CN114743609A - Simulation method and device for solidification process of lead-bismuth alloy in lead-water reaction - Google Patents

Abstract

The invention provides a method and device for simulating the solidification process of a lead-bismuth alloy in a lead-water reaction, and relates to the technical field of nuclear reactors. The simulation environment for the solidification of bismuth alloy; the initial working conditions of the lead-water reaction are obtained, and the solidification and transformation heat transfer process of the lead-bismuth alloy is simulated in the simulation environment based on the initial working conditions, and the high-speed incident water flow is injected into the lead within the preset time. Water reaction area distribution information. The invention can realize the composite simulation of the solidification process of the lead-bismuth alloy in the lead-water reaction, and improve the reliability of the solidification simulation simulation of the lead-bismuth alloy in the lead-water reaction.

Description

Simulation method and device for solidification process of lead-bismuth alloy in lead-water reaction

technical field

The invention relates to the technical field of nuclear reactors, in particular to a method and device for simulating the solidification process of a lead-bismuth alloy in a lead-water reaction.

Background technique

Lead-based fast reactors usually use liquid lead or lead-bismuth alloy as coolant. However, when a steam generator heat transfer tube rupture (SGTR) accident occurs, water and lead-bismuth alloy will undergo a solidification reaction, resulting in flow blockage in the reactor. This will affect the core and cause serious damage to the core. In order to study the actual consequences and possible influences of the lead-water reaction, it is necessary to study the thermophysical process of the heat transfer in transition during the solidification of lead-bismuth alloys. At present, the numerical simulation of transformation heat transfer in the solidification process of lead-bismuth alloy still has the problem of incomplete consideration, resulting in unreliable simulation results.

SUMMARY OF THE INVENTION

In view of this, the object of the present invention is to provide a method and device for simulating the solidification process of lead-bismuth alloy in lead-water reaction, which can realize the composite simulation of lead-bismuth alloy solidification process in lead-water reaction, and improve the lead-bismuth alloy solidification process in lead-water reaction. Reliability of Bismuth Alloy Solidification Simulation Simulations.

In order to achieve the above purpose, the technical solutions adopted in the embodiments of the present invention are as follows:

In a first aspect, an embodiment of the present invention provides a method for simulating the solidification process of a lead-bismuth alloy in a lead-water reaction, including: coupling a preset fluid calculation model, a preset turbulence model, and a solidification heat transfer model to establish a lead-bismuth alloy The simulation environment for alloy solidification; obtain the initial working conditions of the lead-water reaction, and simulate the solidification and transformation heat transfer process of the lead-bismuth alloy based on the initial working conditions in the simulation environment, and obtain the high-speed incident water flow injection preset Time distribution information of lead-water reaction area.

Further, the embodiment of the present invention provides a first possible implementation of the first aspect, wherein the simulation of the solidification and transformation heat transfer process of the lead-bismuth alloy based on the initial working condition is performed in the simulation environment The step of simulating includes: constructing a solidification phase change heat transfer model of the lead-water reaction in the simulation environment in a preset simulation software based on a preset solidification phase change heat transfer condition; The disguised heat transfer model is used for 2D transient simulation.

Further, the embodiment of the present invention provides a second possible implementation manner of the first aspect, wherein the preset solidification transformation heat transfer conditions include: the heat transfer mode of the solid region during the solidification process of the lead-bismuth alloy is heat conduction, and the liquid phase heat transfer mode is heat conduction. The mode of heat transfer in the zone is heat convection.

Further, the embodiments of the present invention provide a third possible implementation of the first aspect, wherein the solidification phase-change heat transfer model includes a heat transfer equation in a solid region, a heat transfer equation in a liquid region, and a paste at the solid-liquid interface. The heat transfer equation for the region.

Further, the embodiment of the present invention provides a fourth possible implementation manner of the first aspect, wherein the heat transfer equation of the solid state region is:

Among them, ρ _s is the solid phase temperature, c _s is the solid phase specific heat, k _s is the solid phase thermal conductivity, T _s is the solid phase temperature, t is the time, and S _s is the solid phase source term.

Further, the embodiment of the present invention provides a fifth possible implementation manner of the first aspect, wherein the heat transfer equation of the liquid region is:

Among them, ρ _l is the liquid phase temperature, c _l is the liquid phase heat, k _l is the liquid phase thermal conductivity, T _l is the liquid phase temperature, v is the velocity vector, and S _l is the liquid phase source term.

Further, the embodiment of the present invention provides a sixth possible implementation manner of the first aspect, wherein the heat transfer equation of the mushy zone is:

where ρ _s is the solid phase temperature, k _s is the solid phase thermal conductivity, k _l is the liquid phase thermal conductivity, T _l is the liquid phase temperature, v is the velocity vector, S _l is the liquid phase source term; Δh _m is the phase transition Latent heat, _v∑ is the velocity vector of the mixture, and T is the temperature in the mushy zone.

In the second aspect, the embodiment of the present invention also provides a simulation device for the solidification process of lead-bismuth alloy in lead-water reaction, including: establishing a module for performing calculation on a preset fluid calculation model, a preset turbulence model and a solidification heat transfer model. Coupling to establish a simulation environment for the solidification of lead-bismuth alloy; simulation module, used to obtain the initial working condition of lead-water reaction, in the simulation environment, based on the initial working condition, the solidification transformation heat transfer process of the lead-bismuth alloy Simulation is carried out to obtain the distribution information of lead-water reaction area within the preset time of high-speed incident water injection.

