A space heat pipe nuclear reactor design method based on shutdown safety physical modeling and computer program product

Abstract

The present application relates to the technical field of nuclear power plant nuclear reactor safety, and is a space heat pipe nuclear reactor design method and computer program product based on shutdown safety physical modeling, which solves the problem that the existing space heat pipe nuclear reactor design method is insufficient in consideration and cannot take into account the safety, power capacity and lightweight requirements; the present application comprises the following steps: establishing a mass model, a safety model and a power model of the nuclear reactor; inputting the constraint conditions of the safety model into the model to make the design meet the shutdown safety requirements; inputting the constraint conditions of the mass model and the power model into the corresponding models respectively and performing framework optimization; the present application constructs an interpretable shutdown neutronics equivalent model, takes the influence of the absorber drum assembly and the reflector on the shutdown criticality as a hard safety constraint, and on this basis, jointly designs the reactor power level and the system mass.

Description

Technical Field

[0001] This invention relates to the field of nuclear power plant nuclear reactor safety technology, and in particular to a design method and computer program product for a space heat pipe nuclear reactor based on shutdown safety physical modeling. Background Technology

[0002] Space heat-pipe reactors (SHPRs) are compact space nuclear reactors that use multiple parallel heat pipes as heat transfer and dissipation channels. They feature passive heat transfer, simplified structure, high system reliability, and suitability for microgravity environments. In applications such as deep space exploration, high-power electric propulsion, and lunar-based energy systems, there are increasingly higher requirements for reactors, demanding both high power levels and low system mass.

[0003] In the design of space heat pipe nuclear reactors, the achievable power level of the reactor is not only limited by the heat transfer capacity of the heat pipe and the thermal constraints of the fuel, but also by neutron safety conditions, especially the strict constraints on the subcritical safety margin in the shutdown state. Shutdown is usually achieved by switching from the reflective state to the absorber state through the control drum or safety drum. The absorption coverage, angular position, and geometric relationship with the reflector directly affect the neutron leakage characteristics and effective multiplication factor in the shutdown state.

[0004] On the other hand, space applications are extremely sensitive to system mass. The thickness of the reflector, the size and number of drum assemblies, the core dimensions, and the configuration of heat pipes and structural components all significantly affect the total mass of the reactor. If only operational criticality or thermal performance is considered during the power design process, without incorporating shutdown safety and structural mass into a unified design framework, it is easy to introduce excessive structural redundancy in high-power schemes or weaken the shutdown safety margin in lightweight schemes.

[0005] There is an urgent need for a new design method for space heat pipe nuclear reactors that can solve the above problems, based on shutdown safety physical modeling, while taking into account power enhancement and quality control. Summary of the Invention

[0006] This invention proposes a design method and computer program product for a space heat pipe nuclear reactor based on shutdown safety physical modeling, which solves the problem that the existing space heat pipe nuclear reactor design methods do not take into account sufficient considerations and cannot simultaneously meet the requirements of safety, power capability and lightweighting.

[0007] The technical solution of this invention is implemented as follows: a design method for a space heat pipe nuclear reactor based on shutdown safety physical modeling, comprising the following steps:

[0008] I. Establish the mass model, safety model, and power model of the nuclear reactor; specifically, establish the equivalent model of the nuclear reactor, the equivalent model of the reflection structure, and the equivalent model of the drum assembly under shutdown conditions.

[0009] The nuclear reactor core is modeled as a cylinder, including the core and multiple parallel heat pipes. The equivalent radius and height of the core are defined. The radial and axial thicknesses of the reflector are introduced, and the effect of the reflector on neutron leakage is described by extrapolation of the boundary and reflection savings.

[0010] The specific steps are as follows:

[0011] By introducing extrapolated boundary lengths, the actual boundary conditions are equivalent to extensions of geometric dimensions;

[0012] The extrapolated boundary length of the core material is defined as:

[0013]

[0014] in, is the core equivalent diffusion coefficient. Its value is related to the transport cross section of the core material. It can be calculated based on the material cross section data or obtained through high-fidelity calculation and calibration. It is not a fixed constant and reflects the diffusion ability of neutrons in the core. This represents the equivalent macroscopic absorption cross section of the reactor core. This represents the equivalent size increment caused by the diffusion boundary conditions;

[0015] The reflection savings increase with increasing reflective layer thickness, but tend to saturate at larger thicknesses; therefore, an exponential saturation form is used to describe this.

[0016]

[0017] in, The thickness of the reflective layer, This represents the amount of reflection savings at the corresponding thickness. This represents the limit of the reflection savings. The characteristic saturation length; the limiting value of reflection savings is related to the neutronic properties of the reflective layer material, which can be expressed as:

[0018]

[0019] in, The extrapolated boundary length of the reflective layer material. Let be the core diffusion coefficient; this expression reflects the "diffusion capability advantage" of the reflector layer relative to the core: The parameter describing the lateral diffusion capability of neutrons in the reflector is determined by the macroscopic transport cross-section of the reflector material;

[0020] Define the radial and axial reflection savings separately:

[0021]

[0022]

[0023] in, The radial reflective layer thickness, The thickness of the axial reflective layer. and These represent the radial and axial reflection savings, respectively.

[0024] The equivalent dimensions of the constructed core are as follows:

[0025]

[0026]

[0027] in, , These are the physical radius and height of the reactor core, respectively.

[0028] Define the absorber drum assembly, namely the control drum and the safety drum, in the absorption configuration under shutdown conditions. The enhancement effect of the absorber drum assembly on radial and axial neutron leakage is equivalently described by the circumferential absorption coverage, axial coverage height and geometric relationship with the reflector of the absorber drum assembly.

