A numerical simulation method for lead bismuth fast reactor solid phase oxygen control lead oxide dissolution

Abstract

The application provides a numerical simulation calculation method for lead-bismuth fast reactor solid-phase oxygen control lead oxide dissolution, specifically, numerical simulation of oxygen release amount of oxygen concentration in a mass exchanger under different heating temperatures and flow rates, polyhedral grids and cubic constitutive relations are used in a ball bed and a T-shaped area, generalized cylindrical grid and QCR quadratic constitutive relations are used for other pipeline fluids, more accurate simulation can be obtained under a smaller number of grids, and the Prandtl number is corrected aiming at an energy transmission formula, so that the SST k-omega turbulence model based on RANS can simulate liquid metal heat exchange.

Description

TECHNICAL FIELD

[0001] The application belongs to the technical field of lead-bismuth reactors, and particularly relates to a numerical simulation calculation method for solid-phase oxygen control lead dissolution of a bismuth fast reactor. BACKGROUND

[0002] The main factor restricting the development of the fourth generation lead-bismuth reactor is the corrosion of the liquid lead-bismuth alloy to the coolant pipe. When the reactor operates at a low temperature below 450 DEG C, the corrosion rate is relatively low, but it will directly lead to the reduction of the efficiency of the lead-bismuth reactor. At a high temperature, the dissolution and corrosion of the liquid lead-bismuth to the pipe metal will be more obvious. Controlling the oxygen concentration in the lead-bismuth alloy to form a dense oxide film on the surface of the pipe metal is considered to be an effective method to resist the corrosion of the high-temperature liquid lead-bismuth. This method needs to accurately control the oxygen concentration. If the oxygen concentration is too low, the oxide film cannot exist stably, and if the oxygen concentration is too high, the lead-bismuth alloy will be rapidly oxidized, the steel structure will be degraded, and lead oxide dregs will be formed. The solid-phase oxygen control technology introduces a bypass on the main loop, and a mass exchanger (PbO MX) arranged in the bypass controls the flow and temperature of the PbO small balls in the bypass to control the oxygen concentration in a reasonable range. In order to design the mass exchanger, the oxygen concentration distribution in the mass exchanger needs to be obtained. The mass exchanger is a complex flow field composed of randomly stacked small balls, and it is difficult to directly measure the oxygen concentration on the wall surface of the small balls and the inner wall surface of the pipe. Therefore, a solid-liquid mass transfer computational fluid dynamics (CFD) model conforming to the lead-bismuth coolant experimental loop needs to be established.

[0003] The simulation of oxygen mass transfer currently disclosed is only for the ball bed part, and a tetrahedral grid is used. Moreover, the energy equation is not added. However, the Prandtl number of the liquid metal is very small, usually between 0.01 and 0.001, which means that the heat conduction mechanism is more dominant than the momentum transfer mechanism in the liquid metal, and the flow boundary layer and the temperature boundary layer are separated. For fluids with the same velocity field, the fluid with a lower Pr t number will exhibit a more pronounced temperature boundary layer. This will lead to the inapplicability of the RANS-based turbulence model. Moreover, it is difficult to measure the oxygen concentration inside the ball bed, and the lead-bismuth oxygen sensor technology is not mature. SUMMARY

[0004] In view of the above technical problems, the present application provides a method for quickly simulating the temperature and oxygen mass transfer capacity of lead-bismuth fluid under different heating powers, specifically a numerical simulation method for simulating the oxygen release amount of oxygen concentration in a mass exchanger under different heating temperatures and flow rates. The Prandtl number is corrected using a formula for energy transmission, so that the SST k-omega turbulent flow model based on RANS can simulate liquid metal heat exchange. Moreover, the polyhedral grid and cubic constitutive relationship are used for the ball bed and T-shaped area, and the generalized cylindrical grid and QCR quadratic constitutive relationship are used for other pipeline fluids, so that more accurate simulation can be obtained with less number of grids.