In a third aspect, an embodiment of the present invention provides an electronic device, including: a processor and a storage device; a computer program is stored on the storage device, and the computer program executes the first aspect when executed by the processor The method of any one.

In a fourth aspect, an embodiment of the present invention provides a computer-readable storage medium, where a computer program is stored on the computer-readable storage medium, and when the computer program is run by a processor, any one of the foregoing first aspects is executed. steps of the method.

The embodiment of the present invention provides a method and device for simulating the solidification process of lead-bismuth alloy in lead-water reaction, including: coupling a preset fluid calculation model, a preset turbulence model and a solidification heat transfer model to establish the solidification of lead-bismuth alloy obtain the initial working conditions of the lead-water reaction, and simulate the solidification and phase-change heat transfer process of the lead-bismuth alloy based on the initial working conditions in the simulation environment, and obtain the lead-water reaction area within the preset time after the high-speed incident water flow is injected distribution information. The present invention constructs a simulation environment for lead-water reaction based on the coupling of multiple models, takes into account various influencing factors in the lead-water reaction, realizes the composite simulation of the solidification process of the lead-bismuth alloy in the lead-water reaction, and improves the process of the lead-water reaction. The reliability of the solidification simulation of lead-bismuth alloys is of reference significance for the study of solidification development and solidification elimination in lead-based fast reactor SGTR accidents.

Other features and advantages of embodiments of the present invention will be set forth in the description that follows, or some of the features and advantages may be inferred or unequivocally determined from the description, or may be learned by implementing the above-described techniques of embodiments of the present invention.

In order to make the above-mentioned objects, features and advantages of the present invention more obvious and easy to understand, preferred embodiments are given below, and are described in detail as follows in conjunction with the accompanying drawings.

Description of drawings

In order to illustrate the specific embodiments of the present invention or the technical solutions in the prior art more clearly, the following briefly introduces the accompanying drawings that need to be used in the description of the specific embodiments or the prior art. Obviously, the accompanying drawings in the following description The drawings are some embodiments of the present invention. For those of ordinary skill in the art, other drawings can also be obtained based on these drawings without creative efforts.

Fig. 1 shows the simulation method flow chart of the solidification process of lead-bismuth alloy in a kind of lead-water reaction provided by the embodiment of the present invention;

FIG. 2 shows a schematic diagram of the geometric structure of a reaction vessel provided by an embodiment of the present invention;

3 shows a change diagram of the distribution of lead-water reaction areas within 0 to 8s provided by an embodiment of the present invention;

Fig. 4 shows the comparison diagram of a kind of simulation model monitoring result provided by the embodiment of the present invention and LIFUS-5 experimental data;

FIG. 5 shows a schematic diagram of the geometric structure of another reaction vessel provided in an embodiment of the present invention;

6 shows a change diagram of the distribution of lead-water reaction areas within 0 to 6s provided by an embodiment of the present invention;

Fig. 7 shows the comparison diagram of a simulation model monitoring result and KYLIN-II-S experimental data provided by an embodiment of the present invention;

FIG. 8 shows a graph of changes in the density of lead-bismuth alloys within 0-1s of an accident provided by an embodiment of the present invention;

Fig. 9 shows the variation diagram of the density of lead-bismuth alloy in a kind of accident process within 0～2s provided by the embodiment of the present invention;

FIG. 10 shows a schematic structural diagram of a simulation device for a solidification process of a lead-bismuth alloy in a lead-water reaction provided by an embodiment of the present invention.

Detailed ways

In order to make the purposes, technical solutions and advantages of the embodiments of the present invention clearer, the technical solutions of the present invention will be described below with reference to the accompanying drawings. Obviously, the described embodiments are part of the embodiments of the present invention, not all of the embodiments.

At present, there are few studies on the solidification mechanism of lead-bismuth alloy under lead-water reaction, and the consideration of factors affecting solidification is not comprehensive enough, and the systematic and intuitive kinetic, thermodynamic and phenomenological models are lacking, which leads to the solidification of lead-bismuth alloy in lead-water reaction. Simulation simulation reliability is low. In order to improve this problem, the embodiment of the present invention provides a method and device for simulating the solidification process of lead-bismuth alloy in lead-water reaction, and the technology can be applied to improve the reliability of lead-bismuth alloy solidification simulation simulation in lead-water reaction. The following describes the embodiments of the present invention in detail.

This embodiment provides a method for simulating the solidification process of lead-bismuth alloy in lead-water reaction, which is applied to electronic equipment such as computers. Include the following steps:

Step S102 , coupling the preset fluid calculation model, the preset turbulence model and the solidification heat transfer model to establish a simulation environment for solidification of the lead-bismuth alloy.

The preset fluid calculation model may be a VOF (Volume-of-Fluid) model, and the preset turbulence model may be a Realizable k-ε turbulence model. In the preset simulation software, the VOF model, the Realizable k-ε turbulence model and the solidification heat transfer model are coupled. Due to the lead-water reaction of the lead-based fast reactor SGTR, the high-pressure supercooled water from the steam generator is injected into the coolant at high speed. , which will involve the mass, heat exchange and multi-phase flow heat transfer between multiple substances. By coupling the three models, the simulation environment of lead-water reaction is closer to the actual solidification process, and the rationality of the simulation of the solidification process of lead-bismuth alloys is improved. .

Step S104 , obtaining the initial working conditions of the lead-water reaction, and simulating the solidification and transformation heat transfer process of the lead-bismuth alloy based on the initial working conditions in a simulation environment, and obtaining the distribution information of the lead-water reaction area within the preset time of injection of the high-speed incident water flow.

