A method for synchronously estimating the thickness of thermally grown oxide and the thickness of defects in a thermal barrier coating

Abstract

The present invention discloses a method for synchronously estimating the thickness of thermally grown oxide and the thickness of defects in a thermal barrier coating, comprising: establishing a one-dimensional, unsteady, multi-layer coupled heat transfer equation set of heat conduction-radiation that describes the internal heat transfer mechanism of a thermal barrier coating system including a semi-transparent coating, a defect layer, a thermally grown oxide layer, a bond coat and a substrate layer under a high-temperature environment; solving the heat transfer equation set by using the finite volume method, and obtaining information on observables represented by temperature at the interior and surface of the thermal barrier coating system in combination with the determined boundary condition expressions; determining the observables and the inversion interval; determining an objective function required for synchronously estimating the thickness of the thermally grown oxide and the thickness of the defects based on the observables; obtaining measured values of the observables of the real system required for synchronously estimating the thickness of the thermally grown oxide and the thickness of the defects, and synchronously estimating the thickness of the thermally grown oxide and the thickness of the defects based on the inverse method; the present invention provides theoretical and technical support for non-destructive detection of internal defects and the like in thermal barrier coating materials in engineering practice.

Description

Technical Field

[0001] The present invention belongs to the field of methods for measuring the thickness of thermally grown oxides and defects, and particularly relates to a method for synchronously estimating the thickness of thermally grown oxides and the thickness of defects in a thermal barrier coating. Background Art

[0002] A thermal barrier coating system generally consists of a semi-transparent coating, a bond coat, and a substrate layer. The core components of an aero-engine, represented by turbine blades, operate in a high-temperature environment. In a high-temperature environment, oxygen elements in the external environment will penetrate through the semi-transparent coating and react chemically with metal elements in the bond coat, generating thermally grown oxides at the interface between the bond coat and the semi-transparent coating. The thickness of these thermally grown oxides will increase with the working time of the coating, resulting in continuous accumulation of stress at the interface. When the stress exceeds the critical value, microcracks will form at the interface. Along with the continuous progress of the thermal cycle, the cracks will continuously expand, eventually forming defects and causing the coating to peel off. Given that the growth of thermally grown oxides and the formation of defects are the main reasons for coating failure, developing a method for estimating the thickness of thermally grown oxides and the thickness of defects in a thermal barrier coating system is of crucial significance for evaluating the performance and damage degree of the thermal barrier coating system and ensuring the efficient and safe operation of aero-engines.

[0003] Regarding the problem of synchronous estimation of the thickness of thermally grown oxides and defect thickness in thermal barrier coating systems, methods such as scanning electron microscopy, ultrasonic testing, and active infrared thermography are generally used at present. Among them, scanning electron microscopy can visually observe the structure and morphology of thermally grown oxides and defects in thermal barrier coating samples. However, in order to obtain clear images, sample preparation processes such as cutting, grinding, polishing, and coating are required, which will cause a certain degree of damage to the object being detected. Ultrasonic testing uses the propagation and reflection characteristics of ultrasonic waves inside an object to achieve thickness estimation. For example, ultrasonic waves propagate at a certain speed within the thermal barrier coating system and will reflect when encountering the outer surface of the thermally grown oxide layer and the interface between the thermally grown oxide layer and the bond coat or substrate layer. By measuring the time interval of the reflected signal and the propagation speed of ultrasonic waves within the thermally grown oxide layer, the thickness of the thermally grown oxide layer can be estimated. However, when there are many pores and defects inside the thermal barrier coating system, it may affect the propagation and reflection of ultrasonic waves, resulting in an increase in the error of synchronous estimation. Compared with the first two technologies, active infrared thermography has advantages such as a large single detection area, intuitive detection results, fast detection speed, non-contact, less affected by the external environment, and is suitable for detecting debonding defects in layered structures and coated materials. It is a technical means with great application value in the field of non-destructive testing of thermal barrier coating systems. The principle of active infrared thermography is to actively emit heat to the object to be measured through a thermal excitation source (such as a flash lamp, infrared heating lamp, etc.), causing temperature changes on the surface or inside of the object. For example, when detecting internal defects in materials, the surface of the material is uniformly heated through infrared thermal excitation. Since defects (such as pores, debonding, etc.) existing inside the material will cause abnormalities in heat transfer during the process, different temperature distributions will be formed on the surface. By analyzing the surface temperature distribution information, qualitative and quantitative estimation of internal defects in the material can be carried out.

[0004] To achieve the synchronous estimation of the thickness of thermally grown oxide (TGO) and the thickness of defects in a thermal barrier coating system under high-temperature conditions, it is necessary to establish an unsteady forward numerical model that describes the heat transfer process of the thermal barrier coating system. In this context, for the overall heat transfer problem of a multi-layer structure including a semi-transparent coating, a defect layer, a thermally grown oxide layer, a bond coat, and a substrate layer, the existing technology ignores the thermal radiation effect inside the semi-transparent coating and replaces it with a simple heat conduction model. Considering the working environment of the thermal barrier coating system, the intensity of radiative heat flux inside the semi-transparent coating will increase rapidly in the form of an exponential function of temperature under high-temperature conditions. At this time, ignoring the thermal radiation effect inside the semi-transparent coating will inevitably have a greater impact on the heat transfer simulation inside the system with a complex structure (such as the presence of defects and thermally grown oxides), which will further lead to calculation errors in the system output represented by the temperature field, and ultimately reduce the synchronous estimation accuracy of the thickness of thermally grown oxide and the thickness of defects based on the inverse method. In addition, the measurement errors caused by the strong thermal interference noise existing in the high-temperature environment will also lead to a reduction in the accuracy of thickness synchronous estimation. All of the above factors make it extremely difficult to synchronously estimate the thickness of thermally grown oxide and the thickness of defects in a thermal barrier coating system under high-temperature and strong thermal interference noise conditions. Summary of the Invention

