Boundary Conditions for the Computation of Thermoacoustic Modes in Combustion Chambers

Abstract

In order to carry out reliable LES or Helmholtz solver computations in aeronautical combustion chambers, it is crucial to impose the right boundary conditions at both inlet and outlet of the combustion system. This means providing acoustic boundary impedances that take into account all the stages in compressors and turbines. This study is a follow up of works where the boundary condition were derived from the isentropic and isenthalpic Linearized Euler Equations. Specific terms are added to the quasi-1D LEE in order to account for enthalpy jumps induced by the rotor stages of the compressors and turbines. This system of equations also accounts for the entropyacoustic coupling since, in addition to the continuity and momentum equations, the entropy equation is also considered. The numerical implementation is validated by comparing the numerical results with analytical solutions in several model problems.

Analytic description of flame intrinsic instability in one-dimensional model of open–open combustors with ideal and non-ideal end boundaries

“…In this regard, we must mention that in an industrial gas turbine combustor there is a compressor assembly in the upstream and turbine assembly in the downstream of the combustor, imposing certain limitations on the validity of the perfectly closed or perfectly open assumption of acoustic ends. A detailed analysis of impedances at acoustic boundaries can be found in Lamarque and Poinsot, 25 Silva et al 27 and Marble and Candel. 28 Once the intrinsic instability features for combustors with ideal end conditions are known, we obtain the intrinsic instability features for practical systems through linear perturbations of the acoustic ends of an idealized open-open combustor.…”

“…A detailed analysis of impedances at acoustic boundaries can be found in Lamarque and Poinsot, 25 Silva et al. 27 and Marble and Candel. 28 Once the intrinsic instability features for combustors with ideal end conditions are known, we obtain the intrinsic instability features for practical systems through linear perturbations of the acoustic ends of an idealized open–open combustor.…”

Prediction of stability behaviors of longitudinal and circumferential eigenmodes in a choked thermoacoustic combustor

“…(18)- (20) are set to the LEE method. Analytical forms of entropy and vorticity disturbances cannot be found in linearized Euler equations directly.…”

“…It was assumed that the nozzle is compact and the flow disturbances satisfied the boundary conditions at the throat of the choked nozzle. Candel and Marble's expression has been widely used for predicting the stability behaviors of a combustor with a choked end [18][19][20][21][22][23][24]. Stow et al [25] extended the study of Marble and Candel by making a second order correction and proposing a length correction (also known as effective length) to describe the choked end via conducting asymptotic analysis.…”

“…(40) and (41), Eqs (18). and(20) can also be obtained.The flow in the downstream of the choked nozzle is supersonic. Thus there are no acoustic waves propagating toward upstream of the nozzle.…”