INTRODUCTION

From the indium spectra the temperature can be computed. Temperature was measured along the vertical central axis of the steady, laminar flame at several points. Figure 5.5 shows the height scan for flames A and B (see Table 5.1) at two different equivalence ratios under identical pressures. The smoothness of the temperature profiles demonstrate the excellent precision that is made possible by the use of a rotary chopper and averaging over 50 spectra (see section 5.3.3 for an account of precision). Nevertheless, the smoothness of the profile does not indicate levels of accuracy within the temperature values. An account of potential sources of systematic error is also treated in section 5.3.3.

800 1000 1200 1400 1600 1800

0 5 10 15 20 25 30 35 40

Height above burner (mm)

Temperature (K)

phi=2.05 phi=2.32

Figure 5.5: Temperature profiles for flames A and B at different values of equivalence ratio at a fixed pressure of 26.7 kPa.

The profiles above clearly show a consistent drop in temperature with height in the burned gases. There is an approximate drop of 200 K over a height change of 30 mm in the burned gases for both cases. This is markedly different to the case of stoichiometric premixed laminar flames where there can be very little change in temperature over 30 mm, and even a slight increase in temperature in the burnt gases after the reaction zone (Chen and Mansour 1996) due to the oxidation of CO. The temperature decrease in our flames is attributable to low pressure and the sooting conditions. Low pressure increases the thermal diffusivity, α, according to: α ∝1 P_{, and} hence increases the rate of thermal diffusion to the surroundings. This increases the rate of heat loss in the burned gases, and hence the temperature decreases at a faster rate with height from the burner. The presence of soot in the burned gases also contributes to the increased cooling of the gases, owing

to the thermal radiation from the soot particles to the surroundings. With the trends in the temperature of the burned gases and the abovementioned thermal effects, the results seem to be qualitatively accurate. Furthermore, the temperatures of the above flames are plausible with respect to the adiabatic flame temperature of the two flames of 2400 K and 2150 K at equivalence ratios of 2.05 and 2.32 respectively (Kee et al. 1985). These values are in excess of the peak temperatures in each of the height profiles. Again, this is expected, due to the appreciable heat loss caused by the low pressure and sooting conditions.

It is also clear that the temperatures for the richer flame are lower, as shown by the vertical offset of the profile relative to the leaner flame in Fig. 5.5. This is expected due to the larger deviation of the richer flame from stoichiometry.

A larger soot loading in richer flames further contributes to the cooling of the flame. Additionally, a horizontal offset exists between the two temperature profiles in Fig. 5.5. This is due to the richer flame adopting a position that is higher relative to the burner’s surface. It is believed that this is caused by the lower flame speed of the richer flame in conjunction with the diverging flow pattern of the unburned gases. The divergent flow pattern is caused by the expansion of the unburned gases upon entering the low pressure combustion chamber. Since the flow pattern is divergent, the local gas speed decreases with an increase in height. The increase in height of the flamefront is therefore due to the adoption of a new equilibrium between the lower flame speed and the corresponding lower unburned gas speed. The offset can also be confirmed by the acquisition of OH LIF data within the same flames. This is shown by the OH LIF profiles of the flame in Fig. 5.6. The data were

generated by using a tuneable dye laser by I.S. Burns during the same experimental campaign. The 1 mm offset of the OH profiles are consistent with that of the temperature profiles in Fig. 5.5. This provides further evidence in support of the validity of the temperature profiles.

Figure 5.6: Profiles of OH LIF in flames A and B of Fig. 5.5. (adapted from I.S. Burns)

1 mm offset

Temperature measurements were also made in the richer flame (φ = 2.32) at three different pressures; the profiles are shown in Fig. 5.7.

800 1000 1200 1400 1600 1800

0 5 10 15 20 25 30 35 40

Height above burner (mm)

Temperature (K)

P=26.7 kPa P=21.3 kPa P=18.7 kPa

Figure 5.7: Temperature profiles for flames B, C and D at different values of pressure at a fixed equivalence ratio of 2.32.

For the pressures investigated, it appears that there is hardly any change in the temperature profiles. This apparent independence of temperature is surprising in spite of the variation in soot concentration for the range of pressures studied. The soot concentration had been investigated previously using Laser Induced Incandescence (LII) calibrated with Cavity Ring-Down Spectroscopy (CRDS) (Desgroux et al. 2008). They observed that an increase in pressure from 21.3 to 26.7 kPa induces an order of magnitude increase in soot volume fraction. In spite of this massive increase, there is no observable change in temperature between the two pressures. This suggests that the surprisingly strong dependence of soot volume fraction on pressure does not appear to be

mediated by an effect of pressure on the flame temperature at the conditions studied here.

5.3.3 Potential Sources of Error

Thus far, we have demonstrated the use of indium TLAF in low pressure sooting flames and have shown qualitatively that the fidelity of the measured temperatures is superior in light of the expected trends and smoothness of the temperature profiles. However, a treatment of the accuracy for the laminar flames investigated here is necessary to determine whether indium TLAF can provide useful data for quantitative studies (e.g. validation of flame-chemistry models, as in this study of a low pressure burner). Two main sources of systematic error have been identified. One of which is the black-body thermopile powermeter used to calibrate the laser power recorded on the photodiodes. The powermeter could introduce a percentage error in temperature of up to 1.7 % at 1850 K. This error is conservative and is based on the full range of zero-error of the meter based on the smallest division of the reading; see appendix C for details. The other main error source is the potential for misalignment of the two laser beams. The worse case scenario is where the beams would be misaligned in the vertical direction, in which the temperature gradient is greatest. It was estimated that this could introduce an error of up to ~1 % with a misalignment of 20 µm; see appendix C. This potential for systematic error is greatest at the steep flank of the temperature gradient, however for the burned gases it dramatically drops to about ~0.1 %, where the error from the powermeter would then dominate.

Other sources of systematic error were considered and discovered to be of minor importance, for example, Mie scattering from the soot particles. This occurs as a result of detecting resonance fluorescence at 451 nm, where there is a susceptibility to detecting scattered radiation from the 451 nm laser. An upper estimate for the systematic error in these experiments due to scattering is ~ 0.3 %. This is based on the most fuel-rich flame at a measurement point with the greatest soot volume fraction, xsoot = 1 ppbv (Desgroux et al. 2008).

This corresponds to flame B at a pressure of 26.7 kPa, φ = 2.32, a measurement point of 40 mm above the burner with a temperature of 1630 K;

see appendix C for details. Furthermore, potential error can originate from absorption of the laser beam. As the beam propagates through the seeded flame, the beam power is increasingly attenuated. This would introduce error when normalising the signal by the laser power recorded by the photodiode placed upstream of the measurement volume. To overcome this problem, a photodiode was placed after the flame, as shown in Fig. 5.2, so that the level of beam attenuation could be quantified. Due to the axisymmetry of the flame, the absorbance of the beam at the measurement volume is half of the value across the entire flame. This allows the signal to be normalised by the correct incident laser power at the measurement volume. However, in our experiments the difference between the temperatures with and without this correction is small at ~ 0.2 % at 1800 K with a peak absorption of up to 3 %.

With this level of attenuation at 3 %, it is therefore possible to neglect the correction for absorption. This is beneficial when measuring temperature in flames that are not axisymmetric or are fluctuating in time, where the laser power at the measurement volume cannot be deduced. On top of the estimates of systematic error been made thus far, a typical standard error exists at ~ 0.2