Method for obtaining a three-dimensional temperature field

Abstract

This invention relates to a method and apparatus for obtaining a three-dimensional temperature field. Several fiber optic temperature measuring devices are arranged along each axial direction. The temperature at various points on any fiber optic line is measured in real time, and the real-time temperature is imported into a created two-dimensional temperature field model based on Fourier heat conduction. The two-dimensional temperature field model is then imported into Fourier's law and the first law of thermodynamics to obtain a three-dimensional temperature field model. This model is then transformed into three cascaded one-dimensional temperature field models. Using a tridiagonal matrix, the temperature in the x, y, and z directions is solved to obtain the solution for the three-dimensional temperature field. The results are imported into a main control device to obtain the power output for each temperature segment, resulting in a three-dimensional uniform temperature field or a three-dimensional gradient temperature field. This invention solves the technical problems of current thermocouples, which can only obtain the temperature at a single point, resulting in limited information, large errors, and numerous external interference factors and poor reliability in dynamic temperature field measurements.

Description

Technical Field

[0001] Embodiments of the present invention relate to a method for obtaining a temperature field, and more particularly to a method for obtaining a three-dimensional temperature field. Background Technology

[0002] For medium- and high-temperature heating furnaces, thermocouples remain the most commonly used temperature measurement method. Typically, each temperature zone is controlled by a single temperature-controlled thermocouple, depending on the number of heating zones. This means that the entire temperature zone is controlled by the feedback signal from a single thermocouple (which can be simply considered as the temperature measured by the thermocouple being the same throughout the zone). This obviously leads to non-uniformity in the overall temperature field. Simultaneously, the temperature-measuring thermocouples themselves suffer from the same problem; using the temperature of a single point to represent the temperature of the entire zone is clearly biased and introduces significant errors. Using multiple thermocouples to measure the temperature of a straight line is inconvenient because thermocouples require external protective tubes, which are relatively thick and occupy a large amount of space.

[0003] Currently, thermocouples are also used to dynamically change their position to measure the uniformity of the temperature field, but there is a time lag, and the movement of thermocouples may also cause temperature fluctuations, resulting in poor accuracy.

[0004] The main drawbacks of thermocouple temperature measurement are: 1. Thermocouples can only obtain the temperature of a single point, resulting in limited information; 2. Using information from a single point to represent the overall information leads to larger errors; 3. Dynamic temperature field measurements are subject to many external interference factors, resulting in poor reliability; 4. Multiple thermocouples are used to measure two-dimensional temperature distributions, which occupies a large space, and the measurement points cannot be aligned on a straight line. Summary of the Invention

[0005] The purpose of this invention is to provide a method and apparatus for controlling a three-dimensional temperature field model, thereby overcoming the main drawbacks of current thermocouple temperature measurement.

[0006] To achieve the above objectives, embodiments of the present invention provide a method for obtaining a three-dimensional temperature field, comprising the following steps:

[0007] Step S100: Set up several fiber optic temperature measuring devices along each axis direction;

[0008] Step S200: The temperature at each point on any fiber optic cable is measured in real time using the fiber optic temperature measuring device, and the real-time temperature of each point is obtained.

[0009] Step S300: Establishment of two-dimensional temperature field model: Import the real-time temperature of each point into the created two-dimensional temperature field model of Fourier heat conduction; proceed to step S400.

[0010] Step S400: Establishment of three-dimensional temperature field model: The two-dimensional temperature field model is then imported into Fourier's law and the first law of thermodynamics to obtain a three-dimensional temperature field model; proceed to step S500.

[0011] Step S500: Solving the three-dimensional temperature field model: The three-dimensional temperature field model is transformed into three cascaded one-dimensional temperature field models; using a tridiagonal matrix, the temperature in the x, y, and z directions is solved to obtain the solution results of the three-dimensional temperature field, and then proceed to step S600;

[0012] Step S600: Import the solution results of the three-dimensional temperature field model into the main control device to obtain the power output of each temperature segment, and obtain a three-dimensional uniform temperature field or a three-dimensional gradient temperature field.

[0013] Furthermore, one of the fiber optic temperature measuring devices is arranged along the axial direction; any one of the fiber optic temperature measuring devices is arranged radially from top to bottom; any one of the fiber optic temperature measuring devices is arranged radially from left to right.

[0014] Furthermore, the establishment of the two-dimensional temperature field model also includes the following steps:

[0015] Step S310: Two-dimensional heat conduction analysis, substituting the real-time temperature of each point into the two-dimensional unsteady-state heat conduction equation.

[0016] = +S(1);

[0017] Where λ represents thermal conductivity, ρ represents density, c represents specific heat, T represents temperature, S represents heat source term, and t represents time;

[0018] Step S320: Integrate both sides of the two-dimensional unsteady heat conduction equation based on the time interval (t, t+Δt), where P represents the control volume.

[0019] - )ΔxΔy(2)

[0020] = ΔyΔt+ ΔxΔt (3;

[0021] =( )ΔxΔyΔt (4;

[0022] After simplification, formulas (2), (3), and (4) are obtained as follows:

[0023] +b(5);

[0024] in:

[0025] = ;

[0026] = ;

[0027] = ;

[0028] = ;

[0029] = + + + + - ΔxΔy;

[0030] = ;

[0031] b= +

[0032] Where: E represents the positive half-axis of the two-dimensional X-axis; W represents the negative half-axis of the two-dimensional X-axis; N represents the positive half-axis of the two-dimensional Y-axis; S represents the negative half-axis of the two-dimensional Y-axis.

