A method for aerothermodynamic design and test feedback correction of a radial turbine

Abstract

The application discloses a radial steam turbine aerodynamic thermal design and test feedback correction method, and belongs to the field of turbomachinery design and artificial intelligence technology, comprising: based on one-dimensional multi-physical field top-level design, optimization is carried out with maximum isentropic efficiency and minimum steam condensation as optimization objectives; sample library is constructed after collecting multi-working condition data and judging stability; BPANN model is constructed, geometric structure parameters and operating conditions are taken as inputs, and isentropic efficiency and steam condensation are taken as outputs for training; the trained model is used for wide working condition prediction; the prediction result is compared with the test measured value, and model parameters are feedback corrected according to the prediction error. The application forms a closed loop of 'one-dimensional multi-physical field design-BPANN prediction-test verification feedback'. The final isentropic efficiency is greater than 80%, the steam condensation is controlled within 3%, and the R 2 of the BPANN prediction result and the test result can reach 99%.

Description

Technical Field

[0001] This invention relates to the fields of turbomachinery design and artificial intelligence technology, and in particular to a method for aerodynamic and thermodynamic design and experimental feedback correction of centripetal steam turbines. Background Technology

[0002] Industrial waste heat, waste pressure, waste gas, and waste energy recovery from steam expansion are important directions for industrial energy conservation and energy cascade utilization. The IEA's "World Energy Investment 2025" indicates that global clean energy investment will reach approximately US$2.2 trillion by 2025. CREA data shows that China's clean energy industry reached approximately RMB 13.6 trillion in 2024. GB / T 1028-2018 "Evaluation Methods for Industrial Waste Energy Resources" establishes a technical standard for waste energy evaluation at the standard level, indicating a clear industrial demand for industrial energy-saving equipment and waste energy recovery.

[0003] For gas turbine testing systems, steam expansion waste energy utilization, and small-to-medium power pressure energy recovery scenarios, centripetal turbines offer advantages such as compact structure, adaptability to low-flow and low-to-medium power scenarios, and ease of coupling with test benches or power generation loads, making them suitable as energy conversion components in waste energy recovery and experimental verification systems. Dixon and Hall pointed out that turbine performance is closely related to flow matching, loss distribution, and operating boundaries under eccentric conditions. Augier indicated that non-ideal factors such as tip clearance, secondary flow, and residual velocity loss can lead to efficiency reduction and affect operational stability. Existing waste energy recovery equipment and turbine design methods primarily evaluate output power or isentropic efficiency under rated operating conditions, neglecting performance variations under wide operating conditions such as variable flow rate, variable speed, and variable inlet boundary. Centripetal turbine design for steam working fluids not only requires improving isentropic efficiency but also controlling steam working fluid condensation and possessing wide-condition prediction and experimental feedback correction capabilities. Existing one-dimensional average line design methods can quickly determine the main geometric dimensions and initial operating parameters of the turbine in the early stages of design, offering advantages such as fast modeling speed, convenient parameter adjustment, and suitability for initial screening of schemes. Moustapha, Zelesky, Baines, and Japikse pointed out that the one-dimensional average line method can effectively complete the preliminary design and performance estimation of turbines. Baines further pointed out that the performance of radial turbines is affected by the flow coefficient, load coefficient, speed ratio, and geometric parameters, and the flow characteristics and loss mechanisms differ under different operating conditions. However, traditional one-dimensional design usually relies on empirical loss models and fixed design point assumptions, and has limited ability to describe multi-parameter coupling, steam humidification and condensation, and performance changes under partial operating conditions, making it difficult to accurately reflect the coupling relationship between structural parameters, operating conditions, and steam condensation trends. Therefore, it is necessary to introduce multiphysics constraints and iterative optimization mechanisms in the one-dimensional design stage.

[0004] Computational fluid dynamics (CFD) can analyze the velocity, pressure, temperature, leakage flow, secondary flow, and local loss distribution within a turbine in detail, making it an important tool for revealing flow mechanisms and conducting structural verification. The Denton system analyzed the main mechanisms of boundary layer loss, wake loss, leakage loss, and secondary flow loss within a turbine, demonstrating the significant value of CFD in identifying loss sources and optimizing structures. However, CFD modeling and computation typically involve processes such as 3D modeling, mesh generation, turbulence model selection, boundary condition setting, and post-processing, resulting in high time and computational costs per calculation. For steam working fluid scenarios, the influence of real-world properties, humidification, condensation, and phase change must be considered, further increasing model complexity. Therefore, CFD is more suitable for mechanism analysis and local verification under critical operating conditions, rather than being the sole tool for rapid prediction of multi-parameter, large-scale, and wide-condition scenarios. In recent years, artificial intelligence and machine learning surrogate models have been increasingly used in the rapid prediction of complex engineering systems. Ghosh et al. pointed out that machine learning methods can reduce expensive iterations in gas turbine blade design; studies by Zhang et al., Hora, and Giometto show that machine learning surrogate models have advantages in reducing computational costs, shortening prediction time, and expanding design space. For turbine design, AI models can quickly provide performance predictions across a wide range of operating conditions after training, thereby reducing reliance on point-by-point CFD calculations and numerous repeated experiments, and improving design iteration efficiency. Combining one-dimensional multiphysics design procedures with the BPANN prediction model can maintain the interpretability of the physical model while enabling rapid prediction, error feedback, and continuous model correction based on limited experimental samples.

[0005] In summary, this invention forms a closed loop of "one-dimensional multiphysics design - BPANN prediction - experimental verification feedback". It reduces computation time and experimental cost, improves turbine design efficiency, prediction accuracy, and generalization ability across a wide range of operating conditions, thereby overcoming the shortcomings of existing technologies in terms of reliance on empirical parameters, insufficient steam condensation treatment, high cost of expanding operating conditions, and insufficient rapid prediction capability. Summary of the Invention

[0006] The purpose of this invention is to provide a centripetal steam turbine aerodynamic and thermodynamic design and experimental feedback correction method, aiming to solve the problems of neglecting steam condensation and difficulty in predicting over a wide range of operating conditions in existing designs. This method employs a one-dimensional multiphysics top-level design, with isentropic efficiency and steam condensation rate as co-optimization objectives; it combines a backpropagation artificial neural network, using geometric parameters and operating conditions as inputs, and isentropic efficiency and steam condensation rate as the core prediction outputs; experimental data is used to verify and correct the model, ultimately achieving a closed-loop predictive design with high isentropic efficiency and low steam condensation rate under a wide range of operating conditions.

