Great Country Academician

After verifying the practicality of the Xinghai space shuttle, the design and construction of the second space shuttle was also put on the agenda.

Compared with the Red and Blue Cold War in the last century, whether it was the space shuttle designed and manufactured by the Red Soviet Union or the United States, the advantages of the Xinghai were really too great. It is not an exaggeration to say that it was a leap in quality.

But despite this, the weight of cargo carried by the Xinghai itself, or the amount of materials it can carry to climb the gravity well, is still limited.

Judging from the current experimental and test data of multiple unmanned flights of Xinghai, Xinghai can carry up to nearly 50 tons. The accurate data should be 48.75 tons of materials climbing the gravity well into outer space.

This data has a certain shrinkage and error compared to the more than 60 tons previously calculated through joint simulation of aerospace engines and miniaturized fusion reactors.

But this is a normal situation. After all, the previous simulation data was based on supercomputing and various conditions were basically perfect. In fact, the design of Xinghai has not reached perfection. Whether it is the wings or the fluid balance, they need to be optimized and adjusted after step-by-step experiments.

The low-Earth orbit transfer capacity is close to fifty tons. For the development of aerospace, this load is not small, but it cannot be said to be very large.

After all, if the load of a traditional chemical fuel launch vehicle is large and super heavy, such as the Long March 9 or Space-X's BRF, its low-Earth orbit transfer load starts at a few hundred tons.

The design and manufacture of the second space shuttle is, on the one hand, to fill the gap in the Xinghai Research Institute's load capacity in the aerospace field and increase its space transportation capabilities.

If the two space shuttles carry out manned landings on the moon or the construction of lunar surface bases, their capacity to transport supplies is not 50 tons + 50 tons, but much greater than 50 + 50.

With the volume and size of the cargo compartment of the Xinghai space shuttle, there is no impact of gravity and air resistance in outer space. Xinghai can carry hundreds of tons of supplies to the moon at a time.

In this case, it is completely possible for the two space shuttles to cooperate with each other. The first space shuttle carries supplies to space, enters low-Earth orbit and adjusts its orbit, and then the second space shuttle carries supplies for replenishment.

The method is similar to the docking and material transfer between the space station and the space supply ship.

This was one of the main reasons why the second space shuttle was designed and built.

And another important reason is ‘Interstellar Rescue’!

You must be familiar with aerospace movies such as "The Martian" and "Gravity", which are about interstellar rescue.

In the field of modern aerospace, since we can go to heaven, we will naturally take into account the disaster accidents in which astronauts are trapped in outer space. Each major space country also has corresponding methods of "aerospace rescue" or "space rescue".

However, it is too difficult to implement due to limitations in various technologies.

The Xinghai, which uses electric propulsion, is different. Compared with traditional spacecraft that have little power and endurance after entering outer space, they can complete spaceflight at the fastest speed and have full orbital adjustment capabilities in outer space.

The new generation of electric propulsion space shuttle that uses small fusion reactor + aerospace engine as its function and power system has no problem in terms of power and endurance.

It can adjust its orbit and return to the spacecraft with problems again and again to complete the rescue work even if rescue docking fails countless times.

On the other side, in the Xinghai Research Institute.

After handing over all aerospace-related work to Weng Yunzong, Xu Chuan returned to his office, thinking about how to solve the high temperature and thermal barrier problems faced by the space shuttle when it returned to the atmosphere.

This is a world-class problem that has existed since the space competition between the Soviet Union and the United States in the last century, or since humans developed the first spacecraft to enter space.

Over several decades of development, although researchers and scholars in the aerospace field have thought of countless solutions, they have never been able to solve this problem.

Of course, there are certainly corresponding improvement ideas and methods.

The most famous among them should be the shock wave theory proposed by Professor Henry Allen, a physicist at the NACA Space Agency (the predecessor of NASA) in the United States.

In 1951, Henry Allen discovered in confidential internal research that the front end of a spacecraft re-entering the atmosphere at high speed will produce a strong compression effect on the air.

