Investigation of azimuthal staging concepts in annular gas turbines

Azimuthal instabilities in annular combustors: standing and spinning modes

“…We stress that this statement does not apply to non-symmetric annular combustors, in which the shape function ψ is no longer M-periodic in the azimuthal direction, and in the very specific case where M = 2n in (3.4), where n is the unstable acoustic mode. This latter case is covered by the stability analysis of Noiray et al [7], and shows that mixed modes and standing modes are possible. In this case, the shape function has peaks at the pressure antinodes, and troughs at the pressure nodes of the standing mode.…”

“…In this representation, the addition of a non-zero asymmetry parameter, C 2n , as proposed in Noiray et al [7], shifts the red point of figure 5 towards one of the A, B axes, maintaining it on the same plane φ ± π/2. Doing so, the system exhibits a superposition of standing and spinning modes.…”

“…In this section, we carry out spatial averaging in the azimuthal direction, in the same way carried out in Noiray et al [7]. When annular combustors are subject to azimuthal instabilities, there is usually only one strong Fourier component, which corresponds to the nth lowest acoustic mode of the chamber.…”

“…The analysis carried out in this paper could easily be extended to higher-order terms. The theory developed in Noiray et al [7] based on (3.1) does not predict stable standing modes for symmetric configurations, which are observed as preferred state of the system in Worth & Dawson [4] and Wolf et al [5]. The universal validity of (3.1) is then called into question, particularly the assumptions of (3.1), which are (i) the absence of a time delay in p and (ii) the independence of q on anything else except p.…”

“…This model has been the common starting point of Noiray et al [7] and Noiray & Schuermans [3,10]. It is the one-dimensional counterpart of the model studied by Sensiau et al [12], where the whole three-dimensional field is considered.…”