B URNING V ELOCITY
2.5. FLAME STABILIZATION
heat to the incoming gaseous reactants. Stable, lean limit combustion of CH4–air mixtures was observed down tof¼0:28.
With regard to the filtrational combustion of Figure 2.17(iii), combustion within porous inert media has been reviewed by Howell et al. (1996). Different regimes of flame propagation have been identified by Babkin (1993). A flame established in a tube filled with an inert, porous medium, through which a homogeneous mixture flows, can move either with, or against, the direction of flow. Figure 2.20 shows temperature profiles in the gas and the solid porous medium in alow velocity regime. Heat conducts through the porous medium in the direction upstream from the flame and this heats the cooler flowing mixture. Sufficient heat is transferred to initiate reaction in the gas. As a result, this becomes hotter than the solid, but cools as it transfers heat to it. The high thermal conductivity of the solid effectively conducts sufficient heat from hot gases to cold reactants. The porous medium acts as a recuperator, transferring heat from hot gas to cold reactants, in a not-dissimilar fashion to what occurs in the Swiss roll and the spouted bed burners. Hsuet al. (1993) were able to burn CH4-air down tof¼0:41 in a porous ceramic burner.
With increasing pore size there is a transition to ahigh velocity regimeof the reaction front, with reduced thermal coupling of gas and solid in the reaction zone and no heat recuperation. There is an increasing dominance of aerodynamic and turbulence effects.
A pressure wave builds up in front of the combustion zone and asonic velocity regimeis entered, with a sudden jump in the reaction wave velocity. Finally, there is a transition to a low velocity, subsonic detonation, which evolves spontaneously from deflagrative combustion (Brailovsky and Sivashinsky, 2000).
might proscribe near-stoichiometric burning, but flash-back is still possible with lean premixtures. In laminar flow, flash-back occurs when the burning velocity is greater than the low flow velocity adjacent to the wall of the tube, along which the reactants flow. Prevention requires that the laminar burning velocity be reduced at the wall.
This is achieved by a combination of heat loss to the tube and, for positive Markstein numbers, flame stretch at the wall. Close to the wall, velocity gradients are in the region of 102103 s 1(Berlad and Potter, 1957; Lewis and von Elbe, 1987). These values are comparable to the values of flame extinction stretch rates in Figure 2.2. For high velocity turbulent flow of a flammable mixture along a flat surface, flash-back of a turbulent flame is improbable in the outer region of the flow, as the flow velocity will always exceed the burning velocity. Close to the surface, within the viscous sub-layer, velocity gradients are generally sufficiently high to quench the flame and prevent flash- back (Bradley, 2004).
The stability and overall high volumetric intensity of turbulent combustion in gas turbine and furnace combustion chambers depend upon the patterns of gas recirculation that mix burning and burned gas with the incoming reactants. Computational fluid dynamics is clearly a powerful design tool in this context. Bradleyet al. (1998b) have described a computational and experimental study in which a swirling, turbulent pre- mixture of CH4-air flowed from a burner tube, with a stepped increase in internal diameter, into a cylindrical flame tube at atmospheric pressure. The step generated an outer recirculation zone at the corner, shown by the computed streamlines in Figure 2.21c. A matrix of small diameter hypodermic tubes housed within a cylindrical burner tube rotating at 54 000 rpm produced the swirl. This generated a radially outward cold gas flow and an inward hot gas flow to create a central recirculation zone. The mean axial entry velocity and the swirl number were maintained constant and the equivalence ratio was varied. Computed parameters were obtained from a Reynolds stress, stretched laminar flamelet model.
The computed concentration of NO in the gases leaving the 300 mm long, silica glass flame tube of 39.2 mm diameter, decreased from 20 ppm at f¼0:75 to 2 ppm at f¼0:56. At this lowest attainable value off, the NO was almost entirely created as
“prompt”NO in the flame front, the temperature being too low along the tube for much production of thermal NO. Shown in Figures 2.21 and 2.22 underneath (a) self- luminescent photographs of the flames are computed contours within the flame tube of (b) mean volumetric heat release rate, (c) streamlines, (d) mean temperatures, and (e) Karlovitz stretch factor, K. For both sets of contours, the swirl number was 0.72 and the mean axial entry velocity to the flame tube was 10 m/s. Figure 2.21 shows conditions forf¼0:59 and Figure 2.22 forf¼0:56. In both cases, the outer, corner, doughnut-like recirculation zone was created by the sudden step, and the inner one, with reverse flow along the center line, was created by the swirl. The reverse flow recircu- lated hot gas into the incoming reactants.
