Development of productivity started in 1981

Chapter 213 explains the application of the general solution of the NS equation

"Comrade Jiankun, you're here! Did you have a good rest?"

At around 3:10 p.m., Wang Jiankun came to the conference room under the guidance of the reception comrade from Factory 132. Director Yin was waiting for him at the door.

"I had a good rest. Director Yin, are all the people here? If they are, let's start. Everyone's time is precious."

"Now that we are all here, I would like to trouble you to explain the application of the general solution of the NS equation today. We will then show you the design drawings of this fighter jet. How about you study it first and then participate in the calculation and improvement?"

"Okay, let's go in now."

"Okay, this way in."

Director Yin took Wang Jiankun and entered the conference room guarded by security personnel through the front door.

After entering, Director Yin first introduced Wang Jiankun’s basic situation.

"Comrades, the person next to me is Wang Jiankun. Some of you may have heard of his name from relevant technical materials. Yes, it was the article that solved the most important equation in fluid mechanics, the NS equation. He will explain to us the application of this general solution in engineering."

There were more than 30 experts and researchers below, both young and old. Most of them were elderly, about 20 of them had gray hair and looked to be around 60 years old. There were only a few young people, probably college graduates in recent years. There were very few middle-aged people, and Wang Jiankun saw only three of them.

This situation also verifies the harm caused by the education gap in the previous period. Now the main force of domestic research still relies on a group of elderly people. There are very few middle-aged researchers, and some of them have relatively poor levels. They need to continue learning at work to master new knowledge. Young researchers are even less able to take on big responsibilities, and they need more practice and learning.

However, with the increasing investment in education in recent years and almost nationwide selection, the quality of young researchers who can successfully graduate and pass the assessment is very high and their learning ability is superb. With their joining, the speed of domestic research should become faster and faster.

"Hello everyone, my name is Wang Jiankun. I am currently studying in the Department of Mathematics at Tsinghua University. I was previously interested in fluid mechanics, so I focused my energy on studying the NS equations. I have now found the general solution to this equation. I will explain to you the specific application of this general solution to the equation later."

At this time, the old experts in the audience began to whisper to each other. Seeing that Wang Jiankun was so young and still in college, they could hardly believe that the Wang Jiankun in the confidential publication was him.

"Comrade Wang Jiankun, you said you found the general solution to this equation? You are still in college, shouldn't you have just been exposed to advanced mathematics? How is it possible that you solved such a complex nonlinear partial differential equation in such a short time?"

An old expert sitting in the front row couldn't help but stand up and question Wang Jiankun.

"Mr. He, please sit down first. The paper was indeed written by Wang Jiankun on the stage. It has gone through two rounds of defense by experts in related fields. Otherwise, it would not have been published in that confidential journal. As for why he is so young, that is not important. It is also a great thing. God blesses China. After all, every generation has talented people!"

When Director Yin saw someone questioning Wang Jiankun, he quickly stood up to appease them.

When the old expert named He saw Director Yin come out to speak and pointed out that Wang Jiankun had been confirmed, he sat down.

"Jiankun, I'm sorry that I didn't tell them about your situation in advance. Please don't mind. Please continue to explain to them!"

"It's okay, Director Yin. I understand. I'll continue."

"As we all know, the NS equation is a nonlinear partial differential equation, which has an additional second-order derivative term compared to the Euler equation. This makes it difficult to find an exact solution without restricting the equation.

For example, when the Reynolds number is greater than or equal to 1, outside the boundary layer of the flow object, the viscous force is much smaller than the inertial force, the viscous term in the equation can be ignored, and the NS equation is simplified to the Euler equation in ideal flow;

In the boundary layer, the NS equations can be simplified to boundary layer equations, etc. Their exact solutions can only be obtained in some very simple special flow problems, but they are extremely difficult to solve in general.

But through some mathematical changes, I found the general solution to this equation. The current verification result is that all known engineering problems can be substituted into this general solution. Next, I will explain to you the application of this general solution in aircraft. I will give you some specific examples, and you can try to verify it together. "

Because the process of finding the general solution is very complicated, and the people sitting in the audience are not experts in the field of mathematics, it is very difficult to explain it to them clearly. Therefore, Wang Jiankun did not spend time on the verification of the general solution. He gave a brief introduction and then jumped to the specific engineering application of the solved general solution.

