CN114417229B - Two-dimensional calculation method for nuclear reactor steam explosion - Google Patents

Abstract

A two-dimensional calculation method for nuclear reactor steam explosion, the steps are as follows: 1. Determine the geometric structure of the nuclear reactor calculation area and the environmental pressure and temperature under severe accidents, input the diameter, temperature and speed of the molten material jet, set the end time and initialize the parameters; 2. , Calculate the physical properties of the melt, water vapor, and water according to the interpolation of the physical property table; 3. Calculate the momentum change between the melt, water, and steam due to interphase friction; 4. Calculate the heat transfer between the melt, water, and steam ;5. Determine whether the melt droplet is fragmented, and calculate the diameter change rate during the melt fragmentation process; 6. Solve the mass, momentum, and energy conservation equations, and save the data to the output file. If the set end time is not reached , jump to step 2 to calculate the next time step, and stop the calculation if the set end time has been reached. The method of the invention can simulate and calculate the steam explosion phenomenon of the nuclear reactor, and obtain calculation results such as the temperature and pressure of each fluid.

Description

A Two-Dimensional Calculation Method for Nuclear Reactor Steam Explosion

technical field

The invention relates to the technical field of pressurized water reactors, in particular to a two-dimensional calculation method for nuclear reactor steam explosions.

Background technique

Under the severe accident conditions of nuclear reactors, the molten material that melts through the pressure vessel reacts violently with the water in the pit of the pressurized water reactor, generating a strong shock wave, which may cause the failure of the containment vessel and the leakage of radioactive substances. At the same time, the explosion may also have an impact on the pressure vessel and the primary circuit system. Therefore, the study of the phenomenon of steam explosion plays an important role in the understanding of the contact reaction between high-temperature molten fuel and coolant and the evaluation of the integrity of the safety barrier and the leakage of radioactive substances in the process of severe accidents in existing pressurized water reactors. At the same time, it is important for the design of new reactors And safety assessment is also important.

Contents of the invention

In order to overcome the problems in the above-mentioned prior art, the object of the present invention is to provide a two-dimensional calculation method for nuclear reactor steam explosion, which adopts the multi-fluid Euler method under the cylindrical coordinate system, and separates Simulation can predict melt fragmentation and diffusion process, steam generation rate, shock wave generation and propagation, etc., and give the distribution and time-dependent changes of parameters such as pressure, temperature, void fraction, and coolant fraction in the calculation area. It provides a reference for steam explosion-related experiments, research and evaluation of FCI phenomena in nuclear reactors.

In order to achieve the above object, the present invention has taken the following technical solutions:

A two-dimensional calculation method for a nuclear reactor steam explosion, comprising the following steps:

Step 1. Determine the geometric structure of the nuclear reactor calculation area and the environmental pressure and temperature parameters under severe accidents, input the diameter, temperature and speed of the molten material jet, set the end time and initialize the parameters;

Step 2: Calculate the physical properties of melt, water vapor and water according to the interpolation table of physical properties;

Step 3: Calculate the momentum change between the melt, water, and steam due to interphase friction;

During the interaction between the melt and water, there is interphase friction between the melt, water, and steam, and the momentum change between the discrete phase p and the continuous phase c due to interphase friction is expressed as:

In the formula:

I _pc —momentum change between the discrete phase and the continuous phase due to interphase friction per unit time and unit volume/kg m ^-2 s ^-2

C _pc —coefficient of friction between the discrete phase and the continuous phase

D _p ——diameter of discrete phase/m

α _p ——volume fraction of discrete phase

Cd _pc ——the resistance coefficient between the discrete phase and the continuous phase

ρ _c ——continuous phase density/kg·m ^-3

——连续相与离散相的相对矢量速度/m·s^-1

——the relative vector velocity of continuous phase and discrete phase/m s ^-1

Re _c - the Reynolds number of the continuous phase

Step 4: Calculate the heat transferred between the melt, water and steam;

The heat transfer between steam and water occurs at the phase interface between steam and water. Assuming that the phase interface between steam and water is at the saturation temperature, the heat transferred by steam and water to the phase interface is:

Q _vi ＝h _vi A _vl (T _v -T _sat ) (3)

Q _li ＝h _li A _vl (T _l -T _sat ) (4)

The heat transferred from the melt to steam and water is expressed as:

Q _mv ＝h _mv A _mv (T _m -T _v ) (5)

Q _ml ＝h _ml A _ml (T _m -T _l ) (6)

In the formula:

Q _vi ——in unit time and unit volume, the heat transferred from steam to phase interface/W·m ^-3

Q _li ——the heat transferred from water to the phase interface in unit time and unit volume/W·m ^-3

Q _mv —— heat transfer from melt to steam in unit time and unit volume/W·m ^-3

Q _ml ——the heat transferred from melt to water in unit time and unit volume/W·m ^-3

h _vi ——heat transfer coefficient between steam and phase interface/W m ^-3 K ^-1

h _li ——heat transfer coefficient between water and phase interface/W m ^-3 K ^-1

h _mv ——Heat transfer coefficient between melt and steam/W m ^-3 K ^-1

h _ml ——Heat transfer coefficient between melt and water/W m ^-3 K ^-1

A _vl ——the heat transfer area of water and steam per unit volume/m ² ·m ^-3

A _mv ——heat transfer area of melt and steam per unit volume/m ² ·m ^-3

A _ml ——Heat transfer area between melt and water per unit volume/m ² ·m ^-3

T _v —— steam temperature/K

T _l ——water temperature/K

T _sat ——water saturation temperature/K

T _m ——The temperature of the melt/K

α _m ——The volume fraction of the melt

α _v ——Volume fraction of steam

α _l ——volume fraction of water

D _m ——the diameter of the melt droplet/m

S——water saturation (volume fraction of water in fluid except melt)

