Blade-adjustable high-specific-speed mixed-flow pump blade optimization design method

Abstract

The invention belongs to the technical field of fluid machinery, and particularly relates to a blade-adjustable high-specific-speed mixed-flow pump blade optimization design method which comprises the following steps: S1, establishing an impeller optimization design model; s2, an impeller parametric modeling method; and S3, approximate model establishment and impeller parameter iterative optimization. According to the method, radial distribution of parameters such as two-dimensional section chord length and pitch angle is given, blade inlet and outlet edge shapes are determined, blade modeling is completed, impeller parameters are optimized on the basis of numerical calculation, machine learning and a numerical optimization algorithm, mixed-flow pump impeller design is conducted through the method, the hydraulic performance of a mixed-flow pump can be remarkably improved, and the service life of the mixed-flow pump is prolonged. Dependence on design experience of designers is reduced, and the method has the advantages of being high in design efficiency and low in cost.

Description

Technical Field

[0001] The invention relates to the technical field of fluid machinery, and in particular to a blade optimization design method for a high specific speed mixed flow pump with adjustable blades. Background Art

[0002] The specific speed of a mixed flow pump is usually between 300 and 600, and the head is within 10m to 20m. It is a type of pump between an axial flow pump and a centrifugal pump. The specific speed of an axial flow pump is usually greater than 600, but the high efficiency zone of the axial flow pump is relatively narrow, especially for axial flow pumps with a specific speed of about 650. The high efficiency zone is very close to the saddle zone. The performance of the water pump in the saddle zone has obvious instability. For the stable operation of the unit, the maximum head of the pump station is usually controlled below the saddle zone. In some pumping stations where the maximum head is too different from the design head, it is difficult for the axial flow pump to take into account both the design head and the maximum head requirements at the same time. For this reason, a number of high specific speed (specific speed greater than 600) mixed flow pumps have emerged, but there are still relatively few high specific speed mixed flow pump models available in China, and their design methods are still unclear, making it difficult to meet the needs of engineering applications.

[0003] The hub and rim sections of the blade-adjustable mixed-flow pump are both spherical. The existing mixed-flow pump design methods mainly include: grid conformal transformation method, twisted triangle method, cone surface development method and three-dimensional controllable velocity moment method. The grid conformal transformation method, twisted triangle method and cone surface development method are all direct problem designs. Their basic principle is to convert the radial blade cascade into an inline blade cascade for design and analysis after determining the blade axial plane diagram through conformal transformation. The inlet angle, outlet angle, wrap angle and other parameters of the blade at different blade heights are calculated through one-dimensional flow theory. The blade camber line is fitted by arc, b-spline and other curves and the thickness distribution is superimposed to construct the blade. However, the one-dimensional flow theory is too simple and has a large gap with the actual flow in the impeller. The design result is difficult to meet the design goal, and the shape of the blade camber line has not been optimized. The influence of the maximum camber position on the blade performance is ignored, and the blade itself has a large flow loss. The three-dimensional controllable velocity moment method belongs to the inverse problem design. By giving the impeller outlet circulation and the load distribution along the streamline direction, and assuming that the blade is tangent to the velocity vector, the blade shaping is completed through iteration. However, the load parameter selection along the streamline direction of this method is too blind, and the design efficiency is low, which is far inferior to directly using mature blade shapes with better performance. Therefore, we propose a blade optimization design method for high specific speed mixed flow pumps with adjustable blades to solve the above problems. Summary of the invention

[0004] 1. Technical issues to be solved

[0005] In view of the deficiencies in the prior art, the present invention provides a method for optimizing the blade design of a high specific speed mixed flow pump with adjustable blades, which solves the problems raised in the above-mentioned background technology.

[0006] (II) Technical solution

[0007] In order to achieve the above-mentioned purpose, the present invention specifically adopts the following technical solutions:

[0008] A blade optimization design method for a high specific speed mixed flow pump with adjustable blades comprises the following steps:

[0009] S1: Establishing an impeller optimization design model;

[0010] S2: Impeller parameter modeling method;

[0011] S3: Approximate model establishment and iterative optimization of impeller parameters.

