Designing and optimizing a stirring system for a cold model of a lithium electrolysis cell based on CFD simulations and optical experiments

Abstract

In the electrolysis lithium industry, liquid lithium metal and chloride gas need to be separated quickly because of the recombination of lithium and chloride. A new stirring system can help to separate liquid metal and chloride in lithium electrolysis cells. The stirring system was tried in a cold model to get the right parameters. Computational Fluid Dynamics (CFD) and Particle Image Velocimetry (PIV) were both employed to design and optimize the device parameters which included impeller type, diameter, position and rotational speed. PIV tests and CFD model validation were conducted in a cylindrical stirred tank. Different turbulence models were applied and the standard k–ε model was considered as the most suitable one. The results show that: the propeller agitator properties of a low blade number and low installation position were advantageous to the lithium collection. The impeller diameter and rotational speed have positive effects on the expected flow field. The simulation results were applied in cold model experiments, which showed that the simulations are correct and can be used in real separator design.

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1. Introduction

Lithium is an important strategic resource which is widely used in alloys, batteries, thermonuclear fusion, organic synthesis, etc.^1,2 Now, the industrial production of lithium metal relies on molten salt electrolysis. However, there are two main problems in the industrial production: high energy consumption and low product purity.³ Up to now, different types of electrolysis cells have been proposed to solve these problems.^4–6 Through comprehensive comparison of the different cell structures, a German electrolysis cell⁵ was considered to be a potential one for industry, and is shown in Fig. 1. It has a stirring system for the separation of lithium and chloride to improve the electrolysis efficiency and product purity, because the system can separate lithium and chloride efficiently by providing negative pressure through a small tube. So, a good stirring system is the key feature for this type of electrolysis cell.

Fig. 1 The structural diagram of a lithium electrolysis cell ((1) observing hole, (2) wall of electrolysis cell, (3) surface of liquid electrolysis, (4) anode, (5) cathode, (6) chloride collector, (7) axis of impeller, (8) liquid lithium, and (9) impeller).

In order to design a good stirring system, simulation and experiment are the main two techniques used by researchers. Simulations are carried out through Computational Fluid Dynamics (CFD), which is widely used in research about hydrodynamics.^7,8 In the CFD procedure for stirred tanks, two common models for the rotation characteristics are Multiple Reference Frames (MRF) and Sliding Mesh (SM).⁹ The MRF model has been found to give similar results using less computational expense compared with the SM impeller rotation model for the steady-state simulation of stirred tanks.^10,11 For the MRF model, steady-state calculations are performed with a rotating reference frame in the impeller region and a stationary reference frame in the outer region. In this way, the effects of the blade rotation are accounted for by virtue of the frame of reference, allowing for the explicit modelling of the impeller geometry.^9,12 The related research about the impeller configuration has been reported, especially on the Ruston turbine which has the lowest power number. The impeller type, configuration, size and placed position have obvious effects on the power number or other flow field physical quantities.^13–15 And the geometry of the vessel has been studied as well. The results indicate that the number of baffles has no effect on the maximum turbulence dissipation rate, either as an independent variable, or in the form of interaction with other geometric variables.¹⁶

In simulation processes, rotation is one of the key points, and turbulence is the other key point. In most stirred tanks, turbulence is a common phenomenon because of the high speed of the agitator. Correct turbulence models can save simulation costs and get accurate results. For turbulence flow in stirred tanks, Reynolds-Averaged Navier–Stokes (RANS) and Large Eddy Simulation (LES) models are in practice, however, LES is usually used in small scale simulations due to its high demand of computational resources.^17,18 The k–ε model is the most established turbulence model in RANS for engineering flows and has been widely used for modelling the turbulence flow in stirred tanks.^19,20 Abujelala²¹ and Armentante²² discussed the accuracy of the k–ε model and other researchers^23,24 compared the flow predictions in stirred tanks using variations of the k–ε model such as the Renormalized Group (RNG) k–ε and standard k–ε models. Generally, the different variations have resulted in only slight changes in the turbulence predictions, and in some cases the standard model gave superior results.