[0007] To achieve the above objectives, this invention provides a method for aerodynamic and thermodynamic design and experimental feedback correction of a centripetal steam turbine, comprising the following steps: S1: Based on the top-level design of one-dimensional multiphysics field, under the coupled effect of geometric constraints, aerodynamic constraints and thermodynamic constraints, the key design parameters of the turbine are synergistically optimized with isentropic efficiency and steam working fluid condensation as optimization objectives to obtain the optimal combination of design variables. S2: Build a turbine test bench and collect test data under multiple operating conditions; the test data should include at least the inlet total pressure, inlet total temperature, outlet back pressure, mass flow rate, rotational speed, output power, outlet temperature, and steam working fluid condensation rate; S3: Perform steady-state determination on the collected experimental data and extract steady-state data; divide the steady-state data into training data and validation data; use the geometric structure parameters corresponding to the optimal design variable combination described in S1 and other multiple design variable combinations generated in the collaborative optimization process as the geometric structure parameters of the samples, and construct a sample library containing input features and output labels; the input features include geometric structure parameters and operating condition parameters, and the output labels include at least isentropic efficiency and steam working fluid condensation rate; S4: Construct a backpropagation artificial neural network model, train the backpropagation artificial neural network model using the sample library, and establish a non-linear mapping relationship between input features and output labels; S5: Use a trained backpropagation artificial neural network model to predict the aerodynamic and thermodynamic performance under multiple operating conditions, and output the predicted isentropic efficiency and steam working fluid condensation. S6: Compare and verify the prediction results of the backpropagation artificial neural network model with the experimental measurement values ​​in the verification data, and correct the weights and biases of the backpropagation artificial neural network model based on the prediction error. S7: Input the geometric structural parameters and operating condition parameters under the operating condition to be predicted into the backpropagation artificial neural network model after feedback correction by S6, and output the corresponding isentropic efficiency and steam working fluid condensation amount under the operating condition as the prediction result of the wide operating condition aerodynamic and thermodynamic performance of the centripetal steam turbine.

[0008] Preferably, the collaborative optimization described in S1 is performed under geometric constraints, which include: Relative leaf height Export hub diameter ratio Export flange diameter ratio The ratio of the number of guide vane blades to the number of moving vane blades and blade angle , and flow channel size , Structural boundary conditions; in, For the blade height, This is the impeller reference diameter. For export wheel hub diameter, The diameter of the export rim. The number of guide vane blades, The number of moving leaf blades, The airflow angle at the guide vane outlet. The relative airflow angle at the blade outlet. The width of the guide vane outlet flow channel. The width of the flow channel at the moving blade outlet.

[0009] Preferably, the collaborative optimization in S1 is performed under aerodynamic constraints, which include: The ratio of the relative velocity at the blade exit to the relative velocity at the blade inlet , moving blade inlet angle ; in, The relative velocity at the inlet of the moving blade. The relative velocity at the blade exit is... The angle of attack is at the inlet of the moving blade.

[0010] Preferably, the isentropic efficiency described in S1 is defined as: ; in, For isentropic efficiency, Total enthalpy at the entrance. This represents the total enthalpy of actual exports. The total enthalpy at the outlet is calculated using isentropic expansion. The condensation rate of the working fluid is expressed as a function of the steam state parameters: ; in, This refers to the condensation rate of the steam working fluid. , and These represent the pressure, temperature, and entropy in the steam state parameters, respectively.

[0011] Preferably, the optimization algorithm used in the collaborative optimization in S1 includes one or more of the following: particle swarm optimization, genetic algorithm, grid search method, sequential quadratic programming, or trust region algorithm.

[0012] Preferably, the condensation amount of the steam working fluid in S2 is obtained by a combination of theoretical back-calculation and experimental measurement: In theoretical back-calculation, based on export pressure outlet temperature And determine the outlet dryness by water vapor physical properties. When the outlet is in a wet steam state, the outlet dryness can be determined based on the actual outlet enthalpy. enthalpy of saturated water and latent heat of vaporization Make an estimate: ; in, For export dryness, This represents the total enthalpy of actual exports. export pressure The corresponding saturated enthalpy of water, To correspond to the latent heat of vaporization under the pressure, when At that time, the amount of steam working fluid condensed by theoretical back-calculation can be expressed as: ; in, The amount of steam working fluid condensed is obtained from theoretical back-calculation. For quality flow, when When this time, it indicates that the outlet working fluid has not entered the wet steam zone, and the theoretical condensation capacity can be taken as [value missing]. ; During the test measurement, a condensation collection unit can be installed at the turbine outlet to measure the mass of condensate collected within a set sampling time. The amount of steam working fluid condensed as measured in the test can be expressed as: ; in, The amount of steam working fluid condensed is measured in the experiment. The mass of condensate collected within the sampling time. This corresponds to the sampling time.

[0013] Preferably, the steady-state determination condition in S3 is: ; in, For the first in the steady-state window Each sample value, This is the window average. The number of sampling points. The allowable fluctuation threshold.

[0014] Preferably, the plurality of operating conditions includes at least two of the following: low flow rate, high flow rate, low speed, high speed, high expansion ratio, low expansion ratio, and near-condensation boundary.

[0015] Preferably, the feedback correction in S6 includes: when the prediction error exceeds a set threshold, adding the experimental measurement values ​​and their corresponding operating parameters from the verification data to the sample library, re-dividing the training data and verification data in the expanded sample library, and retraining or fine-tuning the network weights of the backpropagation artificial neural network model.

[0016] Preferably, the prediction accuracy in S6 is determined by the coefficient of determination R. 2 The evaluation is based on the mean relative error (MRE), where the coefficient of determination (R0) is... 2 The formula is: ; in, For the sample size, As the coefficient of determination, For the first One experimental measurement value, For the first Each model predicts a value. This is the average of all test measurements.

[0017] Therefore, the present invention employs the above-mentioned centripetal steam turbine aerodynamic thermodynamic design and experimental feedback correction method, which has the following beneficial effects: (1) A synergistic optimization method for efficiency improvement and condensation suppression in centripetal steam turbines is proposed. Unlike existing technologies that only focus on isentropic efficiency as a single optimization objective, this invention takes the improvement of isentropic efficiency and the reduction of steam working fluid condensation as a unified objective. In the one-dimensional aerodynamic-thermodynamic design stage, by synergistically optimizing key design parameters, the velocity triangle and flow path structure are better matched, reducing irreversible losses such as impeller friction, gap leakage, exhaust residual velocity, and impeller friction, thereby improving the actual enthalpy drop utilization rate. The physical mechanism is that after the key geometric parameters are matched with the flow rate and rotational speed, the inlet angle of attack and relative velocity ratio tend to be reasonable, impeller friction, leakage, separation, and exhaust residual velocity losses are reduced, the conversion ratio of actual enthalpy drop to shaft work is increased, and the outlet dryness is increased while the condensation driving force is reduced. This effect can be quantitatively evaluated through indicators such as isentropic efficiency, outlet dryness, condensation rate, and loss ratio.

