Robustness evaluation method of air film hole based on flow parameter dimensionality reduction

Abstract

A robustness evaluation method for film holes based on flow parameter dimensionality reduction is proposed. This method is used to evaluate the robustness of cooling performance under the influence of laser-drilled film hole defects. The method consists of two uncertainty analyses, namely, prior estimation and deviation correction. The basic film hole defect uncertainty analysis framework is composed of the laser-drilled film hole defect model, the non-invasive chaotic polynomial uncertainty quantification method, and the k-nearest neighbor clustering algorithm to evaluate the robustness of performance under consistent film hole defects. Deviation correction includes extraction of main flow features, probability distribution evaluation of single film hole flow parameters, probability evaluation of total flow parameters, and flow parameter correction uncertainty quantification analysis. This method is easy to use, widely applicable, flexible in evaluation and analysis, and has low computational cost. In addition, this method is compatible with data results from multiple sources, which is more in line with the needs of aircraft engine turbine design engineers.

Description

Technical Field

[0001] The present invention belongs to the technical field of aero-engine turbine aero-thermal performance system design, and in particular relates to a film hole robustness evaluation method based on flow parameter dimensionality reduction, which is used for analyzing the robustness of aero-engine turbine cooling performance. Background Art

[0002] With the advancement and development of aviation technology, the turbine inlet temperature of some aviation gas turbine engines has approached 2000K. However, the ambient operating temperature that the materials used to manufacture turbines (such as nickel-based high-temperature alloys) can withstand is around 1300K. In order to ensure the performance and service life of aviation gas turbine engines, film cooling technology has been introduced into the design of aviation engine turbines and has been widely studied and applied by researchers and turbine engineers. Laser drilling is the main film hole processing and manufacturing process due to its high efficiency and low cost. The cylindrical film holes obtained by laser drilling are often accompanied by random geometric defects: the surface is rough and irregular, and accompanied by the conical characteristics of the inlet aperture of the film hole being larger than the outlet aperture. The traditional research method is to evaluate it as an ideal and determined cylindrical film hole, which undoubtedly causes deviations in the turbine performance and even life evaluation. Although the geometric defects caused by laser drilling have attracted the attention of researchers, related research is still rarely published, mainly due to the following reasons:

[0003] (1) The geometric characteristics of the air film holes obtained by laser drilling are complex and difficult to directly characterize and parameterize, which poses a great challenge to the performance evaluation of scientific researchers and turbine engineers.

[0004] (2) The geometric features of the air film holes made by laser drilling are random. An efficient and low-computational-cost uncertainty quantification algorithm is needed to evaluate the robustness of the aerodynamic, heat transfer and cooling performance of aircraft engines equipped with air film holes. Traditionally, the Monte Carlo simulation method can better evaluate the robustness of the aero-thermal performance of gas turbine engines, but for highly nonlinear problems, tens of thousands of sampling points are often required. Although the development of CFD has saved a lot of experimental time and cost, the current CFD evaluation of gas turbine engine performance still requires several or even more than ten hours, making it impossible for researchers to afford the computational cost of using Monte Carlo to evaluate the robustness of the aero-thermal performance of gas turbine engines.

[0005] (3) In modern advanced aircraft engine turbines, especially the first-stage nozzle guide vanes, there are often dozens or even hundreds of film holes on their surfaces. Considering the random variation of any film hole not only brings difficulties to geometric modeling, but also increases the computational complexity of robustness evaluation to an unacceptable level.

[0006] (4) The robustness evaluation of modern aircraft engines often requires multi-dimensional performance evaluation. However, when the geometry changes, it is difficult to ensure the consistency of the computational grid in CFD, which greatly limits the multi-dimensional robustness evaluation of aircraft engines. Summary of the invention

[0007] In order to overcome the shortcomings of the above-mentioned prior art, the purpose of the present invention is to provide a method for evaluating the robustness of film holes with reduced flow parameters, which greatly reduces the difficulty of evaluating the robustness of the thermal performance of aircraft engine turbines under the influence of defects in film holes formed by laser drilling, and is more in line with the needs of turbine cooling system designers.

[0008] In order to achieve the above object, the technical solution adopted by the present invention is:

[0009] A robustness evaluation method for air film holes based on flow parameter dimension reduction is characterized by comprising the following steps:

[0010] Step 1: Construct a parametric model of the defective film hole of the conical nozzle, and convert the geometric defects and their uncertainties caused by laser drilling into the inlet aperture D of the film hole. in and taper φ are two geometric uncertainty parameters;

[0011] Step 2: adopting the robustness evaluation method of aero-engine turbine aero-thermal performance, taking aerodynamic, heat transfer and cooling performance as random response results, and determining the uncertainty quantification sampling points according to the probability distribution of the geometric uncertainty parameters;

[0012] Step 3: Modify the cylindrical film hole in the computational geometry of the aero-engine into the parametric model of the defective film hole of the conical nozzle, and modify the geometric size of the film hole according to the uncertainty quantification sampling point to obtain the sampling point geometry; generate a corresponding three-dimensional computational grid for the sampling point geometry, i.e., the sampling point computational grid, and calculate the aerodynamic, heat transfer and cooling performance of the sampling point;

[0013] Step 4: Taking the computational geometry of the ideal cylindrical air film hole as the reference geometry and its CFD computational grid as the reference computational grid, the clustering algorithm is used to map the computational performance of the corresponding sampling points to the reference computational grid according to the spatial relationship between the computational grid of the sampling points and the reference computational grid;

