Vane pump high-performance low-noise multi-objective optimization method based on indirect acoustic variable method

Abstract

The invention relates to an indirect acoustic variable method-based vane pump high-performance low-noise multi-objective optimization method, which comprises the following steps of: establishing a relationship between internal flow of a vane pump and turbulent flow noise, extracting a noise source generated by flow induction in a pump, integrating the turbulent flow noise source in the pump and taking the integrated noise source as one of optimization objective function parameters, a sample group is established by taking key hydraulic design parameters of a pump inlet width, a blade outlet setting angle, a blade wrap angle and a blade number as optimization parameters, and optimization solution based on a genetic algorithm is carried out by taking pump lift, efficiency and noise source intensity for integrating indirect acoustic variables as multi-objective optimization parameters, so that excellent hydraulic performance of the vane pump is ensured, and meanwhile, the optimal design of the vane pump is realized. And a vane pump design with a low noise characteristic is obtained. The method considers various requirements of hydraulic performance and noise of the vane pump, and can be popularized and applied to initial hydraulic design of the vane pump so as to comprehensively consider the hydraulic performance and noise characteristics of the vane pump.

Description

Technical Field

[0001] The present invention relates to a high-performance and low-noise multi-objective optimization method for a vane pump, and in particular to a high-performance and low-noise multi-objective optimization method for a vane pump based on an indirect acoustic variable method, which takes into account the various requirements of the hydraulic performance and noise of the vane pump. Background Art

[0002] Vane pumps are rotary hydraulic machines widely used in marine engineering, water conservancy and hydropower engineering, nuclear power engineering, petrochemical engineering and other fields closely related to national economy and people's livelihood. With the development of modern industry and the progress of science and technology, higher requirements are put forward for its vibration and noise characteristics on the basis of meeting hydraulic performance. The noise sources of vane pumps are mainly mechanical vibration noise, motor electromagnetic noise and fluid induced noise, and the noise level is determined by the complex turbulent field. The first two have been controlled by various high-precision processes. Therefore, the turbulent noise caused by the complex flow inside the vane pump has become a difficulty in the design of low-noise vane pumps, and it is also an important factor that must be considered for low-noise vane pumps. However, at the beginning of the design of the key flow components of the vane pump (including the impeller of the rotating working component, the guide vane of the static expansion and drainage component, the volute and the suction chamber, etc.), it is difficult to consider the contribution of complex flow to the noise source, and then it is impossible to establish the relationship between the flow field, the noise source and the hydraulic design parameters, which is the key to the difficulty in realizing the optimization design of the flow noise of the vane pump.

[0003] The research theories and methods for hydraulic noise caused by incompressible flow in vane pumps are completely transplanted from aeroacoustics. In principle, the relevant mechanisms and calculation methods are applicable to hydrodynamic noise, but there are great differences in the compressibility and viscosity of the two media, and the research focus of hydrodynamic noise and aeroacoustics is significantly different. On the one hand, aeroacoustics mostly studies transonic and supersonic problems. Compared with dipole sources, quadrupole Reynolds stress is a more effective sound source and is more fully studied. Hydrodynamic noise problems generally belong to extremely small Mach number problems, and dipole sound sources are the main contribution, but for different flow characteristics, the contribution to turbulent viscosity is also different. On the other hand, the viscosity of water medium is much greater than that of air. Therefore, under the action of strong strain rate, pressure gradient, vortex shedding collision of different scales, wall energy transfer, and disturbance of the flow field by the moving wall in rotating turbulence, the induced noise sources in the shear layer region occupy an important component in the noise. In addition, the acoustic finite element method of flow field-structure-acoustic field multi-flow field coupling based on the traditional Lighthill acoustic analogy theory occupies a very high computing resource and is difficult to be used for the optimal design of low-noise vane pumps.

[0004] Therefore, in order to solve the problem of optimizing the flow noise induced by incompressible complex turbulence in the vane pump and the design difficulty that noise optimization cannot be considered in the initial hydraulic design of the vane pump, the present invention derives and solves the Lamb vector divergence of the noise source term between the turbulence control equation and the acoustic wave equation, and calculates and evaluates the intensity of the flow noise level of the vane pump by volume integration of the indirect acoustic variable Lamb vector divergence, and then establishes a multi-objective optimization method for the hydraulic performance and low noise characteristics of the vane pump, so as to achieve the optimal design of the high-performance and low-noise vane pump. Summary of the invention

[0005] In view of the above problems, the main purpose of the present invention is to provide a high-performance and low-noise multi-objective optimization method for a vane pump based on an indirect acoustic variable method, which takes into account the various requirements of the hydraulic performance and noise of the vane pump.

