Runner blade optimization method of mixed-flow water turbine and runner

Abstract

The invention provides a runner blade optimization method of a mixed-flow water turbine and a runner. The method comprises the steps that a full-flow-channel three-dimensional model of a flow passage component of the mixed-flow water turbine in the water flow direction is established; a mixed turbulence model is selected, boundary conditions are set, simulation results of the runner under different design working conditions and critical working conditions are obtained, and a core loss area restricting maximum output is determined; setting meridian plane parameters, airfoil section parameters and space distortion parameters of the runner blade according to the position of the core loss area; based on the multiple sets of blade parameters, parameterized models of the runner blades are established respectively; comparing and analyzing simulation results of the plurality of parameterized models under the same working condition, and screening target blade parameters with high relevancy with the maximum output; and based on the target blade parameter, optimizing the runner blade so as to improve the maximum output of the mixed-flow water turbine. Through the optimization method provided by the invention, the problems of insufficient flow field coupling consideration, limited parametric modeling dimension, single optimization target and the like are solved.

Description

Technical Field

[0001] This application relates to the field of hydropower technology, and in particular to a method for optimizing the runner blades of a mixed-flow turbine and the runner itself. Background Technology

[0002] As the most widely used main type of turbine in hydropower stations, the runner is one of the core components determining the unit's performance. The geometry of the runner blades and the design of the internal flow channels directly affect the unit's hydraulic efficiency, operational stability, and cavitation characteristics. An unreasonable runner design can not only reduce unit efficiency but also trigger a series of operational problems, such as difficulty in grid connection during low-head startup, severe vibration during load shedding, and even blade fatigue damage and structural instability. Therefore, the research and design of the runner must balance hydraulic performance and structural safety, reserving sufficient design margins to ensure the long-term safe and stable operation of the unit.

[0003] Currently, with the expansion of hydropower station construction, mixed-flow turbines are developing towards higher head and larger capacity. Under these circumstances, the original blade design is no longer sufficient to maintain high efficiency and stability under high load conditions. Therefore, optimizing the design of the turbine runner blades has become an inevitable requirement in order to further improve the unit's operating output and overall energy conversion efficiency.

[0004] However, existing technical solutions for the optimization design of the runner have many shortcomings, such as insufficient consideration of flow field coupling, limited parametric modeling dimensions, and overly simplistic optimization objectives. They cannot significantly improve the maximum output of the mixed-flow turbine while ensuring operational stability. Summary of the Invention

[0005] To address the aforementioned problems, this invention provides an optimization method for runner blades and a runner to improve the maximum output of a mixed-flow turbine, thereby solving the problems commonly found in existing runner design methods, such as insufficient consideration of flow field coupling, limited dimensions of parametric modeling, and overly singular optimization objectives.

[0006] In a first aspect, the present invention provides a method for optimizing the runner blades to improve the maximum output of a mixed-flow turbine, the technical solution of which is: An optimization method for turbine runner blades to improve the maximum output of a mixed-flow turbine, the method comprising: A three-dimensional model of the entire flow channel of the mixed-flow turbine in the direction of water flow is established; the flow-through components include at least the volute, guide vanes, runner, and tailrace. A mixed turbulence model was selected, and boundary conditions were set to simulate the flow field characteristics of the impeller under different design and critical conditions. Based on the flow field characteristic data of the runner, the simulation results of the runner under various working conditions are analyzed to determine the core loss zone that restricts the maximum output of the mixed-flow turbine. Based on the location of the core loss zone, the blade parameters of the runner blades are set; the blade parameters include meridional parameters, airfoil section parameters, and spatial twist parameters; Based on the set of multiple sets of blade parameters, parameterized models of the runner blades are established respectively; Simulate the flow field characteristic data of multiple parameterized models under the same working condition, compare and analyze the simulation results corresponding to multiple sets of flow field characteristic data, and select target blade parameters that are highly correlated with the maximum output of the mixed-flow turbine. Based on the target blade parameters, the runner blades are optimized to improve the maximum output of the mixed-flow turbine.

[0007] As one preferred embodiment, the optimization of the runner blades based on the target blade parameters includes: The main objective function is used to maximize the power of the rotor shaft. Using the constrained objective function, the cavitation margin is controlled to be no greater than the preset cavitation margin, the tangential velocity of the water flow at the impeller outlet is no greater than 0.15 times the average tangential velocity component, and the maximum negative pressure of the impeller blades is no less than the saturated vapor pressure of water. The blade parameters that satisfy the main objective function and the constraint objective function are taken as the target blade parameters.

[0008] As one preferred embodiment, the process of screening target blade parameters that are highly correlated with the maximum output of the mixed-flow turbine includes: Multiple sample parameters are generated from the target blade parameters based on Latin hypercube sampling, and each sample parameter corresponds to each parameterized model; Obtain the simulation results of the parameterized model corresponding to each of the sample parameters after simulation. The Kriging surrogate model is used to fit the mapping relationship between the sample parameters and the simulation results to construct the surrogate model; The step of taking the blade parameters that satisfy the main objective function and the constraint objective function as the target blade parameters includes: Based on the surrogate model, a non-dominated sorting genetic algorithm is used to search for the Pareto optimal solution set under the condition of satisfying the constraint objective function; the Pareto optimal solution set includes a set of multiple target leaf parameters; The target blade parameters in the Pareto optimal solution set are used to perform multi-objective optimization on the runner blade.

[0009] As one preferred embodiment, the step of using a non-dominated sorting genetic algorithm to search for the Pareto optimal solution set under the condition of satisfying the constraint objective function includes: During the iterative process of the non-dominated sorting genetic algorithm, after each preset number of iterations, multiple optimal sample parameters are selected from the current Pareto optimal solution set using the non-dominated sorting genetic algorithm. Obtain the simulation results of the parameterized model corresponding to each of the optimal sample parameters after simulation. Based on the Kriging proxy model, the mapping relationship between the optimal sample parameters and the simulation results is refitted, and the proxy model is updated.

[0010] As one preferred option, the selection of a mixed turbulence model and the setting of boundary conditions to simulate the flow field characteristics of the impeller under different design and critical conditions include: Based on the flow channel region where the volute and guide vane are located in the full-channel 3D model, RNG is used. k - ε Turbulence model is used for operating condition simulation; Based on the flow channel region where the impeller and tailrace pipe are located in the full-channel 3D model, SST is adopted. k-ω Turbulence model is used for operating condition simulation; Based on the selected RNG k-ε Model and the SST k - ω And based on the boundary conditions set according to the preset operating conditions, the process characteristics of the runner under multiple design operating conditions, maximum output operating conditions and minimum head operating conditions are simulated; wherein, the boundary conditions include at least one operating condition parameter among flow rate, head, rotational speed, guide vane opening and pressure.

