CN111753418A - Migration path analysis method for steam bubbles generated by lead-based reactor accidents - Google Patents

Migration path analysis method for steam bubbles generated by lead-based reactor accidents Download PDF

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CN111753418A
CN111753418A CN202010568930.2A CN202010568930A CN111753418A CN 111753418 A CN111753418 A CN 111753418A CN 202010568930 A CN202010568930 A CN 202010568930A CN 111753418 A CN111753418 A CN 111753418A
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lead
steam
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steam bubbles
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CN111753418B (en
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王成龙
于启帆
苏光辉
张大林
田文喜
秋穗正
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Xian Jiaotong University
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    • G06F30/20—Design optimisation, verification or simulation
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    • G06—COMPUTING; CALCULATING OR COUNTING
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    • G06F30/00—Computer-aided design [CAD]
    • G06F30/20—Design optimisation, verification or simulation
    • G06F30/28—Design optimisation, verification or simulation using fluid dynamics, e.g. using Navier-Stokes equations or computational fluid dynamics [CFD]
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    • G21C—NUCLEAR REACTORS
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Abstract

A migration path analysis method for steam bubbles generated by lead-based reactor accidents comprises the steps of 1, modeling according to reactor structure parameters, inputting initial temperature field and pressure field distribution of a first loop and boundary conditions of temperature and pressure of a second loop as initial steady-state calculation values; 2. calling a lead-based alloy physical property relational expression, introducing a porous medium model and a turbulent flow Prandtl model, obtaining a steady-state temperature field and a pressure field of a primary loop of the reactor, and taking the steady-state temperature field and the pressure field as initial values for calculating the accident condition; 3. calling a drag force calculation function of the steam bubble, and selecting a drag coefficient relational expression to calculate the drag force borne by the steam bubble; 4. calling the relation of the number of the steam bubbles along with the size distribution, and inputting the number distribution rule of the steam bubbles at the initial moment of the accident; 5. setting a crevasse position, and calling an Euler-Lagrange algorithm to solve a steam bubble migration path; until the path calculation is converged and the migration time reaches the calculation requirement. The invention provides evaluation and guidance for the design safety of the lead-based reactor and the judgment of the influence degree of the steam generator heat transfer pipe rupture accident.

Description

Migration path analysis method for steam bubbles generated by lead-based reactor accidents
Technical Field
The invention relates to the field of serious accidents of lead-based reactors, in particular to a steam bubble migration path analysis method under a lead-based reactor steam generator heat transfer pipe rupture accident.
Background
The lead-based reactor refers to a reactor using liquid metal lead or lead-based alloy (collectively referred to as lead-based material) as a coolant. The steam generator heat transfer pipe rupture accident of the lead-based reactor is an accident process that under the steam generator heat transfer pipe rupture working condition, the high-pressure water of the second loop is vaporized and enters a reactor core along with the flowing of the coolant of the first loop. Steam bubbles generated by an accident may be entrained and retained in the reactor core, so that positive cavitation reactivity is generated in a local region of the reactor core, and further, the power of the reactor is increased rapidly, and the safety of the reactor is affected. Therefore, the research on the migration path of the steam bubbles in the event of the rupture of the heat transfer tubes of the steam generator of the lead-based reactor provides important early exploration for evaluating the probability of the steam bubbles being entrained into the reactor core and further judging the possibility of the accident inducing the more serious power surge phenomenon, and has important significance for the design and safety evaluation of the lead-based reactor.
Since the lead-based alloy cooling reactor is a novel reactor, research on the lead-based alloy cooling reactor is still under exploration in various countries. Considering the opaque physical characteristics of the liquid lead-based alloy, the existing experimental and theoretical researches are mainly divided into two categories, one is the overall experimental research and theoretical calculation for developing all the thermal and hydraulic processes of accidents, and the research is mainly focused on the change process research of the temperature field and the pressure field in the accident process; the other type focuses on exploring the lead-based alloy-water reaction process, and mainly focuses on the research on the mechanism reaction of the lead-based alloy-water two-phase induced steam explosion. It can be seen that the prior theoretical research on the migration of steam bubbles in the event of the rupture of the heat transfer tubes of the steam generator is still lacking.
Disclosure of Invention
Aiming at the structural characteristics of a primary circuit in a lead-based reactor, the method carries out steady-state thermodynamic and hydraulic calculation by constructing a primary circuit operating environment of the reactor and setting the physical properties of a lead-based alloy working medium, ensures a subsequent accident simulation environment and analyzes the sensitivity of some steady-state operation key parameters; by optimizing the stress analysis of the steam bubbles, setting the quantity distribution relation of the steam bubbles and setting the position of a break, transient thermal hydraulic calculation is carried out by an Euler-Lagrange algorithm, and the possibility that the steam bubbles generated by accidents are transferred to the reactor core and the distribution position of the steam bubbles in the reactor core are analyzed.