[0006] The present invention solves the above technical problems through the following scheme: a high-performance and low-noise multi-objective optimization method for a vane pump based on an indirect acoustic variable method, the optimization method comprising the following steps:

[0007] Step (1), deriving the relationship between the internal flow of the vane pump and the noise source;

[0008] Step (2), establishing an indirect acoustic variable method based on Lamb vector divergence;

[0009] Step (3), construct a multi-objective optimization method for the hydraulic performance and noise characteristics of the vane pump: the key hydraulic design parameters of the vane pump, the outlet width (b2), the blade outlet placement angle (β2), the blade wrap angle The number of blades (z) is used as the optimization parameter to establish a sample group, and the pump head coefficient (ψ), efficiency (η) and noise source intensity based on indirect acoustic variables (L d ) are multi-objective optimization parameters, and the optimization solution is performed based on genetic algorithm.

[0010] In a specific implementation example of the present invention, the derivation of the relationship between the internal flow of the vane pump and the noise source in step (1) specifically includes the following steps: The Navier Stokes equation for the motion of an incompressible viscous fluid has an equivalent form, namely the Lamb form:

[0011]

[0012] The nonlinear convection term of the flow is represented by L = ω × u; any single-valued, continuous and bounded vector field in the space can be decomposed into a potential vector field and a vortex vector field; for this purpose, by performing curl operations on both sides of the incompressible control equation and ignoring the terms that contribute zero to the vorticity change, the incompressible flow vortex transport equation is obtained:

[0013]

[0014] In equation (2) is the Lamb vector divergence;

[0015] Combining the turbulence control equations and the vorticity transport equations, as well as Hamman's research results on Lamb vector divergence, we know that Lamb vector divergence It can reflect the interaction between the turbulent field intensity strain rate region and the mean field; the negative value of Lamb vector divergence indicates that the local motion in space is relatively strong, and has accumulated the ability to affect the time rate of change of linear momentum; although the overall Lamb vector divergence is positive or negative, the positive contribution can only be generated by the buckling product; when a shear layer region appears in the turbulent flow, it is easy to generate strong pulsations of pseudo-vortex energy;

[0016] Therefore, the vortex-acoustic equation and the Lamb form of the Navier Stokes equations, the corresponding continuity equation and the momentum equation without considering the fluid viscosity are written as:

[0017]

[0018] Take the derivative of both sides of equation (3) with respect to time, and then add We can get:

[0019]

[0020] Combining equations (4) and (5), we can obtain:

[0021]

[0022] Equation (6) is a nonlinear acoustic wave equation that ignores fluid viscosity. Equation (6) can be further simplified by analyzing the magnitude of the source term. Density changes will cause pressure changes. The magnitude of each source term on the right side except density is analyzed and compared using dimensional analysis, which are 1:1:Ma 2 :StMa 2 , where Ma is the Mach number and St is the Strahal number;

[0023] Since the flow inside the vane pump is an incompressible low Mach number flow, the last two terms on the right side are high-order small quantities and can be ignored; equation (6) can be further simplified as:

[0024]

[0025] The first term on the right side of equation (7) represents the noise radiation caused by the vortex boundary constraint and space stretching. If it is a compact sound source, the influence of the fluid kinetic energy distribution in the second term on the far field under low-speed conditions can be ignored relative to the first term. Therefore, equation (7) can be transformed into a common form:

[0026]

[0027] Equation (8) is the vortex-acoustic equation derived by Powell, where is the Lamb vector divergence; Different from the Lighthill equation, equation (8) can further reveal the basic relationship between vortex and sound; Lamb vector divergence L d It consists of two parts, namely the flexion product and the negative enthalpy energy, which are defined as and L e = -ω×ω;

[0028] Under adiabatic isentropic conditions, the contributions of nonlinear terms and entropy terms are very low. Therefore, if only the vortex sound problem is considered, the essence of the important vortex source term in the APE equation is the Lamb vector divergence:

[0029]

[0030] The essence of the vortex source term in equation (9) is the Lamb vector divergence, which is an important sound source term. The first term on the right represents the noise caused by the vortex space pull-up, which is usually significantly generated under the no-slip wall constraint. The second term on the right represents the noise caused by the pulsation of the Lighthill tensor and is the dominant term of the spatial quadrupole noise.

