Natural convection heat transfer calculation method under coupled heat transfer condition of radiation and convection

Abstract

The application provides a natural convection heat transfer calculation method and system under the condition of radiation and convection coupling heat exchange, the method comprises the following steps: building an experimental device, the experimental device comprises a non-active residual heat removal heat exchanger and an electric heating rod inserted into the non-active residual heat removal heat exchanger, the non-active residual heat removal heat exchanger has a flow channel for the flow of cooling fluid, and no flow field interference device is arranged in the flow channel; measuring the total heat transfer amount transferred by the electric heating rod to the cooling fluid and the temperature of each wall surface participating in the radiation heat exchange in the experimental device; establishing a radiation heat exchange calculation model corresponding to the experimental device, taking the temperature of each wall surface participating in the radiation heat exchange as the boundary input condition, and calculating the radiation heat exchange amount; based on the principle of energy conservation, the convection heat transfer amount is obtained by subtracting the radiation heat exchange amount from the total heat transfer amount. The application realizes the accurate separation of radiation heat exchange and convection heat exchange under the condition of not interfering with the flow field through the fusion idea of “half experiment-half simulation”.

Description

Technical Field

[0001] This application mainly relates to the fields of nuclear reactor thermal-hydraulic and safety technology, and in particular to a method and system for calculating natural convection heat transfer under coupled radiation and convection heat transfer conditions. Background Technology

[0002] The passive residual heat removal system is the "last line of defense" ensuring core cooling during a loss-of-heat-sink accident. The passive residual heat removal heat exchanger is a key component for residual heat transfer, with its densely packed horizontal tube bundles forming the main heat transfer mechanism. During shutdown, residual heat from the core is transferred to the tube bundle surface and then primarily to the cooling fluid via natural convection and radiation. Natural convection heat transfer characteristics directly determine the system's residual heat removal capacity and long-term operational stability, serving as the core basis for heat exchanger structure optimization, thermal-hydraulic model development, and safety analysis.

[0003] However, existing technologies cannot directly distinguish the radiative heat transfer from the convective heat transfer in the total heat transfer when studying the heat transfer characteristics of such heat exchangers. To address this issue, two main technical exploration schemes exist in the industry, but both have insurmountable drawbacks. One scheme is a complete experimental separation approach, attempting to directly measure radiative heat flow by adding radiation shielding plates, absorbers, or using radiative heat flux meters. However, direct measurement of radiative heat flow is affected by multiple factors: the wall emissivity is affected by the degree of oxidation, resulting in a dynamic deviation of ±50%; mutual obstruction between tube bundles leads to an angle coefficient calculation deviation of up to ±15%; and the combined error in calculating the total radiative heat transfer often exceeds 30%. More importantly, shielding devices alter the geometry of the tube bundle flow channels, disrupting the natural convection flow field morphology, resulting in a convective heat transfer measurement distortion exceeding 50%, completely negating the engineering reference value of the experimental data. Another type is the full simulation analysis scheme, which relies on CFD software to calculate radiation and convection heat transfer simultaneously. However, this scheme lacks effective verification with experimental data: input conditions such as wall emissivity and fluid properties are mostly based on empirical values. The simulation results can deviate from the actual operating conditions by up to 35%, and the model's conservatism cannot be guaranteed, making it difficult to meet the regulatory requirements for nuclear safety equipment design.

[0004] Therefore, there is an urgent need for an experimental and calculation method that can both ensure the authenticity of the experimental flow field and accurately separate the proportions of radiative and convective heat transfer, in order to solve the core heat transfer measurement problem of passive waste heat removal heat exchangers. Summary of the Invention

[0005] This application aims to solve the above-mentioned problems in the prior art and provide a method and system for calculating natural convection heat transfer under coupled radiation and convection heat transfer conditions, so as to achieve accurate separation of radiation heat transfer and convection heat transfer without disturbing the flow field.

[0006] To address the aforementioned technical problems, this application provides a method for calculating natural convection heat transfer under coupled radiation and convection heat transfer conditions, comprising: constructing an experimental setup, the experimental setup including a passive waste heat removal heat exchanger and an electric heating rod inserted inside the passive waste heat removal heat exchanger, the passive waste heat removal heat exchanger having a flow channel for cooling fluid flow, and no flow field interference device being installed in the flow channel; measuring the total heat transfer transferred to the cooling fluid by the electric heating rod and the temperatures of each wall surface participating in radiation heat transfer in the experimental setup; establishing a radiation heat transfer calculation model for the experimental setup, the radiation heat transfer calculation model using the temperatures of each wall surface participating in radiation heat transfer as boundary input conditions to calculate the radiation heat transfer; and, based on the principle of energy conservation, subtracting the radiation heat transfer from the total heat transfer to obtain the convection heat transfer.

