CN116662721B - COMSOL-based heat pipe cooling reactor nuclear thermoelectric internal coupling numerical calculation method - Google Patents
COMSOL-based heat pipe cooling reactor nuclear thermoelectric internal coupling numerical calculation method Download PDFInfo
- Publication number
- CN116662721B CN116662721B CN202310727195.9A CN202310727195A CN116662721B CN 116662721 B CN116662721 B CN 116662721B CN 202310727195 A CN202310727195 A CN 202310727195A CN 116662721 B CN116662721 B CN 116662721B
- Authority
- CN
- China
- Prior art keywords
- heat pipe
- heat
- temperature
- section
- thermoelectric
- Prior art date
- Legal status (The legal status is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the status listed.)
- Active
Links
- 238000001816 cooling Methods 0.000 title claims abstract description 43
- 238000010168 coupling process Methods 0.000 title claims abstract description 40
- 238000005859 coupling reaction Methods 0.000 title claims abstract description 40
- 238000004364 calculation method Methods 0.000 title claims abstract description 36
- 230000008878 coupling Effects 0.000 title claims abstract description 33
- 238000006243 chemical reaction Methods 0.000 claims abstract description 15
- 239000007787 solid Substances 0.000 claims abstract description 8
- 238000009792 diffusion process Methods 0.000 claims abstract description 7
- 230000009257 reactivity Effects 0.000 claims abstract description 7
- 238000000034 method Methods 0.000 claims description 53
- 239000000463 material Substances 0.000 claims description 27
- 239000011159 matrix material Substances 0.000 claims description 18
- 238000001704 evaporation Methods 0.000 claims description 12
- 230000008020 evaporation Effects 0.000 claims description 12
- 230000008569 process Effects 0.000 claims description 12
- 239000000498 cooling water Substances 0.000 claims description 11
- 230000008859 change Effects 0.000 claims description 9
- 230000004907 flux Effects 0.000 claims description 9
- 239000007788 liquid Substances 0.000 claims description 9
- 238000009833 condensation Methods 0.000 claims description 6
- 230000005494 condensation Effects 0.000 claims description 6
- 239000000446 fuel Substances 0.000 claims description 6
- 238000004519 manufacturing process Methods 0.000 claims description 6
- 230000035755 proliferation Effects 0.000 claims description 5
- 238000010521 absorption reaction Methods 0.000 claims description 3
- 229910052797 bismuth Inorganic materials 0.000 claims description 3
- JCXGWMGPZLAOME-UHFFFAOYSA-N bismuth atom Chemical group [Bi] JCXGWMGPZLAOME-UHFFFAOYSA-N 0.000 claims description 3
- 229910001291 heusler alloy Inorganic materials 0.000 claims description 3
- 230000000704 physical effect Effects 0.000 claims description 3
- XSOKHXFFCGXDJZ-UHFFFAOYSA-N telluride(2-) Chemical compound [Te-2] XSOKHXFFCGXDJZ-UHFFFAOYSA-N 0.000 claims description 3
- 238000009834 vaporization Methods 0.000 claims description 3
- 230000008016 vaporization Effects 0.000 claims description 3
- 230000005611 electricity Effects 0.000 claims 2
- 230000005619 thermoelectricity Effects 0.000 abstract 2
- 238000010586 diagram Methods 0.000 description 4
- 238000011160 research Methods 0.000 description 2
- 230000003068 static effect Effects 0.000 description 2
- 229910018989 CoSb Inorganic materials 0.000 description 1
- 239000006185 dispersion Substances 0.000 description 1
- 230000005684 electric field Effects 0.000 description 1
- XLYOFNOQVPJJNP-UHFFFAOYSA-N water Substances O XLYOFNOQVPJJNP-UHFFFAOYSA-N 0.000 description 1
Classifications
-
- G—PHYSICS
- G06—COMPUTING; CALCULATING OR COUNTING
- G06F—ELECTRIC DIGITAL DATA PROCESSING
- G06F17/00—Digital computing or data processing equipment or methods, specially adapted for specific functions
- G06F17/10—Complex mathematical operations
- G06F17/11—Complex mathematical operations for solving equations, e.g. nonlinear equations, general mathematical optimization problems
- G06F17/12—Simultaneous equations, e.g. systems of linear equations
-
- G—PHYSICS
- G06—COMPUTING; CALCULATING OR COUNTING
- G06F—ELECTRIC DIGITAL DATA PROCESSING
- G06F30/00—Computer-aided design [CAD]
- G06F30/20—Design optimisation, verification or simulation
-
- G—PHYSICS
- G06—COMPUTING; CALCULATING OR COUNTING
- G06F—ELECTRIC DIGITAL DATA PROCESSING
- G06F2111/00—Details relating to CAD techniques
- G06F2111/10—Numerical modelling
-
- G—PHYSICS
- G06—COMPUTING; CALCULATING OR COUNTING
- G06F—ELECTRIC DIGITAL DATA PROCESSING
- G06F2119/00—Details relating to the type or aim of the analysis or the optimisation
- G06F2119/08—Thermal analysis or thermal optimisation
-
- Y—GENERAL TAGGING OF NEW TECHNOLOGICAL DEVELOPMENTS; GENERAL TAGGING OF CROSS-SECTIONAL TECHNOLOGIES SPANNING OVER SEVERAL SECTIONS OF THE IPC; TECHNICAL SUBJECTS COVERED BY FORMER USPC CROSS-REFERENCE ART COLLECTIONS [XRACs] AND DIGESTS
