Method for modeling flow and heat transfer in a reactor based on the theory of fixed-point similarity

Abstract

The application discloses a reactor flow heat transfer modeling method based on fixed solution similarity theory, which comprises the following steps: 1, deriving an original control equation; 2, dimensionless processing; 3, applying fixed solution similarity theory; and 4, distortion evaluation. The application considers the universality of the flow heat transfer control equation with the introduction of the continuous medium hypothesis and the limitation of experimental research in the high-temperature and high-pressure operation environment. In view of the fact that the existing modeling theory lacks strict quantitative evaluation standards and transient distortion phenomena, the application provides a general modeling method which is not limited to working medium, thermodynamic state and does not introduce additional physical assumptions, and summarizes a group of dimensionless criterion numbers representing the flow and heat transfer physical laws, so as to provide a reference for the engineering verification experiment of the thermal fluid and reactor engineering research by using the substitute working medium.

Description

Technical Field

[0001] This invention belongs to the interdisciplinary field of thermal fluid and reactor engineering, specifically relating to a reactor flow heat transfer modeling method based on boundary value similarity theory. Background Technology

[0002] Fourth-generation reactors typically employ advanced coolant designs to improve the safety, economy, and sustainability of nuclear reactors. Commonly used coolants include helium, liquid metals (such as lead and sodium), and molten salts. Most of these coolants operate at high temperatures, and some even require high pressure environments to ensure stable reactor operation. Experimental research is needed to verify the effectiveness of these coolants. However, due to the high temperature and pressure conditions, coupled with the fact that some coolants are toxic and invisible, direct experimentation is difficult. Model-based experiments are necessary to better study and verify the design and performance of these reactors. Model-based experiments can be conducted through computer simulations or small-scale experiments, which reduces experimental costs and risks and allows for a better understanding of relevant physical properties and process parameters. Furthermore, model-based experiments can provide valuable references for the future development of the nuclear energy field.

[0003] Currently, modeling methods mainly include linear scaling, power-volume scaling, and the Ishii three-stage method. In recent years, Zuber et al. developed a structured method for modeling complex systems, solving the modeling problem at two levels: a top-down (inductive) system approach and a bottom-up (deductive) process and phenomenon approach, called H2TS. H2TS can be widely applied to various complex systems, no longer limited to individual physical processes, and can deeply understand the essence of different levels and types of physical processes. It can be applied to complex systems and quantitatively evaluate distortion. However, the entire H2TS modeling process relies on the empirically based Phenomenon Identification and Ranking Table (PIRT), and the occurrence of some important phenomena in complex systems is parallel and strongly coupled, and cannot be simply divided into stages based on time progression. The resulting dimensionless characteristic numbers may be contradictory. In 2015, Jose N. Reyes first proposed the Dynamic System Scaling (DSS) method. This method can obtain the scaling scale of the entire system and evaluate the proportional distortion generated by the entire process; it already has some simple applications. The DSS method describes physical processes as trajectories in a typical normalized coordinate system found in dynamical system studies. In this method, both process and geometric approximations are attributed to the invariance of process metrics under coordinate transformations; therefore, if two processes have similar trajectories in phase space, they can be considered similar. Under this normalized coordinate system, five different scaling methods are derived using two-parameter affine transformations, including the well-known power volume method. In summary, H2TS is currently the most theoretically complete and mature modeling method, while DSS is a novel modeling method that requires further application and promotion in complex systems.

