A Numerical Simulation Method for Oxygen Mass Transfer with Liquid Lead-Bismuth and Solid Oxygen Control

Abstract

The present invention discloses a numerical simulation method for solid-state oxygen control and mass transfer of liquid lead-bismuth, which can be used for numerical simulation research on the oxygen dissolution and diffusion characteristics of solid lead oxide particles in a mass exchanger during solid-state oxygen control of liquid lead-bismuth. By studying the oxygen supply characteristics of a randomly stacked pebble bed composed of solid lead oxide particles in a mass exchanger, the lead oxide pebble bed is simplified into a homogeneous porous medium, and a porous medium component transport model can be used to complete the numerical simulation of solid-state oxygen control. The present invention avoids the modeling difficulties of simplifying point contacts between lead oxide particles in current public literature, has the characteristics of low computing resource usage and high result reliability, and can be used for preliminary research on solid-state oxygen control experiments of liquid lead-bismuth, which is beneficial for guiding the design of solid-state oxygen control equipment in lead-bismuth piles of fourth-generation reactors.

Description

Technical Field

[0001] The present invention specifically relates to a numerical simulation method for liquid lead-bismuth solid oxygen controlled oxygen mass transfer. Background Art

[0002] Lead-based fast reactors (FBRRs) are a type of reactor that uses liquid lead or lead-bismuth alloy as a coolant. They are a type of fourth-generation reactor. For example, FBRRs offer numerous advantages due to their excellent chemical and physical properties, including high neutron yield, small capture cross-section, good thermal conductivity, low melting point, high boiling point, low saturated vapor pressure, and low chemical activity. They hold unique advantages for future applications in distributed power generation, marine, and aviation propulsion. Liquid lead-bismuth, with its high heat capacity and inert chemical properties, is particularly well-suited for commercial mobile nuclear power plants. While FBRRs hold many promising applications, they are highly corrosive to reactor structural materials at high temperatures. Currently, the most viable solution to this corrosion problem is to control the dissolved oxygen concentration in liquid lead-bismuth. Research has shown that at varying temperatures, the oxygen concentration in liquid lead-bismuth alloys reaches a certain level where oxygen forms a dense, uniform oxide layer on the surface of iron-based metals. This oxide layer prevents further corrosion of structural steel by the liquid lead-bismuth alloy. However, the oxygen concentration in the liquid lead-bismuth alloy cannot be too high, otherwise a large amount of lead oxide slag will form, blocking the pipes, causing poor heat transfer, and even more seriously, causing a reactor meltdown. Therefore, accurately controlling the oxygen concentration in the liquid lead-bismuth alloy is crucial.

[0003] Internationally, oxygen concentration control methods primarily fall into three categories: gaseous oxygen control, solid-state oxygen control, and oxygen pump control. Gaseous oxygen control is currently the most commonly used method. This method controls the dissolved oxygen concentration in liquid lead and bismuth by injecting a specific ratio of argon / oxygen, argon / hydrogen / water vapor, or carbon monoxide / carbon dioxide mixture into the liquid metal. Solid-state oxygen control rapidly adjusts the oxygen concentration in the liquid metal by controlling the dissolution and precipitation of solid lead oxide. In addition to gaseous and solid-state oxygen control, oxygen pump technology can also be used to control and regulate the oxygen concentration in liquid lead and bismuth. While similar in principle to oxygen sensors, oxygen pump technology operates in contrast to oxygen sensors. It primarily utilizes electrochemical principles to apply a specific voltage between the two electrodes of a solid electrolyte, controlling the passage of oxygen ions through the solid electrolyte into or out of the liquid lead and bismuth.

