A method for deriving turbine blade wall temperature based on effective radiation

Abstract

The application relates to a method for deducing turbine blade wall temperature based on effective radiation, which can achieve the purpose of accurate temperature measurement of the turbine blade by accurately describing the distribution of effective radiation of the turbine blade. In actual measurement, due to the change of the relative position between two surfaces, the proportion of the radiation emitted by one surface to the other surface changes accordingly. The application can quickly and accurately solve the angular coefficient and effective radiation between small grids in the space, more accurately analyze the wall surface temperature distribution of the turbine blade, and based on the radiation correction research of the infrared temperature measurement of the turbine blade, provide a convenient method, which has the advantages of convenient calculation, accuracy, reliable calculation result and the like, and has certain guiding significance in the radiation correction of the infrared temperature measurement of the turbine blade and the accurate measurement of the blade temperature.

Description

Technical Field

[0001] This application relates to the field of aero-engine temperature measurement technology, and more specifically, to a method for deriving turbine blade wall temperature based on effective radiation. Background Technology

[0002] In the field of aero-engine research, obtaining turbine blade wall temperature is crucial. Due to the complex environment of hot-end components and the interference from wall surface and exhaust radiation, obtaining turbine blade wall temperature is extremely difficult. Currently used methods for calculating turbine blade wall temperature lack further refinement of the blade surface mesh, resulting in inaccurate obtained blade wall temperatures. Summary of the Invention

[0003] To overcome at least one deficiency in the prior art, this application provides a method for deriving turbine blade wall temperature based on effective radiation.

[0004] Firstly, a method for deriving turbine blade wall temperature based on effective radiation is provided, including:

[0005] Step 1: Divide the computational domain into a mesh; any surface in the computational domain other than the blade surface is designated as the first surface.

[0006] Step 2: Determine the area of ​​each grid and the distance between any two grids;

[0007] Step 3: Based on the area of ​​each grid and the distance between any two grids, determine the angle coefficient of any grid on the first surface with respect to any grid on the blade surface, and the angle coefficient of any grid on the blade surface with respect to any grid on the first surface.

[0008] Step 4: Construct the angle coefficient matrix based on the angle coefficients;

[0009] Step 5: Based on the angle coefficient matrix and the wall temperature of each grid obtained in the previous iteration, determine the effective radiation column matrix for the current iteration; the elements in the effective radiation column matrix are the effective radiation of each grid.

[0010] Step 6: Determine the wall temperature matrix based on the effective radiation column matrix of the current iteration. The elements in the wall temperature matrix are the wall temperatures of each grid in the current iteration.

[0011] Step 7: Determine whether the difference between the effective radiation of each grid in the current iteration and the effective radiation of the corresponding grid in the previous iteration is less than a set value. If yes, proceed to step 8. If no, return to step 5 and use the wall temperature of each grid in the current iteration as the wall temperature of each grid in the next iteration.

[0012] Step 8: Output the wall temperature of the mesh belonging to the blade surface in each mesh of the current iteration.

[0013] In one embodiment, the angular coefficient of any grid on the first surface with respect to any grid on the blade surface is determined by the following formula:

[0014]

[0015] Where, Φ 1,2 θ1 is the angle coefficient of any grid in the first surface with respect to any grid in the blade surface, θ2 is the area of ​​any grid in the blade surface, θ1 is the angle between the normal vector of any grid in the first surface and the line connecting the two grid center points, θ2 is the angle between the normal vector of any grid in the blade surface and the line connecting the two grid center points, and r is the distance between the two grid center points.

[0016] In one embodiment, the angular coefficient of any grid on the blade surface with respect to any grid on the first surface is determined by the following formula:

[0017]

[0018] Where, Φ 2,1 Let θ1 be the angle coefficient of any grid on the blade surface relative to any grid on the first surface, dA1 be the area of ​​any grid on the first surface, θ1 be the angle between the normal vector of any grid on the first surface and the line connecting the two grid center points, θ2 be the angle between the normal vector of any grid on the blade surface and the line connecting the two grid center points, and r be the distance between the two grid center points.

[0019] In one embodiment, the effective radiation column matrix is ​​expressed by the following formula:

[0020]

[0021] Where [J] is the effective radiation column matrix, σ is the blackbody radiation constant, and [T] is the effective radiation column matrix. 4 [A] is a fourth-order temperature column matrix, where the elements are the wall temperatures of each grid cell, and [A] is the angle coefficient matrix.