[0029] The geometric relationships are as follows:

[0030]

[0031] in, For macroscopic neutron production, fission neutron yield × macroscopic fission cross section; Macroscopic absorption cross section; The diffusion coefficient is denoted as . For geometric buckling; The larger the leakage, the more accurate the calculation. To link leakage to geometry, the core is equivalent to a cylinder, and the fundamental mode buckling occurs.

[0032]

[0033] The thickness of the drum and the reflective layer determines the center radius of the drum. The further out the drum is, the stronger the disruption of the reflection boundary:

[0034]

[0035] in, This is a dimensionless bias coefficient that describes the "relative position" of the drum center inside the reflector layer. The closer it is to 0, the closer the drum is to the core boundary.

[0036] Drum diameter With the center radius of the drum Determine the circumferential blocking angle of a single drum Thus, the circumferential coverage is obtained. :

[0037]

[0038]

[0039] Equivalent description of radial leakage enhancement:

[0040]

[0041] in, To save radial energy for clean reflection, , These refer to the effective coverage ratios of the control drum and the safety drum, respectively. , These are the absorption and saving ratios of the control drum and the safety drum, respectively;

[0042] Equivalent description of axial leakage enhancement:

[0043]

[0044] in, ∈[0,1] is a dimensionless reduction coefficient;

[0045] 2. Input the constraints of the safety model into the model to ensure that the design meets the shutdown safety requirements;

[0046] Based on the equivalent model in operation, the absorption effect of the absorber drum assembly is introduced to reduce the reflection savings, and the equivalent core size in the shutdown state is constructed. The effective growth factor during shutdown is then calculated based on diffusion theory. ;

[0047] when If the value is less than or equal to the preset shutdown safety limit, then the design meets the shutdown safety requirements.

[0048] Calculate runtime reflection savings:

[0049] The equivalent size in operation is obtained by superimposing the "physical size + extrapolated boundary + reflection savings":

[0050]

[0051]

[0052] Calculate the geometric coverage of the drum assembly:

[0053]

[0054]

[0055]

[0056]

[0057] Next, construct the "effective coverage" from the "geometric coverage";

[0058]

[0059]

[0060] in, The effective boundary degradation coefficient;

[0061] Radial introduction method: Subtract the "coverage penalty" from the "clean reflection savings" to obtain the effective radial savings during shutdown:

[0062]

[0063]

[0064] Axial introduction method: Use "attenuation coefficient" to reduce axial savings:

[0065]

[0066] The process of writing back the "reduced savings" to the shutdown equivalent size completes the construction from the running state to the shutdown state:

[0067]

[0068]

[0069] Third, based on step two, input the constraints of the mass model and the power model into the corresponding models respectively, and perform framework optimization;

[0070] A quality assessment is conducted on the main components of the nuclear reactor, which are structural components including fuel, cladding, heat pipes, reflector layer, and drum assembly, to obtain the total system mass under the corresponding design scheme;

[0071] The nuclear reactor's operating state, shutdown state, heat pipe limit, and structural quality are uniformly determined in the same closed loop using a closed-loop physical evaluation model; and the power capacity is evaluated under the condition of satisfying steady-state heat transfer constraints.

[0072] The specific process of building a quality model:

[0073] The close arrangement of hexagons gives the core cross-sectional area, equivalent radius, and core volume:

[0074]

[0075]

[0076]

[0077] in, is the hexagonal lattice pitch, the distance between the centers of adjacent lattice elements; m is the core control quantity for arrangement density and installability. The effective lattice unit number is dimensionless. This refers to the cross-sectional area of ​​the reactor core. The equivalent radius (m) when the hexagonal array is equivalent to a cylindrical core; This refers to the core volume;

[0078] Lattice pitch "mountable diameter" constraint:

[0079]

[0080]

[0081]

[0082] in, This is the maximum allowable outer diameter within a single crystal lattice unit; Minimum mechanical clearance; To allow for manufacturing / assembly margins; The outer diameter of the fuel rod; The outer diameter of the heat pipe;

[0083] Fuel rod quality, including fuel and cladding:

[0084]

[0085]

[0086]

[0087]

[0088]

[0089] in, This refers to the number of fuel rods; , These are the outer and inner diameters of the fuel rod, respectively. and Density of fuel and cladding material;

[0090] Heat pipe quality includes the metal wall, the solid capillary wick, and the working fluid.

[0091]

[0092]

[0093]

[0094]

[0095]

[0096]

[0097]

[0098] in, Number of heat pipes; These are the outer and inner diameters of the heat pipe, respectively. The diameter of the steam chamber; This is the total equivalent length of the heat pipe, including the equivalent lengths of the in-pile evaporation section and the out-of-pile section; Capillary porosity; and Density of wall material and capillary core material; The density of the working fluid in the liquid phase at the evaporation temperature; The working fluid filling coefficient;

[0099] The quality of the reflective layer, specifically, is the outer enveloping cylindrical shell, where the turret cavity is deducted to avoid double weighing;

[0100]

[0101]

[0102] The mass of the drum assembly and absorber, including the drum cavity, drum shell, and absorber sector layers:

[0103]

[0104]

[0105]

[0106]

[0107]

[0108]

[0109]

[0110] in, The total number of drums, including control drums and safety drums; The length of the drum; The absorber sector ratio is (0–1). , , These are the densities of the drum shell / absorbing element / reflective layer materials, respectively.

