Particle granular temperature in gas fluidized beds

In this paper we introduce and validate a novel non-intrusive probe of the average kinetic energy, or granular temperature, of the particles at the wall of a gas fluidized bed. We present data on the granular temperature of monodispersed glass spheres which span region B, and extend into region A, of the Geldart powder classification. The underlying physics of the measurement is the acoustic shot noise excitation of the surface of the fluid bed vessel by random particle impact. Quantitative determination of the average particle granular temperature is obtained through independent measurement of the wail transfer function determining the coupling between the acoustic shot noise excitation at one location and the response of an accelerometer at another location. We validate the concept and calibration of this acoustic shot noise probe in the frequency range 10-20 kHz, through a comprehensive series of laboratory measurements with gasses and cylinders of significantly different acoustic properties. We demonstrate its utility by presenting the first data on the dependence of the granular temperature on gas flow and particle diameter and make the first observation of a change in the character of the fluidization transition from first order (hysteretic and discontinuous) to second order (reversible and continuous) for Geldart B glass spheres as the A/B boundary is approached. We observe a striking difference in the dependence of the granular temperature on gas flow between Geldart B and A glass spheres, that suggests a fundamental difference in particle dynamics between spheres in the two Geldart regimes. Finally we use the vibrational probe to study the time dependence of the granular temperature under bed collapse conditions when fluidizing gas is withdrawn rapidly from the system. We show an exponential time dependence with a time constant of the order of 100 ms, and demonstrate the consistency of this result with a Langevin equation for the sphere velocity with a time constant derived from the sphere fluctuation velocity and a collisional coefficient of restitution of 0.9. From these results for the granular temperature and a kinetic model for a dense granular gas, we present estimates for the inertial pressure, velocity of sound, viscosity, and diffusion constant of the dense phase of a gas fluidized bed as a function of particle diameter and gas superficial velocity. The implication of these results for current models of gas fluidized beds, and the fundamental basis of the Geldart classification is discussed.