[0022] In one embodiment, the wall temperature of each grid is determined using the following formula:

[0023]

[0024] Where T-eff is the wall temperature of each grid, J is the effective radiation of each grid in the effective radiation column matrix, ε is the emissivity of the grid, and σ is the blackbody radiation constant.

[0025] In one embodiment, the method further includes:

[0026] The initial temperature of each grid is preset according to the boundary conditions, and the blackbody radiation force of each grid is calculated.

[0027] To determine whether the magnitude of the blackbody's radiation force is correct;

[0028] If the blackbody radiation force is correct, proceed to step 3.

[0029] In one embodiment, the method further includes:

[0030] The angle coefficient of any mesh on the first surface with respect to any mesh on the blade surface is denoted as the first angle coefficient; the angle coefficient of any mesh on the blade surface with respect to any mesh on the first surface is denoted as the second angle coefficient.

[0031] Based on the area of ​​each grid and the distance between any two grids, calculate the angular coefficient between any two grids on the blade surface, and denote it as the third angular coefficient;

[0032] Summing up all the first and third angle coefficients yields the accumulated value;

[0033] If the accumulated value is approximately equal to 1, then the angle coefficient is calculated accurately; otherwise, the angle coefficient is not calculated accurately.

[0034] If the angle coefficient is calculated accurately, proceed to step 4.

[0035] Secondly, a computer-readable storage medium is provided, which stores a computer program that, when executed by a processor, implements the aforementioned method for deriving turbine blade wall temperature based on effective radiation.

[0036] Thirdly, a computer program product is provided, including a computer program / instructions, which, when executed by a processor, implement the above-described method for deriving turbine blade wall temperature based on effective radiation.

[0037] Compared with existing technologies, this application has the following advantages: This application provides a method for deriving turbine blade wall temperature based on effective radiation. This method achieves accurate temperature measurement of the blade by accurately describing the distribution of effective radiation of the turbine blade. In actual measurement, due to the change in the relative position between the two surfaces, the proportion of radiation emitted from one surface reaching the other surface changes accordingly. This application can quickly and accurately solve for the angle coefficient and effective radiation between fine grids in space, and more accurately analyze the wall temperature distribution of the turbine blade. Based on the radiation correction research of turbine blade infrared thermometry, this application provides a convenient method with advantages such as convenient and accurate calculation and reliable calculation results. It has certain guiding significance in the radiation correction of turbine blade infrared thermometry and the accurate measurement of blade temperature. Attached Figure Description

[0038] This application can be better understood by referring to the description given below in conjunction with the accompanying drawings, which, together with the detailed description below, are incorporated in and form part of this specification. In the drawings:

[0039] Figure 1 A flowchart illustrating a method for deriving turbine blade wall temperature based on effective radiation according to an embodiment of this application is shown.

[0040] Figure 2 The blade wall temperature and error distributions for different inlet radiation intensities are shown, where (a) is the blade wall temperature and error distribution when the inlet radiation intensity is 1400K, (b) is the blade wall temperature and error distribution when the inlet radiation intensity is 1600K, and (c) is the blade wall temperature and error distribution when the inlet radiation intensity is 1800K.

[0041] Figure 3 The distribution of blade wall error along the blade height is shown in the diagram for different inlet radiation intensities. Detailed Implementation

[0042] Exemplary embodiments of the present application will be described below with reference to the accompanying drawings. For clarity and brevity, not all features of the actual embodiments are described in the specification. However, it should be understood that many embodiment-specific decisions can be made in the development of any such actual embodiment to achieve the developer’s specific objectives, and these decisions may vary as the embodiments differ.

[0043] It should also be noted that, in order to avoid obscuring this application with unnecessary details, only the device structure closely related to the solution according to this application is shown in the accompanying drawings, while other details that are not closely related to this application are omitted.

[0044] It should be understood that this application is not limited to the described embodiments by virtue of the following description with reference to the accompanying drawings. In this document, embodiments may be combined with each other, features may be substituted or borrowed between different embodiments, and one or more features may be omitted in one embodiment, where feasible.

[0045] This application provides a method for deriving turbine blade wall temperature based on effective radiation. Figure 1 A flowchart illustrating a method for deriving turbine blade wall temperature based on effective radiation according to an embodiment of this application is shown. See also... Figure 1 The methods include:

[0046] Step 1: Mesh the computational domain. Any surface of the computational domain other than the blade surface is designated as the first surface. The computational domain includes a fluid domain and a solid domain. The solid domain includes the region where the blade is located. Any surface of the computational domain can be the end wall. Here, a hexahedral meshing method can be used to mesh the computational domain.

