Cooling tower for nuclear power plants

Cooling towers for nuclear power plants often have the shape of a hyperboloid. At first glance, I thought that an obvious reason for this would be the smaller sectional area, meaning the tower would be less exposed to wind.

However, I did a quick calculation, based on a cooling tower nearby. I modeled the cooling tower as a hyperboloid and calculated its volume and its sectional area. I then calculated the radius needed for a cylindrical tower with the same volume. Its sectional area was just 1.5% larger. By reducing its height from 150 to 145 meters (and increasing the radius, of course), the sectional areas would have been the same.

I know that hyperboloids can be built using only straight pieces of reinforcement. However, those towers are quite big and the circular shape could be very well approximated by some sort of polygon with e.g. 1000 vertices making circularly shaped reinforcement unnecessary.

I can imagine other reasons:

• The waisted shape could probably lead to a certain compression of the hot vapor and thus help/accelerate the condensation. Is this true? How big could that effect be?

• Some documents I have read say one needs less material to build a hyperboloid cooling tower. Is there really a big difference in terms of concrete? After a rough calculation, assuming a thickness of 1 meter of concrete all around, I'd estimate that a cylindrical shape would only need approximately 1.5% more concrete.

So, why do almost all cooling towers have this particular shape?

• Just a note: that cooling tower design is seen on other power plants that use the Rankine cycle. I've seen pictures of coal-fired plants that use it. Commented Jun 10, 2019 at 16:58
• It's probably also worth a note that many nuclear stations don't have towers - none in the UK do that I know of. Commented Jun 10, 2019 at 20:22
• @Will.W, some older nuclear stations had towers, but the remaining installations are all coastal, and simply use pumped seawater for cooling. Commented Mar 2, 2021 at 12:48
• @Steve True - Calder Hall had cooling towers. Commented Apr 9, 2021 at 17:26

The hyperbolic shape of cooling tower is preferred as this shape is stronger against wind pressure. Consequently, the concrete wall thickness can be reduced and optimised. from 1.5m at the base of the viel, the shell thickness rapidly fall to ~30cm.

The venturi effect resulting in the usage of this shape is, contrary to popular belief, not improving the performance of the cooling tower. Indeed, the Venturi effect increases the speed at the throat which creates a very slight increase in the pressure drop by friction on the walls. This reduces the draft and therefore the air flow available for cooling. This very marginal loss of performance is largely compensated by the gain in resistance of the shell to external winds.

The height of the tower is determined by :

• Local permit for maximal construction height.
• A balance between performance / cost / erection time.

If the tower is high, the draft will be stronger, thus the airflow will be higher thus the cooling effect will be better. However, if the tower is high, the cost increase rapidly with the difficulty to bring concrete at such height. But also due to the increased thickness of the shell (due to self weight and the wind load). Sometimes, construction time is a limiting factor, rule of thumb is 1m of shell per day. If the tower is 200m, it might be too long for a project.

Reference : 20 years as a hyperbolic cooling tower design engineer

• Thanks very much for your insights and explanations. Commented Mar 2, 2021 at 11:55

The shape is to take advantage of the Bernoulli law.

The narrower throat of the tower creates reduced pressure encouraging faster convection discharge of warm, moist vapors.

Hot water from the turbines is sprayed in at roughly 1/3 height. that compared with cool water on the floor, usually from a near river creates uplift and convective ventilation.

That hyperbolic shape of the tower accelerates this vertical flow.

• Thanks for the answer. Do you have any information on how big the effect is? Also, what does that mean with respect to all those explanations about "using less material" and "offering maximum stability"? Commented Jun 10, 2019 at 6:29
• @PhilippImhof, conic-like geometry is highly stable in earthquakes, and any other geometry would have to use more material and reinforcement to resist the same Richter as the hyperboloid, especially the fact that they stay surefooted on the diagonal columns on the lower part. Commented Jun 10, 2019 at 6:39
• Thanks again. Do you have any links where I can read more about that topic? Commented Jun 10, 2019 at 6:53