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Numerical Simulation of the Laminar Diffusion Flame in a Simplified Burner

Lawrence D. Cloutman

This paper was prepared for submittal to the 26th International Symposium on Combustion

Naples, Italy July =August 2,1996

February 1996

T

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NUMERICAL SIMULATION OF THE LAMINAR DIFFUSION

FLAME IN A SIMPLIFIED BURNER

Lawrence D. Cloutman

P. 0. BOX 808, L-14

Lawrence Livermore National Laboratory

Livermom, California 94550, USA

Telephone (510) 422-9307

FAX (510) 422-2644 -

E-mail cloutman@llnl.gov

Text: 3055 words (actual count)

Equations: 11 = 231 words

Figures: 1400 words

Tables: 400 words

Total length: 5086 words

Either poster or oral presentation is acceptable.

Colloquium topic area: Laminar Flames

,

NUMERICAL SIMULATION OF THE LAMINAR DIFFUSION

FLAME IN A SIMPLIFIED BURNER

Lawrence D. Cloutman

ABSTRACT

The laminar ethylene-air diffusion flame in a simple laboratory burner was simulated with the . COYOTE reactive flow program. This program predicts the flow field, transport, and chemistry for the purposes of cade validation and providing physical understanding of the processes occurring in the flame: We show the results of numerical experiments to test the importance of several physical phenomena: including gravity, radiation: and differential diffusion. The computational results compare favorably with the experimental measurements, and all three phenomena are important to accurate simulations.

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I. INTRODUCTION

Flower and Bowman [l-31 measured the temperature and velocity fields in a simple laboratory-

scale burner. Although their primary goal was to study the sooting properties of this burner, these

measurements are suitable for validation of computational fluid dynamics programs. The geometry

is simple, the flow is laminar, and the combustion occurs in an ethylene-air diffusion flame. The

burner is a simple Wolfhard-Parker burner enclosed in a rectangular chamber as shown in Fig. 1.

Fuel is fed through a rectangular tube 0.8 cm wide by 8.0 cm long, and coflowing air surrounds

the tube. Flame stability requires the initial air velocity to exceed the initial fuel velocity, and

these are 22.0 and 7.0 cm/s, respectively. A steel screen was placed 1.5-2.5 cm outside the flame

to reduce flickering. The results reported here are for a pressure of one atmosphere.

The experimental measurements of temperature and vertical velocity are the subject of this

study. A small silica-coated thermocouple was use to measure gas temperatures. The measure-.

ments have been corrected for radiative losses and have estimated uncertainties of f4%. Velocity

measurements were made with standard LDV techniques.

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Simulations of the experiments were performed with the COYOTE computational fluid dy-

namics program [4]. COYOTE is based on the full transient Navier-Stokes equations, and steady-

state solutions, when they exist, are found by assuming an arbitrary initial flow and allowing the

transient to decay. While this approach is less efficient computationally than a direct steady state

approach, it has several advantages. First, it does not make an ad hoc assumption that the final

flow field is truly steady. That is, it allows the final solution to contain quasi-periodic features

such as flame flickering. If the final flow is truly steady, then that type of solution will evolve

naturally. Second, it automatically performs a flame stability study. If, for example, the flame

cannot be sustained, it should be extinguished in the calculation (at least to the extent that the gas

physics included in the calculation is an accurate representation of the physical system). Third, it

allows easy incorporation of complex, realistic gas physics. The model includes a real-gas thermal

equation of state, arbitrary chemical kinetics, transport coefficients from a Lennard-Jones model,

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a simple radiative heat loss model, and mass diffusion based on the full Stefan-Maxwell equations.

The ethylene combustion is modeled by a one-step global Arrhenius kinetics rate. Also included

are three kinetic reactions for thermal NO, production and six molecular dissociation reactions

required to close the thermal NO reaction set and produce accurate temperatures.

Several simulations at a pressure of one atmosphere using different numerical grids and differ-

ent sets of input physics were performed to test the sensitivity of*the solutions to various factors.

