Multi-objective coupling optimization method for internal flow field and stress field of pumped storage unit

Abstract

The invention relates to the technical field of pumped storage, in particular to a multi-objective coupling optimization method for an internal flow field and a stress field of a pumped storage unit, which comprises the following steps of: setting a computational domain coordinate system, constructing an objective function by taking a runner blade shape as a control function, and converting hydraulic optimization into a control problem; deriving variation and splitting a variable contribution item, and introducing a control vector integral; flow variation is eliminated by adapting an adjoint variable, and a control equation and boundary conditions are determined; constructing a multi-objective function based on torque and stress and simplifying the multi-objective function; using COMSOL to solve field quantity, combining MATLAB / C + + to calculate gradient iteration to update the blade, and promoting optimization to generate a three-dimensional model and an external characteristic curve; the flow field does not need to be solved repeatedly, the calculated amount is small, gradient solving is accurate, complex turbulence design is adapted, flow field and stress field optimization is considered, and the method is suitable for efficient runner design.

Description

Technical Field

[0001] This invention belongs to the field of pumped storage technology, specifically relating to a multi-objective coupled optimization method for the internal flow field and stress field of a pumped storage unit. Background Technology

[0002] With the rapid development of wind and solar power capacity in my country, pumped storage technology, as a relatively mature large-scale energy storage method, effectively compensates for the intermittency and instability of wind and solar power, and is crucial for the transformation of the power system and the national energy architecture. Against this backdrop, pumped storage units, as the core component of pumped storage power stations, are rapidly developing towards higher head, higher specific speed, and larger capacity. However, their performance is complexly affected by the internal flow field and fluid-structure interaction stress field, which has become a key challenge for improving the overall efficiency and safe operation of the power station. Simultaneously, the increasing grid connection of renewable energy sources such as wind and solar power leads to frequent start-ups and shutdowns of pumped storage units to balance the grid load, placing higher demands on the flexibility, reliability, and efficient operating range of the pump turbines. Currently, there is no comprehensive optimization design method to guide the improvement of the overall characteristics of pumped storage units by comprehensively considering factors such as the work done by the pumped turbine (torque), the double-sided force on the turbine blades, and the entire stress field within the turbine's rotation domain. Based on this, the present invention establishes a high-efficiency pumped storage unit applicable to pumped storage power stations and a multi-objective coupled optimization design method for the complex flow field and stress field inside the unit.

[0003] In view of this, the present invention is hereby proposed. Summary of the Invention

[0004] To address the aforementioned technical problems in the existing technology, this invention provides a multi-objective coupled optimization method for the internal flow field and stress field of a pumped storage unit. This method has advantages such as accurate gradient solution, adaptability to complex internal turbulent flow design, and low computational cost, and has broad application prospects in the field of pumped storage unit runner optimization design.

[0005] To achieve the above objectives, the technical solution of the present invention is as follows: A multi-objective coupled optimization method for the internal flow field and stress field of a pumped storage unit includes: S1. Based on the NS equation of viscous flow, and combined with control theory, the coordinate system of the computational domain is set, the objective function is constructed, and the boundary shape of the runner blade is used as the control function. The hydraulic optimization design problem is transformed into a control problem, and the constraints are defined as the flow field control equations. S2. Derive the variational objective function and the variational flow field vector flux, separate the contribution terms of the variational flow variables and the variational geometric variables, introduce the integral of the control vector over the runner computational domain, assume that the control vector is differentiable and derive the integral equation. S3. Reconstruct the objective function variation, eliminate the flow variable variation by selecting appropriate adjoint variables, derive the control equations and corresponding boundary conditions, and obtain the final form of the objective function variation that is only related to the geometric variation. S4. Based on the impeller torque and domain stress, an initial multi-objective function is constructed by combining flow field numerical simulation. After reasonable simplification, a practical optimized objective function is obtained through variational processing using advanced mathematics and complex function theory. S5. Solve the flow field and control variable field in COMSOL software and obtain the gradient vector. Use MATLAB or C++ to calculate the gradient, update the runner blade shape through numerical iteration, and generate the optimized three-dimensional runner blade model and unit external characteristic curve.

