1) Fan Laws

The performances of all types of fans follow certain laws which are useful in predicting the effect upon performance of changes in the conditions of operations, the duty required of the installation, or the size of the equipment due to the space, power, or speed limitations. In the following laws, groups 1 to 6, Q = air volume and P = static, velocity or total pressure. The laws pertaining to fan size apply only to fans geometrically similar, i.e., those in which all dimensions are proportional, it may be used; otherwise, fan diameter is commonly used as a size criterion.

(1) Variation in Fan Speed: (RPM)

Constant Air Density - Constant System
(a) Q: Varies as fan speed ratio
(b) P: Varies as square of fan speed ratio.
(c) Power: Varies as cube of fan speed ratio.

(2) Variation in Fan Size: (but same number of blades)

Constant Tip Speed - Constant Air Density
Constant Fan Proportions - Fixed Point of Rating
(a) Q: Varies as square of fan diameter.
(b) P: Remains constant
(c) RPM: Varies inversely as fan diameter.
(d) Power: Varies as square of fan diameter.

(3) Variation in Fan Size: (but same number of blades)

At Constant RPM - Constant Air Density
Constant Fan Proportions - Fixed Point of Rating
(a) Q: Varies as cube of fan diameter.
(b) P: Varies as square of fan diameter.
(c) Tip Speed: Varies as fan diameter.
(d) Power: Varies as fifth power of diameter.

(4) Variation in Air Density:

Constant Volume - Constant System
Fixed Fan Size - Constant Fan Speed
(a) Q: Constant.
(b) P: Varies as density.
(c) Power: Varies as density.

Note: The cooling tower is designed to handle the process requirement on a design summer day. As the inlet air wet bulb temperature drops, the tower will produce colder discharge water temperatures and consume slightly greater fan horse power.

(5) Variation in Air density:

Constant Pressure - Constant System
Fixed Fan Size - Variable Fan Speed
(a) Q: Varies inversely as square root of density.
(b) P: Constant.
(c) RPM: Varies inversely as square root of density.
(d) Power: Varies inversely as square root of density.

(6) Variation in Air density:

Constant Weight of Air - Constant System
Fixed Fan Size - Variable Fan Speed
(a) Q: Varies inversely as density.
(b) P: Varies inversely as density.
(c) RPM: Varies inversely as density.
(d) Power: Varies inversely as square of density.

2) Fan Performance Variables

A change in fan efficiency will have a direct bearing on cooling tower performance. Reduced fan efficiency may be caused by high wind velocity, high exit temperature, poor fan blade balance, incorrect track, dirty blade surfaces, and below major factors.

(1) Airflow Rate: This factor is a primary variable in the design and operation of axial flow fans. It is basically an independent variable for most types of towers, but there are exceptions, for example natural draft towers and towers with constant speed &fixed-pitch fans.

Most mechanical towers are equipped with adjustable pitch fans. Often the blade pitch angle is adjusted on a seasonal and/or load basis to prevent the unnecessary use of fan power and to help maintain fairly uniform outlet water temperature. Many towers are also equipped with multi-speed fan drives to further increase air-handling flexibility.

(2) Fan Speed: The effect of fan speed at constant fan power depends precisely on the effect of fan efficiency. Generally speaking, an increase in fan speed at relatively high static pressure and relatively low fan speed will result in an increase in fan efficiency. For the opposite case, that is, a relatively low static pressure and high fan speed, the speed increase could likely reduce fan efficiency. Specific predictions of the effects of fan speed should be made from a study of appropriate fan curves.

(3) Air Density: Since the density of the air varies with temperature and pressure (altitude), it is necessary to evaluate the effect of air density on the system design and fan performance. The system designer must evaluate the actual air density that will be handled by the system in order to properly determine the volume of flow required and the actual pressure losses in the system. Since fan is essentially constant volume machine, the volume of air handled by the fan will remain constant regardless of the density, but the total pressure developed by the fan and the power required by the fan will vary in direct proportion to density.

(4) Inlet Conditions: Fan stack design can have a significant effect on fan performance. A poorly designed inlet bell is a potential cause of poor air distribution and low fan efficiency. The fan stack should have smooth interior surface, and should be shaped from inlet to outlet to prevent sudden air direction changes or sudden contractions or enlargements. The flow pattern at the fan tip is of major importance. The losses fall into two categories: first Vena Contracta (The point at which the flow area reaches its minimum is called Vena Contracta), or increase in velocity pressure and second Starvation at fan tip. Below Figure gives actual loss in terms of Total Pressure and Efficiency for a fan running in short duct.

(5) Velocity Recovery Stacks: As cooling towers become larger, velocity stacks become more common. The diverging nozzle at the fan discharge is used to save energy by converting a portion of the velocity pressure to static pressure. The regain of static pressure appears at the fan inlet as additional suction pressure. For high velocity recovery designs the normal height/diameter ratio is from 0.6 to 1.0. A well designed stack will enable recovery of from 70 to 90% of the theoretical maximum velocity pressure recovery.

