Optimization method of centrifugal fan impeller

Abstract

The invention discloses a centrifugal fan impeller optimization method, and belongs to the technical field of centrifugal fans. The method comprises the following steps: performing prototype analysis on a target centrifugal fan, and determining parameters and a range to be improved of the target centrifugal fan; aiming at a structure to be improved, a DOE method and a Latin hypercube design sampling method are adopted to generate a plurality of groups of parameter samples, the uniformity and comprehensiveness of the parameter samples are ensured, and Maximin sampling optimization is adopted to improve the uniformity of sample points; key parameters are found through principal component analysis to serve as design variables, and then final model parameters are determined through multiple optimization algorithms. According to the method, Bayesian optimization and multi-target grey wolf optimization are combined, the CFD calculation frequency is reduced, meanwhile, the optimization efficiency is improved, and the method is suitable for the pneumatic optimization problem with high calculation cost and can be widely applied to optimization design of rotating machines such as fans, turbines and compressors.

Description

Technical Field

[0001] The present invention relates to the technical field of centrifugal fans, and particularly to an optimization method for an impeller of a centrifugal fan. Background Art

[0002] Accelerating the energy consumption mainly based on non-fossil energy and natural gas means that the proportion of fossil energy consumption needs to be significantly reduced. The attention to the development of centrifugal fans towards low energy consumption and high efficiency has gradually increased. Optimizing and modifying the fan impeller, as the main means affecting the flow characteristics of the fan, is conducive to improving the aerodynamic performance of the fan and ensuring the rationality of the fan structure. Although traditional intelligent optimization algorithms (such as genetic algorithms, particle swarm algorithms, etc.) have certain global search capabilities, they often have a slow convergence speed and are prone to falling into local optima in high-dimensional complex design spaces, resulting in low optimization efficiency; for multi-objective optimization problems (such as simultaneously optimizing the fan efficiency and static pressure), there is still a lack of effective guarantee in terms of the distribution and balance of solutions, and it is difficult to achieve a reasonable trade-off between performance indicators; as the main evaluation means in the optimization process, the high computational cost of CFD simulation restricts the in-depth exploration and iteration of large-scale parameter spaces. Under this background, developing an intelligent method with both global search capabilities and computational efficiency, which can achieve multi-objective high-performance optimization under limited resource conditions, has become an important direction in the optimization research of centrifugal fans. Summary of the Invention

[0003] Aiming at the deficiencies of the existing technology, the purpose of the present invention is to provide an optimization method for an impeller of a centrifugal fan.

[0004] The purpose of the present invention is achieved through the following technical solutions: An optimization method for an impeller of a centrifugal fan, comprising the following steps:

[0005] Conduct a prototype analysis on the target centrifugal fan, and analyze the aerodynamic performance of the fan based on fluid mechanics theory and simulation technology (CFD) to determine the important geometric parameters affecting the fan performance;

[0006] For the important geometric parameters, use the design of experiment (DOE, Design of Experiment) method to generate multiple groups of sample parameters, and based on the Latin hypercube sampling (LHS) method, ensure that the sample parameters are reasonably distributed within the entire value range of the optimization variables to ensure the uniformity and comprehensiveness of the optimization search; based on the generated multiple groups of sample parameters, optimize the sampling of the sample parameters through Maximin to improve the uniformity of the sample points;

[0007] According to the optimized sample parameters of each group, use CFD to simulate and calculate the performance indicators of the fan (static pressure, fan efficiency, pressure distribution, flow loss, etc.), and construct a fan optimization database;

[0008] Based on the fan optimization database, principal component analysis (PCA) is used to evaluate the contribution degrees of various optimization variables. The importance is determined by calculating the variance of each principal component. A variance threshold is set, and the principal components with variances greater than the threshold are selected and retained as the variables that significantly affect the fan performance, while the variables with small effects are excluded, so as to determine the final set of optimization variables, reduce the computational amount, and improve the optimization efficiency;

