3.1.1 Flow topologies of spray pertaining to design changes of the atomizer

In this sub-section, we discuss the global flow field of the spray with variations in the design parameters. To characterize the flow topology, the non-dimensional numbers W/Df and L/Df represent the mean width and mean length of the CTRZ. Here, Df (Rf) is the flare exit diameter (radius). We have used the momentum-based swirl number (using (1) in the supplementary material) calculated by using velocity components of the flow field measured from the phase doppler particle analyzer experiment. The momentum-based swirl number will represent the true characteristics of swirling flow, provided the velocity components are measured in the same time domain over a plane in such a complex atomizer. In this study, the swirl number (SN ₅) is calculated by using the axial and tangential velocity components acquired simultaneously using three-dimensions PDI measurements at 5 mm from the exit plane.

The streamline contour shown in figure 2 represents the time-averaged flow structure of the CTRZ across all cases. It is noticed in figure 2 that, with a decrease in the flow Reynolds number from the primary swirler, the CTRZ grows spatially. In other words, there is a radial (W/Df) and axial (L/Df) expansion of the CTRZ with a decrease in flow rate through the primary swirler. From the axial velocity contours and profile in figure 3, we notice that a decrease in the air flow rate through the primary swirler results in a drop of the axial velocity of the resultant flow field at the exit. This reduction in axial velocity is more pronounced inside the CTRZ. From the swirl number definition, a decrease in the axial flux of axial momentum will increase the swirl number, as observed in table 1, manifesting as a bigger CTRZ. Comparing cases C1 and C5 (which represents the effect of mixing length), shows that an increase in the mixing length causes shrinkage of the CTRZ in both the radial and axial directions. Further, cases C4 and C5 show that a decrease in flare angle results in the growth of the CTRZ. This elucidates that the size of the CTRZ can be altered through the mixing length or flare angle variation, keeping the internal design of the high-shear atomizer unchanged. It should be noted here that flare is an interchangeable external part of the high-shear atomizer. Thus, flare provides us with more degrees of freedom or feasibility to tune the size of the CTRZ without any modifications to the geometry or design of the atomizer.

Figure 2. Streamline contour of time-averaged velocity over longitudinal plane representing the CTRZ and flow topology; (a) base case, γ = 60 : 40; (b) C2, γ = 50 : 50; (c) C3, γ = 40 : 60; (d) C4, CR $\varTheta$ = 45°, η = 5; (e) C5, CR $\varTheta$ = 50°, η = 5; ( f) C6, COR $\varTheta$ = 50°, η = 0; (g) C7, COR $\varTheta$ = 45°, η = 5; and (h) C8, COR $\varTheta$ = 50°, η = 5.

Figure 3. Time-averaged axial velocity contours (top row) and profile (bottom row, at y/R_f = 0.75) for base case, C1, γ = 60 : 40; C2, γ = 50 : 50; C3, γ = 40 : 60. The flow topology and functional relations of the length scales of the CTRZ with SN ₅ (see supplementary material § 3.1) are similar to what has been reported for the same cases in our previous study (Reference Kumar, Malavalli, Chaudhuri and BasuKumar et al., 2020) with a simplex-pressure-swirl fuel nozzle at ALR = 14.1. This implies that the type of fuel nozzle has a negligible impact on the flow topology in the present design of the atomizer.

Finally, we have introduced the change in relative swirl direction between the two airflows passing through the primary and secondary swirlers to see its effect on the flow topology at the exit of the flare. It should be noted that we have kept the swirl direction of the primary swirler unchanged, and the swirl direction of the secondary swirler has been changed. Comparing case C1 and case C6, it is seen in figure 2 that the relative swirl direction significantly influences the flow topology. It is noticed that, while switching from a counter-rotation to co-rotation swirl motion, there is an increase in swirl number (SN ₅), see table 1. The increase in swirl number is due to the increased tangential velocity of the resultant flow in the co-rotating atomizer compared with the counter-rotating one. In a counter-rotating atomizer, the opposite sense of the primary and secondary swirl flows means that they oppose each other compared with the co-rotating swirl flow, where both the swirling air flows have the same rotational sense. Further, in the case of C6, the increase of SN ₅ has a pronounced effect on the axial length of the CTRZ compared with the radial length. In other words, on switching the relative rotational sense of the airflow from a counter-rotation to co-rotation atomizer, there is negligible change in the radial expansion of the CTRZ and significant change is registered in the axial length with an increase in swirl number. Researchers (Reference Kumar, Malavalli, Chaudhuri and BasuKumar et al., 2020) have reported similar observations in previous experiments. They attributed the CTRZ topology to the function of the local pressure distribution in radial and axial directions.

