阅读说明：本技术 一种锂冷核反应堆与斯特林发电机耦合传热特性分析方法 (Method for analyzing coupling heat transfer characteristics of lithium-cooled nuclear reactor and Stirling generator ) 是由 王成龙 金钊 张大林 苏光辉 田文喜 秋穗正 于 2021-09-13 设计创作，主要内容包括：一种锂冷核反应堆与斯特林发电机耦合传热特性分析方法,主要步骤如下：1、输入锂冷核反应堆以及斯特林发电机的结构、几何参数,确定堆芯燃料的功率分布和冷却剂的温度,输入反应堆堆芯流量及堆芯斯特林发电机冷端温度,设定计算时间；2、对核反应堆堆芯划分控制体并进行初始化计算；3、建立关于堆芯控制体的非线性微分方程,通过吉尔算法得到当前时刻堆芯控制体温度；4、计算当前时刻斯特林发电机换热量；5、根据所有已知条件,利用吉尔算法求解下一时刻的堆芯温度、压力等参数,循环计算直到达到设定时间。本发明的方法可以计算锂冷核反应堆与斯特林发电机耦合时的瞬态传热运行特性,为锂冷核反应堆与斯特林发电机的搭配设计提供建议与指导。(A method for analyzing the coupling heat transfer characteristics of a lithium-cooled nuclear reactor and a Stirling generator mainly comprises the following steps: 1. inputting the structural and geometric parameters of a lithium-cooled nuclear reactor and a Stirling generator, determining the power distribution of reactor core fuel and the temperature of a coolant, inputting the reactor core flow of the reactor and the cold end temperature of the Stirling generator of the reactor core, and setting calculation time; 2. dividing a control body for the reactor core of the nuclear reactor and carrying out initialization calculation; 3. establishing a nonlinear differential equation related to the reactor core control body, and obtaining the temperature of the reactor core control body at the current moment through a Gill algorithm; 4. calculating the heat exchange quantity of the Stirling generator at the current moment; 5. and (4) solving parameters such as the temperature, the pressure and the like of the reactor core at the next moment by utilizing a Gill algorithm according to all known conditions, and circularly calculating until the set time is reached. The method can calculate the transient heat transfer operating characteristics of the lithium-cooled nuclear reactor and the Stirling generator when the lithium-cooled nuclear reactor and the Stirling generator are coupled, and provides suggestions and guidance for matching design of the lithium-cooled nuclear reactor and the Stirling generator.)

1. A method for analyzing the coupling heat transfer characteristics of a lithium-cooled nuclear reactor and a Stirling generator is characterized by comprising the following steps: the method comprises the following steps:

step 1: inputting the structural and geometric parameters of a lithium-cooled nuclear reactor and a Stirling generator, determining the power distribution of reactor core fuel and the temperature of a coolant, inputting the reactor core flow of the reactor and the cold end temperature of the Stirling generator of the reactor core, and setting calculation time;

step 2: dividing a plurality of control bodies for the reactor core of the nuclear reactor along the radial direction and the axial direction, and setting the temperature and the pressure of each control body to be equal to the temperature and the pressure of a coolant at the initial moment;

and step 3: establishing a nonlinear differential equation related to the reactor core control body, and obtaining the temperature of the reactor core control body at the current moment through a Gill algorithm;

the reactor core of the lithium-cooled nuclear reactor consists of a fuel element and liquid lithium coolant, wherein the fuel element mainly consists of a fuel area, a fission gas gap and a fuel cladding;

firstly, solving reactor fission power by adopting a point reactor model dynamic equation considering six groups of delayed neutrons:

in the formula:

p (t) -time t reactor fission power/W;

t-calculating time/s;

Λ -middle offspring time/s;

beta-total effective delayed neutron fraction;

β_i-the ith group of delayed neutron contributions;