[0005] To solve the problem of synchronously estimating the thickness of thermally grown oxide and the thickness of defects in a thermal barrier coating system under high-temperature and strong thermal interference noise conditions, compared with the existing technology that approximates the internal heat transfer of a thermal barrier coating system with defects and thermally grown oxides under high-temperature conditions as a single heat conduction, the present invention considers the thermal radiation effect inside the semi-transparent coating at the top of the thermal barrier coating system, and establishes a one-dimensional, unsteady, conduction-radiation multi-layer coupled heat transfer model of the thermal barrier coating system including a semi-transparent coating, a defect layer, a thermally grown oxide layer, a bond coat, and a substrate layer, which is more suitable for high-temperature environments, and realizes the accurate simulation of the internal heat transfer of a thermal barrier coating system with defects and thermally grown oxides under high-temperature conditions. On this basis, combining the mutual influence mechanism of heat transfer between layers of the thermal barrier coating system and the influence mechanism of the thermal radiation effect inside the semi-transparent coating on the other layers, by setting temperature terms related to the thermal radiation effect of the semi-transparent coating in the objective function, the objective function is reconstructed, improving the accuracy and robustness of the estimation method under strong thermal interference noise, and realizing the synchronous accurate estimation of the thickness of thermally grown oxide and the thickness of defects in a thermal barrier coating system based on the inverse method under high-temperature and strong thermal interference noise conditions.

[0006] The present invention adopts the following technical solutions:

[0007] A method for synchronously estimating the thickness of thermally grown oxide and the thickness of defects in a thermal barrier coating, the method comprising the following steps:

[0008] Establish a one-dimensional, unsteady, conduction-radiation multi-layer coupled heat transfer equation set to describe the internal heat transfer mechanism of a thermal barrier coating system containing a semi-transparent coating, a defect layer, a thermally grown oxide layer, a bond coat, and a substrate layer under high-temperature environments; determine the boundary condition expressions for each layer of the thermal barrier coating system; the multi-layer coupled heat transfer equation set and the boundary condition expressions constitute a numerical heat transfer model of the thermal barrier coating system; among them, considering the influence of the high-temperature environment on the internal heat transfer of the semi-transparent coating, a description of the thermal radiation effect is added to the equation corresponding to the semi-transparent coating;

[0009] Use the finite volume method to solve the established one-dimensional, unsteady, conduction-radiation multi-layer coupled heat transfer equation set, and combine the determined boundary condition expressions to obtain information on observables represented by temperature at the internal and surface parts of the thermal barrier coating system;

[0010] Determine the observables and inversion intervals required for synchronously estimating the thickness of the thermally grown oxide and the thickness of the defect;

[0011] Based on the observables required for synchronously estimating the thickness of the thermally grown oxide and the thickness of the defect, determine the objective function required for synchronously estimating the thickness of the thermally grown oxide and the thickness of the defect;

[0012] Obtain the measured values of the observables of the real system required for synchronously estimating the thickness of the thermally grown oxide and the thickness of the defect, and synchronously estimate the thickness of the thermally grown oxide and the thickness of the defect based on the inverse method.

[0013] Furthermore, the method for establishing a one-dimensional, unsteady, conduction-radiation multi-layer coupled heat transfer equation set to describe the internal heat transfer mechanism of a thermal barrier coating system containing a semi-transparent coating, a defect layer, a thermally grown oxide layer, a bond coat, and a substrate layer under high-temperature environments is as follows:

[0014] Couple the one-dimensional, unsteady radiation transfer equation describing the internal thermal radiation effect of the semi-transparent coating with the one-dimensional, unsteady, heat conduction differential equation with an internal heat source describing its internal heat conduction. The radiation transfer equation is obtained through the PN approximation method, and the internal heat source term in the heat conduction differential equation is the opposite of the divergence of the radiation heat flux density obtained based on the PN approximation method. The above coupling equation can be expressed as:

[0015] ,

[0016] ,

[0017] Among them, are the temperature and radiation power of the semi-transparent coating respectively, is the time, are the density, specific heat capacity, thermal conductivity, attenuation coefficient, and refractive index of the semi-transparent coating respectively, is the Stefan-Boltzmann constant, and They are divergence and gradient respectively.

[0018] Furthermore, the method for establishing a one-dimensional, unsteady, conduction-radiation multi-layer coupled heat transfer equation set to describe the internal heat transfer mechanism of a thermal barrier coating system including a semi-transparent coating, a defect layer, a thermally grown oxide layer, a bond coat, and a substrate layer under high-temperature conditions further includes:

[0019] Use one-dimensional, unsteady, conduction differential equations without internal heat sources to describe the heat transfer in the defect layer, thermally grown oxide layer, bond coat, and substrate layer of the thermal barrier coating system respectively.

[0020] Furthermore, for determining the boundary condition expressions of each layer of the thermal barrier coating system, by considering the radiative heat flux density originating from the inside of the semi-transparent coating in the boundary conditions at the interface between the semi-transparent coating and the defect layer, the quantitative manifestation of the influence of the thermal radiation effect in the semi-transparent coating on the internal heat transfer of the remaining layers is realized. The specific approach is as follows:

[0021] For the interface between the semi-transparent coating and the defect layer, based on the conservation of heat flux density at the boundary, the sum of all heat flux densities entering this interface is equal to the sum of all heat flux densities leaving this interface. Among them, all heat flux densities entering this interface include the conductive heat flux density and radiative heat flux density inside the semi-transparent coating, and all heat flux densities leaving this interface include the conductive heat flux density of the air inside the defect layer and the net radiative heat flux density at the interface between the defect layer and the semi-transparent coating;

[0022] For the interfaces of the remaining layers, the interface between the semi-transparent coating and the external environment, and the interface between the substrate layer and the external environment, the sum of all heat flux densities entering the interface at any moment is equal to the sum of all heat flux densities leaving the interface.

