Davis, M.P., Fleming, J.W., Williams, B.A., and Ladouceur, H.D., "Flow Field Considerations for

Counter Flow Burners," Proceedings of the Fall Technical Meeting of the Eastern States Section of

the Combustion Institute, pp. 200-203, 1999.

Flow Field Considerations for Counter Flow Burners

M.P. Davis', J.W. Fleming, B.A. Williams, H.D. Ladouceur2

Combustion Dynamics Section, Code 6185, Chemistry Division

Naval Research Laboratory, Washington, DC 20375-5342 USA

'Graduate Student, WPI

2Corresponding author: Code 6112, douglad(cVccfml.navv.mil

INTRODUCTION

Many computational combustion tools (e.g. Sandia OPPDIF code [1]) of opposed jet, counter flow

diffusion flames apply a simplified potential flow model for the fluid flow portion of the problem. The resulting

solution (for no flame) yields a stagnation region between the two burners and an axial velocity component that

is independent of radius. Rolon [2] recognized the need for experimental evidence to provide justification for a

potential flow assumption. His results indicate that for a range of velocities and for two common burner designs

(straight tubes with screens and dual converging nozzles) there are large discrepancies between the assumed flat

radial profile and experimental measurements. This paper investigates the flow field that exists between the

nozzles of various counter flow burners through the use of a commercially available CFD package. Better

understanding of this flow regime will lead to improved burner designs that more closely approximate the one

dimensional treatment used in the combustion models.

The potential flow model ignores viscous effects, resulting in a failure to predict boundary layer

development along the tube walls. A no-slip boundary condition at the tube waIIs causes fluid adjacent to the

waIIs to be retarded, thereby increasing the velocity of the fluid along the centerline (in order to satisfy mass

continuity). This results in a much higher centerline velocity (for the same flow rate) than that predicted by the

potential flow model. A simple potential flow model was examined by neglecting viscous effects and solving

the reduced Navier-Stokes equations. The solution is that of Laplace's equation for the velocity potential, which

was evaluated for a geometry describing two I cm diameter tubes separated by 1 em using a [mite element

package (FLEXPDE) [3]. This potential flow model consistently under predicts the observed flow velocity.

This is reasonable since the acceleration of the fluid core within the tubes by viscous boundary layer growth is

neglected.

In the case of two opposed flows, the situation is more complicated. Flow in both tubes wiU develop

boundary layers resulting in the center core being accelerated. If the separation distance between the two tubes

is small, the velocity profile at the tube exits will be greatly affected by the presence of the other tube due to the

higher pressure stagnation region formed by the two impinging streams. The shape and length of the burner

tubes, the tube separation distance, and the inlet flow velocities aII play important roles in determining the shape

of the radial velocity profile at the tube exits.

The opposed flow problem was studied using PHOENICS [4], a widely utilized CFD software. The

geometry and flow conditions can be easily modified, and parametric studies were run to investigate different

burner configurations over the entire desired range of strain rates. PHOENICS is used to better understand the

fluid mechanics involved, as weII as being a useful design tool to determine optimal burner geometries that

produce flow fields more appropriate for the one-dimensional models.

COMPUTATIONAL SETUP

The CFD calculations were performed using PHOENICS version 1.6, running on an SGI workstation.

PHOENICS uses a finite volume approach to provide solutions of differential equations having transient,

convection, diffusion, and source terms. For this application, the appropriate equations are the incompressible

Navier-Stokes equations. The user is able to specify geometry, boundary conditions, fluid properties, as wel1 as

many other options that control the solution procedure, output, etc. Taking advantage of the axisymmetric

nature of the problem, the solution was specified in a single plane and then rotated to produce the desired 3-D

burner. Boundary conditions were specified along each of the four edges of the solution domain as wen as

along the tube waIIs. At each of the tube inlets, a uniform velocity was set, and no-slip conditions were
specified for each tube surface. For the far field radial boundary, a pressure boundary condition was utilized to

set the pressure to 1 atmosphere.

RESULTS

Calculations were performed for a single, 50 cm long, 1 cm diameter straight tube flowing Nz in order to

assess the predictive capability of the code. For comparison, experimental measurements of the radial profile of

the axial velocity were made on a single burner tube having the same dimensions as were used in the

PHOENICS calculation. Data were collected at a height of 1 mm above the tube exit plane and a Nz flow rate of

2.1 SLPM using an LDV system (QSP, Inc.) seeded with 0.3 ).tm diameter alumina particles entrained into the

Nz flow. Figure 1 plots both the measured and PHOENICS calculated axial velocities as a function of tube

radius. Excellent agreement is observed between the measured and calculated velocities.

Calculations were carried out to investigate the effects of tube length on the shape of the radial velocity

profiles. Figure 2 shows radial profiles of the axial velocity for Nz flowing at an inlet velocity of 40 cm/s for

tubes of lengths 3, 5 and 10 cm. The profiles show the viscous effects that predominate along the tube walls,

lowering the local velocity, giving rise to a boundary layer, and accelerating the core fluid. For longer tube

lengths, the boundary layer grows until a parabolic velocity profile results, after which the velocity profile

ceases to change with increasing tube length (fully developed flow). The 10 cm tube demonstrates this, as the

flat portion of the profile near the centerline has nearly vanished. For the 3 cm long tube, the velocity profile

within 2 mm of the tube centerline is flat, closely approximating the one dimensional assumption made in the

flame models. Thus, the degree of flatness in the radial profile can be varied by the length of the tube .. The

optimal tube length depends on several factors including gas properties, temperature, and most importantly flow

rate.

