CN114722498A - Wing section design method based on generation of countermeasure network - Google Patents

Wing section design method based on generation of countermeasure network Download PDF

Info

Publication number
CN114722498A
CN114722498A CN202210350609.6A CN202210350609A CN114722498A CN 114722498 A CN114722498 A CN 114722498A CN 202210350609 A CN202210350609 A CN 202210350609A CN 114722498 A CN114722498 A CN 114722498A
Authority
CN
China
Prior art keywords
network
airfoil
data
output
lift
Prior art date
Legal status (The legal status is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the status listed.)
Pending
Application number
CN202210350609.6A
Other languages
Chinese (zh)
Inventor
季廷炜
谢李兴
谢芳芳
张鑫帅
朱灶旭
郑耀
Current Assignee (The listed assignees may be inaccurate. Google has not performed a legal analysis and makes no representation or warranty as to the accuracy of the list.)
Zhejiang University ZJU
Original Assignee
Zhejiang University ZJU
Priority date (The priority date is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the date listed.)
Filing date
Publication date
Application filed by Zhejiang University ZJU filed Critical Zhejiang University ZJU
Priority to CN202210350609.6A priority Critical patent/CN114722498A/en
Publication of CN114722498A publication Critical patent/CN114722498A/en
Pending legal-status Critical Current

Links

Images

Classifications

    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F30/00—Computer-aided design [CAD]
    • G06F30/10—Geometric CAD
    • G06F30/15—Vehicle, aircraft or watercraft design
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F30/00—Computer-aided design [CAD]
    • G06F30/20—Design optimisation, verification or simulation
    • G06F30/27—Design optimisation, verification or simulation using machine learning, e.g. artificial intelligence, neural networks, support vector machines [SVM] or training a model
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06N—COMPUTING ARRANGEMENTS BASED ON SPECIFIC COMPUTATIONAL MODELS
    • G06N3/00—Computing arrangements based on biological models
    • G06N3/02—Neural networks
    • G06N3/04—Architecture, e.g. interconnection topology
    • G06N3/045—Combinations of networks
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06N—COMPUTING ARRANGEMENTS BASED ON SPECIFIC COMPUTATIONAL MODELS
    • G06N3/00—Computing arrangements based on biological models
    • G06N3/02—Neural networks
    • G06N3/08—Learning methods
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F2119/00—Details relating to the type or aim of the analysis or the optimisation
    • G06F2119/14—Force analysis or force optimisation, e.g. static or dynamic forces
    • Y—GENERAL TAGGING OF NEW TECHNOLOGICAL DEVELOPMENTS; GENERAL TAGGING OF CROSS-SECTIONAL TECHNOLOGIES SPANNING OVER SEVERAL SECTIONS OF THE IPC; TECHNICAL SUBJECTS COVERED BY FORMER USPC CROSS-REFERENCE ART COLLECTIONS [XRACs] AND DIGESTS
    • Y02—TECHNOLOGIES OR APPLICATIONS FOR MITIGATION OR ADAPTATION AGAINST CLIMATE CHANGE
    • Y02T—CLIMATE CHANGE MITIGATION TECHNOLOGIES RELATED TO TRANSPORTATION
    • Y02T90/00—Enabling technologies or technologies with a potential or indirect contribution to GHG emissions mitigation

Abstract

The invention provides an airfoil design method based on a generation countermeasure network. The method learns by using the randomly generated profile data as training data. The generating network can generate the wing profile according with the lift-drag coefficient by inputting the target lift-drag coefficient. The problem that the lift-drag coefficient and the wing profile have one-to-many mapping relation is solved by adding a hidden code into a generating network. A covert code is a set of numbers that obey a certain distribution (gaussian in the present invention). The output of the generated network, i.e. the wing profile, can be varied by repeated random sampling of the covert code. Finally, diversified wing profiles meeting the target lift-drag coefficient can be obtained.