[0012] Furthermore, the specific content of S1 is to determine the operating range of the mixed flow pump according to characteristic parameters such as maximum head, design head and average head. In addition to the design working condition, the impeller efficiency at the working point of small flow (high head) and large flow (low head) is taken into account, and the multi-objective problem is converted into a single-objective problem by a weighted method. The optimization objective is defined as:

[0013] maxη d =k1η1+k2η2+k3η3

[0014] Among them, η1, η2, η3 are the impeller efficiencies under low flow, design flow and high flow conditions respectively, and k1, k2 and k3 are weight factors. When optimizing the design, a larger weight is given to the frequently operated conditions of the pump, and a smaller weight is given to the less frequently operated conditions of the pump;

[0015] The impeller head change under the design flow rate should not be too large to ensure that the impeller specific speed before and after optimization is basically the same, and can meet the use requirements in engineering applications. The head change before and after the impeller optimization is constrained to be less than 0.1m. The head constraint is:

[0016] H ipR -0.1≤H ipH ≤H ipR +0.1

[0017] Among them, HipR and HipH are the impeller heads before and after optimization;

[0018] To ensure that the cavitation performance of the pump meets the design requirements, that is, the critical cavitation margin of the impeller is less than the critical cavitation margin NSPHre of the pump, the ratio of the low-pressure isosurface area of ​​the blade surface with a constraint pressure of (101325Pa-ρgNSPHre) to the blade area is less than the set value, and this value is about 12% which is more appropriate and can be further adjusted according to the calculation results;

[0019] The mixed flow pump impeller optimization model can be simplified as follows:

[0020]

[0021] Where RisoH is the ratio of the isosurface after chemical pressure (101325Pa-ρgNSPHre) to the leaf area.

[0022] Furthermore, the specific content of S2 is that after determining the impeller diameter D, the angle θ between the blade rotation center and the axis, and the hub ratio Dh / D isoaxial surface parameters, n flow surfaces are divided along the blade height direction in the axial projection diagram, and the annular blade cascade is converted into a plane blade cascade for modeling by the conformal transformation method. The conformal transformation formula is as follows:

[0023]

[0024] Where ξ is the horizontal coordinate of the plane blade cascade, ψ is the vertical coordinate of the plane blade cascade, χ is the radius of the rotation surface, γ is the angle between the flow surface and the axial direction, and φ is the angle in the circumferential direction of the blade;

[0025] The camber line and thickness distribution of the two-dimensional blade profile adopt the NACA4 series camber distribution and NACA66 thickness distribution respectively. The NACA4 series camber line is defined as:

[0026]

[0027] Among them: x / c is the relative coordinate in the chord direction, fmax is the maximum camber, p is the maximum camber position, and c is the chord length;

[0028] Determine the maximum camber position p of the airfoil, given the radial distribution of parameters such as chord length c / D, pitch angle φ and maximum camber ratio fmax / c, the chord-diameter ratio c / D of each section is linearly distributed along the radial direction, determined by given root and tip section c / D, the placement angle φ and maximum camber ratio fmax / c are distributed according to quadratic functions, determined by given root, mid-span and tip section φ and fmax / c, the maximum thickness adopts approximately equal strength distribution along the radial direction, determined by given maximum thickness of root and tip;

[0029] Projected into three-dimensional space by conformal transformation, the origin of space is set as the center of the spherical surface of the wheel rim, and the impeller rotation axis is located on the Z axis. The coordinates of each data point are (r*, β, z), and the flow length L of each radial section in the axial plane diagram is S Calculate as follows:

[0030]

[0031] Based on the flow length of each radial section calculated by the two-dimensional blade profile parameters, the shapes of the blade inlet and outlet edges are drawn in the axial plane diagram. The angle between the inlet and outlet edges of each radial section and the blade rotation centerline is calculated as follows:

[0032]

[0033] Where α1 is the angle between the inlet edge and the rotation centerline, α2 is the angle between the outlet edge and the rotation centerline, and r is the spherical radius of each radial section;

[0034] On the axial projection diagram, m positions are equally spaced along the flow direction in each radial section. The plane modeling of the two-dimensional blade is completed according to the determined chord-diameter ratio c / D, maximum camber position p, maximum thickness t and maximum camber ratio fmax / c. The stacking center xo of the two-dimensional blade is set to (0.4c~0.5c), and the upper arc point coordinates (x2D_u, y2D_u), the camber line coordinates (x2D_m, y2D_m) and the lower arc line coordinates (x2D_l, y2D_l) of the blade are calculated as follows:

[0035]

[0036] x2D_m(i,j)=x(i,j)-x0

[0037] y2D_m(i,j)=-(f(i,j))

[0038] According to the placement angle φ of each radial section, the two-dimensional blade is rotated to the corresponding angle. After rotation, the upper arc point coordinates (x2D_ur, y2D_ur), the camber line coordinates (x2D_mr, y2D_mr) and the lower arc line coordinates (x2D_lr, y2D_lr) of the blade are calculated as follows:

[0039]

[0040] The rotated two-dimensional blade profile coordinates are projected onto the three-dimensional spherical surface, and the leading edge of the blade is initially taken as the circumferential accumulation point of the blade, that is, the circumferential angle of the leading edge of the blade is 0. Taking the mid-arc as an example, the cylindrical coordinates of each data point on the mid-arc are calculated as follows (r*, β, z):

