 ~ C O + 2 H 2 ,

(9)

CO+0.502~::~CO2,

(10)

H2+0.502~::~H20, (11

Because the methane-air (oxygen) overall reaction (CI-L+202

CO2+2H20), often adopted to the turbulent combustion

simulation for saving calculation time, can not represent CO

and HE which are formed in local fuel-rich region. To consider

the interaction between eddy motion and chemical reaction,

the eddy dissipation concept (EDC) model is used to express

the reaction rate (Magnussen and Hjertager, 1976) as:

p . ( m - o x - - 1

= 4.0__ mm/_ _,mr, oq (12)

J '

where ~ is a stoichiometric oxidant requirement to burn lkg

of fuel, Reddy s eddy mixing rate o f fuel and oxygen and ~ is

eddy characteristic time. The eddy characteristic time z is

estimated with considering K olmogorov scale as below:

where e is eddy dissipation rate. From the assumption that

turbulence energy generation and dissipation are locally equal,

eddy dissipation rate is written as below (written in Cartesian

geometry):

= ~ t.O x - ~ x , -~-xj ' (14 )

Eq. (14) is substituted to Eq. (13), the eddy characteristic time

is finally expressed as below:

I =

( 1 5 )

Considering both the chemical reaction and the eddy motion,

reaction rate is finally expressed a s :

ff~ = - m i n ~ , a ~ , ~ ) , 1 6 )

where A is pre-exponential factor of rate constant, E is

Activation energy, R is universal constant of gases and T is

temperature. The value of coefficients A, E, a and b are

referred from Jones (Jones and Lindstedt, 1988).

N u m e r i c a l S o l u t i o n

The SIMPLE algorithm with TDMA method (Patanker,

1980) is used to solve the partial differential equations sh own

in (1). In this simulation, equatio ns of continuity, mom entum ,

enthalpy and gas species mass fractions are discretized in

space by a control volume method. The convective terms are

differenced in space with the quadratic upstream interpolation

for convective kinematics m ethod (Leonard, 1979) and the

diffusive terms are differenced in space w ith the second-order

central difference scheme. The fully implicit scheme is used

for time marching and time step is 0.05s. The schematic

diagram of computational domain is shown in Fig. 1. The

coaxial combustor has 200m m in internal diam eter and

800mm in length. The inner pipe diameter is 6 5mm and the

annulus pipe diameter is ~ 23mm. A computational grid

number in axial, radial and tangential direction are 120 × 40 x

50, respectively.

~

800 ~[

ir . . . . . . . ~ . . . . ~ . l ~

o - . . . . . J J . . . . . .

Fig. 1 Schematic diagram of computational domain.

The Schem atic diagram of experimental setup is shown in

Fig. 2. This combustor has 200ram in diameter and 800mm in

length. The inner pipe diameter is ~ 5ram and the annulus

pipe diameter is ~ 23 mm The experimental condition is

shown in Table 2. A flame temperature is measured by using

suction pyrometer probe equipped with R-type thermocouple.

Gases are sucked through a water-cooled sampling probe made

of stainless steel. The tip diameter of gas sampling probe is O

4.32mm. Intensive cooling starts at the joint o f the probe tip




with a water jacket cooling system where chemical reaction

halts. Sampling gases are analyzed by a gas chromatograph.

. a m p . i n . e W a l l o . o o

f \

ii2 c o m p ro

Methane cylinders

Combustor

/

Gas chromatograph

Fig 2 Schematic diagram of experimental setup.

Table 2 Experimetal condition.

0.1 lml

Air

CI%

Fig. 4 Calculated instantaneous eddy characteristic time

distribution in computational domain.

Figure 5 shows the radial distribution of temperature in

the equivalence ratio ~ = 1.0 at x= 0.1m dow nstream from the

burner. From the Fig. 5, good agreements are seen except for

the centedine. The reason why thermocouple system indicates

exceed temperature is that the effect of radiation from suction

pyrom eter tip is large.

1800

1600

[-] 1.0 140o

CI-h [Nm3 h l] 0.2 0 ~ 12oo

Air [Nm3 h a] 1.90 ~ 100o

Temp erature [K] 293.15 ~ 800

6 0 0

ReD [-] 33228 w

4 0 0

2OO

0

RESULTS AND DISCUSSION

Figure 3 shows the predicted time mean velocity of

combustion gas flow. The line that axial velocity is zero is

plotted on Fig. 3. The strength of the vortex shedding is much

weaker by heat release, large-scale eddies are broken up

because thermal expansion occurs in the vortex core (Fureby

and L/ffstr0m, 1994).

Figure 4 shows the distribution of eddy characteristic time

calculated by the present model. The eddy characteristic time

in the region whe re CI-h and 0 2 are mixed is short and it is

expected that LES combustion simulation is carried out with

the strict assumption o f eddy dissipation concept model. The

combustion reaction occurs at the moment that fuel and

oxygen are fully mixed in micro-scale eddy.