[0007] Optionally, the radiative heat transfer calculation model calculates the radiative heat transfer by: discretizing each wall surface involved in the radiative heat transfer, dividing it into multiple sub-surfaces along the axial and circumferential directions; randomly sampling within each sub-surface to determine the emission position and direction of the rays, tracing the propagation path of the rays, and determining whether the rays intersect with other wall surfaces; when the rays intersect with a wall surface, determining whether the rays are absorbed or reflected based on the wall surface's absorptivity, and recording the energy and position of the absorbed rays; statistically analyzing the tracing results of all rays, calculating the angular coefficient between each wall surface based on the statistical results, and then calculating the radiative heat transfer.

[0008] Optionally, determining whether the ray intersects with other walls includes: using the line-of-sight method to determine whether the ray intersects with other walls through geometric intersection, and determining the position of the intersection point.

[0009] Optionally, whether the ray intersects other walls is determined by whether the quadratic equation of the ray and the cylindrical surface has positive real solutions, wherein the quadratic equation of the ray and the cylindrical surface is: , , ; in,( , ) is the coordinate of the ray's starting point, ( , Let R be the component of the ray direction vector in the xy plane, R be the radius of the cylinder, and t be the distance along the ray direction.

[0010] Optionally, the sampling formula for the launch position is:

[0011] Where z represents the axial position in the cylindrical coordinate system. Let L be the circumferential position in the cylindrical coordinate system, L be the length of the electric heating rod, and rand() be a uniformly distributed random number in the range [0,1].

[0012] Optionally, the sampling of the emission direction follows the assumption of diffuse emission cosine distribution, and the sampling formula for the emission direction is:

[0013] in, Polar angle, The azimuth angle is given by `rand()`, which generates a uniformly random number in the range [0,1].

[0014] Optionally, determining whether a ray is absorbed or reflected based on the wall's absorptivity includes: generating a random number between 0 and 1; if the random number is less than the wall's absorptivity, then the ray is determined to be absorbed and its energy is recorded; otherwise, it is resampled according to the diffuse reflection direction and the next round of tracking begins; the ray tracking terminates under any of the following conditions: it is absorbed by the surface, escapes the computational domain, or reaches the preset maximum number of reflections.

[0015] Alternatively, the angle factor can be calculated using the following formula:

[0016] in, Let i be the angle coefficient of wall i with respect to wall j. Let i be the number of rays emitted from wall i and absorbed by wall j. Let be the total number of rays emitted from wall surface i.

[0017] Optionally, the radiative heat transfer is calculated based on a gray-body radiative heat transfer network model:

[0018] in, The heat exchanged between wall surface i and wall surface j is radiative. For the radiative heat exchange, It is the Stefan-Boltzmann constant. Let i be the temperature of the wall surface. Let j be the temperature of the wall. Let i be the area of ​​the wall. Let j be the area of ​​the wall. Let i be the emissivity of the wall. Let j be the emissivity of the wall. Let be the angle coefficient of wall i relative to wall j.

[0019] Optionally, after obtaining the convective heat transfer, the method further includes: based on the obtained convective heat transfer, combined with the experimentally measured wall temperatures and fluid temperatures participating in radiative heat transfer, calculating the convective heat transfer coefficient, and fitting the natural convection heat transfer criterion correlation equation:

[0020] Where Nu is the natural convection Nusselt number, and Gr is the Grashof number. Let be the Prandtl number, and C and n be constants, obtained by fitting experimental data.

[0021] Optionally, the method further includes a closed-loop correction step for the radiative heat transfer calculation model: dynamically correcting the boundary conditions of the radiative heat transfer calculation model using the temperatures of each wall surface involved in the radiative heat transfer, and iteratively calibrating the emissivity of the wall surfaces in the model using experimental data under reference conditions, so as to control the calculation error of the radiative heat transfer within a preset range.

[0022] To address the aforementioned technical problems, this application provides a natural convection heat transfer calculation system, comprising: The experimental apparatus includes a passive waste heat removal heat exchanger and an electric heating rod inserted inside the passive waste heat removal heat exchanger. The passive waste heat removal heat exchanger has a flow channel for the flow of cooling fluid, and no flow field interference device is installed in the flow channel. A data measurement unit is used to measure the total heat transfer from the electric heating rod to the cooling fluid and the temperature of each wall surface involved in radiative heat transfer in the experimental apparatus. A radiative heat transfer calculation model is used to calculate the radiative heat transfer using the temperatures of each wall surface involved in the radiative heat transfer as boundary conditions. The data fusion processing unit is used to obtain the convective heat transfer by subtracting the radiative heat transfer from the total heat transfer based on the principle of energy conservation.

[0023] Compared with the prior art, this application has the following advantages: 1. Solving the problem of flow field interference: No flow field interference device is set in the flow channel of the experimental device of this application, which eliminates the physical disturbance to the natural convection flow field between tube bundles, ensures the "flow field fidelity" of the experimental data, and makes the extracted convective heat transfer data have real engineering reference value.

[0024] 2. Solving the problem of missing model validation: By using the experimentally measured temperatures of each wall surface involved in radiative heat transfer as precise input for radiation simulation, the "empirical calculation" of pure simulation is transformed into "data-driven high-reliability calculation", which greatly reduces the calculation error of radiative heat transfer.

