A method and system for calibrating parameters of a hydraulic mechanical turbulent transition model

Abstract

This invention relates to the interdisciplinary fields of fluid machinery design, computational fluid dynamics (CFD), and artificial intelligence, specifically a method and system for calibrating parameters of a turbulent transition model for hydraulic machinery. The method selects a two-dimensional hydrofoil profile model that is similar to the hydraulic machinery blade in both geometric and flow field characteristics. For each set of collected parameter samples, numerical simulation is performed using a computational CFD solver to obtain the distribution data of wall friction coefficient and pressure coefficient along the hydrofoil surface, constructing a training dataset composed of the input parameter set and the output flow field characteristics. This invention introduces a pressure extremum constraint term to adaptively weight the pressure coefficient prediction error in the low-pressure region, enabling the calibrated model to effectively capture the lowest pressure point and corresponding distribution characteristics on the blade surface. Compared to traditional calibration methods, this effectively solves the problem of inaccurate prediction of the initial cavitation location in hydraulic machinery.

Description

Technical Field

[0001] This invention relates to the interdisciplinary fields of fluid machinery design, computational fluid dynamics (CFD), and artificial intelligence, specifically to a method and system for calibrating parameters of a hydraulic machinery turbulent transition model. Background Technology

[0002] In the research and design of hydraulic machinery, accurately predicting the flow state on the surfaces of flow components (such as impeller blades, guide vanes, and volutes) is crucial. The transition of fluid from laminar to turbulent flow directly affects hydraulic efficiency (frictional resistance changes) and operational stability (flow-induced vibration). More importantly, in aquatic media, the location of the transition point is often accompanied by a dramatic change in pressure gradient, which is directly related to the occurrence of cavitation. Cavitation leads to severe noise, vibration, and material erosion, and is a core problem that must be avoided in the design of hydraulic machinery.

[0003] Currently, the industry widely uses the Reynolds-averaged Navier-Stokes (RANS) equation combined with transition models (such as...). or a single equation Simulations are performed using a model. However, the transition model parameters (such as...) in existing commercial software... Hydraulic machinery (etc.) is typically calibrated based on low-speed aerodynamic experiments (flat plate flow). The actual operating environment of hydraulic machinery has the following unique characteristics: (1) Extremely high Reynolds number (usually in to (magnitude) (2) Complex pressure gradient (strong adverse pressure gradient exists on the suction surface of turbine blades); (3) High background turbulence (the turbulence is high after the fluid passes through the volute and guide vanes).

[0004] Using default parameters directly in hydraulic machinery simulation often leads to large deviations in the prediction of transition points, resulting in inaccurate efficiency estimates and misjudgments of the initial cavitation location. Traditional parameter calibration relies on manual trial and error, which is extremely inefficient; while CFD-based direct optimization calibration involves too much computation (a single 3D unsteady calculation can take several days), making it difficult to complete within the engineering design cycle. Summary of the Invention

[0005] The purpose of this invention is to provide a method and system for calibrating parameters of a hydraulic mechanical turbulent transition model, so as to solve the problems mentioned in the background art.

[0006] To solve the above-mentioned technical problems, the present invention provides the following technical solution: a method for calibrating parameters of a hydraulic mechanical turbulence transition model, comprising: S1. Determine a set of empirical closed-loop parameter vectors for the Reynolds-averaged Navier-Stokes transition model to be calibrated. These empirical closed-loop parameter vectors include parameters controlling the correlation between the critical Reynolds number and inflow turbulence intensity, parameters controlling the attenuation characteristics of the critical Reynolds number, parameters controlling the length of the transition region, and parameters controlling the model's sensitivity to pressure gradient response. The empirical closed-loop parameter vectors are determined based on the physical meaning of the selected Reynolds-averaged Navier-Stokes transition model and its influence mechanism on the transition process. Priority is given to selecting key closed-loop parameters that significantly affect the distribution of friction coefficient and pressure coefficient under typical hydraulic machinery operating conditions as the parameters to be inverted. Meanwhile, general constants or numerical stability parameters insensitive to the transition location in the Reynolds-averaged Navier-Stokes transition model are fixed to default values. Based on the Reynolds number range for typical hydraulic machinery operating conditions, the physical boundary values ​​of the parameters to be inverted are set, and multiple sets of parameter samples are generated using Latin hypercube sampling. S2. Select a two-dimensional hydrofoil profile model that is similar to the hydraulic machinery blade in terms of geometric and flow field characteristics. For each set of parameter samples collected in S1, use a computational CFD solver (used for numerically solving the fluid dynamics control equations) to perform numerical simulation, obtain the wall friction coefficient distribution data and pressure coefficient distribution data along the hydrofoil surface, and construct a training dataset consisting of the input parameter set and the output flow field characteristics. S3. Calculate the standard deviation of the wall friction coefficient and pressure coefficient at each grid node in the obtained training dataset in the parameter space. Combine the preset threshold for the obtained standard deviation to filter the flow-insensitive area nodes and key feature points in each grid node of the obtained training dataset. S4. Construct a fully connected deep neural network with the empirical closure parameter vector as input and the wall friction coefficient and pressure coefficient at the selected key feature points as output; use the training dataset generated in S2 as supervised learning samples to train the fully connected deep neural network and obtain the nonlinear mapping relationship between the empirical closure parameter vector and the hydrofoil surface flow field characteristics. S5. Establish an optimization objective function for parameter inversion using the empirical closed-loop parameter vector of the Reynolds-averaged Navier-Stokes transition model as the optimization variable. The optimization objective function is based on the deviation between the predicted values ​​of wall friction coefficient and pressure coefficient at key feature points obtained from the nonlinear mapping relationship between the empirical closed-loop parameter vector and the flow field characteristics of the hydrofoil and the experimental or measurement data. It includes a friction fitting term, a pressure extreme value constraint term, and a parameter range regularization term. S6. The objective function is minimized using a gradient descent optimization algorithm. The nonlinear mapping relationship between the obtained empirical closed parameter vector and the flow field characteristics of the hydrofoil surface is used as a differentiable computational graph. The gradient information of the optimization objective function with respect to the empirical closed parameter vector is obtained through backpropagation, and the empirical closed parameter vector is iteratively updated. The optimal model parameter set that fits the current hydraulic conditions is solved in reverse. The obtained optimal model parameter set is used for computational fluid dynamics calculations of three-dimensional hydraulic machinery to predict the overall machine performance.

[0007] Furthermore, the Reynolds-averaged Navier-Stokes transition model in S1 is a single-equation γ-transition model based on local correlation; the specific definition of the empirical closed-form parameter vector in the governing equations includes: The parameter controlling the length of the transition region is used to determine the magnitude of the turbulent spot generation term in the intermittent factor transport equation in the single-equation γ-transition model, and affects the rate of abrupt change from laminar to turbulent flow. The parameters controlling the transition critical Reynolds number include: parameters controlling the correlation between the transition critical Reynolds number and the inflow turbulence intensity, and parameters controlling the attenuation characteristics of the transition critical Reynolds number. The parameters controlling the transition critical Reynolds number are located in the empirical correlation of the critical momentum thickness Reynolds number and are used to capture the influence of background turbulence intensity. The parameters controlling the pressure gradient response are the corresponding response coefficients in the correction terms related to the pressure gradient parameters, which are used to correct the transition criterion in the strong adverse pressure gradient region.