[0023] Furthermore, the method for solving the established one-dimensional, unsteady, conduction-radiation multi-layer coupled heat transfer equation set by using the finite volume method and obtaining the information of observables represented by temperature at the interior and surface of the thermal barrier coating system in combination with the determined boundary condition expressions is as follows:

[0024] In view of the fact that the thermal radiation effect in the semi-transparent coating is transmitted layer by layer to the remaining adjacent layers through the radiative heat flux density in the boundary conditions, when discretizing each layer region using the finite volume method, local refinement technology is adopted to encrypt the grids in the regions near the boundaries of each layer, so as to better capture the changes in the heat flux density at the boundary caused by the thermal radiation effect of the semi-transparent coating; on this basis, the control equations in each layer are integrated over volume, simplified to obtain the corresponding discrete equations and solved, and finally the information of observables represented by temperature at the interior and surface of the thermal barrier coating system is obtained.

[0025] Further, when determining the observables and inversion intervals required for synchronously estimating the thickness of thermally grown oxide and the thickness of defects,

[0026] Combining the mutual influence mechanism of heat transfer between layers of the thermal barrier coating system, the influence mechanism of the thermal radiation effect in the semi-transparent coating on the remaining layers, and the parameter sensitivity analysis, the temperature at the contact surface between the semi-transparent coating and the external environment and the temperature at the contact surface between the substrate layer and the external environment are selected as the observables required for estimation. After determining the observables required for estimation, the inversion intervals required for estimating the thickness of thermally grown oxide and the thickness of defects are determined according to the sensitivity curve of the observables.

[0027] Further, when determining the objective function required for synchronously estimating the thickness of thermally grown oxide and the thickness of defects based on the observables required for synchronously estimating the thickness of thermally grown oxide and the thickness of defects,

[0028] To enhance the robustness of the estimation method and reduce the estimation error caused by the measurement error of the observables due to environmental thermal interference noise during the thickness synchronous estimation process, a temperature term related to the thermal radiation effect of the semi-transparent coating is set in the objective function to reconstruct the objective function;

[0029] The objective function is: the measured value of the observables of the real system corresponding to the true values of the thickness of thermally grown oxide and the thickness of defects and the measured value of the observables of the numerical heat transfer model of the thermal barrier coating system corresponding to a certain value of the parameter to be estimated during the estimation process The gap between them, and the expression is:

[0030] ,

[0031] where, is the true value of the thickness of thermally grown oxide and the thickness of defects, is the value of the thickness of thermally grown oxide and the thickness of defects during the estimation process; and are the temperatures at the contact surface between the semi-transparent coating and the external environment and the temperature at the contact surface between the substrate layer and the external environment at The value, that is, the measured value of the observables of the real system; and are and at The value, that is, the measured value of the observables of the numerical heat transfer model of the thermal barrier coating system.

[0032] Further, when obtaining the measured values of the observables of the real system required for synchronously estimating the thickness of the thermally grown oxide and the thickness of the defect, and synchronously estimating the thickness of the thermally grown oxide and the thickness of the defect based on the inverse method,

[0033] the measured values of the observables of the real system 、 are achieved by adding noise conforming to the random distribution law to the observable values of the established numerical heat transfer model of the thermal barrier coating system. By changing the intensity of the random noise, different degrees of measurement errors of the observables caused by environmental thermal interference noise in the real situation can be simulated; 、 The estimation based on the inverse method is realized by means of the particle swarm optimization algorithm to find the

[0034] that minimizes the objective function. This minimum value is denoted as , , which are the estimated values of the thickness of the thermally grown oxide and the thickness of the defect.

[0035] The beneficial technical effects of the present invention are as follows:

[0036] 1. To realize the synchronous estimation of the thickness of the thermally grown oxide and the thickness of the defect in the thermal barrier coating system under high-temperature environment based on the inverse method, it is first necessary to establish an unsteady forward numerical model describing the heat transfer process of the thermal barrier coating system. For the overall heat transfer problem of a multi-layer structure including a semi-transparent coating, a defect layer, a thermally grown oxide layer, an adhesive layer, and a substrate layer, the prior art ignores the thermal radiation effect inside the semi-transparent coating and replaces it with a simple heat conduction model. Compared with this approach, the present invention considers the thermal radiation effect inside the top semi-transparent coating of the thermal barrier coating system under high-temperature environment, and establishes a one-dimensional, unsteady, heat conduction-radiation multi-layer coupled heat transfer model of the thermal barrier coating system including a semi-transparent coating, a defect layer, a thermally grown oxide layer, an adhesive layer, and a substrate layer, which is more suitable for high-temperature environment, and realizes the accurate simulation of the internal heat transfer of the thermal barrier coating system with defects and thermally grown oxides under high-temperature environment;

[0037] 2. Relying on the established one-dimensional, unsteady, heat conduction-radiation multi-layer coupled heat transfer model describing the internal heat transfer mechanism of the thermal barrier coating system under high-temperature environment, the present invention realizes the synchronous and accurate estimation of the thickness of the thermally grown oxide and the thickness of the defect under high temperature and strong thermal interference noise: for the general magnitude of measurement errors of the observables caused by environmental thermal interference noise, such as the temperature measurement error of the order of and the heat flux measurement error in the range of [50 W / m 2 , 60000 W / m 2For the measurement error of the radiation power, the relative errors of the average estimated values of the thickness of thermally grown oxides under different thickness combinations are maintained between 0.677% and 2.088%, and the relative errors of the average estimated values of the defect thickness are maintained between 0.001% and 0.052%; for the large measurement errors of the observed quantities caused by environmental thermal interference noise, such as the temperature measurement error of the order of and the radiation power measurement error of the order of [100 W / m 2 , 120000 W / m 2 , the relative errors of the average estimated values of the thickness of thermally grown oxides under different thickness combinations are maintained between 1.369% and 2.199%, and the relative errors of the average estimated values of the defect thickness are maintained between 0.031% and 0.321%. Both are maintained within a small range, proving the strong robustness of the estimation method proposed by the present invention; especially when the thicknesses of thermally grown oxides and defects are relatively thin, even in an environment with strong thermal interference noise, the relative estimation errors of the two still remain at 2.199% and 0.321% respectively; therefore, the estimation method proposed by the present invention can accurately capture the thermally grown oxides and early defects in the initial growth stage, providing technical support for timely warning and accurate intervention;