0.1 [ml 0.4 [m|

i

A i r ~ ~ ~

~ u / U ~ = l . O [-]

Fig. 3 Predicted time mean velocity vectors

in computational domain.

• Experiment ]

.......... LES

0 0.1 0.2 0.3 0.4 0.5

r/D [-I

Fig. 5 Radial distribution of temperature at 0. lm from

burner at ~ =1.0.

Figure 6 shows the radial distribution of CFL mole fraction

in the equivalence ratio 6=1.0 at x=0.1m downstream from

the burner. This calculatio n result ,agrees well with the

measured results of CH4 mole fraction.

0.8

O

0.6

0 .4

0 .2

0

[ o ExperimentLEs1

. . . . . . . . . v v

0 0.1 0.2 0.3 0.4 0.5

rid [-]

Fig. 6 Radial distribution of CI-h mole fraction at 0. lm

fro m bu rne r a t 4~ -- 1.0.




i

Figure 7 shows the radial distribution of CO m ole fraction

in the equivalence ratio ~ =1.0 at x=0.1m downstream from

the burner. This calculation result overestimates experim ental

result near the centerline. The reason is because the CO

consum ption reaction is too simple to estimate the distribution

of CO mole fra ction correctly.

The selection of a reac tion mech anism seriously affects on

the calc ulated results of the distribution o f chemical species.

o.1

0 .08

0

0 .06

0 .04

0 .02

o

• LEsEXperiment I

, O o , o ; • • • • .

0 0.1 0.2 0.3 0.4 0.5

r/D [-]

Fig. 7 Radial distribution of CO mole fraction at 0. lm

fro m burn er at 4~ =1.0.

CONCLUSION

A three-dimensional Large eddy simulation turbulent

combustion simulation in a coaxial combustor is carried out.

We construct an eddy characteristic time model derived from a

large-scale motion to estimate the combustion reaction rate

using eddy dissipation concept model for saving a

computational time. An estimation of eddy characteristic time

considering Kolmogorov scale is effective for knowing subgrid

scale motion of flame region and the present model is more

suitable for the assumption of eddy dissipation concept model

than a model using time averaged turbulent energy and eddy

dissipation rate. In this study, the calculation results of

temperature and CI-h mole fraction distribution agree well with

the m easured results, however the calculated result of CO mole

fraction distribution does no t well agree with m easured result

for the sake of using simple CO reaction mechanism. If we

want to apply LES combustion simulation on engineering

applications such as gas turbine combustor, w e should

thoroughly check the reaction model with reaction mechanism

whe ther it could be suitable f or LES com bustion simulation or

not.

REFERENCES

Cook, A. W. and Bush¢, W. K, 199 9, A Subgrid-Sca le

Model for the Scalar Dissipation Rate in nonpremixed

combustion, P h y s i c s o f F lu i d s , V ol. ll, pp. 746-748.

Fureby, C. and L6fstr6m, C., 1994, Large Eddy

Simulation of Bluff Body Stabilized Flames,

T wen ty -F i f th

S i m p o s i u m ( I n t e r n a t i n a l ) o n C o m b u s t i o n , The Combustion

Institute, Pittsburgh, PA, pp. 1257-1264.

Gosman, A. D. and Lockwood, E C., 19 72 , In

Corporation of a Flux Model for Radiation into a Finite-

Difference Procedure for Furnace Calculation, Fo ur teen th



Gosman, A. D. and Pun, W. M., 1974, Lecture Notes for

Course Entities Computation of Recircu lating Flows, Imp erial

College Hea t Transfe r See. Report HTS/74/2.

Jones, W. P., and Lindstedt, R. P., 198 8, Global Reaction

Schemes for Hydrocarbon Combustion, C o m b u s t i o n a n d

F l a m e . V ol. 73, pp, 233-249.

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with a Two-Equation Model of Turbulence , I n t. J . H e a t M a s s

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Leonard, A., 197 4, On tile Energy Cascade in Large-

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18A, pp. 237-248.

Leonard, B. E, 1979 , A stable and accurate convective

modeling procedure based on quadratic upstream

interpolation,

C o m p u t . M e t h . A p p l . M e c h . E n g . ,

V ol. 19, pp.

59-98.

Magnussen, B. E, and Hjertager, B. H., 19 76 , On '

Mathematical Modeling o f Turbulent C ombustion with Special

Emphasis on Soot Formation and Combustion,

S ix teen th

S im p o s ium ( I ntern a t in a l) o n Co m b us t io n , The Combustion


M611er, S. L., Lundgren, E a nd Fureby. C., 19 96, Large

Eddy Simulation of Unsteady Combustion, T wen ty -S i x th



Patankar, S. V ., 1980, Num erical Heat Transfer and Fluid

Flow, Hemis. pub. co., Washington.

Smagorinsky, J., 1963, Gene ral Circulation Expe rimen ts

with the Primitive Equations, Mo rt. W eath . Rev. , V ol. 91, No.

3, pp. 99-164.

6 Copyright © 2000 by ASM E

15064 gas turbine combustor - eddy characteristics

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