- Y02—TECHNOLOGIES OR APPLICATIONS FOR MITIGATION OR ADAPTATION AGAINST CLIMATE CHANGE
- Y02E—REDUCTION OF GREENHOUSE GAS [GHG] EMISSIONS, RELATED TO ENERGY GENERATION, TRANSMISSION OR DISTRIBUTION
- Y02E30/00—Energy generation of nuclear origin
- Y02E30/30—Nuclear fission reactors
Landscapes
- Engineering & Computer Science (AREA)
- Physics & Mathematics (AREA)
- General Physics & Mathematics (AREA)
- Mathematical Physics (AREA)
- Theoretical Computer Science (AREA)
- Computational Mathematics (AREA)
- Mathematical Analysis (AREA)
- Mathematical Optimization (AREA)
- Pure & Applied Mathematics (AREA)
- General Engineering & Computer Science (AREA)
- Data Mining & Analysis (AREA)
- Operations Research (AREA)
- Software Systems (AREA)
- Databases & Information Systems (AREA)
- Algebra (AREA)
- Computer Hardware Design (AREA)
- Evolutionary Computation (AREA)
- Geometry (AREA)
- Monitoring And Testing Of Nuclear Reactors (AREA)
Abstract
The invention discloses a calculation method of a thermoelectricity internal coupling value of a heat pipe cooling reactor core based on COMSOL, which comprises the steps that a calculation object structure comprises a heat pipe reactor core, a high-temperature heat pipe and a three-section type thermoelectric generator, a neutron diffusion model is firstly built in a COMSOL platform, then a solid heat transfer model of the reactor core, the high-temperature heat pipe and the three-section type thermoelectric generator is built, a current model is introduced, a thermoelectricity multiple physical field is formed, an internal coupling calculation model is built based on a direct solving algorithm and a characteristic value solver of the COMSOL platform, and finally the reactivity and the power distribution of the heat pipe reactor are obtained; temperature distribution of the high-temperature heat pipe; power output and thermoelectric conversion efficiency of the three-stage thermoelectric generator. The patent provides a complete and effective heat pipe cooling reactor nuclear thermoelectric internal coupling numerical calculation method, provides a direct calculation method and a numerical result for the energy conversion efficiency of the heat pipe reactor, greatly reduces the design cost and improves the design efficiency of the heat pipe reactor.
Description
Technical Field
The invention belongs to the field of heat pipe cooling reactors, and relates to a heat pipe cooling reactor nuclear thermoelectric in-coupling numerical calculation method based on a COMSOL platform.
Background
As a nuclear reactor which is recently developed, a heat pipe cooling reactor (heat pipe reactor) has the advantages of simple structure, no single point of failure, high intrinsic safety, and the like. The power system of the heat pipe stack is classified into dynamic conversion and static conversion, and the thermoelectric generator is representative of the static conversion system. The thermoelectric generator can directly convert heat energy into electric energy without the help of other equipment, and therefore, the thermoelectric generator has the advantages of high reliability, full solid state, simple structure, no noise and the like. However, the conventional thermoelectric generator generally has the disadvantage of low thermoelectric conversion efficiency. The use of a segmented thermoelectric generator is also a good solution. The sectional thermoelectric generator is to splice thermoelectric materials (two or three) with optimal performance in different temperature ranges. By using the method, the sectional thermoelectric generator can obtain larger average thermoelectric conversion efficiency in a wider temperature range.
In this context, research on three-stage thermoelectric generators in a heat pipe stack has attracted considerable attention in recent years, but detailed calculations for the entire heat pipe stack system have not been sufficiently validated. To obtain the thermoelectric properties of a heat pipe stack system, detailed modeling of the thermoelectric generator is necessary. However, the three-stage thermoelectric generator has a complex structure, and many researches use an outcoupling mode to calculate thermoelectric characteristics. However, this method lacks feedback of the electric field affecting the temperature field, and lacks integrity in the calculation of the thermoelectric properties.
Disclosure of Invention
In order to solve the problems, on the premise of realizing calculation accuracy, the invention ensures the economical efficiency and high efficiency of calculation, and aims to provide a heat pipe cooling reactor nuclear thermoelectric internal coupling numerical calculation method based on a COMSOL platform.