[0011] As one of the preferred options, the flow field characteristic data includes at least the pressure distribution on the surface of the impeller blades, the velocity vector distribution within the flow channel, and the energy loss coefficient distribution; The analysis of simulation results of the impeller under various operating conditions based on the flow field characteristic data of the impeller includes: Based on the pressure distribution on the surface of the impeller blades, the low-pressure zone and the pressure gradient abrupt change zone of the impeller are identified; Based on the velocity vector distribution within the flow channel, the throat region with excessively high flow velocity and the low-energy region with backflow and vortices are located. Based on the energy loss coefficient distribution within the flow channel, the proportions of inlet impact loss, blade surface friction loss, and outlet wake loss of the runner are quantified.

[0012] As one preferred embodiment, the setting of the blade parameters of the runner blades includes: The meridional parameters of the runner blades are set according to at least one of the runner inlet diameter, runner outlet diameter, and meridional contraction angle. The airfoil section parameters of the runner blade are set based on at least one of the runner blade inlet angle, runner blade outlet angle, runner blade maximum thickness position, runner blade chord length, and runner blade consistency. Based on the torsion angle distribution of the impeller blades, the spatial torsion parameters of the impeller blades are set; The meridional plane parameter, the airfoil section parameter, and the spatial twist parameter, or a combination thereof, are set as the blade parameters of the runner blade.

[0013] As one preferred embodiment, the method further includes: Based on the optimized three-dimensional model of the entire flow channel corresponding to the impeller blades, a solid model of the impeller is prepared at a preset scale. The physical model of the runner was installed on a hydraulic test bench, and multiple guide vane openings and heads were set. The power-flow curves of the physical model of the runner under different guide vane openings and heads were tested to verify the energy characteristics performance of the optimized runner. The critical cavitation margin of the solid model of the impeller was tested using the pressure reduction method to verify the cavitation performance of the optimized impeller. The pressure pulsation at the inlet and outlet of the turbine runner and the vibration amplitude of the unit are monitored by pressure sensors and vibration acceleration sensors to verify the stability performance of the optimized turbine runner. Based on the energy characteristics, cavitation performance, and stability performance, the optimized performance results of the rotor are obtained.

[0014] As one preferred embodiment, the method further includes: Based on the performance results of the runner and the engineering constraints of the actual unit, the blade parameters of the runner blades are adjusted.

[0015] Secondly, the present invention provides a runner suitable for a mixed-flow turbine, the mixed-flow turbine including a volute, guide vanes, a runner and a draft tube; the configuration of the runner is optimized based on the runner blade optimization method for improving the maximum output of the mixed-flow turbine provided in the first aspect of the present invention; wherein, the runner blades of the runner have an asymmetric double curvature blade profile, and the inlet edge of the runner blades has a positive curvature and the outlet edge has a negative curvature; The thickness of the rotor blades varies in a gradient from the rim to the hub. The pressure surface of the rotor blade is coated with a superhydrophobic coating, and the back side is provided with at least one microrib structure.

[0016] Traditional designs often only analyze the flow field within the turbine runner or local flow channels, failing to adequately consider the flow interactions between the volute, guide vanes, runner, and draft tube. Therefore, simulations struggle to accurately reproduce the flow distribution in the actual unit, leading to inaccurate loss source localization and distorted optimization direction. Traditional parametric optimization often only modifies the runner airfoil section in a single dimension (such as adjusting the chord length or thickness), neglecting the coupled influence of meridional profiles and spatial distortion on the overall flow field, making it difficult to balance energy conversion efficiency, cavitation performance, and structural stability. Traditional optimization methods often prioritize maximum efficiency or maximum output as the sole objective, without fully considering constraints such as cavitation performance, vibration stability, and operational reliability.

[0017] Compared to traditional design methods, the optimization method provided by this invention has the following advantages: In this embodiment of the invention, a three-dimensional coupled model of the entire flow channel, consisting of a volute, guide vane, runner, and tailrace, is constructed. Appropriate turbulence models are selected for different flow channel regions to fully reveal the dynamic evolution of flow losses, flow channel capacity, and the coupling effects of cavitation and vibration. By proposing a "three-dimensional mapping method for energy loss coefficients," the spatial distribution of runner inlet impact losses (15%-25%), blade surface friction losses (30%-40%), and outlet wake losses (20%-30%) is simulated and quantified. This allows for the precise location of the "core loss zone" that restricts maximum output. The core loss zone is found to be located in the 1 / 3 chord length section of the blade inlet and the area near the hub at the runner outlet, thus solving the problem of "fuzzy loss location" in traditional methods.

[0018] In this embodiment of the invention, a three-dimensional collaborative modeling method of "meridian plane-airfoil section-spatial distortion" is adopted to decompose the turbine blade into an independently controllable but mutually coupled parameter system. Exploring the multi-dimensional variable space overcomes the limitations of single-dimensional optimization, making the optimization more global and practically applicable in engineering. By solving the parameterized model through simulation, flow field characteristics are compared under the same operating conditions, and then target blade parameters that significantly affect the maximum output of the unit are selected based on correlation analysis. Optimizing the turbine blade through multi-parameter modeling can improve problems such as large flow losses, insufficient flow capacity, strong coupling between cavitation and vibration, and insufficient overall efficiency while ensuring strength and manufacturing feasibility. In this embodiment of the invention, a two-layer optimization function of "main objective - constraint objective" is constructed. The maximum output is taken as the main objective, and the cavitation margin, water flow tangential velocity, and maximum negative pressure on the blade surface are taken as constraint objectives to limit it. This avoids the low pressure, cavitation and vibration problems caused by the traditional pursuit of a single output index. It achieves synergistic optimization of cavitation margin and flow field stability while improving the power of the impeller shaft, thereby fundamentally improving engineering defects such as large flow loss, insufficient flow channel capacity and cavitation vibration coupling.

[0019] The aforementioned wheel and optimization method have the same advantages over existing technologies, which will not be elaborated here. Attached Figure Description

[0020] To more clearly illustrate the technical solution of this application, the drawings used in the description of this application will be briefly introduced below. Obviously, the drawings described below are only some embodiments of this application. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0021] Figure 1 A flowchart illustrating the steps of a method for preparing an optimized runner blade for improving the maximum output of a mixed-flow turbine, as provided in an embodiment of the present invention. Figure 2 A schematic diagram of the flow channel of a full-flow channel three-dimensional model provided in an embodiment of the present invention; Figure 3 The simulation result diagram of the optimized impeller blade provided in one embodiment of the present invention is shown. Figure 4 This is an overall configuration diagram of the optimized impeller blades provided in an embodiment of the present invention; Figure 5 This is a single configuration diagram of an optimized runner blade provided in an embodiment of the present invention; Figure 6 A performance comparison diagram of the runner before and after optimization under different working conditions provided in an embodiment of the present invention; Figure 7 The velocity cloud diagrams of the pre-optimized and post-optimized impellers provided in an embodiment of the present invention are the corresponding velocity cloud diagrams after simulation. Figure 8 The pressure cloud diagrams are obtained from simulations of the pre-optimized and post-optimized impellers according to an embodiment of the present invention. Attached image description: 10. Volute; 20. Runner; 30. Tailwater pipe; 1. Hub; 2. Runner blades; 3. Rim. Detailed Implementation

[0023] 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. The following description of at least one exemplary embodiment is merely illustrative and is in no way intended to limit the present invention or its application or use. Based on the embodiments of the present invention, any product that is the same as or similar to the present invention, derived by any person under the guidance of the present invention or by combining the features of the present invention with other prior art, falls within the protection scope of the present invention. Furthermore, all other embodiments obtained by those skilled in the art without inventive effort are within the protection scope of the present invention.

