A method and system for gas-thermal numerical analysis of variable-thickness ceramic coatings on turbine blades

Abstract

The present invention relates to the field of thermal design verification of gas turbine hot-end components, particularly a method and system for numerical analysis of the aero-thermal properties of variable-thickness ceramic coatings on turbine blades. This method determines the spatial position of the variable-thickness ceramic coating region and normalizes it, then calculates the dimensionless flow position of each node within the variable-thickness region, the corresponding ceramic layer thickness and total thickness, and the local equivalent thermal conductivity of each node. The total thickness of the thermal barrier coating and the corresponding equivalent thermal conductivity of each node within the region are then assigned to the corresponding blade surface boundary conditions, allowing numerical calculation of the aero-thermal properties of the turbine blade with the variable-thickness thermal barrier coating to be performed. This method implements numerical analysis of the aero-thermal properties of the variable-thickness thermal barrier coating on turbine blades. This method ensures stable and efficient numerical calculations while accurately simulating the barrier effect of the variable-thickness ceramic coating on the gas heat load. This method addresses the issue of inaccurate numerical analysis of the aero-thermal properties of variable-thickness ceramic coatings on turbine blades.

Description

Technical Field

[0001] The present invention relates to the technical field of thermal design verification of gas turbine hot end components, and in particular to a gas-thermal numerical analysis method and system for variable-thickness ceramic coatings on turbine blades. Background Art

[0002] Turbine blades are a key component in the hot-end of aircraft engines and heavy-duty gas turbines. Thermal barrier ceramic coatings are often applied to their surfaces to mitigate the heat load from the combustion gases. Compared to designs that apply uniform ceramic coating thickness throughout the blade, advanced thermal barrier coating designs vary the coating thickness at the blade's trailing edge split and suction throat to minimize its impact on aerodynamic efficiency.

[0003] The use of variable-thickness thermal barrier ceramic coatings presents challenges to traditional numerical calculations of gas-heat coupling and temperature calibration. Two approaches are commonly used in traditional numerical calculations of uniform-thickness coatings to simulate the thermal insulation effect of ceramic coatings: one is to assign a fixed thermal resistance value to the blade surface to calculate the temperature difference generated by the coating; the other is to directly draw a mesh based on the actual geometry of the ceramic coating, assign thermal conductivity properties to the ceramic material, and apply numerical methods to the calculations.

[0004] However, when faced with the design of variable thickness ceramic coatings, the above traditional methods cannot be used for effective analysis. The reasons are: for the first thermal resistance value method, the thermal resistance value assigned is a constant value, which cannot accurately simulate the change of thermal resistance value when the thickness of the ceramic coating changes;

[0005] For the second method, as the thermal barrier ceramic coating gradually becomes thinner, it geometrically forms a wedge-shaped body with a very small angle. During the discretization of the numerical calculation domain, it is impossible to divide the grid that meets the solver requirements, making it impossible for the numerical calculation to proceed normally. Summary of the Invention

[0006] In view of the problem of inaccurate gas-thermal numerical analysis of variable-thickness ceramic coatings on turbine blades in the prior art, the present invention provides a gas-thermal numerical analysis method and system for variable-thickness ceramic coatings on turbine blades.

[0007] In order to achieve the above object, the present invention adopts the following technical solutions:

[0008] In the pre-established rectangular coordinate system of the calculation domain of the blade as the application object, the spatial positions of the starting edge lower vertex A, the starting edge upper vertex B, the ending edge upper vertex C and the ending edge lower vertex D of the variable thickness ceramic layer area are determined respectively;

[0009] Calculate the characteristic height of the variable thickness ceramic layer region according to the spatial positions of the lower vertex A of the starting edge, the upper vertex B of the starting edge, the upper vertex C of the ending edge, and the lower vertex D of the ending edge;

[0010] Calculate the dimensionless flow position of any node E in the variable thickness ceramic layer region based on the characteristic height of the variable thickness ceramic layer region;

[0011] According to the dimensionless position of the flow direction of node E, the thickness of the ceramic layer and the total thickness corresponding to node E are calculated;

[0012] According to the ceramic layer thickness and total thickness corresponding to node E, calculate the local equivalent thermal conductivity corresponding to node E;

[0013] Calculate the ceramic layer thickness, total thickness and corresponding local equivalent thermal conductivity coefficient corresponding to each node in the variable thickness ceramic layer area respectively;

[0014] The gas-heat value of the variable thickness ceramic coating on the turbine blade is analyzed based on the corresponding ceramic layer thickness, total thickness and corresponding local equivalent thermal conductivity coefficient of all points in the variable thickness ceramic layer area.

[0015] Furthermore, the method for calculating the characteristic height of the variable thickness ceramic layer region is:

[0016]

[0017] Where H is the characteristic height of the variable thickness ceramic layer area, y B 、y C 、y A and y D They are the y-direction coordinate values of vertex B on the starting edge, vertex C on the ending edge, vertex A on the starting edge, and vertex D on the ending edge, respectively.

