Chapter 1177 I am here to solve the problem

Compared with the experienced Yu Hongru, Jiang Zongli and Chen Hong's mentality is obviously much simpler.

It was not until Chang Haonan finished his even-handed speech that the two realized that the former was not prepared to choose between these two directions at all.

At the beginning, it was naturally a surprise.

As long as there are enough resources, who wouldn’t want to get it done in one go?

But the joyful mood did not last long.

After Yu Hongru stepped down to the second line, they were the ones who were truly responsible for implementing the wind tunnel research and development.

Many problems cannot be solved simply by having money.

"Academician Chang."

After Chang Haonan finished his speech, Chen Hong took over the conversation first:

“I don’t mean to target anyone… But the experience we have accumulated in the JF8 and JF10 wind tunnels in the past is based on the reverse detonation unloading technology, while the forward detonation combined with the shock wave reflection principle is a core technology route that affects the overall structure of the wind tunnel. If we want to achieve high total airflow temperature and long experimental time in the same wind tunnel, then the construction period…”

Everyone basically knows how fast Chang Haonan works.

If it took four or five years just to build a wind tunnel, it would probably be difficult to meet his requirements.

Therefore, even Jiang Zongli, who was not specifically targeted, did not immediately refute.

After all, the problems that Chen Hong mentioned do exist objectively.

But now that the project is right in front of him, he can't let go of this opportunity no matter what.

So Jiang Zonglin gritted his teeth and said firmly:

“The design methods of the shock wave reflection chamber and the auxiliary detonation section are still at the stage of theoretical analysis and numerical simulation. To implement them in the wind tunnel, more sufficient test data support is needed. However, we have basically solved the problem of applying the one-dimensional combustion model under detonation wave conditions…”

"Academician Chang, you are an expert in numerical calculations. You should know that in actual work, the one-dimensional model can be generalized to obtain the fundamental waves of high-dimensional solutions, so the efficiency should be much faster than expected... My team and I promise that we will not hinder the entire project!"

Chen Hong on the opposite side did not really want to suppress Jiang Zongli, so he did not add insult to injury.

Just waiting quietly for Yu Hongru or Chang Haonan to give feedback.

"The JF10 wind tunnel has been in use for six years and is about to enter a routine maintenance and upgrade..."

Yu Hongru said as he looked at Chen Hong:

"Xiao Chen, if you can move fast enough, you can put the two technologies of start-up shock wave reflection control and shock wave/boundary layer contamination suppression on the JF10 wind tunnel for a few rounds of testing... After the research on other parts has made progress, you can put them together and comprehensively consider the specific design plan for the new wind tunnel."

"As for Xiao Jiang..."

At this point, he was a little stuck.

On the one hand, Jiang Zonglin was his direct disciple, so it was difficult for him to show too much bias.

On the other hand, Yu Hongru has spent his entire career studying reverse detonation coupling and explosion unloading technology. He can only say that he has some understanding of the theory proposed by Jiang Zongli, but he is not sure about the specific progress.

Seeing the other party's embarrassment, Chang Haonan quickly stepped forward to help:

"In fact, Researcher Jiang doesn't have to worry too much about the progress."

As he spoke, he bent down, took out his laptop from his bag, and placed it on the table:

"The reason I came here this time is actually to solve the theoretical problem of detonation calculation..."

Jiang Zonglin was stunned at first, then quickly turned to surprise.

But he quickly forced himself to control the expression on his face, as if he couldn't believe such a coincidence:

"Calculate... you mean the Chapman-Jouguet combustion equation?"

As we all know, combustion is essentially a redox reaction that produces light and heat.

Since the reaction itself generates heat, and the three elements of combustion include an ignition point, combustion can usually spread spontaneously if there are sufficient combustible materials and oxidants.

Conventionally, people call the low-speed combustion process deflagration, and the high-speed and violent combustion process detonation.

Therefore, the problem of propagation and reflection of detonation waves is essentially a combustion problem.

