Pump turbine inverse problem optimization method based on multi-physical-quantity optimal collaboration

Abstract

The invention relates to the field of pump turbine optimization design, in particular to a pump turbine inverse problem optimization method based on multi-physical-quantity optimal collaboration. The pump turbine inverse problem optimization method comprises the following steps: selecting collaborative parameters, and determining a physical flow constraint basis of a pump turbine; collaborative parameters are constructed, and equation additional items during optimal collaboration are obtained; the equation additional item and the physical flow constraint basis are combined to form an optimal cooperation equation; and performing numerical solution on the optimal coordination equation to obtain the pump turbine flow field meeting optimal coordination of the coordination parameters. According to the pump turbine reverse problem optimization method based on multi-physical-quantity optimal collaboration, the optimization result can be directly obtained, calculation resource consumption in the repeated iteration process of traditional forward problem optimization, blindness of design depending on artificial experience and the like are avoided, the optimization cost is reduced, and the optimization efficiency is improved.

Description

Technical Field

[0001] The invention relates to the field of water pump turbine optimization design, and in particular to a water pump turbine inverse problem optimization method based on optimal coordination of multiple physical quantities. Background Art

[0002] As the core equipment in pumped-storage power stations, the hydraulic performance of pump-turbines is directly related to the safe, stable and efficient operation of the entire power station. In recent years, with the vigorous development of renewable energy and the advancement of smart grid construction, the performance requirements for pump-turbines have been increasing. In particular, the existing design methods still face many challenges in eliminating or improving this unstable characteristic in order to reduce losses and ensure stable operation of the main flow structures (volute, impeller and tailwater pipe) under strong velocity pulsation and pressure pulsation.

[0003] The existing pump-turbine flow field optimization mainly adopts the direct problem design approach, that is, engineers redesign the local flow structure based on experience, and then carry out computational fluid dynamics numerical simulation, and judge the optimization effect based on the simulation results. If the effect is not good, it needs to be redesigned until it reaches the expected result. However, the above direct problem optimization has two main disadvantages. First, the optimization design relies on the existing experience of engineers. This kind of trial-and-error optimization process requires a considerable amount of computing resources in the numerical simulation of complex variable working conditions of pump-turbines. The calculation amount is large and time-consuming, and there is a great deal of blindness. Secondly, the existing optimization is mostly focused on the optimization of a single physical quantity (such as local velocity pulsation, pressure pulsation, cavitation pressure, etc.), ignoring the mutual influence and synergy between multiple physical quantities. It is difficult to maintain or improve other performances while improving a certain performance, resulting in poor overall performance optimization.

[0004] Therefore, this field needs a new technical solution to solve the above problems. Summary of the invention

[0005] In order to improve or solve the technical problems of large amount of calculation and poor overall performance optimization effect in the prior art, the present invention provides a pump-turbine inverse problem optimization method based on optimal coordination of multiple physical quantities, which can achieve global coordinated optimization of multiple physical quantities at a relatively low computational cost. The pump-turbine inverse problem optimization method comprises: selecting coordination parameters and determining the physical flow constraint basis of the pump-turbine; constructing additional terms of the equation when the coordination parameters achieve optimal coordination; combining the additional terms of the equation with the physical flow constraint basis to form an optimal coordination equation; numerically solving the optimal coordination equation to obtain a pump-turbine flow field that satisfies the optimal coordination of the coordination parameters.

[0006] The pump-turbine inverse problem optimization method of the present invention is based on the optimal coordination of multiple physical quantities. Through the inverse problem optimization idea of ​​"cooperative parameter selection-construction and solution of optimal cooperative equation-obtaining optimal cooperative flow field", the optimization result can be directly obtained, avoiding the consumption of computing resources in the repeated iterative process of traditional forward problem optimization and the blindness of relying on manual experience for design, thereby reducing the optimization cost and improving the optimization efficiency. At the same time, based on the optimization idea of ​​optimal coordination of multiple physical quantities, the coordinated optimization of multiple physical quantities in a global range can be realized, avoiding the local optimization problem caused by the traditional optimization of a single physical quantity, thereby improving the optimization effect.