[0018] Furthermore, the method for calculating the dimensionless position of the flow direction of any node E in the variable thickness ceramic layer region is:

[0019] Calculate the dimensionless spanwise height of node E according to the spatial positions of the starting edge lower vertex A, the starting edge upper vertex B, the ending edge upper vertex C, and the ending edge lower vertex D of the variable thickness ceramic layer region;

[0020] According to the dimensionless spanwise height of node E, calculate the starting point E from node E to node E in the flow direction. s distance;

[0021] According to the node E to the starting point E s The distance is calculated to calculate the span of the variable thickness ceramic layer area in the flow direction of node E;

[0022] The dimensionless position of node E in the flow direction is calculated based on the span of the variable thickness ceramic layer region in the flow direction of node E.

[0023] Furthermore, the dimensionless spanwise height of node E is calculated as follows:

[0024]

[0025] in, is the dimensionless spanwise height of point E, y E is the coordinate value of point E in the y direction.

[0026] Furthermore, calculate the starting point E from node E to node E in the flow direction s The distance method is:

[0027]

[0028]

[0029]

[0030] in, Starting point E s The coordinate value on x, Starting point E s The coordinate value on z, l is from node E to starting point E s The distance, z E is the coordinate value of node E in the z direction, x E is the coordinate value of node E in the x direction.

[0031] Furthermore, the method for calculating the span of the variable thickness ceramic layer region in the flow direction of node E is:

[0032]

[0033] Where L is the span of the variable thickness ceramic layer area in the flow direction of point E, |BC| is the distance from the upper vertex B of the starting edge to the upper vertex C of the ending edge, and |AD| is the distance from the lower vertex A of the starting edge to the lower vertex D of the ending edge.

[0034] Furthermore, the method for calculating the dimensionless position of the flow direction of node E is:

[0035]

[0036] in, is the dimensionless position of the flow direction of point E.

[0037] Furthermore, the method for calculating the ceramic layer thickness and total thickness corresponding to node E is:

[0038]

[0039] d=d c +Da (9)

[0040] Among them, d c is the thickness of the ceramic layer corresponding to node E, d is the total thickness corresponding to node E, D c is the thickness of the ceramic layer in the uniform ceramic coating area, D a is the thickness of the bonding layer in the uniform ceramic coating area.

[0041] Furthermore, the method for calculating the local equivalent thermal conductivity corresponding to node E is:

[0042]

[0043] Where λ is the local equivalent thermal conductivity corresponding to node E, λ c is the thermal conductivity of ceramic material, λ a is the thermal conductivity of the bonding material, d c is the thickness of the ceramic layer corresponding to node E, d is the total thickness corresponding to node E, D a is the thickness of the bonding layer in the uniform ceramic coating area.

[0044] A gas-thermal numerical analysis system for variable thickness ceramic coatings on turbine blades, comprising:

[0045] Spatial position determination module: used to determine the spatial positions of the starting edge lower vertex A, the starting edge upper vertex B, the ending edge upper vertex C and the ending edge lower vertex D of the variable thickness ceramic layer region in the pre-established calculation domain rectangular coordinate system of the application object blade;

[0046] Feature height calculation module: used to calculate the feature height of the variable thickness ceramic layer area according to the spatial positions of the lower vertex A of the starting edge, the upper vertex B of the starting edge, the upper vertex C of the ending edge and the lower vertex D of the ending edge;

[0047] Dimensionless position calculation module: used to calculate the dimensionless position of the flow direction of any node E in the variable thickness ceramic layer area according to the characteristic height of the variable thickness ceramic layer area;

[0048] Thickness calculation module: used to calculate the thickness of the ceramic layer and the total thickness corresponding to node E according to the dimensionless flow position of node E;

[0049] Equivalent thermal conductivity calculation module: used to calculate the local equivalent thermal conductivity corresponding to node E based on the ceramic layer thickness and total thickness corresponding to node E;

[0050] Numerical calculation module for each node in the region: used to calculate the thickness of the ceramic layer, the total thickness and the corresponding local equivalent thermal conductivity of each node in the variable thickness ceramic layer region;

[0051] Numerical analysis module: used to analyze the thermal value of variable thickness ceramic coating on turbine blades based on the ceramic layer thickness, total thickness and equivalent thermal conductivity coefficient corresponding to each node in the variable thickness ceramic layer area.

