It is better for the rate of water loss to be small so that you do not have to replenish the circulating condenser water as often. If the rate of water loss is too large, the tower should be checked to make sure that there are no severe leaks in the piping system, that the trickle plates are not damaged, etc.
Evaluation of Heat Load
The heat load of the cooling tower is the total heat to be removed from the circulating water by the cooling tower per unit time, and can be calculated two ways, both of which are in units of BTU/hr. The first way is based on the amount of heat that is released from the water, and is calculated by determining the heat (in BTU) available in the inlet water versus the heat (in BTU) available in the outlet water:
The second way is based on the amount of heat that is absorbed by the ambient air fed through the cooling tower, which is calculated by the difference in heat in the outlet air and the inlet air:
where DT1 = Tair out – Treference, and DT2 = Tair in – Treference. lavg is the average latent heat, calculated from the latent heat for the inlet and outlet conditions:
The unit “tons of refrigeration” is a unit used to measure the amount of heat removed by a chiller per unit time, and is equal in value to 12000 BTU/hr. It is a refrigerating effect equal to melting one ton of ice in 24 hours. Using the following equation expresses the heat load calculated by either equation 12 or equation 13 in tons of refrigeration:
It is important to know the heat load of the cooling tower in order to evaluate its overall capacity to reject heat from the “condenser water”, so that (in this particular case) accurate calculations can be made as to how much volume the air conditioning system can effectively cool. The heat load should be a large number, as the larger the heat load, the larger the amount of heat that can be removed from the water per hour, and the more condenser water that can be pumped through to absorb the heat rejected from the heat pump.
RESULTS AND DATA ANALYSIS
Cooling Diagram
The cooling diagram for the Bryan Hall cooling tower as constructed from the raw data listed in Appendix C is shown in figure 3. In developing this diagram, a counterflow assumption was made, even though the tower exhibits a crossflow pattern. In assuming counterflow, air and water conditions are assumed to be constant across any horizontal section of the tower. This differs from crossflow towers since both air and water conditions vary vertically and horizontally in crossflow towers. Some errors result from these differences. For instance, colder water can be obtained from a counterflow tower (Burger, 1999). Colder water would effect both of the temperature and air operating lines. If temperature of water out was cooler, the slope of the air operating line (L/G) and the driving force would also be smaller, therefore increasing the number of transfer units. Since in this case the number of transfer units for the counterflow tower would be larger than for a crossflow tower, using the counterflow theory overestimates the tower characteristics.
Figure 3. Counterflow cooling diagram for Bryan Hall Cooling Tower
On the cooling diagram, the water operating line exhibits a curved shape that increases as temperature increases. As water falls vertically, it tends to move towards colder air. The water approaches the wet-bulb temperature as a limit (Baker and Shryock, 1961). The saturation line also lies on the water operating line. This is true because it is assumed that at points on this line, a film (saturated with water vapor) surrounds each water particle. If a particle is at conditions above this line, it exists as water. The water operating line displays the same behavior as the saturation line.
The air operating line on the cooling diagram exhibits a straight line. Air that moves through a section always moves towards hotter water and this can be seen in the cooling diagram (figure 3). The air approaches the hot water temperature as a limit. As the hot air enters the bottom of the cooling tower, it wants to move towards hotter water (hot water is located at the top of the tower). This is why the air operating line goes from cold water temperature to hot water temperature.
The slope of the air operating line was used to calculate L/G and (L/G)max. Equations 1 and 2 (calculated in Appendix A), respectively, were used to calculate these values and they are presented in Table 1:
Table 1. Results for L/G and (L/G)max.
L/G .7738 Btu/lb ?F
(L/G)max 1.5344 Btu/lb ?F
The L/G ratio is simply the ratio of the mass flow rates of water to air. The L/G ratio increases as the air flow rate decreases and the driving force is decreased. Therefore, the NTU would be increased. This is not a desired situation since the extent of the equipment that allows the transfer to come to equilibrium is large. Therefore it is more desirable to have a low L/G ratio. A low ratio means the gas flow rate is much larger than the liquid flow rate. More heat can be transferred from the water to the air faster if the gas flow rate is larger.
The driving forces at the top and bottom of the tower were calculated using eq. 3 (calculations in appendix A). Table 2 summarizes the results of the driving forces:
Table 2: Driving Forces at top and bottom of cooling tower.
