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CN114818186B - Wet spraying machine nozzle structural parameter optimization design method and computer readable storage medium - Google Patents

Wet spraying machine nozzle structural parameter optimization design method and computer readable storage medium Download PDF

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CN114818186B
CN114818186B CN202210462130.1A CN202210462130A CN114818186B CN 114818186 B CN114818186 B CN 114818186B CN 202210462130 A CN202210462130 A CN 202210462130A CN 114818186 B CN114818186 B CN 114818186B
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CN114818186A (en
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刘飞香
廖金军
胡及雨
蒋海华
王永胜
凡遵金
吴士兰
吴鑫
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China Railway Construction Heavy Industry Group Co Ltd
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Abstract

The invention provides a method for optimally designing nozzle structural parameters, which comprises the steps of establishing a wet spraying machine nozzle structural test design; performing sensitivity analysis on the structural test design of the nozzle of the wet spraying machine to obtain key parameters of the nozzle of the wet spraying machine; acquiring a curve equation of an outlet mixing uniformity coefficient and an outlet speed; and obtaining an expression of the wet spraying machine nozzle performance evaluation parameter, optimally designing and predicting an evaluation parameter function, and searching for an optimal solution. The invention also provides a computer readable storage medium for storing the simulation optimization design program of the nozzle structural parameters of the wet spraying machine, and the specific steps of the nozzle structural parameter optimization design method can be realized. The invention has the advantages that the structural parameters of the nozzle can be screened, and the screened parameters are optimally designed, so that the blindness of single discrete and optimization of the structural parameters is avoided, the design quality of the nozzle is purposefully improved, and the design optimization period and cost are shortened.

Description

Wet spraying machine nozzle structural parameter optimization design method and computer readable storage medium
Technical Field
The invention relates to the technical field of engineering machinery, relates to a design of a structural parameter of a nozzle of a wet spraying machine, and particularly discloses an optimal design method of the structural parameter of the nozzle of the wet spraying machine and a computer readable storage medium.
Background
The wet spraying machine is an important tool for spraying concrete to support the wall surface of a tunnel, and is widely used for mine roadways, railway and highway tunnels, hydraulic culverts, various underground projects, military projects and the like.
The existing wet spraying machine is used for conveying concrete to a nozzle through a pump during construction operation, fully mixing the concrete with compressed air and an accelerator in the nozzle, and finally spraying the uniformly mixed high-pressure wet concrete to the wall surface to form a supporting layer. The nozzle is a key component of the wet spraying machine, and the unreasonable structure of the wet spraying machine can cause uneven discharge of the nozzle and insufficient spraying speed, so that the nozzle is blocked or the concrete rebound rate is high, and the construction progress, quality and cost are seriously affected. The method improves the non-uniform discharge of the nozzle, reduces the rebound rate, and finds the optimal design parameters of the nozzle to be one of the key technical problems of the wet spraying machine.
The traditional optimization method of the nozzle usually carries out theoretical analysis, simulation analysis and design test verification design on the structural parameters of the nozzle one by one, but the sensitivity of the variables of the structural parameters is uncertain, the range of the values of the parameters is discrete and fuzzy, the optimal structural parameters and the values of the structural parameters cannot be found accurately, and the mixing uniformity of the nozzle outlet is difficult to improve and the nozzle outlet speed is difficult to ensure.
In a general wet-jet nozzle structure parameter simulation optimization method, a simulation engineer needs to determine key parameters and the value range of the key parameters based on a large amount of practical experience and rich theoretical basis, and manually compares simulation results by repeatedly manually adjusting input parameters, so that a more reasonable parameter value is obtained. Although the method can effectively reduce the test cost of the product, engineers are required to manually perform a large amount of simulation calculation in the design stage, and the method has the defects of misjudgment of key parameters, unreasonable parameter value range, manual misoperation, high labor intensity and the like.
In view of the above, it is important to develop a method for obtaining the structural parameters of the nozzle of the wet spraying machine at a high speed and with high precision.