[0052] Compared with the prior art, the present invention has the following beneficial effects:

[0053] The present invention provides a method for numerically analyzing the thermal conductivity of variable-thickness ceramic coatings on turbine blades. This method determines the spatial positions of the starting edge lower vertex A, starting edge upper vertex B, ending edge upper vertex C, and ending edge lower vertex D of the variable-thickness ceramic layer region within a pre-established rectangular coordinate system of the blade's computational domain. The method then calculates the characteristic height of the variable-thickness ceramic layer region, the dimensionless position of any node E within the variable-thickness ceramic layer region, the ceramic layer thickness and total thickness corresponding to node E, and the local equivalent thermal conductivity corresponding to point E. Finally, the ceramic layer thickness, total thickness, and local equivalent thermal conductivity corresponding to each node within the variable-thickness ceramic layer region are calculated based on the calculation method for node E. This method enables numerical analysis of the thermal conductivity of variable-thickness ceramic coatings on turbine blades. Compared to traditional calculation methods using a constant thermal resistance value, this method can determine the local ceramic coating thickness based on the spatial position of different regions on the blade surface, thereby assigning different equivalent thermal conductivities to the blade wall. This method accurately simulates the barrier effect of the variable-thickness ceramic coating on the heat load of gas. Secondly, compared to direct meshing calculation methods, this method avoids the generation of wedge-shaped geometry and low-quality meshes, ensuring stable and efficient numerical calculations. All calculations in this method involve only four arithmetic operations on geometric and thermal parameters, eliminating complex computational processes such as judgment, iteration, and equation solving. This method utilizes low hardware resources and offers high computational efficiency, avoiding computational divergence and floating-point overflow. The method is simple and easy to implement, and provides more accurate numerical analysis of the thermal state of variable-thickness ceramic coatings on turbine blades.

[0054] The present invention also provides a gas-thermal numerical analysis system for variable-thickness ceramic coatings on turbine blades. The system implements the above-mentioned method steps for gas-thermal numerical analysis of variable-thickness ceramic coatings on turbine blades through a spatial position determination module, a characteristic height calculation module, a dimensionless position calculation module, a thickness calculation module, an equivalent thermal conductivity coefficient calculation module, a numerical calculation module for each node in the area, and a numerical analysis module. The system has a simple structure, low hardware resource occupation, and high computational efficiency. BRIEF DESCRIPTION OF THE DRAWINGS

[0055] Figure 1 Schematic diagram of a gas-thermal numerical analysis method for variable thickness ceramic coatings on turbine blades according to the present invention.

[0056] Figure 2Schematic diagram of applying the gas-thermal numerical analysis method of the variable thickness ceramic coating on a turbine blade of the present invention to a turbine blade with a variable thickness ceramic coating in an embodiment.

[0057] Figure 3 Schematic diagram of the relative position relationship between the variable thickness ceramic coating area and any node therein in the embodiment.

[0058] Figure 4 1 is a cross-sectional view of a variable thickness ceramic coating region in an embodiment.

[0059] Figure 5 The figure is a schematic structural diagram of a gas-thermal numerical analysis system for variable thickness ceramic coatings on turbine blades according to the present invention.

[0060] Among them, 1-metal part, 2-ceramic layer, 3-area covered by uniform thickness ceramic layer, 4-area covered by variable thickness ceramic layer at the trailing edge of the blade, 5-area of the trailing edge of the blade not covered by the ceramic layer, 6-area covered by variable thickness ceramic layer at the suction surface of the blade, 7-bonding layer of the turbine blade coating. DETAILED DESCRIPTION

[0061] To make the objectives, technical solutions, and advantages of the embodiments of the present invention more clear, the technical solutions of the embodiments of the present invention will be clearly and completely described below in conjunction with the accompanying drawings of the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Generally, the components of the embodiments of the present invention described and shown in the drawings herein can be arranged and designed in various different configurations.

[0062] Therefore, the following detailed description of the embodiments of the present invention provided in the accompanying drawings is not intended to limit the scope of the invention as claimed, but rather merely represents selected embodiments of the present invention. All other embodiments derived by persons of ordinary skill in the art based on the embodiments of the present invention without creative effort shall fall within the scope of protection of the present invention.

[0063] It should be noted that similar reference numerals and letters denote similar items in the following drawings, and therefore, once an item is defined in one drawing, it does not need to be further defined or explained in subsequent drawings.

[0064] In the description of the embodiments of the present invention, it should be noted that if the terms "upper," "lower," "horizontal," "inner," etc. appear, the orientation or positional relationship indicated is based on the orientation or positional relationship shown in the accompanying drawings, or the orientation or positional relationship in which the inventive product is typically placed when in use. These terms are merely for the convenience of describing the present invention and simplifying the description, and do not indicate or imply that the device or component referred to must have a specific orientation, be constructed, or operate in a specific orientation. Therefore, they should not be construed as limitations on the present invention. In addition, the terms "first," "second," etc. are used only to distinguish descriptions and should not be construed as indicating or implying relative importance.