[0018] (2) A BPANN aerodynamic and thermodynamic prediction and experimental feedback correction method for wide operating conditions is proposed. Unlike traditional empirical models that can only predict a single performance index and are difficult to adapt to varying operating conditions, this invention constructs a backpropagation artificial neural network (BPANN) model, establishing a nonlinear mapping relationship between geometric parameters, operating conditions, isentropic efficiency, and steam condensation rate. Using isentropic efficiency and steam condensation rate as the core prediction outputs, a comprehensive evaluation of efficiency and condensation trends under wide operating conditions is achieved. The outlet total pressure and outlet total temperature serve as auxiliary aerodynamic and thermodynamic responses, used to characterize pressure and temperature changes during flow and heat transfer. Further verification data collected from the test bench is used to compare and validate the model, and the weights and biases of the backpropagation artificial neural network model are corrected based on the prediction error feedback. Its computer mechanism is as follows: BPANN performs a hidden layer nonlinear mapping on the normalized input and continuously updates the weights and biases through experimental error backpropagation, gradually approximating the actual aerodynamic and thermodynamic response function. For existing experimental samples, the BPANN prediction results show good consistency with the experimental results, with a determination coefficient R0. 2 The accuracy rate can reach over 99%, indicating that the model can effectively capture the nonlinear coupling effect of geometric and operating parameters on isentropic efficiency and steam working fluid condensation, and improve the prediction accuracy and generalization ability of the model under a wide range of operating conditions such as variable flow rate, variable speed, and variable inlet pressure.

[0019] (3) The high isentropic efficiency, low condensation, and BPANN prediction accuracy of the present invention under a wide range of operating conditions were verified through experiments. Unlike existing technologies that only provide design point efficiency and lack multi-condition experimental data, the present invention constructed a centripetal turbine test rig and collected isentropic efficiency and steam working fluid condensation data under multiple mass flow rate and speed conditions, comparing the results with the BPANN model predictions. Experimental results show that when the mass flow rate increases from approximately 0.45 kg / s to 0.65 kg / s, the isentropic efficiency remains within the range of approximately 0.72–0.82, and the overall steam working fluid condensation is approximately 2%–3.5%. When the speed increases from approximately 5000 rpm to 25000 rpm, the isentropic efficiency increases from approximately 0.69 to approximately 0.82, and the steam working fluid condensation mainly remains at a low level of approximately 2%–3%. Simultaneously, the BPANN prediction results are highly consistent with the experimental data, accurately reflecting the variation law of efficiency with flow rate and speed, as well as the trend of condensation. This consistency indicates that the data-driven model constructed in this invention can effectively capture the nonlinear coupling effect of geometry and operating parameters on aerodynamic and thermodynamic performance under a wide range of operating conditions, which can reduce some repeated experiments and significantly improve the efficiency of performance prediction.

[0020] The technical solution of the present invention will be further described in detail below with reference to the accompanying drawings and embodiments. Attached Figure Description

[0021] Figure 1 This is a flowchart of a centripetal steam turbine aerodynamic and thermodynamic design and experimental feedback correction method according to the present invention; Figure 2 This is a schematic diagram of the multiphysics coupling analysis of the one-dimensional aerothermal design of this invention; Figure 3 This is a flowchart of the training, prediction, and feedback correction of the backpropagation artificial neural network model in the centripetal steam turbine aerodynamic thermodynamic design and experimental feedback correction method of the present invention. Figure 4 This is a schematic diagram of the structure of the centripetal turbine test bench in an embodiment of the present invention; Figure 5 This is a schematic diagram of the structure of the centripetal turbine test specimen in an embodiment of the present invention; Figure 6 The following is a comparison of the experimental results and BPANN prediction results of the isentropic efficiency and steam working fluid condensation amount of the centripetal turbine test specimen in this invention with the changes of mass flow rate and rotational speed: (a) is the mass flow rate, (b) is the rotational speed. Figure Labels 1. Air compressor; 2. Storage tank; 3. Throttling valve; 4. Electric valve; 5. Air filter; 6. Vortex flow meter; 7. Heating unit; 8. Pressure gauge; 9. Centripetal turbine test specimen; 10. Generator; 11. Electrical load; 12. Speed ​​sensor; 13. Ammeter; 14. Voltmeter. Detailed Implementation

[0022] The technical solution of the present invention will be further described below with reference to the accompanying drawings and embodiments.

[0023] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, 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, 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.

[0024] Example like Figure 1 As shown in the figure, this embodiment provides a method for aerodynamic and thermodynamic design and experimental feedback correction of a centripetal steam turbine.

[0025] Step 1: One-dimensional multiphysics top-level design based on computer program for high isentropic efficiency and low steam working fluid condensation. Within a one-dimensional average line design framework, a multiphysics-based top-level design method is established for high isentropic efficiency and low vapor condensation. Subsequently, geometric, aerodynamic, and thermodynamic constraints are uniformly incorporated into the computer program. The coupling analysis relationship between geometric constraints, aerodynamic performance, and thermodynamic performance is as follows: Figure 2 The overall logic of this step consists of three parts: geometric constraints, aerodynamic performance, and thermodynamic performance, which are combined and solved through iterative optimization.

[0026] First, in the geometric constraint section, the system constrains the key geometric quantities of the turbine structure, including: Relative leaf height Export hub diameter ratio Export flange diameter ratio The ratio of the number of guide vane blades to the number of moving vane blades and blade angle , and flow channel size , Structural boundary conditions; in, For the blade height, This is the impeller reference diameter. For export wheel hub diameter, The diameter of the export rim. The number of guide vane blades, The number of moving leaf blades, The airflow angle at the guide vane outlet. The relative airflow angle at the blade outlet. The width of the guide vane outlet flow channel. The width of the flow channel at the moving blade outlet.

[0027] In terms of aerodynamic performance, the system is based on mass conservation, momentum conservation, and an empirical loss model, and references the Navier-Stokes momentum relation to analyze the internal velocity field, velocity distribution, and pressure characteristics of the turbine, combined with the total inlet pressure. mass flow rate and rotational speed The total pressure loss is evaluated based on key parameters such as... For the total turbine inlet pressure, To achieve the mass flow rate entering the turbine, This refers to the rotor speed. Simultaneously, a constraint is imposed: the ratio of the relative velocity at the blade exit to the relative velocity at the inlet. , moving blade inlet angle To control unfavorable angle of attack, secondary flow, and residual velocity loss; in, The relative velocity at the inlet of the moving blade. The relative velocity at the blade exit is... The angle of attack at the blade inlet represents the deviation between the incoming flow direction and the metal angle at the blade inlet. These aerodynamic constraints can improve the flow matching degree and aerodynamic work capacity within the turbine.

[0028] Specifically, the aerodynamic performance analysis is based on the continuity equation and the Navier-Stokes momentum equation. The continuity equation (mass conservation) is used to ensure the continuity of flow within the channel: ; in, For the working fluid density, For time, It is a velocity vector. This represents the mass flux divergence.

[0029] The momentum equation describes the velocity distribution, pressure gradient, and viscous loss of the working fluid in the guide vane and moving vane passages. Its differential form is: ; in, For pressure, For dynamic viscosity, Indicates the pressure gradient. This represents the velocity diffusion term.