According to different flow patterns and boiling methods, the calculation methods of interphase heat transfer coefficient and heat transfer area are also different, which can be divided into the following situations:

1) Heat transfer coefficient and heat transfer area between water and steam and phase interface under bubbly flow conditions

h _vi =1000 (10)

In the formula:

Nu _l - Nusselt number of water

D _v ——diameter of bubbles in bubbly flow/m

k _l ——The thermal conductivity of water/W m ^-1 K ^-1

Pr _l — Prandtl number of water

Re _l - Reynolds number of water

vol - the volume of the control body/m ^-3

2) Heat transfer coefficient and heat transfer area between water and steam and phase interface under the condition of diffuse flow

In the formula:

Nu _v —— Nusselt number of steam

D _l ——diameter of dispersed water droplet/m

k _v ——heat transfer coefficient of steam/W m ^-1 K ^-1

Pr _v —— Prandtl number of steam

Rev _- Reynolds number of steam

ρ _l ——density of water/kg·m ^-3

Cp _l ——Specific heat of water/J kg ^-1 K ^-1

——水与蒸汽的相对速度/m·s^-1

——The relative speed of water and steam/m·s ^-1

3) Heat transfer coefficient and heat transfer area between water and steam and phase interface under transitional flow conditions

When the water saturation is in the range of 0.25 to 0.75, it is considered to be a transitional flow state; in this state, through the critical bubbly flow, that is, the water saturation S=0.75, and the critical diffuse flow, that is, the water saturation S= Perform linear interpolation between the values calculated at 0.25 to obtain the heat transfer coefficient and heat transfer area;

h _vi ＝(1-f ₁ )h _vi,mist +f ₁ h _vi,bubbly (18)

h _li ＝(1-f ₁ )h _li,mist +f ₁ h _li,bubbly (19)

A _vl ＝(1-f ₁ )A _vl,mist +f ₁ A _vl,bubbly (20)

In the formula:

h _vi,mist ——heat transfer coefficient between diffuse flow steam and phase interface/W m ^-3 K ^-1

h _vi,bubbly ——heat transfer coefficient between bubbly steam and phase interface/W m ^-3 K ^-1

h _li,mist ——heat transfer coefficient between dispersed flowing water and phase interface/W m ^-3 K ^-1

h _li,bubbly ——heat transfer coefficient between bubbly flowing water and phase interface/W m ^-3 K ^-1

A _vl,mist — heat transfer area of water and steam in diffuse flow state per unit volume/m ² ·m ^-3

A _vl,bubbly ——the heat transfer area of water and steam in bubbly flow state per unit volume/m ² ·m ^-3

4) Heat transfer coefficient between melt and coolant under convective conditions

Natural convection:

Nu _nc ＝2.0+0.6Gr _co ^1/4 Pr _co ^1/3 (24)

Forced convection:

In the formula:

h _m,co ——Heat transfer coefficient between melt and coolant/W m ^-3 K ^-1

Nu _co — Nusselt number of coolant

Nu _nc — Nusselt number of the coolant under natural convection conditions

Nu _fc — Nusselt number of the coolant under forced convection conditions

k _co ——Coefficient of thermal conductivity of coolant/W m ^-1 K ^-1

Gr _co - the Grashof number of the coolant

Pr _co - the Prandtl number of the coolant

Re _co - the Reynolds number of the coolant

5) Heat transfer coefficient between melt and coolant under nucleate boiling conditions

Under nucleate boiling conditions, use Chen's formula to calculate the heat transfer coefficient between the melt and water; use the interpolation method to calculate the heat transfer coefficient between the melt and steam, so that the heat transfer coefficient between the melt and steam is at T _m = T _sat When T _m = T _CHF , it is the value of the heat transfer coefficient of the CHF point. When T _m is between T _sat and T _CHF , the heat transfer coefficient between the melt and the steam is calculated by interpolation:

h _mv ＝(3y ² -2y ³ )h _mv,film (T _CHF ) (26)

In the formula:

h _mv,film (T _CHF )——Heat transfer coefficient between melt and steam corresponding to CHF point when T _m =T _CHF /W·m ^-3 ·K ^-1

T _CHF ——melt temperature when critical heat flux occurs/K

6) Heat transfer coefficient between melt and coolant under film boiling conditions

Under film boiling conditions, the heat transfer coefficient between the melt and water is calculated using the following formula:

h _ml ＝max(h _free ,h _force )+h _rad (28)

Use the Dhir-Purohit relation to calculate h _free , h _free represents the heat transfer coefficient when the relative velocity between the melt and water is small; use the Epstein-Hauser relation to calculate h _force , h _force represents the relative velocity difference between the melt and water Larger heat transfer coefficients. The radiation heat transfer coefficient h _rad between the melt and water is:

ε=α _v +α _l (30)

In film boiling, the melt-to-vapour heat transfer coefficient is set to zero; however, note that the total value of the heat transfer coefficient may not be zero since it is the sum of the boiling part and the convective part;

In the formula:

h _free ——Heat transfer coefficient when the relative velocity between melt and water is small/W m ^-3 K ^-1

h _force ——the heat transfer coefficient when the relative speed difference between the melt and water is large/W m ^-3 K ^-1

h _rad ——radiative heat transfer coefficient/W m ^-3 K ^-1

σ——Boltzmann constant/W m ^-2 K ^-4

ε——coolant volume fraction

7) Heat transfer coefficient between melt and coolant under transition boiling conditions