Receive the initial working condition of the lead-water reaction input by the user. The initial working condition of the lead-water reaction is the initial value set by the simulation experiment. The initial working condition can include the temperature difference between the lead-bismuth alloy and the water set by the user, and the initial speed of the water jet. , the initial values of parameters such as water injection pipe diameter, wall temperature, lead-bismuth alloy composition, initial pressure, size of reaction domain and injection back pressure.

The solidification phase change heat transfer model of the lead-water reaction is constructed in the above-mentioned composite simulation environment, and the above initial working condition is set as the initial value of the solidification phase change heat transfer model for simulation simulation, so as to obtain the lead within the preset time after the high-speed incident water flow is injected into the reflection container. The water reflects the regional distribution, and the above-mentioned reaction area distribution information includes the proportion distribution information of the liquid phase composition of the lead-bismuth alloy in the reaction vessel.

The method for simulating the solidification process of lead-bismuth alloy in the above-mentioned lead-water reaction provided in this embodiment, by constructing a simulation environment for lead-water reaction based on multiple models coupling, taking into account various influencing factors in the lead-water reaction, realizes the realization of the lead-water reaction. The composite simulation of the solidification process of lead-bismuth alloy in the reaction improves the reliability of the solidification simulation of lead-bismuth alloy in the lead-water reaction. .

In a feasible implementation manner, this embodiment provides an implementation manner of simulating the solidification and transformation heat transfer process of lead-bismuth alloy based on initial working conditions in a simulation environment. For details, please refer to the following steps 1) to 2) implement:

Step 1): Based on the preset solidification transformation heat transfer conditions, in the preset simulation software, build a solidification transformation heat transfer model of the lead-water reaction in the simulation environment.

The above-mentioned preset simulation software may be CFD (Computational Fluid Dynamics, computational fluid dynamics) simulation software, such as ANSYS FLUENT 2020R2 software. The lead-water reaction process involves complex flow, heat transfer, and mass transfer processes, and various phases of various substances appear in the reaction process. A numerical model for lead-water reaction in the lead-based fast reactor SGTR accident was established using CFD. , which is conducive to rapid, large-scale and accurate simulation research on the solidification mechanism analysis of lead-bismuth alloys under lead-water reaction.

In the lead-water reaction, the solidification process of the lead-bismuth alloy will produce a solid region, a liquid region and a mushy region at the solid-liquid interface. The corresponding heat transfer methods are set for different regions to accurately simulate the solidification process of the lead-bismuth alloy. In a specific embodiment, the above-mentioned preset solidification transformation heat transfer conditions include: during the solidification process of the lead-bismuth alloy, the heat transfer mode in the solid region is heat conduction, and the heat transfer mode in the liquid region is thermal convection.

According to the solidification transformation heat transfer conditions of lead-bismuth alloy in the lead-water reaction, the solidification heat transfer process is analyzed to build a solidification transformation heat transfer model. In the solidification of liquid metal, the methods that can be used include temperature variable method, enthalpy method, and interface function. Among them, the temperature variable method can be used as an optimal replacement for the energy equation in FLUENT simulation, replacing the energy equation at the solid-liquid interface with the latent heat energy equation with temperature as a single variable.

In a specific embodiment, in the process of establishing a simulation environment for the solidification of lead-bismuth alloys in the preset simulation software, the basic control equations that need to be considered for the fluid are three conservation laws: the law of conservation of mass, the law of conservation of momentum, and the law of conservation of energy. law.

The VOF model is often used to solve the multiphase flow problem between a variety of immiscible fluids. In the calculation of the VOF model, the different physical states of different substances are regarded as a separate phase. The lead-water reaction process is a complex multiphase flow process between various fluids. The main phases involved are: liquid lead-bismuth alloy, water vapor, liquid water, and other insoluble gases (such as lead-bismuth alloy protective gas: argon, xenon, etc.) , in which the gas-liquid two-phase flow of water involves a phase transition process of rapid evaporation. The chemical reaction between liquid lead-bismuth alloy and water and protective gas is weak, and the interphase substances are relatively stable when they are fused together, and the surface tension of liquid lead-bismuth alloy is large, and the density is much greater than that of water, which can be combined with other three-phase substances (ie water vapor, liquid Water and other insoluble gases) form a clear phase interface, and there will be no large-scale dispersion in gases and other liquids, so the assumptions of the VOF model for the lead-water reaction process are suitable for the lead-water reaction process.

In the calculation of the VOF model, set the volume fraction of a certain phase q as α _q , the phase volume fraction sum of each control unit is 1, and the volume fractions of different phases indicate that they form a mixture under their respective volume fractions, then there is the following formula ( 1) Constraints:

Among them, n represents the total number of phases in the corresponding mixture, and the above solidification transformation heat transfer model is 4. Under this constraint, the corresponding mass conservation equation between phases is formula (2):

为q相到q′相的质量输送值；

为q′相到q相的质量输送值。Among them, ρ is the density; v is the velocity;

is the mass transfer value from q phase to q'phase;

is the mass transfer value for the q' phase to the q phase.

In the composite simulation environment of FLUENT software, the velocity field is shared by each phase, so the momentum conservation equation is formula (3):

Among them, τ is the laminar shear stress; τ ^t is the turbulent shear stress; P is the pressure; t is the time; g is the acceleration of gravity; F is the interface force.

