Optimization design method for inhibiting vortex strip of draft tube under multiple working conditions of water turbine

Abstract

The invention belongs to the technical field of water turbine design, and particularly provides an optimal design method for turbine multi-working-condition draft tube vortex strip suppression. Performing CFD numerical simulation calculation on the vortex strip of the draft tube of the mixed-flow water turbine; carrying out draft tube vortex strip identification and volume objective function calculation based on a lambda2 criterion; a draft tube vortex strip inhibition optimization design problem is constructed; and solving an optimization design problem based on an EGO algorithm. By means of the method, the design efficiency and the design effect of modification or optimization design of various draft tubes, runner cones and the like can be improved, dependence on the experience of designers is avoided, and therefore the operation stability of the mixed-flow water turbine is better improved.

Description

Technical Field

[0001] The invention belongs to the technical field of water turbine design, and in particular relates to an optimization design method for suppressing vortex belts in a draft tube of a water turbine under multiple working conditions. Background Art

[0002] The turbine is the heart of hydroelectric power generation, used to convert the potential energy of the river into rotational mechanical energy, which in turn drives the generator to generate electricity. Because the Francis turbine has a compact structure, high efficiency, and can adapt to a very high head range, it is currently the most widely used model in countries around the world. As the proportion of intermittent renewable energy in the power grid continues to increase, hydropower units are more frequently responsible for peak and frequency regulation tasks, and they are inevitably operating at deviations from the optimal operating conditions. The tailwater vortex is a special vortex phenomenon that occurs in the tailwater when the Francis turbine deviates from the optimal operating conditions. It will excite low-frequency, high-amplitude pressure pulsations in the tailwater. The pressure pulsations generated may propagate throughout the entire pipeline system and cause hydraulic resonance, and even excite the subsynchronous free oscillation of the prototype turbine, seriously threatening the operating stability of the turbine unit.

[0003] In order to suppress the strength of the vortex belt in the tailwater tube and thus ensure the operation stability of the Francis turbine unit, researchers have been committed to modifying or optimizing the design of the tailwater tube, the discharge cone, etc., such as the discharge cone modification design, the discharge cone perforation design, the design of the guide vane installed on the inner wall of the tailwater tube, etc., and have achieved certain design effects. However, due to the lack of a direct and efficient optimization design method for the tailwater tube vortex belt suppression facilities, the current modification or optimization design of various tailwater tubes, discharge cones, etc. still completely relies on the "trial and error" design method, design-test-modification, and cycle until a satisfactory design is obtained. However, this design method requires multiple manual corrections and tests, so the design cycle is long and the cost is high. In the design process, the correction of related geometric shapes is completely dependent on the designer's experience, which requires a high level of professional knowledge of the designer, and it is difficult to obtain the global optimal design. In addition, it is difficult to obtain an optimized design with good tailwater tube vortex belt suppression effect under a wide range of operating conditions. Summary of the invention

[0004] The technical problem to be solved by the present invention is to provide an optimization design method for vortex suppression in a multi-operating-condition tailwater tube of a hydraulic turbine, thereby improving the design efficiency and design effect of the modification or optimization design of various tailwater tubes, spillway cones, etc., and avoiding dependence on the designer's experience, thereby better improving the operating stability of the mixed flow turbine.

[0005] In order to solve the above technical problems, the technical solution adopted by the present invention is: an optimization design method for suppressing vortex belts in multi-operating state tailwater tubes of a hydraulic turbine, comprising the following steps: Step 1: Select multiple optimized operating points; Step 2: CFD numerical simulation calculation of the vortex belt of the Francis turbine draft tube; Step 3: Based on l 2. Draft tube vortex identification and volume objective function calculation based on the criterion; Step 4: Constructing the optimization design problem of vortex suppression in tailwater tube; Step 5: Solve the optimization design problem based on the EGO algorithm.

[0006] In the preferred scheme, in step one, the optimal Latin hypercube sampling method is used to evenly distribute points on the comprehensive operating characteristic curve of the turbine, and then the operating points in the operating area of ​​the turbine under study that is greatly affected by the tailwater tube vortex (such as high head and low load conditions and low head and high load conditions) are used as multiple optimized operating points.