Location Driving Force
Top 13.39 Btu/lb BDA
Bottom 9.44 Btu/lb BDA
The driving force increases when going from the bottom of the cooling tower to the top of the cooling tower.
The cooling range is the difference between inlet hot water temperature and the outlet cold water temperature and the heat load is fixed. It is better if the range is low because then the L/G ratio will be small, which in turn means the required coefficient (NTU) is small and performance of the tower is better. Thus, a larger cooling range means a smaller extent of equipment is needed for the transfer to come to equilibrium, which is desirable. The cooling tower approach is the difference between outlet cold water temperature and entering air wet-bulb temperature. Size and efficiency of the tower fix approach.
Number of Transfer Units
The number of transfer units measures the size or the extent of the equipment that allows the transfer to come to equilibrium. It was calculated three different ways: 1) numerical estimation; 2) adiabatic assumption based on mass transfer; 3) adiabatic assumption based on heat transfer. In order to solve the equations 4 and 5, the Hsat,inlet and Tsat,inlet were found (the values are found in Appendix C). In the numerical estimation, equations for the water operating line and air operating line (both labeled in figure 3) were found using regression analysis. Table 3 summarizes the results of NTU calculations (refer to appendix A for sample calculations):
Table 3: Results for NTU calculations.
Method NTU
Numerical Estimation 1.895
Mass Transfer Basis .0117
Heat Transfer Basis -.2097
The numerical estimation gives the most reliable value out of the three. In estimation using mass transfer, the Hairout was not able to be found. This is because the dry-bulb temperature of the air out was higher than the dry-bulb temperature coming in. And with the adiabatic humidification assumption, it was not possible to find Hairou. Having the outlet dry-bulb temperature higher than the inlet dry-bulb temperature also led to error in estimation of NTU using heat transfer basis.
NTU is an important value for the tower performance because it is a measure of the degree-of-difficulty of the problem (Baker and Shryock, 1961). It is better for NTU to be small. A smaller NTU means it is easier for the transfer to come to equilibrium.
REFERENCES
Al-Dahhan, Muthanna. ChE 374 Laboratory Manual: Experiments in Heat-Mass-
Momentum Transport. Washington University, 1997.
Baker, Donald, and Shryock, Howark. Journal of Heat Transfer. “A comprehensive approach to the analysis of cooling tower performance.” August, 1961
Hensley, J.C., ed. Cooling Tower Fundamentals. The Marley Cooling Tower Co. 1982.
McCabe, W.L., Smith, J.C., and Harriott, P. Unit Operations of Chemical Engineering.
5th edition. McGraw-Hill, 1993.
Perry, R., Green, D., and Maloney, J. Perry’s Chemical Engineers’ Handbook. 6th
edition. McGraw-Hill, 1984.
Smith, J.M., and Van Ness, H.C. Introduction to Chemical Engineering
Thermodynamics. 4th edition. McGraw-Hill, 1987.
Welty, James R., Wicks, Charles E., and Wilson, Robert E. Fundamentals of Momentum,
Heat, and Mass Transfer. 3rd edition. John Wiley & Sons, 1984.
Convert Crossflow to Counterflow – National Engineer by Bob Burger
Bibliography
Al-Dahhan, Muthanna. ChE 374 Laboratory Manual: Experiments in Heat-Mass-
Momentum Transport. Washington University, 1997.
Baker, Donald, and Shryock, Howark. Journal of Heat Transfer. “A comprehensive approach to the analysis of cooling tower performance.” August, 1961
Hensley, J.C., ed. Cooling Tower Fundamentals. The Marley Cooling Tower Co. 1982.
McCabe, W.L., Smith, J.C., and Harriott, P. Unit Operations of Chemical Engineering.
5th edition. McGraw-Hill, 1993.
Perry, R., Green, D., and Maloney, J. Perry’s Chemical Engineers’ Handbook. 6th
edition. McGraw-Hill, 1984.
Smith, J.M., and Van Ness, H.C. Introduction to Chemical Engineering
Thermodynamics. 4th edition. McGraw-Hill, 1987.
Welty, James R., Wicks, Charles E., and Wilson, Robert E. Fundamentals of Momentum,
Heat, and Mass Transfer. 3rd edition. John Wiley & Sons, 1984.