[0005] The present application provides a numerical simulation calculation method for solid-phase oxygen control lead bismuth fast reactor lead oxide dissolution, comprising:

[0006] Loop bypass and mass exchanger modeling: the discrete element method is used to randomly stack and fill the mass exchanger with PbO and Al2O3 particles in the solid-phase oxygen control mass exchanger, the point contact between the spheres and the spheres, and the spheres and the pipelines is approximated to a cylinder with a diameter of 10% of the diameter of the spheres, and then modeled together with the loop. The fluid domain part between the stacked small balls and the pipeline is extracted, and the oxygen control device simulation only includes the fluid domain part.

[0007] Mesh generation: In order to better capture the complex geometry of the stacked pebble bed, a quadrilateral dominated mesh is generated. The pebble bed part and other pipes are divided into different regions and processed separately. The contact surface mesh of the pebble bed part and other pipes is a conformal mesh. The pebble bed part refers to the stacked spheres and the cylindrical pipes present, and the conformal mesh part is the upper and lower inlet and outlet planes of the cylindrical pipes in the pebble bed part. In the model, the pebble bed part corresponds to the stacked pebble bed region, and the other pipes are divided into the side branch inlet and outlet T-shaped pipe region and the main side branch flow channel cylindrical pipe region. For the side branch inlet and outlet T-shaped pipe region, polyhedral mesh is used, and the intersection line of the vertical cylinder and the horizontal cylinder of the T-shaped pipe region is encrypted by lines. For the cylindrical pipe region, generalized cylindrical mesh is used. The cylindrical pipe region includes the cylindrical mesh region of the main road and the cylindrical mesh region of the branch (including the turn). Because the fluid domain part of the stacked pebble bed region needs to be calculated more finely, the stacked pebble bed region uses polyhedral mesh, and the surface of the stacked sphere wall and the pipe interface of the pebble bed inlet and outlet are encrypted. The surface of the stacked sphere wall refers to the surface of the PbO sphere and the Al2O3 sphere in the stacked pebble bed region, and the pipe interface of the pebble bed inlet and outlet refers to the cross section of the cylindrical pipe inlet and outlet of the pebble bed part. The mesh of the stacked sphere wall and the pipe interface of the pebble bed inlet and outlet all adopts enhanced layer mesh. All the near-wall mesh is processed according to the prismatic layer mesh to solve the near-wall flow problem, including the wall surface of each sphere and the pipe wall surface. The prismatic layer mesh growth rate adopts the hyperbolic tangent rule to adapt to the small gap between the spheres. The reason for adopting the hyperbolic tangent is that the gap between the sphere contact points is too small, and the prismatic layer thickness needs to be unevenly changed. If a uniform thickness is adopted, it cannot generate a prismatic layer in the narrow gap. Finally, mesh optimization is carried out, preferably, the mesh optimization cycle is 8 times, and the mesh quality threshold is set to 1. Preferably, the proportion of mesh quality in the range of 0.6-1.0 is 80%, the mesh can be used for calculation, and the calculation result is more accurate. The preferred embodiment of the present application is summarized, and the proportion of mesh quality above 0.9 is 90%.

[0008] Flow diffusion model selection: The fluid domain part of the stacked pebble bed region in the mass exchanger and the fluid domain part of other pipes are processed in blocks. The flow of oxygen and lead-bismuth liquid both use multiphase liquid components, and the turbulent flow model selects SST k-ω model; the PbO sphere wall surface of the fluid domain part of the stacked pebble bed region is set to be permeable, and the internal oxygen concentration is the saturated concentration of oxygen in lead-bismuth at the temperature of the sphere wall surface of the stacked pebble bed region after fluid heat transfer. Because there is large-curvature flow in the stacked pebble bed region in the geometric model, the stacked pebble bed region uses second-order upwind convection format and cubic constitutive relation; the fluid domain part of other pipes uses QCR quadratic constitutive relation. Because the turbulent flow of the flow does not need to be accurately simulated, but needs to be prevented from diverging, the turbulent flow suppression is turned on, and the full-wall y+ processing is used. The turbulent Schmidt number of the lead-bismuth liquid is 0.9; the energy model selects the separated fluid temperature model.