[0006] Furthermore, it also includes: S6. The optimization loop is advanced with twice the amount of flow equation calculation. The performance curve is generated using COMSOL post-processing function. It is adapted to hardware, software or hardware-software combination implementation forms and realizes the full process function through computer program instructions.

[0007] Furthermore, the expression for the objective function is:

[0008] in, To calculate the spatial surface integral unit, To compute the spatial integration unit, The flow variables include flow velocity and pressure in three directions. To calculate the spatial geometric boundary, , They are respectively and At the boundary Computational domain Functions on.

[0009] Furthermore, the variational decomposition of the objective function is as follows:

[0010]

[0011] in, For changes in flow variables On the boundary The disturbance For changes in flow variables within the volume domain The disturbance Variation for geometric boundary On the boundary The disturbance Variation for geometric boundary within the volume domain The disturbance The variational form of the geometric boundary is equal to Tiny perturbations, For the variation of the flow variable, it equals Tiny perturbations; Will Written with The relevant contribution, the variational decomposition of the flow field vector flux, is as follows:

[0012]

[0013] in, For inviscid vector flux, Let be the viscous vector flux. The Cartesian coordinate system is square. For changes in flow variables The contribution caused For changes caused by geometric variables The contribution caused.

[0014] Furthermore, the expression for the control vector is: After introducing this, integrating over the entire computational domain of the rotor region yields:

[0015] in, For inviscid vector flux, Let be the viscous vector flux.

[0016] Furthermore, in step S3, the adapted adjoint variable has differentiability. By making the coefficient term of the flow variable variation in the objective function variation zero, the variation of the objective function and the variation of the flow variable are decoupled, resulting in a variational form of the objective function containing only geometric variation.

[0017] Furthermore, in step S4, the flow field numerical simulation adopts a turbulence model, which is adapted to the complex turbulence separation and recirculation characteristics in the rotating domain of the impeller.

[0018] Further, in step S4, the expression for the initial multi-objective function is:

[0019] in, For the working face, The back side, For the lower ring, For the crown, It is an inland basin, encompassing core influencing factors such as pressure and shear stress.

[0020] Furthermore, in step S5, the numerical iterative update method is to update the shape of the impeller blade along the opposite direction of the gradient vector of the objective function. The update method includes multi-curve iteration or least squares fitting of the relevant variable function.

[0021] Furthermore, in step S5, the three-dimensional turbine blade model is generated using three-dimensional modeling software, including UG, SolidWorks, or Pro / E; the external characteristic curve of the unit is calculated based on the derived value sequence in the post-processing function of COMSOL software.

[0022] Compared with existing technologies, the multi-objective coupled optimization method for the internal flow field and stress field of a pumped storage unit provided by this invention includes: setting a computational domain coordinate system, constructing an objective function and using the runner blade shape as the control function to transform hydraulic optimization into a control problem; deriving the variational values ​​of the objective function and the flow field vector flux, splitting variable contribution terms and introducing control vector integrals; eliminating flow variable variation by adapting adjoint variables, establishing control equations and boundary conditions, and obtaining an objective function variation that is only related to geometric variation; constructing a multi-objective function based on runner torque and domain stress, and obtaining a practical model after simplification and variational processing; solving the flow field and control variable field using COMSOL, calculating gradients using MATLAB / C++ and iteratively updating the blade shape, and promoting cyclic optimization to generate a three-dimensional model and external characteristic curves; this invention does not require repeated solutions to the flow field, has low computational load, accurate gradient solution, is adaptable to complex turbulent design, takes into account both flow field and stress field optimization, and is suitable for efficient runner design. Attached Figure Description

[0023] Figure 1 The flowchart illustrates the multi-objective coupling optimization method for the internal flow field and stress field of a pumped storage unit provided in this embodiment of the invention. Detailed Implementation

[0024] The technical solution of the present invention will be clearly described below with reference to the accompanying drawings. Obviously, the described embodiments are not all embodiments of the present invention. All other embodiments obtained by those skilled in the art without creative effort are within the protection scope of the present invention.