In the next hour or so, Wang Jiankun listed three specific application examples, namely aerodynamic analysis, rotor airfoil design, and aerothermal design.

The aerodynamic analysis example is to solve the pressure analysis of various parts of the wing. Wang Jiankun used data from a US P51 propeller aircraft during World War II. It can be found in the library, so it is very suitable for use as an example.

The rotor airfoil design was also that of the P51 propeller plane, but after giving the example, he also drew an optimized application of the rotor on a helicopter on the blackboard, indicating that by optimizing the rotor structure, a helicopter rotor can be manufactured that improves the aerodynamic performance of the rotor airfoil at multiple design points such as hovering, forward flight and maneuvering, and under multiple constraint conditions. However, his new example did not attract the attention of these people. They were all researchers of fixed-wing aircraft and looked down on this type of rotor.

The example of aerodynamic thermal design is the German V2 rocket. Information about this rocket can be found in some domestic libraries, so there is no need to specify the source of the information when using it as an example, and the researchers below will be able to accept it quickly.

Wang Jiankun kept writing on the blackboard, completing one version after another. The old experts in the audience did not believe him at first and did not even write. They just sat and watched. Only the three middle-aged experts and several young researchers followed Wang Jiankun's blackboard writing to do the calculations.

As Wang Jiankun wrote more and more on the blackboard and his explanations became more and more fluent, these old experts could no longer sit still. They began to pick up paper and pen and follow Wang Jiankun in calculating. Then their eyes became brighter and brighter, and their mood became more and more excited.

After following the calculations, they found that this general solution equation can indeed greatly simplify the calculations. While calculating these examples, they combined the difficulties they encountered in the design and unconsciously began to calculate the part of the drawings they were responsible for.

Since they were designing a fighter jet that could fly at supersonic speeds, the shape of the wing surface, the shape of the nose section, the shape of the air intake, and especially the size, shape and position of the pair of canards all needed to be determined through wind tunnel testing and finite element analysis.

Unfortunately, their factory lacks funds, and domestic wind tunnels are still conducting more important research. They cannot get the quota nor the funds to go and blow the wind tunnels, so they need to complete the paper calculations first, and then after multiple reviews, they can enter the model manufacturing and wind tunnel blowing stage.

Originally they thought that paper calculations would not be difficult, as the design of atomic bombs and missiles could be completed through paper calculations in the 5s and 60s. They now have several computers that can perform tens of millions of times per second, so it should be very fast.

Unfortunately, they have not done any work in this area, and they do not know the difficulty involved, and they underestimate the complexity of the NS equations.

Because the aerodynamic shape of this aircraft with canards is more complex than that of the American F16, the materials available in China are different from those in the United States, and the thrust and size of the engine are even more different, so the difficulty of calculation is greatly increased.

They had been stuck at the step of calculating the drawings for several months. If Director Yin and several leading people had not insisted on the canard, they might have started over again and designed a similar model based on the F16. Now with this general solution equation, they found that it was too convenient and quick to calculate, so they no longer underestimated Wang Jiankun, knowing that this young man was really capable in this regard. He solved such a complex mathematical problem and was able to explain to them how to apply it to specific engineering problems. The examples he gave were also more representative, allowing them to quickly master the relevant methods.

"Okay, that's all for the application of this general solution. Does anyone have any questions? If not, let's end it."

"Comrade Wang Jiankun, you spoke very well. I want to apologize to you for questioning you before." The old expert named He who had questioned the youth of Wang Jiankun before the meeting apologized to Wang Jiankun.

"Mr. He, I can't stand it. You don't need to apologize to me. You were right before. According to common sense, it is impossible for someone to solve this problem in such a short time and at such a young age.

However, I am indeed good at mathematics. I had completed advanced mathematics courses in college during high school. After entering college, I began to research some cutting-edge topics.

