Numerical simulation of a cyclone separator to recycle the active components of waste lithium batteries

ABSTRACT In this paper, cyclone separator is proposed for the first time to separate particles according to density, and it is applied to the recovery of lithium iron phosphate (LFP) from spent lithium battery materials for the first time. The effect of the flow field on the motion of injected particles in a cyclone separator is studied by means of computational fluid dynamics (CFD). It is found that there is a classification phenomenon caused by the difference in the particle densities and the separation process is simulated accordingly. The results show that 60% LiFePO4 in the original feed can be separated after 7 separations, and the mass purity is 91%, with 7% Al and 2% Fe under instantaneous surface injection conditions. Compared with the original feed, LFP is effectively recycled. After 15 separations, the efficiency increases to 76%. Under simulated continuous injection conditions, the separation efficiency of LFP is 61.22% after 20 simulated separations, and the mass purities of the separated products are 92.53% LFP, 6.92% Al, 0.44% Fe and 0.11% Cu. Compared with the traditional method, the new method has advantages of low energy consumption, low cost, theoretically no pollution, and great development potential.


Introduction
Cyclone separators are generally used in the field of gas-solid or liquid-solid separation in industry. The strong swirl in the gas cyclone causes the particles to flow down the inner wall to be collected, while clean air is discharged from the vortex finder. Hence, the cyclones play an important role in the field of particle control such as air purification (Lim & Yook, 2022). Although the working principle of cyclones is simple, the gas flow inside them is a complicated three-dimensional flow. Researchers use the combination of experiment and simulation to prove the accuracy of computational fluid dynamics in simulating the complex flow field in the cyclone (Lan et al., 2022;Song et al., 2017;Wang & Wu, 2018). At present, noncontact experimental methods such as particle image velocimetry (PIV) (Celis et al., 2022;Wasilewski et al., 2020Wasilewski et al., , 2021 and phase doppler particle analysis (PDPA) (Gao et al., 2019;Liu et al., 2019) are used to measure the flow field data in cyclones, but the equipment is extremely CONTACT Wei Yang wyang@gzhu.edu.cn; Shengzhou Chen szchen@gzhu.edu.cn Supplemental data for this article can be accessed here. https://doi.org/10. 1080/19942060.2022.2053343 costly. As a result, computational fluid dynamics (CFD) combined with discrete phase model (DPM) or discrete element method (DEM) to simulate the flow of fluid and particles is more and more favored (Dong et al., 2020;Fu et al., 2021;Ghalandari et al., 2019;Shamshirband et al., 2020;Yang et al., 2019). These models can provide particle trajectories and statistical information and are widely used to study the gas-solid separation efficiency of cyclones. However, there are few studies on the use of cyclones to separate two or more solid materials with different densities. Many studies have reported the deposition of large particles and the dispersion of small particles in the cyclone by turbulent entrainment (Baltrenas & Chlebnikovas, 2019;Duan, Gao, Hou, et al., 2020;Youn et al., 2021). After entering the cyclone, the particles of large size immediately adhered to the wall, while the concentration of small particles was higher in the short-circuit flow (Shukla et al., 2011). Separation is an interaction between centrifugal motion caused by centrifugal force and dispersion due to turbulence. Bogodage and Leung (2015) conducted CFD numerical simulation of gas-solid flow in cyclone separator. The results show that when a particle follows the secondary flow (short circuit flow), it has the maximum probability of escape, otherwise it will undergo a longer residence time before being collected. Dong et al. (2020) studied the flow field in a gas cyclone by CFD simulation. It is found that multi-inlet can increase the symmetry of the gas flow field, thus reducing the particles escaping from the short-circuit flow. In the above research, short-circuit flow is considered to be a crucial factor to reduce the separation efficiency. Hence, most of the current studies are focused on stabilizing the flow field and improving the efficiency of gas-solid separation by optimizing the geometric parameters (Babaoglu et al., 2021;Hosseini, 2020;Lan et al., 2022;Liu et al., 2021;Shastri & Brar, 2020;Wei et al., 2020) and operating conditions (Morin et al., 2021;Nakhaei et al., 2020;Zhang et al., 2020) of the cyclone. However, the presence of shortcircuit flow impedes fluid-solid separation but facilitates the classification of solid particles (density classification).
In short, none of the above work has break away the cyclone from gas-solid separation. In this work, the application of a gas cyclone to the separation of solids with same particle size but different density is proposed for the first time, and it is applied to the recycling of spent lithium battery materials firstly. A set of active component LFP is built to simulate the industrial separation process. Compared with the traditional method, it has the advantages of low energy consumption, low cost and no pollution in theory. The purpose of this study is to provide an innovative idea for the extended application of cyclone separator, and to provide theoretical guidance for the design and control of the new recovery process.

