thermal science
Cooling Tower Performance vs. Relative Humidity BASIC THEORY AND PRACTICE
Total Heat Exchange A mechanical draft cooling tower is a specialized heat exchanger G = mass rate of dry air [lb/min] in which two fluids (air and water) are in direct contact with each L = mass rate of circulating water [lb/min] other to induce the transfer of heat. Le = mass rate of evaporated water [lb/min] THW = temperature of hot water entering tower [°F] Ignoring any negligible amount of sensible heat exchange that TCW = temperature of cold water leaving tower [°F] hin = enthalpy of air entering [Btu/lb/dry air] may occur through the walls (casing) of the cooling tower, the heat hout = enthalpy of air leaving [Btu/lb/dry air] gained by the air must equal the heat lost by the water. This is Cp = specific heat of water = 4.18 [Btu/lb-°F] an enthalpy driven process. Enthalpy is the internal energy plus Win = humidity ratio of air entering [lb water/lb dry air] the product of pressure and volume. When a process occurs at Wout = humidity ratio of air leaving [lb water/lb dry air] constant pressure (atmospheric for cooling towers), the heat In order to know how much heat the air flowing through a cooling absorbed in the air is directly correlated to the change in enthalpy. tower can absorb, the enthalpy of the air entering the tower must This is shown in Equation 1. be known. This is shown on the psychrometric chart Figure 1. G (hout - hin) = L x Cp (THW - 32°) - Cp (L - Le)(TCW - 32°) (1) The lines of constant enthalpy are close to parallel to the lines of constant wet bulb. This is why cooling towers are most often sized using the inlet wet bulb conditions.
55 60 210 Figure 1: PSYCHROMETRIC CHART 70 90 50 200 1.3 Enthalpy Barometric Pressure 15.5 190 85 15.0 85 1.2 180 45 65 8 WET B LB TE PER T RE - °F 170 1.1
160 80 40 80
150 1
60 80 140 .9 L E F C T T H T R T 35 75 130 75 L E F C T T E TH LP 14.5
120 L E F C T T REL T E H T 75 .8
25% 55 70 L E F C T T WET B LB 30 110 70 E TH LP - BT PER P F R R .7 T R T TE PER T RE - °F 70 100 65 65 90 .6 25 14.0 PEC F C L E ft /lb F R R
65 50
80 E TH LP - BT PER P F R R
60 P R PRE RE - CHE F ERC R 20 90% 60 .5 70 80% 55 60 15%
H T R T - GR F T RE PER P R R 55 15 60 70% .4 50 55 50 60% 45 13.5 50
10 45 50 45 .3 50% 40 40 45 8% 40 40% 35 5 40 30 35 .2 13.0 6% 30 30% 35 30 25 20 40 30 4% 25 20 20%
25 12.5 0 15 20 .1 20 10 10 EW P T - °F 5 15 2% 10 0 10 12.0 -5 5 10 REL T E H T 0 0 -20 -10 -5 0 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 80 85 90 95 100 105 110 115 120 125 130
Linric Company Psychrometric Chart, www.linric.com R B LB TE PER T RE - °F 35 10 15 20 25 30 Effects of Relative Humidity – Thermal Performance Cooling towers are rated most often using the inlet wet bulb before becoming saturated over the same change in enthalpy temperature because these values are closely consistent with the (heat exchange). Therefore, the lower the entering RH, the higher enthalpy of the air. As the relative humidity changes along constant the evaporation loss in the tower will be. Equation 2 shows the wet bulb lines, the enthalpy stays close to constant. This relationship relationship between evaporation and humidity ratio. is shown in Figure 1. Therefore, changes in humidity along a constant wet bulb temperature will result in almost no change to the Le = G (Wout - Win) 2) tower’s overall performance. G = mass rate of dry air [lb/min] Le = mass rate of evaporated water [lb/min] The inlet enthalpy of the air increases by only 0.5% when relative Win = humidity ratio of air entering [lb water/lb dry air] humidity increases by 60% at 68°F. Under standard conditions Wout = humidity ratio of air leaving [lb water/lb dry air] (78°F wet bulb, 95°F entering water temperature, and 85°F exiting water temperature), the overall nominal tonnage performance of an Figure 2 illustrates the changes in humidity ratio in the air entering evaporative cooling tower model improves only a couple tenths of a and exiting an evaporative cooling tower, showing the relative percent when the inlet relative humidity is 90% compared to 10%. percentage change in evaporation due to the change in the relative humidity of the entering air. The difference in evaporation between Evaporation 30% RH and 90% RH entering air is approximately 62%. At standard conditions, this may be as much as 0.62% of the circulating Unlike enthalpy, the relative humidity (RH) does affect the rate of water flow rate. This value is completely dependent on heat load evaporation within the cooling process. It is assumed that exiting and water load as well as the ambient conditions. A general rule air leaves the tower saturated (100% RH). The lower the RH of the to estimate evaporation (at 50% RH) is 1% of the recirculating ambient air entering the tower, the more water the air can absorb water flow for every 12°F of range. This is shown in Equation 3.
55 60 210 Figure 2: PSYCHROMETRIC CHART 70 90 50 200 1.3 Relative Humidity 15.5 190 85 15.0 85 1.2 180 45 65
8 WET B LB TE PER T RE - °F 170 1.1
160 80 40 156 80 8°F WET B LB 0 RH E TER G R 150 1 H 60 (ΔH = GR /LB) R 80 T 140 8°F WET B LB 30 RH E TER G R .9 35 75 T 75 (ΔH = 0 GR /LB) 130 14.5 C 120 .8 80°F WET B LB 100 RH E T G R 75 F 25% 55 70 30 E 110 70 E TH LP - BT PER P F R R 68 L .7
70 100 T R T TE PER T RE - °F 65 65 14.0 PEC F C L E ft /lb F R R 90 25 .6
65 50 80 E TH LP - BT PER P F R R 60 P R PRE RE - CHE F ERC R 20 90% 60 .5 70 80% 60 15% 55 66
H T R T - GR F T RE PER P R R 55 15 60 70% .4 50 55 50 60% 45 13.5 50
10 45 50 45 .3 50% 40 40 45 8% 40 40% 35 5 40 30 35 .2 13.0 6% 30 30% 35 30 25 20 40 30 4% 25 20 20%
25 12.5 0 15 20 .1 20 10 10 EW P T - °F 5 15 10 REL T E H T 2% 10 0 10 12.0 -5 5 0 0 -20 -10 -5 0 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 80 85 90 95 100 105 110 115 120 125 130
Linric Company Psychrometric Chart, www.linric.com R B LB TE PER T RE - °F 35 10 15 20 25 30 Le = L x R x 0.0008 (3)
Le = evaporation rate (gpm) L = tower water flow rate (gpm) R = design range (°F) Conclusion
• Evaporative cooling is an enthalpy driven process. • The lines of constant enthalpy on a psychrometric chart are close to parallel with lines of constant wet bulb temperature. • Relative humidity does NOT affect the performance of an evaporative cooling tower. • Relative humidity DOES affect the rate of evaporation from the tower. The relationship is inversely proportional.
Although RH does not have an effect on mechanical draft cooling towers (relative to the design wet bulb condition), dry bulb temperature and relative humidity are needed to determine the thermal performance for hyperbolic natural draft, fan-assisted natural draft, dry towers and plume-abated towers. thermal science
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