1. A zigzag hydrofoil leading edge optimization method based on a proxy model is characterized in that: comprises the following steps of (a) carrying out,

the method comprises the following steps: establishing a hydrofoil model with a sawtooth-shaped leading edge based on three-dimensional modeling software;

step two: carrying out grid division on the hydrofoil model with the sawtooth-shaped leading edge established in the step one, importing a divided fluid domain grid file into three-dimensional fluid simulation calculation software, simulating a flow surrounding field around the hydrofoil through the three-dimensional fluid simulation software, setting a speed inlet, a pressure outlet and a non-slip wall surface on the surface of the hydrofoil by adding boundary conditions, and further carrying out numerical simulation calculation on the hydrofoil flow surrounding field to obtain turbulent flow field data of the sawtooth-shaped leading edge hydrofoil;

step three: carrying out post-processing analysis according to the turbulent flow field data obtained by calculation and solution to obtain the strength R and the pressure pulsation SPL peak value of the surface vortex system structure of the hydrofoil;

step four: preprocessing the combination of the wave amplitude and the wave length of the convex knot at the front edge of the sawtooth hydrofoil and the corresponding hydrodynamic performance data by adopting a Central Composite Design (CCD) method to obtain n₁Sample points combined with Latin hypercube design (LHSD, Latin)Hypercube sampling) method randomly generates n uniformly covering the whole sample space₂Sample points are arranged, and the precision of the response surface model is improved; n is to be₁A sample point and n₂Combining the sample points to obtain n which is n of the whole sample space₁+n₂A sample point;

step five: n is n for the whole sample space obtained in step four₁+n₂Carrying out response surface fitting on each sample point, namely fitting the relation between a target variable and a design variable through a functional relation to obtain a response surface model of the sawtooth-shaped structure parameters A and lambda, the vortex intensity R and the pressure pulsation SPL, which is called the response surface model for short;

step six: based on the decision coefficient S²Sum root mean square difference σ_RMSEEvaluating the prediction capability of the response surface model obtained in the step five, and quantitatively evaluating the accuracy of the fitted response surface;

step seven: if the accuracy of the fitting response surface quantitatively evaluated in the sixth step does not meet the expected value, reselecting a sample data point to establish a new polynomial response surface fitting function; otherwise, further adopting a variance-based Sobol global sensitivity analysis method to establish sensitivity analysis of the independent variable on the target variable to obtain a polynomial response surface model meeting the fitting precision;

step eight: respectively drawing a trend graph of the vortex intensity R and the pressure pulsation SPL along with the change of the sawtooth amplitude A and the wavelength lambda according to the polynomial response surface model meeting the fitting precision obtained in the step seven; obtaining an independent variable value boundary corresponding to the optimal target variable by analyzing a trend graph, wherein the independent variable comprises a sawtooth amplitude A and a wavelength lambda;

step nine: establishing a multi-objective optimization problem with the vortical intensity R and the pressure pulsation SPL as optimization targets based on the polynomial response surface model meeting the fitting precision obtained in the seventh step and the independent variable value boundary obtained in the eighth step, and solving and optimizing the established multi-objective optimization problem to obtain a Pareto optimal solution set;

and realizing the proxy model optimization based on the polynomial response surface fitting function through the fourth step to the ninth step.

2. The method for optimizing the leading edge of the zigzag hydrofoil based on the proxy model as claimed in claim 1, wherein: the method comprises the following steps of performing surrogate model optimization on the structure size of the front edge of the sawtooth-shaped hydrofoil through the fourth step to the ninth step to obtain sawtooth-shaped parameter combination based on Pareto optimal solution, namely, efficiently obtaining the combination of the convex node amplitude and the wavelength of the front edge of the sawtooth-shaped hydrofoil, enabling the vortex intensity and the pressure pulsation value of the surface of the hydrofoil subjected to the sawtooth-shaped front edge optimization to meet the requirements of required working conditions, enabling the lift drag coefficient of the hydrofoil with the sawtooth-shaped front edge to be superior to that of a smooth hydrofoil, effectively inhibiting or delaying the flow separation of the surface of the hydrofoil, further improving the hydrodynamic performance of the hydrofoil with the sawtooth-shaped front edge, and solving the technical problem of engineering in the field of flow control application;

step ten, solving the engineering technical problem in the flow control application field comprises improving hydrodynamic performance and noise performance of the hydrofoil, saving energy and improving economic benefit.

