Ph.D. Thesis Proposal

Haotian Sun

"Data-Enabled Analysis of Linear Combustion Instability in a Distributed System"

Wednesday, June 19th
2:30 P.M.
Montgomery Knight 317

Abstract: 
This thesis proposal addresses an integrated theoretical and numerical study of combustion instability, which impacts the performance and reliability of various chemical conversion systems across diverse applications. The proposal begins by introducing the motivation for studying combustion instability, emphasizing its significance for advancing combustion technology and the broader field of dynamical systems. The research work starts with the development of a single-point combustion response model, and then expands into a distributed domain using machine learning techniques with a complete workflow established.

A comprehensive theoretical framework is first established by deriving a generalized wave equation from the conservation equations of mass, momentum, and energy in three dimensions. The acoustic pressure is used as the primary variable. An approximation method based on the Galerkin method is implemented to reduce the governing partial differential equations to a system of ordinary differential equations, facilitating stability analysis. The discussion includes Rayleigh's criterion, a fundamental concept in combustion dynamics research, helping to predict and analyze the stability of combustion systems. Additionally, the limitations of traditional models, such as the time-lag  model, are identified, underscoring the need for improved models to enhance the accuracy of combustion instability predictions. A baseline study demonstrates the foundational approach planned to be used to develop the novel methods proposed in this research.

The proposal then delves into the specific research objectives and methodologies. The first objective focuses on developing a single-point combustion response model, including impulse response analysis, application of the Lasso method for model development, and the creation of a transfer function. The second objective expands this model into a domain-distributed focus, addressing challenges such as selecting influential points in the domain, reducing the entire domain using emulation, and balancing time and resource costs. The third objective establishes a workflow using existing software, discussing the challenges of achieving a unified framework and balancing time and resource costs. The development from theoretical analysis to practical application outlines the methodologies to be employed in achieving the research objectives.

Overall, this thesis proposal aims to bridge the gap between theoretical models and practical applications in the study of combustion instability. By addressing the identified gaps and improving upon existing models, the proposed research seeks to contribute valuable insights into the field of combustion stability and the broader study of dynamical systems.

Committee: 

• Dr. Vigor Yang (AE)
• Dr. Yingjie Liu (Math)
• Dr. Joseph OefeLein (AE)