Cooling CoolTowerTheory

7/28/2019 Cooling CoolTowerTheory

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Cooling Towers

A cooling tower is a counter-flow or cross-flow heat exchanger that removes heat from waterand transfers it to air. Cooling towers come in many configurations. An induced-draft coolingtower, which is common in HVAC and industrial applications, is shown in Figure 1a. As

warm water from the process falls through the tower, some of it evaporates, which cools theremaining water. The cooled water collects at the bottom of the cooling tower and is returnedto the plant. Figure 1b shows an evaporative condenser, which is common in industrialrefrigeration applications. Water is circulated from the bottom to the top of the tower, to cool afluid (typically a refrigerant) which passes through a closed heat exchanger.

Figure 1a) open circuit cooling tower, 1b) closed circuit evaporative cooler. Source: BAC Parts andMaintenance Guild, Baltimore Aircoil Company, 2008.

The temperature difference of water through a tower, dT = Tw1-Tw2, is determined by theload, Ql, and the mass flow rate of water, mw. Neither the size of the tower nor the state of theoutside air influences the temperature difference; however, larger towers or lower outdoor airwet-bulb temperatures will decrease the exit water temperature, Tw2.

Sensible and Latent Cooling

Depending on the entering air and water temperatures, the water may be cooled by sensible andlatent cooling of the air, or simply by latent cooling of the air. In either case, latent, i.e.

evaporative, cooling is dominant. For example, consider the case in which the air enters at alower temperature than the water (Figure 3a). The air will leave completely saturated and thecooling is part sensible and part latent. The sensible portion occurs as the air temperatureincreases by absorbing heat from the water. The latent portion occurs as some of the waterevaporates, which draws energy out of the water.

If the air enters at the same wet bulb temperature as before, but at a higher dry-bulbtemperature than the water, then the air will cool as it saturates (Figure 3b). Thus, the sensible

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cooling component is negative, and the all the cooling is due to evaporation. In general,cooling is dominated by latent cooling.

Figure 2. Psychrometric process lines for air through a cooling tower, if the entering airtemperature is a) less than the entering water temperature, and b) greater than the enteringwater temperature.

The total cooling, ma (ha2 ha1) is the same for both cases since enthalpy is a function of wet-bulb temperature alone. However, the dry-bulb temperature significantly influences theevaporation rate, mwe = ma (wa2-wa1). The rate of evaporation increases as the dry-bulbtemperature increases for a given wet-bulb temperature.

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Cooling Towers as Heat Exchangers

Based on the previous discussion, it is clear that cooling tower performance is a function of thewet-bulb temperature of the entering air. In an infinite cooling tower, the leaving air wet-bulbtemperature would approach the entering water temperature, and the leaving water temperaturewould approach the web-bulb temperature of the entering air. The difference between the

leaving water temperature and the entering air wet-bulb temperature is called the approach.The relationship between air wet-bulb and water temperature is shown in the figure below. Inan infinite cooling tower, the approach would be zero.

Source: ASHRAE Handbook, HVAC Systems and Equipment, 2004.

Neglecting fan power and assuming steady state operation, an energy balance on a coolingtower gives:

mw1 cpw Tw1 mw2 cpw Tw2 + ma (ha1 ha2) = 0

Assuming steady state operation, a mass balance on water flow gives:

mw1 mw2 + ma (wa1 wa2) = 0mw2 = mw1 + ma (wa1 wa2)

Substituting mw2 into the energy balance gives:

mw1 cpw Tw1 [mw1 + ma (wa1 wa2)] cpw Tw2 + ma (ha1 ha2) = 0mw1 cpw Tw1 mw1 cpw Tw2 - ma (wa1 wa2) cpw Tw2 + ma (ha1 ha2) = 0

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The fraction of incoming water that is evaporated, ma (wa2-wa1) / mw1, is typically less than 1%.Thus, ma (wa1 wa2) is much less than mw1,and the term ma (wa1 wa2) cpw Tw2 can be neglectedwith negligible error to give:

mw1 cpw (Tw1 Tw2) = ma (ha2- ha1)

Both sides of this equation represent the total cooling capacity of the tower.