[0009] Turbulent boundary condition setting: Turbulent boundary conditions include mass flow rate at inlet, turbulent intensity at inlet and outlet, and oxygen concentration. It can be directly set through software.

[0010] The wall surface oxygen concentration of PbO pellets is saturated oxygen concentration, that is:

[0011]

[0012] In the formula: C s Boundary oxygen concentration, unit: w.t.%; T-temperature, unit: K.

[0013] For fluid working medium oxygen diffusion rate, density, thermal conductivity, specific heat, dynamic viscosity, the following formula is used:

[0014]

[0015] In the formula: D0-the diffusion rate of oxygen in LBE, unit: m 2 / s; R-ideal gas constant; T-temperature, unit: K.

[0016] ρ=11096-1.3236T

[0017] In the formula: ρ-density, unit: kg / m 3 ; T-temperature, unit: K;

[0018]

[0019] In the formula: λ-thermal conductivity, unit: W / (m·K); T-temperature, unit: K;

[0020] c p,LBE =160-0.0239T

[0021] In the formula: c p,LBE -specific heat, unit: J / (kg·K); T-temperature, unit: K;

[0022]

[0023] In the formula: η-dynamic viscosity, unit: Pa·s; T-temperature, unit: K.

[0024] Energy heat transfer boundary condition setting: In the stacked sphere bed, there is a heating device outside the pipe, and the heating power is input according to the actual setting temperature; other pipes are wrapped with insulation layer, and the heat flux is measured according to the actual measurement.

[0025] For liquid metals such as lead bismuth, the Prandtl number is too small, and there is a defect that the thermal boundary layer cannot be accurately described in the Reynolds stress average, so it is necessary to modify the Prandtl number of lead bismuth, and the formula is as follows:

[0026]

[0027] Pr t Prandtl number; v t Kinematic viscosity, unit m 2 / s; v Turbulent viscosity, unit m 2 / s.

[0028] SIMPLE steady operation, until bypass flow, bypass average oxygen concentration and outlet average oxygen concentration is stable, then calculate the dissolution value.

[0029] The beneficial technical effects of the present application: compared with the prior art for lead bismuth fast reactor solid phase oxygen control stack ball bed oxygen mass transfer simulation calculation method, the present application has the following advantages: 1) the quadrilateral main control mode is used in the surface grid part, and the hyperbolic tangent growth rate is used in the prism layer, so that the grid can better capture the complex geometric structure. 2) The whole model of the loop mass exchanger is established, not only the stack ball bed area, but also the stack ball bed area and other fluid pipeline parts are processed in blocks. Considering the turbulent flow in different areas, the generalized cylindrical grid is used in the cylindrical pipeline area, and the polyhedral grid is used in the T-shaped area of the bypass inlet and outlet and the complex flow channel of the stack ball bed, so that the turbulent flow model calculation is more accurate and fast. 3) The energy heat transfer equation is added to correct the Prandtl number, so that the SST k-ω turbulent flow model based on RANS can calculate the heat transfer of liquid lead bismuth metal under different temperature control conditions. 4) Thus, a two-dimensional variable comprehensive model of the loop oxygen control under different temperature and flow rate is established, which makes up for the deficiency of the current one-dimensional model of flow rate under constant temperature condition. BRIEF DESCRIPTION OF DRAWINGS

[0030] Figure 1 The flow chart of the method of the present application is calculated;

[0031] Figure 2 The stack ball bed and loop model in the calculation method of the present application;

[0032] Figure 3 The grid of the loop mass exchanger in the model of the calculation method of the present application;

[0033] Figure 4 The oxygen concentration and velocity streamline distribution under the temperature of 425℃ and the flow rate of 4kg / s in an embodiment of the present application;

[0034] Figure 5 The simulation results in the embodiment of the present application and the comparison with CRAFT. Specific implementation method

[0035] The present application will be further described below in combination with the drawings and specific embodiments.