[0004] However, existing H2TS and DSS modeling theories have two main problems: 1. The modeling theory lacks rigorous quantitative evaluation criteria. According to the similarity principle, when two physical processes are similar, the entire set of dimensionless quantities must be equal. Clearly, the similarity principle has very strict requirements. However, existing modeling principles achieve similarity by keeping some dimensionless numbers or sets of dimensionless quantities (similarity criterion numbers) unchanged. These criterion numbers are merely local or global parameters. In reality, physical processes evolve in the form of spatiotemporal fields, therefore, there is no quantitative mathematical theory to prove the correctness of the modeling, and the selection of similarity criterion numbers often relies heavily on engineering experience. 2. H2TS struggles to capture transient distortions. Furthermore, although this method has many applications, it is mainly used to determine the consistency of similarity criterion numbers and design modeling structures. This work is usually done for steady-state conditions. For transient processes, only the Strouhal number can be used to evaluate initial distortion, and it cannot track and capture the subsequent spatiotemporal evolution of the physical field. 3. The DSS method, based on double affine transformation, is currently only applied to a few simple problems and requires further research and analysis to clarify its applicability. In summary, improving and refining existing modeling theories both transiently and quantitatively, and applying them to the study of the flow and heat transfer characteristics of fourth-generation reactor coolants, combined with experimental verification, is also an important task that urgently needs to be carried out. Summary of the Invention

[0005] To address the problems existing in the prior art, the present invention aims to propose a reactor flow heat transfer modeling method based on boundary value similarity theory. By treating the general flow heat transfer control equations dimensionlessly and comprehensively considering the morphology, thermodynamic state, and compressibility of the flowing working fluid, a set of dimensionless equations is obtained, including five basic types of dimensionless energy equations, regardless of the working fluid or thermodynamic state. A set of dimensionless criterion numbers for characterizing flow heat transfer phenomena is also proposed. Dimensional and dimensionless solutions are obtained by applying boundary value similarity theory to the prototype and model, respectively. This avoids direct experiments on high-temperature, high-pressure, and invisible environments for high-temperature, high-pressure coolants, simplifies the modeling method, reduces experimental costs, and enables the study of reactor coolant flow heat transfer characteristics. Therefore, this method can serve as a general flow heat transfer characteristic modeling method for engineering experiments in the fields of thermal fluids and reactor engineering.

[0006] To achieve the above objectives and technical effects, the present invention adopts the following technical solutions:

[0007] A reactor flow heat transfer modeling method based on boundary value similarity theory includes the following steps:

[0008] Step 1: The reactor flow heat transfer system is the fourth-generation reactor coolant and its flow heat transfer system. Define the system's operating time, geometry, boundary conditions, initial state, flow heat transfer medium, and external source terms. The operating time is limited to a finite domain greater than 0. The geometry is limited to finite domains in one-dimensional, two-dimensional, and three-dimensional spaces. The boundary conditions include first, second, and third types of boundary conditions. The initial state is: temperature 10K-1500K, pressure 0-30MPa. The flow heat transfer medium is limited to a fluid that satisfies the continuous medium assumption. The external source terms are limited to time-varying bounded mass, momentum, and energy source terms.

[0009] Step 2: Describe the reactor flow heat transfer system using the general flow heat transfer control equations:

[0010] (1) Continuity equation:

[0011]

[0012] (2) Momentum equation:

[0013]

[0014] (3) Five types of energy equations:

[0015] Total energy equation:

[0016]

[0017] Total enthalpy equation:

[0018]

[0019] Internal energy equation:

[0020]

[0021] Enthalpy equation:

[0022]

[0023] Temperature equation:

[0024]

[0025] Equations (1) to (7) only introduce the flux differentiability assumption and the Stokes assumption. The meanings of their symbols in the reactor fluid system are as follows:

[0026] ρ: density of the working fluid / kg·m -3 ; Speed ​​of motion / m·s -1 ; Viscous force / Pa; acceleration / m·s-2 p: Pressure acting on the surface element / Pa; μ: Dynamic viscosity / Pa·s; t: Time / s; e: Specific total energy / J·kg -1 λ: Thermal conductivity / W·m -1 ·K -1 T: Temperature / K; u: Specific internal energy / J·kg -1 ; Specific total enthalpy / J·kg -1 h: Enthalpy / J·kg -1 c p Specific heat at constant pressure / J·K -1 ·kg -1 ; Unit second-order tensor;