[0111] Pressure vessel mass, approximately a thin-walled cylindrical shell:

[0112]

[0113]

[0114]

[0115]

[0116]

[0117] in, For design internal pressure; This is for assembly clearance; Minimum manufacturable thickness; Density of the container material;

[0118] Additional structural mass: a lumped model using "volume scale, end face area scale", including supports, end plates, and grids;

[0119]

[0120] in, Density of the structural material; It is a dimensionless volume scaling factor, i.e., the ratio of the structure to the core volume; This is the area scaling factor;

[0121]

[0122] in, The equivalent mass of the drive mechanism for a single drum includes the lumped mass of the motor, bearings, seals, and transmission.

[0123] Total mass summary:

[0124]

[0125] The total mass of the system consists of fuel rods, including fuel and cladding; heat pipes, including wall material, capillary wick, and working fluid; a reflective layer, including reflective material after deducting the drum cavity; a drum assembly, including drum shell and absorber; a pressure vessel; additional structures; and a drum drive mechanism. This summary formula ensures that each geometric space and material is weighed only once and can be directly used in the "mass minimization" objective function in multi-objective optimization.

[0126] The equivalent neutronics model under shutdown conditions is used as a safety constraint for reactor power and mass design. Specifically, the power model is:

[0127]

[0128] in, Target electrical power; For electrical conversion efficiency; For the required thermal power;

[0129]

[0130] Design reactor configuration The heat pipes are responsible for transferring heat from the reactor core. This represents the total thermal power of the reactor core. This represents the average heat transfer power of a single heat pipe.

[0131] Further define the equivalent heat transfer area of ​​the heat pipe evaporator section:

[0132]

[0133] in, The outer diameter of the heat pipe; This refers to the length of the evaporation section;

[0134] The average heat flux density of the evaporation section was obtained:

[0135]

[0136] in, This refers to the length of the evaporation section; The average heat flux density of the evaporation section;

[0137] The maximum sustainable heat transfer capacity of a heat pipe is determined by several limits, including the capillary limit and the sonic blockage limit. The allowable power of a heat pipe is defined as the minimum allowable power of each of these limits.

[0138]

[0139]

[0140]

[0141] in, The surface tension of the working fluid; For wetting contact angle; The equivalent aperture of the capillary core; These represent the pressure drop during liquid / vapor flow, respectively. This is the term related to gravity.

[0142] The speed of sound limit is as follows:

[0143]

[0144] in, This represents the maximum permissible steam mass flow rate under the speed of sound limit. Latent heat of vaporization;

[0145] Because each heat pipe needs to meet the following requirements Therefore, the upper limit of the total thermal power of the reactor core is:

[0146]

[0147] Power models typically correlate "heat generation per unit length" with "radial thermal conduction temperature rise"; if the number of fuel rods is... Core height is Then the average linear power is:

[0148]

[0149] The average volumetric power density is:

[0150] .

[0152] Preferably, the process also includes step four: while ensuring that the shutdown safety requirements are always met, the MOPIMO (Multi-Objective Projection-Iterative Methods Optimization) optimization algorithm is used to optimize the core size, reflector data, absorber drum assembly data, and heat pipe data.

[0153] The space heat pipe nuclear reactor design method and computer program product based on shutdown safety physical modeling disclosed in this invention have the following beneficial effects:

[0154] 1. Establish an equivalent neutronics physical model of a space heat pipe nuclear reactor under shutdown conditions to quantitatively describe the influence of absorber drum assembly absorption coverage and reflector layer configuration on the effective growth factor during shutdown.

[0155] 2. Clarify the constraints of shutdown safety on core dimensions, reflector structure, and power levels to form physical criteria that can be used for design;

[0156] 3. With shutdown safety as a prerequisite constraint, ensure that the high-power, lightweight design scheme still has sufficient subcritical safety margin in non-operational state;

[0157] 4. Under the premise of meeting the shutdown safety limits, the power level of the reactor and the system mass are synergistically balanced to obtain a design scheme with high power and controlled mass; this is conducive to obtaining a high specific power space heat pipe nuclear reactor scheme and improving the reactor power output per unit mass.

[0158] 5. The design process has a clear physical meaning, which makes it easier for engineers to make reasonable trade-offs between safety, power and quality. Attached Figure Description

[0159] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0160] Figure 1 : Flowchart of the design method of this invention;

[0161] Figure 2 The front view of the structure with extrapolated length of the security model and the savings in the reflective layer;

[0162] Figure 3 The equivalent model diagram of the top view of the security model;

[0163] Figure 4 Schematic diagram of nuclear reactor operating and shutdown states;

[0164] Figure 5 : Optimization algorithm flowchart;

[0165] Figure 6 Pareto front plot under MOPIMO algorithm results;

[0166] Figure 7 : Heat pipe stack structure under optimization results. Detailed Implementation

[0167] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0168] like Figure 1The flowchart of the design method of this invention shows a design method for a space heat pipe nuclear reactor based on shutdown safety physics modeling, which includes the following steps:

[0169] I. Establish the mass model, safety model, and power model of the nuclear reactor; specifically, establish the equivalent model of the nuclear reactor, the equivalent model of the reflection structure, and the equivalent model of the drum assembly under shutdown conditions.

[0170] like Figure 2 The structural front view of the extrapolated length of the security model and the savings in the reflective layer, Figure 3 The equivalent model diagram of the top view of the security model and Figure 4 The schematic diagram of the nuclear reactor in operation and shutdown states shows that the nuclear reactor core is equivalent to a cylindrical model, including the core and multiple parallel heat pipes. The equivalent radius and height of the core are defined. The radial and axial thicknesses of the reflector are introduced, and the suppression effect of the reflector on neutron leakage is described by extrapolation boundary and reflection savings.