The heat flux of the melt to water is assumed to be approximately an interpolation between the critical heat flux _qCHF and the minimum stable film boiling heat flux _qmin ; the interpolation formula applied is:

f ₁ =(3y ² -2y ³ ) (32)

It is assumed that the heat transfer coefficient of the melt to the steam can be approximated by interpolating between the critical heat flux heat transfer coefficient and the minimum stable film boiling heat transfer coefficient; the interpolation formula applied is:

h _mv ＝f ₁ h _mvCHF +(1-f ₁ )h _mvmin (35)

In the formula:

q _CHF ——Critical Heat Flux/W·m ^-2

q _min,rad ——minimum film boiling heat flux considering radiation heat transfer/W·m ^-2

q _min ——Minimum film boiling heat flux without considering radiation heat transfer/W·m ^-2

T _min ——Minimum stable film boiling temperature/K

h _mvCHF ——heat transfer coefficient between melt and steam at critical heat flux/W m ^-3 K ^-1

h _mvmin ——the heat transfer coefficient between the melt and steam when the melt temperature is equal to the minimum stable film boiling temperature/W m ^-3 K ^-1

Step 5: Determine whether the melt droplet is fragmented, and calculate the diameter change rate during the melt fragmentation process;

The fragmentation of the melt in the coolant is divided into two situations: (1) the coarse mixing fragmentation of the melt injected into the water due to hydraulic instability; (2) the fine fragmentation of the melt droplets by the thermodynamic action crack;

In the case of coarse mixing, the melt will be fragmented only if the following fragmentation criterion is met:

We represent the Weber number:

Ae ^* denotes the modified aeroelastic coefficient:

Fragmentation Calculate the rate of change of melt diameter for coarse mixing using the fragmentation model of Pilch theory:

During the occurrence of fine fragmentation, the mass change rate of melt fragmentation is calculated by the following formula:

In the formula:

v _r ——relative speed of melt and coolant/m·s ^-1

ρ _co ——average density of coolant/kg·m ^-3

ρ _m ——density of melt/kg·m ^-3

We - Weber number

We _cri ——Critical Weber number, take 4π

Ae——Corrected aeroelastic coefficient

Ae ^* _cri ——Critical corrected aeroelastic coefficient, take 8π ³

σ _m ——surface tension of melt/N·s ^-1

χ—Poisson’s ratio of the melt material

δ—thickness of the solidified shell on the surface of the melt droplet/m

E——Young's modulus after solidification of the melt/Pa

m _frag ——the amount of molten material that has been finely fragmented/kg

C _f —— fine fragmentation constant

m _i ——the amount of molten material in the control body/kg

P - control internal pressure

P _th ——threshold of fine fragmentation pressure/Pa

Step 6: Use the estimated stability method to solve the mass, momentum, and energy conservation equations, and save the data to the output file. If the set end time has not been reached, skip to step 2 to calculate the next time step. If it has reached the set the end time, stop calculation;

The thermal-hydraulic equation is solved by the pre-estimation calculation stability method. This method is mainly divided into three steps: (1) use the pressure of the previous time step to solve the momentum conservation equation to obtain the predicted value of the velocity; (2) express the predicted velocity as this The function of the time step pressure, and form a pressure equation system with the mass and energy conservation equations, which can be solved by pressure iteration to obtain the pressure, velocity, void fraction and temperature of this time step; (3) use this The mass and energy conservation equations are solved for the pressure of the time step to obtain the macroscopic density and internal energy of each phase, which are used as the corresponding quantities in the mass and energy conservation equations in the next time step.

Using the multi-fluid Euler method in the cylindrical coordinate system, the interaction among the three phases of steam, water and melt is considered. The conservation equation for the i-th phase is shown in (41)~(43), j and k represent phase different from i;

Mass Conservation Equation:

Momentum Conservation Equation:

Energy Conservation Equation:

In the formula:

t——time/s

α _i ——volume fraction of phase i

ρ _i ——density of phase i/kg·m ^-3

——i相的速度/m·s^-1

——Velocity of phase i/m·s ^-1

Γ _ji —mass of phase j transformed into phase i in unit time and unit volume/kg m ^-3 s ^-1

Γ _ki —mass of phase k transformed into phase i per unit time and unit volume/kg m ^-3 s ^-1

Γ _s ——mass produced by the external mass source per unit time and unit volume/kg m ^-3 s ^-1

P——pressure/Pa

x——Indicates the other two phases different from phase i, that is, phase j or phase k

C _xi ——the coefficient of friction between phase x and phase i

——x相的速度/m·s^-1

——Velocity of phase x/m s ^-1

C _wi —coefficient of friction between phase i and the wall

——重力加速度/m·s^-2

——Gravity acceleration/m·s ^-2

u _i ——internal energy per unit mass of phase i/J·kg ^-1

H _ji ——The enthalpy change of phase j to phase i per unit mass/J kg ^-1

H _ki ——the enthalpy change of unit mass phase k to phase i/J kg ^-1

Q _ji ——The amount of heat transferred from phase j to phase i in unit time and unit volume/W·m ^-3

Q _ki ——the heat transferred from phase k to phase i in unit time and unit volume/W·m ^-3

Q _s ——the heat generated by the external heat source per unit time and unit volume/W·m ^-3 .

Compared with the prior art, the present invention has the following prominent features:

The calculation area can be calculated without modeling, so as to obtain two-dimensional calculation results. Compared with the one-dimensional calculation results, the radial difference of steam explosion can be analyzed and evaluated.