[0027] Step 3: Dimensionlessize the reactor flow and heat transfer control equations:

[0028] Dimensionless continuity equation:

[0029]

[0030] Dimensionless momentum equation:

[0031]

[0032] Dimensionless total energy equation:

[0033]

[0034] Dimensionless total enthalpy equation:

[0035]

[0036] Dimensionless internal energy equation:

[0037]

[0038] Dimensionless enthalpy equation:

[0039]

[0040] Dimensionless temperature equation:

[0041]

[0042] The dimensionless parameters introduced in equations (8) to (14) are as follows:

[0043] ρ': dimensionless density; t': dimensionless time; Dimensionless velocity; p': dimensionless pressure; The unit vector of the direction of gravitational acceleration; Dimensionless viscous force; e′: dimensionless total energy; u′: dimensionless internal energy; h′: dimensionless enthalpy; Dimensionless total enthalpy; λ′: dimensionless thermal conductivity; μ′: dimensionless dynamic viscosity; Γ: dimensionless temperature; C' p : Dimensionless isobaric specific heat; T0: Reference temperature / K; ρ0: Reference density / kg·m³ -3 v0: Reference speed / m·s -1 ;

[0044] Equations (8) to (14) contain common similarity criteria numbers:

[0045] Strouhal number: a similarity criterion characterizing unsteady and periodic flows;

[0046] Re – Reynolds number: Characterized by the ratio of inertial force to viscous force;

[0047] Fr – Froude number: a ratio representing the relative magnitude of fluid inertial force and gravity;

[0048] Pe – Peckley number: Characterizes the ratio of convection to heat diffusion in a fluid;

[0049] And the similarity criterion number group:

[0050]

[0051] In equation (15), the meanings of each similarity criterion number are as follows:

[0052] —Based on the similarity criterion number derived from the Euler number Eu, it characterizes the ratio of absolute fluid pressure to dynamic head;

[0053] —Based on the similarity criterion number of the Ekert number Ec, it characterizes the ratio of fluid kinetic energy to approximate specific enthalpy;

[0054] Su e —Characterizes the ratio of total energy to kinetic energy of a fluid;

[0055] —Characterizes the ratio of total enthalpy to kinetic energy of a fluid;

[0056] Su u —Characterizes the ratio of a fluid's specific internal energy to its kinetic energy;

[0057] Su h —Characterizes the ratio of specific enthalpy to kinetic energy of a fluid;

[0058] In equation (15), the meanings of each reference physical quantity are as follows:

[0059] v0: Reference speed; c p0: Reference isobaric specific heat; T0: Reference temperature; p0: Reference pressure; ρ0: Reference density; Δp: Pressure drop; e0: Reference total energy; u0: Reference specific internal energy; Reference specific enthalpy; h0: Reference specific enthalpy; ΔT: Temperature difference;

[0060] Step 4: Apply boundary value similarity theory to the dimensionless reactor flow heat transfer control equations to determine the same dimensionless spacetime coordinates, steady dimensionless coefficients, and unsteady dimensionless coefficients for the prototype and model, thus obtaining a set of identical dimensionless solutions. Boundary value similarity theory states that after defining the dependent variable and domain and making the spacetime differential-algebraic equation system dimensionless, under the same dimensionless coordinates and nonlinear parameters, a set of boundary value conditions is introduced and Newton's iteration is performed to obtain a unique dimensionless spacetime solution. Mapping back to any dimensional physical process based on this dimensionless spacetime solution yields similar results. The dimensionless spacetime differential-algebraic equation system is described using the following formula:

[0061]

[0062] The meanings of the symbols in equation (16) are as follows:

[0063] Y′: Dimensionless spacetime solution; r′: Dimensionless spatial coordinates; t′: Dimensionless time coordinates; F s : a steady dimensionless coefficient; F us (Y′): Unsteady dimensionless coefficient;

[0064] Then, the principle of similarity is applied:

[0065] 1. The similarity criterion between the prototype and the experiment, i.e., the coefficients of all terms in the dimensionless spacetime differential algebraic equation are equal;

[0066] 2. Make the dimensionless independent variables equal, that is, satisfy the linear transformation of all coordinates in geometry;

[0067] 3. For transient experiments, the dimensionless time should be kept constant;

[0068] 4. Make the dimensionless initial and boundary conditions equal;

[0069] 5. Using nonlinear programming methods, obtain the reference values, geometric structure, and time-varying source terms corresponding to the experimental system that minimizes the deviations from the prototype's dimensionless similarity criterion numbers, initial conditions, and boundary conditions;

[0070] Furthermore, since the pressure values ​​of incompressible and weakly compressible fluids are independent of their thermophysical properties, it is also necessary to ensure that there is the same dimensionless pressure field as the source term. For compressible fluids, only the total energy, total enthalpy, internal energy, and enthalpy equations can be used for modeling, while incompressible or weakly compressible fluids can also use the temperature equation. However, the physical processes described by all energy equations are equivalent, and the differences in dependent variables reflect different viewpoints on the conservation of energy, thus resulting in different modeling results.

[0071] The main and secondary parameters affecting the physical quantities are selected to conduct a model distortion evaluation of the simulation results, as follows:

[0072] A distortion factor is introduced to describe the distortion of a module j in a phenomenon n. It can evaluate features such as the time ratio, dimensionless number, or scaling parameter between the prototype and the model.

[0073]

[0074] In equation (17):

[0075] [Π j,n ] p : Dimensionless criterion number of the prototype; [Π j,n ] m : Dimensionless criterion number of the model; DF j,n : Represents the fractional difference between the prototype and the model of the conserved quantity transported through a phenomenon n in each module j, and its value reflects the degree of distortion between the prototype and the model.

[0076] Compared with the prior art, the present invention has the following advantages:

[0077] 1. Rigorous theoretical framework. The method of this invention proposes a boundary value similarity theory, which explains the selection of alternative working fluids, confirmation of boundary conditions, and evaluation of dimensionless criterion numbers for numerical simulation and experimentation in the modeling research from the perspective of differential systems, which helps in the selection of the final modeling scheme.

[0078] 2. Good versatility. Based on the fundamental general governing equations for flow and heat transfer, this invention proposes a universal modeling method that is unrestricted by working fluid or state and does not introduce physical assumptions. A new set of dimensionless number groups, Ec, is obtained through this method. Su Eu Su The method uses the Su dimensionless number group, and these dimensionless numbers are interconvertible, which can characterize the basic physical phenomena of flow and heat transfer and have strict physical meaning. Since no assumptions are introduced in the derivation process, this method is applicable to the modeling study of any flowing working fluid and has good universality.

[0079] 3. High accuracy. Since no assumptions are introduced in the derivation process, the method of this invention can not only replace the existing H2TS method, but also make up for the defects of the existing dynamic modeling theoretical framework. It can quantitatively track the distortion terms of dimensionless equations and improve the accuracy of theoretical prediction. Attached Figure Description

[0080] Figure 1 This is a flowchart of the reactor flow heat transfer modeling method based on boundary value similarity theory of the present invention. Detailed Implementation

[0081] The following is in conjunction with the appendix Figure 1 Taking the steady-state flow of liquid lead-bismuth in the main loop system of a lead-bismuth pile as an example, the specific implementation of the method of the present invention will be described in detail.

[0082] The reactor flow heat transfer modeling method based on boundary value similarity theory includes the following steps:

[0083] Step 1: The working fluid is determined to be liquid lead-bismuth. The analysis object is the main loop system component of the lead-bismuth stack. The operating pressure is limited to 0.1 MPa, the temperature in the loop is limited to 573 K-773 K, the operating state is steady state, and the liquid lead-bismuth is considered to be an incompressible fluid.

