**3.2 Multi-burner annular combustor**

In most modern jet engines, multiple burners are aligned circumferentially to achieve high thermal power within a compact volume. As a result, the unsteady heat release of these individual flames interact with the annular geometry of the combustion chamber, which gives rise to self-excited azimuthal instabilities [60]. Compared to longitudinal modes observed for a single flame, e.g., flame B of the DLR dual-swirl burner discussed earlier in this section, azimuthal modes are more dominant and destructive in practical applications because the circumference is usually shorter than the longitudinal length of the combustor resulting in higher resonant frequencies [61]. Thus, azimuthal instability is recognised as a primary issue for jet engine manufacturers.

Due to the complexity and high cost, only few laboratory model annular combustors have been studied experimentally so far, e.g., [62, 63], and the numerical works are scarce. To bridge this gap and gain physical insight into azimuthal instabilities, the annular burner of Worth et al. [62, 64] is simulated using the FlaRe model in this subsection. A photograph along with the schematic of this burner is shown in **Figure 5**. Fully premixed ethylene-air mixture was supplied at the bottom of the plenum and then passed through a honeycomb flow straightener before splitting into 12 bluff-body tubes by a hemispherical flow divider. Both swirling [62] and non-swirling [64] cases were investigated with and without the swirlers below the bluff-bodies. The experiments were operated at room temperature and atmospheric pressure. A bulk mean velocity evaluated at the bluff-body exit was kept constant at 18 m/s for all cases and pronounced azimuthal instability was observed for equivalence ratio ranging from *ϕ* ¼ 0*:*8 to 1.0. Three pressure transducers, denoted as P1, P2 and P3, were mounted on the tube wall 45 mm upstream of the bluff-body exit and they were separated by 120° to measure the azimuthal pressure waves travelling in the *θ*-direction.

The typical computed flame structures of the non-swirling and swirling cases for *ϕ* ¼ 0*:*8 are presented in **Figure 6** using volumetric rendering of the reaction rate for the 12 burners. The instantaneous axial velocity field is also shown for the mid-
