Mechanics of raceway hysteresis in a packed bed
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I. INTRODUCTION
A common feature of packed, spouted, and fluidized beds is that they all show hysteresis. For example, a horizontally oriented jet of gas into a packed bed of particles forms a raceway, an important element of a blast furnace. Figure 1 shows a plot of the raceway diameter and gas velocity in a packed bed and illustrates hysteresis. It is evident from the figure that the raceway size increased with increasing gas velocity. When the gas velocity was decreased from the maximum value (point A), there was initially almost no change in the raceway size. However, when a critical velocity was reached (point B), the raceway size began shrinking with decreasing velocity, but was always larger than that for the corresponding increasing velocity. This serves to illustrate the raceway hysteresis phenomenon. Hysteresis is also often observed in fluidized and spouted beds. It is broadly accepted[1–6] that this hysteresis comes about as a result of interparticle and wall-particle forces. In most practical systems, these are predominantly contact and frictional forces, to which this study is confined. Previous investigators have applied force-balance analysis to cross flow–packed beds,[7,8] upward-forcing jets[9] in moving beds,[10] and packed beds.[10,11] The stress distribution in moving beds with lateral gas injection and in stationary packed beds with bottom gas injection, in a two-dimensional case and for an increasing gas velocity, has been studied by a few authors.[8,9] Recently, it has been shown[7] that particle-particle and wall-particle stresses play an important role in describing the packed-bed behavior during increasing gas velocity. Considering the importance of frictional forces, some investigators[10–13] have G.S. GUPTA, Associate Professor, and S. RAJNEESH, V. SINGH, and S. SARKAR, Graduate Students, are with the Department of Metallurgy, Indian Institute of Science, Bangalore – 560 012, India. Contact e-mail: [email protected] V. RUDOLPH, Professor, Division of Chemical Engineering, and J.D. LITSTER, Professor and Head, School of Engineering, are with the University of Queensland, St. Lucia, QLD-4072, Australia. Manuscript submitted February 14, 2004. METALLURGICAL AND MATERIALS TRANSACTIONS B
attempted to include its effect in the analysis of raceway size. Litster et al.[14] explained the hysteresis phenomena by proposing that the stress term in the force balance would act in different directions, depending upon the increasing or decreasing gas flow. This approach has, subsequently, been used in packed[7] and fluidized[15] beds. This concept[16] is based on the following expression: Pressure force bed weight (force) frictional forces (stresses) 0
[1]
The physical interpretation of this equation is that when the raceway is expanding, the particles near and above the raceway are being pushed in the upward direction. The frictional stresses tend to oppose this and, hence, act generally in the downward direction. When the blast velocity is decreased from a maximum value, the particle
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