[0038] 3. In addition, compared with a class of methods based on wave transmission and reflection represented by ultrasonic detection technology and active infrared thermal wave technology, this method does not have the problem of overlapping and mutual influence of wave reflection information in complex structures, and has great advantages in the synchronous estimation of multiple thicknesses in complex structures represented by thermal barrier coating systems. Description of the Drawings

[0039] Figure 1 is a schematic flow chart of a method for synchronously estimating the thickness of thermally grown oxides and defect thickness in a thermal barrier coating in Embodiment 1 of the present invention;

[0040] Figure 2 is a schematic structural diagram and boundary condition diagram of a thermal barrier coating system including a semi-transparent coating, a defect layer, a thermally grown oxide layer, a bonding layer, and a substrate layer in Embodiment 2 of the present invention;

[0041] Figure 3 is a technical principle diagram of the reverse method part in a method for synchronously estimating the thickness of thermally grown oxides and defect thickness in a thermal barrier coating in an embodiment of the present invention. Detailed Embodiments Embodiment 1

[0042] The following further clearly and completely describes a method for synchronously estimating the thickness of thermally grown oxides and defect thickness in a thermal barrier coating system proposed by the present invention in conjunction with the drawings:

[0043] AsFigure 1 As shown in the figure, a method for synchronously estimating the thickness of thermally grown oxide and the thickness of defects in a thermal barrier coating, the method comprising the following steps:

[0044] S1. Establish a one-dimensional, unsteady, conduction-radiation multi-layer coupled heat transfer equation set that describes the internal heat transfer mechanism of a thermal barrier coating system containing a semi-transparent coating, a defect layer, a thermally grown oxide layer, a bonding layer, and a substrate layer under high-temperature environments;

[0045] Given that the thickness of the thermal barrier coating system is much smaller than its dimensions in other directions, when the local curvature change is small, its internal heat transfer can be approximated as a one-dimensional case. For the semi-transparent coating located at the top of the thermal barrier coating system, in this embodiment, the internal thermal radiation effect is considered on the basis of the prior art. First, the radiative transfer equation describing the internal thermal radiation of the semi-transparent coating is obtained based on the PN approximation method. Subsequently, the internal heat source term in the heat conduction differential equation is replaced by the opposite of the divergence of the radiative heat flux density obtained based on the PN approximation method, and finally, a one-dimensional, unsteady, conduction-radiation coupled equation describing the internal heat transfer law of the semi-transparent coating is obtained:

[0046] ,

[0047] ,

[0048] wherein, are respectively the temperature and radiative power of the semi-transparent coating, is time, are respectively the density, specific heat capacity, thermal conductivity, attenuation coefficient, and refractive index of the semi-transparent coating, is the Stefan-Boltzmann constant, and are respectively divergence and gradient.

[0049] Different from the semi-transparent coating, the bonding layer and the substrate layer are usually alloy materials, and the thermally grown oxide layer is mainly composed of metal oxides. Compared with the semi-transparent coating, the radiative heat transfer in the thermally grown oxide layer, the bonding layer, and the substrate layer can be ignored. Therefore, a single heat conduction differential equation is used to describe the one-dimensional, unsteady, heat transfer process without internal heat sources inside them:

[0050] ,

[0051] wherein, are respectively the density, specific heat capacity, and thermal conductivity of the thermally grown oxide layer, are respectively the density, specific heat capacity, and thermal conductivity of the bonding layer, are respectively the density, specific heat capacity, and thermal conductivity of the substrate layer, are respectively the temperatures of the thermally grown oxide layer, the bonding layer, and the substrate layer.

[0052] For the defect layer inside the thermal barrier coating system, since the defects at the interface are mainly debonding defects, the medium inside the defect layer can be approximated as dry air. The water vapor content in dry air is extremely low and can be approximated as a transparent medium. The radiative heat flux density emitted from the defect layer wall will not be lost when passing through the defect interior. In addition, the emissivity of dry air is extremely low, and the thermal radiation of the air itself inside can be ignored. Therefore, only the one-dimensional, unsteady, heat transfer process without internal heat source inside is described by the heat conduction differential equation:

[0053] ,

[0054] where, are the density, specific heat capacity, thermal conductivity, and temperature of the defect layer respectively.

[0055] The radiative heat flux density emitted from the defect wall can be calculated using the Stefan-Boltzmann formula:

[0056] ,

[0057] where, is the Stefan-Boltzmann constant, is the temperature of the defect wall.

[0058] S2. Determine the expressions for the boundary conditions of each layer of the thermal barrier coating system;

[0059] For the interfaces of the semi-transparent coating, defect layer, thermally grown oxide layer, bond coat, and substrate layer, the boundary conditions are established by the conservation of heat flux density, that is, the sum of all heat flux densities entering the interface at any moment is equal to the sum of all heat flux densities leaving the interface: At the interface between the semi-transparent coating and the defect layer, the sum of the conductive and radiative heat flux densities on the semi-transparent coating side is equal to the sum of the conductive heat flux density on the defect layer side and the net radiative heat flux density at the interface between the defect layer and the semi-transparent coating; At the interface between the defect layer and the thermally grown oxide layer, the sum of the conductive heat flux density on the defect layer side and the net radiative heat flux density at the interface between the defect layer and the thermally grown oxide layer is equal to the conductive heat flux density on the thermally grown oxide layer side; At the interface between the thermally grown oxide layer and the bond coat, the conductive heat flux density on the thermally grown oxide layer side is equal to the conductive heat flux density on the bond coat side; At the interface between the bond coat and the substrate layer, the conductive heat flux density on the bond coat side is equal to the conductive heat flux density on the substrate layer side.

[0060] For the boundary side where the semi-transparent coating and the substrate layer are in contact with the external environment, considering the radiative heat transfer and convective heat transfer between them and the external environment, the boundary conditions are established by the conservation of heat flux density in the same way: at the boundary where the semi-transparent coating is in contact with the external environment, the sum of the conductive and radiative heat flux densities on the semi-transparent coating side is equal to the sum of the net heat flux densities exchanged through convective heat transfer and thermal radiation between this side and the external environment; at the boundary where the substrate layer is in contact with the external environment, the conductive heat flux density on the substrate layer side is equal to the sum of the net heat flux densities exchanged through convective heat transfer and thermal radiation between this side and the external environment.

