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 influence of thermocapillary forces on buoyancy-driven convection is numerically simulated for shallow open cavities with differentially heated endwalls and filled with low-Prandtl-number fluid. Calculations are carried out by solving two-dimensional Navier-Stokes equations coupled to the energy equation, for three aspects ratios A = (length/height) = 4, 12.5 and 25, and several values of the Grashof number (up to 6 × 104) and Reynolds number (|Re| ≤ 1.67 × 104). Thermocapillarity can have a quite significant effect on the stability of a primarily buoyancy-driven flow. The result of the combination of the two basic mechanisms (thermo-capillarity) and buoyancy) depends on whether their effects are additive (positive Re) or opposing (negative Re); counter-acting mechanisms yield more complex flow patterns. The critical Grashof number Grc for the onset of the unsteady regime is found to decrease substantially within a small range of negative Re, and to increase for positive Re (and also for large negative Re). For Gr = 4 × 104, A = 4 and small negative Reynolds numbers, −2.4 × 103 ≤ Re < 0, mono-periodic and bi- or quasi-periodic regimes are shown to exist successively, followed by a reverse transition. The development of the instabilities from an initial steady-state regime has been investigated by varying Re for Gr = 1.5 × 104 (below Grc at Re = 0); the onset of buoyant instabilities is enhanced in a narrow range of Re only (-1200 < Re < -200). It is also noteworthy that for small enough Grashof numbers (e.g. Gr = 3 × 103), a steady-state solution prevails over the whole range of Reynolds numbers investigated. This means that a critical Grashof number exists below which the effect of the thermocapillary forces is no longer destabilizing.

https://www.cambridge.org/core/services/aop-cambridge-core/content/view/S0022112092001009

Buoyancy- and thermocapillary-driven flows in differentially heated cavities for low-Prandtl-number fluids

Thermocapillary convection arising in small-depth layers (long horizontal cavities) subject to a horizontal temperature gradient is studied numerically. A broad range of values of the Reynolds-Marangoni number, Re, is considered for three values of the aspect ratio (A = length/height). For the largest aspect ratio considered, A = 25, the fully developed Poiseuille-Couette solution is reached, but only for moderate Re. The limiting Re value for the observability of such a fully developed solution is derived as a function of A(Re [les ] 20A). For Re [les ] 20A, the flow exhibits three distinct regimes, in the upwind, central and downwind regions, respectively. The Poiseuille-Couette solution (when it exists) fills the central region, and the flow is accelerated, in the upwind region, to reach this Poiseuille-Couette solution at a distance that is proportional to Re. In the downwind region, where the flow is deflected by the endwall, a multi-roll structure is exhibited for Re [ges ] 1330. The number of rolls increases with Re. When Re > 20A, the upwind and downwind regions coalesce and some of the downwind rolls can be suppressed. Most of the computations concern interfacial conditions (with fixed temperature distribution) for which the dynamical solution is decoupled from the thermal one. A few thermal solutions are given herein, for Pr = 0.015 only.

Thermocapillary convection in long horizontal layers of low-Prandtl-number melts subject to a horizontal temperature gradient

Convection is an important parameter in crystal growth from the melt. A driving force for convection besides buoyancy, crystal rotation and crucible rotation, is the surface-tension gradient due to temperature or concentration gradients in the free melt surface. This article points out that in the various melt-growth techniques with free melt surface, e.g. the floating-zone technique, the Czochralski technique and the open-boat zoning, surface-tension-driven flow is likely to occur and to influence the growth. Surface-tension-driven flow is especially important in small melt volumes, near the free surface of larger volumes, or under conditions of weightlessness (e.g. in Spacelab). Under the large temperature gradients encountered in crystal growth, surface-tension-driven flow can become time dependent. Numerical studies, experiments on surface-tension-driven flow, and observations in real growth systems are reviewed.

A. Scharmann

Papers

Prandtl-number dependence of the onset of thermocapillary flow in floating zones

Microgravity experiments on the transition from laminar to oscillatory thermocapillary convection in floating zones

Marangoni and buoyant convection in an open cavity under reduced and under normal gravity

The magnitude of thermocapillary convection in larger melt volumes