FVM-HBM coupling algorithm for solving flow mass transfer problem

Abstract

The invention belongs to the field of solving flow mass transfer, and particularly relates to an FVM-HBM coupling algorithm for solving a flow and mass transfer process, which is characterized in that the coupling algorithm combines a finite volume method with a half-boundary method, the finite volume method is used for solving a Navier-Stokes equation, the half-boundary method is used for solving a convective mass transfer equation, and in the FVM-HBM coupling algorithm, the finite volume method is used for solving the Navier-Stokes equation, and the half-boundary method is used for solving the convective mass transfer equation. The concentration field can be solved by the HBM only through a small number of grids, the calculation amount is greatly reduced, and the calculation efficiency is improved. According to the coupling algorithm, the node requirement can be reduced, the node relation can be simplified, and therefore the storage requirement is reduced, iteration is not needed in the solving process, the calculation speed is increased, and meanwhile high calculation precision is kept. Through verification and analysis of a series of numerical simulation examples, the flow field and the concentration field can be quickly and accurately obtained in the flow mass transfer problem of the coolant in the lead-bismuth reactor through the FVM-HBM coupling algorithm.

Description

Technical Field

[0001] The invention belongs to the field of solving flow and mass transfer, and particularly relates to a FVM-HBM coupling algorithm for solving flow and mass transfer processes. Background Art

[0002] The lead-based fast neutron reactor is a fourth-generation nuclear fission reactor that uses liquid lead or lead-bismuth alloy as the reactor coolant. It can operate at normal pressure and high temperature and has inherent safety and passive safety. As the main reactor type of future advanced nuclear energy, lead-based reactors can be used in many fields of industrial production such as power generation, low-temperature hydrogen production, seawater desalination, and civilian radioisotopes. In a lead-based fast neutron reactor, the operating temperature is generally around 400-600℃. At this time, the temperature becomes crucial to the corrosion rate of the lead-bismuth alloy pipeline. The corrosion rate of iron-based structural materials in lead-bismuth alloy is relatively high. From the perspective of controlling pollution and avoiding corrosion, chemical control and measurement methods for liquid lead-bismuth alloy are crucial.

[0003] The flow of liquid lead-bismuth alloy in the core is controlled by the Navier-Stokes equation, and the transport of corrosion products is controlled by the convective mass transfer equation. The coupling algorithm uses FVM to solve the Navier-Stokes equation and HBM to solve the convective mass transfer equation.

[0004] The flow field in the calculation domain can be solved according to the inlet and outlet boundary conditions, and then a small number of points can be selected in the solution domain to use HBM to solve the convection mass transfer equation to obtain the corrosion product concentration field. At the same time, the use of HBM greatly reduces the number of nodes required, simplifies the relationship between nodes, and does not require iteration. It has high calculation accuracy and speeds up the solution speed, which can better meet the requirements of real-time detection and feedback. Summary of the invention

[0005] The present invention adopts numerical calculation means, focuses on the flow and mass transfer problem of coolant in a lead-bismuth pile, and invents a new method for solving the flow and mass transfer based on the FVM-HBM coupling algorithm.

[0006] In view of the large amount of computation required for simulating flow and mass transfer problems based on the existing finite volume method, a new method based on the FVM-HBM coupling algorithm to solve the flow and mass transfer problem of coolant in lead-bismuth piles is proposed. This method combines traditional FVM with HBM, uses FVM to spatially discretize the macroscopic Navier-Stokes equations, and uses HBM to solve the corrosion product concentration field. The calculation process is simple, efficient and accurate. HBM requires a small amount of grids to obtain accurate results, which greatly expands the application scope of HBM in the field of numerical calculation of flow and mass transfer.