The energy conservation equation is formula (4):

Among them, h is the enthalpy; λ is the thermal conductivity; T is the temperature; μ _t is the turbulent viscosity; σ _k is the turbulent Prandtl number;

The standard k-ε turbulence model is a turbulence model widely used in complex geometry external flow, but there are certain problems in adaptability and accuracy. The Realizable k-ε turbulence model is an improvement of the standard k-ε turbulence model with certain experience. It introduces a turbulent viscosity formula and an energy dissipation rate transfer equation. Compared with the standard k-ε model, the model can be better than the standard k-ε model. The calculation of rotational flow, boundary layer flow, flow separation and secondary flow in the flow field under strong adverse pressure gradient is more in line with the simulation requirements of the solidification process of lead-bismuth alloy in the lead-water reaction.

The composite simulation environment constructed by the Realizable k-ε turbulence model includes formula (5) and formula (6):

Among them, x _i and x _j are the coordinates of the precession fluid before and after the turbulent flow; k _t is the turbulent kinetic energy; K _V is the turbulent kinetic energy generated by the velocity gradient; K _b is the turbulent kinetic energy generated by the buoyancy; ε is the turbulent kinetic energy dissipation rate; μ _l is the laminar eddy viscosity; Y _M is the fluctuation due to diffusion; _Sk and S _ε are user-defined parameters; σ _k , C _1ε , C _2ε , C _3ε are model constants.

The above solidification heat transfer model adopts the enthalpy-porosity formula, which assumes that the solid-liquid mixing zone of the coolant can be regarded as a porous medium with porosity equal to the fluid zone, and introduces the liquid volume fraction to characterize the unsolidified lead-bismuth alloy in the cell Volume fraction, that is, when the porosity of the liquid lead-bismuth alloy in a certain element drops to zero, the liquid phase volume fraction at this point drops to zero, and this point is regarded as completely solidified and does not participate in the calculation of the turbulent velocity. This method for solving the solidification and melting fluid problem can extend the solidification and melting time from a specific melting point to a temperature range, so that when dealing with the solidification and melting problem, a fluid part, a solid part and a mushy part can appear in the flow field at the same time. .

The enthalpy-porosity formula defines the porosity by defining a certain volume percentage of fluid in the discrete computational domain. The solid-liquid mixed paste part is regarded as a completely porous medium, and the porous part is the liquid part of the solid-liquid mixed paste. During the solidification process, the lead-bismuth alloy is solidified from a liquid state, the solid volume percentage increases, and the liquid volume percentage decreases, and the porosity of the lead-bismuth alloy gradually decreases from 1 to 0. When all the liquid lead-bismuth alloys in a computing grid are solidified into solids , the porosity of this region becomes 0, and the calculated velocity is also 0 at this time. The relationship between the liquid volume percentage and temperature in the mushy region can be expressed by formula (7):

Among them, T _solidus is the solidus temperature of the phase change medium in the grid; T _liquidus is the liquidus temperature of the phase change medium in the grid.

For a single medium (T _solidus = T _liquidus ), an obvious solid-liquid interface and its corresponding curve will inevitably appear when the phase transition occurs; for a non-single medium, there will be T _solidus > T _liquidus , in the grid One or more mushy regions are bound to occur, in which the flow velocity becomes a function of beta.

For the density of lead-bismuth alloy, Boussinesq assumption can be made in FLUENT's solidification and melting model: the physical properties of lead-bismuth alloy except density are all constants or functions of density. The volume term in the momentum conservation equation is only affected by β, and the density in the equation is treated as a constant. The viscous dissipation of lead-bismuth alloys is excluded.

The relationship between density and liquid volume percentage β can be obtained

ρ=ρ _ref [1-β(TT _ref )] (8)

Among them, ρ _ref is the reference density value, generally the melting point under normal pressure can be taken: T _ref is the reference temperature value, generally the melting temperature under normal pressure can be taken.

Considering the natural convection caused by the density change of lead-bismuth alloy, the preset simulation software FLUENT has the following corrections to the basic control equation during the model coupling process:

For the source term of the conservation of momentum equation, it is modified to formula (9) and formula (10):

For the energy conservation equation, the source term is modified to formula (11):

For the enthalpy value H in the energy conservation equation, it is corrected to formula (12) and formula (13):

H=h+ΔH (12)

Among them, a is the volume expansion coefficient; L is the latent heat of phase transition: h is the specific enthalpy of sensible heat; _ΔH is the specific enthalpy of latent heat; h _ref is the reference specific enthalpy; is a continuous number for the mushy area.

Step 2): perform a two-dimensional transient simulation on the solidification transformation heat transfer model based on the initial working conditions.

The initial working conditions are set for the solidification phase change heat transfer model, so that the solidification phase change heat transfer model performs a two-dimensional transient simulation simulation of the solidification phase change heat transfer process of the lead-bismuth alloy in the above composite simulation environment. Simulation results of the percentage change in the liquid phase composition of bismuth alloys in the experimental computational domain mixture.

Phase change heat transfer is a complex heat transfer process, and there will be phase change heat transfer, heat conduction and heat convection at the same time before and after the phase change occurs. For the solidification process of the lead-bismuth alloy, the main heat transfer mode in the lead-bismuth alloy in the liquid part is thermal convection, while the main heat transfer mode in the lead-bismuth alloy in the solid part is heat conduction. There will be two-phase substances in the mushy zone at the same time. As the supercooled water evaporates and the phase transition takes away the heat in the lead-bismuth alloy, the liquid substance in the mushy zone gradually solidifies, and the latent heat of solidification is transferred to the supercooled water at the solidification front. For a given quality of supercooled water, the heat required for all evaporation after injection is relatively fixed, and it is only necessary to study the latent heat of solidification of the lead-bismuth alloy corresponding to this part of the heat.