[0007] In the preferred solution, the optimal Latin hypercube sampling method is to randomly exchange two elements in each dimension after obtaining the sample points using the Latin hypercube sampling method, and use an evaluation function Optimize the sample points and evaluate the function The expression is: ; in, express n The distance between every two sample points in i indivual; Indicates that the distance is equal to The number of sample point pairs; there will be s Unequal distance values , ; is a positive integer and a constant.

[0008] In the preferred scheme, in the step 2, the CFD numerical simulation calculation of the vortex belt of the tailwater tube of the mixed flow turbine is performed, and the operation method is: first, a three-dimensional modeling software is used to construct a geometric model of the entire flow basin of the turbine, including a volute, fixed guide vanes, movable guide vanes, a runner, and a tailwater tube; then a meshing tool is used to perform structured or unstructured meshing of the entire flow basin of the turbine according to the complexity of the geometric features; finally, the physical model of the simulation and the cavitation two-phase flow simulation are set according to the operating parameters of multiple optimized operating points, and the simulation calculation is implemented.

[0009] In the preferred embodiment, in the step 2, in the cavitation two-phase flow calculation, the cavitation model adopts the homogeneous multiphase flow Zwart-Gerber-Belamri model based on the Rayleigh-Plesset equation. The cavitation model controls the mass transfer rate between water and gas through the transport equation, and the expression is: ; in, is the empirical coefficient of vaporization; is the empirical coefficient of condensation; is the gas core volume fraction; is the bubble radius; is the gas phase volume fraction; is the gas phase density; is the liquid density; is the gas phase pressure; It's local pressure.

[0010] In the preferred embodiment, in step 3, based on l The method for identifying the draft tube vortex belt and calculating the volume objective function based on the 2-criterion is as follows: Based on the CFD numerical simulation results of the Francis turbine draft tube vortex belt, the l 2 criteria and thresholds are used to automatically identify the tailwater vortex belt, and then the volume of the tailwater vortex belt is calculated by integration. V , the calculated volume V As the optimization objective function of the vortex intensity of the tailwater tube.

[0011] In the preferred embodiment, the l The 2nd criterion is based on the local velocity gradient tensor The decomposition expression is: ; in, is a symmetric tensor, are antisymmetric tensors, representing the deformation and rotation parts of the fluid respectively; Represent the three directions of the Cartesian coordinate system; Respectively represent the velocity components in the three coordinate directions; Represents the partial derivative of the physical quantity in the corresponding coordinate direction; ; The characteristic equation is: ; in, P , Q , R are the three invariants of the velocity tensor gradient; Q Defined as: ; Q If it is greater than 0, it means that the vorticity plays a dominant role, that is, the rotation is greater than the deformation, and it is considered that there is vortex motion; l 2 criterion believes that the condition to ensure that a vortex-induced cross-sectional pressure is minimal is: The three eigenvalues ​​of have the following relationship: ; when When it is less than 0, there is a vortex, which is equivalent to The criterion defines the vortex as Region with two negative eigenvalues.

[0012] In a preferred solution, in step 4, the construction of the tailwater tube vortex suppression optimization design problem includes the following steps: S401, determining optimization design variables according to optimization design object , determine the value range of the optimization design variables through parametric research; S402, linearly combining the optimization objective functions of multiple optimization operating points to obtain the total objective function of the flow field optimization design problem for the purpose of suppressing the vortex bands in the draft tube under multiple operating conditions : ; in, m Indicates the number of optimized operating points; Represents the weight coefficient of each operating point, ; S403, to minimize In order to achieve the coordinated suppression optimization of the draft tube vortex belt of the Francis turbine under multiple working conditions, and take the hydraulic efficiency of the turbine as the optimization constraint, the entire draft tube vortex belt suppression optimization design problem can be constructed as follows:

[0013] in, It means that after the turbine is equipped with tailwater tube vortex suppression measures, i Hydraulic efficiency at the optimal operating point; It means that the turbine is not equipped with tailwater tube vortex suppression measures. i Hydraulic efficiency at the optimal operating point; It means that after the turbine is equipped with tailwater tube vortex suppression measures, i The maximum hydraulic efficiency loss allowed at an optimal operating point.

