POD based methods for Force & Flow Structure Estimation

Abstract

Separated flows arise when boundary layers detach from solid surfaces and form shear layers that roll into vortical structures. These vortices redistribute momentum, amplify pressure fluctuations, and produce unsteady forces that govern the performance and reliability of engineering systems. Interpreting these forces requires not only measuring their magnitude, but resolving how the underlying coherent motions form, evolve, and interact with the surrounding geometry. This thesis applies flow–field decomposition techniques to experimental velocity data in two representative separated–flow environments: a vortex–induced vibration (VIV) cylinder wake and an immersion heat–exchanger rod–bundle.

The first study examines the wake of a one–degree–of–freedom elastically mounted circular cylinder operating within the lock–in regime, where wake shedding synchronizes with structural oscillation. Experiments were conducted in the University of Calgary recirculating water tunnel using a rigid circular cylinder mounted on a linear elastic guide, for a reduced–velocity range of U* = 3 – 12, corresponding to Reynolds numbers Re ≈ 3.2 × 10^3 – 1.3 × 10^4. Time–resolved particle image velocimetry (PIV) is analyzed using a moving–reference Spectral Proper Orthogonal Decomposition (mr–SPOD), which extracts frequency–ranked coherent structures in a body–fixed frame aligned with the cylinder motion. The dominant shedding modes captures more than 80% of the fluctuating kinetic energy, and its modal coefficient exhibits a approximately proportional relationship with the vorticity–induced lift obtained from an auxiliary–potential force partitioning framework. This structure–resolved decomposition separates kinematic contributions from vorticity–driven loading and attributes fluctuations directly to individual coherent motions in the wake. Using only the leading modes, the modal reconstructions reproduce over 85% of the measured instantaneous lift fluctuations. This demonstrates that a small set of modes governs the majority of hydrodynamic loading in nominally two–dimensional VIV and provides a physically interpretable route to force estimation from experimental velocity fields.

The second study applies proper orthogonal decomposition to planar PIV measurements acquired in the meridional mid-plane of a full-scale immersion heat exchanger, designed and constructed by the author in partnership with Thermon. Measurements span 3000 ≤ Re ≤ 17000 and capture the cross-flow past a transparent rod–baffle arrangement. Across the explored Reynolds number range, the leading POD modes identify the principal separated–flow mechanisms: gap–vortex formation between rods, baffle–edge shedding at structural discontinuities, and large–scale recirculation spanning multiple subchannels. The kinetic energy captured by the dominant mode decreases with increasing Reynolds number, indicating a shift from quasi–periodic gap dynamics to multi–scale turbulent exchange and intermittent cross–channel transport. These modal trends clarify how separation, mixing, and unsteady loading emerge in rod–bundle geometries where the flow is tightly confined and strongly influenced by the baffle and rod arrangement.

Together, the results establish low–order modal decomposition as a quantitative bridge between experimental velocity fields and the fluid–mechanical processes responsible for unsteady forces, providing a coherent framework for interpreting separated–flow physics in both canonical and industrial environments.