1. Introduction
The molten salt reactor (MSR) is a Generation IV reactor that shows promise in terms of its ability to satisfy increasing electricity demands. Due to its many remarkable advantages—being safe, economic, and applying sustainable development of fissile resources and nuclear non-proliferation [1]—it has attracted interest from various researchers [2, 3]. The thorium-based molten salt reactor (TMSR) has become increasingly prominent, based on its excellent breeding capability in both thermal and fast spectrum reactors, and less long-lived minor actinides resulting from fission—and due to the abundance of thorium reserves that are available [4]. The fluoride-salt-cooled, high-temperature reactor (FHR), which is basically an MSR with solid fuel, can deliver heat at high temperatures—above 600 oC—and exhibits attractive economic performance while achieving outstanding safety and security standards [5–8]. In order to verify the technical feasibility and practicality of large-scale thorium-based FHRs, the Shanghai Institute of Applied Physics (SIAP) initiated a pioneering Molten Salt Reactor Experiment (MSRE) research program that involved designing and planning the construction of a 2 MWth Th-U pebble-bed TMSR-SF with Solid Fuel in 2020 [9–12]. In this nuclear system (as shown in Fig. 1), the process gas will be cooled to < 100 oC after reaction, in the aerosol condenser, in preparation for release. However, the high temperature salt spray, which includes beryllium, lithium, uranium, and other radioactive materials, will escape with the argon gas, and will be condensed into solid particles 0.03–10 μm in diameter. Direct emission of this nuclear waste gas will cause environmental pollution, indicating that a high efficiency exhaust removal system is needed, and will form basic emission control equipment in future TMSR–SF reactor designs.
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At present, gas–solid separation equipment that is based on activated carbon adsorption technology is the most popular cleaning equipment in nuclear power systems [13]. Due to particle wear, the activated carbon is easily damaged and needs frequent replacement—which causes high pressure drop and considerable economic loss [14]. Mechanical separation equipment, however, such as a cyclone, has not only good wear resistance, but also has a simple structure, with the added advantages of low cost and convenient maintenance [15]. Its disadvantage is that it has high separation efficiency only for particles > 5 μm [16]; thus, one or more separators need to be added in series to separate particles < 5 μm, which consumes more materials and floor space, involves complicated structures, and reduces low efficiency.
These issues show that separation equipment with a compact structure, with high efficiency, operating with a low pressure drop and exhibiting a long service life, is urgently needed for the next generation nuclear system TMSR-SF. Considering the advantages of both filters and axial cyclone separators, a novel combined separator has been proposed [17], for application to TMSR-SF technology, as shown in Fig. 2. In order to optimize design and to manufacture this new equipment, its internal flow field and separation performance have required further study.
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Many numerical studies have been performed on filters and cyclone separators. Tronville et al [18] and Hu et al [19] modelled the influence of filter structure on a flow field and identified an optimal filter structure size. Zhou et al [20] and Tian et al [21] used the standard k-ε model and Reynolds Stress model to simulate the separator—and compared it with measured results to verify the feasibility of a numerical simulation method. Azadi et al [22] simulated gas particulate flow inside different-sized cyclones, while Nor et al [23] and Wasilewski [24] numerically studied the influence of cyclone separator structure on flow field performance. All these studies were conducted for a single filter or separator; while there have been few studies on the flow field of a setup like the new combined separator. Therefore, a feasible and accurate numerical model or method is necessary, in order to study the separation performance of this combined separator. It is also important, in terms of design optimization and to facilitate wide application of this new separator, that its separation mechanism and the influence of structural parameters on pressure drop and separation efficiency are clarified.
In this study, a numerical model of the new combined separator has been established. Based on the optimum turbulence model, the gas-phase flow field and the gas–solid two-phase flow field have been numerically simulated, using the commercial FLUENT 16.0 software. The pressure drop and gas–solid separation performance were studied further by systematically examining the influence of structural parameters on separation performance. Finally, an optimized blade structure—the key component of the combined separator—was identified.
2. Geometric model
The new separator is compact and consists of two stages, as shown in Fig. 2. The first stage includes a settlement chamber and an axial blade cyclone separator, and is mainly used for the inertial separation of large particles. The second stage consists mainly of a filter and an air purification chamber, for capturing very small particles. The complete separator is 0.08 m in diameter and 0.325 m high. The axial blade cyclone separator is 0.15 m high, and consists of six blades at a 60° angle of inclination. The diameter of the blade structure is 0.045 m. The filter is 0.175 m high and consists of two flower boards, with 22 and 43 holes, respectively.
