Pressure drop of liquid–solid two-phase flow in a down-flow circulating fluidized bed

Liquid–solid fluidized beds with varying particle diameters encompass extensive application across hydrometallurgy, mineral separation, and biochemistry. In the present work, the numerical model based on the multiphase particle-in-cell method is developed to study the liquid–solid polydisperse fluidized bed system with continuous particle size distribution (PSD). After the proposed model is well validated with experimental data, the effects of PSD width on fluidization dynamics and particle behaviors are analyzed and discussed. The key findings can be summarized as follows. Following a full fluidization, noticeable layering emerges among particles, with larger particles primarily accumulating at the system bottom, necessitating higher slip velocity and particle Reynolds number (Re p ) to remain suspended, thereby resulting in a reduced flow area and heightened solid holdup. A wider PSD width leads to a more even spread of particles across the diameters, enhancing the visibility of stratification. It also creates a more consistent distribution of solid holdup changes and pressure drops along the bed height. Moreover, it is found that particles around 1.09 mm in diameter, representing the average size, consistently gather at a dimensionless axial height of 0.1, irrespective of variations in PSD widths. Simultaneously, when considering this axial position as the boundary, there exists a contrary relationship between the variations in particle solid content, particle size distribution, fluid velocity, and bed pressure drop with the PSD width. Finally, decreasing particle size correlates with reduced slip velocity and Re p , intensifying the particle susceptibility to fluid motion.

Section: Pressure Signalsmentioning

confidence: 85%

Numerical Investigation of Wide Continuous Particle Size Distribution Effect on the Liquid–Solid Fluidized System

Yu,

Sun,

Yang

et al. 2024

“…In liquid–solid fluidized beds, for example, the electrolyte tracer technique was employed to investigate the axial and radial mixing behaviors of the liquid phase; the radioactive particle tracking technique was applied to measure the solid flow pattern and mixing behaviors; the conductivity probe technique was used for measuring the local solid holdups; and the particle image velocimetry (PIV), as a nonintrusive technique, was employed to determine the particle velocity. , These reported experimental data gave a comprehensive understanding of the mechanism of liquid–solid fluidization. Based on these experimental data, many empirical equations of the voidage and pressure drop were proposed. − However, experiments were usually expensive and time-consuming, especially to obtain a complete experimental data set.…”

Section: Introductionmentioning

confidence: 99%

Customized Software Package for the Simultaneous Prediction of Multiple Fluidization Characteristic Parameters in Liquid–Solid Fluidized Beds

He,

Lei,

Xie

2024

In liquid−solid fluidized beds, there are many parameters that need to be determined for their optimization design. This study develops four machine learning models for the simultaneous prediction of the bed expansion ratio, voidage, and drag coefficient in liquid−solid fluidized beds. The Ridge regression model, K-nearest neighbor model, support vector regression, and XGBoost model are trained and tested based on the liquid−solid fluidization experimental data set. The methods of grid-search and nested cross-validation are employed for hyperparameter tuning. It is found that the XGBoost model is the best-performing model. The results of 5-fold cross-validation and Leave-One-Out confirm that there is no overfitting problem. The voidage, drag coefficient, and bed expansion ratio are all accurately predicted, and the average R 2 is 0.992, 0.976, and 0.974, respectively. Furthermore, the method of principal component analysis is employed to analyze the high-dimensional fluidization data, and the feature importance of each principal component is obtained. For convenience in use, a customized software package is developed by Python language. The software has a good graphical interface function and supports user-defined models, which can be trained using users' own data set and customized model parameters. The software is expected to benefit the preliminary design of fluidized beds.

“…The earliest research on liquid–solid fluidization can be traced back to 1948; Wilhelm and Kwauk have investigated the fluidization of lead particles . Since then, many empirical correlations for the voidage, pressure drop, and drag coefficient prediction have been derived from liquid–solid fluidized beds. − It is known that both pressure drop and drag coefficient are dependent on the voidage. Therefore, much attention has been focused on accurately predicting the voidage over the past few decades.…”

Section: Introductionmentioning

confidence: 99%

Development of Effective Voidage Correlations in Pilot-Scale Liquid–Solid Fluidized Bed Based on Data-Driven Modeling

Xie

Zhou

Huo

et al. 2023

Liquid−solid fluidized beds can meet many different demands from chemical, environmental, and pharmaceutical processes, and it is very crucial to accurately predict their voidages, which, however, are usually underestimated by the classical Richardson−Zaki equation. In this study, a data-driven modeling method was applied to develop the voidage correlation based on the experimental data from pilot-scale liquid−solid fluidized bed where the fluidization experiments of spherical glass beads were performed at different particle sizes, particle densities, liquid superficial velocities, and operating temperatures. By selecting different parametric spaces, various high-accuracy voidage correlations based on different dimensionless numbers (i.e., Re, Re t , Ar, Fr, St) were discovered and all of the values of R 2 were approximately 0.99. In comparison, the combination of Re and Ar numbers could better characterize the voidage and the mean square error was as low as 2.29 × 10 −4 . The proposed correlation also performed very well in predicting the voidage of the fluidization of irregular calcite pellets in a pilot-scale fluidized bed and the voidage of the fluidization of coarse coal particles in a laboratory-scale fluidized bed, thus indicating its universality.