[0014] Step 5: Feedback the calculated performance of the clustered sampling points to the evaluation method of the robustness of the aero-engine turbine thermal performance to construct a random surrogate model, and evaluate the robustness of the performance of interest through the random surrogate model, i.e., a priori prediction;

[0015] Step 6: Based on the a priori prediction, the flow parameters concerned by the aircraft engine are calculated, the random fluctuation probability distribution thereof under the influence of the random changes in the defective air film hole parameters is calculated, and the flow parameters exceeding the set threshold are selected as flow uncertainty parameters;

[0016] Step 7: Convert the geometric uncertainty parameters into flow uncertainty parameters;

[0017] Step 8: Use the fluctuation range of the flow uncertainty parameters obtained in step 7 to conduct a secondary evaluation and analysis on the robustness of the aerodynamic, heat transfer and cooling performance of the aircraft engine turbine, i.e., deviation correction.

[0018] Compared with the prior art, the present invention has the following beneficial effects:

[0019] (1) The present invention can study and analyze the robustness of the thermal performance of various aircraft engine turbines from multiple data sources.

[0020] (2) The present invention proposes a parametric model for characterizing cylindrical air film holes formed by laser drilling, which facilitates the performance evaluation of aircraft engines equipped with cylindrical air film holes formed by laser drilling.

[0021] (3) The present invention can evaluate the robustness of the performance of an aircraft engine provided with cylindrical air film holes formed by laser drilling at a relatively low computational cost.

[0022] (4) The present invention can ensure the consistency of the spatial characteristics of CFD calculation results, and then perform multi-dimensional and flexible robustness evaluation. BRIEF DESCRIPTION OF THE DRAWINGS

[0023] Figure 1 It is a flow chart of a method for evaluating robustness of air film holes based on flow parameter dimensionality reduction of the present invention.

[0024] Figure 2 It is a gas turbine end wall calculation model and calculation grid used in the embodiment.

[0025] Figure 3 It is a parameterized model of the conical nozzle defective air film hole in the embodiment.

[0026] Figure 4 : is the probability density distribution of the mass flow rate ratio under the influence of random changes of 20 air film holes upstream of the stator blade in the embodiment.

[0027] Figure 5 This is the robustness analysis of the end wall cooling performance under the condition of random fluctuation of the mass flow rate ratio in the embodiment. DETAILED DESCRIPTION

[0028] The embodiments of the present invention are described in detail below with reference to the accompanying drawings and examples.

[0029] The present invention is a robustness evaluation method for air film holes based on flow parameter dimension reduction, which realizes the robustness evaluation of air film hole performance through dual uncertainty analysis, namely, prior prediction and deviation correction. Figure 1 As shown, it mainly includes the following steps:

[0030] Step 1: Construct a parametric model of the defective film hole of the conical nozzle, and convert the geometric defects and their uncertainties caused by laser drilling into the inlet aperture D of the film hole. in And taper φ are two geometric uncertainty parameters, and the parameter variation range is determined according to the specific laser drilling process.

[0031] The cylindrical air film holes obtained by laser drilling are often accompanied by geometric defects: the surface is rough and irregular, and the inlet aperture of the air film hole is larger than the outlet aperture. To this end, the present invention proposes to construct a parametric model of conical nozzle defective air film holes based on the consistent air film hole inlet and outlet area ratio feature. The parametric model of conical nozzle defective air film holes has a consistent air film hole inlet and outlet area with the air film holes obtained by actual laser drilling, that is, a consistent inlet and outlet area ratio AR. The model is based on the inlet aperture of the air film hole (D in The random probability distribution of the inlet aperture and taper is determined by the actual processing technology.

[0032] Parameterized model of film hole with conical nozzle defect The inlet aperture D of the film hole in The area ratio AR is controlled parametrically by the taper φ, and the inlet aperture D in The random probability distribution of the taper φ is determined by the actual laser drilling process. The parameter variation range of the model is determined according to the laser drilling process, which is expressed as:

[0033]

[0034]

[0035] Where L is the length of the air film hole, D ex is the outlet aperture of the air film hole.

[0036] Step 2: Adopt the robustness evaluation method of aero-engine turbine aero-thermal performance, take the aerodynamic, heat transfer and cooling performance as the random response results, and determine the uncertainty quantification sampling points according to the probability distribution of the uncertainty parameters.

[0037] Taking the aerodynamic, heat transfer and cooling performance as the random response results of the physical model, the robustness evaluation method of the aero-thermal performance of the aircraft engine turbine can realize the robustness evaluation of the performance under the conditions of multiple uncertainty parameter dimensions, multiple uncertainty sources and multiple uncertainty probability distributions. This step uses the aforementioned geometric uncertainty parameters as uncertainty inputs, and determines the optimal sampling points according to the robustness evaluation method of the aero-thermal performance of the aircraft engine turbine. The robustness evaluation method of the aero-thermal performance of the aircraft engine turbine constructs a random proxy model with the non-invasive chaotic polynomial (NIPCE) as the core, selects the optimal sampling points according to the probability distribution of the uncertainty parameters, and solves the aerodynamic, heat transfer and cooling performance of the aircraft engine, that is, the random response result y of the calculation geometry is considered under the consideration of the actual air film hole defects, and then a robustness evaluation that meets engineering accuracy is realized with a small sample size. This method constructs a d-dimensional hyperplane space according to the number of uncertain parameters d, and determines the orthogonal polynomial basis function according to the probability density function followed by the uncertainty parameters. The non-invasive chaotic polynomial is expressed as follows:

[0038]

[0039] In the formula, represents d uncertain parameters, are the coefficients of the polynomials, and I represents a series of orthogonal polynomial bases.

