A method for rapid calculation of flat plate wall temperature with gas film and thermal barrier coating

Abstract

The present application belongs to the field of aero-engine and gas turbine, and relates to a kind of flat plate wall surface temperature rapid calculation method containing gas film and thermal barrier coating.The calculation method described in the present application has higher calculation efficiency compared with conventional three-dimensional numerical simulation method, and is oriented to flat plate structure design problem with gas film hole and thermal barrier coating, and a large number of different structures, different materials and different working conditions of each wall surface temperature can be obtained in a short time, which is used to prove the establishment of design scheme and optimization, etc.In the present application, by zoning each wall surface, the heat transfer process of each region is topologically converted into a solvable heat transfer model, which realizes the simplification of complex three-dimensional partial differential equation set into a series of simple one-dimensional formulas.The method of the present application can avoid a large number of repeated processes (modeling, mesh division, solution calculation, etc.) and the connection and switching between many software, thereby greatly saving time cost.

Description

Technical Field

[0001] This invention belongs to the field of aero-engines and gas turbines, and relates to a method for rapid calculation of the temperature of a flat plate wall containing an air film and a thermal barrier coating. Background Technology

[0002] With the rapid development of aero-turbine engines and gas turbines, breaking through high-performance bottlenecks has become increasingly important. This mainly relies on higher turbine inlet gas temperatures, which also means higher requirements for the temperature resistance of blades. A single cooling technology is insufficient to bridge this gap between the required cooling capacity and the material's temperature resistance. Currently, turbine blades often employ a combination of cooling measures to further improve their temperature resistance. A common approach is the combination of film cooling and thermal barrier coatings. Cool airflow enters the mainstream gas flow through film cooling holes, forming a film on the gas surface to cool the outer wall. However, this still doesn't achieve sufficient cooling. Therefore, a thermal barrier coating needs to be applied to the metal substrate surface, relying on its low thermal conductivity to isolate the gas from heating and provide thermal protection. To maximize cooling efficiency, a design where film cooling and thermal barrier coatings are interleaved can be used. However, this introduces significant challenges to blade design and temperature analysis.

[0003] Currently, the determination of wall temperature for such parts mainly employs 3D simulation analysis software. The existing technical process first uses 3D modeling software to model the metal substrate, thermal barrier coating, and film pore structure. Then, it discretizes the computational domain using mesh generation tools to obtain a mesh model. Finally, it uses 3D numerical simulation software for flow and heat transfer to solve the problem, thereby obtaining the 3D temperature field distribution within the metal substrate and coating entity. Typical results are shown below. Figure 1 As shown, the contour lines and cloud maps reveal a relatively complex temperature distribution pattern on the solid wall surface. For ease of observation, only half of the symmetrical structure is shown.

[0004] Obtaining the aforementioned temperature field distribution requires solving a system of multiple partial differential equations, involving numerical discretization over millions of grids and computation of large matrices. This necessitates reliable software and powerful computer hardware, resulting in high costs and significant time and effort, hindering engine development. Furthermore, because the thermal barrier coating also affects film cooling—its low thermal conductivity not only blocks the heating of high-temperature combustion gases but also weakens heat dissipation from the hot wall to the film—it's necessary to obtain numerous wall temperature parameters under different operating conditions to guide the design of the two cooling measures and ensure their synergy to maximize the blade's temperature resistance. This also complicates simulation analysis. Moreover, for a flat plate model combining the two cooling measures, comparing wall temperatures under different structures and operating conditions means remodeling, meshing, and numerical simulation each time, repeatedly performing the above processes and involving numerous software programs, further increasing time costs and reducing overall design efficiency.

[0005] Therefore, how to quickly and accurately obtain the wall temperature under complex heat transfer processes is an urgent problem to be solved, which is of great significance for improving the development capability of aero-engines. Summary of the Invention

[0006] To address the shortcomings of existing technologies, this invention provides a rapid calculation method for the temperature of a flat plate wall containing an air film and a thermal barrier coating. This invention solves these problems by rationally partitioning, simplifying, and transforming the computational domain, and by simplifying the complex three-dimensional partial differential equations into a series of simple one-dimensional formulas, thus forming a faster calculation method.

[0007] A rapid calculation method for the surface temperature of a flat plate containing an air film and a thermal barrier coating, the main calculation process of which is as follows: Figure 2 As shown, the specific process is as follows:

[0008] The first step is to establish computational models for typical flat plate and cylindrical film-film atomizing structures based on the input structural parameters, physical property parameters, and operating conditions. Due to symmetry, only half of the computational model is established. The length, width, and thickness of the flat plate are l, b, and h, respectively, and the distance from the center point of the cold air side film-film atomizing hole to the upstream of the flat plate is l. h The diameter of the air film vent is φD, and the angle between the axis of the air film vent and the plate surface is β, such as... Figure 3 As shown. The flat gas surface is divided into a gas-covered area and a gas-film-covered area based on whether or not it is covered by a gas film. The gas temperature in the gas-covered area is T. g The convective heat transfer coefficient is α g The temperature of the outflowing cold air in the air-supported area is T. c The convective heat transfer coefficient is α c1 The temperature of the cold air on the inner surface of the air film pores is T. c The convective heat transfer coefficient is α c2 The temperature of the air conditioning unit on the flat panel is T. c The convective heat transfer coefficient is α c3 .

[0009] The second step is to partition, discretize, deform, and integrate each region of the board, and extract the dimensional parameters of each region.

[0010] 2.1 Divide the flat gas surface into regions and simplify the shape of each region, such as... Figure 4 As shown, the details are as follows:

[0011] 2.1.1 The width of the flat gas surface is b, and the length is l. The area of ​​this region is A. g The area A of the flat-plate gas-fired side gh zone gh .

[0012] 2.1.2 The flat gas-fuel side g1 area is simplified into a rectangle with a width of 0.5D and a length of l. a The area of ​​this region is A. g1 .

[0013] 2.1.3 The air-supported membrane covering area c1 is simplified into a rectangle with a width of 0.5D and a length of l. a The area of ​​this region is A. c1 .

[0014] 2.1.4 The flat gas-fuel side g2a zone is simplified to a rectangle with a width of (BR-0.2)D and a length of l. b The area of ​​this region is A. g2a .

[0015] 2.1.5 The flat gas-fuel side g2b zone is simplified to an L-shape, with a total width of (1.6BR-0.32)D and a total length of 1.25l. b The area of ​​this region is A. g2b .

