Topological Analysis of Turbulent Wake Behind a Trapezoidal Mixing Tab Using DES and Velocity Gradient Tensor Invariants

Abstract

This study numerically investigates the complex three-dimensional turbulent flow around a trapezoidal mixing tab, which acts as a vortex generator in an infrared signature Suppression System(IRSS). While previous studies heavily relied on steady Reynolds-averaged Navier-Stokes(RANS) models, this research employs the Detached Eddy Simulation(DES) to precisely capture unsteady vortex shedding and micro-scale mixing mechanisms. The simulation was conducted for an incompressible pipe flow at a Reynolds number of 150,000. Grid convergence was verified using Pope’s criterion, and the DES results demonstrated a superior agreement with experimental velocity profiles compared to the RANS predictions. Furthermore, the turbulent kinetic energy spectrum closely followed Kolmogorov’s -5/3 decay law in the inertial subrange, confirming the validity of the resolved flow scales. By utilizing the Q-R topological diagram based on the invariants of the velocity gradient tensor, the dynamic evolution of vortical structures was quantitatively classified. The analysis revealed that the stable focus/stretching(SFS) and unstable focus/compressing(UFC) topologies actively govern the turbulent energy cascade, reflecting a dynamic equilibrium of vortex creation and viscous dissipation. Ultimately, the high-fidelity DES successfully captures the intricate fragmentation of hairpin vortices, providing profound insights for optimizing fluid mixing systems.