[0009] Bayesian optimization (BO) is used for intelligent search. Based on the set of optimization variables, the optimal solution is found with the least amount of CFD calculations; within the search space after Bayesian optimization is completed, multi-objective grey wolf optimization (MOGWO) is used for fine optimization; the Pareto solution set is maintained to ensure the balance of multi-objective optimization. After optimization is completed, the Pareto front is plotted, the trade-off relationship between fan efficiency and static pressure is analyzed, the optimal design parameters are extracted, and the effectiveness of the optimization scheme is verified through CFD simulation. Finally, an optimized scheme for a high-performance centrifugal fan is obtained.

[0010] Further, the prototype analysis of the target centrifugal fan includes:

[0011] Based on fluid mechanics theory, theoretical analysis of the fan is carried out to determine the factors affecting the fan performance, where the fan performance includes fan efficiency and static pressure; CFD simulation technology is used to simulate the flow field of the fan to obtain the flow field characteristics (such as velocity distribution, pressure gradient, turbulence structure, etc.) of the fan; through global sensitivity analysis, the parameters with sensitivity indices greater than the preset threshold are used as important geometric parameters affecting the fan performance, and the important geometric parameters include blade shape, blade angle distribution, hub diameter, blade spacing, and front and rear disc distances.

[0012] Further, the intelligent search using Bayesian optimization includes:

[0013] Bayesian optimization uses Gaussian process regression (GPR) as a surrogate model to establish an approximate model of the CFD results, and selects the optimal search point through the expected improvement (EI) acquisition function, gradually narrowing the search space and improving the optimization efficiency.

[0014] Further, the fine optimization using multi-objective grey wolf optimization includes:

[0015] The high-performance sample points screened by Bayesian optimization are used as the initial population of the multi-objective grey wolf, and the optimal individuals are screened by non-dominated sorting (Pareto Sorting). During the optimization process, the fan efficiency and static pressure of the population individuals are calculated as fitness values, and the population position is updated through the grey wolf optimization hunting mechanism, where the leader wolf, secondary leader wolf, and third-level leader wolf are respectively selected from the Pareto front solution set to ensure the global and local convergence capabilities of the search.

[0016] The present invention also provides an electronic device, including a memory and a processor, where the memory is coupled to the processor. Among them, the memory is used to store program data, and the processor is used to execute the program data to implement the optimization method of a centrifugal fan impeller.

[0017] The present invention also provides a computer-readable storage medium, on which a computer program is stored, and when the program is executed by a processor, it implements the optimization method of a centrifugal fan impeller.

[0018] The beneficial effects of the present invention are as follows: The present invention combines Bayesian optimization with multi-objective grey wolf optimization (MOGWO), reduces the number of CFD calculations while improving the optimization efficiency, is applicable to pneumatic optimization problems with high computational costs, and can be widely applied to the optimization design of rotating machinery such as fans, turbines, and compressors. Description of the Drawings

[0019] Figure 1 is a flow chart of the present invention;

[0020] Figure 2 is a schematic diagram of the impeller structure;

[0021] Figure 3 is a comparison cloud chart of the velocity before and after optimization;

[0022] Figure 4 is a comparison cloud chart of the pressure before and after optimization. Detailed Embodiments

[0023] Here, the exemplary embodiments will be described in detail, and the examples are shown in the drawings. When the following description refers to the drawings, unless otherwise indicated, the same numbers in different drawings represent the same or similar elements. The embodiments described in the following exemplary embodiments do not represent all embodiments consistent with the present invention. On the contrary, they are only examples of devices and methods consistent with some aspects of the present invention as detailed in the appended claims.