In view of the existing problems, the present invention provides a two-dimensional steam explosion calculation method, the understanding of the contact reaction between high-temperature molten fuel and coolant, and the evaluation of the integrity of the safety barrier and the leakage of radioactive substances during the serious accident process of the existing pressurized water reactor. Whether it plays an important role or not, it is also of great significance to the design and safety assessment of new reactors.

Description of drawings

Fig. 1 is a flow chart of the method of the present invention.

Detailed ways

Below in conjunction with accompanying drawing and specific embodiment the present invention is described in further detail:

The present invention is a two-dimensional calculation method for nuclear reactor steam explosion, as shown in Figure 1, the specific flow of the method includes the following steps:

Step 1. Determine the geometric structure of the nuclear reactor calculation area and the environmental pressure and temperature parameters under severe accidents, input the diameter, temperature, and speed of the molten material jet, and set the end time as the initial value of the calculation variable;

Step 2: Calculate the physical properties of melt, water vapor, and water according to the physical property table interpolation, so that the physical property data of each phase can be used in the subsequent calculation process;

Step 3: Calculate the momentum change between the melt, water, and steam due to interphase friction;

During the interaction between melt and water, there is phase friction among melt, water and steam. The discrete phase is approximately regarded as a sphere, and the continuous phase is the continuous fluid existing around the discrete phase. Under certain circumstances, the three phases of steam, water, and melt can be used as the discrete phase or the continuous phase. The momentum change between the discrete phase p and the continuous phase c due to interphase friction is expressed as:

In the formula:

I _pc —momentum change between the discrete phase and the continuous phase due to interphase friction per unit time and unit volume/kg m ^-2 s ^-2

C _pc —coefficient of friction between the discrete phase and the continuous phase

D _p ——diameter of discrete phase/m

α _p ——volume fraction of discrete phase

Cd _pc ——the resistance coefficient between the discrete phase and the continuous phase

ρ _c ——continuous phase density/kg·m ^-3

——连续相与离散相的相对矢量速度/m·s^-1

——the relative vector velocity of continuous phase and discrete phase/m s ^-1

Re _c - the Reynolds number of the continuous phase

Step 4: Calculate the heat transferred between the melt, water and steam;

The heat transfer between steam and water occurs at the phase interface between steam and water. Assuming that the phase interface between steam and water is at the saturation temperature, the heat transferred by steam and water to the phase interface is:

Q _vi ＝h _vi A _vl (T _v -T _sat ) (3)

Q _li ＝h _li A _vl (T _l -T _sat ) (4)

The heat transferred from the melt to steam and water is expressed as:

Q _mv ＝h _mv A _mv (T _m -T _v ) (5)

Q _ml ＝h _ml A _ml (T _m -T _l ) (6)

In the formula:

Q _vi —— heat transfer from steam to phase interface in unit time and unit volume/W·m ^-

Q _li ——the heat transferred from water to the phase interface in unit time and unit volume/W·m ^-3

Q _mv ——The heat transferred from the melt to the steam per unit time and unit volume/W m

Q _ml ——the heat transferred from melt to water in unit time and unit volume/W·m ^-3

h _vi ——heat transfer coefficient between steam and phase interface/W m ^-3 K ^-1

h _li ——heat transfer coefficient between water and phase interface/W m ^-3 K ^-1

h _mv ——Heat transfer coefficient between melt and steam/W m ^-3 K ^-1

h _ml ——Heat transfer coefficient between melt and water/W m ^-3 K ^-1

A _vl ——the heat transfer area of water and steam per unit volume/m ² ·m ^-3

A _mv ——heat transfer area of melt and steam per unit volume/m ² ·m ^-3

A _ml ——Heat transfer area between melt and water per unit volume/m ² ·m ^-3

T _v —— steam temperature/K

T _l ——water temperature/K

T _sat ——water saturation temperature/K

T _m ——The temperature of the melt/K

α _m ——The volume fraction of the melt

α _v ——Volume fraction of steam

α _l ——volume fraction of water

D _m ——the diameter of the melt droplet/m

S——water saturation (volume fraction of water in fluid except melt)

According to different flow patterns and boiling modes, the calculation methods of interphase heat transfer coefficient and heat transfer area are also different, and the heat transfer coefficient and heat transfer area under different conditions can be calculated more accurately. Divided into the following situations:

1) Heat transfer coefficient and heat transfer area between water and steam and phase interface under bubbly flow conditions

h _vi =1000 (10)

In the formula:

Nu _l - Nusselt number of water

D _v ——diameter of bubbles in bubbly flow/m

k _l ——The thermal conductivity of water/W m ^-1 K ^-1

Pr _l — Prandtl number of water

Re _l - Reynolds number of water

vol - the volume of the control body/m ^-3

2) Heat transfer coefficient and heat transfer area between water and steam and phase interface under the condition of diffuse flow

In the formula:

Nu _v —— Nusselt number of steam

D _l ——diameter of dispersed water droplet/m

k _v ——heat transfer coefficient of steam/W m ^-1 K ^-1

Pr _v —— Prandtl number of steam

Rev _- Reynolds number of steam

ρ _l ——density of water/kg·m ^-3

Cp _l ——Specific heat of water/J kg ^-1 K ^-1

——水与蒸汽的相对速度/m·s^-1

——The relative speed of water and steam/m·s ^-1

3) Heat transfer coefficient and heat transfer area between water and steam and phase interface under transitional flow conditions

When the water saturation is in the range of 0.25 to 0.75, it is considered to be a transitional flow state; in this state, through the critical bubbly flow, that is, the water saturation S=0.75, and the critical diffuse flow, that is, the water saturation S= Perform linear interpolation between the values calculated at 0.25 to obtain the heat transfer coefficient and heat transfer area;

h _vi ＝(1-f ₁ )h _vi,mist +f ₁ h _vi,bubbly (18)

h _li ＝(1-f ₁ )h _li,mist +f ₁ h _li,bubbly (19)