[0024] To better understand the technical solution of this application, the common impeller structure and traditional impeller blade optimization methods will now be further explained: During the design phase: Insufficient consideration of flow field coupling: Current hydraulic optimization studies mostly focus on the local flow field analysis of the runner 20, while neglecting the full-channel coupling effect between the volute 10, guide vanes, draft tube 30 and the runner 20. This "local flow field analysis" mode makes the flow field boundary conditions unrealistic, which can easily lead to deviations in the location of energy loss sources, making it difficult to truly reflect the flow characteristics within the entire unit.

[0025] Parametric modeling has limited dimensions: Existing parametric designs only optimize the airfoil section of blades, mainly by adjusting two-dimensional parameters such as chord length, thickness distribution, or inlet / outlet angles, lacking comprehensive control over meridional shape, channel contraction characteristics, and spatial distortion patterns. This single-dimensional modeling approach often struggles to balance flow capacity, flow uniformity, and energy conversion efficiency.

[0026] The optimization objectives are too singular: Traditional optimization methods often take maximum efficiency or maximum output as the sole objective, without fully considering constraints such as cavitation performance, vibration stability, and operational reliability. Under high head and high flow conditions, pursuing only output improvement often leads to the expansion of the low-pressure area on the back of the blades, resulting in intensified cavitation and increased flow field pulsation, which in turn generates unit vibration and noise, affecting long-term operational safety.

[0027] Therefore, although the impeller structure in the existing technical solutions has been optimized to some extent, it still has the following defects in practical engineering applications, for example: Large flow loss due to water flow around the blades: The blade angle design of the impeller 20 is unreasonable, which causes the blade inlet angle and outlet angle to be mismatched with the actual incoming flow direction. This results in boundary layer separation of the water flow on the blade surface. Especially under high load conditions, the separation area expands and forms a "separation vortex", causing energy dissipation.

[0028] Insufficient flow capacity of the flow channel: The blade profile (curvature distribution, chord length) of the impeller 20 is not designed properly, which leads to uneven velocity distribution in the flow channel of the impeller 20 and the occurrence of "throat effect" in some areas, which limits the flow rate and thus restricts the maximum output.

[0029] Cavitation and vibration coupling effects: Cavitation bubbles are easily generated in the low-pressure area on the back of the blades of the runner 20. The bursting of bubbles not only causes material erosion, but also causes flow field pulsation, which leads to increased unit vibration, forcing operators to reduce the load to avoid risks, and indirectly reducing the actual output.

[0030] Therefore, even after optimization, the runner blades 2 of existing mixed-flow turbines generally suffer from problems such as water flow around losses, insufficient flow channel capacity, and coupling of cavitation and vibration. These factors together affect the unit, making it unable to operate stably under high head and high load conditions, and jointly limiting the operating output and maximum output improvement of the mixed-flow turbine.

[0031] In view of this, in order to enable mixed-flow turbines to maintain their maximum operating power within a safe operating range under high head and large capacity conditions, it is necessary to establish a comprehensive optimization design method based on CFD, including full-channel flow analysis and parametric modeling, multi-objective optimization algorithms and strategies, and experimental verification and engineering adaptation of optimization schemes. This method aims to solve problems in the existing optimization design of mixed-flow turbine runners, such as insufficient flow field coupling analysis, single parametric dimension, and one-sided optimization objectives. Furthermore, it aims to address problems in actual operation, such as large water flow around losses, insufficient flow channel capacity, and the coupling effects of cavitation and vibration.

[0032] Based on the above description, the technical solution of this invention application will be described as follows: Reference Figure 1 As shown, Figure 1 This is a flowchart illustrating the steps of preparing the optimized runner blades for improving the maximum output of a mixed-flow turbine, as described in this invention. This invention proposes a method for optimizing runner blades to improve the maximum output of a mixed-flow turbine, the method comprising the following steps: S1. Establish a three-dimensional model of the entire flow channel of the mixed-flow turbine in the direction of water flow; the flow channel includes at least the volute 10, guide vanes, runner 20 and tailrace pipe 30; S2. Select the mixed turbulence model and set the boundary conditions to simulate the flow field characteristics of the runner 20 under different design and critical conditions. S3. Based on the flow field characteristic data of the runner 20, analyze the simulation results of the runner 20 under various working conditions, and determine the core loss area that restricts the maximum output of the mixed-flow turbine. S4. Based on the location of the core loss zone, set the blade parameters of runner blade 2; the blade parameters include meridional parameters, airfoil section parameters, and spatial twist parameters; S5. Based on the set multiple sets of blade parameters, establish parameterized models of runner blade 2 respectively; S6. Simulate the flow field characteristic data of multiple parameterized models under the same working condition, compare and analyze the simulation results corresponding to multiple sets of flow field characteristic data, and screen the target blade parameters that are highly correlated with the maximum output of the mixed-flow turbine. S7. Based on the target blade parameters, optimize the runner blade 2 to improve the maximum output of the mixed-flow turbine.

[0033] Specifically, steps S1-S7 aim to achieve flow field analysis and parametric modeling based on CFD (Computational Fluid Dynamics). Steps S1-S4 are mainly used for full-channel CFD simulation and bottleneck location; steps S5-S7 are mainly used for blade parametric modeling and variable selection. In step S1, the flow components of the mixed-flow turbine along the flow path from the inlet to the outlet are first completely modeled. The flow components include the volute 10, guide vanes ( Figure 2 (Due to being obscured by the volute 10, it is not shown); impeller 20 (including upper crown, impeller blades 2, lower ring, hub 1, rim 3, etc.); and tailrace pipe 30. The volute 10 is a spiral channel used to evenly distribute water from the pressure pipe to each guide vane; the guide vanes are used to adjust the angle and flow rate of water flowing into the impeller 20; the impeller 20, as the core energy conversion component, is used to convert water flow energy into mechanical energy; the tailrace pipe 30 is used to recover the kinetic energy at the impeller outlet and guide it downstream. This embodiment models all flow components covering the entire hydraulic flow channel of the unit in a unified manner, so that the flow field characteristics between each component can be realistically reflected during simulation. Figure 2 As shown, Figure 2 The diagram shows the flow channel of the full flow channel 3D model. A complete full flow channel 3D model can be obtained using professional 3D modeling software. The full flow channel 3D model is then imported into CFD software, and the full flow channel of the mixed-flow turbine is numerically simulated using CFD software.

[0034] In step S2, a hybrid turbulence model is selected, and turbulence model parameters, such as turbulence intensity, turbulence viscosity ratio, and turbulence length scale, are set for numerical solutions of water flow velocity, pressure, and turbulence energy. The hybrid turbulence model is a combination of at least one turbulence model; for example, the turbulence model could be the commonly used SST (Self-Stage Turbulence Model). k-ω Turbulence model k-ε Turbulence model, RNG k-ε Turbulence models, etc. Preferably, this embodiment selects SST. k-ω Turbulence model and RNG k-ε turbulence model, RNG for volute 10 and guide vane k-ε The turbulence model simulates strong swirling flow; the runner 20 and tailrace pipe 30 use SST. k-ω Turbulence models accurately capture boundary layer separation. SST k-ω Turbulence models can more accurately simulate near-wall flow and separated flow, and are particularly suitable for the complex flow characteristics in mixed-flow turbines.

