Effects of the Mean Flow Field on the Thermo-Acoustic Stability of Aero-Engine Combustion Chambers

Abstract

This paper presents a finite element methodology to predict the thermoacoustic eigenmodes of combustion chambers using the linearized Navier-Stokes equations (LNSE) in frequency space. The effect of the mean flow on the acoustics is accounted for. Besides scattering and refraction of acoustic waves in shear layers, this set of equation describes two main damping mechanisms. One is related to the generation of entropy waves, so called hot-spots, in flame regions. The other is related to the transformation of acoustic energy into vorticity waves at sharp leading or trailing edges. Both fluctuation types, i.e. entropy and vorticity, are convected by the mean flow, leading to significant damping when the fluid discharges into an open outlet. In combustion chamber environments these waves are accelerated in the downstream high pressure distributor and are partially transformed back into acoustic waves constituting to the feedback loop of thermo-acoustic instabilities. Accurate prediction of the eigenmodes and eigenfrequencies of instability require therefore to take these interaction effects into account. First, the accuracy of the LNSE approach, to capture the damping generated by the first mechanism of entropy generation and convection, is investigated for a generic premixed flame configuration. Solutions of the LNSE are compared to the analytic solutions as well as eigenvalues determined by an Helmholtz ansatz. Later methodology assumes a quiescent medium and neglects all interactions of acoustics with the mean flow. It is shown that large errors are introduced with increasing Mach-number. To illustrate errors assuming a quiescent medium for realistic combustion chambers, the LNSE are used to assess the eigenmodes of a two-dimensional aero-engine combustor including strong shear regions, in the next step. The non-isothermal mean flow field is obtained performing an incompressible RANS simulation. It features an expanding jet with inner and outer recirculation zones. The acoustic computations using LNSE reveal a set of unstable and neutral hydrodynamic modes in addition to acoustic modes. Both damping mechanisms are present and contribute to the overall system stability. Again the obtained solution is compared to the solution of an Helmholtz code and differences are discussed.

Boundary Conditions for the Computation of Thermoacoustic Modes in Combustion Chambers

“…T t2 (19) in which it has been assumed that the fluid has a constant specific heat c p and thereforeĥ = c pT .…”

“…The total pressure ratio π c is defined by a second order polynomial π c = aṁ 2 + bṁ + c and clearly depends on the performance characteristics of the compressor. The logarithmic derivative of T t can be then computed as: Adding a compact one dimensional compressor to the system is therefore equivalent to add an additional term to the left hand side of the energy equation (19), as follows :…”

“…The development of LEE solvers for complex geometries associated to combustion chambers is still in a nascent state. In such an approach the stability not only of acoustic modes, but also vortical and entropy modes is studied [19]. Nevertheless, the mean flow velocity field in typical combustion chambers is very low, and assuming that convective terms do not significantly contribute in the analysis of combustion instabilities is reasonable.…”

Numerical Investigation of Indirect Noise Generation by Accelerated Vorticity

“…For that purpose a hybrid CFD/CAAapproach (Computational Fluid Dynamics and Computational Aeroacoustics) is applied, which may not only be utilized for noise prediction problems, but also in the frame of thermoacoustic stability analyses in gas turbine combustors. 12,13 The hybrid approach relies on the separation of the flow field into a time-averaged statistically stationary mean part and an instationary fluctuating part. The fluctuations are assumed to be linear and represent the coherent acoustic and vortical structures.…”

Prediction of Combustion Noise in a Model Combustor Using a Network Model and a LNSE Approach

“…In this way the influence of the acoustic propagation model and the source term on the resulting pressure spectrum can be identified and separated, which are the two major goals of this study. Both the LOTAN and LNSE solver have already demonstrated their capabilities for accurate combustion noise predictions in academic cases [1,2] as well as industry-relevant combustor geometries [22,23]. Moreover, LOTAN and LNSE were already validated against each other in the frame of a simple model combustor [24].…”