Description

Wing section design method based on generation of countermeasure network
Technical Field
The invention relates to a wing section design method based on a generation countermeasure network, which can efficiently design a wing section conforming to a lift-drag coefficient under a certain flight state according to the lift-drag coefficient, can generate diversified wing sections by repeatedly sampling hidden codes in input, meets the target lift-drag coefficient, and belongs to the field of aircraft appearance design.
Background
Aircraft design is a large and complex project that relies heavily on the design experience of engineers. The problem that the design cycle time is long exists in the design of the aircraft at the present stage, wherein each design stage needs a large amount of simulation verification, a large amount of data is generated, how to combine deep learning with the design process of the aircraft, self-learning is realized through data modeling, the design efficiency is improved, the cost is reduced, the design cycle is reduced, the design automation process is optimized, and the design method has important engineering and theoretical significance.
Disclosure of Invention
In order to realize the combination of deep learning and an aircraft design process, the problems that engineering data are few in the aircraft pneumatic design process, a one-to-many mapping relation exists in the aircraft design process and the like are solved through the deep learning. The invention constructs a wing profile design model based on a generation countermeasure network (GAN), and obtains a wing profile capable of meeting target lift and drag coefficients by inputting a lift coefficient and a drag coefficient; for a group of lift coefficient and drag coefficient, a plurality of airfoils possibly correspond to or approximate to the lift coefficient and the drag coefficient, so that hidden codes which obey Gaussian distribution are added into the input of the neural network, the shape of the airfoil is changed by randomly sampling the hidden codes, and the one-to-many mapping problem is solved.
In order to achieve the purpose, the technical idea adopted by the invention is as follows:
by randomly sampling hidden codes which obey Gaussian distribution and taking the hidden codes and the target aerodynamic coefficient as the input of the generation network G, the generation network outputs diversified airfoil geometric data, so that the airfoil design is realized. The training process of the encoder E and the generated network specifically includes:
at step S1, airfoil data is collected for training. The airfoil data comprises geometric data of an airfoil and target aerodynamic coefficient data, wherein the geometric data of the airfoil are coordinates x and y of discrete points of the airfoil, and x of different airfoils is fixed and unified to the same value. The target aerodynamic coefficient C is a lift coefficient ClAnd/or coefficient of resistance Cd。
And step S2, constructing an encoder E to input the airfoil profile data y and output the distribution z of the hidden codes. Expressed as:
Figure BDA0003579964950000011
wherein
Figure BDA0003579964950000012
Is a standard Gaussian distribution; mu.szAnd σzAn average value and a standard deviation of z, respectively, indicate a dot product.
And step S3, random sampling of the hidden code. Wherein the hidden code z1Randomly sampling from z, latent code z2From
Figure BDA0003579964950000013
Randomly sampling;
step S4, converting the hidden code z1And z2Respectively forming an array with the target parameters as the input of a generation network G, and outputting predicted airfoil profile coordinates y 'by the generation network G'1、y′2. Generation of airfoil data y 'with encoder E input simultaneously'2Output hidden code z'2。
Step S5, constructing a discrimination network D to input the airfoil profile data y and y'1、y′2And a target aerodynamic coefficient, and judging the authenticity of the data;
step S6, updating the neural network parameters through the target function training, finishing the training when the generating network G reaches convergence, and obtaining the trained generating network and the hidden codes which obey Gaussian distribution, wherein the target function is expressed as:
Figure BDA0003579964950000021
wherein λ isb、λz、λKLIs a hyper-parameter;
Figure BDA0003579964950000022
Figure BDA0003579964950000023
Figure BDA0003579964950000024
Figure BDA0003579964950000025
Figure BDA0003579964950000026
wherein p isdataData representing a training data set;
Figure BDA0003579964950000027
to expect, | × | purple1D (×) represents the output of the discriminator D, G (×) represents the output of the generation network G, E (×) represents the output of the encoder E,
Figure BDA0003579964950000028
to measure the similarity of two distributions for divergence, p (y) represents the implicit function of y.
Further, the step S1 specifically includes the following sub-steps:
step S1.1, fixing x as
Figure BDA0003579964950000029