[0041]

[0042] β(i,j)=(x2D_mr(i,j)-x2D_mr(i,j-1)) / r * (i,j)+β(i,j-1)

[0043]

[0044] Where i represents the i-th radial section, j represents the j-th data point on each radial section, and x(j) is the ratio of the flow length of the j-th point to the total length;

[0045] Referring to the existing mixed flow pump model, the ratio x1 of the circumferential overlap point position to the blade chord length is selected, and the circumferential angle at each radial section x1 is obtained by interpolation of the circumferential angle distribution. The circumferential angle at the overlap center x1 is subtracted from the circumferential angle of each radial section data point to ensure that the circumferential angle at the circumferential overlap point is 0;

[0046] Considering the influence of the circumferential curvature of the blade, a quadratic function is used to fit the circumferential curvature angle of each radial section. The circumferential angle of the blade overlap point at the hub is taken as 0. The circumferential curvature angles at the mid-span and blade tip are given to describe the radial distribution of the curvature angle. The curvature of the blade toward the working surface is recorded as positive curvature, and the curvature toward the back surface is recorded as negative curvature.

[0047] Generate corresponding functions or scripts through programming software such as Python and Matlab to realize automatic calculation of the above steps, which is convenient for calling during optimization design.

[0048] Furthermore, the two-dimensional blade profile stacking point is located at 0.4 to 0.5 times the blade chord length.

[0049] Furthermore, when the maximum camber position p of the airfoil is close to the trailing edge, it is beneficial to improve the performance near large flow and low head, and when the maximum camber position p is close to the leading edge, it is more beneficial to improve the performance near small flow and high head. The maximum camber position can be determined according to operation requirements.

[0050] Furthermore, the specific content of S3 is to obtain sample data in the design space through optimized Latin hypercube sampling (OHLS), establish a sample library, and complete the numerical simulation of the impeller at each sample point through three-dimensional modeling software, meshing software and finite element analysis software. Considering that the flow components such as the rear guide vane have little effect on the performance of the upstream impeller, in order to improve the optimization efficiency, only single-channel calculation is performed on the impeller;

[0051] After obtaining enough sample points, Gaussian process regression (GPR) is used to fit the approximate relationship between the design variables and the optimization target. The hyperparameters of the GPR model include kernel function, basis function and standard deviation σ, etc. Bayesian optimization is used to determine the hyperparameter combination of the GPR model. Bayesian optimization is based on the data using Bayesian theorem to estimate the posterior distribution of the objective function, and selects the next sampled hyperparameter combination according to the distribution, which has a high hyperparameter optimization efficiency. Cross-validation is used to prevent overfitting during GPR model training, with 100 iterations and the minimum mean square error (MSE) as the hyperparameter update principle. In order to take into account the overall prediction accuracy of the model, the method of minimizing the upper confidence bound (UCB) is used to select the best parameter point from the iteration results. MSE is defined as

[0052]

[0053] The approximate model is solved by the multi-island genetic algorithm (MIGA) to obtain the optimal parameter combination, and the optimization results are further verified by numerical simulation methods. If the requirements are met, the optimization design is completed, otherwise the above steps are repeated.

[0054] (III) Beneficial effects

[0055] Compared with the prior art, the present invention provides a blade optimization design method for a high specific speed mixed flow pump with adjustable blades, which has the following beneficial effects:

[0056] 1. In the existing mixed flow pump design method, it is necessary to first determine the inlet and outlet edge positions of the blades in the axial plane diagram, and calculate the blade parameters of each radial section based on the determined axial plane diagram, but the selection of the inlet and outlet edge positions is relatively arbitrary. The fully parameterized high specific speed mixed flow pump blade optimization design method described in the present invention gives the radial distribution of parameters such as chord length and placement angle and projects them into three-dimensional space to complete the blade shaping. The radial distribution of parameters such as blade chord length has a larger adjustment space, and has the characteristics of diverse blade shapes, simple control, and intuitive and easy to understand.

[0057] 2. The fully parameterized high specific speed mixed flow pump blade optimization design method described in the present invention comprehensively considers the influence of the maximum arch position of the cross-sectional blade profile and the circumferential bend on the performance of the mixed flow pump impeller during the design, which is beneficial to improving the performance of the mixed flow pump impeller.