λ_i-decay constant/s of slow neutrons of group i^-1；

C_i(t) -concentration/m of slow-release neutrons in ith group at time t^-3；

n_c-number of delayed neutron bursts;

ρ (t) -Total reactivity/$;

the reactor fission power is obtained by calculating a point reactor model dynamic equation, and the reactor fission power is converted into a heat source in a control body:

Q_V,i-internal heat source/W.m of fuel control body i^-3；

P (t) -time t reactor fission power/W;

λ_P,i-inputting the power distribution coefficient of the ith control body

V_iControl volume/m of body i³；

The fuel pellet and cladding, air gap zone temperature change rates were calculated as follows:

in the formula:

ρ_Udensity of fuel pellets/kg m^-3；

c_USpecific heat of Fuel pellets/J.kg^-1·K^-1；

T_U-temperature/K of the fuel pellets;

λ_Uthermal conductivity of the fuel pellets/W.m^-1·K^-1；

r-radius of fuel pellet/m;

Q_V-fuel controlHeat source density/W.m of product^-3；

ρ_iThe density of the region i/kg m^-3；

c_iThe specific heat/J.kg of the region i^-1·K^-1；

T_i-temperature/K of zone i;

λ_i-thermal conductivity/W.m of area i^-1·K^-1；

r_i-radius/m of area i;

g₁envelope area

g₂-air gap region

Assuming that the flow of liquid lithium coolant within the core is an incompressible one-dimensional unidirectional flow, the control equation is as follows:

quality control equation:

the momentum control equation:

energy control equation:

in the formula:

rho-density of coolant/kg. m^-3

t-time/s

W-coolant flux/kg.s^-1

P-coolant pressure/Pa

f-coefficient of friction

A-coolant flow area/m²

h-specific enthalpy of CoolantJ·kg^-1

z-axial height of coolant/m

U-coolant heating circumference/m

D-hydraulic diameter of coolant/m

The equation sets (6) - (7) obtain the change rate of the reactor core flow along with time and space, and the equation (8) is solved to obtain the change of the reactor core fluid temperature along with time; solving the heat transfer equation sets (4), (5) and (8) of the reactor core of the lithium-cooled nuclear reactor by using a Gill algorithm to obtain the temperature distribution of the pellets, the cladding, the air gap and the fluid in the reactor core;

and 4, step 4: calculating the heat exchange quantity of the Stirling generator at the current moment;

the fluid of the reactor core flows through the hot end of the Stirling generator from the outlet of the reactor core and then flows into the inlet of the reactor core again, and the temperature of the hot end of the Stirling generator is the average temperature of the inlet and the outlet of the reactor core; the Stirling generator model comprises a Stirling generator cold and hot end wall surface, a gas working medium and a heat regenerator part; the following thermal balance equation is for the cold and hot end enclosure of the stirling generator:

in the formula:

T_Hcore outlet fluid temperature

T_CTemperature of Stirling Cold end

Π_In-hot end heat exchange perimeter

Π_In-cold end heat exchange perimeter

ρ_In-hot end cladding material density/kg · m^-3

ρ_Out-cold end cladding material density/kg m^-3

T_In-hot end cladding inner wall temperature/K

T_Out-CoolingEnd cladding inner wall temperature/K

T_fIs gas temperature/K

A_In-hot end cross-sectional area/m²

A_Out-hot end cross-sectional area/m²

λ_In-hot end material thermal conductivity/W.m^-1·K^-1

λ_Out-cold end material thermal conductivity/W.m^-1·K^-1

δ_In-thickness of hot end cladding wall surface/m

δ_Out-cold end cladding wall thickness/m

c_In-specific heat capacity/J.kg of hot end cladding material^-1·K^-1

c_Out-specific heat capacity/J.kg of cold end cladding material^-1·K^-1

η_STEfficiency of Stirling Generator

The heater, the cooler and the heat regenerator are in limited temperature difference heat transfer, have similar control equations, and the circulating heat exchange quantity is as follows:

