It is essential for the operation of a wide variety of industrial plants that heat be transferred in some way from the plants to their surroundings. Sometimes, this is done by direct convection to the atmosphere, as in an air-cooled internal combustion engine. More frequently, a stream of water, "cooling water", is used. If a plant is near a river, a lake or the sea, an abundant supply of such cooling water can be supplied to it at a low temperature and returned to where it came from at a somewhat higher temperature. But often the choice of site for a plant is dominated by other factors, such as the location of raw materials, coal for example. There may be a river or a lake nearby but it may be unacceptable to raise the temperature of its waters any further. In such cases, the cooling water itself has to be cooled after use by heat transfer to the atmosphere and returned to the plant for reuse. Cooling towers are designed for precisely this purpose: to transfer heat from a stream of cooling water to the atmosphere.

In most large cooling towers, the cooling water and air are in *direct contact* (Figure 1). The cooling water is pumped into a system of sprayer pipes and nozzles within the tower and is drawn by gravity into a pond below. Air from the atmosphere enters the base of the tower and flows through the falling water. A "packing" is provided across the whole cross-section of the tower to ensure that the water, in its descent, presents a large surface area to the air. Water flows as a film or splashes and is provided across the whole cross-section of the tower to ensure that the water, in its descent, presents a large surface area to the air. Water flows as a film or splashes and trickles over the surfaces of the packing while air flows between the surfaces. Depending on the particular design, air may flow predominantly upwards (counter-flow) or horizontally (crossflow). As water temperature decreases, air temperature increases. When, as in most towers, the water and air are in direct contact, the "driving force" for heat transfer is not the local temperature difference but a local enthalpy difference; namely, the difference (h*S* – h*G*) where h*S* is the specific enthalpy of saturated air at the local temperature of the water/air interface and h*G* is the local bulk specific enthalpy of the moist air. The local heat flux from the water to the air is the product of this driving force and an empirical coefficient having the units of a mass flux. It is several times greater than it would be if the local temperature difference were the driving force, as is the case with "dry" heat transfer where the fluids are separated by a solid wall and no evaporation occurs.

Flow of air through the tower can be created in two ways: by natural draft or by mechanical draft. In natural draft towers, the packing region is located inside the base of what is, in effect, a large chimney (Figure 2). After its contact with warm cooling water, the density of the air above the packing is 5% or so less than that of the atmosphere. The difference in weight between the air in the "chimney" and the air outside provides the driving force to overcome pressure losses that resist the flow of air through the tower. The typical "hyperbolic" profile of such towers (as sketched in Figure 2) is chosen mainly for structural and economic reasons—it is much more resistant to wind-induced stress and vibration than a plain cylindrical shell and requires less material.

Mechanical draft towers use fans, driven by electric motors, to produce the flow of air (Figure 3). The tower is called "forced draft" when the fan is located in the air entry at the base of the tower; "induced draft" when the fan is located in the air exit at the top of the tower. Both centrifugal and axial flow fans are used, but axial fans are usual with induced draft.

**Figure 3. Mechanical draft cooling tower layouts: (a) Forced draft, counter flow; (b) Induced draft, mixed flow; (c) Induced draft, cross flow. From Singham, J. R. (1990) in Heat Exchanger Design Handbook, Hemisphere.**

The relative merits of natural and mechanical draft towers are summarized in Table 1. In some situations, there may be an economic compromise in the form of an "assisted draft" tower—a natural draft tower with fans added around the base in the air entry, the size of the tower being much less than would be necessary without the fans.

In the majority of towers, i.e., direct contact or "wet" towers of the type discussed above, about 1% of the water flow rate is lost to the atmosphere by evaporation and by entrainment of fine droplets of water by the air. (The larger droplets are intercepted by "eliminators," typically an array of slats covering the whole cross-section of the tower just above the water spray system.) This loss has to be supplemented by an external supply and, to keep the concentration of salts in the water acceptably low, the supply of make-up water may have to be around 3%. In some locations, such a quantity may be too difficult or too costly to provide and a "dry" tower may be economic.

In dry towers, the water and air are not in direct contact so there is no loss of water by evaporation. In effect, the packing is replaced by a heat exchanger in which metal walls separate the two streams. Dry towers may be natural, mechanical or assisted draft. But there is a big penalty for eliminating water loss by evaporation. The evaporative cooling effect is also eliminated and it is estimated that the air flow rate required to achieve the same cooling capacity will have to be three or more times greater than in a wet tower; so the tower will have to be much larger and much more expensive. Moreover, the set of heat exchangers for the tower will be more costly to produce than a corresponding packing. "Wet-dry" towers have been proposed as a compromise between wet and dry towers. [Singham (1990)]

A wide variety of materials and geometric design have been used for packing: corrugated roofing sheets made of cement-based or plastic material; timber laths of triangular or rectangular cross-section; plastic-impregnated paper "honeycomb"; complex cellular geometries made of thin plastic material. [Singham (1990); Hill, Pring & Osborne (1990) and Johnson (1990)]

The required performance of a proposed cooling tower can be specified by listing the values of the following five quantities:

the mass-flow rate of the water;

the inlet temperature of the water;

the exit temperature of the water;

the atmospheric wet-bulb temperature;

the atmospheric dry-bulb temperature.

