A method, system and medium for constructing a non-uniformly distributed CHF number table

Abstract

The present invention relates to the field of reactor thermal hydraulic technology, and specifically, to a method, system, and medium for constructing a non-uniformly distributed CHF table. The critical heat flux (CHF) is a key input parameter of the reactor thermal design criteria and is also the key to characterizing the core heat exchange limit. The prediction accuracy of CHF can be improved based on interpolation calculation of the table. Starting from the nonlinear influence of the main thermal parameters on CHF, the present invention proposes a nonlinear CHF table construction method for high-precision interpolation calculation based on the table. The core content is the connotation, form, and specific determination method of the non-uniform distribution of the table. It can support high-precision calculation of CHF based on the table, while reducing the total amount of data required for the table and saving experimental costs, thereby achieving the engineering purpose of helping to improve the calculation accuracy of CHF and releasing the core design margin.

Description

Technical Field

[0001] The present invention relates to the technical field of reactor thermal hydraulics, and in particular to a method, system and medium for constructing a non-uniformly distributed CHF table. Background Art

[0002] Critical heat flux (CHF) is a key input parameter in reactor thermal design criteria and is also the key to characterizing the core heat transfer limit.

[0003] Improving CHF prediction accuracy can reduce design penalties and free up design margins. Currently, CHF calculations are primarily based on experimentally fitted equations. These equations are artificially assumed, and due to the limited number of undetermined coefficients, there is a significant deviation of approximately ±20% between the fitted equation and the experimental data, resulting in a large design penalty. Furthermore, as experimental data expand, the equation becomes difficult to cover and must be refitted. Consequently, these fitted equations inherently suffer from low accuracy and difficulty extrapolating data.

[0004] When there are enough CHF experimental data points, CHF can be calculated directly by interpolation based on the table. In theory, the interpolation accuracy can continue to improve with data encryption; however, the total amount of data in the multidimensional table increases with the data encryption exponentially. Summary of the Invention

[0005] The purpose of the present invention is to provide a method, system and medium for constructing a non-uniformly distributed CHF number table to solve the above-mentioned problems in the prior art.

[0006] The embodiments of the present invention are achieved through the following technical solutions:

[0007] In a first aspect, the present invention provides a method for constructing a non-uniformly distributed CHF number table, comprising:

[0008] Step 1: Obtain the midpoint of the table and determine the mass flow rate through the midpoint of the table;

[0009] Step 2: Step the mass flow rate, keep other parameters unchanged, and obtain different mass flow rates. For different mass flow rates, change the critical vapor fraction value, and keep other parameters unchanged.

[0010] Step 3: Based on steps 1 and 2, increase or decrease the pressure value, while keeping other parameters unchanged;

[0011] Step 4: Determine the new thermal diameter;

[0012] Step 5: Based on the determined mass flow rate, critical vapor fraction value, pressure value and thermodynamic diameter, the corresponding CHF is obtained through experiments to obtain a complete non-uniform distribution CHF table.

[0013] Preferably, obtaining the midpoint of the table includes taking the rated design operating condition of the core as the center point of the table, and the thermal diameter is the value of a typical coolant sub-channel:

[0014] CHF0={p0,G0,xe0,Dh0}

[0015] Where CHF0 is the center point of the table, p0 represents the rated operating pressure of the core, G0 represents the average mass flow rate at the rated operating condition, xe0 represents the steam content at the hot channel outlet, and Dh0 represents the thermal diameter of the typical sub-channel.

[0016] Preferably, the other parameters remaining unchanged include:

[0017] A designated value is set so that when the critical vapor fraction value and the pressure value change, the difference in CHF values ​​between two adjacent points in the CHF table is no greater than the designated value. The designated value is recorded as ΔCHF.

[0018] Preferably, determining the new thermal diameter includes:

[0019]

[0020] Where Dh0 represents the typical sub-channel thermal diameter, Dh is the new sub-channel thermal diameter, CHF0 is the center point value of the table, and ΔCHF is the difference in CHF between two adjacent points.

[0021] Preferably, the interpolation of the non-uniformly distributed CHF number table includes:

[0022] Based on the given input parameters, a table is used to perform interpolation calculation to obtain a CHF calculation value for the corresponding working condition. The calculation result of the interpolation function does not exceed the maximum value of the four corner points in the CHF table and does not fall below the minimum value.

[0023] Preferably, the interpolation function includes:

[0024] Calculate the Euclidean distance between the point to be interpolated and its adjacent points, and calculate the CHF value of the point through interpolation.