[0004] To date, the most mature oxygen control technology used in lead-based fast reactors internationally is gaseous oxygen control. Experience with solid-state oxygen control technology is still lacking. This is primarily due to the lack of maturity in the design of mass exchangers for solid-state oxygen control equipment and the use of lead oxide. More precise design and analysis of the oxygen supply characteristics of lead oxide loading in liquid lead-bismuth systems are needed. Therefore, numerical simulation analysis of the designed solid-state oxygen control equipment is necessary before experiments. Currently, no research has been reported on numerical methods for solid-state oxygen control and mass transfer in liquid lead-bismuth systems based on porous media models. Summary of the Invention

[0005] In response to the above-mentioned technical problems, the present invention provides a numerical simulation method for solid-state oxygen control and mass transfer of liquid lead-bismuth, which can be used for numerical simulation research on the oxygen dissolution and diffusion characteristics of solid lead oxide particles in the mass exchanger during the solid-state oxygen control process of the liquid lead-bismuth system. By studying the oxygen supply characteristics of the randomly stacked pebble bed composed of solid lead oxide particles in the mass exchange, the lead oxide pebble bed is simplified to a homogeneous porous medium, and the numerical simulation of solid-state oxygen control is completed using the porous medium component transport model. It avoids the modeling difficulties of simplifying the point contact between lead oxide particles in the current public literature, has the characteristics of low computing resource usage and high result reliability, can be used for liquid lead-bismuth solid-state oxygen control experimental pre-study, and is conducive to guiding the design of solid-state oxygen control equipment in the fourth-generation lead-based fast reactor.

[0006] The present invention solves the above-mentioned technical problems by adopting the following technical solutions: a numerical simulation method for controlling oxygen mass transfer in liquid lead-bismuth solid oxygen, comprising the following steps:

[0007] Step 1: Solid-state oxygen control equipment modeling: The randomly stacked ball bed composed of solid lead oxide particles in the mass exchange is simplified into a homogeneous porous medium, and the fluid dynamics modeling of the porous medium region and the liquid lead-bismuth fluid channel is performed separately;

[0008] Step 2: Mesh generation: The solid lead oxide in the solid-state oxygen control equipment has been simplified into a homogeneous porous medium. The porous medium area is meshed separately, and then the other liquid lead-bismuth flow channels are meshed. The two different areas are in contact, and the contact interface is the internal connected surface, ensuring that the liquid lead-bismuth fluid can flow through the porous medium area to transport the oxygen component.

[0009] Step 3: Physical property call and solid-state oxygen control equipment calculation model setting: Since the dissolved oxygen concentration in liquid lead bismuth is very low, the thermophysical property parameters are based on the liquid lead bismuth itself. After solid lead oxide is washed and dissolved by liquid lead bismuth, it is mixed and transported with the main fluid in the dissolved liquid phase. Therefore, a multi-component liquid model and a multi-component transport model are selected for solution and calculation. The K-Epsilon turbulence model is selected as the turbulence model, and a two-layer full y+ wall treatment is selected for the porous medium region. For the liquid lead bismuth main fluid, the turbulent Schmidt number is set to 0.9. Since the liquid lead bismuth is only supplied with oxygen by solid lead oxide, chemical reactions are ignored. The physical properties of the porous medium are characterized by the average value of the lead oxide ball bed volume, lead oxide ball density, and number.

[0010] Step 4: Solid-state oxygen control equipment calculation model and boundary condition setting: Boundary conditions include inlet flow rate, initial oxygen concentration, inlet turbulence intensity, initial temperature and porous area boundary conditions;

[0011] The porous region boundary conditions include component source terms and initial condition options;

[0012] The component source term provides the boundary oxygen concentration, which is converted into the dissolved oxygen concentration that can be supplied by the saturated oxygen boundary of the porous media region based on the number, density, and volume of the solid lead oxide pellets. The calculation formula is as follows:

[0013] The saturated oxygen concentration when lead oxide dissolves is:

[0014]

[0015] Where:

[0016] C S ——the saturated oxygen concentration when lead oxide is dissolved, in wt.%;

[0017] T——temperature, in K;

[0018] The specific oxygen component source term is converted into a homogeneous porous medium component source based on the designed number, density and ball bed volume of solid lead oxide balls;

[0019] The initial condition options include viscous resistance coefficient, inertial resistance coefficient, porosity, and tortuosity. The calculation formula for the inertial resistance coefficient is as follows:

[0020]

[0021] Where:

[0022] a——viscous resistance coefficient, unit is kg / (m 3 s);

[0023] μ——dynamic viscosity, unit is Pa·s;

[0024] ε——porosity;

