Session: 04-09 Combustion Dynamics III

Submission Number: 175717

Flame Describing Function of Jet in Crossflow Flames Using the G-Equation 

The jet in crossflow (JICF) emerges as an important configuration in modern gas turbine combustors, particularly in axially-staged systems designed to achieve high turbine inlet temperatures while reducing NOx emissions. In such systems, the collision of the injected jet with the crossflow results in complex flame structures formed by the interaction of the two streams. These interactions make the flame highly sensitive to acoustic and convective perturbations, and therefore directly relevant to thermoacoustic instabilities. In theoretical studies, two dimensional JICF configurations were studied. However, three-dimensional configuration would exhibit fundamentally different behavior, which requires more complex mathematical treatment and makes numerical investigations particularly necessary. This highlights the need for systematic investigations of acoustic–flame interactions in JICF configurations.

Systematic studies of the response of JICF flames to acoustic forcing remain limited, thereby constraining the predictive capability of thermoacoustic instability models. In this context, the G-equation provides a kinematic simplification that avoids solving the full reactive flow field, while still capturing the essential flame kinematic mechanisms relevant to instability. By avoiding the direct solution of chemical kinetics and turbulence, and retaining only the flame surface kinematics, the method enables efficient parametric exploration while preserving physical consistency in flame propagation. Those characteristics make the G-equation an attractive approach for investigating instability mechanisms in canonical configurations such as JICF flames.

This study aims to quantify the frequency response of laminar JICF flames using the G-equation framework and to calculate the corresponding flame describing functions. To this end, a three-dimensional G-equation is employed to compute the kinematic evolution of the flame surface under prescribed velocity forcing. Perturbations are introduced through harmonic modulation of the jet velocity, the crossflow velocity, or both simultaneously, representing different acoustic–convective coupling pathways. Frequency is varied over a wide Strouhal number range, and forcing amplitudes are adjusted from small perturbations in the linear regime to larger values that elicit nonlinear responses. Flame response is measured by evaluating surface integrated quantities based on the G=0 isosurface, which serve as indicators of global heat release fluctuations. This methodology enables detailed analysis of frequency dependent gain/phase behavior and amplitude-dependent nonlinear effects. It there by offer a clearer picture of instability mechanisms in JICF flames.

The present study yields the following key outcomes. First, the FDF of laminar JICF flames will be obtained, enabling quantitative assessment of the quasi-steady response in the low frequency regime as well as the convective delay associated with jet penetration. Second, the variation of the flame describing function (FDF) with increasing forcing amplitude will be characterized, highlighting gain saturation, a progressive phase shift, and the emergence of second harmonic components. Third, mean-shift phenomena and nonlinear effects will be identified, which are particularly relevant to instability development.

These results will provide a kinematic baseline dataset that contributes to a deeper understanding of the instability mechanisms in JICF flames. In addition, the G-equation approach offers a simple yet physically consistent framework that can serve as a useful reference for comparison with high fidelity LES, DNS, and experimental studies. Such a baseline is essential for isolating the role of geometry and kinematics in thermoacoustic instability, and for developing more reliable reduced order models of flame dynamics in crossflow fed combustors.

Presenting Author: Juhoon Son Korea Advanced Institute of Science and Technology

Presenting Author Biography: Juhoon Son is a Ph.D. candidate in the Combustion Modeling Laboratory at KAIST, South Korea. His research focuses on flame dynamics and thermoacoustic instabilities in premixed combustion systems, with particular emphasis on applying the G-equation framework to a wide range of combustion configurations.

Authors:

Juhoon Son Korea Advanced Institute of Science and Technology
Jaewon Yoon korea advanced institute of science and technology
Yong Jea Kim korea advanced institute of science and technology
Dong-Hyuk Shin korea advanced institute of science and technology