arXiv subjects

Eunok Yim

Publications and source records attributed to Eunok Yim.

5 recordsLinked to original sources

arXiv2026

A minimal model of pump foil dynamics

Pump foiling enables a hydrofoil surfboard to sustain forward motion on flat water using only periodic leg pumping, converting vertical oscillations into hydrodynamic lift and thrust. We present a minimal mechanical model of pump foil propulsion, formulated as a coupled second-order system for horizontal and vertical translation and pitch in an inertial frame. The rider-board system is modeled in reduced form, with the rider mass concentrated at the body center and the foil mass assigned to the mast-linker pivot, about which the front and rear wing dynamics are written. Hydrodynamic loading includes quasi-steady lift and drag, buoyancy, and rotational effects, including rotational lift and nonlinear rotational drag. Under simplified control assumptions in which the pumping frequency is fixed and the net rider pumping input is represented by a single effective force-amplitude parameter, the model predicts sustained stable forward-propulsion regimes at modest forcing amplitude and small positive pitch angle. In this regime, the front wing acts primarily as the main lifting surface, while the rear wing, although contributing less to vertical support, is essential for pitch stability because of its longer moment arm. These results provide a mechanistic interpretation of pump foil propulsion and identify measurable quantities and parameter sensitivities that can guide targeted field and laboratory experiments and help refine assumptions on rider control inputs and hydrodynamic loading.

physics.flu-dyn↗

arXiv2026

Vortex breakdown in a hydro turbine draft tube swirling jet

The swirling flow in a Francis type hydropower turbine is known to be susceptible to the formation of a large helical structure, commonly referred to as a vortex rope. This vortex rope can be interpreted as an unstable mode associated with vortex breakdown. This perspective is adopted here in a simplified laminar flow setting. The helical vortex rope mode is shown to bifurcate supercritically from an axisymmetric baseflow in a Hopf bifurcation within a turbine draft tube. When wall friction effects are neglected, a large recirculation region at the axis can form and a range of subcritical solutions is identified for a flow regime corresponding to partial load of the turbine. The existence of these subcritical solutions promotes the emergence of a hysteresis loop. We further describe a regular dynamics of a formation of recirculation bubble at the axis and its destruction due to the emergence of a helical vortex rope at its periphery. Increasing the axial flow discharge towards the regime corresponding to nominal turbine load leads to an unfolding of the steady solutions branch in a transcritical bifurcation. This bifurcation takes place at finite Reynolds number and complements existing evidence of transcritical bifurcation of the swirling jet flows, previously reported only in the inviscid limit.

physics.flu-dyn↗

arXiv2026

Linear Stability and Structural Sensitivity of a Swirling Jet in a Francis Turbine Draft Tube

Motivated by the need to better understand flow unsteadiness in hydraulic turbines, we perform a local linear stability and adjoint-based sensitivity analysis of the turbulent swirling jet at the outlet of a Francis turbine. We use measured mean flow and turbulence profiles at several operating conditions (below, at, and above the best efficiency point (BEP) flow rate) and perform a stability analysis. Incorporating eddy viscosity $\nu_t$ into the analysis strongly damps inviscid growth rates and restricts instability to low azimuthal modes $m\in [-1,2]$, in better agreement with experiments. Three turbulent viscosity closures (constant, mixing-length and measured $k-\varepsilon$ based) yield similar spectra, with close agreement between mixing length and measured models, all identify partial load (0.92 BEP) as the most unstable regime. Sensitivity results show that axial velocity modifications primarily control growth rates, whereas azimuthal velocity changes mainly shift frequencies. We also derive the sensitivity kernel of the spectrum to turbulent viscosity modifications and find that spatial variations of eddy viscosity are essential for predicting the unstable mode range. The predictions accurately estimate stability changes for small variations in operating point. We further analyze the flow using classical inviscid swirling jet instability criteria (the generalized Rayleigh discriminant) and WKB analysis to predict the stability to broader operating points and reconcile these results to the stability and sensitivity analyses. The approach used in this study is fast and simple to model, but it neglects draft tube geometry (non-parallel effects), motivating future global stability and sensitivity analyses.

physics.flu-dyn↗

arXiv2022

Leidenfrost flows: instabilities and symmetry breakings

Leidenfrost drops were recently found to host strong dynamics. In the present study, we investigate both experimentally and theoretically the {flows structures and stability} inside a Leidenfrost water drop as it evaporates, starting with a large puddle. As revealed by infrared mapping, the drop base is warmer than its apex by typically 10$^{\circ}$C, which is likely to trigger bulk thermobuoyant flows and Marangoni surface flows. Tracer particles unveil complex and strong flows that undergo successive symmetry breakings as the drop evaporates. We investigate the linear stability of the baseflows in a non-deformable, quasi-static, levitating drop induced by thermobuoyancy and effective thermocapillary surface stress, using only one adjustable parameter. The stability analysis of nominally axisymmetric thermoconvective flows, parametrized by the drop radius $R$, yields the most unstable, {thus, dominant, azimuthal modes (of wavenumber $m$). Our theory predicts well the radii $R$ for the mode transitions and cascade with decreasing wavenumbers from $m=3$, $m=2$, down to $m=1$ (the eventual rolling mode that entails propulsion) as the drop shrinks in size}. The effect of the escaping vapor is not taken into account here, which may further destabilize the inner flow and couple to the liquid/vapor interface to give rise to motion Bouillant et al. (2018) [8] and Brandao et al. (2020) [9].

physics.flu-dyn↗

arXiv2019

Nonlinear evolution of the centrifugal instability using a semi-linear model

We study the nonlinear evolution of the centrifugal instability developing on a columnar anticyclone with a Gaussian angular velocity using a semi-linear approach. The model consists in two coupled equations: one for the linear evolution of the most unstable perturbation on the axially averaged mean flow and another for the evolution of the mean flow under the effect of the axially averaged Reynolds stresses due to the perturbation. Such model is similar to the self-consistent model of \cite{Vlado14} except that the time averaging is replaced by a spatial averaging. The non-linear evolutions of the mean flow and the perturbations predicted by this semi-linear model are in very good agreement with DNS for the Rossby number $Ro=-4$ and both values of the Reynolds numbers investigated: $Re=800$ and $2000$ (based on the initial maximum angular velocity and radius of the vortex). An improved model taking into account the second harmonic perturbations is also considered. The results show that the angular momentum of the mean flow is homogenized towards a centrifugally stable profile via the action of the Reynolds stresses of the fluctuations. The final velocity profile predicted by \cite{Kloosterziel07} in the inviscid limit is extended to finite high Reynolds numbers. It is in good agreement with the numerical simulations.

physics.flu-dyn↗