[0065] In addition, if the term "horizontal" appears, it does not mean that the component must be absolutely horizontal, but can be slightly tilted. For example, "horizontal" only means that its direction is more horizontal than "vertical", and does not mean that the structure must be completely horizontal, but can be slightly tilted.

[0066] In the description of the embodiments of the present invention, it should be noted that, unless otherwise expressly specified or limited, the terms "disposed," "installed," "connected," and "connected" should be understood in a broad sense. For example, they can refer to fixed connections, detachable connections, or integral connections; they can refer to mechanical connections or electrical connections; they can refer to direct connections or indirect connections through an intermediate medium; and they can refer to internal connections between two components. Those skilled in the art will understand the specific meanings of the above terms in the present invention based on specific circumstances.

[0067] The present invention will be further described in detail below with reference to specific embodiments, which are intended to explain the present invention rather than to limit it.

[0068] See also Figure 1 The present invention discloses a gas-thermal numerical analysis method for a variable thickness ceramic coating on a turbine blade, comprising the following steps:

[0069] S1: In the pre-established rectangular coordinate system of the calculation domain of the application object blade, the spatial positions of the starting edge lower vertex A, the starting edge upper vertex B, the ending edge upper vertex C and the ending edge lower vertex D of the variable thickness ceramic layer area are determined respectively;

[0070] That is, in the rectangular coordinate system of the blade calculation domain, the spatial position of the variable thickness ceramic layer area is determined, and the vertex near the lower part of the starting edge of the ceramic coating thickness change is recorded as the starting edge lower vertex A, the vertex near the upper part of the starting edge of the ceramic coating thickness change is recorded as the starting edge upper vertex B, the vertex near the upper part of the ending edge of the ceramic coating thickness change is recorded as the ending edge upper vertex C, and the vertex near the lower part of the ending edge of the ceramic coating thickness change is recorded as the ending edge lower vertex D, and the coordinate values of the above four boundary vertices are obtained; the directions of the starting edge and the ending edge of the ceramic coating thickness change, that is, the line segments AB and CD, are defined as the span direction, and the directions of the lower edge and the upper edge of the ceramic coating thickness change area, that is, the line segments BC and AD, are defined as the flow direction.

[0071] S2: Calculate the characteristic height of the variable thickness ceramic layer region based on the spatial positions of the lower vertex A of the starting edge, the upper vertex B of the starting edge, the upper vertex C of the ending edge, and the lower vertex D of the ending edge. Specifically, the characteristic height of the variable thickness ceramic coating region is calculated by the difference between the average heights of the upper and lower edges of the variable thickness ceramic coating region, that is:

[0072] Calculate the average height of the upper edge of the variable thickness ceramic coating area, that is:

[0073]

[0074] Calculate the average height of the lower edge of the variable thickness ceramic coating area, that is:

[0075]

[0076] The characteristic height of the variable thickness ceramic coating area is calculated from the difference in average height between the upper edge and the lower edge of the variable thickness ceramic coating area, that is:

[0077] H=y high -y low (3)

[0078]

[0079] Among them, y high is the average height of the upper edge of the variable thickness ceramic coating area, y low is the average height of the lower edge of the variable thickness ceramic coating area, H is the characteristic height of the variable thickness ceramic layer area, and y B 、y C 、y A and y D The y-coordinate values of vertex B on the starting edge, vertex C on the ending edge, vertex A on the starting edge, and vertex D on the ending edge are respectively;

[0080] Thus, by obtaining the coordinates of the four points and calculating the characteristic height H, the spatial position determination and normalization processing of the variable thickness ceramic coating area are completed.

[0081] S3: Calculate the dimensionless flow position of any node E in the variable thickness ceramic layer region based on the characteristic height of the variable thickness ceramic layer region. The method is:

[0082] S3.1: Calculate the dimensionless spanwise height of node E based on the spatial positions of the starting edge lower vertex A, the starting edge upper vertex B, the ending edge upper vertex C, and the ending edge lower vertex D of the variable thickness ceramic layer region. Specifically,

[0083]

[0084]

[0085] in, is the dimensionless spanwise height of node E, y E is the coordinate value of point E in the y direction;

[0086] S3.2: Based on the dimensionless spanwise height of point E, calculate the starting point E from node E to node E in the flow direction. s The distance is:

[0087] First, according to the dimensionless spanwise height of node E, the starting point E of node E in the flow direction is calculated. s The coordinate values in the x and z directions are:

[0088]

[0089]

[0090] Then, according to the starting point E of node E in the flow direction s Coordinate values in the x and z directions, calculating the starting point E from node E to node E in the flow direction s The distance, that is:

[0091]

[0092] in, Starting point E s The coordinate value on x, Starting point E s The coordinate value on z, l is from point E to the starting point E s The distance, z E is the coordinate value of point E in the z direction, x E is the coordinate value of point E in the x direction;

[0093] S3.3: From node E to starting point E s The distance between the two points is calculated to calculate the span of the variable thickness ceramic layer area in the flow direction of point E, specifically:

[0094]

[0095] Where L is the span of the variable thickness ceramic layer area in the flow direction of node E, |BC| is the distance from the upper vertex B of the starting edge to the upper vertex C of the ending edge, and |AD| is the distance from the lower vertex A of the starting edge to the lower vertex D of the ending edge.