[0040] In the robustness evaluation of aero-engine thermal and cooling performance, the third-order chaotic polynomial is usually sufficient to meet the calculation accuracy of engineering design, then:

[0041]

[0042] In the formula, P represents the number of terms of the polynomial under d-dimensional uncertain parameters and q-order accuracy, and its calculation formula is as follows:

[0043]

[0044] Ψ j (ξ) represents the jth orthogonal polynomial basis with ξ as input, i.e., I j (ξ i1 ,ξ i2 ,ξ i3 ,…). Then the full tensor product method is used to solve the required sampling point combination of uncertain parameters. The number of sampling points (under the third-order chaotic polynomial) is 4 d The coefficients of the chaotic polynomial are calculated using the Galerkin projection method in the spectral method and the corresponding calculation performance under the sampling point combination:

[0045]

[0046] Where Ω represents the probability space of uncertainty parameter ξ, and ρ(ξ) represents the joint probability density function of uncertainty parameter ξ.

[0047] After the above operations, the non-invasive chaotic polynomial equation (NIPCE) can be constructed and used for the robustness evaluation of aero-engine turbine aero-thermal performance.

[0048] This method uniformly converts the uncertainty sources into uncertainty parameters in a non-invasive form as input parameters for the robustness evaluation method of aircraft engine turbine aero-thermal performance, and flexibly constructs chaotic polynomials based on the number d of uncertainty parameters and the probability density function of uncertainty parameters. Therefore, the robustness evaluation of aerodynamic, heat transfer and cooling performance can be realized under flexible conditions of multiple uncertainty parameter dimensions, multiple uncertainty sources and multiple uncertainty probability distributions through the robustness evaluation method of aircraft engine turbine aero-thermal performance.

[0049] Specifically, in step 1, the geometric defects and their uncertainties caused by laser drilling are converted into the inlet aperture D of the film hole through the parametric model of the conical nozzle defect film hole. in and taper φ are two geometric uncertainty parameters. in The two geometric uncertainty parameters and the corresponding probability density distribution of taper φ are used as input parameters to construct the chaotic polynomial, and the full tensor product method is used to solve the required inlet aperture D. in The chaotic polynomial to be constructed can be expressed as follows:

[0050]

[0051] Formula (6) is a random proxy model constructed in the form of chaotic polynomials, which is based on the inlet aperture D in The two geometric uncertainty parameters of φ and taper φ are used as inputs, and the random response result y of the computational geometry of the aerodynamic, heat transfer and cooling performance of the aircraft engine under the actual consideration of the film hole defects is directly obtained by substituting them into formula (6).

[0052] Step 3: According to the uncertain quantitative sampling points, the geometric part of the film hole in the computational geometry is corrected, that is, the cylindrical film hole in the computational geometry of the aero-engine is modified to the parametric model of the conical nozzle defective film hole, and the geometric size of the film hole is modified according to the uncertain quantitative sampling points to obtain the sampling point geometry; generate a corresponding three-dimensional computational grid for the sampling point geometry, that is, the sampling point computational grid, and use CFD software to calculate the aerodynamic, heat transfer and cooling performance of the sampling point.

[0053] In the present invention, computational geometry is the geometric model of the aircraft engine. In this step, defective film holes are modeled so that the geometric features of all film holes in a sampling point geometry remain consistent, that is, the same film hole inlet aperture and taper, and then CFD is called for calculation.

[0054] Specifically, according to the inlet aperture D obtained by the full tensor product solution in step 2 in The sampling point geometry is modified by the sampling point combination composed of the ideal cylindrical air film hole and the taper φ. That is, the original computational geometry using the ideal cylindrical air film hole is changed to the computational geometry using the conical nozzle defective air film hole. It is particularly important to ensure that the geometric features of all conical nozzle defective air film holes in the sampling point geometry are consistent, that is, the inlet aperture D of each defective air film hole in each sampling point geometry in and taper φ are the inlet aperture D in the corresponding sampling point combination in And taper φ.

[0055] Then, a three-dimensional computational grid (i.e., sampling point computational grid) is generated for each sampling point geometry using mesh generation software (such as ICEM, fluent meshing, etc.), and the corresponding aerodynamic, heat transfer, and cooling performance (i.e., sampling point computational performance) is calculated using CFD software.

[0056] Step 4: For each sampling point, evaluate its similarity with the grid of the benchmark condition (i.e., the calculation condition of the ideal cylindrical hole), and cluster each sampling point grid onto the calculation grid of the benchmark condition to ensure that the spatial characteristics of the calculation results are consistent.