A _vl ＝(1-f ₁ )A _vl,mist +f ₁ A _vl,bubbly (20)

In the formula:

h _vi,mist ——heat transfer coefficient between diffuse flow steam and phase interface/W m ^-3 K ^-1

h _vi,bubbly ——heat transfer coefficient between bubbly steam and phase interface/W m ^-3 K ^-1

h _li,mist ——heat transfer coefficient between dispersed flowing water and phase interface/W m ^-3 K ^-1

h _li,bubbly ——heat transfer coefficient between bubbly flowing water and phase interface/W m ^-3 K ^-1

A _vl,mist — heat transfer area of water and steam in diffuse flow state per unit volume/m ² ·m ^-3

A _vl,bubbly ——the heat transfer area of water and steam in bubbly flow state per unit volume/m ² ·m ^-3

4) Heat transfer coefficient between melt and coolant under convective conditions

Under convective conditions, the melt exists in single-phase water or single-phase steam in the form of droplets or fragments, and the heat transfer coefficient between the melt and steam or water is:

Natural convection:

Nu _nc ＝2.0+0.6Gr _co ^1/4 Pr _co ^1/3 (24)

Forced convection:

In the formula:

h _m,co ——Heat transfer coefficient between melt and coolant/W m ^-3 K ^-1

Nu _co — Nusselt number of coolant

Nu _nc — Nusselt number of the coolant under natural convection conditions

Nu _fc — Nusselt number of the coolant under forced convection conditions

k _co ——Coefficient of thermal conductivity of coolant/W m ^-1 K ^-1

Gr _co - the Grashof number of the coolant

Pr _co - the Prandtl number of the coolant

Re _co - the Reynolds number of the coolant

5) Heat transfer coefficient between melt and coolant under nucleate boiling conditions

Under nucleate boiling conditions, use Chen's formula to calculate the heat transfer coefficient between the melt and water; use the interpolation method to calculate the heat transfer coefficient between the melt and steam, so that the heat transfer coefficient between the melt and steam is at T _m = T _sat When T _m = T _CHF , it is the value of the heat transfer coefficient at the CHF point. When T _m is between T _sat and T _CHF , the heat transfer coefficient between the melt and the steam is calculated by interpolation:

h _mv ＝(3y ² -2y ³ )h _mv,film (T _CHF ) (26)

In the formula:

h _mv,film (T _CHF )——Heat transfer coefficient between melt and steam corresponding to CHF point when T _m =T _CHF /W·m ^-3 ·K ^-1

T _CHF ——melt temperature when critical heat flux occurs/K

6) Heat transfer coefficient between melt and coolant under film boiling conditions

Under film boiling conditions, the heat transfer coefficient between the melt and water is calculated using the following formula:

h _ml ＝max(h _free ,h _force )+h _rad (28)

Use the Dhir-Purohit relation to calculate h _free , h _free represents the heat transfer coefficient when the relative velocity between the melt and water is small; use the Epstein-Hauser relation to calculate h _force , h _force represents the relative velocity difference between the melt and water Larger heat transfer coefficients. The radiation heat transfer coefficient h _rad between the melt and water is:

ε=α _v +α _l (30)

In film boiling, the melt-to-vapour heat transfer coefficient is set to zero; however, note that the total value of the heat transfer coefficient may not be zero since it is the sum of the boiling part and the convective part;

In the formula:

h _free ——Heat transfer coefficient when the relative velocity between melt and water is small/W m ^-3 K ^-1

h _force ——the heat transfer coefficient when the relative speed difference between the melt and water is large/W m ^-3 K ^-1

h _rad ——radiative heat transfer coefficient/W m ^-3 K ^-1

σ——Boltzmann constant/W m ^-2 K ^-4

ε——coolant volume fraction

7) Heat transfer coefficient between melt and coolant under transition boiling conditions

The heat flux of the melt to water is assumed to be approximately an interpolation between the critical heat flux _qCHF and the minimum stable film boiling heat flux _qmin ; the interpolation formula applied is:

f ₁ =(3y ² -2y ³ ) (32)

It is assumed that the heat transfer coefficient of the melt to the steam can be approximated by interpolating between the critical heat flux heat transfer coefficient and the minimum stable film boiling heat transfer coefficient; the interpolation formula applied is:

h _mv ＝f ₁ h _mvCHF +(1-f ₁ )h _mvmin (35)

In the formula:

q _CHF ——Critical Heat Flux/W·m ^-2

q _min,rad ——minimum film boiling heat flux considering radiation heat transfer/W·m ^-2

q _min ——Minimum film boiling heat flux without considering radiation heat transfer/W·m ^-2

T _min ——Minimum stable film boiling temperature/K

h _mvCHF ——heat transfer coefficient between melt and steam at critical heat flux/W m ^-3 K ^-1

h _mvmin ——the heat transfer coefficient between the melt and steam when the melt temperature is equal to the minimum stable film boiling temperature/W m ^-3 K ^-1

Step 5: Determine whether the melt droplet is fragmented, and calculate the rate of change in diameter during the melt fragmentation process;

The fragmentation of the melt in the coolant is divided into two situations: (1) the coarse mixing fragmentation of the melt injected into the water due to hydraulic instability; (2) the fine fragmentation of the melt droplets by the thermodynamic action crack;

In the case of coarse mixing, the melt will be fragmented only if the following fragmentation criterion is met:

We represent the Weber number:

Ae ^* denotes the modified aeroelastic coefficient:

