Boundary Conditions for Acoustic Eigenmodes Computation in Gas turbine Combustion Chambers

Abstract

Understanding and predicting acoustic instabilities in gas turbine combustion chambers requires the knowledge of the acoustic behaviour of all the elements feeding the combustion chamber (characterized by their impedance). Inlets and outlets of chambers are often represented as one-dimensional ducts and existing methods to evaluate impedances of choked and unchoked nozzles are described: (1) analytical formulae, 1-3 (2) numerical methods using the linearized Euler equations and a finite-difference solver in Fourier space and (3) full spacetime solver where the response of the nozzle is studied by forcing its inlet (or outlet) and measuring its response in the time domain. These three methods are compared in reference cases (a straight duct and a subsonic distributor). Practical implications for gas turbines * Post-doctoral fellow † Research Director, AIAA Associate Fellow Heat release amplitude(rad/s) φ Real-valued function ρ Volume mass (kg/m 3) ϕ Adimensionalized pressure fluctuation

Large eddy simulation of spark ignition in a turbulent methane jet

“…For the present study, a two-step Taylor Galerkin numerical scheme [43] is used, which provides a third order accuracy in space and time. Explicit time-advancement is employed to minimize numerical dissipation.…”

Accounting for convective effects in zero-Mach-number thermoacoustic models

“…The theory of the energy flux conservation indicates that using a formulation which neglects the mean flow (method II pu ) leads to significant errors, because the error on the imposed energy flux is OðMÞ. This statement goes against the previous assumption of Lamarque and Poinsot [21] that prescribed the use of a boundary condition formulated with purely acoustic state variablesp andû. As discussed by Peters et al [35], many authors in the aeroacoustic community prescribe the use of a so-called energetical correction of the reflection coefficient which is the ð1ÀMÞ=ð1 þ MÞ term in Eq.…”

“…1b), namely a complex-valued impedance noted Z. These impedances can be deduced from transfer functions describing the response of acoustic elements to acoustic or entropic perturbations, either analytically under the compact hypothesis [20] or numerically by solving the LEE [21].…”

Thermo-acoustic characterization of the burner-turbine interface in a can-annular combustor using CFD

“…For no flow, the transfer matrix method based on equation (3.3) was preferred. Since the transfer matrix method was not yet implemented for cases with higher Mach numbers, the low frequency approximation was used in situation of flow as reference since its validity is proven in literature by Marble & Candel [19], Lamarque & Poinsot [24] and Ehrenfried [41].…”

“…Kaji & Okazaki [22], [23] have analyzed a method focused on the acceleration potential to study the sound transmission through a 2D rectilinear cascade. Review papers by Lamarque & Poinsot [24] and Duran et al [25] provide an overview of the experimental and numerical studies related to the reflection coefficient analysis. They represent inlets and outlets of chambers as one-dimensional ducts and evaluate impedances of subsonic and choked compact nozzles through analytical formulae and numerical methods using the Linearized Euler Equations (LEE).…”