## 1 Introduction  
Air classifiers are widely used in various fields as a core piece of equipment in the powder material preparation process. In practice, there are different classification principles and a variety of air classifiers, such as gravitational, centrifugal, dry, wet, cascade, fluidized bed, inertial, external, vortex, and circulating air classifiers [1, 2, 3, 4]. The selection of an air classifier type is performed based on the technical characteristics of the classifiers and the classification materials, as well as the criteria for the classification products, technological advances, and economic factors [1, 2]. Rotor-type classification devices can achieve high classification efficiency, a wide range of capacities, fineness, and the adjustment of the fineness through controlling the operating parameters and improving their structures. Therefore, rotor-type classifiers are widely used in various industrial fields, particularly in the production of quartz-based artificial stone. However, the practical requirements may not be fully met by commercially available air classifiers. At present, there are many air classifiers that have been developed to enhance the classification efficiency and address specific industrial issues. The complexity of the gas-solid two-phase flow behavior inside the air classifier presents a challenge in developing a more economical and efficient new design [5]. The influence of the process parameters has been studied by many researchers seeking to improve the performance of air classifiers [6]. Nevertheless, only certain requirements of specific types of sample production are satisfied by these improvements. Numerous investigations have been undertaken to enhance the structures of different parts of lab-scale air classifiers, primarily focusing on the rotor cage, which potentially influences the flow field of the classifier [7]. With the advancements in materials science, further research on the flow field distribution law in air classifiers and the optimization of the air classifier structure has been conducted by researchers [8]. For an under-feed classifier, it is better to use an inverted cone-type rotor cage, while a positive conical rotor cage is inadequate. Rotor cage structures with diameter ratios of 1:0.8 and 1:0.7 were found to be the best, resulting in high classification efficiency and accuracy [9]. An appropriate number of blades contributed to efficiently improving particle gradation. The inertial anti-vortex between the blades was eliminated due to the streamlined blades of the classifier, which led to a decrease in the velocity gradient; this was beneficial for conveyance and particle classification [10]. The _Z_-blade shape not only resulted in high classification efficiency but also effectively decreased the pressure drop in the classifier, resulting in reduced power consumption [11]. A classifier with non-radial arc rotor blades led to an increase in classification efficiency and accuracy and a narrow particle size distribution [12]. For a turbo-pneumatic classifier, positive bending arc blades with optimal installation angles help to reduce the fishhook depth and increase the classification accuracy, especially in comparison to straight blades [13]. The tangential and radial velocities fluctuate significantly if the radius of the rotor cage is too large or too small, which is not beneficial for the classification process. Two rotor cage structures with outer-inner radii of 100-70 and 90-60, respectively, demonstrated a superior flow field distribution and classification performance [8]. In the turbo air classifier, the closed bottom plate of the rotor cage was more favorable for classification than a flat circular ring [14]. Regarding a dynamic separator, the influence of the geometry of the fine powder outlet on the pressure drop and separation performance was also investigated [15]. Four tangential-shaped fine exit tubes provided better separation with a smaller fish-hook effect in comparison with one cylinder-shaped tube.