A method and system for multi-factor sensitivity analysis of turbine blade cooling

Abstract

The application discloses a kind of turbine blade cooling multi-factor sensitivity analysis method and system.The method comprises: establishing value interval and probability distribution for each input parameter, and first round sampling is carried out, to obtain multiple samples.CFD simulation is carried out on the blade geometry model corresponding to each sample respectively.The simulation result is used to train the proxy model.The second round sampling is carried out to each input parameter, and the sample is input into the proxy model to predict the corresponding blade thermal response index.The statistical characteristics of the quantified blade thermal response index uncertainty are extracted.The first-order sensitivity index of each input parameter, total effect sensitivity index, the sensitivity ranking of each input parameter change is calculated.The application trains the proxy model by a small amount of sample CFD simulation, and then uses the proxy model to replace large-scale CFD simulation, effectively reduces the calculation amount and time cost, so as to efficiently complete turbine blade uncertainty quantification and sensitivity analysis under the condition of limited resources.

Description

Technical Field

[0001] This invention belongs to the field of turbine blade parameter analysis technology, specifically relating to a method and system for analyzing the multi-factor sensitivity of turbine blade cooling. Background Technology

[0002] Since the advent of aero engines, gas turbine engines, as the core component of aero propulsion systems, have undergone over a century of technological innovation and development. To improve the thermal efficiency and power output of gas turbine engines, this is typically achieved by increasing the turbine inlet temperature. However, with the continuous rise in turbine inlet temperature, the heat carried by the high-temperature gas entering the turbine blades increases significantly, leading to a substantial increase in the thermal stress on the blades, directly affecting their service life and operational reliability. Therefore, efficient cooling technologies must be employed to effectively cool the turbine blades to ensure their normal operation in high-temperature environments and prevent failure or even erosion damage due to overheating.

[0003] In actual operation, the flow and heat transfer characteristics of turbine blades are significantly affected by a variety of uncertainties. These factors include fluctuations in engine operating conditions, differences in material properties, geometric machining errors, and changes in external environmental conditions. These uncertainties not only lead to fluctuations and instability in blade cooling effects but may also weaken the overall performance of the blades and even pose a potential threat to engine safety. For example, in film cooling, the cooling effect may change significantly due to fluctuations in cooling airflow, temperature differences, or changes in gas pressure. If these uncertainties are not effectively suppressed or assessed, localized overheating on the blade surface can easily occur, leading to serious damage or even functional failure.

[0004] Therefore, how to scientifically quantify these uncertainties and consider them in the design and optimization of turbine blade cooling systems has become a key issue in ensuring their long-term stable operation under complex conditions. Based on this, current research is gradually shifting from simply improving cooling efficiency to focusing on the quantification and analysis of uncertainties, in order to ensure the stability and reliability of turbine blade cooling performance in complex operating environments. Summary of the Invention

[0005] The purpose of this invention is to provide a method and system for multi-factor sensitivity analysis of turbine blade cooling. This method combines computational fluid dynamics (CFD) simulation to establish a surrogate model and performs uncertainty quantification and sensitivity analysis on the cooling effect of turbine blades under different operating conditions and geometric machining errors, thereby obtaining the effect law and contribution of each operating condition parameter and geometric parameter on the blade cooling performance.

[0006] In a first aspect, the present invention provides a method for multi-factor sensitivity analysis of turbine blade cooling, comprising: Multiple input parameters are selected from the operating and / or geometric parameters of the turbine blades. Value ranges and probability distributions are established for each input parameter, and a first round of sampling is performed to obtain multiple samples.

[0007] CFD simulations were performed on the blade geometry model corresponding to each sample to obtain the blade thermal response indices for different samples; each sample and its corresponding blade thermal response indices constituted a dataset. A surrogate model based on the Kriging model was trained using this dataset.

[0008] A second round of sampling is performed on each input parameter, and the resulting samples are input into the surrogate model to predict the corresponding blade thermal response index. Statistical characteristics of the uncertainty in the quantified blade thermal response index are extracted. These statistical characteristics include variance. .

[0009] For each input parameter The variance of the blade thermal response index was calculated with the blade itself remaining constant and other parameters varying. The variance of the blade's thermal response index with its own changes and other parameters remaining constant. .

[0010] Variance With variance The ratio of the two values ​​is used as a first-order sensitivity index. ; take variance With variance The ratio of the two values ​​is used as the sensitivity index of the total effect. .

[0011] Using the first-order sensitivity index and / or total effect sensitivity index The sensitivity of the blade thermal response index to changes in various input parameters was ranked.

[0012] Preferably, the number of samples in the first round of sampling is 10 to 20 times the dimension of the input parameters. The number of samples in the second round of sampling is 5,000 to 20,000.

[0013] As a preferred option, the effect sensitivity index is used. The input parameters are ranked from largest to smallest in terms of sensitivity. The higher the input parameter ranks, the more sensitive the blade's thermal response index is to changes in that input parameter.