Cyclone mathematic model
In this paper, the cyclone mathematic model of Obermair and Staudinger (2001) and Obermair et al. (2003) was used as a reference model for subsequent work, and their experimental results will be used in this CFD validation. The same size parameters and inlet velocity as the reference model are used to ensure that the compared flow field has the same initial conditions and solved by the simulation method in this paper. The specific design and size are shown in Figure 1 and Table 1, respectively, and its volume is 0.1175 m 3 .

The turbulence model
The choice of the turbulence model is related to the correctness and credibility of the simulation. Common models for describing turbulent flow are the k-ε doubleequation model, Reynolds stress model (RSM), and large eddy simulation (LES) model. However, the performance of the k-ε model is not satisfactory under strong swirl conditions, and the LES model requires a very highquality grid, which is difficult to achieve in the inlet section of the cyclone. Nevertheless, the accuracy of the RSM model in describing the three-dimensional flow field of cyclones has been confirmed by many scholars (Kumar & Jha, 2019;Sakin et al., 2019;Zhao et al., 2020).

Reynolds averaged Naiver-Stokes (RANS) and the RSM model
In this study, the gas phase flow velocity is low, so the gas can be considered an incompressible gas, and the inlet velocity is assumed to be uniform and turbulent. In this case, the Reynolds-averaged Navier-Stokes equations can be expressed as (Misiulia et al., 2020;Wasilewski, 2016): where −ρu i u j is the Reynolds stress tensor, which is used for modeling to solve Equation (2). The Reynolds stress transfer equation is as follows (Dong et al., 2020;Gao et al., 2019;Wasilewski, 2016): where ρ, u i , u i and x i are the fluid density, velocity, velocity fluctuation and position coordinates, respectively, and D T,ij represents stress diffusion, P ij represents shear production, ij is the pressure-strain correlation term and ε ij is the dissipation term. They are given as (Wang et al., 2006): where s is the source term, p stands for pressure, and μ is the dynamic viscosity of gas.

Discrete phase modeling (DPM)
The dispersed phase model in Fluent is based on the Euler-Lagrange (E-L) method, which assumes that the distribution of the dispersed phase in the main phase is thin enough to ignore the interaction between particles and the effect of the particle volume fraction on the continuous phase. Generally, the volume fraction of the dispersed phase in the continuous phase is less than 10%. The trajectory of a particle is predicted by its force. The equation for particle motion is as follows (Duan, Gao, Lu, et al., 2020): where F D (u − u p ) is the drag force per unit mass of the particle, F D = 18μ ρ p d 2 p C D Re p 24 (Wasilewski et al., 2021).
The drag coefficient of spherical particles is calculated by Schiller-Naumann drag model and deduced from the value of Re: Among them, u, u p , μ, ρ p , d p , and Re p = ρd p |u p −u| μ are the gas velocity, particle velocity, dynamic viscosity of gas, particle density, particle diameter and relative Reynolds number for a particle, respectively.