[0025] In a second aspect, the present invention further provides a system for constructing a non-uniformly distributed CHF number table, comprising:

[0026] The data determination module is configured to obtain a midpoint of the numerical table and determine the mass flow rate using the midpoint of the numerical table; step the mass flow rate while keeping other parameters constant to obtain different mass flow rates; for the different mass flow rates, change the critical vapor fraction value while keeping other parameters constant; increase or decrease the pressure value based on steps one and two while keeping other parameters constant; and determine a new thermal diameter;

[0027] The table building module is configured to conduct experiments on these operating conditions to obtain CHF values ​​based on the determined mass flow rate, critical vapor fraction value, pressure value and thermodynamic diameter, thereby obtaining a complete non-uniform distribution CHF table.

[0028] In a third aspect, the present invention further provides a computer-readable storage medium storing a computer program, wherein the computer program, when executed by a processor, implements the above-mentioned method for constructing a non-uniformly distributed CHF number table.

[0029] The technical solutions of the embodiments of the present invention have at least the following advantages and beneficial effects:

[0030] The method provided by the present invention mainly includes obtaining the midpoint of a numerical table and determining the mass flow rate through the midpoint of the numerical table; stepping the mass flow rate to obtain mass flow rates of different sizes, changing the critical vapor fraction value for each mass flow rate, and increasing or decreasing the pressure value; determining a new thermodynamic diameter, and based on the determined mass flow rate, critical vapor fraction value, pressure value, and thermodynamic diameter, conducting experiments on these operating conditions to obtain CHF values, thereby obtaining a complete non-uniformly distributed CHF numerical table. This method supports high-precision CHF calculations based on the numerical table, while reducing the total amount of data and saving experimental costs, thereby achieving the engineering goal of helping to improve CHF calculation accuracy and release core design margin. BRIEF DESCRIPTION OF THE DRAWINGS

[0031] In order to more clearly illustrate the technical solutions of the embodiments of the present invention, the following briefly introduces the drawings required for use in the embodiments. It should be understood that the following drawings only illustrate certain embodiments of the present invention and therefore should not be regarded as limiting the scope. For ordinary technicians in this field, other relevant drawings can be obtained based on these drawings without paying any creative work.

[0032] Figure 1 Schematic diagram of the nonlinear relationship between CHF-p of the present invention.

[0033] Figure 2 Schematic diagram of the process of constructing a non-uniform number table of the present invention. DETAILED DESCRIPTION

[0034] To make the objectives, technical solutions, and advantages of the embodiments of the present invention more clear, the technical solutions of the embodiments of the present invention will be clearly and completely described below in conjunction with the accompanying drawings of the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Generally, the components of the embodiments of the present invention described and shown in the drawings herein can be arranged and designed in various different configurations.

[0035] The division of modules in this application is a logical division. In actual application, there may be other division methods. For example, multiple modules can be combined or integrated into another system, or some features can be ignored or not executed.

[0036] Independently described modules or submodules may or may not be physically separate; they may be implemented in software or hardware. Some modules or submodules may be implemented in software, with the processor invoking the software to implement the functionality of these modules or submodules, while other modules or submodules may be implemented in hardware, such as hardware circuits. Furthermore, some or all of the modules may be selected based on actual needs to achieve the objectives of the present application.

[0037] Existing CHF tables have uniform distributions of parameters, with small spacing between points. The data volume is enormous, primarily due to the extensive availability of CHF experimental results for circular tubes in the public literature. Constructing such a large-scale table is unthinkable for engineering projects with specialized channels, limited access to public data, and strict experimental and funding constraints.

[0038] Figure 1 The nonlinear effect of pressure on CHF is demonstrated. This suggests that we can optimize the table by combining the CHF parameter variation patterns: in the high slope region or near the inflection point, the experimental conditions can be increased; conversely, the experimental conditions can be significantly reduced.

[0039] The present invention provides a method for constructing a non-uniformly distributed CHF number table, comprising:

[0040] Step 1: Obtain the midpoint of the table and determine the mass flow rate through the midpoint of the table;

[0041] Specifically, obtaining the midpoint of the table includes taking the rated design condition of the core as the center point of the table, and the thermal diameter as the value of a typical coolant subchannel:

[0042] CHF0={p0,G0,xe0,Dh0}

[0043] Where CHF0 is the center point of the table, p0 represents the rated operating pressure of the core, G0 represents the average mass flow rate at the rated operating condition, xe0 represents the steam content at the hot channel outlet, and Dh0 represents the thermal diameter of the typical sub-channel.

[0044] Step 2: Step the mass flow rate, keep other parameters unchanged, and obtain different mass flow rates. For different mass flow rates, change the critical vapor fraction value, and keep other parameters unchanged.