That is, when the space shuttle returns, the head of the aircraft will form an umbrella-shaped shock cone in the atmosphere ahead, and the air density at the front of the shock wave will increase sharply, eventually becoming like a moving wall in front of the spacecraft. The spacecraft moves forward in the wake of the shock cone.

To put it simply, it can be understood that when the space shuttle returns, the hottest thing is not the space shuttle itself, but the 'shock cone' generated at the head of the space shuttle.

The 'aerodynamic heating' is also mainly caused by the compression and friction between the shock wave front and the static air in front.

Based on this theory, Henry Allen believed that if the spacecraft surface and the shock front were kept at a certain distance, the friction temperature of the spacecraft surface could be greatly reduced.

With this idea, Henry Allen designed a blunt spacecraft head, and through experiments and final demonstration, confirmed that this theory worked.

This is why the heads of spacecraft, space shuttles, and intercontinental missiles currently studied by various countries all use blunt-nosed cones.

Because the blunt nose of the spacecraft can effectively push out a wide and strong shock wave at the bow during the deceleration process, and push the wave front away from the bow and surroundings, just like the waves pushed away by the bow of a flat-headed barge.

These days, Xu Chuan has been searching and reading relevant information and papers, thinking about how to further improve Professor Henry Allen's shock cone theory.

Compared with traditional materials and technologies such as heat insulation, heat dissipation, and heat resistance, the shock cone theory is currently his most promising route.

This is determined by the extremely high speed of the space shuttle.

In daily life and the physics that most people have learned, if you want to reduce aerodynamic resistance to reduce aerodynamic heating, then the volume of the object should be made as small as possible.

Because when the volume of an object becomes smaller, the friction area with air will also decrease. Therefore, in fields where speed and efficiency are emphasized, the smallest possible object design is usually chosen.

But on a spacecraft, this theory is invalid, especially during the process of returning to the atmosphere. The extremely high speed of the spacecraft causes the aerodynamic heating to heat up too fast, and the sharp head reduces the effect of aerodynamic heating. Very little.

The nose cone is subject to a highly concentrated heat load in time and space, and has no time to dissipate heat, and will be burned out quickly.

Traditional heat-resistant materials or heat insulation, heat dissipation, and thermal conduction technologies can only slightly delay the timing of being burned, but they cannot fundamentally change the outcome of being burned.

The shock cone route is more suitable for extremely high-speed space shuttles.

In the office, Xu Chuan was thinking about theories related to shock cones.

Although Professor Henry Allen's shock cone theory has brought certain optimization methods to the blunt head of the spacecraft, this problem still exists, and the most core mathematical theory has not been solved.

Behind the desk, after thinking for a while, he took out a stack of draft paper from the drawer, pondered for a while and then stroked the ballpoint pen in his hand.

【∑i=1·/xi(H(φ)φxi)= 0】

This is the system of equations for the 'supersonic spoiler problem'.

To put it simply, when a flying object flies at supersonic speed in the air, a shock wave will generally be generated in front of the flying object. From the perspective of relative motion, it can also be understood that when a supersonic airflow passes over a fixed object, a shock wave will be formed in front of the object due to the obstruction of the object.

It is the shock cone at the head of the spacecraft mentioned before. The formation of this shock cone will greatly change the state of the airflow, thereby changing the force on the object.

Studying the position of the shock wave surface generated after this 'supersonic airflow' is blocked by a fixed object and the flow field behind the wave is called the problem of 'supersonic flow around'.

If expressed using mathematical formulas, Euler equation or Navier-Stokes equation is usually used to describe the flow in aerodynamics.

It is a hyperbolic equation in the supersonic region and an elliptical equation in the subsonic region.

The study of this equation is crucial to the development of modern high-speed flight technology and the solution of the supersonic spoiler problem equations.

Unfortunately, since the distribution of fluid velocity in the flow field is unknown, the transformation line from the hyperbolic equation to the elliptical equation is also unknown. In addition, the fluid motion equation is nonlinear.

