Large-flow centrifugal fan impeller optimization design method

Abstract

The invention discloses an optimization design method for a large-flow centrifugal fan impeller, and belongs to the field of centrifugal rotating machinery. The method mainly relates to impeller components and comprises a design part and an optimization part. In the design part, design parameters of the centrifugal fan impeller are finally obtained according to a series of calculation results and given parameters; in the optimization part, an MOEA / D optimization algorithm is adopted, a multi-target optimization problem is decomposed into a plurality of single-target sub-problems, and each sub-problem is defined by a weight vector. The algorithm initializes the population and allocates a solution to each sub-problem, and then iterative optimization is performed: neighbor sub-problems are selected, new individuals are generated through crossover and mutation, and the new individuals are used to update the optimal solution of the related sub-problems. According to the method, the fitness is evaluated by using a weighted summation method, and uniform distribution of a solution set on a Pareto leading edge is ensured. According to the method, the multi-target problem in the design process of the centrifugal fan impeller is effectively solved, and efficient and stable operation of the centrifugal fan in different use scenes is ensured.

Description

Technical Field

[0001] The invention relates to an optimization design method for a large-flow centrifugal fan impeller, and belongs to the field of centrifugal rotating fluid machinery. Background Art

[0002] With the increasing global awareness of environmental protection and energy efficiency, centrifugal fans and their impeller technology have also ushered in new development opportunities and challenges. As an indispensable and important equipment in the industrial, commercial and civil fields, centrifugal fans play a key role in air conditioning systems, ventilation engineering, air purification, exhaust gas treatment and other aspects. As a key component of a centrifugal fan, the main function of the impeller is to convert the mechanical energy of the drive motor into the kinetic energy and pressure energy of the gas. When the impeller rotates, it exerts centrifugal force on the incoming gas through the blades, so that the gas is thrown out along the radius of the impeller, and gains kinetic energy and pressure energy in the process. This is the fundamental reason why centrifugal fans can increase gas pressure and promote gas flow. Constructing a reliable optimization design method for centrifugal fan impellers is of great significance to the design of high-performance fans. A high-performance impeller can not only significantly improve the working efficiency of the fan and reduce energy loss, but also extend the service life of the equipment and reduce maintenance costs. However, the traditional single-objective optimization method is difficult to meet the problems between multiple design objectives at the same time, and the complex numerical simulation and optimization process requires a lot of computing resources, resulting in a long design cycle. Summary of the invention

[0003] In order to solve the problems existing in the prior art, the purpose of the present invention is to provide a method for optimizing the design of a large-flow centrifugal fan impeller based on the existing centrifugal fan design method, so as to improve the aerodynamic performance of the fan.

[0004] The technical solution adopted to achieve the purpose of the present invention is:

[0005] A method for optimizing the design of a large flow centrifugal fan impeller comprises the following steps:

[0006] Step 1: Given the target design parameters of the centrifugal impeller, including the design flow rate, speed, outlet diameter and impeller inlet density;

[0007] Step 2: Given the blade outlet installation angle β 2A ;

[0008] Step 3: Calculate the outlet circumferential velocity u2;

[0009] Step 4: Determine the inlet diameter D2;

[0010] Step 5: Determine the number of blades Z;

[0011] Step 6: Given the blade trailing edge thickness δ2, calculate the outlet absolute velocity component c 2r, and then determine the inlet width b1 and the outlet width b2;

[0012] Step 7: Calculate the inlet circumferential velocity u1;

[0013] Step 8: Calculate the inlet absolute velocity component c 1r ;

[0014] Step 9: Calculate the inlet blade installation angle β 1A ;

[0015] Step 10: Check the total pressure value ∆p;

[0016] Step 11: Adopt the MOEA / D optimization algorithm to finally obtain the optimal solution.