Boundary conditions
Air was selected as the continuous phase with a density of 1.225 kg/m 3 and a viscosity of 1.789 × 10 −5 kg·m −1 ·s −1 . Commercial lithium iron phosphate power batteries mainly consist of lithium iron phosphate, super-P, poly (vinylide fluoride) (PVDF), N-methyl-2-pyrrolidone (NMP), aluminum foil, copper foil, a polar ear and membrane. Among them, super-P, PVDF, NMP and so on can be removed by high-temperature calcination. In this study, the focus of recycling is to realize the separation of lithium iron phosphate from aluminum, copper and steel materials. Hence, the particle phases were lithium ferrous phosphate (LFP) (1523 kg·m −3 ), Al (2719 kg·m −3 ), Cu (8978 kg·m −3 ) and Fe (7874 kg·m −3 ). The inlet and outlet types of the cyclone are defined as the velocity inlet and pressure outlet. The turbulence intensity is 5%, the hydraulic diameter is 0.1286 and 0.15 m, and the inlet velocity is 12.69 m·s −1 . In the discrete phase model, the number of particles is converted according to the mass ratio of the battery, and then the particles are injected by surface injection. This study takes the lithium iron phosphate battery produced by a battery company in Zhuhai as a reference, and its material ratio and the number of injected particles are shown in Table 2. It is assumed that the particle shape is spherical, and the particle size is 3 × 10 −6 m; these particles have the same initial velocity as the continuous phase. The stochastic trajectory model is used to simulate the turbulent diffusion of particles. The particles will bounce back when they come into contact with the inner wall of the cyclone, then escape from the pressure outlet and are captured in the dust hopper.
To explore the particle collection status of the dust hopper, two collecting surfaces are set up, namely, wall_dustbin1 and wall_dustbin2, as shown in Figure 2.

Convergence strategy
Simulation software ANSYS Fluent 2021 R1 was used to solve the flow field of cyclone separator and the subsequent simulation. A workstation with an Intel R i7 CPU @3.80 GHz is used to perform the computations. The solution algorithm is the semi-implicit method pressurelinked equations consistent (SIMPLEC) algorithm, and the pressure difference format is PRESTO. The interpolation scheme of turbulence parameters and Reynolds stress parameters is a first-order upwind scheme. Under the steady-state condition, the iterative calculation decreases by less than three orders of magnitude after 1000 steps, and then its residual fluctuates between 10 −4 and 10 −3 . The velocity at the outlet tends to be stable, and it can be considered that the calculation has reached preliminary convergence. By switching the transient solver, the interpolation scheme of turbulence parameters and Reynolds stress parameters is adjusted to the secondorder upwind scheme to further improve the accuracy. The average residence time of the gas t res = V Q in = 0.452 s. As a result, a time step of 0.0005 s is sufficient. When the time step is set to 0.001 and 0.0005 s successively, it can be observed that the residual gradually drops below 10 −4 , and then the flow field can be considered to reach the final convergence state. This strategy can save substantial simulation time.

Mesh independency
ICEM-CFD was used to create a structured mesh for the cyclone to improve the simulation accuracy, and the mesh was encrypted for the wall and the area with a high fluid velocity gradient. Five sets of hexahedral grids with numbers of 325,147, 546,743, 753,981, 1,013,661 and 1,296,831 were simulated for 12,000 steps under the same conditions. The pressure drop and tangential velocity distribution were used as the parameters to judge the grid independence. The tangential velocities at Z = 0.5, 0.745, 0.99 and 1.29 m were compared. The tangential velocity at each height presents a symmetrical inverted 'W' pattern, namely, the Rankine vortex. When the number of grid cells exceeds 753,981, the tangential velocity of each position tends to be consistent, especially at Z = 0.5 and 0.745 m, as shown in Figure 3. Moreover, the symmetry center (vortex core) of tangential velocity under different grid numbers under these two heights is offset from the geometric center and rotates with a certain frequency and amplitude, which is called the PVC. The swinging of the vortex core tends to be stable with increasing height. In addition, with an increase in the number of grids, the simulated pressure drop of the cyclone tends to be stable, as shown in Figure 4, and the relative errors are 2.87%, 6.34%, 0.801% and 2.30%.
To reduce the effect of accidental factors and improve the simulation accuracy, a grid with 1,013,661 elements is selected as the grid used in this simulation.