[0047] Step 2: Determine the area of ​​each grid cell and the distance between any two grid cells. Here, Fluent software can be used to calculate the area of ​​the resulting grid cells and the distance between any two grid cells.

[0048] Step 3: Based on the area of ​​each grid and the distance between any two grids, determine the angle coefficient of any grid on the first surface with respect to any grid on the blade surface, denoted as the first angle coefficient, and the angle coefficient of any grid on the blade surface with respect to any grid on the first surface, denoted as the second angle coefficient.

[0049] Specifically, the angle coefficient of any grid on the first surface with respect to any grid on the blade surface is calculated using the following formula:

[0050]

[0051] Where, Φ 1,2 θ1 is the angle coefficient of any grid in the first surface with respect to any grid in the blade surface, θ2 is the area of ​​any grid in the blade surface, θ1 is the angle between the normal vector of any grid in the first surface and the line connecting the two grid center points, θ2 is the angle between the normal vector of any grid in the blade surface and the line connecting the two grid center points, and r is the distance between the two grid center points.

[0052] The angular coefficient of any grid on the blade surface with respect to any grid on the first surface is given by the following formula:

[0053]

[0054] Where, Φ 2,1 Let θ1 be the angle coefficient of any grid on the blade surface relative to any grid on the first surface, dA1 be the area of ​​any grid on the first surface, θ1 be the angle between the normal vector of any grid on the first surface and the line connecting the two grid center points, θ2 be the angle between the normal vector of any grid on the blade surface and the line connecting the two grid center points, and r be the distance between the two grid center points.

[0055] Step 4: Construct the angle coefficient matrix based on the angle coefficients.

[0056] Here, any element a in the angle coefficient matrix, Where φ is the angle coefficient, including the first angle coefficient and the second angle coefficient; δ is the Kronecker operator, where δ = 1 when the two grids corresponding to φ are aligned, otherwise δ = 0; ε is the emissivity of the grid, which is a set value.

[0057] Step 5: Determine the effective radiation column matrix for the current iteration based on the angle coefficient matrix and the wall temperature of each grid obtained in the previous iteration; the elements in the effective radiation column matrix are the effective radiation of each grid.

[0058] Specifically, the effective radiation column matrix is ​​calculated using the following formula:

[0059]

[0060] Where [J] is the effective radiation column matrix, and σ is the blackbody radiation constant with a value of 5.67 × 10⁻⁶. -8 W / (m 2 ·K 4 ), [T 4 [A] is a fourth-order temperature column matrix, where the elements are the wall temperatures of each grid cell, and [A] is the angle coefficient matrix.

[0061] Step 6: Determine the wall temperature matrix based on the effective radiation column matrix of the current iteration. The elements in the wall temperature matrix are the wall temperatures of each grid in the current iteration.

[0062] Specifically, the wall temperature of each grid is calculated using the following formula:

[0063]

[0064] Where T-eff is the wall temperature of each grid, J is the effective radiation of each grid in the effective radiation column matrix, ε is the emissivity of the grid, and σ is the blackbody radiation constant with a value of 5.67 W / (m²). 2 ·K 4 ).

[0065] Step 7: Determine whether the difference between the effective radiation of each grid in the current iteration and the effective radiation of the corresponding grid in the previous iteration is less than a set value, which can be 10e-3. If yes, proceed to step 8; otherwise, return to step 5 and use the wall temperature of each grid in the current iteration as the wall temperature of each grid in the next iteration.

[0066] Step 8: Output the wall temperature of the mesh belonging to the blade surface in each mesh of the current iteration.

[0067] In this embodiment, the accurate temperature measurement of the turbine blade is achieved by precisely describing the distribution of effective radiation. In actual measurements, the relative positions of the two surfaces change, causing the proportion of radiation emitted from one surface to reach the other to vary. This application can quickly and accurately solve for the angle coefficient and effective radiation between fine grids in space, enabling a more accurate analysis of the turbine blade's wall temperature distribution. Based on radiation correction research in turbine blade infrared thermometry, this application provides a convenient method with advantages such as convenient and accurate calculation, and reliable results. It has certain guiding significance for radiation correction in turbine blade infrared thermometry and accurate blade temperature measurement.