Disclosure of Invention
The invention aims to provide a method for optimally designing structural parameters of a wet spraying machine nozzle, which is used for carrying out sensitivity analysis on the structural parameters on the basis of a simulation result of a parameterized model of the wet spraying machine nozzle, finding out key structural parameters influencing the performance of the nozzle and establishing a mathematical model of the key structural parameters; establishing constraint conditions by taking nozzle outlet mixing non-uniformity and outlet speed as targets; and obtaining the optimal structural parameter value through optimal design calculation. The specific technical scheme is as follows:
the optimized design method of the structural parameters of the nozzle comprises the following steps:
Establishing a wet spraying machine nozzle structure test design;
carrying out sensitivity analysis on the structural test design of the wet spraying machine nozzle to obtain key parameters of the wet spraying machine nozzle, wherein the key parameters are as follows: the diameter d and the length l of the material collecting pipe, the angle BETA between the air inlet pipe and the axis, the air inlet pipe diameter air_d and the air inlet pipe diameter number N2;
A curve equation of the outlet mixing uniformity coefficient y 1 and the outlet speed y 2 is obtained:
y1=a1+b1x1+c1x2+d1x3+e1x4+f1x5+g1x1 2+h1x3 2+i1x5 2+j1x1x3+k1x1x5+l1x3x5;
wherein: x 1、x2、x3、x4、x5 represents key parameters air_ d, BETA, d, l and N2;a1、b1、c1、d1、e1、f1、g1、h1、i1、j1、k1、l1、a2、b2、c2、d2、e2、f2、g2、h2、i2、j2、k2、l2、m2、n2、o2、p2、q2、r2 and s 2 are coefficients, and the values are constants;
obtaining an expression of a wet spraying machine nozzle performance evaluation parameter y, and optimally designing an evaluation parameter function y to predict optimal solutions of the diameter d and the length l of the material gathering pipe, the angle BETA of the air inlet pipe and the axis, the air inlet pipe diameter air_d and the air inlet pipe diameter number N2; where y=10y 1+0.1y2.
Preferably ,a1=0.0943;b1=0.0312,c1=-0.0005,d1=0.0241,e1=0.0002,f1=-0.0023,g1=-0.0007,h1=-0.0001,i1=0.0002,j1=-0.0005,k1=0.0004,l1=0.0001;a2=52.4191,b2=-11.5052,c2=0.6605,d2=-0.8622,e2=0.0345,f2=-3.7082,g2=-0.5317,h2=-0.0007,i2=-0.0091,j2=0.0206,k2=-0.0110,l2=0.4523,m2=-0.0014,n2=0.0695,o2=-0.0132,p2=-0.0006,q2=-0.0004,r2=0.0735,s2=0.0014.
Preferably, the larger the variation of the response of the main effect diagram along with the parameter factor in the sensitivity analysis process, the larger the influence of the factor on the response is, and then the key parameter is selected.
Preferably, the method for establishing the wet spraying machine nozzle structure test design specifically comprises the following steps of:
Step S1, a three-dimensional CAD software is adopted to build a three-dimensional model of a wet spraying machine nozzle, and a parameterized model of the wet spraying machine nozzle is further obtained;
performing CFD fluid simulation calculation on the nozzle structure parameterized model by adopting fluid simulation CFD software to obtain a wet-jet nozzle CFD fluid simulation model;
And S2, integrating the wet sprayer nozzle parameterized model and the wet sprayer nozzle CFD fluid simulation model in the step S1 by using the optimization design software, and automatically driving and calling the wet sprayer nozzle parameterized model and the wet sprayer nozzle CFD fluid simulation model by using the optimization design software to finish the structural test design of the wet sprayer nozzle.
Preferably, the method further comprises the step of establishing an optimal design software process component test design sensitivity analysis before performing sensitivity analysis on the wet spraying machine nozzle structure test design.
Preferably, the sensitivity analysis of the test design of the process component of the optimization design software is established, specifically, an optimization Latin hypercube design algorithm is adopted to ensure that all design test points are uniformly distributed in a design space as much as possible.
Preferably, a curve equation for obtaining the outlet mixing uniformity coefficient y 1 and the outlet speed y 2 is obtained by adopting an approximate model; an approximation model error of no more than 10% is considered satisfactory.
Preferably, the approximation model is a response surface algorithm model.
Preferably, the optimal solution is obtained by a multi-island genetic algorithm.