[0008] Specifically, the intermittent factor transport equation in the single-equation γ-transition model is as follows: ; in, For the turbulent spot generation term (source term); the parameter controlling the length of the transition zone is in the empirical formula. The term exists as a proportionality coefficient: In the standard model, The parameter used to control the length of the transition zone is usually set to a fixed value (such as 0.5). However, under high Reynolds number and high pressure gradient conditions in hydraulic machinery, the standard value will lead to an excessively long predicted transition zone. This invention corrects the physical "steepness" of the transition process by inverting this parameter. The empirical correlation for the critical momentum-thickness Reynolds number is as follows: ; in, The critical momentum thickness Reynolds number; To capture background turbulence; This is the turbulence attenuation function; The parameter used to control the correlation between the critical Reynolds number of transition and the inflow turbulence intensity is specifically the inflow turbulence intensity control coefficient in the empirical correlation of the critical momentum thickness Reynolds number. It mainly controls the sensitivity of the inflow turbulence intensity to the advance of the transition start point. Correcting this value can solve the problem of early transition under high turbulence background inside hydraulic machinery. The parameter used to control the decay characteristics of the critical Reynolds number at transition is specifically the generation rate control constant in the source term of the intermittent factor transport equation in the single-equation γ transition model (usually a standard value of 0.03 or 0.06, which is used as a variable in this invention). These are the pressure gradient parameters; To be related to pressure gradient parameters Related corrections.

[0009] Compared with existing general transition model parameter calibration methods, the core difference of this invention lies in the introduction of a pressure extremum constraint term oriented towards the cavitation characteristics of hydraulic machinery into the loss function of the inverse problem solution. This applies a higher weight to the prediction error of the pressure coefficient in the low-pressure zone, enabling the inversion parameters to not only fit the friction distribution and transition location but also accurately capture the minimum pressure point and its distribution characteristics. Since pressure extrema directly determine the initial cavitation risk in hydraulic machinery, these distinguishing features can significantly improve the reliability of cavitation prediction and the accuracy of overall machine performance evaluation, providing a targeted improvement effect for hydraulic machinery engineering applications.

[0010] Furthermore, the two-dimensional hydrofoil profile model in S2 is selected from a publicly available standard hydrofoil model library, and the criteria for determining its similarity to the hydraulic machinery blade in terms of geometric and flow field characteristics are as follows: Geometric similarity: the error of the maximum relative thickness of the hydrofoil compared to the average cross-section of the hydraulic machinery blade is within a first preset range; Similarity in flow field characteristics: Under the same Reynolds number, the pressure recovery coefficient gradient of the standard hydrofoil suction surface is within a second preset range compared to the error of the hydraulic mechanical blade suction surface. When constructing the training dataset consisting of an input parameter set and output flow field features, the input parameter set represents the empirical closed parameter vector used in numerical calculations of the Reynolds-averaged Navier-Stokes transition model. The parameter values ​​in the empirical closed parameter vector are generated by Latin hypercube sampling and are used to drive the CFD solver to generate flow field results under different transition responses. The output flow field features represent the obtained wall friction coefficient distribution data and pressure coefficient distribution data along the hydrofoil surface.

[0011] The hydrofoil profile model described in this invention is selected from the NACA or Eppler series hydrofoils, and the computational domain boundary conditions are set to incompressible liquid water medium. The inflow turbulence intensity is adjusted to match the actual operating environment of the hydraulic machinery. To ensure that the two-dimensional hydrofoil data matches the real operating environment of the hydraulic machinery blades, this invention adopts a condition similarity matching strategy. Specifically, it sets boundary conditions such as the Reynolds number range, inflow turbulence intensity Tu, and angle of attack based on typical hydraulic machinery operating conditions, and performs CFD calculations in incompressible liquid water medium. This ensures that the generated hydrofoil flow field data is consistent with the hydraulic machinery blades in terms of pressure gradient intensity and low-pressure region distribution. The above matching process is not a simple copy of existing technologies, but rather a setting specifically for the characteristics of hydraulic machinery: "high Reynolds number + complex pressure gradient + high background turbulence intensity," thereby ensuring that the trained surrogate model and inversion parameters have engineering transferability. Existing general methods only fit frictional resistance (affecting efficiency) and ignore pressure extrema. The cavitation initiation of hydraulic machinery is determined by the formula... Decision. By accurately capturing This directly improves the accuracy of predicting the initial critical point of cavitation. This allows designers to accurately locate cavitation risk zones on blades, rather than just assessing efficiency, thus solving the unique cavitation erosion problem of hydraulic machinery.

[0012] Furthermore, the preset threshold in S3 is determined using a statistical adaptive method, specifically: the average and variance of the standard deviation of all grid nodes are calculated, and the sum of the obtained average and variance by a preset multiple is used as the preset threshold. In the process of filtering the flow-insensitive nodes and key feature points in each grid node of the obtained training dataset, the standard deviation of the wall friction coefficient and pressure coefficient at each grid node in the obtained training dataset within the parameter space is compared with a preset threshold. If the standard deviation of the wall friction coefficient and pressure coefficient at the corresponding grid node in the obtained training dataset within the parameter space is less than or equal to the preset threshold, then the corresponding grid node in the obtained training dataset is determined to be a flow-insensitive node; if the standard deviation of the wall friction coefficient and pressure coefficient at the corresponding grid node in the obtained training dataset within the parameter space is greater than the preset threshold, then the corresponding grid node in the obtained training dataset is determined to have a significant response to changes in the parameter space, and the corresponding grid node in the obtained training dataset is a key feature point. Key feature points in this invention include transition zone nodes, separation / reattachment zone nodes, and cavitation initiation sensitive zone nodes. Specifically, the nodes can be identified based on the pressure coefficient and its extreme value distribution, the location of abrupt changes in the friction coefficient, and its gradient change characteristics: when the wall friction coefficient distribution at a node rises rapidly from a low value accompanied by abrupt changes in the gradient along the flow path, the node can be identified as a transition-related node; when the pressure coefficient at a node is at a low pressure level and near the minimum pressure, the node can be identified as a cavitation sensitive node; when the wall friction coefficient at a node shows an abnormal decrease or a decline in distribution characteristics, combined with flow field separation characteristics, the node can be identified as a separation-related node, thus forming a set of key feature points oriented towards multi-physical process constraints.