Q＝hA_w(T_w-T_g)(1/n) (11)

in the formula:

q-quantity of circulating Heat exchange/W

h-average heat exchange coefficient/W.m of working medium and wall surface^-2·K^-1

T_wTemperature of inner wall surface/K

T_gTemperature of gas/K

n-crankshaft speed/r.s^-1

For an actual Stirling generator heat regenerator, certain heat regeneration loss exists, and the effectiveness epsilon is defined and is the ratio of actual circulating heat quantity to ideal circulating heat quantity; the heat capacity flow rate of the cold and hot fluid of the heat regenerator part is the same, if neglecting the heat conduction resistance of the heat regenerator, then there are:

in the formula:

A_wg-heat transfer area/m²

c_pWorking medium heat capacity/J.kg^-1·K^-1

A-free flow area of working medium/m²

St-Stenton number, St 0.46Re for working helium^-0.4Pr^-1。

The axial heat loss of the regenerator can be calculated by:

in the formula:

Q_lossaxial heat loss/W

λ_r-heat conductivity coefficient/W.m at regenerator shell^-1·K^-1

A_r-regenerator cross-sectional area/m²

l_rAs regenerator length/m

T_h-average temperature of hot side of regenerator/K

T_c-average temperature of regenerator cold side/K

n-crankshaft speed/r.s^-1

Through the solving of the formulas (11) to (13), the actual heat exchange quantity of the Stirling generator at the current moment is obtained:

Q_ac＝Q·ε-Q_loss (14)

in the formula:

epsilon-degree of effectiveness

Q-quantity of circulating Heat exchange/W

Q_lossAxial heat loss/W

Q_ac-actual heat exchange quantity/W

And 5: and (4) solving parameters such as the temperature and the pressure of the reactor core at the next moment by using a Gill algorithm, and circularly calculating until the set time is reached.

Technical Field

The invention relates to the heat exchange technology in the field of nuclear reactors, in particular to a method for analyzing the coupling heat transfer characteristics of a lithium-cooled nuclear reactor and a Stirling generator.

Background

At present, dynamic energy conversion such as stirling cycle, brayton cycle, etc. has become the main energy conversion mode adopted by the design of high-power space nuclear reactors due to its high conversion efficiency. The Stirling cycle is combined with liquid metal lithium to cool the reactor, so that hundreds of kilowatts of power output can be realized, and the method is one of feasible design schemes of large space reactors. In order to determine the influence of transient heat transfer characteristics of the lithium-cooled reactor coupled Stirling generator in a complex universe environment, a reactor core thermal hydraulic model and a Stirling generator system heat exchange model are established, so that a basis is provided for more comprehensively and effectively evaluating the safe operation characteristics of the Stirling generator coupled lithium-cooled reactor system in the complex universe environment.

Disclosure of Invention

In order to overcome the problems in the prior art, the invention aims to provide a method for analyzing the coupling heat transfer characteristics of a lithium-cooled nuclear reactor and a stirling generator, which can accurately reflect the operating characteristics of a system, can realize the calculation of space lithium-cooled nuclear power supply systems with different structures and powers, including a reactor core and the stirling generator, reduce the requirements on the structures and parameters of the space lithium-cooled nuclear power supply, and effectively increase the adaptability of the method to different problems.

In order to achieve the purpose, the invention adopts the following technical scheme:

a method for analyzing the heat transfer characteristics of a lithium-cooled nuclear reactor and a Stirling generator in a coupling mode comprises the following steps:

step 1: inputting the structural and geometric parameters of a lithium-cooled nuclear reactor and a Stirling generator, determining the power distribution of reactor core fuel and the temperature of a coolant, inputting the reactor core flow of the reactor and the cold end temperature of the Stirling generator of the reactor core, and setting calculation time;

step 2: dividing a plurality of control bodies for the reactor core of the nuclear reactor along the radial direction and the axial direction, and setting the temperature and the pressure of each control body at the initial moment;

and step 3: establishing a nonlinear differential equation related to the reactor core control body, and obtaining the temperature of the reactor core control body at the current moment through a Gill algorithm;

the reactor core of the lithium-cooled nuclear reactor consists of a fuel element and liquid lithium coolant, wherein the fuel element mainly consists of a fuel area, a fission gas gap and a fuel cladding;

firstly, solving reactor fission power by adopting a point reactor model dynamic equation considering six groups of delayed neutrons:

in the formula:

p (t) -time t reactor fission power/W;

t-calculating time/s;

