Analysis of acoustic, entropy and vorticity waves in a non-uniform annular combustor

Theoretical analysis of sound propagation and entropy generation across a distributed steady heat source

“…The acoustic transfer functions are still determined by the impedance of Z u = −1 at X = X u = 0 as expressed in Eq. (48). The WKB solution derived in our previous work [39] is presented in Appendix B.…”

“…One strategy is to directly divide the distributed region into multiple subregions with constant or approximately linearly varying flow properties. Known analytical expressions can be applied in each subregion and subregions connected via matching conditions [46][47][48][49]. Another theoretical strategy to analyse the energy transport of an acoustic wave propagating through complicated flow distributions is using perturbation expansions [18,50].…”

Analytical solutions for the acoustic field in thin annular combustion chambers with linear gradients of cross-sectional area and mean temperature

“…When dealing with a geometry whose cross-sectional area and flow field change gradually, the chamber can be segmented into a series of elements whose individual axial lengths are sufficiently smaller than the dominant acoustic wavelengths. The cross-sectional area and flow field in each element is then assumed uniform, so that analytical solutions for the acoustic field within each element can be obtained directly and used [14,15,16]. However, if it is possible to directly derive analytical solutions for the acoustic fields in these complex geometries, the computing cost could be further reduced and it would also be possible to obtain more physical insights into the mechanisms.…”