Mechanics/heat-transfer relation for particulate materials. Final report

Abstract

The original goal of this study was to try and understand the relationship between the thermal and mechanical properties of particulate flows. Two situations were examined. The first is a study of the effects of simple shear flows, as a embryonic flow type on the apparent thermal conductivity and apparent viscosity of a dry granular flow. This program has demonstrated that both quantities increase linearly with the imposed velocity gradient, implying that both are driven by the square root of the granular temperature (just as the viscosity and thermal conductivity of a billiard ball gas varies as the square root of the thermodynamic temperature). In addition, the studies the differences in the mechanism of internal transport of the two quantities. They indicate that both heat and momentum may be transported in the streaming mode, i.e. by the random motions of the constituent particles, but, as heat transfer is a relatively slow process, only momentum is exchanged in interparticle collisions. The second study involved fluidized beds. The original idea was to try and relate the heat transfer behavior of a fluidized bed to the "particle pressure _, the forces by only the particle phase of the twophase mixture. This part of the study was really two steps in itself. While terms involving the particle pressure and other interparticle forces have long appeared in multiphase flow models, these terms have never been measured. Consequently, there is great value in simply measuring the particle pressures. We performed this study in a gas fluidized bed and determined that the principle generation of particle pressure came from the motion of bubbles and that the particle pressure could be related to the bubble size. The second phase of the study was to relate the particle pressure to the heat transfer• This, unfortunately proved unsuccessful. TABLE OF CONTENTS 1.0 Introduction 2.0 Reynolds' Analogy for Particle Flows: The Relationship between the 3 Apparent Thermal Conductivity and Viscosity for a Sheared Granular Material 2.1 Exp_rimental Apparatus 2.2 Experimental Procedure 2.3 Calculation of the Apparent Thermal Conductivity 2.4 Results and Discussion 14 2'5 Conclusions 3.0 Particle Pressures in Gas Fluidized Beds 3.1 The Particle Pressure Transducer 3.2 T_ting of the Particle Pressure Transducer 28 3.3 Flwldized Bed 33 3.4 Partick\: Pressures in Gas-Fluidized Beds 33 3.5 The New Particle Pressure Transducer 44 3.6 Particle Pressure in Gas-Fluidized Beds Undergoing Particulate Fluidization 46 3.7 The Relationship between the Particle Pressure and Reat Transfer 50 3.8 Conclusions 52 4.0 Appendix-Experimental Innovations 54 4.1 Heater Control Circuit 54 4.2 Thermocouple Connections through Slip Rings 55 References 58 , CIIAPTER2: REYNOLDS' ANALOGY FOR PARTICLE FLOWS: THE RELATIONSHIP BETWEEN THE APPAKENT THERMAL CONDUCTIVITY AND VISCOSITY FOR A SHEARED GRANULAR MATERIAL "Reynolds analogy" for fluids is a term that is commonly used to describe relationships between their mechanical behavior-e.g. the shear force exerted on a s...