[0033] Step S330: Perform the derivation in the cylindrical axisymmetric coordinate system and substitute the formula. (6) The derivation is performed; we get:

[0034] = ;

[0035] = ;

[0036] = ;

[0037] = ;

[0038] = + + + + - V;

[0039] = ;

[0040] b= + ;

[0041] =0.5( + x(7);

[0042] Where r is the radius of the arc and V is the volume with radius r; proceed to step S400.

[0043] Furthermore, the establishment of the three-dimensional temperature field model also includes the following steps:

[0044] Step S410: Based on the function T=f(x,y,z, ..., ...) used to establish the three-dimensional temperature field ), = (8);

[0045] = (9).

[0046] The internal heat element per unit volume is , Infinite element dV=dxdydz; Proceed to step S420;

[0047] Step S420, according to the aforementioned Fourier law, calculate as follows:

[0048] The net heat output along the x-axis is - =- xdydzd ;

[0049] The net heat output along the Y-axis is - =- xdydzd ;

[0050] The net heat output along the Z-axis is - =- xdydzd ;

[0051] Proceed to step S430;

[0052] Step S430: According to the first law of thermodynamics:

[0053] Net heat of importing and exporting infinitesimal elements = xdydzd ;

[0054] The heat generated in a infinitesimal element = ;

[0055] The increase in the thermodynamic energy of a infinitesimal element = xdydzd Proceed to step S440;

[0056] Step S440: According to the formula: net heat of the infinitesimal element + heat generated in the infinitesimal element = increase in the thermodynamic energy of the infinitesimal element; after simplification, = + + Proceed to step S450;

[0057] Step S450: Apply the steps from step S440 to the axial coordinate system to obtain a three-dimensional heat conduction model, which can be represented by the formula... ;

[0058] Proceed to step S500.

[0059] Furthermore, the solution of the three-dimensional temperature field also includes:

[0060] Step S510: Assuming that the y and z directions are implicit and the x direction is explicit, the solution of the three-dimensional temperature field will be transformed into a one-dimensional problem, which is solved using a tridiagonal matrix; proceed to step S511.

[0061] Step 511: Simplify the formula

[0062] +b(5);

[0063] Ignoring the temperature in the y direction, we can obtain formula (10).

[0064] (10);

[0065] By moving all temperature terms to the left side of the formula and keeping the source term b on the right side of the formula, we get formula (11).

[0066] - (11);

[0067] make = , = and = ,

[0068] Formula (12) is obtained:

[0069] - (12); Proceed to step S512; Step S512: Because it is assumed that heat conduction is one-dimensional, therefore =1, = , = In a tridiagonal matrix, - , and - A tridiagonal matrix is ​​created for i=1, i=2...i=6, where i=3 is... = When i=4 = When i=5 = From this, we can obtain a tridiagonal matrix. Proceed to step S513;

[0070]

[0071] Step S513: Source Item Matrix The calculation of the source term matrix Given that all values ​​of b are the same, b = x, =1, =Device power output Proceed to step S514;

[0072] Step S514: Solve the tridiagonal matrix The reverse , = Thus obtain = , = , = ;

[0073] = = = ;

[0074] Proceed to step S520;

[0075] Step S520: Assuming that the x and z directions are implicit and the y direction is explicit, the three-dimensional problem of solving the three-dimensional temperature field will be transformed into a one-dimensional problem; solve it using a tridiagonal matrix; proceed to step S521;

[0076] Step S521: Establish a tridiagonal matrix. Similarly to formulas (10)-(12), formulas (13)-(15) can be obtained.

[0077] (13);

[0078] - (14);

[0079] - (15);

[0080] Proceed to step S522;

[0081] Step S522: Because we assume one-dimensional heat conduction, therefore x=1, = , = In a tridiagonal matrix, - , and - A tridiagonal matrix is ​​created for i=1, i=2...i=6, where i=3... = When i=4 = When i=5 = ; obtain a tridiagonal matrix

[0082]

[0083] Proceed to step S523;

[0084] Step S523: Assume the source term matrix Given that all values ​​of b are the same. Source term vector Solve for b in the middle;

[0085] b= Proceed to step S524;

[0086] Step S524: = × Seeking , , ;

[0087] = × =

[0088] Step S530: Assuming the x and y directions are implicit and the z direction is explicit, the three-dimensional problem of solving the three-dimensional temperature field will be transformed into a one-dimensional problem; solve it using a tridiagonal matrix; proceed to step S531;

[0089] Step S531: Establish a tridiagonal matrix. Similarly to formulas (10)-(12), formulas (16)-(18) can be obtained.

[0090] (16);

[0091] - (17);

[0092] - (18);

[0093] Proceed to step S532:

[0094] Step S532: Assuming one-dimensional heat conduction, r=1, = , = In a tridiagonal matrix, - , and - A tridiagonal matrix is ​​created for i=1, i=2...i=6, where i=3... = When i=4 = When i=5 = The tridiagonal matrix is ​​obtained.

[0095]

[0096] Step S533: Source Item Proceed to step S534;

[0097] Step SS534: = × Thus, to obtain , , ;

[0098] A numerical calculation of a three-dimensional temperature field is obtained; steps S510-S534 are continuously repeated to obtain a real-time three-dimensional temperature field model; proceed to step S600.