3. The method for optimizing the leading edge of the zigzag hydrofoil based on the proxy model as claimed in claim 1 or 2, wherein: the modeling of a prototype hydrofoil is realized by introducing a hydrofoil tangent plane contour curve and stretching, on the basis, the original point of a Cartesian coordinate system is fixed at the front edge point of the prototype hydrofoil, the positive x is along the flow direction, the positive y is along the span direction, and the z axis can be determined by the right-hand rule; taking the span length of the hydrofoil as an axis y, the chord length as an axis x, and the guide edge as a sawtooth-shaped leading edge reference line, establishing a sine wave curve as a guide line, and realizing the modeling of the sawtooth-shaped leading edge hydrofoil by drawing a boss; the sine wave curve satisfies the following formula:

wherein: x is the number of_LEIs the abscissa of the waveform curve, A and λ are the amplitude and wavelength of the waveform, y is the spanwise coordinate, y is the wavelength₀Is the spanwise coordinate of the guide edge of the prototype hydrofoil.

4. The method for optimizing the leading edge of the zigzag hydrofoil based on the proxy model as claimed in claim 3, wherein: in the third step, the first step is that,

the intensity and pressure pulsation satisfy the following formula:

SPL＝20log(p/p_ref)

wherein: where R in the rotation intensity R is a true eigenvector representing the rotation axis, ω is the vorticity, λ_ciIs a pseudo-time averaged angular velocity; p in the pressure pulsation sound pressure level SPL is the instantaneous pressure in the flow field, p_refIs a reference sound pressure.

5. The method for optimizing the leading edge of the zigzag hydrofoil based on the proxy model as claimed in claim 4, wherein: in the fifth step, the first step is that,

fitting the relation between the target variable and the design variable through the functional relation, and fitting by adopting a 2-order polynomial, wherein the specific expression is as follows:

in the formula:fitting values of target variables; n is the number of design points; y is_iIs the ith design point; beta is a₀、β_i、β_ijAre regression coefficients.

6. The method for optimizing the leading edge of the zigzag hydrofoil based on the proxy model as claimed in claim 5, wherein: the sixth realization method comprises the following steps of,

based on the decision coefficient S²Sum root mean square difference σ_RMSEEvaluating the prediction capability of the response surface model obtained in the step five, and responding to the fitting according to the following formulaQuantitative evaluation of surface accuracy:

in the formula: z is a radical of_iObserved values for design points;is the response surface function fit value; according to S²And σ_RMSEDefinition of (1), S²The closer to 1, σ_RMSEThe closer to 0, the higher the response surface fitting accuracy.

7. The method for optimizing the leading edge of the zigzag hydrofoil based on the proxy model as claimed in claim 6, wherein: the seventh implementation method comprises the following steps of,

if the accuracy of the fitting response surface quantitatively evaluated in the sixth step does not meet the expected value, reselecting a sample data point to establish a new polynomial response surface fitting function; otherwise, further adopting a variance-based Sobol global sensitivity analysis method to establish sensitivity analysis of the independent variable on the target variable, wherein the sensitivity analysis formula is as follows:

in the formula: v_iIs the effect of the independent variable on the target variable; v_izFor the interaction of other independent variables; v is the influence of all independent variables on the target variable;expressing global sensitivity, local sensitivity of independent variable and other independent variables can be comprehensively considered through a sensitivity analysis formulaThe amount interacts with it.