In Figure 2.21, high values of K marginally inhibited combustion close to the corners. With a slightly higher value of f, the value ofK was halved in this region and a more compact flame was generated, with heat release close to the end face and tube walls. At this value off, small changes in velocity and fcaused experimental flame extinctions and re-ignitions. The corresponding fluctuations in heat release rate generated pressure oscillations. These could amplify due to resonances with the natural acoustic wavelengths of the tube and Rayleigh–Taylor instabilities. The combination of the streamline flow pattern and the contours ofK, with flame extinctions at the higher
values, determined the location of the flame. At the lower value off¼0:56, Figure 2.22 shows how the higher upstream values ofKcaused the flame to move downstream, where a V-flame anchored precariously between the two stagnation-saddle points. As the mixture was leaned off further, the leading edge of the flame moved towards the downstream stagnation-saddle point. The flame was very unstable, with small changes in velocity orfcausing it to fluctuate with periodic extinctions and re-ignitions, and eventually blew off.
(a) self-luminescent flame photograph
(b) mean heat release rate (MW/m3)
(c) streamlines
(d) mean temperature (K)
(e) Karlovitz stretch factor
x (mm)
r (mm)r (mm)r (mm)r (mm)
10 0
−10 10 0
−10 10 0
−10 10 0
−10
0 10 20 30 40 50 60 70 80 90 100 110 120 130 140 150 160 3.00
2.00 1.50 1.00 0.75 0.50 0.30
450 550 700 900 1100 1300 1500 10 20 30 40 50
Figure 2.21 Swirling, pre-mixed CH4-air flame forf 0:59: (a) flame photograph, (b) contours of heat release rate, (c) streamlines, (d) mean temperature, and (e) Karlovitz stretch factor (Bradleyet al., 1998).
De Zilwaet al. (2002) also have shown how extinctions and oscillations are related to stabilization. Candel (1992) has reviewed combustion oscillations arising from the coupling of flame fluctuations with acoustic waves and described how actively perturb- ing combustion parameters can control and suppress instabilities. An example of this is the active control system of Evesqueet al. (2002), in which fuel was injected unsteadily to alter the heat release rate in response to an input signal triggered by the oscillations.
(a) self-luminescent flame photograph
(b) mean heat release rate (MW/m3)
(c) streamlines
(d) mean temperature (K)
(e) Karlovitz stretch factor
x (mm)
r (mm)r (mm)r (mm)r (mm)
10 0
−10 10 0
−10 10 0
−10 10 0
−10
0 10 20 30 40 50 60 70 80 90 100 110 120 130 140 150 160 5.0
3.0 2.5 2.0 1.5 1.0 0.6 0.4
450 550 700 900 1100 1300 1500 10 15 20 25 30
Figure 2.22 Swirling, pre-mixed CH4-air flame forf 0:56: (a) flame photograph, (b) contours of heat release rate, (c) streamlines, (d) mean temperature, and (e) Karlovitz stretch factor (Bradleyet al., 1998).
Another technique is to inject fuel locally into regions of highK. Some of these issues are discussed in Chapter 7.
Upstream of a combustion chamber, if the residence time of a premixture at an elevated temperature is greater than ti, autoignition will occur. Temperatures and pressures, and hence ti, may not be constant, in which case autoignition will occur when the Livengood and Wu (1955) integral
ðt
0
dt ti
(2:19) attains a value of unity. This becomes more probable when recirculation zones are created, within which the reactants might have an increased residence time.
With regard to the lift-off and stability of non-premixed fuel jet flames in still air, the underlying mechanism for the lift-off has been described in Section 2.1. If the jet velocity increases, the flame lifts further from the burner tube, until eventually it blows-off. Dimensionless correlations of lift-off heights and blow-off velocities have been developed that summarize the results of both computations and experiments (Bradleyet al., 1998a). Surrounding a fuel jet with hot recirculated gases with added air enables very lean mixtures to be burned. The high strain rate that otherwise inhibits combustion and the enhanced mixing at the base of the lifted flame contribute to flame stability. This system is characterized as a fuel jet in hot co-flow. With hot co-flows at 1300 K and as little as 3% oxygen by mass, Dallyet al. (2002) measured temperature increases due to combustion, which were as low as 100 K. Concentrations of NO were less than 5 ppm and were fairly uniformly dispersed. Combustion was governed by low temperature chemical kinetics, rather than the high temperature kinetics associated with a propagating flame.