[0068] In one embodiment, the method further includes:

[0069] Based on the predefined initial temperature of each grid according to the boundary conditions, the magnitude of the blackbody radiation force E of each grid is calculated. b E b =σT 4 Where σ is the blackbody radiation constant, with a value of 5.67 × 10⁻⁶. -8 W / (m 2 ·K 4 Here, boundary conditions include turbulence intensity, atmospheric pressure, composition, etc.

[0070] To determine if the magnitude of the blackbody's radiant force is correct; here, the difference between the magnitude of the blackbody's radiant force and the theoretical value should not exceed 10 W / m. 2 If the result is correct, the calculation is considered correct; otherwise, return to step 2 and calculate again to eliminate the calculation error.

[0071] If the blackbody radiation force is correct, proceed to step 3.

[0072] In one embodiment, the method further includes: verifying the integrity of the diagonal coefficients, which can be done by:

[0073] Based on the area of ​​each grid and the distance between any two grids, calculate the angular coefficient between any two grids on the blade surface, and denote it as the third angular coefficient;

[0074] Summing up all the first and third angle coefficients yields the accumulated value;

[0075] If the accumulated value is approximately equal to 1, then the angle coefficient is calculated accurately; otherwise, the angle coefficient is not calculated accurately.

[0076] If the angle coefficient is calculated accurately, proceed to step 4; if the angle coefficient is not calculated accurately, return to step 2 and recalculate the area of ​​the grid and the distance between any two grids to eliminate the calculation error.

[0077] This application provides a computer-readable storage medium storing a computer program. When the computer program is executed by a processor, it implements the above-described method for deriving turbine blade wall temperature based on effective radiation.

[0078] This application provides a computer program product, including a computer program / instructions, which, when executed by a processor, implement the above-described method for deriving turbine blade wall temperature based on effective radiation.

[0079] To further verify the effectiveness of the method in this application, experimental analysis was conducted. The influence of different inlet radiation intensities on the heat transfer characteristics of turbine blades under endwall reflected radiation was studied, and the effective radiation distribution was output. The inlet radiation intensities were changed to 1400K, 1600K, and 1800K, while ensuring that the proportions of gas components H2O, CO2, N2, and O2 were 0.05, 0.1, 0.7, and 0.15, respectively; the blade emissivity was 0.6; and the outlet blackbody radiation temperature was the same at 1400K. The blade wall temperature under different inlet radiation intensities was obtained without considering the influence of gas combustion radiation. Figure 2 The blade wall temperature and error distributions for different inlet radiation intensities are shown, where (a) is the blade wall temperature and error distribution when the inlet radiation intensity is 1400K, (b) is the blade wall temperature and error distribution when the inlet radiation intensity is 1600K, and (c) is the blade wall temperature and error distribution when the inlet radiation intensity is 1800K. Figure 2 In this context, T-eff represents the blade wall temperature obtained according to the method of this application, T-wall is the theoretical value of the blade wall temperature, T-dif is the temperature error, and T-dif = T-eff - T-wall.

[0080] according to Figure 2 It can be seen that, under the condition of changing the temperature of the imported blackbody radiation, the effect on the blade wall temperature is mainly concentrated in the blade pressure surface region, where the blade pressure surface temperature is significantly higher than that of the blade suction surface region. The second most affected region is the blade leading edge region, because the imported blackbody radiation temperature input mainly irradiates the blade pressure surface and the vicinity of the leading edge of the blade pressure surface, and this part of the region receives a large radiative energy flow.

[0081] The error distribution is obtained by outputting the error distribution along the leaf height direction. Figure 3The diagram shows the distribution of blade wall surface error along the blade height under different inlet radiation intensities. By comparing the blade error distribution under different inlet radiation temperatures, it can be qualitatively observed that the increase in inlet radiation temperature has the greatest impact on the temperature change of the blade leading edge and pressure surface, followed by the trailing edge, and the error is more pronounced in areas with film cooling holes. Because the inlet is directly radiated by the combustion chamber outlet gas, the blade leading edge is sensitive to changes in inlet radiation temperature, and the trailing edge has less cooling, resulting in a higher temperature rise due to the larger radiative heat flux at this point. Combined with... Figure 2 The calculation error was most significant in the leading edge region of the blade, reaching as high as 37.68K.

[0082] Under the combined influence of the main and secondary flows, the calculated error on the pressure surface is only around 25K. The effective radiation distribution calculated in this application further corrects the wall error distribution of the blade under different inlet radiation intensities.