Pressure field and validation
Pressure drop is considered to be one of the main indexes to measure the performance of cyclone separator. The contours of the axial and the tangential pressure drop on different planes are shown to gain an in-depth understanding of the internal flow field of cyclone, as shown in Figure 5. The high-pressure area corresponds to the outer vortex, and the low-pressure area is near the geometric centerline. The axial pressure drop shows a symmetrical distribution, a pressure gradient attenuating from both sides to the center, and a negative pressure region. The air flow enters the cyclone from the inlet, and collides at the position where the inlet is tangent to the cylinder, thus showing a squeeze shape, as shown in the blue dashed frame of the contour at z = 1.4 m. Moreover, the tangential pressure drop at the other two positions shows an almost completely symmetrical shape, and the slight offset shows the swing of the inner vortex, namely precessing vortex core (PVC). This offset increases gradually from top to bottom because the diameter of the cylinder of the cyclone becomes smaller, the gas accelerates and the turbulence increases.
At the same time, the pressure field and solution time solved by RSM, k-ε and LES large eddy simulation are compared to prove the credibility of the model selection.
The flow field simulated by LES and RSM model has similar pressure field distribution, but the k-ε model is not satisfactory, which shows its defect in the prediction of strong swirl flow, as shown in Figure 6. In addition, under the same initial conditions, the iteration time of 12,000 steps for the three models is shown in Table 3. The simulation time of LES large eddy simulation is about 3.3times of RSM model and 7.1 times of k-ε model, and the calculation cost is high.

Velocity field and validation
To verify the accuracy of the model, the tangential and axial velocity distributions of the cyclone separator at z = 0.5 m (A-A') are compared with the experimental data of Obermair et al. (2003), and the simulation data of Park et al. (2020). As shown in Figure 7, both tangential velocity and axial velocity show a certain symmetrical structure, and increase at first and then decrease along the geometric central axis of the inner wall in the radial direction. However, there is a certain deviation between the symmetry center and the geometric center of the velocity field, which indicates that the PVC and vortex core oscillation phenomenon (Duan, Gao, Hou, et al., 2020;Shukla et al., 2013) appear in the cyclone due to the single tangential inlet. A similar phenomenon has appeared in many previous studies. The tangential velocity distribution of cyclone separator consists of the forced vortex and free vortex regions, and the combination of them shows the typical characteristics of strong swirl flow: the Rankine vortex, showing a symmetrical inverted 'W' shape, as shown in Figure 7(a). From the wall to the central axis, the axial velocity changes from negative to positive, which represents the transition from downflow to upflow. At the center of the cyclone, the axial velocity stagnates, and the local minimum appears, as shown in Figure 7(b). However, it is obvious that the prediction of tangential velocity and axial velocity of k-ε model shows a big error with the experimental value, and the prediction performance of LES model and RSM model is better. Considering comprehensively, the RSM model is considered to be an appropriate method. In summary, the calculated results of CFD are in terrific agreement with the experimental data and can accurately capture the information of flow field distribution. The CFD modeling of this cyclone predicts promising results.