An appreciable amount of the energy spent for the achievement of air flow through the cooling tower is wasted in the form of the kinetic energy of the exit air. Particularly in the case of towers in which the fan velocity pressure is very high in comparison with the stack pressure differential, much affection is directed toward the gradual reduction in air velocity from the fan plane to the discharge plane. The resultant reduction in the exit air kinetic energy results in substantial power savings.

For example, a cooling tower with fan rings (designed with a height/diameter ratio of about 0.2) capable of only negligible kinetic energy reduction from fan to exit is operating at the following conditions:

• Fan driver - output horsepower: 147.2 hp
• Static pressure, inch water gage: 0.5100
• Net velocity pressure, inch water gage: 0.1963

Then, if the fan ring is replaced by a velocity pressure recovery design that reduces the net velocity press. to 0.1687 inch water gage, assuming no change in fan efficiency or air flow, the fan power is reduced as ff.: HP₂ = HP₁ x (TP₂ / TP₁) = 147.2 x [(0.5100 + 0.1687) / (0.5100 + 0.1963)] = 141.4 HP

(6) Blade Tip Clearance: The clearance between the tip of the blade of the axial flow fan and the fan stack is an often neglected parameter which influences fan and cooling tower performance. Large clearances allow the shedding of a vortex from the upper surface of the blade back to the low pressure area beneath the fan; this produces lowered air flow rates and reduced fan efficiency.

Fans are often installed in cooling towers with tip clearance of up to two (2) inches because of the manufacturing tolerances inherent in large fiberglass stack segments. In addition, clearances also vary by as much as an inch due to eccentricity of the stack. Fan manufacturers recommend that tip clearance be minimized to insure proper fan performance. To achieve a small clearances is difficult in cooling tower installations without very careful attention to the design and installation of the fan stack. In addition, small clearances less than about 1/2?are often undesirable and impracticable in large cooling tower applications due to differential thermal expansion between the fan blade and the stack.

The tip clearance of many factors reducing the actual fan performance must be carefully studied. Losses up to 20% of fan efficiency are possible with excessive clearance. Since most of the work is done by the outer third of the fan blade, excessive tip clearance allows "spillover" of the air flow from the high -pressure region to the low-pressure region in the inlet side. "Excessive" tip clearance means greater than about 0.3% of fan diameter for cooling tower fans. This would be no more than 1 inch clearance for 28 feet diameter fan or about 0.32 inch for a 9 feet diameter fan. Sometimes this is not always possible to attain a small tip clearance in a practical sense especially for the large diameter cooling tower fans due to the thermal expansion differences and the constructional accuracy of the fan stack. The followings are, however, Hudson's recommendation for tip clearance and they have been successfully used.

The reasons that the fan efficiency is improved with the reduced blade tip clearance are basically due to the followings;

• By minimizing air tip losses between the blade tips and fan stack, the average vertical air velocity and, therefore, the volumetric air flow rate is increased.
• The exit air, vertical velocity profile is more uniform so that the air flow is more evenly distributed across the fan stack.

If the average tip clearance between the fan and fan stack is larger than above the maximum values, a pressure loss due to the increase of fan casing sectional area will occur. There will be a rapid decline in the efficiency due to the decrease of total pressure and airflow, and will be a slight decrease in the brake horsepower due to the decrease of fan efficiency. If this cannot be avoid, consult with Chungrok about an accurate calculation of pressure loss and efficiency. The following multiplying factors are in general being used to correct the fan total efficiency given in the fan performance curve.

The power consumption is generally decreased as much as the tip clearance is increased, since the volumetric air flow rate is significantly decreased. The efficiency at the larger tip clearance is decreased, because the input power is not reduced as much as the airflow is decreased.

(7) Fan Performance Tolerance: The fan performance also has a tolerance which must be considered. The AMCA allowable certified ratings tolerance is ?2.5% in flow and 5% on pressure.

It is quite common practice to anticipate the system tolerance by applying a safety factor to the design. This is most often done by adding some (10%) additional static pressure requirement to the calculated static and some (5%) additional airflow requirement to the calculated air flow. So, the actual point of fan operation will be different from the design fan performance, since the estimated system resistance and airflow are usually result in excess of actual system.

Assuming the fan is rated correctly, the three most common causes of deficient performance of the fan are "improper air discharge through fan stack", "non-uniform inlet airflow", and "swirl at the fan inlet". These conditions alter the aerodynamic characteristics of the fan so that its full flow potential is not realized. They will occur if the fan inlet and outlet are not properly designed or installed. Other major causes of deficient performance are:

• The air performance characteristics of the installed system are significantly different from the system design.
• Dirty fills will increase the system resistance and consequently reduce the air flow rate.