If it is determined that the melt will be fragmented under rough mixing conditions, the rate of change of melt diameter under coarse mixing is calculated using the fragmentation model of Pilch theory:

During the occurrence of fine fragmentation, the fragmentation mass change rate of the melt to be fragmented is calculated by the following formula:

In the formula:

v _r ——relative speed of melt and coolant/m·s ^-1

ρ _co ——average density of coolant/kg·m ^-3

ρ _m ——density of melt/kg·m ^-3

We - Weber number

We _cri ——Critical Weber number, take 4π

Ae——Corrected aeroelastic coefficient

Ae ^* _cri ——Critical corrected aeroelastic coefficient, take 8π ³

σ _m ——surface tension of melt/N·s ^-1

χ—Poisson’s ratio of the melt material

δ—thickness of the solidified shell on the surface of the melt droplet/m

E——Young's modulus after solidification of the melt/Pa

m _frag ——the amount of molten material that has been finely fragmented/kg

C _f —— fine fragmentation constant

m _i ——the amount of molten material in the control body/kg

P - control internal pressure

P _th ——threshold of fine fragmentation pressure/Pa

Step 6: Use the estimated stability method to solve the mass, momentum, and energy conservation equations, and save the data to the output file. If the set end time has not been reached, skip to step 2 to calculate the next time step. If it has reached the set the end time, stop calculation;

The thermal-hydraulic equation is solved by the pre-estimation calculation stability method. This method is mainly divided into three steps: (1) use the pressure of the previous time step to solve the momentum conservation equation to obtain the predicted value of the velocity; (2) express the predicted velocity as this The function of the time step pressure, and form a pressure equation system with the mass and energy conservation equations, which can be solved by pressure iteration to obtain the pressure, velocity, void fraction and temperature of this time step; (3) use this The mass and energy conservation equations are solved for the pressure of the time step to obtain the macroscopic density and internal energy of each phase, which are used as the corresponding quantities in the mass and energy conservation equations in the next time step. The stability of the steam explosion process can be properly improved by using the estimated stability method.

Using the multi-fluid Euler method in the cylindrical coordinate system, the interaction among the three phases of steam, water and melt is considered. The conservation equation for the i-th phase is shown in (41)~(43), j and k represent phase different from i;

Mass Conservation Equation:

Momentum Conservation Equation:

Energy Conservation Equation:

In the formula:

t——time/s

α _i ——volume fraction of phase i

ρ _i ——density of phase i/kg·m ^-3

——i相的速度/m·s^-1

——Velocity of phase i/m·s ^-1

Γ _ji —mass of phase j transformed into phase i in unit time and unit volume/kg m ^-3 s ^-1

Γ _ki —mass of phase k transformed into phase i per unit time and unit volume/kg m ^-3 s ^-1

Γ _s ——mass produced by the external mass source per unit time and unit volume/kg m ^-3 s ^-1

P——pressure/Pa

x——Indicates the other two phases different from phase i, that is, phase j or phase k

C _xi ——the coefficient of friction between phase x and phase i

——x相的速度/m·s^-1

——Velocity of phase x/m s ^-1

C _wi —coefficient of friction between phase i and the wall

——重力加速度/m·s^-2

——Gravity acceleration/m·s ^-2

u _i ——internal energy per unit mass of phase i/J·kg ^-1

H _ji ——The enthalpy change of phase j to phase i per unit mass/J kg ^-1

H _ki ——the enthalpy change of unit mass phase k to phase i/J kg ^-1

Q _ji ——The amount of heat transferred from phase j to phase i in unit time and unit volume/W·m ^-3

Q _ki ——the heat transferred from phase k to phase i in unit time and unit volume/W·m ^-3

Q _s ——the heat generated by the external heat source per unit time and unit volume/W·m ^-3 .

Claims (1)

1. A nuclear reactor steam explosion two-dimensional calculation method is characterized in that: comprise the following steps: Step 1. Determine the geometric structure of the nuclear reactor calculation area and the environmental pressure and temperature parameters under severe accidents, input the diameter, temperature and speed of the molten material jet, set the end time and initialize the parameters; Step 2: Calculate the physical properties of melt, water vapor and water according to the interpolation table of physical properties; Step 3: Calculate the momentum change between the melt, water, and steam due to interphase friction; During the interaction between the melt and water, there is interphase friction between the melt, water, and steam, and the momentum change between the discrete phase p and the continuous phase c due to interphase friction is expressed as:

In the formula: I _pc —momentum change between the discrete phase and the continuous phase due to interphase friction per unit time and unit volume/kg m ^-2 s ^-2 C _pc —coefficient of friction between the discrete phase and the continuous phase D _p ——diameter of discrete phase/m α _p ——volume fraction of discrete phase Cd _pc ——the resistance coefficient between the discrete phase and the continuous phase ρ _c ——continuous phase density/kg·m ^-3

——the relative vector velocity of continuous phase and discrete phase/m s ^-1 Re _c - the Reynolds number of the continuous phase Step 4: Calculate the heat transferred between the melt, water and steam; The heat transfer between steam and water occurs at the phase interface between steam and water. Assuming that the phase interface between steam and water is at the saturation temperature, the heat transferred by steam and water to the phase interface is: Q _vi ＝h _vi A _vl (T _v -T _sat ) (3) Q _li ＝h _li A _vl (T _l -T _sat ) (4) The heat transferred from the melt to steam and water is expressed as: Q _mv ＝h _mv A _mv (T _m -T _v ) (5) Q _ml ＝h _ml A _ml (T _m -T _l ) (6)