[0096] S3.4: Calculate the dimensionless flow position of point E based on the span of the variable thickness ceramic layer region in the flow direction of node E, specifically:

[0097]

[0098] in, is the dimensionless position of the flow direction of point E.

[0099] S4: Calculate the ceramic layer thickness and total thickness corresponding to node E based on the dimensionless flow position of node E, specifically:

[0100]

[0101] d=d c +D a (13)

[0102] Among them, d c is the thickness of the ceramic layer corresponding to node E, d is the total thickness corresponding to node E, D c is the thickness of the ceramic layer in the uniform ceramic coating area, D a is the thickness of the bonding layer in the uniform ceramic coating area.

[0103] S5: Calculate the local equivalent thermal conductivity corresponding to node E based on the ceramic layer thickness and total thickness corresponding to node E, specifically:

[0104]

[0105] Where λ is the local equivalent thermal conductivity corresponding to node E, λ c is the thermal conductivity of ceramic material, λ a is the thermal conductivity of the bonding material.

[0106] S6: Calculate the ceramic layer thickness, total thickness and corresponding local equivalent thermal conductivity of each node in the variable thickness ceramic layer area respectively. That is, according to the calculation method steps of the above-mentioned node E, for the discretized calculation domain, calculate the ceramic layer thickness, total thickness and corresponding local equivalent thermal conductivity of each node in the variable thickness ceramic layer area on the blade surface respectively. No further details will be given here.

[0107] S7: Based on the corresponding ceramic layer thickness, total thickness and corresponding local equivalent thermal conductivity of all points in the variable thickness ceramic layer area, the gas-thermal numerical analysis of the variable thickness ceramic coating of the turbine blade is carried out. Specifically, the total thickness and equivalent thermal conductivity of the thermal barrier coating at each node in the variable thickness ceramic layer area are assigned to the blade surface boundary conditions of the variable thickness ceramic coating area, and the gas-thermal coupling numerical calculation of the turbine blade is carried out.

[0108] See also Figure 2 Taking a turbine blade with a variable-thickness ceramic coating as an example, the structure of this turbine blade includes a metal portion 1, the surface of which is covered with a thermal barrier ceramic coating composed of a bonding layer 7 and a ceramic layer 2. The metal portion 1 also includes an area 5 at the blade's trailing edge that is not covered by the ceramic layer. A uniform-thickness ceramic layer, i.e., uniform-thickness ceramic layer covering area 3, is typically sprayed on the front half of the blade's pressure surface, leading edge, and trailing half of the suction surface. A ceramic layer with a thickness that varies linearly along the local flow direction is sprayed on the front portion of the pressure surface's trailing edge slit, i.e., variable-thickness ceramic layer covering area 4, and the throat portion of the suction surface, i.e., variable-thickness ceramic layer covering area 6. A ceramic layer is typically not sprayed on the trailing edge due to the large amount of cooling outflow. The present invention is applied to the gas-thermal coupled numerical analysis and calculation of spraying a linearly varying thickness ceramic layer in variable-thickness ceramic layer covering area 4 and variable-thickness ceramic layer covering area 6 on the blade's suction surface.

[0109] It should be pointed out that in engineering applications, the bonding layer thickness of thermal barrier ceramic coating is usually around 0.05mm, and the uniform thickness of the ceramic layer is around 0.2mm, which is much smaller than the chord length or blade height of the turbine blade. For high-pressure turbine blades, this size is usually 40 to 200mm. Figure 2 The ceramic layer shown is only for illustrating its position on the blade surface and the form of thickness variation, and does not represent the thickness of the coating relative to the blade in proportion.

[0110] Here, the variable thickness ceramic coating area in front of the split on the trailing edge of the pressure surface, that is, the variable thickness ceramic layer covering area 4 on the trailing edge of the blade is selected to illustrate the specific method of the present invention.

[0111] In the pre-established rectangular coordinate system of the calculation domain of the blade as the application object, the spatial positions of the starting edge lower vertex A, the starting edge upper vertex B, the ending edge upper vertex C and the ending edge lower vertex D of the variable thickness ceramic layer area are determined respectively;

[0112] That is, in the rectangular coordinate system of the blade calculation domain, the spatial position of the variable thickness ceramic layer area is determined, and the vertex near the lower part of the starting edge of the ceramic coating thickness change is recorded as the starting edge lower vertex A, the vertex near the upper part of the starting edge of the ceramic coating thickness change is recorded as the starting edge upper vertex B, the vertex near the upper part of the ending edge of the ceramic coating thickness change is recorded as the ending edge upper vertex C, and the vertex near the lower part of the ending edge of the ceramic coating thickness change is recorded as the ending edge lower vertex D; the directions of the starting edge and the ending edge of the ceramic coating thickness change, i.e., the line segments AB and CD, are defined as the span direction, and the directions of the lower edge and the upper edge of the ceramic coating thickness change area, i.e., the line segments BC and AD, are defined as the flow direction.

