Standard deviation of absolute and differential pressure fluctuations in fluidized beds of group B particles

Abstract

Keywords: Fluidization; Gas-solid bed; Pressure fluctuations IntroductionKnowledge of bed fluctuations in a gas-solid fluidized bed is important for its design and/or operation as they provide information on indexes of fluidization quality, which include formation, rise and eruption of gas bubbles, movement of solids and pressure waves propagation through the bed. These indexes are commonly considered as an indicative of the dynamic behaviour of the fluidized bed and can be explored as a way of monitoring the process (Felipe and Rocha, 2007). Due to the ease of measurement and its significance in understanding dynamic behaviours, pressure time series and pressure fluctuations have been investigated by numerous researchers (Bi, 2007). It is accepted that the complex pressure signal is a result of the superposition of local fluctuations caused mainly by traveling gas bubbles and fast-traveling pressure waves arising due to bubble formation, coalescence and eruption. In order to characterize the hydrodynamics of the bed, statistical methods and spectral analysis have been used to identify these phenomena and to establish the different fluidization regimes (Lirag and Littman, 1971;Fan et al., 1981;Johnsson et al., 2000;van der Schaaf et al., 2002;Bai et al., 2005;Puncochar and Drahos, 2005 ity (Puncochar et al., 1985;Wilkinson, 1995;Felipe and Rocha, 2007). In spite of the measurement simplicity the nature of pressure fluctuations in a fluidized bed is a complex function of particle properties, bed geometry, flow conditions, pressure and temperature. Fan et al. (1981) investigated the effect of particle size, static bed height and gas velocity. Svoboda et al. (1984) showed that the magnitude of the pressure fluctuations increases with both excess gas velocity and particle diameter. Svoboda et al. (1983) also reported that the amplitude of pressure fluctuations depends upon the height above the distributor. Pressure fluctuations can be very different at different locations on the axis of the bed (the region of bubble coalescence is displaced as the gas velocity increases) and thus the position at which pressure fluctuations are measured becomes an important factor in determining the relationship between the standard deviation of pressure fluctuations and the gas velocity. The effect of the probe location was studied by Hong et al. (1990) and Wilkinson (1995) for several particle sizes and static bed heights. The use of absolute or differential probes has also been discussed in order to elucidate weather or not they provide similar or different information: Roy and Davidson (1989) showed that single point pressure measurements were different from differential pressure measurements because the former included contributions from all 0263-8762/$ -see front matter

Feature of acoustic sound signals involved in vapor bubble condensation and its application in identification of condensation regimes

“…The variations in the two deviations were often used to determine the regime transformation (Salehi-Nik et al, 2009;van Ommen et al, 2004;Sobrino et al, 2008), while it was unsuccessful for the DCC in present work. As a result, higherorder moments, skewness (third moment) and kurtosis (fourth moment) were given for insight into DCC.…”

Early detection of agglomeration in a polyethylene fluidized bed at high temperature and pressure by vibration signature analysis

“…Standard deviation of signals from fluidized beds have been used to identify regime transitions (Bi et al, 2000;Azizpour et al, 2011), determine the minimum fluidization velocity (Sobrino et al, 2008;Abbasi et al, 2009) and detect defluidization in industrial fluidized-bed reactors as an on-line tool . Standard deviation of time series x i shows the deviation of the distribution from a normal distribution in time interval of N and is defined as follows:…”

Pressure drop and pressure fluctuations in spouted beds with binary mixtures of particles

“…Standard deviations of the pressure fluctuations has been widely used to identify a regime change in gas-solid fluidized beds [26][27][28][29][30]. Table 2 shows the averaged values and standard deviations of differential pressure fluctuations collected at different bed sections in a spouted bed.…”

“…In the literature, it has been reported that A C C E P T E D M A N U S C R I P T ACCEPTED MANUSCRIPT 4 the standard deviation or the average absolute deviation is often used to identify a flow regime change [26][27][28][29][30]. The statistical analysis in time domain is the simplest and the most commonly employed; it is also very fast and easily applicable.…”