[0025] It should be noted that, unless otherwise specifically stated, the relative arrangement and numerical expressions of the components and steps described in these embodiments should not be construed as limiting the scope of the invention.

[0026] The following description of exemplary embodiments is merely illustrative and is not intended to limit the invention or its application or use in any way. Techniques, methods, and apparatus known to those skilled in the art may not be discussed in detail herein, but where applicable, such techniques, methods, and apparatus should be considered part of this specification.

[0027] Example See Figure 1 , Figure 1 This is a flowchart of a multi-objective coupled optimization method for the internal flow field and stress field of a pumped storage unit proposed in this invention. Specific steps may include: S1. Basic Settings and Core Equation Construction: Based on the viscous flow Navier-Stokes equations and combined with control theory, the computational domain coordinate system is set up (each boundary surface corresponds to a certain coordinate). (Constant values, geometric changes corresponding to coordinate transformation matrix changes), construct the objective function and use the runner blade boundary shape as the control function, transforming the hydraulic optimization design problem into a control problem, and clarifying the constraints as the flow field control equations; specifically including: S11. The viscous flow control equation (NS equation) is selected as the core equation for hydraulic performance analysis. At the same time, the principle of general control equation and objective function in control theory is integrated, and the core of the study is clearly the influence of the runner and blade shape changes on hydraulic performance.

[0028] S12. Set the computational domain coordinate system to a constant value corresponding to a certain coordinate ξi for each boundary surface. At this time, the change in the geometric shape of the runner blade can be directly equivalent to the change in the coordinate transformation matrix, which greatly simplifies the description of the subsequent geometric and flow relationship.

[0029] S13. Construct the objective function:

[0030] in, To calculate the spatial surface integral unit, To compute the spatial integration unit, The flow variables include flow velocity and pressure in three directions. To calculate the spatial geometric boundary, , They are respectively and At the boundary Computational domain Functions on; The design problem is transformed into a control problem, and the boundary shape of the impeller blade is represented as a control function. The selection of the control function should ensure that the objective function... Take the minimum value. The constraints refer to the flow field control equations. Changes in the hydraulic shape of the runner, airfoil, etc., will lead to variational changes in the flow variables. Variation with geometric boundary .

[0031] S2. Variational Derivation and Constraint Handling: Derive the variational objective function and the variational flow field vector flux, and decompose the variational flow variables. In conjunction with the variational contribution of geometric variables, the control vector is integrated over the runner computational domain, assuming the control vector is differentiable and deriving the integral equation. This step establishes the correlation between hydraulic shape changes and flow field variables through variational decomposition and integration, laying the foundation for subsequent elimination of redundant variables. Specifically, this includes: S21. Variational derivation of the objective function, based on the variation caused by changes in hydraulic shape, and the variation of the objective function. The expression is:

[0032] Will , The contributions are broken down into flow variables and geometric variables:

[0033]

[0034] in, For changes in flow variables On the boundary The disturbance For changes in flow variables within the volume domain The disturbance Variation for geometric boundary On the boundary The disturbance Variation for geometric boundary within the volume domain The disturbance The variational form of the geometric boundary is equal to Tiny perturbations, For the variation of the flow variable, it equals Tiny perturbations; S22. Constraint equations and vector flux variation: The constraint equations for the change of hydraulic shape under steady conditions are as follows:

[0035] in, For inviscid vector flux, Let be the viscous vector flux.