[0024] As Figure 1 shown, the embodiment of the present invention provides an optimization method for a centrifugal fan impeller, including the following steps:

[0025] (1) Prototype analysis and parameter determination: As Figure 2 shown, it is the impeller structure of the prototype fan. When optimizing the design of the centrifugal fan, it is first necessary to conduct an in-depth analysis of the prototype fan to clarify key parameters such as its aerodynamic performance and energy efficiency indicators. Specifically, it includes:

[0026] Theoretical analysis: Based on fluid mechanics theory, determine the main factors affecting the fan efficiency and pressure characteristics. The outer diameter R2 of the impeller determines the linear velocity of the fluid at the end of the impeller and is the core factor affecting the static pressure head; the inner diameter R1 of the impeller affects the inlet linear velocity and the suction capacity of the impeller, etc.; the outlet installation angle β of the impeller affects the movement direction of the fluid and the magnitude of the centrifugal force; the number of blades directly affects the width of the blade passage and the guiding ability.

[0027] Numerical simulation: Using CFD simulation technology, conduct steady-state and transient flow field calculations on the prototype fan, and analyze the flow characteristics, pressure distribution, turbulent structure, secondary flow loss, etc. of the internal air flow. Take cross-sections at different blade heights (h) along the axial direction of the centrifugal fan impeller for flow field analysis, and take 0.8h, 0.5h, and 0.2h respectively (the 0.8h cross-section is close to the inlet of the centrifugal fan impeller). At 0.8h, the pressure distribution is asymmetric, especially the pressure gradient at the blade outlet is significant; the pressure increase at the blade outlet at 0.5h is reduced; the 0.2h cross-section close to the rear disc shows a larger low-pressure area, indicating a lower kinetic energy in this area.

[0028] In the embodiment, through the analysis of theory and numerical simulation, it is obtained that the four parameters to be initially modified can be the inner diameter R1 of the impeller, the outer diameter R2 of the impeller, the outlet installation angle β of the impeller, and the blade thickness θ.

[0029] (2) Using the Latin hypercube design in the DOE method, take the four parameters of the inner diameter R1 of the impeller, the outer diameter R2 of the impeller, the outlet installation angle β of the impeller, and the blade thickness θ as input variables to generate multiple sets of sample parameter data containing different parameter combinations. Each set of data represents a possible fan design scheme.

[0030] (3) Adopt Maximin sampling optimization to ensure the maximization of the minimum distance between sample points, improve the sampling uniformity, and prevent the over-aggregation of sample points. Calculate the Euclidean distance matrix of all sample points, adjust the positions of the sample points, and make them evenly cover the entire search space. The four centrifugal fan design parameters selected according to the above process are used as sample space variables, respectively:

[0031] The blade outlet angle β, the inner diameter R1 of the impeller, the outer diameter R2 of the impeller, and the blade thickness θ.

[0032] Each set of sample points is composed of the above four variables and can be represented as a 4D vector:

[0033] X i = [βi , R1 i , R2 i , θ i .

[0034] Since the dimensions of each variable are different, directly calculating the Euclidean distance may lead to misjudgment due to scale differences. Therefore, it is necessary to normalize the original sample data. The normalization formula is as follows:

[0035]

[0036] Where, X i,k is the original value of the k-th variable in the i-th sample; min(X k ), max(X k ) are respectively the minimum and maximum values of the k-th variable in all samples; is the normalized value.

[0037] Calculate the Euclidean distance between any two sample points for the normalized sample set:

[0038]

[0039] The above process is executed for all sample pairs (i, j), and a symmetric distance matrix D of n×n is constructed.

[0040] Where, D i,j = D j,i, represents the Euclidean distance between the i-th sample and the j-th sample; D i,i = 0 indicates that the distance between a sample and itself is zero.

[0041] Finally, it is calculated that: D min = 0.341.

[0042] It shows that in the four-dimensional parameter space after normalization, the minimum distance between any two points is 0.341.

[0043] In order to reduce the complexity of the optimization calculation, the principal component analysis method is used to perform dimensionality reduction analysis on the data. During the principal component analysis process, the contribution degree of each parameter to the fan performance index is calculated, and the final optimization variables are determined. Finally, the three parameters of the impeller inner diameter R1, the impeller outer diameter R2, and the impeller outlet installation angle β are selected as the final variables. Table 1 shows 45 groups of sample parameter data generated with the impeller inner diameter R1, the impeller outer diameter R2, and the impeller outlet installation angle β as the final variables.