[0061] The above one-dimensional, unsteady, conduction-radiation multi-layer coupled heat transfer equations describing the internal heat transfer mechanism of the thermal barrier coating system containing a semi-transparent coating, a defect layer, a thermally grown oxide layer, a bond coat and a substrate layer under high-temperature conditions, together with the boundary conditions of each layer of the thermal barrier coating system, constitute the numerical heat transfer model of the thermal barrier coating system.

[0062] S3. Solve the established one-dimensional, unsteady, conduction-radiation multi-layer coupled heat transfer equations by the finite volume method, and combine the determined boundary condition expressions to obtain the information of the observables represented by temperature inside and on the surface of the thermal barrier coating system;

[0063] The solution process based on the finite volume method will sequentially traverse the semi-transparent coating, the defect layer, the thermally grown oxide layer, the bond coat and the substrate layer. The following takes the semi-transparent coating as an example for illustration: First, discretize the solution domain to determine the temperature nodes and control volumes. Given that the thermal radiation effect in the semi-transparent coating is transferred layer by layer to the remaining layers adjacent to it through the radiative heat flux density in the boundary conditions, when using the finite volume method to discretize each layer region, local refinement technology is used to encrypt the grids in the regions near the boundaries of each layer to better capture the change of the heat flux density at the boundary caused by the thermal radiation effect of the semi-transparent coating; Subsequently, perform volume integration on the control equation in the semi-transparent coating, that is, the conduction-radiation coupling equation, and simplify it to obtain the discrete equations for temperature and radiation power, and solve the above discrete equations to obtain the temperature and radiation power inside the semi-transparent coating.

[0064] For the heat conduction differential equations describing the heat transfer in the defect layer, the thermally grown oxide layer, the bond coat and the substrate layer, the finite volume method is also used for solution. The basic idea is the same as that for solving the conduction-radiation coupling equation in the semi-transparent coating. Finally, the temperatures inside the defect layer, the thermally grown oxide layer, the bond coat and the substrate layer can be obtained.

[0065] S4. Determine the observables and inversion intervals required for synchronously estimating the thickness of the thermally grown oxide and the thickness of the defect;

[0066] Combined with the mutual influence mechanism of heat transfer between the layers of the thermal barrier coating system and the influence mechanism and parameter sensitivity analysis of the thermal radiation effect in the semi-transparent coating on the other layers, the temperature at the contact surface between the semi-transparent coating and the external environment is and the temperature at the interface between the substrate and the external environment Select the observations needed for estimation.

[0067] The sensitivity is the derivative of the observed value relative to the thermally grown oxide thickness and defect thickness to be estimated. Since the observed value changes with time, the derivative value of the observed value relative to the parameter to be estimated at each moment is connected to obtain the sensitivity curve that changes with time. For the problem of simultaneous estimation of thermally grown oxide thickness and defect thickness, after determining the observed value required for estimation, the inversion interval required for parameter estimation is determined according to the sensitivity curve of the above observed value.

[0068] S5, determining an objective function required for simultaneously estimating the thickness of the thermally grown oxide and the thickness of the defect based on the observed amount required for simultaneously estimating the thickness of the thermally grown oxide and the thickness of the defect;

[0069] The objective function is the true value of the parameters to be estimated (thermally grown oxide thickness and defect thickness) The corresponding observed value of the real system and a value of the parameter to be estimated during the estimation process Corresponding observed values ​​of the numerical heat transfer model of the thermal barrier coating system The gap between (two norm), its general form is:

[0070] ,

[0071] In order to enhance the robustness of the estimation method and reduce the estimation error caused by the measurement error of the observation quantity caused by the environmental thermal interference noise during the thickness synchronization estimation process, the temperature term related to the thermal radiation effect of the semi-transparent coating is set in the objective function to reconstruct the objective function. Since there are multiple observation quantities in the current problem, the objective function is in the form of adding multiple bi-norms:

[0072] ,

[0073] in, is the true value of thermally grown oxide thickness and defect thickness, is the value of thermally grown oxide thickness and defect thickness in the estimation process; and is the temperature of the interface between the semi-transparent coating and the external environment and the temperature at the interface between the substrate and the external environment exist The value under is the measured value of the real system observation; and is and at the value of , that is, the measured value of the observable quantity of the numerical heat transfer model of the thermal barrier coating system.

[0074] S6. Obtain the measured values of the observable quantities of the real system required for synchronously estimating the thickness of the thermally grown oxide and the thickness of the defect, and synchronously estimate the thickness of the thermally grown oxide and the thickness of the defect based on the inverse method;

[0075] The synchronous estimation of the thickness of the thermally grown oxide and the thickness of the defect belongs to an inverse problem, and its essence is to invert the unknown input of the system related to the output from the known output of the system. Specifically, that is, from the known output of the real system (i.e., the measured value of the determined observable quantity invert the unknown input of the real system related to these observable quantities (i.e., the thickness of the thermally grown oxide and the thickness of the defect to be estimated), and the inversion method is the inverse method, and its principle is as Figure 3 shown:

[0076] First, establish a one-dimensional, unsteady, conduction-radiation multi-layer coupled heat transfer model that describes the internal heat transfer process of the real thermal barrier coating system. Subsequently, select the parameters to be estimated as the input of the model, and select the determined observable quantities as the output. When the output value of the model is close enough to the output value of the real system , the model input value corresponding to the current model output value can be considered as the input value of the real system approximate value (also called the estimated value, denoted as: ). Finally, the output value of the real system required for synchronous estimation, that is, the measured value of the observable quantity is achieved by adding noise that conforms to the random distribution law to the observable quantity value of the established numerical heat transfer model of the thermal barrier coating system. By changing the intensity of the random noise, different degrees of measurement errors of the observable quantity caused by environmental thermal interference noise in the real situation can be simulated.

