Comparison of inviscid and viscous vortex shedding from translating and rotating plates

TL;DR

The authors develop and validate an inviscid vortex-sheet model with continuous leading-edge shedding and compare its predictions to direct Navier–Stokes simulations at $Re \approx 1000$ across ~70 unsteady plate maneuvers. They find strong agreement in body-dominated regimes for normal-force histories and near-edge vorticity structure, while flow-dominated cases, particularly at low angles of attack, show reduced quantitative accuracy due to absence of viscous dissipation and sensitivity to near-body dynamics. The study demonstrates that stable LE shedding in an inviscid framework enables robust, high-throughput exploration of unsteady high-$Re$ flows and clarifies regimes where inviscid models are reliable for force prediction and interpretation. It also highlights the necessity of viscous simulations to capture flow-dominated phenomena and Reynolds-number dependent effects.

Abstract

We compare an inviscid vortex sheet model with continuous leading-edge shedding with direct Navier-Stokes simulations over a wide range of unsteady plate motions at moderate Reynolds number ($\mathrm{Re} \approx 1000$). Approximately $70$ distinct kinematic configurations are examined, spanning both body-dominated and flow-dominated regimes. In body-dominated motions, where the fluid dynamics are primarily driven by prescribed plate accelerations, the inviscid model accurately reproduces normal force histories and the qualitative structure of the induced vorticity field. In flow-dominated configurations, with quasi-periodic vortex shedding, agreement with force predictions is good but reduced at low angles of attack, reflecting the greater sensitivity of vortex shedding dynamics to physical and computational parameters. The ability of the present formulation to accommodate stable, continuous leading-edge vortex shedding enables uniform comparisons across diverse motions and clarifies the regimes in which inviscid vortex sheet models can be used reliably for force prediction and physical interpretation.

Figures (23)

• Figure 1: Schematic showing the plate in $(a)$ the lab frame and $(b)$ the body frame.
• Figure 2: (a) The drag coefficient $F_D$ and (b) the length of the recirculation bubble $S$ over time for an impulsively started flat plate moving normal to itself with unit speed at $\mathrm{Re} = 1000$, compared with data obtained from figure 13 in Koumoutsakos_Shiels_1996.
• Figure 3: Vorticity fields (labeled by color bar) for an impulsively started plate at times $t$ = 0.5, 2.5, 6, and 10, with circulation bubble outlined in black and $\mathrm{Re} = 1000$. The streamlines (top half) and vorticity contours (bottom half) from figure 20 in Koumoutsakos_Shiels_1996 are overlaid on each panel.
• Figure 4: The net normal force up to time $t = \textrm{KC}$ (top) and time $t = 3\textrm{KC}$ (bottom) for both the viscous (blue) and inviscid (orange) models.
• Figure 5: Vorticity $\omega$ at $t = \textrm{KC}$ for an oscillating plate with $\textrm{KC} = 0.4,\ \ldots, 3.6$ in inviscid (right) and viscous (left) models.