[0025] 3. Achieve precise separation of radiation and convection: Through the technical approach of "experimental measurement of total heat - simulation calculation of radiative heat - separation to obtain convective heat", precise separation of radiation and convection heat transfer under complex coupled heat transfer conditions is achieved, providing a clean data foundation for subsequent analysis of convective heat transfer characteristics. Attached Figure Description

[0026] The accompanying drawings are included to provide a further understanding of this application. They are incorporated into and constitute a part of this application. The drawings illustrate embodiments of this application and, together with this specification, serve to explain the principles of this application.

[0027] Figure 1 This is a flowchart of a method for calculating natural convection heat transfer under coupled radiation and convection heat transfer conditions according to an embodiment of this application.

[0028] Figure 2 This is a schematic diagram showing the positions of the passive waste heat removal heat exchanger and the electric heating rod.

[0029] Figure 3 This is a flowchart of a ray tracing program based on the Monte Carlo method for calculating radiative heat transfer according to an embodiment of this application.

[0030] Figure 4 This is a system block diagram of a natural convection heat transfer calculation system according to an embodiment of this application. Detailed Implementation

[0031] The technical solutions of the embodiments of this application will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of this application, and not all embodiments. Based on the embodiments of this application, all other embodiments obtained by those skilled in the art without creative effort should fall within the scope of protection of this application.

[0032] This application aims to solve the technical problem of accurately separating radiative and convective heat transfer in passive waste heat removal heat exchangers under dense tube bundles and wide temperature range conditions.

[0033] To address this, this application proposes a "semi-experimental-semi-simulation" heat transfer separation measurement method and system. The core technical solution is as follows: the temperature parameters of the tube bundle surface and the fluid, as well as the total heat transfer, are obtained through a high-fidelity experimental device. Simultaneously, a radiation heat transfer calculation model based on the Monte Carlo method is established, and the radiation heat transfer is dynamically calculated using the experimentally measured wall temperature as the boundary condition. Finally, the radiation fraction is subtracted from the total heat transfer to achieve accurate extraction of pure convective heat transfer.

[0034] Figure 1 This is a flowchart illustrating a method for calculating natural convection heat transfer under coupled radiation and convection heat transfer conditions, according to an embodiment of this application. Figure 1As shown, the calculation method 100 for natural convection heat transfer under coupled radiation and convection heat transfer conditions includes: Step S1: Construct an experimental setup, which includes a passive waste heat removal heat exchanger and an electric heating rod inserted inside the passive waste heat removal heat exchanger. The passive waste heat removal heat exchanger has a flow channel for the flow of cooling fluid, and no flow field interference device is installed inside the flow channel. Step S2: Measure the total heat transfer from the electric heating rod to the cooling fluid and the temperature of each wall surface involved in radiative heat transfer in the experimental setup; Step S3: Establish a radiation heat transfer calculation model corresponding to the experimental setup. The radiation heat transfer calculation model uses the temperature of each wall surface involved in radiation heat transfer as the boundary input condition to calculate the radiation heat transfer. Step S4: Based on the principle of energy conservation, subtract the radiation heat transfer from the total heat transfer to obtain the convective heat transfer.

[0035] The following provides a detailed explanation of steps S1 to S4: Figure 2 This is a schematic diagram showing the positions of the passive waste heat removal heat exchanger and the electric heating rod. (See diagram for example.) Figure 2 As shown, the experimental setup includes a passive residual heat removal heat exchanger and an electric heating rod inserted into the passive residual heat removal heat exchanger. The electric heating rod simulates the transfer of residual heat from the reactor core after shutdown. The passive residual heat removal heat exchanger has an air outlet and an air inlet located at opposite positions at the top and bottom. Driven by the density difference between the inlet and outlet, air flows upward through the residual heat removal heat exchanger. The air is heated by the electric heating rod, generating an upward airflow. This upward airflow carries heat and is discharged into the atmosphere, achieving natural circulation heat dissipation.

[0036] Optionally, the passive waste heat removal heat exchanger is a tube bundle heat exchanger, which includes a closed shell with densely arranged horizontal tube bundles inside.

[0037] The experimental setup uses a data measurement unit to measure data. This unit includes a power measurement module, a temperature measurement module, and a calculation module. The power measurement module is electrically connected to the electric heating rod and is used to measure the total input power of the heating rod in real time. .

[0038] The temperature measurement module includes multiple thermocouples. Thermocouples are placed at key locations in the experimental setup; for example, a first set of thermocouples is placed on the inner wall of the heat exchanger shell, and a second set of thermocouples is placed on the outer wall of the heat exchanger shell. The two sets of thermocouples are used to monitor the radial temperature difference of the heat exchanger shell in real time.

[0039] In the experimental setup of this application, the electric heating rod is tightly inserted into the tube bundle. Because the surface of the electric heating rod is tightly wrapped by the tube bundle, thermocouples cannot be directly placed. Therefore, this application employs an equivalent measurement method: multiple thermocouple measuring points are arranged along the axial and circumferential directions on the outer wall of the tube bundle, and the measured tube bundle wall temperature is taken as the electric heating rod wall temperature. The approximate value represents the radiant temperature of the heat source surface. The inner wall of the heat exchanger shell is the main cold surface for radiative heat transfer, receiving radiant heat from the heat source surface and other structural components. Multiple thermocouple measuring points are arranged on the inner wall surface of the shell to measure the inner wall temperature. As a boundary condition for the cold wall surface in radiative heat transfer calculations.