The base case includes gravity and gas-phase radiative losses. These runs were made with Fick's

law and a unit Lewis number for all species. Additional cases were run with the full mass dif-

fusion model, including thermal diffusion. We will present comparisons between the calculated

and measured temperatures and velocities. The computational results compare favorably with

.the experimental measurements. We find that the solutions are quite sensitive to gravity: NO,

predictions will require the use of the radiation model to get adequate accuracy in the temperature

field, and the solutions are sensitive to the mass transport model.

Section I1 presents the governing equations and describes the gas physics. Section I11 describes

the geometry of the experimental apparatus and the problem setup. Section IV describes several

solutions for this burner. Conclusions are presented in Section V.

11. GOVERNING EQUATIONS

The program is based on the Navier-Stokes equations for a mixture of compressible gases. We

use the single (mass weighted) velocity representation and Eulerian coordinates.

Mass conservation is expressed by the continuity equation for each species CY:

(1) dP0 - + v (p,G) = -v - fa + R,: at

where pa .is the density of species cy, u' is the fluid velocity, fa is the diffusional mass flux of species

cy: and R, is the rate of change of species a by chemical reactions. The diffusional flux is a complex

function of the flow that is approximated by Fick's law,

A = -PDV(P, /P) :

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.

in some of the solutions. D is the species diffusivity (assumed here independent of a), and p is the

total density. We also use the formalism of Ramshaw [5; 61, which is an approximate treatment of

the full Stefan-Maxwell equations. The R, are assumed to be known functions of the composition

and thermodynamical variables. The global rate for ethylene oxidation, for example, is

R c ~ H ~ = 6.4 x 1012 W C ~ H ~ [02]1.65 [CZH~]'.' exp(-15000/T) g/cm 3 -s: (3)

where W C ~ H ~ is the molecular weight of ethylene. This rate predicts the correct laminar flame

speed under stoichiometric conditions at one atmosphere.

The momentum equation is

1 - at + v - (PUG) = Cp,@, - VP - v . s, (4)

.where P is the pressure: and

applications is the gravitational acceleration 3. The viscous stress tensor is

is the body force per unit mass acting on species a' which in most

s = -p[VG + (VG)T] - 1-11 (V - Z) u, ( 5 )

where p is the coefficient of viscosity, 1-11 is the second coefficient of viscosity, pb is the bulk viscosity

and U is the unit tensor.

We choose the thermal internal energy equation to express energy conservation:

where I is the specific thermal internal energy, and H , is the heat of formation of species cy. Note

that for = 9': the next-to-the-last term vanishes. The heat flux a i s approximated by the sum

of Fourier's law and enthalpy diffusion:

where h, is the specific enthalpy of species cy.

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The radiative heat loss term Grad is described in [7]. A complete treatment of the radiative

transfer would be extremely complex and computationally challenging, so we consider only highly

simplified models. Two limits lead to such models. The first case is a diffusion approximation,

which is appropriate in optically thick flows. In this approximation, K is the sum of molecular

and radiative conductivities and Grad = 0. The second case is a local radiative heat sink, which is *

appropriate in the limit of optically thin flows. Our applications tend to be optically thin, so we

adopt a slight generalization of the local heat sink approximation used by Chao, Law, and T’ien

[SI: namely

, where u is the Stefan-Boltzmann constant. The wall temperature Tw is assumed to be the same

for all walls. The function Kp is related to the Planck mean opacity, np; by

where {pa} is the set of all species densities, k, is the monochromatic absorption coefficient, and

B, is the Planck function.

The equation ocstate is assumed to be given as the sum of the partial pressures of an ideal

gas for each species. Transport coefficients are computed from the Lennard-Jones model [9]. The

JANAF tables [lo-121 provide a homogeneous set of thermochemical data for a large collection

of materials, and these tables are used to supply the specific enthalpy and heat of formation for

each species of interest. Chemical reactions are divided into two groups. The first group is treated

kinetically, with the rates assumed to be of generalized Arrhenius form; The second group is

assumed to be in chemical equilibrium. Table 1 shows the reactions used in this study.

111. PROBLEM DESCRIPTION

The geometry of the experiment is shown in Fig. 1. The burner is nothing more than a 0.8

by 8.0 cm rectangular metal tube through which ethylene flows. The tube is surrounded by the

Table 1.

