9.5 Cooling Towers: Range, Approach, Evaporation, Blowdown & Legionella Control

9.5 Cooling Towers: Range, Approach, Evaporation, Blowdown & Legionella Control

Cooling towers are the primary heat rejection machinery for water-cooled central chiller plants, water-source heat pump loops, and industrial refrigeration systems. A cooling tower discharges heat directly into the atmosphere through the evaporative cooling of recirculating condenser water. Because latent heat of vaporization of water is high ($h_{fg} \approx 1,050\text{ Btu/lbm}$), cooling towers reject massive thermal loads with modest water consumption, lowering condenser water temperatures toward the ambient wet-bulb temperature (WBT). On the PE Mechanical: HVAC and Refrigeration exam, cooling tower problems frequently test Range and Approach thermodynamics, psychrometric mass balances, Cycles of Concentration (COC), blowdown and makeup flow rates, and ASHRAE Standard 188 Legionella control standards.

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1. Cooling Tower Fundamentals & Psychrometric Operating Principle

Unlike dry air-cooled condensers that reject sensible heat against ambient dry-bulb temperature (DBT), an open cooling tower brings warm condenser water into direct physical contact with an induced or forced airstream.

+-----------------------------------------------------------------------------------------+
| COOLING TOWER HEAT TRANSFER MECHANISM                                                   |
+-----------------------------------------------------------------------------------------+
| 1. Latent Heat Transfer (Evaporation): ~75% to 85% of Total Heat Rejection.             |
|    A small fraction (~1.0% to 1.5%) of circulating water evaporates into the airstream, |
|    absorbing h_fg (~1,050 Btu/lbm) and cooling the remaining water pool.                |
| 2. Sensible Heat Transfer (Convection): ~15% to 25% of Total Heat Rejection.            |
|    Sensible heat transfer occurs due to dry-bulb temperature differences between the    |
|    water and air streams (can be positive or negative depending on ambient DBT).        |
| 3. Theoretical Lower Temperature Limit: The Ambient Wet-Bulb Temperature (WBT).        |
|    By the Second Law of Thermodynamics, leaving cold water can never reach or fall      |
|    below ambient WBT (0°F approach requires an infinitely large cooling tower).         |
+-----------------------------------------------------------------------------------------+

Primary Tower Configurations

   CROSSFLOW (Induced Draft)                     COUNTERFLOW (Induced Draft)
        [  Fan Motor  ]                              [  Fan Motor  ]       
        /             \                              /             \       
   ====/   Fan Stack   \====                    ====/   Fan Stack   \====  
       |               |                            |               |      
  Water| +-----------+ |Water                  Water| +-----------+ |Water 
  In ->| | Film Fill | |<- In                  In ->| | Drift Elim| |<- In 
       | |  (Air ->) | |                            | +-----------+ |      
  Air  | |           | |  Air                   Air | | Film Fill | |  Air 
  In ->| +-----------+ |<- In                   In->| |  (Air ^)  | |<- In 
       |               |                            | +-----------+ |      
       +---------------+                            +---------------+      
         [ Cold Basin ]                               [ Cold Basin ]       

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2. Core Thermodynamic Metrics: Range, Approach & Thermal Effectiveness

+-----------------------------------------------------------------------------------------+
| DEFINITION OF COOLING TOWER TEMPERATURE METRICS                                         |
+-----------------------------------------------------------------------------------------+
|                                                                                         |
| Warm Water From Chiller (T_EWT / T_hot, e.g., 95.0°F)                                   |
|       |                                                                                 |
|       |  <--- RANGE = T_EWT - T_LWT (e.g., 95°F - 85°F = 10.0°F)                        |
|       V                                                                                 |
| Cold Water To Chiller (T_LWT / T_cold, e.g., 85.0°F)                                    |
|       |                                                                                 |
|       |  <--- APPROACH = T_LWT - T_wb (e.g., 85°F - 78°F = 7.0°F)                       |
|       V                                                                                 |
| Ambient Wet-Bulb Temperature (T_wb, e.g., 78.0°F)                                       |
|                                                                                         |
+-----------------------------------------------------------------------------------------+

1. Cooling Tower Range ($\Delta T_{\text{range}}$)

The temperature difference between warm water entering the tower ($T_{\text{EWT}}$) and cold water leaving the tower basin ($T_{\text{LWT}}$):

$\text{Range} = T_{\text{EWT}} - T_{\text{LWT}}$

Engineering Principle: Range is established strictly by the thermal cooling load ($\text{THR}$) and the circulating water flow rate ($\text{GPM}$): $\text{Range} = \frac{\text{THR (Btu/hr)}}{500 \times \text{GPM}}$ Changing tower fan speed or ambient weather conditions does not change the Range if cooling load and flow rate are constant; it shifts both $T_{\text{EWT}}$ and $T_{\text{LWT}}$ up or down together.