[0036] Will Written with The relevant contribution, the variational decomposition of the flow field vector flux, is as follows:

[0037]

[0038] in, For inviscid vector flux, Let be the viscous vector flux. The Cartesian coordinate system is square. For changes in flow variables The contribution caused For changes caused by geometric variables The contribution caused.

[0039] S23. Introduction and Integration of Control Vectors: Introduction of Control Vectors Integrate over the entire computational domain of the pumped storage unit's runner region:

[0040] assumed Differentiable, we can derive:

[0041] S3. Establishment of governing equations and boundary conditions: Reconstructing the objective function variation, eliminating the flow variable variation by selecting suitable adjoint variables, deriving the governing equations and corresponding boundary conditions, and obtaining the final form of the objective function variation that is only related to the geometric variation; specifically including: S31, Variation of the Objective Function The specific formula for reconstruction is as follows:

[0042] Accompany variables Differentiable, then The value of can make No longer appearing in The objective function expression is only related to the geometric variation. Related to; in this formula, the variation of the flow variable in the spatial integral term. The coefficients are combined to obtain the governing equations.

[0043] S32. Derivation of governing equations and boundary conditions With the coefficient term set to zero, the governing equation is obtained:

[0044] Variation of flow variables in the surface integral The coefficient terms yield the boundary conditions:

[0045] S33. The final variational form is determined by adapting the accompanying variables. eliminate , get only with Related variables:

[0046] The above equation shows the gradient solution and the variational solution of the flow field variables. Since it is irrelevant, the variational objective function can be obtained without repeatedly solving the flow field. The gradient of the objective function with respect to the design variables. After obtaining the gradient of the objective function with respect to the design variables, the gradient is combined with the optimal algorithm to obtain the geometric boundary changes, thus obtaining the geometric boundary of the pumped storage turbine runner blades with better hydraulic performance.

[0047] S4. Construction and Optimization of Multi-Objective Functions: Using the impeller torque and intra-domain stress as references, an initial multi-objective function is constructed based on flow field numerical simulation. After reasonable simplification, a practical optimization objective function is obtained through variational processing using advanced mathematics and complex variable function theory. Specifically, this includes: S41. Initial function construction: Taking the impeller torque and intra-domain stress as references, select a suitable turbulence model, define the x-axis as the rotation axis, and set the blade placement angle. With equal parameters, the initial objective function is:

[0048] in, For the working face, The back side, For the lower ring, For the crown, It is an inland basin, encompassing core influencing factors such as pressure and shear stress.

[0049] In formulating the above objective function, the following important references were taken into account: (1) The shear stress on the working surface and back wall of the impeller blade is the minimum; (2) The small runner torque improves the efficiency of the pumped storage unit and further enhances the static benefits of the entire power station; (3) The torque can be used as the objective function to embed the wall shear stress into the relevant expression in a non-explicit way, so as to comprehensively reflect the relevant stress. In addition, the pressure is also taken into account. The pressure surface, back surface, upper crown and lower ring of the impeller blade are all taken into account. (4) Under the condition that all other conditions are fixed, the head of the pumped storage unit is only related to the outer diameter of the runner. Rotor outlet width and the angle of the rotor blades Therefore, the above considerations can also reflect the placement angle at each point of the blade rib line; (5) Incorporating the shear stress at each spatial point in the flow domain within the runner into the objective function is crucial for minimizing the stress in the entire runner's rotation domain.

[0050] S42. Simplifying the objective function: In the initial objective function formula, the second term on the right, H and X, represent the torques generated by the viscous shear stress on the lower ring and upper crown of the impeller, respectively. These are very small compared to the torques generated on the working surface G and the back surface B, and can be ignored. This is because during optimization, if the torques generated on the working surface and back surface of the impeller blades are optimized to below or at their minimum value, then the torques generated by H and X will be even smaller and more acceptable. Similarly, on the back surface of the working surface, the torque generated by the wall shear stress is very small compared to the torque generated by the pressure term P, and can also be ignored. This is because if the torque generated by the pressure is optimized to its minimum, then the torque generated by the shear stress will be even smaller.