[0036] In a specific embodiment of the present application, a method for numerical simulation of solid phase oxygen control lead bismuth fast reactor lead dissolution is provided, Figure 1 The specific flow chart is shown in the figure. The working condition of this embodiment is heating temperature 425℃, inlet flow rate 4kg / s.

[0037] Step 1: modeling of loop bypass and mass exchanger, as shown in the figure, for the solid phase oxygen control mass exchanger, the discrete element method is used to randomly stack the spheres to fill the mass exchanger. In this embodiment, the sphere diameter is 10mm, and the filling is 68 spheres. The middle sphere is selected as PbO, a total of 14; the upper and lower two layers are Al2O3, 54. The point contact between the spheres and the spheres and the pipe is treated as a cylinder with a diameter of 10% of the sphere, and then modeled together with the loop. Extract the fluid domain part between the stacked small balls and the pipe, and the oxygen control device simulation only includes the fluid domain part. Figure 2

[0038] Step 2: meshing, as shown in the figure: the area in the model is divided into stacked bed area, T area, and cylindrical pipe area. The stacked bed area and the T area use polyhedral mesh, the surface of the spheres is face-encrypted, and the pipe junction is line-encrypted. The cylindrical pipe area uses generalized cylindrical mesh. The surface of the prismatic layer spheres is 13 layers, and the other parts are 3 layers, with a hyperbolic tangent growth rate. The final number of meshes is 3.9 million. Figure 3 Step 3: all turbulence models are selected as SST k-ω model, the PbO sphere wall surface of the stacked bed fluid domain part is set as permeable, and the internal oxygen concentration is the oxygen saturation concentration of lead bismuth after fluid heat of the stacked bed area sphere wall surface. The stacked bed area uses second-order upwind convection format and cubic constitutive relationship; other pipe fluid domain parts use QCR quadratic constitutive relationship; open turbulence suppression, and use full wall y+ treatment; the turbulent Schmidt number of lead bismuth liquid is 0.9. The energy model selects the separated fluid temperature model.

[0039] Step 4: turbulence boundary condition setting: the boundary conditions include mass flow rate 4kg / s, inlet and outlet turbulence intensity 0.05, and oxygen concentration 1×10 -7 w.t.%, temperature 400℃, and turbulent Schmidt number 0.9. The PbO sphere wall oxygen concentration is the saturation oxygen concentration, i.e.,

[0040]

[0041]

[0042] C s Boundary oxygen concentration, unit: w.t.%; T-temperature, unit: K;

[0043] The formulas used for lead bismuth fluid working medium oxygen diffusion rate, density, thermal conductivity, specific heat, and dynamic viscosity are:​​

[0044]

[0045] wherein: D0 - diffusion rate of oxygen in lead bismuth, unit m 2 R - ideal gas constant; T - temperature, unit K;

[0046] p = 11096 - 1.3236T

[0047] wherein: p - density, unit kg / m 3 T - temperature, unit K;

[0048]

[0049] wherein: λ - thermal conductivity, unit W / (m·K); T - temperature, unit K;

[0050] c p,LBE = 160 - 0.0239T

[0051] wherein: c p,LBE - specific heat, unit J / (kg·K); T - temperature, unit K;

[0052]

[0053] wherein: η - dynamic viscosity, unit Pa·s; T - temperature, unit K;

[0054] Boundary condition setting of energy heat transfer: there is a heating device outside the stacked ball bed pipe, and the heating power is input according to the actual setting temperature, so that the surface temperature of the PbO ball is controlled at about 425℃; other pipes are wrapped with insulation layer, and the heat flux is measured according to the actual measurement.

