RANS Study of Hydrogen-Air Turbulent Non-Premixed Flames

D. Dovizio1, E. Giacomazzi

2, C. Bruno

1, A. Ingenito

1, N. Arcidiacono

2

1. Univ. "Sapienza", Dept. Mechanics and Aeronautics , Rome - ITALY

2. ENEA, TER-ENE-IMP, Rome, ITALY

1. Test case description

The coaxial air nozzle is concentric to the fuel nozzle, and the inner (da) and the outer

diameter are 30 and 38 mm, respectively. The coaxial air is injected parallel to the fuel jet. In

addition, coflow air is provided to the flame to keep the global equivalence ratio within a

certain range. The velocity of the coflow air is kept low enough not to affect flame

characteristics [1-2]. Flame stabilization is obtained by the thickness t of the hydrogen duct, t

= 5 mm. The fuel is hydrogen, flowing in the central duct, while the primary air stream flows

inside the annular duct: the two jets are ducted for 40mm prior to entering the combustion

chamber.

Fig. 1 Coaxial combustor schematic section.

Three simulations were performed, corresponding to three different injection velocities of the

fuel and oxidizer streams: 25, 50 and 106 m/s for the hydrogen stream and 10.6, 17.7 and 28.3

m/s for the air stream respectively. Buoyancy effects were studied by simulating each of these

cases with and without gravity force. The Reynolds number is always larger than 2000

(turbulent flow).

The turbulence model adopted is the standard K- model [3]. The combustion model is based

on a mixture fraction approach (ZH is the elemental mass fraction) and on an assumed-shape

probability density function (PDF) approach. A turbulent non premixed combustion diagram

was used to determine the combustion regime. The values of Ret are of the order of 102,

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while Da is of the order of 103: the laminar flamelet assumption (LFA) limit is justified for

the present study, offering tremendous computational savings.

2. Flame structure

In the flamelet approach the flame structure is described using the mixture fraction [4]. The

computed flame structure is plotted in Figure 2. This result underlines that in the flamelet

approach finite rate chemistry can be taken into account. Diffusion flame usually lies along

the points where mixing produces a stoichiometric mixture. ZH = Zst iso-surfaces give an idea

of the flame shape as shown in Figure 3.

Fig. 2 Temperature versus ZH plot defining flame structure (UH2=106m/s with gravity).

Fig. 3 Stoichiometric mixture fraction iso-surface defining flame shape. 1 UH2=25m/s with

gravity, 2 UH2=25m/s without gravity; 3 UH2=50m/s with gravity; 4 UH2=50m/s

without gravity; 5 UH2=106m/s with gravity; 6 UH2=106m/s without gravity.

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Ischia, June, 27-30 - 2010

Figure 3 shows results performed with URANS simulations for the three different injection

velocities configurations. For each of them gravity effect was considered by comparing

simulations with the gravity force included (on the left of each couple) and not (on the right).

These first results can be summarized with three mean features:

flame length increases when the inlet velocity increases,

gravity field makes the flame shorter,

but this effect is more evident for low injection velocities.

Physics interpretation of this behavior can be found recalling Froude number definition and

considering that increasing inlet velocity means increasing initial momentum flux with

respect to buoyant forces (i.e. Froude number): flame length (associated with the momentum

flux) increases. The second feature can be interpreted intuitively: gravity force acts opposing

to the flow motion and the flame is strongly affected due to the low hydrogen density value.

4. Temperature and velocity fields

Thermal field analysis, predicted by URANS simulations, show a well anchored flame with

the combustion initially limited to the thin shear layer where hydrogen and air mix. A cold

zone (blue depicted) can be identified, where only fuel exists and is generally called inertial or

potential core. Maximum temperature is reached on the axis, on a location increasing as

velocity injection increases. Buoyancy effects are evidenced by the presence of external

vortices at low axial locations. Fig. 6 shows instantaneous temperature fields comparing the

case with gravity force included with the one in absence of gravity.

Fig. 4 Instantaneous temperature fields for the three different cases: on the left is depicted

the case with .