Except in special circumstances, atmospheric pressure is assumed to be the standard atmospheric pressure. The mass flow rate of the air is not specified and it is the first task of the designer to determine its value. For prediction of the performance of an existing tower, the mass flow rate of the air replaces the exit water temperature in the above list and it is the latter that has to be determined. *Merkel 's Equation* enables both these calculations—for proposed and for existing towers—to be carried out. It relates the above variables to variables associated with the heat transfer performance of the proposed or existing packing. It is based on the assumption of uniform, one-dimensional counterflow, but can be adapted to other conditions. The equation can be stated as [Singham (1990)]:

where

and

In Eqs. (2) and (3),

h_{w} = specific enthalpy of the water at any level; |

h_{G} = specific enthalpy of bulk moist air at the same level; |

h_{S} = specific enthalpy of saturated air at temperature of water at the same level; |

= mass flow rate of water per unit area; |

= mass flow rate of moist air ("gas") per unit area; |

NTU = "number of transfer units" for the packing. |

The quantity I_{M}, defined by Eq. (2), is a measure of the cooling requirement. The quantity I_{p}, defined by Eq. (3), is a measure of the performance of the packing. Merkel's equation, Eq. (1), requires them to be equal.

NTU is an empirical quantity and may be thought of as the product of a Stanton Number and a geometric feature of the packing, namely, the surface area of the water-air interface per unit plan area of packing. Often packing performance is expressed instead as another empirical group for which the conventional symbols are "KaV/L". The relation between NTU and KaV/L is a simple one [Singham (1990)]. (See also NTU.)

With the above five design quantities specified and with enthalpy property data for water and moist air, I_{M} can be evaluated for any value of the water/air mass flow ratio. The performance of a chosen packing, expressed as I_{p}, is also an empirical function of flow ratio. Thus the equality of these two quantities, required by Merkel's equation, allows flow ratio to be found. Since the water mass flow rate is specified, air mass flow rate is now known, without need for other details concerning tower design. This is true for both natural and mechanical draft towers. The rest of the design procedure, however, depends on which type of tower is under consideration. For a natural draft tower, the height and cross-sectional area of the tower have to be such as to make the sum of the estimated pressure losses that occur with this now-known air flow rate equal to the driving pressure difference caused by the buoyancy of warm moist air. For a mechanical draft tower, a fan has to be selected to supply the now-known air flow rate with a pressure rise equal to the estimated pressure loss.

Any design which satisfies these heat transfer and pressure loss requirements is technically valid. An infinite number of designs is possible, differing from one another in shape, height, cross-sectional areas, type of packing, depth of packing, etc. The final choice is made after taking into account economic, environmental and operational considerations, often in conjunction with some cost-optimization procedure.

With an existing tower a slightly different calculation procedure is required. The aim is to determine the value of the third variable in the above list—water exit temperature—for any set of the other four that may be of interest. The first step is to determine air mass flow rate by matching buoyancy and pressure loss for a natural draft tower; or fan pressure rise and pressure loss for mechanical draft. Since the water mass flow rate is already known (specified), the water/air mass flow ratio can be calculated and used to find I_{p} from the known characteristics of the packing; and hence I_{M}, from Merkel's equation. The final step is similar to that outlined above: find by trial the value of exit water temperature that results in the required value of I_{M}.

It is well-established that air and water flows in real towers are far from the uniform one-dimensional flows often assumed in design and analysis. The discrepancy can be taken into account by the introduction of correction coefficients whose values are estimated from full-scale test data on towers. Such data are in short supply and even when available, there remains some doubt as to the validity of the correction; some "over-design" may be prudent depending on contractual terms. Another approach is to return to the fundamental equations of fluid mechanics and heat and mass transfer and to arrive at numerical solutions with the aid of Computational Fluid Dynamics (CFD) techniques. These solutions can, in principle, be used as the sole basis of design; or they can be used to modify and improve existing simpler methods.

#### REFERENCES

Singham, J. R. (1990) Hemisphere Handbook of Heat Exchanger Design, Section 3.12 (Cooling Towers), Hemisphere Publishing Corporation, New York.

Hill, G. B., Pring, E. J., and Osborn, P. D. (1990) Cooling Towers: Principles and Practice, Third Edition, Butterworth-Heinemann, London.

Johnson, T. (1990) *Plastic Packings for Large Cooling Towers*, Chem. Eng. (London), pp. 18-24.

British Standard 4485, (1988) Water Cooling Towers, Part 2, *Methods for Performance Testing*; Part 3, *Code of Practice for Functional and Thermal Design*.

Bibliography of Technical Papers (1993) Cooling Tower Institute, Houston, Texas 77273, USA.