[0055] For liquid metals such as lead bismuth, the Prandtl number of lead bismuth needs to be corrected, and the formula is as follows:

[0056]

[0057] wherein: Pr t - Prandtl number; v t - kinematic viscosity, unit m 2 / s; v - turbulent viscosity, unit m 2 / s;

[0058] Step 5: SIMPLE steady-state operation until the bypass flow, bypass average oxygen concentration and outlet average oxygen concentration are stable.

[0059] The final calculation result is that the bypass flow is 0.7966 kg / s, the bypass oxygen concentration is 1.626×10-6 w.t.%, 3.901 x 10 -7 w.t.% is the average oxygen concentration at the outlet. Figure 4 The oxygen concentration and velocity streamline distribution are shown.

[0060] The average dissolution rate is the amount of oxygen carried away by the LBE fluid in a certain period of time, and the formula is as follows:

[0061]

[0062] q is the average dissolution rate, in kg / s; is the mass flow rate, in kg / s; C out is the average oxygen concentration of the cross-section plane in the middle of the branch, in wt%; C in is the average oxygen concentration of the cross-section at the inlet, in wt%.

[0063] In the above embodiment of the present application, 14 PbO balls with a diameter of 10 mm are treated, and the dissolution rate is 1.215 x 10 -6 kg / s under the conditions of a temperature of 425°C and a main path flow rate of 4 kg / s.

[0064] The average mass transfer coefficient represents the size of the mass transfer capacity of the PbO ball, which is related to the average dissolution rate q, and the calculation formula is as follows:

[0065]

[0066] k is the average mass transfer coefficient, in kg / (m 2 ·s); A is the mass transfer area, that is, the surface area of the PbO ball, in m 2 ; C s is the saturated oxygen concentration, in w.t.%; C bulk is the volume oxygen concentration, which is obtained by averaging the inlet and outlet oxygen concentrations, in w.t.%.

[0067] The Sherwood number is a dimensionless form of the mass transfer coefficient, and is the ratio of the rates of convective mass transfer and diffusive mass transfer, and the expression is as follows:

[0068]

[0069] ρ is the LBE density, in kg / m 3 , D is the diffusion coefficient, in m 2 / s; l is the characteristic length, dimensionless, and is defined as follows:

[0070]

[0071] where V void is the entire void volume, in m2 ; s is the area in the void that is in contact with the LBE, in m 2 ; ε0 is the volume porosity; d is the sphere diameter, in m.

[0072] The Peclet number is the product of the Reynolds number and the Schmidt number, as follows:

[0073] P e = R e · S C

[0074]

[0075]

[0076] P e is the Peclet number, Re is the Reynolds number, S C is the Schmidt number, all three are dimensionless; u is the average velocity, in m / s; v is the kinematic viscosity, in m 2 / s, expressed as

[0077]

[0078] η is the dynamic viscosity, in Pa·s.

[0079] The simulation results at different temperatures and different flow rates are shown in Table 1.

[0080] Table 1 Simulation results at different temperatures and different flow rates

[0081]

[0082]

[0083] As can be seen from the above specific embodiments, the present application can successfully complete the oxygen mass transfer in the PbO ball bed in the loop mass exchanger and the diffusion process of oxygen in the loop at different heating temperatures and different main flow rates, so as to obtain the mass exchanger outlet concentration and the PbO ball dissolution rate, and the oxygenation effect can be pre-evaluated.

[0084] The accuracy of the simulation is verified by the relationship between Pe and Sh, and as long as the relationship trend is consistent with CRAFT, it can be considered reasonable. CRAFT loop uses 14mm balls, and CRAFT is a relatively well-known and authoritative data in the field. The balls used in the simulation in the present application are very close to CRAFT, so the simulation results of the present application are compared with the data of CRAFT to verify the accuracy of the simulation of the present application. For example, Figure 5The image of the CFD simulation data result of the present application is shown. It can be seen that the image of the CFD simulation data result of the present application is more consistent with the CRAFT experimental result, proving that the simulation by the method of the present application is effective and accurate.