[0083] The above descriptions are merely various embodiments of this application, but the scope of protection of this application is not limited thereto. Any variations or substitutions that can be easily conceived by those skilled in the art within the scope of the technology disclosed in this application should be included within the scope of protection of this application. Therefore, the scope of protection of this application should be determined by the scope of the claims.

Claims

1. A method for deriving turbine blade wall temperature based on effective radiation, characterized in that, include: Step 1: Divide the computational domain into a grid; The computational domain, excluding any surface of the blade, is denoted as the first surface; Step 2: Determine the area of ​​each grid and the distance between any two grids; Step 3: Based on the area of ​​each grid and the distance between any two grids, determine the angle coefficient of any grid in the first surface with respect to any grid in the blade surface, and the angle coefficient of any grid in the blade surface with respect to any grid in the first surface. Step 4: Construct an angle coefficient matrix based on the angle coefficients; Step 5: Determine the effective radiation column matrix for the current iteration based on the angle coefficient matrix and the wall temperature of each grid obtained in the previous iteration; The elements in the effective radiation column matrix are the effective radiation of each grid. Step 6: Determine the wall temperature matrix based on the effective radiation column matrix of the current iteration, wherein the elements in the wall temperature matrix are the wall temperatures of each grid in the current iteration; Step 7: Determine whether the difference between the effective radiation of each grid in the current iteration and the effective radiation of the corresponding grid in the previous iteration is less than a set value. If yes, proceed to step 8. If no, return to step 5 and use the wall temperature of each grid in the current iteration as the wall temperature of each grid in the next iteration. Step 8: Output the wall temperature of the grid belonging to the blade surface in each grid of the current iteration; The angular coefficient of any grid in the first surface with respect to any grid in the blade surface is given by the following formula: in, Let be the angle coefficient of any grid in the first surface with respect to any grid in the blade surface. Let be the area of ​​any grid on the blade surface. Let be the angle between the normal vector of any grid in the first surface and the line connecting the center points of the two grids. Let be the angle between the normal vector of any grid on the blade surface and the line connecting the center points of the two grids. The distance between the center points of the two grids; The angle coefficient of any grid on the blade surface with respect to any grid on the first surface is given by the following formula: in, Let be the angle coefficient of any grid on the blade surface with respect to any grid on the first surface. Let be the area of ​​any grid in the first surface. Let be the angle between the normal vector of any grid in the first surface and the line connecting the center points of the two grids. Let be the angle between the normal vector of any grid on the blade surface and the line connecting the center points of the two grids. The distance between the center points of the two grids; The method further includes: The angle coefficient of any grid in the first surface with respect to any grid in the blade surface is denoted as the first angle coefficient; the angle coefficient of any grid in the blade surface with respect to any grid in the first surface is denoted as the second angle coefficient. Based on the area of ​​each grid and the distance between any two grids, calculate the angle coefficient between any two grids on the blade surface, and denot it as the third angle coefficient; Summing up all the first and third angle coefficients yields the accumulated value; If the accumulated value is approximately equal to 1, then the angle coefficient is calculated accurately; otherwise, the angle coefficient is not calculated accurately. If the angle coefficient is calculated accurately, proceed to step 4.

2. The method as described in claim 1, characterized in that, The effective radiation column matrix is ​​defined by the following formula: in, For an effective radiation column matrix, Let be the blackbody radiation constant. This is a fourth-order column matrix of temperatures, where each element represents the wall temperature of each grid cell. This is the angular coefficient matrix.

3. The method as described in claim 1, characterized in that, The wall temperature of each grid is determined using the following formula: in, The wall temperature for each grid, For the effective radiation of each grid in the effective radiation column matrix, For the emissivity of the grid, is the blackbody radiation constant.

4. The method as described in claim 1, characterized in that, The method further includes: The initial temperature of each grid is preset according to the boundary conditions, and the blackbody radiation force of each grid is calculated. Determine whether the magnitude of the blackbody radiation force is correct; If the blackbody radiation force is correct, proceed to step 3.

5. A computer-readable storage medium, characterized in that, The computer-readable storage medium stores a computer program that, when executed by a processor, implements the method for deriving turbine blade wall temperature based on effective radiation as described in any one of claims 1-4.

6. A computer program product, characterized in that, Includes a computer program / instruction, which, when executed by a processor, implements the method for deriving turbine blade wall temperature based on effective radiation as described in any one of claims 1-4.

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