[0045] Gradually increase or decrease the mass flow rate G, while keeping other parameters constant, so that the difference in CHF between two adjacent points is close to a specified value, such as 15%. The difference ΔCHF can be approximately estimated using an existing relationship.

[0046] Similarly, by changing the critical vapor fraction value while keeping other parameters constant, the difference in CHF between two adjacent points (the upper and lower points in the figure) is no greater than a specified value, such as 15%. Because the impact of the critical vapor fraction value is related to G, the resulting point array is non-uniformly distributed.

[0047] Step 3: Based on steps 1 and 2, increase or decrease the pressure value, while keeping other parameters unchanged;

[0048] Increasing or decreasing the pressure p, while keeping other parameters constant, ensures that the difference in CHF between two adjacent layers is no greater than a specified value, such as 15%. Since the effect of p is nonlinear, the lattice is non-uniformly distributed with respect to pressure.

[0049] There is an inflection point in the pressure effect, so the density can be appropriately increased near the inflection point.

[0050] Step 4: Determine the new thermal diameter;

[0051] Specifically, the design needs to examine the impact of flow channel deformation or flow channel size changes on CHF. Usually, only three different thermal diameters need to be covered. The new thermal diameter can be determined using the following formula. The new thermal diameter includes:

[0052]

[0053] Where Dh0 represents the typical sub-channel thermal diameter, Dh is the new sub-channel thermal diameter, CHF0 is the center point value of the table, and ΔCHF is the difference in CHF between two adjacent points.

[0054] If the CHF ratio is taken as 1.15, the increased thermal diameter can be obtained; if the ratio is taken as 0.85, the reduced thermal diameter can be obtained.

[0055] Step 5: Based on the determined mass flow rate, critical vapor fraction value, pressure value and thermodynamic diameter, conduct experiments to determine the CHF under the corresponding operating conditions to obtain a complete non-uniform distribution CHF table.

[0056] In practical applications, a 10% to 20% difference in CHF between adjacent points is feasible, which mainly depends on the requirements for interpolation accuracy and the control of experimental costs.

[0057] The method provided by the present invention mainly includes obtaining the midpoint of the table, determining the mass flow rate through the midpoint of the table; stepping the mass flow rate to obtain mass flow rates of different sizes, changing the critical steam content value for different mass flow rates, and increasing or decreasing the pressure value; determining a new thermodynamic diameter, and based on the determined mass flow rate, critical steam content value, pressure value and thermodynamic diameter, conducting experiments to determine the CHF under the corresponding working conditions to obtain a complete non-uniformly distributed CHF table. Interpolation calculations are performed using the table, etc. The above method realizes high-precision calculation of CHF based on the table, while reducing the total amount of data and saving experimental costs, thereby achieving the engineering purpose of helping to improve the accuracy of CHF calculation and releasing the core design margin.

[0058] Based on the above, it also includes:

[0059] Taking the rated operating condition as the origin and keeping other parameters unchanged, first step the mass flow rate G. The advancing direction is shown in Figure 2 The horizontal red line in the figure is then plotted. For different G values, the critical vapor fraction xe is varied to obtain two sets of points, one above the other, and so on. Because the points are set based on the CHF variation, the spacing between them varies, resulting in a non-uniform distribution, significantly reducing the number of experiments and cost.

[0060] Figure 2 The red rectangle and green diagonal lines in the middle illustrate interpolation calculations based on the table. Because the CHF variation between adjacent data points is very small (e.g., 15%), the CHF variation within this small quadrilateral region can be considered monotonic. By selecting an appropriate interpolation function and ensuring that the result is bounded (the interpolated result does not exceed the maximum value of the four corner points and does not fall below the minimum value), it is easy to rigorously prove that the interpolation error is well below 15%.

[0061] In an exemplary embodiment of the present invention, interpolating a non-uniformly distributed CHF table includes:

[0062] Based on the given input parameters, a numerical table is used for interpolation calculation to obtain the CHF calculation value of the corresponding working condition. The numerical table is constructed. The numerical table represents the mapping relationship between the independent variable and the function value CHF. The key point of the present invention is to achieve the non-uniform distribution of the dot matrix by controlling the CHF difference between adjacent points. Non-uniform means that the step length between each independent variable, that is, the interval, is not equal. Figure 2 and attached Figure 1 . This is the core principle of the invention;

[0063] Application of the table. Given the independent variables {p, G, xe, Dh}, an interpolation algorithm is used based on the table to obtain the CHF calculation value (interpolation result) under the corresponding working condition. The calculation result of the interpolation function does not exceed the maximum value of the four corner points in the CHF table, nor is it lower than the minimum value.