[0058] 3. The fully parameterized high specific speed mixed flow pump blade optimization design method described in the present invention combines machine learning, numerical simulation and intelligent optimization algorithm to automatically optimize the impeller design parameters, reducing the dependence on the design experience of researchers and having the advantages of high design efficiency and low cost. BRIEF DESCRIPTION OF THE DRAWINGS

[0059] Figure 1 Optimize the design flow chart for mixed flow pumps;

[0060] Figure 2 This is a schematic diagram of the axial projection of the impeller of a mixed flow pump;

[0061] Figure 3 It is a schematic diagram of blade parameters;

[0062] Figure 4 Schematic diagram of blade profile camber lines at different maximum camber positions;

[0063] Figure 5 Schematic diagram of leaf shape at different leaf heights;

[0064] Figure 6 This is a schematic diagram of the blade shape;

[0065] Figure 7 This is a schematic diagram of single-channel calculation;

[0066] Figure 8 This is a comparison chart of the external characteristics of the impellers of different schemes. DETAILED DESCRIPTION

[0067] The following will be combined with the drawings in the embodiments of the present invention to clearly and completely describe the technical solutions in the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0068] Example

[0069] like Figure 1-8 As shown, a blade optimization design method for a high specific speed mixed flow pump with adjustable blades is provided in one embodiment of the present invention, comprising the following steps:

[0070] S1: Establishing an impeller optimization design model;

[0071] S2: Impeller parameter modeling method;

[0072] S3: Approximate model establishment and iterative optimization of impeller parameters.

[0073] In this embodiment, the specific content of S1 is to determine the operating range of the mixed flow pump according to characteristic parameters such as maximum head, design head and average head. In addition to the design working condition, the impeller efficiency at the working point of small flow (high head) and large flow (low head) is taken into account, and the multi-objective problem is converted into a single-objective problem by a weighted method. The optimization target is defined as:

[0074] maxη d =k1η1+k2η2+k3η3

[0075] Among them, η1, η2, η3 are the impeller efficiencies under low flow, design flow and high flow conditions respectively, and k1, k2 and k3 are weight factors. When optimizing the design, a larger weight is given to the frequently operated conditions of the pump, and a smaller weight is given to the less frequently operated conditions of the pump;

[0076] The impeller head change under the design flow rate should not be too large to ensure that the impeller specific speed before and after optimization is basically the same, and can meet the use requirements in engineering applications. The head change before and after the impeller optimization is constrained to be less than 0.1m. The head constraint is:

[0077] H ipR -0.1≤H ipH ≤H ipR +0.1

[0078] Among them, HipR and HipH are the impeller heads before and after optimization;

[0079] To ensure that the cavitation performance of the pump meets the design requirements, that is, the critical cavitation margin of the impeller is less than the critical cavitation margin NSPHre of the pump, the ratio of the low-pressure isosurface area of ​​the blade surface with a constraint pressure of (101325Pa-ρgNSPHre) to the blade area is less than the set value, and this value is about 12% which is more appropriate and can be further adjusted according to the calculation results;

[0080] The mixed flow pump impeller optimization model can be simplified as follows:

[0081]

[0082] Where RisoH is the ratio of the isosurface after chemical pressure (101325Pa-ρgNSPHre) to the leaf area.

[0083] In this embodiment, the specific content of S2 is that after determining the impeller diameter D, the angle θ between the blade rotation center and the axis, and the hub ratio Dh / D isoaxial surface parameters, n flow surfaces are divided along the blade height direction in the axial plane projection diagram, and the annular cascade is converted into a plane cascade for modeling by the conformal transformation method. The conformal transformation formula is as follows:

[0084]

[0085] Where ξ is the horizontal coordinate of the plane blade cascade, ψ is the vertical coordinate of the plane blade cascade, χ is the radius of the rotation surface, γ is the angle between the flow surface and the axial direction, and φ is the angle in the circumferential direction of the blade;

[0086] The camber line and thickness distribution of the two-dimensional blade profile adopt the NACA4 series camber distribution and NACA66 thickness distribution respectively. The NACA4 series camber line is defined as:

[0087]

[0088] Among them: x / c is the relative coordinate in the chord direction, fmax is the maximum camber, p is the maximum camber position, and c is the chord length;

[0089] Determine the maximum camber position p of the airfoil, given the radial distribution of parameters such as chord length c / D, pitch angle φ and maximum camber ratio fmax / c, the chord-diameter ratio c / D of each section is linearly distributed along the radial direction, determined by given root and tip section c / D, the placement angle φ and maximum camber ratio fmax / c are distributed according to quadratic functions, determined by given root, mid-span and tip section φ and fmax / c, the maximum thickness adopts approximately equal strength distribution along the radial direction, determined by given maximum thickness of root and tip;

[0090] Projected into three-dimensional space by conformal transformation, the origin of space is set as the center of the spherical surface of the wheel rim, and the impeller rotation axis is located on the Z axis. The coordinates of each data point are (r*, β, z), and the flow length L of each radial section in the axial plane diagram isS Calculate as follows:

[0091]