Although CFD simulations have resulted in effective design and optimization in many fields,^25–28 experiments are still the most reliable way to get accurate results or credible validation for a mathematical model.^29,30 Laser Doppler Velocimetry (LDV) and Particle Image Velocimetry (PIV) are the main means of flow field measurements for stirred tanks now.^31–33 These two techniques have their own advantages: the former is a single-point measurement and provides more flow field information while PIV is a multi-dimensional measurement with a bigger testing area.³⁴ The main problem of PIV measurement is the resolution which is related to the captured image area. This problem can be resolved with a large PIV method which was proposed by Sheng and Drumm.^35,36 Now, three-dimensional measurements also appear to provide much more real flow field information.³⁷ In PIV procedure, the density of the particles in an image is the most important factor. P. Pianko-Oprych³⁸ did many experiments to find the best density of particles for spatial resolution. He and Deshpande³⁹ showed that 5–15 particles per unit searching area can result in the best resolution. In order to get the best results, Khan⁴⁰ proposed angle-resolved stereo-PIV to study the different angles of the impeller, and Sharp⁴¹ studied the averaged PIV treatment for steady flow fields in stirred tanks. In practice, averaged PIV is an effective and highly efficient measurement for steadily stirred tanks, compared with angle-resolved stereo-PIV which is more effective for time dependent flow fields.

In all, CFD and PIV have their own advantages. Combining PIV and CFD to study the flow field of a stirred tank can benefit from each of their advantages and overcome each of their disadvantages. This combination can let each method validate the other. So, in this study, CFD and PIV were both employed to optimize a cold model of a stirred device in a lithium electrolysis cell of which is little reported in literature. The accuracy of the CFD model was validated in an ordinary stirred tank with the help of PIV. The geometry and operation parameters of the stirred device including impeller type, diameter, position and rotational speed were optimized with the commercial software Fluent 6.3. Parts of the optimized results were compared to the PIV results again to validate the simulation further. As discussed at the end of the paper, cold model experiments were carried out to validate the design and optimization.

2. Experimental instrumentation

2.1. Introduction of lithium and chloride separation device

The details of the lithium and chloride separation device structure are shown in Fig. 1. In this figure, the main liquid made up of electrolytes including KCl, NaCl, LiCl etc. The liquid lithium flows on the surface of the electrolyte for its density is smaller than that of the electrolyte. The liquid lithium released from the cathode and the chloride released from the anode go up along the electrodes to the surface of the electrolyte, and they will recombine into LiCl again if the liquid lithium is not removed in time. So the stirring system is installed to separate the lithium. An impeller is utilized to generate negative pressure in the collection chamber, as shown on the right-hand side of Fig. 1. Then the liquid lithium will be transferred from the electrolysis chamber to the collection chamber due to the pressure difference. Hence, the design and optimization of such a collection device is especially important.

2.2. Experimental device

In order to design the collection device shown in Fig. 2b, the preliminary model validation for PIV was carried out in a stirred cylindrical tank of diameter t = 240 mm. The vessel was filled with tap water and the liquid height h was 200 mm. Four baffles were mounted equidistance around the cylindrical vessel to eliminate the vortex. Their width B was one tenth of the vessel diameter. The vessel and all of the baffles were made of polymethyl methacrylate. The cylindrical stirred tank was located in a square glass vessel. Tap water was also injected into the square vessel to minimize the effect of optical refraction. A four-blade propeller of diameter d = 100 mm was employed in this test. The impeller blade and disk thickness was 2 mm. A space of c = h/3 was employed between the bottom of the vessel and the impeller disk plane. The impeller counter clockwise rotational speed n was set to be 150 rpm to generate an obvious axial flow. Fig. 2a is a simple schematic diagram.

Fig. 2 Cross-sectional view of the vessels: (a) the validation stirred tank; (b) the simplified electrolysis stirred device.

The stirred device in an electrolysis cell was the emphasis of this research. It was not necessary to model the whole electrolysis cell. Proper simplification was essential and reasonable. Fig. 2b shows the simplified device, and its detailed geometry parameters are shown in Table 1. In fact, the immersed internal component was a tube which consisted of three parts: a large pipe, a small pipe and a transition pipe. All of the components were made of glass to ensure enough transparence. A space of C = 95 mm was employed between the bottom of the vessel and the internal tube. A three-blade propeller of diameter D = 100 mm and rotational speed N = 300 rpm was installed in the centre of the large pipe while the optimization was focused on the axial velocity magnitude in the small pipe.