3.1.2 Flow topologies of spray at different values of ALR for base case C1

In this subsection, we have focused on the response of an atomizer with the variation of ALR. From a gas turbine engine perspective, it becomes crucial for the engine to stabilize the flame across different load conditions. Hence, an atomizer must create a CTRZ at all operating conditions. The authors believe that the ALR values considered in the present study cover the region of interest for the gas turbine community. Flow topology of spray at selected ALR (4.72; 7.08; 9.44, left to right) conditions is shown in figure 4, which shows that the atomizer is capable of creating the reverse flow zone across a wide ALR range. Interestingly, with an increase in ALR, the CRTZ is stretched radially, left to right, W/Df = 0.74; 0.79; 0.86 and contracted axially, L/Df = 1.183; 1.185; 1.60, respectively. The droplets are small enough, resulting in excellent air/fuel mixing within a short distance of the exit. The rich and uniform mixture is the key point to reduce NO_x in rich-quench-lean concept-based combustors (Reference McKinney, Sepulveda, Sowa and CheungMcKinney et al., 2007).

Figure 4. Streamline contour of spray flow field for base case C1 across various ALR values; (a) 4.72, (b) 7.08 and (c) 9.44.

3.2.1 Droplet characteristics pertaining to design changes in the atomizer.

Droplet lifetime and evaporation rate are strong functions of the drop size which influences the low-emission combustion characteristics. Hence, the study of droplet size is as important as flow structure. In this subsection, we will discuss the effect of the geometrical design parameters of the atomizer on the droplet size distribution at fixed ALR = 14.1. The variation in droplet size in the radial direction is recorded for three axial locations at y/R_f = 0.5, y/R_f = 1.5 and y/R_f = 2.5, as shown in figure 5. Smaller droplets are found near the centre (r/Rf = 0) of the spray, while larger size droplets are found near the spray's edge. This happens since bigger droplets experience larger centrifugal forces than smaller droplets in such a turbulent swirl flow. If we notice the variation in droplet size across the cases at a given axial position, there is not much difference between y/R_f = 0.5 and 1.5 within r/R_f = 1.5. Beyond radial position, r/R_f = 1.5, we observed differences for a few cases. At y/R_f = 2.5, a considerable difference is observed in droplet sizes across all of the cases. This large difference in drop size of 9%–27 % is between the cases C5 and C6, and 2%–26 % for cases C1 and C6 from the centre to the edge. The reason for this can be answered from the streamline contours of cases C5 and C6. If we look at y/R_f = 2.5 for case C5 (see figure 2), the flow surrounding the CTRZ gets merged, which may lead to coalescence of droplets, resulting in an increase of droplet size. The effect of co- and counter-swirl (C6 and C1) is also observed in the study. The difference in drop size is relatively small near the exit, y/R_f = 0.5, and can be considered negligible. However, the difference in droplet size is noticeable at y/R_f = 1.5 and 2.5.

Figure 5. Droplet size at ALR ~ 14.1 across all the test cases C1:C8 for axial positions; (a) y/R_f = 0.5, (b) y/R_f = 1.5 and (c) y/R_f = 2.5.

At y/R_f = 1.5 from the exit of flare, the droplet sizes up to r/R_f = 2 are almost similar and beyond this co-rotation atomizer (C6) yields smaller droplet sizes compared with the counter-rotation atomizer (C1). This could result from the coalescence of droplets in the counter-rotation case. The streamline contours, see figure 2(a–f), clearly show that co-rotation (C6) has radially expanding flow which prevents coalescence, whereas the spray gets coalesced in the counter-rotation case. Finally, at y/R_f = 2.5, the droplet size for co-rotation is relatively smaller than for the corresponding counter-rotation atomizers at all radial locations. The difference in droplet size is more pronounced beyond r/R_f = 1.5. This results from the flow topology (see figure 2a–f) of counter- and co-rotation. Beyond y/R_f = 1.5 downwards, the flow (outer shear layer (OSL)) bends inward and goes straight while the ISL gets merged at y/R_f = 2.25, which may lead to the coalescence of droplets at the centre in counter-rotation. Contrarily, co-rotation leads to diverging flow (OSL and inner shear layer (ISL)), which prevents droplet coalescence.

3.2.2 Droplet size distribution at different values of ALR

In this subsection, we present the effect of ALR on the size of the droplet distribution. It should be noticed that the droplet size variation only for case C1; base case, is carried out at various ALR values. The droplet size variation is measured at three locations, namely y/R_f = 1.5, y/R_f = 2.0 and y/R_f = 2.5 downstream of the flare exit.

