XYLENE POWER LTD.

FNR COOLING TOWERS

By Charles Rhodes, P.Eng., Ph.D.

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 fan-coil heat exchanger which uses warm condenser cooling water discharge to heat the rising 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 potential modes of operation, "dry" and "wet". However, due to pressure issues the wet mode is not easily adaptable to district heating.

In the "dry" mode there is about a 40 degree C temperature difference between the tower inlet water temperature (condenser water discharge temperature) and the rising 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 tower 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 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.

The corresponding tower discharge air temperature is:
30 C + 20 C = 50 C.
The corresponding tower inlet water temperature is:
50 C + 40 C = 90 C.

the corresponding tower water discharge temperature (condenser inlet water temperature) is:
90 C - 20 c = 70 C.
A disadvantage of this state of operation is that the electricity generation efficiency is significantly reduced.

Ideally, 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 two of the four independent on-site cooling towers.

Each on-site cooling tower is sized and piped to safely reject at least 45 MWt. Thus at all times at least 2 of the 4 on-site cooling towers must 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. The critical isue is that the on-site cooling towers must have sufficient capacity to remove fission product decay heat.
 

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 17.5 m in diameter has a bottom cross sectional area A of:
A = Pi X (17.5 m / 2)^2 = 240.5 m^2

However, internal water coils reduce this area a bit. To minimize this problem the cooling tower open area should increase through the use of side perforations near its bottom.

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 cooling tower internal air temperature rise of dT = 20 degrees C, corresponding to an outside air temperature of 25 degrees C and a turbogenerator condenser cooling water discharge temperature of 85 degrees C.

Then the thermal power removed by one cooling tower is:
A V Rhoa Cp dT
= (245.2 m^2) X 7 m / s X 1.225 kg / m^3 X 1.00 kJ / kg deg C X 20 deg C
= 42,051.8 kJ / s
= 42.051 MWt

Thus two operating cooling towers can remove 80 MWt of fission product decay heat.

Hence for 45 MWt of cooling the rising air velocity must become: (45 MWt / 42.051 MWt) X 7 m / s = 7.491 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 17.5 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 (17.5 m / 2)^2] / 2 = Pi (25 m) (ground clearance)
or
(ground clearance) = Pi (25 m / 2)^2 / 2 Pi (25 m) = (17.5 m / 8) = 2.19 m

It appears that including ground clearance the dry cooling towers should extend at least:
42.86 + 2.19 = 45 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 47 m above grade.
 

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 17.5 m diameter available at the base of the cooling tower.

We need 12 more similar or larger 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. A plot of land 120 feet X 120 feet (40 m X 40 m) loses 15 m in eachdirection due to setback, but allows a cooling tower base diameter of 25 m. This diameter can reduce to:
25 m / 1.41 = 17.7 m at its throat.
 

This web page last updated February 16, 2026.