The phase transition heat transfer process of lead-bismuth alloy solidification has the following characteristics: the phase transition temperature of the mixture is not a fixed temperature value like a single substance, but a temperature range, in which the existence of the paste can change with the phase transition. The solid-liquid interface that occurs and gradually moves. For a computing unit, this solid-liquid interface will always exist until the phase transition of the material in this unit is completed. The release of the latent heat of solidification and the absorption of the latent heat of evaporation together become a function of time, and can also be a function of the moving distance of the solid-liquid interface. The moving speed of the solid-liquid interface is not linear, and the release rate of the latent heat of solidification is not linear, so it cannot be normalized by the superimposed phase transition model. The physical properties of the solidified material will change greatly before and after solidification, mainly reflected in the viscosity and density curves, and some special materials will also have a large change in specific heat capacity.

In a specific embodiment, the above-mentioned solidification phase-change heat transfer model includes a heat transfer equation in a solid region, a heat transfer equation in a liquid region, and a heat transfer equation in a mushy region at the solid-liquid interface.

In the solid-state region where conduction is the main heat transfer mode, there is the basic equation (14):

Among them, ρ _s is the solid phase temperature, c _s is the solid phase specific heat, k _s is the solid phase thermal conductivity, T _s is the solid phase temperature, t is the time, and S _s is the solid phase source term.

In the liquid region where heat convection is the main heat transfer mode, there is a basic equation (15):

Among them, ρ _l is the liquid phase temperature, c _l is the liquid phase heat, k _l is the liquid phase thermal conductivity, T _l is the liquid phase temperature, v is the velocity vector, and S _l is the liquid phase source term.

For the solid-liquid interface in the mushy zone, there is the basic equation (16):

where ρ _s is the solid phase temperature, k _s is the solid phase thermal conductivity, k _l is the liquid phase thermal conductivity, T _l is the liquid phase temperature, v is the velocity vector, S _l is the liquid phase source term; Δh _m is the phase transition Latent heat, _v∑ is the velocity vector of the mixture, and T is the temperature in the mushy zone.

There are also boundary condition formula (17), formula (18) and formula (19):

T= _Tw (17)

Among them, α is the external heat transfer coefficient (which can be regarded as a constant value in this simulation); q _ω is the external heat flux density (which can be regarded as a constant value in this simulation); _Tw is the external reference temperature (which can be regarded as a constant value in this simulation) as the wall temperature).

Using the enthalpy method, a characteristic enthalpy equation can be established for calculating the time at which solidification occurs. When solidification occurs, the enthalpy of the mushy zone is shown in equation (20):

Among them, h is the enthalpy of the mushy zone; T _m is the phase transition temperature of the lead-bismuth alloy, such as 125°C; Δh _m represents the latent heat of phase transition; t is the time; C _p is the constant pressure specific heat capacity; T is the fluid temperature

If the relationship between enthalpy and temperature is directly combined with the energy equation, then when t= _Tm , the enthalpy is not a function of temperature, and the enthalpy equation does not hold, so continuity assumptions are required.

Assuming that the temperature T is in (T _m - θ, T _m + θ), the enthalpy and temperature have a simple linear relationship. When θ tends to infinity, formula (21) can be obtained:

Substituting formula (21) back into formula (20) can obtain formula (22):

Combining Equation (22) with the energy conservation equation of Equation (23), the enthalpy equation expressing the heat transfer of solidification can be obtained immediately.

Among them, t represents time; x, y represent the coordinates in the X and Y directions of space; C _p represents the constant pressure specific heat capacity; k represents the thermal conductivity; _H is the energy at any time; Sh is the source term of the energy conservation equation.

The solidification heat transfer enthalpy equation derived by the continuous process can be further derived to obtain the solidification time enthalpy equation, and the characteristic enthalpy equation of the solidification time of lead-bismuth alloy in the lead-water reaction at the macro scale can be expressed as Equation (24) :

Among them, t' _{solidification} is the solidification time, A _injection is the diameter of the water injection pipe, v _injection is the initial velocity of the water jet, T _{lbe, ave} are the average temperatures of the initial lead-bismuth alloy, T _{water, ave} are the average temperatures of the injected water, ρ _w is the density of water, h _{f, ave} is the average convective heat transfer coefficient, C′ _SGTR is the characteristic constant of the characteristic enthalpy equation, m _t is the mass of the material participating in the transformation process, and Δh is the latent heat of solidification transformation.

In the above-mentioned lead-water reaction, the lead-bismuth alloy can be selected from the lead-bismuth alloy of 44.5% (mass fraction) Pb+55.5% Bi, and the physical parameters of the lead-bismuth alloy under this ratio are shown in Table 1 below:

Table 1 Physical parameters of lead-bismuth alloy (44.5%(mass fraction)Pb+55.5%Bi)

In order to verify the reliability of the simulation of the above solidification transformation heat transfer model, two more mature experimental systems in the domestic and foreign lead-water reaction experimental systems (LIFUS-5 lead-water reaction experimental system and KYLIN-II-S experimental system) were selected. The experimental data are compared and verified, and the geometry of the reaction vessel in the solidification transformation heat transfer model is changed to make it as close as possible to the reaction vessel structure.