[0084] Step 2: Describe the reactor flow heat transfer system using the general flow heat transfer control equations:

[0085] (1) Continuity equation:

[0086]

[0087] (2) Momentum equation:

[0088]

[0089] (3) Five types of energy equations:

[0090] Total energy equation:

[0091]

[0092] Total enthalpy equation:

[0093]

[0094] Internal energy equation:

[0095]

[0096] Enthalpy equation:

[0097]

[0098] Temperature equation:

[0099]

[0100] Equations (1) to (7) only introduce the flux differentiability assumption and the Stokes assumption. The meanings of their symbols in the reactor fluid system are as follows:

[0101] ρ LBE Density of liquid lead bismuth / kg·m -3 ; Velocity of liquid lead bismuth / m·s -1 ; Viscous force / Pa; Acceleration of liquid lead-bismuth / m·s -2 p: Pressure acting on the surface element / Pa; μ LBE : Dynamic viscosity of liquid lead-bismuth / Pa·s; t: time / s; e LBE Specific total energy of liquid lead-bismuth / J·kg -1 ;λ LBE Thermal conductivity of liquid lead-bismuth / W·m -1 ·K -1 ;T LBE Temperature of liquid lead-bismuth in K; u LBE Specific internal energy of liquid lead-bismuth / J·kg -1 ; Specific total enthalpy of liquid lead-bismuth / J·kg -1 h LBE Specific enthalpy of liquid lead-bismuth / J·kg -1 c p,LBE Specific heat at constant pressure of liquid lead-bismuth / J·K -1 ·kg -1 ; Unit second-order tensor;

[0102] Step 3: Dimensionlessly transform the reactor flow and heat transfer control equations. Since liquid lead-bismuth has been considered an incompressible fluid, all five types of energy equations are applicable. In this embodiment, the temperature equation is used as an example for dimensionless transformation. The dimensionless transformation methods for other types of energy equations are similar, resulting in the following three major dimensionless equations:

[0103] Dimensionless continuity equation:

[0104]

[0105] Dimensionless momentum equation:

[0106]

[0107] Dimensionless temperature equation:

[0108]

[0109] The dimensionless parameters introduced in equations (8) to (10) are as follows:

[0110] ρ': dimensionless density; t': dimensionless time; Dimensionless velocity; p': dimensionless pressure; The unit vector of the direction of gravitational acceleration; Dimensionless viscous force; λ′: dimensionless thermal conductivity; Γ: dimensionless temperature; C' p : Dimensionless isobaric specific heat; T0: Reference temperature / K; ρ0: Reference density / kg·m³ -3 v0: Reference speed / m·s -1 ;

[0111] Equations (8) to (10) contain common similarity criteria numbers:

[0112] Strouhal number: a similarity criterion characterizing unsteady and periodic flows;

[0113] Re – Reynolds number: Characterized by the ratio of inertial force to viscous force;

[0114] Fr – Froude number: a ratio representing the relative magnitude of fluid inertial force and gravity;

[0115] Pe – Peckley number: Characterizes the ratio of convection to heat diffusion in a fluid;

[0116] And the similarity criterion number proposed in this invention:

[0117]

[0118] In equation (11), the similarity criterion number has the following meaning:

[0119] —Based on the similarity criterion number of the Ekert number Ec, it characterizes the ratio of fluid kinetic energy to approximate specific enthalpy;

[0120] In equation (11), the meanings of each reference physical quantity are as follows:

[0121] v0: Reference speed; c p0 : Reference isobaric specific heat; T0: Reference temperature; ΔT: Temperature difference; The reference values ​​are selected as the physical quantity values ​​corresponding to liquid lead-bismuth and the alternative working fluid at the inlet in the model and prototype;