[0030] In the thermodynamic performance section, the system analyzes the enthalpy drop distribution, heat transfer process, and condensation characteristics during steam expansion based on energy and heat transfer equations. It also evaluates the isentropic efficiency and steam condensation rate by combining key parameters such as inlet total temperature and rotational speed. This calculation allows for the assessment of thermodynamic state changes and terminal condensation trends during steam expansion, providing a basis for low-condensation-rate design.

[0031] The energy equation is used to calculate the enthalpy drop, temperature change, and shaft work output during the expansion of the working fluid; the heat transfer equation describes the effect of heat exchange between the blades and the working fluid on the total outlet temperature. The energy equation can be expressed as: ; in, For enthalpy, The mass derivative represents the mass derivative as the working fluid moves. Thermal conductivity, For temperature, This is a viscous dissipation term.

[0032] The heat transfer equation can be expressed as: ; in, This represents the heat flux density.

[0033] Condensation rate via pressure ,temperature ,entropy Isostate parameters are characterized as The results were verified using outlet dryness, theoretically calculated condensation, and experimentally measured condensation. The condensation constraint refers to the lower limit requirement for turbine outlet dryness, meaning the outlet dryness must not be lower than a preset threshold (e.g., 0.85–0.95) to avoid droplet erosion and efficiency loss due to excessive humidification. This constraint can be used as an independent screening condition in the optimization iteration.

[0034] By solving the above-mentioned continuity equation, momentum equation, energy equation and condensation mechanism in a coupled manner, the system performs synergistic optimization with the goal of maximizing isentropic efficiency and minimizing the amount of steam working fluid condensed, while satisfying geometric constraints. Finally, the optimal combination of design variables and the corresponding aerodynamic and thermodynamic performance evaluation results are output.

[0035] Figure 2 The one-dimensional aerodynamic-thermodynamic design of this invention employs a multiphysics coupled analysis framework. This framework first reads the design variables and operating condition inputs, including geometric parameters and operating condition parameters. Subsequently, the system solves for geometric constraints, aerodynamic performance, and thermodynamic performance in a parallel coupled manner. Geometric constraints: used to limit the relative blade height, outlet hub diameter ratio, outlet rim diameter ratio, guide vane / moving blade number ratio, as well as manufacturability boundaries such as blade angle and flow channel size, to ensure channel area, structural manufacturability and strength requirements.

[0036] Aerodynamic performance: Based on the continuity equation and the Navier-Stokes momentum equation, the velocity distribution, pressure gradient, total pressure loss, angle of attack, and relative velocity ratio are analyzed. Unfavorable angles of attack, secondary flow, and residual velocity losses are reduced through constraints, and the degree of velocity triangle matching is evaluated.

[0037] Thermodynamic performance: Enthalpy drop distribution, heat transfer process, and condensation characteristics are analyzed based on energy and heat transfer equations. Isentropic efficiency, output power, temperature drop, enthalpy drop, and steam condensation rate are used as evaluation indicators.

[0038] Through the above coupling, the system performs rapid iterative design with the optimization objectives of maximizing isentropic efficiency and minimizing steam working fluid condensation, while satisfying geometric, aerodynamic and thermodynamic constraints. Finally, it outputs an optimized design scheme with high isentropic efficiency and low steam working fluid condensation.

[0039] The output of this step includes the optimal combination of design variables, main geometric dimensions, design point isentropic efficiency, outlet dryness, steam working fluid condensation, main loss components, and design data for subsequent backpropagation artificial neural network (BPANN) model.

[0040] Isoentropy efficiency is defined as: ; in, For isentropic efficiency, Total enthalpy at the entrance. This represents the total enthalpy of actual exports. This is the total enthalpy at the outlet calculated using isentropic expansion.

[0041] The amount of steam working fluid condensed is expressed as: ; in, This refers to the condensation rate of the steam working fluid. , and These represent the pressure, temperature, and entropy in the steam state parameters, respectively.

[0042] The design results are verified with isentropic efficiency ≥80% and steam working fluid condensation ≤3%, and the optimization effect is evaluated in combination with outlet dryness, steam working fluid condensation, output power and loss ratio.

[0043] Step 2: Turbine test bench setup and test data acquisition During turbine expansion, the steam working fluid first enters the guide vane or nozzle passage, where it is accelerated by the pressure gradient and develops an absolute velocity with a specific direction. It then enters the moving blade passage, where it exchanges momentum with the high-speed rotating impeller, causing changes in both the absolute and relative velocities of the working fluid, thus outputting shaft work to the rotor. This process simultaneously involves the conversion of pressure energy to kinetic energy, the conversion of kinetic energy to shaft work, mechanical energy dissipation due to wall friction, heat exchange between the blades and the casing, and potential local condensation of the steam working fluid. Therefore, the turbine expansion process must simultaneously satisfy the conservation of mass, momentum, and energy (see step one for the corresponding governing equations). Using the aforementioned flow and heat transfer governing equations, the velocity distribution, pressure changes, enthalpy drop distribution, heat transfer process, and condensation trend during turbine expansion can be analyzed.

[0044] The system establishes design point, low load point, medium load point, high load point, and off-peak operating point by adjusting inlet pressure, inlet temperature, mass flow rate, rotational speed, and outlet back pressure, thus constructing a test sample covering a wide range of operating conditions. Test measurement parameters include at least the following: total inlet pressure, total inlet temperature, outlet static pressure or back pressure, outlet temperature, mass flow rate, rotor speed, shaft end torque or generator end voltage and current, casing wall temperature, and steam working fluid condensation rate.

[0045] Output power can be calculated from electrical power or shaft power, and is expressed as: ; in, For effective output power, This is the voltage at the generator end. For the generator current, For generator efficiency, This refers to the shaft end torque. ω is the angular velocity.

[0046] The isentropic efficiency based on experimental data is: ; in, To test isentropic efficiency, For quality flow, Total enthalpy at the entrance. This is the isentropic total enthalpy at the outlet.

[0047] To clarify the method for obtaining the condensation amount of the steam working fluid, this step adopts a combination of theoretical back-calculation and experimental measurement.

[0048] When performing theoretical back-calculation, first consider the export pressure. outlet temperature And determine the outlet dryness by water vapor physical properties. When the outlet is in a wet steam state, the outlet dryness can be determined based on the actual outlet enthalpy. enthalpy of saturated water and latent heat of vaporization Make an estimate: ; in, For export dryness, This represents the total enthalpy of actual exports. export pressure The corresponding saturated enthalpy of water, This represents the latent heat of vaporization under the corresponding pressure. When At that time, the amount of steam working fluid condensed by theoretical back-calculation can be expressed as: ; in, The amount of steam working fluid condensed is obtained from theoretical back-calculation. For mass flow rate. When When this time, it indicates that the outlet working fluid has not entered the wet steam zone, and the theoretical condensation capacity can be taken as [value missing]. .

[0049] During the test measurement, a condensation collection unit can be installed at the turbine outlet to measure the mass of condensate collected within a set sampling time. The measured steam working fluid condensation rate can be expressed as: ; in, The amount of steam working fluid condensed is measured in the experiment. The mass of condensate collected within the sampling time. This corresponds to the sampling time.