In order to achieve the above purpose, the technical scheme adopted by the invention is as follows:
a calculation method for the thermoelectric in-coupling value of a heat pipe cooling reactor core based on COMSOL is characterized by comprising the following steps: according to a direct solving algorithm and a eigenvalue solver of the COMSOL platform, a nuclear thermoelectric internal coupling calculation model is established, and finally the reactivity, the power distribution, the temperature distribution of a high-temperature heat pipe, the power output and the thermoelectric conversion efficiency of a three-section thermoelectric generator of the heat pipe cooling reactor are obtained;
the structure of the heat exchanger of the calculation object comprises a fuel rod 1, a heat pipe cooling reactor matrix 2, a high-temperature heat pipe 3, a thermoelectric generator mounting platform 4, a three-section thermoelectric generator 5 and a cooling water plate 6; the fuel rod 1 is arranged in the heat pipe cooling reactor matrix 2, the heat pipe reactor matrix 2 and the thermoelectric generator mounting platform 4 are connected together through the high-temperature heat pipe 3, the three-section thermoelectric generator 5 is arranged on the surface of the thermoelectric generator mounting platform 4, and the cooling water plate 6 is arranged on the surface of the three-section thermoelectric generator 5;
in performing the calculations, the following parameters need to be known or can be obtained initially: selected structural materials and physical properties of the heat pipe cooling reactor, the high-temperature heat pipe and the three-section type thermoelectric generator, and design temperature T of the cooling water plate cold Group constant G of heat pipe cooled reactor constant ；
The numerical value calculation method specifically comprises the following steps:
step 1, establishing a neutron diffusion model of a heat pipe cooling reactor in a COMSOL platform: given the group constants of a heat pipe cooled reactor, the following set of equations is established:
wherein, the subscript is 1, which is a fast neutron energy group; subscript 2 is the slow neutron energy group; d is a diffusion coefficient; sigma and method for producing the same a Is a macroscopic absorption cross section; v Σ f Is a macroscopic scattering cross section; sigma and method for producing the same 1→2 A scattering cross section from fast neutrons to slow neutrons; k (k) eff Is the effective proliferation coefficient of the reactor; d, Σ, νΣ f Together, these variables are collectively referred to as the group constant G constant The method comprises the steps of carrying out a first treatment on the surface of the Is neutron flux distribution, which is also the power distribution of the heat pipe cooling reactor;calculating the available neutron flux distribution in the COMSOL by using a eigenvalue solver and a direct solver, so as to obtain power distribution;
step 2, constructing a solid heat transfer model of a heat pipe cooling reactor core, a high-temperature heat pipe and a three-section thermoelectric generator in the COMSOL, coupling the power distribution obtained in the step 1 into the model, and simultaneously coupling the design temperature T of a cooling water plate cold Inputting a model to serve as a constant temperature cooling condition of the whole model;
the general solid heat transfer model is suitable for a heat pipe reactor core and a three-section type thermoelectric generator, and the equation is as follows:
wherein ρ is the density of the material; c (C) p Is the constant pressure heat capacity of the material; k is the thermal conductivity of the material; q is the heat flow calculated in the process of obtaining, and T is the temperature of the calculated value to be obtained;representing the change in temperature with time;
the heat transfer model of the high-temperature heat pipe is a thermal resistance network model and uses thermal resistance R 1 The form of (2) represents the heat loss of the heat pipe in the heat transfer process, and the final temperature distribution is obtained, and an equation set is established as follows:
wherein: d, d o Is the outer diameter of the pipe wall of the heat pipe; d, d i Is the inner diameter of the pipe wall of the heat pipe; lambda (lambda) w Is the heat conductivity of the pipe wall material of the heat pipe; l (L) 1 The length of the evaporation section of the heat pipe;
radial heat conduction of wick at evaporation section of heat pipe and thermal resistance R of radial heat conduction 2 The method comprises the following steps:
wherein: d, d v The diameter of the air cavity in the heat pipe; lambda (lambda) e Equivalent thermal conductivity is related to the thermal conductivity of the wick material and the working medium;
radial heat conduction of wick at condensation section of heat pipe and thermal resistance R of radial heat conduction 3 The method comprises the following steps:
wherein L is 2 The length of the condensing section of the heat pipe;
radial heat conduction and thermal resistance R of tube wall of evaporation section of heat tube 4 The method comprises the following steps:
phase change heat transfer of gas-liquid interface of evaporation section of heat pipe and thermal resistance R thereof 5 The method comprises the following steps:
wherein: r is a gas constant; t (T) v Is the vapor temperature; r is the latent heat of vaporization; p is p v Is the vapor pressure;
vapor axial flow heat transfer and thermal resistance R thereof 6 The method comprises the following steps:
wherein: l (L) e Is the effective length of the heat pipe; mu (mu) v Is the kinetic viscosity coefficient of the vapor; ρ v Is vapor density;
phase change heat transfer of gas-liquid interface of condensation section of heat pipe and thermal resistance R thereof 7 The method comprises the following steps:
axial heat conduction of heat pipe liquid suction core and heat resistance R thereof 8 The method comprises the following steps:
wherein L is the length of the heat pipe;
axial heat conduction of heat pipe wall and thermal resistance R thereof 9 The method comprises the following steps:
step 3, constructing a thermoelectric coupling model of the three-section thermoelectric generator in the COMSOL;
building a corresponding thermoelectric coupling equation according to the topological structure of the three-section thermoelectric generator, wherein the equation is as follows:
wherein:is a current density vector; [ alpha ]]Is a Seebeck coefficient matrix; [ kappa ]]Is a heat conduction coefficient matrix; [ Sigma ]]Is a conductivity matrix; t (T) te Is the temperature inside the three-section thermoelectric generator; />Is a scalar potential;
and step four, coupling a eigenvalue solver and a steady state solver in the COMSOL platform, and selecting a direct solving method to solve the problems of the reactivity of the heat pipe cooling reactor, namely an effective proliferation coefficient, the temperature distribution of the high-temperature heat pipe, and the energy output and thermoelectric conversion efficiency of the three-stage thermoelectric generator in the same solving process.