Wherein n ispThe number of discrete points on the upper surface of the airfoil profile is the same as the x-axis coordinate of the discrete points on the lower surface of the airfoil profile; i is 1 to npIs a positive integer of (1). Generating an airfoil shape by using a CST parameterization method to obtain a geometric shape represented by the sample point;
step S1.2, performing aerodynamic calculation on the airfoil shape generated in the step S1.1 under a certain inflow condition by adopting open source aerodynamic software XFOIL;
and S1.3, analyzing the aerodynamic calculation result in the step S1.2 to obtain a required aerodynamic coefficient and obtain airfoil profile data.
Further, in step S2, the network structure of the encoder E is 3 fully-connected layers, and each fully-connected layer is followed by a batch normalization layer and a LeakyReLU activation function.
Further, the network structure for generating the network G employs a Unet network.
Further, in step S5, the network structure of the network D is determined to be connected by multiple fully connected layers, and each fully connected layer is followed by the batch normalization layer and the ReLU activation function.
Further, the airfoil with the inconsistent lift-drag coefficient is removed from the airfoil geometric data of the diversity output by the generation network, and the airfoil with the largest lift-drag ratio is selected as a design result.
Further, in the step S6, the convergence criterion is
Figure BDA0003579964950000031
The invention has the beneficial effects that:
1. by inputting a target lift-drag coefficient and a hidden code which follows Gaussian distribution, the generating network can generate an airfoil profile which meets the target lift-drag coefficient under certain flight conditions.
2. By repeatedly and randomly sampling the hidden codes in the generated network input, the result of the generated network can be changed, and different wing profiles can be obtained, wherein the wing profiles can meet the target lift-drag coefficient under certain flight conditions. The problem that the lift drag coefficient and the wing profile have one-to-many mapping relation is solved to a certain extent.
Drawings
FIG. 1 is a flow chart of the present invention;
FIG. 2 is a sampling range of airfoil training data and test data;
FIG. 3 is a schematic diagram of various neural network structures;
FIG. 4 is a schematic diagram of a Unet network structure in a generating network;
FIG. 5 is a cross-sectional view of a mission of an unmanned aerial vehicle;
FIG. 6 shows the design results of different airfoils obtained by the generation network according to the present invention after inputting the same lift coefficient and different hidden codes;
FIG. 7 is a result of overlaying the different airfoils of FIG. 6;
fig. 8 is a schematic diagram of the wing profile design result provided by the present invention applied to an unmanned aerial vehicle.
Detailed Description
The present invention will be described in detail below with reference to the accompanying drawings.
FIG. 1 is a flow chart of an airfoil design method based on generation of a countermeasure network according to the present invention.
The present embodiment contemplates a drone aerofoil that has an engine start warm-up, a roll-off, a takeoff, a climb acceleration, a cruise, a descent, a landing, a roll-off, a shutdown (as shown in fig. 5). The unmanned aerial vehicle is mainly determined to have the flight performance of the unmanned aerial vehicle during stalling, takeoff, climbing rate, climbing speed and cruise. The cruise stage of the aircraft is selected as a design target, and the lift coefficient required by the aircraft in the cruise state is 0.2272 and is used as an input, so that the airfoil profile meeting the target is obtained.
Specifically, the method for training the encoder and generating the network to obtain the hidden code obeying the Gaussian distribution comprises the following steps:
step S1, airfoil data and corresponding lift coefficient data are collected for training. Specifically, the method comprises the following steps:
s1.1, randomly generating wing profile data by adopting a CST parameterization method, wherein the sampling range of the training data and the testing data of the wing profile is shown in figure 2. The geometrical data of the airfoil is that the coordinates x, y and x of discrete points of the airfoil are fixed
Figure BDA0003579964950000041
Wherein n ispTaking 99 out of the embodiment, the x-axis coordinate of the discrete points on the lower surface of the airfoil is the same as that of the upper surface; i is 1 to npIs a positive integer of (1).
Step S1.2, adopting open source aerodynamic software XFOIL to make the incoming flow speed of the airfoil shape generated in step S1.1 be 50m/S at an attack angle of 1.1319 degrees and the Reynolds number be 1.46 multiplied by 106Performing aerodynamic calculations under the conditions of (a);
and S1.3, analyzing the aerodynamic calculation result in the step S1.2 to obtain a lift coefficient.