8. The method for optimizing the leading edge of the zigzag hydrofoil based on the proxy model as claimed in claim 1 or 2, wherein: selecting solidworks as three-dimensional modeling software;

ANSYS CFX is selected as three-dimensional fluid simulation software; and selecting a Reynolds time-average N-S equation (RANS) to carry out numerical simulation calculation on the hydrofoil flow-around field.

Background

Flow separation is a phenomenon that often exists when a fluid flows on a solid wall surface, and large-scale vortex shedding caused by the flow separation is a main reason for causing the hydrofoil to stall and deviate from an operating point, and can cause strong vibration and noise to greatly influence the hydrodynamic performance of the hydrofoil. The sawtooth-shaped hydrofoil leading edge can increase the energy of the wall fluid by generating a flow direction vortex, so that the effect of inhibiting flow separation is achieved, and therefore a new opportunity is provided for improving the hydrodynamic performance of the solid wall flow field by applying the sawtooth-shaped hydrofoil leading edge to act on the solid wall flow field. But current research has less analysis of the structural dimensions of the leading edge of a zigzag hydrofoil applied in water. In order to improve the hydrodynamic performance of the hydrofoil with the additional sawtooth-shaped hydrofoil leading edge, scholars at home and abroad carry out a great deal of research on the numerical calculation of the flow separation control of the various sawtooth-shaped hydrofoil leading edges and put forward various optimization design methods. However, the existing optimization method is too large in calculation amount and too dependent on finite element software, and the existing optimization method is not universal. The agent model is an analysis model which has small calculation amount, but the calculation result is similar to the calculation analysis result of the high-precision model. At present, the research of applying the proxy model to the hydrofoil with the sawtooth-shaped front edge is not carried out. .

Disclosure of Invention

The invention discloses a proxy model-based sawtooth hydrofoil leading edge optimization method, which aims to solve the technical problems that: the structural size of the sawtooth-shaped hydrofoil leading edge is optimized based on the proxy model, the combination of the protruding node amplitude and the wavelength of the sawtooth-shaped hydrofoil leading edge can be efficiently obtained, the vortex strength and the pressure pulsation value of the hydrofoil surface optimized by the sawtooth-shaped leading edge meet the requirements of required working conditions, the lift drag coefficient of the hydrofoil with the sawtooth-shaped leading edge is superior to that of a smooth hydrofoil, the flow separation of the surface of the hydrofoil is effectively inhibited or delayed, the hydrodynamic performance of the hydrofoil with the sawtooth-shaped leading edge is further improved, and the technical problem of engineering in the field of flow control application is solved. The invention has the advantage of high optimization efficiency.

The purpose of the invention is realized by the following technical scheme:

the invention discloses a proxy model-based sawtooth-shaped hydrofoil leading edge optimization method, which comprises the steps of establishing a hydrofoil model with a sawtooth-shaped leading edge through three-dimensional modeling software, carrying out grid division on the hydrofoil model with the sawtooth-shaped leading edge, and placing the hydrofoil model into fluid mechanics simulation software to carry out turbulence field numerical calculation to obtain turbulence field data of the hydrofoil with the sawtooth-shaped leading edge. And carrying out post-processing analysis according to the turbulent flow field data obtained by calculation and solution to obtain the strength R of the surface vortex system structure of the hydrofoil and the pressure pulsation SPL peak value. And preprocessing the combination of the wave amplitude and the wavelength of the convex knot at the front edge of the sawtooth hydrofoil and the corresponding hydrodynamic performance data by adopting a Central Composite Design (CCD) method and a Latin Hypercube Sampling (LHSD) method to obtain all n sample points in the whole sample space. And then carrying out response surface fitting on the n sample points, namely fitting the relation between the target variable and the design variable through a functional relation to obtain a response surface model of the sawtooth-shaped structure parameters A and lambda, the vortex intensity R and the pressure pulsation SPL. Based on the decision coefficient S²Sum root mean square difference σ_RMSEAnd evaluating the prediction capability of the obtained response surface model, and quantitatively evaluating the accuracy of the fitted response surface. And if the accuracy of the fitting response surface of the quantitative evaluation does not meet the expected value, reselecting the sample data points to establish a new polynomial response surface fitting function. Otherwise, further adopting a variance-based Sobol global sensitivity analysis method to establish sensitivity analysis of the independent variable on the target variable to obtain a polynomial response surface meeting the fitting precisionAnd (4) modeling. And respectively drawing a trend graph of the vortex intensity R and the pressure pulsation SPL along with the change of the sawtooth amplitude A and the wavelength lambda according to the obtained polynomial response surface model meeting the fitting precision. And searching an independent variable value boundary corresponding to the optimal target variable by analyzing the trend graph, wherein the independent variable comprises a sawtooth amplitude A and a wavelength lambda. And establishing a multi-objective optimization problem with the vortical intensity R and the pressure pulsation SPL as optimization targets, solving and optimizing the established multi-objective optimization problem to obtain a Pareto optimal solution set, and realizing the proxy model optimization based on a polynomial response surface fitting function. A serrated parameter combination based on Pareto optimal solution is obtained through proxy model optimization, namely, the combination of the convex node amplitude and the wavelength of the front edge of the serrated hydrofoil is obtained at high efficiency, so that the vortex intensity and the pressure pulsation value of the surface of the hydrofoil optimized by the serrated front edge meet the requirements of required working conditions, the lift drag coefficient of the hydrofoil with the serrated front edge is superior to that of a smooth hydrofoil, the flow separation of the surface of the hydrofoil is effectively inhibited or delayed, the hydrodynamic performance of the hydrofoil with the serrated front edge is improved, and the technical problem of engineering in the flow control application field is solved.

The invention discloses a zigzag hydrofoil leading edge optimization method based on a proxy model, which comprises the following steps:

the method comprises the following steps: and establishing a hydrofoil model with a sawtooth-shaped leading edge based on three-dimensional modeling software.

The modeling of the prototype hydrofoil is realized by introducing a hydrofoil tangent plane contour curve and stretching, on the basis, the original point of a Cartesian coordinate system is fixed at the front edge point of the prototype hydrofoil, the positive x is along the flow direction, the positive y is along the spanwise direction, and the z axis can be determined by the right-hand rule. The hydrofoil span length is used as a y axis, the chord length is used as an x axis, the guide edge is a sawtooth-shaped leading edge reference line, a sine wave curve is established to be used as a guide line, and the modeling of the sawtooth-shaped leading edge hydrofoil is realized through the extension of a boss. The sine wave curve satisfies the following formula:

wherein: x is the number of_LEOn the abscissa of the wave curve, A and λ are the amplitude andwavelength, y is the spanwise coordinate, y₀Is the spanwise coordinate of the guide edge of the prototype hydrofoil.

Preferably, the three-dimensional modeling software is solidworks.

Step two: and (2) carrying out grid division on the hydrofoil model with the sawtooth-shaped leading edge established in the step one, importing the divided fluid domain grid file into three-dimensional fluid simulation calculation software, simulating a flow winding field around the hydrofoil through the three-dimensional fluid simulation software, setting a speed inlet, a pressure outlet and a non-slip wall surface on the surface of the hydrofoil by adding boundary conditions, and further carrying out numerical simulation calculation on the hydrofoil flow winding field to obtain turbulent flow field data of the sawtooth-shaped leading edge hydrofoil.

Preferably, the three-dimensional fluid simulation software selects ANSYS CFX; and selecting a Reynolds time-average N-S equation (RANS) to carry out numerical simulation calculation on the hydrofoil flow-around field.

Step three: carrying out post-processing analysis according to turbulent flow field data obtained by calculation and solution to obtain the intensity R and pressure pulsation SPL peak value of the surface vortex system structure of the hydrofoil, wherein the intensity and pressure pulsation satisfy the following formula:

SPL＝20log(p/p_ref)

wherein: where R in the rotation intensity R is a true eigenvector representing the rotation axis, ω is the vorticity, λ_ciIs the pseudo-time averaged angular velocity. P in the pressure pulsation sound pressure level SPL is the instantaneous pressure in the flow field, p_refIs a reference sound pressure.