Particle distribution and motion
When the gas-solid feed is injected into the cyclone, there is a centrifugal force in the radial direction due to inertia, which leads to the centrifugal movement of the solid particles and the radial pressure gradient of the gas phase flow field. Solid particles are affected by fluid drag and centrifugal force in the radial direction. The existence of these two forces hinders the separation of particles from the fluid but is beneficial for the classification of particles. The sedimentation and collection of solid particles mainly depend on the centrifugal force F c and the fluid drag force F d . In the axial direction, if the gravity of the particles is greater than the resistance provided by the rising air flow, then the particles go down into the dust hopper; inversely, the particles escape from the vortex finder. In the radial direction, when the centrifugal force on the particles is greater than the drag force of the fluid, the particles move centrifugally and fall along the wall to be collected. This indicates that the particles are light and easily carried into the inner vortex for upward movement and escape from the vortex finder. When the resultant force in the radial direction is zero, the particles rotate constantly on the interface between the inner vortex and the outer vortex, and this diameter is the cut diameter. The axial velocity on this interface is zero and is called the locus of zero vertical velocity (LZVV). Similarly, this phenomenon will also occur when the particle diameter is constant and the density changes, so it is theoretically feasible to separate solid particles with different densities by cyclone.
The particles in Table 2 are injected into the cyclone by instantaneous surface injection to minimize the trajectory deviation caused by the collision between particles, and the motion trajectory is shown in Figure 8(a). The trajectory of the particles in the continuous injection process is also visualized, as shown in Figure 8(b), which provides more intuitive and statistically based proof of the motion of the particles. For the animation files of the two separation processes, see the supplementary 'Continuous surface injection.zip' and 'Instantaneous surface injection.zip'.
The statistics of captured particles are shown in Table 4. In the first separation, 75 of the 399 injected LFP particles escaped from the vortex finder, accounting for 19% of the total LFP particles, and 1 out of 32 Al particles escaped, while the much denser Fe and Cu particles did not escape from the vortex finder at all. Under the same operating conditions and particle size, Fe and Cu particles have greater mass, and when entering the annular space, the centrifugal force is greater under the same conditions. Consequently, when particles rotate downward in the annular space, particles with a small mass tend to move centripetally due to the drag force of the fluid, which can be intuitively reflected in the red circles in Figure 8(a) and (b). In contrast, particles with a large mass mainly move toward the inner wall due to centrifugal force. This particle motion law is also reflected in the study of El-Emam, Ahmed, et al. (2019) and El-Emam, Shi, et al. (2019). They designed a pneumatic harvesting and cleaning machine whose main component is a cyclone separator. The jojoba seeds and their leaves from the soil surface are inhaled in a cyclone to achieve separation. In the same year, they optimized the structure parameters of the cyclone by CFD-DEM oneway coupling numerical simulation, and improved the efficiency of separation and cleaning of jojoba beans from impurities (leaves, etc.). When visualizing the motion trajectories of seeds and leaves, some of the lighter leaves escape from the vortex finder, while the denser seeds are discharged from the dust hopper. From the top view, there are also some leaves distributed near the axis of the separator, but there are almost no seeds. This indicates that seeds are subjected to a greater centrifugal force, while leaves tend to move centripetally due to their small mass and large surface area, so they are more likely to be carried away by short-circuit flow and inner vortex.
However, not all light particles can escape from the vortex finder. Figure 9 shows the axial velocity cloud diagram in the cyclone. The black boundary is LZVV, which shows good symmetry. However, as a single air inlet is used, the upflow areas on both sides are not exactly  equal. There is an upflow beyond the range of the pipe wall near the lower end of the vortex finder, as shown in the red dotted box. Part of the upflow continues to flow upward along the outer wall of the vortex finder, while a part of the fluid flows directly from the downflow to the upflow at the lower end of the vortex finder, which is the flow area of the short-circuit flow. In the annular space, the difference in radial motion also directly leads to a greater probability for low-density particles to escape through the short-circuit flow region, which can also explain why only LFP and Al particles escape, and LFP particles account for the majority of the particles. However, it is worth noting that the short-circuit flow area accounts for only a small part of the whole annular space, so not all particles can successfully reach this area. In this study, LFP and Al are defined as low-density particles, while Fe and Cu are defined as height-density particles. Therefore, a particle classification phenomenon exists near the lower end of the vortex finder. In addition, there is a similar classification phenomenon near the dust hopper, which is clearly reflected in the pink circle in the 0.5 s time step in Figure 8(a) and 0.8 s time step in Figure 8(b). At this time, the low-density particles are mainly concentrated in the dust hopper, some of which are carried by the inner vortex and move in a circle away from the wall (pink circle). The root cause of this phenomenon is the imbalance between the centrifugal force and fluid drag force. Therefore, LZVV is taken as the particle classification boundary, which is also the reason why the diameter of Wall_dustbin1 is 0.9b. The particles collected by dustbin1 are mainly LFP particles, and sporadic Fe and Cu particles can be interpreted as backmixing of particles, which is caused by the random mixing zone of upflow and downflow near the dust hopper, as shown in the blue dotted box in Figure 10. Separation flow diagram. Figure 9. The particle data collected in dustbin2 indicate that most particles mainly follow the outer vortex after injection, especially particles close to the inner wall, and it is difficult for these particles to escape from the vortex finder. Therefore, it can be considered that there are two particle classification phenomena at the lower end of the vortex finder and the dust hopper in the cyclone, which provide the possibility for the separation of the active component LFP in the waste lithium battery. In the supplementary animation file, 'Continuous surface injection.mp4', these two classification phenomena are intuitively reflected.

