4.1. Experimental Results
Gas impingement was initially omitted to observe the influence of flow conditions on the jet angle without external interaction. The solid/gas loading ratio (
) in the conveying line was observed to have a direct impact on the jet half-angle; as the loading ratio is increased, the jet half-angle decreases (
Table 1). In order to ensure this is not a direct result of varying individual flow rates, two test conditions with similar loading ratios (±1%) are compared. Conditions 3 and 4 result in the same jet half-angle despite a difference in solid flow of 12% and a difference in gas flow of 11% (
Table 1). For the cases with gas impingement, the impinging gas flow rate was approximately four times larger than the conveying gas flow rate (40 kg/h compared to 8–10 kg/h). As shown in
Table 1, the relation between the loading ratio and jet half-angle holds true when introducing impinging gas; all cases with impinging gas have a lower loading ratio and thus a higher jet half-angle than all cases without impinging gas. For the cases with impinging gas (i.e., conditions 10–13), the changes in loading ratio were not sufficient to have a significant impact on the jet half-angle. The sleeve gas flow rate was also varied between two values of 0 and 10 kg/h N
2. These values were selected based on hot flow conditions used with CanmetENERGY’s pilot-scale gasifier, which was operated with a steam (i.e., sleeve gas) flow rate of up to 20 kg/h H
2O [
26]. A value of 10 kg/h N
2 was selected to remain within the range of momentum of the steam entering the reactor (10 kg/h N
2 having the momentum equivalent of 8 kg/h H
2O). The flow of sleeve gas did not impact the jet half-angle during cold flow testing (e.g., condition 11 vs. condition 13 in
Table 1). However, during reactive conditions the introduction of steam as sleeve gas may influence the jet half-angle by affecting the temperature surrounding the jet, which should influence the jet half-angle as discussed in the Theory section.
4.2. Jet Half-Angle Variability
It is important to track jet half-angle variability as it affects gasifier operation, and can potentially lead to unsafe conditions and/or poor syngas quality. The jet half-angle standard deviation was determined using 300 images taken for select conditions in order to determine the influence of the solid/gas loading ratio, impinging gas flow, and sleeve gas flow.
Table 2 shows the jet half-angle mean value and standard deviation for each test, as well as the corresponding conditions for each test (loading ratios and various gas flows). Note that the jet half-angles in this table vary slightly from those in
Table 1 since they were determined by measuring angles for each image in a set of 300 images. In contrast, values in
Table 1 are from measuring the angles from 3 images which are each the result of averaging 300 images. An F-test, with a 90% confidence interval, was applied to determine the significance of the different standard deviations measured for each condition. The results indicate that conditions 4 and 6 have statistically similar variance, as well as conditions 10, 11 and 13. The analysis thus suggests that the presence of the impinging gas influences the variability of the jet half-angle. The presence of the sleeve gas, as well as varying the solid/gas loading ratio (excluding the impinged gas), was found to not influence the variability of the jet half-angle. For certain applications, it may be more important to minimize the relative variability, represented by the coefficient of variation, rather than the (absolute) variability, represented by the standard deviation. The coefficients of variation, i.e., the ratios of the standard deviation to the mean, are included in
Table 2 and are similar for all conditions.
Beyond the magnitude, whether absolute or relative, of the jet half-angle variability, the frequency of the variability can also have an impact on gasifier performance. For instance, reactor temperatures and syngas composition are sensitive to the jet angle [
8]; hence, changing the frequency of the jet half-angle variability could cause refractory thermal shock or syngas consistency issues. Furthermore, analyzing the variability in the frequency domain can help determine causes of the variability. The data for the conditions presented in
Table 2 were subjected to a fast Fourier transformation to analyse the data in the frequency domain. Frequency spectra are shown in
Figure 5. Conditions 4 and 6 have similar frequency spectra; they do not have a mean squared amplitude greater than 0.01°
2 at frequencies greater than 0.3 Hz. Conditions 10, 11 and 13 have similar frequency spectra; they have several frequencies with amplitudes of 0.01–0.03°
2 in the range of 0.3–5.0 Hz. The added variability with impinging gas, i.e., conditions 11, 10, and 13, could be a result of high frequency, i.e., >0.3 Hz, fluctuations in the control valve position for the impinging gas; the control valve (Samson Type 3760 Electropneumatic Positioner, Samson Controls Inc., Markham, ON, Canada) requires ≤2 s to transit from fully open to fully closed. This highlights how operating conditions can be sensitive to certain aspects of control systems.