[0013] Furthermore, in step S4, the output layer of the fully connected deep neural network performs standardized sorting and vectorization processing on the selected key feature points, specifically including: S41. Arrange the dimensionless coordinates of the extracted key feature points in the airfoil chord direction in ascending order; S42. Represent the physical properties of each key feature point after sorting in S41 as a sub-vector. The sub-vector includes the corresponding dimensionless coordinates, wall friction coefficient and pressure coefficient value. S43. Concatenate the sub-vectors corresponding to all key feature points in sequence to obtain the corresponding one-dimensional output vector, so that each neuron in the output layer of the neural network always corresponds to the physical properties of a specific geometric position on the airfoil.

[0014] Furthermore, the friction fitting term in S5 is used to measure the deviation between the predicted value of the wall friction coefficient and the measured value in the water tunnel experiment. The parameter range regularization term is used to limit the interval in which the inversion parameters are located by a smooth boundary function; The pressure extreme value constraint term is used to apply a higher weight to the pressure coefficient prediction error in the low-pressure area, and the calculation formula involved is as follows: ; in, This refers to the set of surface region nodes in the experimental data where the pressure coefficient is less than the critical cavitation number. The empirical closed parameter vector of the Reynolds-averaged Navier-Stokes transition model; Let be the pressure coefficient obtained at the i-th low-pressure zone node through the water tunnel experiment; For empirically closed parameter vectors Under the given conditions, the pressure coefficient at the i-th low-pressure node is predicted by the nonlinear mapping relationship between the empirical closed parameter vector and the flow field characteristics of the hydrofoil surface; The cavitation zone weighting coefficient is used to assign a higher weight to the pressure error of the low-pressure zone node than to other regions.

[0015] Furthermore, the cavitation zone weighting coefficient is adaptively adjusted based on the distance function between the pressure coefficient at the node and the critical cavitation number, and the relevant calculation formula is as follows: ; in, Let be the pressure coefficient at the i-th low-pressure node. This represents the minimum pressure coefficient at each low-pressure node in the current flow field. This is the gain coefficient. As the attenuation factor, the k is a preset dimensionless scaling factor.

[0016] Furthermore, the gradient descent optimization algorithm of S6 employs the L-BFGS algorithm to accelerate the convergence speed of the iterative update of the empirical closed parameter vector. The convergence criterion is set as the objective function descent amplitude being lower than a preset amplitude threshold or reaching the maximum number of iterations. A multi-point restart strategy is adopted, selecting multiple initial points in the parameter space for optimization. In each iteration, the error between the predicted values ​​of the wall friction coefficient and pressure coefficient of key feature points predicted based on the nonlinear mapping relationship between the obtained empirical closed parameter vector and the hydrofoil surface flow field characteristics and the experimental data is used to calculate the optimized objective function. Gradient information is obtained through backpropagation, and the empirical closed parameter vector is updated until convergence. The solution with the minimum final loss function value is taken as the global optimum to avoid getting trapped in local minima.

[0017] Furthermore, the specific process in S6 of using the obtained optimal model parameter set for computational fluid dynamics calculations of three-dimensional hydraulic machinery to predict the overall machine performance includes: The flow field of turbine runner blades or pump impellers is simulated using the calibrated optimal model parameter set. Based on the location of the fluid separation point and the minimum pressure distribution obtained from the simulation, the blade airfoil rib line or thickness distribution is modified. The blade geometry modification is driven by the airfoil parameterization method, which maps the cross-sectional airfoil geometric features of the turbine or pump blades to a set of geometric control parameters. When the calibrated simulation results show that the transition initiation position is within the preset chord length range of the suction surface and the minimum pressure coefficient is lower than the critical cavitation threshold, the correction strategy is automatically executed. The leading edge radius is selected as the design variable for iterative optimization to delay the occurrence of transition or suppress the initiation of cavitation.

[0018] A parameter calibration system for a hydraulic mechanical turbulence transition model, comprising: The sample generation module is used to generate Reynolds-averaged Navier-Stokes transition model parameter samples through Latin hypercube sampling; The flow field calculation module is used to call the CFD solver to calculate the hydrofoil flow field data in batches. The surrogate model training module is used to train fully connected deep neural networks to replace computational CFD solvers; The parameter inversion module is used to solve for the optimal model parameters by minimizing the physical constraint loss function based on the water tunnel experimental data.

[0019] Compared with the prior art, the beneficial effects achieved by the present invention are: (1) This invention introduces a pressure extreme value constraint term to adaptively weight the pressure coefficient prediction error in the low-pressure zone, enabling the calibrated model to effectively capture the lowest pressure point and corresponding distribution characteristics on the blade surface. Compared with traditional calibration methods, this invention effectively solves the problem of inaccurate prediction of the initial cavitation location in hydraulic machinery. At the same time, in the experimental comparison between the standard hydrofoil and the Francis turbine model, the efficiency prediction error of the calibrated model is reduced from 3% of the default parameter to less than 0.5%, and the predicted location of the initial cavitation point is significantly improved in agreement with the experimental results. (2) Compared with the traditional genetic algorithm that directly calls the CFD solver, the present invention can shorten the calibration time from several weeks to several hours; (3) The parameter set obtained by calibration in this invention has physical meaning and can be extended from 2D hydrofoils to complex flow simulation of 3D turbine blades. Attached Figure Description

[0020] The accompanying drawings are provided to further illustrate the invention and form part of the specification. They are used in conjunction with embodiments of the invention to explain the invention and do not constitute a limitation thereof. In the drawings: Figure 1 This is a flowchart illustrating a method for calibrating parameters of a hydraulic mechanical turbulence transition model according to the present invention. Figure 2 This is a schematic diagram illustrating the influence range of parameter changes on the pressure coefficient distribution of the hydrofoil suction surface in an embodiment of the hydraulic mechanical turbulence transition model parameter calibration method of the present invention; Figure 3 This is a schematic diagram comparing the turbine efficiency curves and model experimental data before and after calibration in an embodiment of the hydraulic machinery turbulent transition model parameter calibration method of the present invention. Detailed Implementation

