Luminescence interference to two-colour toluene laser-induced fluorescence thermometry in a particle-laden flow

Abstract

We present the use of two-colour toluene planar laser-induced fluorescence (LIF) to obtain spatially resolved measurements of the gas temperature ($T_\mathrm{g}$) in a particle-laden turbulent flow under sufficiently dense particle loading that the interference from laser interactions with the particles is significant. The effect of the ratio of volumetric flow rates of the particle phase to the gas phase ($\phi$) on the accuracy and precision of two-colour toluene LIF thermometry was systematically investigated for three particle materials, alumina, zinc activated zinc oxide (ZnO:Zn) and polymethyl methacrylate (PMMA), each of which has differing interactions with the excitation laser. The PMMA particles were spherical and mono-disperse with diameters of 6 to $40\, \upmu \hbox {m}$, while the alumina and ZnO:Zn particles had diameters in the range 1–40  $\upmu \hbox {m}$ and 2–200 $\upmu \hbox {m},$ respectively. The results show that the accuracy of the gas temperature measurement is insensitive to particle size for the PMMA particles, but dependent on the instantaneous particle loading. Importantly, reliable measurements can be performed in the dense two-way coupling regime, with the measurement being accurate to within 5 °C for $\phi$ < $2.5\times 10^{-4}$ for the PMMA particles and for $\phi<$$7.6\times 10^{-4}$ for the alumina and ZnO:Zn particles.

Graphic abstract

Appendix

The accuracy of the two-colour thermometry is significantly influenced by the strength of the fluorescence signals relative to the noise, as shown in Fig. 9. In particular, because the temperature is inferred from the fluorescence intensity ratio rather than directly from the individual fluorescence intensities, the errors in temperature measurement can be particularly significant where the signal strength of the denominator term, in the present case the blue channel, is on the order of the noise strength. To reduce this effect, we employ two commonly used post-processing techniques – thresholding and smoothing. Here, we investigate the effect of these two technique on the prevalence of errors in the temperature measurement for a single image. To quantify the errors, we first calculate the difference between the measured and actual temperature, ${\varDelta T_\mathrm{dep}}$, on a pixel-by-pixel basis for the entire region of the image that is above the specified threshold. The mean ($\overline{\varDelta T_\mathrm{dep}}$) and standard deviation ($\sigma _{\varDelta T}$) of this ensemble were then calculated for the case where the jet is unheated, because the actual gas temperature is uniform and known for this case.

Figure 16 presents the effect of the threshold value, $\epsilon$, on both $\overline{\varDelta T_\mathrm{dep}}$ and $\sigma _{\varDelta T}$. The threshold is normalised by $I_\mathrm{base}$, which is the temporally and spatially averaged fluorescence intensity, within the region $-0.1 < r/D<$ 0.1, 0.5 $< x/D < 3$, where the toluene tracer is not mixed with the co-flow. The thresholding procedure was performed separately for each channel, such that the temperature at each pixel was only calculated if the intensity in both channels satisfy their respective threshold requirements. The values of $I_\mathrm{base}$ correspond to SNR = 38.4 and 19.6 for the blue and red channels, respectively. The results show that $\overline{\varDelta T_\mathrm{dep}}< 0.1$ °C for $\epsilon /I_\mathrm{base}>$ 7%, while $\sigma _{\varDelta T}$ reduces monotonically as $\epsilon /I_\mathrm{base}$ increases. While the errors in the measured temperature can be further reduced at larger $\epsilon$, this also reduces the number of usable data points in each image, particularly near to the jet edges (see Figs. 8 and 10). Therefore, as a compromise, a threshold value of $\epsilon /I_{base}$ of 10% was used for the present investigation. This resulted in pixels with SNR $\le$ 3.84 or 1.96 for the blue and red channels, respectively, being excluded from the temperature measurement.

Fig. 16

Effect of threshold magnitude ($\epsilon$) as a percentage of $I_\mathrm{base}$ on the mean temperature error and corresponding standard deviation ($\overline{\varDelta T_\mathrm{dep}}$ and $\sigma _{\varDelta T}$) for two-colour LIF measurements in an unheated jet without particles

Figure 17 presents the influence of smoothing kernel size, N, on ($\overline{\varDelta T_\mathrm{dep}}$) and ($\sigma _{\varDelta T}$). Here, the smoothing kernel applied to the instantaneous temperature measurements is a $N\times N$ pixel mean filter. Pixels below the $\epsilon /I_\mathrm{base}$ threshold were excluded from the smoothing procedure. Each pixel measures a region of cross-section 32.$7 \times 32.7\, \upmu \hbox {m}$, so that the minimum spatial resolution of the filtered images is 32.7$\times N\, \upmu \hbox {m}$. A threshold value of 10% was applied to the images before filtering. It can be seen that both $|\overline{\varDelta T_\mathrm{dep}}|$ and $\sigma _{\varDelta T}$ decrease as the filter size is increased. Without filtering (i.e. $N = 1$), $\overline{\varDelta T_\mathrm{dep}} = -1.7$ °C, with a standard deviation of 25.7 °C. For all values of $N \ge$ 9, $\overline{\varDelta T_\mathrm{dep}}<$ 0.025 °C, with the corresponding $\sigma _{\varDelta T}$ for $N = 9$ and 15 being 8.3 °C and 5.7 °C, respectively. While a larger smoothing kernel decreases both $|\overline{\varDelta T_\mathrm{dep}}|$ and $\sigma _{\varDelta T}$, this comes at the expense of spatial resolution. Hence, a kernel size of $9 \times 9$ pixels was chosen because it has a near zero mean error with a relatively low standard deviation, while still preserving a reasonable spatial resolution of $294\, \upmu \hbox {m}$. As the light sheet thickness for the current experiments is $\approx 300\, \upmu \hbox {m}$, this results in a roughly cubic measurement volume of $294 \times 294\times 300 \upmu \hbox {m}$ for each pixel.

Fig. 17

Effect of square filter kernel size (N) on the mean temperature error and corresponding standard deviation (($\overline{\varDelta T_\mathrm{dep}}$) and $\sigma _{\varDelta T}$) for two-colour LIF thermometry of a single image in an unheated jet without particles