The LIFUS-5 lead-water reaction experimental system is set up to inject lead-bismuth alloy from the bottom to the top of the reaction vessel through the water injection hole with high-pressure supercooled water, and mainly monitor the temperature and pressure parameters in the reaction process. The geometric structure of the reaction vessel in the solidification phase change heat transfer model is shown in Figure 2. The experimental parameters of the LIFUS-5 experiment are input as the initial working conditions into the preset simulation software to carry out the two-dimensional transient simulation of the lead-water reaction experiment, as shown in Figure 3 The change diagram of the distribution of the lead-water reaction area in the shown 0-8s, T in Figure 3 is the time elapsed since the start of water injection, when T=0, the proportion of the liquid phase composition of the upper lead-bismuth alloy in the reaction vessel is 0, and the lower part is 0. The liquid phase composition of the lead-bismuth alloy accounts for 100%. Figure 3 shows the simulation results of the percentage change of the liquid phase composition of the lead-bismuth alloy in the experimental calculation domain when the high-speed incident water flow is injected for 8s. Under the experimental parameters, the lead-water reaction is intense, and the high-speed incident water flow makes the lead-water reaction area basically fill the entire reaction vessel.

The temperature of the area close to the actual LIFUS-5 test point is monitored by means of preset measuring points, and compared with the experimental data, see the simulation model monitoring results and LIFUS-5 experiment as shown in Figure 4 The comparison chart of the data, Figure 4 shows the temperature monitoring results of the monitoring points at the horizontal lines 10mm, 50mm and 100mm away from the water injection inlet. It can be seen from Figure 4 that at the instant of high-speed flow incidence, the lead-bismuth alloy reaches the lowest temperature, and then due to The water vapor rises rapidly, and the temperature of the lead-bismuth alloy rises. The general trend of the simulation model results is similar, and the minimum temperature is similar.

The KYLIN-II-S experimental system sets high-pressure supercooled water to inject lead-bismuth alloy from the liquid surface. The water injection method, the amount of participating substances, and the degree of reaction intensity in the simulated lead-water reaction process in this group of experiments are different from those in the LIFUS-5 experiment. larger. The geometric structure of the reaction vessel in the solidification phase change heat transfer model is shown in Figure 5. The experimental parameters of the KYLIN-II-S experiment are used as the initial working conditions and input into the preset simulation software to carry out the two-dimensional transient simulation of the lead-water reaction experiment. The results of the percentage change of the liquid phase composition of the lead-bismuth alloy in the experimental computational domain mixture during the lead-water reaction obtained by transient modeling and simulation.

Referring to the change diagram of the distribution of the lead-water reaction area in 0-6s as shown in Figure 6, T in Figure 6 is the time elapsed since the start of water injection, and the proportion of the liquid phase composition of the upper lead-bismuth alloy in the reaction vessel when T=0 is 0, and the proportion of the liquid phase composition of the lower lead-bismuth alloy is 100%. Figure 6 shows the simulation results of the liquid phase composition of the lead-bismuth alloy accounting for the percentage change of the mixture in the experimental calculation domain after the high-speed incident water flow is injected for 6s. It can be seen that the lead-water reaction process in the KYLIN-II-S experiment is relatively gentle, the lead-bismuth alloy in most of the containers does not participate in the reaction process, and the water flow pressure is not enough to break through the liquid level of the liquid lead-bismuth alloy, causing the main phase transition and gasification. The heat transfer is concentrated between the interface between the liquid lead-bismuth alloy and the inert gas.

The temperature is also monitored by preset measuring points (the measuring points are located at the inlet nozzle), and the monitoring results of the simulation model are compared with the experimental data. See the monitoring results of the simulation model and KYLIN-II-S shown in Figure 7. As can be seen from Figure 7, the experimental data shows that the lead-bismuth alloy reaches the lowest temperature of 378°C at 0.8s from the start of water injection, and stabilizes at 404°C after 8s. The simulation verification model shows that the lead-bismuth alloy reaches the lowest temperature of 369℃ in 0.3s. The oscillation amplitude of the simulation model (that is, the solidification transformation heat transfer model built in the preset simulation software) is larger than the experimental value, but the general trend is similar, and the minimum temperature difference is within 10 °C.

By comparing the experimental values of the above two groups of experimental systems (LIFUS-5 lead-water reaction experimental system and KYLIN-II-S experimental system) with the simulation values of the solidification transformation heat transfer model, the numerical model of this paper (solidification transformation Heat transfer model) can be applied to the environmental simulation of lead-water reaction in different situations, and the simulation results are reliable. The above solidification transformation heat transfer model can also simulate the solidification process of lead-bismuth alloy by adjusting parameters, and explore the solidification mechanism of lead-bismuth alloy in lead-water reaction.

In order to study the solidification phenomenon of lead-bismuth alloy in the lead-water reaction under actual accident conditions, two typical fracture situations were simulated.

First, set the position of the break in working condition A at the bottom of the heat transfer tube, and the water injection direction is vertically downward. Figure 8 is a graph showing the change in the density of lead-bismuth alloys within 0-1s of the accident. It can be seen from Figure 8 that the solidification of the lead-bismuth alloy under this condition starts from the water injection area, and first solid components appear around the water injection flow, and then this part of the solidified material precipitates to the bottom of the container, and gradually melts during the precipitation process. The rapid evaporation occurs in the heat transfer tube bundle gap, and there is a temperature drop area in the heat transfer tube bundle gap, and the solidified component around the steam begins to appear in the tube bundle gap. This part of the solidified material will be pushed up by the steam along the gap, causing a certain degree of blockage.