[0007] Furthermore, the steps of selecting synergistic parameters and determining the physical flow constraint basis of the pump-turbine include: clarifying the key physical quantities to be optimized and selecting at least two of the key physical quantities as synergistic parameters; and selecting constraint conditions associated with the synergistic parameters as the physical flow constraint basis of the pump-turbine.

[0008] Furthermore, the synergistic parameters include flow field velocity V and pressure gradient The physical flow constraint is based on the incompressible flow Navier-Stokes equations of fluid mechanics:

[0009]

[0010] Where ρ is the fluid density, V is the flow velocity, is the velocity gradient, is the pressure gradient, μ is the viscosity coefficient, X is the external force vector, ρX is the external force term, and Δ is the Laplace operator.

[0011] Furthermore, the step of constructing the additional term of the equation when the synergy parameter obtains the optimal synergy includes: taking the synergy parameter as the target variable and the physical flow constraint basis as the constraint condition, and using the Lagrange multiplier method to construct the target functional J:

[0012]

[0013] Where F is the Lagrangian function, including the target variable a, constraints b1, b2, ..., b n and its derivatives b1', b2', ..., b n ', and is second-order continuously differentiable; x, y, z are the three-dimensional flow field coordinates inside the pump-turbine;

[0014] Construct the auxiliary functional J* according to the target functional J and the complete constraint condition φ:

[0015] φ i (a,b i )=0

[0016]

[0017] Among them, the undetermined function λ i is the Lagrange multiplier; H i It is composed of the Lagrangian function F and the Lagrangian multiplier λ i The expression formed by combining and the complete constraint φ;

[0018] By varying the auxiliary functional J*, we obtain the Euler equations:

[0019]

[0020]

[0021]

[0022] Solve the Euler equations based on the boundary conditions of the target functional J to obtain the Lagrange multiplier λ i The expression of the Lagrange multiplier λ i The additional terms in the equation when forming the optimal synergy together with the synergy parameters.

[0023] Furthermore, when the synergistic parameters are flow field velocity V and pressure gradient When the physical flow constraint basis is the Navier-Stokes equations for incompressible flow in fluid mechanics,

[0024] The target functional J:

[0025]

[0026] The complete constraint φ is:

[0027]

[0028] The auxiliary functional J*:

[0029]

[0030] Furthermore, the boundary conditions include no-slip wall conditions and conservation of inlet and outlet flow rates;

[0031] The no-slip wall condition:

[0032] y0=0, u0=0; y1=δ1, u1=U1

[0033] Among them, y0=0 represents the position of the wall, that is, the distance from the wall is zero; u0=0 means that at the wall, the velocity of the flow field in the y direction is zero; y1=δ1 represents the position at a certain distance from the wall; u1=U1 means that at y1=δ1, the velocity of the flow field is U1;

[0034] The import and export flow conservation: G in =G out .

[0035] Furthermore, the optimal synergy equation is:

[0036]

[0037] In summary, compared with the prior art, the present invention has the following beneficial effects:

[0038] (1) Through the inverse problem optimization idea of ​​"cooperative parameter selection - construction and solution of optimal cooperative equation - acquisition of optimal cooperative flow field", the optimization result can be directly obtained, avoiding the consumption of computing resources in the iterative process of traditional forward problem optimization and the blindness of relying on manual experience for design, thereby reducing the optimization cost and improving the optimization efficiency; at the same time, based on the optimization idea of ​​optimal cooperation of multiple physical quantities, the coordinated optimization of multiple physical quantities in a global scope can be realized, avoiding the local optimization problem caused by the traditional optimization of a single physical quantity, thereby improving the optimization effect. BRIEF DESCRIPTION OF THE DRAWINGS

[0039] The preferred embodiments of the present invention are described below in conjunction with the accompanying drawings, in which:

[0040] Figure 1 It is a schematic diagram comparing the optimization ideas of the inverse problem and the optimization ideas of the direct problem in the inverse problem optimization method of the pump-turbine based on the optimal coordination of multiple physical quantities of the present invention;

[0041] Figure 2 It is a flow chart of the pump-turbine inverse problem optimization method based on optimal coordination of multiple physical quantities of the present invention;

[0042] Figure 3 It is a schematic diagram of the construction process of the optimal coordination equation in the pump-turbine inverse problem optimization method based on the optimal coordination of multiple physical quantities of the present invention;

[0043] Figure 4 It is a schematic diagram comparing the prototype impeller flow field and the optimal coordinated flow field in the pump-turbine inverse problem optimization method based on optimal coordination of multiple physical quantities of the present invention;

[0044] Figure 5 It is a schematic diagram comparing the loss reduction effects of the pump-turbine inverse problem optimization method based on optimal coordination of multiple physical quantities of the present invention. DETAILED DESCRIPTION

[0045] The preferred embodiments of the present invention are described below with reference to the accompanying drawings. It should be understood by those skilled in the art that these embodiments are only used to explain the technical principles of the present invention and are not intended to limit the protection scope of the present invention.

[0046] It should be noted that in the description of the present invention, the terms "upper", "lower", "left", "right", "inner", "outer" and the like indicating directions or positional relationships are based on the directions or positional relationships shown in the drawings, which are only for the convenience of description, and do not indicate or imply that the device or element must have a specific orientation, be constructed and operated in a specific orientation, and therefore cannot be understood as limiting the present invention. In addition, the terms "first" and "second" are used for descriptive purposes only, and cannot be understood as indicating or implying relative importance.

[0047] In addition, it should be noted that in the description of the present invention, unless otherwise clearly specified and limited, the terms "installation", "setting", and "connection" should be understood in a broad sense, for example, it can be a fixed connection, a detachable connection, or an integral connection; it can be a direct connection, an indirect connection through an intermediate medium, or the internal connection of two components. For those skilled in the art, the specific meanings of the above terms in the present invention can be understood according to specific circumstances.

[0048] In order to improve or solve the technical problems of large amount of calculation and poor overall performance optimization effect in the prior art, the present invention provides a pump-turbine inverse problem optimization method based on optimal coordination of multiple physical quantities, which can achieve global coordinated optimization of multiple physical quantities at a relatively low computational cost. The pump-turbine inverse problem optimization method includes: selecting coordination parameters and determining the physical flow constraint basis of the pump-turbine; constructing equation additional terms when the coordination parameters achieve optimal coordination; combining the equation additional terms with the physical flow constraint basis to form an optimal coordination equation; numerically solving the optimal coordination equation to obtain a pump-turbine flow field that satisfies the optimal coordination of the coordination parameters.

[0049] Figure 1 It is a schematic diagram comparing the optimization ideas of the inverse problem and the optimization ideas of the direct problem in the inverse problem optimization method of the pump-turbine based on the optimal coordination of multiple physical quantities of the present invention. Figure 2 Flow chart of the pump-turbine inverse problem optimization method based on the optimal coordination of multiple physical quantities of the present invention. Figure 1 and Figure 2 As shown, the pump-turbine inverse problem optimization method based on optimal coordination of multiple physical quantities of the present invention includes:

[0050] Step S1, selecting synergistic parameters and determining the physical flow constraint basis of the pump-turbine; wherein the synergistic parameters refer to the key physical quantities to be optimized, including flow field velocity, pressure gradient, temperature, temperature gradient, velocity gradient, vorticity, etc.; the physical flow constraint basis refers to the constraint conditions of the internal flow of the pump-turbine, including the Navier-Stokes equations of incompressible flow in fluid mechanics, the specified inlet flow angle, head, etc.;

[0051] Step S2, constructing additional terms of the equation when the coordination parameters are optimally coordinated, that is, solving the optimization problem of the coordination parameters under the constraints;

[0052] Step S3, combining the equation additional terms with the physical flow constraint basis to form an optimal synergistic equation;

[0053] Step S4, numerically solving the optimal coordination equation to obtain the pump-turbine flow field that satisfies the optimal coordination of coordination parameters; wherein the optimal coordination equation can be transplanted into a computational fluid dynamics solver, and numerically solved by the fluid dynamics solver to directly obtain the pump-turbine flow field that satisfies the optimal coordination.