[0092] Based on the flow length of each radial section calculated by the two-dimensional blade profile parameters, the shapes of the blade inlet and outlet edges are drawn in the axial plane diagram. The angle between the inlet and outlet edges of each radial section and the blade rotation centerline is calculated as follows:

[0093]

[0094] Where α1 is the angle between the inlet edge and the rotation centerline, α2 is the angle between the outlet edge and the rotation centerline, and r is the spherical radius of each radial section;

[0095] On the axial projection diagram, m positions are equally spaced along the flow direction in each radial section. The plane modeling of the two-dimensional blade is completed according to the determined chord-diameter ratio c / D, maximum camber position p, maximum thickness t and maximum camber ratio fmax / c. The stacking center xo of the two-dimensional blade is set to (0.4c~0.5c), and the upper arc point coordinates (x2D_u, y2D_u), the camber line coordinates (x2D_m, y2D_m) and the lower arc line coordinates (x2D_l, y2D_l) of the blade are calculated as follows:

[0096]

[0097] x2D_m(i,j)=x(i,j)-x0

[0098] y2D_m(i,j)=-(f(i,j))

[0099] According to the placement angle φ of each radial section, the two-dimensional blade is rotated to the corresponding angle. After rotation, the upper arc point coordinates (x2D_ur, y2D_ur), the camber line coordinates (x2D_mr, y2D_mr) and the lower arc line coordinates (x2D_lr, y2D_lr) of the blade are calculated as follows:

[0100]

[0101] The rotated two-dimensional blade profile coordinates are projected onto the three-dimensional spherical surface, and the leading edge of the blade is initially taken as the circumferential accumulation point of the blade, that is, the circumferential angle of the leading edge of the blade is 0. Taking the mid-arc as an example, the cylindrical coordinates of each data point on the mid-arc are calculated as follows (r*, β, z):

[0102]

[0103] β(i,j)=(x2D_mr(i,j)-x2D_mr(i,j-1)) / r * (i,j)+β(i,j-1)

[0104]

[0105] Where i represents the i-th radial section, j represents the j-th data point on each radial section, and x(j) is the ratio of the flow length of the j-th point to the total length;

[0106] Referring to the existing mixed flow pump model, the ratio x1 of the circumferential overlap point position to the blade chord length is selected, and the circumferential angle at each radial section x1 is obtained by interpolation of the circumferential angle distribution. The circumferential angle at the overlap center x1 is subtracted from the circumferential angle of each radial section data point to ensure that the circumferential angle at the circumferential overlap point is 0;

[0107] Considering the influence of the circumferential curvature of the blade, a quadratic function is used to fit the circumferential curvature angle of each radial section. The circumferential angle of the blade overlap point at the hub is taken as 0. The circumferential curvature angles at the mid-span and blade tip are given to describe the radial distribution of the curvature angle. The curvature of the blade toward the working surface is recorded as positive curvature, and the curvature toward the back surface is recorded as negative curvature.

[0108] Generate corresponding functions or scripts through programming software such as Python and Matlab to realize automatic calculation of the above steps, which is convenient for calling during optimization design.

[0109] In this embodiment, the position of the two-dimensional blade profile overlap point is 0.4 to 0.5 times the blade chord length.

[0110] In this embodiment, when the maximum camber position p of the airfoil is close to the trailing edge, it is beneficial to improve the performance near large flow and low head. When the maximum camber position p is close to the leading edge, it is more beneficial to improve the performance near small flow and high head. The maximum camber position can be determined according to the operation requirements.

[0111] In this embodiment, the specific content of S3 is to obtain sample data in the design space through optimized Latin hypercube sampling (OHLS), establish a sample library, and complete the numerical simulation of the impeller at each sample point through three-dimensional modeling software, meshing software and finite element analysis software. Considering that the flow components such as the rear guide vane have little effect on the performance of the upstream impeller, in order to improve the optimization efficiency, only a single-channel calculation is performed on the impeller;

[0112] After obtaining enough sample points, Gaussian process regression (GPR) is used to fit the approximate relationship between the design variables and the optimization target. The hyperparameters of the GPR model include kernel function, basis function and standard deviation σ, etc. Bayesian optimization is used to determine the hyperparameter combination of the GPR model. Bayesian optimization is based on the data using Bayesian theorem to estimate the posterior distribution of the objective function, and selects the next sampled hyperparameter combination according to the distribution, which has a high hyperparameter optimization efficiency. Cross-validation is used to prevent overfitting during GPR model training, with 100 iterations and the minimum mean square error (MSE) as the hyperparameter update principle. In order to take into account the overall prediction accuracy of the model, the method of minimizing the upper confidence bound (UCB) is used to select the best parameter point from the iteration results. MSE is defined as

[0113]

[0114] The approximate model is solved by the multi-island genetic algorithm (MIGA) to obtain the optimal parameter combination, and the optimization results are further verified by numerical simulation methods. If the requirements are met, the optimization design is completed, otherwise the above steps are repeated.