[0040] The temperature measurement module also includes multiple thermocouples arranged at the fluid inlet and outlet for acquiring the fluid temperature. .

[0041] Experimental measurements were conducted while maintaining the original morphology of the natural convection flow field between the tube bundles without introducing any flow field interference devices (such as radiation shielding plates, heat absorbers, etc.). The calculation module calculated the system heat loss using the following formula, based on the average inner wall temperature and average outer wall temperature of the shell collected by the temperature measurement module, the known shell surface area, and the pre-calibrated heat transfer coefficient of the insulation layer. :

[0042] in, This represents the average temperature of the inner wall of the shell. The average temperature of the outer wall of the shell. For the surface area of ​​the shell, The heat transfer coefficient of the insulation layer.

[0043] According to the law of conservation of energy, the total heat transfer from radiation to convection is... The heat loss of the system is obtained by subtracting the input power of the electric heating rod; that is, the calculation module is also used based on the formula: The total heat transfer from radiation to convection is calculated.

[0044] In this application, "the temperature of each wall surface involved in radiative heat transfer" refers to the surface temperature of all solid walls in the experimental setup that may interact with each other through radiative heat transfer, including at least the wall temperature of the electric heating rod. and the temperature of the inner wall of the heat exchanger shell Using these two types of measured wall temperatures as boundary input conditions for the radiative heat transfer calculation model ensures both the realism of the radiation simulation and the feasibility of engineering implementation.

[0045] In traditional full-experiment separation schemes, invasive devices such as radiation shielding plates and absorbers must be inserted to directly measure radiative heat flux. Although these devices are for measurement, they themselves change the geometry of the flow channel, disrupt the flow field morphology, and alter the heat transfer boundary conditions. The result of these disturbances is that although the intention is to measure radiation, the flow field has changed, and the measured total heat transfer and convective heat transfer data are "distorted".

[0046] This application avoids introducing any flow field interference devices (such as radiation shielding plates, heat absorbers, etc.) during experimental measurements, completely preserving the original morphology of the natural convection flow field between tube bundles. This key design avoids the systematic errors introduced by changes in the flow channel and flow field disturbances in traditional full-experiment separation methods, ensuring that the measured wall temperature, fluid temperature, and total heat transfer accurately reflect the actual physical process. Error analysis shows that the error in the total heat transfer of this application can be controlled within ±5%, laying a solid experimental foundation for the accurate simulation of subsequent radiative heat transfer and the reliable separation of convective heat transfer.

[0047] In step S3, a full-size three-dimensional geometric model is first constructed based on the actual dimensions of the experimental setup to fully reproduce the relative positional relationships between the electric heating rods and the passive waste heat removal heat exchanger. The passive waste heat removal heat exchanger includes multiple tube bundles, a heat exchanger shell, and a guide tube; the tube bundle obstruction relationships are automatically identified. Then, a Monte Carlo-based ray tracing method is used to calculate the radiative heat transfer.

[0048] like Figure 3 As shown, the calculation of radiative heat transfer based on the Monte Carlo ray tracing method includes the following steps: Step S31: Discretize each wall surface involved in radiative heat transfer in the experimental setup, dividing it into multiple sub-surfaces along the axial and circumferential directions.

[0049] To ensure the statistical uniformity of radiation emission and reception, this application discretizes all walls involved in radiative heat transfer within the experimental setup. These walls mainly include: Heat source surface: outer surface of the electric heating rod (equivalently represented by the tightly fitted outer wall of the tube bundle); Cold wall surface: the inner wall surface of the heat exchanger shell; Other structural component surfaces: such as guide tubes, etc.

[0050] The discretization method involves dividing each wall surface into multiple sub-surfaces along its geometric features. In this embodiment, cylindrical surfaces such as the surface of the electric heating rod and the inner wall of the shell are treated using a cylindrical coordinate system, divided into 10 layers axially and 10 layers circumferentially, resulting in 100 sub-surfaces for each electric heating rod surface. The inner wall of the shell is processed using the same logic. Each sub-surface serves as an independent ray-emitting unit and energy-receiving unit in subsequent ray tracing, and its area, temperature, emissivity, and other attributes are recorded separately.

[0051] Step S32: Randomly sample within each sub-face to determine the emission position and direction of the ray, trace the propagation path of the ray, and determine whether the ray intersects with other walls.

[0052] Before performing ray tracing, enter the following key parameters: Physical parameters: Emissivity of the surface of the electric heating rod =0.8, shell emissivity =0.7, fluid temperature electric heating rod wall temperature and the temperature of the inner wall of the shell ; Calculation parameters: Number of rays 1×10 5 Strip / sub-surface (control statistical error ≤ 5%), maximum number of reflections 5.