[0014] In a preferred solution, in step 5, solving the optimization design problem based on the EGO algorithm includes the following steps: S501, using the optimal Latin hypercube sampling method to evenly arrange a certain number of initial sample points in the design space, and using the initial sample points and the optimization objective function values ​​corresponding to the initial sample points to construct an initial Kriging proxy model; S502. The second step is the iterative update of the optimal solution. The correction points are iteratively selected using the differential evolution algorithm and the improved expectation criterion based on the Kriging proxy model, and the optimization objective function values ​​corresponding to the correction points are calculated to determine whether they have converged. If not, the correction points are added to the sample point database and the loop iteration is continued. If converged, the loop iteration ends. The convergence of the optimization is determined by monitoring the changing trend of the objective function. If the optimization objective function value remains unchanged or changes slightly after multiple optimization iterations, the optimization is considered to have converged. During the optimization process, the penalty function method is used to process the design points that do not converge in the simulation or do not meet the constraints defined in step four.

[0015] In the preferred solution, in step S502, the basic idea of ​​improving the expectation criterion is to calculate the unknown points in the design space by using the Gaussian probability model. x The response value at the position is relative to the current optimal value The expected possibility of improvement is calculated, and the point with the largest expected value of improvement in the design space is selected as the correction point. The expression is: ; in, Indicates the current minimum value; Indicates unknown point x The true value at Indicates that the Kriging surrogate model is at an unknown point x The predicted value at s Indicates that the Kriging surrogate model is at an unknown point x The root mean square error of the prediction at ; and They are the cumulative function and probability density function of the standard normal distribution respectively.

[0016] The present invention provides an optimization design method for suppressing vortex belts in a multi-operating-condition draft tube of a hydraulic turbine, which has the following beneficial effects: 1. This method can significantly improve the design efficiency and design effect of the modification or optimization design of various tailwater pipes, discharge cones, etc., and can suppress the strength of the tailwater pipe vortex and the pressure pulsation caused by it in a wider range of working conditions, greatly improve the operating stability of the Francis turbine, and better enable hydropower generation to play a role in peak load regulation and frequency regulation in the new energy system.

[0017] 2. Step 1 of the present invention uses the optimal Latin hypercube experimental design method to select multiple optimized operating points, thereby achieving the purpose of covering the largest possible optimized operating range with as few optimized operating points as possible. While comprehensively considering the operating range of the turbine affected by the vortex belt of the tailwater tube, it reduces the amount of optimization calculation and improves the efficiency of the optimization design.

[0018] 3. Step three of the present invention proposes an optimization objective function that is easy to evaluate and can characterize the strength of the tailwater tube vortex belt, namely, the volume of the tailwater tube vortex belt, thereby realizing the direct optimization design of the tailwater tube vortex belt strength, making the optimization effect of suppressing the tailwater tube vortex belt strength more obvious.

[0019] 4. Step 4 of the present invention takes the weighted average of the volumes of the tailwater tube vortex belts at multiple optimized operating points as the optimization objective function, thereby achieving the purpose of simultaneously reducing the strength of the tailwater tube vortex belts under multiple operating conditions of the turbine, and at the same time, the designer's intention or the needs of actual production conditions can be met by adjusting the weight coefficient.

[0020] 5. Step five of the present invention uses an efficient global optimization algorithm to solve the optimization design problem, which not only avoids dependence on the designer's experience and improves the efficiency of the optimization design, but also reduces the possibility of falling into a local optimal solution and increases the probability of obtaining a global optimal solution.