The position of the break in working condition B is close to the bottom of the heat transfer tube (100mm from the bottom of the heat transfer tube), and the water injection direction is horizontal. Fig. 9 is a graph showing the change of the density of lead-bismuth alloy in the accident process within 0-2s. It can be seen from Figure 9 that the solidification phenomenon of the lead-bismuth alloy is more severe under this working condition. First, the lead-bismuth alloy rapidly solidifies at the flow channel of the water injection position and blocks the flow channel, causing a huge pressure shock to the adjacent pipeline, and the solidification zone persists. As the water flows to the bottom of the heat transfer tube bundle and evaporates rapidly, there is a temperature drop area in the gaps of other heat transfer tube bundles, and the temperature drop is huge, causing a large area of solidification in a short time.

Corresponding to the method for simulating the solidification process of lead-bismuth alloy in the lead-water reaction provided by the above-mentioned embodiment, the embodiment of the present invention provides a simulation device for the solidification process of lead-bismuth alloy in the lead-water reaction. Schematic diagram of the structure of the simulation device for the solidification process of lead-bismuth alloy in the lead-water reaction. The device includes the following modules:

The establishment module 11 is used for coupling the preset fluid calculation model, the preset turbulence model and the solidification heat transfer model to establish a simulation environment for the solidification of the lead-bismuth alloy.

The simulation module 12 is used for obtaining the initial working condition of the lead-water reaction, and simulating the solidification and phase-change heat transfer process of the lead-bismuth alloy based on the initial working condition in the simulation environment, and obtaining the lead-water reaction area within the preset time after the injection of the high-speed incident water flow distribution information.

The simulation device for the solidification process of the lead-bismuth alloy in the lead-water reaction provided in this embodiment, through the coupling of multiple models to construct a simulation environment for the lead-water reaction, taking into account various influencing factors in the lead-water reaction, realizes the realization of the lead-water reaction. The composite simulation of the solidification process of lead-bismuth alloy in the reaction improves the reliability of the solidification simulation of lead-bismuth alloy in the lead-water reaction. .

In one embodiment, the simulation module 12 is further configured to construct, in a preset simulation software based on preset solidification and phase-change heat transfer conditions, a solidification phase-change heat transfer model of the lead-water reaction in a simulation environment; based on the initial working conditions A two-dimensional transient simulation is carried out on the solidification transformation heat transfer model.

In an embodiment, the above-mentioned preset solidification transformation heat transfer conditions include: the heat transfer mode of the solid region during the solidification process of the lead-bismuth alloy is heat conduction, and the heat transfer mode of the liquid region is thermal convection.

In one embodiment, the above-mentioned solidification phase-change heat transfer model includes a heat transfer equation in a solid region, a heat transfer equation in a liquid region, and a heat transfer equation in a mushy region at the solid-liquid interface.

In one embodiment, the heat transfer equation for the solid state region is:

Among them, ρ _s is the solid phase temperature, c _s is the solid phase specific heat, k _s is the solid phase thermal conductivity, T _s is the solid phase temperature, t is the time, and S _s is the solid phase source term.

In one embodiment, the heat transfer equation of the above-mentioned liquid region is:

Among them, ρ _l is the liquid phase temperature, c _l is the liquid phase heat, k _l is the liquid phase thermal conductivity, T _l is the liquid phase temperature, v is the velocity vector, and S _l is the liquid phase source term.

In one embodiment, the heat transfer equation of the above-mentioned mushy zone is:

where ρ _s is the solid phase temperature, k _S is the solid phase thermal conductivity, k _l is the liquid phase thermal conductivity, T _l is the liquid phase temperature, v is the velocity vector, S _l is the liquid phase source term; Δh _m is the phase transition Latent heat, _v∑ is the velocity vector of the mixture, and T is the temperature in the mushy zone.

The implementation principle and the technical effects of the device provided in this embodiment are the same as those in the foregoing embodiments. For brief description, for the parts not mentioned in the device embodiment, reference may be made to the corresponding content in the foregoing method embodiments.

An embodiment of the present invention provides an electronic device, including: a processor and a storage device; a computer program is stored on the storage device, and the computer program executes the method described in the foregoing embodiments when executed by the processor.

An embodiment of the present invention provides a computer-readable medium, wherein the computer-readable medium stores computer-executable instructions, and when the computer-executable instructions are invoked and executed by a processor, the computer-executable instructions cause the The processor implements the methods described in the above embodiments.

Those skilled in the art can clearly understand that, for the convenience and brevity of description, for the specific working process of the system described above, reference may be made to the corresponding process in the foregoing embodiments, and details are not repeated here.

The computer program product of the method and device for simulating the solidification process of a lead-bismuth alloy in a lead-water reaction provided by the embodiment of the present invention includes a computer-readable storage medium storing program codes, and the instructions included in the program codes can be used to execute the preceding method. For the specific implementation of the method described in the embodiment, reference may be made to the method embodiment, which will not be repeated here.

In addition, in the description of the embodiments of the present invention, unless otherwise expressly specified and limited, the terms "installed", "connected" and "connected" should be understood in a broad sense, for example, it may be a fixed connection or a detachable connection , or integrally connected; it can be a mechanical connection or an electrical connection; it can be a direct connection, or an indirect connection through an intermediate medium, or the internal communication between the two components. For those of ordinary skill in the art, the specific meanings of the above terms in the present invention can be understood in specific situations.