Table 1 The geometry parameters of the stirred device in the electrolysis cell

Physical quantities	Value (mm)
Side length of the square vessel T	250
Diameter of the large cylinder T1	140
Diameter of the small cylinder T2	40
Height of the water in the square vessel H	550
Height of the large pipe H1	200
Height of the transition pipe H2	55
Height of the small pipe H3	100

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2.3. Measurement instruments

2D PIV (TSI) was employed for the experiments concerning the flow field in this study. Fig. 3 is the schematic diagram of the PIV system. The fluid was seeded with 10 μm neutral hollow glass spheres which had the excellent following performance. The pulse laser (Continuum) provided a sheet laser to illuminate the glass spheres flowing with the fluid. The laser plane was 1 mm thick, and the wavelength was 532 nm. A Charge Coupled Device (CCD) camera (Nikon 4M) was located vertical to the laser plane to capture the illuminated particles. The particles were recorded twice at the times t and t + Δt respectively. The coherence between the laser pulse and the digital camera at different times was realized with the help of a synchronizer. According to the recorded particle information, the corresponding software Insight 3G calculated the physical quantities of the flow field based on cross-correlation processing with interrogation cell sizes of 32 pixels. At the same time, an overlap of 50% was employed for the processing. In addition, the number of captured images was one of the most important operation parameters.³⁸ Its effect on the result accuracy was considered.

Fig. 3 The schematic diagram of the PIV system.

3. Mathematical and physical model

3.1. Mathematical model

The flow of the stirred tank was simulated with a single-phase model. The minimum Reynolds number of 15 923 indicates that the turbulence model must be adopted in this study. The main governing equations of continuity and momentum equations are written as follows:

For the velocity components:

where is the mean velocity and u’_i is the fluctuating velocity. The difficulty in the equation solution procedure focuses on the Reynolds stress term . The Reynolds averaged numerical simulation (RANS) employs models based on the Boussinesq approach (k–ε models) and the Reynolds stress transport models (Reynolds stress model), to close eqn (2). It provides an effective way to balance the contradiction between prediction accuracy and computational cost.

The Boussinesq hypothesis adopts an isotropic turbulence viscosity μ_t to close the Reynolds stress term. The expression is shown in eqn (4). Standard, RNG, realizable k–ε models belong to this type.

The standard k–ε model calculates the turbulence viscosity μ_t with the turbulence kinetic energy k and the turbulence dissipation ε which are calculated from the following transport equations:

where G_k and G_b represent the generation of turbulence kinetic energy due to the mean velocity gradients and buoyancy, respectively. Y_M represents the contribution of the fluctuating dilatation in compressible turbulence to the overall dissipation rate. The default value of the model constants are C_1ε = 1.44, C_2ε = 1.92 and C_μ = 0.09. The constant turbulent Prandtl numbers for k and ε are σ_k = 1.0 and σ_ε = 1.3.

The Re-normalization Group (RNG) k–ε model was derived based on a statistical technique called renormalization group theory. It has the same model equations as the standard k–ε model except for the main difference in the dissipation rate transport equation where an additional term R_ε is added to increase the accuracy for rapidly strained flows. The variable Prandtl number and the effective viscosity are also adopted to improve its performance. Thus, it is more accurate and reliable for a wider class of flows than the standard k–ε model.

The realizable k–ε model differs from the standard k–ε model in two ways: the turbulence viscosity involves a variable C_μ and the improved dissipation rate transport equation, evolved from the exact dynamic equation of the mean-square vorticity fluctuation.

In eqn (10) the absence of G_k better represents the spectral energy transfer, and the destruction term on the right-hand side does not have any singularity. It has better performance than the traditional k–ε models in many cases including rotating homogeneous shear flows, boundary layer flows and separated flows.

Although k–ε models have many advantages, their application is limited due to the isotropic assumption in the turbulent viscosity. The alternative approach is to solve transport equations for each of the terms in the Reynolds stress tensor, which is well known as the Reynolds Stress Model (RSM). Seven additional transport equations are required to be solved in three dimensional simulations. The exact Reynolds stress transport equation is written as follows:

where the two terms on the left are the local time derivative and convection, respectively. The terms on the right D_T,ij, D_L,ij, P_ij, G_ij, ϕ_ij, ε_ij, F_ij and S represent the turbulent diffusion, molecular diffusion, stress production, buoyancy production, pressure strain, dissipation, production by system rotation, and the additional source term, respectively. Among all of them, D_L,ij, P_ij and F_ij do not require any modeling while different modeling assumptions are employed to close the terms of D_T,ij, G_ij, ϕ_ij and ε_ij. Because the effects of streamline curvature, swirl, rotation, and rapid changes in the strain rate are considered, the RSM has greater potential to predict complex flows accurately, especially anisotropic flows.

