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Observations of liquid vortex sloshing and Kelvin's equilibrium states were made inside a cylindrical container using a spinning disk near its base. Both steady and periodic free-surface sloshing phenomena were found to take place. During periodic sloshing, the air core sustained shape transformations, assuming an elliptical cross-section at the end, and then collapsed forming a pair of vortices. Kelvin's equilibrium states emerged at lower liquid levels. These were stable within an interval of rotational speeds. The bandwidth of stationary states decreased as the wavenumber (N) increased. For N greater than six, the states appeared critically stable. Between equilibria, unstable transitional regions were found to exist. As the liquid level was decreased, the core shape spectrum shifted towards smaller frequencies.

We experimentally corroborate the core analytical deductions of Thomson's 124-year-old theorem, vis-à-vis the stability of a ring of N vortices. Observations made in water vortices produced inside a cylinder via a revolving disk confirm that the regular N-gons are stable for Nor=8. The N

A study of the liquid behaviour in horizontal cylindrical road containers undergoing a steady turning manoeuvre is presented and discussed. The steady state solutions are derived analytically from the hydrostatic equations. The transient solutions are obtained by numerical integration of the Navier-Stokes, continuity and free-surface equations. The non-dimensional governing equations are solved in primitive variables by using a modified marker-and-cell technique which involves the interpolation-reflection type boundary conditions developed for this investigation. The mathematical model of the liquid motion includes all essential non-linear effects and allows the damped natural frequencies of liquid vibrations to be obtained as well as the magnitudes of the liquid slosh loads. This study also enables the coupled directional dynamics of the ‘vehicle-liquid tank’ system undergoing different road manoeuvres to be investigated by integrating the non-linear fluid slosh model and an appropriate vehicle model simultaneously.

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Strongly swirling vortex chamber flows are examined experimentally and numerically using the Reynolds stress model (RSM). The predictions are compared against the experimental data in terms of the pressure drop across the chamber, the axial and tangential velocity components, and the radial pressure profiles. The overall agreement between the measurements and the predictions is reasonable. The predictions provided by the numerical model show clearly the forced and free vortex modes of the tangential velocity profile. The reverse flow (or back flow) inside the core and near the outlet, known from experiments, is captured by the numerical simulations. The swirl number has been found to have a measurable impact on the flow features. The vortex core size is shown to contract with the swirl number which leads to higher pressure drop, higher peak tangential velocity, and deeper radial pressure profiles near the axis of rotation. The adequate agreement between the experimental data and the simulations using RSM turbulence model provides a valid tool to study further these industrially important swirling flows.

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