Λ -middle offspring time/s;

beta-total effective delayed neutron fraction;

β_i-the ith group of delayed neutron contributions;

λ_i-decay constant/s of slow neutrons of group i^-1；

C_i(t) -concentration/m of slow-release neutrons in ith group at time t^-3；

n_c-number of delayed neutron bursts;

ρ (t) -Total reactivity/$;

the reactor fission power is obtained by calculating a point reactor model dynamic equation, and the reactor fission power is converted into a heat source in a control body:

Q_V,i-internal heat source/W.m of fuel control body i^-3；

P (t) -time t reactor fission power/W;

λ_P,i-inputting the power distribution coefficient of the ith control body

V_iControl volume/m of body i³；

The fuel pellet and cladding, air gap zone temperature change rates were calculated as follows:

in the formula:

ρ_Udensity of fuel pellets/kg m^-3；

c_USpecific heat of Fuel pellets/J.kg^-1·K^-1；

T_U-temperature/K of the fuel pellets;

λ_Uthermal conductivity of the fuel pellets/W.m^-1·K^-1；

r-radius of fuel pellet/m;

Q_V-heat source density/W.m of fuel control body^-3；

ρ_iThe density of the region i/kg m^-3；

c_iThe specific heat/J.kg of the region i^-1·K^-1；

T_i-temperature/K of zone i;

λ_i-thermal conductivity/W.m of area i^-1·K^-1；

r_i-radius/m of area i;

g₁envelope area

g₂-air gap region

Assuming that the flow of liquid lithium coolant within the core is an incompressible one-dimensional unidirectional flow, the control equation is as follows:

quality control equation:

the momentum control equation:

energy control equation:

in the formula:

rho-density of coolant/kg. m^-3

t-time/s

W-coolant flux/kg.s^-1

P-coolant pressure/Pa

f-coefficient of friction

A-coolant flow area/m²

h-specific enthalpy of coolant/J.kg^-1

z-axial height of coolant/m

U-coolant heating circumference/m

D-hydraulic diameter of coolant/m

The equation sets (6) - (7) obtain the change rate of the reactor core flow along with time and space, and the equation (8) is solved to obtain the change of the reactor core fluid temperature along with time; solving the heat transfer equation groups (4), (5) and (8) of the reactor core of the lithium-cooled nuclear reactor by using a Gill algorithm to obtain the temperature distribution of the pellets, the cladding, the air gap and the fluid in the reactor core;

and 4, step 4: calculating the heat exchange quantity of the Stirling generator at the current moment;

after flowing through the hot end of the Stirling generator from the outlet of the reactor core, the fluid of the reactor core flows into the inlet of the reactor core again, and the temperature of the hot end of the Stirling generator is the average temperature of the inlet and the outlet of the reactor core; the Stirling generator model comprises a cold and hot end wall surface of the Stirling generator, a gas working medium and a heat regenerator part; the following heat balance equation is provided for the cold and hot end cladding of the Stirling generator:

in the formula:

T_Hcore outlet fluid temperature

T_CTemperature of Stirling Cold end

Π_In-hot end heat exchange perimeter

Π_In-cold end heat exchange perimeter

ρ_In-hot end cladding material density/kg · m^-3

ρ_Out-cold end cladding material density/kg m^-3

T_In-hot end cladding inner wall temperature/K

T_Out-cold end cladding inner wall temperature/K

T_fIs gas temperature/K

A_In-hot end cross-sectional area/m²

A_Out-hot end cross-sectional area/m²

λ_In-hot end material thermal conductivity/W.m^-1·K^-1

λ_Out-cold end material thermal conductivity/W.m^-1·K^-1

δ_In-thickness of hot end cladding wall surface/m

δ_Out-cold end cladding wall thickness/m

c_In-specific heat capacity/J.kg of hot end cladding material^-1·K^-1

c_Out-specific heat capacity/J.kg of cold end cladding material^-1·K^-1

η_STEfficiency of Stirling Generator

The heater, the cooler and the heat regenerator are in limited temperature difference heat transfer, have similar control equations, and the circulating heat transfer capacity is as follows:

Q＝hA_w(T_w-T_g)(1/n) (11)

in the formula:

q-quantity of circulating Heat exchange/W

h-average heat exchange coefficient/W.m of working medium and wall surface^-2·K^-1

T_wTemperature of inner wall surface/K

T_gTemperature of gas/K

n-crankshaft speed/r.s^-1

For an actual Stirling generator heat regenerator, certain heat regeneration loss exists, and the effectiveness epsilon is defined and is the ratio of actual circulating heat quantity to ideal circulating heat quantity; the heat capacity flow rate of the cold and hot fluid of the heat regenerator part is the same, if neglecting the heat conduction resistance of the heat regenerator, then there are:

in the formula:

A_wg-heat transfer area/m²

c_pWorking medium heat capacity/J.kg^-1·K^-1

A-free flow area of working medium/m²

St-Stenton number, St 0.46Re for working helium^-0.4Pr^-1。

The axial heat loss of the regenerator can be calculated by:

in the formula:

Q_lossaxial heat loss/W

λ_r-heat conductivity coefficient/W.m at regenerator shell^-1·K^-1

A_r-regenerator cross-sectional area/m²

l_rAs regenerator length/m

T_h-average temperature of hot side of regenerator/K

T_c-average temperature of regenerator cold side/K

n-crankshaft speed/r.s^-1

Through the solving of the formulas (11) to (13), the actual heat exchange quantity of the Stirling generator at the current moment is obtained:

Q_ac＝Q·ε-Q_loss (14)

in the formula:

epsilon-degree of effectiveness

Q-quantity of circulating Heat exchange/W

Q_lossAxial heat loss/W

Q_ac-actual heat exchange quantity/W

And 5: and (4) solving parameters such as the temperature, the pressure and the like of the reactor core at the next moment by utilizing a Gill algorithm according to all known conditions, and circularly calculating until the set time is reached. Compared with the prior art, the invention has the following outstanding characteristics:

the system for coupling the lithium-cooled nuclear reactor and the Stirling generator is researched, the whole temperature distribution of the system can be accurately calculated, the system safety analysis of the lithium-cooled nuclear reactor and the Stirling generator with different structures and powers can be realized, the heat transfer calculation of the reactor core and the Stirling generator is included, the requirements on the structure and parameters of the lithium-cooled nuclear reactor are reduced, and the adaptability of the method to different problems is effectively improved. The method can calculate the transient heat transfer characteristic of the coupling of the general lithium-cooled nuclear reactor and the Stirling generator, and provides a research method for an operation strategy, an electric system control scheme and the like during the transient operation of the system.

Drawings

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

Detailed Description

The invention is described in further detail below with reference to the following figures and detailed description:

the invention relates to a method for analyzing the coupling heat transfer characteristics of a lithium-cooled nuclear reactor and a Stirling generator. As shown in fig. 1, the specific process of the method includes the following steps:

step 1: inputting the structural and geometric parameters of a lithium-cooled nuclear reactor and a Stirling generator, determining the power distribution of reactor core fuel and the temperature of a coolant, inputting the reactor core flow of the reactor and the cold end temperature of the Stirling generator of the reactor core, and setting calculation time;

the lithium-cooled reactor is a reactor using liquid lithium as a coolant, and the Stirling generator can realize dynamic energy conversion for converting reactor heat energy into electric energy. The geometric and structural parameters of the lithium-cooled nuclear reactor and the Stirling generator in the step 1 are set, and the coupling heat transfer calculation of the lithium-cooled nuclear reactor and the Stirling generator with different geometric structures can be realized through the steps 2 to 5.