[0115] The present invention aims at the problem that the existing mixed flow pump impeller design method is inefficient and overly dependent on the experience of designers. A fully parameterized adjustable mixed flow pump impeller blade optimization design method is proposed. This method can be used to optimize the mixed flow pump blades in all parameters, thereby improving the impeller efficiency. Taking a mixed flow pump impeller with a specific speed of about 700 as an example, its design parameters include: speed n = 1200r / min, design flow Qd = 0.324m3 / s, design head Hd = 5.76m, the blade is adjustable, the water pump is mostly operated under large flow and low head conditions, and the cavitation margin requirement under the design flow condition is less than 8.08m.

[0116] According to the existing mixed flow pump model, the impeller diameter D = 0.3m, the hub diameter Dh = 0.15m, the number of blades Z = 3, the angle between the blade rotation centerline and the axis θ = 55°, and the specific parameters of the blade axial plane diagram are shown in Figure 2 .

[0117] Determine the pump impeller optimization function model. According to the pump operation data, while ensuring the efficiency at the design flow rate, give a higher weight to the efficiency at large flow conditions. Referring to relevant literature, the weighted efficiency weights k1, k2, and k3 in this example are 0.279, 0.406, and 0.315 respectively.

[0118] Refer to the relevant mixed flow pump model to determine the optimization parameters and value ranges. This example does not consider the influence of the circumferential bending of the blade. The specific parameters and value ranges are shown in the following table. The subscripts 0, 0.5 and 1 in the table correspond to the root, mid-span and tip sections respectively:

[0119] Table 1 Impeller design parameters and value ranges

[0120]

[0121] A total of 260 groups of samples were generated by optimizing the Latin hypercube algorithm. In order to prevent individual sample points from affecting the prediction accuracy, the points with excessive head deviation in the sample set were removed. The sample set was divided into a training set and a test set, of which 75% was used to train the approximate model and 25% was used to test the prediction effect of the approximate model. The Bayesian method was used to optimize the hyperparameters of the Gaussian process model. It can be seen from the optimization model that the optimization indicators mainly include weighted efficiency ηd, impeller head HipH and low pressure area ratio RisoH. The approximate functional relationship between the design parameters and each optimization index was established through the GPR model, and the determination coefficient R2 was introduced to evaluate the prediction accuracy of the model (the closer the determination coefficient R2 is to 1, the more accurate the prediction result is). The determination coefficient R2 of the GPR model prediction results for ηd, HipH and RisoH is required to be greater than 0.9, otherwise continue to add sample points. The correlation coefficient R2 of the prediction results of the GPR model is above 0.94. The approximate model established by solving the multi-island genetic algorithm is used to obtain the impeller parameter combination that meets the optimization model.

[0122] Based on the above embodiment, the final shapes of the blades at the maximum camber relative positions p=0.4, 0.5 and 0.6 are obtained, which are respectively recorded as F1, F2 and F3. The specific design parameters are shown in Table 2:

[0123] Table 2 Combination of impeller parameters after optimization

[0124]

[0125]

[0126] Figure 8The performance comparison of the impeller F0 obtained by the optimized schemes and the traditional design method is shown in the figure. Compared with F0, the impeller efficiency of the optimized model is improved in the flow range of 0.8Qd to 1.2Qd. The weighted efficiencies of the four schemes are 88.27%, 88.70%, 88.72% and 88.77%, respectively. The weighted efficiency of the optimized model is improved by about 0.5 percentage points. The impeller heads of the four models at the design flow rate are 5.76, 5.80, 5.79 and 5.76m, respectively. The head changes little, which meets the optimization design goal of improving efficiency and keeping the specific speed basically unchanged. Under the flow conditions of 0.8Qd, Qd and 1.2Qd, the hydraulic efficiency of the benchmark model F0 is 88.20%, 90.35% and 85.66% respectively. Compared with F0, under the flow conditions of 0.8Qd, Qd and 1.2Qd, the hydraulic efficiency of scheme F1 increases by 0.57, 0.35 and 0.41 percentage points respectively, the hydraulic efficiency of scheme F2 increases by 0.35, 0.33 and 0.70 percentage points respectively, and the hydraulic efficiency of scheme F3 increases by 0.20, 0.32 and 0.98 percentage points respectively. The efficiency of scheme F1 and scheme F3 differs by about 0.37 percentage points under the flow condition of 0.8Qd and by about 0.57 percentage points under the flow condition of 1.2Qd. For the mixed flow impeller design, the maximum efficiency of the impeller designed with different camber lines is not much different. The maximum camber position of the airfoil mainly affects the distribution range of the high-efficiency zone. When the maximum camber position of the airfoil is close to the trailing edge, it is beneficial to improve the performance near large flow and low head. When the maximum camber position is close to the leading edge, it is more beneficial to improve the performance near small flow and high head. For this research example, considering the impeller performance under different flow conditions, the maximum camber position p = 0.5 was finally selected.