[0014] As a preferred approach, optimization weights are calculated for each input parameter separately. as follows: Where i = 1, 2, ..., n ; n This represents the number of input parameters.

[0015] Preferably, the blade thermal response index is the average blade wall temperature and / or the highest blade wall temperature.

[0016] As a preferred option, the statistical characteristics of the uncertainty of the blade thermal response index also include one or more of the mean, variance, standard deviation, and confidence interval.

[0017] Preferably, the input parameters include four operating condition parameters. The four operating condition parameters are the pressure at the front chamber cold air inlet, the temperature at the front chamber cold air inlet, the pressure at the rear chamber cold air inlet, and the temperature at the rear chamber cold air inlet.

[0018] Preferably, the blade geometry model used for CFD simulation employs unstructured mesh generation. The mesh on the blade surface and the upper and lower endwall regions of the blade geometry model utilizes a localized mesh refinement strategy. The minimum mesh element size for the film cooling hole outlet and inner wall of the blade geometry model is controlled to remain constant at preset values. The mesh height setting in the near-wall region ensures that the dimensionless distance parameter... y +The overall control is kept below 3.

[0019] Preferably, the expression for the proxy model is as follows: in, The prediction results output by the surrogate model; x For input parameters; For regression functions; These are coefficients to be determined; It is a systematic bias.

[0020] The undetermined coefficients The estimated value for: in, The sample coefficient matrix, This is the response matrix corresponding to the sample; Let be the covariance matrix of the observation error vector.

[0021] Systematic bias variance The estimated value for: in, This represents the number of samples.

[0022] Secondly, the present invention provides a multi-factor sensitivity analysis system for turbine blade cooling, which is used to execute the aforementioned turbine blade cooling performance optimization method. The multi-factor sensitivity analysis system for turbine blade cooling includes a sampling module, a CFD simulation module, a surrogate prediction module, a statistical module, and a sensitivity ranking module.

[0023] The sampling module is configured to sample the operating parameters and / or geometric parameters of the turbine blades according to a probability distribution within the range of values.

[0024] The CFD simulation module is configured to: receive the first batch of samples from the sampling module and generate a blade geometry model, and perform mesh generation and CFD simulation on the generated blade geometry model.

[0025] The surrogate prediction module is configured to: train a surrogate model using the blade thermal response index output by the CFD simulation module, and use the second batch of samples from the trained surrogate model to predict the blade thermal response index.

[0026] The statistical module is configured to receive the blade thermal response index output by the theoretical prediction module, extract statistical characteristics, and generate the first-order sensitivity index and the total effect sensitivity index for each operating condition parameter and / or geometric parameter.

[0027] The sensitivity ranking module is configured to receive the first-order sensitivity index and the total effect sensitivity index output by the statistics module, and to rank the sensitivity of each operating condition parameter and / or geometric parameter.

[0028] Thirdly, the present invention provides a method for optimizing the cooling performance of turbine blades, comprising: The aforementioned method for multi-factor sensitivity analysis of turbine blade cooling is used to obtain optimized weights for multiple operating parameters and / or geometric parameters. .

[0029] Establish a system that includes optimization weights The multi-objective optimization objective function and constraints are defined. The multi-objective optimization objective function is used to iteratively optimize the operating parameters and / or geometric parameters. Optimization weights are also defined. High operating parameters and / or geometric parameters allow for greater adjustment range in iterative optimization.

[0030] Preferably, the optimized parameters include the turbine blade geometry. The machining accuracy of each geometry is adjusted according to its sensitivity ranking. The machining accuracy of the geometry parameters with higher sensitivity rankings is improved.

[0031] Fourthly, the present invention provides a computer device including a memory and a processor, wherein the memory stores a computer program that can run on the processor; when the processor executes the computer program stored in the memory, it implements the aforementioned method for multi-factor sensitivity analysis of turbine blade cooling.

[0032] Fifthly, the present invention provides a readable storage medium storing a computer program; when the computer program is executed by a processor, it implements the aforementioned method for multi-factor sensitivity analysis of turbine blade cooling.

[0033] The present invention has the following beneficial effects.

[0034] 1. Significantly improves computational efficiency while ensuring result accuracy: This invention trains a surrogate model using a small number of CFD simulation samples, and then uses the surrogate model to replace large-scale CFD simulations, effectively reducing computational load and time costs. This allows for efficient completion of turbine blade uncertainty quantification and sensitivity analysis under limited resource conditions. Simultaneously, the surrogate model fully retains the key response characteristics of the physical model during sampling and training, enabling it to approximate the real system with high accuracy, ensuring the reliability and scientific validity of the analysis results.