[0021] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0022] Please see Figure 1 This embodiment provides a method for calibrating parameters of a hydraulic mechanical turbulence transition model, including: S1. Determine a set of empirical closed-loop parameter vectors for the Reynolds-averaged Navier-Stokes transition model to be calibrated. These empirical closed-loop parameter vectors include parameters controlling the correlation between the critical Reynolds number and inflow turbulence intensity, parameters controlling the attenuation characteristics of the critical Reynolds number, parameters controlling the length of the transition region, and parameters controlling the model's sensitivity to pressure gradient response. The empirical closed-loop parameter vectors are determined based on the physical meaning of the selected Reynolds-averaged Navier-Stokes transition model and its influence mechanism on the transition process. Priority is given to selecting key closed-loop parameters that significantly affect the distribution of friction coefficient and pressure coefficient under typical hydraulic machinery operating conditions as the parameters to be inverted. Meanwhile, general constants or numerical stability parameters insensitive to the transition location in the Reynolds-averaged Navier-Stokes transition model are fixed to default values. Based on the Reynolds number range for typical hydraulic machinery operating conditions, the physical boundary values ​​of the parameters to be inverted are set, and multiple sets of parameter samples are generated using Latin hypercube sampling. Specifically, key closure parameters that control the boundary layer transition initiation point, transition zone length, and sensitivity to pressure gradients are preferentially selected. These parameters significantly influence the friction coefficient and pressure coefficient distributions under typical hydraulic machinery operating conditions, thus enabling effective inversion to obtain parameter combinations suitable for the current operating conditions through inverse problem solving. General constants in the model or numerical stability parameters insensitive to transition points, such as diffusion coefficients in turbulence models, attenuation rate parameters at far-field boundaries, and general source term constants in intermittent factor transport equations, are not preferred. These parameters typically have universality in a wide range of fluid dynamics problems, or their influence on the "transition initiation point" and "pressure extrema" under high Reynolds number conditions in hydraulic machinery is much lower than the aforementioned preferred parameters; therefore, they are fixed as default values ​​to reduce the dimensionality of the inverse problem solution.

[0023] The Reynolds-averaged Navier-Stokes transition model in S1 is a single-equation γ-transition model based on local correlation; the specific definition of the empirical closed-form parameter vector in the governing equations includes: The parameter controlling the length of the transition region is used to determine the magnitude of the turbulent spot generation term in the intermittent factor transport equation in the single-equation γ-transition model, and affects the rate of abrupt change from laminar to turbulent flow. The parameters controlling the transition critical Reynolds number include: parameters controlling the correlation between the transition critical Reynolds number and the inflow turbulence intensity, and parameters controlling the attenuation characteristics of the transition critical Reynolds number. The parameters controlling the transition critical Reynolds number are located in the empirical correlation of the critical momentum thickness Reynolds number and are used to capture the influence of background turbulence intensity. The parameters controlling the pressure gradient response are the corresponding response coefficients in the correction terms related to the pressure gradient parameters, which are used to correct the transition criterion in the strong adverse pressure gradient region.

[0024] Specifically, the intermittent factor transport equation in the single-equation γ-transition model is as follows: ; in, For the turbulent spot generation term (source term); the parameter controlling the length of the transition zone is in the empirical formula. The term exists as a proportionality coefficient: In the standard model, The parameter used to control the length of the transition zone is usually set to a fixed value (such as 0.5). However, under high Reynolds number and high pressure gradient conditions in hydraulic machinery, the standard value will lead to an excessively long predicted transition zone. This invention corrects the physical "steepness" of the transition process by inverting this parameter. The empirical correlation for the critical momentum-thickness Reynolds number is as follows: ; in, The critical momentum thickness Reynolds number; To capture background turbulence; This is the turbulence attenuation function; The parameter used to control the correlation between the critical Reynolds number of transition and the inflow turbulence intensity is specifically the inflow turbulence intensity control coefficient in the empirical correlation of the critical momentum thickness Reynolds number. It mainly controls the sensitivity of the inflow turbulence intensity to the advance of the transition start point. Correcting this value can solve the problem of early transition under high turbulence background inside hydraulic machinery. The parameter used to control the decay characteristics of the critical Reynolds number at transition is specifically the generation rate control constant in the source term of the intermittent factor transport equation in the single-equation γ transition model (usually a standard value of 0.03 or 0.06, which is used as a variable in this invention). These are the pressure gradient parameters; To be related to pressure gradient parameters Related corrections.

[0025] In this embodiment, Latin hypercube sampling (LHS) is used to generate N sets of parameter samples. Compared with simple random sampling, LHS can ensure that the projection of the parameter space in each dimension is uniformly distributed, avoiding the problems of "sample clustering" or "missing corner points due to sparsity" that may occur in random sampling. When training the surrogate model corresponding to the fully connected deep neural network, using LHS can cover the boundary and interior of the 4-dimensional parameter space with a smaller number of samples (e.g., N=200 sets), thereby significantly reducing the number of expensive CFD calculations and improving the "information density" of the training data.

[0026] S2. Select a two-dimensional hydrofoil profile model that is similar to the hydraulic machinery blade in terms of geometric and flow field characteristics. For each set of parameter samples collected in S1, use a computational CFD solver (used for numerically solving the fluid dynamics control equations) to perform numerical simulation, obtain the wall friction coefficient distribution data and pressure coefficient distribution data along the hydrofoil surface, and construct a training dataset consisting of the input parameter set and the output flow field characteristics. The two-dimensional hydrofoil profile model in S2 is selected from a publicly available standard hydrofoil model library (in this embodiment, it is selected from the NACA series or Eppler series hydrofoils). The criteria for determining similarity with hydraulic machinery blades in terms of geometric and flow field characteristics are as follows: Geometric similarity: the error of the maximum relative thickness of the hydrofoil relative to the average cross-section of the hydraulic machinery blade is within a first preset range (±5%). Similarity in flow field characteristics: Under the same Reynolds number, the pressure recovery coefficient gradient of the standard hydrofoil suction surface is within the second preset range (±10%) compared to that of the hydraulic machinery blade suction surface. This approach ensures that both have similar adverse pressure gradient environments, thus guaranteeing the physical similarity of the separation and transition mechanisms. A high-fidelity dataset reflecting the low-pressure zone and transition characteristics of the suction surface of hydraulic machinery is constructed, thereby ensuring the transferability of the established surrogate model for hydraulic machinery applications.

[0027] When constructing the training dataset consisting of an input parameter set and output flow field features, the input parameter set represents the empirical closed parameter vector used in the numerical calculation of the Reynolds-averaged Navier-Stokes transition model. The parameter values ​​in the empirical closed parameter vector are generated by Latin hypercube sampling and are used to drive the CFD solver to generate flow field results under different transition responses. The output flow field features represent the obtained wall friction coefficient distribution data and pressure coefficient distribution data along the hydrofoil surface, and can further extract key feature points of the transition region, separation region, and low-pressure region for surrogate model training.

