Preface Introduction 1. Fluid field equations and modal analysis in rigid containers 2. Linear forced sloshing 3. Viscous damping and sloshing suppression devices 4. Weakly nonlinear lateral sloshing 5. Equivalent mechanical models 6. Parametric sloshing (Faraday's waves) 7. Dynamics of liquid sloshing impact 8. Linear interaction of liquid sloshing with elastic containers 9. Nonlinear interaction under external and parametric excitations 10. Interactions with support structures and tuned sloshing absorbers 11. Dynamics of rotating fluids 12. Microgravity sloshing dynamics Bibliography Index.

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Liquid Sloshing Dynamics

The paper reviews the roots, the state-of-the-art and perspectives of multibody system dynamics. Some historical remarks show that multibody system dynamics is based on classical mechanics and its engineering applications ranging from mechanisms, gyroscopes, satellites and robots to biomechanics. The state-of-the-art in rigid multibody systems is presented with reference to textbooks and proceedings. Multibody system dynamics is characterized by algorithms or formalisms, respectively, ready for computer implementation. As a result simulation and animation are most important. The state-of-the-art in flexible multibody systems is considered in a companion review by Shabana.

https://hosting.umons.ac.be/html/mecara/grasmech/PaperSchiehlen.pdf

Multibody System Dynamics: Roots and Perspectives

A simpler model for concentrated vortices

Lift-generated vortex wakes of subsonic transport aircraft

The vortex tube or Ranque–Hilsch vortex tube is a device that enables the separation of hot and cold air as compressed air flows tangentially into the vortex chamber through inlet nozzles. Separating cold and hot airs by using the principles of the vortex tube can be applied to industrial applications such as cooling equipment in CNC machines, refrigerators, cooling suits, heating processes, etc. The vortex tube is well-suited for these applications because it is simple, compact, light, quiet, and does not use Freon or other refrigerants (CFCs/HCFCs). It has no moving parts and does not break or wear and therefore requires little maintenance. Thus, this paper presents an overview of the phenomena occurring inside the vortex tube during the temperature/energy separation on both the counter flow and parallel flow types. The paper also reviews the experiments and the calculations presented in previous studies on temperature separation in the vortex tube. The experiment consisted of two important parameters, the first is the geometrical characteristics of the vortex tube (for example, the diameter and length of the hot and cold tubes, the diameter of the cold orifice, shape of the hot (divergent) tube, number of inlet nozzles, shape of the inlet nozzles, and shape of the cone valve. The second is focused on the thermo-physical parameters such as inlet gas pressure, cold mass fraction, moisture of inlet gas, and type of gas (air, oxygen, helium, and methane). For each parameter, the temperature separation mechanism and the flow-field inside the vortex tubes is explored by measuring the pressure, velocity, and temperature fields. The computation review is concentrated on the quantitative, theoretical, analytical, and numerical (finite volume method) aspects of the study. Although many experimental and numerical studies on the vortex tubes have been made, the physical behaviour of the flow is not fully understood due to its complexity and the lack of consistency in the experimental findings. Furthermore, several different hypotheses based on experimental, analytical, and numerical studies have been put forward to describe the thermal separation phenomenon.

/pdf/review-of-ranque-hilsch-effects-in-vortex-tubes-3lx1l9q9ac.pdf

Review of Ranque–Hilsch effects in vortex tubes

Analytical and experimental studies to investigate selected fluid parameters in vortex chambers are presented. From the analytical model, the dimensionless quantities of the core size, static pressure drop across the chamber, and radial static pressure distribution are shown to be functions of the chamber geometry only. Experimental results confirm all of the findings.

Theoretical and experimental studies on vortex chamber flows

Determination du rayon de l'ecoulement inverse adimensionnel a partir des equations de mouvement et d'energie. Ce rayon ne depend que des parametres geometriques de la chambre a tourbillon

Reverse flow radius in vortex chambers

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.

https://www.cambridge.org/core/services/aop-cambridge-core/content/view/S0022112090000702

A note on liquid vortex sloshing and Kelvin's equilibria

A new model that is capable of generating singleor double-celled steady, incompressible, intense vortices is proposed. As was evident in earlier experiments, depending on the values of scaling constants, it is shown that the axial-velocity component may attain pro les ranging from jet-like to wake-like. In general, the radial-velocity pro le has a similar shape as the tangential velocity, developing a direction reversal near the axis of rotation when the two-celled vortex appears. For the case of a one-celled vortex, the tangential velocity behaves like that of Rankine’s vortex with viscous smoothing near the core. However, as the reverse  ow inside the core matures the tangential velocity reduces gradually from the forcedvortex pro le while its maximum value is augmented. The evolution from a one-celled to a two-celled vortex is also characterized by a migration of the vorticity peak from the central axis toward the core. The present theory suggests that the implementation of the experimental data for the tangential velocity near the core depends on the quality of the secondary  ow.

Georgios H. Vatistas

Papers

Theoretical and experimental studies on vortex chamber flows

Reverse flow radius in vortex chambers

A note on liquid vortex sloshing and Kelvin's equilibria

New Model for Intense Self-Similar Vortices

Liquid sloshing in rectangular road containers