In order to achieve the purpose, the invention adopts the following technical scheme to implement:
a migration path analysis method for steam bubbles generated by lead-based reactor accidents comprises the following steps:
step 1: building a lead-based reactor model and inputting steady-state operation parameters, wherein the building and the steady-state operation parameters comprise modeling according to anti-lead-based reactor structure parameters, inputting initial temperature field distribution and pressure field distribution of a first loop and boundary conditions of temperature and pressure of a second loop as initial values of steady-state calculation;
step 2: calling a lead-based alloy physical property relational expression, introducing a porous medium model and a turbulent flow Prandtl model, carrying out steady-state thermal hydraulic calculation of a primary circuit of the lead-based reactor through a computational fluid dynamics program, and converging a to-be-calculated residual curve to 10-5Then obtaining a steady-state temperature field and a steady-state pressure field of a primary circuit of the lead-based reactor, and using the steady-state temperature field and the steady-state pressure field as initial values for calculating the accident condition;
the method comprises the following steps of (1) introducing physical property relational expression optimization calculation of the lead-based alloy in consideration of the influence of physical property setting of the liquid lead-based alloy on the flow and heat exchange of the liquid lead-based alloy; the introduced relation is the physical property relation of the liquid lead-based alloy:
ρLBE＝11096-1.3236T (1)
Cp,LBE＝159-2.72×10-2T+7.12×10-6T2(2)
λLBE＝3.61+1.517×10-2T-1.741×10-6T2(3)
μLBE(T)＝(4.56-7.03×10-3T+3.61×10-6T2)×10-3(4)
in the formula:
ρLBEdensity of lead-based alloy/kg. m-3
T-lead-based alloy temperature/K
Cp,LBE-lead base alloy heat capacity/J.K-1
λLBE-lead-based alloy thermal conductivity/W.m-1·K-1
μLBE(T) -kinetic viscosity of lead-base alloy/Ns.m-2
Introducing a porous medium model for optimizing and simulating the flow resistance of the liquid lead-based alloy in the steam generator and the core, wherein the viscous resistance coefficient and the inertial resistance coefficient in the porous medium model are determined by the flow resistance characteristics of the steam generator and the core:
Δp＝ΔpViscous+ΔpInertial(5)
ΔpViscous＝CViscousμLBE(T)uΔx (6)
Figure BDA0002548628170000031
in the formula:
Δ p-porous Medium pressure drop/Pa
ΔpViscousViscous drag pressure drop/Pa
ΔpInertial-inertial resistance pressure drop/Pa
CViscousCoefficient of viscous drag
u-lead base alloy flow velocity/m.s-1
Deltax-unit distance of flow of lead-base alloy per m in calculated step length
CInertialCoefficient of inertial resistance
Introducing a turbulent flow Prandtl model for optimizing and simulating a turbulent flow heat exchange process of the liquid lead-based alloy in a primary loop of the lead-based reactor:
Figure BDA0002548628170000041
Figure BDA0002548628170000042
Pe＝ul/D (10)
in the formula:
Prt-turbulent Plantt number
Pe-Bekeley number
Characteristic dimension of l-lead base alloy flow field/m
Molecular diffusion coefficient of D-lead base alloy flow field
And step 3: starting a DPM Euler-Lagrange model in a computational fluid dynamics program, calling a steam bubble drag force calculation function in the DPM Euler-Lagrange model, and calculating the drag force borne by a steam bubble, wherein the calculation result of the drag force is determined by selecting and correcting different drag coefficient relational expressions:
Figure BDA0002548628170000043
Figure BDA0002548628170000044
in the formula:
FDthe drag force/N experienced by the steam bubble
ub-vapor bubble flow velocity/m.s-1
ρb-steamBubble density/kg. m-3
dbDiameter of the steam bubble/m
CD-vapor bubble drag coefficient
Re-relative Reynolds number of vapor bubble
And 4, step 4: inputting a distribution rule of the number of the steam bubbles at the initial moment of the accident along with the size, namely the ratio of the number of the steam bubbles of each size generated at the initial moment to the number of all the steam bubbles, at the initial number setting position of the steam bubbles in the DPM Euler-Lagrange model;
and 5: setting the position of a crevasse in a steam generator at the initial position of a steam bubble in a DPM Euler-Lagrange model, and solving a steam bubble migration path; if the calculated residual curve of the steam bubble migration path continuously fluctuates, the calculation is not converged, and at the moment, a new drag coefficient relation formula is updated in the DPM Euler-Lagrange model, and the calculation is restarted; if the calculated residual curve of the steam bubble migration path tends to be stable and does not fluctuate any more, the calculation convergence is indicated, and whether the calculated steam bubble migration time length meets the calculation requirement or not is further judged at the moment; if the calculated migration time of the steam bubbles meets the calculation requirement, stopping the calculation and obtaining the migration calculation result of the steam bubbles; otherwise, the distribution result of the steam bubbles at the stopping time is read as an initial condition, and the migration path calculation of the steam bubbles is continued until the calculated migration time of the steam bubbles reaches the calculation requirement.