[0050] like Figure 4 As shown, the turbine test bench in this embodiment has the following connection relationships and working process: (a) Connection relationship: Gas path connection (flow path of the test working fluid) The gas flows unidirectionally from left to right, and the components are connected in series through pipes: Air compressor 1 generates the test working fluid, which is delivered to storage tank 2 via pipeline. Storage tank 2 serves to stabilize pressure and store the gas. Its outlet pipeline is connected in sequence to throttle valve 3 and electric valve 4 to control the gas flow rate and on / off state of the system. After passing through the electric valve, the gas enters air filter 5 for purification. The purified gas flows through vortex flow meter 6 to measure the volumetric flow rate. Subsequently, the gas flows through heating unit 7 to regulate the temperature of the test working fluid. The heated gas flows through pressure gauge 8 to detect the pressure of the gas before entering the turbine. Finally, the gas, with a certain pressure and flow rate, enters vertically downwards from the upper pipeline into the centripetal turbine test specimen 9. After expanding and doing work inside the turbine, the gas is discharged from the "exhaust" port on the right side.

[0051] Mechanical transmission connection The centripetal turbine test specimen 9 generates rotational mechanical energy under the impact and expansion of gas. The turbine's rotating shaft is connected to the rotating shaft of the generator 10 below via a coupling, and the turbine's rotation directly drives the generator rotor. Speed ​​sensors 12 are installed near the turbine and generator bearings to monitor the unit's rotational speed (rotational speed) in real time.

[0052] Electrical circuit connection (power generation and load) Generator 10 is driven by a turbine to generate electricity, which is then output through conductors. An ammeter 13 is connected in series in the output circuit to measure the current in the circuit. A voltmeter 14 is connected in parallel after the ammeter to measure the voltage output by the generator. The circuit after the ammeter and voltmeter measurements is finally connected to an electrical load 11, which is used to simulate the generator's output under different load conditions.

[0053] (II) Work Process: Air compressor 1 serves as the source of compressed working fluid for the test bench, generating a test working fluid with specific pressure and flow rate. The test working fluid first enters storage tank 2, which reduces pressure pulsations at the air compressor output and stabilizes and buffers the test working fluid, making the airflow into subsequent pipelines more stable. The outlet of storage tank 2 is connected to throttle valve 3, which is used to initially regulate the gas pressure and flow rate in the pipeline to create test conditions under different inlet pressures and flow rates.

[0054] An electric valve 4 is installed after the throttle valve 3. The electric valve is used to precisely adjust the pipeline opening, changing the air supply according to test requirements, and working with the data acquisition system to achieve automatic switching or semi-automatic adjustment at different operating points. An air filter 5 is connected to the outlet of the electric valve 4. The air filter removes impurities, oil mist, or particulate matter from the test medium, reducing the risk of impurities entering the centripetal turbine test specimen 9 and causing wear or blockage to the impeller, bearings, and flow channels, thereby improving the stability of test data and the reliability of equipment operation.

[0055] The outlet of air filter 5 is sequentially connected to a vortex flow meter 6, a heating unit 7, and a pressure gauge 8. The vortex flow meter measures the volumetric flow rate or equivalent mass flow rate of the gas entering the centripetal turbine test specimen 9 in real time, providing crucial parameters for calculating turbine input energy, aerodynamic performance, and isentropic efficiency. The heating unit heats or regulates the temperature of the working fluid before it enters the turbine, ensuring the inlet temperature meets the set operating conditions. The pressure gauge is installed on the pipeline before the inlet of the centripetal turbine to monitor the pressure at the turbine inlet. Through the combined measurements of the flow meter, heating unit, and pressure gauge, the turbine inlet boundary conditions under different throttling openings, electric valve openings, and supply pressures can be determined, providing fundamental data for subsequent performance calculations and BPANN model training.

[0056] After undergoing the aforementioned pressure stabilization, regulation, filtration, flow measurement, heating, and pressure measurement, the test working fluid enters the centripetal turbine test specimen 9. The centripetal turbine is the core working component of the test bench. Inside it, the test working fluid expands and drives the impeller to rotate, converting the pressure energy and internal energy of the working fluid into the mechanical energy of the rotor shaft. The expanded exhaust gas is discharged from the exhaust port of the centripetal turbine, which can be directly discharged into the atmosphere or connected to a silencing or after-treatment device. Changes in the inlet pressure, flow rate, and rotational speed of the centripetal turbine directly affect the output power and isentropic efficiency.

[0057] The rotor shaft of the centripetal turbine test specimen 9 is connected to the input shaft of the generator 10 via a coupling. The mechanical energy output by the centripetal turbine drives the generator to rotate, and the generator converts the mechanical energy into electrical energy. The output terminal of the generator is connected to an electrical load 11 to simulate the power output state of the turbine under different load conditions. By changing the gas supply pressure, flow rate, or load conditions, the variation patterns of speed, voltage, current, and output power under different operating conditions can be obtained, thereby evaluating the energy conversion capability of the turbine within multiple operating ranges.

[0058] Speed ​​sensor 12 is installed near the shaft between the centripetal turbine test piece 9 and the generator 10 to measure the rotational speed of the turbine rotor or generator input shaft in real time. Rotational speed is a crucial parameter for determining the turbine's operating status, calculating shaft power, and analyzing aerodynamic matching relationships. Ammeter 13 is connected in series in the generator output circuit to measure the generator output current; voltmeter 14 is connected in parallel at the generator output terminal to measure the output voltage. The voltage and current data collected by the voltmeter and ammeter can be used to calculate the generator output power; combined with parameters such as generator efficiency, flow rate, and inlet pressure, the effective turbine output power and experimental isentropic efficiency can be further calculated.

[0059] During the test run, the signals collected by the vortex flow meter 6, pressure gauge 8, velocity sensor 12, ammeter 13 and voltmeter 14 were all transmitted to the data acquisition card and displayed, recorded and processed in real time by the industrial control computer.

[0060] like Figure 5 As shown, the centripetal turbine test specimen 9 includes: a turbine volute, a fluid inlet channel, a nozzle ring, a turbine hub, and a rotor assembly. The turbine volute is an annular turbine volute flow channel structure, with one end connected to the fluid inlet channel; the dimensions of the fluid inlet channel and the annular flow channel are determined according to the design operating conditions. The test gas, after being stabilized, regulated, filtered, flow-measured, heated, and pressure-measured in the front-end pipeline, enters the turbine volute through the fluid inlet channel and is distributed along the circumference of the turbine volute, making the flow rate and pressure before entering the nozzle ring more uniform.

[0061] The nozzle ring is coaxially arranged inside the turbine volute and connected to the annular flow channel inside the turbine volute. The nozzle ring has multiple nozzle channels or nozzle blades circumferentially to convert the pressure energy inside the turbine volute into a high-speed jet with a predetermined direction and velocity, and to guide the working fluid to the inlet of the moving blade rotor assembly according to the designed incident angle, so as to reduce incident deviation, local separation and secondary flow loss.