[0054] Continue to see Figure 1 and Figure 2 In one or more embodiments, step S1 of selecting coordination parameters and determining the physical flow constraint basis of the pump turbine includes:

[0055] Step S11, clarify the key physical quantities to be optimized, and select at least two key physical quantities as collaborative parameters; first, select the structure that needs to be improved in the pump-turbine, which can be an impeller, a volute, a tailwater pipe, etc. The following description takes the impeller as the improved structure. Secondly, the energy loss caused by pressure pulsation, local cavitation and local flow separation are all unfavorable factors that affect the efficient and stable operation of the pump-turbine. According to literature research (Shao et al., Physics of Fluids, 2023, 35:115113; Shao et al., Physics of Fluids, 2023, 35:105101), the flow field velocity V and the pressure gradient These are the two key physical quantities for regulating the stable operation of the pump turbine. It is understood that structures such as volutes and draft tubes can also be improved by this method, and the synergistic parameters can be set to two, three or other suitable numbers; exemplary, the synergistic parameters can include flow field velocity, temperature and vorticity.

[0056] The following is based on the flow field velocity V and pressure gradient As an example of coordinated parameters: set the flow field velocity V and pressure gradient There is some optimal synergy between them to meet the minimum loss and stable operation of the pump turbine; the synergy relationship S between the two can be expressed as:

[0057]

[0058] Among them, x, y, and z are the three-dimensional flow field coordinates inside the pump-turbine.

[0059] Step S12: select the constraint conditions associated with the coordination parameters as the physical flow constraint basis of the pump turbine; wherein the simplest constraint conditions associated with the coordination parameters can be selected as the constraint basis. For example, the simplest constraint conditions for the internal flow of the pump turbine, that is, satisfying the incompressible flow Navier-Stokes equations of fluid mechanics, are selected as the physical flow constraint basis:

[0060]

[0061] Where ρ is the fluid density, V is the flow velocity, is the velocity gradient, is the pressure gradient, μ is the viscosity coefficient, X is the external force vector, ρX is the external force term, and Δ is the Laplace operator.

[0062] Figure 3 Schematic diagram of the construction process of the optimal coordination equation in the pump-turbine inverse problem optimization method based on the optimal coordination of multiple physical quantities of the present invention. Figure 2 and Figure 3 As shown, in one or more embodiments, the step of constructing the additional terms of the equation when the synergy parameters are obtained to obtain the optimal synergy in step S2 includes:

[0063] Step S21, taking the synergy parameter as the target variable and the physical flow constraint basis as the constraint condition, the Lagrange multiplier method is used to construct the target functional J:

[0064]

[0065] Where F is the Lagrangian function, including the target variable a, constraints b1, b2, ..., b n and its derivatives b1', b2', ..., b n ', and is second-order continuously differentiable; x, y, z are the three-dimensional flow field coordinates inside the pump-turbine.

[0066] The flow field velocity V, pressure gradient and Navier-Stokes equations into the target functional J:

[0067]

[0068] By solving the optimization problem of the target variable under the constraints through the Lagrange multiplier method and incorporating the constraints into the optimization process, the optimization problem can be transformed into a mathematically tractable form, so that the optimal solution under the constraints can be obtained more conveniently.

[0069] Step S22: construct an auxiliary functional J* according to the target functional J and the complete constraint condition φ:

[0070] φ i (a,bi )=0

[0071]

[0072] Among them, the undetermined function λ i is the Lagrange multiplier; H i It is composed of the Lagrangian function F and the Lagrangian multiplier λ i The expression composed of and the complete constraint condition φ.