[0031] In a specific implementation example of the present invention, step (2) of establishing an indirect acoustic variable method based on Lamb vector divergence specifically includes the following steps:

[0032] The noise source intensity caused by the complex flow inside the vane pump can be obtained by the indirect acoustic variable Lamb vector divergence L d Perform volume integration to characterize:

[0033]

[0034] Where D2 is the outlet diameter of the vane pump impeller, m; g0 is the reference acceleration, m / s 2 ;

[0035] Based on formula (10), the indirect acoustic variable Lambvector divergenceL is calculated for different operating conditions and different flow areas of the vane pump. d The volume integral of the vane pump is used to obtain the prediction of the noise source intensity induced by the internal flow of the vane pump.

[0036] (3) Construct a multi-objective optimization method for the hydraulic performance and noise characteristics of the vane pump:

[0037] The key hydraulic design parameters of the vane pump are outlet width (b2), blade outlet placement angle (β2), and blade wrap angle. The number of blades (z) is used as the optimization parameter to establish a sample group, and the pump head coefficient (ψ), efficiency (η) and noise source intensity based on indirect acoustic variables (L d ) are multi-objective optimization parameters, and a genetic algorithm-based optimization solution is performed to achieve a vane pump design with low noise characteristics while ensuring excellent hydraulic performance of the vane pump.

[0038] In a specific implementation example of the present invention, step (3) specifically includes the following steps:

[0039] Step (301): Determine the optimization target: The optimization target is the vane pump head (ψ), efficiency (η) and the noise source intensity (L d );

[0040] Step (302): Select optimization parameters and set the value range: Based on the vane pump design theory, the outlet width (b2), blade outlet placement angle (β2), and blade wrap angle of the optimized variable vane pump are preliminarily given. Optimization interval of blade number (z);

[0041] Step (303): Generate a sample space according to the test method;

[0042] Step (304): Sensitivity analysis: Perform sensitivity analysis on the design parameter variables to analyze how to quantitatively distribute the output changes to different input variables, and then remove the parameter variables that have little impact on the optimization target, and only retain the parameter variables that have a great impact on the optimization target, so as to achieve the purpose of reducing the complexity of the model and improving the accuracy of the model;

[0043] Step (305): Construct an approximate model between the optimization variables and the optimization target: construct an approximate model of the approximate input variables and the output variables based on the response surface method.

[0044] Step (306): Solve the global optimal solution for the approximate model based on the NSGA-II multi-objective genetic algorithm.

[0045] The positive progressive effect of the present invention is that the high-performance and low-noise multi-objective optimization method of the vane pump based on the indirect acoustic variable method provided by the present invention has the following advantages: the present invention takes into account the various requirements of the hydraulic performance and noise of the vane pump, and can be extended to the initial hydraulic design of the vane pump to comprehensively consider the hydraulic performance and noise characteristics of the vane pump. BRIEF DESCRIPTION OF THE DRAWINGS

[0046] Figure 1 It is a flow chart of the multi-objective optimization design of the present invention.

[0047] Figure 2 It is a simulation diagram of the multi-objective optimization process of the vane pump of the present invention.

[0048] Figure 3-1 This is a three-dimensional spatial diagram of the head response surface constructed based on the Kriging method.

[0049] Figure 3-2 A two-dimensional top view of the head response surface constructed based on the Kriging method.

[0050] Figure 4 Schematic diagram of the Pareto front and the optimal solution in the present invention. DETAILED DESCRIPTION

[0051] Preferred embodiments of the present invention are given below in conjunction with the accompanying drawings to illustrate the technical solutions of the present invention in detail.