[0035] 2. Achieving Uncertainty Quantification and Sensitivity Analysis of Thermal Response Indicators: This invention extracts the variance of the blade thermal response index when one input parameter remains constant while the others change, as well as the variance of the blade thermal response index when one input parameter changes while the others remain constant. This enables first-order sensitivity analysis and overall effect sensitivity analysis for each input parameter. It maintains convergence and stability even in the presence of multi-parameter interactions, thereby ranking the multi-parameter sensitivity of complex turbine blade cooling and obtaining the independent contribution and interaction effect of different input parameters on the blade thermal response. It clearly identifies key sources of uncertainty and provides a quantitative basis for optimizing design and manufacturing tolerance control.

[0036] 3. More efficient and targeted optimization process: This invention uses a weighted optimization method based on sensitivity analysis results. It can assign higher optimization weights to key parameters according to the sensitivity contribution of input parameters to the uncertainty of cooling performance, so that they are adjusted first in the design, while reducing the optimization intensity of low-sensitivity parameters, thereby achieving more efficient and targeted optimization of turbine blade cooling performance. Attached Figure Description

[0037] Figure 1 This is a flowchart of Embodiment 1 of the present invention.

[0038] Figure 2 This is a schematic diagram of the blade geometry and calculation boundary in Embodiment 1 of the present invention.

[0039] Figure 3This is a diagram showing the first round of sampling results in Embodiment 1 of the present invention.

[0040] Figure 4 This is a graph showing the evaluation results of the proxy model in Embodiment 1 of the present invention.

[0041] Figure 5 This is a graph showing the results of uncertainty quantification analysis in Embodiment 1 of the present invention.

[0042] Figure 6 This is a graph showing the sensitivity analysis results in Embodiment 1 of the present invention. Detailed Implementation

[0043] The present invention will be further described below with reference to the accompanying drawings.

[0044] Example 1 A multi-factor sensitivity analysis method for turbine blade cooling is proposed. Based on the quantification of comprehensive operating condition uncertainties, this method takes high-pressure turbine guide vanes as the research object and analyzes the impact of changes in multiple operating parameters affecting the flow and heat transfer characteristics of the turbine guide vanes on the blade cooling effect, ranking them according to their sensitivity. In this embodiment, four operating parameters are analyzed: the pressure at the inlet of the front chamber cold air, the temperature at the inlet of the front chamber cold air, the pressure at the inlet of the rear chamber cold air, and the temperature at the inlet of the rear chamber cold air. The blade cooling effect is quantified using the blade wall temperature. The four operating parameters analyzed are the main factors affecting the system response, and their uncertainties arise from measurement errors, operational fluctuations, and changes in the external environment.

[0045] like Figure 1 As shown, the multi-factor sensitivity analysis method for turbine blade cooling mainly includes the following steps: input parameter sampling, CFD high-fidelity calculation, surrogate model establishment, uncertainty quantification, and sensitivity analysis.

[0046] Step 1: Input Parameter Sampling Based on the fluctuation characteristics of the engine's actual operating conditions and experimental statistical data, the value ranges and probability distributions of four operating condition parameters to be analyzed are established. Using these four operating condition parameters as input parameters, an input parameter space is established. Within this input parameter space, small-batch sampling is performed on the operating condition parameters to obtain multiple samples. In some embodiments, the probability distribution of the input parameters adopts a normal distribution.

[0047] To ensure a uniform distribution of finite samples in the high-dimensional input space, this embodiment employs the Latin hypercube sampling (LHS) method to generate sample points. Compared to traditional random sampling, the Latin hypercube sampling method achieves stratified uniform sampling within each input parameter value range, improving sample utilization and result stability. The number of samples is determined based on the dimension of the input parameters and the nonlinear complexity of the target response, typically taken as 10 to 20 times the parameter dimension.

[0048] In this embodiment, the results of sampling the four operating parameters using the Latin hypercube sampling method are as follows: Figure 3 As shown.

[0049] Step 2: Establish the blade geometric model and perform numerical simulation. For each sample, a corresponding blade geometric model is created and meshed. For example... Figure 2 As shown, when performing mesh generation, considering the complex geometry of the guide vane channel, especially the significant curvature changes and local flow separation in the leading edge, trailing edge, and film cooling hole regions, an unstructured mesh is used to improve the accuracy of geometric fitting. The unstructured mesh can simultaneously accommodate the discretization of complex surface geometry and the controllability of local meshes, avoiding distortion in high-curvature regions caused by structured meshes.

[0050] Specifically, a localized mesh refinement strategy is adopted for the blade surface and upper and lower end edge regions to ensure that the surface mesh can fully resolve aerodynamic and thermal flux changes. In the mainstream region of the blade surface, the mesh size is set at 0.1 mm to ensure a smooth transition of the overall flow field. In the film cooling hole region, due to the strong shearing and mixing between the cooling airflow and the mainstream, the local flow structure has a high velocity and temperature gradient, making it difficult for traditional medium-density meshes to accurately distinguish the adhesion and diffusion characteristics of the cooling film. Therefore, in the film cooling hole outlet and the inner wall region of the hole, the minimum mesh cell size is strictly controlled to 0.01 mm to ensure the resolution of the initial shear layer and vortex structure of the jet. Furthermore, considering the complex flow and turbulence effects of the flow field, this embodiment uses the SST k-ω model to ensure accurate simulation of the thermal-fluid coupling process.