[0044] Table 1

[0045] Serial number R1 (mm) β(°) R2 (mm) 1 180.73 19.78 83.85 2 180.73 20.77 81.26 3 180.73 21.76 78.75 4 182.23 22.29 78.53 5 180.87 21.52 79.53 6 182.59 20.93 82.52 … … … … 43 182.23 20.61 83.06 44 181.12 19.88 83.96 45 181.98 19.27 82.83

[0046] (4) To improve the efficiency of multi-objective optimization of the fan, this paper introduces the Bayesian Optimization (BO) method, which is used to intelligently select candidate points with the greatest potential for performance improvement based on the Gaussian Process Regression (GPR) model, thereby reducing the number of CFD simulations. First, using the existing 45 groups of CFD simulation data, GPR surrogate models for static pressure (Ps) and volume flow rate (V) are trained respectively. On this basis, the Expected Improvement (EI) acquisition function is used to score 100 groups of candidate samples and evaluate their potential for performance improvement compared to the current optimal solution. The EI is defined as follows:

[0047] EI(x) = E[maxf(x) - f * , 0)];

[0048] where, f * is the maximum static pressure value, and f(x) is the predicted value of the candidate point under the surrogate model. Its analytical solution can be expressed under the Gaussian process assumption as:

[0049]

[0050] where, μ(x) and σ(x) are the predicted mean and standard deviation of point x respectively, f * is the optimal objective value in the current training samples, φ(Z) and are the cumulative distribution function and probability density function of the standard normal distribution respectively, and ξ is the exploration factor, usually taking the value of 0.01. The predicted results of a candidate point x are μ(x) = 3381, σ(x) = 1, f * = 3491, and it can be calculated that Z = -110.01. Since Z is extremely small and φ(Z) ≈ 0, then EI(x) ≈ 0. This indicates that the predicted value of this candidate point is much lower than the current optimal value and has almost no possibility of performance improvement. Therefore, it should not be preferentially selected for CFD calculation.

[0051] By calculating the EI values of all candidate points and selecting the top 10 groups of points for real CFD simulations, the training set is updated and the accuracy of the surrogate model in the high-performance region is improved. To construct a representative and diverse initial population of MOGWO, subset optimization is performed on the top 50 high-potential samples with EI values in combination with the Maximin sampling strategy to maximize the minimum distance between population sample points. Finally, 20 groups of parameters are selected to initialize the MOGWO population. These points cover the directions of the maximum static pressure and the maximum flow rate, which helps MOGWO to carry out multi-objective optimization search in the high-performance region. The 20 groups of data shown in Table 2 are the initial population of multi-objective grey wolf optimization.

[0052] Table 2

[0053] Serial number R1 (mm) β(°) R2 (mm) 1 183.36 17.17 80.19 2 183.06 17.47 82.28 3 185.14 24.32 83.91 4 180.5 24.17 73.17 5 186.1 21.14 72.26 6 182.58 18.33 90.18 … … … … 18 185.93 22.06 77.24 19 184.26 18.84 78.7 20 181.02 25.49 83.76

[0054] (5) In the optimization of the fan, 20 groups of high-potential search points provided by Bayesian optimization (BO) are used as the initial population of multi-objective grey wolf optimization (MOGWO) to optimize the static pressure (P) and efficiency (η) of the fan. First, based on the population provided by BO, each individual consists of the inner diameter of the impeller (R1), the outer diameter of the impeller (R2), and the installation angle of the impeller outlet (β), and its fitness value is calculated, that is, the predicted values of static pressure and efficiency. The Gaussian process regression (GPR) surrogate model is used for preliminary evaluation, and only some key individuals are subjected to real CFD calculations to reduce the computational amount and continuously optimize the surrogate model. Subsequently, in the MOGWO iteration process, the α (leader wolf), β (secondary wolf), and δ (third-rank wolf) individuals with the optimal static pressure and efficiency in the current population are selected, and the positions of the remaining individuals are dynamically adjusted using the hunting mechanism to make them approach the optimal solution. Taking a common individual in the population as an example, the position update process in one round of iteration is demonstrated. The selected individual number is the 6th, and its original design parameters are:

[0055] X i = [R1, R2, β] = [183.03, 80.18, 22.83].