The effectiveness, E, of a heat exchanger is the ratio of the actual to maximum heat transfer.

E = Qactual / Qmax

For a heat exchanger, Qmax occurs if the air leaves the cooling tower completely saturated atthe temperature of the incoming water. Thus, effectiveness is

E = Qactual / Qmax = [mw1 cpw (Tw1 Tw2)] / [ ma (ha,sat,tw1- ha1)]

Energy Efficiency of Counterflow and Crossflow Towers

The two most common tower designs for HVAC applications are forced-air counterflow andinduced air cross-flow. Cooling tower energy use is a function of fan and pump power. Togenerate the same quantity of cooling, forced-air counterflow towers require more fan andmore pump energy then induced-air crossflow towers. Thus, induced-air crossflow towers arealmost always more energy efficient.

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Forced-air counterflow towers require more fan energy because centrifugal fans are made togenerate low flow against high pressure, but cooling towers generally need high flow at lowpressure. In comparison, induced air crossflow towers use propeller fans, which generate highflow against low pressure, which is more suited to cooling towers.

Forced-air counterflow towers require more pump energy because these towers are taller inorder to facilitate the counterflow heat transfer as the water falls through the tower. Thisheight increases elevation head in the piping system. In addition, forced-air counterflowtowers spray water through nozzles, which increases pressure drop. In comparision, induced-

air crossflow towers are shorter and wider since the path of the air through the water ishorizontal. In addition, the supply water simply drains from feeding pans into fill, whicheliminates the need for nozzles.

A comparison of cooling tower energy use for the same loads is shown below.

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Source: Marley Technical Report H-001A, Cooling Tower Energy and Its Management,October, 1982.

Cooling Tower Control

In HVAC applications, chiller evaporator loads vary depending on weather and buildingoccupancy, and the quantity of heat rejected by the condenser varies accordingly. The cooling

tower will always reject the all the heat from the condenser. However, the temperature of thecold water return to the condenser will decline at lower loads.

Various methods are used to control cooling tower capacity to generate the desired cold waterreturn temperature. The two control points for cooling towers are water flow and air flow.However, cooling tower manufacturers strongly recommend that water flow remain constant atall times. Thus, primary control methods generally rely on varying air flow. The commoncontrol methods are listed below.

Run Fans ContinuouslyThis type of control results in the coldest possible return water temperature, which reduces

chiller energy use. However, it also results in the highest cooling tower fan energy use.Because the improvement of chiller efficiency with lower condenser water temperature isasymptotical at some minimum temperature, this method of control rarely results in the bestoverall energy efficiency.

Cycle Fans On and OffThis type of control reduces excess fan energy use at cold outsider air temperatures, and iswidely used. At relatively cold temperatures, however, the fan may cycle on and off toofrequently. The maximum number of fan cycles is about 8 per hour. Thus, many coolingtowers are equipped with water bypass loops. In most applications, water bypass control isonly used at low temperatures when fan cycling could be a problem.

Use Two-Speed FanThis method of control adds an intermediate level of cooling between full-on and full-off. Thisresults in considerable fan energy savings, since fan energy varies with the cube of flow. Thus,fan energy at 50% air flow is only 12% of the fan energy at full air flow. This type of steppedcontrol can be further extended with two cell towers with one fan in each cell. This leads tofour possible steps of control. A typical relationship between cold water temperature and fanflow is shown below.

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Continuously Control Fan Speed with VSDThis method results in the lowest fan energy use by continuously achieving savings, due to thefan law that fan energy varies with the cube of flow.