[0051] Mesh design in the near-wall region is crucial for the accuracy of turbulent heat transfer calculations; therefore, boundary layer meshes are set on the blade surface and endwall regions. According to the applicability criteria of the SST k-ω model, when the dimensionless distance parameter... y When the velocity distribution is + < 5, the turbulence model can directly analyze the velocity distribution within the viscous sublayer and buffer layer without using empirical wall functions, thus avoiding the additional assumption errors introduced by wall functions. Therefore, this invention sets the height of the first mesh layer (the first mesh layer is the first mesh layer extending from the boundary of the fluid domain) to 0.001 mm, so that the dimensionless distance parameter... y + The overall thickness is controlled below 3, and 12 boundary layer units are arranged. The interlayer thickness increases exponentially with a growth rate of 1.2 to ensure that the viscous sublayer on the blade surface, endwall, and inner wall of the cooling hole is completely resolved.

[0052] Each sample corresponds to a set of input parameters. A validated high-fidelity CFD solver is used to perform steady-state or transient calculations on the blade geometry model corresponding to each sample, obtaining the blade thermal response indices for each sample. These indices include cooling efficiency, average wall temperature, and maximum wall temperature. Each sample and its corresponding blade thermal response indices constitute the input-output dataset. This dataset provides the data foundation for training the surrogate model.

[0053] Step 3: Establish the proxy model The surrogate model is used to establish an approximate mathematical mapping relationship between input parameters and blade thermal response indicators. It forms the basis for this embodiment's accurate sensitivity analysis of multiple input parameters with low computational requirements. In this embodiment, the surrogate model is trained on a limited sample of the input-output dataset obtained in step two, enabling it to quickly predict the response characteristics of complex systems and achieve an effect similar to CFD calculation results.

[0054] In this embodiment, the proxy model is built based on the Kriging model and has the following characteristics: (1) The surrogate model provided in this embodiment adopts a local approximation method based on Gaussian process regression, which can accurately fit the nonlinear characteristics of the response surface and provide prediction confidence. The surrogate model provided in this embodiment describes the similarity between sample points through a covariance function (or kernel function) and uses known data to predict unknown data. It can not only effectively model complex nonlinear systems, but also quantify the uncertainty of each prediction, providing more reliable information for decision-making.

[0055] (2) The surrogate model provided in this embodiment can quickly predict the response characteristics of complex systems by training and learning the relationship between input parameters and blade thermal response indices based on limited sample data. Compared with traditional CFD methods, the surrogate model provided in this embodiment provides the ability to approximate CFD calculation results while significantly improving computational efficiency. The combination of the two ensures both overall prediction accuracy and effectively captures local changes in complex regions.

[0056] The specific expression for the proxy model is shown below: in, The prediction results output by the surrogate model; x For input parameters; yes The regression function is given, and a global approximation model in the design space is presented; These are coefficients to be determined; It is a function with a mean of zero and a variance of . A stationary random process, representing an approximation System deviations that occur at that time.

[0057] The covariance between any input parameters can be expressed as: in, This represents the variogram between any two sample points. Common variograms include cubic functions, Gaussian functions, linear functions, and spherical functions.

[0058] The undetermined coefficients can be obtained using the generalized least squares estimation method. The estimated value for: in, The sample coefficient matrix, This is the response matrix corresponding to the sample; Let be the covariance matrix of the observation error vector.

[0059] variance The estimated value for: in, This represents the number of samples.

[0060] From the above model parameters, the predicted points can be obtained. Predicted response value at [location] and prediction variance They are respectively: in, This is the correlation matrix between sample points and prediction points.

[0061] The training process of the proxy model is as follows: (1) Data preprocessing: Normalize and perform necessary dimensionality reduction on each sample in the dataset to improve the convergence speed of the model and reduce computational complexity.

[0062] (2) Model structure optimization: Select appropriate model hyperparameters and optimize the model structure through methods such as cross-validation to ensure its generalization ability on various types of samples. The model hyperparameters include function type, variance, and length scale.

[0063] (3) Model accuracy verification: Calculate the determination coefficient of the surrogate model after training. The root mean square error (RMSE) is used to verify the model's accuracy. A surrogate model is considered to fit well when the RMSE is greater than 0.75 and less than 10% of the sample output variance.

[0064] In this embodiment, the evaluation result of the proxy model is as follows: Figure 4 As shown, the validated surrogate model requires only milliseconds of computation time in a single prediction, which is thousands of times more efficient than the hours or even days required for traditional CFD calculations.

