Global linear stability analysis of a slit flame subject to intrinsic thermoacoustic instability

The present study makes use of the adjoint modes of the Linearized Reactive Flow (LRF) equations to investigate the Intrinsic Thermoacoustic (ITA) feedback loop of a laminar premixed slit flame. The analysis shows that the ITA feedback loop is closed by vorticity generated in the boundary layer of the slit by impinging acoustic waves penetrating the slit. In this region, adjoint vorticity shows a high sensitivity of the flow. It is also hypothesised that the ITA eigenmode smoothly transitions to a purely hydrodynamic mode -- vortex shedding -- for a passive flame. The computational domain is chosen sufficiently short so as to isolate the ITA feedback loop from cavity modes. This analysis is made possible by the holistic character of the LRF model, i.e. a direct linearization of the non-linear reactive flow equations, including explicit finite rate chemistry and avoiding idealization of the flow.Comment: 11 pages, 6 figures. Presented at the International Congress on Sound and Vibration, July 2023, Pragu

Effect of hydrogen addition on the consumption speed of lean premixed laminar methane flames exposed to combined strain and heat loss

This study presents a numerical analysis of the impact of hydrogen addition on the consumption speed of premixed lean methane-air laminar flames exposed to combined strain and heat loss. Equivalence ratios of 0.9, 0.7, and 0.5 with fuel mixture composition ranging from pure methane to pure hydrogen are considered to cover a wide range of conditions in the lean region. The 1-D asymmetric counter-flow premixed laminar flame aCFPF with heat loss on the product side is considered as a flamelet configuration that represents an elementary unit of a turbulent flame and the consumption speed is used to characterize the effect of strain and heat loss. Due to the ambiguity in the definition of the consumption speed of multi-component mixtures, two definitions are compared. The definition of the consumption speed based on the heat release results in lower values of the stretched flame speed and even an opposite response to strain rate for some methane-hydrogen-air mixtures compared to the definition based on the fuel consumption. Strain rate leads to an increase in the flame speed for the lean methane-hydrogen mixtures, reaching a maximum value after which the flame speed decreases with strain rate. Heat loss decreases the stretched flame speed and leads to a sooner extinction of the flamelet due to combined strain and heat loss. Hydrogen addition and equivalence ratio significantly impact the maximum consumption speed and the flame response to combined strain rate and heat loss. The effect of hydrogen on the thermo-diffusive properties of the mixture, characterized by the Zel'dovich number and the effective Lewis number, are also analyzed and related to the effect on the consumption speed. Two definitions of the Lewis number of the multi-component fuel mixture are evaluated against the results from the aCFPF.Comment: Submitted to journal Combustion Theory and Modelling - Manuscript ID TCTM-2022-06-6

Learning Hidden States in a Chaotic System: A Physics-Informed Echo State Network Approach

International audienceWe extend the Physics-Informed Echo State Network (PI-ESN) framework to reconstruct the evolution of an unmeasured state (hidden state) in a chaotic system. The PI-ESN is trained by using (i) data, which contains no information on the unmeasured state, and (ii) the physical equations of a prototypical chaotic dynamical system. Non-noisy and noisy datasets are considered. First, it is shown that the PI-ESN can accurately reconstruct the unmeasured state. Second, the reconstruction is shown to be robust with respect to noisy data, which means that the PI-ESN acts as a denoiser. This paper opens up new possibilities for leveraging the synergy between physical knowledge and machine learning to enhance the reconstruction and prediction of unmeasured states in chaotic dynamical systems

Quantitative comparison of presumed-number-density and quadrature moment methods for the parameterisation of drop sedimentation

In numerical weather prediction models, parameterisations are used as an alternative to spectral modelling. One type of parameterisations are the so-called methods of moments. In the present study, two different methods of moments, a presumed-number-density-function method with finite upper integration limit and a quadrature method, are applied to a one-dimensional test case (‘rainshaft’) for drop sedimentation. The results are compared with those of a reference spectral model. An error norm is introduced, which is based on several characteristic properties of the drop ensemble relevant to the cloud microphysics context. This error norm makes it possible to carry out a quantitative comparison between the two methods. It turns out that the two moment methods presented constitute an improvement regarding two-moment presumed-number-density-function methods from literature for a variety of initial conditions. However, they are excelled by a traditional three-moment presumed-number-density-function method which requires less computational effort. Comparisons of error scores and moment profiles reveal that error scores alone should not be taken for a comparison of parameterisations, since moment profile characteristics can be lost in the integral value of the error norm

Categorization of Thermoacoustic Modes in an Ideal Resonator with Phasor Diagrams

A recent study (Yong, Silva, and Polifke, Combust. Flame 228 (2021)) proposed the use of phasor diagrams to categorize marginally stable modes in an ideal resonator with a compact, velocity-sensitive flame. Modes with velocity phasors that reverse direction across the flame were categorized as ITA modes. The present study extends this concept to growing and decaying modes. In other words, with the method proposed, it is possible to distinguish whether a given thermoacoustic mode -- regardless of its stability -- should be categorized as acoustic or ITA. The method proposed does not rely on any parametric sweep, but on the angle relating the velocity phasors across the flame. This method of categorization reveals distinct regions in the complex plane where acoustic and ITA eigenfrequencies are localized. Additionally, we analyze the medium oscillation at the flame location to construct a physically intuitive understanding of the proposed categorization method.Comment: to be published in Combustion and Flam

Causality and intrinsic thermoacoustic instability modes

International audienceDirect numerical simulation of a confined laminar premixed flame has been performed in an anechoic combustor, showing self-sustained intrinsic thermoacoustic oscillations. Theoretical predictions based on acoustic jump relations and the n − τ model for the flame are presented and causality concerns are discussed. The instability’s frequency and mode structure are recovered numerically with very good accuracy. A detailed discussion on the interplay of the physical phenomena responsible for this dynamical coupling is also carried out