Table 1

Characteristics relating to combustion instabilities of two combustors

Fig.1

Illustration of thermoacoustic feedback loop

Fig.2

Instantaneous topology of an isothermal bluff body flow［22］

Fig.3

Axial distribution of ratio of Sinuous mode energy to total energy of Sinuous mode and Varicose mode at different forcing frequencies［23］

Fig.4

Variation of local unsteady heat release amplitude with forcing frequency［23］

Fig.5

Experimental configuration of swirling flame burner and flame describing function results ［44］

Fig.6

Mechanisms generating unsteady heat release rate fluctuations in swirling flows［43］

Fig.7

PIV results of axial velocity of flow field［48］

Fig.8

Schematic diagram of thermoacoustic network model of an aero-engine combustor chamber［58］

Fig.9

Simplified schematic diagram of one-dimensional combustion thermoacoustic system

Fig.10

Complex eigenfrequencies as a function of temperature ratio across flame ［63］

Fig.11

Schematic diagram of radial modal coupling

Fig.12

Experimental setup of model combustion chamber ［68］

Fig. 13

Variation of sound pressure level in combustion chamber with equivalence ratio for liners with different bais flows［68］

Fig.14

Schematic diagram of simplified premixed annular combustor［70］

Fig.15

Comparison of variation of complex eigenfrequencies with length of liner obtained by COMSOL and our 3D model under different radial truncated mode numbers ［74］

Fig.16

Variation of complex eigenfrequencies with length of liner obtained by our 3D model under different radial truncated mode numbers with unsteady heat release rate ［74］

Fig.17

Mode shapes for Mode 2L0A （L2/Lc=0,L3/Lc=0.47）［74］

Fig.18

Mode shapes for Mode 2L0A （L2/Lc=0.26,L3/Lc=0.47）［74］

Fig.19

Comparison of variation of complex eigenfrequencies with length of liner obtained by COMSOL and our 3D model ［70］

Fig.20

Comparison of variation of complex eigenfrequencies with length of liner for circumferential uniform liner and segmented liners［70］

Fig.21

Pressure mode shapes of Mode 1L1A at default cutting plane and acoustic absorption of perforated plates for circumferential uniform liner case［70］

Fig.22

Pressure mode shapes of Mode 1L1A+ at default cutting plane and acoustic absorption of perforated plates for circumferential segmented liners case［70］

Fig.23

Pressure mode shapes of Mode 1L1A- at default cutting plane and acoustic absorption of perforated plates for circumferential segmented liners case［70］

Fig.24

Configurations of segmented liners （shaded regions denote sector backing cavity and short line segments denote rigid plates）［70］

Fig.25

Complex eigenfrequencies of Modes 1L1A+ and 1L1A- for different liner configurations［70］

Fig.26

Results of complex eigenfrequencies for uniform liner and segmented liners with unsteady heat release rate［70］

Fig.27

Sketch of perforated injector mounting surface［79］

Fig.28

Variation of complex eigenfrequencies with perforation ratio for different bias flow conditions［79］

Fig.29

Sketch of nonuniform radial perforated injector mounting surface［79］

Fig.30

Variation of complex eigenfrequencies with perforation ratio σdo， radius of aperture rdow， and Mach number of mean bias flow Madow［79］