[0035] This embodiment sets boundary conditions based on the operating conditions to be simulated. Different boundary conditions correspond to different operating conditions. For example, the input boundary conditions may include parameters such as fluid properties, flow rate, head, inlet velocity, inlet total pressure, outlet pressure, runner speed, angular velocity, temperature, tailrace level, and guide vane opening. By combining these different parameters, different operating conditions can be simulated. The operating conditions to be simulated in this embodiment are divided into design conditions and critical conditions. Design conditions can characterize the normal operating state under parameters such as rated head and flow rate, so different parameters such as flow rate, head, and runner speed can be set as boundary conditions. Critical conditions may include maximum output conditions and minimum head conditions. Maximum output conditions can characterize the maximum power that the unit can output under safe operating conditions, and the maximum flow rate and maximum head are usually set as boundary conditions. Minimum head conditions can characterize the extreme situation of the unit operating at low water level and low flow rate, and the minimum flow rate and minimum head are usually set as boundary conditions. Different boundary conditions correspond to different operating conditions under which the flow field pressure distribution, streamline morphology, flow velocity, and turbulent energy of the unit will vary. Therefore, after CFD simulation, each operating condition can output a set of process characteristic data. The process characteristic data includes the pressure field, velocity field, turbulent energy field, and energy loss coefficient distribution calculated by CFD in conjunction with the turbulence model under the corresponding operating condition.

[0036] In some embodiments, the flow characteristic data of the runner 20 under different guide vane openings can be simulated to simulate and analyze the power-flow curves of the runner 20 under different guide vane openings and heads. Then, the results are compared with the actual test results in the model test verification stage to confirm whether the maximum output has reached the design target and to further evaluate the feasibility of the simulation optimization stage.

[0037] In step S3, the flow field characteristic data output by the CFD software can be further calculated, extracted, statistically analyzed, and visualized using a dedicated post-processing module or tool. This includes extracting flow field characteristic data such as pressure field, velocity field, and energy loss coefficient distribution, ultimately outputting simulation results for various operating conditions. Simultaneously, CFD can present the simulation results through various visualization graphics, enabling bottleneck diagnosis. For example, the simulation results may include post-processed pressure contour maps, velocity contour maps, and energy loss contour maps, further yielding parameters such as the power, efficiency, loss distribution, and cavitation index of the impeller 20.

[0038] Specifically, the simulation results can be used for in-depth analysis: Pressure distribution on the surface of the runner blade: The pressure distribution on the surface of runner blade 2 obtained by CFD solution is post-processed to output a pressure contour map. The pressure contour map can show the static pressure or total pressure distribution at various points on the surface of runner blade 2 or inside the flow field. By analyzing the pressure contour map, low-pressure areas (cavitation risk areas) and areas of abrupt pressure gradient changes (flow loss areas) can be quickly identified.

[0039] Velocity vector distribution within the flow channel: The velocity field obtained from CFD solutions is post-processed to output a velocity contour map. The velocity contour map visually displays the fluid flow path, separation zones, recirculation zones, vortices, and stagnation points. By analyzing the velocity contour map, "throat" regions with excessively high velocities and low-energy regions with recirculation and vortices can be located.

[0040] Energy loss coefficient distribution: CFD was used to integrate the energy loss ratios of different components (guide vanes, runner 20, and draft tube 30) to obtain the energy loss coefficient distribution. This distribution was then post-processed to output an energy loss contour map. The energy loss contour map reflects parameters such as turbulent kinetic energy, turbulent dissipation rate, and total pressure loss coefficient. By analyzing the energy loss contour map, the proportions of inlet impact loss, blade surface friction loss, and outlet wake loss of runner 20 can be quantified, clearly identifying the core loss area limiting maximum output. Therefore, the "bottleneck" region limiting the maximum output of runner 20 can be accurately located through simulation results. Finding the "bottleneck" region provides the most direct basis for subsequent optimization (such as setting blade parameters).

[0041] In step S4, the blade parameters of the runner are specifically optimized for the identified low-pressure zone, pressure gradient abrupt change zone, throat zone, low-energy zone, and core loss zone to improve optimization efficiency and engineering feasibility. Then, the blade parameters are further subdivided into meridional parameters, airfoil section parameters, and spatial twist parameters. This three-dimensional collaborative modeling decomposes the complex three-dimensional blade geometry into two relatively independent yet interconnected levels, thereby systematically controlling the blade shape. In step S5, the runner blade 2 of the mixed-flow turbine is a three-dimensional curved surface. This embodiment employs a three-dimensional collaborative modeling method of "meridional plane-airfoil section-spatial twist" to parametrically model the runner blade 2. Each set of parameter values ​​corresponds to a new three-dimensional runner blade geometric model. By establishing a parametric model, only the combination of each set of blade parameters needs to be adjusted to automatically generate a new geometric model, greatly improving optimization efficiency.

[0042] In step S6, after establishing a parametric model containing several sets of design variables, directly optimizing all design variables would be too computationally intensive. Therefore, in this embodiment, several sets of parametric models are first imported into CFD for steps S2 and S3, with the same boundary conditions and turbulence model set to obtain simulation results of the runner blades 2 under various operating conditions. By comparing multiple sets of simulation results, the influence of at least one design variable on performance indicators (such as maximum output) is analyzed, and several design variables most sensitive to output are finally selected, namely, the target blade parameters. Simultaneously, the multiple sets of target blade parameters most sensitive to output can also be used as optimization input parameters in subsequent multi-objective optimization algorithms. The optimization algorithm (such as NSGA-II) automatically searches for the optimal combination within the target blade parameter range to maximize output and satisfy constraints. In step S7, the finally selected target blade parameters are used as optimized blade parameters to optimize the runner blades 2, thereby improving the maximum output of the mixed-flow turbine.

[0043] Thus, traditional designs often only perform flow field analysis within the individual runner 20 or a local flow channel, without fully considering the flow interactions between the volute 10, guide vanes, runner 20, and tailrace pipe 30. Therefore, simulations struggle to accurately reproduce the flow distribution in the actual unit, leading to errors in loss source localization and distortion of optimization direction. This embodiment constructs a three-dimensional coupled model of the entire flow channel from the volute 10 to the guide vanes, runner 20, and tailrace pipe 30, and selects appropriate turbulence models for different flow channel regions, thereby fully revealing the dynamic evolution of water flow losses around the flow path, flow channel capacity, and the coupling effects of cavitation and vibration. By proposing the "three-dimensional mapping method of energy loss coefficient", the spatial distribution of impact loss at the runner inlet (accounting for 15%-25%), blade surface friction loss (accounting for 30%-40%), and exit wake loss (accounting for 20%-30%) is simulated and quantified. The "core loss area" that restricts the maximum output can be accurately located. It can be found that the core loss area is located in the 1 / 3 chord length section of the blade inlet and the area near the hub 1 at the runner outlet, which solves the problem of "fuzzy loss location" in traditional methods.