The nozzle structural parameter optimization design method provided by the invention has the beneficial effects that: the optimization design method provided by the invention can screen a plurality of structural parameters of the nozzle, screen out parameters with larger influence on the working performance of the nozzle, and then carry out targeted optimization design on the screened parameters, thereby avoiding blindness when single discrete and optimization are respectively carried out on a plurality of structural parameters when the structural parameters of the nozzle are optimally designed, improving the design quality of the nozzle in a targeted manner, and shortening the period and cost of design optimization.
The invention also provides a computer readable storage medium, wherein the computer readable storage medium is stored with a wet-jet nozzle structural parameter simulation optimization design program, and the wet-jet nozzle structural parameter simulation optimization design program realizes the steps of the nozzle structural parameter optimization design method when being executed by a processor.
In addition to the objects, features and advantages described above, the present invention has other objects, features and advantages. The present invention will be described in further detail with reference to the drawings.
Drawings
The accompanying drawings, which are included to provide a further understanding of the application and are incorporated in and constitute a part of this specification, illustrate embodiments of the application and together with the description serve to explain the application. In the drawings:
FIG. 1 is a schematic view of a wet spraying machine nozzle according to an embodiment of the invention;
FIG. 2 is a flow chart of the method for optimizing the design parameters of the nozzle structure of the wet spraying machine;
FIG. 3 is a plot of the main effects of the response of the aggregate tube diameter d and length l, the air inlet tube angle with the axis BETA, the air inlet tube diameter air_d, and the air inlet tube diameter number N2 as a function of the parameter factor mixing uniformity coefficient in the sensitivity analysis of the present invention;
FIG. 4 is a plot of the main effect of the response of the aggregate tube diameter d and length l, air inlet tube angle with axis BETA, air inlet tube diameter air_d, and air inlet tube diameter number N2 as a function of the parametric factor outlet velocity in the sensitivity analysis of the present invention;
Wherein, 1, a wet spraying machine nozzle, 1.1, a concrete inlet; 1.2, a nozzle outlet, 1.3, a compressed air inlet.
Detailed Description
Embodiments of the invention are described in detail below with reference to the attached drawings, but the invention can be implemented in a number of different ways, which are defined and covered by the claims.
Examples:
Referring to fig. 1, the wet sprayer nozzle 1 mainly comprises a concrete inlet 1.1, a nozzle outlet 1.2 and a compressed air inlet 1.3, wherein parameters include a gathering pipe diameter d, a gathering pipe length l, an angle BETA (BETA in fig. 1) between an air inlet pipe and an axis, an air inlet pipe diameter air_d, an air inlet pipe diameter number N2 and the like.
The method for optimally designing the structural parameters of the nozzle of the wet spraying machine disclosed by the embodiment, as shown in fig. 2, specifically comprises the following steps:
Step one, building a wet spraying machine nozzle structure test design (the part of which is not disclosed in the prior art, and can be realized by a person skilled in the art), wherein the specific scheme is as follows:
1. And establishing a three-dimensional model of the nozzle of the wet spraying machine by adopting three-dimensional CAD software, carrying out parameterization on the structure sizes, namely, parameterizing the model of the nozzle of the wet spraying machine, deriving a parameterized expression file, and applying a script file to realize the functions of modifying parameters, updating the model, saving the model and the like. Programming a program code file in a batch processing bat format of three-dimensional CAD software, and realizing the process of automatically updating and saving the geometric model.
Performing CFD fluid simulation calculation on the parameterized nozzle structure model by adopting fluid simulation CFD software to obtain a CFD fluid simulation model, and completing replacement of a geometric model, model mesh division, simulation parameter setting and result analysis and output by applying a script file based on a CFD template file, wherein the output nozzle outlet concrete and air mixing distribution uniformity coefficient and outlet speed are used as comparison evaluation result parameters with an initial nozzle structure scheme, and the calculation result file is in a text format. Programming a program code file in a batch processing bat format of fluid simulation CFD software, and realizing the processes of model replacement, grid division, simulation parameter setting, post-processing result output and the like of a simulation model.
2. And integrating a CAD parameterized model by using an optimization design software, adopting an optimization software program integration component, taking a parameterized file in the parameterized model of the nozzle of the wet spraying machine as an input file of the component, writing structural parameters of the nozzle into the optimization design software as input of the optimization design parameters, and taking a bat batch processing file as a program execution file. And executing the optimal design command to update the nozzle geometric model, and outputting an updated model file to realize the integration of automatically driving and calling CAD three-dimensional software by the optimal design software.
