Statistical study of the distribution of voidage in a bubbling fluidized bed with a constant section

Highlights

• Statistics were used to characterize the voidage signals.

• The distribution of voidage was more discrete for high gas velocities.

• The maximum of voidage occurred in the center of the upper bed.

• The voidage reached the minimum near the upper wall of the bed.

Abstract

The distribution of voidage was statistically studied in a plexiglass bubbling fluidized bed with a constant section. Four statistics, including average, standard deviation, skewness, and kurtosis, were analyzed. The vertical, horizontal, and three-dimensional distributions of voidage with various gas velocities were investigated. The results showed that both the vertical and horizontal distributions of voidage were more discrete for high gas velocities, i.e., the difference between different positions was greater. At the highest gas velocity, both voidage and the bubble size reached the maximum in the upper bed center. The minimum of voidage occurred near the upper bed wall, and the bubble was small both at the bottom and near the wall. The region of the sufficient bubbling fluidization was the maximum region of voidage, while the region of the particulate fluidization was the minimum region of voidage.

Introduction

Gas–solid fluidization is a process where the solid particles and gas are mixed and contacted intensely (Fotovat et al., 2017; Grace et al., 1999; Squires et al., 1985; Xu et al., 2021). Gas–solid fluidized beds have been used in many fields owing to the outstanding mixing and heat transfer characteristics (Bi and Grace, 1995b; Hamzehlouia et al., 2018; Mei et al., 2006). The internal mechanism of gas–solid fluidized beds is essential to improve the performance of the fluidized bed. The fundamental mechanism of the fluidized bed depends on the gas–solid flow (Mori and Wen, 1975; Taghipour et al., 2005; Zhou et al., 2021). However, the gas–solid flow in the fluidized bed is complex due to the physical properties of approximate fluids (Bi et al., 2000; Peirano and Leckner, 1998; Svensson et al., 1996), which has received significant attention in recent years.

Measuring the dynamic physical signals inside the fluidized bed is a widely used way to explore the internal characteristics of the bed. The dynamic physical signals include voidage, pressure, vibration, and sound (Johnsson et al., 2000; Ren et al., 2001; Rüdisüli et al., 2012; Sasic et al., 2007; van Ommen et al., 2011). Xiang et al. (2019) investigated the effects of bed size on pressure fluctuations in bubbling fluidized beds with different sections. They found that the pressure fluctuation was lower in the large bed (Xiang et al., 2019). Azizpour et al. (2011) studied the characteristics of the gas–solid fluidized bed by analyzed the vibration signals. The results showed that the variation of standard deviation and kurtosis of vibration signals against the gas velocity of the bed could be used to predict the transition of gas–solid flow states (Azizpour et al., 2011). Zhao et al. (2005) constructed a model for the shock wave of gas–solid flow based on the two-phase sound velocity. They found that the two-phase sound velocity model results were more accurate than the single-phase sound velocity model (Zhao et al., 2005). Many studies on the dynamic physical signals in the gas–solid fluidized bed have been carried out, while few studies paid attention to the voidage.

Voidage is a fundamental signal in the fluidized bed, reflecting the essential characteristics of the gas–solid flow state (Bi and Grace, 1995b; Zhou and Zhu, 2020; Zijerveld et al., 1998). The gas–solid fluidization is essentially the uneven distribution consisting of the dense phase of solid particles and the dilute phase of gas in the gas–solid fluidized bed (Bai et al., 2021; Das et al., 2008; Grbavcic et al., 2006), the external reflection of which is the voidage signal. The distribution of voidage in a fluidized bed can reflect the behavior of bubbles and can be used to identify the patterns of the gas–solid flow (Hills, 1974; Makkawi and Wright, 2003; Yang et al., 2003). Therefore, the distribution of voidage in gas–solid fluidized beds needs to be further investigated.

As a dynamic physical signal, voidage is changeable in the time dimension (Gu et al., 2020; Hamzehei et al., 2010; Ren et al., 2001). These changes need to be eliminated to obtain valuable information from the voidage signals. Statistical methods, such as average, standard deviation, skewness, and kurtosis, are a suitable way to extract the invariant property from the changeable voidage signals (Bi and Grace, 1995a; Ellis et al., 2003; Issangya et al., 2000; Tebianian et al., 2015), which can be used to obtain sufficient information from the signals.

In this study, the distribution of voidage characterized by statistics was investigated in a bubbling fluidized bed with a constant section. Four statistics, including average, standard deviation, skewness, and kurtosis, were applied to analyze the voidage signals. Four measuring probes were set at different vertical positions of the fluidized bed to explore the vertical distribution of voidage. The horizontal distribution of voidage was studied by changing the distances of probes into the bed. The vertical and horizontal distributions of voidage with various gas velocities were analyzed, and the three-dimensional distribution of voidage at the highest gas velocity was obtained.