In step S2, the encoder E inputs the airfoil data y and outputs a hidden code distribution z, denoted as E (y). The encoder E is a neural network for reducing the high-dimensional data samples into low-dimensional data, the input is the y value of the airfoil data, and the output is the distribution z of the hidden codes. The network structure of encoder E (fig. 3) is 3 layers of fully-connected layers, each layer of fully-connected layers followed by a bulk normalization layer and a leakyreu activation function. Since the output implicit code is approximately normal to the standard distribution, the output of the encoder E is the average value mu of zzAnd standard deviation σz。
Figure BDA0003579964950000042
Wherein
Figure BDA0003579964950000043
Is a standard Gaussian distribution; an indication of a dot product;
and step S3, random sampling of the hidden code. Wherein the hidden code z1From E (y) random sampling, implicit code z2From
Figure BDA0003579964950000044
Random sampling;
step S4, generating network G input lift coefficient ClAnd a hidden code z1Generating airfoil y'1. Wherein the generation network G is used for generating diversified airfoils with the input of lift coefficient ClAnd hidden code
Figure BDA0003579964950000045
The output is the y value which generates the airfoil profile coordinate points. The network structure (fig. 3) of the generated network G adopts a net network model, and the network structure is relatively symmetrical and is often used for models with consistent input and output dimensions. The diversity of the wing profiles is realized by repeatedly sampling the hidden code z from the standard normal distribution;
step S5, generating a network G input lift coefficient ClAnd a hidden code z2Generating airfoil y'2. Wherein, the generation network G is the same as the generation network in step S4;
in step S6, encoder E inputs generation airfoil profile data y'2Output hidden code z'2. Wherein, the encoder E is the same as the encoder in step S2;
in step S7, airfoil profile data y and y 'are inputted to the discrimination network D'1、y′2And coefficient of lift ClTo obtain an output D (C)l，y)、D(Cl，y′1)、D(Cl，y′2). The judgment network D is used as a judge to distinguish whether the input data is from the real sample or generated by the generation network G, if the input data is from the real sample, the output tends to 1, and if the input data is from the generation network G, the output tends to 0. The network structure of discrimination network D (fig. 3) is connected by multiple fully-connected layers, each followed by a bulk normalization layer and a ReLU activation function.
Step S8, calculating an objective function:
Figure BDA0003579964950000051
Figure BDA0003579964950000052
Figure BDA0003579964950000053
Figure BDA0003579964950000054
Figure BDA0003579964950000055
wherein p isdataData representing a training data set; wherein D (_) denotes the output of the discriminator D, G (_) denotes the output of the generation network G, E (_) denotes the output of the encoder E,
Figure BDA0003579964950000056
to measure the similarity of two distributions for divergence, p (y) represents the implicit function of y.
Step S9, updating the neural network parameters through the objective function:
Figure BDA0003579964950000057
wherein λ isb、λz、λKLFor hyper-parameters, here 10, 1, 10;
in step S10, the training is repeated from step two, and when the generated network G converges, the training is terminated. Wherein the convergence criterion is
Figure BDA0003579964950000058
After training is finished, the wing profile is designed by taking the lift coefficient of the wing to be 0.2272 in the cruise state as a final consideration in the embodiment. The hidden code is repeatedly sampled to obtain a design result shown in figure 6, 16 different wing profiles can be selected, the wing profiles are numbered from left to right and from top to bottom as numbers 1-16, and the lift-drag coefficient calculated by pneumatic software is arranged above the wing profiles. Overlapping these airfoils, see fig. 7, it can be seen that the resultant airfoils are relatively close in profile, differing in detail, with the major variation being at the leading edge of the airfoil lower surface.
As can be seen from the lift-drag coefficients of the airfoils shown in fig. 6, the lift coefficients of the airfoils nos. 2, 3, 7 and 14 do not reach 0.2272, which is not satisfactory for the intended purpose, and thus are left out. In order to compare the advantages and disadvantages of other airfoils, the lift-drag ratio is calculated to obtain the following table. The following table shows that the lift-drag ratio of the 13 # airfoil is the largest, the lift coefficient is 0.251, the lift requirement of the aircraft in the cruise state is met, and the 13 # airfoil can be considered as a design result. Fig. 8 is a schematic view of a drone using a No. 13 airfoil.
Figure BDA0003579964950000061
It should be understood that the above examples are only for clarity of illustration and are not intended to limit the embodiments. Other variations and modifications will be apparent to persons skilled in the art in light of the above description. This need not be, nor should all embodiments be exhaustive. And obvious variations or modifications of the invention may be made without departing from the scope of the invention.