The droplet size variation at different ALR is shown in figure 6. At low ALR = 4.72, the droplet size is comparably larger than the other two ALR cases. Further, the variation in droplet size is found to be negligible inside the CTRZ, r/R_f = 1; this is because the finer droplet gets trapped inside it. Across shear layers, there is a considerable difference in droplet size with vertical distance from the flare exit. At y/R_f = 1.5, the droplet size is larger than that at y/R_f = 2.5. This suggests that, in downstream locations, secondary atomization occurs in the flow at ALR = 4.72. Additionally, with an increase in ALR from 4.72 to 9.44, this difference in the Sauter mean diameter (SMD) value of droplets with downstream position (y/R_f) becomes smaller and at ALR = 9.44 becomes negligible. This shows that the location of secondary atomization shifts near to the flare exit with an increase of ALR and no further atomization take place downstream. Furthermore, the maximum droplet size is reduced to 34 μm at ALR = 9.44 and further reduces to 30 μm at ALR = 14.1 (see figure 5b,c: y/Rf = 1.5 and 2.5), at the spray edge for base case C1.

Figure 6. Droplet size variation with ALR, 4.72–9.44, for base case at three axial locations; C1: CR, γ = 60 : 40.

3.2.3 Comparison of droplet size between present atomizer and recent atomizer experiment

The global Sauter mean diameter (GSMD) is presented for base case C1 and compared with the GSMD of the airblast atomizer reported in the literature (Reference Shanmugadas, Chakravarthy, Chiranthan, Sekar and KrishnaswamiShanmugadas et al., 2018) to mark the atomization performance of both the atomizer configurations, see table 2. The ALR studied in the current experiment is 14.1, close to ALR ~ 16 reported in the literature. The GSMD is chosen to represent the overall atomization capability of the atomizer and calculation is based on the volume flux-averaged SMD (Reference Bhayaraju and HassaBhayaraju & Hassa, 2009). The GSMD at an axial location can be defined as the local volume flux-averaged SMD over given radial locations (see (3.1)), where V_i (r, y) is the local volume flux at a radial location, r, and axial location, y, from the atomizer exit. Comparing the GSMD values of both atomizers shows that the present atomizer configuration has excellent overall atomization performance. Further, the SMD of the base case C1 of the present study at ALR ~ 14 and that of atomizer at ALR ~ 16 reported in the literature (Reference Shanmugadas and ChakravarthyShanmugadas & Chakravarthy, 2017) are compared to mark the performance capability of the present configuration of the atomizer with

(3.1)\begin{equation}GSMD(\kern0.7pt y) = \frac{{\sum\limits_{i = 1}^n {({V_i}(r,y)SM{D_i}(r,y)} }}{{\sum\limits_{i = 1}^n {{V_i}(r,y)} }},\end{equation}

a discrete jet as shown in figure 7. The SMD values of the present configuration are well below at given positions. It is to be noticed that the SMD reported in the literature (green marker) is at 15 mm from the exit plane and ALR ~ 16. Thus, the comparison of GSMD and SMD of the present atomizer configuration with a similar atomizer for a gas turbine reported in the literature shows that the current design of a high-shear atomizer would be an excellent candidate to achieve desirable atomization in a gas turbine engine. Further, the GSMD of all test cases is given in table S4 and for case C1 at various ALR is given in table S5 of the supplementary material.

Table 2. Comparison of GSMD of the present study and available in the literature.

Notes: d is the venturi throat diameter, and y/d is the non-dimensional axial locations measured from the exit of the venturi in both the study. The present atomizer is the base case C1.

Figure 7. Comparison of SMD produced by airblast atomizer, base case C1, in the present study (ALR ~ 14) at three axial locations to the location given in the literature (green marker) at ALR ~ 16 (Reference Shanmugadas and ChakravarthyShanmugadas & Chakravarthy, 2017). Note: axial location is measured from exit plane in both the atomizers.

3.3.1 Azimuthal spray volume distribution with swirl cup design parameters of the atomizer

The distribution of liquid volume across the six jets of the fuel nozzle is measured before spray patternation, see table S6. The standard deviation across six jets is 7.44 % from the mean due to a manufacturing defect. Subsequently, the spray patternation of the atomizer with its various configurations has been tested at 50 mm from the flare to check the consistency of the high-shear atomizer, fitted with a discrete radial-jet fuel nozzle. The volume of liquid collected in each cylinder is normalized by the total volume collected and represented to show the spray distribution in figure 8. Based on the atomizer configuration, the generated spray varies from the hollow cone (case C1) to the solid cone (case C4, C5). This structure of the spray is directly connected to the CTRZ size. The spray with small CTRZ has a downstream stagnation point far above the position where the patternation is carried out. Therefore, the presence of the CTRZ is not reflected in the spray patternation contours for cases C4 and C5.