For the rotation characteristics, Multiple Reference Frames (MRF) of steady-state calculations were performed with a rotating reference frame in the impeller region and a stationary reference frame in the outer region. In this way, the effects of the blade rotation are accounted for by virtue of the frame of reference, allowing for the explicit modelling of the impeller geometry. MRF models in Fluent software are expressed in two ways, relative velocity formulation and absolute velocity formulation. This paper uses the latter, and the governing equations are written as follows:

Conservation of mass:

Conservation of momentum:

where [small omega, Greek, macron] is the angular velocity, [small nu, Greek, vector] is the absolute velocity (the velocity viewed from the stationary frame), [small nu, Greek, vector]_r is the relative velocity (the velocity viewed from the moving frame), F⃑ is the source term, and is expressed by eqn (14).where I is the unit tensor.

3.2. Numerical simulation strategies

The simulation model of the stirred tank was established with CFD software. The size of the tank and the operation parameters have been described above. The geometrical model of the same scaled stirred tank was established in Gambit 2.4.6. The whole vessel was divided into four parts to simulate impeller revolution with the Multiple Reference Frame (MRF): one rotational zone (impeller) and three static zones. Corresponding tetrahedral and hexahedral grids were employed respectively. The inner stirred zone was meshed with a hybrid mesh which included tetrahedron and pyramid grids because of the irregular impeller while the other three zones were meshed with structural hexahedron grids. In total, 104 682 elements were generated by this process after the mesh independence tests. Fig. 4 shows the global and local grid distributions.

Fig. 4 The mesh of the validation model: (a) the global grid distribution; (b) the cross section view of the grid distribution.

At the same time, the CFD model of the electrolysis stirred device was meshed with the same generation method. Only the irregular stirred zone and the conical zone were meshed with a tetrahedron and pyramid grid while the others were meshed with a hexahedron grid. 786 724 elements were generated as discrete volumes after the mesh independence tests as well.

Simulations were carried out with the commercial software Fluent 6.3. The Semi_Inplicit Method for Pressure-Linked Equations (SIMPLE) scheme was adopted for the pressure–velocity coupling. The standard pressure spatial discretization was selected, coupling the second order upwind for the spatial discretization of momentum, turbulent kinetic energy and turbulent dissipation rate. The default under the relaxation factors was employed. A residual of 10⁻⁴ was forced on except for 10⁻³ for the continuity and 10⁻⁵ for the velocity criteria. The time step size was 0.01 s.

3.3. Cold model experiment setup

Based on the PIV experiments and simulation results, a 1 : 1 cold model of an industrial lithium electrolytic cell was designed and manufactured. As is shown in Fig. 5, the cathode, anode, pipes, stirring tank and collection tank were all made from polymethyl methacrylate and were installed in a glass tank. The glass tank had a size of 900 × 700 × 800 mm and was made from stalinite with a thickness of 10 mm. The liquid level was maintained at 600 mm during the experimental process.

Fig. 5 The cold model of the lithium electrolyzer.

According to the similarity principle, lithium was replaced by silicone oil and the electrolyte was replaced by water. Silicone oil was fed to the electrolytic zone. The time the silicone oil spent flowing from the electrolytic zone to collection zone was measured by a chronograph.

4. Results and discussion

4.1. The PIV results analysis

The fluid instantaneous velocity consists of two parts: averaged velocity and fluctuating velocity. The single PIV image shows the instantaneous flow field. The measured velocity is random and does not present general information because of the fluctuating velocity. To obtain a steady flow field, it’s necessary for the images to be averaged. To find the best number of averaged images, different quantities of images were averaged. The numbers of averaged images are 25, 50, 75, 100, 125, 150, 175, 200, 225, 250, 275, 300, 325, 350, 375, 400, 425, 450, 475 and 500.

