Source: Steam Turbine Major
Original name: Why is the side of the cooling tower curved? Why is this surface hyperboloid shaped, and why is the opening on the top small?
1. Why are the sides of the cooling tower curved?
2. Why is this surface hyperboloid shaped?
3. Why is the opening on it small?
In order to distinguish the degree of priority of the factors, we have to sort it out.
First of all, the earliest cooling towers were of various shapes, such as straight and octagonal cylinders.
And after Iterson first invented the hyperboloid tower in 1915, this configuration quickly became popular in thermal power stations, so why this shift? The answer is scale.
This is a chain of relationships: 1 The installed capacity of the power station is increased - 2 Larger cooling towers need to be built - 3 Cooling capacity is directly affected by area and height, so cooling towers need to be taller and larger - 4 Tall cylindrical structures are unstable and even if they are built, they are expensive to build - 5 Large cooling towers need to be built economically - 6 Hyperboloid towers are the most economical.
Needless to say, 1 and 2 require a formula in process 3, that is, the cooling capacity (pumping force per unit area) is only related to the height of the cooling tower and the difference between the density of the internal and external gases, so the cooling towers are built higher and higher, and now they are usually above 100 meters, while the new towers are more than 200 meters.
This caused the problem in 4, the 200-meter-high straight wall is very unstable, and in order for it to withstand wind resistance and deformation, it has to be thickened or a lot of steel bars added, and eventually a tower will be like a skyscraper, and the cost is unacceptable.
Therefore, in 5, we have to find an economical way to reduce the cost of the cooling tower, which is the shell curved structure, which means that the curvature can produce strength.
This is because the Gaussian curvature of a surface is not 0, and it can be deduced from the "Theorema Egregium" proposed by the great mathematician Gauss that you can bend a surface at will, as long as you do not elongate, compress or tear it, the Gaussian curvature will not change.
In other words, for a structure with a non-zero Gaussian curvature, the Gaussian curvature will only change when it is torn or beyond the bearing capacity of the material, so the structural strength and deformation resistance of the surface are very strong.
Therefore, we need to build the cooling tower in the shape of a curved surface.
It should be noted here that cylindrical and conical structures have a Gaussian curvature of 0, which means that they can be rolled into a cylinder or conical with a plane, so their strength is not as good as that of other surfaces.
From left to right: Negative Gaussian curvature surfaces (hyperboloids), zero Gaussian curvature surfaces (cylindrical), and positive Gaussian curvature surfaces (spherical surfaces).
Virtually all thin-shell structures are material-efficient, and there are also cooling towers of other shapes, and the exploration of structures is endless.
The Kozienice thermal power plant, the second largest in Poland, has a straight cylinder in the upper part of the cooling tower
The typical large cooling tower is about 150m high and has a diameter of about 150m at the bottom, which means that it can accommodate a football field at the bottom.
However, it is very thin, only 20cm at its thinnest point. If the cooling tower is scaled down to the size of an eggshell, it is thinner than an eggshell, only 1/5 the thickness of an eggshell.
So why is the hyperboloid structure the most economical?
First of all, according to the structure of the cooling tower, it can be seen that the design of the middle narrowing allows the air inlet area to be larger with the same water spraying area, which helps to increase the air volume.
Therefore the surface should be incurved (negative Gaussian curvature).
The cooling tower is shaped like a hyperboloid
Calculate the minimum surface area of a continuously connected surface when it is known that the bottom and top surfaces are circular, and solve the equation to find that the connected surface is a hyperbolic rotating surface.
Therefore, the biggest benefit of the hyperboloid shape of the cooling tower design is that the minimum amount of material used in the construction of the tower is proportional to the surface area under the same cooling capacity (the same size of the bottom and top surfaces, the same height, and the same cooling medium together determine the same maximum cooling capacity).
This is actually wrong, the minimum surface area of a continuous connected surface is a "minimum surface" problem, the German mathematician Euler solved in his paper in 1744, the "catenary surface" is the kind of rotating surface with the smallest surface area, and the catenary surface is obtained by the rotation of the catenary around its alignment.
Hyperboloids, on the other hand, are generated by hyperbolic alignments (or straight lines around a non-coplanar alignment), so the two surfaces appear to be similar in shape, but they are completely different.
The reason for the economy of the hyperboloid is not because it is the most material-efficient, but because of the way it is constructed, a straight-grained surface that is made up of a straight line through continuous motion, which is its most important geometric property.
Therefore, the reinforcement does not need to be bent when arranged, that is, it can be parallel to the oblique straight line of space.
The Canton Tower, also known as the small waist, can see that each main steel beam is straight
Therefore, after the Dutch engineer Iterson implemented this scheme in 1915, the hyperboloid form of cooling towers became popular.
Of course, with the increase in size, the construction method of hyperbolic cooling towers is to be staged concrete cast-in-situ.
The construction process of the world's first hyperboloid cooling tower
After years of engineering practice, the mechanical properties and windproof properties of this structure have been well tested, and it has become the most common form of cooling tower, so the use of hyperboloid is also a historical inertia.
In fact, in engineering practice, the construction is not completely in accordance with the geometric shape, and the curve form is different from the construction design, and the surface in the actual construction is mostly approached by multi-segment plane steel formwork.
So, strictly speaking, today's tower shapes are the result of the interaction of optimal design, engineering practices, and construction habits, and there are subtle differences from the geometric hyperboloids.
The cooling tower of the Kozienice power station in Poland mentioned above has slight differences in its initial geometry and construction drawings.
There is an additional feature of the structure of the middle inward bend, the Venturi effect, the narrowing of the air flow channel can increase the speed of the gas, which helps to increase the gas velocity near the evaporator, but this part is doubtful, according to some sources, the contribution of this part is very small, and it is necessary to ask the expert in fluid mechanics to explain.