According to the COMSOL-based heat pipe cooling reactor nuclear thermoelectric internal coupling numerical calculation method, a nuclear thermoelectric multi-physical field coupling model is built in a COMSOL platform, and nuclear thermoelectric numerical calculation results are obtained in the same solving process, and the method belongs to an internal coupling calculation method and has strong relevance.
The COMSOL-based heat pipe cooling reactor nuclear thermoelectric in-coupling numerical calculation method uses a three-section type thermoelectric generator as a thermoelectric conversion device of a heat pipe stack, wherein the low-temperature Duan Redian material of the three-section type thermoelectric generator is bismuth telluride; thermoelectric materials in the middle temperature section are skutterudite; the thermoelectric material of the high temperature section is a half heusler alloy. The three-section thermoelectric generator has a large-span applicable temperature range in design, and the design temperature reaches more than 1000K.
Compared with the prior art, the invention has the following advantages:
1. the neutron diffusion equation is constructed in COMSOL, the step of calculating neutron flux distribution by using external software is omitted, and the calculation flow is simplified.
2. All solving equations are solved in a coupling mode in the COMSOL, an internal coupling mode is realized, and compared with external coupling (external software calculates neutron flux distribution and leads the neutron flux distribution to the COMSOL for conducting heat calculation), the solving process is solved in a physical field, and the accuracy is high.
Drawings
FIG. 1 is a schematic diagram of a method for calculating the thermoelectric in-coupling value of a heat pipe cooling reactor core based on a COMSOL platform;
FIG. 2 is a schematic diagram of the overall structure of a design object;
FIG. 3 is a schematic diagram of a calculation model of a thermal resistance network of a high-temperature heat pipe;
fig. 4 is a schematic diagram of a three-stage thermoelectric generator.
Detailed Description
For the purpose of making the objects, technical solutions and advantages of the embodiments of the present invention more apparent, the technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings in the embodiments of the present invention, and it is apparent that the described embodiments are some embodiments of the present invention, but not all embodiments of the present invention. All other embodiments, which can be made by those skilled in the art based on the embodiments of the invention without making any inventive effort, are intended to be within the scope of the invention.
A heat pipe cooling reactor nuclear thermoelectric internal coupling numerical calculation method based on a COMSOL platform establishes a nuclear thermoelectric internal coupling calculation model according to a direct solving algorithm and a characteristic value solver of the COMSOL platform, and finally obtains the reactivity, the power distribution, the temperature distribution of a high-temperature heat pipe and the power output and the thermoelectric conversion efficiency of a three-section thermoelectric generator.
As shown in fig. 2, the heat exchanger structure to be calculated by the numerical calculation method of the invention comprises a fuel rod 1, a heat pipe cooling reactor matrix 2, a high-temperature heat pipe 3, a thermoelectric generator mounting platform 4, a three-stage thermoelectric generator 5 and a cooling water plate 6; wherein the fuel rod 1 is arranged in the heat pipe reactor matrix 2, the heat pipe cooling reactor matrix 2 and the thermoelectric generator mounting platform 4 are connected together through the high temperature heat pipe 3, the three-stage thermoelectric generator 5 is arranged on the surface of the thermoelectric generator mounting platform 4, and the cooling water plate 6 is arranged on the surface of the three-stage thermoelectric generator 5.