[0057] This step uses the computational geometry of the ideal cylindrical film hole as the reference geometry, and its CFD computational grid as the reference computational grid. In order to achieve a multi-dimensional and flexible robustness evaluation of aero-engine performance, it is necessary to ensure that the spatial characteristics of the performance indicators extracted from each sample are consistent. Because the geometric dimensions of the conical nozzle defect film holes in the sampling point geometry are inconsistent, the grid nodes of the corresponding generated sampling point computational grids are also difficult to correspond to each other. The sampling point computational performance can only directly obtain the performance at the sampling point computational grid (grid node). To this end, the k-nearest neighbor clustering algorithm (kNN) is used to process the performance of each sampling point, and the corresponding sampling point performance is mapped to the reference computational grid according to the spatial relationship between the sampling point computational grid and the reference computational grid; after the above operation, subsequent calculations and evaluations can be performed under the same computational grid (grid node), and the spatial characteristics of the computational performance of each sampling point are consistent. The sampling point computational performance proposed in the present invention is the performance after being processed by the k-nearest neighbor clustering algorithm and mapped to the reference computational grid.

[0058] Specifically, in the parameterized model of the film hole with conical nozzle defect, the inlet aperture D of the film hole is inand the random changes of taper φ are used to characterize the geometric uncertainty of the actual defective film hole. Therefore, the geometric features of the defective film holes of the conical nozzle in the sampling point geometry are inconsistent with each other, which leads to the inconsistency of the corresponding generated sampling point calculation grids, that is, the spatial coordinates of the grid nodes are not one-to-one corresponding. The sampling point calculation performance can only directly obtain the performance at the sampling point calculation grid (grid node). This is inconsistent with the consistency of the spatial coordinates of the calculation performance of each sampling point required for the multi-angle flexible aviation engine performance robustness evaluation. To solve this problem, the computational geometry of the ideal cylindrical film hole is first used as the reference geometry, and the corresponding generated three-dimensional calculation grid is used as the reference grid. Then, the k-nearest neighbor clustering algorithm (kNN) is used to process the calculation performance of each sampling point, and the sampling point calculation performance is mapped to the reference calculation grid according to the spatial relationship between the corresponding sampling point calculation grid and the reference calculation grid. The specific process of k-nearest neighbor clustering is as follows (taking the geometry of the i-th sampling point as an example, hereinafter referred to as the sampling point geometry G i ):

[0059] Based on the sampling point geometry G i The generated sampling point calculation grid M i , the number of grid nodes is N mesh Mi The number of grid nodes of the benchmark computational grid (using the computational geometry of an ideal cylindrical air film hole) is N mesh ideal Calculate M i The spatial similarity L2 between each grid node in the reference calculation grid and each grid node in the reference calculation grid is calculated. The spatial similarity evaluation index uses the Cartesian distance. The specific formula is as follows:

[0060]

[0061] In the formula, x i ideal and x j Mi They represent the spatial coordinates of the i-th grid node in the reference grid and the j-th grid node in the sampling point calculation grid. The superscript l represents the spatial dimension, which is 2 for a two-dimensional calculation grid and 3 for a three-dimensional calculation grid.

[0062] Select and x i ideal The k M with the highest similarity (closest distance) i The selection of k is based on the geometry type of the computational grid and the number of corresponding grid nodes, such as 4 for tetrahedral grids and 8 for hexahedral grids. The clustering calculation formula is as follows:

[0063]

[0064] In the formula, g(xi ideal ) are the k M with the highest similarity i The computational performance on the grid nodes in g(x p Mi ) is mapped to the i-th grid node x in the base grid i ideal The computational performance after spatial coordinates. p is the similarity / distance weight.

[0065] In addition, in high-fidelity aero-engine turbine CFD calculations, the number of computational grids (N mesh ) is often as high as millions or even tens of millions. It is directly possible to use a linear scan algorithm or a brute force search algorithm to find the k grid nodes with the highest similarity (the computational complexity is O(N mesh 2 )), which means at least one trillion calculations, and such a high number of calculations will significantly reduce the efficiency of the algorithm. Therefore, the kd tree algorithm is used to construct the data structure of the similarity between the reference grid and the sampling point calculation grid, thereby reducing the algorithm complexity to O(N mesh logN mesh ).

[0066] Step 5: Feedback the performance of the clustered sampling points (with consistent spatial features) to the NIPCE in the evaluation method of the robustness of the aero-engine turbine thermal performance, and then construct a random surrogate model to evaluate the robustness of the performance of interest, i.e., a priori prediction.

[0067] Specifically, the calculation performance of the sampling points processed by the k-nearest neighbor clustering algorithm in step 4 is provided to the robustness evaluation method of the aero-engine turbine thermal performance in step 2, that is, the calculation performance of the sampling points is used as the y value in formula (5), and the coefficient α of the chaotic polynomial is solved by formula (5) j , and then complete the construction of the random agent model of chaotic polynomial form (NIPCE), that is, formula (6).

[0068] Through the random surrogate model, i.e., formula (6), the robustness of the performance of interest (such as aerodynamics, heat transfer and cooling performance of the aircraft engine) is calculated, i.e., a priori prediction.

[0069] At this time, the constructed random proxy model realizes the geometric parameters (D in The mapping relationship between φ and the performance of interest. That is, each input of a set of geometric parameters within the tolerance range (D inand φ) can be obtained by the random proxy model (Formula (6)) to obtain the aerodynamic, heat transfer and cooling performance indicators of the corresponding aircraft engine. In addition, the geometric parameters of the defective film hole of the conical nozzle (inlet aperture D in The performance statistical moments of aircraft engines with a taper (φ) within their probability distribution (such as the mean, variance, standard deviation, etc. of aerodynamic, heat transfer and cooling performance).