4.3. Model Fitting
The relationship put forth by Roy et al. (Equation (2)) shows that the jet half-angle is inversely proportional to the jet core density. This dependence is extended to the solid/gas loading ratio,
, via Equation (3); as the solid/gas loading ratio increases, the density of the suspension also increases. Thus, the jet half-angle should be inversely proportional to the solid/gas loading ratio. This relationship is exemplified in
Table 1, where the jet half-angle increases as the solid/gas loading ratio decreases.
Least squares regression was applied to the experimental data (i.e., conditions 1–13 in
Table 2) with Equation (2) and yielded a value of 17.3 for constant
. The coefficient of determination, average absolute relative error and bias factor (as presented by Macchi et al. [
27]) of the resulting model are 0.86, 10% and 0.93, respectively. The model is compared to experimental results in
Figure 6. The application of a model including the square-root of density ratios implies that the jet half-angle can be related to the entrainment of surrounding gas into the jet, for the system and operating conditions at hand (solid/gas loading ratios varying from 1–18 kg
solid/kg
gas; solid fuel flow rates ranging from 25–100 kg/h; conveying gas flow rates ranging from 4.7–10 kg/h, and impinging gas flow rates up to 40 kg/h). Note that these conditions correspond to density ratios ranging 0.07–0.5.
Two CFD simulations, with similar conditions as the experiments [
28], were analyzed to determine the jet half-angle for reactive flow (
Table 3). The jet core in both cases remains at ambient temperature (~300 K), while the surrounding temperatures differ between the two cases; estimated at 1231 K and 1165 K for cases 1 and 2, respectively (
Figure 7). The jet half-angles, estimated using particle volume fraction thresholds, are, respectively, 3.6–5.2° and 4.6–6.7° (
Figure 8). The particle volume fraction thresholds, i.e., 2.5 × 10
−4–1.0 × 10
−3, were selected based on the range of the solids volume fraction in the bulk jet surroundings. Similarly, change in mean particle volume fraction is used to define the characteristics lengths of gas jets penetrating into a fluidized bed [
29]. Also indicated in
Table 3 are the jet half-angles predicted using the same correlation that was applied to the cold flow cases, i.e., Equation (2) with an
factor of 17.3, which falls within the predicted value boundaries of the CFD simulations. However, although the CFD results suggest that the impact of increased surrounding temperature is greater than the increased loading ratio, leading to a rise in jet half-angle from case 1 to 2, the proposed model predicts a negligible difference in jet half-angles. Since the injector geometries are the same for the experiments and CFD simulations, further investigation is required to determine whether the difference in CFD and proposed model predictions are due to the proposed model not explicitly accounting for gradients in the surrounding temperature and the solids volume fraction.
It can be noted that the feed flowrates used in this study are approximately three orders of magnitude less than those of typical commercial entrained flow gasifiers. Nonetheless, commercial gasifiers can have similar, although scaled-up, injector geometries to the one used in this study, resulting in similar gas volumetric fractions in the jet core (i.e., ~0.85). However, the pressure in commercial dry feed gasifiers is typically 2–4 times higher than the pressure applied in this study. This difference in pressure affects the jet core density and the jet surroundings density. Assuming a jet core gas fraction of 0.85 and a solid density of 1200 kg/m3, increasing the jet gas pressure by a factor of 3 increases the jet core density by a factor of 1.15. Increasing the jet core density by a factor of 1.15 and the jet surroundings density by a factor of 3 in Equation (2) results in an increase of the jet angle by a factor of 1.61. Hence, it is expected that commercial gasifiers will have jet angles ~60% greater than those obtained in this study.