3. Numerical methods
3.1. Mathematical model
3.1.1. Governing equations
Based on the Boussinesq hypothesis, Reynolds-averaged Navier-Stokes equations were solved to predict the continuous phase. For steady and incompressible fluid flow in the separator, ignoring mass forces, the equations are described as shown in (1) and (2) [25]:
Mass conservation equation:
Momentum conservation equation:
In (1) and (2), u, p, ρ, and μ represent the carrying fluid velocity, pressure, density, and viscosity, respectively, and
is defined as the Reynolds stress tensor, which represents the effects of turbulent fluctuations on fluid flow.
When modeling a confined swirling flow, an accurate description of the flow’s turbulence is important. A number of turbulence models are available, such as the standard k–ε model, the RNG k–ε model, the Realizable k-ε model, and the Reynolds stress model (RSM). In this study, the standard k-ε model was used to simulate turbulence transport effects. The turbulence kinetic energy k and its rate of dissipation ε were obtained from transport Eqs. (4) and (5) [26].
In Eqs. (4) and (5), Gk represents the generation of turbulence kinetic energy, and is defined as shown:
Sij is defined as
YM is included in the k equation to account for compressibility effects in k-ε models, and the turbulent viscosity μT is computed by combining k and ε as follows:
The model constants were: C1ε = 1.44, C2ε = 1.92, Cμ = 0.09, σk = 1.0, and σε = 1.3.
3.1.2. Porous medium model
According to filtration theory, the porous medium model uses an empirical formula to define flow resistance in porous media. Si is included in the momentum equation, to represent the resistance of a porous medium to fluids—and for simple homogeneous porous media, it is defined as shown in Eq.(6) [27]:
When calculating the porous media model, the viscosity resistance coefficient K (1/α) and the inertia resistance coefficient C2 also need to be set.
3.1.3. Gas–solid two-phase flow model
In this study, beryllium (Be) was selected for the particle phase in the gas–solid, two-phase flow. The particle phase volume fraction was < 10%, and in the discrete phase model (DPM) used to calculate the trajectories of particles in flow, it was assumed that particle–particle interactions were negligible and that they did not affect the flow field. The force balance equation for particle movement in a Lagrangian reference frame is as shown in (7)–(10) [28].
In Equations (7)–(10), uA, μA, and ρA represent the argon velocity, viscosity, and density, respectively, up, ρp, and dp represent particulate velocity, density, and diameter, respectively; ReP is the relative Reynolds number, CD is the drag coefficient, and C1 to C3 are constants that depend on the range of ReP [29].
3.2. Boundary conditions
3.2.1. Gas-phase flow field
The fluid medium was argon, with a pressure of 0.15 MPa, and temperature of 100 ℃; the density, ρ, was 1.93 kg/m 3, and viscosity, μ, was 2.745×10 −5 Pa∙s. Boundary conditions at each zone were as follows:
(1) Inlet: Inlet velocity. The velocity at inlet vin was 50 m/s, and it was assumed that the entrance turbulence was well developed and was scattered evenly across the entire inlet cross-section. At the same time, entrance turbulence was determined by setting turbulence intensity I and hydraulic diameter at the inlet cross-section (Intensity and Hydraulic Diameter)—and the hydraulic diameter, DH, was 30 mm.
Flow Reynolds number:
Turbulence Intensity:
(2) Outlet: Pressure outlet. Pressure was set to 0 Pa.
(3) Wall: The wall parameters were standard, and there was no slip condition.
(4) Porous media: The viscous drag coefficient, inertial drag coefficient, and porosity of porous media were calculated using (13) and (14), where Df is fiber diameter, ε1 is the porosity and C4, C5 are constants
We defined Df = 20 μm, and ε1 = 0.92, as mentioned in the literature [30]. Then C4 and C5 were solved using Eq. (14), to be 3.08210734 × 109 m-2 and 17978.95948 m-1, respectively.
