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

Introduction The theory of liquid sloshing dynamics in partially filled containers is based on developing the fluid field equations, estimating the fluid free-surface motion, and the resulting hydrodynamic forces and moments. Explicit solutions are possible only for a few special cases such as upright cylindrical and rectangular containers. The boundary value problem is usually solved for modal analysis and for the dynamic response characteristics to external excitations. The modal analysis of a liquid free-surface motion in a partially filled container estimates the natural frequencies and the corresponding mode shapes. The knowledge of the natural frequencies is essential in the design process of liquid tanks and in implementing active control systems in space vehicles. The natural frequencies of the free liquid surface appear in the combined boundary condition (kinematic and dynamic) rather than in the fluid continuity (Laplace's) equation. For an open surface, which does not completely enclose the field, the boundary conditions usually specify the value of the field at every point on the boundary surface or the normal gradient to the container surface, or both. The boundary conditions may be classified into three classes (Morse and Fesbach, 1953): the Dirichlet boundary conditions , which fix the value of the field on the surface; the Neumann boundary conditions , which fix the value of the normal gradient on the surface; and the Cauchy conditions , which fix both value of the field and normal gradient on the surface. Each class is appropriate for different types of equations and different boundary surfaces.

Liquid Sloshing Dynamics: Fluid field equations and modal analysis in rigid containers

In this work, we study the effect of fluid flow on the growth dynamics during solidification of tetragonal Ni2B from the undercooled melt. Different experimental techniques are applied to generate varying fluid flow velocities in undercooled samples, electromagnetic levitation under 1 g conditions (1 g EML) and in reduced gravity (μg EML) as well as the melt-fluxing technique and electrostatic levitation. The propagation of the solid-liquid interface apparent on the surface of solidifying samples is observed by high-speed video imaging while the non-contact measurement of the undercooling prior to solidification is accomplished by IR-pyrometry. It is demonstrated that fluid flow has a substantial influence on the growth kinetics. As revealed by an extended sharp-interface model, this effect is mainly attributed to the substantial change in growth kinetics caused by a convection induced transition from dendrites to more faceted solidification structures.

The effect of fluid flow on the solidification of Ni2B from the undercooled melt

Liquid Sloshing Dynamics: Equivalent mechanical models

Liquid Sloshing Dynamics: Introduction

The combined effect of thermal Marangoni convection induced by a gradient of temperature imposed upon the free surface of a liquid sphere and the residual natural convection steming from the still existing micro-gravity field in an orbiting space laboratory has been investigated The case of a constant and linearly dependent axial residual gravity field has been considered, for which the Stokes equation in the approximation of Boussinesq have been solved By the introduction of a dynamic Bond-number derived as the ratio of the Grashof number to the Reynoldsnumber based upon the Marangoni flow the predominance of Marangoni- (for Bo 0) or natural convection (for Bo ∞) could be determined Streamlines, radial- and angular velocity distributions have been obtained analytically The combined effect of Marangoni- and natural convection is of importance for space processings In addition the isothermal lines are presented for various imposed temperature distributions at the free surface of the liquid sphere



Es wird das Zusammenwirken thermischer Marangonikonvektion und der von der Restschwere in einem Weltraumlabor herruhrenden naturlichen Residualkonvektion in einer Flussigkeitskugel bestimmt Dabei wird die Oberflache der Kugel (Schmelze) einer axialsymmetrischen Temperatur ausgesetzt und in einem konstanten und linear variablen Mikrogravitationsfeld behandelt Stromfunktion und Geschwindigkeitsverteilung werden aus der Stokesgleichung in der Approximation von Boussinesq analytisch gelost Der Einflus des Residualschwerefeldes im Raumfluglabor wird durch das Einfuhren der dynamischen Bondzahl angegeben, wobei diese aus dem Verhaltnis der Grashofzahl zur Reynoldszahl, welche auf der Marangonikonvektion basiert, abgeleitet wird Fur verschwindende Bondzahlen dominiert die Marangonikonvektion, wahrend fur sehr grose Bondzahlen die naturliche Konvektion vorherrscht Fur lineare und quadratische Temperaturverteilungen werden die Stromlinien numerisch bestimmt

H. F. Bauer

Papers

Combined Residual Natural and Marangoni Convection in a Liquid Sphere Subjected to a Constant and Variable Micro‐Gravity Field