van den Cm Bleek

Non-intrusive determination of bubble and slug length scales in fluidized beds by decomposition of the power spectral density of pressure time series

Abstract In this paper we show that spectral analysis of non-intrusive time dependent pressure measurements in bubbling and circulating gas–solid fluidized beds permits to obtain the first estimates of bubble, gas slug, and solids cluster length scales from pressure fluctuation data. These length scales are calculated from the incoherent cross power spectra of pressure signals measured in the bubbling or circulating bed and in the plenum. Remarkable quantitative agreement with bubble diameter data is found, and equally remarkable agreement is obtained with independent estimates of gas slug lengths by others in circulating fluidized beds. These results demonstrate the possibility of greatly expanding the information that can be obtained non-intrusively from gas–solid fluidized beds.

Origin, propagation and attenuation of pressure waves in gas-solid fluidized beds

Abstract Recently reported results on the origin, propagation and attenuation of pressure waves in bubbling gas—solid fluidized beds are re-evaluated and the results are compared with additional experiments reported here. It is found that the measured pressure fluctuations are a result of slow and fast propagating pressure waves. Pressure waves with high propagation velocities (> 10 m/s) are unambiguously identified as compression waves, which move upwards and downwards. Upward moving compression waves originate from gas bubble formation and gas bubble coalescence. The amplitude of upward moving pressure waves is linearly dependent on the distance to the bed surface. Downward moving compression waves are caused by gas bubble eruptions at the fluidized bed surface, bubble coalescence and by changes in bed voidage. In this case the pressure wave amplitude is independent of the distance to the bed surface. Pressure waves with propagation velocities of less than 2 m/s are caused by rising gas bubbles. These pressure waves move upwards only, with an amplitude proportional to the bubble size. The average wave propagation velocity measured in a freely bubbling bed is lower than that predicted from the pseudo-homogeneous compressible wave theory owing to the presence of slowly rising gas bubbles. The average propagation velocity of pressure waves in a gas—solid circulating fluidized bed is adequately described as a function of local voidage by pseudo-homogeneous compressible wave theory. At low voidages in the bottom of the riser, the propagation velocity is lowered by the presence of gas bubbles or large gas voids.

Eulerian simulations of bubbling behaviour in gas-solid fluidised beds

Abstract In literature little attempt has been made to verify experimentally Eulerian-Eulerian gas-solid model simulations of bubbling fluidised beds with existing correlations for bubble size or bubble velocity. In the present study, a CFD model for a free bubbling fluidised bed was implemented in the commercial code CFX of AEA Technology. This CFD model is based on a two fluid model including the kinetic theory of granular flow. Simulations of the bubble behaviour in fluidised beds at different superficial gas velocities and at different column diameters are compared to the Darton et al. (1977) equation for the bubble diameter versus the height in the column and to the Hilligardt and Werther (1986) equation, corrected for the two dimensional geometry using the bubble rise velocity correlation of Pyle and Harrison (1967). It is shown that the predicted bubble sizes are in agreement with the Darton et al. (1977) bubble size equation. Comparison of the predicted bubble velocity with the Hilligardt and Werther (1986) equation shows a deviation for the velocity of smaller bubbles. To explain this, the predicted bubbles are divided into two bubble classes : bubbles that have either coalesced, broken-up or have touched the wall, and bubbles without these occurrences. The bubbles of this second class are in agreement with the Hilligardt and Werther (1986) equation. Fit parameters of Hilligardt and Werther (1986) are compared to the fit parameters obtained in this work. It is shown that coalescence, break-up, and direct wall interactions are very important effects, often dominating the dynamic bubble behaviour, but these effects are not accounted for by the Hilligardt and Werther (1986) equation.