[0016] 2.1.6 The flat gas-fuel side g3a zone is simplified to a rectangle with a width of bD and a length of l. a +l e The area of ​​this region is A. g3a .

[0017] 2.1.7 The gas-bearing section g3b on the flat plate is simplified to a rectangle with a width of b - (1.6BR - 0.32)D and a length of 1.25l. b The area of ​​this region is A. g3b .

[0018] 2.1.8 The flat gas-fuel side g3c zone is simplified to a rectangle with a width of b and a length of l. c The area of ​​this region is A. g3c .

[0019] 2.1.9 The flat gas-fuel side g3d region is simplified to a rectangle with a width of b and a length of l. d The area of ​​this region is A. g3d .

[0020] 2.1.10 The flat gas-fuel side gh zone is simplified to a rectangle with a width of D and a length of l. e The area of ​​this region is A. gh .

[0021] To facilitate calculation, the g3a and g3d regions on the flat-plate gas side are combined and topologically transformed into a merged region of g3a and g3d on the flat-plate gas side, with an area of ​​A. g3ad , can be represented as:

[0022] A g3ad =A g3a +A g3d (1)

[0023] The flat-plate gas-side regions g3b and g3c are combined and their topology transformed into a merged region of g3b and g3c on the flat-plate gas-side, with an area of ​​A. g3bc , can be represented as:

[0024] A g3bc =A g3b +A g3c (2)

[0025] 2.2 Divide the inner surface of the air film pore into regions by projecting along the pore axis in a direction perpendicular to the plane of symmetry, such as... Figure 5 As shown, the details are as follows:

[0026] 2.2.1 The area of ​​region c2a on the inner surface of the air film pore is A. c2a .

[0027] 2.2.2 The area of ​​region c2b on the inner surface of the air film pore is A. c2b .

[0028] 2.3 Divide the flat air conditioning surface into zones and simplify the shape of each zone, such as... Figure 6 As shown, the details are as follows:

[0029] 2.3.1 The width of the flat air-cooled surface is b, the length is l, and the area of ​​this region is A. c Area A of the flat-plate cooling side ch zone ch .

[0030] 2.3.2 The c3a area on the flat-plate cooling side is simplified into a rectangle with a width of b and a length of l. a +l e The area of ​​this region is A. c3a .

[0031] 2.3.3 The c3b area on the flat-plate cooling side is simplified into a rectangle with a width of b and a length of 1.25l. b The area of ​​this region is A. c3b .

[0032] 2.3.4 The c3c area on the flat-plate cooling side is simplified into a rectangle with a width of b and a length of l. c -l f The area of ​​this region is A. c3c .

[0033] 2.3.5 The c3d region on the flat-plate cooling side is simplified to a rectangle with a width of b and a length of l. d The area of ​​this region is A. c3d .

[0034] 2.3.6 The ch-zone on the flat-plate cooling side is simplified to a rectangle with a width of b and a length of l. f The area of ​​this region is A. ch .

[0035] The c3a and c3d regions on the flat-plate cooling side are combined and their topology transformed into a merged c3a and c3d region on the flat-plate cooling side, with an area of ​​A. c3ad , can be represented as:

[0036] A c3ad =A c3a +A c3d (3)

[0037] The c3b and c3c regions on the flat-plate cooling side are combined and their topology transformed into a merged c3b and c3c region on the flat-plate cooling side, with an area of ​​A. c3bc , can be represented as:

[0038] A c3bc =A c3b +A c3c (4)

[0039] The third step involves converting the heat transfer topology of each region into a solvable heat transfer model. A simplified calculation method is then used to solve for the convective heat transfer coefficient of the region covered by the thermal barrier coating. The heat flow conservation equation for the heat transfer model is established, and based on this, the wall temperature of each region is calculated. The specific heat transfer model and the wall temperature solutions for each region are as follows:

[0040] 3.1 The convective heat transfer coefficient of the area covered by the thermal barrier coating is calculated using a simplified calculation method:

[0041] 3.1.1 Equivalent convective heat transfer coefficient α of the gas-covered area after coating application g 'for:

[0042]

[0043] 3.1.2 Equivalent convective heat transfer coefficient α of the air film covering region c1 after coating c1 'for:

[0044]

[0045] In formulas (5) and (6), L TBC and λ TBC These represent the thickness and thermal conductivity of the thermal barrier coating, respectively.

[0046] 3.2 Establish the heat flow conservation equation for the heat transfer model, and based on this, solve for the wall temperature in each region.

[0047] 3.2.1 Convert the topology of the g1-c1 region to a thickness of 0.5D and a width of l. a A heat transfer model for a flat plate of length δ, such as Figure 7 As shown. Based on the law of conservation of energy, it is assumed that the heat Q transferred from the gas combustion gas to the flat plate gas combustion side g1 region through convective heat transfer is... g1 The heat Q1 transferred from the flat gas-fired side (g1 zone) to the gas-film-covered (c1 zone) via thermal conduction; and the heat Q carried away by the cold air exiting the gas-film-covered (c1 zone) via convective heat transfer. c1 Equal, that is:

[0048] Q g1 =Q1=Q c1 (7)

[0049]

[0050] Solving the above equation yields:

[0051] Wall temperature T in zone g1 of the flat gas side Wg1 for:

[0052]

[0053] The wall temperature T of the air-supported membrane covering region c1 Wc1 for:

[0054]

[0055] The thermal resistance R of convective heat transfer between the gas and the flat gas side g1 zone g1 for:

[0056]

[0057] If the gas-covered area is coated with a thermal barrier coating, then the equivalent convective heat transfer coefficient α of the gas-covered area is used. g Replace α in formula (11) g Perform the calculation.

[0058] The thermal resistance R1 between the flat gas-propelled gas side region g1 and the gas film-covered region c1 is:

[0059]

[0060] In formula (12), λ s Let be the thermal conductivity of the flat plate.

[0061] The thermal resistance R between the air film covering region c1 and the convective heat transfer of the outflowing cold air is... c1 for:

[0062]

[0063] If the air film covering region c1 is coated with a thermal barrier coating, then the equivalent convective heat transfer coefficient α of region c1 covered by the air film is... c1 Replace α in formula (13) c1 Perform the calculation.

