Many practical combustion systems such as residential gas burners contain dense groupings or clusters of jet flames with sufficiently small spacing between them, which causes flame interaction. The interaction effect, due in part to Oxygen deficiency in the interstitial space between the flames, causes the spreading of flames, which may merge together to form larger group flames. This interactive effect is studied analytically by revisiting the laminar isolated flame theory for 2D jets, for which similarity solutions are readily available in compressible form, and symmetrical interaction zones can be observed. Flame characteristics were studied by obtaining analytical expressions for flame specific parameters such as height and width, lift-off height and blow-off velocity, air entrainment and mixing layer growth. The theory for multiple interacting jets describes an approximate criterion for interburner spacing at which flame interaction and group flame formation are first observed. The analytical framework presented in this paper presented in this paper produced results which were compared with experimental measurements. The experimental apparatus allowed the interburner spacing to be varied from 7.87 mm to 50.8 mm, and measurements of flame height, width, lift-off height and group-flame formation under interactive modes. Images of the evolving flow field were taken and Schlieren images of the multiple 2D jets were also recorded using a digital camera.
In order to study the stability and combustion behavior of interacting jet diffusion flames, laminar single flame stability theory must be developed for a burner and extended to include the effect of multiple burners. In this current work, a stability theory for jets is introduced and the appropriate generalized conservation equations for momentum, species, and energy for 2D compressible systems with boundary conditions are presented. The governing equations are solved to give explicit solutions for axial and radial gas velocities, flame height, maximum flame width and its axial location, amount of air entrainment, lift-off height and blow-off velocity as a function of injection Reynolds number (
Some of the relevant endeavors are summarized here. Van quickenborne and Van Tiggelen [
The above studies focused on circular burners. However, 2D jets where (
Burner configurations.
2D jet geometry (
Top view of a linear array of 2D jets spaced at a distance
In light of the numerous practical applications of multiple burner arrays in industry and elsewhere, fundamental information regarding the factors governing flame interaction is required. The separation distance between individual burners in many combustion systems is often small enough to cause the flames to interact with one another resulting in a change of flame structure (such as greater flame length and width) and a change in stability characteristics of the flame (such as higher blow-off velocity). Multiple flame interaction also exhibits reduced NOx production [
Whereas literature regarding isolated jet flames is quite extensive (as discussed earlier), literature regarding stability characteristics of interacting multiple flames is scarce. One of the earliest studies of multiple flames was conducted by Putnam and Speich [
The primary objective of the current work is to describe the physics of the interactive processes between multiple 2D jets. Particular interest will be paid to the dependence of flame geometry (flame height, flame width, mixing layer growth, etc.) and stability characteristics (lift-off height and blow-off velocity) on interburner spacing,
Therefore, the current work is organized to present analytical models for isolated and multiple burner jets followed by experimental results for comparison with the models. A review of the conservation equations for an isolated 2D jet in compressible form, a presentation of flame stability theory in Section
For the pure mixing problem, the axial velocity
Profiles describing various aspects of the flame.
Profiles of axial velocity, fuel, and oxygen mass fraction for a 2D jet under mixing conditions. A qualitative illustration of the mass fraction of oxygen and fuel is shown
Expanded view of the combustible mixture tube
Four possible scenarios exist as shown in Figure
Qualitative illustrations of stoichiometric (solid) and flame speed (dashed) contours;
Unstable flame
Nozzle attached flame
Lifted flame
Partial flame
As will be explained in the upcoming discussion, Schmidt number plays a key role in defining the various possibilities shown in Figures
For the isolated 2D jet, the equations of mass, momentum, energy, and species were transformed from compressible form into incompressible form (Annamalai and Sibulkin, [
Summary of single, laminar jet results for 2D planar jet under non-buoyant conditions.
Row# | Parameter | 2D Jet | Remarks |
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1 | Properties | Variable | For 2D, |
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4 | Stretched coordinate |
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5 | Similarity Coordinate, |
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6 | Modified Similarity variable, |
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7 | Momentum equation in |
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8 | Species equation in |
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9 | Axial velocity |
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10 | Lateral velocity |
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11a | Mixing layer thickness, |
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Note mix layer varies as |
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11b | Jet half-width, |
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11c | Velocity contour |
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12 | Mass flow within or |
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Used for estimating the mass flow within |
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13 | Total mass flow |
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14 | Height at which two adjacent mixing layers intersect |
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Burners are located |
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15a | Air entrained at |
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15b | Air entrained |
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Buoyancy affects air entrained for 2D | ||
within interburner spacing/injected flow for which |
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15c | Air entrained at |
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16 | Species and non dimensional Shvab-Zeldovich, |
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17a | Height of Contours, |
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18 | Maximum width of flame, |
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19 | Ratio of flame height and max width |
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20 | Distance |
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22 | Flame angle with axis, |
tan |
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tan |
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tan |
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23 | Lift-off Height, |
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24 | Blow-off velocity |
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For variable density see Fay [
In order to determine the lift-off height and blow-off velocity of 2D jets, the mixing problem must be solved. By setting
and
Using the solution given in row 9 for axial velocity
Qualitative growth of the flame speed and stoichiometric contours with
Velocity contours for
Flame speed contour
Stoichiometric contour
Stoichiometric (dashed) and flame speed (solid) contour growths with increasing
The solution for
Equation (
The flame speed and stoichiometric contour growth, for a fixed
The Schmidt number (
If
For
From the above discussion, an explicit solution can be found for the lift-off height (or unignitable height) if
The flame height is nondimensionalized by the diameter (
Theoretical predictions for
The blow-off velocity can also be found from (
For application to multiple jets the growth of mixing layer and the ratio of amount air entrained by each jet to the amount of gas injected are very important since they affect oxygen concentration in the interstitial space between the burners. Setting
For a pure fuel jet, it was seen that as
Excess air variation at
Interactive processes within liquid drops and coal particle clouds have been dealt in earlier literature [
Based on this hypothesis, simple criteria for predicting the stages of interaction can be developed. First, consider Figure
Qualitative illustration of the effect of flame interaction: (a) isolated flames, (b) individual flames, (c) group flame, and (d) sheath flame.
