A novel modal expansion method for low-order modeling of thermoacoustic instabilities in complex geometries

Abstract

This work proposes an improvement to existing methods based on modal expansions used for the prediction of thermoacoustic instabilities in zero Mach number flow conditions. Whereas the orthogonal basis made of the acoustic eigenmodes of the domain bounded by rigid walls is classically used, an alternative method based on a modal expansion onto an over-complete set of acoustic eigenmodes is proposed. This allows avoiding the misrepresentation of the acoustic velocity field often observed near non rigid-wall boundaries. A Low Order Model network utilizing a state-space framework is then built upon this novel type of modal expansion. Several test cases, going from non reacting ducts to a complex geometry with combustion, are studied to assess the potential of the approach. The methodology not only successfully mitigates the misrepresentation in the acoustic field in the presence of non-rigid-wall boundaries, but it also drastically improves the convergence speed. The modularity of the method and its ability to handle complex geometries are illustrated by considering a configuration featuring an annular chamber, an annular plenum, as well as multiple burners. This novel technique is expected to bring worthy improvements to existing Low Order Models using modal expansions for the prediction of combustion instabilities.

Symmetry breaking of azimuthal waves: Slow-flow dynamics on the Bloch sphere

“…In previous studies dealing with thermoacoustic instabilities in annular configurations, the time delay between the acoustic field and the heat release rate oscillations has been accounted for in different ways: i) by using the simple n-τ formulation (e.g. [48,19]) and its state-space equivalent [49] for modelling the linear thermoacoustic problem in time and frequency domain, ii) by using measured flame describing functions (e.g. [50,28]) for modelling the nonlinear thermoacoustic problem in frequency domain, and iii) by modelling the flame response to acoustic perturbations with a distribution of time delays [14], or by using state-space representations of experimentally measured FTFs [15,26] for simulating the nonlinear thermoacoustic problem in time domain.…”

Phenomenological Reduced-order Modeling of Sub-critical Combustion in Cryogenic Rocket Engines: an Application to the Prediction of High-frequency Combustion Instabilities

“…Following the work conducted at ONERA over the last decade [11,14,29], high-fidelity Large Eddy Simulations of a representative case are being carried out to confront the results of the ROM, using the CEDRE platform showcased in this study. Finally, the a priori choice of a suitable modal basis is still a current topic of research [25] and will need to be tackled.…”

“…This is typically done by considering the acoustic eigenmodes of the cavity; however, these modes may not be optimal for the disperse phase, which is generally localized in the vicinity of the injectors, thus requiring high-frequency acoustic modes to be properly resolved. Using a specific basis for each variable alleviates this issue and allows better faster spectral convergence [25].…”

Vibration Analysis and Parameter Optimization of the Longitudinal Axial Flow Threshing Cylinder

“…A low order frequency is harmful to the structure; therefore, the influence of a high order vibration frequency on the threshing cylinder was not considered [31]. The modal analysis of a threshing cylinder in the free state showed that the six degrees of freedom of movement and rotation of the model were unconstrained, and the simulation results showed that the first six rigid body modes had zero natural frequency [32,33].…”