Vary Air Flow Using Inlet Air DampersBefore VSDs, cooling towers were sometimes controlled by running the fan at full speed whilevarying the inlet air dampers to modulate air flow. This method of control results inintermediate energy savings between fan cycling and continuous VSD control. However, israrely used now that the VSD control is now commonplace.Comparison of Energy Use with Various Methods of Cooling Tower ControlTotal chiller and cooling tower energy use for these control methods for a typical HVACapplication are shown below.

Source: Marley Technical Report H-001A, Cooling Tower Energy and Its Management,

October, 1982.

Variable Cold Water Set-Point TemperatureThe energy efficiency of all the control discussed above can be improved by varying the coldwater set-point temperature with the outdoor air wet bulb temperature. This type of controltakes into account the fact that towers can only produce water at a few degrees above the wet-bulb temperature (this temperature difference is called the approach); hence fan energy canbe reduced when that temperature is achieved, since continued fan operation results in minimalfurther reductions in cold water temperature.

Fan Motor Power with Fan Speed and Air Volume Flow Rate

The figure below shows fan motor power draw as a function of input frequency for a coolingtower fan equipped with a VFD. The fan affinity laws would predict a relationship betweenfraction power (FP) and fraction speed (FS) of:

FP = FS3

Regression of the data show a slightly better fit using the exponent 2.8:

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FP = FS2.8

Since fan speed is proportional to volume flow rate, this relation also hold for fraction volumeflow rate, FV.

FP = FV2.8

The slightly reduced exponent is caused by declining VFD, motor and fan efficiencies atreduced speed.

Source: An Application of Adjustable Speed Drives for Cooling Tower Capacity Control,Welch, W. and Beckman, J.

Cooling Tower Bypass Plumbing

Bypass control is typically used only at low outdoor air wetbulb temperatures in order toreduce fan cycling. Bypass should not be used in sub-freezing temperatures since this can leadto tower freeze up. The preferred tower bypass plumbing is shown below. The preferred valveis a single two-way butterfly valve placed in the bypass line.

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Source: BAC Product and Application Handbook, Volume 1, 2005.

Cooling Tower Pumping Pressure DropTypical cooling tower pressure drops are shown below. The Estimated Head Loss column isfor a standard condenser and 15 year old piping. The Actual Head Loss column is for a low-pressure loss condenser and new piping.


Cooling Tower Selection

In HVAC applications, the starting place for cooling towers selection is typically to match thenominal cooling tower tons, as supplied by the tower manufacturer, to the cooling capacityof the chiller or chiller plant. The water flow rate through the cooling tower is initially set at 3gpm per nominal cooling tower ton. Subsequent design optimization may occur from thisstarting point. Engineering data for a typical model of induced-air crossflow cooling towersare shown below. Based on these data, fan motor hp is about 0.1 hp/ton and air flow rates areabout 2,000 cfm/hp.

A nominal cooling tower ton is defined as cooling 3 gpm of water from 95 F to 85 F at an airwetbulb temperature of 78 F. Thus, the actual cooling associated with a nominal coolingtower ton is:

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Qact = 3 gpm x 8.33 lb/gal x 60 min/hr x 1 Btu/lb F x (95 85) F = 15,000 Btu/hr

This strange convention exists to make it easy for users to select cooling towers by matchingthe nominal cooling capacity of the chiller with the chiller cooling capacity. The conventionworks because most chillers have a COP of about 3, and total heat rejected by the condenser to

the cooling tower is about 15,000 Btu/hr for every 12,000 Btu/hr through the evaporator.


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Source: Marley Cooling Towers, 2000.

Cooling Tower Performance

The performance of typical cooling towers at water flow rates of 3 gpm/ton and 5 gpm/ton isshown below. Similar performance data for specific cooling towers can usually be obtainedfrom the manufacturer. These curves predict the temperature of the cold water leaving thecooling tower as a function of the water temperature range (Th-Tc) and entering air web bulbtemperature. Temperature range is generally known and can be used as an input value in thesecharts, since the temperature range is set by the water flow rate and heat rejection rate of thecondenser.