[0007] The technical solution of the present invention:

[0008] The FVM-HBM coupling algorithm for solving the convective mass transfer problem first uses FVM to solve the NS equation, uses the SIMPLE algorithm to achieve decoupling of pressure and velocity, and after obtaining a stable flow field, uses HBM to solve the convective mass transfer equation. The FVM-HBM coupling algorithm is implemented in the following steps in the calculation process:

[0009] The simplified pipeline flow in the lead-bismuth alloy pile is controlled by the two-dimensional NS equations, including the mass conservation equation and the momentum conservation equation;

[0010] The mass conservation equation:

[0011] Momentum conservation equation:

[0012] The solution order of the SIMPLE algorithm is to first discretize the momentum equation based on FVM:

[0013] Discretization in the x direction:

[0014] Discretization in the y direction:

[0015] Then, the pressure correction relationship is constructed based on the mass conservation equation:

[0016] a I,J P′ I,J =a I+1 , J P′ I+1,J +a I-1,J P′ I-1,J +a I,J+1 P′ I,J+1 +a I,J-1 P′ I,J-1 +b′ I,J

[0017] Correct pressure and speed based on the pressure correction amount:

[0018] Pressure correction:

[0019] Speed ​​u correction:

[0020] Speed ​​v correction:

[0021] The iterative solution obtains the convergence result and the numerical solution of the flow field. Then a small number of nodes are selected to extract the velocity information on the nodes as the flow field information for HBM to solve the convective mass transfer equation.

[0022] The expression of the two-dimensional steady-state convective mass transfer equation is:

[0023] Where, ρ—density, kg / m 3 , Γ—mass transfer coefficient, m 2 / s

[0024] The characteristic of HBM is that firstly, two new variables are used to reduce the order of the differential equation, and the relationship between the unknown quantities at the four adjacent nodes is derived, and then the relationship between the concentration and concentration gradient at half of the boundary and the concentration and concentration gradient at the other half of the boundary is derived, and the variables V and W are introduced:

[0025]

[0026]

[0027] Convert a partial differential equation with one variable and two independent variables containing second-order derivatives into a system of partial differential equations with three variables and two independent variables containing only first-order derivatives:

[0028]

[0029] The three equations are combined to obtain a system of equations, and the three equations are integrated with respect to space to obtain the relationship between the three variables in space:

[0030]

[0031] After integration, the relationship between the four adjacent nodes is as follows:

[0032] A i+1,j+1 X i+1,j+1 =A i,j+1 X i,j+1 +A i+1,j X i+1,j +A i,j X i,j

[0033] in

[0034]

[0035]

[0036]

[0037]

[0038] By iterating the above relationship, the relationship between the concentration and concentration gradient at one half of the boundary and the concentration and concentration gradient at the other half of the boundary can be obtained.

[0039] The introduced variables are solved according to the conditions on the boundary to obtain the concentration field.

[0040] The specific calculation process of the present invention is:

[0041] Import geometric information and physical property parameters;

[0042] Discretize the solution domain;

[0043] Using SIMPLE to solve the momentum equation and pressure correction equation based on FVM;

[0044] Correcting pressure and speed based on the correction amount;

[0045] Continue to iterate until convergence to obtain flow field information;

[0046] Select some nodes in the solution domain;

[0047] Use HBM to solve the concentration equation and obtain the concentration field;

[0048] The beneficial effects of the present invention are:

[0049] HBM is used to solve the convection mass transfer equation. The equation is reduced in order by introducing two variables, which simplifies the relationship between nodes and speeds up the solution.

[0050] The matrix equation is always fourth order during the solution process, so the calculation amount is small and the calculation speed is fast;

[0051] Applicable to situations where geometric or physical parameters vary;

[0052] No iteration is required during the solution process, and the computational memory requirements are small;

[0053] This algorithm can be used to simulate the coolant flow and corrosion product concentration field inside the lead-bismuth alloy in real time, and to quickly and accurately control and measure the chemical state of the liquid lead-bismuth alloy. BRIEF DESCRIPTION OF THE DRAWINGS

[0054] Figure 1 The computational process of solving flow and mass transfer problems using the FVM-HBM coupling method;

[0055] Figure 2 It is a schematic diagram of the grid on the computational domain;

[0056] Figure 3 The flow field calculated by FVM when the number of grids is 40000;

[0057] Figure 4 This is the concentration field calculated by HBM when the grid number is 930. DETAILED DESCRIPTION

[0058] The present invention provides a FVM-HBM coupling algorithm for solving flow mass transfer problems, which will be further described below in conjunction with the accompanying drawings and specific examples.