[0056] In this round of iteration, according to the principle of the maximum static pressure Ps, the maximum efficiency η, and the balance of the two objectives, three "leader wolf" individuals are selected as the reference update targets, specifically as follows:

[0057] α individual (maximum static pressure): x α = [187.00, 87.08, 22.36];

[0058] β individual (maximum efficiency): x β = [183.06, 82.28, 17.47];

[0059] δ individual (compromise between static pressure and efficiency): x δ = [183.36, 80.19, 17.17].

[0060] The search factor in the current iteration step is set to α = 1.5, and random numbers are generated (taking the α direction as an example):

[0061]

[0062] Calculate the control parameters:

[0063] A1 = 2aγ1 - a = 0.3, C1 = 2γ2 = 1.4.

[0064] Taking the α individual as the guiding direction, calculate:

[0065] D α = |C1·X α - X i | = [78.77, 41.73, 8.47];

[0066] X1 = X α - A1·D α = [163.37, 74.56, 19.82].

[0067] Repeat the steps to calculate the β direction and the δ direction. The final new individual position is:

[0068]

[0069] While ensuring the optimization directionality, this update mechanism takes into account the exploration and diversity of the design space, thus effectively promoting the population to converge to the Pareto front, providing a solid foundation for the subsequent extraction of multi-objective optimal solutions and the improvement of fan performance.

[0070] Subsequently, for the population generated in each iteration, the current Pareto optimal solution set is extracted through non-dominated sorting (Pareto Sorting), and the crowding distance is used to maintain the distribution uniformity of its solution set. After the optimization is terminated, a performance comparison and analysis of the final Pareto front is carried out, and a design scheme that shows balance between static pressure and efficiency or has engineering significance is selected as the recommended solution for the optimization of the fan structure parameters.

[0071] The final optimal data obtained after optimization is: R1 = 185.8, R2 = 74.72, β = 25.57.

[0072] Figure 3 、 Figure 4 Are the velocity contour maps and pressure contour maps before and after optimization respectively. From Figure 3 It can be seen that the gas flow velocity in the optimized fan is slightly greater than that in the prototype fan, which can reduce the turbulent loss and pressure loss of the flow and reduce the occurrence of flow separation phenomena. From Figure 4 It can be seen that the total pressure of the optimized fan is greater than that of the prototype fan, and the static pressure distribution is also more uniform after the flow is fully developed, which improves the fan performance and working efficiency.

[0073] The embodiment of the present invention also provides an electronic device, including a memory and a processor, the memory is coupled to the processor; wherein, the memory is used to store program data, and the processor is used to execute the program data to implement the optimization method of a centrifugal fan impeller described above.

[0074] An embodiment of the present invention also provides a computer-readable storage medium, on which a computer program is stored, and when the program is executed by a processor, the optimized method for a centrifugal fan impeller described above is implemented.

[0075] The computer-readable storage medium may be an internal storage unit of any device with data processing capabilities described in any of the foregoing embodiments, such as a hard disk or a memory. The computer-readable storage medium may also be any device with data processing capabilities, such as a plug-in hard disk, a Smart Media Card (SMC), an SD card, a Flash Card, etc. equipped on the device. Further, the computer-readable storage medium may also include both an internal storage unit of any device with data processing capabilities and an external storage device. The computer-readable storage medium is used to store the computer program and other programs and data required by any device with data processing capabilities, and may also be used to temporarily store data that has been output or will be output.