[0062] The moving blade rotor assembly is located inside the nozzle ring and coaxially connected to the rotor shaft. The moving blade rotor assembly consists of a turbine hub and multiple circumferentially arranged moving blades, with the moving blade inlet opposite to the nozzle ring outlet. The working fluid, accelerated by the nozzle ring, enters the moving blade passage, where momentum exchange occurs and it expands to perform work, converting the pressure energy, internal energy, and kinetic energy of the working fluid into the mechanical energy of the rotor shaft, which is then output to the generator. The turbine hub supports the moving blades, defines the inner flow channel, and maintains the rotational stiffness of the moving blade rotor assembly, ensuring the relative positional stability between the moving blades and the nozzle ring.

[0063] Through the above structure, the fluid intake channel undertakes the function of introducing flow, the annular channel inside the turbine casing and the nozzle ring together achieve circumferential uniform gas distribution and directional acceleration, the moving blade rotor assembly realizes energy conversion, and the turbine hub ensures rotor support and flow channel geometric stability. Thus, the centripetal turbine test piece 9 forms a test bench connection relationship with the front-end flow meter, heating unit, pressure gauge and rear-end generator, which is "intake regulation - uniform gas distribution - nozzle acceleration - moving blade work - shaft power output".

[0064] Step 3: Steady-state determination, data partitioning, and sample library construction To ensure sample reliability, instead of directly inputting all raw time-series data into the backpropagation artificial neural network (BPANN), steady-state determination and sample window extraction are performed first. A window is considered a steady-state window when the mean change rate and fluctuation amplitude of inlet total pressure, inlet total temperature, mass flow rate, rotational speed, and output power within a set time window are all less than a threshold. The steady-state sample selection criteria are as follows: ; in, For the first in the steady-state window Each sample value, This is the window average. The number of sampling points. The allowable fluctuation threshold.

[0065] After extracting the steady-state data, the experimental data are first cleaned and preprocessed, specifically including: (1) Data integrity check and missing value handling: Identify missing values ​​of key parameters such as inlet total pressure, inlet total temperature, mass flow rate, speed, and output power. For a small number of missing values, linear interpolation is performed first based on the physical trend of adjacent steady-state windows, or the values ​​are filled based on repeated tests under the same operating conditions; for abnormal data points that cannot be reasonably repaired, they are directly removed from the training samples to avoid the neural network learning incorrect mapping relationships.

[0066] (2) Outlier removal: based on physical constraints and statistical methods (such as 3) The principle or interquartile range method is used to identify and eliminate outliers caused by sensor malfunction, external disturbances, or recording errors. For the output label of steam working fluid condensation, when its calculated or measured value deviates significantly from the physically possible range (e.g., dryness <0 or >1), it is eliminated.

[0067] (3) Feature construction: Input features include geometric structural parameters (relative blade height, outlet hub diameter ratio, outlet rim diameter ratio, guide vane / moving blade number ratio, blade angle, flow channel size, etc.) and operating condition parameters (mass flow rate, rotational speed, inlet pressure); output labels include isentropic efficiency, steam working fluid condensation, etc., among which the core prediction output of the backpropagation artificial neural network model is isentropic efficiency and steam working fluid condensation.

[0068] After data cleaning, the steady-state data is divided into training data and validation data (in this embodiment, the ratio is 70% training and 30% validation). A sample library containing input features and output labels is constructed by combining the geometric structural parameters corresponding to one or more sets of design variable combinations generated during the co-optimization process in step one.

[0069] It should be noted that although step one obtains a set of optimal design variable combinations through collaborative optimization, this embodiment also includes other sets of design variable combinations generated during the optimization process in step one (such as geometric parameters corresponding to different iteration steps), or other geometric structural parameters obtained through design space sampling, in order to enhance the generalization ability of the BPANN model when constructing the sample library. Therefore, the geometric structural parameters in the sample library are no longer limited to a single optimal design, enabling the neural network to learn the influence of geometric parameter changes on aerodynamic and thermodynamic performance. In another embodiment, only the geometric structural parameters corresponding to the optimal design variable combinations can be used, but in this case, the geometric parameters are used as fixed inputs, and the neural network will mainly learn the mapping relationship between operating condition parameters and output labels.

[0070] To eliminate the impact of dimensional differences between different features on neural network training, input features and output labels are normalized. This embodiment uses the min-max normalization method, with the following formula: ; in, Original features The features are normalized. and These are the minimum and maximum values ​​of the feature in the sample set, respectively.

[0071] All input features and output labels are normalized according to the above formula. The output quantities in the sample library should include at least the experimental isentropic efficiency and the steam working fluid condensation rate.

[0072] Step 4: Build the BPANN model and train it using the sample database. like Figure 3As shown, the Backpropagation Artificial Neural Network (BPANN) model of this invention performs data processing, training, and prediction according to the following process: First, geometric parameters, mass flow rate, rotational speed, inlet pressure, and corresponding experimental measurements and design calculation data are read from the sample library, and normalized, training / validation set partitioning and feature construction are performed; then, the preprocessed features are input into the BPANN model for training, and the weights and biases are continuously corrected through the error backpropagation algorithm; after training, the generalization ability is verified, and predictions are made under multiple different operating conditions, outputting isentropic efficiency and steam working fluid condensation; finally, the prediction results are compared with the experimental measurements, the prediction error is calculated, and when the error exceeds the set threshold, feedback correction is initiated to re-optimize the model parameters (i.e., update the weights and biases of the BPANN model).

[0073] A turbine aerodynamic and thermodynamic prediction model is established using a feedforward backpropagation artificial neural network (BPANN) with multiple inputs and multiple outputs. The input layer receives geometric parameters, operating condition parameters, and physically derived features; the hidden layer extracts the coupling relationships between variables through weighted summation and nonlinear activation; the output simultaneously provides predictions for isentropic efficiency, steam condensation rate, and performance under a wide operating condition. The outlet total pressure and outlet total temperature serve as auxiliary aerodynamic and thermodynamic responses. For non-negative outputs such as steam condensation rate, non-negative constraints or non-negative activation functions can be set in the output layer to ensure that the prediction results conform to physical meaning.

[0074] The network training process consists of three basic steps: forward propagation, error calculation, and backpropagation. In forward propagation, the input features are transformed through each hidden layer to obtain the predicted output. In error calculation, the predicted value is compared with the experimental measurement value to obtain the training error. In backpropagation, the network parameters are updated according to the gradient of the error with respect to the weights and biases, so that the prediction result gradually approaches the experimental result.

[0075] The hidden layer mapping relationship can be represented as: ; in, For the input feature vector, This is the weight matrix from the input layer to the hidden layer. This is the hidden layer bias vector. It is a non-linear activation function. This is the output vector of the hidden layer.

[0076] The output layer mapping relationship can be represented as: ; in, Predict the output vector for BPANN. This is the weight matrix from the hidden layer to the output layer. This represents the output layer bias vector. For this model, the core prediction output can be expressed as: ; in, Predicting isentropic efficiency for BPANN Predict the condensation rate of the working fluid for BPANN.

