Effects of inflow perturbations generated with hydrodynamic stability concept on the time dependent flow development

Abstract

This study investigates the influence of inflow conditions on the development of turbulence in axially rotating pipe flow, with the aim of improving our understanding of turbulence onset in transitional regimes and generation of proper inflow conditions. The flow configuration is motivated by both fundamental interest and practical relevance in rotating machinery and pipe transport systems, where inflow disturbances and swirl can significantly affect transition dynamics. The analysis begins with the spatial inviscid hydrodynamic stability problem, solved for six configurations involving distinct mean axial velocity profiles, both with and without rotation. The parallel-shooting method is employed to compute eigenvalues and mode shapes. The inviscid results reveal both stable and unstable wave-like solutions, with mode shapes resembling Bessel functions in simpler cases. The propagation direction and growth rates of these modes seemed to vary with rotation and velocity profile. To capture viscous effects, the spatial viscous stability problem is then solved for two physically relevant cases, laminar axial profile without swirl and a turbulent profile with swirl. The viscous spectrum reveals two mode families, one converging to inviscid modes with slightly different dispersion characteristics, and a second "viscous subset" exhibiting distinct spatial structures and primarily downstream propagation. These include wall and centre modes, whose spatial coherence decreases with increasing Reynolds number and frequency. No unstable viscous modes are observed within the investigated parameter space. Large Eddy Simulations (LES) are performed using OpenFOAM with a radius-based Reynolds number of 2500 and a swirl number of 0.5, employing the Smagorinsky subgrid-scale model. Inflow perturbations are constructed from hydrodynamic stability modes, selected based on orthogonality to ensure a representative and non-redundant perturbation basis. A control case without inflow perturbations is also simulated. The results show that inflow conditions derived from viscous stability theory significantly improve the accuracy of turbulent statistics. Specifically, turbulence characteristics begin to converge approximately 40 pipe diameters downstream when perturbations are imposed, in contrast to the delayed and less realistic transition observed in the unperturbed case. Overall, this study demonstrates that accurately prescribed inflow perturbations, grounded in linear stability theory, can substantially enhance the fidelity of LES in transitional pipe flows with swirl. These findings underscore the importance of coupling theoretical stability analysis with numerical simulations to better predict and control turbulence onset.