[0171] The specific steps are as follows:

[0172] Under a group diffusion theory framework, the neutron flux at the core boundary is not strictly zero at the geometric boundary, but decays to zero at a certain distance outside the geometric boundary. To reflect this physical property, an extrapolated boundary length is introduced, which equates the actual boundary condition to an extension of the geometric dimension.

[0173] The extrapolated boundary length of the core material is defined as:

[0174]

[0175] in, is the core equivalent diffusion coefficient. Its value is related to the transport cross section of the core material. It can be calculated based on the material cross section data or obtained through high-fidelity calculation and calibration. It is not a fixed constant and reflects the diffusion ability of neutrons in the core. Among them, the equivalent transport macroscopic cross section of the reactor core When the reactor core is composed of multiple materials (including fuel, structural materials, coolant, and absorbers), the equivalent transport cross section can be determined using a volume-weighted method. ,in, .in, The equivalent total macroscopic cross section of the reactor core is given in units of 1000 m / s. ; The equivalent scattering macroscopic cross section of the reactor core, in units of ; The cosine of the core average scattering angle is dimensionless. For the first in the core similar materials, For the core material assembly, For the first The volume fraction of this type of material in the reactor core, dimensionless; For the first The total macroscopic cross section, the macroscopic scattering cross section, and the average scattering angle cosine of the material;

[0176] This represents the equivalent macroscopic absorption cross section of the reactor core. This represents the equivalent size increment caused by the diffusion boundary conditions; its physical meaning is "neutrons still have an effective range of existence outside the geometric boundary". By introducing this extrapolated boundary length, complex boundary conditions can be equivalent to geometric size corrections without explicitly solving for the boundary flux distribution.

[0177] The reflector layer reduces the neutron leakage rate by scattering leaked neutrons and reflecting them back to the reactor core. Its equivalent effect can be described as further increasing the effective size of the reactor core. Therefore, a reflection saving is introduced to quantitatively describe the reflector layer's ability to suppress neutron leakage. The reflection saving is defined as the additional increment in the equivalent core size when the reflector layer is present, relative to the case considering only extrapolated boundary conditions. The reflection saving increases with the reflector layer thickness, but tends to saturate at larger thicknesses; therefore, an exponential saturation form is used to describe it.

[0178]

[0179] in, The thickness of the reflective layer, This represents the amount of reflection savings at the corresponding thickness. The limit value for reflection savings represents the maximum equivalent dimensional increment that can be provided when the reflective layer is infinitely thickened. The characteristic saturation length reflects the decay rate of the reflective layer thickness's contribution to the reflection savings; the limiting value of the reflection savings is related to the neutronic properties of the reflective layer material, and can be expressed as:

[0180]

[0181] in, The extrapolated boundary length of the reflective layer material. Let be the core diffusion coefficient; this expression reflects the "diffusion capability advantage" of the reflector layer relative to the core: The parameter describing the lateral diffusion capability of neutrons in the reflector is determined by the macroscopic transport cross-section of the reflector material; The macroscopic cross section of the reflective layer transport The unit is In this invention, the reflective layer is made of a single material, BeO, and the group constant data of BeO are directly used for calculation. The total macroscopic cross-section of the reflective layer is given in units of 1000 m / s. , The macroscopic cross section of the reflector layer is given in units of . , The value is the cosine of the average scattering angle of the reflector, which is dimensionless. The stronger the reflector's ability to diffuse and scatter neutrons, the higher the proportion of neutrons it can reflect back to the reactor core, and the greater the corresponding reflection savings.

[0182] Since the reflective layer may have different thicknesses in the radial and axial directions, and there are two end faces in the axial direction, the radial and axial reflection savings are defined separately:

[0183]

[0184]

[0185] in, The radial reflective layer thickness, The thickness of the axial reflective layer. and These represent the radial and axial reflection savings, respectively.

[0186] Taking into account the core physical dimensions, extrapolated boundary length, and reflection savings, the equivalent dimensions of the constructed core are as follows:

[0187]

[0188]

[0189] in, , These are the physical radius and height of the reactor core, respectively.

[0190] Define the absorber drum assembly, namely the control drum and the safety drum, in the absorption configuration under shutdown conditions. The enhancement effect of the absorber drum assembly on radial and axial neutron leakage is equivalently described by the circumferential absorption coverage, axial coverage height and geometric relationship with the reflector of the absorber drum assembly.

[0191] The geometric relationships are as follows:

[0192]

[0193] in, The term for macroscopic neutron production is calculated as fission neutron yield multiplied by macroscopic fission cross section, which determines the "source strength". The macroscopic absorption cross section determines the "material absorption loss"; The diffusion coefficient determines the "diffusion rate"; For geometric buckling, it is equivalent to characterizing leakage strength; The larger the core, the stronger the leakage; to link leakage to geometry, the core is equivalent to a cylinder, and the fundamental mode buckles:

[0194]

[0195] The thickness of the drum and the reflective layer determines the center radius of the drum. The further out the drum is, the stronger the disruption of the reflection boundary:

[0196]

[0197] in, This is a dimensionless bias coefficient that describes the "relative position" of the drum center inside the reflector layer. The closer it is to 0, the closer the drum is to the core boundary.