Compared with the prior art, the invention has the following advantages:
1. the analysis method can solve the steam bubble migration path under the accident of the rupture of the heat transfer pipe of the steam generator of the lead-based reactor, and fills the blank of the existing calculation requirement;
2. according to the analysis method, a porous medium model and a turbulent flow Prandtl model are added, so that the flow characteristic and the heat transfer characteristic of the coolant in the steady-state operation of a primary circuit of the lead-based reactor can be more accurately calculated;
3. the analysis method can obtain the most accurate steam bubble stress analysis by correcting the drag coefficient relational expression, thereby ensuring the calculation accuracy of the steam bubble migration path;
4. the analysis method can obtain the steam bubble migration paths under different accident conditions by introducing different steam bubble number distribution relations and different breaking positions, and improves the universality of the method.
Drawings
FIG. 1 is a block diagram of the computational process of the present invention.
FIG. 2 is a schematic diagram of a primary loop structure of a lead-based reactor.
Fig. 3 is a graph of the distribution of the number of certain vapor bubbles with size.
Detailed Description
The process of the present invention is described in further detail below with reference to the accompanying drawings and the detailed description:
as shown in FIG. 1, the present invention
A migration path analysis method for steam bubbles generated by lead-based reactor accidents comprises the following steps:
step 1: building a lead-based reactor model and inputting steady-state operation parameters, wherein the building and the steady-state operation parameters comprise modeling according to anti-lead-based reactor structure parameters, inputting initial temperature field distribution and pressure field distribution of a first loop and boundary conditions of temperature and pressure of a second loop as initial values of steady-state calculation;
step 2: calling a lead-based alloy physical property relational expression, introducing a porous medium model and a turbulent flow Prandtl model, carrying out steady-state thermal hydraulic calculation of a primary circuit of the lead-based reactor through a computational fluid dynamics program, and converging a to-be-calculated residual curve to 10-5Then obtaining a steady-state temperature field and a steady-state pressure field of a primary circuit of the lead-based reactor, and using the steady-state temperature field and the steady-state pressure field as initial values for calculating the accident condition;
the method comprises the following steps of (1) introducing physical property relational expression optimization calculation of the lead-based alloy in consideration of the influence of physical property setting of the liquid lead-based alloy on the flow and heat exchange of the liquid lead-based alloy; the introduced relation is the physical property relation of the liquid lead-based alloy:
ρLBE＝11096-1.3236T (1)
Cp,LBE＝159-2.72×10-2T+7.12×10-6T2(2)
λLBE＝3.61+1.517×10-2T-1.741×10-6T2(3)
μLBE(T)＝(4.56-7.03×10-3T+3.61×10-6T2)×10-3(4)
in the formula:
ρLBEdensity of lead-based alloy/kg. m-3
T-lead-based alloy temperature/K
Cp,LBE-lead base alloy heat capacity/J.K-1
λLBE-lead-based alloy thermal conductivity/W.m-1·K-1
μLBE(T) -kinetic viscosity of lead-base alloy/Ns.m-2
Introducing a porous medium model for optimizing and simulating the flow resistance of the liquid lead-based alloy in the steam generator and the core, wherein the viscous resistance coefficient and the inertial resistance coefficient in the porous medium model are determined by the flow resistance characteristics of the steam generator and the core:
Δp＝ΔpViscous+ΔpInertial(5)
ΔpViscous＝CViscousμLBE(T)uΔx (6)
Figure BDA0002548628170000071
in the formula:
Δ p-porous Medium pressure drop/Pa
ΔpViscousViscous drag pressure drop/Pa
ΔpInertial-inertial resistance pressure drop/Pa
CViscousCoefficient of viscous drag
u-lead base alloy flow velocity/m.s-1
Deltax-unit distance of flow of lead-base alloy per m in calculated step length
CInertialCoefficient of inertial resistance
Introducing a turbulent flow Prandtl model for optimizing and simulating a turbulent flow heat exchange process of the liquid lead-based alloy in a primary loop of the lead-based reactor:
Figure BDA0002548628170000081
Figure BDA0002548628170000082
Pe＝ul/D (10)
in the formula:
Prt-turbulent Plantt number
Pe-Bekeley number
Characteristic dimension of l-lead base alloy flow field/m
Molecular diffusion coefficient of D-lead base alloy flow field
And step 3: starting a DPM Euler-Lagrange model in a computational fluid dynamics program, calling a steam bubble drag force calculation function in the DPM Euler-Lagrange model, and calculating the drag force borne by a steam bubble, wherein the calculation result of the drag force is determined by selecting and correcting different drag coefficient relational expressions:
Figure BDA0002548628170000083
Figure BDA0002548628170000084
in the formula:
FDthe drag force/N experienced by the steam bubble
ub-vapor bubble flow velocity/m.s-1
ρbDensity of steam bubbles/kg. m-3
dbDiameter of the steam bubble/m
CD-vapor bubble drag coefficient
Re-relative Reynolds number of vapor bubble
And 4, step 4: inputting a distribution rule of the number of the steam bubbles at the initial moment of the accident along with the size, namely the ratio of the number of the steam bubbles of each size generated at the initial moment to the number of all the steam bubbles, at the initial number setting position of the steam bubbles in the DPM Euler-Lagrange model;
and 5: setting the position of a crevasse in a steam generator at the initial position of a steam bubble in a DPM Euler-Lagrange model, and solving a steam bubble migration path; if the calculated residual curve of the steam bubble migration path continuously fluctuates, the calculation is not converged, and at the moment, a new drag coefficient relation formula is updated in the DPM Euler-Lagrange model, and the calculation is restarted; if the calculated residual curve of the steam bubble migration path tends to be stable and does not fluctuate any more, the calculation convergence is indicated, and whether the calculated steam bubble migration time length meets the calculation requirement or not is further judged at the moment; if the calculated migration time of the steam bubbles meets the calculation requirement, stopping the calculation and obtaining the migration calculation result of the steam bubbles; otherwise, the distribution result of the steam bubbles at the stopping time is read as an initial condition, and the migration path calculation of the steam bubbles is continued until the calculated migration time of the steam bubbles reaches the calculation requirement.
The effect of the invention is explained below by combining a specific calculation object, taking a schematic diagram of a loop structure of a certain lead-based reactor shown in fig. 2 as an example, firstly, through step 1, a reactor model is built according to the design structure and design parameters of the reactor, and initial temperature field and pressure field distribution of a loop, and temperature and pressure boundary conditions of a secondary loop are input as initial values of steady-state calculation; calling a physical property relation of the liquid lead-bismuth alloy, a porous medium model and a turbulence Plantt model according to the step 2 to calculate and obtain a steady-state temperature field and a pressure field of a primary loop of the reactor; obtaining a calculation mode of the steam bubble drag force in the lead-based alloy according to the step 3; introducing a distribution curve of the number of the steam bubbles along with the size as shown in figure 3 according to the step 4, wherein the distribution curve is used as a distribution rule of the number of the steam bubbles at the initial moment of the accident; setting a position of a break opening according to the step 5, calculating to obtain a calculation result of steam bubble migration to the reactor core, outputting the result mainly including the calculated cloud map distribution of the steam bubble migration to the reactor core of the reactor and the change curve of the number of the steam bubbles captured at different positions of the reactor core, and contributing to further evaluating the possibility of positive cavitation bubble reactivity of the local area caused by the steam bubbles, thereby providing a basis for more comprehensively evaluating the severity of accidents caused by the steam generator heat transfer tube rupture accidents.