The functions, if implemented in the form of software functional units and sold or used as independent products, may be stored in a computer-readable storage medium. Based on this understanding, the technical solution of the present invention can be embodied in the form of a software product in essence, or the part that contributes to the prior art or the part of the technical solution. The computer software product is stored in a storage medium, including Several instructions are used to cause a computer device (which may be a personal computer, a server, or a network device, etc.) to execute all or part of the steps of the methods described in the various embodiments of the present invention. The aforementioned storage medium includes: U disk, mobile hard disk, Read-Only Memory (ROM, Read-Only Memory), Random Access Memory (RAM, Random Access Memory), magnetic disk or optical disk and other media that can store program codes .

In the description of the present invention, it should be noted that the terms "center", "upper", "lower", "left", "right", "vertical", "horizontal", "inner", "outer", etc. The indicated orientation or positional relationship is based on the orientation or positional relationship shown in the accompanying drawings, which is only for the convenience of describing the present invention and simplifying the description, rather than indicating or implying that the indicated device or element must have a specific orientation or a specific orientation. construction and operation, and therefore should not be construed as limiting the invention. Furthermore, the terms "first", "second", and "third" are used for descriptive purposes only and should not be construed to indicate or imply relative importance.

Finally, it should be noted that the above-mentioned embodiments are only specific implementations of the present invention, and are used to illustrate the technical solutions of the present invention, but not to limit them. The protection scope of the present invention is not limited thereto, although referring to the foregoing The embodiment has been described in detail the present invention, those of ordinary skill in the art should understand: any person skilled in the art who is familiar with the technical field within the technical scope disclosed by the present invention can still modify the technical solutions described in the foregoing embodiments. Or can easily think of changes, or equivalently replace some of the technical features; and these modifications, changes or replacements do not make the essence of the corresponding technical solutions deviate from the spirit and scope of the technical solutions of the embodiments of the present invention, and should be covered in the present invention. within the scope of protection. Therefore, the protection scope of the present invention should be based on the protection scope of the claims.

Claims (10)

1. A method for simulating a lead-bismuth alloy solidification process in a lead-water reaction is characterized by comprising the following steps:

coupling a preset fluid calculation model, a preset turbulent flow model and a solidification heat transfer model to establish a simulation environment for lead-bismuth alloy solidification;

acquiring the initial working condition of the lead-water reaction, and carrying out simulation on the solidification phase-change heat transfer process of the lead-bismuth alloy based on the initial working condition in the simulation environment to obtain the distribution information of the lead-water reaction area in the preset time of injecting high-speed incident water flow.

2. The method of claim 1, wherein the step of performing simulation on the solidification, transformation and heat transfer process of the lead-bismuth alloy based on the initial working condition in the simulation environment comprises:

constructing a solidification phase-change heat transfer model of the lead-water reaction in the simulation environment in preset simulation software based on preset solidification phase-change heat transfer conditions;

and carrying out two-dimensional transient simulation on the solidification phase-change heat transfer model based on the initial working condition.

3. The method of claim 2, wherein the predetermined freeze phase change heat transfer conditions comprise: the heat transfer mode of the solid area in the solidification process of the lead bismuth alloy is heat conduction, and the heat transfer mode of the liquid area is heat convection.

4. The method of claim 2, wherein the solidification-to-phase heat transfer model includes a heat transfer equation for a solid region, a heat transfer equation for a liquid region, and a heat transfer equation for a mushy region at a solid-liquid interface.

5. The method of claim 4, wherein the heat transfer equation for the solid-state region is:

wherein ρ_sIs a solid phase temperature, c_sIs specific heat of solid phase, k_sIs a solid phase thermal conductivity coefficient, T_sIs the solid phase temperature, t is the time, S_sIs a solid phase source item.

6. The method of claim 4, wherein the heat transfer equation for the liquid zone is:

where ρ is_lIs a liquid phase temperature, c_lIs liquid phase specific heat, k_lIs liquid phase thermal conductivity coefficient, T_lIs the liquidus temperature, v is the velocity vector, S_lIs a liquid phase source item.

7. The method of claim 4, wherein the heat transfer equation for the mushy zone is:

where ρ is_sIs the temperature of the solid phase, k_sIs a solid phase thermal conductivity coefficient, k_lIs liquid phase thermal conductivity coefficient, T_lIs the liquidus temperature, v is the velocity vector, S_lIs a liquid phase source item; Δ h_mFor latent heat of phase change, v_∑Is the mixture velocity vector and T is the temperature of the mushy zone.

8. A simulation device for a lead bismuth alloy solidification process in a lead-water reaction is characterized by comprising the following steps:

the establishing module is used for coupling the preset fluid calculation model, the preset turbulence model and the solidification heat transfer model to establish a simulation environment for solidifying the lead-bismuth alloy;

and the simulation module is used for acquiring the initial working condition of the lead-water reaction, and carrying out simulation on the solidification phase-change heat transfer process of the lead-bismuth alloy based on the initial working condition in the simulation environment to obtain the distribution information of the lead-water reaction area in the preset time of high-speed incident water flow injection.

9. An electronic device, comprising: a processor and a storage device;

the storage device has stored thereon a computer program which, when executed by the processor, performs the method of any one of claims 1 to 7.

10. A computer-readable storage medium, on which a computer program is stored, which, when being executed by a processor, carries out the steps of the method according to any one of the claims 1 to 7.

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