If we can conquer, even partially, the Chapman-Jouguet combustion equation under high-dimensional conditions, then many problems that originally required experiments can be solved on paper.

Chang Haonan smiled and nodded:

"Yes, some time ago, I used the high-dimensional conservation law to study the self-similarity problem of the two-dimensional simplified CJ model..."

While they were talking, Jiang Zongli had already taken the initiative to connect Chang Haonan's computer to the projector.

The original line of titles on the screen suddenly disappeared and was replaced by a new page of PPT.

The above is an equation that is quite familiar to everyone present.

"Researcher Jiang just said that you have already studied the one-dimensional CJ ​​combustion model, so I will start from there..."

Chang Haonan turned around and gestured slightly, then continued:

"For the global solution of a class of n-dimensional combustion models, the initial boundary is an n-1-dimensional smooth manifold, which can be a curved bounded complex surface, or any other form that meets the requirements. In short, after appropriate coordinate transformation, the solution of the original equation can be reconstructed."

"Considering the working characteristics of the wind tunnel, we will not consider higher-dimensional problems for the time being and limit this equation to two dimensions..."

"In the actual combustion process, the boundaries of combustibles are basically curves or surfaces... We construct a non-self-similar solution of the combustion model and analyze its complex geometric structure. By comparing the difference between the high-dimensional non-self-similar solution and the one-dimensional self-similar solution, it is easy to discover the new spatial structure characteristics of the detonation wave..."

"..."

Soon, a phased conclusion appeared on the PPT:

"If for any x∈R, [-Φ'(x)f(u+)+g(u+)]-[-Φ'(x)f(u-)+g(u-)]>0 holds, then when q0<Qg, the combustion reaction will only produce a strong detonation wave, and the analytical solution to the two-dimensional CJ ​​equation is..."

"..."

Jiang Zongli was not a mathematics major, so he was somewhat confused when he first faced long sections of derivations and calculations, as well as expressions that could not be written on a single page of PPT.

But Chang Haonan did not intend to explain the entire process from a theoretical perspective.

Therefore, after ruling out the existence of self-similar solutions to the original equation and starting to discuss the intensity and waveform of the blast wave in different situations, I became much more sober.

The pen in my hand began to quickly record the contents of the PPT.

In the end, a very beautifully structured expression appeared in the notebook.

Jiang Zonglin looked at the final result of the two-dimensional equation in front of him and couldn't help holding his breath:

"So... after adding the piecewise expression of q(t, x), the structure of the solution actually has the structural characteristics of a hyperbolic system of equations?"

For a moment, he even doubted the authenticity of all this.

Such a direct analysis process, but I was totally unaware of it...

But when I thought about the terrifying calculation process in the first half, I quickly felt relieved.

"Not only that."

Chang Haonan changed the form of the solution and gave a preset initial condition:

"When strong detonation and detonation occur simultaneously, the combustion wave interface and the sparse wave weak discontinuity behind the wave converge together to form a trifurcated structure. This is the result of the interaction of three sets of waves."

At this time, Jiang Zongli was already immersed in his own thoughts, and began the subsequent engineering analysis with rapid writing.

Out of curiosity, several people nearby leaned over and wanted to see the contents of Jiang Zongli's notebook.

But he was stopped by Chang Haonan.

He knew very well that this "flow" state was very rare, so he didn't intend to disturb the other party.

It’s still early anyway.

A ten-minute burst of inspiration now may be worth weeks or even months of follow-up work later.

It was not until about half an hour later that Jiang Zongli's hand movements gradually slowed down.

In this room which was less than 20 square meters, his forehead was already covered with sweat.

This is enough to show how intensely the brain was working just now.

"I see……"

Jiang Zonglin raised his head again:

"The FC-WENO hybrid method can be constructed for the hyperbolic conservation law equations in a single-region framework. Because the smooth and non-smooth regions in the single-region framework change with the state of the numerical solution in the flow field at all times, the high-precision linear format can be used to the maximum extent, improving the accuracy and efficiency of the calculation!"