5. Flame – vortex interaction

An instantaneous iso-temperature color visualization of the computed flame (UH2 = 106 m/s, no

gravity) is shown in Fig. 5a. It should be pointed out that no artificial perturbations were intro-

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duced to generate buoyancy-driven structures external to the flame. Once a vortex is developed it

rolls along the flame surface while it is convected downstream. During this process, the vortex

interacts strongly with the flame, making the flame surface bulge and squeeze. This motion is

simulated by the time-dependent calculations.

Fig. 5 Comparison of computed hydrogen/air flames for fuel-jet velocity of 106 m/s: (a)

instantaneous temperature contours of computed flame; (b) iso-temperature contours

obtained from time-averaged flame; (c) iso-temperature contours of steady-state

flame.

Since the mean temperature reflects the time the flame spends at a given location, the

presence of the first bulge indicates that the flame spends considerable time in the bulged

position at an axial location between 110 and 140 mm. The isotherms in the interior of the jet

(r < 5 mm) are only moderately affected by the dynamic motion of the outer structures, as

evidenced by the similarity of the instantaneous (Fig. 5a) and averaged (Fig. 5b) isotherms.

To illustrate the importance of simulating the dynamic flames using unsteady CFD codes,

calculations were also performed for the same flame using the steady-state option of

FLUENT. Solution for this case converged to a flame having perfectly smooth surface. The

iso-temperature visualization of the resulted flame is shown in Fig. 5c, which does not

resemble either the instantaneous flame (Fig. 5a) or time-averaged flame (Fig. 5b).

Fig. 6 Impact of outer and inner vortices on temperature for the flame shown in Fig. 5.

Blowups of the two different vortex-flame interactions are shown insets.

Vortex-flame interactions result in the presence of two types of vortices: one located on the

fuel side of the flame and the other on the air side. Both types of vortices create positive

(stretch) and negative (compression) stretch regions when interacting with the flame, as

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Ischia, June, 27-30 - 2010

shown in Fig. 6. The outer vortex-flame interaction is shown in the left insert, and the fuel

side vortex-flame interaction is shown on the right. Vortices are more evident in the iso-

radial-velocities contours of Fig. 7: red and blue colors represent positive (outward) and

negative (inward) radial velocities, respectively.

Fig. 7 Instantaneous radial velocity fields in the first part of the combustor for

: on the left is depicted the case with

Vortices motion are time dependent. Frequency spectra from the temperature fluctuations

(measured on a single point in the domain, x=10cm; y=0.95cm) are obtained using FFT

method. Figure 8 shows frequency spectra obtained from temperature data collected at a

radial location of 9.5 mm within the shear-layer at a distance of 100 mm from the nozzle exit.

The data, stored from 60000 time-steps, covered a real time of 0.6 s. We can distinguish two

peaks over a frequency range between 0 to 1000 Hz. The one at 273.9 Hz corresponds to the

fundamental frequency, and the subharmonic of this (547.8 Hz) appears as the second peak.

The frequency of the highest peak can be compared with a dimensional analysis that defines a

frequency as the ratio of mean velocity and characteristic length of the vortices:

(1)

where Lv is the distance between two consecutive vortices. Vortex frequency value is very

close to the peak obtained from the FFT and displayed on Fig. 10. Physically this

phenomenon can be explained considering turbulent fluctuations as different spatial and

temporal scales vortical structure overlap. When these move inwards the fluid they induce a

perturbation on the characteristic scalars.

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Fig. 8 Frequency spectra obtained from temperature measured on a single point into the

domain ( ): , with gravity effects.

6. Conclusions

RANS and URANS simulations were performed for a turbulent jet diffusion flame. Buoyancy

effects were demonstrated by comparing temperature fields for cases with and without gravity

force included for different injection velocities. This analysis shows that buoyancy effects are

less evident for high injection velocities. Finally URANS simulations showed that in certain

cases transient phenomena such as flame vortex interactions can be predicted.

7. References

[1] J.F. Driscoll, R.H. Chen, and Y. Yoon: Combust. Flame 88:37-49, 1992.

[2] J.-Y. Chen and W. Kollmann: Combust. and flame 88, 1992.

[3] B.E. Launder and D.B. Spalding: Lectures in Mathematical Models of Turbulence.

London: academic Press., 1972.

[4] T. Poinsot and D. Veynante, Theoretical and numerical combustion, Edwards, 2005.

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