[0122] Step 4: Apply boundary value similarity theory to the dimensionless reactor flow heat transfer control equations to determine the same dimensionless spacetime coordinates, steady dimensionless coefficients, and unsteady dimensionless coefficients for the prototype and model, thus obtaining a set of identical dimensionless solutions. Boundary value similarity theory states that after defining the dependent variable and domain and making the spacetime differential-algebraic equation system dimensionless, under the same dimensionless coordinates and nonlinear parameters, a set of boundary value conditions is introduced and Newton's iteration is performed to obtain a unique dimensionless spacetime solution. Mapping back to any dimensional physical process based on this dimensionless spacetime solution yields similar results. The dimensionless spacetime differential-algebraic equation system is described using the following formula:

[0123]

[0124] The meanings of the symbols in equation (12) are as follows:

[0125] Y′: Dimensionless spacetime solution; r′: Dimensionless spatial coordinates; t′: Dimensionless time coordinates; F s : a steady dimensionless coefficient; F us (Y′): Unsteady dimensionless coefficient;

[0126] Then, the principle of similarity is applied:

[0127] 1. The similarity criterion between the prototype and the experiment, i.e., the coefficients of all terms in the dimensionless spacetime differential algebraic equations are equal. In this embodiment, the flow is steady-state, therefore the dimensionless time term can be ignored, i.e., the coefficients of the dimensionless continuity equation, the dimensionless momentum equation, and the dimensionless temperature equation are equal. and This can be omitted; for incompressible liquid lead-bismuth, the dimensionless temperature equation... This can also be ignored; to ensure that liquid lead-bismuth and the alternative working fluid satisfy flow and heat transfer similarity, Re, Fr, Pe, and Ec in the dimensionless equations should be guaranteed. Su For each corresponding element to be equal, the liquid lead-bismuth and the alternative working fluid must satisfy the two flow similarities, resulting in v' LBE =v' sub ,p' LBE =p' sub That is, the dimensionless velocity and dimensionless pressure of the two flows are equal; v' LBE v' sub p' represents the dimensionless velocities of liquid lead-bismuth and the alternative working fluid, respectively. LBE p' sub These are the dimensionless pressures of liquid lead-bismuth and the alternative working fluid, respectively.

[0128] 2. Set the dimensionless independent variables to be equal, which satisfies the linear transformation of all geometric coordinates. Here, we are in a steady state and do not consider the time coordinate, ensuring the dimensionless coordinate x' of liquid lead-bismuth. LBE ,y' LBE ,z'LBE and the dimensionless coordinate x' of the alternative working fluid sub ,y' sub ,z' sub Corresponding equal;

[0129] 3. Let the dimensionless initial conditions and boundary conditions be equal. For steady-state flow, there are no requirements for the dimensionless initial conditions, while v' = 0 is satisfied on the dimensionless solid wall.

[0130] 4. Using nonlinear programming methods, obtain the reference values, geometric structure, and time-varying source terms corresponding to the experimental system that minimizes the deviations from the prototype's dimensionless similarity criterion numbers, initial conditions, and boundary conditions;

[0131] Finally, based on the results of the physical quantities of the coolant working fluid in the prototype and model obtained in steps 1 to 4 above, the main and secondary parameters affecting the results are selected to conduct a model distortion evaluation of the simulation results; a distortion factor is introduced to describe the distortion degree of a certain part j in a certain phenomenon n, which can evaluate the characteristic time ratio, dimensionless number or proportional parameters of the prototype and model.

[0132]

[0133] In equation (13):

[0134] [Π j,n ] p : Dimensionless criterion number of the prototype; [Π j,n ] m : Dimensionless criterion number of the model; DF j,n : Represents the fractional difference between the prototype and the model of the conserved quantity transported through a phenomenon n in each module j, and its value reflects the degree of distortion between the prototype and the model.

[0135] It should be noted that this embodiment only describes the steady-state flow of liquid lead-bismuth in a lead-bismuth fast reactor, assuming it to be an incompressible fluid and using a dimensionless temperature equation as an example. For compressible fluids, only the total energy, total enthalpy, internal energy, and enthalpy equations can be used for modeling. However, the physical processes described by all energy equations are equivalent; the differences in the dependent variables reflect different perspectives on energy conservation, thus leading to different modeling results. In fact, this invention is also applicable to other flow and heat transfer phenomena involved in thermal fluids and reactor engineering, and is not limited to the objects listed in this embodiment.