Step four: preprocessing the combination of the wave amplitude and the wave length of the convex knot at the front edge of the sawtooth hydrofoil and the corresponding hydrodynamic performance data by adopting a Central Composite Design (CCD) method to obtain n₁Randomly generating n uniformly covering the whole sample space by combining a Latin Hypercube Sampling (LHSD) method₂And the accuracy of the response surface model is improved by the sample points. N is to be₁A sample point and n₂Merging of sample pointsObtaining n-n of the whole sample space₁+n₂And (4) sampling points.

Step five: n is n for the whole sample space obtained in step four₁+n₂And (3) carrying out response surface fitting on each sample point, namely fitting the relation between the target variable and the design variable through a functional relation to obtain a response surface model of the parameters A and lambda of the sawtooth structure, the vortex intensity R and the pressure pulsation SPL, which is called the response surface model for short.

And fitting the relation between the target variable and the design variable through the functional relation, and preferably fitting by adopting a 2-order polynomial, wherein the specific expression is as follows:

in the formula:fitting values of target variables; n is the number of design points; y is_iIs the ith design point; beta is a₀、β_i、β_ijAre regression coefficients.

Step six: based on the decision coefficient S²Sum root mean square difference σ_RMSEAnd evaluating the prediction capability of the response surface model obtained in the step five, and quantitatively evaluating the accuracy of the fitted response surface.

Based on the decision coefficient S²Sum root mean square difference σ_RMSEEvaluating the prediction capability of the response surface model obtained in the step five, and quantitatively evaluating the accuracy of the fitting response surface according to the following formula:

in the formula: z is a radical of_iObserved values for design points;is the response surface function fit value. According to S²And σ_RMSEDefinition of (1), S²The closer to 1, σ_RMSEThe closer to 0, the higher the response surface fitting accuracy.

Step seven: and if the accuracy of the fitting response surface quantitatively evaluated in the sixth step does not meet the expected value, reselecting the sample data points to establish a new polynomial response surface fitting function. Otherwise, further adopting a variance-based Sobol global sensitivity analysis method to establish sensitivity analysis of the independent variable on the target variable, and obtaining a polynomial response surface model meeting the fitting precision.

And if the accuracy of the fitting response surface quantitatively evaluated in the sixth step does not meet the expected value, reselecting the sample data points to establish a new polynomial response surface fitting function. Otherwise, further adopting a variance-based Sobol global sensitivity analysis method to establish sensitivity analysis of the independent variable on the target variable, wherein the sensitivity analysis formula is as follows:

S_i ^tot＝(V_i+V_iz)/V

in the formula: v_iIs the effect of the independent variable on the target variable; v_izFor the interaction of other independent variables; v is the influence of all independent variables on the target variable; s_i ^totThe global sensitivity is expressed, and the local sensitivity of the independent variable and the interaction of other independent variables can be comprehensively considered through a sensitivity analysis formula.

Step eight: and respectively drawing a trend graph of the vortex intensity R and the pressure pulsation SPL along with the change of the sawtooth amplitude A and the wavelength lambda according to the polynomial response surface model meeting the fitting precision obtained in the step seven. And obtaining an independent variable value boundary corresponding to the optimal target variable by analyzing the trend graph, wherein the independent variable comprises a sawtooth amplitude A and a wavelength lambda.

Step nine: and based on the polynomial response surface model meeting the fitting precision obtained in the seventh step and the independent variable value boundary obtained in the eighth step, establishing a multi-objective optimization problem with the vortex intensity R and the pressure pulsation SPL as optimization targets, and solving and optimizing the established multi-objective optimization problem to obtain a Pareto optimal solution set.

And realizing the proxy model optimization based on the polynomial response surface fitting function through the fourth step to the ninth step.