[0099] Furthermore, by setting the boundary conditions for each temperature measurement zone, the numerical values ​​of the three-dimensional temperature field obtained by the model of the three-dimensional temperature field are compared with the actual temperature measured by the fiber optic temperature measuring device.

[0100] This invention also provides an apparatus for obtaining a three-dimensional temperature field, comprising:

[0101] A fiber optic temperature measurement amplification device is provided. A main control device is connected to the fiber optic temperature measurement amplification device. The main control device transmits the temperature values ​​of each point in the three-dimensional heat conduction model obtained from the three-dimensional model to the fiber optic temperature measurement amplification device. The fiber optic temperature measurement amplification device performs digital-to-analog conversion on the temperature values ​​of each point in the three-dimensional model. The fiber optic temperature measurement amplification device amplifies the temperature values ​​of each point in the three-dimensional model after digital-to-analog conversion.

[0102] The fiber optic driven heating device transmits the amplified temperature values ​​of each point in the three-dimensional model to the fiber optic driven heating device; the fiber optic driven heating device drives the heater to heat; the fiber optic temperature measuring device measures the temperature in the three-dimensional heat conduction model; the measured temperature is returned to the main control device, which cyclically sends the temperature values ​​of each point in the three-dimensional model to the three-dimensional heat conduction model to obtain the temperature values ​​of each point in the next three-dimensional model and adjusts the temperature.

[0103] Furthermore, in the device for obtaining the three-dimensional temperature field, the main control device is communicatively connected to the fiber optic temperature measurement and amplification device, the fiber optic temperature measurement and amplification device is electrically connected to the fiber optic driven heating device, and the fiber optic driven heating device is electrically connected to the heater.

[0104] Furthermore, in the aforementioned device for obtaining a three-dimensional temperature field, the fiber-optic driven heating device and the heater are controlled by a PID heating control method.

[0105] Furthermore, in the device for obtaining a three-dimensional temperature field, the main control device compares the temperature of each point in the three dimensions obtained in the calculation of the three-dimensional heat conduction model with a preset value.

[0106] Compared with the prior art, the embodiments of the present invention obtain a three-dimensional temperature field by means of the following steps:

[0107] Step S100: Set up several fiber optic temperature measuring devices along each axis direction;

[0108] Step S200: The temperature at each point on any fiber optic cable is measured in real time using the fiber optic temperature measuring device, and the real-time temperature of each point is obtained.

[0109] Step S300: Establishment of two-dimensional temperature field model: Import the real-time temperature of each point into the created two-dimensional temperature field model of Fourier heat conduction; proceed to step S400.

[0110] Step S400: Establishment of three-dimensional temperature field model: The two-dimensional temperature field model is then imported into Fourier's law and the first law of thermodynamics to obtain a three-dimensional temperature field model; proceed to step S500.

[0111] Step S500: Solving the three-dimensional temperature field model: The three-dimensional temperature field model is transformed into three cascaded one-dimensional temperature field models; using a tridiagonal matrix, the temperature in the x, y, and z directions is solved to obtain the solution results of the three-dimensional temperature field, and then proceed to step S600;

[0112] Step S600: Import the solution results of the three-dimensional temperature field model into the main control device to obtain the power output of each temperature segment, and obtain a three-dimensional uniform temperature field or a three-dimensional gradient temperature field.

[0113] It solves the main shortcomings of current thermocouple temperature measurement: thermocouples can only obtain the temperature of a single point, resulting in limited information; using information from a single point to replace the overall information leads to large errors; dynamic temperature field measurement is subject to many external interference factors, resulting in poor reliability; multiple thermocouples are used to measure two-dimensional temperature distribution, which occupies a large space and the temperature measurement points cannot be on a straight line, etc. Attached Figure Description

[0114] Figure 1 This is a schematic diagram of the temperature zone structure of a single fiber optic temperature measuring device according to the present invention;

[0115] Figure 2 This is a schematic diagram of the temperature distribution along the axial direction of the temperature zone of a single fiber optic temperature measuring device according to the present invention;

[0116] Figure 3 This is a schematic diagram of the temperature distribution along the radial direction of the temperature zone in a single fiber optic temperature measuring device of the present invention.

[0117] Figure 4 This is a schematic diagram illustrating the temperature gradient distribution principle of the present invention;

[0118] Figure 5 This is a schematic diagram of the radial temperature distribution of the temperature zones of the multiple fiber optic temperature measuring devices of the present invention;

[0119] Figure 6 This is a schematic diagram showing the temperature gradient distribution of the multiple fiber optic temperature measuring devices of the present invention.

[0120] Figure 7 This is a schematic diagram illustrating the two-dimensional heat conduction axial analysis distribution principle of multiple fiber optic temperature measurement devices in this invention.

[0121] Figure 8This is a schematic diagram illustrating the distribution principle of multiple fiber optic temperature measurement devices in a two-dimensional heat conduction cylindrical axisymmetric coordinate system.

[0122] Figure 9 This is a schematic diagram illustrating the distribution principle of the three-dimensional temperature field model of the multiple fiber optic temperature measuring devices in the present invention, in a three-dimensional heat conduction model in a unit coordinate system.

[0123] Figure 10 This is a schematic diagram illustrating the distribution principle of the three-dimensional heat conduction model in the axial coordinate system of the three-dimensional temperature field model of the multiple fiber optic temperature measuring devices of the present invention.