[0070] Step 6: Based on the prior prediction, that is, the influence of the uncertainty of the defective air film hole obtained in step 5 on the flow parameters, calculate the flow parameters of concern to the aircraft engine (such as flow coefficient, momentum flow rate ratio, mass flow ratio, etc.) and their fluctuation range, compare the differences between the ideal cylindrical air film hole and the conical nozzle defective air film hole, and calculate the random fluctuation probability distribution under the influence of random changes in the defective air film hole parameters, and use the set threshold to screen the flow parameters. If the ratio of the standard deviation of a flow parameter to its mean exceeds the threshold, the random fluctuation of the flow parameter is considered to obtain the flow uncertainty parameter; if it does not exceed the threshold, the random fluctuation is ignored and only considered as a determined value.

[0071] In this step, the flow parameters affected by the air film hole defect and their variation range are determined through the robustness analysis results. At this time, since the geometric features of all air film holes are consistent, the impact on the flow parameters is consistent, that is, the random proxy model constructed in the prior prediction can be used to evaluate the impact of a single defective air film hole on performance robustness.

[0072] Specifically, based on the influence of the defective film holes of the conical nozzle obtained in step 5 and their geometric uncertainty on the aerodynamic parameters, the important flow parameters FR of the aeroengine (such as the flow coefficient Cd, the momentum flow rate ratio I, the mass flow ratio MFR) and their fluctuation range are calculated. At this time, since the geometric parameters of each defective film hole are consistent, the above-mentioned aerodynamic parameters are uniformly affected by the defective film holes at any position. That is, the random proxy model constructed in step (5) can be used to calculate the influence of a single defective film hole of a conical nozzle on the flow parameter performance.

[0073] At this time, formula (6) can be written as:

[0074]

[0075] Taking the flow coefficient Cd, momentum flow rate ratio I, and mass flow ratio MFR as examples:

[0076]

[0077] Geometric parameters of defective air film holes in a single conical nozzle (inlet aperture D in Under the random changes of the flow coefficient (Cd), momentum flow rate ratio (I), mass flow ratio (MFR) and their fluctuation probability distribution of the aircraft engine are calculated as follows:

[0078] Assuming that the processing of each air film hole obeys independent and identical distribution, Latin hypercube sampling is used to randomly generate multiple groups of sample points within the variation range of the air film hole inlet aperture and taper, that is, the random value combination of the inlet aperture and taper within the tolerance range (the specific number of sample points is based on the convergence of the statistical characteristics of the calculation problem, and 1000000 is recommended). The generated sample points are substituted into formula (9) in turn to obtain the corresponding flow parameters, and the calculated flow parameters are statistically analyzed using the Monte Carlo method to obtain the probability distribution of flow parameter fluctuations.

[0079] The flow parameters are then screened. If the ratio of the standard deviation of a flow parameter to its mean exceeds 5%, the random fluctuation of the flow parameter is considered, that is, the flow uncertainty parameter. If it is less than 5%, the random fluctuation of the flow parameter is ignored and only considered as a determined value.

[0080] Step 7: Based on the idea of ​​flow parameter dimensionality reduction, the high-dimensional geometric uncertainty parameters are converted into the flow uncertainty parameters.

[0081] If the aircraft engine is equipped with N hole When the parametric model of the conical nozzle defect film hole is adopted, the number of geometric uncertainty parameters is 2×N. hole According to step (2), it can be estimated that the number of sampling points required to construct a random proxy model with chaotic polynomial as the core is 4 2×Nhole This computational cost is unacceptable for aircraft engine engineering design.

[0082] Assuming that the quality of the air film holes obtained by laser drilling follows an independent and identical distribution, the impact of random changes in all air film holes on the overall flow parameters is evaluated as follows: Latin hypercube sampling is used to randomly generate multiple groups of sample points within the range of the change in the inlet aperture and taper of the air film hole (the specific number of sample points depends on the convergence of the statistical characteristics of the calculation problem, and 1000000 is recommended). Each group of sample points consists of N hole The number of film holes in the calculation geometry of the aircraft engine turbine and the control parameters of the conical nozzle model (the diameter of the film hole inlet D in and taper φ), that is, (2×N hole The process aims to generate a set of random inlet apertures and tapers for each air film hole.

[0083] The inlet aperture D of each defective air film hole in each sample point in Substitute the taper φ into formula (9) to calculate the flow parameters screened in step 6, that is, the influence of a defective air film hole in the sample point on the flow parameters. hole The air film holes are executed in sequence, and the obtained N holeThe flow parameters of the group (after screening in step 6) are summed or averaged to obtain the overall impact of the sample on the flow parameters.

[0084] Then, Monte Carlo simulation is used to statistically analyze the overall performance of the generated multiple groups of sample points, and the probability density distribution of flow parameter fluctuations caused by air film hole defects can be obtained. At this time, since the calculation of the random proxy model with chaotic polynomial as the core (i.e., formula (9)) is an algebraic calculation, even if the above operation is performed for estimation, the time cost required is much less than the time required for a single CFD evaluation.