[0017] This method specifically includes the following steps:

[0018] An optimization design method for the impeller of a large-flow centrifugal fan, including the following steps:

[0019] Step 1. Given the design target parameters of the centrifugal impeller, including the design flow rate Q, rotational speed n, impeller outlet diameter D2, and impeller inlet density ρ in ;

[0020] Step 2. Given the blade outlet installation angle β 2A , generally, the blade outlet angle range of the backward impeller is 35~60°, preferably 38~42°;

[0021] Step 3. Calculate the outlet circumferential velocity u2, and the calculation formula is as follows:

[0022]

[0023] Step 4. Determine the inlet diameter D1, and the calculation formula is as follows:

[0024]

[0025] To this end, first calculate the flow coefficient φ

[0026]

[0027] Step 5. Determine the number of blades Z, and the calculation formula is as follows:

[0028]

[0029] Step 6. Given the blade trailing edge thickness δ2, combined with the result in Step 3, according to the empirical formula β 2A = 35~48°, C 2r / u2 = 0.21~0.25, calculate the outlet absolute velocity component c 2r, and then determine the inlet width b1 and the outlet width b2. The calculation formulas are as follows;

[0030]

[0031]

[0032] ,

[0033]

[0034] Among them, ∧ represents the hem of the blade, t2 is the pitch, σ is the tangential blade thickness, and τ2 is the outlet blockage coefficient;

[0035] Step 7: Calculate the inlet circumferential velocity u1. The calculation formula is as follows:

[0036]

[0037] Step 8: Calculate the inlet absolute velocity component c 1r , and the calculation formula is as follows:

[0038]

[0039] Among them, τ1 is the inlet blockage coefficient and τ2 is the outlet blockage coefficient

[0040] Step 9: Calculate the inlet blade installation angle β 1A , and the calculation formula is as follows:

[0041]

[0042]

[0043] Among them, β 1A represents the air flow angle, i represents the incidence angle, and i takes ±0~8°;

[0044] Step 10: Check the total pressure value ∆p. If the error is large, reselect the outlet installation angle β 2A and the number of blades Z. The checking formula is as follows:

[0045]

[0046]

[0047] It is judged whether the total pressure value is within the error range by whether ΔP - ΔP tf is less than 1%. If it exceeds the error range, reselect the outlet installation angle β 2A and the number of blades Z for checking.

[0048] According to steps 1 to 10, an initial model of an optimization design method for a large-flow centrifugal fan impeller can be obtained.

[0049] Step 11-1: Determine the key parameters, design space, and optimization objectives in the centrifugal impeller;

[0050] According to the flow separation and distortion generated in the direction of the impeller tip of the fan impeller, advance the key parameters: the control points of the hub line in the meridian plane of the impeller, the control points of the shroud line in the meridian plane, the leading edge endpoint of the impeller tip, the leading edge endpoint of the impeller root, the blade installation angle of the mid-arc line at the impeller tip, and the blade installation angle of the mid-arc line at the impeller root;

[0051] At the same time, clarify the objective functions f1(x), f2(x),.... f j (x), and adjust the initial values corresponding to the geometric parameters when the impeller has the optimal objective result;

[0052] Step 11-2: Use regular network sampling to standardize the value range of each objective function to the interval (0,1). The objective space is represented as an m-dimensional unit hypercube, and the center point of each grid cell is taken as the weight vector; divide each dimension into h equal parts, then there will be a total of h m grid points;

[0053] Select the midpoint of each grid cell as the weight vector, and its corresponding weight vector is:

[0054]

[0055] where m represents the number of objectives of the optimization problem, and i k is an integer from 0 to h−1, representing the index position on the kth dimension; then normalize the weight vector, and the specific formula is as follows:

[0056]

[0057] where w i ＇ is the normalized value, and w i is the original data value; organize the obtained data to obtain the initial sample library;

[0058] Step 11-3: For each weight vector w i ＇ , use the weighted summation model to construct a corresponding single-objective sub-problem:

[0059]

[0060] where w j represents the jth component of the weight vector w i ＇ ;

[0061] Step 11-4: For each sub-problem g i Randomly generate an initial solution x i , where the initial solution satisfies the boundary conditions of the decision variables; randomly generate an initial solution set P = {x1, x2, …, x N}), where N is the number of sub-problems; for each individual x i in the current population, calculate its fitness value g i on the corresponding sub-problem g i (x i |w i ＇ );

[0062] For each sub-problem g i Maintain an optimal solution w i * , that is, the best-known solution to this sub-problem;

[0063] Step 11-5: Determine the neighbor set B(i) of each sub-problem g i ; based on the sub-problems corresponding to the T closest weight vectors, where T is the neighborhood size parameter;