In performing the calculations, the following parameters need to be known or can be obtained initially: selected structural materials and physical properties of the heat pipe cooling reactor, the high-temperature heat pipe and the three-section type thermoelectric generator, and design temperature T of the cooling water plate cold Group constant G of heat pipe cooled reactor constant ；
As shown in fig. 1, the numerical calculation method of the present invention specifically includes the following steps:
step 1, establishing a neutron diffusion model of a heat pipe cooling reactor in a COMSOL platform: given the group constants of a heat pipe cooled reactor, the following set of equations is established:
wherein, the subscript is 1, which is a fast neutron energy group; subscript 2 is the slow neutron energy group; d is expansionA dispersion coefficient; sigma and method for producing the same a Is a macroscopic absorption cross section; v Σ f Is a macroscopic scattering cross section; sigma and method for producing the same 1→2 A scattering cross section from fast neutrons to slow neutrons; k (k) eff Is the effective proliferation coefficient of the reactor; d, Σ, νΣ f Together, these variables are collectively referred to as the group constant G constant The method comprises the steps of carrying out a first treatment on the surface of the Is neutron flux distribution, which is also the power distribution of the heat pipe cooling reactor; calculating the available neutron flux distribution in the COMSOL by using a eigenvalue solver and a direct solver, so as to obtain power distribution;
and 2, building a solid heat transfer model of the heat pipe pile cooling reactor core, the high-temperature heat pipe and the three-section type thermoelectric generator in the COMSOL. Coupling the power distribution obtained in step 1 into the model while simultaneously cooling the design temperature T of the water sheet cold And inputting the model as a constant temperature cooling condition of the whole model.
The general solid heat transfer model is suitable for a heat pipe reactor core and a three-section type thermoelectric generator, and the equation is as follows:
wherein ρ is the density of the material; c (C) p Is the constant pressure heat capacity of the material; k is the thermal conductivity of the material; q is the heat flow calculated in the process of obtaining, and T is the temperature of the calculated value to be obtained;representing the change in temperature over time.
The heat transfer model of the high-temperature heat pipe is a thermal resistance network model, and the thought of the heat transfer model is shown in fig. 3:
by thermal resistance R 1 The form of (2) represents the heat loss of the heat pipe in the heat transfer process, and the final temperature distribution is obtained, and an equation set is established as follows:
wherein: d, d o Is the outer diameter of the pipe wall of the heat pipe; d, d i Is the inner diameter of the pipe wall of the heat pipe; lambda (lambda) w Is the heat conductivity of the pipe wall material of the heat pipe; l (L) 1 Is the length of the evaporation section of the heat pipe.
Radial heat conduction of wick at evaporation section of heat pipe and thermal resistance R of radial heat conduction 2 The method comprises the following steps:
wherein: d, d v The diameter of the air cavity in the heat pipe; lambda (lambda) e For equivalent thermal conductivity, related to the thermal conductivity of the wick material and working medium
Radial heat conduction of wick at condensation section of heat pipe and thermal resistance R of radial heat conduction 3 The method comprises the following steps:
wherein L is 2 Is the length of the condensing section of the heat pipe.
Radial heat conduction and thermal resistance R of tube wall of evaporation section of heat tube 4 The method comprises the following steps:
phase change heat transfer of gas-liquid interface of evaporation section of heat pipe and thermal resistance R thereof 5 The method comprises the following steps:
wherein: r is a gas constant; t (T) v Is the vapor temperature; r is the latent heat of vaporization; p is p v Is the vapor pressure.
Vapor axial flow heat transfer and thermal resistance R thereof 6 ：
Wherein: l (L) e Is the effective length of the heat pipe; mu (mu) v Is the kinetic viscosity coefficient of the vapor; ρ v Is the vapor density.
Phase change heat transfer of gas-liquid interface of condensation section of heat pipe and thermal resistance R thereof 7 The method comprises the following steps:
axial heat conduction of heat pipe liquid suction core and heat resistance R thereof 8 The method comprises the following steps:
wherein L is the length of the heat pipe
Axial heat conduction of heat pipe wall and thermal resistance R thereof 9 The method comprises the following steps:
and 3, constructing a thermoelectric coupling model of the three-section thermoelectric generator in the COMSOL. The topological structure is shown in figure 4, and the low-temperature Duan Redian material of the three-section thermoelectric generator is bismuth telluride (P 1 Is Bi 0.5 Sb 1.5 Te 3 ,N 1 Is Bi 2 Te 2.7 Se 0.3 ) The method comprises the steps of carrying out a first treatment on the surface of the The thermoelectric material of the middle temperature section is skutterudite (P) 2 Is CeFe 3 CoSb 12 ,N 2 Is Yb 0.3 Co 4 Sb 12 ) The method comprises the steps of carrying out a first treatment on the surface of the The thermoelectric material of the high temperature section is half heusler alloy (P 3 Is ZrCoSb, N 3 ZrNiSn).