Fig. 6a shows the velocity vectors and velocity contours which are the averaged result of 25 pairs. To compare the different averaged results, three zones were selected which are marked as A–C in the figure. The radial averaged velocity in A and C and the axial averaged velocity in B are shown in Fig. 6a. Fig. 6b shows the numerical velocity at every point for the different averaged images. When 100 images were averaged, the error of velocities stayed within 3%. And the results were basically steady when the quantity of images reached 300. These results are consistent with the literature⁴¹ which reported similar results. Hence, 300 images were selected to acquire a reliable averaged flow field for validation.

Fig. 6 The effect of the number of averaged images on the velocity field. (a) The averaged velocity field of the stirred tank with 25 instantaneous images. (b) The effect of the number of averaged images on the velocity.

4.2. The validation of the CFD model

As mentioned above, different turbulence models were applied to simulate the flow field of the stirred tank. First, three kinds of k–ε model were tested: the standard k–ε model, the RNG k–ε model and the realizable k–ε model. Fig. 7a shows the velocity contours of the different k–ε models. It was found that the results of the different models were almost the same. The impeller generated an obvious axial flow, especially in the impeller volume. It is hard to compare these models from the contours. For a detailed comparison, the velocity radial distribution at different heights z was treated as the comparable physical quantity, meanwhile, the location information and definitions for height z and distance x are shown in Fig. 2a and 6a.

Fig. 7 Turbulence model comparison: (a) velocity contours of the standard k–ε model, RNG k–ε model and realizable k–ε model from left to right. (b) Velocity radial distribution of various k–ε models at the heights of 100, 110 and 120 mm from left to right.

Fig. 7b shows the velocity radial distribution of the different k–ε models at different heights. The measured velocity with PIV is also included. It is obvious that the experimental values are close to the simulation values. All of the k–ε models were satisfactory while the standard k–ε model is the simplest one to solve. Hence, by comparison, it is better to choose the standard k–ε model.

Up to now, the k–ε model is a typical CFD model because of its wide applicability. At the same time, more complex models have been developed to simulate hard problems or improve the accuracy, like the Large Eddy Simulation (LES) and the Reynolds Stress Model (RSM). Each model has its own application or advantages. The only purpose of the comparison between the different models was to find the most suitable one. Fig. 8 shows the comparison results between the standard k–ε model, LES and RSM. Generally, the result of RSM agreed well with the data of the standard k–ε model and PIV. The deviation was reasonable and acceptable. But the consumed time of RSM was longer than the standard k–ε model during the calculation process. Thus, the standard k–ε model has more advantages. On the other hand, it was interesting that the LES model turned out to be the worst one. From the velocity contours, the difference of LES was clear. The flow was not symmetric and regular. The velocity distribution also demonstrated the deviation of LES. It was deduced that this may happen because the mesh size was not enough to resolve the scales characteristic of small turbulence, especially for the boundary layer grids.⁸ Other CFD models like k–ε have already shown a good performance in simulations of the stirred tank. Hence, it was not worth simulating the LES with a refined mesh because of the high computer requirements.

Fig. 8 Turbulence model comparison: (a) velocity contours of the standard k–ε model, RSM model and LES model from left to right. (b) Velocity radial distribution of various turbulence models at the heights of 100, 110 and 120 mm from left to right.

From the experimental and simulation results, it can be concluded that the standard k–ε model, RNG k–ε model, realizable k–ε model and RSM can all simulate the stirring process with acceptable error. Considering the consumed time and computational resources, the standard k–ε model was applied in this study.

4.3. Optimization of impeller type

The stirring device is crucial for the liquid lithium collection. The axial flow which can generate a negative pressure under the impeller was expected. The type of impeller has an important effect on the flow pattern. Hence, the selection of impeller type is very significant.

Three typical types of impeller were selected for comparison: a three flat-blade turbine, a three inclined-blade turbine and propeller agitators. The last one also included four subtypes: three blades, four blades, five blades and six blades. All of the impellers had the uniform diameter of 100 mm. It should be noticed that the height of the large pipe became 20 mm which was optimized.

Flow fields with different impellers were simulated. The contours shown in Fig. 9a display the differences obviously. The flat blade turbine and inclined blade turbine had a higher radial velocity and lower axial velocity than the propeller agitators, especially the inclined blade turbine, where the axial velocity in the bottom pipe was close to zero. The variations of the propeller agitators with different blades were hard to identify from the contours. Hence, the detailed axial velocity distribution along the centre of the small pipe is shown in Fig. 9b. The results show that the propeller agitator behaved much better. Moreover, it indicates that the axial velocity increased as the number of blades increased from three to six but the increments (4–7%) were not very large. In another words, increasing the blade number was not an efficient way of improving the axial velocity. Hence, the three blade propeller agitator was selected.