Converging nozzles are also used to generate flat radial profiles. However, the flat radial profile for an

unopposed nozzle is affected by the presence of an opposing nozzle. Figure 3 presents the axial velocity across

the nozzle exit for flow between two opposed converging nozzles. The contour of the nozzles is that specified

by Rolon [2] and is described by an exponential curve. The opposed flows are presented for five strain rates, a,

defmed as the maximum axial velocity gradient in the streamwise direction. For higher flow velocities, a higher

pressure area develops along the centerline at the stagnation plane, causing an axial velocity depression

transverse to the flow. This results in the "M" or "w" shaped profiles seen in Figure 3. Such profiles were

observed experimentally by Rolon [2] at similar strain values. This same nozzle produces an extremely flat

profile in isolation.

The same phenomenon that causes the dip in the profile for the opposed converging nozzles will tend to

flatten out the curvature trom viscous effects seen in an unopposed straight tube. Thus, in order to achieve a flat

profile near the flame zone, the exit radial profile for the isolated burner must lie somewhere between that of a

fully developed parabolic flow and that of a nozzle designed to yield a completely flat profile. Computational

determination of the optimum nozzle shape is an inverse problem, one that is not easily solved. Calculations

with various contours suggest that a cubic or fourth order curve does a better job at producing flatter radial

profiles for opposed flow conditions. Calculations are continuing to address this issue as well as to predict the

results of Figure 2 for opposed tubes.

The choice of the optimum counter flow burner design depends on several parameters including choice

of fuel and oxidizer, strain rate range of interest and whether one will be using powders or liquid aerosols in

either flow. Straight tubes with movable flow straighteners are much easier to build than a converging nozzle,

although flow straighteners complicate the introduction of aerosols. The structures imposed on the profile due

to individual screen openings must also be considered. However, the possibility of producing flatter velocity

profiles over a larger range of strain rates by varying the lengths of straight tubes ·will have clear advantages.

CONCLUSIONS

It has been shown that CFD can provide valuable insight into the flow physics of counter flow diffusion

flame burners. Although no combustion is modeled here, many CFD software packages have the ability to

tackle both the flow geometry and the chemistry (e.g., PHOENICS 3.1).
These results can serve as a starting point for those interested in designing an opposed flow burner that

provides a one dimensional flow field more amenable to one dimensional flame models. For a given burner

design, the radial velocity profiles will be very different depending on flow velocity, tube separation, length, and

burner shape. It is possible to obtain a relatively flat radial velocity profile although this can only strictly be

accomplished at a specific flow velocity and tube separation. Either straight tubes, converging nozzles, or

variable length sections of straight tubes have the potential of being able to extend the range of strain that could

be studied while maintaining some aspect of one dimensionality.

ACKNOWLEDGEMENTS

This research is sponsored by the Department of Defense's Next Generation Fire Suppression

Technology Program funded by the DoD Strategic Environmental Research and Development Program. The

authors would like to thank Will Gorton and Mike Kozma for their assistance ..

REFERENCES

[1]. OPPDIF: A Fortran Program for Computing Opposed-Flow Diffusion Flames", SANDIA Report SAND96-

8243, UC-1409, May 1997.

[2]. "Counter Jet Stagnation Flows", J.c. Rolon, D. Veynante, and J.P. Martin, Exp. in Fluids, 11, 313-324

(1991).

[3]. FLEXPDE: Finite Element Analysis for Partial Differential Equations, SPDE, Inc., Fremont, CA (1995)

[4]. PHOENICS, Version 1.6, Concentration Heat and Momentum, Limited (CHAM), Bakery House, London,

(1992).

Figure 1: Axial Velocity V5. Radial Position

for a Single 50 cm Tube

70 1-"""""""" """""" I" ""'" I""'" ,. '-

I ",) I I· I \ I I ,I, I I I I I I I I I, II I '

2 4

Radial Distance (mm)

,

0(10

o.L

o

o

o

8

b

6

LDA Data

Phoenics

Calculation

•

o

65 i60 f=.

~

~ 55 t

E .

<.> '-

z: 50 ~

~ F ~ 45 r co ~

Lo~35

f- 30 ~ != 25L.
Figure 2: Phoenics Calculations for a Single Tube of

Axial Velocity vs Radius for Varying Tube Lengths

0.8 "1

•••• L=IO em •••

oooooo~~ 0 L=5 em

ooooooooS8G 0 L=3em 00

6e

66

6

e

e

o

0.6

- --(/) g

>-

0.4 - >'0Q)0

.~

0.2

x

<{

:: J

o 2 3 4

Radius (mm)

5

1

6

Rgure 3: f\.Jc:maizedAxial Velodty at Tube Exit

\IS Radial Positim fa- Spedfied Strain Rates, a·

Fa- T\M) QJpJsed Converging f\bzzIes

1.2 ~ Q Q i 0 , 22.~ .0

~ 2 2 2 v t

.z-. to ••• • , t i i ••• v '8~ 0.8 • • •

• • v 0 

• • 

a = 11.0 S~11I • •

• v

a = 34.1 s .

~ : • a = 62.0 S-1 I • v

0

a = 00.5 S·1

•

a= 124s·1 I

.,

0.0

0.426 1.00.8

Radial PJSition (y/R)