[0085] Through the above operation, we can obtain hole Defective air film holes (air film hole inlet diameter D in The overall impact and range of the flow parameters caused by the independent random changes of the taper φ within the tolerance range. In actual aircraft engines, there are usually dozens or even hundreds of air film holes, that is, there are dozens or even hundreds of defective air film holes with geometric uncertainty. This means that dozens or even hundreds of geometric uncertainty parameters are converted into several flow parameter uncertainties under their influence (after screening in step 6, the flow parameters with random fluctuations need to be considered).

[0086] It should be noted that since the independent random changes in the geometry of defective air film holes at any position are taken into account, the obtained probability distribution of flow parameters is inconsistent with the probability distribution of flow parameters in step (5) assuming that the geometric characteristics of all defective air film holes are consistent, that is, the probability distribution of flow distribution is corrected.

[0087] Step 8: Use the flow uncertainty parameters and their fluctuation probabilities determined in step 7 to conduct a secondary evaluation and analysis of the robustness of the aerodynamic, heat transfer, and cooling performance of the aircraft engine turbine, i.e., deviation correction.

[0088] Specifically, the fluctuation range of the flow uncertainty parameters obtained in step 7 is used as the uncertainty input. Combined with the robustness evaluation method of the aero-engine turbine aerodynamic and thermal performance and the k-nearest neighbor clustering algorithm, a secondary robustness evaluation is performed on the aerodynamic, heat transfer, and cooling performances of the aero-engine turbine after the flow parameters are corrected, i.e., deviation correction.

[0089] In one embodiment of the present invention, the robustness analysis of the end wall aero-thermal performance is conducted using the first stage stator blade of a gas turbine. The calculation model is as follows: Figure 2As shown. A double row of discrete cylindrical film holes (20 in total) are arranged upstream of the stationary blades. Considering that the cylindrical film holes are processed by laser drilling and have typical conical features and random fluctuations in geometric features. This embodiment evaluates and analyzes the robustness of the end wall cooling performance in this case. In this embodiment, the probability density distribution of the inlet aperture and taper in the parametric model of the conical nozzle refers to the statistical data in the literature, and its corresponding parameters are shown in Table 1, and its schematic diagram is shown in Figure 3 shown.

[0090] Table 1 Conical nozzle model parameters and their variation range

[0091]

[0092] Reference Figure 1 The evaluation method of this embodiment includes the following steps:

[0093] 1. Determine the parameter variation range of the conical nozzle parametric model

[0094] In this embodiment, the probability density distribution of the inlet aperture and taper in the tapered nozzle parameterized model refers to the statistical data in the literature, and the corresponding parameters are shown in Table 1.

[0095] 2. Construct a chaotic polynomial (NIPCE) based on the robustness evaluation method of aircraft engine turbine thermal performance.

[0096] In this embodiment, the first stage is a priori prediction, which directly quantifies the uncertainty of the parameter changes of the conical nozzle parameterized model. The parameters of the conical nozzle parameterized model are the inlet aperture and the taper, so the dimension is two-dimensional. Considering the accuracy and computational cost required for the project, the non-intrusive generalized chaotic polynomial adopts third-order accuracy (q=3). The random response results are expressed as follows using the non-intrusive generalized chaotic polynomial method:

[0097]

[0098] The optimal sampling point combination of inlet aperture and taper is determined according to the probability distribution and NIPCE in Table 1.

[0099] 3. According to the sampling point combination generated in 2, the 20 discrete air film holes upstream of the stator are modeled and made to have consistent hole geometric characteristics. Then, the CFD software is called for mesh generation and performance prediction.

[0100] 4. Clustering of sample point calculation results

[0101] Since the geometric features of the defective air film holes in each group of sample points are inconsistent, it is difficult to keep the corresponding generated computational grids consistent. In order to perform multi-dimensional and flexible robustness analysis, it is necessary to unify them to the same spatial features, such as mapping the calculation results of each group of sample points to the same set of calculation coordinates. In this embodiment, the calculation geometry and calculation grid of the ideal cylindrical air film hole are used as the benchmark, and the calculation results of each group of samples are clustered onto the benchmark calculation grid.

[0102] 5. Constructing NIPCE random proxy model and robustness evaluation (prior prediction)

[0103] The film hole flow coefficient, mass flow rate ratio, momentum flow rate ratio, etc. obtained at each sample point are fed back to the robustness evaluation method of the aero-engine turbine aero-thermal performance, and then the corresponding NIPCE stochastic surrogate model is constructed. The robustness of the film hole flow coefficient, cold air inlet mass flow rate, momentum flow rate ratio, etc. is evaluated through the constructed NIPCE stochastic surrogate model.

[0104] 6. Screen out the key geometric parameters affected by the random changes in the geometric characteristics of the defective air film holes, and determine their random fluctuation probability distribution

[0105] Table 2 gives the selected key flow parameters and their fluctuation ranges. It can be seen from the table that the fluctuation range of the momentum flow rate ratio is small (less than the set threshold of 5%), and has little effect on the aero-thermal performance of the first-stage stator end wall, so its fluctuation is ignored. However, the defective film holes have a greater impact on the momentum flow rate ratio, so the momentum flow rate ratio is set to 4.78 as one of the flow parameter conditions for the secondary robustness evaluation. The mass flow rate ratio listed in Table 2 is the overall value of the 20 discrete holes upstream. Since the geometric parameters of each film hole are consistent, the mass flow rate ratio of a single hole is 1 / 20 of that in Table 2. Thus, the values ​​and probability distributions of the key flow parameters (momentum flow rate ratio, mass flow rate ratio) under the influence of film hole defects are obtained.