[0059] Examples The simplified two-dimensional flow mass transfer problem is as follows Figure 2 As shown, the area is 0.3m long, 0.032m wide, and the density ρ = 1.04*10 5 kg / m 3 , the mass transfer coefficient is 4e-9m 2 / s, the source term S is simplified to 0;

[0060] The boundary conditions are as follows: the lower boundary and the upper boundary are wall boundary conditions, the left boundary is the fluid inlet, the right boundary is the fluid outlet, the inlet velocity is 0.5 m / s, and the outlet static pressure is 0 Pa;

[0061] Solve the flow field and concentration field distribution of the pipeline based on the FVM-HBM coupling algorithm;

[0062] The above data comparison shows that for the numerical simulation of coolant flow and mass transfer in a lead-bismuth pile, the FVM-HBM coupling algorithm of the present invention can accurately obtain the flow field and concentration field distribution of the pipeline at the same time.

Claims

1. The FVM-HBM coupling algorithm for solving flow and mass transfer problems is characterized by: The coupling algorithm combines the finite volume method with the semi-boundary method, uses the finite volume method to solve the Navier-Stokes equation, and uses the semi-boundary method to solve the convective mass transfer equation. In the FVM-HBM coupling algorithm, HBM only needs a small number of grids to solve the concentration field, which greatly reduces the amount of calculation and improves the calculation efficiency.

2. The FVM-HBM coupling algorithm for solving flow mass transfer problems according to claim 1, characterized in that: Use FVM to solve the NS equations. The flow in the pipeline of the lead-bismuth alloy pile is controlled by the two-dimensional NS equations, including the mass conservation equation and the momentum conservation equation; The mass conservation equation: Momentum conservation equation: The solution order of the SIMPLE algorithm is to first discretize the momentum equation based on FVM: Discretization in the x direction: Discretization in the y direction: Then, the pressure correction relationship is constructed based on the mass conservation equation: a I,J P′ I,J =a I+1,J P′ I+1,J +a I-1,J P′ I-1,J +a I,J+1 P′ I,J+1 +a I,J-1 P′ I,J-1 +b′ I,J Correct pressure and speed based on the pressure correction amount: Pressure correction: Speed ​​u correction: Speed ​​v correction: The iterative solution obtains the convergence result and the numerical solution of the flow field. Then a small number of nodes are selected to extract the velocity information on the nodes as the flow field information for HBM to solve the convective mass transfer equation.

3. The FVM-HBM coupling algorithm for solving flow mass transfer problems according to claim 2, characterized in that: Use HBM to solve the convective mass transfer equation. The expression of the two-dimensional steady-state convective mass transfer equation is: Where, ρ—density, kg / m 3 , Γ—mass transfer coefficient, m 2 / s The characteristic of HBM is that firstly, two new variables are used to reduce the order of the differential equation, and the relationship between the unknown quantities at the four adjacent nodes is derived, and then the relationship between the concentration and concentration gradient at half of the boundary and the concentration and concentration gradient at the other half of the boundary is derived, and the variables V and W are introduced: Convert a partial differential equation with one variable and two independent variables containing second-order derivatives into a system of partial differential equations with three variables and two independent variables containing only first-order derivatives: The three equations are combined to obtain a system of equations, and the three equations are integrated with respect to space to obtain the relationship between the three variables in space: After integration, the relationship between the four adjacent nodes is as follows: A i+1,j+1 X i+1,j+1 =A i,j+1 X i,j+1 +A i+1,j X i+1,j +A i,j X i,j in By iterating the above relationship, we can get the relationship between the concentration and concentration gradient at one half of the boundary and the concentration and concentration gradient at the other half of the boundary. According to the conditions on the boundary, we solve the introduced variables and get the concentration field.

4. The FVM-HBM coupling algorithm for solving flow mass transfer problems according to claim 3, characterized in that: In the process of solving the convection mass transfer equation by HBM, the matrix used by the computer for calculation is always fourth-order and does not increase with the increase of the number of grids, so the calculation speed is fast.

5. The FVM-HBM coupling algorithm for solving flow mass transfer problems according to claim 4, characterized in that: The specific calculation process is: Import geometric information and physical property parameters; Discretize the solution domain; Using SIMPLE to solve the momentum equation and pressure correction equation based on FVM; Correcting pressure and speed based on the correction amount; Continue to iterate until convergence to obtain flow field information; Select some nodes in the solution domain; The concentration equation is solved using HBM to obtain the concentration field.

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