[0113] According to the spatial positions of the lower vertex A of the starting edge, the upper vertex B of the starting edge, the upper vertex C of the ending edge, and the lower vertex D of the ending edge, the characteristic height of the variable thickness ceramic layer area is calculated. For details, see formulas (1)-(4). Thus, by obtaining the coordinates of the four points and calculating the characteristic height H, the spatial position determination and normalization processing of the variable thickness ceramic coating area are completed.

[0114] See also Figure 3 , according to the characteristic height of the variable thickness ceramic layer area, the dimensionless position of the flow direction of any node E in the variable thickness ceramic layer area is calculated as follows:

[0115] According to the spatial positions of the starting edge lower vertex A, the starting edge upper vertex B, the ending edge upper vertex C, and the ending edge lower vertex D of the variable thickness ceramic layer area, the dimensionless spanwise height of the node E is calculated, see formulas (5)-(6);

[0116] According to the dimensionless spanwise height of node E, calculate the starting point E from node E to node E in the flow direction. s First, according to the dimensionless spanwise height of node E, calculate the starting point E of node E in the flow direction. s The coordinate values in the x and z directions are as follows: s Coordinate values in the x and z directions, calculating the starting point E from node E to node E in the flow direction s The distance, see formula (9);

[0117] According to the node E to the starting point E sThe distance between the two sides is used to calculate the span of the variable thickness ceramic layer area in the flow direction of point E. For details, see formula (10);

[0118] According to the span of the variable thickness ceramic layer area in the flow direction of point E, the dimensionless flow position of node E is calculated, as shown in formula (11).

[0119] According to the dimensionless position of the flow direction of node E, the thickness of the ceramic layer and the total thickness corresponding to node E are calculated. Figure 4 Specifically, a thermal barrier ceramic coating is sprayed onto the surface of the metal portion 1. The thermal barrier ceramic coating consists of a bonding layer 7 and a ceramic layer 2. The bonding layer 7 has a uniform thickness. In the variable thickness coating region, the thickness of the ceramic layer decreases proportionally with the dimensionless distance in the flow direction. Therefore, the dimensionless position of any point in the variable thickness coating region in the flow direction is equal to the ratio of the reduced thickness of the ceramic layer to the original thickness. For details, see formulas (12)-(13).

[0120] According to the thickness of the ceramic layer and the total thickness corresponding to the node E, the local equivalent thermal conductivity corresponding to the node E is calculated. For details, see formula (14).

[0121] Calculate the ceramic layer thickness, total thickness and corresponding local equivalent thermal conductivity of each node in the variable thickness ceramic layer area respectively; calculate the ceramic layer thickness, total thickness and corresponding local equivalent thermal conductivity of each node in the variable thickness ceramic layer area respectively according to the calculation method steps of node E.

[0122] Based on the corresponding ceramic layer thickness, total thickness, and corresponding local equivalent thermal conductivity at all points within the variable thickness ceramic layer region, the gas-heat numerical analysis of the variable thickness ceramic coating on the turbine blade is performed. The total thickness d and equivalent thermal conductivity λ of the thermal barrier coating at each point in the region are assigned to the blade surface boundary conditions of the variable thickness ceramic coating region. The specific implementation method can be to write a function based on the calculation formula of the above method and fill it into the wall heat transfer setting column of the blade in the numerical solver. Alternatively, the total thickness d and equivalent thermal conductivity λ of each discrete point on the surface of the region can be calculated by programming and imported into the numerical solver. The remaining parts are then set up according to conventional numerical solution methods. Finally, the gas-heat coupling numerical calculation of the turbine blade is carried out to complete the coupled heat transfer analysis of the variable thickness thermal barrier ceramic coating.