[0064] 3.2.2 Convert the topology of the g2a-c2a region to the axis length l b Central angle in radians θ 2a The radii of the gas-fired side and the air-cooled side are r and r, respectively. g2a and r c2a Wall thickness Δr 2a A heat transfer model for a sector-shaped section of a straight circular tube with uniform wall thickness, such as... Figure 8 As shown. Based on the law of conservation of energy, it is assumed that the heat Q transferred from the gas combustion gas to the flat plate gas combustion side g2a region through convective heat transfer is... g2a The heat Q transferred by conduction from region g2a on the flat gas side to region c2a on the inner surface of the gas film pores. 2a The heat Q carried away by the cold air inside the film vent from region c2a on the inner surface of the film vent through convective heat transfer. c2a Equal, that is:

[0065] Q g2a =Q 2a =Q c2a (14)

[0066]

[0067] Solving the above equation yields:

[0068] Wall temperature T in the gas-fired zone g2a of the flat plate Wg2a for:

[0069]

[0070] The wall temperature T of region c2a on the inner surface of the air film pore Wc2a for:

[0071]

[0072] The thermal resistance R of convective heat transfer between the gas and the flat gas side g2a zone g2a for:

[0073]

[0074] If the gas-covered area is coated with a thermal barrier coating, then the equivalent convective heat transfer coefficient α of the gas-covered area is used. g Replace α in formula (18) g Perform the calculation.

[0075] The thermal resistance R between the gas-propelled gas side region g2a and the inner surface region c2a of the film gas vent is significantly reduced. 2a for:

[0076]

[0077] The thermal resistance R between region c2a on the inner surface of the film film vent and the convective heat transfer of the cold air inside the vent is... c2a for:

[0078]

[0079] When the area A of the gas-propelled zone g2a on the flat plate... g2a The area A of region c2a, which is smaller than the inner surface of the air film pore, is... c2a When calculating using the above formula, the bending direction of the circular tube's arc surface is different from that of the other tubes. Figure 8 Conversely, when the area A of region g2a on the flat gas side... g2a Equal to the area A of region c2a on the inner surface of the air film pore c2a At that time, the heat transfer model becomes a length l b Width (BR-0.2)D, Thickness Δr 2a In the flat plate heat transfer model, the thermal resistance R between the gas combustion side region g2a and the inner surface region c2a of the gas film pores is... 2a It becomes:

[0080]

[0081] At this point, the calculation of wall temperature formulas (16) and (17) adopts formula (21).

[0082] 3.2.3 Convert the topology of the g2b-c2b region to the axis length l b Central angle in radians θ 2b The radii of the gas-fired side and the air-cooled side are r and r, respectively. g2b and r c2b Wall thickness Δr 2b A heat transfer model for a sector-shaped section of a straight circular tube with uniform wall thickness, such as... Figure 9 As shown. Based on the law of conservation of energy, it is assumed that the heat Q transferred from the gas combustion gas to the g2b zone on the flat gas side via convective heat transfer is... g2b The heat Q transferred by conduction from region g2b on the flat gas side to region c2b on the inner surface of the gas film pores. 2b The heat Q carried away by the cold air inside the film vent from the c2b region on the inner surface of the film vent through convective heat transfer. c2b Equal, that is:

[0083] Q g2b =Q 2b =Q c2b (twenty two)

[0084]

[0085] Solving the above equation yields:

[0086] Wall temperature T in the gas-fired zone g2b of the flat plate Wg2b for:

[0087]

[0088] The wall temperature T of region c2b on the inner surface of the air film pore Wc2b for:

[0089]

[0090] Thermal resistance R of convective heat transfer between the gas and the flat gas side g2b zone g2b for:

[0091]

[0092] If the gas-covered area is coated with a thermal barrier coating, then the equivalent convective heat transfer coefficient α of the gas-covered area is used. g Replace α in formula (26) g Perform the calculation.

[0093] The thermal resistance R between the g2b region on the gas-propellant side of the flat plate and the c2b region on the inner surface of the gas film vent is high. 2b for:

[0094]

[0095] The thermal resistance R between the c2b region on the inner surface of the film film vent and the convective heat transfer of the cold air inside the vent. c2b for:

[0096]

[0097] When the area A of the gas-bearing side of the flat plate is... g2b The area A of region c2b smaller than the inner surface of the air film pore c2b When calculating using the above formula, the bending direction of the circular tube's arc surface is different from that of the other tubes. Figure 9 Conversely, when the area A of the gas-bearing zone g2b on the flat plate is... g2b Equal to the area A of region c2b on the inner surface of the air film pore c2b At that time, the heat transfer model becomes a length l b Width (BR-0.2)D, Thickness Δr 2b In the flat plate heat transfer model, the thermal resistance R between the gas combustion side region g2b and the inner surface region c2b of the gas film pore is... 2b It becomes:

[0098]

[0099] At this point, the calculation of wall temperature formulas (24) and (25) adopts formula (29).

[0100] 3.2.4 Convert the topology of the merged region of g3a and g3d—the merged region of c3a and c3d—to the axis length b and the central angle radian θ. 3ad The radii of the gas-fired side and the air-cooled side are r and r, respectively. g3ad and r c3ad Wall thickness Δr 3ad A heat transfer model for a sector-shaped section of a straight circular tube with uniform wall thickness, such as... Figure 10 As shown. Based on the law of conservation of energy, it is assumed that the heat Q transferred from the gas combustion gas to the merging zone of g3a and g3d on the flat plate gas side is in the form of convective heat transfer. g3ad The heat Q transferred by conduction from the combined region of g3a and g3d on the flat gas side to the combined region of c3a and c3d on the flat cold air side. 3ad The heat Q carried away by the cold air from the combined c3a and c3d region of the flat-plate cold air surface through convection heat transfer. c3ad Equal, that is:

[0101] Q g3ad =Q 3ad =Q c3ad (30)

[0102]

[0103] Solving the above equation yields:

[0104] The wall temperature T in the combined zone of g3a and g3d on the flat gas side Wg3ad for:

[0105]

[0106] The wall temperature T in the combined zone of C3b and C3c on the flat plate cooling side Wc3ad for:

[0107]

[0108] The thermal resistance R of convective heat transfer in the combined region of gas and flat plate gas side g3a and g3d g3ad for:

[0109]

[0110] If the gas-covered area is coated with a thermal barrier coating, then the equivalent convective heat transfer coefficient α of the gas-covered area is used. g Replace α in formula (34) g Perform the calculation.