[0136] The above description is a further detailed explanation of the present invention in conjunction with specific preferred embodiments. It should not be construed that the specific embodiments of the present invention are limited to this. The scope of application is not limited to the working fluid or thermodynamic state. The lead-bismuth fast reactor mentioned in the embodiments is only one solution of the present invention. For those skilled in the art, several simple deductions or substitutions can be made without departing from the concept of the present invention, and the invention can be applied and extended to other types of reactors. All of these should be considered as falling within the scope of patent protection determined by the submitted claims.

Claims

1. A reactor flow heat transfer modeling method based on boundary value similarity theory, characterized in that: Includes the following steps: Step 1: The reactor flow heat transfer system is the fourth-generation reactor coolant and its flow heat transfer system. The working fluid of the system is liquid lead-bismuth. The object of analysis is the main loop system component of the lead-bismuth reactor. The system's operating time, geometry, boundary conditions, initial state, flow heat transfer fluid, and external source terms are defined. The operating time is limited to a finite domain greater than 0. The geometry is limited to finite domains in one-dimensional, two-dimensional, and three-dimensional spaces. The boundary conditions include the first, second, and third types of boundary conditions. The initial state is: temperature 10K-1500K, pressure 0-30MPa. The flow heat transfer fluid is limited to a fluid that satisfies the continuous medium assumption. The external source terms are limited to time-varying bounded mass, momentum, and energy source terms. Step 2: Describe the reactor flow heat transfer system using the general flow heat transfer control equations: (1) Continuity equation: (1) (2) Momentum equation: (2) (3) Five types of energy equations: Total energy equation: (3) Total enthalpy equation: (4) Internal energy equation: (5) Enthalpy equation: (6) Temperature equation: (7) Equations (1) to (7) only introduce the flux differentiability assumption and the Stokes assumption. The meanings of their symbols in the reactor fluid system are as follows: Density of liquid lead bismuth / ; : Velocity of liquid lead bismuth / ; : Viscous force / ; Acceleration of liquid lead-bismuth / ; Pressure acting on a surface element / ; : Dynamic viscosity of liquid lead bismuth / ; :time / ; Specific total energy of liquid lead bismuth / ; Thermal conductivity of liquid lead-bismuth / ; Temperature of liquid lead bismuth / ; Specific internal energy of liquid lead-bismuth / ; Specific total enthalpy of liquid lead bismuth / ; Specific enthalpy of liquid lead bismuth / ; Specific heat at constant pressure of liquid lead-bismuth / ; Unit second-order tensor; Step 3: Dimensionlessize the reactor flow and heat transfer control equations: Dimensionless continuity equation: (8) Dimensionless momentum equation: (9) Dimensionless total energy equation: (10) Dimensionless total enthalpy equation: (11) Dimensionless internal energy equation: (12) Dimensionless enthalpy equation: (13) Dimensionless temperature equation: (14) The dimensionless parameters introduced in equations (8) to (14) are as follows: Dimensionless density; Dimensionless time; : Dimensionless velocity; Dimensionless pressure; : The unit vector in the direction of gravitational acceleration; : Dimensionless viscous force; Dimensionless total energy; Dimensionless internal energy; Dimensionless enthalpy; Dimensionless total enthalpy; : Dimensionless thermal conductivity; Dimensionless dynamic viscosity; Dimensionless temperature; Dimensionless specific heat at constant pressure; Reference temperature / K; Reference density / ; Reference speed / ; Equations (8) to (14) contain common similarity criteria numbers: —Strauhal number: a similarity criterion characterizing unsteady and periodic flows; —Reynolds number: Characterized by the ratio of inertial forces to viscous forces; —Froude number: a ratio representing the relative magnitudes of fluid inertial forces and gravity; —Peckley number: a ratio that characterizes the convection to thermal diffusion in a fluid; And the similarity criterion number group: (15) In equation (15), the meanings of each similarity criterion number are as follows: —Based on Euler number The similarity criterion number of evolution represents the ratio of fluid absolute pressure to dynamic