Validation of the Eulerian simulated dynamic behaviour of gas-solid fluidised beds

In this paper, a Eulerian–Eulerian CFD model for a freely bubbling gas–solid fluidised bed containing Geldart-B particles is developed for studying its dynamic characteristics. This CFD model is based on the kinetic theory of granular flow. Van Wachem et al. (1998a) Comput. Chem. Engng 22 (Suppl.), S299–S307 have shown that this model is capable of providing reasonable predictions of the time-averaged properties. In this paper, the dynamic characteristics of the gas–solids behaviour at different superficial gas velocities, at different column diameters, and at different pressures are evaluated, namely (A) the velocity of pressure and voidage waves through the bed, (B) the power of the low and high frequencies of the pressure and voidage fluctuations, (C) the reorientation of the gas–solids flow just above minimum fluidisation and the effect of elevated pressure upon this reorientation, and (D) the Kolmogorov entropy. The CFD simulation results for items (A)–(D) are compared with published experimental data and with appropriate correlations from the literature. A good agreement is found between the Eulerian–Eulerian CFD simulations of bubbling fluidised-bed dynamics, and the data from experiments in the literature. This is a strong incentive for the further development of this type of simulation models in fluidised-bed reactor design and scale-up.

Experimental validation of Lagrangian-Eulerian simulations of fluidized beds

Abstract The present study aims to validate two-dimensional Lagrangian–Eulerian simulations of gas–solid fluidized beds by comparing these with dedicated experimental data obtained with polystyrene Geldart type D particles of 1.545 mm size. Experimental data on pressure, voidage, and bed height fluctuations, and the power spectral density are compared with three different implementations of the Lagrangian–Eulerian model. Though qualitative trends found in the experiment are correctly reproduced by the simulations, it is found that the simulations are particularly sensitive to porosity estimation procedures used in the three different simulation strategies employed. Furthermore, the phenomenon of particle clustering predicted by the model does not conform to experimental observations; this is because the physics of the break-up of clusters is not properly captured in the Lagrangian-Eulerian model.

SCALE-UP OF CHAOTIC FLUIDIZED BED HYDRODYNAMICS

This paper focuses on scale-up of the dynamic behavior of gas-solids fluidized bubbling reactors. An empirical approach is followed that is based on the observation that the non-linear, hydrodynamic behavior of bubbling fluidized beds is of a chaotic nature. The degree of chaos is quantified by the Kolmogorov entropy, which is a measure of the rate of loss of information in the system (expressed in bits of information per second). The basic idea of the ‘chaos scale-up methodology’ proposed in this paper is that the rate of information loss 3hould be kept similar when scaling up a bubbling bed from the small scale to the larger scale, in order to ensure dynamic (i.e. chaotic) similarity between the scaled beds. For a set of Geldart-B and -D particle systems, and for a range of bed diameters (from 0.1 m ID up to 0.8 m ID), an empirical correlation (Equation 4 in the paper) is derived that relates Kolmogorov entropy to main bubbling bed design parameters, viz. (i) fluidization conditions (superficial gas velocity, settled bed height), (ii) particle properties (minimum fluidization velocity), and (iii) bed size (diameter). It is illustrated by numerical examples how this correlation might be used in scaling up the chaotic dynamics of bubbling fluidized reactors. It is further shown that a similar type of correlation for Kolmogorov entropy can also be derived theoretically (Equations 1 and 5 in the paper).

Structure heterogeneity, regime multiplicity and nonlinear behavior in particle-fluid systems

This paper is devoted to the understanding of the structure heterogeneity, regime multiplicity and behavior nonlinearity of particle-fluid systems which give rise to predominant difficulties in their modeling and scale-up. Possible approaches are explored for dealing with these aspects of complexities. Two types of nonlinearity are recognized in particle-fluid systems - intrinsic, as related directly to particle-fluid interaction, and secondary, as related to particle geometric and system scale-up. It is indicated that multiple resolution with respect to energy, process, movement and structure may be a promising approach to coping with intrinsic nonlinearity, though understanding of secondary nonlinearity calls for more specific analysis of the effects of external factors on intrinsic nonlinearity.

Monitoring Fluidization by Dynamic Pressure Analysis

In industrial practice, it is important to have a method for early detection of changes in fluidized bed behaviour, e.g., to warn about upcoming bed agglomeration. Recently, a number of new monitoring methods based on observing the non-linear dynamics of measured pressure fluctuations have been reported. In this paper, these methods for monitoring fluidization are discussed and the expected future developments are described.