[0198] Drum diameter With the center radius of the drum Determine the circumferential blocking angle of a single drum Thus, the circumferential coverage is obtained. :

[0199]

[0200]

[0201] Equivalent description of radial leakage enhancement:

[0202]

[0203] in, To save radial energy for clean reflection, , These refer to the effective coverage ratios of the control drum and the safety drum, respectively. , These are the absorption and saving ratios of the control drum and the safety drum, respectively;

[0204] Equivalent description of axial leakage enhancement:

[0205]

[0206] in, ∈[0,1] is a dimensionless reduction coefficient;

[0207] 2. Input the constraints of the safety model into the model to ensure that the design meets the shutdown safety requirements;

[0208] Based on the equivalent model in operation, the absorption effect of the absorber drum assembly is introduced to reduce the reflection savings, and the equivalent core size in the shutdown state is constructed. The effective growth factor during shutdown is then calculated based on diffusion theory. ;

[0209] when If the value is less than or equal to the preset shutdown safety limit, then the design meets the shutdown safety requirements.

[0210] Calculate runtime reflection savings:

[0211] The equivalent size in operation is obtained by superimposing the "physical size + extrapolated boundary + reflection savings":

[0212]

[0213]

[0214] Calculate the geometric coverage of the drum assembly:

[0215]

[0216]

[0217]

[0218]

[0219] Next, "effective coverage" is constructed from "geometric coverage", converting geometric quantities into equivalent neutron boundary degradation intensity;

[0220]

[0221]

[0222] in, The effective boundary degradation coefficient;

[0223] Radial introduction method: Subtract the "coverage penalty" from the "clean reflection savings" to obtain the effective radial savings during shutdown:

[0224]

[0225]

[0226] Axial introduction method: The "attenuation coefficient" is used to reduce the axial savings, reflecting the increased end leakage caused by insufficient axial coverage height.

[0227]

[0228] The process of writing back the "reduced savings" to the shutdown equivalent size completes the construction from the running state to the shutdown state:

[0229]

[0230]

[0231] Third, based on step two, input the constraints of the mass model and the power model into the corresponding models respectively, and perform framework optimization;

[0232] A quality assessment is conducted on the main components of the nuclear reactor, which are structural components including fuel, cladding, heat pipes, reflector layer, and drum assembly, to obtain the total system mass under the corresponding design scheme;

[0233] The nuclear reactor's operating state, shutdown state, heat pipe limit, and structural quality are uniformly determined in the same closed loop using a closed-loop physical evaluation model; and the power capacity is evaluated under the condition of satisfying steady-state heat transfer constraints.

[0234] The specific process of building a quality model:

[0235] The close arrangement of hexagons gives the core cross-sectional area, equivalent radius, and core volume:

[0236]

[0237]

[0238]

[0239] in, is the hexagonal lattice pitch, the distance between the centers of adjacent lattice elements; m is the core control quantity for arrangement density and installability. The effective lattice unit number is dimensionless and represents the number of available positions / lattice points within the cross-section of the core. This refers to the cross-sectional area of ​​the reactor core. To convert the hexagonal array into the equivalent radius (m) of a cylindrical core, and to unify the geometry to a cylindrical model; This refers to the core volume;

[0240] The "mountable diameter" constraint of the lattice pitch is used to avoid geometrically unfeasible placement:

[0241]

[0242]

[0243]

[0244] in, This is the maximum allowable outer diameter within a single crystal lattice unit; Minimize mechanical clearance to ensure that assembly and thermal expansion do not interfere; To allow for manufacturing / assembly margins to absorb machining errors; The outer diameter of the fuel rod; The outer diameter of the heat pipe;

[0245] Fuel rod quality, including fuel and cladding:

[0246]

[0247]

[0248]

[0249]

[0250]

[0251] in, This refers to the number of fuel rods; , These are the outer and inner diameters of the fuel rod, respectively. and Density of fuel and cladding material;

[0252] Heat pipe quality includes the metal wall, the solid capillary wick, and the working fluid.

[0253]

[0254]

[0255]

[0256]

[0257]

[0258]

[0259]

[0260] in, Number of heat pipes; These are the outer and inner diameters of the heat pipe, respectively. The diameter of the steam chamber; This is the total equivalent length of the heat pipe, including the equivalent lengths of the in-pile evaporation section and the out-of-pile section; The capillary porosity is a value that indicates a smaller solid mass but more pores. and Density of wall material and capillary core material; The density of the working fluid in the liquid phase at the evaporation temperature; The working fluid filling coefficient;

[0261] The quality of the reflective layer, specifically, is the outer enveloping cylindrical shell, where the turret cavity is deducted to avoid double weighing;

[0262]

[0263]

[0264] The mass of the drum assembly and absorber, including the drum cavity, drum shell, and absorber sector layers:

[0265]

[0266]

[0267]

[0268]

[0269]

[0270]

[0271]

[0272] in, The total number of drums, including control drums and safety drums; The length of the drum; The sector ratio of the absorber (0–1) reflects the "proportion of the circumferential coverage of the absorbent material"; , , These are the densities of the drum shell / absorbing element / reflective layer materials, respectively.

[0273] Pressure vessel mass, approximately a thin-walled cylindrical shell:

[0274]

[0275]

[0276]

[0277]

[0278]

[0279] in, For design internal pressure; This is an assembly clearance to ensure proper installation and thermal expansion. Minimum manufacturable thickness; Density of the container material;

[0280] Additional structural mass: a lumped model using "volume scale, end face area scale", including supports, end plates, and grids;

[0281]

[0282] in, Density of the structural material; It is a dimensionless volume scaling factor, i.e., the ratio of the structure to the core volume; This is the area scaling factor;

[0283]

[0284] in, The equivalent mass of the drive mechanism for a single drum includes the lumped mass of the motor, bearings, seals, and transmission.