3.2.2. Gas–solid two-phase flow field
The boundary condition for the gas fluid was as noted in subsection 3.2.1, and the discrete phase model was used to simulate the gas–solid, two-phase flow in the proposed separator. Particles were injected with the gas into the flow stream, normal to the separator inlet surface.
The high temperature, molten salt cooling experiment was carried out in the SIAP lab. In terms of sample analysis, particle size and corresponding mass fractions were measured, giving the results shown in Table 1.
Particle diameter (D,μm) | 0.17 | 0.26 | 0.65 | 1.0 | 1.6 | 2.5 | 4.4 | 6.8 | 10 |
Mass fraction (w%) | 4 | 4 | 18 | 33 | 18 | 6 | 8 | 8 | 1 |
The total mass fractions for the different particle size range were statistically calculated, as shown in Fig. 3. It should be noted that the corresponding mass fraction was for all particles larger than the referenced particle diameter.
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According to the Rosin–Rammler equation [31], the solid particle distribution index could be calculated using Equation (15), where Dm represented the medium particle diameter, as Y = 36.8%, and was defined as 1.13 μm, from Fig. 3.
Using the inputs above, the distribution index was then calculated to be n = 1.17.
DPM boundary conditions were as follows:
(1) Inlet: Escape, indicating that particles could pass through this section.
(2) Outlet: Escape, indicating that particles that were not separated, escaped.
(3) Bottom wall: Trap, indicating that particles collected here.
(4) Filter walls: Trap.
(5) Other walls: Reflect.
3.3. Computational methodology
Fluid flow numerical simulations were obtained with computer code ANSYS 16.0, which is based on a finite volume technique, while the SIMPLE algorithm was used to solve the flow and pressure equations, and the standard method was employed in the pressure term. The second order, upwind algorithm mentioned in reference [32] was employed in simulating the boundary layer motion of the fluid. All of the governing equations were solved using the pressure-based, coupled algorithm, so that the residual for all equations was < 10-3.
3.4. Mesh Generating and grid independence verification
The accuracy of a CFD solution is strongly determined by the number and type of meshed elements within the computational domain [33, 34]. In order to obtain the best results, the whole model was divided into blocks, and a non-uniform, unstructured grid, using tetrahedrons as elements, was employed, as shown in Fig. 4. The mesh in the blade and porous media regions was locally refined.
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The grid independence test was performed, in order to ensure calculation accuracy: the calculations were therefore primarily carried out using five different grid sizes, with 1.15 × 106, 1.64 × 106, 2.82 × 106, 3.11 × 106, and 3.83 × 106 grids, respectively. The computational pressure drop deviation between each two adjacent grid sets was 1.42%, 1.27%, 0.86%, and 0.69%, respectively, which indicated that this CFD numerical model and method had high precision and was reasonable. After comprehensively considering calculation accuracy and efficiency, our final calculations were performed using the fourth grid set—that is, that with grid number of 3.11 × 106.
4. Model verification
The blade and the filter were the two key parts of the proposed combined separator. The filter was generally taken as porous media, and its flow field was simulated using a laminar model, however, the blade zone flow field needed to be studied using a turbulence model. In order to obtain accurate results, optimal selection of turbulent models should be conducted for the blade zone, by referring to experimental data in the literature [35].
The experimental cyclone structure was similar to the blade structure of the combined separator. The inlet pressure and temperature were 100020 Pa and 19 ℃, respectively. To decrease measuring error, experiments were repeated seven times, and the resultant data standardized. The maximum and minimum deviations were 11.6% and -3.59%, respectively. The final, standardized experimental results for the seven flow runs were published in reference [35], where the numerical axial cyclone separator dimensions were the same as that used in this experiment, except that, in order to make the fluid flow fully, the inlet and outlet were extended by 100 mm and 840 mm, respectively. Four turbulent models were used to simulate the structure flow fields, as mentioned above, and the numerical pressure drops obtained were compared with experimental results—and have been displayed in Fig. 5.
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Comparing the experimental pressure drops, as illustrated in Figure 5, the deviation of the numerical results obtained using the standard k-ε model was the least—within ± 10%—while the others’ deviations were > 10%. This indicated that the standard k-ε turbulence model, and this numerical calculation method, were both appropriate and accurate.