Original Partial Equilibrium Mechanism

Kinetic Reactions Equilibrium Reactions

C2H.4 + 302 + 2C02 + 2H20 O + N z + N O + N

N + 0 2 + N O + O OH + N + NO + H

H2 +2H Nz + 2 N

0 2 $ 2 0 0 2 + H2 + 20H

0 2 + 2H20 + 4 0 H

0 2 + 2CO + 2C02

axial air flow, which is confined in a rectangular chamber whose walls are several centimeters from

the tube. The long slot at the open end of the tube makes it a good approximation to assume

the flame is uniform along most of the length of the slot. The two dimensional simulations were

made in a plane perpendicular to the long direction of the slot. We also assume bilateral symmetry

about a line bisecting the slot the long way, so we place the lower left hand corner of the grid at

the center of the slot, but 0.5 cm below the apening. The wall of the slot is assumed to be a sheet

of metal 0.1 cm thick and is represented in the two-dimensional plots as a series of x's. The base

case uses a uniform grid of 1 mm square zones and has 30 by 60 zones. Some runs were made with

0.5 mm square zones. The fuel, ethylene, is allowed to flow into the bottom of the mesh through

horizontal zones numbers 2 through 5 in the coarse grid (number 1 is the fictitious zone at the left

side of the mesh), and air flows in through zones 6 through 31. An obstacle representing the edge

of the burner occupies the first 6 zones vertically (including the bottom fictitious zone) of the 6th

column.

Our inflow boundary condition is the type (ii) with specified density of Rudy and Strikwerda

[13]. In addition, we impose a restriction against inflow along any outflow boundary for reasons

discussed in an earlier report [14]: although it was not needed in these calculations. We assume

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that the inflowing gases are at a temperature of 300 K and a pressure of 1.013 x lo6 dynes/cm2.

The inflow velocities are 7 cm/s for the ethylene and 22 cm/s for the air velocity. The inflow

density is 1.131 x g/cm3 for the ethylene. The air was assumed to be a mixture of five species

with densities of 2.688 x lo-* g/cm3 0 2 , 8.766 x lV4 N2: 5.292 x CO2, 7.217 x lo-' H20:

and 1.489 x lov5 argon. Unless otherwise noted, the gravitational acceleration is assumed to be

-980 cm/s2.

IV. NUMERICAL SOLUTIONS

A series of five cases were run out to steady state using a variety of numerical parameters

and physical submodels. The base case has a resolution of 1 mm and Fick's law is used for the

species diffusion. The same diffusivitg is used for all species and is calculated from the mixture

viscosity and a Schmidt number of 0.7. The radiation model was included. The same problem was

run with 0.5 mm zones. There was no significant change in the solution, demonstrating the grid

independence of the solutions. It is somewhat surprising that the solution with 1 mm resolution

is so well converged. Another variation of the base case was to use a fuel oxidation rate that is

half that of Eq. (3) . This had no effect on the solution. This is not surprising since it takes

approximately 0.01 s for the fluid to cross a computational zone: but the chemical time scale for

oxidizing the fuel is approximately three orders of magnitude smaller,. A similar insensitivity to

the reaction rates: however; will not occur for the much slower thermal NO reactions.

Another case was the same as the base case except Fick's law was replaced by the detailed

mass transport model. A comparison between these two cases is given in the next five figures.

Figure 2 shows the isotherms for both cases. The multicomponent diffusion model produces a

higher peak temperature (2422 K, as compared to 2317 K with Fick's law). The height of the

flame was not measured in the experiment, but it was observed to be well beyond the height of

this computational grid, as predicted here. The axial temperature gradient in the core of the flame

is significantly smaller in the multicomponent case.

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I:

Figure 3 shows the calculated and experimental horizontal temperature profiles. The left edge

of each plot is at the center of the flame, and the peak temperature occurs approximately above

the edge of the slot. The Fick's law calculation does very well except in the center of the flame.

The multicomponent calculation does better in the center, but is systematically a little hotter than

the experimental values. The experimental flame was intended to produce sooting conditions, and

the calculations do not yet have a soot production or soot radiation model. The fact that the

multicomponent calculation is systematically slightly too hot is consistent with the radiative losses

expected from the soot.