[0285] Total mass summary:

[0286]

[0287] The total mass of the system consists of fuel rods, including fuel and cladding; heat pipes, including wall material, capillary wick, and working fluid; a reflective layer, including reflective material after deducting the drum cavity; a drum assembly, including drum shell and absorber; a pressure vessel; additional structures; and a drum drive mechanism. This summary formula ensures that each geometric space and material is weighed only once and can be directly used in the "mass minimization" objective function in multi-objective optimization.

[0288] The equivalent neutronics model under shutdown conditions is used as a safety constraint for reactor power and mass design. Specifically, the power model is:

[0289]

[0290] in, Target electrical power; For electrical conversion efficiency; For the required thermal power;

[0291]

[0292] Design reactor configuration The heat pipes are responsible for transferring heat from the reactor core. This represents the total thermal power of the reactor core. This represents the average heat transfer power of a single heat pipe.

[0293] Further define the equivalent heat transfer area of ​​the heat pipe evaporator section:

[0294]

[0295] in, The outer diameter of the heat pipe; This refers to the length of the evaporation section;

[0296] The average heat flux density of the evaporation section was obtained:

[0297]

[0298] in, This refers to the length of the evaporation section; The average heat flux density of the evaporation section;

[0299] The maximum sustainable heat transfer capacity of a heat pipe is determined by several limits, including the capillary limit and the sonic blockage limit. The allowable power of a heat pipe is defined as the minimum allowable power of each of these limits.

[0300]

[0301]

[0302]

[0303] in, The surface tension of the working fluid; For wetting contact angle; The equivalent aperture of the capillary core is the smaller the aperture, the larger the capillary head. These represent the pressure drop in the liquid phase and vapor phase, respectively, and their values ​​increase with increasing heat load. This is the term related to gravity.

[0304] The speed of sound limit is as follows:

[0305]

[0306] in, This represents the maximum permissible steam mass flow rate under the speed of sound limit. Latent heat of vaporization;

[0307] Because each heat pipe needs to meet the following requirements Therefore, the upper limit of the total thermal power of the reactor core is:

[0308]

[0309] Meeting the heat pipe limits alone is insufficient; the temperatures of the fuel, cladding, and structure must also be kept within limits. Power models typically correlate "heat generation per unit length" with "radial thermal conduction temperature rise." If the number of fuel rods is... Core height is Then the average linear power is:

[0310]

[0311] The average volumetric power density is:

[0312] .

[0314] like Figure 5 As shown in the optimization algorithm flowchart, step four is also included: under the premise of always meeting the shutdown safety requirements, the MOPIMO (Multi-Objective Projection-Iterative Methods Optimization) optimization algorithm is used to optimize the core size, reflector data, absorber drum assembly data and heat pipe data, so as to maximize the reactor power and control the total mass of the system, thereby achieving a collaborative design of high power and lightweight.

[0315] The specific optimization process is as follows: Figure 6 Pareto front plot and results from MOPIMO algorithm Figure 7 The optimized heat pipe stack structure is shown below:

[0316] Definition of optimization problem:

[0317] Based on the equivalent neutronics model, mass model, and power model, the key structural and operational parameters of the reactor system are defined as a design variable vector. Its general form is:

[0318]

[0319] Based on the system design requirements, the following bi-objective optimization problem is constructed:

[0320] Objective 1: Maximize the sustainable thermal power of the reactor core.

[0321]

[0322] Objective 2: Minimize the total mass of the system.

[0323]

[0324] To ensure the feasibility of the project, the following constraints must be met:

[0325] Shutdown safety constraints:

[0326] Power feasibility constraints:

[0327] Heat pipe temperature constraints:

[0328] Design variable boundary constraints: ;

[0329] Initial population generation and boundary projection:

[0330] To solve the above multi-objective constrained optimization problem, a scale of is introduced. Design population;

[0331] Random initialization: ,in: , represents a uniform random vector;

[0332] If the variable is out of range, then perform boundary projection: This ensures that design variables always remain within the physically feasible range.

[0333] Physical safety and operational status assessment:

[0334] Perform the following for each individual in the population:

[0335] (1). Call the neutronics model → Calculate ,

[0336] (2). Call the power model → Calculate

[0337] (3). Call the quality model → Calculate

[0338] If safety constraints are violated, the action is deemed infeasible.

[0339] Non-dominated sorting and elite solution maintenance:

[0340] If the following conditions are met: , ;

[0341] And at least one objective is strictly superior, then Dominate The elite solution set is used to retain the optimal design solution for the current generation. Update format for each generation: , For the projection direction, The step size.

[0342] Among them, residual guided projection (RGP): This is used to enhance convergence.

[0343] Double Random Projection (DRP): This enhances global search capabilities.

[0344] Weighted Random Projection (WRPU): Balance exploration and development.

[0345] Lévy Flight Guided Projection (LFGP): It is used to escape local optima.

[0346] Environmental selection:

[0347] Merging parent and child generations: Before choosing Individual: ;

[0348] Termination criteria and output results:

[0349] Termination conditions include: or The final output is the Pareto optimal solution set: .

[0350] This invention discloses a computer program product for a space heat pipe nuclear reactor based on shutdown safety physical modeling, including a computer program. When the computer program is run, it causes the design method of a space heat pipe nuclear reactor based on shutdown safety physical modeling described above to be executed.