[0111] The thermal resistance R between the combined region of g3a and g3d on the flat gas side and the combined region of c3a and c3d on the flat air cooling side is [missing information]. 3ad for:

[0112]

[0113] The thermal resistance R of the combined region of c3a and c3d on the cold air side of the flat plate with the cold air surface for convective heat transfer is... c3ad for:

[0114]

[0115] Due to the area A of the merged region of g3a and g3d on the flat gas side g3ad It must be smaller than the area A of the merged region of c3a and c3d on the flat-plate cooling side. c3ad Therefore, the heat transfer model and formulas mentioned above do not need to be changed.

[0116] 3.2.5 Topological transformation of the merged region of g3b and g3c—the merged region of c3b and c3c—to axis length b and central angle radian θ. 3bc The radii of the gas-fired side and the air-cooled side are r and r, respectively. g3bc and r c3bc Wall thickness Δr 3bc A heat transfer model for a sector-shaped section of a straight circular tube with uniform wall thickness, such as... Figure 11 As shown. Based on the law of conservation of energy, it is assumed that the heat Q transferred from the gas combustion gas to the merging zone of g3b and g3c on the flat gas side is in the form of convective heat transfer. g3bc The heat Q transferred by conduction from the combined zone of g3b and g3c on the flat gas side to the combined zone of c3b and c3c on the flat cold air side. 3bc The heat Q carried away by the cold air from the flat-plate cooling surface from the combined zone of C3b and C3c via convection heat transfer is... c3bc Equal, that is:

[0117] Q g3bc =Q 3bc =Q c3bc (37)

[0118]

[0119] Solving the above equation yields:

[0120] The wall temperature T in the combined zone of gas-fired flat plate gas side g3b and g3c Wg3bc for:

[0121]

[0122] The wall temperature T in the combined zone of C3b and C3c on the flat plate cooling side Wc3bc for:

[0123]

[0124] The thermal resistance R of convective heat transfer in the combined region of gas and flat plate gas side g3b and g3c g3bc for:

[0125]

[0126] If the gas-covered area is coated with a thermal barrier coating, then the equivalent convective heat transfer coefficient α of the gas-covered area is used. g Replace α in formula (41) g Perform the calculation.

[0127] The thermal resistance R between the combined region of g3b and g3c on the flat gas side and the combined region of c3b and c3c on the flat air conditioning side is [missing information]. 3bc for:

[0128]

[0129] The thermal resistance R of the combined area of ​​C3b and C3c on the cold air side of the flat plate and the cold air surface for convective heat transfer is... c3bc for:

[0130]

[0131] When the area A of the merged region of g3b and g3c on the flat gas side g3bc The area A of the combined region of C3b and C3c on the flat-plate cooling side is greater than that of the plate cooling side. c3bc When calculating using the above formula, the bending direction of the circular tube's arc surface is different from that of the other tubes. Figure 11 Conversely, when the area A of the merged region of g3b and g3c on the flat gas side is... g3bc Equal to the area A of the combined region of c3b and c3c on the flat-plate cooling side c3bc At that time, the heat transfer model became 1.25 l in length. b +l c -l f Width b, thickness Δr 3bc In the flat plate heat transfer model, the thermal resistance R between the combined region of g3b and g3c on the gas side and the combined region of c3b and c3c on the cold gas side is... 3bc It becomes:

[0132]

[0133] At this time, the calculation of wall temperature formulas (39) and (40) adopts formula (44).

[0134] The fourth step is to combine the wall temperature and area values ​​of each sub-region and calculate the wall temperature using an area-weighted average method.

[0135] 4.1 Temperature T of the flat gas surface Wg for:

[0136]

[0137] 4.2 Temperature T on the inner surface of the air film pores Wc2 for:

[0138]

[0139] 4.3 Temperature T of the flat-plate air conditioning surface Wc3 for:

[0140]

[0141] The beneficial effects of this invention are:

[0142] 1. High computational efficiency, quickly obtaining the temperature of each wall surface:

[0143] The computational method described in this invention offers higher computational efficiency compared to conventional three-dimensional numerical simulation methods. Addressing the design problem of flat plate structures with film vents and thermal barrier coatings, it can quickly obtain a large number of wall temperatures under various structures, materials, and operating conditions to validate design schemes and for optimization. In this invention, by partitioning each wall surface, the heat transfer process in each region is topologically transformed into a solvable heat transfer model, simplifying complex three-dimensional partial differential equations into a series of simple one-dimensional formulas. Furthermore, for surfaces coated with thermal barrier coatings, the convective heat transfer coefficient equivalent conversion method in this invention allows for the reproduction of the same insulation effect without establishing the physical structure of the thermal barrier coating; only the coating thickness and thermal conductivity need to be considered to calculate the reduction in heat transfer. In summary, this invention avoids numerous repetitive processes (modeling, meshing, solving calculations, etc.) and the need to switch between various software programs, thus significantly saving time and costs.

[0144] 2. Comprehensive calculation functions, capable of calculating the wall temperature of flat plate components under various working conditions and structures:

[0145] This invention provides a method for rapidly calculating the wall temperature of flat plate components with film cooling and thermal barrier coating protection, as well as their optimized combinations, under different structures, materials, and operating conditions. This provides guidance for the design of hot-end components in aero-engines and gas turbines, such as combustion chambers and turbines. Its comprehensive functionality is reflected in its ability to consider the influence of multiple factors on the heat transfer process and wall temperature, which can be categorized into three aspects: geometric structure, material properties, and operating conditions.

[0146] a) Geometric structure: Plate length l, plate width b, plate thickness h, film gas aperture diameter φD, distance l from the center point of the cold air side film gas aperture to the upstream end of the plate (gas inlet end). h 1. Angle β between the axis of the air film pore and the plate surface; 2. Thickness L of the thermal barrier coating TBC .

[0147] b) Physical properties: Thermal conductivity λ of the flat plate s Thermal barrier coating thermal conductivity λ TBC .

[0148] c) Operating conditions: Gas temperature T g Air conditioning temperature T c Air-to-air ratio (BR) and convective heat transfer coefficient (α) of the gas-fired coverage area g The convective heat transfer coefficient α of the air-film covered area c1 The convective heat transfer coefficient α of the inner surface of the film pores c2 The convective heat transfer coefficient α of a flat air-cooled surface c3 .