Figure 4 shows the horizontal profile of axial velocity for the experiment and both calculations.

Both calculations agree with the experiment out to 1.0 cm. It is not known why the outer flow of

air is systematically higher than the 22 cm/s flow speed reported by Bowman and Flower.

Figure 5 shows mass fractions of H:! for both calculations. Since differential diffusion effects

are largest for the very light species, we expect some differences between these two plots. Not only

are the details of the internal distributions in the flame different, but the peak values are different

by a factor of nearly two.

.Figure Gshows mass fractions of NO. As in the case of H2, there are some significant differences

in the spatial distribution. With Fick's law, the peak NO mass fraction occurs in a sheet in the

outer part of the flame, coincident with the high temperatures. In the multicomponent model, the

peak NO mass fraction occurs in an island just above the lip of the burner, and there is nearly a

factor of four difference in the peak NO mass fraction. The NO flow rates at the top of the grid

are 2.5 x g/s-cm and 6.4 x lob6 g/s-cm for the Fick's law and multicomponent solutions,

respectively. These results strongly suggest that burner models that are expected to produce

reliable solutions that include any significant level of chemical detail must include a detailed mass

transport model.

The base case was rerun without, the radiative heat loss model. The peak temperature is

2355 K, close to the adiabatic skoichiometric flame temperature of 2380 K. The isotherms are

qualitatively the same as in the base case. Temperatures are typically 50 to 100 K higher at points

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in the flame zone as compared to the base case. The Hz mass Gaction peaks at 8.6 x a little

over twice the base case value. The peak NO mass fraction is 3.5 x and has a different spatial

distribution than in the first two cases. Far more NO production is occurring as the hot gases rise

through the grid than in the base case. The NO flow rate is 6.8 x g/s-cm and clearly would

be higher if the grid were taller.

The importance of buoyancy forces is demonstrated by rerunning the base case with zero

gravitational acceleration. Figure 7 shows the isotherms and NO mass fractions for the zero-

gravity case. The flame is now much wider than before: and the lower temperatures suppress NO

pro duct ion.

V. CONCLUSIONS

The COYOTE hydrodynamics program has been used to simulate reactive flows in a simplified

experimental burner. One objective of this study is validation of the program and demonstration of

its capability to simulate laminar diffusion flames. The second objective is to study the importance

of several physical submodels in burner simulations.

While detailed comparison of the computational and experimental results is still in progress,

we can make the following general observations:

1) The model successfully predicts the velocity and temperature fields with surprisingly coarse

zoning (1 mm resolution).

2) It is critical to include gravity in the calculations as buoyancy effects are quite pronounced.

3) Even with the simple chemical mechanism used in these solutions, the results showed a

surprising sensitivity to the mass transport model.

4) The radiative cooling model lowers local combustion temperatures on the order of 50-100

K for non-sooting flames. While this change has little effect on the gross dynamics of the flow: it

is significant for the calculation of NO, production due to the high temperature sensitivity of the

thermal NO, mechanism.

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5) More work is needed on several physics submodels. First, we need soot chemistry and

radiation to improve the temperature predictions. Second: we need more detailed chemical mech-

anisms. Third, we need an improved model for the radiative transfer. Work is in progress on these

items.

ACKNOWLEDGMENTS

I thank Bill Flower for supplying additional information on several aspects of the experiment.

This work was performed under the auspices of the U. S. Department of Energy and the Lawrence

Livermore National Laboratory under contract number W-7405-ENG-48.

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REFERENCES

1. Flower, W. L. and Bowman, C. T., Symposium (International) on Combustion, The Combus-

2. Flower, W. L. and Bowman, C. T., Combust. Sci. Tech. 37:93 (1984).

3. Flower, W. L., “The Effect of Elevated Pressure on the Rate of Soot Production in Laminar Diffusion Flames,’‘ presented at the Spring Meeting of the Western States Section .of the Combustion Institute, 1985.

tion Institute, Pittsburg, 1984, pp. 1035-1044.

4. Cloutman, L. D., “COYOTE: A Computer Program for 2-D Reactive Flow Simulations,’’ Lawrence Livermore National Laboratory report UCRL-ID-103611, 1990.