Fig. 9 Effects of the different impeller types: (a) velocity contours of the three flat-blade turbine, the three inclined-blade turbine and the propeller agitators with three, four, five and six blades from left to right. (b) Velocity radial distribution of the three flat-blade turbine, the three inclined-blade turbine and the propeller agitators with three, four, five and six blades from left to right.

4.4. Optimization of impeller diameter

Impeller diameter is an important parameter to describe any impeller. It represents the size of an impeller and its effect on the velocity field is remarkable. Different propeller agitators with three blades of diameters 60, 70, 80, 90, 100, 110, 120 and 125 mm were employed to study the effects of impeller diameter.

The results are shown in Fig. 10. From the contours in Fig. 10a, it is obvious that the velocity in the center of the small pipe increases with the increment of impeller diameter. The detailed data in Fig. 10b also describes the same conclusion. This result is related to the size of impeller swept region and the circulation in the axial flow of the stirred device.

Fig. 10 Effects of the impeller diameters: (a) velocity contours of different blade diameters which increase from left to right, and (b) velocity radial distribution of the different blade diameters.

As is known, when the impeller rotates counter clockwise, the direction of fluid motion in the impeller swept region is upward. Then the upper fluid will move downwards in the outer region, because of gravity, to generate the balanced circulation which can be observed in Fig. 10a clearly. When the impeller diameter was increased, the impeller swept region became larger and the outer region became smaller. Then the upward flow must become larger too. Compared to increasing the downward flow in the outer region, it was much easier to supply the increased upward flow from the bottom small pipe in this special system. Then the axial velocity in the pipe increased with the larger required flow accordingly. To reach balance again, the fluid flowing out from the top large pipe was also increased which can be confirmed from the velocity contours.

At the same time, it should be noted that a larger stirring device is not always favorable. First, the energy consumption will rise with a larger impeller. Second, with a constant amount of lithium, a large liquid surface means a small liquid height which is hard to pump. Therefore, it is not good for the collection of liquid lithium. Third, collision will occur when the impeller is too close to the wall because of eccentric rotation in industrial operation. Hence, the 100 mm impeller was selected as the optimal diameter in this study.

4.5. Optimization of impeller position

The installation of the impeller has an important effect on the flow field. In chemical engineering, some impellers are even installed eccentrically to get a special flow field. In this system, eccentric installation was not needed. The main point of concern was the height of the impeller. In this study, the horizontal bottom of the big cylinder was defined as height 0, and the upper levels had positive height. Here, to study the effects of impeller heights which exceed 20 mm, the height of the large pipe should be changed to 200 mm to guarantee the axial flow in the small pipe.

The heights of 0, 25, 50, 75, 100, 125 and 150 mm were selected to simulate the corresponding flow fields which are shown in Fig. 11a. The height of 0 mm had an obvious advantage and the velocity radial distributions in Fig. 11b display the same result. From the data comparison, the effect of impeller height on the axial velocity was significant. This is easy to understand. First, it is generally known that the effects between the impeller and fluid decrease with the increment of their distance because of the fluid viscosity. Therefore, the axial velocity in the small pipe must be smaller with the higher impeller. Second, the fluid which is transferred upwards by the impeller must be replaced by peripheral fluid which consists of two parts: the flow from the outer region and the flow from the small pipe. If the impeller is close to the small pipe, the supplementing fluid would be almost all from the small pipe, while the outer fluid region would be the main supplement if the impeller was far from the small pipe. In other words, the height of the impeller had a significant effect on the stirring performance. The height of 0 was proven to provide maximum axial velocity.

Fig. 11 Effects of impeller installed height: (a) velocity contours of different impeller heights which increase from left to right. (b) Velocity radial distribution of the different impeller heights.

4.6. Optimization of impeller rotational speed

As an operation parameter, the importance of impeller rotational speed is well known. Just like impeller diameter, this parameter decides the flow pattern directly because of its effect on the Reynolds number. Hence, the simulations were conducted with the impeller rotational speeds of 100, 200, 300, 400 and 500 rpm. The corresponding results are shown in Fig. 12.

Fig. 12 Effects of impeller speed: (a) velocity contours of different impeller rotational speeds which increase from left to right, and (b) velocity radial distribution of the different impeller rotational speeds.