[0064] Specifically, the interpolation function includes.

[0065] The interpolation calculation algorithm adopted by the present invention is the "Euclidean distance inverse interpolation method". First, the Euclidean distance between the point to be interpolated and the adjacent point is calculated:

[0066] s i =[(pp i ) 2 +(GG i ) 2 +(xe-xe i ) 2 +(Dh-Dh i ) 2 ] 0.5

[0067] Where the subscript i represents the i-th adjacent point near the interpolation point, and is the Euclidean distance between the interpolation point and the i-th adjacent point.

[0068] Where s i is the Euclidean distance, p is the core pressure interpolation point, p i is the ith adjacent point near the core pressure interpolation point, G is the average mass flow rate interpolation point, G i is the ith adjacent point near the average mass flow rate interpolation point, xe is the steam content interpolation point at the hot channel outlet, and xe i is the i-th adjacent point near the interpolation point of the steam content at the hot channel outlet, Dh is the interpolation point of the thermal diameter of the typical sub-channel, Dh i is the i-th adjacent point near the interpolation point of the thermal diameter of a typical sub-channel.

[0069] The total distance is defined as:

[0070]

[0071] Where n represents the number of adjacent points and s is the total Euclidean distance.

[0072] Weighting coefficient λ i Defined as:

[0073]

[0074] The interpolation calculation shows that the CHF value at this point is:

[0075]

[0076] Where CHF i is the adjacent CHF value to be interpolated.

[0077] In a second aspect, the present invention further provides a system for constructing a non-uniformly distributed CHF number table, comprising:

[0078] The data determination module is configured to obtain a midpoint of the numerical table and determine the mass flow rate using the midpoint of the numerical table; step the mass flow rate while keeping other parameters constant to obtain different mass flow rates; for the different mass flow rates, change the critical vapor fraction value while keeping other parameters constant; increase or decrease the pressure value based on steps one and two while keeping other parameters constant; and determine a new thermal diameter;

[0079] The table construction module is configured to conduct experiments to determine the CHF under corresponding operating conditions based on the determined mass flow rate, critical vapor fraction, pressure, and thermodynamic diameter, thereby generating a complete non-uniform CHF table. The table interpolation calculation module performs multi-dimensional interpolation calculations based on the constructed non-uniform table and specified inputs to obtain the calculated CHF value for the corresponding input.

[0080] In addition, the functional units in the various embodiments of the present invention may be integrated into a single processing unit, each unit may exist physically separately, or two or more units may be integrated into a single unit. The aforementioned integrated units may be implemented in the form of hardware or software functional units.

[0081] If the integrated unit is implemented as a software functional unit and sold or used as an independent product, it can be stored in a computer-readable storage medium. The computer software product is stored in a storage medium and includes a number of instructions for causing a computer device (which can be a personal computer, server, or network device, etc.) to perform all or part of the steps of the various embodiments of the present invention. The aforementioned storage medium includes: USB flash drives, mobile hard drives, read-only memories (ROMs), random access memories (RAMs), magnetic disks, optical disks, and other media that can store program code.

[0082] The above are merely preferred embodiments of the present invention and are not intended to limit the present invention. Those skilled in the art will readily appreciate that various modifications and variations of the present invention are possible. Any modifications, equivalent substitutions, or improvements made within the spirit and principles of the present invention shall be included within the scope of protection of the present invention.

Claims

1. A method for constructing a non-uniformly distributed CHF number table, characterized in that: include: Step 1: Obtain the midpoint of a numerical table, wherein the midpoint of the numerical table includes taking the rated design condition of the core as the center point of the numerical table and the thermal diameter as the value of a typical coolant sub-channel; CHF0={p0,G0,xe0,Dh0} Where CHF0 is the center point of the table, p0 represents the rated operating pressure of the core, G0 represents the average mass flow rate at the rated operating condition, xe0 represents the steam content at the hot channel outlet, and Dh0 represents the thermal diameter of the typical sub-channel. Determine the mass flow rate by the midpoint of the table; Step 2: The mass flow rate is stepped while other parameters remain unchanged, including the rated core operating pressure, the steam fraction at the hot channel outlet, and the typical sub-channel thermal diameter, to obtain different mass flow rates. For each mass flow rate, the critical steam fraction is changed while other parameters remain unchanged, including the mass flow rate, the rated core operating pressure, and the typical sub-channel thermal diameter. Step 3: Based on steps 1 and 2, increase or decrease the pressure value, while keeping other parameters unchanged, including mass flow rate, steam fraction at the hot channel outlet, and typical sub-channel thermodynamic diameter; Step 4: Determine the new thermal diameter; Determining the new thermal diameter includes: Where Dh0 represents the typical sub-channel thermal diameter, Dh is the new sub-channel thermal diameter, CHF0 is the center point value of the table, and ΔCHF is the difference in CHF between two adjacent points. Step 5: Based on the determined mass flow rate, critical vapor fraction value, pressure value and thermodynamic diameter, the CHF value is obtained through experiments, thereby obtaining a complete non-uniform distribution CHF table.