[0053] Within each discretized sub-face, the emission position and direction of the ray are determined by random sampling. Determining the emission position of the ray by random sampling includes the following: In cylindrical coordinates, the sampling formulas for the axial position z and the circumferential position θ are:

[0054] Where z represents the axial position in the cylindrical coordinate system. Let L be the circumferential position in the cylindrical coordinate system, L be the length of the electric heating rod, and rand() be a uniformly distributed random number in the range [0,1].

[0055] Determining the emission direction of rays through random sampling includes: the sampling of the emission direction follows the assumption of diffuse cosine distribution, and the sampling formula for the emission direction is:

[0056] in, Polar angle, The azimuth angle is given by `rand()`, which generates a uniformly random number in the range [0,1].

[0057] After the ray is emitted from the emission position along the emission direction determined by sampling, its propagation path between tube bundles is traced using the line-of-sight method. The core is to determine whether the ray intersects with other walls (such as other tube bundles, shells, etc.) and to determine the nearest intersection point.

[0058] For cylindrical surfaces (tube bundles, shells), the intersection of a ray and a cylindrical surface is determined by solving the quadratic equation between them. The quadratic equation for the ray and the cylindrical surface is: , , ; in,( , ) is the coordinate of the ray's starting point, ( , ) represents the component of the ray direction vector in the xy plane, and R is the radius of the cylinder.

[0059] The judgment logic is to calculate the discriminant. ;like The equation has no real solutions, and the ray does not intersect the cylinder; if Solving for the two roots t1 and t2, we take the smallest positive real root. The intersection point corresponding to a positive real root is taken as the first intersection point between the ray and the cylinder; if no positive real root exists, the ray and the cylinder do not intersect. For multiple potential intersecting walls, the smallest positive real root is selected. The corresponding intersection point serves as the first collision point on the ray propagation path.

[0060] Step S33: When the ray intersects the wall, determine whether the ray is absorbed or reflected based on the wall's absorptivity, and record the energy and position of the absorbed ray.

[0061] After the rays reach the wall surface, absorption or reflection is determined based on the wall's optical properties. According to Kirchhoff's laws, for a gray body surface, the absorptivity α equals the emissivity ε. The judgment logic is as follows: Generate a uniformly random number in the interval [0,1] using rand(); If rand() < ε, then the ray is absorbed by the wall. Record the energy of the ray (usually counted as 1 unit) and the number of the wall and sub-face that were absorbed. If rand()≥ ε, the ray is reflected and resampled in the diffuse reflection direction (using the same directional sampling formula as the emission), and then enters the next round of tracking.

[0062] Tracking of the ray will be terminated and further processing of the ray will cease under any of the following conditions: Surface absorption: When the radiation energy is absorbed by a wall surface, the energy contribution is attributed to that wall surface. Escape computational domain: When a ray propagates beyond the predefined geometric computational domain boundary (such as flying out of the heat exchanger shell), it no longer interacts with any wall surface; Maximum number of reflections: In this embodiment, it is set to 5 times. If the number of reflections is exceeded, the calculation will be forcibly terminated even if the reflections are not absorbed, in order to balance the accuracy and efficiency of the calculation.

[0063] Step S34: Statistically analyze the tracking results of all rays, calculate the angle coefficient between each wall based on the statistical results, and then calculate the radiative heat transfer.

[0064] First, the emission and absorption data of all sub-surfaces belonging to the same macroscopic wall are summarized. Defined as the total number of rays emitted from all sub-faces of wall i. Defined as the total number of rays emitted from all sub-faces of wall i and ultimately absorbed by all sub-faces of wall j. Angular coefficient. Defined from the wall Launched and hit by the wall The proportion of absorbed rays.

[0065] The angle coefficient between the walls is calculated using the following formula:

[0066] in, Let i be the angle coefficient of wall i with respect to wall j. Let i be the number of rays emitted from wall i and absorbed by wall j. Let be the total number of rays emitted from wall surface i.

[0067] In this embodiment, each subplane emits 1×10 5 For each ray, the statistical error of the angle coefficient can be controlled within 5% (95% confidence interval).

[0068] This application addresses the complex geometry of densely packed tube bundles in passive waste heat removal heat exchangers by employing the Monte Carlo method to directly simulate the radiation propagation process through random ray tracing. This completely avoids the difficulty of calculating angular factors in complex shading relationships encountered by traditional analytical methods. Through discretization and line-of-sight intersection methods, the mutual shading relationships between tube bundles can be automatically identified, and the radiation angular factor of each tube bundle to the shell and between tube bundles can be accurately calculated, solving the traditional problem of radiation calculation for densely packed tube bundles.

[0069] In one embodiment, the radiative heat transfer between any two walls is calculated based on a gray-body radiative heat transfer network model. For wall i and wall j, the radiative heat transfer between them is:

[0070] in, The heat exchanged between wall surface i and wall surface j is radiative. It is the Stefan-Boltzmann constant. Let i be the temperature of the wall surface. Let j be the temperature of the wall. Let i be the area of ​​the wall. Let j be the area of ​​the wall. Let i be the emissivity of the wall. Let j be the emissivity of the wall. Let be the angle coefficient of wall i relative to wall j.