[0106] Table 2 Flow parameters under ideal conditions and uncertainty conditions

[0107]

[0108] 7. Based on the idea of ​​flow parameter dimensionality reduction, high-dimensional geometric uncertainty parameters are converted into a small number of aerodynamic uncertainty parameters.

[0109] Assuming that the quality of the air film holes obtained by laser drilling follows an independent and identical distribution, the impact of random changes in all air film holes on the overall flow parameters is evaluated as follows: 1,000,000 groups of sampling points are randomly generated within the range of the air film hole inlet aperture and taper using Latin hypercube sampling. Each group of sampling points consists of 20 pairs of conical nozzle model control parameters (air film hole inlet aperture D inThe process aims to generate a set of random inlet aperture and taper for each air film hole.

[0110] The NIPCE random proxy model corresponding to the mass flow rate ratio in the prior prediction is used to calculate the influence of each random defect air film hole in each sampling point, that is, the mass flow rate ratio of a single hole at the sampling point. Then, the mass flow rate ratio under the influence of 20 air film holes is summed, that is, the overall mass flow rate ratio of the sampling point.

[0111] Monte Carlo simulation is then used to statistically analyze the overall mass flow rate ratio of the generated 1,000,000 sets of sampling points to obtain the probability density distribution of the overall mass flow rate ratio caused by the air film hole defect. The results are as follows: Figure 4 The above process only takes a few minutes for a single core to obtain the probability distribution of the mass flow rate ratio under the influence of random changes in all air film hole geometric parameters, which is much less than the dozens of cores required for a single CFD calculation in this embodiment.

[0112] At this time, the robustness evaluation problem of this embodiment is transformed from the original 40-dimensional (2×20) geometric uncertainty problem to a 1-dimensional overall mass flow rate random fluctuation problem.

[0113] 8. Robustness evaluation of aerodynamic, heat transfer and cooling performance of aircraft engine turbines under flow parameter fluctuations

[0114] The momentum flow rate ratio I = 4.78 is used as the flow parameter constraint. Figure 4 The mass flow rate ratio shown in is the uncertainty input. Combining the robustness evaluation method of aero-engine turbine aero-thermal performance and the k-nearest neighbor clustering algorithm, a secondary robustness evaluation of the aerodynamic, heat transfer, and cooling performance of the aero-engine turbine after the flow parameters are corrected is performed, i.e., deviation correction. The evaluation results are shown in Figure 5 shown.

[0115] Depend on Figure 5 It can be seen that there is a significant difference between the cooling performance of the end wall under the condition of aerodynamic parameter fluctuation and the cooling performance under the condition of an ideal cylindrical hole. And the main cooling performance fluctuation mainly occurs downstream of the end wall throat. The present invention can help researchers and aeroengine design engineers to perform robustness analysis of structural design, and then guide the robustness design of aeroengine turbines, and has extremely high engineering application value.

Claims

1. A robustness evaluation method for air film holes based on flow parameter dimension reduction, characterized in that: The following steps are involved: Step 1: Construct a parametric model of the defective film hole of the conical nozzle, and convert the geometric defects and their uncertainties caused by laser drilling into the inlet aperture D of the film hole. in and taper φ are two geometric uncertainty parameters; Step 2: adopting the robustness evaluation method of aero-engine turbine aero-thermal performance, taking aerodynamic, heat transfer and cooling performance as random response results, and determining the uncertainty quantification sampling points according to the probability distribution of the geometric uncertainty parameters; Step 3: Modify the cylindrical film hole in the computational geometry of the aero-engine into the parametric model of the conical nozzle defect film hole, and modify the geometric dimensions of the film hole according to the uncertainty quantification sampling point to obtain the sampling point geometry; Generating a corresponding three-dimensional computational grid for the sampling point geometry, i.e., the sampling point computational grid, and calculating the aerodynamic, heat transfer, and cooling performance of the sampling point; Step 4: Taking the computational geometry of the ideal cylindrical air film hole as the reference geometry and its CFD computational grid as the reference computational grid, the clustering algorithm is used to map the computational performance of the corresponding sampling points to the reference computational grid according to the spatial relationship between the computational grid of the sampling points and the reference computational grid; Step 5: Feedback the calculated performance of the clustered sampling points to the evaluation method of the robustness of the aero-engine turbine thermal performance to construct a random surrogate model, and evaluate the robustness of the performance of interest through the random surrogate model, i.e., a priori prediction; Step 6: Based on the a priori prediction, the flow parameters concerned by the aircraft engine are calculated, the random fluctuation probability distribution thereof under the influence of the random changes in the defective air film hole parameters is calculated, and the flow parameters exceeding the set threshold are selected as flow uncertainty parameters; Step 7: Convert the geometric uncertainty parameters into flow uncertainty parameters; Step 8: Use the fluctuation range of the flow uncertainty parameters obtained in step 7 to conduct a secondary evaluation and analysis on the robustness of the aerodynamic, heat transfer and cooling performance of the aircraft engine turbine, i.e., deviation correction.

2. The robustness evaluation method for air film holes based on flow parameter dimensionality reduction according to claim 1 is characterized in that: In the step 1, the parameterized model of the conical nozzle defect film hole has the same film hole inlet and outlet areas as the film hole obtained by actual laser drilling, that is, the same inlet and outlet area ratio AR; the parameter variation range of the model is determined according to the laser drilling process; Where, L is the length of the air film hole, D ex is the outlet aperture of the air film hole.