[0064] Calculate the Euclidean distance between each weight vector and store it in a distance matrix D, where D[i][j] represents the distance between w i and w j , and select the T closest ones as neighbors. The calculation formula is as follows:

[0065]

[0066] where m is the number of objective functions, create a neighborhood matrix N, where N[i][j] = 1 indicates that sub-problem g j belongs to the neighbor set of g i ; otherwise N[i][j] = 0;

[0067] For each sub-problem g i and its neighbor B(i), randomly select several parent individuals from the solutions corresponding to the sub-problems for crossover operations, and use the crossover operator in the genetic algorithm to combine the characteristics of the parent individuals to generate offspring individuals y;

[0068] Step 11-6: Insert the newly generated offspring y into the associated sub-problem g i and check whether it is better than the existing solution;

[0069] Determine whether the iteration process terminates by whether w i * is less than f j (y). If w i* <f j (y), then let w i * =f j (y), otherwise continue the iteration until the last round of optimization to generate the Pareto solution set, screen out the required optimal solution, generate the corresponding optimal model of the fan and calculate the optimization result.

[0070] Compared with the prior art, the beneficial effects of the present invention are as follows:

[0071] The method includes two parts: design and optimization. In the design part, the relevant parameters of the centrifugal impeller are given to determine the relevant parameters of the optimization objective; in the optimization part, based on the MOEA / D optimization algorithm, the multi-objective problem is decomposed into multiple single-objective sub-problems. Through iterative optimization, the best solutions of the relevant sub-problems are updated with new individuals to ensure the uniform distribution of the solution set on the Pareto front.

[0072] Given the design flow rate, rotational speed, outlet diameter, and inlet density of the centrifugal impeller; given the blade outlet installation angle; calculate the outlet circumferential velocity; calculate the inlet diameter; calculate the number of blades.

[0073] Given the blade trailing edge thickness; calculate the outlet absolute velocity component; calculate the inlet width; calculate the outlet width; calculate the inlet circumferential velocity; calculate the inlet absolute velocity component; calculate the inlet blade installation angle.

[0074] Check the total pressure value. If the error is large, reselect the outlet installation angle and the number of blades.

[0075] Determine the variation ranges of the control points of the impeller meridian hub line, the control points of the impeller meridian shroud line, the leading edge endpoints of the blade tip, the leading edge endpoints of the blade root, the blade installation angle of the blade tip mean camber line, and the blade installation angle of the blade root mean camber line.

[0076] Decompose the multi-objective optimization problem into multiple single-objective sub-problems, and each sub-problem is defined by a weight vector. The algorithm initializes the population and assigns solutions to each sub-problem, and then performs iterative optimization: select neighbor sub-problems, generate new individuals through crossover and mutation, and update the best solutions of the relevant sub-problems with the new individuals to obtain the optimal solution.

[0077] MOEA / D solves the multi-objective optimization problem by decomposing it into multiple sub-problems, can optimize multiple objectives simultaneously, and has higher computational efficiency and convergence speed. This method can not only significantly improve the overall performance of the fan, but also promote the realization of the environmental protection and energy conservation goals, meeting the needs of modern society for efficient, low-noise, and reliable equipment. Description of the Drawings

[0078] Figure 1 It is a flowchart of an optimization design method for the impeller of a large-flow centrifugal fan according to an embodiment of the present invention.

[0079] Figure 2 It is the structural parameter diagram of the fan impeller designed in the embodiment of the present invention.

[0080] Figure 3 It is the distribution diagram of the sample performance parameters after sampling in the embodiment of the present invention.

[0081] Figure 4 It is the sampling model diagram in the embodiment of the present invention.

[0082] Figure 5 It is the blade fitting curve diagram in the embodiment of the present invention.

[0083] Figure 6 It is the performance curve diagram in the embodiment of the present invention. Specific implementation method

[0084] Embodiment: The design process of a certain centrifugal fan is as follows:

[0085] Given the design target parameters of the centrifugal impeller, including the design flow rate Q = 5 kg / s, the rotational speed n = 2950 rpm, the impeller outlet diameter D2 = 0.651 m, and the impeller inlet density ρ in = 1.2 kg / m 3 ;

[0086] Given the blade outlet installation angle β 1A = 45°;

[0087] Calculate the outlet circumferential velocity u2:

[0088]

[0089] It is calculated that u2 = 100.5545 m / s.