[0127] Finally, it should be noted that the above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. Although the present invention has been described in detail with reference to the aforementioned embodiments, those skilled in the art can still modify the technical solutions described in the aforementioned embodiments or replace some of the technical features therein by equivalents. Any modification, equivalent replacement, improvement, etc. made within the spirit and principle of the present invention shall be included in the protection scope of the present invention.

Claims

1. A blade optimization design method for a high specific speed mixed flow pump with adjustable blades, characterized in that: The steps include: S1: Establishing an impeller optimization design model; S2: Impeller parameter modeling method; S3: Approximate model establishment and iterative optimization of impeller parameters.

2. The blade optimization design method for a high specific speed mixed flow pump with adjustable blades according to claim 1 is characterized by: The specific content of S1 is to determine the operating range of the mixed flow pump according to characteristic parameters such as maximum head, design head and average head. In addition to the design working condition, the impeller efficiency at the working point of small flow (high head) and large flow (low head) is taken into account, and the multi-objective problem is converted into a single-objective problem by a weighted method. The optimization target is defined as: maxi d =k1η1+k2η2+k3η3 Among them, η1, η2, η3 are the impeller efficiencies under low flow, design flow and high flow conditions respectively, and k1, k2 and k3 are weight factors. When optimizing the design, a larger weight is given to the frequently operated conditions of the pump, and a smaller weight is given to the less frequently operated conditions of the pump; The impeller head change under the design flow rate should not be too large to ensure that the impeller specific speed before and after optimization is basically the same, and can meet the use requirements in engineering applications. The head change before and after the impeller optimization is constrained to be less than 0.1m. The head constraint is: S.t.H ipR -0.1≤H ipH ≤H ipR +0.1 Among them, HipR and HipH are the impeller heads before and after optimization; To ensure that the cavitation performance of the pump meets the design requirements, that is, the critical cavitation margin of the impeller is less than the critical cavitation margin NSPHre of the pump initial setting, the ratio of the low-pressure isosurface area of ​​the blade surface with a constraint pressure of (101325Pa-ρgNSPHre) to the blade area is less than the set value; The mixed flow pump impeller optimization model can be simplified as follows: Where RisoH is the ratio of the isosurface after chemical pressure (101325Pa-ρgNSPHre) to the leaf area.