[0077] The training error can be expressed as: ; in, For training error, The number of training samples. For the first The experimental measurements of each sample, This is the corresponding predicted value.

[0078] In terms of model structure, a shared hidden layer plus multiple output branches can be used, allowing the network to first learn the common features of the geometric structure and operating parameters, and then output different aerodynamic and thermodynamic indices separately. For cases with limited sample size, L2 regularization or early stopping mechanisms can be added to prevent the model from over-memorizing training samples.

[0079] Through the above-mentioned input feature processing, hidden layer mapping, output prediction, experimental comparison and error feedback process, the model can establish a nonlinear mapping relationship between geometric structural parameters, mass flow rate, rotational speed, inlet pressure and isentropic efficiency, and steam working fluid condensation rate, providing a basis for subsequent wide-condition performance prediction and feedback correction.

[0080] Step 5: Use the trained BPANN model to predict multiple operating conditions. Centripetal steam turbine expansion tests typically do not involve a single stable design point, but rather multidimensional variations in inlet pressure, inlet temperature, mass flow rate, rotational speed, and outlet back pressure. Therefore, the BPANN model cannot only achieve high accuracy near the design point; it also needs to maintain stable predictive capabilities under multiple operating conditions, including low flow rate, high flow rate, low rotational speed, high rotational speed, high expansion ratio, low expansion ratio, and near the condensation boundary. To improve generalization ability, for data from adjacent geometries or new test rigs, transfer learning can be used to retain the lower-level feature extraction layers while only fine-tuning the higher-level weights, thereby reducing retraining costs.

[0081] Multiple operating conditions include at least two of the following: low flow rate, high flow rate, low speed, high speed, high expansion ratio, low expansion ratio, and near-condensation boundary (outlet dryness 0.85–0.95).

[0082] When predicting multiple operating conditions, new geometric parameters and operating condition parameters are input into the trained BPANN model, which outputs the corresponding isentropic efficiency and steam condensation rate. If the model's prediction uncertainty is high, the operating condition can be marked as a region to be supplemented for testing, and the next round of testing sampling can be prioritized. In this way, the BPANN model is not only used for prediction, but can also guide the supplementation of test operating conditions and the expansion of the design space.

[0083] The generalization loss function with regularization is: ; in, This represents the total loss after regularization. The value of the loss function. The regularization coefficient is . For the sum of squares of all weights.

[0084] The evaluation index for model prediction accuracy is: ; in, For the sample size, As the coefficient of determination, For the first One experimental measurement value, For the first Each model predicts a value. This is the average of all test measurements.

[0085] To verify the prediction accuracy of the BPANN model, the model predictions were compared with experimental measurements. For example... Figure 6 As shown, the experimental results and BPANN predictions for isentropic efficiency and water vapor condensation as a function of mass flow rate and rotational speed are compared. The scatter plots represent experimental measurements, and the dashed lines represent BPANN model predictions.

[0086] As shown in the figure, when the mass flow rate increases from approximately 0.45 kg / s to 0.65 kg / s, the isentropic efficiency remains within the range of approximately 0.72–0.82, and the overall condensation rate of the steam working fluid is approximately 2%–3.5%. When the rotational speed increases from approximately 5000 rpm to 25000 rpm, the isentropic efficiency increases from approximately 0.69 to approximately 0.82, while the condensation rate of the steam working fluid remains at a relatively low level of approximately 2%–3%. The BPANN prediction curve and the experimental data points show good consistency in both overall trend and numerical position, effectively capturing the changing trends of aerodynamic and thermodynamic properties under a wide range of operating conditions.

[0087] Step Six: Experimental Comparison, Verification, and Feedback Correction Several design points, partial operating points, and boundary operating points were selected for experimental verification to obtain experimental measurements of temperature, pressure, mass flow rate, speed, output power, and experimental isentropic efficiency. For the condensation of the steam working fluid, a combination of theoretical back-calculation and experimental measurement was used to obtain the values, which were then used as a benchmark for comparison and verification with the BPANN predicted values.

[0088] If the prediction error is within the allowable range (e.g., relative error not exceeding 5%), the current model can be used for rapid prediction within this operating condition range; if the error exceeds the set threshold, feedback correction is initiated. The coefficient of determination R is the primary validation metric. 2 The accuracy of a model is evaluated using two core metrics: Ri and Mean Relative Error (MRE). 2 The mean squared error (MRE) is used to characterize the consistency between BPANN predictions and experimental results, while the mean squared error (MRE) characterizes the average deviation of predicted values ​​from experimental measurements. If R... 2 The high efficiency and low MRE indicate that BPANN can effectively reflect the variation patterns of isentropic efficiency and steam condensation under real-world operating conditions. For predicting steam working fluid condensation, the accuracy of determining whether condensation has occurred can also be calculated separately.

[0089] Compare the BPANN predicted values ​​with the experimental measured values, and calculate the coefficient of determination R. 2 And mean relative error (MRE).

[0090] The feedback correction in this step includes: adding the experimental measurements and their corresponding operating parameters from the validation data to the sample library, re-dividing the training data and validation data in the expanded sample library, and then retraining or fine-tuning the network weights of the backpropagation artificial neural network model.

[0091] Furthermore, based on the comparison between the prediction error and the experimental measurements, relevant parameters in the one-dimensional aerodynamic-thermal design model can be corrected in reverse. Specifically, this includes: correcting loss model coefficients (such as empirical coefficients for blade loss and clearance leakage loss), adjusting the weight coefficients in the comprehensive objective function, or optimizing the value range of key design variables (such as reaction degree, speed ratio, and wheel diameter ratio). This feedback mechanism enables the one-dimensional design model to continuously learn from experimental data, forming a complete closed loop of "experiment → design → re-optimization".

[0092] Through the above-mentioned experimental verification and feedback correction process, the system can continuously improve the model prediction accuracy and generalization ability, and finally form a closed-loop optimization mechanism of "experimental verification - error feedback - model correction - re-prediction".

[0093] Step 7: Application of Model Inference Input the geometric structural parameters and operating condition parameters under the operating condition to be predicted into the backpropagation artificial neural network model after feedback correction in step six. The model then outputs the corresponding isentropic efficiency and steam working fluid condensation amount under the operating condition, which serve as the prediction results of the wide-condition aerodynamic and thermodynamic performance of the centripetal steam turbine.

[0094] Specifically, for a centripetal turbine designed using the optimal design variable combination in step one, its geometric parameters are fixed values. When it is necessary to evaluate the aerodynamic and thermodynamic performance of the turbine under a new operating condition (given mass flow rate, speed, and inlet pressure), simply input the set of geometric parameters and operating condition parameters into the BPANN model after feedback correction in step six, and the model can quickly output the corresponding isentropic efficiency and steam condensation rate.

[0095] The one-dimensional aerothermal design of this invention comprehensively considers the coupled effects of multiple physical factors such as flow, heat transfer, loss and steam condensation, and achieves a balance between efficiency and condensation through the synergistic optimization of key parameters.