[0065] Two surrogate models were constructed for the two parameters of interest (average wall temperature and maximum wall temperature), and the results are as follows. Figure 4 As shown. From Figure 4 As shown in the left figure, the sample points of the average wall temperature are basically distributed along the diagonal and have a small degree of dispersion, indicating that the surrogate model can accurately capture the overall trend of temperature changes. Its coefficient of determination R0 2 =0.952, indicating that the model has a high fitting accuracy for the average wall temperature response. The root mean square error (RMSE) is 8.876 K and the mean absolute error (MAE) is 3.906 K, both at low levels, indicating that the model prediction error is small and there is no obvious systematic bias. Overall, the predicted points are most densely distributed in the medium and low temperature range, almost overlapping with the actual values, with only a slight deviation in the high temperature range (around 1180 K).

[0066] exist Figure 4 In the right-hand figure, the predicted results for the highest wall temperature also show a strong linear correlation, with a coefficient of determination R0. 2 =0.962, slightly higher than the average wall temperature prediction result, indicating that the model has a stronger fitting ability in capturing temperature changes in the hot spot area of ​​the blade. RMSE is 5.466 K and MAE is 4.435 K, indicating good error control. All sample points are closely distributed on both sides of the ideal diagonal, with no obvious systematic shift or outlier points.

[0067] In summary, the constructed surrogate model maintains good prediction accuracy and stability under different output responses. The surrogate model achieves high consistency, high correlation, and low error response approximation within the sample space, providing a reliable foundation for subsequent analysis.

[0068] Step 4: Quantification of Uncertainty A large-scale sampling process (typically 5,000–20,000 groups) is performed based on the probability distribution of each input parameter to obtain samples for uncertainty quantification. A surrogate model is then used to quickly predict from this large sample size, enabling uncertainty propagation analysis. Specifically, the uncertainty of the input parameters is transmitted to the blade thermal response index through the surrogate model, and the statistical characteristics of the output are analyzed. The specific steps are as follows: (1) Input space sampling: In order to estimate the statistical properties of the output, a large number of samples are collected from the input space based on the probability distribution of each input parameter. These samples represent the random variations of the input parameters under their probability distribution.

[0069] (2) Calculation of blade thermal response index: The corresponding blade thermal response index is calculated for each input sample through a surrogate model. The surrogate model provides prediction results for each sample during this process, and also provides the variance or standard deviation of the blade thermal response index. In this embodiment, the blade thermal response index is the average blade wall temperature and the highest temperature on the blade wall surface.

[0070] (3) Statistical analysis: By constructing the probability distribution of the output through a large number of input samples corresponding to the blade thermal response index, and calculating its mean, variance and other statistics, the uncertainty of the system response can be understood. The statistical characteristics of the output help to analyze the behavior of the blade in the face of uncertainty. The uncertainty of the input parameters includes operating condition uncertainty and geometric manufacturing uncertainty.

[0071] Through these steps, we can intuitively see the impact of input uncertainty on the system response and estimate the reliability of the final output. The statistical characteristics of the blade thermal response index include one or more of the following: mean, variance, standard deviation, and confidence interval.

[0072] In this embodiment, the statistical characteristics of the blade thermal response index are defined as follows: in, The mathematical expectation (average) of the target quantity. Variance is used to measure the degree of dispersion of the output results.

[0073] By analyzing the statistical results, the response range and probability distribution characteristics of the system under input uncertainty can be obtained. For example, the mean value of the average wall temperature on the blade surface. It represents typical operating conditions, while variance It reflects the fluctuation amplitude affected by input disturbances.

[0074] The quantitative results of the average wall temperature and the maximum wall temperature of the two blade thermal response indices are as follows: Figure 5 As shown, this achieves the quantification of the uncertainty of changes in operating parameters. Figure 5The uncertainty quantification results of the average and maximum wall temperatures of the guide vane surface calculated based on the surrogate model are presented. Through Monte Carlo propagation analysis of a large number of input samples, the probability density function (PDF) of the quantity of interest and its statistical characteristic parameters are obtained. The blue solid line represents the probability density distribution obtained through kernel density estimation, the red dashed line represents the sample mean location, and the black dashed line represents the 95% confidence interval range.

[0075] from Figure 5 As shown in the left figure, the distribution of the average wall temperature exhibits a distinct multi-peak pattern, with a standard deviation of 42.4 K and a relative fluctuation of approximately 3.7% relative to the mean of 1137.8 K. This result indicates that the overall thermal response of the guide vane possesses strong stability. The 95% confidence interval is [1063.5 K, 1213.7 K], implying that within the typical operating fluctuation range, the variation in the average wall temperature of the blade is approximately ±6%, indicating that the system as a whole has good thermal stability.

