Otto Molerus

Heat transfer in fluidized beds

Preface. Introduction. Particle migration at solid surfaces and heat transfer in bubbling fluidized beds. Heat transfer in particle beds. Heat transfer mechanisms in bubbling fluidized beds. Prediction of minimum fluidization velocity. Physical properties of the media. Prediction of heat transfer in bubbling fluidized beds at Ar10 8. Physical background to convective heat transfer. Heat transfer at elevated temperatures. Historical remarks. Fluid dynamics of circulating fluidized beds. Experimentally determined wall-to-suspension heat transfer coeffients in circulating fluidized beds. Prediction of the heat transfer in circulating fluidized beds without considering the influence radiation. Prediction of the heat transfer in circulating fluidized beds at elevated temperatures. Heat transfer in homogenous multiphase flows. Prediction of the heat transfer with particulate fluidization. General aspects of heat transfer in fixed and fluidized beds percolated by a gas at Re>1. References. Index

Particle migration at solid surfaces and heat transfer in bubbling fluidized beds—II. Prediction of heat transfer in bubbling fluidized beds

In a gas fluidized bed, heat to and from a heat exchanger surface can be transferred by the gas and/or particle convection. Despite more than 40 years of intensive research on this topic, the contribution through particle convection remains inadequately described, while the gas convective component has been straightforward to predict. In Part 1 of this paper, the pulsed light method of tracing particles in a fluidized bed close to a wall has been introduced, allowing a better understanding of how particle convective heat transfer works. In Part 2, a correlation is proposed, which allows prediction of the heat transfer coefficient in dependence of the superficial gas velocity. The correctness of the prediction is tested by comparison with more than 20 measurements covering the following range of system data and operational conditions: particle size 74–4000 μm particle density 26-11,800 kg m−3 gas pressure 0.03-2 MPa bed temperature 290–1050 K excess gas velocities up to 2.5 ms−1. In the investigated temperature range of 290–1050 K there appears to be no significant contribution to the heat transfer due to radiation.

Heat transfer in moving beds with a stagnant interstitial gas

The contact resistance for the heat transfer between adjacent particles is identified as the limiting factor for heat transfer in moving beds of particles consisting of rather hard solid materials and filled with a stagnant interstitial gas. It defines the short time heat transfer, which is determined by the thermal conductivity of the gas between the heated surface and the first row of particles, as well as the long time heat transfer which is characterized by the progression of the temperature front into the bulk of the bed. It also governs the steady heat conduction through a stationary bed kept at different temperatures at its ends.

Particle migration at solid surfaces and heat transfer in bubbling fluidized beds—I. Particle migration measurement systems

Abstract Heat transfer between submerged surfaces and fine particle fluidized beds is affected by particle migration to and from the exchanger surface. Owing to the lack of appropriate measurement techniques up to now, however, modelling of particle migration to and from heat exchanger surfaces was based primarily on speculation and less on experimental evidence. The present work has therefore the following two objectives. In this part of the paper, the measuring and analysing systems are described. A collection of luminous particles adjacent to a transparent solid surface is marked by a light pulse transmitted via fibre optics. The fate of the initially bright spot is recorded on videotape. Digital image analysis of spot migration gives statistically determined migration velocities along the heating surface, whereas the decay in luminosity defines the particle exchange frequency in the direction perpendicular to the solid surface. Comparison of the measured particle exchange frequencies with the simultaneously measured heat transfer coefficients reveals a direct correspondence between particle migration and heat transfer. The measured velocities of particles parallel to the wall provide an explanation for the well-known effect of probe size on the measured heat transfer coefficients. Details of fine particle behaviour and visualized by inspection of microscopic video images. Part 2 of this paper deals with the prediction of heat transfer in bubbling fluidized beds, using the results obtained with the experimental technique, described in Part 1.