[0021] 6. An optimization design method for suppressing vortex belts in tailwater tubes of hydraulic turbines under multiple operating conditions developed based on the above technology can significantly improve the design efficiency and design effect of the modification or optimization design of various tailwater tubes, spill cones, etc., and can suppress the strength of tailwater tube vortex belts and the pressure pulsation caused by them in a wider range of operating conditions, greatly improve the operating stability of mixed flow turbines, and better enable hydropower generation to play a role in peak load regulation and frequency regulation in new energy systems. BRIEF DESCRIPTION OF THE DRAWINGS

[0022] The present invention will be further described below in conjunction with the accompanying drawings and embodiments: Figure 1 This is a flow chart of the optimization design method for vortex suppression in the draft tube of a hydraulic turbine under multiple operating conditions; Figure 2 A method for selecting multiple optimized operating points; Figure 3 Schematic diagram of the vortex belt in the tailwater tube. DETAILED DESCRIPTION

[0023] In order to make the purpose, technical solution and advantages of the present invention more clearly understood, the present invention is further described in detail below in conjunction with the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are only used to explain the present invention and are not used to limit the present invention.

[0024] like Figure 1 As shown in FIG, an optimization design method for suppressing vortex belts in the draft tube of a hydraulic turbine under multiple operating conditions includes selecting multiple optimized operating points, CFD numerical simulation calculation of vortex belts in the draft tube of a Francis turbine, and l 2 criteria for the identification of tailwater vortex belts and the calculation of volume objective function, the construction of the tailwater vortex belt suppression optimization design problem, and the efficient solution of the optimization design problem based on the EGO algorithm. Each step is now explained in detail.

[0025] Step 1: The specific process of selecting multiple optimized operating points is as follows: use the optimal Latin hypercube sampling method to evenly distribute points on the turbine comprehensive operating characteristic curve, and then select the operating points in the operating area where the turbine under study is greatly affected by the vortex belt of the tailwater tube (such as high head and low load conditions and low head and high load conditions) as multiple optimized operating points, such as Figure 2 As shown, this can not only fully consider the working conditions of the turbine affected by the vortex belt of the tailwater tube, but also reduce the amount of optimization calculation.

[0026] The optimal Latin hypercube sampling method is improved on the basis of the Latin hypercube sampling method. After obtaining the sample points using the Latin hypercube sampling method, two elements are randomly exchanged in each dimension, and an evaluation function is used. Optimize the sample points, and the expression of the evaluation function is: ; in, express n The pairwise distances of the sample points i indivual; Indicates that the distance is equal to Considering that there may be pairs of sample points with equal distances, there will be s Unequal distance values , ; is a positive integer, which is a constant. In this embodiment, 5 is selected.

[0027] In this way, the optimized operating points can be evenly arranged in the operating area where the turbine is greatly affected by the vortex belt of the tailwater tube.

[0028] Step 2: The specific process of CFD numerical simulation calculation of the vortex belt of the draft tube of a mixed flow turbine is as follows: first, a three-dimensional modeling software is used to construct a geometric model of the entire flow basin of the turbine, including the volute, fixed guide vanes, movable guide vanes, runner, and draft tube. Then, a meshing tool is used to perform structured or unstructured meshing of the entire flow basin of the turbine according to the complexity of the geometric features. Finally, the physical model of the simulation and the cavitation two-phase flow simulation are set according to the operating parameters of multiple optimized operating points, and the simulation calculation is implemented. In the cavitation two-phase flow calculation, the cavitation model adopts the homogeneous multiphase flow Zwart-Gerber-Belamri model based on the Rayleigh-Plesset equation. The cavitation model controls the mass transfer rate between water and gas through the transport equation, and the expression is: ; in, is the empirical coefficient of vaporization; is the empirical coefficient of condensation; is the gas core volume fraction; is the bubble radius; is the gas phase volume fraction; is the gas phase density; is the liquid density; is the gas phase pressure; It's local pressure.

[0029] By recording macro files and writing batch files, the above CFD numerical simulation process can be automatically implemented and called at any time during the optimization process.

[0030] Step 3: Based on l The specific process of the tailwater tube vortex identification and volume objective function calculation based on the 2-criterion is as follows: Based on the CFD numerical simulation results of the tailwater tube, l 2 criteria and appropriate thresholds for automatic identification of tailwater vortex zones, such as Figure 3 As shown, the volume of the tailwater vortex is then calculated by integration V , the calculated volume V As the optimization objective function of the vortex intensity of the tailwater tube.