[0124] Figure 11 This is a flowchart of the three-dimensional temperature field model of the present invention;

[0125] Figure 12 This is a flowchart of the two-dimensional temperature field calculation of the present invention;

[0126] Figure 13 This is a flowchart of the three-dimensional temperature field calculation of the present invention;

[0127] Figure 14 This is a flowchart of the X-axis in the three-dimensional temperature field solution method of the present invention;

[0128] Figure 15 This is a flowchart of the Y-axis in the three-dimensional temperature field solution method of the present invention;

[0129] Figure 16 This is a flowchart of the Z-axis in the three-dimensional temperature field solution method of the present invention;

[0130] Figure 17 This is a schematic diagram of the three-dimensional temperature field device of the present invention;

[0131] Figure 18 This is a schematic diagram illustrating the principle of one-dimensional heat conduction in this invention. Detailed Implementation

[0132] To make the objectives, technical solutions, and advantages of this invention clearer, the various embodiments of this invention will be described in detail below with reference to the accompanying drawings. However, those skilled in the art will understand that many technical details have been provided in the various embodiments of this invention to facilitate a better understanding of this application. However, the technical solutions claimed in the claims of this application can be implemented even without these technical details and with various variations and modifications based on the following embodiments.

[0133] The first embodiment of the present invention relates to a method for obtaining a three-dimensional temperature field, such as... Figures 1 to 17 As shown, it includes the following steps:

[0134] Step S100: Set up several fiber optic temperature measuring devices along each axis direction;

[0135] Step S200: Measure the temperature at each point on any fiber optic cable in real time using the fiber optic temperature measuring device, and obtain the real-time temperature at each point; proceed to step S300.

[0136] Step S300: Establishment of two-dimensional temperature field model: Import the real-time temperature of each point into the created two-dimensional temperature field model of Fourier heat conduction; proceed to step S400.

[0137] Step S400: Establishment of three-dimensional temperature field model: The two-dimensional temperature field model is then imported into Fourier's law and the first law of thermodynamics to obtain a three-dimensional temperature field model; proceed to step S500.

[0138] Step S500: Solving the three-dimensional temperature field model: The three-dimensional temperature field model is transformed into three cascaded one-dimensional temperature field models; using a tridiagonal matrix, the temperature in the x, y, and z directions is solved to obtain the solution results of the three-dimensional temperature field, and then proceed to step S600;

[0139] Step S600: Import the solution results of the three-dimensional temperature field model into the main control device to obtain the power output of each temperature segment, thus obtaining a three-dimensional uniform temperature field or a three-dimensional gradient temperature field. This solves the main shortcomings of current thermocouple temperature measurement: thermocouples can only obtain the temperature of a single point, resulting in limited information; using single-point information to replace overall information leads to large errors; dynamic temperature field measurement is subject to many external interference factors, resulting in poor reliability; multiple thermocouples are used to measure two-dimensional temperature distribution, occupying a large space, and the temperature measurement points cannot be aligned on a straight line, among other technical problems.

[0140] To achieve the aforementioned technical effects, the method for obtaining a three-dimensional temperature field in the first embodiment, such as... Figures 2 to 6 As shown, fiber optic temperature measurement is used to measure the temperature at various points along a line in real time, thus obtaining the real-time temperature at each point and acquiring more temperature information. Combined with simulation methods, the three-dimensional distribution of the entire temperature field is calculated. The temperature measurement method is as follows: Figure 1 As shown, the measured temperature field distribution inside the furnace is shown in the figure. Figure 2-6 One of the fiber optic temperature measuring devices 100 is arranged along the axial direction; any one of the fiber optic temperature measuring devices is arranged radially from top to bottom; any one of the fiber optic temperature measuring devices 100 is arranged radially from left to right. This arrangement of the fiber optic temperature measuring devices 100 in the first embodiment forms an axial and radial arrangement in physical space, facilitating the subsequent construction of the three-dimensional temperature field. The axial and radial arrangement does not necessarily have to be in a 90° right angle direction.

[0141] To achieve the aforementioned technical effects, the method for obtaining a three-dimensional temperature field in the first embodiment, such as... Figures 7 to 8 and Figure 12As shown, the establishment of the two-dimensional temperature field model in the first embodiment also includes the following steps:

[0142] Step S310: Two-dimensional heat conduction analysis, substituting the real-time temperature of each point into the two-dimensional unsteady-state heat conduction equation, such as... Figure 7 As shown;

[0143] = +S(1);

[0144] Where λ represents thermal conductivity, ρ represents density, c represents specific heat, T represents temperature, S represents heat source term, and t represents time;

[0145] Step S320: Integrate both sides of the two-dimensional unsteady heat conduction equation based on the time interval (t, t+Δt), where P represents the control volume, such as... Figure 7 As shown;

[0146] - )ΔxΔy(2;

[0147] = ΔyΔt+ ΔxΔt (3;

[0148] =( )ΔxΔyΔt (4;

[0149] After simplification, formulas (2), (3), and (4) are obtained as follows:

[0150] +b(5);

[0151] in:

[0152] = ;

[0153] = ;

[0154] = ;

[0155] = ;

[0156] = + + + + - ΔxΔy;

[0157] = ;

[0158] b= + ;

[0159] Where: E represents the positive half-axis of the two-dimensional X-axis; W represents the negative half-axis of the two-dimensional X-axis; N represents the positive half-axis of the two-dimensional Y-axis; S represents the negative half-axis of the two-dimensional Y-axis.