5. Ramshaw, J. D., J. Non-Equilib. Thermodyn. 15:295 (1990).

6. Ramshaw, J. D., J. Non-Equiiib. Thermodyn. 18:121 (1993).

7. Cloutman, L. D., “Numerical Simulation of Radiative Heat Loss in an Experimental Burner,” Lawrence Livermore National Laboratory report UCRL-JC-115048, presented at the 1993 Fall Meeting of the Western States Section Meeting of the Combustion Institute, 1993.

8. Chao, B. H., Law, C. K., and TYen, J. S., Twenty-Third Symposium (International) on Combustion, The Combustion Institute, 1990, 523.

9. Cloutman, L. D.; “A Database of Selected Transport Coefficients for Combustion Studies,’’ Lawrence Livermore National Laboratory report UCRL-ID-115050, 1993.

10. Stull, D. R. and Prophet, H., JANAF Thermochemical Tables, 2nd ed. (U. S. Department of .Commerce/National Bureau of Standards, NSRDS-NBS 37, June 1971).

11. Chase, M. W., Curnutt, J. L., Hu, A. T., Prophet, H.: Syverud, A. N., and Walker, L. C., JANAF Thermochemical Table, 1974 Supplement,. J. Phys. Chem. Ref. Data 3:311 (1974).

12. Chase, M. W. Jr., Davies, C. A., Downey, J. R. Jr., F’rurip, B. J., McDonald, M. A., and Syverud, A. N., JANAF Thermochemical Tables, Third Edition, Parts I and II. Supplement No. 1, J. Phys. Chem. Ref. Data 14 (1985).

.

I

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13. Rudy, D. H. and Strikwerda, J. C., Computers 64 Fluids 9:327 (1981).

14. Cloutman, L. D., “Numerical Simulation of Turbulent Mixing and Combustion Near the Inlet of a Burner,” Lawrence Livermore National Laboratory report UCRL-JC-112943, 1993.

12

i T I

air

t t ethylene

22 cm/s 7 cm/s'

T air

air grid

Fig. 1. Top and side views of the slot burner. The location of the two-dimensional computational grid is also shown.

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TEMPERA'

Fick's Law

MIN = 2;7103990+02 MAX = 2.3167040+03

WRE

Multicomponent

MIN = 2.55062604-02 MAX = 2.4215020+03

Fig. 2. Isotherms for the base case (Fick's law mass transport) and multicomponent mass transport solutions.

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x 0 0 N

x e 8 s 8 n N

s? -0 eo

8

8 0 n

x n N

9 .O

9 8 0 N

9 0

B 8 0 2

9 -0 xu, -52 c

x x x

0 0

x

0 .I2

8. N

x.

Fick’s Law

I , 1 3 02 0.4 0.6 0.8 LO 12 1.4 1.6

x (cm>

Calc. Y 1 I I I I I

0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6

x (cm)

3. Horizontal profiles of temperature 2.0 cm above the burner.

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9 E : 8

8

8

.-

0

9

00

9 e h

$2

' C C 5

C

5

5 C

C C

C c C C

> x n

9 z 2

8 n

N

9 0

8

Fick's Law

I I 1 1 I I I I .o 0.2 0.4 0.6 0.8 10 K 1.4 16

x (an)

Multicomponent

I I I I 0.0 0.2 0.4 0.6 0.8 1.0 12 1.4 1.6

x (4

4. Horizontal profiles of axial velocity 2.0 cm above the burner.

. 1. G

, 3 1

3

3

7

?

L MAX = 3.841191D-04 MAX = 6.4389251)-04

Fig. 5. H2 mass fraction contours for the base case (Fick's law mass transport) and multicomponent mass transport solutions.

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NO MASS FRACTION

Fick’s Law Multicomponent

I

J

MAX = 9.6806720-05 = 3.4679800-04

Fig. 6. NO mass fraction contours for the base case (Fick’s law mass transport) and multicomponent mass transport solutions.

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i MAX = 2.3133970+03 MAX = 9.079066D-05

Fig. 7. Isotherms and NO mass fraction contours for the zero-gravity solution.

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