[0025] d——diameter, in m;

[0026] The porosity calculation formula is as follows:

[0027]

[0028] Where:

[0029] V - total volume of the pebble bed including all lead oxide particles;

[0030] V F - the volume of all lead oxide particles contained in the pebble bed;

[0031] The calculation formula of inertial resistance coefficient is as follows:

[0032]

[0033] Where:

[0034] b——Inertial resistance coefficient, unit is kg / m 4 ;

[0035] ρ——density, unit is kg / m 3 ;

[0036] The curvature calculation formula is as follows:

[0037]

[0038] τ——curvature;

[0039] Step 5: Use the SIMPLE algorithm, set the discretization format to second-order upwind, and perform steady-state calculations until the average dissolved oxygen concentration at the outlet converges to a stable value.

[0040] Compared with the prior art, the present invention has the following advantages:

[0041] 1. The present invention avoids the difficulty of simplifying the modeling of point contacts between lead oxide particles in the current public literature;

[0042] 2. The analysis method and calculation model of the present invention have the characteristics of low computing resource usage and high reliability of results, and can be used for preliminary research on solid-state oxygen control experiments of liquid lead and bismuth;

[0043] 3. The analysis method of the present invention is helpful in guiding the design of solid-state oxygen control equipment in the fourth-generation lead-based fast reactor. BRIEF DESCRIPTION OF THE DRAWINGS

[0044] Figure 1 It is a calculation flow chart of the present invention;

[0045] Figure 2 A schematic diagram of a modeling method for simplifying a randomly stacked pebble bed composed of solid lead oxide particles in a mass exchanger of a solid-state oxygen control device of the present invention into a porous medium region;

[0046] Figure 3 Mesh settings for the liquid lead-bismuth flow channels and porous media regions in a solid-state oxygen control device. DETAILED DESCRIPTION

[0047] The following will clearly and completely describe the technical solutions in the embodiments of the present invention in conjunction with the drawings in the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, rather than all the embodiments. Based on the embodiments in the invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0048] Implementation Case 1:

[0049] A numerical simulation method for solid-state oxygen control and mass transfer in liquid lead-bismuth is used for solid-state oxygen control, and the steps are as follows:

[0050] Step 1: Modeling of solid-state oxygen control equipment, such as Figure 2 As shown in the figure, the randomly stacked ball bed composed of solid lead oxide particles in the mass exchange is simplified into a homogeneous porous medium, and the fluid mechanics modeling of the porous medium region and the liquid lead-bismuth fluid channel is carried out separately;

[0051] Step 2: Mesh generation, such as Figure 3 As shown, Figure 1 is the inlet flow channel of the solid-state oxygen control device; Figure 2 is the aluminum oxide porous medium area, the purpose of which is to stabilize the fluid flow rate flowing into the lead oxide porous medium area, and this area is a non-source item; Figure 3 is the lead oxide porous medium area, which is the source item in the solid-state oxygen control simulation and provides dissolved oxygen for the liquid lead-bismuth alloy; Figure 4 is the outlet flow channel of the solid-state oxygen control device; Figure 3 The interface where the four regions contact each other is the flowable interface;

[0052] Step 3: Physical property call and solid-state oxygen control equipment calculation model setting: Since the dissolved oxygen concentration in liquid lead bismuth is very low, the thermophysical property parameters are based on the liquid lead bismuth itself. After solid lead oxide is washed and dissolved by liquid lead bismuth, it is mixed and transported with the main fluid in the dissolved liquid phase. Therefore, a multi-component liquid model and a multi-component transport model are selected for solution and calculation. The K-Epsilon turbulence model is selected as the turbulence model, and a two-layer full y+ wall treatment is selected for the porous medium region. For the liquid lead bismuth main fluid, the turbulent Schmidt number is set to 0.9. Since the liquid lead bismuth is only supplied with oxygen by solid lead oxide, chemical reactions are ignored. The physical properties of the porous medium are characterized by the average of the volume, density, and number of lead oxide pellets.