Separation of battery materials
To explore the feasibility of using cyclones to separate the active component LFP in waste lithium batteries, a set of simulated separation processes was built, as shown in Figure 10. The original feed composition is shown in Table 2. After feeding, a part of the low-density particles is separated from the top of the cyclone, the particles enter the dust hopper cycle to the next separation link, and a part of the supplementary feed is added to ensure that the quality of the imported LFP remains unchanged. It is obvious that the number of LFP in the supplementary feed is equal to that separated from the top. However, since Al, Fe and Cu are little or no separated, the addition of supplementary feed will increase their proportion in the feed. In this way, after each separation, some LFP and Al particles escape from the top and become separation products, while the height-density particles are enriched in the dust hopper.
The material particles were simulated for 15 separations. Table 4 lists the particle data collected in each trap area during the first five separations. The data of each separation can support the two classification phenomena mentioned above. It is obvious that the total number of injected particles increases with the number of separations, while the number of escaped LFP particles remains relatively stable in each separation. This indicates that under the condition of instantaneous surface injection, the number of LFP particles escaping is not affected by the number of other particles and can be regarded as a constant proportion, which is 17% when calculated by an average of 15 times. The recycling efficiency is defined as the ratio of the number of LFP particles escaped from the vortex finder to the total injected LFP particles. The material proportion of the dust hopper and the recycling efficiency of LFP after each separation are shown in Figure 11 (The purity of the material separated for the 0-th time represents the composition of the feed). With increasing separation times, LFP is constantly recycled, and its mass proportion to the dust hopper keeps decreasing, while height-density particles are always enriched in the dust hopper. The mass proportion of Al first increases and then decreases slightly. This is because Al and LFP are quite close in density, and the increase in the number of Al particles injected provides more opportunities for them to escape. This finding indicates that there is a positive correlation between the escape number of particles and their own injection number, which is also reflected in height-density particles. After 15 separations, 76% of the LFP particles in the total feed were separated. However, it should be noted that with the improvement in the separation efficiency of LFP, its growth rate decreases. Even when the number of separation times is small, the recycling benefit of LFP is quite considerable. For example, after 7 separations, 60% LFP of the feed can be separated. The quality purity of the product is 91%, including 7% Al, 2% Fe and no Cu impurities. Compared with the original feed, the purity of the LFP is greatly improved.