[0149] The method of this invention can also set whether the gas coverage area and the gas film coverage area have a coating, thereby realizing the calculation and analysis of three different designs: no coating, full coating, and optimized coating, to adapt to different design requirements and reflect the comprehensiveness and power of the function.

[0150] 3. The calculation results are reliable and accurately provide the temperature of each wall surface:

[0151] The wall temperatures calculated by the method of this invention are close to the calculation results of three-dimensional numerical simulation that strictly conforms to the flow and heat transfer equations. The relative errors of the wall temperatures in the three calculation regions (based on the three-dimensional numerical simulation results) are all within ±2%, which shows high accuracy.

[0152] For flat gas-fired surfaces, Figure 12 Taking the typical calculation results shown as an example, the three-dimensional numerical simulation results are as follows: Figure 12 As shown in (b), the isotherms extend outwards around the film vents and the film-covered area, with the color of the bands changing from light to dark to indicate that the wall temperature gradually increases from these two regions outwards; for the inner surface of the film vents, the isotherms are... Figure 13 Taking the typical calculation results shown as an example, the three-dimensional numerical simulation results are as follows: Figure 13 As shown in (b), the isotherms run approximately parallel to the axis of the film gas vent, and the color of the stripes, from light to dark, indicates that the temperature gradually increases from the cold gas side to the combustion gas side of the vent; for a flat cold gas surface, with Figure 14 Taking the typical calculation results shown as an example, the three-dimensional numerical simulation results are as follows: Figure 14 As shown in (b), the isotherms extend outwards around the film cooling holes, and are approximately perpendicular to the length of the plate downstream of the holes, indicating that the influence of the cold gas inside the holes gradually weakens in this area, consistent with the trend of the stripes changing from light to dark. The method of this invention divides the same surface into sections (the three surfaces are divided in the same way). Figure 5 , Figure 6 and Figure 7 ) Perform separate calculations, and the calculated wall temperatures for each zone are as follows: Figure 12As shown in (a), 13(a), and 14(a), the temperature values ​​are represented by the color intensity of the scale on their left sides. Similar to the results of their respective 3D numerical simulations, they exhibit the same trend. Furthermore, the color comparison shows that the wall temperature of each region is close to the average wall temperature of the corresponding region in the 3D simulation calculation. It can be considered that although the wall temperature distribution depicted by this method is not as detailed as the 3D simulation results, it still has high accuracy in terms of average values. Attached image description:

[0153] Figure 1 This is a cloud map showing the wall temperature distribution of a typical flat plate under film cooling and thermal barrier coating protection.

[0154] Figure 2 A flowchart for rapid calculation of flat plate wall temperature;

[0155] Figure 3 This is a structural diagram of a flat plate;

[0156] Figure 4 A diagram showing the calculation area division for a flat gas surface;

[0157] Figure 5 This is a diagram showing the computational region division of the inner surface of the air film pores.

[0158] Figure 6 This is a diagram showing the calculation area division for a flat-plate cooling surface.

[0159] Figure 7 The heat transfer model after the topology transformation of region g1 to c1;

[0160] Figure 8 The heat transfer model after the topology transformation of the g2a-c2a region;

[0161] Figure 9 The heat transfer model after the topology transformation of the g2b-c2b region;

[0162] Figure 10 The heat transfer model after the topology transformation of the g3a and g3d merged region to the c3a and c3d merged region;

[0163] Figure 11 The heat transfer model after the topology transformation of the merged region of g3b and g3c to the merged region of c3b and c3c.

[0164] Figure 12 (a) is a flat gas surface temperature contour map calculated by the method of the present invention;

[0165] Figure 12 (b) is a temperature cloud map of the flat gas surface calculated by three-dimensional simulation;

[0166] Figure 13(a) is a cloud map of the inner surface temperature of the air film pores calculated by the method of the present invention;

[0167] Figure 13 (b) is a temperature cloud map of the inner surface of the air film pores calculated by three-dimensional simulation;

[0168] Figure 14 (a) is a temperature cloud map of the flat cooling surface calculated by the method of the present invention;

[0169] Figure 14 (b) is a temperature cloud map of the flat plate cooling surface calculated in three-dimensional simulation.

[0170] The labels in the diagram correspond as follows: 1- Flat gas surface; 2- Inner surface of the film gas vent; 3- Flat cold air surface; 4- Flat gas side g1 zone; 5- Film gas coverage c1 zone; 6- Flat gas side g2a zone; 7- Flat gas side g2b zone; 8- Flat gas side g3a zone; 9- Flat gas side g3b zone; 10- Flat gas side g3c zone; 11- Flat gas side g3d zone; 12- Flat gas side gh zone; 13- Inner surface of the film gas vent c2a zone. 14-Inner surface of the air film pore, c2b region; 15-C3a region on the flat plate cooling side; 16-C3b region on the flat plate cooling side; 17-C3c region on the flat plate cooling side; 18-C3d region on the flat plate cooling side; 19-Ch region on the flat plate cooling side; 20-Combined region of g3a and g3d on the flat plate gas side; 21-Combined region of c3a and c3d on the flat plate cooling side; 22-Combined region of g3b and g3c on the flat plate gas side; 23-Combined region of c3b and c3c on the flat plate cooling side. Detailed Implementation

[0171] To make the content of this invention easier to understand, the invention will be further described in detail below with reference to specific embodiments and accompanying drawings.

[0172] Example 1:

[0173] For a flat plate component with cylindrical air film vents and no thermal barrier coating on its surface, the required geometric parameters, operating conditions, and physical properties are shown in Table 1.

[0174] Table 1. Parameters required for calculation in Example 1

[0175]

[0176] First, the regions of the flat plate wall are discretized, deformed, and integrated. Then, the local wall temperature is solved based on the heat flow conservation equation. Finally, the average wall temperature is solved based on area weighting, i.e., the wall temperature T of the flat plate gas-fired surface is calculated using formulas (45), (46), and (47). Wg The wall temperature T on the inner surface of the air film pores Wc2 The wall temperature T of the flat-panel air conditioner surfaceWc3 .

[0177] The wall temperature results obtained by the method of this invention are similar to those obtained by three-dimensional simulation calculation. The temperature difference between the two is within 15K, and the relative error of the wall temperature (based on the three-dimensional numerical simulation calculation results) does not exceed ±1%. The specific calculation results are shown in Table 2.