[0090] Determine the inlet diameter D1:

[0091]

[0092] It is calculated that D1 = 0.4138 m.

[0093] Therefore, first calculate the flow coefficient φ

[0094]

[0095] It is calculated that φ = 0.1509.

[0096] Determine the number of blades Z:

[0097]

[0098] It is calculated that Z = 15.

[0099] Calculate the component velocity c of the absolute velocity at the outlet 2r , and then determine the inlet width b1 and the outlet width b2:

[0100]

[0101]

[0102]

[0103]

[0104]

[0105] The calculated component velocity c of the absolute velocity at the outlet 2r = 23.12 m / s, the outlet blockage coefficient τ2 = 0.908, the inlet width b1 = 0.1874, and the outlet width b2 = 0.1191.

[0106] Calculate the circumferential velocity u1 at the inlet. The calculation formula is as follows:

[0107]

[0108] The calculated u1 = 63.91 m / s.

[0109] Calculate the component velocity c of the absolute velocity at the inlet 1r , and the calculation formula is as follows:

[0110]

[0111] The calculated c 1r = 21.8186 m / s, the inlet blockage coefficient τ1 = 0.7474, and the outlet blockage coefficient τ2 = 0.908.

[0112] Calculate the inlet blade installation angle β 1A , and the calculation formula is as follows:

[0113]

[0114]

[0115] The calculated β 1A = 23.37°.

[0116] Check the total pressure value ∆p. If the error is large, reselect the outlet installation angle β 2A and the number of blades Z. The checking formula is as follows:

[0117]

[0118]

[0119] After 14 iterations, ΔP - ΔP tf = -26.19, meeting the requirements.

[0120] The MOEA / D optimization algorithm is adopted. It simplifies the solution process by decomposing a multi-objective optimization problem into multiple single-objective sub-problems and uses a set of weight vectors to guide the optimization of these sub-problems.

[0121] Determine the key parameters, design space, and optimization objectives in the centrifugal impeller. Specifically, based on the flow separation and distortion generated in the direction of the impeller tip in the fan impeller, extract the key parameters with greater influence, including the control points of the hub line in the meridian plane of the impeller, the control points of the shroud line in the meridian plane, the leading edge endpoints at the impeller tip, the leading edge endpoints at the impeller root, the blade installation angle of the mid-arc line at the impeller tip, and the blade installation angle of the mid-arc line at the impeller root. At the same time, clarify the objective functions of optimization, including the power, static pressure, total pressure, static pressure efficiency, and total pressure efficiency at the design point. Adjust the initial values of the geometric parameters corresponding to the optimal objective results of the impeller, and reasonably set the change ranges of the above parameters. The parameter ranges are as shown in the following table;

[0122] Table 1: Parameter Optimization Variables and Ranges

[0123]

[0124] Table 2: Objective Functions

[0125]

[0126] Adopt regular network sampling to standardize the value range of each objective function to the interval (0, 1). The objective space can be represented as a 3D unit hypercube. Then, take the center point of each grid cell as the weight vector. Divide each dimension into 5 equal parts, then there will be a total of 5 3 = 125 grid points. Select the midpoint of each grid cell as the weight vector, and its corresponding weight vector can be calculated by the following formula:

[0127]

[0128] Normalize each weight to obtain the initial sample library. The specific formula is as follows:

[0129]

[0130] For each weight vector w i ', construct a corresponding single-objective sub-problem. Here, the weighted summation model is adopted. The specific formula is as follows:

[0131]

[0132] Randomly generate an initial solution x for each sub-problem gi i such that these solutions satisfy the boundary conditions of the decision variables. Randomly generate an initial solution set P = {x1, x2, …, x N}, for each individual x i in the current population, calculate its fitness value g i on the corresponding sub-problem g i (x i ∣w i ). For each sub-problem g i , maintain an optimal solution w i * , that is, the best known solution to this sub-problem.

