4.0 THEORY

Basic Principle

First consider an air stream passing over the surface of a warm water droplet or film. If we assume that the water is hotter than the air, then the water temperature will be cooled down by radiation, conduction and convection, and evaporation. The radiation effect is normally very small and may be neglected. Convection and conduction depend on the temperature difference, the surface area, air velocity, etc. the effect of evaporation is the most significant where cooling takes place as water molecules diffuse from the surface into the surrounding air. During the evaporation process, the water molecules are replaced by others in a liquid form which the energy required is taken.

Psychometric Chart

The psychometric chart is very useful in in determining the properties of air/water vapour mixture. Among the properties that can be defined with psychometric chart are Dry Bulb Temperature, Wet Bulb Temperature, Relative Humidity, Humidity Ratio, Specific Volume and Specific Enthalpy. Knowing two of these properties, any other properties can be easily identified from the chart provided the air pressure is approximately atmospheric.

In the Bench Top Cooling Tower application, the air inlet and outlet sensor show the dry bulb temperature and wet bulb temperature. Therefore, the specific enthalpy, specific volume, humidity ratio and relative humidity can be readily read from the psychometric chart.

Orifice Calibration

As mentioned above, the psychometric chart can be used to determine the value of the specific volume. However the values given in the chart are for 1 kg of dry air at the stated total pressure.For every 1 kg of dry air, there is w kg of water vapour, yielding the total mass of 1+w kg. Therefore, the actual specific volume of the air/vapour mixture is given by:

(7)

The mass flow rate of air and steam mixture through the orifice is given by

(8)

Where,

ṁ = Mass flow rate of air/vapour mixture = Actual specific volume end x = Orifice differential in mmH2OThus,

(9)

The mass flow rate of dry air,

(10)

A simplification can be made since in this application, the value of ω is unlikely to exceed0.025. As such, neglecting would not yield significant error.

Application of Steady Flow Energy Equation

Consider System A for the cooling tower defined as in Figure 2. It can be seen that for this system, indicated by the dotted line,

a) Heat transfer at the load tank and possibly a small quantity to surroundings.

b) Work transfer at the pump.

c) Low humidity air enters at point A.

d) High humidity air leaves at point B.

e) Make-up enters at point E, the same amount as the moisture increase in the air stream.

From the steady flow equation,

(11)

Note: The pump power, P is a work input. Therefore, it is negative.

If the enthalpy of the air includes the enthalpy of the steam associated with it, and this quantity is in terms of per unit mass of dry air, the equation may then be written as:

(12)

Note:a) The mass flow rate of the air through a cooling tower is a constant, whereas the mass

flow rate of moist air increases as the result of evaporation process.

b) The term can usually be neglected since its value is relatively small.

Under steady state conditions, by conservation of mass flow rate of dry air and of water (as liquid or vapour) must be the same at inlet and outlet to any system.

Therefore,

(14)

The ratio of steam to air (ω) is known for the initial and final state points on the psychometric charts. Therefore,

(17)

If the cooling tower system is redefined, where the process heat and pump work does not cross the boundary of the system. In this case warm water enters the system at point C and cool water leaves at point D. Again from steady flow energy equation,

and P=0, may have a small value due to heat transfer between the unit and its surroundings.

(18)

Rearranging,

(19)

Again, the term can be neglected.