[0071] The total radiative heat transfer is obtained by summing the radiative heat transfer between all the walls:

[0072] in, For radiative heat exchange, Let be the radiative heat exchange between wall i and wall j.

[0073] In step S4, based on the principle of energy conservation, the total heat exchange measured in step S2 is... Subtract the radiative heat transfer calculated in step S3 from the middle This results in pure natural convection heat exchange.

[0074] in, Heat exchange is achieved through natural convection.

[0075] Optionally, after obtaining the convective heat transfer, the process further includes: Based on the obtained convective heat transfer, combined with the experimentally measured wall temperature of the electric heating rod... With fluid temperature Calculate the convective heat transfer coefficient :

[0076] in, This refers to the total surface area of ​​the electric heating rod involved in heat exchange.

[0077] Furthermore, to extend the experimental results to prototype design and safety analysis, a dimensionless analysis method was used to establish the criterion correlation for natural convection heat transfer. The following dimensionless numbers are defined: Natural convection Nusel number ; Glaschov number ; Prandtl number ; Where D is the characteristic diameter of the tube bundle. Let g be the thermal conductivity of the fluid, and g be the acceleration due to gravity. denoted as the coefficient of volumetric expansion of the fluid. For kinematic viscosity, For dynamic viscosity, This is the specific heat capacity at constant pressure.

[0078] The correlation of the natural convection heat transfer criterion is fitted using a power function form:

[0079] Where Nu is the natural convection Nusselt number, and Gr is the Grashof number. Let Nu be the Prandtl number, and C and n be undetermined constants in the model, obtained by fitting experimental data. The calculated Nu under different operating conditions is then compared with... Plotted in a log-log coordinate system, the slope n and intercept C are determined through linear regression. This correlation can be directly used for the engineering design and safety analysis of passive waste heat removal heat exchangers.

[0080] Optionally, to improve calculation accuracy, this application also includes a closed-loop correction step for the radiative heat transfer calculation model. The boundary conditions of the radiation simulation are dynamically corrected using the temperatures of each wall surface involved in radiative heat transfer measured in step S2, and the emissivity of the walls in the model is iteratively calibrated using experimental data under reference conditions. Through the above corrections, the calculation error of the radiative heat transfer is controlled within 15%.

[0081] In terms of error control, the comprehensive measurement error of convective heat transfer is controlled within 20% by calibrating the power measuring instrument (accuracy 0.1%), averaging multiple sets of data, and using an error propagation model, ensuring the engineering reliability of the final result.

[0082] This application also provides a natural convection heat transfer calculation system. For example... Figure 4 As shown, the natural convection heat transfer calculation system 400 includes: Experimental apparatus 41 includes a passive waste heat removal heat exchanger and an electric heating rod inserted inside the passive waste heat removal heat exchanger. The passive waste heat removal heat exchanger has a flow channel for the flow of cooling fluid, and no flow field interference device is installed in the flow channel. The data measurement unit 42 is used to measure the total heat transfer from the electric heating rod to the cooling fluid and the temperature of each wall surface involved in radiative heat transfer in the experimental setup. Radiation heat transfer calculation model 43 is used to calculate the amount of radiation heat transfer using the temperature of each wall surface involved in radiation heat transfer as the boundary condition. The data fusion processing unit 44 is used to obtain the convective heat transfer by subtracting the radiation heat transfer from the total heat transfer based on the principle of energy conservation.

[0083] Verification Example: To verify the correctness and calculation accuracy of the Monte Carlo ray tracing method used in this invention, this embodiment designs a series of benchmark test cases to systematically verify the program from two dimensions: angle factor calculation and radiative heat transfer calculation.

[0084] The verification process follows this logic: Angular coefficient verification: Using a concentric cylinder model, the length of the cylinder is changed from finite to infinite to verify whether the angle coefficient calculated by the program approaches the theoretical analytical solution; Radiative heat transfer verification: Under the same geometric model, with defined temperature boundaries and surface emissivity, verify whether the radiative heat transfer calculated by the program is consistent with the theoretical solution of the gray body radiation network model; Energy conservation verification: Verify whether the radiation energy emitted and absorbed by all surfaces within a closed cavity satisfies the law of conservation of energy.

[0085] In this embodiment, the surface of the heating rod is divided into 500 axial layers and 10 circumferential layers. Each grid emits 10 rays, the maximum number of reflections is set to 0, the reflectivity is set to 0, and the gas absorption effect is turned off. The theoretical analytical solution for an infinitely long concentric cylinder is 1. When the heating rod is 9000 mm, the Monte Carlo simulation result is 0.99747, with a relative error of 0.25%.

[0086] The theoretical heat transfer was calculated to be 7839.28 W. The heat transfer calculated by the program was approximately 7839.78 W, with an absolute error of 0.5 W and a relative error of 0.0064%. This result not only verifies the calculation accuracy but also confirms that the program can correctly handle the reciprocity of angle coefficients between surfaces of unequal area and the energy conservation of the closed cavity.