head; —Based on Ekert numbers The similarity criterion number of evolution represents the ratio of fluid kinetic energy to approximate specific enthalpy; —Characterizes the ratio of total energy to kinetic energy of a fluid; —Characterizes the ratio of total enthalpy to kinetic energy of a fluid; —Characterizes the ratio of a fluid's specific internal energy to its kinetic energy; —Characterizes the ratio of specific enthalpy to kinetic energy of a fluid; In equation (15), the meanings of each reference physical quantity are as follows: Reference speed; Reference specific heat at constant pressure; Reference temperature; Reference pressure; Reference density; Pressure drop; Reference ratio to total energy; Reference specific internal energy; Reference total enthalpy; Reference enthalpy; Temperature difference, the reference value is selected as the physical quantity value corresponding to liquid lead bismuth and alternative working fluid at the inlet in the model and prototype; Step 4: Apply boundary value similarity theory to the dimensionless reactor flow heat transfer control equations to determine the same dimensionless spacetime coordinates, steady dimensionless coefficients, and unsteady dimensionless coefficients for the prototype and model, thus obtaining a set of identical dimensionless solutions. Boundary value similarity theory states that after defining the dependent variable and domain and making the spacetime differential-algebraic equation system dimensionless, under the same dimensionless coordinates and nonlinear parameters, a set of boundary value conditions is introduced and Newton's iteration is performed to obtain a unique dimensionless spacetime solution. Mapping back to any dimensional physical process based on this dimensionless spacetime solution yields similar results. The dimensionless spacetime differential-algebraic equation system is described using the following formula: (16) The meanings of the symbols in equation (16) are as follows: : Dimensionless spacetime solution; Dimensionless spatial coordinates; Dimensionless time coordinates; : Steady dimensionless coefficient; : Unsteady dimensionless coefficient; Then, the principle of similarity is applied: 1) The similarity criterion between the prototype and the experiment, i.e., the coefficients of all terms in the dimensionless spacetime differential algebraic equation are equal; 2) Make the dimensionless independent variables equal, that is, satisfy the linear transformation of all coordinates in geometry; 3) For transient experiments, the dimensionless time should be made equal; 4) Make the dimensionless initial conditions and boundary conditions equal; 5) Using nonlinear programming methods, obtain the reference values, geometric structure, and time-varying source terms corresponding to the experimental system that minimizes the deviations from the dimensionless similarity criterion numbers, initial conditions, and boundary conditions of the prototype; Furthermore, since the pressure values ​​of incompressible and weakly compressible fluids are independent of their thermophysical properties, it is also necessary to ensure that there is the same dimensionless pressure field as the source term. For compressible fluids, only the total energy, total enthalpy, internal energy, and enthalpy equations can be used for modeling, while incompressible or weakly compressible fluids can also use the temperature equation. However, the physical processes described by all energy equations are equivalent, and the differences in dependent variables reflect different viewpoints on the conservation of energy, thus resulting in different modeling results.

2. The reactor flow heat transfer modeling method based on boundary value similarity theory according to claim 1, characterized in that, The main and secondary parameters affecting the physical quantities are selected to conduct a model distortion evaluation of the simulation results, as follows: Introducing a distortion factor to describe a module In a certain phenomenon The distortion can be evaluated for features such as the time ratio, dimensionless number, or scaling parameters of the prototype and the model. (17) In equation (17): The dimensionless criterion number of the prototype; The dimensionless criterion number of the model; : Representation in each module In the middle, through a certain phenomenon The fractional difference between the prototype and the model for the conserved transport quantity reflects the degree of distortion between the prototype and the model.

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