Coherent Structure Dynamics of Heat Transfer in Wakes of an Inclined Elliptical Cylinder: A Novel Lagrangian Framework

TL;DR

This paper presents a new Lagrangian framework to analyze heat transfer in the wake of an inclined elliptical cylinder, linking flow structures with heat transfer dynamics across various angles.

Contribution

It introduces a novel Lagrangian-based method to predict heat transfer behavior by analyzing the evolution of coherent flow structures in unsteady wakes.

Findings

Active saddle points correlate with surface heat transfer trends.

Displacement of saddle points influences heat transfer efficiency.

The framework predicts key transitional events in heat transfer profiles.

Abstract

This work introduces a novel Lagrangian-based framework to analyze forced convective heat transfer in the unsteady wake of a heated elliptical cylinder inclined at angles ranging from $\theta = 0^\circ$ to $90^\circ$, in $15^\circ$ increments with $Pr = 0.71$ at a fixed Reynolds number of $Re = 100$. The framework correlates the temporal evolution of the surface-averaged Nusselt number with the dynamic behavior of Lagrangian saddle points, formed at the intersection of repelling and attracting Lagrangian Coherent Structures (LCSs) extracted via Finite-Time Lyapunov Exponent (FTLE) fields.The study is carried out within a precisely constructed observational domain, a previously unreported influential region in the near-wake, where the trajectory analysis of the newly defined key saddle points (active saddle points) consistently aligns with the trends in surface heat transfer. This domain enables predictive identification of key transitional events in the Nusselt number profile, including local extrema and slope inflections, across all inclination angles. The analysis reveals that oblique displacement of active saddle points enhances heat transfer by promoting the shedding of repelling LCSs, while parallel displacement leads to weakened heat transfer due to the delayed detachment of repelling coherent structures. The proposed framework enables the construction of a temporal function that closely replicates the monotonicity and transitional features of the Nusselt number evolution. Furthermore, threshold displacement metrics are defined for dominant repelling LCSs to correspond with peak heat transfer efficiency. The proposed methodology not only generalizes across a wide range of inclination angles but also provides a physically interpretable framework for predicting heat transfer enhancement based on coherent structure evolution in unsteady flows.