[0087] This application adopts the method of "experimental measurement of total heat exchange". — Simulation calculation of radiative heat transfer —Separation yields convective heat transfer The three-part architecture avoids the flow field disruption caused by the need to add radiation shielding plates in the "full experimental separation method" and the lack of verification caused by the reliance on empirical parameters in the "full simulation analysis method". This fusion path is neither a simple experimental measurement nor a pure numerical simulation, but a deep coupling of the two, which realizes the precise separation of radiation and convection heat transfer and obtains accurate convection heat transfer data.

[0088] This application establishes a deep coupling mechanism between experiment and simulation: the experimentally measured wall temperature is used as the direct boundary input condition for radiation simulation, rather than relying on empirical estimates. The program receives the heat pipe wall temperature (equivalently measured from the outer wall of the tube bundle) and the shell wall temperature from the experimental setup in real time, ensuring that the radiation calculations are based on actual operating conditions. This deep coupling mechanism transforms the radiation heat transfer calculation from the traditional "open-loop estimation" to "closed-loop correction," fundamentally eliminating calculation biases caused by uncertain boundary conditions. Through closed-loop correction, the calculation error of radiation heat transfer is controlled within 15%, solving the fundamental problem in pure simulation analysis where "input parameters rely on experience, and calculation results lack verification."

[0089] This application also provides a computer program product containing instructions. The computer program product may be software or program products containing instructions capable of running on a network device or stored on any available medium. When the computer program product is run on at least one device, it causes the at least one device to perform a method for calculating natural convection heat transfer under conditions of coupled radiation and convection heat transfer.

[0090] This application also provides a computer-readable storage medium. The computer-readable storage medium can be any available medium that a network device can store, or a data storage device such as a data center containing one or more available media. The available medium can be a magnetic medium (e.g., floppy disk, hard disk, magnetic tape), an optical medium (e.g., DVD), or a semiconductor medium (e.g., solid-state drive). The computer-readable storage medium includes instructions that instruct the device to perform a natural convection heat transfer calculation method under conditions of coupled radiation and convection heat transfer.

[0091] Flowcharts are used in this application to illustrate the operations performed by the system according to embodiments of this application. It should be understood that the preceding or following operations are not necessarily performed in exact order. Instead, various steps can be processed in reverse order or simultaneously. Furthermore, other operations may be added to these processes, or one or more steps may be removed from these processes.

[0092] To make the objectives, technical solutions, and advantages of this application clearer, the application will be described in further detail below with reference to the accompanying drawings. The specific operating methods and functional descriptions in the method embodiments can also be applied to the device embodiments or system embodiments.

[0093] Furthermore, it should be noted that the use of terms such as "first" and "second" to define components is merely for the purpose of distinguishing the corresponding components. Unless otherwise stated, these terms have no special meaning and therefore should not be construed as limiting the scope of protection of this application. In addition, although the terminology used in this application is selected from commonly known and used terms, some terms mentioned in this application's specification may have been chosen by the applicant according to his or her judgment, and their detailed meanings are explained in the relevant sections of this description. Moreover, this application should be understood not only through the actual terms used, but also through the meaning implied by each term.

[0094] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, and not to limit them; although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some of the technical features; and these modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the protection scope of the technical solutions of the embodiments of the present invention.

[0095] Those skilled in the art will understand that embodiments of this application can be provided as methods, systems, or computer program products. Therefore, this application can take the form of a completely hardware embodiment, a completely software embodiment, or an embodiment combining software and hardware aspects. Furthermore, this application can take the form of a computer program product embodied on one or more computer-usable storage media (including but not limited to disk storage, CD-ROM, optical storage, etc.) containing computer-usable program code.

[0096] Obviously, those skilled in the art can make various modifications and variations to this application without departing from the spirit and scope of this application. Therefore, if such modifications and variations fall within the scope of the claims of this application and their equivalents, this application also intends to include such modifications and variations.

Claims

1. A method for calculating natural convection heat transfer under coupled radiation and convection heat transfer conditions, characterized in that, include: An experimental setup is constructed, comprising a passive waste heat removal heat exchanger and an electric heating rod inserted inside the passive waste heat removal heat exchanger. The passive waste heat removal heat exchanger has a flow channel for the flow of cooling fluid, and no flow field interference device is installed in the flow channel. The total heat transfer from the electric heating rod to the cooling fluid and the temperature of each wall surface involved in radiative heat transfer were measured in the experimental apparatus. A radiation heat transfer calculation model corresponding to the experimental device is established. The radiation heat transfer calculation model uses the temperature of each wall surface involved in radiation heat transfer as the boundary input condition to calculate the radiation heat transfer. Based on the principle of energy conservation, the convective heat transfer is obtained by subtracting the radiative heat transfer from the total heat transfer. The calculation of radiative heat transfer using the radiative heat transfer calculation model includes: discretizing each wall surface involved in radiative heat transfer, dividing it into multiple sub-surfaces along the axial and circumferential directions; randomly sampling within each sub-surface to determine the emission position and direction of rays, tracing the propagation path of the rays, and determining whether the rays intersect with other wall surfaces; when the rays intersect with a wall surface, determining whether the rays are absorbed or reflected based on the wall surface's absorptivity, and recording the energy and position of the absorbed rays; statistically analyzing the tracing results of all rays, calculating the angular coefficient between each wall surface based on the statistical results, and then calculating the radiative heat transfer.