3. The robustness evaluation method for air film holes based on flow parameter dimensionality reduction according to claim 1 is characterized in that: In step 2, the robustness evaluation method for the aero-engine turbine thermal performance is to construct a random proxy model with a non-invasive chaotic polynomial as the core, and the inlet aperture D of the air film hole is in The two geometric uncertainty parameters and the corresponding probability density distribution of taper φ are used as input parameters to construct the chaotic polynomial, and the full tensor product method is used to solve the required inlet aperture D. in and the uncertainty quantification sampling point combination composed of the taper φ.

4. The robustness evaluation method for air film holes based on flow parameter dimensionality reduction according to claim 1 is characterized in that: In step 3, the geometric features of all defective air film holes of the conical nozzle in each sampling point geometry are ensured to be consistent, that is, the inlet aperture D of each defective air film hole in each sampling point geometry is in and taper φ are the inlet aperture D in the corresponding sampling point combination in And taper φ.

5. The robustness evaluation method for air film holes based on flow parameter dimensionality reduction according to claim 1 is characterized in that: In step 4, the clustering algorithm is the k-nearest neighbor clustering algorithm. For the i-th sampling point geometry G i , which is the sampling point calculation grid M i , the clustering method is as follows: Calculate M i The spatial similarity between each grid node in the and each grid node in the benchmark computational grid; Select the spatial coordinate x of the i-th grid node in the benchmark calculation grid i ideal The nearest k M i Cluster the grid nodes in and get the k M nodes with the highest similarity. i The computational performance on the grid nodes in is mapped to the i-th grid node x in the benchmark grid. i ideal Computational performance after spatial coordinates.

6. The robustness evaluation method for air film holes based on flow parameter dimensionality reduction according to claim 1 is characterized in that: In step 5, the calculated performance of the clustered sampling points is used as the random response result y in the robustness evaluation method of the aero-engine turbine thermal performance, and its chaotic polynomial coefficient α is solved. j : Thus, a random agent model in the form of chaotic polynomial is constructed: In the formula, P represents the number of terms of the polynomial under d-dimensional uncertain parameters and q-order accuracy, and its calculation formula is as follows: Ψ j (ξ) represents the jth orthogonal polynomial basis with ξ as input, i.e., I j (ξ i1 ,ξ i2 ,ξ i3 ,…), Ω represents the probability space of uncertainty parameters ξ, and ρ(ξ) represents the joint probability density function of uncertainty parameters ξ.

7. The robustness evaluation method for air film holes based on flow parameter dimensionality reduction according to claim 1 is characterized in that: In step 6, based on the influence of the defective film hole of the conical nozzle and its geometric uncertainty on the aerodynamic parameters obtained by prior prediction, the flow parameters of the aeroengine and their fluctuation probability distribution are calculated as follows when the geometric parameters of the defective film hole of the conical nozzle vary randomly: Latin hypercube sampling is used to randomly generate multiple groups of sample points within the variation range of the inlet aperture and taper of the air film hole, that is, the random value combination of the inlet aperture and taper within the tolerance range. The generated sample points are substituted into the following formula in turn to obtain the corresponding flow parameters: Calculate the flow parameters FR of aircraft engines and their fluctuation range; The Monte Carlo method is used to perform statistical analysis on the obtained flow parameters and obtain the probability distribution of flow parameter fluctuations.

8. The robustness evaluation method for air film holes based on flow parameter dimensionality reduction according to claim 1 is characterized in that: The method for selecting the flow parameters exceeding the set threshold value as the flow uncertain parameters in step 6 is: If the ratio of the standard deviation of a flow parameter to its mean exceeds the set threshold, the random fluctuation of the flow parameter is considered, that is, the flow uncertainty parameter. If it does not exceed the set threshold, the random fluctuation of the flow parameter is ignored and only considered as a determined value.

9. The robustness evaluation method for air film holes based on flow parameter dimensionality reduction according to claim 1 is characterized in that: In step 7, Latin hypercube sampling is used to randomly generate multiple groups of sample points within the variation interval of the geometric uncertainty parameter, and each group of sample points consists of N hole The random value composition of the geometric uncertainty parameter; the inlet aperture D of each defective air film hole in each sample point in Substitute the taper φ into the following formula: The screened flow uncertainty parameters are calculated, that is, the influence of a defective air film hole in the sample point on the flow parameters; each air film hole in the sample point is executed in turn, and the obtained N hole The flow parameters of the group are summed or averaged to obtain the overall influence of the sample on the flow parameters; Finally, Monte Carlo simulation is used to statistically analyze the overall performance of multiple groups of sample points generated, and the probability density distribution of flow parameter fluctuations caused by air film hole defects is obtained.

10. The robustness evaluation method for air film holes based on flow parameter dimensionality reduction according to claim 1, characterized in that: In the step 8, the fluctuation range of the flow uncertainty parameter obtained in the step 7 is used as the uncertainty input, and the robustness evaluation method of the aero-engine turbine aero-thermal performance and the k-nearest neighbor clustering algorithm are combined to perform a secondary robustness evaluation on the aerodynamic, heat transfer and cooling performance of the aero-engine turbine after the flow parameters are corrected, i.e., deviation correction.

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