[0073] The flow field velocity V, pressure gradient and Navier-Stokes equations with the full constraint φ:

[0074]

[0075] Auxiliary functional J*:

[0076]

[0077] Among them, the expression of the integrand H is:

[0078]

[0079] By constructing the auxiliary functional J*, the target functional J and the complete constraint φ can be more closely combined. In the subsequent variational operation, the influence of the complete constraint can be considered to obtain more accurate results.

[0080] Step S23, vary the auxiliary functional J* to obtain the Euler equations:

[0081]

[0082]

[0083]

[0084] Among them, H is composed of the Lagrangian function F, the Lagrangian multiplier λ i The expression is composed of the complete constraint condition φ; x, y, z are the three-dimensional flow field coordinates inside the pump-turbine.

[0085] Specifically, the integrand H is expanded into partial differential equations in the three directions of x, V, and z:

[0086]

[0087]

[0088]

[0089] Among them, u, v, and w are the components of the flow field velocity V in the x, y, and z directions.

[0090] By performing variational operations on the above partial differential equations, we obtain the Euler equations:

[0091]

[0092]

[0093]

[0094] Among them, u, v, and w are the components of the flow field velocity V in the x, y, and z directions.

[0095] Step S24, based on the boundary conditions of the target functional J, solve the Euler equations to obtain the expression of the Lagrange multiplier λ, and the Lagrange multiplier λ and the coordination parameter constitute the additional terms of the equations when the optimal coordination is achieved. Specifically, the boundary conditions include no-slip wall conditions and conservation of inlet and outlet flow. No-slip wall conditions:

[0096] y0=0, u0=0; y1=δ1, u1=U1

[0097] Among them, y0=0 represents the position of the wall, that is, the distance from the wall is zero; u0=0 means that at the wall, the velocity of the flow field in the y direction is zero; y1=δ1 represents the position at a certain distance from the wall; u1=U1 means that at y1=δ1, the velocity of the flow field is U1.

[0098] Conservation of import and export flow: G in =G out , under incompressible flow conditions, it is simplified to:

[0099] V1A1=V2A2

[0100] Among them, V is the flow field velocity and A is the cross-sectional area.

[0101] Based on the above boundary conditions, we solve the Euler equations and obtain the Lagrange multiplier λ:

[0102]

[0103] Specifically, the expression of the above boundary conditions is brought into the Euler equations, and the Euler equations with the boundary conditions are solved using numerical methods or analytical methods. The specific solution method is not the invention of this patent, and can be the finite difference method, spectral method, etc. in the prior art, which will not be limited or specifically expanded here.

[0104] Continue to see Figure 2 and Figure 3 In one or more embodiments, the optimal synergy equation in step S3 is:

[0105]

[0106] in, As the basis of physical flow constraints, Add the term to the equation.

[0107] Figure 4 It is a schematic diagram comparing the prototype impeller flow field and the optimal coordinated flow field in the pump-turbine inverse problem optimization method based on the optimal coordination of multiple physical quantities of the present invention. Figure 5 Schematic diagram showing the comparison of the loss reduction effect of the pump-turbine inverse problem optimization method based on the optimal coordination of multiple physical quantities in the present invention. Figure 4 and Figure 5 As shown, the optimal cooperative equation is transplanted into the computational fluid dynamics solver and solved to directly obtain the solution that satisfies the flow field velocity V and pressure gradient. Compared with the impeller flow field of the prototype pump-turbine, the optimal coordinated pump-turbine flow field has a uniform velocity field distribution, an increased pressure load on the suction surface, and eliminates the local backflow caused by low-pressure pulsation in the prototype flow field.

[0108] So far, the technical scheme of the present invention has been described in conjunction with the preferred embodiments shown in the accompanying drawings. However, it is easy for those skilled in the art to understand that the protection scope of the present invention is obviously not limited to these specific embodiments. Without departing from the principle of the present invention, those skilled in the art can make equivalent changes or substitutions to the relevant technical features, and the technical schemes after these changes or substitutions will fall within the protection scope of the present invention.