2. The method as described in claim 1, characterized in that, Determining whether the ray intersects with other walls includes: using the line-of-sight method to determine whether the ray intersects with other walls through geometric intersection, and determining the location of the intersection point.

3. The method as described in claim 2, characterized in that, Whether a ray intersects other walls is determined by whether the quadratic equation of the ray and the cylindrical surface has positive real solutions. The quadratic equation of the ray and the cylindrical surface is: ， ， ； in,( , ) is the coordinate of the ray's starting point, ( , Let R be the component of the ray direction vector in the xy plane, R be the radius of the cylinder, and t be the distance along the ray direction.

4. The method as described in claim 1, characterized in that, The sampling formula for the launch location is: Where z represents the axial position in the cylindrical coordinate system. Let L be the circumferential position in the cylindrical coordinate system, L be the length of the electric heating rod, and rand() be a uniformly distributed random number in the range [0,1].

5. The method as described in claim 1, characterized in that, The sampling of the emission direction follows the assumption of diffuse emission cosine distribution, and the sampling formula for the emission direction is: in, Polar angle, The azimuth angle is given by `rand()`, which generates a uniformly random number in the range [0,1].

6. The method as described in claim 1, characterized in that, Determining whether rays are absorbed or reflected based on the absorptivity of the wall surface includes: Generate a random number between 0 and 1. If the random number is less than the absorption rate of the wall, it is determined that the ray is absorbed and the energy is recorded; otherwise, resample according to the diffuse reflection direction and enter the next round of tracking. The ray will terminate tracking under any of the following conditions: it is absorbed by the surface, escapes the computational domain, or reaches the preset maximum number of reflections.

7. The method as described in claim 1, characterized in that, The angle coefficient between the walls is calculated using the following formula: in, Let i be the angle coefficient of wall i with respect to wall j. Let i be the number of rays emitted from wall i and absorbed by wall j. Let be the total number of rays emitted from wall surface i.

8. The method as described in claim 1, characterized in that, The radiative heat transfer is calculated based on a gray-body radiative heat transfer network model: in, The heat exchanged between wall surface i and wall surface j is radiative. For the radiative heat exchange, It is the Stefan-Boltzmann constant. Let i be the temperature of the wall surface. Let j be the temperature of the wall. Let i be the area of ​​the wall. Let j be the area of ​​the wall. Let i be the emissivity of the wall. Let j be the emissivity of the wall. Let be the angle coefficient of wall i relative to wall j.

9. The method as described in claim 1, characterized in that, After obtaining the convective heat transfer, the method further includes: Based on the obtained convective heat transfer, combined with the experimentally measured wall temperatures and fluid temperatures involved in radiative heat transfer, the convective heat transfer coefficient is calculated, and the correlation formula for the natural convection heat transfer criterion is obtained by fitting: Where Nu is the natural convection Nusselt number, and Gr is the Grashof number. Let be the Prandtl number, and C and n be constants, obtained by fitting experimental data.

10. The method as described in claim 1, characterized in that, It also includes a closed-loop correction step for the radiative heat transfer calculation model: The boundary conditions of the radiation heat transfer calculation model are dynamically corrected using the temperatures of each wall surface involved in the radiation heat transfer, and the emissivity of the wall surfaces in the model is iteratively calibrated using experimental data under the reference operating conditions, so that the calculation error of the radiation heat transfer is controlled within a preset range.

11. A natural convection heat transfer calculation system, characterized in that, include: The experimental apparatus includes a passive waste heat removal heat exchanger and an electric heating rod inserted inside the passive waste heat removal heat exchanger. The passive waste heat removal heat exchanger has a flow channel for the flow of cooling fluid, and no flow field interference device is installed in the flow channel. A data measurement unit is used to measure the total heat transfer from the electric heating rod to the cooling fluid and the temperature of each wall surface involved in radiative heat transfer in the experimental apparatus. A radiative heat transfer calculation model is used to calculate the radiative heat transfer using the temperatures of each wall surface involved in the radiative heat transfer as boundary conditions. The calculation of the radiative heat transfer includes: discretizing each wall surface involved in the radiative heat transfer by dividing it into multiple sub-surfaces along the axial and circumferential directions; randomly sampling and determining the emission position and direction of rays within each sub-surface, tracing the propagation path of the rays, and determining whether the rays intersect with other wall surfaces; when the rays intersect with a wall surface, determining whether the rays are absorbed or reflected based on the wall surface's absorptivity, and recording the energy and position of the absorbed rays; statistically analyzing the tracing results of all rays, calculating the angular coefficients between each wall surface based on the statistical results, and then calculating the radiative heat transfer. The data fusion processing unit is used to obtain the convective heat transfer by subtracting the radiative heat transfer from the total heat transfer based on the principle of energy conservation.

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