Claims (1)

1. A migration path analysis method for steam bubbles generated by lead-based reactor accidents is characterized by comprising the following steps: the method comprises the following steps:
step 1: building a lead-based reactor model and inputting steady-state operation parameters, wherein the building and the steady-state operation parameters comprise modeling according to anti-lead-based reactor structure parameters, inputting initial temperature field distribution and pressure field distribution of a first loop and boundary conditions of temperature and pressure of a second loop as initial values of steady-state calculation;
step 2: calling a lead-based alloy physical property relational expression, introducing a porous medium model and a turbulent flow Prandtl model, carrying out steady-state thermal hydraulic calculation of a primary circuit of the lead-based reactor through a computational fluid dynamics program, and converging a to-be-calculated residual curve to 10-5Then obtaining a steady-state temperature field and a steady-state pressure field of a primary circuit of the lead-based reactor, and using the steady-state temperature field and the steady-state pressure field as initial values for calculating the accident condition;
the method comprises the following steps of (1) introducing physical property relational expression optimization calculation of the lead-based alloy in consideration of the influence of physical property setting of the liquid lead-based alloy on the flow and heat exchange of the liquid lead-based alloy; the introduced relation is the physical property relation of the liquid lead-based alloy:
ρLBE＝11096-1.3236T (1)
Cp,LBE＝159-2.72×10-2T+7.12×10-6T2(2)
λLBE＝3.61+1.517×10-2T-1.741×10-6T2(3)
μLBE(T)＝(4.56-7.03×10-3T+3.61×10-6T2)×10-3(4)
in the formula:
ρLBEdensity of lead-based alloy/kg. m-3
T-lead-based alloy temperature/K
Cp,LBE——Lead-base alloy heat capacity/J.K-1
λLBE-lead-based alloy thermal conductivity/W.m-1·K-1
μLBE(T) -kinetic viscosity of lead-base alloy/Ns.m-2
Introducing a porous medium model for optimizing and simulating the flow resistance of the liquid lead-based alloy in the steam generator and the core, wherein the viscous resistance coefficient and the inertial resistance coefficient in the porous medium model are determined by the flow resistance characteristics of the steam generator and the core:
Δp＝ΔpViscous+ΔpInertial(5)
ΔpViscous＝CViscousμLBE(T)uΔx (6)
Figure FDA0002548628160000021
in the formula:
Δ p-porous Medium pressure drop/Pa
ΔpViscousViscous drag pressure drop/Pa
ΔpInertial-inertial resistance pressure drop/Pa
CViscousCoefficient of viscous drag
u-lead base alloy flow velocity/m.s-1
Deltax-unit distance of flow of lead-base alloy per m in calculated step length
CInertialCoefficient of inertial resistance
Introducing a turbulent flow Prandtl model for optimizing and simulating a turbulent flow heat exchange process of the liquid lead-based alloy in a primary loop of the lead-based reactor:
Figure FDA0002548628160000022
Figure FDA0002548628160000023
Pe＝ul/D (10)
in the formula:
Prt-turbulent Plantt number
Pe-Bekeley number
Characteristic dimension of l-lead base alloy flow field/m
Molecular diffusion coefficient of D-lead base alloy flow field
And step 3: starting a DPM Euler-Lagrange model in a computational fluid dynamics program, calling a steam bubble drag force calculation function in the DPM Euler-Lagrange model, and calculating the drag force borne by a steam bubble, wherein the calculation result of the drag force is determined by selecting and correcting different drag coefficient relational expressions:
Figure FDA0002548628160000031
Figure FDA0002548628160000032
in the formula:
FDthe drag force/N experienced by the steam bubble
ub-vapor bubble flow velocity/m.s-1
ρbDensity of steam bubbles/kg. m-3
dbDiameter of the steam bubble/m
CD-vapor bubble drag coefficient
Re-relative Reynolds number of vapor bubble
And 4, step 4: inputting a distribution rule of the number of the steam bubbles at the initial moment of the accident along with the size, namely the ratio of the number of the steam bubbles of each size generated at the initial moment to the number of all the steam bubbles, at the initial number setting position of the steam bubbles in the DPM Euler-Lagrange model;
and 5: setting the position of a crevasse in a steam generator at the initial position of a steam bubble in a DPM Euler-Lagrange model, and solving a steam bubble migration path; if the calculated residual curve of the steam bubble migration path continuously fluctuates, the calculation is not converged, and at the moment, a new drag coefficient relation formula is updated in the DPM Euler-Lagrange model, and the calculation is restarted; if the calculated residual curve of the steam bubble migration path tends to be stable and does not fluctuate any more, the calculation convergence is indicated, and whether the calculated steam bubble migration time length meets the calculation requirement or not is further judged at the moment; if the calculated migration time of the steam bubbles meets the calculation requirement, stopping the calculation and obtaining the migration calculation result of the steam bubbles; otherwise, the distribution result of the steam bubbles at the stopping time is read as an initial condition, and the migration path calculation of the steam bubbles is continued until the calculated migration time of the steam bubbles reaches the calculation requirement.
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CN113782105A (en) * 2021-08-31 2021-12-10 西安交通大学 Method for analyzing flow heat transfer characteristics of liquid metal lead bismuth alloy under swinging condition
CN113782105B (en) * 2021-08-31 2022-12-09 西安交通大学 Method for analyzing flow heat transfer characteristics of liquid metal lead-bismuth alloy under swinging condition

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