The accumulation of various complex factors has led mathematicians to study this system of equations. When dealing with mathematical analysis, it will involve nonlinearity, mixed types, free boundaries, global solutions, etc., which are generally considered to be in the theory of partial differential equations. The most difficult factor.

Therefore, for the problem of supersonic flow around a blunt object, due to the inevitable deformation of the equation, there is currently a lack of results that have been rigorously proven by mathematical theory, whether it is about the existence, stability or structure of the solution.

Although its difficulty is not as high as the NS equation and the Euler equation, there has not been much research progress in the mathematical community to prove its difficulty.

Staring at the formula on the draft paper, Xu Chuan fell into deep thought.

To deduce the problem of supersonic flow around a blunt object, according to his mathematical intuition, the best way is not to deal with it directly.

It is a system of partial differential equations evolved from Euler equations and NS equations. To solve it, according to his current mathematical intuition, it is best to further decompose it first.

Of course, he is not the only one who has this idea. Many mathematicians are doing it, but everyone has different understandings and perspectives.

After thinking for a while, Xu Chuan continued to write, transforming the three-dimensional inviscid compressible steady flow equations into a boundary value problem with fixed boundaries, and further transformed it.

". Then: given the curve i in the three-dimensional space oxyz: x h (z), y = g (z) and given the airfoil with i as the leading edge, ∑ y = ψ (x, z)."

"When the incoming flow is supersonic, a shock wave S+ attached to the front edge will be generated: y=p. When only discussing the local solution near the origin, there is μ·f/x-υ+ω·f/z=0, and y=f(x,y)”

The ballpoint pen in his hand kept falling on the white manuscript paper. Xu Chuan was immersed in it, constantly expanding his thinking.

Although he usually advises and teaches his students and attends classes at NTU to stay active in mathematics, to be honest, he has not had such focused and in-depth thinking on mathematics for a long time.

Originally, Xu Chuan thought it would take him a few days to fully recover his sense of mathematics, but unexpectedly, when he wrote the first line of calculations, the thoughts that had been dormant in his mind for a long time became active again.

It's like muscle memory. No, it may be more appropriate to describe this feeling with the instinct carved in DNA. When he decomposes and derives the problem of supersonic flow around blunt objects, the mathematical knowledge in his mind is It came alive automatically like running water.

The transformation, decomposition, twisting and processing of each item are as natural and smooth as breathing.

A long time passed little by little, and when the last line of calculations fell on the manuscript paper, the desk was already covered with calculation papers with the calculations listed.

Putting down the ballpoint pen in his hand, Xu Chuan looked at the calculation he had derived.

[||(Un+2-Un+1,φm+2-φm+1)||E〃N-1(T)≤CT||(Un+1-Um,φm+1-φm)||]

When T is sufficiently small, the limit of {(Um, φm in E〃N-1) is the solution of equations (7) to (9), and then the existence of the local solution is obtained by returning to the original scale.

Since N can be made arbitrarily large in the theorem proof, this solution is C∞ and smooth!

A phased result on the problem of supersonic flow around blunt objects was completed in his hands.

The whole process was incredibly smooth, as if a clear stream was flowing smoothly like jade.

Even he himself felt a little surprised by this.

After all, he hadn't focused on mathematics for a long time.

And for any thing, if you put it down for a period of time, it will definitely take time to get back to the state. This is for sure.

Just like ordinary people playing games, if you haven't played a game for a long time, when you pick it up again, your status will definitely deteriorate and your level will decrease.

For a scholar, when he is idle in his professional field for too long, the skills he originally mastered will gradually weaken.

This is also the reason why most researchers or scholars cannot take time off.

Even many of them have entered their old age, such as his mentors Professor Deligne and Professor Witten. The reason why they are still studying academics is precisely because they cannot bear the knowledge they once mastered to pass away from their minds.

However, in today's mathematical deduction, Xu Chuan felt as if he had skipped the restorative training process directly, and the thoughts in his mind kept supporting him to move forward.

Even though the NS equation had been solved long before, he still couldn't believe that he could so successfully make a preliminary result on the problem of supersonic flow around blunt objects.