[0051] The relevant control variations are mapped to the integral calculations of each part of the pumped storage unit; finally, considering the order of magnitude of the objective variation on the upper crown and lower ring, the final optimization objective function is written as:

[0052] S43. Applying advanced mathematics and related theories of complex functions to perform variational analysis on the objective function:

[0053]

[0054]

[0055]

[0056]

[0057]

[0058] S5. Program Solution and Blade Optimization: Solve the flow field and control variable field in COMSOL software and obtain the gradient vector. Calculate the gradient using MATLAB or C++, update the runner blade shape through numerical iteration, and generate the optimized 3D runner blade model and unit external characteristic curves; specifically including: S51. Solve the flow field and control variable field in COMSOL Multiphysics, and obtain the gradient vector of the objective function based on the flow field results.

[0059] S52. Use multi-strip curve iteration or least squares fitting to update the blade shape based on gradient vector; generate spline curves in 3D modeling software to construct a 3D optimized impeller.

[0060] S53. Prioritize using MATLAB and C++ to calculate gradient vectors, and iterate and update them in the opposite direction of the gradient to reduce optimization difficulties.

[0061] S6. Cyclic Optimization and Output: The optimization cycle is advanced with twice the computational load of the flow equations. Performance curves are generated using COMSOL post-processing functions. It is adapted to hardware, software, or a combination of hardware and software implementations. The entire process is realized through computer program instructions.

[0062] Because the solution methods for the control equations and flow control equations are consistent, there is no need to consider the correlation of design variables. The computational cost of each optimization cycle is approximately twice that of the flow equations, significantly improving iteration efficiency. Data is processed using derived value sequences obtained through COMSOL post-processing to generate key performance data such as unit external characteristic curves. It can be implemented entirely in hardware, entirely in software, or a combination of both; it can also be stored as a computer program product on media such as disks and CD-ROMs, and deployed on various computer devices via program instructions to achieve optimization functions.

[0063] In summary, the present invention has the following advantages: 1. No need to repeatedly solve the flow field; the computational cost of the optimization loop is only about twice that of the flow equation, and it is independent of the number of design variables, which greatly reduces the iteration cost. 2. By coupling the Navier-Stokes equations with control theory, the variational form of the objective function, which is only related to the geometric variation, is derived. The gradient solution is accurate, ensuring the optimization effect. 3. It can adapt to the complex turbulent design requirements inside the runner, and is compatible with multi-objective coupling optimization of flow field and stress field, fully covering core performance indicators such as torque and shear stress.

[0064] The above specific embodiments are only used to illustrate the technical solutions of the present invention and are not intended to limit it. Although the present invention has been described in detail with reference to examples, those skilled in the art should understand that modifications or equivalent substitutions can be made to the technical solutions of the present invention without departing from the scope of the technical solutions of the present invention, and all such modifications or substitutions should be covered within the scope of the claims of the present invention.

Claims

1. A multi-objective coupled optimization method for the internal flow field and stress field of a pumped storage unit, characterized in that, include: S1. Based on the NS equation of viscous flow, and combined with control theory, the coordinate system of the computational domain is set, the objective function is constructed, and the boundary shape of the runner blade is used as the control function. The hydraulic optimization design problem is transformed into a control problem, and the constraints are defined as the flow field control equations. S2. Derive the variational objective function and the variational flow field vector flux, separate the contribution terms of the variational flow variables and the variational geometric variables, introduce the integral of the control vector over the runner computational domain, assume that the control vector is differentiable and derive the integral equation. S3. Reconstruct the objective function variation, eliminate the flow variable variation by selecting appropriate adjoint variables, derive the control equations and corresponding boundary conditions, and obtain the final form of the objective function variation that is only related to the geometric variation. S4. Based on the impeller torque and domain stress, an initial multi-objective function is constructed by combining flow field numerical simulation. After reasonable simplification, a practical optimized objective function is obtained through variational processing using advanced mathematics and complex function theory. S5. Solve the flow field and control variable field in COMSOL software and obtain the gradient vector. Use MATLAB or C++ to calculate the gradient, update the runner blade shape through numerical iteration, and generate the optimized three-dimensional runner blade model and unit external characteristic curve.

