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**COOLING TOWERS:**

The process of thermal electricity generation with a nuclear reactor produces about 2 kWht of low grade heat for every 1 kWhe of electricity generated. In order for the electricity generation to be dependable a FNR must be able to dispose of the corresponding amount of low grade heat regardless of the outside air temperature.

On cold days in the winter all of the low grade heat can be used for meeting the district heating load. However, on warmer days part or all of the low grade heat must be rejected either to a large body of water or to the atmosphere via cooling towers.

To a first approximation a natural draft cooling tower is a tall vertical cylinder that is open to the outside at both its top and bottom. Near the inside bottom of the cooling tower there is a heat exchanger which uses warm condenser discharge water to heat the air. The resulting lower density of air inside the tower as compared to air outside the tower creates a natural draft and hence an ongoing air flow up the inside of the tower which continuously removes heat from the heat exchanger.

Cooling towers have two modes of operation, "dry" and "wet". The "dry" mode should be used when the outside air temperature is less than 5 degrees C. The "wet" mode is should used when the outside air temperature is greater than 5 degrees C.

In the "dry" mode there is about a 40 degree C temperature difference between the condenser water discharge temperature and the outside air temperature. That temperature difference is sufficient to provide about a 20 degree C temperature difference between the cooling tower discharge air temperature and the cooling tower inlet air temperature. That air temperature difference provides enough natural draft that the cooling towers when operated "dry" can reject all of the available low grade heat. The advantages of operating a cooling towers in its "dry" mode are that there is no consumption of water and there is no water vapor emission that from that cooling tower that can potentially lead to vapor condensation and icing of exposed surfaces in the vicintity of the cooling tower.

In the "wet" mode there is about a 20 degree C temperature difference between the condenser water discharge temperature and the outside air temperature. That temperature difference is sufficient to provide about a 10 degree C temperature difference between the cooling tower discharge air temperature and the cooling tower inlet air temperature. That temperature difference does not cause enough draft driven air flow to reject all of the available low grade heat.

In the "wet" mode the heat rejection is increased by spraying liquid water into the rising warm air stream. Part of the water spray evaporates and in so doing absorbs its latent heat of evaporation which adds to the rate of heat rejection. The disadvantages of "wet" mode cooling tower operation are the costs of the evaporated water and potential local area icing if the outside air temperature dips below 0 degrees C.

The heat disposal challenge is in the summer when there is little capacity at the buildings to absorb heat from the district heating system and the performance of the cooling towers is diminished by the higher outside air temperature. In order to operate the electricity generation at maximum capacity in the summer when the outside air temperature is 30 degrees C each of the 16 cooling towers must be able to continuously sink:

**45 MWt**

at an outside air temperature of 30 degrees C.

This heat rejection objective is met through the use of dual mode cooling towers that operate wet in the summer and dry in the winter. The wet/dry mode switch occurs at an outside air temperature of about 5 degrees C and is accompanied by a corresponding change in the extended district heating loop water flow as described on the web page titled FNR District Heating.

Iseally, for good atmospheric heat distribution, each cooling tower should be about 6 blocks away from its nearest neighbour.

In the event of a loss of AC power at a load or cooling tower location the the system performance will be diminished due to partial loss of pump power for water circulation.

In circumstances of a city wide AC power failure the reactor must be able to reject 80 MWt of fission product decay heat using just natural fluid circulation.

On the reactor site there are four independent cooling towers. Each on-site cooling tower is sized and piped to safely reject at least 45 MWt by natural air circulation. Thus at all times at least 2 of the 4 on-site cooling towers should be kept operational.

The capacity limitation of the on-site cooling towers is addressed by connecting the district heating pipe network to 12 remote cooling towers that provide the required additional cooling capacity.

**COOLING TOWER AIR DAMPERS:**

Each cooling tower requires air dampers which during the heating season are position adjausted to prevent coil freezeup. During the heating season the water circulation through each cooling tower coil is controlled to balance water flow changes through the building isolation heat exchangers so that the electricity generation can maintain constant operation.

A complication with the cooling tower dampers is that in the winter, on loss of AC power, they must spring closed to provide cooling tower coil freeze protection. However, on loss of station power these dampers must remain open sufficiently to dump fission product decay heat.

**WATER RESERVIORS**

It is prudent to have on the reactor site sufficient water to remove fission product decay heat by evaporation in emergency circumstances when the normal heat sink such as an air cooled cooling tower is unavailable. This source of water might take the form of suitably sloped district heating pipes, a large swimming pool, a large decorative pond, or the like. Reserve water storage tanks can potentially be located underneath each on-site cooling tower.

Assume that emergency cooling water is stored in four on-site below grade cylindrical tanks, each 20 m high by 25 m diameter, located directly below the cooling towers. Then the volume of water immediately available on-site for emergency cooling is:

4 X Pi (25 m / 2)^2 20 m

= 39, 269 m^3

= 39.269 X 10^6 kg

The latent heat of vaporization of water is:

22.6 X 10^5 J / kg

Hence evaporation of this stored water requires:
22.6 X 10^5 J / kg X 39.269 X 10^6 kg

= 887.48 X 10^11 J

Without any use of the cooling tower dry cooling capacity that amount of water is sufficient to remove maximum ongoing fission product decay heat of:

0.01 X 1000 MWt = 10 MWt for:

887.48 X 10^11 J / (10 X 10^6 J / s)

= 887.48 X 10^4 s

= 887.48 X 10^4 s / (3600 s / h)

= 2465 hours.