[0076] Figure 5 The right figure shows the uncertainty distribution of the highest wall temperature, which is closer to a unimodal quasi-normal distribution than the average wall temperature. The standard deviation is ±51.3 K, corresponding to a relative fluctuation of approximately 3.6% in the mean of 1395.5 K. The 95% confidence interval is [1306.2 K, 1508.5 K]. It can be seen that although the overall fluctuation range is narrow, the tail of the temperature distribution is slightly skewed to the right, indicating the existence of a certain probability of high-temperature anomalies. These high-temperature samples mainly occur under combined disturbances of decreasing cooling gas pressure or increasing temperature in the front cavity, corresponding to conditions where the cooling film adhesion in the leading edge region is weakened and the local convective heat transfer coefficient is reduced.

[0077] Step 5: Sensitivity Analysis To identify the input factors that have the greatest impact on the blade's thermal response, this embodiment employs the Sobol global sensitivity analysis method based on variance decomposition. This method can quantitatively evaluate the contribution of each input parameter and its interaction to the output results in high-dimensional, strongly nonlinear systems.

[0078] The variance of the blade thermal response index is decomposed into the sum of the independent effects and interaction effects of each input parameter. Based on this, the following two main sensitivity indices are defined: First-order sensitivity index Sensitivity index of total effect These are used to measure the direct impact of a single input parameter on the output and its overall importance in all interactions, respectively. The first-order sensitivity index is used to measure these effects. Indicates input parameters Independent contribution to the variance of the blade thermal response index.

[0079] in With other input parameters fixed, only the different input parameters are considered. The variance of the calculated blade thermal response index.

[0080] Total effect sensitivity index Indicates input parameters The interaction contribution to the output variance takes into account the input parameters. The interaction with all other input parameters.

[0081] in, Indicates fixed input parameters The variance of the blade thermal response index caused by the influence of other input parameters.

[0082] This embodiment calculates the aforementioned sensitivity index based on a surrogate model, identifying the operating parameters that have the most significant impact on the average and maximum wall temperatures of the blade surface, providing a basis for cooling design and optimization. In some embodiments, only the magnitude of the average wall temperature of the blade surface is used as an indicator to measure the blade's thermal response performance.

[0083] The sensitivity analysis results in this embodiment are as follows: Figure 6 As shown, the temperature in the front chamber and the pressure in the rear chamber are factors that significantly affect the blade wall temperature. In this embodiment, only 50 simulation examples are needed to complete a comprehensive quantification of operational uncertainties and sensitivity analysis.

[0084] Step 6: Optimization of blade cooling performance based on sensitivity analysis results The sensitivity analysis results clearly demonstrate the contribution of different input parameters to the uncertainty of turbine blade cooling performance and their relative importance. Based on this ranking of importance, sensitivity information is incorporated into the optimization design process to achieve targeted improvements to key parameters.

[0085] Specifically, after obtaining the global sensitivity analysis results of the input parameters, the adjustment intensity of different input parameters during the optimization process is weighted according to the contribution of each input parameter to the uncertainty of the cooling performance blade thermal response index: First, the first-order sensitivity index corresponding to each input parameter is calculated based on the surrogate model. Sensitivity index of total effect And with the total effect sensitivity index This serves as an indicator of the overall importance of the parameters. Subsequently, the sensitivity index of the total effect of each input parameter is used. The size is determined, and a parameter weighting relationship is constructed so that input parameters that have a greater impact on cooling performance receive higher adjustment priority during the optimization process.

[0086] Based on this, the aforementioned weights are incorporated into the cooling performance optimization model, and the control method for the operating parameters is adjusted accordingly. This approach ensures that the optimization process focuses on highly sensitive parameters, reducing the interference of low-sensitivity parameters on overall optimization efficiency, thereby achieving more efficient, stable, and engineering-feasible optimization of turbine blade cooling performance.

[0087] In this embodiment, to quantitatively reflect the relative importance of each input parameter in the optimization process, the sensitivity analysis results are incorporated into the weight calculation. Assume there are n input parameters in the system, and their corresponding total effect sensitivity indices are as follows: , , ..., Then the optimization weight of the i-th input parameter. Defined as: in, This represents the relative weight of the i-th input parameter in the optimization process, and its value directly reflects the overall impact of the parameter on the uncertainty of cooling performance.

[0088] When constructing an optimization model, the aforementioned weights can be incorporated into the objective function or constraints. For example, when the optimization objective is the average or maximum blade wall temperature, a weighted optimization objective function can be constructed, allowing highly sensitive parameters to have a larger adjustment range during the optimization iteration process, while the adjustment range of less sensitive parameters is correspondingly reduced.

[0089] This weighted strategy allows the optimization process to focus on improving key parameters that significantly affect cooling performance, thereby effectively reducing computational costs and engineering implementation difficulties while ensuring optimization results.

[0090] The turbine blade cooling multi-factor sensitivity analysis method provided in this embodiment significantly reduces the computational cost of complex computational fluid dynamics (CFD) simulation while ensuring computational accuracy, and realizes uncertainty propagation and global sensitivity assessment of multi-input parameter systems.