Claims

1. A pump-turbine inverse problem optimization method based on optimal coordination of multiple physical quantities, characterized in that: include: Select synergy parameters and determine the physical flow constraint basis for pump turbines; Constructing additional terms of the equation when the synergy parameters achieve optimal synergy; Combining the equation addition term with the physical flow constraint basis to form an optimal synergistic equation; The optimal coordination equation is numerically solved to obtain a pump-turbine flow field that satisfies the optimal coordination of the coordination parameters.

2. The pump-turbine inverse problem optimization method based on optimal coordination of multiple physical quantities according to claim 1 is characterized in that: The steps of selecting the coordination parameters and determining the physical flow constraint basis of the pump turbine include: Identify key physical quantities to be optimized, and select at least two of the key physical quantities as synergistic parameters; Constraints associated with the synergistic parameters are selected as a basis for physical flow constraints of the pump-turbine.

3. The pump-turbine inverse problem optimization method based on optimal coordination of multiple physical quantities according to claim 2 is characterized in that: The synergistic parameters include flow field velocity V and pressure gradient The physical flow constraint is based on the incompressible flow Navier-Stokes equations of fluid mechanics: Where ρ is the fluid density, V is the flow velocity, is the velocity gradient, is the pressure gradient, μ is the viscosity coefficient, X is the external force vector, ρX is the external force term, and Δ is the Laplace operator.

4. The pump-turbine inverse problem optimization method based on optimal coordination of multiple physical quantities according to claim 2 is characterized in that: The step of constructing the equation additional term when the synergy parameter obtains the optimal synergy includes: taking the synergy parameter as the target variable and the physical flow constraint basis as the constraint condition, and using the Lagrange multiplier method to construct the target functional J: Where F is the Lagrangian function, including the target variable a, constraints b1, b2, ..., b n and its derivatives b1', b2', ..., b n ', and is second-order continuously differentiable; x, y, z are the three-dimensional flow field coordinates inside the pump-turbine; Construct the auxiliary functional J* according to the target functional J and the complete constraint condition φ: f i (a,b) i )=0 Among them, the undetermined function λ i is the Lagrange multiplier; H i It is composed of the Lagrangian function F and the Lagrangian multiplier λ i The expression formed by combining and the complete constraint φ; By varying the auxiliary functional J*, we obtain the Euler equations: Solve the Euler equations based on the boundary conditions of the target functional J to obtain the Lagrange multiplier λ i The expression of the Lagrange multiplier λ i The additional terms in the equation when forming the optimal synergy together with the synergy parameters.

5. The pump-turbine inverse problem optimization method based on optimal coordination of multiple physical quantities according to claim 4 is characterized in that: When the synergistic parameters are the flow field velocity V and the pressure gradient When the physical flow constraint basis is the Navier-Stokes equations for incompressible flow in fluid mechanics, The target functional J: The complete constraint φ is: The auxiliary functional J*:

6. The pump-turbine inverse problem optimization method based on optimal coordination of multiple physical quantities according to claim 5 is characterized in that: The boundary conditions include no-slip wall conditions and conservation of inlet and outlet flow rates; The no-slip wall condition: y0=0, u0=0; y1=δ1, u1=U1 Among them, y0=0 represents the position of the wall, that is, the distance from the wall is zero; u0=0 means that at the wall, the velocity of the flow field in the y direction is zero; y1=δ1 represents the position at a certain distance from the wall; u1=U1 means that at y1=δ1, the velocity of the flow field is U1; The import and export flow conservation: G in =G out .

7. The pump-turbine inverse problem optimization method based on optimal coordination of multiple physical quantities according to claim 5 is characterized in that: The optimal synergy equation:

8. The pump-turbine inverse problem optimization method based on optimal coordination of multiple physical quantities according to claim 1 is characterized in that: The optimal cooperative equation is numerically solved by a fluid dynamics solver.

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