[0133] Determine the neighbor set B(i) of each sub-problem g i . This is usually based on the sub-problems corresponding to the T closest weight vectors, where T is the neighborhood size parameter. Calculate the Euclidean distance between each weight vector and store it in a distance matrix D, where D[i][j] represents the distance between w i and w j , and select the T closest ones as neighbors. The calculation formula is as follows:

[0134]

[0135] Create a neighborhood matrix N, where N[i][j] = 1 indicates that the sub-problem g j belongs to the neighbor set of g i ; otherwise it is 0. For each sub-problem g i and its neighbors B(i), randomly select several parent individuals from the solutions corresponding to these sub-problems. One to three parent individuals can be selected for crossover operations, and use the crossover operator in the genetic algorithm to combine the characteristics of the parent individuals to generate offspring individuals y.

[0136] Insert the newly generated offspring y into the associated sub-problem g i , and check whether it is better than the existing solution. Compare the fitness values. If w i * <f j (y), then let w i * = f j (y). After 60 iterations, the Pareto front has approached the stable solution set. As Figure 5 shown, the number of iterations is no longer increased, and this is taken as the final optimization result. Figure 6 is the performance curve graph of the embodiment of the present invention. It can be seen from the graph that the performance of power, total pressure and static pressure has been greatly improved compared with the original model.

[0137] The foregoing has shown and described the basic principles, main features and advantages of the present invention. For those skilled in the art, it is obvious that the present invention is not limited to the details of the above-described exemplary embodiments, and without departing from the spirit or basic characteristics of the present invention, the present invention can be implemented in other specific forms. Therefore, in any regard, the embodiments should be regarded as exemplary and non-limiting. The scope of the present invention is defined by the appended claims rather than the above description. Therefore, all changes falling within the meaning and scope of the equivalent elements of the claims are intended to be embraced within the present invention. Any reference signs in the claims should not be construed as limiting the claims concerned.

[0138] The above content is a further detailed description of the present invention in combination with specific preferred technical solutions, and it cannot be determined that the specific implementation of the present invention is only limited to these descriptions. For those of ordinary skill in the technical field to which the present invention pertains, without departing from the concept of the present invention, several simple deductions or substitutions can still be made, and all should be regarded as belonging to the protection scope of the present invention.

Claims

1. A method for optimizing the design of a large flow centrifugal fan impeller, characterized in that: The steps include: Step 1: Given the target design parameters of the centrifugal impeller, including the design flow rate Q, speed n, impeller outlet diameter D2, impeller inlet density ρ in ; Step 2: Given the blade outlet installation angle β 2A ; Step 3: Calculate the outlet circumferential velocity u2; Step 4: Determine the inlet diameter D2; Step 5: Determine the number of blades Z; Step 6: Given the blade trailing edge thickness δ2, calculate the outlet absolute velocity component c 2r , and then determine the inlet width b1 and outlet width b2; Step 7: Calculate the inlet peripheral speed u1; Step 8: Calculate the absolute inlet velocity c 1r ; Step 9: Calculate the inlet blade installation angle β 1A ; Step 10: Verify the total pressure value ∆p; Step 11: Use the above steps to obtain the initial model, use the MOEA / D optimization algorithm, and finally get the optimal solution; specifically, it includes the following sub-steps: Step 11-1: Determine the key parameters, design space and optimization objectives of the centrifugal impeller; According to the flow separation and distortion in the direction of the fan impeller blade tip, key parameters are set in advance: the impeller meridian hub line control point, the meridian wheel cover line control point, the blade tip leading edge endpoint, the blade root leading edge endpoint, the blade tip mid-camber line blade installation angle, and the blade root mid-camber line blade installation angle; At the same time, the optimization objective function f1(x), f2(x), f3(x)... f j (x), adjusting the initial values ​​corresponding to the geometric parameters when the impeller has the optimal target result; Step 11-2: Use regular network sampling to standardize the range of each objective function to the interval (0,1). The objective space is represented as an m-dimensional unit hypercube. The center point of each grid cell is taken as the weight vector. Each dimension is divided into h equal parts, so there will be a total of h m grid points; The midpoint of each grid cell is selected as the weight vector, and its corresponding weight vector is: ； Where m represents the number of objectives in the optimization problem, i k is an integer from 0 to h−1, indicating the index position on the kth dimension; the weight vector is then normalized, and the specific formula is as follows: ； Among them, w i ＇ is the normalized value, w i is the original data value; sort the obtained data to obtain the initial sample library; Step 11-3: For each weight vector w i ＇ , a corresponding single-objective subproblem is constructed using the weighted sum model: ； Among them, w j Represents the weight vector w i ＇ The jth component of Step 11-4: For each sub-problem g i Randomly generate an initial solution x i , the initial solution satisfies the boundary conditions of the decision variables; the initial solution set P={x1,x2,…,x N }, where N is the number of subproblems; for each individual x in the current population i , calculate its corresponding subproblem g i The fitness value g on i (x i ∣w i ＇ ); For each subproblem g i Maintain an optimal solution w i * , which is the best known solution to this subproblem; Step 11-5: Determine each sub-problem g i The neighbor set B(i) of ; based on the subproblems corresponding to the closest T weight vectors, where T is the neighborhood size parameter; The Euclidean distance between each weight vector is calculated and stored in a distance matrix D, where D[i][j] represents w i and w j The distance between them is calculated and the nearest T ones are selected as neighbors. The calculation formula is as follows: ； Where m is the number of objective functions, create a neighborhood matrix N where N[i][j]=1 for subproblem g j Belong to g i Neighbor set; otherwise N[i][j]=0; For each subproblem g i and its neighbors B(i), randomly select several parent individuals from the solutions corresponding to the subproblems for crossover operations, use the crossover operator in the genetic algorithm to combine the characteristics of the parent individuals, and generate offspring individuals y; Step 11-6: Insert the newly generated offspring y into the associated subproblem g i , check whether it is better than the existing solution; By i * Is it less than f? j (y) Determine whether the iteration process is terminated. If w i * <f j (y), then let w i * =f j (y), otherwise, continue to iterate until the last round of optimization and generate the Pareto solution set, screen out the required optimal solution, generate the corresponding wind turbine optimal model and calculate the optimization result.