3. The blade optimization design method for a high specific speed mixed flow pump with adjustable blades according to claim 1, characterized in that: The specific content of S2 is that after determining the impeller diameter D, the angle θ between the blade rotation center and the axis, and the hub ratio Dh / D isoaxial surface parameters, n flow surfaces are divided along the blade height direction in the axial projection diagram, and the annular blade cascade is converted into a plane blade cascade for modeling by the conformal transformation method. The conformal transformation formula is as follows: Where ξ is the horizontal coordinate of the plane blade cascade, ψ is the vertical coordinate of the plane blade cascade, χ is the radius of the rotation surface, γ is the angle between the flow surface and the axial direction, and φ is the angle in the circumferential direction of the blade; The camber line and thickness distribution of the two-dimensional blade profile adopt the NACA4 series camber distribution and NACA66 thickness distribution respectively. The NACA4 series camber line is defined as: Among them: x / c is the relative coordinate in the chord direction, fmax is the maximum camber, p is the maximum camber position, and c is the chord length; Determine the maximum camber position p of the airfoil, given the radial distribution of parameters such as chord length c / D, pitch angle φ and maximum camber ratio fmax / c, the chord-diameter ratio c / D of each section is linearly distributed along the radial direction, determined by given root and tip section c / D, the placement angle φ and maximum camber ratio fmax / c are distributed according to quadratic functions, determined by given root, mid-span and tip section φ and fmax / c, the maximum thickness adopts approximately equal strength distribution along the radial direction, determined by given maximum thickness of root and tip; Projected into three-dimensional space by conformal transformation, the origin of space is set as the center of the spherical surface of the wheel rim, and the impeller rotation axis is located on the Z axis. The coordinates of each data point are (r*, β, z), and the flow length L of each radial section in the axial plane diagram is S Calculate as follows: Based on the flow length of each radial section calculated by the two-dimensional blade profile parameters, the shapes of the blade inlet and outlet edges are drawn in the axial plane diagram. The angle between the inlet and outlet edges of each radial section and the blade rotation centerline is calculated as follows: Where α1 is the angle between the inlet edge and the rotation centerline, α2 is the angle between the outlet edge and the rotation centerline, and r is the spherical radius of each radial section; On the axial projection diagram, m positions are equally spaced along the flow direction in each radial section. The plane modeling of the two-dimensional blade is completed according to the determined chord-diameter ratio c / D, maximum camber position p, maximum thickness t and maximum camber ratio fmax / c. The stacking center xo of the two-dimensional blade is set to (0.4c~0.5c), and the upper arc point coordinates (x2D_u, y2D_u), the camber line coordinates (x2D_m, y2D_m) and the lower arc line coordinates (x2D_l, y2D_l) of the blade are calculated as follows: x2D_m(i,j)=x(i,j)-x0 y2D_m(i,j)=-(f(i,j)) According to the placement angle φ of each radial section, the two-dimensional blade is rotated to the corresponding angle. After rotation, the upper arc point coordinates (x2D_ur, y2D_ur), the camber line coordinates (x2D_mr, y2D_mr) and the lower arc line coordinates (x2D_lr, y2D_lr) of the blade are calculated as follows: The rotated two-dimensional blade profile coordinates are projected onto the three-dimensional spherical surface, and the leading edge of the blade is initially taken as the circumferential accumulation point of the blade, that is, the circumferential angle of the leading edge of the blade is 0. Taking the mid-arc as an example, the cylindrical coordinates of each data point on the mid-arc are calculated as follows (r*, β, z): β(i,j)=(x2D_mr(i,j)-x2D_mr(i,j-1)) / r * (i,j)+β(i,j-1) Where i represents the i-th radial section, j represents the j-th data point on each radial section, and x(j) is the ratio of the flow length of the j-th point to the total length; Referring to the existing mixed flow pump model, the ratio x1 of the circumferential overlap point position to the blade chord length is selected, and the circumferential angle at each radial section x1 is obtained by interpolation of the circumferential angle distribution. The circumferential angle at the overlap center x1 is subtracted from the circumferential angle of each radial section data point to ensure that the circumferential angle at the circumferential overlap point is 0; Considering the influence of the circumferential curvature of the blade, a quadratic function is used to fit the circumferential curvature angle of each radial section. The circumferential angle of the blade overlap point at the hub is taken as 0. The circumferential curvature angles at the mid-span and blade tip are given to describe the radial distribution of the curvature angle. The curvature of the blade toward the working surface is recorded as positive curvature, and the curvature toward the back surface is recorded as negative curvature. Generate corresponding functions or scripts through programming software such as Python and Matlab to realize automatic calculation of the above steps, which is convenient for calling during optimization design.

4. The blade optimization design method for a high specific speed mixed flow pump with adjustable blades according to claim 3 is characterized by: The position of the two-dimensional blade profile stacking point is 0.4 to 0.5 times the blade chord length.

5. The blade optimization design method for a high specific speed mixed flow pump with adjustable blades according to claim 3 is characterized by: When the maximum camber position p of the airfoil is close to the trailing edge, it is beneficial to improve the performance near large flow and low head. When the maximum camber position p is close to the leading edge, it is more beneficial to improve the performance near small flow and high head. The maximum camber position can be determined according to operation requirements.

6. The blade optimization design method for a high specific speed mixed flow pump with adjustable blades according to claim 1, characterized in that: The specific content of S3 is to obtain sample data in the design space through optimized Latin hypercube sampling (OHLS), establish a sample library, and complete the numerical simulation of the impeller at each sample point through three-dimensional modeling software, meshing software and finite element analysis software. Considering that the flow components such as the rear guide vane have little effect on the performance of the upstream impeller, in order to improve the optimization efficiency, only single-channel calculation is performed on the impeller; After obtaining enough sample points, Gaussian process regression (GPR) is used to fit the approximate relationship between the design variables and the optimization target. The hyperparameters of the GPR model include kernel function, basis function and standard deviation σ, etc. Bayesian optimization is used to determine the hyperparameter combination of the GPR model. Bayesian optimization is based on the data using Bayesian theorem to estimate the posterior distribution of the objective function, and selects the next sampled hyperparameter combination according to the distribution, which has a high hyperparameter optimization efficiency. Cross-validation is used to prevent overfitting during GPR model training, with 100 iterations and the minimum mean square error (MSE) as the hyperparameter update principle. In order to take into account the overall prediction accuracy of the model, the method of minimizing the upper confidence bound (UCB) is used to select the best parameter point from the iteration results. MSE is defined as The approximate model is solved by the multi-island genetic algorithm (MIGA) to obtain the optimal parameter combination, and the optimization results are further verified by numerical simulation methods. If the requirements are met, the optimization design is completed, otherwise the above steps are repeated.

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