[0044] Traditional parametric optimization often only modifies the airfoil section of the runner 20 in a single dimension (such as adjusting the chord length or thickness), ignoring the coupling effect of the meridional profile and spatial distortion on the overall flow field, making it difficult to simultaneously consider energy conversion efficiency, cavitation performance, and structural stability. This embodiment employs a three-dimensional collaborative modeling method of "meridian plane-airfoil section-spatial distortion," decomposing the runner blade 2 into an independently adjustable but mutually coupled parameter system. Exploring the multi-dimensional variable space overcomes the limitations of single-dimensional optimization, making the optimization more global and practically applicable. By solving the parametric model through simulation, flow field characteristics are compared under the same operating conditions, and then target blade parameters that significantly affect the unit's maximum output are selected based on correlation analysis. Optimizing the runner blade 2 through multi-parameter modeling can improve problems such as large flow losses, insufficient flow capacity, strong coupling between cavitation and vibration, and insufficient overall efficiency while ensuring strength and manufacturing feasibility.

[0045] Further, step S4 includes: S41. Set the meridional parameters of the runner blade 2 according to at least one of the runner inlet diameter, runner outlet diameter, and meridional contraction angle; S42. Set the airfoil section parameters of the runner blade 2 based on at least one of the runner blade inlet angle, runner blade outlet angle, runner blade maximum thickness position, runner blade chord length, and runner blade consistency. S43. Based on the torsion angle distribution of the rotor blade 2, set the spatial torsion parameters of the rotor blade 2; S44. Set any one or a combination of the meridional parameters, airfoil section parameters, and spatial twist parameters as the blade parameters of the runner blade 2.

[0046] In this embodiment, during the multi-parameter collaborative blade parameterization modeling process, the meridional parameters, airfoil section parameters, and spatial twist parameters in each set of blade parameters can be adjusted. The meridional parameters can be adjusted by modifying the inlet diameter, outlet diameter, and meridional contraction angle of the runner blade 2. The runner inlet diameter determines the cross-sectional area of ​​the water entering the runner 20, the runner outlet diameter determines the outflow area and tailrace direction, and the meridional contraction angle represents the degree of contraction of the flow channel from inlet to outlet, determining the variation law of the flow area along the flow channel direction, thereby controlling the velocity distribution. For the airfoil section parameters, a section is cut along the blade height (from hub 1 to rim 3), and the blade inlet angle, outlet angle, maximum thickness position, chord length, and consistency of the runner blade 2 for each airfoil section are adjusted, including the consistency (number of blades / chord length ratio). The blade inlet angle is the angle at which the water enters the blade. During the design process, the blade inlet angle is well matched with the actual incoming flow direction from the guide vane to reduce flow around the blade. The blade outlet angle is the angle at which the water leaves the blade, affecting the outflow direction and tailrace energy. The location of maximum thickness is where the blade exhibits the greatest thickness distribution along the chord direction. The chord length, the straight-line distance from the leading edge to the trailing edge of the airfoil section, determines the blade envelope area. Consistency is closely related to flow uniformity. For spatial torsion parameters, these parameters are adjusted by regulating the torsion angle distribution. Adjusting the blade's torsion angle distribution can adapt to variations in circumferential velocity at different radii, reducing secondary flow losses and improving flow field uniformity.

[0047] Therefore, this embodiment can achieve comprehensive optimization of the overall and local flow field of the runner by adjusting the meridional plane parameters, airfoil section parameters, and spatial twist parameters, and allowing arbitrary combinations of these parameters as the blade parameters for optimizing the runner blade 2. This enables the multi-parameter optimized runner blade 2 to significantly reduce flow losses, improve flow capacity, and suppress cavitation and vibration coupling phenomena while increasing the maximum output of the unit, thus balancing performance and engineering adaptability.

[0048] For example, when adjusting blade parameters, for meridional parameters: the designed inlet diameter D1 is 1.2D2-1.5D2, where D2 is the outlet diameter; the designed meridional contraction angle α is 8°-12°, and the flow area gradient of the flow channel is controlled by adjusting the meridional contraction angle. For airfoil section parameters: the designed inlet angle β1 varies with the radius from 15° to 45°, the outlet angle β2 varies with the radius from 5° to 20°, the designed maximum thickness position is 30%-40% of the inlet chord length from the runner blade 2, and the designed consistency (the ratio of the number of blades Z to the average chord length L) is 0.8-1.2.

[0049] As a further improvement to this embodiment, it aims to address the problem of traditional optimization having a single objective. Step S7 further includes: S71. Maximize the rotor shaft power of rotor 20 using the main objective function; S72. Using the constraint objective function, control the cavitation margin to be no greater than the preset cavitation margin, the water flow tangential velocity at the impeller outlet to be no greater than 0.15 times the average tangential velocity component, and the maximum negative pressure of impeller blade 2 to be no greater than the saturated vapor pressure of water. S73. Use the blade parameters that satisfy the main objective function and the constraint objective function as the target blade parameters.

[0050] In this embodiment, during the optimization of the target blade parameters of the runner blade 2, a multi-objective optimization function is constructed with "maximum output improvement" as the core objective and combined with operational stability requirements. The main objective function can be expressed by the following formula: Formula 1 Where P is the maximum power of the impeller shaft; ρ is the water density; g is the gravitational acceleration; Q is the flow rate; H is the head; and η is the impeller efficiency.

[0051] Therefore, the main objective function can maximize the turbine shaft power, thereby maximizing the unit output under given head and flow conditions. Specifically, the flow rate and turbine efficiency can be directly extracted from CFD simulation results to calculate the shaft power, ensuring that the optimization focuses on "dual improvement of flow rate and efficiency".

[0052] The objective function of the constraint can include the following formulas 2, 3 and 4: NPSH≤M NPSH Formula 2 Where NPSH is the cavitation margin; M NPSH This is the preset cavitation margin allowed by the design.

[0053] Therefore, by constraining the objective function to ensure that the cavitation margin does not exceed a preset cavitation margin, cavitation can be prevented even when the maximum output is increased. Otherwise, while maximizing output, the blades will suffer erosion damage, significantly shortening their service life. Specifically, the pressure distribution near the blade inlet can be extracted from the CFD simulation results to obtain the cavitation margin value. By ensuring that the cavitation margin is less than the design value while maximizing the rotor shaft power—reducing it by 0.2m-0.5m compared to the prototype—cavitation can be avoided.

[0054] C 4u ≤0.15C4 formula 3 Where C4u is the tangential velocity of the water flow at the turbine outlet; C4 is the absolute velocity at the turbine outlet.

[0055] Therefore, by constraining the objective function, the tangential velocity of the water flow at the runner outlet is limited to no more than 0.15 times the average tangential velocity component. This constraint reduces the backflow vortex region within the tailrace pipe 30, improves the axial flow characteristics of the water flow, and ensures flow field stability. Specifically, the velocity vector at the runner outlet section can be extracted from the CFD simulation results, and the average tangential velocity component C can be calculated.4u Calculate the total speed C4 and check if the ratio of the two speeds is ≤0.15.

