An Inverted Conical Flame, anchored at a central bluff-body, in an unconfined burner configuration, is a flame that may be used to further understand more complex flame configurations, such as in aeronautical engines combustion chambers. This article involves the modeling of an unconfined laminar premixed ICF, anchored at a central cylindrical rod. The computational fluid dynamic modeling of this flame configuration involves the solution of transport equations of species mass, momentum and energy, which is computationally expensive. A skeletal methane/air chemical kinetic mechanism is used to capture a plethora of time and length scales. Reduced Order Models (ROM) have been shown to increase the computational efficiency of dynamical systems modeling. Accordingly, in this work a ROM of the steady ICF is developed, using the volume flow rate of the combustible mixture as input variable of the ROM, and the velocity components and the temperature fields as the output. The aim is to optimize the flame modeling computational time, thus paving the way to the reduced order modeling of acoustically excited, unstable, laminar premixed inverted conical flames. A model of the ICF has been developed with Fluent 2019 R2, and the analysis of a diversity of properties and species included in the combustion process has been made. Since a skeletal chemical kinetic model is used, the characterization of the flame is marked by its different property scales, allowing the flame front recognition over the field of CH 2 . However, this CFD model does not present a static convergence behavior, but oscillates over a pseudo-steady state point. Thus an approximation of the statistical steady state has only been achieved by ensemble averaging the results. Therefore, the ROM of the ICF has been developed over a set of averaged data generated with Fluent, and its results shows agreement with CFD results, presenting an average overall error smaller than 3 %.

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With the rising complexity of dynamical systems generating ever more data, learning dynamics models appears as a promising alternative to physics-based modeling. However, the data available from physical platforms may be noisy and not cover all state variables. Hence, it is necessary to jointly perform state and dynamics estimation. In this paper, we propose interconnecting a high-gain observer and a dynamics learning framework, specifically a Gaussian process state-space model. The observer provides state estimates, which serve as the data for training the dynamics model. The updated model, in turn, is used to improve the observer. Joint convergence of the observer and the dynamics model is proved for high enough gain, up to the measurement and process perturbations. Simultaneous dynamics learning and state estimation are demonstrated on simulations of a mass-spring-mass system.

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The study of combustion-thermoacoustic instabilities is a topic of interest in the development of engines. However, the modeling of these systems involves a high computational burden. This paper focuses on a simpler class of systems that still features such instabilities: inverted conical flames anchored on a central bluff-body. Here these flames are modeled by solving species mass momentum and energy transport equations, coupled with a skeletal methane/air chemical kinetic mechanism. The aim is to characterize the dynamic behavior of inverted conical flames, both due to their natural dynamics and to external incoming velocity fluctuations. The main contribution is the detailed model of the flames, including the smallest scales. The analysis of the impact of the mesh adaption on the flame response shows a trade-off between model accuracy and computational burden that can be adjusted by changing the temperature gradient threshold. The flame response analysis in terms of the temperature and OH mass fraction gives a detailed characterization of the flame front behavior in its different scales, both in time and space. The analysis of the flame front dynamic response employing FFT shows that these have a natural frequency of 35 Hz, and this frequency interacts with the flame response due to incoming velocity excitations. More specifically, when forcing the flame with low frequencies (f ≤ 125 Hz) the flame responds only to the forcing and some harmonics, whereas when forcing between 125 < f ≤ 172 Hz the flame response comprises both the natural and forced behavior. Forcing beyond 200 Hz shows the natural flame response only. KEYWORDSlaminar premixed flame; thermo-acoustic instability; flame transfer function; flame frequency response; computational fluid dynamics CONTACT L. da Costa Ramos.