Appropriately defined dimensionless groups for the description of flow phenomena in disperse systems

In process design, the state of flow in a disperse system must be taken into consideration not only with respect to the aerodynamic resistance, but also with respect to heat and mass transfer as well as chemical reactions. According to the state-of-the-art, convective heat transfer, for example, is usually described by relations of the form of Nu = Nu(Re, Pr). From the definition of the Reynolds number, it follows conclusively, that unique functions Nu = Nu(Re, Pr) are obtained only for geometrically similar systems. With disperse systems, however, geometrical similarity is lost in two ways: with a change in the particle shape, and also with a change in the void fraction. These peculiarities result in a corresponding complexity, e.g. the observed heat transfer phenomena. An alternative approach is proposed as following: For the description of the aerodynamic resistance R of the elements of a disperse system as usual the Reynolds number Re = (ud)v, but also a new drag number, Dr = (6ϱfR)(πμ2) are introduced, i.e. it is proposed to represent the aerodynamic resistance of disperse systems in the form of Dr = Dr(Re) instead of the usual form cD(Re), because the drag number is free from the kinematic variables u, and d of the flow field. In particular, within reasonable limits of accuracy, two geometrically dissimilar systems exhibit the same Nusselt number, when their drag numbers coincide, i.e. the alternative form Nu = Nu(Dr, Pr) seems to be more appropriate. This latter feature will be shown in detail by the prediction of the heat transfer coefficients between submerged surfaces and fixed as well as fluidized beds percolated by a gas at higher Reynolds numbers.

Fluid mechanics in terms of eigenparameters: Part I: Fundamentals

Abstract Three different types of flow are investigated, namely viscous flow, “no length” problems, i.e. flow along straight walls, and “single length” problems in the cases of the flow around geometrically similar objects, respectively, fully developed laminar or turbulent flow in straight tubes. With these types of flow a maximum number of four eigenparameters is identified, namely the two material properties: fluid density ρ F and viscosity μ , and two system parameters: characteristic length D and characteristic velocity u . With the help of these eigenparameters the respective dimensionless and invariant forms of the Navier–Stokes equation are derived. The invariant forms result in dimensionless coordinates and velocities in the form of ratios, respectively, Reynolds numbers. Aerodynamic resistance manifests in the form of single scaling factors with the dimensions of pressure gradients. In Part II of the paper exemplary applications, in particular with respect to the influence of fluid dynamics on the heat transfer, are discussed.

The relevance of dimensionless frequencies for turbulent flow phenomena observed in chemical engineering practice

Abstract Turbulent flows are powerful means for promoting many processes of chemical engineering. Through more than a century of specialists’ research, various more or less complex calculating procedures for the prediction of turbulent mean flow are available. As a rule, however, these approaches do not provide an intuitive understanding of the underlying physics of flow. Therefore, an approach based on the physical property frequency is proposed which may be seen as a step towards an easier interpretation of turbulent flow phenomena. The significance of the physical property frequency is exemplified by two classical examples of theoretical fluid mechanics, namely the flow around cylindrical objects and fully developed turbulent pipe flow

Theorie der Fließeigenschaften kohäsiver Schüttgüter

Kohasive Schuttguter sind dadurch gekennzeichnet, das sie in begrenztem Mase fahig sind, Zugspannungen zu ubertragen. Diese Eigenart insbesondere feinkorniger Schuttguter hat ihre Ursache darin, das bei diesen die zwischen den Partikeln wirksamen Haftkrafte im Vergleich zu den eingepragten Kraften nicht mehr vernachlassigbar klein sind. Die eigentumliche Schwierigkeit fur Theorie und Experiment beim Umgang mit kohasiven Schuttgutern besteht nun darin, das die zwischen den Partikeln wirksamen Haftkrafte in ihrer Intensitat ihrerseits von der Belastungsvorgeschichte des Schuttgutes abhangen. Aus diesem komplexen Materialverhalten folgt fur jede theoretische Darstellung, das sie einerseits hinreichend einfach sein mus, damit sie in der Praxis uberhaupt auswertbar ist, das sie aber andererseits keine Ubervereinfachung sein darf, wenn sie noch wesentliche Zuge der Realitat enthalten soll.

Fluid mechanics in terms of eigenparameters. Part II : Exemplary applications

Abstract In chemical engineering, fluid mechanics is a tool for the successful design of processes, which involve heat and mass transfer as well as chemical reactions. In order to exemplify this particular role of fluid mechanics, the implications of fluid mechanics on the heat transfer are demonstrated exemplarily.

Vibration induced pneumatic conveying of friable materials

A new transport system has been developed which combines vibration of the conveying pipe with amplitudes in the order of fractions of a millimeter with rather low superficial velocities of the carrying gas. The observed rates of fracture or attrition, respectively show that even very fragile materials are conveyed gently with the new system. This effect is achieved mainly by a drastically reduced minimum velocity for reliable transport of the particulate material.