[0077] It can be seen from the principle of the inverse method that the essence of parameter inversion is the process of finding the model input value that makes the gap between the model output value and the real system output value small enough. From a mathematical point of view, the gap between the model output value and the real system output value can be quantitatively represented by the established objective function. The essence of the synchronous estimation process of the thickness of the thermally grown oxide and the thickness of the defect is to find the objective function to take the minimum value. In this embodiment, the process of minimizing the above objective function is realized by means of the particle swarm optimization algorithm. It can be considered that the number of particles is set to 15 and the maximum number of iterations is set to 80. Embodiment 2

[0078] For example, in this embodiment, a one-dimensional, unsteady, conduction-radiation multi-layer coupled heat transfer model of a thermal barrier coating system containing a semi-transparent coating, a defect layer, a thermally grown oxide layer, a bond coat, and a substrate layer is established, and based on this model, the thicknesses of the thermally grown oxide and the defect in the thermal barrier coating system are synchronously estimated.

[0079] As Figure 2 shown, considering the convective heat transfer and radiative heat transfer between the thermal barrier coating system and the external environment, where the ambient temperature outside the semi-transparent coating is 2000 K, the convective heat transfer coefficient is 250 W / m 2 / K, the ambient temperature outside the substrate layer is 300 K, the convective heat transfer coefficient is 110 W / m 2 / K, and the initial temperature of the thermal barrier coating system is 300 K. The thermal conductivities of the semi-transparent coating, the defect layer, the thermally grown oxide layer, the bond coat, and the substrate layer are 0.62 W / m / K, 0.026 W / m / K, 21 W / m / K, 17 W / m / K, and 33 W / m / K respectively, and the volume heat capacities are 3.5×10 6 J / m 3 / K, 1690 J / m 3 / K, 5.2668×10 6 J / m 3 / K, 9.45×3×10 6 J / m 3 / K, 4.25×10 6 J / m 3 / K. The thicknesses of the semi-transparent coating, the bond coat, and the substrate layer are 150, 50, and 1.4 mm respectively, and the spatial step sizes of the semi-transparent coating, the bond coat, and the substrate layer are 10 -6 m, and the spatial step sizes of the defect layer and the thermally grown oxide layer are 10 -7 m. The simulation duration is 20 s, and the time step size is 0.005 s. The absorption coefficient of the semi-transparent coating is 30 m -1 , the scattering coefficient is 10 4 m -1 , the refractive index is 1.58, the emissivity of the surface of the semi-transparent coating exposed to the environment side is 0.97, the emissivity of the surface of the semi-transparent coating at the junction with the defect layer is 0.92, the emissivity of the surface of the thermally grown oxide layer at the junction with the defect layer is 0.35, and the emissivity of the surface of the substrate layer exposed to the environment side is 0.6; the finite volume method is used to solve the one-dimensional, unsteady, conduction-radiation multi-layer coupled heat transfer model of the above thermal barrier coating system, and the temperature field and radiation power field inside the thermal barrier coating system are obtained.

[0080] Based on the inspiration of parameter sensitivity, combined with the mutual influence mechanism of heat transfer between layers of the thermal barrier coating system and the influence mechanism of the thermal radiation effect in the semi-transparent coating on the remaining layers, a temperature term related to the thermal radiation effect of the semi-transparent coating is set in the objective function to reconstruct the objective function, and the temperature at the contact surface between the semi-transparent coating and the external environment and the temperature at the contact surface between the substrate layer and the external environment are selected as the observables required for estimation. Specifically, since the time interval from 0 to 20 s covers more than 50% of the peak region of the sensitivity curve, the interval [0, 20 s] is selected as the inversion interval. Use to represent the true values of the thermally grown oxide thickness and the defect thickness, and use to represent a certain value of the thermally grown oxide thickness and the defect thickness during the estimation process. The objective function is defined as:

[0081] ,

[0082] where, is the true value of the thermally grown oxide thickness and the defect thickness, is the value of the thermally grown oxide thickness and the defect thickness during the estimation process. and are the temperatures at the contact surface between the semi-transparent coating and the external environment and the temperature at the contact surface between the substrate layer and the external environment at , that is, the measured values of the true system observables. and are and at , that is, the observable values of the numerical heat transfer model of the thermal barrier coating system.

[0083] The essence of the synchronous estimation process of the thermally grown oxide thickness and the defect thickness is to find the process that makes the objective function take the minimum value. The above process is realized by the particle swarm optimization algorithm, where the inversion boundaries of the thermally grown oxide thickness and the defect thickness are set to and respectively, the number of particles is 15, the maximum number of iterations is 80, the maximum number of stagnant iterations is 15, the function tolerance is 10 -8 , and both the individual learning factor and the social learning factor are 1.49.

[0084] Table 1 shows the results of the synchronous estimation of the thermally grown oxide thickness and the defect thickness based on the above idea for different degrees of measurement errors of observables caused by environmental thermal interference noise when considering the thermal radiation effect inside the semi-transparent coating. Specifically, two combinations of the thermally grown oxide thickness and the defect thickness are considered, which are thickness combination 1: , thickness combination 2: and two cases of measurement errors of observables with different degrees caused by environmental thermal interference noise.

[0085] For the measurement error of observables with a general magnitude caused by environmental thermal interference noise, such as the temperature measurement error with an order of magnitude of and the radiation power measurement error with an order of magnitude of [50 W / m 2 , 60000 W / m 2 (Case 1), the relative error of the average estimated value of the thermally grown oxide thickness under different thickness combinations remains between 0.677% and 2.088% (the relative error is the percentage of the absolute value of the difference between the average estimated value and the true value of the thickness to the true value), and the relative error of the average estimated value of the defect thickness remains between 0.001% and 0.052%.

[0086] For the measurement error of observables with a large magnitude caused by environmental thermal interference noise, such as the temperature measurement error with an order of magnitude of and the radiation power measurement error with an order of magnitude of [100 W / m 2 , 120000 W / m 2 (Case 2), the relative error of the average estimated value of the thermally grown oxide thickness under different thickness combinations remains between 1.369% and 2.199%, and the relative error of the average estimated value of the defect thickness remains between 0.031% and 0.321%.

