What is the difference between a hyperbolic cooling tower and a mechanical tower?

Hyperbolic cooling towers are commonly used in power plants to supply cooling water to the turbine systems. Their main advantages are high water treatment capacity and low operating costs, but the downside is that they result in a smaller decrease in water temperature compared to vertical cooling towers of the same capacity. Mechanical cooling towers are commonly used for water in chemical processing systems; they cool the circulating water by using fans to blow air in counterflow. Their main advantage is that they can reduce water temperature significantly, but their operating costs are high. The applications of the two differ to some extent, each having its own advantages and disadvantages; it is necessary to choose the appropriate one depending on the specific situation.

A cooling tower is a device that uses water as a circulating coolant to absorb heat from a system and release it into the atmosphere, thereby reducing the water temperature； It works by utilizing the heat exchange that occurs when water comes into contact with moving air to generate steam; the evaporation of this steam carries away heat, thereby enabling heat dissipation through processes such as evaporation, convection, and radiation. This mechanism is used to remove excess heat generated in industrial processes or in refrigeration and air conditioning systems, thus reducing the water temperature and ensuring the proper operation of the system. The device is usually barrel-shaped, which is why it is called a cooling tower. Features making natural ventilation hyperbolic cooling towers suitable for power plants: 1 Increased installed capacity of power plants – 2 The need to build larger cooling towers – 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 their construction is also costly – 5 There is a need to construct large cooling towers in an economical manner – 6 Hyperbolic towers are the most economical option. Whether made of concrete or steel, a 200-meter-high vertical wall is extremely unstable; to enable it to withstand wind forces and deformation, it is necessary to thicken it or use more rebar, and as a result the tower would end up resembling a skyscraper, with costs that are unacceptably high. We need to find an economical way to reduce the cost of cooling towers, and that is through a shell-like curved surface structure – in other words, the curvature itself provides strength. This is because the Gaussian curvature of a surface is not zero; as stated in the \"Theorema Egregium\" proposed by the great mathematician Gauss, it can be inferred that you can bend a surface however you like, as long as you do not stretch, compress, or tear it, its Gaussian curvature will remain unchanged. In other words, for structures with a non-zero Gaussian curvature, the Gaussian curvature only changes when the structure is torn or exceeds the material’s bearing capacity; therefore, the structural strength and deformation resistance of such surfaces are very high. Therefore, we need to build the cooling tower in a curved shape. It should be noted here that the Gaussian curvature of cylindrical and conical shapes is 0; in other words, a plane can be rolled into a cylinder or cone, which means their strength is lower than that of other surfaces. All thin-shell curved surface structures feature high strength and material savings; there are also cooling towers in other shapes and materials, and the exploration of such structures is endless. Typical large cooling towers today are about 150 meters tall and have a diameter of around 150 meters at the base; in other words, their base is large enough to accommodate a football field. However, their thickness is very low, with the thinnest parts being only 20 cm thick. If such a cooling tower were scaled down to the size of an eggshell, it would be even thinner than an eggshell, with a thickness equal to only 1/5 of that of an eggshell.

So why is the hyperbolic surface structure the most economical? Firstly, based on the structure of the cooling tower, it can be seen that the tapered design in the middle allows for a larger inlet area at the same wetting surface area, which helps to increase the air flow volume. Therefore, this surface should be concave (negative Gaussian curvature). The reason for the economic efficiency of hyperboloids is not due to minimal material usage, but rather to their method of construction. A hyperboloid is a ruled surface, formed by a straight line in continuous motion – this is its most important geometric property. Therefore, the rebar does not need to be bent when arranged; it can simply be placed parallel to the inclined lines in space. After years of practical application in engineering, the mechanical properties and wind resistance of this structure have been thoroughly tested, making it the most common type of cooling tower; thus, the use of hyperbolic surfaces is also a result of historical inertia. In practice, construction work does not strictly follow the geometric shape of the surface; instead, surfaces are usually constructed in segments. Given the radius of the cylinder wall’s generatrix and its wall thickness, multiple flat steel formworks are used to approximate that shape. Therefore, strictly speaking, its final shape differs from that of a hyperbolic paraboloid; the tower shape we see today is the result of the interaction between optimized design, engineering practices, and construction conventions, and it thus differs from a geometric hyperboloid. Cooling towers are designed in a hyperbolic shape to improve cooling efficiency. The bottom part has the largest circumference, allowing maximum intake of cold air. When this cold air reaches the narrowest section, it comes into contact with hot water. Firstly, as the pipe diameter decreases, the flow rate of the air increases, enabling it to remove heat from the hot water more quickly. Secondly, the decrease in pipe diameter also compresses the volume of the cold air, resulting in an increase in pressure. An increase in pressure enhances the heat-carrying capacity of the fluid; thus, in the narrow section, the cold air can absorb as much heat from the hot water as possible, thereby cooling it. At the very top, the diameter of the tube expands again; the air, which has carried a large amount of heat, slows down, its pressure decreases, and it releases the heat it contained, forming white water vapor.