[0160] Step S330: Perform the derivation in the cylindrical axisymmetric coordinate system and substitute the formula. (6) Perform the derivation; obtain: as Figure 8 As shown:

[0161] = ;

[0162] = ;

[0163] = ;

[0164] = ;

[0165] = + + + + - V;

[0166] = ;

[0167] b= + ;

[0168] =0.5( + x;

[0169] Where r is the radius of the arc, and V is the volume with radius r.

[0170] Then, proceed to step S400.

[0171] To achieve the aforementioned technical effects, the method for obtaining a three-dimensional temperature field in the first embodiment, including the calculation of the three-dimensional temperature field, further comprises the following steps: Figure 9, Figure 10 , Figure 11 , Figure 12 , Figure 13 and Figure 14 As shown

[0172] Step S410: Based on the function T=f(x,y,z, ..., ...) used to establish the three-dimensional temperature field ), = (8);

[0173] = (9).

[0174] The internal heat element per unit volume is , Infinite element dV=dxdydz; Proceed to step S420;

[0175] Step S420, according to the aforementioned Fourier law, calculate as follows:

[0176] The net heat output along the x-axis is - =- xdydzd ;

[0177] The net heat output along the Y-axis is - =- xdydzd ;

[0178] The net heat output along the Z-axis is - =- xdydzd ;

[0179] Proceed to step S430.

[0180] Step S430: According to the first law of thermodynamics:

[0181] Net heat of importing and exporting infinitesimal elements = xdydzd ;

[0182] The heat generated in a infinitesimal element = ;

[0183] The increase in the thermodynamic energy of a infinitesimal element = xdydzd Proceed to step S440;

[0184] Step S440: According to the formula: net heat of the infinitesimal element + heat generated in the infinitesimal element = increase in the thermodynamic energy of the infinitesimal element; after simplification, = + + Proceed to step S450;

[0185] Step S450: Apply the steps from step S440 to the axial coordinate system to obtain a three-dimensional heat conduction model, which can be represented by the formula... ;

[0186] Proceed to step S500.

[0187] To achieve the aforementioned technical effects, the method for obtaining a three-dimensional temperature field in the first embodiment, such as... Figure 15 As shown, the solution of the three-dimensional temperature field also includes:

[0188] Step S510: Assuming that the y and z directions are implicit and the x direction is explicit, the solution of the three-dimensional temperature field will be transformed into a one-dimensional problem, which is solved using a tridiagonal matrix; proceed to step S511.

[0189] Step S511: Simplify the formula

[0190] +b(5);

[0191] Ignoring the temperature in the y direction, we can obtain formula (10).

[0192] (10);

[0193] By moving all temperature terms to the left side of the formula and keeping the source term b on the right side of the formula, we get formula (11).

[0194] - (11);

[0195] make = , = and = ,

[0196] Formula (12) is obtained:

[0197] - (12); Proceed to step S512;

[0198] Step S512: Because we assume one-dimensional heat conduction, therefore =1, = , = In a tridiagonal matrix, - , and - A tridiagonal matrix is ​​created for i=1, i=2...i=6, where i=3 is... = When i=4 = When i=5 = From this, we can obtain a tridiagonal matrix. Proceed to step S513;

[0199]

[0200] Step S513: Source Item Matrix The calculation of the source term matrix Given that all values ​​of b are the same, b = x, =1, =Device power output Proceed to step S514;

[0201] Step S514: Solve the tridiagonal matrix The reverse , = Thus obtain = , = , = ;

[0202] = = = ;

[0203] Proceed to step S520;

[0204] Step S520: Assuming that the x and z directions are implicit and the y direction is explicit, the three-dimensional problem of solving the three-dimensional temperature field will be transformed into a one-dimensional problem; solve it using a tridiagonal matrix; proceed to step S521;

[0205] Step S521: Establish a tridiagonal matrix. Similarly to formulas (10)-(12), formulas (13)-(15) can be obtained.

[0206] (13);

[0207] - (14);

[0208] - (15);

[0209] Proceed to step S522;

[0210] Step S522: Because we assume one-dimensional heat conduction, therefore x=1, = , = In a tridiagonal matrix, - , and - A tridiagonal matrix is ​​created for i=1, i=2...i=6, where i=3... = When i=4 = When i=5 = ; obtain a tridiagonal matrix

[0211]

[0212] Proceed to step S523;

[0213] Step S523: Assume the source term matrix Given that all values ​​of b are the same. Source term vector Solve for b in the middle;

[0214] b= Proceed to step S524;

[0215] Step S524: = × Seeking = , ;

[0216] = × =

[0217] Step S530: Assuming the x and y directions are implicit and the z direction is explicit, the three-dimensional problem of solving the three-dimensional temperature field will be transformed into a one-dimensional problem; solve it using a tridiagonal matrix; proceed to step S531;

[0218] Step S531: Establish a tridiagonal matrix. Similarly to formulas (10)-(12), formulas (16)-(18) can be obtained.

[0219] (16);

[0220] - (17);

[0221] - (18);

[0222] Proceed to step S532:

[0223] Step S532: Assuming one-dimensional heat conduction, r=1, = , = In a tridiagonal matrix, - , and - A tridiagonal matrix is ​​created for i=1, i=2...i=6, where i=3... = When i=4 = When i=5 = The tridiagonal matrix is ​​obtained.

[0224]

[0225] Step S533: Source Item Proceed to step S534;

[0226] Step S534: = × Thus, to obtain , , ;

[0227] = × = ;

[0228] A numerical calculation of a three-dimensional temperature field is obtained; steps S510-S534 are continuously repeated to obtain a real-time three-dimensional temperature field model; proceed to step S600.

