Thierry Poinsot

Acoustic modes in combustors with complex impedances and multidimensional active flames

two approaches for solving the corresponding nonlinear eigenvalue problem are proposed. The first one is based on an asymptotic expansion of the solution, the baseline being the acoustic modes and frequencies for a steady (or passive) flame and appropriate boundary conditions. This method allows a quick assessment of any acoustic mode stabilitybutisvalidonlyforcaseswherethecouplingbetweenthe flameandtheacousticwavesissmallinamplitude. The second approach is based on an iterative algorithm where a quadratic eigenvalue problem is solved at each subiteration. It is more central processing unit demanding but remains valid even in cases where the response of the flametoacousticperturbationsislarge.Frequency-dependentboundaryimpedancesareaccountedforinbothcases. A parallel implementation of the Arnoldi iterative method is used to solve the large eigenvalue problem that arises fromthespacediscretization ofthe Helmholtzequation.Several academicandindustrial testcasesareconsideredto illustrate the potential of the method.

Flow forcing techniques for numerical simulation of combustion instabilities

Investigation of combustion instabilities in gas turbine combustors require the knowledge of flame transfer functions. Those can be obtained by experimental measurement or by Large Eddy Simulations (LES). Because calculations are usually limited to a portion of the whole combustor, boundary conditions are of crucial importance. It is common practice to inject acoustic perturbations for the flame transfer function measurement in form of velocity perturbations (u(t)). We present an alternative method based on a characteristic treatment of the Euler Equations. It consists of injecting sound waves traveling into the computational inlet while letting outgoing waves leave the domain without reflection. This method has several advantages concerning the study of flame transfer functions compared to injecting velocity perturbations. Both techniques are compared for cases where analytical solutions may be derived (a duct without flame and a planar laminar flame) and for one case where a CFD code is necessary (a laminar Bunsen-type flame).

Analysis and Modeling of Entropy Modes in a Realistic Aeronautical Gas Turbine

A combustion instability in a combustor typical of aeroengines is analyzed and modeled thanks to a low order Helmholtz solver. A Dynamic Mode Decomposition (DMD) is first applied to the Large Eddy Simulation (LES) database. The mode with the highest amplitude shares the same frequency of oscillation as the experiment (approx. 350 Hz) and it shows the presence of large entropy spots generated within the combustion chamber and convected down to the exit nozzle. The lowest purely acoustic mode being in the range 650-700 Hz, it is postulated that the instability observed around 350 Hz stems from a mixed entropy/acoustic mode where the acoustic generation associated with the entropy spots being convected throughout the choked nozzle plays a key role. A Delayed Entropy Coupled Boundary Condition is then derived in order to account for this interaction in the framework of a Helmholtz solver where the baseline flow is assumed at rest. When fed with appropriate transfer functions to model the entropy generation and convection from the flame to the exit, the Helmholtz solver proves able to predict the presence of an unstable mode around 350 Hz, in agreement with both the LES and the experiments. This finding supports the idea that

Combustion Noise in Modern Aero-Engines

Combustion noise has recently been the subject of attention of both the aeroacoustic and the combustion research communities. Over the last decades, engine manufacturershave made important efforts to significantly reduce fan and jet noise, which increased the relative importance of combustion noise. Two main mechanisms of combustion-noise generation have been identified: direct combustion noise, generated by acoustic waves propagating to the outlet, and indirect combustion noise, caused by the acceleration of entropy waves (or hot spots) and vorticity waves through turbine blades. The purpose of this paper is to describe some of the predicting tools used in combustion noise, as well as to present an overview on some recent experimental studies.

Using Boundary Conditions to Account for Mean Flow Effects in a Zero Mach Number Acoustic Solver

The present study is devoted to the modeling of mean flow effects while computing thermoacoustic modes under the zero Mach number assumption. It is first recalled that the acoustic impedance modelling a compressor or a turbine must be pre- scribed under an energetical form instead of the classical acous- tic variables. Then we demonstrate the feasibility to take into ac- count the coupling between acoustic and entropy waves in a zero Mach number framework to capture a family of low frequency entropic modes. The proposed approach relies on a new Delayed Entropy Coupled Boundary Condition (DECBC) and proves able to capture a family of Low frequency entropic mode even though no mean flow term is included into the fluctuating pressure equa- tion.