Building a corresponding thermoelectric coupling equation according to the topological structure, wherein the thermoelectric coupling equation is as follows:
wherein:is a current density vector; [ alpha ]]Is a Seebeck coefficient matrix; [ kappa ]]Is a heat conduction coefficient matrix; [ Sigma ]]Is a conductivity matrix; t (T) te Is the temperature inside the three-section thermoelectric generator; />Is a scalar potential.
And step four, coupling a eigenvalue solver and a steady state solver in the COMSOL platform, and selecting a direct solving method to solve and obtain the reactivity (effective multiplication coefficient) of the heat pipe cooling reactor, the temperature distribution of the high-temperature heat pipe, the energy output and the thermoelectric conversion efficiency of the three-stage thermoelectric generator in the same solving process.
Claims (3)
1. A calculation method for the thermoelectric in-coupling value of a heat pipe cooling reactor core based on COMSOL is characterized by comprising the following steps: according to a direct solving algorithm and a eigenvalue solver of the COMSOL platform, a nuclear thermoelectric internal coupling calculation model is established, and finally the reactivity, the power distribution, the temperature distribution of a high-temperature heat pipe, the power output and the thermoelectric conversion efficiency of a three-section thermoelectric generator of the heat pipe cooling reactor are obtained;
the structure of the heat exchanger to be calculated by the method comprises a fuel rod (1), a heat pipe cooling reactor matrix (2), a high-temperature heat pipe (3), a thermoelectric generator mounting platform (4), a three-section thermoelectric generator (5) and a cooling water plate (6); the fuel rod (1) is arranged in the heat pipe cooling reactor matrix (2), the heat pipe reactor matrix (2) and the thermoelectric generator mounting platform (4) are connected together through the high-temperature heat pipe (3), the three-section thermoelectric generator (5) is arranged on the surface of the thermoelectric generator mounting platform (4), and the cooling water plate (6) is arranged on the surface of the three-section thermoelectric generator (5);
in performing the calculations, the following parameters need to be known or can be obtained initially: selected structural materials and physical properties of the heat pipe cooling reactor, the high-temperature heat pipe and the three-section type thermoelectric generator, and design temperature T of the cooling water plate cold Group constant G of heat pipe cooled reactor constant ；
The numerical value calculation method specifically comprises the following steps:
step 1, establishing a neutron diffusion model of a heat pipe cooling reactor in a COMSOL platform: given the group constants of a heat pipe cooled reactor, the following set of equations is established:
wherein, the subscript is 1, which is a fast neutron energy group; subscript 2 is the slow neutron energy group; d is a diffusion coefficient; sigma and method for producing the same a Is a macroscopic absorption cross section; v Σ f Is a macroscopic scattering cross section; sigma and method for producing the same 1→2 A scattering cross section from fast neutrons to slow neutrons; k (k) eff Is the effective proliferation coefficient of the reactor; d, Σ, νΣ f Together, these variables are collectively referred to as the group constant G constant The method comprises the steps of carrying out a first treatment on the surface of the Is neutron flux distribution, which is also the power distribution of the heat pipe cooling reactor; calculating the available neutron flux distribution in the COMSOL by using a eigenvalue solver and a direct solver, so as to obtain power distribution;
step 2, constructing a solid heat transfer model of a heat pipe cooling reactor core, a high-temperature heat pipe and a three-section thermoelectric generator in the COMSOL, coupling the power distribution obtained in the step 1 into the model, and simultaneously coupling the design temperature T of a cooling water plate cold Inputting a model to serve as a constant temperature cooling condition of the whole model;
the general solid heat transfer model is suitable for a heat pipe reactor core and a three-section type thermoelectric generator, and the equation is as follows:
wherein ρ is the density of the material; c (C) p Is constant pressure of materialA heat capacity; k is the thermal conductivity of the material; q is the heat flow calculated in the process of obtaining, and T is the temperature of the calculated value to be obtained;representing the change in temperature with time;
the heat transfer model of the high-temperature heat pipe is a thermal resistance network model and uses thermal resistance R 1 The form of (2) represents the heat loss of the heat pipe in the heat transfer process, and the final temperature distribution is obtained, and an equation set is established as follows:
wherein: d, d o Is the outer diameter of the pipe wall of the heat pipe; d, d i Is the inner diameter of the pipe wall of the heat pipe; lambda (lambda) w Is the heat conductivity of the pipe wall material of the heat pipe; l (L) 1 The length of the evaporation section of the heat pipe;
