Characterization and detection of high-frequency combustion oscillations in a rocket model combustor

We present a numerical study on the characterization and early detection of high-frequency combustion oscillations on the basis of the theories of complex networks and synchronization. In this study, we deal with a cylindrical combustor with an off-center installed coaxial injector as a liquid rocket model combustor. The turbulence network proposed by Taira et al. [J. Fluid Mech. 795, R2 (2016).] in which weighted networks are constructed by connecting each fluid element to other fluid elements, enables us to identify vortical interactions in a turbulent combustor [S. Murayama et al., Phys. Rev. E. 97, 022223 (2018)]. We observe a clear power-law decay in terms of the vertex strength in the turbulence network during combustion oscillations, indicating the presence of scale-free structure. In the transition process to combustion oscillations, the coherence structure begins to appear in the phase field consisting of pressure fluctuations p' and heat release fluctuations q'. The Kuramoto order parameter considering the mutual coupling between p' and q' [S. Mondal et al., J. Fluid Mech. 811, 659 (2017).] is valid for capturing the precursor of high-frequency combustions oscillations in a cylindrical combustor with an off-center installed coaxial injector.