After these sections were characterised, the analysis was completed using a MatLab program. The program gathered all results, isolating the specified regions of low velocity in the ‘‘radial” analysis for the PVC or negative velocity in the ‘‘axial” plane for the CRZ. New planes were overlapped and isosurfaces produced. This allowed the visualization of the low speed region or the zero velocity contour for the PVC and CRZ zones, respectively. Experiments using 40 images per section showed reasonable results. Increasing the images per section to 150 gave considerable improvement. This methodology gave better accuracy with only 2.5% vectors substitution. For the later studies, the velocity maps were developed in the range of 0.0–12.0 m/s in the radial plane and 3.0 to 11.0 m/s in the axial direction for the PVC and CRZ, respectively. It was found that the PVC boundaries had a good correlation between the planes at 3.2 m/s, whilst the CRZ boundaries were defined at 0.7 m/s.

The effect of burner exhaust confinement on the system was the next step in the investigation, providing a basis for future comparison with similar configurations when in the combustion mode. Square and circular confinements were studied with different outlets. The same conditions used for the most stable case in the unconfined state, were then applied to all the confined studies. Fig. 4 shows the cases investigated where the swirl burner fires into a simulated combustor ‘‘can”. The same procedure as previously mentioned was used to obtain the coherent structures in‘‘axial” and ‘‘radial” planes, respectively.

The first confinement had a square transversal area of 2.00  2.00 D2 (Fig. 4A). Its total length was designed to be larger than the total visualised length of the CRZ under unconfined conditions, 1.67 D. Hence, the confinement was designed to be 2.50 D (200 mm) long, this being typical of industrial practice [10]. Three types of confinement exhaust were used. The second case used a pyramidal exhaust with length of 1.00 D and square transversal open area of 1.00  1.00 D2 (Fig. 4.B). Finally, the third configuration used a sudden flat obstruction at the end of the confinement with a circular 0.50 D hole (Fig. 4.C).

Circular confinements were also used to allow the assessment of structures in a more common type of burner/furnace arrangement. Thus, the design of the circular confinement was 2.00 D diameter and the length of the burner was kept at 2.50 D (200 mm). Hence, to match results with the previous square cases, three similar exhausts were used. An open case (Fig. 4D), a conical obstruction similar to the pyramidal case (Fig. 4E), and a sudden flat sharp 0.5 D exit (Fig. 4F) were studied.

The range of validation tests for the velocity maps of the confined trials was set at 0.0–9.0 m/s and 5.0 to 8.0 m/s for the ‘‘radial” and ‘‘axial” analysis, respectively. The percentage of substitution was only 1.5% and 2.1% for the ‘‘radial” and ‘‘axial” cases respectively, confirming satisfactory results.

 Fig. 5. Sr vs. Re dependency, denoting the asymptotic value of Sr at high Re. Case IC50_50, Sg = 1.86. N First harmonic, j second harmonic.

3. Experimental approach

3.1. Signal analysis

Extracts from initial unconfined tests were used to characterise the frequency of the precession, Fig. 5. The relationship of the Strouhal number with the Reynolds number is clearly evident, showing an independent relationship at high Re. It is clear that both harmonics are constant at high Re, as discussed by Syred [13], being more consistent with uniform inserts in the inlets. When analysing configuration IC-50 (an asymmetric case), despite nearly doubling the swirl number (Sg) from 1.86 to 3.70, the Sr only increases from 1.25 to 1.6. This was also observed by other researchers [13].

A comparison of the use of different sized inserts in the tangential inlets (Fig. 2) was also made for similar swirl numbers. Configuration IC-50_50 and IC-25 had similar Sg numbers of 1.86 and 1.97, respectively. Similar asymptotic Strouhal numbers of 1.24 and 1.18 were found, only a 5% difference being noted. A summary of all the various swirl number results under unconfined conditions with their respective Strouhal numbers is shown in Fig. 6. Scatter from the fitted curve arises from the asymmetric single inlet cases. Above Re = 20,000, Sr was sensibly constant at 1.2 for the first harmonic and 2.4 for the second.