[0229] To achieve the aforementioned technical effects, the method for obtaining a three-dimensional temperature field in the first embodiment involves setting boundary conditions for each temperature measurement zone, calculating the numerical value of the three-dimensional temperature field from the model of the three-dimensional temperature field, and comparing it with the actual temperature measured by the fiber optic temperature measuring device.

[0230] In a second embodiment of the present invention, a device for obtaining a three-dimensional temperature field is also provided, such as... Figure 18 As shown, it includes:

[0231] The main control device 200 is connected to the fiber optic temperature amplification device 300. The main control device 200 transmits the temperature values ​​of each point in the three-dimensional heat conduction model obtained from the three-dimensional model to the fiber optic temperature amplification device 300. The fiber optic temperature amplification device 300 performs digital-to-analog conversion on the temperature values ​​of each point in the three-dimensional model and amplifies the temperature values ​​of each point in the three-dimensional model after digital-to-analog conversion. The main function of the fiber optic temperature amplification device 300 is to amplify the temperature values.

[0232] The fiber optic temperature amplification device 300 transmits the amplified temperature values ​​of each point in the three-dimensional model to the fiber optic driven heating device 400; the fiber optic driven heating device 400 drives the heater 500 to heat; the fiber optic temperature measuring device 100 measures the temperature in the three-dimensional heat conduction model; the measured temperature is returned to the main control device 200, which cyclically sends the temperature values ​​of each point in the three-dimensional model to the three-dimensional heat conduction model to obtain the temperature values ​​of each point in the next three-dimensional model and adjusts the temperature accordingly. The fiber optic driven heating device 400 mainly serves to drive the heater 500 to heat.

[0233] The apparatus for obtaining a three-dimensional temperature field in the second embodiment of the present invention, such as Figure 15 As shown, the main control device 200 is communicatively connected to the fiber optic temperature amplification device 300, which is electrically connected to the fiber optic driven heating device 400. The fiber optic driven heating device 400 is also electrically connected to the heater 500. After the main control device 200 and the fiber optic temperature amplification device 300 are communicatively connected, the main control device 200 controls the fiber optic temperature amplification device 300 to perform digital-to-analog conversion and amplification of the temperature values ​​of each point in the three-dimensional heat conduction model obtained from the three-dimensional heat conduction model. After the fiber optic driven heating device 400 is electrically connected to the heater 500, the fiber optic driven heating device 400 drives the heater 500 to heat the heater. At the same time, the fiber optic temperature measuring device 100 measures the temperature. The main control device 200 performs temperature control and simulated temperature control through the three-dimensional heat conduction model.

[0234] The apparatus for obtaining a three-dimensional temperature field in the second embodiment of the present invention, such as Figure 15 As shown, the fiber optic driven heating device 400 and the heater 500 are controlled by a PID heating control method.

[0235] The apparatus for obtaining a three-dimensional temperature field in the second embodiment of the present invention, such as Figure 15 As shown, the main control device 200 of the device for obtaining the three-dimensional temperature field compares the temperature of each point in the three-dimensional heat conduction model with a preset value. This mainly serves another function in the present invention: when the main control device 200 uses the three-dimensional heat conduction model to obtain the temperature of each point in the three-dimensional temperature field, it compares the temperature with the preset value to perform simulation.

[0236] In a third embodiment of the present invention, a method for a three-dimensional temperature field is provided, such as... Figure 13 , Figure 14 , Figure 15 , Figure 16 , Figure 18 As shown, the details are as follows.

[0237] First, assume that the y and z directions are implicit, and the x direction is explicit; the three-dimensional problem will then be transformed into a one-dimensional problem. For example... Figure 13 , Figure 17 As shown, there are respectively Based on formula (5) derived from the two-dimensional temperature field, omitting the temperature along the y-axis, we obtain formula (10). Reintegrating formula (10) yields formula (11). , Use respectively , This allows us to obtain formula (12), which in turn yields a tridiagonal matrix. Source term vector And temperature vector - = , , =c.

[0238] (10)

[0239] - (11)

[0240] - (12)

[0241]

[0242] = ;

[0243] =

[0244] Because we assume one-dimensional heat conduction, therefore =1, = , = . = =The thermal conductivity of air =0.023W / mK (does not change with the value of i), when i=1, = =0.001, i=2, = =0.002, i=3, = =0.003, i=4, = =0.004, i=5, = =0.005, i=6, = =0.006. In one-dimensional heat conduction, = + - x, =10, =1, x = 0.001. Substituting these values, we can obtain the corresponding... , ; , , ; , , ; , , ; , , ; , The corresponding tridiagonal matrix .

[0245]

[0246] By finding the matrix The reverse Source term vector All values ​​of b are the same, b= x, =1, x=0.001, the equipment power is 1kW, and it takes 22 minutes to heat to 300 degrees Celsius at 25% output. =1000×0.25×22×60=330000J. Source term vector. b=330. Temperature vector. It can be done × get.

[0247] = ;

[0248] = = × = × = ;

[0249] in They are , The temperatures were 298.6℃, 325.3℃, and 294℃, respectively.

[0250] Similarly, assuming the x and z directions are implicit and the y direction is explicit, we can solve for the temperature in the y direction. , .