[0123] See also Figure 5 The present invention also provides a gas-thermal numerical analysis system for variable thickness ceramic coatings on turbine blades, comprising:

[0124] Spatial position determination module: used to determine the spatial positions of the starting edge lower vertex A, the starting edge upper vertex B, the ending edge upper vertex C and the ending edge lower vertex D of the variable thickness ceramic layer region in the pre-established calculation domain rectangular coordinate system of the application object blade;

[0125] Feature height calculation module: used to calculate the feature height of the variable thickness ceramic layer area according to the spatial positions of the lower vertex A of the starting edge, the upper vertex B of the starting edge, the upper vertex C of the ending edge and the lower vertex D of the ending edge;

[0126] Dimensionless position calculation module: used to calculate the dimensionless position of the flow direction of any node E in the variable thickness ceramic layer area according to the characteristic height of the variable thickness ceramic layer area;

[0127] Thickness calculation module: used to calculate the thickness of the ceramic layer and the total thickness corresponding to node E according to the dimensionless flow position of node E;

[0128] Equivalent thermal conductivity calculation module: used to calculate the local equivalent thermal conductivity corresponding to node E based on the ceramic layer thickness and total thickness corresponding to node E;

[0129] Numerical calculation module for each node in the region: used to calculate the thickness of the ceramic layer, the total thickness and the corresponding local equivalent thermal conductivity of each node in the variable thickness ceramic layer region;

[0130] Numerical analysis module: used to analyze the thermal value of variable thickness ceramic coating on turbine blades based on the ceramic layer thickness, total thickness and equivalent thermal conductivity coefficient corresponding to each node in the variable thickness ceramic layer area.

[0131] The system has a simple structure, low hardware resource occupation and high computational efficiency.

[0132] In summary, the present invention provides a method and system for numerical analysis of the aerothermal behavior of variable-thickness ceramic coatings on turbine blades. This method determines the spatial location of the variable-thickness ceramic coating region and normalizes it, calculating the dimensionless position of any point within the region. The corresponding ceramic layer thickness and total thickness are then calculated, and the local equivalent thermal conductivity is calculated. The total thickness and equivalent thermal conductivity of the thermal barrier coating at each point within the region are then assigned to the corresponding blade surface boundary conditions, enabling numerical calculation of the aerothermal behavior of turbine blades with variable-thickness thermal barrier coatings. Specifically, the local ceramic coating thickness and equivalent thermal conductivity are inferred based on the spatial geometric coordinates of the blade surface, thereby enabling numerical analysis of the aerothermal behavior of variable-thickness thermal barrier coatings on turbine blades. The method is simple and easy to use, avoiding the generation of wedge-shaped geometry and low-quality meshes, ensuring stable and efficient numerical calculations. Compared to traditional calculation methods using a constant thermal resistance value, the present invention can assign varying thicknesses and equivalent thermal conductivities to the blade wall, enabling accurate simulation of the barrier effect of variable-thickness ceramic coatings on gas heat loads.

[0133] The above description is merely a preferred embodiment of the present invention and is not intended to impose any limitation on the technical solution of the present invention. Those skilled in the art should understand that, without departing from the spirit and principles of the present invention, the technical solution can also be subjected to several simple modifications and replacements, and these modifications and replacements are also within the scope of protection covered by the claims.

Claims

1. A method for aero-thermal numerical analysis of variable thickness ceramic coatings on turbine blades, characterized in that: The following steps are involved: In the pre-established rectangular coordinate system of the calculation domain of the blade as the application object, the spatial positions of the starting edge lower vertex A, the starting edge upper vertex B, the ending edge upper vertex C and the ending edge lower vertex D of the variable thickness ceramic layer area are determined respectively; Calculate the characteristic height of the variable thickness ceramic layer region according to the spatial positions of the lower vertex A of the starting edge, the upper vertex B of the starting edge, the upper vertex C of the ending edge, and the lower vertex D of the ending edge; According to the characteristic height of the variable thickness ceramic layer area, the dimensionless position of the flow direction of any node E in the variable thickness ceramic layer area is calculated as follows: According to the spatial positions of the starting edge lower vertex A, the starting edge upper vertex B, the ending edge upper vertex C and the ending edge lower vertex D in the variable thickness ceramic layer area, the dimensionless spanwise height of the node E is calculated. in, is the dimensionless spanwise height of point E, y B 、 y C 、 y A and y D They are the y-coordinate values of the vertex B on the starting edge, the vertex C on the ending edge, the vertex A on the starting edge, and the vertex D on the ending edge. y E is the coordinate value of point E in the y direction; According to the dimensionless spanwise height of node E, calculate the starting point E from node E to node E in the flow direction. s distance; According to the node E to the starting point E s The distance is calculated to calculate the span of the variable thickness ceramic layer area in the flow direction of node E. in, L is the span of the variable thickness ceramic layer area in the flow direction of point E, is the distance from vertex B on the starting edge to vertex C on the ending edge, is the distance from the vertex A under the starting edge to the vertex D under the ending edge; H is the characteristic height of the variable thickness ceramic layer area; According to the span of the variable thickness ceramic layer area in the flow direction of node E, the dimensionless flow position of node E is calculated. in, is the dimensionless position of the flow direction of point E, l From node E to starting point E s distance; According to the dimensionless flow position of node E, the thickness of the ceramic layer and the total thickness corresponding to node E are calculated as follows: in, d c is the thickness of the ceramic layer corresponding to node E, d is the total thickness corresponding to node E, D c The thickness of the ceramic layer in the uniform ceramic coating area is D a is the thickness of the bonding layer in the uniform ceramic coating area; According to the ceramic layer thickness and total thickness corresponding to node E, the local equivalent thermal conductivity corresponding to node E is calculated as follows: in, is the local equivalent thermal conductivity corresponding to node E, is the thermal conductivity of the ceramic material, is the thermal conductivity of the bonding material; Calculate the ceramic layer thickness, total thickness and corresponding local equivalent thermal conductivity coefficient corresponding to each node in the variable thickness ceramic layer area respectively; The gas-heat value of the variable thickness ceramic coating on the turbine blade is analyzed based on the corresponding ceramic layer thickness, total thickness and corresponding local equivalent thermal conductivity coefficient of all points in the variable thickness ceramic layer area.

