Abstract: Accurately capturing the interaction between fluid motion, chemical reactions, and electric fields is essential for understanding flame behavior in advanced combustion systems relevant to propulsion, energy conversion, and emissions control. In this work, we present a two-dimensional computational framework in cylindrical coordinates for simulating laminar non-premixed flames with electrostatic coupling representative of weakly ionized plasma-assisted combustion environments. The solver employs a high-order compact finite difference scheme for spatial discretization, enabling improved resolution of steep gradients commonly observed in reacting flows, together with a fourth-order temporal integration method to ensure numerical stability and accuracy. Detailed combustion chemistry is incorporated through a steady flamelet formulation, providing an efficient yet robust description of chemical kinetics within the CFD framework. To account for electric field-assisted effects in a simplified and physically consistent manner, the governing equations are extended to include Poisson’s equation for the electric potential and transport equations for one positively and one negatively charged species, assuming a weakly ionized regime in which neutral species dominate the flow dynamics. Electric field effects are modeled by solving species continuity equations for one positively charged and one negatively charged species, coupled with Poisson’s equation for the electric potential to obtain a self-consistent electric field. The resulting electrostatic and plasma-induced effects enter the governing equations through explicit source terms in the momentum and energy equations, accounting for electric body forces and Joule heating for weakly ionized plasma. A systematic parametric study is conducted using a canonical co-flow methane–air diffusion flame to examine the influence of flow conditions and combustor geometry. The results show that plasma forcing leads to a noticeable increase in flame length, as identified by extended OH and CH radical distributions. This behavior is attributed to a combination of electric-field-driven charged species drift, enhanced convective transport, and localized Joule heating, which collectively modify scalar transport and delay radical recombination along the axial direction. Overall, the proposed high-order framework provides a validated and computationally efficient tool for high-resolution simulation of chemically reacting flows with weak plasma coupling, offering new insight into the role of electric fields in laminar non-premixed flame dynamics.

Abstract: Cracks in planetary gearbox casings generate vibration responses, which, when properly isolated and analyzed, can be used for monitoring structural degradations. This paper provides a signal processing framework to effectively track casing crack related features in planetary gearboxes using carrier synchronous signal average (C-SSA). The proposed algorithm is based on processing the hunting-tooth synchronous signal average (H-SSA) to extract the C-SSA which contains the cyclic interaction between the gear loadings and the corresponding casing response. The root mean square (RMS) of the C-SSA signal can then serve as a health condition indicator (CI) to track crack propagation. Further enhancement can be achieved by applying the Hilbert transform (HT) on the C-SSA using the full bandwidth to derive squared envelope signal, which clearly shows the modulations from the crack response and further enhances the trending capability. To remove cyclic temperature influences observed in the trends, singular spectrum analysis technique (SSAT) has been used, ensuring the trend reflects the changes purely due to the damage progression. Experiments using three casing-mounted sensors show good capability to track crack progression. Tests under 100%, 125%, and 150% load levels show consistent performance across these operating conditions, with better results seen at higher loads. The results demonstrate that C-SSA and its squared envelope signal effectively enhances the sensitivity and reliability of vibration-based crack detection, providing a practical tool for long-term structural health monitoring of planetary gearbox.