[0091] The execution subject of this embodiment may be a computer device; the computer device includes a memory and a processor, the memory stores executable code, and when the processor executes the executable code, it implements the method provided in this embodiment, specifically by executing each step of the method.

[0092] The memory may include high-speed random access memory (RAM) and may also include non-volatile memory, such as at least one disk storage device. Communication between this system network element and at least one other network element is achieved through at least one communication interface (which can be wired or wireless), such as the Internet, wide area network, local area network, metropolitan area network, etc. The bus can be an ISA bus, PCI bus, or EISA bus, etc. The bus can be divided into address bus, data bus, control bus, etc.

[0093] The memory is used to store programs. After receiving an execution instruction, the processor executes the program. The method executed by the device for defining the flow process disclosed in any of the foregoing embodiments of the present invention can be applied to the processor or implemented by the processor.

[0094] The processor may be an integrated circuit chip with signal processing capabilities. In implementation, each step of the above method can be completed by integrated logic circuits in the processor's hardware or by instructions in software form. The processor can be a general-purpose processor, including a Central Processing Unit (CPU) or other programmable logic devices. It can implement or execute the methods and steps disclosed in this embodiment. The general-purpose processor can be a microprocessor or any conventional processor. The steps of the method disclosed in this embodiment can be directly manifested as being executed by a hardware decoding processor, or executed by a combination of hardware and software modules in the decoding processor. The software modules can reside in random access memory, flash memory, read-only memory, programmable read-only memory, electrically erasable programmable memory, registers, or other mature storage media in the art. This storage medium is located in memory; the processor reads information from the memory and, in conjunction with its hardware, completes the steps of the above method.

[0095] In some other embodiments, the computer device may also be one or more desktop computers, notebooks, workstations, databases, or servers.

[0096] Traditional high-fidelity CFD simulations can accurately describe three-dimensional flow and heat transfer behavior, but direct Monte Carlo sampling or other repetitive calculation methods typically require significant computational resources, making them unsuitable for engineering applications. This embodiment establishes a high-precision surrogate model to replace CFD calculations, achieving efficient uncertainty propagation and sensitivity assessment, thereby significantly improving analysis efficiency. Therefore, the method provided in this embodiment combines high efficiency, accuracy, and versatility, significantly enhancing the level of uncertainty analysis and design optimization for turbine blade cooling, and possessing broad engineering application prospects.

[0097] Example 2 A multi-factor sensitivity analysis method for turbine blade cooling is disclosed in this embodiment, which differs from Embodiment 1 in that the input parameters include not only operating parameters but also geometric parameters. The geometric parameters include the diameter of the film cooling orifice, the expansion angle, the angle between the orifice axis and the Z-axis, and the width of the impact orifice. Sensitivity analysis yields a ranking of the thermal response indicators' sensitivity to changes in various operating and geometric parameters. For geometric parameters with high sensitivity ranking, the machining accuracy level is increased to improve the stability of the thermal response indicators. For geometric parameters with low sensitivity ranking, the machining accuracy level is maintained or reduced to lower production costs.

[0098] In some embodiments, a multi-objective genetic algorithm is used to perform joint iterative optimization of the values ​​of geometric parameters. During iterative optimization, corresponding perturbation points are generated based on the probability distribution of the key geometric parameters, processing errors, and operational condition fluctuations for each individual. A surrogate model is used to predict the blade thermal response index corresponding to each perturbation point. The expected variance of the blade thermal response index at each perturbation point is used as the fitness of the individual during the corresponding iteration process.

[0099] Example 3 A multi-factor sensitivity analysis system for turbine blade cooling includes a sampling module, a CFD simulation module, a surrogate prediction module, a statistics module, and a sensitivity ranking module; the multi-factor sensitivity analysis system for turbine blade cooling provided in this embodiment can execute the sensitivity analysis method in Embodiment 1.

[0100] The sampling module is configured to sample the operating parameters and / or geometric parameters of the turbine blades according to a probability distribution within the range of values. The CFD simulation module is configured to: receive the first batch of samples from the sampling module and generate a blade geometric model, and perform mesh generation and CFD simulation on the generated blade geometric model; The surrogate prediction module is configured to: train the surrogate model using the blade thermal response index output by the CFD simulation module, and use the second batch of samples from the trained surrogate model to predict the blade thermal response index. The statistical module is configured to receive the blade thermal response index output by the theoretical prediction module, extract statistical characteristics, and generate the first-order sensitivity index and the total effect sensitivity index for each operating condition parameter and / or geometric parameter. The sensitivity ranking module is configured to receive the first-order sensitivity index and the total effect sensitivity index output by the statistics module, and to rank the sensitivity of each operating condition parameter and / or geometric parameter.

[0101] In some embodiments, the sampling module, CFD simulation module, surrogate prediction module, statistics module, and sensitivity ranking module each employ different computer devices.