[0351] The space heat pipe nuclear reactor design method and computer program product based on shutdown safety physical modeling disclosed in this invention have the following beneficial effects:

[0352] 1. Establish an equivalent neutronics physical model of a space heat pipe nuclear reactor under shutdown conditions, and quantitatively describe the influence of absorber drum assembly absorption coverage and reflector layer configuration on the effective growth factor during shutdown.

[0353] 2. Clarify the constraints of shutdown safety on core dimensions, reflector structure, and power levels to form physical criteria that can be used for design;

[0354] 3. With shutdown safety as a prerequisite constraint, ensure that the high-power, lightweight design scheme still has sufficient subcritical safety margin in non-operational states;

[0355] 4. Under the premise of meeting the shutdown safety limits, the power level of the reactor and the system mass are synergistically balanced to obtain a design scheme with high power and controlled mass; this is conducive to obtaining a high specific power space heat pipe nuclear reactor scheme and improving the reactor power output per unit mass.

[0356] 5. The design process has a clear physical meaning, which makes it easier for engineers to make reasonable trade-offs between safety, power and quality.

[0357] Of course, those skilled in the art should be able to make various corresponding changes and modifications based on the present invention without departing from its spirit and essence, but all such changes and modifications should fall within the protection scope of the appended claims.

Claims

1. A design method for a space heat pipe nuclear reactor based on shutdown safety physical modeling, characterized in that: Includes the following steps: I. Establish the mass model, safety model, and power model of the nuclear reactor; specifically, establish the equivalent model of the nuclear reactor, the equivalent model of the reflection structure, and the equivalent model of the drum assembly under shutdown conditions. The nuclear reactor core is modeled as a cylinder, including the core and multiple parallel heat pipes. The equivalent radius and height of the core are defined. The radial and axial thicknesses of the reflector are introduced, and the effect of the reflector on neutron leakage is described by extrapolation of the boundary and reflection savings. The specific steps are as follows: By introducing extrapolated boundary lengths, the actual boundary conditions are equivalent to extensions of geometric dimensions; The extrapolated boundary length of the core material is defined as: in, The core equivalent diffusion coefficient reflects the diffusion capability of neutrons within the core. This represents the equivalent macroscopic absorption cross section of the reactor core. This represents the equivalent size increment caused by the diffusion boundary conditions; The reflection savings increase with increasing reflective layer thickness, but tend to saturate at larger thicknesses; therefore, an exponential saturation form is used to describe this. in, The thickness of the reflective layer, This represents the amount of reflection savings at the corresponding thickness. This represents the limit of the reflection savings. The characteristic saturation length; the limit of reflection savings is related to the neutronic properties of the reflective layer material, which can be expressed as: in, The extrapolated boundary length of the reflective layer material. Let be the core diffusion coefficient; this expression reflects the "diffusion capability advantage" of the reflector layer relative to the core: for; Define the radial and axial reflection savings separately: in, The radial reflective layer thickness is... The thickness of the axial reflective layer. and These represent the radial and axial reflection savings, respectively. The equivalent dimensions of the constructed core are as follows: in, , These are the physical radius and height of the reactor core, respectively. Define the absorber drum assembly, namely the control drum and the safety drum, in the absorption configuration under shutdown conditions. The enhancement effect of the absorber drum assembly on radial and axial neutron leakage is equivalently described by the circumferential absorption coverage, axial coverage height and geometric relationship with the reflector of the absorber drum assembly. The geometric relationships are as follows: in, For macroscopic neutron production, fission neutron yield × macroscopic fission cross section; Macroscopic absorption cross section; The diffusion coefficient is denoted as . For geometric buckling; The larger the leakage, the more accurate the calculation. To link leakage to geometry, the core is equivalent to a cylinder, and the fundamental mode buckling occurs. The thickness of the drum and the reflective layer determines the center radius of the drum. The further out the drum is, the stronger the disruption of the reflection boundary: in, This is a dimensionless bias coefficient that describes the "relative position" of the drum center inside the reflector layer. The closer it is to 0, the closer the drum is to the core boundary. Drum diameter With the center radius of the drum Determine the circumferential blocking angle of a single drum Thus, the circumferential coverage is obtained. : Equivalent description of radial leakage enhancement: in, To save radial energy for clean reflection, , These refer to the effective coverage ratios of the control drum and the safety drum, respectively. , These are the absorption and saving ratios of the control drum and the safety drum, respectively; Equivalent description of axial leakage enhancement: in, ∈[0,1] is a dimensionless reduction coefficient; 2. Input the constraints of the safety model into the model to ensure that the design meets the shutdown safety requirements; Based on the equivalent model in operation, the absorption effect of the absorber drum assembly is introduced to reduce the reflection savings, and the equivalent core size in the shutdown state is constructed. The effective growth factor during shutdown is then calculated based on diffusion theory. ; when If the value is less than or equal to the preset shutdown safety limit, then the design meets the shutdown safety requirements. Calculate runtime reflection savings: The equivalent size in operation is obtained by superimposing the "physical size + extrapolated boundary + reflection savings": Calculate the geometric coverage of the drum assembly: Next, construct the "effective coverage" from the "geometric coverage"; in, The effective boundary degradation coefficient; Radial introduction method: Subtract the "coverage penalty" from the "clean reflection savings" to obtain the effective radial savings during shutdown: Axial introduction method: Use "attenuation coefficient" to reduce axial savings: The process of writing back the "reduced savings" to the shutdown equivalent size completes the construction from the running state to the shutdown state: Third, based on step two, input the constraints of the mass model and the power model into the corresponding models respectively, and perform framework optimization; A quality assessment is conducted on the main components of the nuclear reactor, which are structural components including fuel, cladding, heat pipes, reflector layer, and drum assembly, to obtain the total system mass under the corresponding design scheme; The nuclear reactor's operating state, shutdown state, heat pipe limit, and structural quality are uniformly determined in the same closed loop using a closed-loop physical evaluation model; and the power capacity is evaluated under the condition of satisfying steady-state heat transfer constraints.