Claims (7)

1. An airfoil design method based on a generation countermeasure network is characterized in that hidden codes which obey Gaussian distribution are randomly sampled, and a target aerodynamic coefficient is used as the input of a generation network G, so that airfoil geometric data of the generation network output diversity is realized, and airfoil design is realized; the training process for generating the network G specifically includes:
step S1, collecting airfoil profile data for training; the airfoil data comprises geometric data of an airfoilThe target aerodynamic coefficient data are obtained, wherein the geometrical data of the airfoil are coordinates x and y of discrete points of the airfoil, and the x of different airfoils are fixed and respectively unified into the same value; the target aerodynamic coefficient C is a lift coefficient ClAnd/or coefficient of resistance Cd；
Step S2, constructing an encoder E to input airfoil data y and output the distribution z of the hidden codes; expressed as:
Figure FDA0003579964940000011
wherein
Figure FDA0003579964940000012
Is a standard Gaussian distribution; mu.szAnd σzThe mean and standard deviation of z, respectively; an indication of a dot product;
step S3, sampling the hidden code randomly; wherein the hidden code z1Randomly sampling from z, latent code z2From
Figure FDA0003579964940000013
Random sampling;
step S4, hiding the code z1And z2Respectively forming an array with the target parameters as the input of a generation network G, and outputting predicted airfoil profile coordinates y 'by the generation network G'1、y′2(ii) a Generation of airfoil data y 'with encoder E input simultaneously'2Output hidden code z'2；
Step S5, constructing a discrimination network D to input the airfoil profile data y and y'1、y′2And the target aerodynamic coefficient, and judging the authenticity of the data;
step S6, updating the neural network parameters through the target function training, finishing the training when the generating network G reaches convergence, and obtaining the trained generating network and the hidden codes which obey Gaussian distribution, wherein the target function is expressed as:
Figure FDA0003579964940000014
wherein λ isb、λz、λKLIs a hyper-parameter;
Figure FDA0003579964940000015
Figure FDA0003579964940000016
Figure FDA0003579964940000017
Figure FDA0003579964940000018
Figure FDA0003579964940000019
wherein p isdataData representing a training data set;
Figure FDA00035799649400000110
to expect, | | × | cage1D (×) represents the output of the discriminator D, G (×) represents the output of the generation network G, E (×) represents the output of the encoder E,
Figure FDA0003579964940000021
to measure the similarity of two distributions for divergence, p (y) represents the implicit function of y.
2. The method as claimed in claim 1, wherein the step S1 comprises the following sub-steps:
step S1.1, fixing x as
Figure FDA0003579964940000022
Wherein n ispThe number of discrete points on the upper surface of the airfoil profile is the same as the x-axis coordinate of the discrete points on the lower surface of the airfoil profile; i is 1 to npA positive integer of (d); generating an airfoil shape by using a CST parameterization method to obtain a geometric shape represented by the sample point;
step S1.2, performing aerodynamic calculation on the airfoil shape generated in the step S1.1 under a certain inflow condition by adopting open source aerodynamic software XFOIL;
and S1.3, analyzing the aerodynamic calculation result in the step S1.2 to obtain a required aerodynamic coefficient and obtain airfoil profile data.
3. The method of claim 1, wherein in the step S2, the network structure of the encoder E is 3 layers of fully-connected layers, and each layer of fully-connected layers is followed by a batch normalization layer and a leakyreu activation function.
4. The method of claim 1, wherein the network fabric that generates network G employs a Unet network.
5. The method according to claim 1, wherein in step S5, the network structure of the discrimination network D is connected by a plurality of fully-connected layers, each layer being followed by a bulk normalization layer and a ReLU activation function.
6. The method of claim 1, wherein airfoils with non-compliant lift-drag coefficients are removed from the diverse airfoil geometry data that generate the net output, and the airfoil with the largest lift-drag ratio is selected as the design result.
7. The method according to claim 1, wherein in step S6, the convergence criterion is
Figure FDA0003579964940000023
CN202210350609.6A 2022-04-02 2022-04-02 Wing section design method based on generation of countermeasure network Pending CN114722498A (en)