Step ten: the structural size of the sawtooth-shaped hydrofoil front edge is optimized by a proxy model through the fourth step to the ninth step, so that a sawtooth-shaped parameter combination based on a Pareto optimal solution is obtained, namely, a combination of the convex node amplitude and the wavelength of the sawtooth-shaped hydrofoil front edge is obtained at high efficiency, the vortex strength and the pressure pulsation value of the hydrofoil surface subjected to the sawtooth-shaped front edge optimization meet the requirements of required working conditions, the lift drag coefficient of the hydrofoil with the sawtooth-shaped front edge is superior to that of a smooth hydrofoil, the flow separation of the surface of the hydrofoil is effectively inhibited or delayed, the hydrodynamic performance of the hydrofoil with the sawtooth-shaped front edge is further improved, and the technical problem of engineering in the field of flow control application is solved.

Step ten, solving the engineering technical problem in the flow control application field comprises improving hydrodynamic performance and noise performance of the hydrofoil, saving energy and improving economic benefit.

Has the advantages that:

1. the invention discloses a proxy model-based sawtooth hydrofoil leading edge optimization method, which is characterized in that the structural size of the sawtooth hydrofoil leading edge is optimized based on a proxy model, the combination of the convex node amplitude and the wavelength of the sawtooth hydrofoil leading edge can be efficiently obtained, the vortex strength and the pressure pulsation value of the hydrofoil surface subjected to the sawtooth leading edge optimization meet the requirements of required working conditions, the lift drag coefficient of the hydrofoil with the sawtooth leading edge is superior to that of a smooth hydrofoil, the flow separation of the surface of the hydrofoil is effectively inhibited or delayed, the hydrodynamic performance of the hydrofoil with the sawtooth leading edge is further improved, and the technical problem of engineering in the field of flow control application is solved.

2. The invention discloses a proxy model-based sawtooth-shaped hydrofoil leading edge optimization method, which is characterized in that the high nonlinearity between the sawtooth-shaped structure size and the hydrofoil hydrodynamic performance is realized, the relation is very complex, the time consumption of the traditional simulation calculation optimization method is long, and the difficulty is high.

3. The invention discloses a proxy model-based sawtooth-shaped hydrofoil leading edge optimization method, which adopts a Central Composite Design (CCD) method to preprocess the combination of the amplitude and the wavelength of a sawtooth-shaped hydrofoil leading edge convex knot and the corresponding hydrodynamic performance data to obtain n₁Randomly generating n uniformly covering the whole sample space by combining a Latin Hypercube Sampling (LHSD) method₂And the accuracy of the response surface model is improved by the sample points.

Drawings

FIG. 1 is a flow chart of a method for sawtooth hydrofoil leading edge optimization based on a proxy model;

FIG. 2 is a schematic view of a sawtooth foil leading edge;

FIG. 3 is a schematic diagram of a spatial sample obtained based on a center composite design method and a Latin hypercube design method;

FIG. 4 is a goodness of fit plot of a 2 nd order polynomial response surface plotted based on sample space design points;

FIG. 5 is a global sensitivity diagram of independent variables to target variables based on a Sobol analysis method;

FIG. 6 is a graph of the quantitative trend of target variables with independent variation, wherein: FIG. 6(a) is a graph of pressure pulsation versus target variable global sensitivity, and FIG. 6(b) is a graph of vortex intensity versus target variable global sensitivity;

FIG. 7 is a graph of a Pareto optimal solution set distribution obtained by solving a multi-objective optimization problem.

Detailed Description

For a better understanding of the objects and advantages of the present invention, reference should be made to the following detailed description taken in conjunction with the accompanying drawings and examples.