When
When
When
Sheath combustion—all of the required air must come from the far field
The mass fraction of O2 available within the interstitial space between the flames is graphically illustrated in Figure
Oxygen profiles for (a) single flames and (b) multiple flames.
Isolated flame:
Individual flames:
As the spacing between the burners is reduced further (
Based on the qualitative observations illustrated in Figure
Note that
From (
In other words, the expansion of gases requires the interburner spacing to be at a larger distance to form an individual flame. Equation (
where
The following hypotheses are used in arriving at a criterion for group flame formation.
Following the group combustion literature [
As a second approximation, group flames will be assumed to form when the entrained air becomes insufficient to burn the fuel issuing from the central burner (Figure
Equation (
Non-dimensionalizing equation (
Using typical values of
The experimental apparatus shown in Figure
Experimental apparatus.
Figure
Ratio of maximum flame width to visible flame height as a function of injection
Two possibilities will be considered. First, the gases will be assumed incompressible (
Theoretical predictions follow the basic trend of experimental data showing that the ratio decreases as the injection
Calculated Froude number versus Reynolds number for isolated jet.
Froude number, |
0.167 | 0.283 | 0.383 | 0.489 | 0.537 |
Injection Reynolds number |
0.784 | 1.62 | 2.95 | 5.28 | 6.86 |
It can be observed from the table that buoyancy forces appear to be important (
Figure
Ratio of axial location of the maximum flame width to the visible flame height as a function of injection
As previously discussed in Section
Lift-off height for 85% N2-15% C3H8 by volume mixture,
The comparison between the laminar flame theory’s prediction of blow-off velocity (as given in row 24) and the experimental measurements of blow-off for a single 2D jet fired with N2-diluted mixtures of C3H8 is given in Figure
Blow-off velocity for nitrogen-diluted mixtures of C3H8.
Recently a test method was proposed to determine the degree of flammability of refrigerants [
The experimental apparatus shown in Figure
Figure
Ratio of multiple flame length to single flame length as a function of interburner spacing and injection velocity for 100% CH4 fuel.
As previously mentioned, as the interburner spacing decreases, the flames must widen and lengthen to obtain the necessary oxygen for combustion. This effect was qualitatively illustrated in Figure
Interaction stages with
Figure
Interburner spacing required for flame interaction and group flame formation as a function of injection velocity for 100% CH4 fuel.
Individual flames (as shown in Figure
Figure
Comparison of theoretical predictions (given in (4d), (5b), and (10c)) and experimentally observed interburner spacing nondimensionalized by the visible flame height of a single isolated jet for CH4 fuel.
A Schlieren system was used to study the interaction of multiple flames at various interburner spacings. Figure
Sequence of Schlieren images for 14.8 mL/min/burner of C3H8 (
As the spacing is reduced to 16 burner widths (12.7 mm) as shown in Figure
Since no lift-off was observed for CH4 (
Lift-off height for 85% N2 and 13% C3H8 mixture.
Comparison between the laminar flame theory’s prediction of blow-off velocity (as given in row 24) and the experimental measurements of blow-off in a linear array of three planar burners fired with N2-diluted mixtures of C3H8 is given in Figure
Blow-off velocity for nitrogen-diluted mixtures of C3H8.
Solutions for the compressible form of the governing equations of mass, momentum, energy, and species for a single 2D jet were solved to give explicit solutions for flame height and width, mixing layer growth, lift-off height, and blow-off velocity. A flame stability theory (lift-off, blow-off velocity, etc.) was offered based on two important parameters: the flame speed contour, giving the positions in space where the axial gas velocity equals the laminar flame speed and the stoichiometric contour giving the positions in space where fuel and air are in stoichiometric proportions. For fuels with Schmidt number was found to play a key role in flame stabilization processes. For Laminar flame theory predictions compared favorably with experimental data collected for a single 2D jet.
Laminar single flame theory was modified to include multiple burner effects to obtain simple expressions which predict the interburner spacing at which flame interaction begins and at which formation of group flames occurs. Four distinctive modes of flame interaction were identified: (a) isolated, (b) individual, (c) group, and (d) sheath. For a given burner geometry and combustible fuel properties, these modes were found to be a function of interburner spacing and injection Reynolds number. At low injection Reynolds numbers, flame interaction can cause flame flicker. Laminar isolated flame theory underpredicts the blow-off velocity in linear arrays of 2D burners by approximately 40% for interburner spacings from 64 to 16 burner widths.
The authors wish to acknowledge the partial financial support provided for this research by the Energy Resources Program of the State of Texas and Paul Pepper Professorship to one of the authors. The authors appreciate the assistance with the Schlieren imaging system provided by Prof. K. Kihm of Texas A&M University and the time and effort dedicated to the project by Daniel Snook of Auburn University.