[0028] S3. Calculate the standard deviation of the wall friction coefficient and pressure coefficient at each grid node in the obtained training dataset within the parameter space. Combined with a preset threshold for the obtained standard deviation, filter the flow-insensitive nodes and key feature points in each grid node of the obtained training dataset. For each set of parameter samples (empirical closed parameter vector), the same set of geometric models and consistent grid topology are used for CFD calculation to ensure that grid nodes at the same spatial location under different parameter samples have a one-to-one correspondence. Remove flow-insensitive nodes. The preset threshold in S3 is determined using a statistically adaptive method. Specifically, the average and variance of the standard deviations of all grid nodes are calculated, and the sum of the average and variance by a preset multiple is used as the preset threshold. This dynamic threshold selection strategy ensures that the transition core region with the most drastic flow field changes can be automatically captured under different Reynolds numbers or operating conditions without manual intervention. Nodes in the transition region and cavitation initiation sensitive region that show significant responses to changes in transition parameters are retained as key feature points. In the process of filtering the flow-insensitive nodes and key feature points in each grid node of the obtained training dataset, the standard deviation of the wall friction coefficient and pressure coefficient at each grid node in the obtained training dataset within the parameter space is compared with a preset threshold. If the standard deviation of the wall friction coefficient and pressure coefficient at the corresponding grid node in the obtained training dataset within the parameter space is less than or equal to the preset threshold, then the corresponding grid node in the obtained training dataset is determined to be a flow-insensitive node; if the standard deviation of the wall friction coefficient and pressure coefficient at the corresponding grid node in the obtained training dataset within the parameter space is greater than the preset threshold, then the corresponding grid node in the obtained training dataset is determined to have a significant response to changes in the parameter space, and the corresponding grid node in the obtained training dataset is a key feature point. Key feature points in this invention include transition zone nodes, separation / reattachment zone nodes, and cavitation initiation sensitive zone nodes. Specifically, the nodes can be identified based on the pressure coefficient and its extreme value distribution, the location of abrupt changes in the friction coefficient, and its gradient change characteristics: when the wall friction coefficient distribution at a node rises rapidly from a low value accompanied by abrupt changes in the gradient along the flow path, the node can be identified as a transition-related node; when the pressure coefficient at a node is at a low pressure level and near the minimum pressure, the node can be identified as a cavitation sensitive node; when the wall friction coefficient at a node shows an abnormal decrease or a decline in distribution characteristics, combined with flow field separation characteristics, the node can be identified as a separation-related node, thus forming a set of key feature points oriented towards multi-physical process constraints.

[0029] S4. Construct a fully connected deep neural network with the empirical closure parameter vector as input and the wall friction coefficient and pressure coefficient at the selected key feature points as output; use the training dataset generated in S2 as supervised learning samples to train the fully connected deep neural network and obtain the nonlinear mapping relationship between the empirical closure parameter vector and the hydrofoil surface flow field characteristics. The specific architecture of the fully connected deep neural network (DNN) described in this embodiment is as follows: The input layer contains 4 neurons, corresponding to the empirical closure parameter vector; the hidden layer consists of 5 layers, each containing 64 neurons, and the activation function is Swish(…). To address the vanishing gradient problem in deep networks; the output layer contains M neurons (e.g., M=100), corresponding to the wall friction coefficient and pressure coefficient values ​​at the selected key feature points; the training hyperparameters use the Adam optimizer, with an initial learning rate set to... The batch size is 32, the training epochs are 2000, and the loss function is mean squared error (MSE). The input layer receives an empirical closed-form parameter vector, taking into account the stress coefficient before inputting the data into the neural network. With friction coefficient There are significant differences in numerical magnitude ( for Magnitude, and for Direct training on small-scale features (of a certain magnitude) can lead to the model becoming insensitive to them. Therefore, before feeding the labeled training data into the model for training, min-max normalization is performed. Statistical analysis of all sample points in the training set and The maximum and minimum values; Using formula Map both values ​​to interval; After the model outputs the predicted values, the inverse function is used to restore the physical dimensions.

[0030] This step eliminates the influence of different physical quantities' dimensions, making the weights of each physical field in the loss function practically equivalent. For the pressure coefficient and friction coefficient at the output, Z-Score standardization (i.e., subtracting the mean and dividing by the standard deviation) is used to accelerate network convergence and prevent gradient explosion. After the model predicts the output, it is then denormalized back to the physical quantity values. The output layer corresponds to the physical quantity values ​​(including those at the key feature points selected in step S3) at the key feature points. and ).

[0031] In step S4, the output layer of the fully connected deep neural network performs standardized sorting and vectorization processing on the selected key feature points, specifically including: S41. Arrange the dimensionless coordinates of the extracted key feature points in the airfoil chord direction in ascending order; S42. Represent the physical properties of each key feature point after sorting in S41 as a sub-vector. The sub-vector includes the corresponding dimensionless coordinates, wall friction coefficient and pressure coefficient value. S43. Concatenate the sub-vectors corresponding to all key feature points in sequence to obtain the corresponding one-dimensional output vector, so that each neuron in the output layer of the neural network always corresponds to the physical properties of a specific geometric position on the airfoil.

[0032] S5. Establish an optimization objective function for parameter inversion using the empirical closed-loop parameter vector of the Reynolds-averaged Navier-Stokes transition model as the optimization variable. The optimization objective function is based on the deviation between the predicted values ​​of wall friction coefficient and pressure coefficient at key feature points obtained from the nonlinear mapping relationship between the empirical closed-loop parameter vector and the flow field characteristics of the hydrofoil and the experimental or measurement data. It includes a friction fitting term, a pressure extreme value constraint term, and a parameter range regularization term. Specifically, the objective function of the optimization process treats the empirical closed-loop parameter vector of the transition model to be inverted. That is, the empirical closed-loop parameter vector is used as the optimization variable, and parameter inversion is achieved by minimizing the loss function. The loss function is based on the deviation between the predicted values ​​of wall friction coefficient and pressure coefficient at key feature points output by the surrogate model and the data from water tunnel experiments or high-fidelity measurements. By introducing multiple physical constraints, the inverted parameters can characterize both boundary layer friction and transition locations, and accurately capture the extreme pressure characteristics of the low-pressure zone in hydraulic machinery, thus adapting to the real operating environment of hydraulic machinery.

[0033] The friction fitting term in S5 is used to measure the deviation between the predicted value of the wall friction coefficient and the measured value of the water tunnel experiment. The parameter range regularization term is used to limit the interval in which the inversion parameters lie through a smooth boundary function; specifically, the smooth boundary function is used... The inversion parameters are constrained to be within a physically reasonable range; among which When the empirical closed parameter vector Within the interval, both terms are softplus (negative) ≈ 0, when the empirical parameter vector is closed. Going out of bounds will result in continuously differentiable penalties, and the more times the boundary is crossed, the greater the penalty.

[0034] The pressure extreme value constraint term is used to apply a higher weight to the pressure coefficient prediction error in the low-pressure area, and the calculation formula involved is as follows: ; in, This refers to the set of surface region nodes in the experimental data where the pressure coefficient is less than the critical cavitation number. The empirical closed parameter vector of the Reynolds-averaged Navier-Stokes transition model; Let be the pressure coefficient obtained at the i-th low-pressure zone node through the water tunnel experiment; For empirically closed parameter vectors Under the given conditions, the pressure coefficient at the i-th low-pressure node is predicted by the nonlinear mapping relationship between the empirical closed parameter vector and the flow field characteristics of the hydrofoil surface; The cavitation zone weighting coefficient is used to assign a higher weight to the pressure error of the low-pressure zone node than to other regions.