2. The design method for a space heat pipe nuclear reactor based on shutdown safety physical modeling according to claim 1, characterized in that: The specific process of constructing the quality model is as follows: The close arrangement of hexagons gives the core cross-sectional area, equivalent radius, and core volume: in, is the hexagonal lattice pitch, the distance between the centers of adjacent lattice elements; m is the core control quantity for arrangement density and installability. The effective lattice unit number is dimensionless. This refers to the cross-sectional area of ​​the reactor core. The equivalent radius (m) when the hexagonal array is equivalent to a cylindrical core; This refers to the core volume; Lattice pitch "mountable diameter" constraint: in, This is the maximum allowable outer diameter within a single crystal lattice unit; Minimum mechanical clearance; To allow for manufacturing / assembly margins; The outer diameter of the fuel rod; The outer diameter of the heat pipe; Fuel rod quality, including fuel and cladding: in, This refers to the number of fuel rods; , These are the outer and inner diameters of the fuel rod, respectively. and Density of fuel and cladding material; Heat pipe quality includes the metal wall, the solid capillary wick, and the working fluid. in, Number of heat pipes; These are the outer and inner diameters of the heat pipe, respectively. The diameter of the steam chamber; This is the total equivalent length of the heat pipe, including the equivalent lengths of the in-pile evaporation section and the out-of-pile section; Capillary porosity; and Density of wall material and capillary core material; The density of the working fluid in the liquid phase at the evaporation temperature; The working fluid filling coefficient; The quality of the reflective layer, specifically, is the outer enveloping cylindrical shell, where the turret cavity is deducted to avoid double weighing; The mass of the drum assembly and absorber, including the drum cavity, drum shell, and absorber sector layers: in, The total number of drums, including control drums and safety drums; The length of the drum; The absorber sector ratio is (0–1). , , These are the densities of the drum shell / absorbing element / reflective layer materials, respectively. Pressure vessel mass, approximately a thin-walled cylindrical shell: in, For design internal pressure; This is for assembly clearance; Minimum manufacturable thickness; Density of the container material; Additional structural mass: a lumped model using "volume scale, end face area scale", including supports, end plates, and grids; in, Density of the structural material; It is a dimensionless volume scaling factor, i.e., the ratio of the structure to the core volume; This is the area scaling factor; in, The equivalent mass of the drive mechanism for a single drum includes the lumped mass of the motor, bearings, seals, and transmission. Total mass summary: The total mass of the system consists of fuel rods, including fuel and cladding; heat pipes, including wall material, capillary wick, and working fluid; reflective layer, including reflective material after deducting the drum cavity; drum assembly, including drum shell and absorber; pressure vessel; additional structures; and drum drive mechanism. This summary formula ensures that each geometric space and material is weighed only once and can be directly used in the "mass minimization" objective function in multi-objective optimization.

3. The design method for a space heat pipe nuclear reactor based on shutdown safety physical modeling according to claim 2, characterized in that: The equivalent neutronics model under shutdown conditions is used as a safety constraint for reactor power and mass design. Specifically, the power model is: in, Target electrical power; For electrical conversion efficiency; For the required thermal power; Design reactor configuration The heat pipes are responsible for transferring heat from the reactor core. This represents the total thermal power of the reactor core. This represents the average heat transfer power of a single heat pipe. Further define the equivalent heat transfer area of ​​the heat pipe evaporator section: in, The outer diameter of the heat pipe; This refers to the length of the evaporation section; The average heat flux density of the evaporation section was obtained: in, This refers to the length of the evaporation section; The average heat flux density of the evaporation section; The maximum sustainable heat transfer capacity of a heat pipe is determined by several limits, including the capillary limit and the sonic blockage limit. The allowable power of a heat pipe is defined as the minimum allowable power of each of these limits. in, The surface tension of the working fluid; For wetting contact angle; The equivalent aperture of the capillary core; These represent the pressure drop during liquid / vapor flow, respectively. This is the term related to gravity. The speed of sound limit is as follows: in, This represents the maximum permissible steam mass flow rate under the speed of sound limit. Latent heat of vaporization; Because each heat pipe needs to meet the following requirements Therefore, the upper limit of the total thermal power of the reactor core is: Power models typically correlate "heat generation per unit length" with "radial thermal conduction temperature rise"; if the number of fuel rods is... Core height is Then the average linear power is: The average volumetric power density is: 。 4. The design method for a space heat pipe nuclear reactor based on shutdown safety physical modeling according to claim 3, characterized in that: It also includes step four, which optimizes the core size, reflector data, absorber drum assembly data, and heat pipe data using the MOPIMO (Multi-Objective Projection-Iterative Methods Optimization) algorithm while ensuring that the shutdown safety requirements are always met.

5. A computer program product for a space heat pipe nuclear reactor based on shutdown safety physical modeling, characterized in that: The system includes a computer program that, when run, causes the design method for a space heat pipe nuclear reactor based on shutdown safety physical modeling, as described in any one of claims 1-4, to be executed.

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