[0076] After considering the specification and practicing the content disclosed herein, those skilled in the art will readily think of other embodiments of the present application. The present application is intended to cover any variations, uses, or adaptations of the present application, which follow the general principles of the present application and include common general knowledge or conventional technical means in the technical field not disclosed in the present application. The specification and the embodiments are only regarded as exemplary.

[0077] It should be understood that the present application is not limited to the exact structure described above and shown in the drawings, and various modifications and changes can be made without departing from its scope.

Claims

1. An optimization method for the impeller of a centrifugal fan, characterized in that, The steps are as follows: Conduct a prototype analysis on the target centrifugal fan, analyze the aerodynamic performance of the fan based on fluid mechanics theory and simulation technology to determine the important geometric parameters affecting the fan performance; For the important geometric parameters, use the Design of Experiments (DOE) method to generate multiple groups of sample parameters, and based on the Latin Hypercube Sampling method, ensure that the sample parameters are reasonably distributed within the entire value range of the optimization variables; Based on the generated multiple groups of sample parameters, sample and optimize the sample parameters through Maximin to improve the uniformity of the sample points; According to the optimized groups of sample parameters, use CFD simulation to calculate the performance indicators of the fan and construct a fan optimization database; Based on the fan optimization database, use principal component analysis to evaluate the contribution degree of each optimization variable, determine its importance by calculating the variance of each principal component, set a variance threshold, screen out the principal components with variances greater than the threshold, retain them as variables that significantly affect the fan performance, and eliminate variables with small effects, thereby determining the final set of optimization variables; Use Bayesian optimization for intelligent search, and based on the set of optimization variables, find the optimal solution with the least amount of CFD calculations; Within the search space after completing Bayesian optimization, use multi-objective grey wolf optimization for fine optimization; Maintain the Pareto solution set to ensure the balance of multi-objective optimization. After optimization, plot the Pareto front, analyze the trade-off relationship between fan efficiency and static pressure, extract the optimal design parameters, and verify the effectiveness of the optimization scheme through CFD simulation. Finally, obtain an optimized scheme for a high-performance centrifugal fan.

2. The optimization method of a centrifugal fan impeller according to claim 1, characterized in that, The prototype analysis of the target centrifugal fan includes: Conduct a theoretical analysis of the fan based on fluid mechanics theory to determine the factors affecting the fan performance, where the fan performance includes fan efficiency and static pressure; Use CFD simulation technology to simulate the flow field of the fan to obtain the flow field characteristics of the fan; Through global sensitivity analysis, take the parameters with sensitivity indices greater than the preset threshold as the important geometric parameters affecting the fan performance, and the important geometric parameters include blade shape, blade angle distribution, hub diameter, blade spacing, and front and rear disc distances.

3. An optimization method for an impeller of a centrifugal fan according to claim 1, characterized in that, The intelligent search using Bayesian optimization includes: Bayesian optimization uses Gaussian process regression as a surrogate model to establish an approximate model of the CFD results, and selects the optimal search point through the expected improvement acquisition function to gradually narrow the search space.

4. An optimization method for an impeller of a centrifugal fan according to claim 1, characterized in that, The fine optimization using multi-objective grey wolf optimization includes: Use the high-performance sample points screened by Bayesian optimization as the initial population of multi-objective grey wolves, and screen the optimal individuals through non-dominated sorting; During the optimization process, calculate the fan efficiency and static pressure of the population individuals as fitness values, and update the population position through the grey wolf optimization hunting mechanism, where the lead wolf, secondary lead wolf, and third-level lead wolf are respectively selected from the Pareto front solution set to ensure the global and local convergence capabilities of the search.

5. An electronic device, comprising a memory and a processor, characterized in that, The memory is coupled to the processor; wherein, the memory is used for storing program data, and the processor is used for executing the program data to implement an optimization method for an impeller of a centrifugal fan as described in any one of claims 1-4.

6. A computer-readable storage medium having a computer program stored thereon, characterized in that, When the program is executed by the processor, it implements an optimization method for an impeller of a centrifugal fan as described in any one of claims 1-4.

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