Hence no matter what the disaster, it is essential to either replenish the stored emergency cooling water or restore 50% operation of at least one of the four cooling towers within 3 months of the disaster.

The required rate of water evaporation to reject the prolonged fission product decay heat is:

10 MWt X (10^6 Wt / MWt) X (1 J / s-Wt) X (1 kg H2O / 22.6 X 10^5 J)

=

**DRY COOLING CAPACITY:**

A cylindrical cooling tower 25 m in diameter has a bottom cross sectional area A of:

A = Pi X (25 m / 2)^2 = 490.87 m^2

However, water coils reduce this area by about a factor of two.

The heat capacity of air is:BR> Cp = 1.00 kJ / kg deg C

The density of air is about:

Rhoa = 1.225 kg / m^3

Assume that in normal operation the cooling tower axial rising air velocity is:

V = 7 m / s

Assume in the dry cooling mode a cooliong tower internal air temperature rise of dT = 20 degrees C, corresponding to an outside air temperature of 5 degrees C and a turbogenerator condenser cooling water discharge temperature of 45 degrees C.

Then the thermal power removed by one cooling tower is:

A V Rhoa Cp dT

= (490.87 m^2 / 2) X 7 m / s X 1.225 kg / m^3 X 1.00 kJ / kg deg C X 20 deg C

= 42,092 kJ / s

= 42.092 MWt

Hence for 45 MWt of cooling the rising air velocity must become: (45 MWt / 42.092 MWt) X 7 m / s = 7.484 m / s

For natural draft operation the cooling tower must be tall enough that the required axial flow velocity is developed by warm air buoyancy.

The gas kinetic flow power is:

(mass / s) (V^2 / 2) = (Rhoa A V) V^2 / 2

The driving power = dP A V

Conservation of energy gives:

dP A V = (Rhoa A V) V^2 / 2

or

dP = (Rhoa) V^2 / 2

dP = (dRhoa) H g

where H = height of cooling tower.

Thus:

(dRhoa) H g = (Rhoa) V^2 / 2

or

H = (Rhoa) V^2 / [2 (dRhoa) g]

Rhoa = 1.225 kg / m^3

dRhoa = (20 deg C / 300 deg C) X Rhoa

= 1.225 kg / m^3 / 15

= 0.08167 kg / m^3

Thus:

H = (Rhoa) V^2 / [2 (dRhoa) g]

= (1.225 kg / m^3) (7.484 m / s)^2 / [2 (0.08167 kg / m^3)(9.8 m / s^2]

= 42.86 m

Thus this is the theoretical minimum height for a 25 m base diameter dry tower with an internal air temperature rise of 20 degrees C to remove 45 MWt by dry cooling. A higher condenser discharge temperature than 45 degrees C will significantly reduce the efficiency of electricity generation.

The minimum required cooling tower ground clearance is given by:

[Pi (25 m / 2)^2] / 2 = Pi (25 m) (ground clearance)

or

(ground clearance) = Pi (25 m / 2)^2 / 2 Pi (25 m)
= (25 m / 8) = 3.125 m

It appears that including ground clearance the dry cooling towers should extend at least:

42.86 + 3.125 = **46 m**

above grade. Tyoically the ground cleareance is further doubled to minimize suction of ground level debris into the cooling tower heat exchange coils.
Thus the top of the cooling tower is about 50 m above grade.

The cooling tower base diameter is 25 m and the cooling tower throat diameter with 50% of the inlet area obstructed by water coils is about:

25 m / (2^0.5) = **17.7 m**

With the additional ground clearance the radial air velocity at the perimeter of the cooling tower base is about:

(7.484 m / s) / 2 = **3.7 m / s**

**COIL AIR FLOW RESISTANCE:**

A significant problem poorly addressed in the above calculations is the air flow resistance introduced into the cooling tower by the water coil. This air flow resistance is minimized by doubling the cooling tower diameter at its bottom relative to its throat so as to maintain a constant open area for air flow. However, on the reactor site there is only a 25 m diameter available at the base of the cooling tower. Hence to make the cooling towers operate by natural draft with 50% of the inlet area obstructed the throat area is increased by a factor of two.

When the cooling tower is in its "wet" mode the air flow above the coil is increased by the water vapor flow.

We need 12 more similar cooling towers spaced along the district heating pipe routes. Real estate for cooling towers is a significant issue in a major city. Frequently these cooling towers will be significantly taller than other nearby structures.

ON SITE COOLING TOWERS:

In order to provide redundance the four on-site cooling towers can be shared between two district heating loops. Since these two loops in general operate at different head pressures, the on site cooling towers must have two isolated heat exchange coils.

This web page last updated May 20, 2022.

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