Step 2: dividing a plurality of control bodies for the reactor core of the nuclear reactor along the radial direction and the axial direction, and setting the temperature and the pressure of each control body at the initial moment;

the number of the control bodies can be set at will, the number of the control bodies is increased, the calculation precision can be increased, and the temperature and pressure of each control body of the reactor core at the initial moment are consistent with the parameters of the initially input coolant.

And step 3: establishing a nonlinear differential equation related to the reactor core control body, and obtaining the temperature of the reactor core control body at the current moment through a Gill algorithm;

the reactor core of the lithium-cooled nuclear reactor consists of a fuel element and liquid lithium coolant, wherein the fuel element mainly consists of a fuel area, a fission gas gap and a fuel cladding; the heat transfer calculation flow for the core comprises the steps of determining the fuel element power generation, the fuel element heat conduction and the liquid lithium coolant flowing heat transfer process.

Firstly, solving reactor fission power by adopting a point reactor model dynamic equation considering six groups of delayed neutrons:

in the formula:

p (t) -time t reactor fission power/W;

t-calculating time/s;

Λ -middle offspring time/s;

beta-total effective delayed neutron fraction;

β_i-the ith group of delayed neutron contributions;

λ_i-decay constant/s of slow neutrons of group i^-1；

C_i(t) -concentration/m of slow-release neutrons in ith group at time t^-3；

n_c-number of delayed neutron bursts;

ρ (t) -Total reactivity/$;

the reactor core fission power is obtained by calculating the point reactor model dynamic equation, and the fission power is converted into a heat source in the control body:

Q_V,i-internal heat source/W.m of fuel control body i^-3；

P (t) -time t reactor fission power/W;

λ_P,i-inputting the power distribution coefficient of the ith control body

V_iControl volume/m of body i³；

The fuel pellet and cladding, air gap zone temperature change rates were calculated as follows:

in the formula:

ρ_Udensity of fuel pellets/kg m^-3；

c_USpecific heat of Fuel pellets/J.kg^-1·K^-1；

T_U-temperature/K of the fuel pellets;

λ_Uthermal conductivity of the fuel pellets/W.m^-1·K^-1；

r-radius of fuel pellet/m;

Q_V-heat source density/W.m of fuel control body^-3；

ρ_iThe density of the region i/kg m^-3；

c_iThe specific heat/J.kg of the region i^-1·K^-1；

T_i-temperature/K of zone i;

λ_i-thermal conductivity/W.m of area i^-1·K^-1；

r_i-radius/m of area i;

g₁envelope area

g₂-air gap region

Assuming that the flow of liquid lithium coolant within the core is an incompressible one-dimensional unidirectional flow, the control equation is as follows:

quality control equation:

the momentum control equation:

energy control equation:

in the formula:

rho-density of coolant/kg. m^-3

t-time/s

W-coolant flux/kg.s^-1

P-coolant pressure/Pa

f-coefficient of friction

A-coolant flow area/m²

h-specific enthalpy of coolant/J.kg^-1

z-axial height of coolant/m

U-coolant heating circumference/m

D-hydraulic diameter of coolant/m

The equation sets (6) - (7) obtain the change rate of the reactor core flow along with time and space, and the equation (8) is solved to obtain the change of the reactor core fluid temperature along with time; solving the heat transfer equation groups (4), (5) and (8) of the reactor core of the lithium-cooled nuclear reactor by using a Gill algorithm to obtain the temperature distribution of the pellets, the cladding, the air gap and the fluid in the reactor core;