[0052] The present invention aims at the difficulty of low-noise design of vane pump, establishes the relationship between the internal flow and turbulent noise of vane pump, extracts the noise source induced by the flow in the pump, integrates the turbulent noise source in the pump and takes it as one of the optimization objective function parameters, establishes a sample group with the key hydraulic design parameters of the pump, namely, pump outlet width, blade outlet placement angle, blade wrap angle, and number of blades as optimization parameters, and performs optimization based on genetic algorithm with pump head, efficiency, and noise source intensity integrated by indirect acoustic variables as multi-objective optimization parameters, so as to achieve the design of vane pump with low noise characteristics while ensuring the excellent hydraulic performance of vane pump. The detailed invention contents are as follows:

[0053] (1) Derivation of the relationship between the internal flow and noise source of the vane pump:

[0054] The Navier Stokes equations for the motion of incompressible viscous fluids have a particularly important equivalent form, the Lamb form:

[0055]

[0056] The nonlinear convection term of the flow can be expressed as L = ω × u. Any single-valued, continuous and bounded vector field in the space can be decomposed into a potential vector field and a vortex vector field. To this end, by performing curl operations on both sides of the incompressible control equation and ignoring the terms that contribute zero to the vorticity change, the incompressible flow vorticity transport equation can be obtained:

[0057]

[0058] In equation (2) is the Lamb vector divergence.

[0059] Combining the turbulence control equations and the vorticity transport equations, as well as Hamman's research results on Lamb vector divergence, we know that Lamb vector divergence It can reflect the interaction between the turbulent field intensity strain rate region and the mean field. The negative value of Lamb vector divergence indicates that the local motion in space is relatively strong and has accumulated the ability to affect the time rate of change of linear momentum. Although the overall Lamb vector divergence can be positive or negative, positive contributions can only be generated by the buckling product. When a shear layer region appears in the turbulent flow, strong pulsations of pseudo-vortex energy can be easily generated.

[0060] Therefore, the simultaneous vortex-acoustic equation and Lamb form of the Navier Stokes equation, the corresponding continuity equation and the momentum equation without considering the fluid viscosity can be written as:

[0061]

[0062] Take the derivative of both sides of equation (3) with respect to time, and then add We can get:

[0063]

[0064] Combining equations (4) and (5), we can obtain:

[0065]

[0066] Equation (6) is a nonlinear acoustic wave equation that ignores fluid viscosity. Equation (6) can be further simplified by analyzing the magnitude of the source term. Density changes will cause pressure changes. The magnitude of each source term on the right side except density is analyzed and compared using dimensional analysis, which are 1:1:Ma 2 :StMa 2 , where Ma is the Mach number and St is the Strahal number. Since the flow inside the vane pump is an incompressible low Mach number flow, the last two terms on the right side are high-order small quantities and can be ignored. Equation (6) can be further simplified as:

[0067]

[0068] The first term on the right side of equation (7) represents the noise radiation caused by the vortex boundary constraint and space stretching. If it is a compact sound source, the influence of the fluid kinetic energy distribution in the second term on the far field under low-speed conditions can be ignored relative to the first term. Therefore, equation (7) can be transformed into a common form:

[0069]

[0070] Equation (8) is the vortex-acoustic equation derived by Powell, where is the Lamb vector divergence. Different from the Lighthill equation, this equation can further reveal the basic relationship between vortex and sound. dIt consists of two parts, namely the flexion product and the negative enthalpy energy, which are defined as and L e =-ω×ω.

[0071] Under adiabatic isentropic conditions, the contributions of nonlinear terms and entropy terms are very low. Therefore, if only the vortex sound problem is considered, the essence of the important vortex source term in the APE equation is the Lamb vector divergence:

[0072]

[0073] The essence of the vortex source term in equation (9) is the Lamb vector divergence, which is an important sound source term. The first term on the right represents the noise caused by the vortex space pull-up, which is usually obvious under the no-slip wall constraint; the second term on the right represents the pulsation of the Lighthill tensor, which is the dominant term of the spatial quadrupole noise. Therefore, for multi-wall, strong rotation, and strong shear flows such as vane pumps, the Lamb vector divergence can effectively predict and measure the contribution of the internal flow of the vane pump to the noise source.

[0074] (2) Establish an indirect acoustic variable method based on Lamb vector divergence:

[0075] The noise source intensity caused by the complex flow inside the vane pump can be obtained by the indirect acoustic variable Lamb vector divergence L d Perform volume integration to characterize:

[0076]

[0077] Where D2 is the outlet diameter of the vane pump impeller, m; g0 is the reference acceleration, m / s 2 .

[0078] Based on formula (10), the indirect acoustic variable Lambvector divergenceL is calculated for different operating conditions and different flow areas of the vane pump. d The volume integral of the vane pump can be used to predict the intensity of the noise source induced by the internal flow of the vane pump.