[0085] This embodiment is only a preferred specific implementation of the present application, but the protection scope of the present application is not limited to this, any person skilled in the art can easily think of changes or replacements within the technical scope disclosed by the present application, which should be covered in the protection scope of the present application. Therefore, the protection scope of the present application should be subject to the protection scope of the claims.

Claims

1. A method for calculating the numerical simulation of the dissolution of lead oxide in a lead-bismuth fast reactor with solid phase oxygen control, comprising: Modeling of the loop bypass and mass exchanger: using the discrete element method to randomly stack the PbO and Al2O3 particles in the mass exchanger of the solid phase oxygen control to fill the mass exchanger, approximating the point contact between the spheres and the pipeline as a cylinder with a diameter of 10% of the diameter of the spheres, and modeling the oxygen control device simulation only including the fluid domain part between the stacked small balls and the pipeline; Mesh generation: using a quadrilateral master control method to generate a mesh, dividing the pebble bed part and other pipelines into different areas for separate processing, and using conformal mesh for the contact surface mesh of the pebble bed part and other pipelines; the pebble bed part corresponds to the stacked pebble bed area, and the other pipelines are divided into a bypass inlet and outlet T-shaped pipeline area and a main bypass flow channel cylindrical pipeline area; for the bypass inlet and outlet T-shaped pipeline area, polyhedral mesh is used, and the intersection line of the vertical cylinder and the horizontal cylinder is encrypted; for the cylindrical pipeline area, generalized cylindrical mesh is used; the stacked pebble bed area uses polyhedral mesh, and the surface of the stacked sphere wall and the interface between the pebble bed inlet and outlet and the pipeline are encrypted; The mesh of the stacked sphere wall and the interface between the pebble bed inlet and outlet and the pipeline all uses enhanced layer mesh; the near-wall mesh is processed according to the prismatic layer mesh, and the prismatic layer mesh growth rate uses the hyperbolic tangent rule; Flow diffusion model selection: both oxygen and lead bismuth liquid use multiphase liquid component, and the turbulent flow model selects SST Model; The fluid domain part of the stacked sphere bed area is set as permeable, and the inner oxygen concentration is the saturated concentration of oxygen in lead bismuth after the temperature of the sphere bed area sphere wall surface after fluid heat transfer; The stacked pebble bed area uses a second-order upwind convection scheme and a cubic constitutive relationship; the fluid domain part of the other pipelines uses a QCR quadratic constitutive relationship; turbulence suppression is turned on, and full-wall y+ processing is used; Turbulence boundary condition setting, including setting the mass flow rate of the inlet, the turbulence intensity of the inlet and outlet, and the oxygen concentration; Energy heat transfer boundary condition setting: in the stacked pebble bed area, the actual temperature input heating power is set; the heat flux of the other pipelines is measured according to the actual measurement; The Prandtl number of the lead-bismuth is corrected, and the formula is as follows: ， wherein is the Prandtl number, is the kinematic viscosity, in m 2 / s, is the turbulent viscosity, in m 2 / s; Until the bypass flow, the average oxygen concentration of the bypass, and the average oxygen concentration of the outlet are stable, the SIMPLE steady-state operation is performed, and then the dissolution value is calculated.

2. The method according to claim 1, wherein the method is characterized in that: The pebble bed part refers to the stacked spheres and the cylindrical pipeline in which they exist, and the conformal mesh part is the upper and lower inlet and outlet planes of the cylindrical pipeline of the pebble bed part.

3. The method of claim 1, wherein the method is characterized by: The cylindrical pipeline area includes the cylindrical mesh area of the main pipeline and the cylindrical mesh area of the branch pipeline.

4. The method of claim 1, wherein the method is characterized by: When optimizing the mesh, the mesh optimization cycle is 8 times, the mesh quality threshold is 1, and the 90% mesh quality is controlled to be above 0.

9.

5. The method of claim 1, wherein the method is characterized by: The Schmidt number of the turbulent flow of the lead-bismuth liquid is 0.9.

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