[0178] Table 2. Wall temperature calculation results and relative errors in Example 1

[0179]

[0180] Example 2:

[0181] For a flat plate component with cylindrical gas film pores and a thermal barrier coating that fully covers the gas-burning surface of the plate, the required parameters for calculation are shown in Table 3, and the remaining parameters are the same as those in Table 1.

[0182] Table 3 Parameters required for calculation in Example 2

[0183]

[0184] First, the regions of the flat plate wall are discretized, deformed, and integrated. Then, the local wall temperature is solved based on the heat flow conservation equation. Finally, the average wall temperature is solved based on area weighting. That is, the wall temperature T of the flat plate gas surface is calculated using formulas (45), (46), and (47). Wg The wall temperature T on the inner surface of the air film pores Wc2 The wall temperature T of the flat-panel air conditioner surface Wc3 .

[0185] The wall temperature results obtained by the method of this invention are similar to those obtained by three-dimensional simulation calculation. The temperature difference between the two is within 20K, and the relative error of the wall temperature (based on the three-dimensional numerical simulation calculation results) does not exceed ±1.5%. The specific calculation results are shown in Table 4.

[0186] Table 4. Wall temperature calculation results and relative errors in Example 2

[0187]

[0188] Example 3:

[0189] For a flat plate component with cylindrical gas film vents, the thermal barrier coating is designed in an optimized manner, i.e., the thermal barrier coating is applied only to the gas film coverage area, and no thermal barrier coating is applied to the surface of the gas film coverage area c1. The required parameters are shown in Table 5, and the other parameters are the same as those in Table 1.

[0190] Table 5 Parameters required for calculation in Example 3

[0191]

[0192] First, the regions of the flat plate wall are discretized, deformed, and integrated. Then, the local wall temperature is solved based on the heat flow conservation equation. Finally, the average wall temperature is solved based on area weighting, i.e., the wall temperature T of the flat plate gas-fired surface is calculated using formulas (45), (46), and (47). Wg The wall temperature T on the inner surface of the air film pores Wc2 The wall temperature T of the flat-panel air conditioner surface Wc3 .

[0193] The wall temperature results obtained by the method of this invention are similar to those obtained by three-dimensional simulation calculation. The temperature difference between the two is within 20K, and the relative error of the wall temperature (based on the three-dimensional numerical simulation calculation results) does not exceed ±1.5%. The specific calculation results are shown in Table 6.

[0194] Table 6. Wall temperature calculation results and relative errors in Example 3

[0195]

Claims

1. A method for rapid calculation of the surface temperature of a flat plate containing an air film and a thermal barrier coating, characterized in that, The steps are as follows: The first step is to establish computational models for typical flat plate and cylindrical film-film atomizing structures based on the input structural parameters, physical property parameters, and operating conditions. Due to symmetry, only half of the computational model is established, with the length, width, and thickness of the flat plate being l, b, and h, respectively, and the distance from the center point of the cold air side film-film atomizing hole to the upstream of the flat plate being l. h The diameter of the gas film vent is ϕD, and the angle between the axis of the gas film vent and the plate surface is β, where the upstream of the plate refers to the gas inlet. The flat plate gas surface is divided into a gas-covered area and a gas-film-covered area based on whether or not it is covered by a gas film. The gas temperature in the gas-covered area is T. g The convective heat transfer coefficient is α g The temperature of the outflowing cold air in the air-supported area is T. c The convective heat transfer coefficient is α c1 The temperature of the cold air on the inner surface of the air film pores is T. c The convective heat transfer coefficient is α c2 The temperature of the air conditioning unit on the flat panel is T. c The convective heat transfer coefficient is α c3 ; The second step is to partition, discretize, deform, and integrate each region of the board surface, and extract the dimensional parameters of each region. 2.1 The flat gas surface is divided into regions and the shape of each region is simplified, as follows: 2.1.1 The width of the flat gas surface is b, and the length is l. The area of ​​this region is A. g The area A of the flat-plate gas-fired side gh zone gh ; 2.1.2 The gas-fired plate side g1 region is simplified into a rectangle with a width of 0.5D and a length of l. a The area of ​​this region is A. g1 ; 2.1.3 The air-supported membrane covering region c1 is simplified into a rectangle with a width of 0.5D and a length of l. a The area of ​​this region is A. c1 ; 2.1.4 The flat gas-fuel side g2a zone is simplified to a rectangle with a width of (BR-0.2)D and a length of l. b The area of ​​this region is A. g2a ; 2.1.5 The flat gas-fuel side g2b zone is simplified to an L-shape, with a total width of (1.6BR-0.32)D and a total length of 1.25l. b The area of ​​this region is A. g2b ; 2.1.6 The flat gas-fuel side g3a zone is simplified to a rectangle with a width of bD and a length of l. a +l e The area of ​​this region is A. g3a ; 2.1.7 The gas-bearing section g3b on the flat plate is simplified into a rectangle with a width of b - (1.6BR - 0.32)D and a length of 1.25l. b The area of ​​this region is A. g3b ; 2.1.8 The gas-fired plate side g3c zone is simplified into a rectangle with a width of b and a length of l. c The area of ​​this region is A. g3c ; 2.1.9 The g3d region on the flat gas side is simplified to a rectangle with a width of b and a length of l. d The area of ​​this region is A. g3d ; 2.1.10 The flat gas-fired side gh zone is simplified to a rectangle with a width of D and a length of l. e The area of ​​this region is A. gh ; To facilitate calculation, the g3a and g3d regions on the flat-plate gas side are combined and topologically transformed into a merged region of g3a and g3d on the flat-plate gas side, with an area of ​​A. g3ad , can be represented as: (1) The flat-plate gas-side regions g3b and g3c are combined and their topology transformed into a merged region of g3b and g3c on the flat-plate gas-side, with an area of ​​A. g3bc , can be represented as: (2) 2.2 The inner surface of the air film pore is divided into regions by projecting along the pore axis in a direction perpendicular to the plane of symmetry, as follows: 2.2.1 The area of ​​region c2a on the inner surface of the air film pore is A. c2a ; 2.2.2 The area of ​​region c2b on the inner surface of the air film pore is A. c2b ; 2.3 The flat air conditioning surface is divided into zones and the shape of each zone is simplified, as follows: 2.3.1 The width of the flat air-cooled surface is b, the length is l, and the area of ​​this region is A. c The area A of the flat-plate cold air side ch zone (19) ch ; 2.3.2 Simplify the c3a area on the flat-plate cooling side into a rectangle with a width of b and a length of l. a +l e The area of ​​this region is A. c3a ; 2.3.3 The c3b area on the flat-plate cooling side is simplified into a rectangle with a width of b and a length of 1.25l. b The area of ​​this region is A. c3b ; 2.3.4 The c3c area on the flat-plate cooling side is simplified into a rectangle with a width of b and a length of l. c -l f The area of ​​this region is A. c3c ; 2.3.5 Simplify the c3d region on the flat-plate cooling side into a rectangle with width b and length l. d The area of ​​this region is A. c3d ; 2.3.6 The ch-zone on the flat-plate cooling side is simplified to a rectangle with a width of b and a length of l. f The area of ​​this region is A. ch ; The c3a and c3d regions on the flat-plate cooling side are combined and their topology transformed into a merged c3a and c3d region on the flat-plate cooling side, with an area of ​​A. c3ad , is represented as: (3) The c3b and c3c regions on the flat-plate cooling side are combined and their topology transformed into a merged c3b and c3c region on the flat-plate cooling side, with an area of ​​A. c3bc , is represented as: (4) The third step involves converting the heat transfer process topology of each region into a solvable heat transfer model. A simplified calculation method is then used to solve for the convective heat transfer coefficient of the region covered by the thermal barrier coating. The heat flow conservation equation for the heat transfer model is established, and based on this, the wall temperature of each region is calculated. The specific heat transfer model and the wall temperature solutions for each region are as follows: 3.1 The convective heat transfer coefficient of the area covered by the thermal barrier coating is calculated using a simplified calculation method: 3.1.1 Equivalent convective heat transfer coefficient α of the gas-covered area after coating application g for: (5) 3.1.2 Equivalent convective heat transfer coefficient α of the air film covering region c1 after coating c1 for: (6) In formulas (5) and (6), L TBC and λ TBC These are the thickness and thermal conductivity of the thermal barrier coating, respectively. The fourth step is to combine the wall temperature and area values ​​of each sub-region and calculate the wall temperature using an area-weighted average method.