radial heat conduction of wick at evaporation section of heat pipe and thermal resistance R of radial heat conduction 2 The method comprises the following steps:
wherein: d, d v The diameter of the air cavity in the heat pipe; lambda (lambda) e Equivalent thermal conductivity is related to the thermal conductivity of the wick material and the working medium;
radial heat conduction of wick at condensation section of heat pipe and thermal resistance R of radial heat conduction 3 The method comprises the following steps:
wherein L is 2 The length of the condensing section of the heat pipe;
radial heat conduction and thermal resistance R of tube wall of evaporation section of heat tube 4 The method comprises the following steps:
phase change heat transfer of gas-liquid interface of evaporation section of heat pipe and thermal resistance R thereof 5 The method comprises the following steps:
wherein: r is a gas constant; t (T) v Is the vapor temperature; r is the latent heat of vaporization; p is p v Is the vapor pressure;
vapor axial flow heat transfer and thermal resistance R thereof 6 The method comprises the following steps:
wherein: l (L) e Is the effective length of the heat pipe; mu (mu) v Is the kinetic viscosity coefficient of the vapor; ρ v Is vapor density;
phase change heat transfer of gas-liquid interface of condensation section of heat pipe and thermal resistance R thereof 7 The method comprises the following steps:
axial heat conduction of heat pipe liquid suction core and heat resistance R thereof 8 The method comprises the following steps:
wherein L is the length of the heat pipe;
axial heat conduction of heat pipe wall and thermal resistance R thereof 9 The method comprises the following steps:
step 3, constructing a thermoelectric coupling model of the three-section thermoelectric generator in the COMSOL;
building a corresponding thermoelectric coupling equation according to the topological structure of the three-section thermoelectric generator, wherein the equation is as follows:
wherein:is a current density vector; [ alpha ]]Is a Seebeck coefficient matrix; [ kappa ]]Is a heat conduction coefficient matrix; [ Sigma ]]Is a conductivity matrix; t (T) te Is the temperature inside the three-section thermoelectric generator; />Is a scalar potential;
and step four, coupling a eigenvalue solver and a steady state solver in the COMSOL platform, and selecting a direct solving method to solve the problems of the reactivity of the heat pipe cooling reactor, namely an effective proliferation coefficient, the temperature distribution of the high-temperature heat pipe, and the energy output and thermoelectric conversion efficiency of the three-stage thermoelectric generator in the same solving process.
2. The method for calculating the thermoelectric in-coupling value of the heat pipe cooling reactor core based on COMSOL according to claim 1, wherein the method comprises the following steps of: a multi-physical field coupling model of nuclear heat and electricity is built in a COMSOL platform, and numerical calculation results of the nuclear heat and electricity are obtained in the same solving process, and the method belongs to an internal coupling calculation method and has strong relevance.
3. The method for calculating the thermoelectric in-coupling value of the heat pipe cooling reactor core based on COMSOL according to claim 1, wherein the method comprises the following steps of: the three-section type thermoelectric generator is used as a thermoelectric conversion device of the heat pipe stack, and the low-temperature Duan Redian material of the three-section type thermoelectric generator is bismuth telluride; thermoelectric materials in the middle temperature section are skutterudite; the thermoelectric material of the high temperature section is half heusler alloy; the three-section thermoelectric generator has a large-span applicable temperature range in design, and the design temperature reaches more than 1000K.
Priority Applications (1)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| CN202310727195.9A CN116662721B (en) | 2023-06-19 | 2023-06-19 | COMSOL-based heat pipe cooling reactor nuclear thermoelectric internal coupling numerical calculation method |
Applications Claiming Priority (1)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| CN202310727195.9A CN116662721B (en) | 2023-06-19 | 2023-06-19 | COMSOL-based heat pipe cooling reactor nuclear thermoelectric internal coupling numerical calculation method |
Publications (2)
| Publication Number | Publication Date |
|---|---|
| CN116662721A CN116662721A (en) | 2023-08-29 |
| CN116662721B true CN116662721B (en) | 2024-04-02 |
Family
ID=87720597
Family Applications (1)
| Application Number | Title | Priority Date | Filing Date |
|---|---|---|---|
| CN202310727195.9A Active CN116662721B (en) | 2023-06-19 | 2023-06-19 | COMSOL-based heat pipe cooling reactor nuclear thermoelectric internal coupling numerical calculation method |
Country Status (1)
| Country | Link |
|---|---|
| CN (1) | CN116662721B (en) |
Families Citing this family (1)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN117473873B (en) * | 2023-11-13 | 2024-04-26 | 上海交通大学 | Nuclear thermal coupling realization method based on DeepM & Mnet neural network |
Citations (5)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN109063235A (en) * | 2018-06-19 | 2018-12-21 | 中国原子能科学研究院 | A kind of coupling of multiple physics system and method for reactor simulation |