[0096] Therefore, this invention adopts the above-mentioned centripetal steam turbine aerodynamic thermodynamic design and experimental feedback correction method. It quickly grasps the core parameters through one-dimensional multi-physics field top-level design, establishes the sample basis through experimental measurements, realizes wide-condition prediction of isentropic efficiency and steam working fluid condensation through BPANN, and continuously writes back the model parameters through experimental errors. Thus, it achieves the unity of high isentropic efficiency, low steam working fluid condensation and wide-condition generalization prediction capability, which can be applied to gas turbine testing, waste heat and waste pressure recovery and small power recovery devices.

[0097] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention and not to limit them. Although the present invention has been described in detail with reference to preferred embodiments, those skilled in the art should understand that modifications or equivalent substitutions can still be made to the technical solutions of the present invention, and these modifications or equivalent substitutions cannot cause the modified technical solutions to deviate from the spirit and scope of the technical solutions of the present invention.

Claims

1. A method for aerodynamic and thermodynamic design and experimental feedback correction of a centripetal steam turbine, characterized in that, Includes the following steps: S1: Based on the top-level design of one-dimensional multiphysics field, under the coupled effect of geometric constraints, aerodynamic constraints and thermodynamic constraints, the key design parameters of the turbine are synergistically optimized with isentropic efficiency and steam working fluid condensation as optimization objectives to obtain the optimal combination of design variables. S2: Build a turbine test bench and collect test data under multiple operating conditions; the test data should include at least the inlet total pressure, inlet total temperature, outlet back pressure, mass flow rate, rotational speed, output power, outlet temperature, and steam working fluid condensation rate; S3: Perform steady-state determination on the collected experimental data and extract steady-state data; divide the steady-state data into training data and validation data; use the geometric structure parameters corresponding to the optimal design variable combination described in S1 and other multiple design variable combinations generated in the collaborative optimization process as the geometric structure parameters of the samples, and construct a sample library containing input features and output labels; the input features include geometric structure parameters and operating condition parameters, and the output labels include at least isentropic efficiency and steam working fluid condensation rate; S4: Construct a backpropagation artificial neural network model, train the backpropagation artificial neural network model using the sample library, and establish a non-linear mapping relationship between input features and output labels; S5: Use a trained backpropagation artificial neural network model to predict the aerodynamic and thermodynamic performance under multiple operating conditions, and output the predicted isentropic efficiency and steam working fluid condensation. S6: Compare and verify the prediction results of the backpropagation artificial neural network model with the experimental measurement values ​​in the verification data, and correct the weights and biases of the backpropagation artificial neural network model based on the prediction error. S7: Input the geometric structural parameters and operating condition parameters under the operating condition to be predicted into the backpropagation artificial neural network model after feedback correction by S6, and output the corresponding isentropic efficiency and steam working fluid condensation amount under the operating condition as the prediction result of the wide operating condition aerodynamic and thermodynamic performance of the centripetal steam turbine.

2. The method according to claim 1, characterized in that, The collaborative optimization described in S1 is performed under geometric constraints, which include: Relative leaf height Export hub diameter ratio Export flange diameter ratio The ratio of the number of guide vane blades to the number of moving vane blades and blade angle , and flow channel size , Structural boundary conditions; in, For the blade height, This is the impeller reference diameter. For export wheel hub diameter, The diameter of the export rim. The number of guide vane blades, The number of moving leaf blades, The airflow angle at the guide vane outlet. The relative airflow angle at the blade outlet. The width of the guide vane outlet flow channel. The width of the flow channel at the moving blade outlet.

3. The method according to claim 1, characterized in that, The collaborative optimization described in S1 is performed under aerodynamic constraints, which include: The ratio of the relative velocity at the blade exit to the relative velocity at the blade inlet , moving blade inlet angle ; in, The relative velocity at the inlet of the moving blade. The relative velocity at the blade exit is... The angle of attack is at the inlet of the moving blade.

4. The method according to claim 1, characterized in that, The isentropic efficiency described in S1 is defined as follows: ； in, For isentropic efficiency, Total enthalpy at the entrance. This represents the total enthalpy of actual exports. The total enthalpy at the outlet is calculated using isentropic expansion. The condensation rate of the working fluid is expressed as a function of the steam state parameters: ； in, This refers to the condensation rate of the steam working fluid. , and These represent the pressure, temperature, and entropy in the steam state parameters, respectively.

5. The method according to claim 1, characterized in that, The optimization algorithm used in the collaborative optimization described in S1 includes one or more of the following: particle swarm optimization, genetic algorithm, grid search method, sequential quadratic programming, or trust region algorithm.

6. The method according to claim 1, characterized in that, The condensation rate of the steam working fluid mentioned in S2 was obtained by a combination of theoretical back-calculation and experimental measurement. In theoretical back-calculation, based on export pressure outlet temperature And determine the outlet dryness by water vapor physical properties. When the outlet is in a wet steam state, the outlet dryness can be determined based on the actual outlet enthalpy. enthalpy of saturated water and latent heat of vaporization Make an estimate: ； in, For export dryness, This represents the total enthalpy of actual exports. export pressure The corresponding saturated enthalpy of water, To correspond to the latent heat of vaporization under the pressure, when At that time, the amount of steam working fluid condensed by theoretical back-calculation can be expressed as: ； in, The amount of steam working fluid condensed is obtained from theoretical back-calculation. For quality flow, when When this time, it indicates that the outlet working fluid has not entered the wet steam zone, and the theoretical condensation capacity can be taken as [value missing]. ; During the test measurement, a condensation collection unit can be installed at the turbine outlet to measure the mass of condensate collected within a set sampling time. The amount of steam working fluid condensed as measured in the test can be expressed as: ； in, The amount of steam working fluid condensed is measured in the experiment. The mass of condensate collected during the sampling period. This corresponds to the sampling time.

7. The method according to claim 1, characterized in that, The steady-state determination condition described in S3 is: ； in, For the first in the steady-state window Each sample value, The average value is the window value. The number of sampling points. The allowable fluctuation threshold.

8. The method according to claim 1, characterized in that, The multiple operating conditions include at least two of the following: low flow rate, high flow rate, low speed, high speed, high expansion ratio, low expansion ratio, and near-condensation boundary.

9. The method according to claim 1, characterized in that, The feedback correction described in S6 includes: when the prediction error exceeds a set threshold, adding the experimental measurement values ​​and their corresponding operating parameters from the verification data to the sample library, re-dividing the training data and verification data in the expanded sample library, and retraining or fine-tuning the network weights of the backpropagation artificial neural network model.

10. The method according to claim 1, characterized in that, In S6, the prediction accuracy is determined by the coefficient of determination R. 2 The evaluation is based on the mean relative error (MRE), where the coefficient of determination R0 is... 2 The formula is: ； in, For the sample size, As the coefficient of determination, For the first One experimental measurement value, For the first Each model predicts a value. This is the average of all test measurements.

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