2. The multi-objective coupled optimization method for the internal flow field and stress field of a pumped storage unit according to claim 1, characterized in that, Also includes: S6. The optimization loop is advanced with twice the amount of flow equation calculation. The performance curve is generated using COMSOL post-processing function. It is adapted to hardware, software or hardware-software combination implementation forms and realizes the full process function through computer program instructions.

3. The multi-objective coupled optimization method for the internal flow field and stress field of a pumped storage unit according to claim 1, characterized in that, The expression for the objective function is: in, To calculate the spatial surface integral unit, To compute the spatial integration unit, The flow variables include flow velocity and pressure in three directions. To calculate the spatial geometric boundary, , They are respectively and At the boundary Computational domain Functions on.

4. The multi-objective coupled optimization method for the internal flow field and stress field of a pumped storage unit according to claim 1, characterized in that, The variational decomposition of the objective function is as follows: in, For changes in flow variables On the boundary The disturbance For changes in flow variables within the volume domain The disturbance Variation for geometric boundary On the boundary The disturbance Variation for geometric boundary within the volume domain The disturbance The variational form of the geometric boundary is equal to Tiny perturbations, For the variation of the flow variable, it equals Tiny perturbations; Will Written with The relevant contribution, the variational decomposition of the flow field vector flux, is as follows: in, For inviscid vector flux, Let be the viscous vector flux. The Cartesian coordinate system is square. For changes in flow variables The contribution caused For changes caused by geometric variables The contribution caused.

5. The multi-objective coupled optimization method for the internal flow field and stress field of a pumped storage unit according to claim 1, characterized in that, The expression for the control vector is: After introducing this, integrating over the entire computational domain of the rotor region yields: in, For inviscid vector flux, Let be the viscous vector flux.

6. The multi-objective coupled optimization method for the internal flow field and stress field of a pumped storage unit according to claim 1, characterized in that, In step S3, the adapted adjoint variable has differentiability. By making the coefficient term of the flow variable variation in the objective function variation zero, the variation of the objective function and the variation of the flow variable are decoupled, resulting in a variational form of the objective function containing only geometric variation.

7. The multi-objective coupled optimization method for the internal flow field and stress field of a pumped storage unit according to claim 1, characterized in that, In step S4, the flow field numerical simulation adopts a turbulence model, which is adapted to the complex turbulence separation and recirculation characteristics in the rotating domain of the impeller.

8. The multi-objective coupled optimization method for the internal flow field and stress field of a pumped storage unit according to claim 1, characterized in that, In step S4, the expression for the initial multi-objective function is: in, For the working face, The back side, For the lower ring, For the crown, It is an inland basin, encompassing core influencing factors such as pressure and shear stress.

9. The multi-objective coupled optimization method for the internal flow field and stress field of a pumped storage unit according to claim 1, characterized in that, In step S5, the numerical iterative update method is to update the shape of the impeller blade along the opposite direction of the gradient vector of the objective function. The update method includes multi-curve iteration or least squares fitting of the relevant variable function.

10. The multi-objective coupled optimization method for the internal flow field and stress field of a pumped storage unit according to claim 1, characterized in that, In step S5, the three-dimensional turbine blade model is generated using three-dimensional modeling software, including UG, SolidWorks, or Pro / E; the external characteristic curve of the unit is calculated based on the derived value sequence in the post-processing function of COMSOL software.

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