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Source: ASHRAE Handbook, HVAC Systems and Equipment, 2004.

A relation for the temperature of cooling water leaving the tower, Tc, can be dervived fromregressing data from the 3 gpm/ton and 5 gpm/ton curves shown above. The relation andregression coefficients are shown below. The R2 for these relations exceeds 0.995 and theaverage error, [abs(Tc Tc,pred)], is less than 0.8 F.

Tc = a + b Twb + c Tr + d Twb2 + e Tr2 + f Tr Twb

Coef 3 gpm/ton 5 gpm/ton

A 16.790751 2 4. 629 9229B 0. 6464308 0 .4500 7792C 2. 2221763 3 .3222 9591D 0. 0016061 0 .0026 1818E -0 .0159268 -0. 0324886F -0.015954 -0. 0190476

These equations can be incorporated into software to predict cooling tower performance withvarying ambient conditions. For example, CoolSim (Kissock, 1997) calculates exit water

temperatures, and the fraction of time that a cooling tower can deliver water at a targettemperature, based on water temperature range Tr and TMY2 weather data. This informationis useful in determining how often a cooling tower can replace a chiller in cooling applications.

Cooling Tower Performance at Reduced Air Flow RatesComparison of the 3 gpm/ton and 5 gpm/ton performance maps can be used to predict coolingtower performance at reduced air flow rates. For example, for a cooling tower operating with awater flow rate of 3 gpm/ton, the 3 gpm/ton performance map shows tower performance at a

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set water-to-air flow rate ratio. The 5 gpm/ton chart shows tower performance for a higherwater-to-air flow ratio, or, inversely, at a lower air-to-water flow rate ratio. Thus, the 5gpm/ton performance map indicates tower performance if water flow rate is held steady whilethe air flow rate is reduced to 3/5 = 60% of maximum airflow.

Regressing the data from the 3 gpm/ton and 5 gpm/ton performance curves, with fraction of airflow, FV, set to 1.0 for the 3 gpm/ton data and 0.6 for the 5 gpm/ton data gives the followingrelation for the temperature of cooling water leaving the tower, Tc, at reduced air flow. The R2

for this relation is R2 = 0.978 and the average error [abs(Tc Tc,pred)] is 1.9 F. Theoretically,the fraction of air flow, FV, could vary between 0 and 1.0. However, this relation wasgenerated using data that represent peak air flow at 0.6 and 1.0. Thus, it is not recommendedthat this relationship be used outside of this range.

Tc = a + b Twb + c Tr + d Twb2 + e Tr2 + f Tr Twb + g FV

Coef Value

a39.24367

b 0.548254c 2.772236d 0.002112e -0.02421f -0.0175g -23.1667

Evaporation RateAs discussed in the previous section, cooling in cooling towers is dominated by evaporation.

The evaporation rate can be calculated from the pyschrometric relations in the previoussection, if the inlet and exit conditions of the air are known. For example, consider the case inwhich the cooling load, Ql, mass flow rate of air, ma, (which can be calculated based on thefan cfm and specific volume of the inlet air), and inlet conditions of air are known. Theenthalpy of the exit air, ha2, can be calculated from an energy balance.

Ql = ma (ha2 ha1)ha2 = ha1+ Ql / ma

The state of the exit air can be fixed by assuming that it is 100% saturated with an enthalpyha2. The evaporation rate, mwe, can be determined by a water mass balance on the air.

mwe = ma (wa2- wa1)

The fraction of water evaporated is:

mwe / mw

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Using this method for entering air temperatures from 50 F to 90 F, we determined that thefraction of water evaporated typically ranges from about 0.5% to 1%, with an average value ofabout 0.75%.

Another way to estimate the fraction of water evaporated is to assume that all cooling, Ql, is

from evaporation, Qevap. The cooling load Ql, is the product of the water flow rate, mw,specific heat, cp, and temperature difference, dT. The evaporative cooling rate is the productof the water evaporated, mwe, and the latent heat of cooling, hfg.