2. The method for optimizing the design of a large flow centrifugal fan impeller according to claim 1, characterized in that: In step 2, the blade outlet installation angle β is given 2A =35~48°.

3. The method for optimizing the design of a large flow centrifugal fan impeller according to claim 2, characterized in that: In step 3, the calculation formula of the outlet circumferential speed u2 is as follows: 。 4. The method for optimizing the design of a large flow centrifugal fan impeller according to claim 3, characterized in that: The calculation formula of the inlet diameter D1 in step 4 is as follows: ； The flow coefficient φ is: 。 5. The method for optimizing the design of a large flow centrifugal fan impeller according to claim 4, characterized in that: The calculation formula of the number of blades Z in the step is as follows: 。 6. The method for optimizing the design of a large flow centrifugal fan impeller according to claim 5, characterized in that: In step 6, according to the empirical formula C 2r / u2=0.21~0.25, calculate the exit absolute velocity fraction C 2r : C 2r =(0.21～0.25)； ； Given the blade trailing edge thickness δ2, the inlet width b1 and outlet width b2 are determined by the following calculation formula: ； ； ； ； ； Among them, ∧ represents the folded edge of the blade, t2 is the pitch, σ2 is the outlet tangential blade thickness, and τ2 is the outlet blocking coefficient.

7. The method for optimizing the design of a large flow centrifugal fan impeller according to claim 6, characterized in that: The calculation formula of the inlet peripheral speed u1 in step 7 is as follows: 。 8. The method for optimizing the design of a large flow centrifugal fan impeller according to claim 7, characterized in that: In step 8, the inlet absolute speed component c 1r The calculation formula is as follows: ； Among them, τ1 is the inlet blocking coefficient and τ2 is the outlet blocking coefficient.

9. The method for optimizing the design of a large flow centrifugal fan impeller according to claim 8, characterized in that: In step 9, the inlet blade installation angle β is calculated. 1A , the calculation formula is as follows: ； ； Among them, β1 represents the airflow angle, i represents the angle of attack, and i ranges from ±0 to 8°.

10. The method for optimizing the design of a large flow centrifugal fan impeller according to claim 9, characterized in that: In step 10, the total pressure value ∆p is calculated as follows: ； ； By ΔP-ΔP tf If it is less than 1%, judge whether the total pressure value is within the error range. If it exceeds the error range, reselect the outlet installation angle β 2A And the number of blades Z are calculated.

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