| CN112086210A (en) * | 2020-10-15 | 2020-12-15 | 中国原子能科学研究院 | Heat exchange calculation method and system for nuclear reactor cooling system |
| CN112989651A (en) * | 2021-02-06 | 2021-06-18 | 西安交通大学 | Multi-physical field coupling method for reactor core |
| CN113094947A (en) * | 2021-03-29 | 2021-07-09 | 西安交通大学 | Nuclear thermal coupling analysis method for nuclear reactor core |
| CN114707394A (en) * | 2022-06-07 | 2022-07-05 | 西安交通大学 | Reactor transient neutron flux simulation method considering deformation effect under fixed grid |
-
2023
- 2023-06-19 CN CN202310727195.9A patent/CN116662721B/en active Active
Patent Citations (5)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN109063235A (en) * | 2018-06-19 | 2018-12-21 | 中国原子能科学研究院 | A kind of coupling of multiple physics system and method for reactor simulation |
| CN112086210A (en) * | 2020-10-15 | 2020-12-15 | 中国原子能科学研究院 | Heat exchange calculation method and system for nuclear reactor cooling system |
| CN112989651A (en) * | 2021-02-06 | 2021-06-18 | 西安交通大学 | Multi-physical field coupling method for reactor core |
| CN113094947A (en) * | 2021-03-29 | 2021-07-09 | 西安交通大学 | Nuclear thermal coupling analysis method for nuclear reactor core |
| CN114707394A (en) * | 2022-06-07 | 2022-07-05 | 西安交通大学 | Reactor transient neutron flux simulation method considering deformation effect under fixed grid |
Non-Patent Citations (2)
| Title |
|---|
| 核反应堆物理热工耦合的瞬态分析方法研究;王昆鹏 等;核安全;20191230(第06期);全文 * |
| 电磁发射装置轨道热管理冷却管道的力学设计;林灵淑 等;强激光与粒子束(第02期);全文 * |
Also Published As
| Publication number | Publication date |
|---|---|
| CN116662721A (en) | 2023-08-29 |
Similar Documents
| Publication | Publication Date | Title |
|---|---|---|
| He et al. | Recent development and application of thermoelectric generator and cooler | |
| Huang et al. | Geometry optimization of thermoelectric coolers using simplified conjugate-gradient method | |
| Meng et al. | Multi-objective and multi-parameter optimization of a thermoelectric generator module | |
| CN116662721B (en) | COMSOL-based heat pipe cooling reactor nuclear thermoelectric internal coupling numerical calculation method | |
| Kyono et al. | Conversion of unused heat energy to electricity by means of thermoelectric generation in condenser | |
| CN108763670B (en) | Method for solving Brayton cycle transient process of supercritical carbon dioxide reactor | |
| Yang et al. | Annular thermoelectric generator performance optimization analysis based on concentric annular heat exchanger | |
| Kwan et al. | Exergetic and temperature analysis of a fuel cell-thermoelectric device hybrid system for the combined heat and power application | |
| Yang et al. | Evaluation method for assessing heat transfer enhancement effect on performance improvement of thermoelectric generator systems | |
| Zhang et al. | Numerical analysis of segmented thermoelectric generators applied in the heat pipe cooled nuclear reactor | |
| CN113255105B (en) | Load flow calculation method of electric and thermal comprehensive energy system with bidirectional coupling network structure | |
| Zhang et al. | Modelling and experimental validation of advanced adiabatic compressed air energy storage with off‐design heat exchanger | |
| Hao et al. | Multi-parameters analysis and optimization of a typical thermoelectric cooler based on the dimensional analysis and experimental validation | |
| Li et al. | Characteristics and optimation of heat pipe radiator for space nuclear propulsion spacecraft | |
| Ma et al. | A review on thermoelectric-hydraulic performance and heat transfer enhancement technologies of thermoelectric power generator system | |
| Huang et al. | Performance investigation of an updated alkali metal thermoelectric converter-thermally regenerative electrochemical cycles-thermoelectric generator hybrid system | |
| Xu et al. | Experimental study on performances of flat-plate pulsating heat pipes coupled with thermoelectric generators for power generation | |
| Mojumder et al. | An empirical analysis on photovoltaic thermal system with fin design by forced air circulation | |
| Zhang et al. | Thermal-hydraulic analysis of heat pipe reactor experimental device with thermoelectric generators | |
| He et al. | Analysis on optimal length scale of thermoelectric generators when using different circuit layouts | |
| Almajali et al. | Parametric study on the performance of combined power plant of steam and gas turbines | |
| CN114549232A (en) | Hybrid energy flow calculation method for electricity-heat comprehensive energy system | |
| Zhao et al. | An alkali metal thermoelectric converter/thermally regenerative electrochemical cycles/absorption refrigerator coupling system for power and cooling | |
| Zhang et al. | Multi-criteria decision analysis and experimental study on heat pipe thermoelectric generator for waste heat recovery | |
| He et al. | Analysis of the influence of different thermal boundary conditions on thermoelectric generators |
Legal Events
| Date | Code | Title | Description |
|---|---|---|---|
| PB01 | Publication | ||
| PB01 | Publication | ||
| SE01 | Entry into force of request for substantive examination | ||
| SE01 | Entry into force of request for substantive examination | ||
| GR01 | Patent grant | ||
| GR01 | Patent grant |