The CFD fluid simulation model is integrated by using the optimization design software, an optimization software program integration component is adopted, a result file of the CFD fluid simulation model is used as an output file of the component, and as the result parameter of fluid simulation steady-state calculation changes along with the number of iteration steps, after a certain number of iteration steps is calculated, the result tends to be in a steady state, and calculation convergence can be considered, so that the average value of the number of iteration steps of the last 100 steps of the result file is used as the output of the result parameter, and a bat batch processing file is used as a program execution file of CFD simulation calculation. Executing the optimal design command to update the CFD simulation calculation of the nozzle, and outputting an updated simulation result file to realize automatic driving of the optimal design software to call CFD fluid simulation software;
3. And (3) establishing sensitivity analysis of an optimal design software process component test Design (DOE), and adopting an optimal Latin hypercube design algorithm to ensure that all design test points are distributed in a design space as uniformly as possible. The test design was performed with the objective of selecting different combinations of design parameters and calculating the simulation results for each set of parameter combinations, where the test sample data size was selected as 100 sets.
Step two, performing sensitivity analysis on the structural test design of the wet spraying machine nozzle to obtain key parameters of the wet spraying machine nozzle, wherein the key parameters are as follows:
The main effect diagram shown in fig. 3-4 is obtained through sensitivity analysis and calculation, the larger the response changes along with the parameter factors, the larger the influence of the parameter factors on the response is, and the preferred key parameters are: the diameter d and length l of the converging tube, the angle BETA of the air inlet tube to the axis, the air inlet tube diameter air_d and the number N2 of air inlet tube diameters.
Step three, establishing an approximate model component of the optimizing design software application program, which specifically comprises the following steps: the approximate model is established based on the calculation input and output of 100 groups of sample points of the test design, is obtained by fitting the relation between factors and responses of sample point data in a mathematical model mode through an algorithm, and can be used for predicting an optimal solution through a subsequent optimization algorithm; the approximate model selects a Response Surface (RSM) algorithm model, and the RSM approximate model can fit a complex response relation through the selection of a regression model, so that the method has good robustness, and the accuracy of the approximate model is verified by adopting R-Squared. Fitting calculation of an approximate model is carried out on the key parameter factors and the result response; if the error of the approximation model is less than 10%, the result prediction of the approximation model is considered acceptable, if the error is more than 10%, the result prediction of the approximation model is considered unacceptable, and an algorithm for eliminating irrelevant sample points, adding test design sample points or replacing the approximation model is required;
fourth, based on sample point data of key structural parameters, obtaining curve equations of an outlet mixing uniformity coefficient y 1 and an outlet speed y 2 by fitting an RSM response surface algorithm model, wherein the curve equations are respectively expressed as 1) and 2):
y1=a1+b1x1+c1x2+d1x3+e1x4+f1x5+g1x1 2+h1x3 2+i1x5 2+j1x1x3+k1x1x5+l1x3x5 1);
Wherein: x 1、x2、x3、x4、x5 represents that the key parameters air_ d, BETA, d, l and N2;a1、b1、c1、d1、e1、f1、g1、h1、i1、j1、k1、l1、a2、b2、c2、d2、e2、f2、g2、h2、i2、j2、k2、l2、m2、n2、o2、p2、q2、r2 and s 2 are coefficients, respectively, and the values are constant, preferably :a1=0.0943;b1=0.0312,c1=-0.0005,d1=0.0241,e1=0.0002,f1=-0.0023,g1=-0.0007,h1=-0.0001,i1=0.0002,j1=-0.0005,k1=0.0004,l1=0.0001;a2=52.4191,b2=-11.5052,c2=0.6605,d2=-0.8622,e2=0.0345,f2=-3.7082,g2=-0.5317,h2=-0.0007,i2=-0.0091,j2=0.0206,k2=-0.0110,l2=0.4523,m2=-0.0014,n2=0.0695,o2=-0.0132,p2=-0.0006,q2=-0.0004,r2=0.0735,s2=0.0014.
Step five, acquiring an expression (shown as expression 3) of a wet-jet nozzle performance evaluation parameter y based on a normalization principle and combining engineering practice experience, and optimally designing and predicting optimal solutions of the diameter d and the length l of the material gathering pipe, the angle BETA of the air inlet pipe and the axis, the air inlet pipe diameter air_d and the air inlet pipe diameter number N2 of the wet-jet nozzle;
Where y=10y 1+0.1y2 3).