Example 1:

with the NACA66 hydrofoil model as an embodiment, as shown in fig. 1 to 7, the zigzag hydrofoil leading edge optimization method based on the proxy model disclosed in this embodiment specifically includes the following steps:

the method comprises the following steps: a NACA66 hydrofoil model with a sawtooth-shaped front edge is established on the basis of solidworks three-dimensional modeling software. The modeling of the prototype hydrofoil is realized by introducing a hydrofoil tangent plane contour curve and stretching, on the basis, the original point of a Cartesian coordinate system is fixed at the front edge point of the prototype hydrofoil, the positive x is along the flow direction, the positive y is along the spanwise direction, and the z axis can be determined by the right-hand rule. The hydrofoil span length is used as a y axis, the chord length is used as an x axis, the guide edge is a sawtooth-shaped leading edge reference line, a sine wave curve is established to be used as a guide line, and the modeling of the sawtooth-shaped leading edge hydrofoil is realized through the extension of a boss. The sine wave curve satisfies the following formula:

wherein: x is the number of_LEIs the abscissa of the waveform curve, A and λ are the amplitude and wavelength of the waveform, y is the spanwise coordinate, y is the wavelength₀Is the spanwise coordinate of the guide edge of the prototype hydrofoil. The built-up serrated hydrofoil leading edge is shown in figure 2.

Step two: and (2) carrying out grid division on the hydrofoil model with the sawtooth-shaped leading edge established in the step one, importing a divided fluid domain grid file into three-dimensional fluid simulation calculation software ANSYS CFX, simulating a flow winding field around the hydrofoil through the three-dimensional fluid simulation software, setting a speed inlet, a pressure outlet and a non-slip wall surface of the hydrofoil by adding boundary conditions, and carrying out numerical simulation calculation on the flow winding field of the hydrofoil through a Reynolds-time-average N-S equation (RANS) to obtain turbulence field data of the hydrofoil with the sawtooth-shaped leading edge.

Step three: carrying out post-processing analysis according to turbulent flow field data obtained by calculation and solution to obtain the intensity R and pressure pulsation SPL peak value of the surface vortex system structure of the hydrofoil, wherein the intensity and pressure pulsation satisfy the following formula:

SPL＝20log(p/p_ref)

wherein: where R in the rotation intensity R is a true eigenvector representing the rotation axis, ω is the vorticity, λ_ciIs the pseudo-time averaged angular velocity. P in the pressure pulsation sound pressure level SPL is the instantaneous pressure in the flow field, p_refIs a reference sound pressure.

Step four: the method comprises the steps of preprocessing the combination of wave amplitude and wave length of a convex knot at the front edge of the sawtooth-shaped hydrofoil and corresponding hydrodynamic performance data by adopting a Central Composite Design (CCD) method to obtain 9 sample points, and randomly generating 76 sample points uniformly covering the whole sample space by combining a Latin Hypercube Sampling (LHSD) method to improve the precision of a response surface model. Combining the 9 sample points and the 76 sample points yields all 85 sample points of the entire sample space.

The test points obtained first with the Central Composite Design (CCD) method consist of the following 3 parts:

1) one sample spatial center point (a, λ) ═ 25mm, 35mm, as the red square point in fig. 3;

2)2 × 2 sample space axial points (a, λ) ═ 25mm, 5mm), (25mm, 65mm), (10mm, 35mm), (40mm, 35mm), as in the green triangle in fig. 3;

3)2ⁿsample spatial factorial points (a, λ) ═ 10mm, 5mm), (40mm, 5mm), (10mm, 65mm), 40mm, 65mm), as in the blue square point in fig. 3.

In order to improve the accuracy of the response surface model, 76 sample points uniformly covering the whole sample space, such as dots in fig. 3, are randomly generated by combining a latin hypercube design (LHSD) method, and the total number of the sample points is 85.

Step five: n is n for the whole sample space obtained in step four₁+n₂And (3) carrying out response surface fitting on each sample point, namely fitting the relation between the target variable and the design variable through a functional relation to obtain a response surface model of the parameters A and lambda of the sawtooth structure, the vortex intensity R and the pressure pulsation SPL, which is called the response surface model for short. Fitting the relation between the target variable and the design variable through the functional relation, and fitting by adopting a 2-order polynomial, wherein the specific expression is as follows:

in the formula:fitting values of target variables; n is the number of design points; y is_iIs the ith design point; beta is a₀、β_i、β_ijAre regression coefficients.