[0035] The cavitation zone weighting coefficient is adaptively adjusted based on the distance function between the pressure coefficient at the node and the critical cavitation number, and the relevant calculation formula is as follows: ; in, Let be the pressure coefficient at the i-th low-pressure node. This represents the minimum pressure coefficient at each low-pressure node in the current flow field. This is the gain coefficient. As the attenuation factor, the , where k is a preset dimensionless scaling factor. This function increases the weight of nodes closer to the lowest pressure point. The weight of nodes far from the low-pressure area increases exponentially, while the weight of nodes close to 1. This enables the optimization process to automatically focus on the region with the highest cavitation risk.

[0036] S6. The objective function is minimized using a gradient descent optimization algorithm. The nonlinear mapping relationship between the obtained empirical closed parameter vector and the flow field characteristics of the hydrofoil surface is used as a differentiable computational graph. The gradient information of the optimization objective function with respect to the empirical closed parameter vector is obtained through backpropagation, and the empirical closed parameter vector is iteratively updated. The optimal model parameter set that fits the current hydraulic conditions is solved in reverse. The obtained optimal model parameter set is used for computational fluid dynamics calculations of three-dimensional hydraulic machinery to predict the overall machine performance.

[0037] The gradient descent optimization algorithm of S6 uses the L-BFGS algorithm to accelerate the convergence speed of the iterative update of the empirical closed parameter vector. The convergence criterion is set as the objective function descent amplitude being lower than a preset amplitude threshold or reaching the maximum number of iterations. A multi-point restart strategy is adopted, selecting multiple initial points in the parameter space for optimization. In each iteration, the error between the predicted values ​​of the wall friction coefficient and pressure coefficient of key feature points predicted by the nonlinear mapping relationship between the obtained empirical closed parameter vector and the flow field characteristics of the hydrofoil surface and the experimental data is used to calculate the optimization objective function. Gradient information is obtained by backpropagation, and the empirical closed parameter vector is updated until convergence. The solution with the minimum final loss function value is taken as the global optimum to avoid getting trapped in local minima.

[0038] The specific process in S6 of using the obtained optimal model parameter set for computational fluid dynamics calculations of three-dimensional hydraulic machinery to predict the overall performance includes: The flow field of turbine runner blades or pump impellers is simulated using the calibrated optimal model parameter set. Based on the location of the fluid separation point and the minimum pressure distribution obtained from the simulation, the blade airfoil rib line or thickness distribution is modified. The blade geometry modification is driven by the airfoil parameterization method, which maps the cross-sectional airfoil geometric features of the turbine or pump blades to a set of geometric control parameters. When the calibrated simulation results show that the transition initiation position is within the preset chord length range of the suction surface and the minimum pressure coefficient is lower than the critical cavitation threshold, the correction strategy is automatically executed. The leading edge radius is selected as the design variable for iterative optimization to delay the occurrence of transition or suppress the initiation of cavitation.

[0039] Specifically, firstly, CFD simulation is performed on the turbine runner blades or pump impeller using calibration parameters to identify the fluid separation point location, transition initiation location, and lowest pressure distribution area. Then, based on these key locations and cavitation risk areas, the airfoil rib line, thickness distribution, or leading / trailing edge curvature are adjusted according to preset modification rules, and simulation verification is performed again until the design goals of suppressing cavitation initiation or improving efficiency are met, thus realizing a closed-loop optimization modification process for engineering design. The blade geometry modification is driven by the PARSEC airfoil parameterization method or the Hicks-Henne type function method. Specifically, the cross-sectional airfoil geometry features of the turbine or pump blade are mapped to a set of geometric control parameters, which at least include the leading edge radius (…). ), the location of maximum thickness on the upper surface ( ) and maximum thickness value ( When the calibrated simulation results show that the transition initiation position is within 0-20% of the chord length of the suction surface and the minimum pressure coefficient is... Below the critical cavitation threshold At that time, the following correction strategy is automatically executed: lock the chord length and trailing edge parameters, and select the leading edge radius parameter. As a design variable, according to the preset step size Iterative increase The value, until Or it may reach the geometric constraint boundary; if the fluid separation point occurs earlier than the design value, then the position parameter of the maximum thickness of the upper surface is selected. It moves toward the trailing edge to delay the generation of the adverse pressure gradient.

[0040] This embodiment takes the calibration of the transition model of a mixed-flow turbine (Francis Turbine) as an example, as detailed below: Baseline model selection: SST was chosen. Turbulence model coupled with single equation Transition model. Determine the set of parameters to be optimized. .

[0041] Data generation: Select NACA 0012 and NACA 4412 hydrofoils that are similar to the cross-section of the turbine blades.

[0042] Operating conditions: Reynolds number Angle of attack range .

[0043] Using the LHS algorithm with default parameter values Generate 1000 samples within the range, and compute them using Star-CCM+ or OpenFOAM. and distributed.

[0044] During neural network training: Input: 4-dimensional parameter vector.

[0045] Output: 100 key points after screening the hydrofoil surface and value.

[0046] Network structure: 5 fully connected layers, 64 neurons per layer, with Swish activation function.

[0047] Inverse problem solving: Obtain actual measurements of hydrofoils in water tunnel experiments Curves and pressure distribution.

[0048] Define the loss function: .in Weights are set to Twice that, emphasizing the fit to the low-pressure region. Frictional fitting term. Used to measure the deviation between predicted friction distribution and experimental measurements, in order to calibrate the boundary layer transition location; pressure extreme value constraint term. This method is used to assign high weight to the pressure coefficient prediction error in low-pressure areas, taking into account the cavitation characteristics of hydraulic machinery. To ensure the model accurately captures the minimum pressure point, the set of nodes in the low-pressure zone is as follows: (It meets the experimental pressure coefficient) (node ​​region); parameter range regularization term This is used to constrain inversion parameters within a physically reasonable range using smooth boundary functions, thereby preventing numerical divergence or loss of physical meaning caused by inversion parameters going out of bounds. For any parameter Set its value range as Then the parameter range regularization term can be expressed as: in This is used to generate a continuously differentiable penalty when parameters approach or exceed the boundary, thereby improving the stability and engineering usability of inverse problem solutions.

[0049] Using the L-BFGS optimizer, convergence is achieved in approximately 50 iterations, yielding the corrected parameters. .

[0050] Will It was applied to the 3D simulation of the entire flow channel of a mixed-flow turbine in a power station.

[0051] The results show that the corrected model successfully captured the trailing edge transition phenomenon of the guide vane, and the predicted range of the cavitation zone on the suction surface of the runner blade is more consistent with the actual observation.

[0052] like Figure 2As shown, when simulating the hydrofoil's operating conditions using the default transition model parameters of existing commercial software (i.e., the baseline distribution shown by the black solid line in the figure), the predicted peak value of the minimum suction surface pressure coefficient is approximately... ; However, in the water tunnel experiment under this typical working condition, the measured minimum pressure coefficient was... (The corresponding value is deep within the gray shaded area in the image).