[0053] The physical properties are as follows:

[0054] ρ LBE =11065-1.293T

[0055] c P,LBE =164.8-3.94×10 -2 T+1.25×10 -5 T 2 -4.56×10 5 T -2

[0056] λ LBE =3.284+1.617×10 -2 T-2.305×10 -6 T 2

[0057]

[0058]

[0059] Where:

[0060] ρ LBE ——Density of lead-bismuth alloy, kg / m 3 ;

[0061] T——lead-bismuth alloy temperature, unit is K;

[0062] c P,LEB ——heat capacity of lead-bismuth alloy, in J / (kg·K);

[0063] λ LBE ——Thermal conductivity of lead-bismuth alloy, in W / (m·K);

[0064] η LBE ——dynamic viscosity of lead-bismuth alloy, in Pa·s;

[0065] D O,LBE ——Diffusion coefficient of oxygen in liquid lead-bismuth alloy, unit is m 2 / s;

[0066] R——ideal gas constant, value is 8.31441, unit is J / (mol·K);

[0067] In this example, the K-Epsilon turbulence model is selected as the turbulence model, and a two-layer full y+ wall treatment is selected for the porous medium region. For the liquid lead-bismuth main fluid, the turbulent Schmidt number is set to 0.9. Since the liquid lead-bismuth only relies on solid lead oxide for oxygen supply, chemical reactions are ignored. The physical properties of the porous medium are calculated using the average of the volume, density, and number of lead oxide pellets.

[0068] Step 4: Solid-state oxygen control equipment calculation model and boundary condition setting: Boundary conditions include inlet flow rate, initial oxygen concentration, inlet turbulence intensity, initial temperature and porous area boundary conditions;

[0069] The porous region boundary conditions include component source terms and initial condition options;

[0070] The component source term provides the boundary oxygen concentration, which is converted according to the number, density and volume of solid lead oxide pellets.

[0071] The dissolved oxygen concentration that can be supplied to the saturated oxygen boundary of the porous media area is calculated as follows:

[0072] The saturated oxygen concentration when lead oxide dissolves is:

[0073]

[0074] Where:

[0075] C S ——the saturated oxygen concentration when lead oxide is dissolved, in wt.%;

[0076] T——temperature, in K;

[0077] The specific oxygen component source term is converted into a homogeneous porous medium component source based on the designed number, density and volume of solid lead oxide pellets;

[0078] The initial condition options include viscous resistance coefficient, inertial resistance coefficient, porosity, and tortuosity. The calculation formula for the inertial resistance coefficient is as follows:

[0079]

[0080] Where:

[0081] a——viscous resistance coefficient, unit is kg / (m 3 s);

[0082] μ——dynamic viscosity, unit is Pa·s;

[0083] ε——porosity;

[0084] d——diameter, in m;

[0085] The porosity calculation formula is as follows:

[0086]

[0087] Where:

[0088] V - total volume of the pebble bed including all lead oxide particles;

[0089] V F - the volume of all lead oxide particles contained in the pebble bed;

[0090] The calculation formula of inertial resistance coefficient is as follows:

[0091]

[0092] Where:

[0093] b——Inertial resistance coefficient kg / m 4 ;

[0094] ρ——density, unit is kg / m 3 ;

[0095] The curvature calculation formula is as follows:

[0096]

[0097] τ——curvature;

[0098] In this example, the inlet flow rate is 1.99 kg / s, the temperature is 642 K, and the inlet oxygen concentration is 9.00 × 10 -6 wt.%, turbulence intensity is 0.01, turbulence viscosity ratio is 10; flow channel diameter is 47mm; designed lead oxide pellets have a particle size of 12mm and a number of 78 pellets. The average density of lead oxide pellets is about 92.4% of the theoretical density of PbO, which is converted into the oxygen component source term in the porous medium boundary condition of 0.00244kg / (m 3 ·s); the viscous drag coefficient is 8165kg / (m 3 ·s); the inertial drag coefficient is 1.07×10 7 kg / m 4 ;Porosity is 0.43;Tortuosity is 1.414;

[0099] Step 5: Use the SIMPLE algorithm, set the discretization format to second-order upwind, and perform steady-state calculations until the average dissolved oxygen concentration at the outlet converges to a stable value.