[0031] The l The 2nd criterion is based on the local velocity gradient tensor The decomposition expression is: ; in, is a symmetric tensor, are antisymmetric tensors, representing the deformation and rotation parts of the fluid respectively; Represent the three directions of the Cartesian coordinate system; Respectively represent the velocity components in the three coordinate directions; Represents the partial derivative of the physical quantity in the corresponding coordinate direction.

[0032] ; The characteristic equation of is as follows:

[0033] in, P , Q , R are the three invariants of the velocity tensor gradient. Q Defined as: ; generally Q When it is greater than 0, it means that vorticity plays a dominant role, that is, rotation is greater than deformation, and vortex motion is considered to exist.

[0034] l2 criterion believes that the condition to ensure a minimum cross-sectional pressure induced by a vortex is the determinant The three eigenvalues ​​of have the following relationship: ; And when When it is less than 0, there is a vortex, which is equivalent to The criterion defines the vortex as Region with two negative eigenvalues.

[0035] Step 4: The specific process of constructing the tailwater tube vortex suppression optimization design problem is as follows: First, determine the optimization design variables according to the optimization design object. (such as the diameter and length of the discharge cone, the diameter and distribution of the holes in the discharge cone, etc.), the optimization design objects include the discharge cone modification design, the discharge cone hole design, the design of adding guide vanes to the inner wall of the tailwater pipe, etc., the optimization design variables Including the diameter and length of the spillway cone, the diameter and distribution of the holes in the spillway cone, etc.

[0036] The range of values ​​of the optimization design variables is determined through parametric research; then the optimization objective functions of multiple optimization operating points are linearly combined to obtain the total objective function of the flow field optimization design problem for the purpose of suppressing the vortex bands in the tailwater tube under multiple operating conditions. In this embodiment, the optimization objective function is the tailwater tube vortex volume corresponding to each operating point , the overall objective function The expression is:

[0037] in, m Indicates the number of optimized operating points; It represents the weight coefficient of each operating point, which can be adjusted according to the vortex belt strength of the original turbine at each operating point or the designer's intention. .

[0038] Finally, minimize The goal is to achieve the coordinated suppression optimization of the vortex belt in the draft tube of a Francis turbine under multiple operating conditions, and the hydraulic efficiency of the turbine is used as the optimization constraint during the optimization process to better guide the optimization algorithm to quickly find the optimal design that meets the actual requirements.

[0039] In this embodiment, the optimization constraint is set to that the hydraulic efficiency of the water turbine cannot be much lower than the original value.

[0040] Step 5. The specific process of efficiently solving the optimization design problem based on the EGO algorithm is: using the efficient global optimization algorithm EGO to efficiently solve the optimization design problem of vortex suppression in tailwater tubes under multiple working conditions, which can be divided into two major steps.

[0041] The first step is the experimental design (DOE), which uses the optimal Latin hypercube sampling method to evenly arrange a certain number of initial sample points in the design space, and uses the initial sample points and their corresponding objective functions to construct an initial Kriging surrogate model to achieve a preliminary search of the design space.

[0042] The second step is the iterative update of the optimal solution. The differential evolution (DE) algorithm and the improved expectation (EI) criterion based on the Kriging surrogate model are used to iteratively select correction points that take into account both exploratory and exploitative aspects, thereby achieving an efficient and comprehensive search of the design space. The iteration is repeated until the optimization convergence conditions are reached.

[0043] With the help of the adaptive Kriging proxy model, the selection of sample points is no longer blind, but is gradually selected according to the characteristics of the optimization problem, which can greatly reduce the demand for overall sample points and significantly improve the optimization efficiency. For all new designs, the CFD simulation module is automatically called in batch processing to perform geometric construction, meshing, numerical simulation, and automatically post-processing to calculate the corresponding objective function value, which is the volume of the tailwater vortex in this embodiment. For those designs that cannot converge in numerical simulation or do not meet the optimization constraints, the penalty function method is used in the optimization process.