2. The method for rapid calculation of the surface temperature of a flat plate containing an air film and a thermal barrier coating as described in claim 1, characterized in that, The specific operation method in step 3.2 is as follows: 3.2.1 Convert the topology of the g1-c1 region to a thickness of 0.5D and a width of l. a In a flat plate heat transfer model of length δ, based on energy conservation, it is assumed that the heat Q transferred from the gas combustion gas to the gas combustion gas side g1 region of the flat plate is in the form of convective heat transfer. g1 The heat Q1 transferred between the flat gas-fired side (g1 zone) and the gas-film-covered zone (c1 zone) via thermal conduction; and the heat Q carried away by the cold air exiting the gas-film-covered zone (c1 zone) via convective heat transfer. c1 Equal, that is: (7) (8) Solving the above equation yields: Wall temperature T in zone g1 of the flat gas side Wg1 for: (9) The wall temperature T of the air-supported membrane covering region c1 Wc1 for: (10) The thermal resistance R of convective heat transfer between the gas and the flat gas side g1 zone g1 for: (11) If the gas-covered area is coated with a thermal barrier coating, then the equivalent convective heat transfer coefficient α of the gas-covered area is used. g Replace α in formula (11) g Perform calculations; The thermal resistance R1 between the flat gas-propelled gas side region g1 and the gas film-covered region c1 is: (12) In formula (12), λ s Let be the thermal conductivity of the flat plate; The thermal resistance R between the air film covering region c1 and the convective heat transfer of the cold air flowing out of the air film is... c1 for: (13) If the air film covering region c1 is coated with a thermal barrier coating, then the equivalent convective heat transfer coefficient α of region c1 covered by the air film is... c1 Replace α in formula (13) c1 Perform calculations; 3.2.2 Convert the topology of the g2a-c2a region to the axis length l b Central angle in radians θ 2a The radii of the gas-fired side and the air-cooled side are r and r, respectively. g2a and r c2a Wall thickness ∆r 2a A heat transfer model for a sector-shaped section of a straight circular tube with uniform wall thickness is used. Based on energy conservation, it is assumed that the heat Q transferred from the gas combustion gas to the gas-bearing side g2a zone of the flat plate is transferred in the form of convective heat transfer. g2a The heat Q transferred by conduction from region g2a on the flat gas side to region c2a on the inner surface of the gas film pores. 2a The heat Q carried away by the cold air inside the film vent from region c2a on the inner surface of the film vent through convective heat transfer. c2a Equal, that is: (14) (15) Solving the above equation yields: Wall temperature T in the gas-fired zone g2a of the flat plate Wg2a for: (16) The wall temperature T of region c2a on the inner surface of the air film pore Wc2a for: (17) The thermal resistance R of convective heat transfer between the gas and the flat gas side g2a zone g2a for: (18) If the gas-covered area is coated with a thermal barrier coating, then the equivalent convective heat transfer coefficient α of the gas-covered area is used. g Replace α in formula (18) g Perform calculations; The thermal resistance R between the gas-propelled gas side region g2a and the inner surface region c2a of the film gas vent is significantly reduced. 2a for: (19) The thermal resistance R between region c2a on the inner surface of the film film vent and the convective heat transfer of the cold air inside the vent is... c2a for: (20) When the area A of the gas-propelled zone g2a on the flat plate... g2a The area A of region c2a, which is smaller than the inner surface of the air film pore, is... c2a When the above formula is used for calculation, but the bending direction of the circular pipe arc surface is opposite; when the area A of the gas-propelled plate side g2a region... g2a Equal to the area A of region c2a on the inner surface of the air film pore c2a At that time, the heat transfer model becomes a length l b Width (BR-0.2)D, Thickness ∆r 2a In the flat plate heat transfer model, the thermal resistance R between the gas combustion side (g2a region) and the inner surface of the gas film pores (c2a region) is... 2a It becomes: (21) At this time, the calculation of wall temperature formulas (16) and (17) adopts formula (21); 3.2.3 Convert the topology of the g2b-c2b region to the axis length l b Central angle in radians θ 2b The radii of the gas-fired side and the air-cooled side are r and r, respectively. g2b and r c2b Wall thickness ∆r 2b A heat transfer model for a sector section of a straight circular tube with uniform wall thickness; based on energy conservation, it is assumed that the heat Q transferred from the gas combustion gas to the g2b zone on the flat plate gas side is in the form of convective heat transfer. g2b The heat Q transferred by conduction from region g2b on the flat gas side to region c2b on the inner surface of the gas film pores. 2b The heat Q carried away by the cold air inside the film vent from the c2b region on the inner surface of the film vent through convective heat transfer. c2b Equal, that is: (22) (23) Solving the above equation yields: Wall temperature T in the gas-fired zone g2b of the flat plate Wg2b for: (24) The wall temperature T of region c2b on the inner surface of the air film pore Wc2b for: (25) Thermal resistance R of convective heat transfer between gas and flat gas side g2b zone (7) g2b for: (26) If the gas-covered area is coated with a thermal barrier coating, then the equivalent convective heat transfer coefficient α of the gas-covered area is used. g Replace α in formula (26) g Perform calculations; The thermal resistance R between the g2b region on the gas-propellant side of the flat plate and the c2b region on the inner surface of the gas film vent is high. 2b for: (27) The thermal resistance R between the c2b region on the inner surface of the film film vent and the convective heat transfer of the cold air inside the vent. c2b for: (28) When the area A of the gas-bearing side of the flat plate is... g2b The area A of region c2b smaller than the inner surface of the air film pore c2b At that time, the above formula is still used for calculation, but the bending direction of the circular pipe arc surface is reversed; when the area A of the gas-bearing side g2b region on the flat plate... g2b Equal to the area A of region c2b on the inner surface of the air film pore c2b At that time, the heat transfer model becomes a length l b Width (BR-0.2)D, Thickness ∆r 2b In the flat plate heat transfer model, the thermal resistance R between the gas combustion side g2b region and the gas film pore inner surface c2b region is calculated. 