NUSSELT NUMBER FOR DIRECT CONTACT EVAPORATION OF A MOVING ELLIPSOIDAL DROP IN AN IMMISCIBLE LIQUID

Since Sideman et al.^[1] derived an analytical solution of the Nusselt number for a spherical drop in the direct contact evaporation in an immiscible liquid, many researchers have performed theoretical research on this field under different assumptions [2]-[6]. However drops moving in another immiscible liquid do not take a spherical form, but oblate form, which may be well approximated as an ellipsoid. This paper establishes the mathematical model of heat transfer for a moving ellipsoidal drop in an immiscible liquid, and presents results from numerical calculation. The relationship of the Nusselt number with the Weber number and the Peclet number is given, which is suitable for a relatively large range of We and Pe. The theoretical results for the Nusselt number show good agreement with experimental data. Some important conclusions are obtained.     

Hydrodynamische Einlauflänge und Widerstandsgesetz von reibungsmindernden kationschen Tensidlösungen

Zusammenfassung Durch Zugabe geeigneter Tensidsysteme in Wasser kann der Str?mungsdruckverlust in geraden Rohren erheblich gesenkt werden. Die diesem Effekt zugrunde liegenden Mechanismen wurden in früheren Arbeiten eingehend diskutiert. In dieser Arbeit werden neue Ergebnisse vorgestellt, die sowohl die Bestimmung der hydrodynamischen Einlaufl?nge als auch die Ermittlung der Widerstandsbeiwerte im ausgebildeten Str?mungszustand erm?glichen. Für den Bereich der ausgebildeten Rohrstr?mung wird eine neue Berechnungsgleichung vorgeschlagen. Durch Erweiterung der bisherigen Modellvorstellungen ergibt sich ein Widerstandsgesetz für den gesamten Wirkungsbereich des Tensids. Die Ergebnisse stützen sich auf Untersuchungen mit zwei verschiedenen Additivsystemen, bei denen die Parameter Str?mungsgeschwindigkeit, Temperatur und Einsatzkonzentration variiert wurden.     

Gas/liquid interfacial area per unit volume and volumetric mass transfer coefficient in stirred slurry reactors

In three-phase systems, where the liquid constitutes the continuous phase, solid is the catalyst and gas represents the dispersed phase, there are decisive criteria which have to be observed in reactor design. These are e.g. the interfacial area per unit volume between gas and liquid, the volumetric mass transfer coefficient and the mass transfer coefficient. The basic aim of the present work was therefore the investigation of these parameters in relation to the main influencing parameters. Process parameters stirrer speed and superficial gas velocity were varied as well as the physical properties such as liquid viscosity, solids concentration, particle diameter and a geometrical parameter, i.e. reactor diameter. The sulphite method was employed for the determination of these values. The test results confirmed the known relationships of power consumption and superficial gas velocity. An increase in the liquid viscosity leads to a decrease in all the tested values. In most cases, suspended solid particles lead to a lowering of the test values. The influence of the tank diameter on the plots of the test values against specific power consumption turned out to be invariant so that a scale-up of geometrically similar systems can be carried out at constant power consumption, superficial gas velocity and liquid viscosity.