Actual working condition simulation
To be closer to the actual production, the particles were injected continuously for 0.1 s to simulate the separation performance during continuous feeding. The remaining operating conditions are the same as for instantaneous surface injection, and the data are shown in Table 5. At this time, it was observed that more Fe and Cu particles were separated together, reducing the purity of LFP, which was not expected. Therefore, the particle diameter is set to 4.5e-6m to increase the centrifugal force, ensuring that the particles coming out of the vortex finder consist of only LFP and a small amount of Al, and the separation process is the same as that of instant injection. Twenty simulated separations were carried out, and the data of the first five separations are shown in Table 6. Although the number of other particles injected continues to increase with the separation, the escape number of LFP particles remains within the range of 7 ∼ 8%, which provides a theoretical basis for industrial steady-state operation. After 20 separations, a total of 116,760 LFP particles were separated from the 190,715 injected particles, with a separation efficiency of 61.22%. The mass purity of the four materials in the recycled products was 92.53%, 6.92%, 0.44% and 0.11%. At this time, the cyclone can separate 61.22% of the feed LFP, with a purity of 92.53%, and its impurities are mainly Al; this result means that the cyclone can effectively realize the separation of the active component LFP in waste lithium-ion battery materials. The enrichment of height-density particles in the dust hopper and the recycling efficiency of LFP are shown in Figure 12. As in Figure 11, the LFP recycling efficiency curve shows  an obvious 'marginal diminishing effect'. In the initial separation, the recycling benefit of LFP is outstanding, and this benefit begins to decline with an increase in the number of separations. Therefore, it is expected that to find the optimal separation times, the efficiency curve, equipment investment, energy consumption and other factors need to be comprehensively considered rather than blindly increasing the separation times. Moreover, the data of the two capture areas at the dust hopper also support the existence of the second density classification phenomenon. In the Wall_dustbin1 capture area, the purity of LFP in the material collected in the first separation is 84.58%, which is greatly improved compared with that of the feed. Near the dust hopper, as mentioned above, particles are backmixed in the random mixing zone between upflow and downflow. An increase in incident particles aggravates the backmixing, resulting in a decrease in the purity of LFP collected in Wall_dustbin1. However, as far as the author knows, there is no cyclone separator that can collect particles of the two areas mentioned above in the dust hopper at present. When simply separated by a metal plate, the addition of the metal plate will interfere with the flow field. As a consequence, the material collected by Wall_dustbin1 is not regarded as a product flow in the simulation. Otherwise, the effect of separation will be greatly improved to reduce the number of separations and the cost of industrialization.

Conclusion
In this study, it is proposed for the first time that the gas cyclone separator is applied to the separation of solids with equal particle size and different density, and this discovery is applied to the recycling of spent lithium battery materials for the first time. Compared with most of the current research work, this study makes the cyclone separator break away from the mainstream field of gas-solid separation and expand to solid-solid separation, and successfully set up a simulation process for the recycling of active component LFP. The internal flow field of the cyclone separator is in good agreement with the previous experimental results. The conclusions of the study are summarized as follows: (1) Under preset operating conditions, there are two kinds of particle classification phenomena caused by the density difference at the lower end of the cyclone vortex finder and the dust outlet. The greater the density difference is, the more obvious the grading effect.
(2) Under instantaneous surface injection conditions, 60% of LFP in the original feed can be separated after 7 separations, and its mass purity is 91%, with 7% Al and 2% Fe and no Cu. Compared with the original feed, LFP is effectively recycled. The recycling efficiency increases with the number of separations; for example, the efficiency is 76% after 15 separations. (3) Under the same operating conditions, the escape number of each particle is positively correlated with its own injection number but is unrelated to the injection number of other particles. When the injection number of LFP is constant, the escape number is in a stable range, which can be applied to industrial steady-state operation. (4) Under simulated actual working conditions, the theoretical separation efficiency of 20 cycles is 61.22%, the mass purity of the recycled material is 92.53%, the main impurities are aluminum (6.92%), and trace amounts of Fe (0.44%) and Cu (0.11%). A cyclone separator can separate and recycle LiFePO 4 from waste lithium-ion battery materials, but the benefit of recycling exhibits an obvious marginal decline effect. Consequently, optimal separation times can be obtained by comprehensively considering the efficiency curve, equipment investment, energy consumption and other factors.
Compared with traditional recycling methods, this method is more environmentally friendly. These results may provide theoretical guidance for the recycling of LFP or other solid materials by cyclone separators in industry. This work is to throw a brick to attract jade, because the scenario of solid-solid separation does not exist only in the recycling of LFP from spent lithium batteries. In theory, as long as there is a sufficient density difference between the two particles, a cyclone separator can be used for separation. However, the recycling efficiency of this method still needs to be improved. In the future, if the new cyclone separator can form two dust hoppers similar to Wall_dustbin1 and Wall_dustbin2 mentioned above, then Wall_dustbin1 will be equivalent to an additional stream of products, which can not only improve the recycling efficiency of the LFP but also vastly reduce the separation times and the industrial cost of the process. In addition, the future work should provide a more comprehensive and in-depth study on the application of solid-solid separation and the optimization of structural parameters of cyclone separator by the combination of experiment and simulation.

Disclosure statement
No potential conflict of interest was reported by the author(s).