[0079] (3) Construct a multi-objective optimization method for the hydraulic performance and noise characteristics of the vane pump:

[0080] The key hydraulic design parameters of the vane pump are outlet width (b2), blade outlet placement angle (β2), and blade wrap angle. The number of blades (z) is used as the optimization parameter to establish a sample group, and the pump head coefficient (ψ), efficiency (η) and noise source intensity based on indirect acoustic variables (L d) are multi-objective optimization parameters, and a genetic algorithm-based optimization solution is performed to achieve a vane pump design with low noise characteristics while ensuring excellent hydraulic performance of the vane pump.

[0081] Therefore, the multi-objective optimization method for the hydraulic performance and noise characteristics of the vane pump constructed in this invention is a way to solve the multi-objective optimization problem by combining experimental design, approximate model and intelligent algorithm. The specific process is as follows Figure 1 The multi-objective optimization process of the hydraulic performance and noise characteristics of the vane pump is shown in the attached Figure 2 As shown in the figure, the process can realize automated simulation calculation, which mainly includes:

[0082] The first step is to determine the optimization target. The optimization targets of the present invention are mainly the vane pump head (ψ), efficiency (η) and the noise source intensity (L d );

[0083] Step 2: Select optimization parameters and set the value range. Based on the vane pump design theory, the outlet width (b2), blade outlet placement angle (β2), and blade wrap angle of the optimized variable vane pump are preliminarily given. Optimization interval of blade number (z);

[0084] Step 3: Generate sample space according to the experimental method. Latin Hypercube Sampling (LHS) is a strategy for approximate random sampling from a multivariate parameter distribution. It uses a classical algorithm to eliminate the correlation between sample points that exceeds expectations. This algorithm can reduce the correlation between input variables to a certain extent, achieve uniform stratification, and obtain tail sample values ​​even with less sampling. It is particularly effective when processing large-scale data. However, when there is a high correlation between input variables, the effect of LHS may be reduced; in some cases, LHS may also produce some unreasonable samples, affecting the accuracy of the simulation. Therefore, this method adopts the optimal Latin hypercube design ALHS (Advanced Latin hypercube design, ALHD), which can add optimized samples based on the existing LHS sample set to minimize the correlation between sample points and achieve optimal sample coverage of the design space. It can better deal with the situation where there is a high correlation between input variables, generate more reasonable samples, and improve simulation accuracy. The final implementation method is through the attached Figure 2 The experimental design module (Design of experiment, DOE) generates the sample space. Figure 2 The Chinese equivalents of the English in are shown in Table 1, see the last page of the instruction manual.

[0085] Step 4: Sensitivity analysis: In the process of vane pump optimization design, excessive optimization parameters will cause a sharp increase in calculation amount and time cost, resulting in a significant increase in the optimization cycle. The numerous optimization variables lead to the so-called "curse of dimensionality". Therefore, a sensitivity analysis (Sensitivity analysis) is performed on the design parameter variables to analyze how to quantitatively allocate the output changes to different input variables, and then remove the parameter variables that have little effect on the optimization target, and only retain the parameter variables that have a great influence on the optimization target, so as to achieve the purpose of reducing the complexity of the model and improving the accuracy of the model. The final implementation method is through the attached Figure 2 The best prediction meta-module (Metamodel of Optimal, MOP) in is used to reduce the data dimension;

[0086] Step 5: Construct an approximate model between the optimization variables and the optimization targets. Based on the response surface methodology (RSM), an approximate model of the input variables (independent variables) and the output variables (response variables) is constructed. Since the relationship between the input variables, flow state, structure, and target changes of the vane pump is a complex nonlinear problem, and the Kriging method can accurately predict linear and nonlinear functions, the database is very small, which can reduce the number of required parameters. Therefore, the present invention adopts the Kriging method to fit the response surface model between the design variables and the target function, and the final implementation method is to attach Figure 2 The Metamodel of Optimal (MOP) in the algorithm is used as an alternative solver for subsequent optimization calculations. The optimal sample point can be used as the initial value of the optimization to accelerate the optimization process. Figure 3-1 This is a three-dimensional spatial diagram of the head response surface constructed based on the Kriging method. Figure 3-2 A two-dimensional top view of the head response surface constructed based on the Kriging method.