[0087] Table 1

[0088]

[0089] Table 2 shows the estimation results when the internal thermal radiation effect of the semi-transparent coating is ignored under the same conditions. By comparing with the results in Table 1, it can be seen that when the internal thermal radiation effect of the semi-transparent coating is ignored under high-temperature environments, the errors of the synchronous estimation of the thermally grown oxide thickness and the defect thickness based on the inverse method become larger, verifying the necessity of considering the thermal radiation effect.

[0090] Table 2

[0091]

[0092] In addition, even for the case of strong environmental thermal interference noise (Case 2), the estimation method of the present invention still controls the estimation errors of the thermally grown oxide thickness and the defect thickness at an extremely low level (2.199% and 0.321% respectively). With this advantage, the method proposed by the present invention can accurately capture the thermally grown oxide in the initial growth stage and early defects, providing technical support for timely warning and intervention.

[0093] In summary, regarding the problem of synchronous estimation of the thickness of thermally grown oxides and defect thickness in a thermal barrier coating system based on the inverse method, compared with the existing technology that ignores the internal thermal radiation effect of the semi-transparent coating, the present invention incorporates the internal thermal radiation effect of the semi-transparent coating into the thermal barrier coating system with defects and thermally grown oxides, and establishes a one-dimensional, unsteady, heat conduction-radiation multi-layer coupled heat transfer model of the thermal barrier coating system that includes a semi-transparent coating, a defect layer, a thermally grown oxide layer, a bond coat, and a substrate layer, which is more suitable for high-temperature environments. The synchronous estimation of the thickness of thermally grown oxides and defect thickness in the thermal barrier coating system under high-temperature conditions based on the inverse method is realized, and it has better accuracy. Specifically:

[0094] For the measurement error of the observed quantity with a general magnitude caused by environmental thermal interference noise, such as the temperature measurement error of the order of and the radiation power measurement error of the order of [50 W / m 2 , 60000 W / m 2 , the relative error of the average estimated value of the thickness of thermally grown oxides under different thickness combinations remains between 0.677% and 2.088%, and the relative error of the average estimated value of the defect thickness remains between 0.001% and 0.052%. For the measurement error of the observed quantity with a large magnitude caused by environmental thermal interference noise, such as the temperature measurement error of the order of and the radiation power measurement error of the order of [100W / m 2 , 120000 W / m 2 , the relative error of the average estimated value of the thickness of thermally grown oxides under different thickness combinations remains between 1.369% and 2.199%, and the relative error of the average estimated value of the defect thickness remains between 0.031% and 0.321%. Both are within a relatively small range, demonstrating the strong robustness of the estimation method proposed by the present invention. Especially when the thickness of thermally grown oxides and defect thickness are relatively thin, even in an environment with strong thermal interference noise, the relative errors of their estimations still remain at 2.199% and 0.321% respectively. Therefore, the estimation method proposed by the present invention can accurately capture the thermally grown oxides in the initial growth stage and early defects, providing technical support for timely warning and accurate intervention.

[0095] In addition, compared with a class of methods based on wave transmission and reflection represented by ultrasonic detection technology and active infrared thermography technology, this method does not have the problem of overlapping and interfering reflection information of waves in complex structures, and has great advantages in the synchronous estimation of multiple thicknesses in complex structures represented by thermal barrier coating systems.

[0096] So far, the technical solution of the present invention has been described in conjunction with the preferred embodiments shown in the accompanying drawings. However, it is easily understood by those skilled in the art that the protection scope of the present invention is obviously not limited to these specific embodiments. Without departing from the principle of the present invention, those skilled in the art can make equivalent changes or substitutions to the relevant technical features, and the technical solutions after these changes or substitutions will fall within the protection scope of the present invention.

Claims

1. A method for synchronously estimating the thickness of thermally grown oxide and the thickness of defects in a thermal barrier coating, characterized in that The method includes the following steps: Establish a one-dimensional, unsteady, conduction-radiation multi-layer coupled heat transfer equation set that describes the internal heat transfer mechanism of a thermal barrier coating system including a semi-transparent coating, a defect layer, a thermally grown oxide layer, a bond coat, and a substrate layer under high-temperature conditions; determine the boundary condition expressions for each layer of the thermal barrier coating system; the multi-layer coupled heat transfer equation set and the boundary condition expressions constitute a numerical heat transfer model of the thermal barrier coating system; among them, considering the influence of the high-temperature environment on the internal heat transfer of the semi-transparent coating, a description of the thermal radiation effect is added to the equation corresponding to the semi-transparent coating; Use the finite volume method to solve the established one-dimensional, unsteady, conduction-radiation multi-layer coupled heat transfer equation set, and combine the determined boundary condition expressions to obtain information on observables represented by temperature at the internal and surface parts of the thermal barrier coating system; Determine the observables and inversion intervals required for synchronously estimating the thickness of the thermally grown oxide and the thickness of the defect; Based on the observables required for synchronously estimating the thickness of the thermally grown oxide and the thickness of the defect, determine the objective function required for synchronously estimating the thickness of the thermally grown oxide and the thickness of the defect; Obtain the measured values of the observables of the real system required for synchronously estimating the thickness of the thermally grown oxide and the thickness of the defect, and synchronously estimate the thickness of the thermally grown oxide and the thickness of the defect based on the inverse method.

2. The method for synchronously estimating the thickness of thermally grown oxide and the thickness of defects in a thermal barrier coating according to claim 1, wherein The method for establishing a one-dimensional, unsteady, conduction-radiation multi-layer coupled heat transfer equation set that describes the internal heat transfer mechanism of a thermal barrier coating system including a semi-transparent coating, a defect layer, a thermally grown oxide layer, a bond coat, and a substrate layer under high-temperature conditions is as follows: Couple the one-dimensional, unsteady radiation transfer equation that describes the internal thermal radiation effect of the semi-transparent coating with the one-dimensional, unsteady, heat conduction differential equation with internal heat sources that describes its internal heat conduction, where the radiation transfer equation is obtained through the PN approximation method, and the internal heat source term in the heat conduction differential equation is the opposite of the divergence of the radiation heat flux density obtained based on the PN approximation method. The above coupled equation can be expressed as: ， ， wherein, are respectively the temperature and radiation power of the semi-transparent coating, is time, are respectively the density, specific heat capacity, thermal conductivity, attenuation coefficient and refractive index of the semi-transparent coating, is the Stefan-Boltzmann constant, and are respectively divergence and gradient.