Common cooling towers are either square or circular in shape, and they are equipped with fans at the top; these fans function similar to exhaust fans, serving to accelerate the removal of water vapor and hot air. When these gases escape from the cooling tower, they create a white mist, just like when we exhale in winter. What is the shape of the cooling towers in power plants? According to Wikipedia, the cooling tower structures of many power plants are of the single-leaf hyperbolic shape. Since a single-sheeted hyperboloid is a doubly ruled surface, it can be constructed using straight steel beams. In this way, wind resistance is reduced. At the same time, the integrity of the structure can be maintained with the minimum amount of material. This is in terms of structure (a hyper surface is actually composed of straight lines) and flow lines (to reduce wind resistance). So, what are the internal fluid principles? Let’s first examine the principle of smoke extraction in chimneys. Chimneys are used to convey hot fluids, which are characterized by being lighter than air and therefore rise upward. To reduce pollution, chimneys need to be made very tall, and fluid flow generates resistance losses. Since hot fluids rise due to buoyancy, it is necessary to maintain their temperature; therefore, chimneys are made of materials with good insulating properties. So how can that flow resistance be overcome? The lower the flow velocity, the less the resistance. Logically, a chimney should have an increasing diameter as it goes upward, so that the flow velocity slows down and the resistance decreases, which is more conducive to emissions. For example, the exhaust pipe of a car has an enlarged outlet. Why is it actually designed to get thinner as it goes upward? Because hot air rises due to buoyancy, and buoyancy is generated by lower density; as hot air rises, its temperature decreases, and this drop in temperature causes the density of the gas to increase. At this point, it is necessary to reduce the air pressure in order to maintain a low density; this is achieved by converting the pressure of the hot air into velocity, that is, by reducing the flow path of the chimney. Whether this analysis is correct is just an attempt to stimulate further discussion. Then why isn’t the outlet of that power plant’s cooling tower narrowed like a chimney, but rather widened? Cooling towers utilize the simple chimney effect (Chimney effect_Baidu Baike) to drive air (or cold water with spray) to exchange heat with the hot mass, thereby achieving cooling. In fact, no matter what the shape is, as long as a space with a certain vertical slope is created, a chimney effect can occur. Then why is it designed this way in the diagram? Conclusion: The shape of the cooling tower in the diagram is a hyperurface. Given that the bottom and top surfaces are circular, to find the minimum surface area of a continuously connected surface, solving the equations reveals that the connecting surface is a surface generated by the rotation of a hyperbolic function. Therefore, the greatest advantage of designing a cooling tower in a hyperbolic shape is that, for the same cooling capacity (the same size of base and top surface, the same height, and the same cooling medium all determining the same maximum cooling capacity), the least amount of material is required for its construction. (It can be approximated that, with a constant wall thickness, the amount of material used is proportional to the surface area.) An additional advantage: the building materials for cooling towers are generally reinforced concrete. If a hyperbolic building is to be constructed using steel, straight steel members can be used for everything, which saves a lot on processing costs (see the Canton Tower, where all the bracing members are straight steel tubes).

One is a cooling tower commonly used in power plants, and the other is a cooling tower used for cooling circulating water or industrial water