[0087] Step 6: Solve the global optimal solution (set) for the approximate model based on the NSGA-II (Non-dominated Sorting Genetic Algorithm II) multi-objective genetic algorithm. Figure 4 Schematic diagram of the Pareto front and the optimal solution in the present invention. The NSGA-II multi-objective genetic algorithm introduces mechanisms such as elite retention strategy, fast non-dominated sorting and crowding calculation, which make the convergence and robustness of the calculation better. At the same time, the fast non-dominated sorting significantly reduces the computational complexity. The elite retention strategy retains excellent individuals by letting the parent and offspring compete together, while the crowding calculation ensures the diversity of solutions by determining whether individuals stay or leave. Individuals with greater crowding are generally considered to be superior. Through these methods, NSGA-II can effectively find balanced and high-quality solutions in multi-objective optimization problems. The final line of sight is to attach Figure 2 The solution is obtained in the optimization calculation module (NSGA-IIOptimization Algorithm, NOA2).

[0088] Finally, the high performance and low noise multi-objective optimization of the vane pump is achieved based on the indirect acoustic variable method.

[0089] Based on the NSGA-Ⅱ algorithm, the MOP response surface model is optimized by multiple objectives and the corresponding Pareto optimal solution set is obtained. The Pareto solution consisting of the solution set objective function mapping is shown in the attached figure. Figure 4 As shown. The blue points are advanced Latin hypercube sampling points, and the red line is the fitted Pareto curve. Since the optimization goal is to find the sound source intensity level L under the premise of optimizing the head and efficiency as much as possible, d Therefore, in order to perform global optimization, the appropriate design point can be selected as the final optimization result based on the Pareto frontier. The optimization goal of a vane pump in the present invention is to select the sound source intensity level L on the Pareto frontier under the premise of ensuring that the numerical efficiency is greater than 0.92. d The best solution is attached Figure 4 shown.

[0090] Table 1 Figure 2 (Chinese and English)

[0091]

[0092]

[0093] The present invention takes into account the various requirements of the hydraulic performance and noise of the vane pump, and can be widely used in the initial hydraulic design of the vane pump to comprehensively consider the hydraulic performance and noise characteristics of the vane pump.

[0094] The above shows and describes the basic principles and main features of the present invention and the advantages of the present invention. Those skilled in the art should understand that the present invention is not limited to the above embodiments, and the above embodiments and descriptions are only for explaining the principles of the present invention. Without departing from the spirit and scope of the present invention, the present invention may have various changes and improvements, which fall within the scope of the present invention to be protected, and the scope of the present invention to be protected is defined by the attached claims and their equivalents.

Claims

1. A high-performance, low-noise multi-objective optimization method for a vane pump based on an indirect acoustic variable method, characterized by: The optimization method comprises the following steps: Step (1), deriving the relationship between the internal flow of the vane pump and the noise source; Step (2), establishing an indirect acoustic variable method based on Lamb vector divergence; Step (3) construct a multi-objective optimization method for the hydraulic performance and noise characteristics of the vane pump: the key hydraulic design parameters of the vane pump are outlet width (b2), blade outlet placement angle (β2), blade wrap angle The number of blades (z) is used as the optimization parameter to establish a sample group, and the pump head coefficient (ψ), efficiency (η) and noise source intensity based on indirect acoustic variables (L d ) are multi-objective optimization parameters, and the optimization solution is performed based on genetic algorithm.