Fig. 12a shows the velocity contours with the different impeller rotational speeds. In the case of 100 rpm, the flow was weak. With the increment of impeller rotational speed, the flow got more turbulent gradually. When the impeller rotational speed reached 400 rpm, the turbulence became remarkable. The magnitude of the central velocity in the pipe also showed a clear improvement which changed from light blue to crimson in the contours. Fig. 12b expresses the same result.

In order to validate the accuracy of the CFD model in this stirred device, PIV experiments with different impeller rotational speeds were also conducted in the collection device. The numerical simulations are in accordance with the experimental results, in general, in the comparison which is shown in Fig. 13, especially for the results of 100 and 200 rpm. However, the velocity fluctuation in the PIV results of 300 and 400 rpm should also be noticed. As mentioned above, the flow got much more turbulent when the rotational speed was raised up from 100 rpm to 400 rpm. In this process, the fluctuating velocity also increased. The 300 averaged images which corresponded to 150 rpm were not enough for the higher rotational speeds. Maybe 500 pairs were suitable for 300 rpm. In other words, though parts of the PIV results were not steady, the velocity magnitude and tendency were still in accordance with the simulation. Hence, the result was still credible and the CFD model was available.

Fig. 13 Comparison between the PIV and simulation of the maximum central velocity with different impeller rotational speeds.

4.7. Cold model experiments

The velocity of the silicone oil drops varied with their positions in the pipe, with larger values in the center and smaller values in the wall of the pipe. Therefore, the experimental data had to be averaged to get a correct result.

The operation parameters were based on the optimization results: stirring speed of 400 rpm, impeller height of 0 and stirring tank height of 20 mm. The total pipe length was 710 mm, so the average velocity of the silicone oil in the pipe can be calculated from the time it spent in the pipe. 5 pairs of data with different drop diameters and random positions in the pipe were measured and the consumed times for the drops to flow through the whole pipe are shown in Table 2 and the experimental setup is shown in Fig. 5.

Table 2 Velocity in the tube

No.	1	2	3	4	5	Average
Consumed time (s)	3.72	4.47	3.85	4.09	4.63	4.15
Velocity (m s^−1)	0.19	0.16	0.18	0.17	0.15	0.17

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From Table 2 we can see that the average velocity in the pipe was 0.17 m s⁻¹. The consumed time for the lithium production to flow from the farthest position to the entrance of the pipe can be calculated as: t = πr_cathode/[small nu, Greek, macron] = 3.14 × 0.15/0.17 = 2.77 s. In the same way, when the stirring speed was 450 rpm and 500 rpm, the average velocity in the pipe was found to be 0.24 m s⁻¹ and 0.31 m s⁻¹, respectively. Thus the consumed time for the production to flow from the farthest position to the entrance of the pipe was 1.96 s and 1.52 s. A higher stirring speed will result in stronger turbulence in the collection tank. According to the literature,⁵ the time taken for the molten salt and lithium to leave the electrolytic zone should be better than 2 s, so the stirring speed can be 450 rpm.

5. Conclusion

The stirring device in a lithium electrolysis cell which is used for liquid lithium collection was optimized. CFD was used to optimize the flow field because of the experimental difficulties of high temperatures and high costs. The PIV experiments which were used to select and validate the suitable CFD model were tested in a cylindrical stirred tank. The impeller type, diameter, position and rotational speed were selected as the optimized parameters. A cold model of an industrial lithium electrolysis cell was designed based on the optimized results and cold model experiments were carried out.

The results show that the PIV result with 300 averaged pairs had enough accuracy. The standard k–ε model was considered to be the best CFD model which was verified with PIV in the stirred tank. The optimization indicated that the propeller agitator had a much better performance than the other types while the effect of the impeller blade number on the velocity magnitude was not obvious. The impeller was also much better when installed close to the small pipe. The effects of the impeller diameter and rotational speed were significant which was related to the circulation in the flow field. A high diameter and speed were expected while the feasibility of actual operation should be noted. The CFD turbulence single phase model is effective for stirring systems with medium angle speed and low velocity.

Acknowledgements

We acknowledge the financial support provided by the National Natural Science Foundation of China (Grant 21206038), the Specialized Research Fund for the Doctoral Program of Higher Education (New Teachers) (Grant 20120074120014).

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