Nivel de conocimiento que tiene el docente en el ámbito del liderazgo y

tiny quantities of cool gas in the measurement volume when using CARS.

This point is elucidated further in section 4.3.2.

Figure 4.13: Standard deviation and phase-averaged temperature shown for a phase angle of 90^o along with sample temperature histograms.

Here, it is seen that regions of relatively high standard deviation correspond to lower temperatures in contrast to the region of burned gases close to the bluff body with standard deviations to within ~100 K. The large values of standard deviation are thought to stem from the flickering of the flamefront from measurement shot-to-shot over the phase-average, as discussed earlier in relation to Fig. 4.12. Owing to the combination of a large temperature gradient present at the flamefront and the instability in its position, any series of temperature measurements taken close to the flamefront would show a

larger distribution of temperature. These measured temperatures do not necessarily represent accurately the phase-averaged temperature using the non-linear CARS technique.

CARS results show a much cooler region in the top left of the images, which is far from agreement with URANS and OH PLIF. The relatively cool region is considered to be an artefact due to the lack of spatial resolution in the CARS experiments. When the volume is too large it poses a problem when zones with temperature gradients are probed. This is particularly the case for probed position (c) in Fig. 4.13, whereupon the flamebrush curls round to this position. Figure 4.13 also shows histograms of temperature derived from instantaneous CARS spectra for points (a), (b) and (c) within the maps of Fig.

4.13, where it is clear that point (c) is not Gaussian unlike (a). The combination of low spatial resolution and the non-linear nature of CARS leads to a distorted histogram. This results from the combination of spectra from the pockets of cool and hot gases within the measurement volume, which yields a ‘mixed’ spectrum. Due to the squared relationship between CARS signal intensity and nitrogen density, cold spectral contributions significantly outweigh the weaker hot spectra. This leads to biasing towards cooler temperatures, and hence towards a larger spread in the distribution of temperatures and a negative skew from what would otherwise be a Gaussian distribution (Chen and Bilger 2002; Guo et al. 2003).

To resolve the problem of spatial resolution, attempts to correct for the biasing inherent in mixed CARS spectra have been investigated before (Boquillon et al. 1988; Shepherd et al. 1990; Thumann et al. 1995;

Parameswaran and Snelling 1996; Seeger et al. 2006). This involves taking the difference between the measured and true-averaged temperature within the CARS measurement volume. Figure 4.14 shows three plots of temperature of measurement volume versus proportion of hot and cold gas, at Tmax and Tmin

respectively. For each pair of plots, the dashed and solid lines represent respectively the averaged- and CARS measured temperature.

Figure 4.14: Thermodynamic temperature, Tth, and CARS temperature, TCARS, versus α, the fraction of hot gas in the probe volume, for three pairs of high- and low-temperature values (adapted from Boquillon et al. 1988).

The averaged-temperature is computed from considering that the gases contained in the measurement volume are a homogeneous mixture of the hot and cold gases; this is known as the thermodynamic temperature, Tth

(Boquillon et al. 1988). CARS measured temperatures are derived from the fitting of theoretical spectra for homogeneous samples to mixed spectra of varying proportions of hot gas, α; this yields the curve as shown by the solid lines. The mixed spectra can be derived theoretically by considering the signal contributions from the two pockets of hot and cold gas, at Tmin and Tmax, to the

α^∗

T2

T1

overall signal. By fitting theoretical spectra for homogeneous samples to the theoretically derived mixed spectra for different compositions α, the solid-lined curves are generated, as shown in Fig. 4.14. This allows the correction to be made for the biasing present in the measured temperature towards the cold pockets in the measurement volume. The correction is made by inferring the temperature T1 from the fit to an experimentally obtained mixed spectrum, then reading the corresponding hot gas proportion, α^*, on Fig. 4.14, thus allowing the real averaged-temperature to be read as T2.

However, this method is not free from problems, which is attributable to the limited range of α values that can be used in correcting temperature. Due to the flat part of the curve for the CARS temperature (solid curve in Fig. 4.14), the precision in the corrected temperature, T2 is significantly reduced by the very large sensitivity of the change of α to any imprecision in the measured temperature from the mixed spectra, T1. The flatness of the curve for low values of α becomes more prominent with a lowering of the cold pocket temperature, Tmin, thus limiting the range over which temperatures can be corrected for α in excess of 0.5. Furthermore, the technique above relies on the division of the measurement volume into two distinct temperatures, Tmin

and Tmax, which assumes that the flamefront sharply demarcates the two proportions in the measurement volume, usually at room and the adiabatic flame temperature. However, in reality a series of temperatures would exist within the measurement volume for turbulent flames. This further complicates the correction for biasing originating from the non-linearity of the CARS technique. Therefore, in light of the two aspects of this method, it was deemed

impractical to apply correction, and hence improve the resolution of the measured temperature at the flamefront.