The nozzle design requirement y 1 is more than 0.8 and y 2 is more than 20, and the maximum value of the wet-jet nozzle performance evaluation parameter y is found for different optimization working conditions; if the corresponding y 1、y2 meets the constraint requirements, the flow of the nozzle of the wet spraying machine can be characterized, and the verification result is shown in the following table 1:
Table 1 results of iterative verification of function y
Key parameter value range Maximum value of y y1 y2
x1∈[2,6],x2∈[10,30],x3∈[20,40],x4∈[10,100],x5∈[2,10] 10.26 0.810 21.60
x1∈[6,12],x2∈[50,90],x3∈[40,70],x4∈[200,300],x5∈[20,32] 10.391 0.812 22.71
x1∈[4,8],x2∈[40,80],x3∈[45,75],x4∈[300,450],x5∈[10,20] 10.38 0.817 22.10
Verifying the function y through multiple groups of data, and finding that when the function y is maximum, the corresponding y 1 and y 2 are numerical values conforming to constraint conditions; the wet-jet nozzle flowability was demonstrated using y.
Step six, establishing an optimization component of an optimization design software process, wherein an optimization design algorithm is a calculation method for predicting an optimal value after an approximate model is established, MIGA (multi-island genetic algorithm) is selected as the optimization design algorithm, MIGA has better global solving capability and calculation efficiency than the traditional genetic algorithm, and the combination containing the optimal solution or the better solution is searched from data through iteration. And carrying out optimal design and prediction on the evaluation parameter function y to obtain an optimal solution, wherein the optimal solution is as follows:
And (3) establishing target constraint conditions, wherein the uniformity coefficients of the mixing distribution of the concrete and the air at the nozzle outlets of the optimization scheme and the initial scheme are y 1、y1 ', and the outlet speeds are y 2、y2', respectively. The optimization constraint is that the function y takes a maximum value and y 1>y1',y2>y2'. The results of the data before and after the optimization are shown in table 2, and the results are improved in the evaluation index.
Table 2 comparison of data results before and after optimization
Name of the name Outlet mixing uniformity Outlet speed (m/s)
Initial protocol 0.807 21.02
Optimization scheme 0.833 24.50
Relative change amount 3.2% 16.6%
In this embodiment, a computer readable storage medium may be further provided, where a program for simulating and optimizing a structural parameter of a nozzle of a wet spraying machine is stored on the computer readable storage medium, and the program for simulating and optimizing the structural parameter of the nozzle of the wet spraying machine implements the steps of the method for optimizing the structural parameter of the nozzle when the program is executed by a processor. Portions of this embodiment not disclosed in detail may be implemented according to conventional means in the art by those skilled in the art.
The wet spraying machine has a plurality of nozzle structure parameters, the influence degree on the performance of the nozzle is different, and when the nozzle structure is optimized, if the single structure parameter is optimized discretely and fuzzily, the wet spraying machine has a certain blindness, and huge workload and time cost are wasted. The method of the invention firstly obtains the key parameters, finds the parameters with great influence on the working performance, and then carries out targeted optimization, which plays an important role in improving the design quality of the nozzle, greatly shortens the design optimization period and cost, and meets the dual requirements of high speed and high precision.
The above description is only of the preferred embodiments of the present invention and is not intended to limit the present invention, but various modifications and variations can be made to the present invention by those skilled in the art. Any modification, equivalent replacement, improvement, etc. made within the spirit and principle of the present invention should be included in the protection scope of the present invention.