Ql = Qevapmw cp dT = mwe hfg

Assuming the latent heat of evaporation of water, hfg, is 1,000 Btu/lb, and the temperaturedifference of water through the tower, dT, is 10 F, the fraction of water evaporated is:

mwe / mw = cp dT / hfg = 1 (Btu/lb-F) x 10 (F) / 1000 (Btu/lb) = 1%

If on average, 75% of the cooling were from evaporation and 25% from sensible cooling, thenthe evaporation rate would be:

75% x 1% = 0.75%

Thus, both methods suggest that 0.75% is a good estimate of the rate of evaporation; however,we have seen manufacturer data indicating average evaporation rates as low as 0.30%. Waterlost to evaporation should not be subjected to sewer charges. Typical sewer charges are about$2.20 per hundred cubic feet.

Some water may be lost as water droplets are blown from the tower by oversized fans or wind.This type of water loss is called drift. Drift rates are typically about 0.2% of flow (ASHRAEHandbook, HVAC Systems and Equipment, 2000); however, we generally assume that driftlosses are included in the 0.75% evaporation rate.

Water Treatment and Blow Down RateCooling tower water must be treated to prevent bacterial growth and maintain the concentrationof dissolved solids at acceptable levels to prevent scale and corrosion.

Bacterial Growth

The typical method of controlling bacterial growth is to add biocides at prescribed intervalsand to keep the cooling tower water circulating. If the tower will not be operated for asustained period of time, then the cooling water should be drained.

Dissolved SolidsWater evaporated from a cooling tower does not contain dissolved solids. Thus, theconcentration of dissolved solids will increase over time if only enough water is added to thetower to compensate for evaporation. To maintain the dissolved solids at acceptable levels,

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most towers periodically discharge some water and replace it with fresh water. This process iscalled blow down. It the level of dissolve solids increases too high, scale will be begin to form,and/or the water may become corrosive and damage piping, pumps, cooling tower surfaces andheat exchangers. Usually, the primary dissolved solid to control is calcium carbonate CaCO3.

Blow down can be accomplished by continuously adding and removing a small quantity ofwater, periodically draining and refilling the cooling tower reservoir, or by metering theconductivity of water and adding fresh water only when needed. By far the most efficientmethod is to meter the conductivity of water, which increases in proportion to the level ofdissolved solids, and add fresh water only when needed.

The required quantity of blow down water depends on the acceptable quantity of dissolvedsolids in the tower water, PPMtarget, the quantity of dissolved solids in the makeup water,PPMmu, and the evaporation rate, mwe. The target level of dissolved solids is typicallyquantified in cycles, where:

Cycles = PPMtarget / PPMmu

For example, if the quantity of dissolved CaCO3 in the makeup water, PPMmu, is 77 ppm andthe maximum level to prevent scaling, PPMtarget, is 231, then the cooling tower water must bemaintained at three cycles:

Cycles = PPMtarget / PPMmu = 231 ppm / 77 ppm = 3

By applying mass balances, it can be shown that the blow down water required to maintain acertain number of cycles is

mwbd = mwe / (Cycles 1)

The total makeup water required mwmu, is the sum of the water added for evaporation andblow down:

mwmu = mwe + mwbd

For example for a 1,000 gpm tower with a 0.75% evaporation rate and CaCO3 concentration at3 Cycles, the quantity of makeup water required would be about:

mwe = (mwe/mw) x mw = 0.75% x 1,000 gpm = 7.5 gpmmwbd = mwe / (Cycles 1) = 7.5 gpm / (3 1) = 3.75 gpmmwmu = mwe + mwbd = 7.5 gpm + 3.75 gpm = 11.25 gpm

The overall makeup water rate would be about:

11.25 gpm / 1,000 gpm = 1.1%

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