[0056] P min ≥P v Formula 4 Among them, P min P represents the maximum negative pressure on the blade surface. v This is the saturated vapor pressure of water.

[0057] Therefore, by constraining the objective function, the maximum negative pressure of the rotor blade 2 is constrained to not exceed the saturated vapor pressure of water, for example, P at 25℃. min ≥-98kPa, this constraint can prevent cavitation erosion.

[0058] In conjunction with the above embodiments, if any one of Formulas 1, 2, 3, and 4 is not satisfied, the selected target blade parameters are considered invalid and discarded. If Formulas 1, 2, 3, and 4 are satisfied simultaneously, the selected target blade parameters are used as optimization parameters to optimize the runner 20. Thus, this embodiment constructs a two-layer optimization function of "main target - constraint target," taking the maximum output as the main target and limiting it with cavitation margin, water flow tangential velocity, and maximum negative pressure on the blade surface as constraint targets. This avoids the low pressure, cavitation, and vibration problems caused by traditional pursuit of a single output index, and achieves synergistic optimization of cavitation margin and flow field stability while improving the runner shaft power. This fundamentally improves engineering defects such as large flow losses, insufficient flow channel capacity, and cavitation-vibration coupling.

[0059] In some embodiments, any one of cavitation margin, water flow tangential velocity, and maximum negative pressure on the blade surface can be used as a constraint target. That is, if Formula 1 is satisfied, and any one of Formula 2, Formula 3, and Formula 4 is satisfied, the selected target blade parameter can be used as the optimization parameter, which still solves the shortcomings of traditional technology in optimizing a single output index to a certain extent.

[0060] Furthermore, in the multi-objective collaborative optimization process, after step S6 and before step S7, the following steps are also included: S11. Based on Latin hypercube sampling, multiple sample parameters are generated from the target blade parameters, and each sample parameter corresponds to each parameterized model; S12. Obtain the simulation results of the parameterized model corresponding to each sample parameter after simulation. S13. Use the Kriging surrogate model to fit the mapping relationship between sample parameters and simulation results, and construct the surrogate model.

[0061] In this embodiment, during the process of selecting target blade parameters and after selecting multiple sets of target blade parameters, CFD simulation needs to be performed on the parameterized model corresponding to each set of blade parameters or target blade parameters to obtain the corresponding simulation results. The design variables of each set of blade parameters have multi-dimensional parameters (such as the inlet angle, outlet angle, thickness, twist angle, etc. mentioned above). The CFD simulation process is computationally expensive and time-consuming. This embodiment adopts a combined optimization strategy of "surrogate model + intelligent algorithm" to balance optimization accuracy and computational efficiency. Specifically, sample points are generated within the range of multiple sets of target blade parameters based on Latin hypercube sampling (LHS). LHS is an efficient multi-dimensional space sampling method that can ensure that sample points are evenly distributed within the value range of each design variable, avoiding sample clustering, thereby revealing the characteristics of the design space to the maximum extent with the fewest possible sample points.

[0062] Using LHS, several sample points are generated from several sets of target sample parameters. Each sample point represents a set of sample parameters. The sample parameters correspond to the design variable combination in any set of blade parameters. The corresponding blade model is generated for the generated sample parameters, and a CFD simulation is performed on each blade model. The performance indicators, such as shaft power, cavitation margin, outlet tangential velocity ratio, and minimum pressure, are calculated through the simulation results.

[0063] After obtaining the performance indicators, a Kriging model is used to fit the mapping relationship between the design variables (input sample parameters) and the objective function (output performance indicators), thereby establishing a surrogate model. This surrogate model can replace computationally expensive CFD simulations, quickly predicting the performance values ​​of the parameterized models corresponding to each set of blade parameters under different operating conditions.

[0064] Correspondingly, step S73 is followed by: S74. Based on the surrogate model, a non-dominated sorting genetic algorithm is used to search for the Pareto optimal solution set under the condition of satisfying the constraint objective function; the Pareto optimal solution set includes a set of multiple target leaf parameters; S75. During the iteration process of the non-dominated sorting genetic algorithm, after a preset number of iterations, multiple optimal sample parameters are selected from the current Pareto optimal solution set using the non-dominated sorting genetic algorithm. S76. Obtain the simulation results of the parameterized model corresponding to each optimal sample parameter after simulation. S77. Based on the Kriging surrogate model, refit the mapping relationship between the optimal sample parameters and the simulation results, and update the surrogate model.

[0065] S78. Using the target blade parameters in the Pareto optimal solution set, perform multi-objective optimization on the runner blade 2.

[0066] After the surrogate model is constructed, a non-dominated sorting genetic algorithm (NSGA-II) can be used as a basis to quickly find the Pareto optimal solution set under the constraints. This Pareto optimal solution set contains a combination of multiple objective blade parameters, and each solution represents the globally optimal balance between the runner shaft power and constraints such as cavitation margin and outlet tangential velocity ratio. Using the objective blade parameters in the Pareto optimal solution set to perform multi-objective optimization of runner blade 2, the maximum output of the mixed-flow turbine can be increased while taking into account cavitation and flow field stability. Finally, CFD is used to verify and correct the optimal samples. During the intelligent algorithm iteration process, every few or dozens of iterations, a portion of the optimal sample points are selected for CFD simulation verification to correct surrogate model errors and ensure the reliability of the optimization results.

[0067] For example, 100-150 sample points are generated based on Latin hypercube sampling (LHS), and the mapping relationship between the design variables and the objective function is fitted using the Kriging surrogate model (fitting accuracy R²≥0.95). Then, the Pareto optimal solution set is searched through 20-30 iterations using the NSGA-Ⅱ algorithm, which solves the problem of "low accuracy and poor efficiency" in traditional optimization.

[0068] In the simulation phase, after optimizing the blades through steps S1-S7, the optimized scheme can be experimentally verified and adapted for engineering applications. In the model testing phase, a runner solid model similar to the optimized scheme can be prepared at a 1:10 or 1:20 scale, and its performance can be experimentally verified on a standard hydraulic test bench. Examples include energy characteristic tests, cavitation tests, and stability tests.

[0069] Energy characteristics test: The power-flow curves of the runner solid model under different guide vane openings and water heads are tested on the hydraulic test bench to confirm whether the maximum output has reached the design target and whether the efficiency has been improved by 3%-5% (the industry's standard improvement range).

[0070] Cavitation test: The critical cavitation margin of the runner solid model was tested using the "pressure reduction method" to verify whether the cavitation performance of the optimized blades met the requirements.

[0071] Stability test: Pressure sensors and vibration acceleration sensors are used to monitor the pressure pulsation at the inlet and outlet of the turbine runner and the vibration amplitude of the unit to ensure that the optimized unit's operational stability has not decreased.

[0072] Through energy characteristic tests, cavitation tests, and stability tests, it can be verified whether the maximum output, cavitation margin, and vibration characteristics of the optimized turbine runner 20 meet expectations. If they do, the project can proceed to the engineering adaptation and adjustment phase, which involves scaling up the model results and applying them to a real unit.