Priority Applications (1)

Application Number Priority Date Filing Date Title
CN202210350609.6A CN114722498A (en) 2022-04-02 2022-04-02 Wing section design method based on generation of countermeasure network

Applications Claiming Priority (1)

Application Number Priority Date Filing Date Title
CN202210350609.6A CN114722498A (en) 2022-04-02 2022-04-02 Wing section design method based on generation of countermeasure network

Publications (1)

Publication Number Publication Date
CN114722498A true CN114722498A (en) 2022-07-08

Family

ID=82241977

Family Applications (1)

Application Number Title Priority Date Filing Date
CN202210350609.6A Pending CN114722498A (en) 2022-04-02 2022-04-02 Wing section design method based on generation of countermeasure network

Country Status (1)

Country Link
CN (1) CN114722498A (en)

Cited By (1)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN116628854A (en) * 2023-05-26 2023-08-22 上海大学 Wing section aerodynamic characteristic prediction method, system, electronic equipment and storage medium

Cited By (1)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN116628854A (en) * 2023-05-26 2023-08-22 上海大学 Wing section aerodynamic characteristic prediction method, system, electronic equipment and storage medium

Similar Documents

Publication Publication Date Title
CN106529093B (en) A kind of pneumatic/structure/pneumostatic bullet for high aspect ratio wing couples optimization method
Wickramasinghe et al. Designing airfoils using a reference point based evolutionary many-objective particle swarm optimization algorithm
Thirumalainambi et al. Training data requirement for a neural network to predict aerodynamic coefficients
CN110516318B (en) Airfoil design method based on radial basis function neural network proxy model
CN110110384A (en) A kind of application method based on the non-dominant genetic algorithm of concentration strategy in the optimization of aircraft wing-type design
CN113777931B (en) Icing wing type pneumatic model construction method, device, equipment and medium
CN112699622B (en) Close formation pneumatic coupling effect modeling method for fixed-wing unmanned aerial vehicle
CN114722498A (en) Wing section design method based on generation of countermeasure network
CN111598435A (en) Quality trend prediction method based on adaptive feature selection and improved thought evolution algorithm
CN115438584A (en) Wing profile aerodynamic force prediction method based on deep learning
Karali et al. Design of a deep learning based nonlinear aerodynamic surrogate model for UAVs
CN113408044A (en) Multi-rotor unmanned aerial vehicle blade optimization design method
Lane et al. A surface parameterization method for airfoil optimization and high lift 2D geometries utilizing the CST methodology
CN109783858A (en) A method of optimize for low Reynolds number airfoil
Johnson et al. Using artificial neural networks and self-organizing maps for detection of airframe icing
CN108009320A (en) A kind of multisystem association modeling method of hypersonic aircraft Control-oriented
CN113110558B (en) Hybrid propulsion unmanned aerial vehicle demand power prediction method
CN115796021A (en) Adaptive PID control parameter setting method for variant aircraft based on neural network
Khurana et al. Development and validation of an efficient direct numerical optimisation approach for aerofoil shape design
CN111625901B (en) Intelligent pressure coefficient curve generation method for wing profile
Ivanov et al. Influence of selected turbulence model on the optimization of a class-shape transformation parameterized airfoil
Kody et al. An efficient methodology for using a multi-objective evolutionary algorithm for winglet design
CN114676639A (en) Aircraft aerodynamic shape optimization method, device and medium based on neural network
Safikhani et al. Pareto optimization of two-element wing models with morphing flap using computational fluid dynamics, grouped method of data handling artificial neural networks and genetic algorithms
Fernando et al. Bio-Inspired Aircraft Wing Modification Analysis in ANSYS Fluent

Legal Events

Date Code Title Description
PB01 Publication
PB01 Publication
SE01 Entry into force of request for substantive examination
SE01 Entry into force of request for substantive examination