[0044] The basic idea of ​​the EI criterion is to calculate the unknown points in the design space through the Gaussian probability model. x The response value at the position is relative to the current optimal value The expected possibility of improvement is calculated, and the point with the largest expected value of improvement in the design space is selected as the correction point. The expression is:

[0045] in, Indicates the current minimum value; Represents the true value at the unknown point x; Represents the predicted value of the Kriging surrogate model at the unknown point x; s Represents the root mean square error of the prediction of the Kriging surrogate model at the unknown point x; and They are the cumulative function and probability density function of the standard normal distribution respectively.

[0046] The optimization design method for suppressing the vortex belt of the tailwater tube of a mixed flow turbine under multiple operating conditions described in the present invention can significantly improve the design efficiency and design effect of the modification or optimization design of various tailwater tubes, spill cones, etc., and can suppress the strength of the tailwater tube vortex belt and the pressure pulsation caused by it within a wider range of operating conditions, greatly improve the operating stability of the mixed flow turbine, and better enable hydropower generation to play a role in peak regulation and frequency regulation in new energy systems.

[0047] It will be easily understood by those skilled in the art that the above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions and improvements made within the spirit and principles of the present invention should be included in the protection scope of the present invention.

Claims

1. An optimization design method for suppressing vortex belts in the draft tube of a hydraulic turbine under multiple operating conditions, characterized in that: The following steps are involved: Step 1: Select multiple optimized operating points; Step 2: CFD numerical simulation calculation of the vortex belt of the Francis turbine draft tube; Step 3: Based on λ 2. Draft tube vortex identification and volume objective function calculation based on the criterion; Step 4: Constructing the optimization design problem of vortex suppression in tailwater tube; Step 5: Solve the optimization design problem based on the EGO algorithm.

2. The optimization design method for suppressing vortex belts in multi-operating state draft tubes of a hydraulic turbine according to claim 1 is characterized in that: In the step 1, the optimal Latin hypercube sampling method is used to evenly distribute points on the comprehensive operating characteristic curve of the turbine, and then the operating points that fall within the operating area of ​​the turbine under study that is greatly affected by the vortex belt of the tailwater tube are used as multiple optimized operating points.

3. The optimization design method for suppressing vortex belts in multi-operating state draft tubes of a hydraulic turbine according to claim 2, characterized in that: The optimal Latin hypercube sampling method is to randomly exchange two elements in each dimension after obtaining the sample points using the Latin hypercube sampling method, and use an evaluation function Optimize the sample points and evaluate the function The expression is: ； in, express n The distance between every two sample points in i indivual; Indicates that the distance is equal to The number of sample point pairs; there will be s Unequal distance values , ; is a positive integer and a constant.

4. The optimization design method for suppressing vortex belts in multi-operating state draft tubes of a hydraulic turbine according to claim 1, characterized in that: In the step 2, the CFD numerical simulation calculation of the vortex belt of the draft tube of the mixed flow turbine is performed as follows: first, a three-dimensional modeling software is used to construct a geometric model of the entire flow basin of the turbine, including a volute, fixed guide vanes, movable guide vanes, a runner, and a draft tube; then a meshing tool is used to perform structured or unstructured meshing of the entire flow basin of the turbine according to the complexity of the geometric features; finally, the physical model of the simulation and the cavitation two-phase flow simulation are set according to the operating parameters of multiple optimized operating points, and the simulation calculation is implemented.

5. The optimization design method for suppressing vortex belts in multi-operating state draft tubes of a hydraulic turbine according to claim 3, characterized in that: In the step 2, in the calculation of cavitation two-phase flow, the cavitation model adopts the homogeneous multiphase flow Zwart-Gerber-Belamri model based on the Rayleigh-Plesset equation. The cavitation model controls the mass transfer rate between water and gas through the transport equation, and the expression is: ； in, is the empirical coefficient of vaporization; is the empirical coefficient of condensation; is the gas core volume fraction; is the bubble radius; is the gas phase volume fraction; is the gas phase density; is the liquid density; is the gas phase pressure; It's local pressure.