2. The high-performance, low-noise multi-objective optimization method for a vane pump based on the indirect acoustic variable method according to claim 1 is characterized by: The derivation of the relationship between the internal flow of the vane pump and the noise source in step (1) specifically includes the following steps: The Navier Stokes equation for the motion of incompressible viscous fluid has an equivalent form, namely the Lamb form: The nonlinear convection term of the flow is represented by L = ω × u. Any single-valued, continuous and bounded vector field in the space can be decomposed into a potential vector field and a vortex vector field. To this end, by performing curl operations on both sides of the incompressible control equation and ignoring the terms that contribute zero to the vorticity change, the vortex transport equation for incompressible flow is obtained: In equation (2) is the Lamb vector divergence; Combining the turbulence control equation and the vortex transport equation, as well as Hamman's research results on Lamb vector divergence, we can know that Lamb vector divergence It can reflect the interaction between the turbulent field intensity strain rate region and the mean field; negative values ​​of the Lamb vector divergence indicate that the local motion in space is relatively strong and has accumulated the ability to affect the time rate of change of linear momentum; although the overall Lamb vector divergence is positive or negative, a positive contribution can only be generated by the buckling product; when a shear layer region appears in the turbulent flow, it is easy to generate strong pulsations of pseudo-vortex energy; Therefore, the simultaneous vortex-acoustic equations and the Lamb form of the Navier-Stokes equations, the corresponding continuity equation and the momentum equation without considering the fluid viscosity are written as: Take the time derivative of both sides of equation (3) and add We can get: Combining equations (4) and (5) we can get: Equation (6) is a nonlinear acoustic wave equation that ignores fluid viscosity. Equation (6) can be further simplified by analyzing the magnitude of the source term. Density changes will cause pressure changes. The magnitude of each source term on the right side except density is analyzed and compared using dimensional analysis, which are 1:1:Ma 2 :StMa 2 , where Ma is the Mach number and St is the Strahal number; Since the flow inside the vane pump is an incompressible low Mach number flow, the last two terms on the right side are high-order small quantities and can be ignored; Equation (6) can be further simplified as: The first term on the right side of equation (7) represents the noise radiation caused by the vortex boundary constraint and spatial stretching. If the sound source is compact, the influence of the fluid kinetic energy distribution in the second term on the far field under low-speed conditions can be ignored relative to the first term. Therefore, equation (7) can be transformed into the common form: Equation (8) is the vortex-acoustic equation derived by Powell, where is the Lamb vector divergence; Different from the Lighthill equation, equation (8) can further reveal the basic relationship between vortex and sound; Lamb vector divergence L d It consists of two parts, namely the flexion product and the negative envrophy, which are defined as and L e = -ω×ω; Under adiabatic isentropic conditions, the contributions of nonlinear terms and entropy terms are very low. Therefore, if only the eddy-acoustic problem is considered, the essence of the important eddy source term in the APE equation is the Lamb vector divergence: The essence of the vortex source term in equation (9) is the Lamb vector divergence, which is an important sound source term; the first term on the right side represents the noise caused by the vortex space pull-up, which is usually significantly generated under the no-slip wall constraint; the second term on the right side represents the noise caused by the pulsation of the Lighthill tensor and is the dominant term of the spatial quadrupole noise.

3. The high-performance, low-noise multi-objective optimization method for a vane pump based on the indirect acoustic variable method according to claim 1 is characterized by: The establishment of the indirect acoustic variable method based on Lamb vector divergence in step (2) specifically includes the following steps: The noise source intensity caused by the complex flow inside the vane pump can be obtained by the indirect acoustic variable Lamb vector divergence L d Perform volume integration to characterize: Where D2 is the outlet diameter of the vane pump impeller, m; g0 is the reference acceleration, m / s 2 ; Based on formula (10), the indirect acoustic variable Lamb vector divergence L is calculated for different operating conditions and different flow areas of the vane pump. d The volume integral of the vane pump is used to obtain the noise source intensity prediction caused by the internal flow of the vane pump; (3) Construct a multi-objective optimization method for the hydraulic performance and noise characteristics of the vane pump: The key hydraulic design parameters of the vane pump are outlet width (b2), blade outlet placement angle (β2), blade wrap angle ( ) and the number of blades (z) as the optimization parameters to establish a sample group, and the pump head coefficient (ψ), efficiency (η) and noise source intensity based on indirect acoustic variables (L d ) is a multi-objective optimization parameter, and a genetic algorithm-based optimization solution is performed to achieve a vane pump design with low noise characteristics while ensuring excellent hydraulic performance of the vane pump.

4. The high-performance, low-noise multi-objective optimization method for a vane pump based on the indirect acoustic variable method according to claim 1 is characterized by: Step (3) specifically includes the following steps: Step 301: Determine the optimization target: The optimization target is the vane pump head (ψ), efficiency (η) and the noise source intensity (L d ); Step 302: Select optimization parameters and set the value range: Based on the vane pump design theory, the outlet width (b2), blade outlet placement angle (β2), and blade wrap angle of the optimized variable vane pump are preliminarily given. Optimization interval of blade number (z); Step 303: Generate sample space according to the experimental method; Step 304: Sensitivity analysis: Perform sensitivity analysis on the design parameter variables to analyze how to quantitatively distribute the output changes to different input variables. Then, remove the parameter variables that have little impact on the optimization target and only retain the parameter variables that have a large impact on the optimization target, thereby reducing the model complexity and improving the model accuracy. Step 305: Construct an approximate model between the optimization variables and the optimization objectives: Construct an approximate model between the input variables and the output variables based on the response surface methodology. Step 306: Solve the global optimal solution of the approximate model based on the NSGA-II multi-objective genetic algorithm.

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