[0251] (13)

[0252] - (14)

[0253] - (15)

[0254] Because we assume one-dimensional heat conduction, therefore =1, = , = . = =The thermal conductivity of air=0.023W / mK (does not change with the value of i), when i=1, = =0.001, i=2, = =0.002, i=3, = =0.003, i=4, = =0.004, i=5, = =0.005, i=6, = =0.006. In one-dimensional heat conduction, = + - y, =10, =1, y = 0.001. Substituting these values, we can obtain the corresponding... , ; , , ; , , ; , , ; , , ; , The corresponding tridiagonal matrix .

[0255]

[0256] By finding the matrix The reverse Source term vector Given that all values ​​of b are the same. We can source term vector Solving for b, we get b = 298.6 ÷ (0.0256 + 0.1025 + 0.2304 + 0.2337 + 0.1951 + 0.1137) = 330.1. (Temperature vector) It can be done × get.

[0257] = ;

[0258] = = × = × = ;

[0259] in They are , The temperatures were 298.6℃, 325.3℃, and 294.1℃, respectively.

[0260] Because we assume one-dimensional heat conduction, therefore =1, = , = In a tridiagonal matrix, - , and - . = =The thermal conductivity of air=0.023W / mK (does not change with the value of i), when i=1, = =0.001, i=2, = =0.002, i=3, = =0.003, i=4, = =0.004, i=5, = =0.005, i=6, = =0.006. Substituting these values, we can obtain the corresponding... , ; , , ; , , ; , , ; , , ; , The corresponding tridiagonal matrix .

[0261] ;

[0262] By finding the matrix The reverse Source term vector Given that all values ​​of b are the same. We can source term vector Solving for b, we get b = 325.3 ÷ (0.0193 + 0.0771 + 0.1732 + 0.3064 + 0.2558 + 0.1538) = 330.1. (Temperature vector) It can be done × get.

[0263] = ;

[0264] = = × = × = ;

[0265] They are , The temperatures were 298.6℃, 325.3℃, and 294.1℃, respectively.

[0266] In the third embodiment of this invention, a 6×6 tridiagonal matrix was used to illustrate the numerical calculation method of the three-dimensional temperature field. Because the matrix size is relatively small, the temperature at the center point is... Temperature of neighboring points , as well as There is a deviation. The main reason is that the size of the tridiagonal matrix is ​​insufficient; in this case, the tridiagonal matrix is ​​6×6, which is too small, resulting in too few iterations and thus a deviation. If the size of the diagonal matrix is ​​increased, the temperature at the center point... Temperature of neighboring points , as well as They will approach each other infinitely, until they are equal. In the third embodiment of the present invention... x、 , When z and Δx, Δy, Δz approach 0 (infinitesimals), the temperature at the center point will also increase. Temperature of neighboring points , as well as They will approach each other infinitely, until they are equal. Meanwhile, in the third embodiment of the present invention, other heat source terms are assumed to be 0 for ease of illustration. In practical applications, however, other heat source terms will not be equal to 0, thus also affecting the center point temperature. Temperature of neighboring points , as well as It will approach infinitely closer until it is equal. In the third embodiment of the invention, increasing the size of the tridiagonal matrix and the number of iterations will reduce the deviation. Similarly, reducing... x、 , As z and Δx, Δy, and Δz are brought closer to 0, the deviation will also decrease. Furthermore, including other heat source terms as boundary conditions in the model will also reduce the deviation until they are equal.

[0267] Those skilled in the art will understand that the above embodiments are specific examples of implementing the present invention, and in practical applications, various changes in form and detail may be made without departing from the spirit and scope of the present invention.

Claims

1. A method of obtaining a three-dimensional temperature field, characterized by, Includes the following steps: Step S100: Set up several fiber optic temperature measuring devices along each axis direction; Step S200: Measure the temperature at each point on any fiber optic cable in real time using the fiber optic temperature measuring device, and obtain the real-time temperature at each point; proceed to step S300. Step S300: Establishment of two-dimensional temperature field model: Import the real-time temperature of each point obtained into the created two-dimensional temperature field model of Fourier heat conduction; Proceed to step S400; Step S400: Establishment of three-dimensional temperature field model: The two-dimensional temperature field model is then imported into Fourier's law and the first law of thermodynamics to obtain a three-dimensional temperature field model; Proceed to step S500; Step S500: Solving the three-dimensional temperature field model: The three-dimensional temperature field model is transformed into three cascaded one-dimensional temperature field models; using a tridiagonal matrix, the temperature in the x, y, and z directions is solved to obtain the solution results of the three-dimensional temperature field, and then proceed to step S600; Step S600: Import the solution results of the three-dimensional temperature field model into the main control device to obtain the power output of each temperature segment, and obtain a three-dimensional uniform temperature field or a three-dimensional gradient temperature field.

2. The method of obtaining a three-dimensional temperature field according to claim 1, wherein, One of the fiber optic temperature measuring devices is arranged along the axial direction; any one of the fiber optic temperature measuring devices is arranged radially from top to bottom; any one of the fiber optic temperature measuring devices is arranged radially from left to right.