Figure 8. Azimuthal spray patternation across all the cases at 50 mm downstream of the exit; (a) base case, γ = 60 : 40; (b) C2, γ = 50 : 50; (c) C3, γ = 40 : 60; (d) C4, CR $\varTheta$ = 45°, η = 5; (e) C5, CR $\varTheta$ = 50°, η = 5; ( f) C6, COR $\varTheta$ = 50°, η = 0; (g) C7, COR $\varTheta$ = 45°, η = 5; and (h) C8, COR $\varTheta$ = 50°, η = 5.

Furthermore, from figure 2(d,e), it is clear that at around 25 mm from the exit in the axial direction, the forward-moving flow merges and behaves similar to the co-flowing spray structure. The patternation results of the spray having a CTRZ size of around 50 mm in the axial direction show a low volume of spray at the centre. Most of the spray volume/mass is collected in the annular region away from the central axis.

To quantitatively discuss the spray patternation of the injectors, the contour of normalized volume is expressed in terms of the sector-wise normalized flux to represent the azimuthal symmetry of the spray. Normalized flux is defined as the normalized volume of spray collecting per unit area over the azimuthal plane. Further, the contour is divided into 36 equal sectors (a detailed explanation is given in the supplementary material, § S4) to find the sector-wise normalized flux. The volume of liquid in each sector and standard deviation across all the sectors have been calculated to represent the azimuthal symmetry; see figure 9. The percentage standard deviation with respect to the mean is calculated and is believed to represent azimuthal symmetry quite well. The percentage standard deviation with respect to the mean varies with atomizer configuration in the 5%–10 % range. Base case: C1 shows the highest azimuthal symmetry with the lowest standard deviation value, while case C3 shows the maximum. Looking closely, four peaks of nearly equal magnitude are found at equal angular intervals, indicating a local high flux in the corresponding sector. The appearance of the four peaks shows that some atomizer configurations, particularly co-rotation atomizers, are not able to mitigate the discrete nature of the fuel nozzle compared with a counter-rotating injector, see figure 9(e–h). Similar peaks are found in the work of Reference Cohen and RosfjordtCohen and Rosfjord (1993), where the six jets retained their coherency as they impinged and filmed on the venturi lip, resulting mild streak in the spray. However, in the present study, only four peaks are present even for some cases (co-rotation cases have greater magnitude), suggesting better atomization in the current atomizer configuration than was the case in former work. However, these four equally spaced local peaks do not reduce the azimuthal symmetry of fuel distribution. Further, spray distribution and azimuthal symmetry are finely resolved at a given radius in figure S12 of the supplementary material.

Figure 9. Sector-wise normalized flux for the respective case; (a) base case, γ = 60 : 40; (b) C2, γ = 50 : 50; (c) C3, γ = 40 : 60; (d) C4, CR $\varTheta$ = 45°, η = 5; (e) C5, CR $\varTheta$ = 50°, η = 5; ( f) C6, COR $\varTheta$ = 50°, η = 0, 7; (g) C7, COR $\varTheta$ = 45°, η = 5; and (h) C8, COR $\varTheta$ = 50°, η = 5.

3.3.2 Azimuthal spray volume distribution with ALR

The injector must be capable of maintaining the spatial uniformity of the reactant mixture across the required power conditions of the engine to keep the emission within acceptable limits. From this point of view, the azimuthal spray volume distribution at various ALR is studied for base case C1. Figure 10 shows the contours of the normalized volume of spray distribution at ALR 4.72, 7.08 and 9.44, represented on the same scale. It is noticed from the contour at ALR 4.72 that the accumulation of spray is least at the centre compared with other ALR. The spray is collected in the annular region, and this hollowness relates to atomization characteristics. At low ALR, the droplet size is relatively bigger. The bigger drops experience more centrifugal force and tends to fall farther from the centre. Further, in a swirl atomizer, the finer drops get trapped within the CTRZ and are drawn towards the centre while bigger drops are thrown away from the jet axis. The normalized radial flux in the radius range of approximately r/Rf = 2.75–3.5 mm is found to be higher. This flux gets lowered with an increase in ALR. The possible cause for this could be the relatively bigger droplet size and reduction in atomization with a decrease in the ALR, as a consequence of the low shear energy available for atomization.

Figure 10. Spray patternation at different values of ALR for base case C1.

However, ALR does not influence the sector-wise azimuthal flux symmetry very much. The standard deviation of normalized flux across the sectors at all ALR values is within 6 % with respect to the mean. This shows the excellent ability of the atomizer even with a discrete radial-jet fuel nozzle to maintain the azimuthal symmetry within a fair value, which was the most concerning factor among designers related to the application of a discrete radial-jet fuel nozzle in a gas turbine combustor.