2b It becomes: (29) At this point, the calculation of wall temperature formulas (24) and (25) adopts formula (29); 3.2.4 Convert the topology of the merged region of g3a and g3d—the merged region of c3a and c3d—to the axis length b and the central angle radian θ. 3ad The radii of the gas-fired side and the air-cooled side are r and r, respectively. g3ad and r c3ad Wall thickness ∆r 3ad The heat transfer model of a sector segment of a straight circular tube with uniform wall thickness is used. Based on the law of conservation of energy, it is assumed that the heat Q transferred from the gas combustion gas to the merging zone g3a and g3d on the flat plate gas side is in the form of convective heat transfer. g3ad The heat Q transferred by conduction from the combined region of g3a and g3d on the flat gas side to the combined region of c3a and c3d on the flat cold air side. 3ad The heat Q carried away by the cold air from the combined c3a and c3d region of the flat-plate cold air surface through convection heat transfer. c3ad Equal, that is: (30) (31) Solving the above equation yields: The wall temperature T in the combined zone of g3a and g3d on the flat gas side Wg3ad for: (32) The wall temperature T in the combined zone of C3b and C3c on the flat plate cooling side Wc3ad for: (33) The thermal resistance R of convective heat transfer in the combined region of gas and flat plate gas side g3a and g3d g3ad for: (34) If the gas-covered area is coated with a thermal barrier coating, then the equivalent convective heat transfer coefficient α of the gas-covered area is used. g Replace α in formula (34) g Perform calculations; The thermal resistance R between the combined region of g3a and g3d on the flat gas side and the combined region of c3a and c3d on the flat air cooling side is [missing information]. 3ad for: (35) The thermal resistance R of the combined region of c3a and c3d on the cold air side of the flat plate with the cold air surface for convective heat transfer is... c3ad for: (36) 3.2.5 Topological transformation of the merged region of g3b and g3c—the merged region of c3b and c3c—to axis length b and central angle radian θ. 3bc The radii of the gas-fired side and the air-cooled side are r and r, respectively. g3bc and r c3bc Wall thickness ∆r 3bc The heat transfer model of a sector segment of a straight circular tube with uniform wall thickness is used. Based on the law of conservation of energy, it is assumed that the heat Q transferred from the gas combustion gas to the merging zone g3b and g3c on the flat plate gas side is in the form of convective heat transfer. g3bc The heat Q transferred by conduction from the combined zone of g3b and g3c on the flat gas side to the combined zone of c3b and c3c on the flat cold air side. 3bc The heat Q carried away by the cold air from the flat-plate cooling surface from the combined zone of C3b and C3c via convection heat transfer is... c3bc Equal, that is: (37) (38) Solving the above equation yields: The wall temperature T in the combined zone of gas-fired flat plate gas side g3b and g3c Wg3bc for: (39) The wall temperature T in the combined zone of C3b and C3c on the flat plate cooling side Wc3bc for: (40) The thermal resistance R of convective heat transfer in the combined region of gas and flat plate gas side g3b and g3c g3bc for: (41) If the gas-covered area is coated with a thermal barrier coating, then the equivalent convective heat transfer coefficient α of the gas-covered area is used. g Replace α in formula (41) g Perform calculations; The thermal resistance R between the combined region of g3b and g3c on the flat gas side and the combined region of c3b and c3c on the flat air conditioning side is [missing information]. 3bc for: (42) The thermal resistance R of the combined area of ​​C3b and C3c on the flat plate cooling side and the cooling surface for convective heat transfer of the cooling air is... c3bc for: (43) When the area A of the merged region of g3b and g3c on the flat gas side g3bc The area A of the combined region of C3b and C3c on the flat-plate cooling side is greater than that of the plate cooling side. c3bc When the above formula is still used for calculation, but the bending direction of the circular pipe arc surface is reversed; when the area A of the merged region of g3b and g3c on the flat gas side is... g3bc Equal to the area A of the combined region of c3b and c3c on the flat-plate cooling side c3bc At that time, the heat transfer model becomes length Width b, thickness ∆r 3bc In the flat plate heat transfer model, the thermal resistance R between the combined region of g3b and g3c on the gas side and the combined region of c3b and c3c on the cold gas side is... 3bc It becomes: (44) At this point, the calculation of wall temperature formulas (39) and (40) adopts formula (44).

3. A method for rapid calculation of the surface temperature of a flat plate containing an air film and a thermal barrier coating as described in claim 1 or 2, characterized in that, The fourth step, as described above, consists of the following steps: 4.1 Temperature T of the flat gas surface Wg for: (45) 4.2 Temperature T on the inner surface of the air film pores Wc2 for: (46) 4.3 Temperature T of the flat-plate air conditioning surface Wc3 for: (47)。

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