In the formula: Q _vi ——in unit time and unit volume, the heat transferred from steam to phase interface/W·m ^-3 Q _li ——the heat transferred from water to the phase interface in unit time and unit volume/W·m ^-3 Q _mv —— heat transfer from melt to steam in unit time and unit volume/W·m ^-3 Q _ml ——the heat transferred from melt to water in unit time and unit volume/W·m ^-3 h _vi ——heat transfer coefficient between steam and phase interface/W m ^-3 K ^-1 h _li ——heat transfer coefficient between water and phase interface/W m ^-3 K ^-1 h _mv ——Heat transfer coefficient between melt and steam/W m ^-3 K ^-1 h _ml ——Heat transfer coefficient between melt and water/W m ^-3 K ^-1 A _vl ——the heat transfer area of water and steam per unit volume/m ² ·m ^-3 A _mv ——heat transfer area of melt and steam per unit volume/m ² ·m ^-3 A _ml ——Heat transfer area between melt and water per unit volume/m ² ·m ^-3 T _v —— steam temperature/K T _l ——water temperature/K T _sat ——water saturation temperature/K T _m ——The temperature of the melt/K α _m ——The volume fraction of the melt α _v ——Volume fraction of steam α _l ——volume fraction of water D _m ——the diameter of the melt droplet/m S—water saturation, that is, the volume fraction of water in fluids other than melt According to different flow patterns and boiling methods, the calculation methods of interphase heat transfer coefficient and heat transfer area are also different, which can be divided into the following situations: 1) Heat transfer coefficient and heat transfer area between water and steam and phase interface under bubbly flow conditions h _vi =1000 (10)

In the formula: Nu _l - Nusselt number of water D _v ——diameter of bubbles in bubbly flow/m k _l ——The thermal conductivity of water/W m ^-1 K ^-1 Pr _l — Prandtl number of water Re _l - Reynolds number of water vol - the volume of the control body/m ^-3 2) Heat transfer coefficient and heat transfer area between water and steam and phase interface under the condition of diffuse flow

In the formula: Nu _v —— Nusselt number of steam D _l ——diameter of dispersed water droplet/m k _v ——heat transfer coefficient of steam/W m ^-1 K ^-1 Pr _v —— Prandtl number of steam Rev _- Reynolds number of steam ρ _l ——density of water/kg·m ^-3 Cp _l ——Specific heat of water/J kg ^-1 K ^-1

——The relative speed of water and steam/m·s ^-1 3) Heat transfer coefficient and heat transfer area between water and steam and phase interface under transitional flow conditions When the water saturation is in the range of 0.25 to 0.75, it is considered to be a transitional flow state; in this state, through the critical bubbly flow, that is, the water saturation S=0.75, and the critical diffuse flow, that is, the water saturation S= Perform linear interpolation between the values calculated at 0.25 to obtain the heat transfer coefficient and heat transfer area; h _vi ＝(1-f ₁ )h _vi,mist +f ₁ h _vi,bubbly (18) h _li ＝(1-f ₁ )h _li,mist +f ₁ h _li,bubbly (19) A _vl ＝(1-f ₁ )A _vl,mist +f ₁ A _vl,bubbly (20)

In the formula: h _vi,mist ——heat transfer coefficient between diffuse flow steam and phase interface/W m ^-3 K ^-1 h _vi,bubbly ——heat transfer coefficient between bubbly steam and phase interface/W m ^-3 K ^-1 h _li,mist ——heat transfer coefficient between dispersed flowing water and phase interface/W m ^-3 K ^-1 h _li,bubbly ——heat transfer coefficient between bubbly flowing water and phase interface/W m ^-3 K ^-1 A _vl,mist — heat transfer area of water and steam in diffuse flow state per unit volume/m ² ·m ^-3 A _vl,bubbly ——the heat transfer area of water and steam in bubbly flow state per unit volume/m ² ·m ^-3 4) Heat transfer coefficient between melt and coolant under convective conditions

Natural convection: Nu _nc ＝2.0+0.6Gr _co ^1/4 Pr _co ^1/3 (24) Forced convection:

In the formula: h _m,co ——Heat transfer coefficient between melt and coolant/W m ^-3 K ^-1 Nu _co — Nusselt number of coolant Nu _nc — Nusselt number of the coolant under natural convection conditions Nu _fc — Nusselt number of the coolant under forced convection conditions k _co ——Coefficient of thermal conductivity of coolant/W m ^-1 K ^-1 Gr _co - the Grashof number of the coolant Pr _co - the Prandtl number of the coolant Re _co - the Reynolds number of the coolant 5) Heat transfer coefficient between melt and coolant under nucleate boiling conditions Under nucleate boiling conditions, use Chen's formula to calculate the heat transfer coefficient between the melt and water; use the interpolation method to calculate the heat transfer coefficient between the melt and steam, so that the heat transfer coefficient between the melt and steam is at T _m = T _sat When T _m = T _CHF , it is the value of the heat transfer coefficient at the CHF point. When T _m is between T _sat and T _CHF , the heat transfer coefficient between the melt and the steam is calculated by interpolation: h _mv ＝(3y ² -2y ³ )h _mv,film (T _CHF ) (26)

In the formula: h _mv,film (T _CHF )——Heat transfer coefficient between melt and steam corresponding to CHF point when T _m =T _CHF /W·m ^-3 ·K ^-1 T _CHF ——melt temperature when critical heat flux occurs/K 6) Heat transfer coefficient between melt and coolant under film boiling conditions Under film boiling conditions, the heat transfer coefficient between the melt and water is calculated using the following formula: h _ml ＝max(h _free ,h _force )+h _rad (28) Use the Dhir-Purohit relation to calculate h _free , use the Epstein-Hauser relation to calculate h _force , and the radiation heat transfer coefficient h _rad between the melt and water is:

ε=α _v +α _l (30) In film boiling, the melt-to-vapor heat transfer coefficient is set to zero; In the formula: h _free ——Heat transfer coefficient when the relative velocity between melt and water is small/W m ^-3 K ^-1 h _force ——the heat transfer coefficient when the relative speed difference between the melt and water is large/W m ^-3 K ^-1 σ——Boltzmann constant/W m ^-2 K ^-4 ε——coolant volume fraction 7) Heat transfer coefficient between melt and coolant under transition boiling conditions The heat flux of the melt to water is assumed to be approximately an interpolation between the critical heat flux _qCHF and the minimum stable film boiling heat flux _qmin ; the interpolation formula applied is:

f ₁ =(3y ² -2y ³ ) (32)

It is assumed that the heat transfer coefficient of the melt to the steam can be approximated by interpolating between the critical heat flux heat transfer coefficient and the minimum stable film boiling heat transfer coefficient; the interpolation formula applied is: h _mv ＝f ₁ h _mvCHF +(1-f ₁ )h _mvmin (35) In the formula: q _CHF ——Critical Heat Flux/W·m ^-2 q _min,rad ——minimum film boiling heat flux considering radiation heat transfer/W·m ^-2 q _min ——Minimum film boiling heat flux without considering radiation heat transfer/W·m ^-2 T _min ——Minimum stable film boiling temperature/K h _mvCHF ——heat transfer coefficient between melt and steam at critical heat flux/W m ^-3 K ^-1 h _mvmin ——the heat transfer coefficient between the melt and steam when the melt temperature is equal to the minimum stable film boiling temperature/W m ^-3 K ^-1 Step 5: Determine whether the melt droplet is fragmented, and calculate the diameter change rate during the melt fragmentation process; The fragmentation of the melt in the coolant is divided into two situations: (1) the coarse mixing fragmentation of the melt injected into the water due to hydraulic instability; (2) the fine fragmentation of the melt droplets by the thermodynamic action crack; In the case of coarse mixing, the melt will be fragmented only if the following fragmentation criterion is satisfied:

Ae ^* denotes the modified aeroelastic coefficient:

Fragmentation Calculate the rate of change of melt diameter for coarse mixing using the fragmentation model of Pilch theory:

During the occurrence of fine fragmentation, the mass change rate of melt fragmentation is calculated by the following formula:

In the formula: v _r ——relative speed of melt and coolant/m·s ^-1 ρ _co ——average density of coolant/kg·m ^-3 ρ _m ——density of melt/kg·m ^-3 We - Weber number We _cri ——Critical Weber number, take 4π Ae——Corrected aeroelastic coefficient Ae ^* _cri ——Critical corrected aeroelastic coefficient, take 8π ³ σ _m ——surface tension of melt/N·s ^-1 χ—Poisson’s ratio of the melt material δ—thickness of the solidified shell on the surface of the melt droplet/m E——Young's modulus after solidification of the melt/Pa m _frag ——the amount of molten material that has been finely fragmented/kg C _f —— fine fragmentation constant m _i ——the amount of molten material in the control body/kg P——pressure/Pa P _th ——threshold of fine fragmentation pressure/Pa Step 6: Use the estimated stability method to solve the mass, momentum, and energy conservation equations, and save the data to the output file. If the set end time has not been reached, skip to step 2 to calculate the next time step. If it has reached the set the end time, stop calculation; The thermal-hydraulic equation is solved by the pre-estimation calculation stability method. This method is mainly divided into three steps: (1) use the pressure of the previous time step to solve the momentum conservation equation to obtain the predicted value of the velocity; (2) express the predicted velocity as this The function of the time step pressure, and form a pressure equation system with the mass and energy conservation equations, which can be solved by pressure iteration to obtain the pressure, velocity, void fraction and temperature of this time step; (3) use this Solve the mass and energy conservation equations for the pressure of the time step to obtain the macroscopic density and internal energy of each phase, which will be used as the corresponding quantities in the mass and energy conservation equations in the next time step; Using the multi-fluid Euler method in the cylindrical coordinate system, the interaction among the three phases of steam, water and melt is considered. The conservation equation for the i-th phase is shown in (41)~(43), j and k represent phase different from i; Mass Conservation Equation:

Momentum Conservation Equation:

Energy Conservation Equation:

In the formula: t——time/s α _i ——volume fraction of phase i ρ _i ——density of phase i/kg·m ^-3

——Velocity of phase i/m·s ^-1 Γ _ji —mass of phase j transformed into phase i in unit time and unit volume/kg m ^-3 s ^-1 Γ _ki —mass of phase k transformed into phase i per unit time and unit volume/kg m ^-3 s ^-1 Γ _s ——mass produced by the external mass source per unit time and unit volume/kg m ^-3 s ^-1 x——Indicates the other two phases different from phase i, that is, phase j or phase k C _xi ——the coefficient of friction between phase x and phase i

——Velocity of phase x/m s ^-1 C _wi —coefficient of friction between phase i and the wall

——Gravity acceleration/m·s ^-2 u _i ——internal energy per unit mass of phase i/J·kg ^-1 H _ji ——The enthalpy change of phase j to phase i per unit mass/J kg ^-1 H _ki ——the enthalpy change of unit mass phase k to phase i/J kg ^-1 Q _ji ——The amount of heat transferred from phase j to phase i in unit time and unit volume/W·m ^-3 Q _ki ——the heat transferred from phase k to phase i in unit time and unit volume/W·m ^-3 Q _s ——the heat generated by the external heat source per unit time and unit volume/W·m ^-3 .

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