5. Results and discussions
5.1 Velocity Field
To understand detailed fluid flow information, velocity distributions at different cross-sections, and for the whole separator, were investigated. Along the z-axis, 11 cross-sections were investigated, as shown in Fig. 2. Z1–Z5 were in the blade zone, from Z = 0.091 m to 0.111 m, and each pair of adjacent cross-sections was 5 mm apart. Cross-sections Z6–Z11 were in the filter zone, and each pair of adjacent cross-sections there was 10 mm apart, from Z = 0.174 m to 0.224 m. Path h’ was defined along the y-axis direction, as the center line of each cross-section.
Fig. 6 (a) shows the velocity magnitude contours of the new combined separator, on the longitudinal section of y = 0, and it can be seen that velocity changed faster in the blade zone, at the flower board, and at the outlet pipe, due to the changes in actual flow area. Velocity distribution in the filter zone was relatively uniform.
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In order to understand the blade zone flow mechanism, velocity was investigated at five cross-sections along the z-axis—and velocity distribution at cross-sections Z1–Z5 in the blade zone have been illustrated in Figs 6 (b)–(f), where it is apparent that the velocity distribution differed with height. Along the z-axis, the maximum velocity magnitude and gradient increased with separator height, with the maximum velocity at cross-section Z1 being 49.8459 m/s, which increased to 112.037 m/s by Z5. In addition, the high velocity areas at Z1 and Z2 were larger and decreased with increased height, while those at Z3–Z5 were smaller and appeared in the corner near the inner cylinder. This phenomenon was caused by reduction in flow area, which was itself dependent on the blade layout.
Velocity contours for filter zone cross-sections have been displayed in Fig. 7, where it can be seen that the velocities were almost centrosymmetric, and appeared relatively uniform for all of the cross-sections.
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Tangential velocity distribution along path h’ in the cross-sections has been displayed in Fig. 8, where it can be seen that, in the blade zone, tangential velocity was antisymmetrically distributed along the radial direction. Due to blade influence, tangential velocity fluctuated, exhibiting rapid changes. The maximum tangential velocities for different cross-sections occurred at different radii, and the greater the tangential velocity, the easier was gas–solid separation.
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Tangential velocity along path h’ was almost 0 in the filter zone, which implied that there was no swirling effect there—and that gas–solid separation was carried out only by the filter.
5.2 Pressure Field
Static pressure distributions on the longitudinal section have been illustrated in Fig. 9 (a), where it can be seen that static pressure gradually decreased along the z-axis, while in the blade zone, static pressure increased in the radial direction. A low-pressure zone appeared in the center of the cyclone, due to its high swirling velocity, and it was apparent that the filter zone pressure gradient was very large, and almost constant in the radial direction.
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Fig. 9 (b)–(f) show static pressure contours for cross-sections Z1–Z5 in the blade zone, and indicate that the maximum static pressure at the cross-sections decreased along the z-axis. The high pressure area at Z1 was smaller and increased with increasing height, while it was larger at Z4–Z5. It should be pointed out that the static pressure in six independent regions behind the blades decreased clockwise, in all cross-sections.
Static pressure contours for filter zone cross-sections have been displayed in Fig. 10, and it can be seen that cross-section static pressures at different heights were almost centrosymmetric, and were relatively uniform. Along the z-axis, maximum static pressure decreased with separator height, and thus, while the maximum static pressure at cross-section Z6 was 122709 Pa, by Z11 it had decreased to 48620 Pa.
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Static pressures along cross-section paths are shown in Fig. 11. In the blade zone, static pressure at different heights increased with increased radius, reaching its maximum near the cylinder wall. In the filter zone, static pressure varied significantly with separator height, while showing constant behavior radially, at any given height.
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5.3 Particle trajectory and separation efficiency
Based on gas field flow, discrete phase particles were added, and their resultant trajectories are shown in Fig. 12.
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From Fig. 12 (a), it can be seen that coarse particles were mainly concentrated in the settlement chamber, then after this first-stage separation, particle concentration was reduced, and most of the unseparated particles escaped from the outlet. Ultimately, 720 particles were emitted, 147 were captured, 553 particles escaped and the trajectories of 20 particles were incomplete. Based on these results, the separation efficiency, η1, of the combined separator— without filter material—was calculated to be 20.42%.
Particles were mostly captured after flowing through the new combined separator, as shown in Fig. 12 (b). Of the 720 particles emitted, 692 particles were captured and 28 particles were recorded as incomplete. Therefore, the combined separator—with filter material—showed that it could separate particles with 96.11% efficiency.