[0053] The predicted values ​​using the default parameters deviate significantly from the experimental true values, failing to capture the actual low-pressure extreme values. Its relative prediction error is as high as: ; Such a significant under-prediction is fatal. If the critical cavitation number... The default result (-0.95) can mislead designers into thinking there is no risk of cavitation, while cavitation has already occurred in actual operation (-1.15). This is the main reason for the early corrosion of hydraulic machinery blades.

[0054] To address the above problems, the present invention utilizes Figure 2 The parameter sensitivity space, indicated by the gray shading, is used to force the optimization algorithm to find the optimal parameters within the shaded area by introducing the pressure extremum constraint term in step S5.

[0055] That is, using the physical characteristics indicated by arrows A (cavitation sensitive region) and B (transition sensitive region), the predicted curve is stretched downwards from the default black solid line to a position close to the lower edge of the gray area. After calibration using the method of this invention, the lowest pressure coefficient predicted by the parameters inverted from the surrogate model is... .

[0056] like Figure 3 As shown, the hydraulic efficiency of a mixed-flow turbine across the entire flow range ( A comparative verification was conducted. The most complex partial load condition was selected. As a typical point of analysis: Experimental truth: The measured efficiency of the model experimental platform is... ; Default parameters: Uncalibrated CFD calculation results show an efficiency of [value missing]. ; Because the default model prematurely predicted the transition from laminar to turbulent flow, the calculated wall friction and separation losses were excessively high, resulting in an absolute efficiency deviation of -3.7 percentage points (a relative error of approximately 4.1%). This prevented designers from accurately assessing unit performance. Applying the model calibrated according to this invention improved the efficiency to [percentage missing]. The predicted curves closely match the experimental results, with an absolute efficiency deviation of only -0.4 percentage points (relative error of approximately 0.4%).

[0057] Therefore, across the entire operating range, this invention reduces the average root mean square error of prediction (RMSE) from 3.5% of the default parameter to 0.45%. This demonstrates that the technical solution proposed in this invention can effectively find the physical parameters suitable for high Reynolds number hydraulic machinery, solving the problem of prediction distortion in existing technologies under non-design conditions.

[0058] This second embodiment provides a hydraulic machinery turbulence transition model parameter calibration system, including: The sample generation module is used to generate Reynolds-averaged Navier-Stokes transition model parameter samples through Latin hypercube sampling; The flow field calculation module is used to call the CFD solver to calculate the hydrofoil flow field data in batches. The surrogate model training module is used to train fully connected deep neural networks to replace computational CFD solvers; The parameter inversion module is used to solve for the optimal model parameters by minimizing the physical constraint loss function based on the water tunnel experimental data.

[0059] It should be noted that, in this document, relational terms such as "first" and "second" are used only to distinguish one entity or operation from another, and do not necessarily require or imply any such actual relationship or order between these entities or operations. Furthermore, the terms "comprising," "including," or any other variations thereof are intended to cover non-exclusive inclusion, such that a process, method, article, or apparatus that comprises a list of elements includes not only those elements but also other elements not expressly listed, or elements inherent to such process, method, article, or apparatus.

[0060] Finally, it should be noted that the above descriptions are merely preferred embodiments of the present invention and are not intended to limit the present invention. Although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art can still modify the technical solutions described in the foregoing embodiments or make equivalent substitutions for some of the technical features. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the protection scope of the present invention.

Claims

1. A method for calibrating parameters of a hydraulic mechanical turbulent transition model, characterized in that, include: S1. Determine a set of empirical closed-loop parameter vectors for the Reynolds-averaged Navier-Stokes transition model to be calibrated. The empirical closed-loop parameter vectors are determined based on the physical meaning of the selected Reynolds-averaged Navier-Stokes transition model and its influence mechanism on the transition process. Prioritize the selection of key closed-loop parameters that have a significant impact on the distribution of friction coefficient and pressure coefficient under typical hydraulic machinery operating conditions as parameters to be inverted. Fix the general constants in the Reynolds-averaged Navier-Stokes transition model or numerical stability parameters that are not sensitive to the transition position to default values. Based on the Reynolds number range of typical hydraulic machinery operating conditions, the physical value boundaries of the parameters to be inverted are set, and multiple sets of parameter samples are generated using Latin hypercube sampling. S2. Select a two-dimensional hydrofoil profile model that is similar to the hydraulic machinery blade in terms of geometric and flow field characteristics. For each set of parameter samples collected in S1, use a computational CFD solver to perform numerical simulation to obtain the wall friction coefficient distribution data and pressure coefficient distribution data along the hydrofoil surface, and construct a training dataset consisting of the input parameter set and the output flow field characteristics. S3. Calculate the standard deviation of the wall friction coefficient and pressure coefficient at each grid node in the obtained training dataset in the parameter space. Combine the preset threshold for the obtained standard deviation to filter the flow-insensitive area nodes and key feature points in each grid node of the obtained training dataset. S4. Construct a fully connected deep neural network with the empirical closure parameter vector as input and the wall friction coefficient and pressure coefficient at the selected key feature points as output. Using the training dataset generated by S2 as supervised learning samples, the fully connected deep neural network is trained to obtain the nonlinear mapping relationship between the empirical closed parameter vector and the flow field characteristics of the hydrofoil surface. S5. Establish an optimization objective function for parameter inversion using the empirical closed-loop parameter vector of the Reynolds-averaged Navier-Stokes transition model as the optimization variable. The optimization objective function is based on the deviation between the predicted values ​​of wall friction coefficient and pressure coefficient at key feature points obtained from the nonlinear mapping relationship between the empirical closed-loop parameter vector and the flow field characteristics of the hydrofoil and the experimental or measurement data. It includes a friction fitting term, a pressure extreme value constraint term, and a parameter range regularization term. S6. The objective function is minimized using a gradient descent optimization algorithm. The nonlinear mapping relationship between the obtained empirical closed parameter vector and the flow field characteristics of the hydrofoil surface is used as a differentiable computational graph. The gradient information of the optimization objective function with respect to the empirical closed parameter vector is obtained through backpropagation, and the empirical closed parameter vector is iteratively updated. The optimal model parameter set that fits the current hydraulic conditions is solved in reverse. The obtained optimal model parameter set is used for computational fluid dynamics calculations of three-dimensional hydraulic machinery to predict the overall machine performance.

2. The method for calibrating parameters of a hydraulic mechanical turbulent transition model according to claim 1, characterized in that, The Reynolds-averaged Navier-Stokes transition model in S1 is a single-equation γ-transition model based on local correlation; the specific definition of the empirical closed-form parameter vector in the governing equations includes: The parameter controlling the length of the transition region is used to determine the magnitude of the turbulent spot generation term in the intermittent factor transport equation in the single-equation γ-transition model, and affects the rate of abrupt change from laminar to turbulent flow. The parameters controlling the transition critical Reynolds number include: parameters controlling the correlation between the transition critical Reynolds number and the inflow turbulence intensity, and parameters controlling the attenuation characteristics of the transition critical Reynolds number. The parameters controlling the transition critical Reynolds number are located in the empirical correlation of the critical momentum thickness Reynolds number and are used to capture the influence of background turbulence intensity. The parameters controlling the pressure gradient response are the corresponding response coefficients in the correction terms related to the pressure gradient parameters, which are used to correct the transition criterion in the strong adverse pressure gradient region.