3. The method of obtaining a three-dimensional temperature field of claim 1, wherein, The establishment of the two-dimensional temperature field model also includes the following steps: Step S310: Two-dimensional heat conduction analysis, substituting the real-time temperature of each point into the two-dimensional unsteady-state heat conduction equation. = +S（1）； Where λ represents thermal conductivity, ρ represents density, c represents specific heat, T represents temperature, S represents heat source term, and t represents time; Step S320: Integrate both sides of the two-dimensional unsteady heat conduction equation based on the time interval (t, t+Δt), where P represents the control volume. - ) ΔxΔy (2); = ΔyΔt+ ΔxΔt (3); =( )ΔxΔyΔt (4); After simplification, formulas (2), (3), and (4) are obtained as follows: +b（5）； in: = ； = ； = ； = ； = + + + + - ΔxΔy; = ； b= + ； Where: E represents the positive half-axis of the two-dimensional X-axis; W represents the negative half-axis of the two-dimensional X-axis; N represents the positive half-axis of the two-dimensional Y-axis; S represents the negative half-axis of the two-dimensional Y-axis. Step S330: Perform the derivation in the cylindrical axisymmetric coordinate system and substitute the formula. (6) The derivation is performed; we get: = ； = ； = ； = ； = + + + + - V； = ； b= + ； =0.5( + x（7）； Where r is the radius of the arc and V is the volume with radius r, proceed to step S400.

4. The method for obtaining a three-dimensional temperature field according to claim 1, characterized in that, The establishment of the three-dimensional temperature field model also includes the following steps: Step S410: Based on the function T=f(x,y,z, ..., ...) used to establish the three-dimensional temperature field ), = (8); = （9）； The internal heat element per unit volume is , micro-element body dV=dxdydz; Proceed to step S420; Step S420, according to the aforementioned Fourier law, the following is calculated: The net heat output along the x-axis is - =- xdydzd ; The net heat output along the Y-axis is - =- xdydzd ; The net heat output along the Z-axis is - =- xdydzd ; Proceed to step S430. Step S430: According to the first law of thermodynamics: Net heat of importing and exporting infinitesimal elements = xdydzd ; The heat generated in a infinitesimal element = ; The increase in the thermodynamic energy of a infinitesimal element = xdydzd ; Proceed to step S440; Step S440: According to the formula: net heat of the infinitesimal element + heat generated in the infinitesimal element = increase in the thermodynamic energy of the infinitesimal element; after simplification, = + + ; Proceed to step S450; Step S450: Apply the steps from step S440 to the axial coordinate system to obtain a three-dimensional heat conduction model, which can be represented by the formula... ; Proceed to step S500.

5. The method for obtaining a three-dimensional temperature field according to claim 1, characterized in that, The solution to the three-dimensional temperature field also includes: Step S510: Assuming that the y and z directions are implicit and the x direction is explicit, the solution of the three-dimensional temperature field will be transformed into a one-dimensional problem, which is solved using a tridiagonal matrix; proceed to step S511. Step S511: Simplify the formula +b（5）； Ignoring the temperature in the y direction, we can obtain formula (10). （10）； By moving all temperature terms to the left side of the formula and keeping the source term b on the right side of the formula, we get formula (11). - （11）； make = , = and = , Formula (12) is obtained: - (12); Proceed to step S512; Step S512: Because we assume one-dimensional heat conduction, therefore =1, = , = In a tridiagonal matrix, - , and - A tridiagonal matrix is ​​created for i=1, i=2...i=6, where i=3 is... = When i=4 = When i=5 = From this, we can obtain a tridiagonal matrix. Proceed to step S513; ； Step S513: Source Term Matrix The calculation of the source term matrix Given that all values ​​of b are the same, b = x, =1, =Device power output Proceed to step S514; Step 514: Solve the tridiagonal matrix The reverse , = Thus obtain = , = , = ; = = = ； Proceed to step S520; Step S520: Assuming that the x and z directions are implicit and the y direction is explicit, the three-dimensional problem of solving the three-dimensional temperature field will be transformed into a one-dimensional problem; solve it using a tridiagonal matrix; proceed to step S521; Step S521: Establish a tridiagonal matrix. Similarly to formulas (10)-(12), formulas (13)-(15) can be obtained. （13）； - （14）； - （15）； Proceed to step S522; Step S522: Because we assume one-dimensional heat conduction, therefore x=1, = , = In a tridiagonal matrix, - , and - A tridiagonal matrix is ​​created for i=1, i=2...i=6, where i=3... = When i=4 = When i=5 = ; obtain a tridiagonal matrix ; Proceed to step S523; Step S523: Assume the source term matrix Given that all values ​​of b are the same. Source term vector Solve for b in the middle; b= Proceed to step S524; Step S524: = × Seeking = , ; = × = ； Step S530: Assuming the x and y directions are implicit and the z direction is explicit, the three-dimensional problem of solving the three-dimensional temperature field will be transformed into a one-dimensional problem; solve it using a tridiagonal matrix; proceed to step S531; Step S531: Establish a tridiagonal matrix. Similarly to formulas (10)-(12), formulas (16)-(18) can be obtained. （16）； - （17）； - （18）； Proceed to step S532: Step S532: Assuming one-dimensional heat conduction, r=1, = , = In a tridiagonal matrix, - , and - A tridiagonal matrix is ​​created for i=1, i=2...i=6, where i=3... = When i=4 = When i=5 = ; obtain a tridiagonal matrix ; Step 533: Source Item Proceed to step S534; Step S534: = × Thus, to obtain , , ; = × = ; A numerical calculation of a three-dimensional temperature field is obtained; steps S510-S534 are continuously repeated to obtain a real-time three-dimensional temperature field model; proceed to step S600.

6. The method for obtaining a three-dimensional temperature field according to claim 5, characterized in that, By setting the boundary conditions for each temperature measurement zone, the numerical values ​​of the three-dimensional temperature field obtained by the model of the three-dimensional temperature field are compared with the actual temperature measured by the fiber optic temperature measuring device.

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