2. The gas-thermal numerical analysis method for variable thickness ceramic coatings on turbine blades according to claim 1, characterized in that: The method for calculating the characteristic height of the variable thickness ceramic layer area is: in, H is the characteristic height of the variable thickness ceramic layer area, y B 、 y C 、 y A and y D They are the y-direction coordinate values of vertex B on the starting edge, vertex C on the ending edge, vertex A on the starting edge, and vertex D on the ending edge, respectively.

3. The gas-thermal numerical analysis method for variable thickness ceramic coatings on turbine blades according to claim 1, characterized in that: Calculate the starting point E from node E to node E in the flow direction s The distance method is: in, Starting point E s exist x The coordinate values on Starting point E s exist z The coordinate values on l From node E to starting point E s distance, z E For node E z The coordinate value of the direction, x E For node E x The coordinate value of the direction.

4. A gas-thermal numerical analysis system for variable thickness ceramic coatings on turbine blades, characterized in that: include: Spatial position determination module: used to determine the spatial positions of the starting edge lower vertex A, the starting edge upper vertex B, the ending edge upper vertex C and the ending edge lower vertex D of the variable thickness ceramic layer region in the pre-established calculation domain rectangular coordinate system of the application object blade; Feature height calculation module: used to calculate the feature height of the variable thickness ceramic layer area according to the spatial positions of the lower vertex A of the starting edge, the upper vertex B of the starting edge, the upper vertex C of the ending edge and the lower vertex D of the ending edge; Dimensionless position calculation module: used to calculate the dimensionless position of the flow direction of any node E in the variable thickness ceramic layer area according to the characteristic height of the variable thickness ceramic layer area, specifically: According to the spatial positions of the starting edge lower vertex A, the starting edge upper vertex B, the ending edge upper vertex C and the ending edge lower vertex D in the variable thickness ceramic layer area, the dimensionless spanwise height of the node E is calculated. in, is the dimensionless spanwise height of point E, y B 、 y C 、 y A and y D They are the y-coordinate values of the vertex B on the starting edge, the vertex C on the ending edge, the vertex A on the starting edge, and the vertex D on the ending edge. y E is the coordinate value of point E in the y direction; According to the dimensionless spanwise height of node E, calculate the starting point E from node E to node E in the flow direction. s distance; According to the node E to the starting point E s The distance is calculated to calculate the span of the variable thickness ceramic layer area in the flow direction of node E. in, L is the span of the variable thickness ceramic layer area in the flow direction of point E, is the distance from vertex B on the starting edge to vertex C on the ending edge, is the distance from the vertex A under the starting edge to the vertex D under the ending edge; H is the characteristic height of the variable thickness ceramic layer area; According to the span of the variable thickness ceramic layer area in the flow direction of node E, the dimensionless flow position of node E is calculated. in, is the dimensionless position of the flow direction of point E, l From node E to starting point E s distance; Thickness calculation module: used to calculate the thickness of the ceramic layer and the total thickness corresponding to node E according to the dimensionless flow position of node E, specifically: in, d c is the thickness of the ceramic layer corresponding to node E, d is the total thickness corresponding to node E, D c The thickness of the ceramic layer in the uniform ceramic coating area is D a is the thickness of the bonding layer in the uniform ceramic coating area; Equivalent thermal conductivity calculation module: used to calculate the local equivalent thermal conductivity corresponding to node E based on the ceramic layer thickness and total thickness corresponding to node E, specifically: in, is the local equivalent thermal conductivity corresponding to node E, is the thermal conductivity of the ceramic material, is the thermal conductivity of the bonding material; Numerical calculation module for each node in the region: used to calculate the thickness of the ceramic layer, the total thickness and the corresponding local equivalent thermal conductivity of each node in the variable thickness ceramic layer region; Numerical analysis module: used to analyze the thermal value of variable thickness ceramic coating on turbine blades based on the ceramic layer thickness, total thickness and equivalent thermal conductivity coefficient corresponding to each node in the variable thickness ceramic layer area.

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