[0100] The final calculated outlet oxygen concentration is 1.91×10 -5 wt.%;

[0101] As can be seen from the above examples, the present invention can successfully complete the study of oxygen mass transfer characteristics in solid-state oxygen control. The calculation results can output the oxygen concentration distribution in the mass exchanger and the average outlet oxygen concentration, and evaluate the performance of the solid-state oxygen control equipment, which is beneficial to guiding the design of solid-state oxygen control equipment in the fourth-generation lead-bismuth reactor.

[0102] The above is only a preferred embodiment of the present invention. It should be pointed out that for ordinary technicians in this technical field, without departing from the principles of the present invention, improvements or changes can be made based on the above description. All these improvements and changes should also be considered within the scope of protection of the present invention.

Claims

1. A numerical simulation method for controlling oxygen mass transfer in liquid lead and bismuth in solid state oxygen, characterized by: Here are the steps: Step 1: Solid-state oxygen control equipment modeling: The randomly stacked ball bed composed of solid lead oxide particles in the mass exchange is simplified into a homogeneous porous medium, and the fluid dynamics modeling of the porous medium region and the liquid lead-bismuth fluid channel is performed separately; Step 2: Mesh Generation: The solid lead oxide in the solid-state oxygen control device has been simplified into a homogeneous porous medium. Therefore, a mesh is created for the porous medium region, followed by a mesh for the other liquid lead-bismuth flow channels. The two different regions are in contact, and the contact interface is the internally connected surface, ensuring that the liquid lead-bismuth fluid can flow through the porous medium region and transport the oxygen component. Step 3: Physical property call and solid-state oxygen control equipment calculation model setting: Since the dissolved oxygen concentration in liquid lead bismuth is very low, the thermophysical property parameters are based on the liquid lead bismuth itself. After solid lead oxide is washed and dissolved by liquid lead bismuth, it is mixed and transported with the main fluid in the dissolved liquid phase. Therefore, a multi-component liquid model and a multi-component transport model are selected for solution and calculation. The K-Epsilon turbulence model is selected as the turbulence model, and a two-layer full y+ wall treatment is selected for the porous medium region. For the liquid lead bismuth main fluid, the turbulent Schmidt number is set to 0.

9. Since the liquid lead bismuth is only supplied with oxygen by solid lead oxide, chemical reactions are ignored. The physical properties of the porous medium are characterized by the average value of the lead oxide ball bed volume, lead oxide ball density, and number. Step 4: Solid-state oxygen control equipment calculation model and boundary condition setting: Boundary conditions include inlet flow rate, initial oxygen concentration, inlet turbulence intensity, initial temperature and porous area boundary conditions; The porous region boundary conditions include component source terms and initial condition options; The component source term provides the boundary oxygen concentration, which is converted into the dissolved oxygen concentration that can be supplied by the saturated oxygen boundary of the porous media region based on the number, density, and volume of the solid lead oxide pellets. The calculation formula is as follows: The saturated oxygen concentration when lead oxide dissolves is: Where: C S ——the saturated oxygen concentration when lead oxide is dissolved, in wt.%; T——temperature, in K; The specific oxygen component source term is converted into a homogeneous porous medium component source based on the designed number, density and ball bed volume of solid lead oxide balls; The initial condition options include viscous resistance coefficient, inertial resistance coefficient, porosity, and tortuosity. The calculation formula for the inertial resistance coefficient is as follows: Where: a——viscous drag coefficient, unit is kg / (m 3. s); μ——dynamic viscosity, unit is Pa . s; ε——porosity; d——diameter, in m; The porosity calculation formula is as follows: Where: V - total volume of the pebble bed including all lead oxide particles; V F - the volume of all lead oxide particles contained in the pebble bed; The calculation formula of inertial resistance coefficient is as follows: Where: b——Inertial resistance coefficient, unit is kg / m 4 ; ρ——density, unit is kg / m 3 ; The curvature calculation formula is as follows: τ——curvature; Step 5: Use the SIMPLE algorithm, set the discretization format to second-order upwind, and perform steady-state calculations until the average dissolved oxygen concentration at the outlet converges to a stable value.

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