Step six: based on the decision coefficient S²Sum root mean square difference σ_RMSEEvaluating the prediction capability of the response surface model obtained in the step five, and quantitatively evaluating the accuracy of the fitting response surface according to the following formula:

in the formula: z is a radical of_iObserved values for design points;is the response surface function fit value. According to S²And σ_RMSEIs defined as S²The closer to 1, σ_RMSEThe closer to 0, the higher the response surface fitting accuracy.

And drawing a 2-order polynomial response surface fitting goodness graph based on the sample space design point, wherein the abscissa is the calculation result of the target variable quantity value of the design point, and the ordinate is the predicted value of the target variable response surface of the design point.

Step seven: and if the accuracy of the fitting response surface quantitatively evaluated in the sixth step does not meet the expected value, reselecting the sample data points to establish a new polynomial response surface fitting function. Otherwise, further adopting a variance-based Sobol global sensitivity analysis method to establish sensitivity analysis of the independent variable on the target variable, wherein the sensitivity analysis formula is as follows:

S_i ^tot＝(V_i+V_iz)/V

in the formula: v_iIs the effect of the independent variable on the target variable; v_izFor the interaction of other independent variables; v is the influence of all independent variables on the target variable; s_i ^totThe global sensitivity is expressed, and the local sensitivity of the independent variable and the interaction of other independent variables are comprehensively considered. As shown in fig. 5, in the sensitivity analysis of 2 target variables R and SPL, it is found that the target variable is greatly influenced by the amplitude a, i.e. the sawtooth amplitude a has a large influence on the hydrodynamic performance of the intake foil.

Step eight: and respectively drawing a trend graph of the vortex intensity R and the pressure pulsation SPL along with the change of the sawtooth amplitude A and the wavelength lambda according to the polynomial response surface model meeting the fitting precision obtained in the step seven. And obtaining an independent variable value boundary corresponding to the optimal target variable by analyzing the trend graph, wherein the independent variable comprises a sawtooth amplitude A and a wavelength lambda. Analysis reveals that the pressure pulsation SPL gradually reaches a minimum value as the sawtooth amplitude a and the wavelength λ decrease. And the vorticity R gradually reaches a minimum as the sawtooth amplitude a and the wavelength λ increase.

Step nine: and based on the polynomial response surface model meeting the fitting precision obtained in the seventh step and the independent variable value boundary obtained in the eighth step, establishing a multi-objective optimization problem with the vortex intensity R and the pressure pulsation SPL as optimization targets, and solving and optimizing the established multi-objective optimization problem to obtain a Pareto optimal solution set formed by all possible solutions.

And realizing the proxy model optimization based on the polynomial response surface fitting function through the fourth step to the ninth step.

Step ten: the method comprises the steps of performing proxy model optimization on the structure size of the leading edge of the sawtooth-shaped hydrofoil through the fourth step to the ninth step to obtain a sawtooth-shaped parameter combination based on a Pareto optimal solution, namely, efficiently obtaining a combination of a convex node amplitude A of the leading edge of the sawtooth-shaped hydrofoil, which is 5mm, and a wavelength lambda, which is 50mm, so that the vortex intensity and the pressure pulsation value of the surface of the hydrofoil subjected to the optimization of the sawtooth-shaped leading edge meet the requirements of required working conditions, the lift drag coefficient of the hydrofoil with the sawtooth-shaped leading edge is superior to that of a smooth hydrofoil, and the flow separation of the surface of the hydrofoil is effectively inhibited or delayed, thereby improving the hydrodynamic performance of the hydrofoil with the sawtooth-shaped leading edge, and solving the technical problem of engineering in the field of flow control application.

The above detailed description is intended to illustrate the objects, aspects and advantages of the present invention, and it should be understood that the above detailed description is only exemplary of the present invention and is not intended to limit the scope of the present invention, and any modifications, equivalents, improvements and the like made within the spirit and principle of the present invention should be included in the scope of the present invention.