Twistower

A contrail is stable because droplets condense in the vortex core. The droplets move to the core outer diameter, leaving behind the latent heat in the core. This heat generates a temperature inversion at the core diameter, which due to the centrifugal force, prevents mixing of the low density core with the higher density ambient. This inversion boundary makes the vortex very stable.

A thin-walled cylinder is stronger than a temperature inversion and will generate more stable vortices. If the air in the cylinder is hot the vortex will be even more stable. If a rotating thin walled tower like the Twistower is applied for a Solar Tower it will generate a stable vortex with low flow losses.

Solar tower application

A solar tower lifts sun heated air by the chimney effect. The kinetic energy of the lifting air is transferred in electrical power by turbines in the tower base.

The tower will float if it is lighter than the lifting force of the low density hot air and the drag force of the flow in the tower. More lift can be provided by helium or hydrogen filled inflatable ribs.

Another idea to apply a thin walled tower is the green tower in Namibia. An idea to apply a vortex is the vortex engine. The problem of a non rotating thin walled tower is the under pressure, which will implode the cylinder. The problem of a non bound vortex is the stability and the small core diameter. Both problems are not present in the Twistower, where the inner pressure on the wall is in equilibrium with the outer pressure on the wall and where the core diameter is automatically the wall diameter. Due to the low loads the wall can be thin if the applied material is strong and light as for instance carbon fiber.
In principle each individual part of the wall will be in equilibrium with the air forces, though the loads on the wall are small. The vortex is generated by a vane grid at the bottom of the tower. The kinetic energy is transformed by windturbines, applied around the tower inlet.

If there is wind the tower will be tilted by the wind force. The tilt angle depends on the acting vertical and horizontal forces on the tower and the inflatable ribs filled with light gas.

The vertical force is due to the density of the hot rotating air, the vertical part of the force due to the inflatable ribs filled with light gas, tower weight and internal tower drag:

Fv = (π/4)d²hg[(ρo – ρi) cos φ+0.5 Ca ρo /(gh) (D/d)² vw²sin φ cos φ
-4 t/d ρw+ρi sin φ λ/(gd) vt²]

The horizontal force is due to wind drag on the tower and inflatable ribs:

Fh = 0.5 ρo vw² (Cd h d sin φ + Ca (π/4)D² cos² φ)

The resulting tower tilt is

φ = arctan (Fa /Fh)

Because the tower cannot support bending moments it is lateral free and only positive axial forces will be supported, so the stress in the tower wall sheet is:

σ = (Fv² + Fh²)½/(πdt)

To provide the lateral freedom the tower is supported at the root by a rotatable hinge, while the connection with the base is provided by a rotatable labyrinth (brush) seal.

For a 60 m diameter, 1000 m high tower with a wall sheet of 0.4 mm the tilt angle and the sheet stress is given for different windspeeds in figure 5 below.

During normal windspeeds up to 5 m/s the tower tilt is between 65o and 80o, which is feasible. At high windspeeds of 22 m/s the tower tilt is 30o and for the short period it will occur, it is feasible. Even at extreme windspeeds the tower will not hit the ground (φ>18o).
In all conditions the wall sheet stress is feasible (σ < 100 MPa) if the sheet is reinforced with high tension fibers. Of course if extreme weather conditions are expected the tower can easely be deployed.

Advantages

The tower will be very cheap and is easy to erect and to maintain. It can be compared with the erection of hot air balloons or zeppelins.
The mass of the tower is only 180 ton, which is orders smaller than for a conventional 60 m diameter 1000 m high tower (estimate: 500000 ton). The estimated cost is only 20 M€ which is also orders cheaper than for a conventional tower (estimate 300 M€).
For a 200 MW solar tower, this is only 0.1 €/W and very feasible.
If provided by a greenhouse driven solar updraft tower the estimated electricity cost is 3 - 6 €ct/kWh. If provided by a solar pond driven updraft tower the estimated cost is 1.5 - 3 €ct/kWh.
The efficiency of an updraft tower is proportional with the height of the updrafting air column, which is the tower height for conventional towers. Because for the Twistower the stable vortex will go on, the height of the updrafting air column will be much higher and is expected to be more than twice of the tower height. This will make the efficiency of the Twistower much higher than for a conventional tower.

Critical points and recommended measures

• Rain and ice will increase the tower mass, which might sink the tower to the ground
• Birds might damage the tower
• Aero-elastic instability might damage the tower and the turbines

To avoid ice deposition it is preferred to place the turbines in ice free places. However if it occurs occasionally at higher levels the ice will melt if the tower goes down and will lift again after melting of the ice.
To avoid rain deposition the wall should be hydrophobe, so the centrifugal force of the rotating tower will get the rain off.

Birds will be driven away by noise. It is expected that the rotating tower will locally transmit sufficient noise to warn the birds. Never the less if a collision might happen, the thin tower sheet will damp the collision. Also because the internal pressure is in equilibrium with the external pressure a small hole is no problem and hardly any leakage of hot air will occur.

Due to the low stiffness and the large aerodynamic damping of a light sheet no dynamic or aero-elastic instability is expected.
Before and during extreme weather with large wind speed gradients (turbulence) like thunder storms the tower should be deployed.

Conclusions

The Twistower is a very cheap tower, which can generate or transfer kinetic energy by air flow with high efficiency. Because conventionally the tower is an expensive component the application of a Twistower will substantially decrease the cost of a solar updraft tower.

Other applications like cheap chimneys or cooling towers might also be possible.