2. The method for constructing a non-uniformly distributed CHF number table according to claim 1, characterized in that: Also includes step lengths for individual parameters: Set the specified value so that the difference in CHF values ​​between two adjacent points in the CHF table does not exceed the specified value when the mass flow rate, critical vapor fraction, or pressure value changes.

3. The method for constructing a non-uniformly distributed CHF number table according to claim 2, wherein: It also includes interpolation of non-uniformly distributed CHF number tables; According to the input parameters and the constructed table, the corresponding CHF calculation results are obtained through the interpolation function; The calculation result of the interpolation function does not exceed the maximum value of the four corner points in the CHF table and is not lower than the minimum value.

4. The method for constructing a non-uniformly distributed CHF number table according to claim 3, characterized in that: The interpolation function includes: Calculate the Euclidean distance between the point to be interpolated and its adjacent points, and calculate the CHF value of the point through interpolation.

5. The method for constructing a non-uniformly distributed CHF table according to claim 4, characterized in that: Calculating the Euclidean distance between the point to be interpolated and the adjacent points includes: s i =[(pp i ) 2 +(GG i ) 2 +(is-is i ) 2 +(D-Go i ) 2 ] 0.5 Where s i is the Euclidean distance, p is the core pressure interpolation point, p i is the ith adjacent point near the core pressure interpolation point, G is the average mass flow rate interpolation point, G i is the ith adjacent point near the average mass flow rate interpolation point, xe is the steam content interpolation point at the hot channel outlet, and xe i is the i-th adjacent point near the interpolation point of the steam content at the hot channel outlet, Dh is the interpolation point of the thermal diameter of the typical sub-channel, Dh i is the i-th adjacent point near the interpolation point of the thermal diameter of a typical sub-channel.

6. The method for constructing a non-uniformly distributed CHF number table according to claim 5, characterized in that: Also included is the total distance: Where n represents the number of adjacent points and s is the total Euclidean distance.

7. A system for constructing a non-uniformly distributed CHF table, characterized in that: include: a data determination module configured to obtain a midpoint of a numerical table, wherein the midpoint of the numerical table includes taking a rated design condition of the core as the center point of the numerical table and a thermal diameter as a value of a typical coolant sub-channel; CHF0={p0,G0,xe0,Dh0} Where CHF0 is the center point of the table, p0 represents the rated operating pressure of the core, G0 represents the average mass flow rate at the rated operating condition, xe0 represents the steam content at the hot channel outlet, and Dh0 represents the thermal diameter of the typical sub-channel. The mass flow rate is determined by the midpoint of the table; the mass flow rate is stepped while other parameters remain unchanged, including the rated core operating pressure, the hot channel outlet steam fraction, and the typical sub-channel thermodynamic diameter, to obtain different mass flow rates; for each different mass flow rate, the critical steam fraction is changed while other parameters remain unchanged, including the mass flow rate, the rated core operating pressure, and the typical sub-channel thermodynamic diameter; Increasing or decreasing the pressure value, while keeping other parameters unchanged, including mass flow rate, hot channel outlet steam fraction and typical sub-channel thermodynamic diameter; Determine the new thermal diameter; Determining the new thermal diameter includes: Where Dh0 represents the typical sub-channel thermal diameter, Dh is the new sub-channel thermal diameter, CHF0 is the center point value of the table, and ΔCHF is the difference in CHF between two adjacent points. A table building module is configured to obtain a complete non-uniformly distributed CHF table by experimentally obtaining a corresponding CHF based on the determined mass flow rate, critical vapor fraction value, pressure value, and thermodynamic diameter; The table interpolation calculation module performs multi-dimensional interpolation calculations based on the constructed non-uniform table and the given input to obtain the CHF calculation value corresponding to the input; A main control module is connected to the data determination module and the number table construction module, and is used to execute a non-uniformly distributed CHF number table construction method according to any one of claims 1 to 6.

8. A computer-readable storage medium, characterized in that The computer-readable storage medium stores a computer program, and when the computer program is executed by a processor, the method for constructing a non-uniformly distributed CHF number table according to any one of claims 1 to 6 is implemented.

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