6. The optimization design method for suppressing vortex belts in multi-operating state draft tubes of a hydraulic turbine according to claim 1, characterized in that: In step 3, based on λ The method for identifying the draft tube vortex belt and calculating the volume objective function based on the 2-criterion is as follows: Based on the CFD numerical simulation results of the Francis turbine draft tube vortex belt, the λ 2 criteria and thresholds are used to automatically identify the tailwater vortex belt, and then the volume of the tailwater vortex belt is calculated by integration. V , the calculated volume V As the optimization objective function of the vortex intensity of the tailwater tube.

7. The optimization design method for suppressing vortex belts in multi-operating state draft tubes of a hydraulic turbine according to claim 6, characterized in that: Said λ The 2nd criterion is based on the local velocity gradient tensor The decomposition expression is: ； in, is a symmetric tensor, are antisymmetric tensors, representing the deformation and rotation parts of the fluid respectively; Represent the three directions of the Cartesian coordinate system; Respectively represent the velocity components in the three coordinate directions; Represents the partial derivative of the physical quantity in the corresponding coordinate direction; ； The characteristic equation is: ； in, P , Q , R are the three invariants of the velocity tensor gradient; Q Defined as: ; Q If it is greater than 0, it means that the vorticity plays a dominant role, that is, the rotation is greater than the deformation, and it is considered that there is vortex motion; λ 2 criterion believes that the condition to ensure that a vortex-induced cross-sectional pressure is minimal is: The three eigenvalues ​​of 、 、 With the following relationship: ； when When it is less than 0, there is a vortex, which is equivalent to The criterion defines the vortex as Region with two negative eigenvalues.

8. The optimization design method for suppressing vortex belts in multi-operating state draft tubes of a hydraulic turbine according to claim 1, characterized in that: In step 4, the construction of the tailwater tube vortex suppression optimization design problem includes the following steps: S401, determining optimization design variables according to optimization design object , and determine the value range of the optimization design variables through parametric research; S402, linearly combining the optimization objective functions of multiple optimization operating points to obtain the total objective function of the flow field optimization design problem for the purpose of suppressing the vortex intensity of the draft tube under multiple operating conditions : ； in, m Indicates the number of optimized operating points; Represents the weight coefficient of each operating point, ; S403, to minimize In order to achieve the coordinated suppression optimization of the draft tube vortex belt of the Francis turbine under multiple working conditions, and take the hydraulic efficiency of the turbine as the optimization constraint, the entire draft tube vortex belt suppression optimization design problem is constructed as follows: ； in, It means that after the turbine is equipped with tailwater tube vortex suppression measures, i Hydraulic efficiency at the optimal operating point; The original turbine is i Hydraulic efficiency at the optimal operating point; It means that after the turbine is equipped with tailwater tube vortex suppression measures, i The maximum hydraulic efficiency loss allowed at an optimal operating point.

9. The optimization design method for suppressing vortex belts in multi-operating state draft tubes of a hydraulic turbine according to claim 1, characterized in that: In step 5, solving the optimization design problem based on the EGO algorithm includes the following steps: S501, using the optimal Latin hypercube sampling method to evenly arrange a certain number of initial sample points in the design space, and using the initial sample points and the optimization objective function values ​​corresponding to the initial sample points to construct an initial Kriging proxy model; S502, the second step is the iterative update of the optimal solution. The correction points are iteratively selected using the differential evolution algorithm and the improved expectation criterion based on the Kriging proxy model, and the optimization objective function value corresponding to the correction point is calculated to determine whether the optimization converges. If not, the correction point is added to the sample point database and the optimization cycle iteration is continued. If converged, the cycle iteration ends.

10. The optimization design method for suppressing vortex belts in multi-operating state draft tubes of a hydraulic turbine according to claim 9, characterized in that: In step S502, the expected criteria are improved EI The basic idea is to calculate the unknown points in the design space through the Gaussian probability model x The response value at the position is relative to the current optimal value The expected possibility of improvement is calculated, and the point with the largest expected value of improvement in the design space is selected as the correction point. The expression is: ； in, Indicates the current minimum value; Indicates unknown point x The true value at Indicates that the Kriging surrogate model is at an unknown point x The predicted value at s Indicates that the Kriging surrogate model is at an unknown point x The root mean square error of the prediction at ; and They are the cumulative function and probability density function of the standard normal distribution respectively.

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