The first half of the proof of the general solution of the NS equation was published in a top American mathematics journal a few months ago. After I completed the proof of the general solution, I found that if it was used to solve practical engineering problems, it could help us simplify calculations and speed up cutting-edge engineering research. So I did not submit it abroad, but published it in a confidential domestic journal. "

Wang Jiankun took this opportunity to demonstrate his achievements in mathematics, and did not forget to praise himself in order to narrow the distance between himself and these experts.

"I see, Comrade Jiankun, you are amazing. Young people nowadays all yearn to go abroad and are eager to show off their good things. You can think of publishing confidentially in order to help domestic scientific research narrow the gap with Europe and the United States. You are very conscious. Many of my students are not as good as you. Let's have dinner together later and have a good chat."

"Okay, I'll go to the guesthouse first, and then to the cafeteria. I also have some questions about aircraft design that I want to discuss with you."

Seeing that Mr. He had extended an olive branch, Wang Jiankun took it and asked to consult him on the issue of aircraft design.

"Okay, I'll walk slowly, so I'll go to the cafeteria first. How about we meet at the seat near the food window?"

"Okay, then it's settled."

……

"Come here, Jiankun, this chicken leg is good. You are young and consume a lot, so eat it. I am old and can't eat it." Old He picked up a big chicken leg and gave it to Wang Jiankun.

"Mr. He, please eat by yourself. You are doing research at this critical time, and you cannot let your body suffer from deficiency."

"It's okay. I beat this chicken drumstick specially for you. Our conditions are much better now. I also have some meat slices. There's enough for you to eat. Please enjoy."

Wang Jiankun couldn't refuse, so he took the chicken leg from He Lao. Wang Jiankun used his superpowers to check and found that He Lao was in good health and there was no disease in his body. It was just that he was old, and the function and vitality of some cells began to decline.

"Mr. He, how old are you? You have a head full of white hair, but you still insist on working on the front line of scientific research."

"I am 65 years old. I went to a farm 20 years ago and wasted more than 10 years there. My hair turned white at that time. Actually, I am in good health. I was worried about my hair turning white at that time. I had just made some progress in my research on airplanes, but I had to stop, so I was worried about my hair turning white.

Now I finally have the opportunity to participate in the design of a new fighter jet, and I will do it even if it means risking my life to make up for the wasted time.

Of course, we also have the problem of insufficient backup forces. You have seen in the conference room that there are very few young and middle-aged researchers. We old guys have to step up and help them. At the same time, we cannot let research stagnate. Our country can no longer stop."

Mr. He talked about his experiences while eating.

"It's not easy for you, but everything will get better and better. Now that we have reform and opening up, our development speed is accelerating. With people like you helping us, I believe our scientific research achievements will become greater and greater."

"Yes, by the way, Jiankun, didn't you say you had some questions about aircraft design? If you have nothing to do tonight, let's find a place and I'll tell you about it."

"Okay, I don't have anything to do tonight, why don't we go to the small conference room in the guesthouse? The conditions there are pretty good."

"Okay, I'll go back after dinner and tell my wife and come over, you go first."

After finishing his meal, Mr. He left the cafeteria with his lunch box. Wang Jiankun washed the lunch box in the cafeteria and put it in the storage room, then walked towards the guesthouse.

In the factories in the distance, workers can be seen coming in and out from time to time. Those are civilian product workshops. Although there are not many orders and the amounts are not high, the factory still runs night shifts so that the workers have work to do and get a basic salary, hoping to keep the workers' jobs and their skills in this way.

……

"Mr. He, you're here pretty quickly. Come, here is some tea. Let's drink tea and chat."

Not long after Wang Jiankun arrived at the guesthouse, he waited for Mr. He, then took him to a small meeting room in the guesthouse, made him some tea and started chatting with him.

"Mr. He, I was invited here not only to explain to you how to apply the general solution of the NS equations, but also to participate in the design of this fighter, so I would like to first understand from you what difficulties you are currently facing."

"Oh? Jiankun, you also research aircraft design? You are a versatile person!"

"I don't deserve it. I have a good brain and I was interested in flying machines before, so I learned a little bit."

"Don't be so modest. The examples you gave before show that you have learned a lot."

After chatting for a while, Mr. He began to explain to him the original intention of designing this third-generation aircraft designed by Factory 132 to compete with the American F16 fighter and the difficulties it is currently encountering.

(End of this chapter)