and 4, step 4: calculating the heat exchange quantity of the Stirling generator at the current moment;

after flowing through the hot end of the Stirling generator from the outlet of the reactor core, the fluid of the reactor core flows into the inlet of the reactor core again, and the temperature of the hot end of the Stirling generator is the average temperature of the inlet and the outlet of the reactor core; the Stirling generator model comprises a cold and hot end wall surface of the Stirling generator, a gas working medium and a heat regenerator part; the following heat balance equation is provided for the cold and hot end cladding of the Stirling generator:

in the formula:

T_Hcore outlet fluid temperature

T_CTemperature of Stirling Cold end

Π_In-hot end heat exchange perimeter

Π_In-cold end heat exchange perimeter

ρ_In-hot end cladding material density/kg · m^-3

ρ_Out-cold end cladding material density/kg m^-3

T_In-hot end cladding inner wall temperature/K

T_Out-cold end cladding inner wall temperature/K

T_fIs gas temperature/K

A_In-hot end cross-sectional area/m²

A_Out-hot end cross-sectional area/m²

λ_In-hot end material thermal conductivity/W.m^-1·K^-1

λ_Out-cold end material thermal conductivity/W.m^-1·K^-1

δ_In-thickness of hot end cladding wall surface/m

δ_Out-cold end cladding wall thickness/m

c_In-specific heat capacity/J.kg of hot end cladding material^-1·K^-1

c_Out-specific heat capacity/J.kg of cold end cladding material^-1·K^-1

η_STEfficiency of Stirling Generator

The heater, the cooler and the heat regenerator are in limited temperature difference heat transfer, have similar control equations, and the circulating heat transfer capacity is as follows:

Q＝hA_w(T_w-T_g)(1/n) (25)

in the formula:

q-quantity of circulating Heat exchange/W

h-average heat exchange coefficient/W.m of working medium and wall surface^-2·K^-1

T_wTemperature of inner wall surface/K

T_gTemperature of gas/K

n-crankshaft speed/r.s^-1

For an actual Stirling generator heat regenerator, certain heat regeneration loss exists, and the effectiveness epsilon is defined and is the ratio of actual circulating heat quantity to ideal circulating heat quantity; the heat capacity flow rate of the cold and hot fluid of the heat regenerator part is the same, if neglecting the heat conduction resistance of the heat regenerator, then there are:

in the formula:

A_wg-heat transfer area/m²

c_pWorking medium heat capacity/J.kg^-1·K^-1

A-free flow surface of working mediumProduct/m²

St-Stenton number, St 0.46Re for working helium^-0.4Pr^-1。

The axial heat loss of the regenerator can be calculated by:

in the formula:

Q_lossaxial heat loss/W

λ_r-heat conductivity coefficient/W.m at regenerator shell^-1·K^-1

A_r-regenerator cross-sectional area/m²

l_rAs regenerator length/m

T_h-average temperature of hot side of regenerator/K

T_c-average temperature of regenerator cold side/K

n-crankshaft speed/r.s^-1

Through the solving of the formulas (11) to (13), the actual heat exchange quantity of the Stirling generator at the current moment is obtained:

Q_ac＝Q·ε-Q_loss (28)

in the formula:

epsilon-degree of effectiveness

Q-quantity of circulating Heat exchange/W

Q_lossAxial heat loss/W

Q_ac-actual heat exchange quantity/W

And 5: and (4) solving parameters such as the temperature, the pressure and the like of the reactor core at the next moment by utilizing a Gill algorithm according to all known conditions, and circularly calculating until the set time is reached.

The steps 1-5 can accurately calculate the heat transfer process from the reactor core to the Stirling generator, obtain the actual heat exchange quantity of the reactor core and the Stirling generator, and calculate the real-time temperature of each control body of the reactor core or the Stirling generator at different moments.