Thermodynamics lab... cooling tower

and continuity equation,

Eqn. 2

Where p is pressure, ρ is air density, v is velocity, and A is the cross-sectional area of the inlet and outlet orifice. It is important to understand Bernoulli’s equation in both fluid mechanics and thermodynamics. Refer to an appropriate text for more information about the Bernoulli equation and its derivation.

By using simple algebra and equations one and two, the exit velocity can be defined as,

Eqn. 3

Theoretical mass flow rate can be defined as,

Eqn. 4

Where is the theoretical mass flow is rate of the air, and is the exit velocity. By combining equation 3 and equation 4, the following is obtained

Eqn. 5

Where the inlet area, A1, is a 150 mm square and the outlet area, A2, is an 80 mm diameter circle.

Actual mass flow rate of the airflow is defined as,

Eqn. 6

Where α is the flow coefficient and ε is the expansion coefficient. For this experiment we will use values of α = 0.605 and ε = 0.98 based upon previous measurements by the manufacturer.

Once the mass flow rate is found, the volumetric flow rate can be obtained. The equation for volumetric airflow is,

Eqn. 7

where ν is the specific volume. Volumetric flow rate is important to know in industry. Volumetric flow rate will help engineers in selecting the proper fan size for their cooling tower design.

Cooling Capacity of air

There a two ways in obtaining the cooling capacity of the air. The first way is to find the enthalpy difference between the inlet and outlet of the airflow. The second way is to calculate the evaporative and convective heat transfer between the water and the air.

The enthalpy difference between the inlet and outlet airflow will be examined first. The heat gained by the air is defined as

Eqn. 8

where is the total heat absorbed by the air, and are the enthalpy values of the air at the inlet and outlet locations. This formula can give a rough estimate of the amount of heat gained by the air, but does not include the enthalpy of the water that in the air.

For a more accurate value of the amount of heat absorbed by the air, the evaporative and convective components must be analyzed separately. The total heat obtained by the air can be defined as

Eqn. 9

where is the heat gained by evaporation and is the heat gained by convection. Before analyzing heat gained by evaporation and the heat gained by convection, the mass flow rate of dry air must be calculated. The equation for the mass flow rate of dry air is as follows,

Eqn. 10

Where is the mass flow rate of dry air, and is the absolute humidity at the air outlet.

Once the mass flow rate of dry air is calculated, the heat of evaporation and convection can be calculated.

The evaporation process is where the majority of the heat transfer will occur. Heat gain by the evaporative process is a result of physical transfer of water into the air. When the air reaches 100% relative humidity, it cannot absorb any more water, which means that there is no more heat transfer due to evaporation. The heat gained by evaporative cooling can be defined as,

Eqn. 11

Where is the heat of vaporization, is the specific heat of water vapor, and are the humidity ratio at the inlet and outlet of the tower, and and is the temperature of the air at the inlet and outlet of the tower.

Convective cooling is pure heat transfer without any transfer of material and depends on air properties as well as the change of temperature of the air. The convective heat transfer is more important in the winter months than the summer months since the air temperature is colder in the winter. This results in a larger temperature change. The convective component of the heat transfer is defined as,

Eqn. 12

where is the specific heat capacity of air. Even though the air is the cooling medium in this process, it is gaining and losing heat from the water at the same time.

Heat Load

The heat load of the water is calculated through basic thermodynamic equations. The definition of heat is defined as,

Eqn. 13

Where is the mass flow rate of the water, is the specific heat of water, and is the change of temperature at the inlet and outlet. Equation 13 can be written in terms of volumetric flow rate and density,

Eqn. 14

Where is the volume flow rate of the water and is the density of water. It is important to know the amount of heat that the water is losing. The more heat that the water is losing, the colder the water will become, which is our ultimate goal. Comparing the amount of heat loss by the water and the heat gained by the air will give an approximate number for the efficiency.

Cooling Coefficient

The cooling coefficient is the same concept as the effectiveness of a heat exchanger. It is comparing actual temperature drop to the maximum temperature drop. The coefficient of cooling can be written as

Eqn. 15

Where Twat,in and Twat,out are the temperatures of the water at the inlet and outlet, and Twb,in is the web bulb temperature of the air at the inlet. The wet bulb temperature is most easily found from a psychrometric chart using the air inlet temperature and relative humidity. The reasoning behind the comparing the temperature of the water and the wet bulb temperature of the air is that the water can only get as cold as the wet bulb temperature of the inlet. The dry bulb temperature can remain the same but the wet bulb temperature changes because of humidity changes. The higher cooling coefficient will result in a larger rate heat transfer.

Water loss

For an open circuit cooling tower, water is lost through airflow. A reservoir is needed to replenish the circulated water. It is important to know the rate of water loss because it is important to know how much water needs to be replenished into the system. The equation needed to calculate water loss is as follows,

Eqn. 16

where is the mass flow rate of the water. Converting from mass flow rate to volume flow rate is simple since one kilogram of water is one liter. The water loss is measured in liters per hour.

Performing the lab

We will conduct this experiment as a response surface DOE (Design of Experiments) to characterize system over a range of water and airflow rates. The four water flow rates will be 40, 60, 80, and 100 l/hr and the three airflow rates will be defined by using the damper on the fan at three settings – open horizontal position, half-open (≈45o angle), and nearly closed. Your lab section will be assigned as either A or B and will test each setting combination two or more times in a random order.

You will then use an Excel spreadsheet to fit a full quadratic function to the cooling coefficient to create model that allows the cooling coefficient can be predicted at other values of the water and airflow rates. An additional handout with examples will be posted on canvas separately.

Report

This will be a short memo style report from a group of 2 or 3 students (not the full lab group) that is only a bit more complicated than a worksheet. You need to include the surface graph of the cooling coefficient vs. the airflow and water flow rates, answer the questions below, and write a set of conclusions.

1. What value of Q do you expect to be higher? Water or Air? Explain.

2. Why is one value of Q larger than the other?

3. When analyzing the heat gained by the air, why is the heat gained by convection negative?

4. Where does the extra heat dissipate?

5. What other variables can be affecting you data?

6. From analyzing the pressure difference in the tower, is it better to have a larger pressure drop or smaller pressure drop? Explain.

7. What are your main controlling factors and what can you do to increase the heat exchange.

8. What climate is works best for a mechanical draft cooling tower? Explain.

Prelab Name ____________________

1. What is the purpose of a cooling tower?

2. How does a cooling tower work?

3. What is a Psychrometric chart and why is it used?

4. Why does it feel much hotter when the temperature is 90 ̊F with a 100% relative humidity than the same temperature at a 40% relative humidity?