Claims (9)

1. The method for optimally designing the structural parameters of the nozzle is characterized by comprising the following steps of:
Establishing a wet spraying machine nozzle structure test design;
carrying out sensitivity analysis on the structural test design of the wet spraying machine nozzle to obtain key parameters of the wet spraying machine nozzle, wherein the key parameters are as follows: the diameter d and the length l of the material collecting pipe, the angle BETA between the air inlet pipe and the axis, the air inlet pipe diameter air_d and the air inlet pipe diameter number N2;
A curve equation of the outlet mixing uniformity coefficient y 1 and the outlet speed y 2 is obtained:
y1=a1+b1x1+c1x2+d1x3+e1x4+f1x5+g1x1 2+h1x3 2+i1x5 2+j1x1x3+k1x1x5+l1x3x5;
Wherein: x 1、x2、x3、x4、x5 represents key parameters air_ d, BETA, d, l and N2;a1、b1、c1、d1、e1、f1、g1、h1、i1、j1、k1、l1、a2、b2、c2、d2、e2、f2、g2、h2、i2、j2、k2、l2、m2、n2、o2、p2、q2、r2 and s 2 are coefficients, and the values are constants; in particular ,a1=0.0943;b1=0.0312,c1=-0.0005,d1=0.0241,e1=0.0002,f1=-0.0023,g1=-0.0007,h1=-0.0001,i1=0.0002,j1=-0.0005,k1=0.0004,l1=0.0001;a2=52.4191,b2=-11.5052,c2=0.6605,d2=-0.8622,e2=0.0345,f2=-3.7082,g2=-0.5317,h2=-0.0007,i2=-0.0091,j2=0.0206,k2=-0.0110,l2=0.4523,m2=-0.0014,n2=0.0695,o2=-0.0132,p2=-0.0006,q2=-0.0004,r2=0.0735,s2=0.0014;
Obtaining an expression of a wet spraying machine nozzle performance evaluation parameter y, and optimally designing an evaluation parameter function y to predict optimal solutions of the diameter d and the length l of the material gathering pipe, the angle BETA of the air inlet pipe and the axis, the air inlet pipe diameter air_d and the air inlet pipe diameter number N2; where y=10y 1+0.1y2.
2. The method for optimizing design of nozzle structural parameters according to claim 1, wherein the larger the response of the main effect diagram along with the change of the parameter factor in the sensitivity analysis process is, the larger the influence of the factor on the response is explained, and then the key parameters are selected.
3. The method for optimizing design of nozzle structural parameters according to claim 1, wherein the step of establishing a wet-jet nozzle structural test design comprises the steps of:
Step S1, a three-dimensional CAD software is adopted to build a three-dimensional model of a wet spraying machine nozzle, and a parameterized model of the wet spraying machine nozzle is further obtained;
performing CFD fluid simulation calculation on the nozzle structure parameterized model by adopting fluid simulation CFD software to obtain a wet-jet nozzle CFD fluid simulation model;
And S2, integrating the wet sprayer nozzle parameterized model and the wet sprayer nozzle CFD fluid simulation model in the step S1 by using the optimization design software, and automatically driving and calling the wet sprayer nozzle parameterized model and the wet sprayer nozzle CFD fluid simulation model by using the optimization design software to finish the structural test design of the wet sprayer nozzle.
4. A method of optimizing nozzle design parameters according to any one of claims 1-3, further comprising creating an optimization design software process component test design sensitivity analysis prior to performing sensitivity analysis on the wet nozzle structure test design.
5. The method for optimizing design parameters of a nozzle according to claim 4, wherein the step of establishing the sensitivity analysis of the design of the process component test of the optimizing design software is to use an optimizing Latin hypercube design algorithm to uniformly distribute all design test points in the design space as much as possible.
6. The method for optimizing design parameters of a nozzle according to claim 4, wherein the curve equation for obtaining the outlet mixing uniformity coefficient y 1 and the outlet speed y 2 is obtained by adopting an approximate model; an approximation model error of no more than 10% is considered satisfactory.
7. The method of claim 6, wherein the approximation model is a response surface algorithm model.
8. The method for optimizing design parameters of a nozzle according to claim 4, wherein the optimal solution is obtained by a multi-island genetic algorithm.
9. A computer readable storage medium, wherein a wet-jet nozzle structural parameter simulation optimization design program is stored on the computer readable storage medium, and the wet-jet nozzle structural parameter simulation optimization design program realizes the steps of the nozzle structural parameter optimization design method according to any one of claims 1-8 when being executed by a processor.
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CN111898308A (en) * 2020-09-15 2020-11-06 中国计量大学 A design scheme for optimizing paint spray gun air nozzles using response surface methodology

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Publication number Priority date Publication date Assignee Title
EP3588331A1 (en) * 2018-06-28 2020-01-01 Dong Han New Energy Automotive Technology Co., Ltd Method and device for optimization design of engine hood
CN111898308A (en) * 2020-09-15 2020-11-06 中国计量大学 A design scheme for optimizing paint spray gun air nozzles using response surface methodology

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