3. The method for calibrating parameters of a hydraulic mechanical turbulent transition model according to claim 1, characterized in that, The two-dimensional hydrofoil profile model in S2 is selected from a publicly available standard hydrofoil model library. The criteria for determining similarity to hydraulic machinery blades in terms of geometric and flow field characteristics are as follows: Geometric similarity: the error of the maximum relative thickness of the hydrofoil compared to the average cross-section of the hydraulic machinery blade is within a first preset range; Similarity in flow field characteristics: Under the same Reynolds number, the pressure recovery coefficient gradient of the standard hydrofoil suction surface is within a second preset range compared to the error of the hydraulic mechanical blade suction surface. When constructing the training dataset consisting of an input parameter set and output flow field features, the input parameter set represents the empirical closed parameter vector used in numerical calculations of the Reynolds-averaged Navier-Stokes transition model; the output flow field features represent the obtained wall friction coefficient distribution data and pressure coefficient distribution data along the hydrofoil surface.

4. The method for calibrating parameters of a hydraulic mechanical turbulent transition model according to claim 1, characterized in that, The preset threshold in S3 is determined using a statistical adaptive method, specifically: the average and variance of the standard deviation of all grid nodes are calculated, and the sum of the average and variance by a preset multiple is used as the preset threshold. In the process of filtering the flow-insensitive zone nodes and key feature points in each grid node of the obtained training dataset, the standard deviation of the wall friction coefficient and pressure coefficient at each grid node in the obtained training dataset in the parameter space is compared with a preset threshold. If the standard deviation of the wall friction coefficient and pressure coefficient at the corresponding grid node in the obtained training dataset in the parameter space is less than or equal to the preset threshold, then the corresponding grid node in the obtained training dataset is determined to be a flow-insensitive zone node. If the standard deviation of the wall friction coefficient and pressure coefficient at the corresponding grid node in the obtained training dataset is greater than the preset threshold in the parameter space, then the corresponding grid node in the obtained training dataset is determined to have a significant response to changes in the parameter space, and the corresponding grid node in the obtained training dataset is a key feature point.

5. The method for calibrating parameters of a hydraulic mechanical turbulent transition model according to claim 1, characterized in that, In step S4, the output layer of the fully connected deep neural network performs standardized sorting and vectorization processing on the selected key feature points, specifically including: S41. Arrange the dimensionless coordinates of the extracted key feature points in the airfoil chord direction in ascending order; S42. Represent the physical properties of each key feature point after sorting in S41 as a sub-vector. The sub-vector includes the corresponding dimensionless coordinates, wall friction coefficient and pressure coefficient value. S43. Concatenate the sub-vectors corresponding to all key feature points in order to obtain the corresponding one-dimensional output vector.

6. The method for calibrating parameters of a hydraulic mechanical turbulent transition model according to claim 1, characterized in that, The friction fitting term in S5 is used to measure the deviation between the predicted value of the wall friction coefficient and the measured value of the water tunnel experiment. The parameter range regularization term is used to limit the interval in which the inversion parameters are located by a smooth boundary function; The pressure extreme value constraint term is used to apply a higher weight to the pressure coefficient prediction error in the low-pressure area, and the calculation formula involved is as follows: ； in, This refers to the set of surface region nodes in the experimental data where the pressure coefficient is less than the critical cavitation number. The empirical closed parameter vector of the Reynolds-averaged Navier-Stokes transition model; Let be the pressure coefficient obtained at the i-th low-pressure zone node through the water tunnel experiment; For empirically closed parameter vectors Under the given conditions, the pressure coefficient at the i-th low-pressure node is predicted by the nonlinear mapping relationship between the empirical closed parameter vector and the flow field characteristics of the hydrofoil surface; This is the weighting coefficient for the cavitation region.

7. The method for calibrating parameters of a hydraulic mechanical turbulent transition model according to claim 6, characterized in that, The cavitation zone weighting coefficient is adaptively adjusted based on the distance function between the pressure coefficient at the node and the critical cavitation number, and the relevant calculation formula is as follows: ； in, Let be the pressure coefficient at the i-th low-pressure node. This represents the minimum pressure coefficient at each low-pressure node in the current flow field. This is the gain coefficient. As the attenuation factor, the k is a preset dimensionless scaling factor.

8. The method for calibrating parameters of a hydraulic mechanical turbulent transition model according to claim 1, characterized in that, The gradient descent optimization algorithm of S6 uses the L-BFGS algorithm to accelerate the convergence speed of the iterative update of the empirical closed parameter vector. The convergence criterion is set as the objective function descent amplitude being lower than a preset amplitude threshold or reaching the maximum number of iterations. A multi-point restart strategy is adopted, selecting multiple initial points in the parameter space for optimization. In each iteration, the error between the predicted values ​​of the wall friction coefficient and pressure coefficient of key feature points predicted by the nonlinear mapping relationship between the obtained empirical closed parameter vector and the flow field characteristics of the hydrofoil surface and the experimental data is used to calculate the optimization objective function. Gradient information is obtained by backpropagation, and the empirical closed parameter vector is updated until convergence. The solution with the minimum final loss function value is taken as the global optimal solution.

9. The method for calibrating parameters of a hydraulic mechanical turbulent transition model according to claim 1, characterized in that, The specific process in S6 of using the obtained optimal model parameter set for computational fluid dynamics calculations of three-dimensional hydraulic machinery to predict the overall performance includes: The flow field of turbine runner blades or pump impellers is simulated using the calibrated optimal model parameter set. Based on the location of the fluid separation point and the minimum pressure distribution obtained from the simulation, the blade airfoil rib line or thickness distribution is modified. The blade geometry modification is driven by the airfoil parameterization method, which maps the cross-sectional airfoil geometric features of the turbine or pump blades to a set of geometric control parameters. When the calibrated simulation results show that the transition initiation position is within the preset chord length range of the suction surface and the minimum pressure coefficient is lower than the critical cavitation threshold, the correction strategy is automatically executed. The leading edge radius is selected as the design variable for iterative optimization to delay the occurrence of transition or suppress the initiation of cavitation.

10. A hydraulic machinery turbulent transition model parameter calibration system, employing the hydraulic machinery turbulent transition model parameter calibration method according to any one of claims 1 to 9, characterized in that, include: The sample generation module is used to generate Reynolds-averaged Navier-Stokes transition model parameter samples through Latin hypercube sampling; The flow field calculation module is used to call the CFD solver to calculate the hydrofoil flow field data in batches. The surrogate model training module is used to train fully connected deep neural networks to replace computational CFD solvers; The parameter inversion module is used to solve for the optimal model parameters by minimizing the physical constraint loss function based on the water tunnel experimental data.

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