3. The method for synchronously estimating the thickness of thermally grown oxide and the thickness of defects in a thermal barrier coating according to claim 2, wherein The method for establishing a one-dimensional, unsteady, conduction-radiation multi-layer coupled heat transfer equation set that describes the internal heat transfer mechanism of a thermal barrier coating system including a semi-transparent coating, a defect layer, a thermally grown oxide layer, a bond coat, and a substrate layer under high-temperature conditions further includes: Use the one-dimensional, unsteady, heat conduction differential equation without internal heat sources to describe the heat transfer in the defect layer, thermally grown oxide layer, bond coat, and substrate layer of the thermal barrier coating system respectively.

4. The method for synchronously estimating the thickness of thermally grown oxide and the thickness of defects of a thermal barrier coating according to claim 1, wherein For the determination of the boundary condition expressions for each layer of the thermal barrier coating system, by considering the radiation heat flux density originating from the inside of the semi-transparent coating in the boundary condition at the interface between the semi-transparent coating and the defect layer, a quantitative representation of the influence of the thermal radiation effect in the semi-transparent coating on the internal heat transfer of the remaining layers is achieved. The specific method is as follows: For the interface between the semi-transparent coating and the defective layer, based on the conservation of heat flux at the boundary, the sum of all heat fluxes entering the interface is equal to the sum of all heat fluxes leaving the interface, where all heat fluxes entering the interface include the heat conduction heat flux and radiation heat flux inside the semi-transparent coating, and all heat fluxes leaving the interface include the heat conduction heat flux of the air inside the defective layer and the net radiation heat flux at the interface between the defective layer and the semi-transparent coating; For the interfaces of the remaining layers, the interface between the translucent coating and the external environment, and the interface between the substrate layer and the external environment, the sum of all heat flux densities entering the interface at any moment is equal to the sum of all heat flux densities leaving the interface.

5. A method for synchronously estimating the thickness of thermally grown oxide and the thickness of defects in a thermal barrier coating according to claim 1, characterized in that The method of using the finite volume method to solve the established one-dimensional, non-steady-state, heat conduction-radiation multilayer coupled heat transfer equations and obtaining the information of the observed quantity represented by the temperature inside and on the surface of the thermal barrier coating system in combination with the determined boundary condition expression is as follows: Considering that the thermal radiation effect in the translucent coating is transmitted layer by layer to the remaining adjacent layers through the radiation heat flux density in the boundary conditions, when the finite volume method is used to discretize the regions of each layer, the local refinement technology is used to encrypt the grids in the areas near the boundaries of each layer in order to better capture the changes in the heat flux density at the boundaries caused by the thermal radiation effect of the translucent coating; on this basis, the control equations in each layer are volume integrated, simplified to obtain the corresponding discrete equations and solved, and finally the information of the observed quantity represented by temperature inside and on the surface of the thermal barrier coating system is obtained.

6. The synchronous estimation method for the thickness of thermally grown oxide and the thickness of defects in a thermal barrier coating according to claim 1, wherein When determining the observations and inversion intervals required to simultaneously estimate the thermally grown oxide thickness and defect thickness, Combined with the mutual influence mechanism of heat transfer between layers of the thermal barrier coating system, the influence mechanism of the internal thermal radiation effect in the semi-transparent coating on the remaining layers, and the parameter sensitivity analysis, the temperature at the contact surface between the semi-transparent coating and the external environment and the temperature at the contact surface between the substrate layer and the external environment are selected as the observables required for estimation. After determining the observables required for estimation, the inversion intervals required for estimating the thickness of the thermally grown oxide and the defect thickness are determined according to the sensitivity curves of the observables.

7. A method for synchronously estimating the thickness of thermally grown oxide and the thickness of defects in a thermal barrier coating according to claim 6, wherein When determining the objective function required for simultaneously estimating the thickness of the thermally grown oxide and the thickness of the defect based on the observation quantity required for simultaneously estimating the thickness of the thermally grown oxide and the thickness of the defect, In order to enhance the robustness of the estimation method and reduce the estimation error caused by the measurement error of the observed quantity caused by the environmental thermal interference noise in the thickness synchronization estimation process, the temperature term related to the thermal radiation effect of the semi-transparent coating is set in the objective function to reconstruct the objective function; The objective function is: the measured value of the observable of the real system corresponding to the true values of the thermally grown oxide thickness and the defect thickness and the observable value of the numerical heat transfer model of the thermal barrier coating system corresponding to a certain value of the parameter to be estimated during the estimation process The difference between them is expressed as: ， Wherein, is the true value of the thickness of the thermally grown oxide and the thickness of the defects, is the value of the thickness of the thermally grown oxide and the thickness of the defects during the estimation process; and are the temperatures at the contact surfaces of the semi-transparent coating with the external environment and the contact surfaces of the substrate layer with the external environment at the values under; and are and at the values under.

8. A method for synchronously estimating the thickness of thermally grown oxide and the thickness of defects in a thermal barrier coating according to claim 7, characterized in that Obtaining the measured values ​​of the real system observation quantities required for simultaneous estimation of the thermally grown oxide thickness and the defect thickness, when the thermally grown oxide thickness and the defect thickness are simultaneously estimated based on the inverse method, Measured values of observables of the real system , are obtained by adding noise that conforms to the random distribution law to the observable values , of the established numerical heat transfer model of the thermal barrier coating system. By changing the intensity of the random noise, different degrees of measurement errors of observables caused by environmental thermal interference noise in real situations can be simulated; The estimation based on the reverse method is to find the one that minimizes the objective function by means of the particle swarm optimization algorithm to achieve, and this minimum value is denoted as , which is the estimated value of the thickness of the thermally grown oxide and the thickness of the defects.

Images