[0073] During the engineering adaptation and adjustment phase, the optimization scheme can be fine-tuned based on the model test results and the actual unit's manufacturing process and operating conditions. For example, if the maximum blade thickness is too small, resulting in insufficient strength, the thickness can be locally increased without significantly affecting the flow field; if the on-site head fluctuation range is greater than the design value, the blade exit angle can be appropriately adjusted to widen the high-efficiency operating range.

[0074] It should be noted that, for the method embodiments, the embodiments of this application are not limited to the described order of actions, because according to the embodiments of this application, some steps may be performed in other orders or simultaneously.

[0075] Correspondingly, according to a second aspect of the invention, such as Figures 3-5 As shown; the present invention also provides a runner 20 suitable for a mixed-flow turbine, the mixed-flow turbine including a volute 10, guide vanes, a runner 20 and a draft tube 30; the configuration of the runner 20 is optimized based on the runner blade optimization method for improving the maximum output of the mixed-flow turbine provided in the first aspect of the present invention; wherein, the runner blade 2 of the runner 20 has an asymmetric double curvature blade profile, and the inlet edge of the runner blade 2 has a positive curvature and the outlet edge has a negative curvature; the thickness of the runner blade 2 varies in a gradient from the rim 3 to the hub 1 of the runner 20; the pressure surface of the runner blade 2 is coated with a superhydrophobic coating, and at least one microrib structure is provided on the back.

[0076] The technical solution of the present invention will be described in more detail below with reference to the accompanying drawings. Please refer to the accompanying drawings. Figures 3-5 The impeller 20 designed using this invention features a blade profile with varying lengths and a gradient thickness distribution. Specifically, the blade profile with a double curvature transition has a positive curvature in the 15% chord length region of the inlet edge of the impeller blade 2, and a negative curvature in the 20% chord length region of the outlet edge. The non-linear thickness distribution from the rim 3 to the hub 1, combined with the WS2 superhydrophobic coating (contact angle 152°) sprayed on the pressure surface, results in a 12% weight reduction while increasing power output by 15.1% at a water head of 550m. The microrib structure at 50-70% chord length on the blade back reduces the cavitation erosion coefficient to 0.76σ.

[0077] After the simulation is completed, the optimized rotor obtained from the optimized design of this invention embodiment and the unoptimized original rotor can be subjected to CFD simulation one by one, and a comparison chart of the simulation results of the two rotors before and after optimization can be output. For example... Figure 6 This chart compares the performance of the unoptimized original impeller and the optimized impeller under different operating conditions. Figure 6 The flow-power curves and flow-efficiency curves are shown under different guide vane opening conditions. Figure 6In the diagram, the curve with solid squares represents the flow-efficiency curve of the original impeller; the curve with intersecting squares represents the flow-efficiency curve of the optimized impeller; the curve with solid triangles represents the flow-power curve of the original impeller; and the curve with intersecting triangles represents the flow-power curve of the optimized impeller. From... Figure 6 The four curves clearly show that the efficiency of the optimized rotor is not significantly improved compared to the original rotor, and may even be lower. However, the power output of the optimized rotor is significantly better than that of the original rotor under different operating conditions. The optimization approach involves sacrificing some efficiency to achieve greater output. For example... Figure 7 The images show the velocity contours of the unoptimized original impeller and the optimized impeller. Figure 7 middle, Figure 7 a represents the velocity contour map of the original rotor; Figure 7 b is a velocity contour plot of the blade 2 of the original rotor viewed from a frontal perspective; Figure 7 c is a velocity cloud diagram of the original runner blade 2 viewed from a top-down perspective; Figure 7 A represents the velocity contour map of the optimized rotor; Figure 7 B is a velocity cloud diagram of the optimized runner blade 2 viewed from a frontal perspective; Figure 7 C is a velocity contour plot of the optimized runner blade 2 viewed from a top-down perspective. Figure 7 The comparison showed that the maximum flow velocity at the outlet edge of the original rotor blade 2 was 34.909 m / s, while the maximum flow velocity at the outlet edge of the optimized rotor blade 2 was 32.102 m / s. While increasing the maximum output of the rotor 20, the maximum flow velocity of the rotor blade 2 did not increase significantly, which effectively controlled the wear problem of the rotor blade 2. Figure 8 Pressure cloud diagrams of the impeller 20 before and after optimization are generated through simulation. Figure 8 middle, Figure 8 a is the pressure cloud diagram of the original impeller; Figure 8 b is the pressure contour diagram of the optimized impeller. From Figure 8 As can be seen from the two pressure cloud maps provided, the area of ​​the low-pressure zone does not change significantly. Therefore, the cavitation performance of the optimized impeller will not deteriorate significantly and meets the cavitation performance requirements.

[0078] The mixed-flow turbine with the impeller 20 provided by this invention achieved a significant increase in maximum output while ensuring the stability of unit operation during the engineering verification phase. Specifically: Taking a 178.6MW mixed-flow turbine of a power station as an example, the performance of runner blade 2 is significantly improved after adopting the above optimization method: At maximum head, the maximum output increased from 181MW to 195MW, breaking through the original rated power limit, with an increase of 7%; The efficiency of the impeller is increased by 2.8% under rated conditions and by 3.5%-4.2% under partial load conditions (70%-90% of rated power), reducing energy loss; The cavitation margin was reduced by 0.3m, which significantly improved the unit's operational stability under low head conditions and reduced the vibration amplitude by 15%-20%.

[0079] It should be noted that, for the above-described runner embodiment, since the above-described method for optimizing the runner blades to improve the maximum output of the mixed-flow turbine has already achieved the technical effects mentioned above, the runner designed using this method should also have similar technical effects, so it will not be elaborated here.

[0080] It should also be noted that, in this document, the terms "upper," "lower," "left," "right," "inner," and "outer," etc., indicate the orientation or positional relationship based on the orientation or positional relationship shown in the accompanying drawings, and are only for the convenience of describing the invention and simplifying the description, and do not indicate or imply that the device or element referred to must have a specific orientation, or be constructed and operated in a specific orientation, and therefore should not be construed as a limitation of the invention. Furthermore, relational terms such as "first" and "second" are only used to distinguish one entity or operation from another entity or operation, and do not necessarily require or imply any such actual relationship or order between these entities or operations, nor should they be construed as indicating or implying relative importance. Moreover, the term "comprising" or any other variation thereof is intended to cover non-exclusive inclusion, such that a process, method, article, or terminal device that comprises a list of elements includes not only those elements, but also other elements not expressly listed, or elements inherent to such a process, method, article, or terminal device.