Claims

1. A method for multi-factor sensitivity analysis of turbine blade cooling, characterized in that: include: Select multiple input parameters from the operating parameters and / or geometric parameters of the turbine blade; For each input parameter, establish the value range and probability distribution, and perform the first round of sampling to obtain multiple samples; CFD simulations were performed on the blade geometry model corresponding to each sample to obtain the blade thermal response indexes for different samples. Each sample and its corresponding blade thermal response index constitute a dataset; the dataset is used to train a surrogate model based on the Kriging model. A second round of sampling is performed on each input parameter, and the resulting samples are input into the surrogate model to predict the corresponding blade thermal response index; statistical characteristics of the uncertainty of the blade thermal response index are extracted and quantified; the statistical characteristics include variance. ; For each input parameter The variance of the blade thermal response index was calculated with the blade itself remaining constant and other parameters varying. The variance of the blade's thermal response index with its own changes and other parameters remaining constant. ; Variance With variance The ratio of the two values ​​is used as a first-order sensitivity index. ; take variance With variance The ratio of the two values ​​is used as the sensitivity index of the total effect. ; Using the first-order sensitivity index and / or total effect sensitivity index The sensitivity of the blade thermal response index to changes in various input parameters was ranked.

2. The method for multi-factor sensitivity analysis of turbine blade cooling according to claim 1, characterized in that: The number of samples in the first round of sampling is 10 to 20 times the dimension of the input parameters; the number of samples in the second round of sampling is 5,000 to 20,000.

3. The method for multi-factor sensitivity analysis of turbine blade cooling according to claim 1, characterized in that: Using the effect sensitivity index The sensitivity of each input parameter is sorted from largest to smallest; the higher the input parameter is in the ranking, the more sensitive the blade thermal response index is to changes in that input parameter.

4. The method for multi-factor sensitivity analysis of turbine blade cooling according to claim 1, characterized in that: Calculate the optimization weights for each input parameter separately. as follows: Where i = 1, 2, ..., n ; n This represents the number of input parameters.

5. The method for multi-factor sensitivity analysis of turbine blade cooling according to claim 1, characterized in that: The blade thermal response index is the average temperature of the blade wall and / or the highest temperature of the blade wall.

6. The method for multi-factor sensitivity analysis of turbine blade cooling according to claim 1, characterized in that: The statistical characteristics of the uncertainty of the quantification of blade thermal response index also include one or more of the mean, variance, standard deviation and confidence interval.

7. The method for multi-factor sensitivity analysis of turbine blade cooling according to claim 1, characterized in that: The input parameters include four operating condition parameters: the pressure at the front chamber cold air inlet, the temperature at the front chamber cold air inlet, the pressure at the rear chamber cold air inlet, and the temperature at the rear chamber cold air inlet.

8. The method for multi-factor sensitivity analysis of turbine blade cooling according to claim 1, characterized in that: The blade geometry model used for CFD simulation employs unstructured mesh generation; the mesh on the blade surface and the upper and lower endwall regions of the blade geometry model uses a local refinement strategy; the minimum mesh element size of the air film aperture outlet and inner wall of the blade geometry model is controlled to remain constant at preset values; the mesh height setting value in the near-wall region ensures that the dimensionless distance parameter... y +The overall control is kept below 3.

9. A multi-factor sensitivity analysis system for turbine blade cooling, characterized in that: The turbine blade cooling performance optimization method as described in claim 1 is used to execute the turbine blade cooling multi-factor sensitivity analysis system, which includes a sampling module, a CFD simulation module, a surrogate prediction module, a statistical module, and a sensitivity ranking module. The sampling module is configured to sample the operating parameters and / or geometric parameters of the turbine blades according to a probability distribution within the range of values. The CFD simulation module is configured to: receive the first batch of samples from the sampling module and generate a blade geometric model, and perform mesh generation and CFD simulation on the generated blade geometric model; The surrogate prediction module is configured to: train the surrogate model using the blade thermal response index output by the CFD simulation module, and use the second batch of samples from the trained surrogate model to predict the blade thermal response index. The statistical module is configured to receive the blade thermal response index output by the theoretical prediction module, extract statistical characteristics, and generate the first-order sensitivity index and the total effect sensitivity index for each operating condition parameter and / or geometric parameter. The sensitivity ranking module is configured to receive the first-order sensitivity index and the total effect sensitivity index output by the statistics module, and to rank the sensitivity of each operating condition parameter and / or geometric parameter.

10. A method for optimizing the cooling performance of turbine blades, characterized in that: include: The optimized weights of multiple operating parameters and / or geometric parameters are obtained using the multi-factor sensitivity analysis method for turbine blade cooling as described in claim 4. ; Establish a system that includes optimization weights The multi-objective optimization objective function and constraints; Iterative optimization of operating parameters and / or geometric parameters is performed using a multi-objective optimization objective function; optimization weights are optimized. High operating parameters and / or geometric parameters allow for greater adjustment range in iterative optimization.

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