The tests showed that first-stage axial cyclone separation greatly influenced the combined separator’s total efficiency. In summary, the higher the first-stage separation efficiency, the smaller the particles that were able to enter the second stage filter—which would result in reduced particle wear and maintenance costs.
6. Influence of structural parameters
Blade structure determines first-stage separation efficiency, so in order to obtain higher separation efficiency and reduced pressure drop, the influence of key blade structure parameters needed to be studied.
6.1 Blade inclination angle
Considering the actual working conditions and due to installation and manufacturing limitations, generally, blade inclination angles were between 15–60°. These limits occur as, firstly, since the blades overlap, they can be easily damaged when the blade inclination angle < 15°, while, secondly, if the angle > 60°, the fluid will flow in parallel fashion along the z-axis, thus decreasing gas–solid separation efficiency.
Using a 6-bladed configuration, numerical studies were conducted on the separation performance of ten combined separators with different blade angles—and the resulting pressure drop and separation efficiency of these combined separators are shown in Fig. 13.
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The combined separator pressure drop showed the same trend in variation with and without filter material, with pressure drop decreasing before becoming constant, with increased blade inclination angle. Blade inclination angle showed great effect on pressure drop when it was < 40°.
The separation efficiency of the combined separator—without filter material—fluctuated with blade inclination angle, reaching its maximum at 45°, but when filter material was introduced, the separation efficiency increased slightly at first, before decreasing with further inclination angel increase. When the blade inclination angle was 45°, separation efficiency jumped to its maximum—as the 45° blade inclination made gas–solid inertial separation and fluid flow relatively stable. Based on these results, it was settled that the optimum blade inclination angle was 45°.
6.2 Blade number
Using 45° blade inclination, numerical simulation of separators designed with a variety of blade numbers was conducted—and the resultant pressure drops and separation efficiencies are displayed in Fig. 14.
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From Fig. 14, the combined separator pressure drop—with or without filter material—shows the same variation trend. With increased blade number, pressure drop increased, with this effect increasing when the blade number > six.
Separation efficiency fluctuated with blade number. For the combined separator without filter material, separation efficiency varied slightly with blade number, reaching a maximum of 30% with four blades. For the combined separator with filter material, the efficiency was constant, at ~ 97%, before suddenly decreasing to ~ 65% when the blade number > six. Separation efficiency was then further reduced when the blade number was > seven, indicating overall that a four-bladed design was optimum.
For the optimized structure without filter material, pressure drop decreased, from 7.12 kPa to 6.66 kPa, while separation efficiency increased, from 20.42% to 29.45%. With filter material, the pressure drop decreased, from 144.13 kPa to 143.95 kPa, while separation efficiency increased from 96.11% to 98.81%. Compared with the original design, separation efficiency per unit of pressure drop improved by 2.99% and 54%, for the optimum structure with or without filter material, respectively.
7. Conclusion
In this study, a new combined separator, designed as exhaust removal equipment for a TMSR-SF, has been proposed. Gas–solid, two-phase flow fields were simulated, using CFD, and then the influence of key structural parameters on separation performance was analyzed. The following conclusions can be drawn from the study:
(1) Using the experimental results, an accurate CFD numerical model and method for the new combined separator have been proposed.
(2) In the blade zone, the maximum velocity magnitude and gradient increased with separator height (along the z-axis), while static pressure increased in the radial direction. A low pressure zone appeared in the center of the cyclone, due to high swirling velocity, while in the filter zone, velocity distribution was relatively uniform. Static pressure decreased along the z-axis, while being almost constant in the radial direction.
(3) Combined separator gas–solid separation efficiencies, with and without filter material, were 96.11% and 20.42%, respectively, with first-stage axial cyclone separation showing significant influence on the combined separator’s total efficiency.
(4) With increased blade inclination angle, the combined separator pressure drop, with or without filter material, decreased, before becoming constant, while it increased with increased blade number. The separation efficiency of the combined separator with or without filter material fluctuated with blade inclination angle and number, and four blades, with a 45° inclination angle was determined to be the optimum combination for the new design. Separation efficiency per unit of pressure drop improved by 2.99% and 54%, for the optimum structure, with or without filter material, respectively.
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