Claims

1. An optimization method for runner blades to improve the maximum output of a mixed-flow turbine. The method, characterized in that it includes: A three-dimensional model of the entire flow channel of the mixed-flow turbine in the direction of water flow is established; the flow-through components include at least the volute, guide vanes, runner, and tailrace. A mixed turbulence model was selected, and boundary conditions were set to simulate the flow field characteristics of the impeller under different design and critical conditions. Based on the flow field characteristic data of the runner, the simulation results of the runner under various working conditions are analyzed to determine the core loss zone that restricts the maximum output of the mixed-flow turbine. Based on the location of the core loss zone, the blade parameters of the runner blades are set; the blade parameters include meridional parameters, airfoil section parameters, and spatial twist parameters; Based on the set of multiple sets of blade parameters, parameterized models of the runner blades are established respectively; Simulate the flow field characteristic data of multiple parameterized models under the same working condition, compare and analyze the simulation results corresponding to multiple sets of flow field characteristic data, and select target blade parameters that are highly correlated with the maximum output of the mixed-flow turbine. Based on the target blade parameters, the runner blades are optimized to improve the maximum output of the mixed-flow turbine.

2. The method for optimizing the runner blades to improve the maximum output of a mixed-flow turbine according to claim 1, characterized in that, The optimization of the runner blades based on the target blade parameters includes: The main objective function is used to maximize the power of the rotor shaft. Using the constrained objective function, the cavitation margin is controlled to be no greater than the preset cavitation margin, the tangential velocity of the water flow at the impeller outlet is no greater than 0.15 times the average tangential velocity component, and the maximum negative pressure of the impeller blades is no less than the saturated vapor pressure of water. The blade parameters that satisfy the main objective function and the constraint objective function are taken as the target blade parameters.

3. The method for optimizing the runner blades to improve the maximum output of a mixed-flow turbine according to claim 2, characterized in that, The process of selecting target blade parameters that are highly correlated with the maximum output of the mixed-flow turbine includes: Multiple sample parameters are generated from the target blade parameters based on Latin hypercube sampling, and each sample parameter corresponds to each parameterized model; Obtain the simulation results of the parameterized model corresponding to each of the sample parameters after simulation. The Kriging surrogate model is used to fit the mapping relationship between the sample parameters and the simulation results to construct the surrogate model; The step of taking the blade parameters that satisfy the main objective function and the constraint objective function as the target blade parameters includes: Based on the surrogate model, a non-dominated sorting genetic algorithm is used to search for the Pareto optimal solution set under the condition of satisfying the constraint objective function; the Pareto optimal solution set includes a set of multiple target leaf parameters; The target blade parameters in the Pareto optimal solution set are used to perform multi-objective optimization on the runner blade.

4. The method for optimizing the runner blades to improve the maximum output of a mixed-flow turbine according to claim 3, characterized in that, The process involves using a non-dominated sorting genetic algorithm to search for the Pareto optimal solution set while satisfying the constraint objective function, followed by: During the iterative process of the non-dominated sorting genetic algorithm, after each preset number of iterations, multiple optimal sample parameters are selected from the current Pareto optimal solution set using the non-dominated sorting genetic algorithm. Obtain the simulation results of the parameterized model corresponding to each of the optimal sample parameters after simulation. Based on the Kriging proxy model, the mapping relationship between the optimal sample parameters and the simulation results is refitted, and the proxy model is updated.

5. The method for optimizing the runner blades to improve the maximum output of a mixed-flow turbine according to claim 1, characterized in that, The selection of a mixed turbulence model and the setting of boundary conditions to simulate the flow field characteristics of the impeller under different design and critical conditions include: Based on the flow channel region where the volute and guide vane are located in the full-channel 3D model, RNG is used. k - ε Turbulence model is used for operating condition simulation; Based on the flow channel region where the impeller and tailpipe are located in the full flow channel three-dimensional model, the SSTk-ω turbulence model is used to simulate the working conditions. Based on the selected RNG k-ε Model and the SST k - ω And based on the boundary conditions set according to the preset operating conditions, the process characteristics of the runner under multiple design operating conditions, maximum output operating conditions and minimum head operating conditions are simulated; wherein, the boundary conditions include at least one operating condition parameter among flow rate, head, rotational speed, guide vane opening and pressure.

6. The method for optimizing the runner blades to improve the maximum output of a mixed-flow turbine according to claim 1, characterized in that, The flow field characteristic data includes at least the pressure distribution on the surface of the impeller blades, the velocity vector distribution within the flow channel, and the energy loss coefficient distribution. The analysis of simulation results of the impeller under various operating conditions based on the flow field characteristic data of the impeller includes: Based on the pressure distribution on the surface of the impeller blades, the low-pressure zone and the pressure gradient abrupt change zone of the impeller are identified; Based on the velocity vector distribution within the flow channel, the throat region with excessively high flow velocity and the low-energy region with backflow and vortices are located. Based on the energy loss coefficient distribution within the flow channel, the proportions of inlet impact loss, blade surface friction loss, and outlet wake loss of the runner are quantified.

7. The method for optimizing the runner blades to improve the maximum output of a mixed-flow turbine according to claim 1, characterized in that, The blade parameters for setting the impeller blades include: The meridional parameters of the runner blades are set according to at least one of the runner inlet diameter, runner outlet diameter, and meridional contraction angle. The airfoil section parameters of the runner blade are set based on at least one of the runner blade inlet angle, runner blade outlet angle, runner blade maximum thickness position, runner blade chord length, and runner blade consistency. Based on the torsion angle distribution of the impeller blades, the spatial torsion parameters of the impeller blades are set; The meridional plane parameter, the airfoil section parameter, and the spatial twist parameter, or a combination thereof, are set as the blade parameters of the runner blade.

8. An optimization method for runner blades to improve the maximum output of a mixed-flow turbine according to any one of claims 1-7. The method, characterized in that, The method further includes: Based on the optimized three-dimensional model of the entire flow channel corresponding to the impeller blades, a solid model of the impeller is prepared at a preset scale. The physical model of the runner was installed on a hydraulic test bench, and multiple guide vane openings and heads were set. The power-flow curves of the physical model of the runner under different guide vane openings and heads were tested to verify the energy characteristics performance of the optimized runner. The critical cavitation margin of the solid model of the impeller was tested using the pressure reduction method to verify the cavitation performance of the optimized impeller. The pressure pulsation at the inlet and outlet of the turbine runner and the vibration amplitude of the unit are monitored by pressure sensors and vibration acceleration sensors to verify the stability performance of the optimized turbine runner. Based on the energy characteristics, cavitation performance, and stability performance, the optimized performance results of the rotor are obtained.

9. The method for optimizing the runner blades to improve the maximum output of a mixed-flow turbine according to claim 8, characterized in that, The method further includes: Based on the performance results of the runner and the engineering constraints of the actual unit, the blade parameters of the runner blades are adjusted.

10. A runner suitable for a mixed-flow turbine, the mixed-flow turbine comprising a volute, guide vanes, a runner, and a draft tube; characterized in that, The configuration of the runner is optimized based on the runner blade optimization method for improving the maximum output of a mixed-flow turbine as described in any one of claims 1-9; wherein, The impeller blades have an asymmetric double curvature blade profile, and the inlet edge of the impeller blades has a positive curvature while the outlet edge has a negative curvature. The thickness of the rotor blades varies in a gradient from the rim to the hub. The pressure surface of the rotor blade is coated with a superhydrophobic coating, and the back side is provided with at least one microrib structure.

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