2. Cooling Tower Approach ($\Delta T_{\text{approach}}$)

The temperature difference between cold water leaving the tower basin ($T_{\text{LWT}}$) and ambient wet-bulb temperature ($T_{\text{wb}}$):

$\text{Approach} = T_{\text{LWT}} - T_{\text{wb}}$

Approach is the true indicator of cooling tower sizing and thermal performance capability. Typical commercial approaches range from $6.0^\circ\text{F}$ to $10.0^\circ\text{F}$. Sizing for an approach below $5.0^\circ\text{F}$ exponentially increases tower fill volume, fan horsepower, and physical footprint.

3. Thermal Effectiveness (Efficiency, $\varepsilon$)

The ratio of actual water cooling achieved to the theoretical maximum possible cooling (if water cooled all the way to ambient wet-bulb):

$\varepsilon_{\text{tower}} = \frac{T_{\text{EWT}} - T_{\text{LWT}}}{T_{\text{EWT}} - T_{\text{wb}}} = \frac{\text{Range}}{\text{Range} + \text{Approach}}$

4. Nominal Cooling Tower Ton

A Nominal Cooling Tower Ton is defined by the Cooling Technology Institute (CTI) as the heat rejection of $15,000\text{ Btu/hr}$ ($12,000\text{ Btu/hr}$ evaporator cooling $+ 3,000\text{ Btu/hr}$ compressor work, representing a chiller with $\text{COP} = 4.0$ or $0.88\text{ kW/ton}$). Standard CTI rating conditions:

• Circulate $3.0\text{ GPM}$ of water per nominal ton.
• Cool water from $95.0^\circ\text{F}$ ($T_{\text{EWT}}$) to $85.0^\circ\text{F}$ ($T_{\text{LWT}}$) ($ ext{Range} = 10.0^\circ\text{F}$).
• Operating at $78.0^\circ\text{F}$ ambient Wet-Bulb Temperature ($T_{\text{wb}}$) ($ ext{Approach} = 7.0^\circ\text{F}$).

$\text{Heat Rejection} = 500 \times 3.0\text{ GPM} \times 10.0^\circ\text{F} = 15,000\text{ Btu/hr}$

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3. Water Mass Balance: Evaporation, Drift, Blowdown & Makeup

Water continuously leaves the cooling tower through three mechanisms: evaporation into the air, mechanical droplet drift entrained in exhaust air, and intentional blowdown (bleed-off) to remove concentrated dissolved minerals.

                                [ Exhaust Air + Water Vapor + Drift (D) ]
                                              ^
                                              |
  [ Circulating Water (GPM) ]                 |
  Warm EWT (95°F) =================> [ Cooling Tower ]
                                              |
                                              +===> Evaporation Loss (E)
                                              |
  [ Makeup Water (M) ] =====================> [ Cold Basin ] ====> Cold LWT (85°F) to Chiller
  (City / Well Water)                         |
                                              +===> Blowdown / Bleed-off (B)

Conservation of Mass for Tower Water

$\dot{M} = \dot{E} + \dot{B} + \dot{D}$

Where $\dot{M}$ is Makeup water, $\dot{E}$ is Evaporation, $\dot{B}$ is Blowdown (bleed), and $\dot{D}$ is Drift loss.

1. Evaporation Rate ($\dot{E}$)

From latent heat considerations, approximately $1\text{ pound of water}$ evaporates for every $1,000$ to $1,050\text{ Btu}$ of heat rejected:

$\dot{E}\text{ (lbm/hr)} = \frac{\text{THR (Btu/hr)}}{h_{fg}} \approx \frac{\text{THR}}{1,050}$

Converting to volumetric flow rate in Gallons per Minute ($\text{GPM}$):

$\dot{E}\text{ (GPM)} = \frac{500 \times \text{GPM}_{\text{circ}} \times \text{Range}}{8.337\text{ lbm/gal} \times 60\text{ min/hr} \times 1,050\text{ Btu/lbm}} = \frac{500 \times \text{GPM}_{\text{circ}} \times \text{Range}}{525,231}$

$\dot{E}\text{ (GPM)} \approx 0.00080 \times \text{GPM}_{\text{circ}} \times \text{Range (}{}^\circ\text{F)}$

$\dot{E}\text{ (GPM per Ton)} \approx \frac{15,000\text{ Btu/(hr}\cdot\text{ton)}}{8.337 \times 60 \times 1,050} \approx 0.0285\text{ GPM/ton} \approx 1.71\text{ to } 1.80\text{ gal/(ton}\cdot\text{hr)}$

2. Drift Losses ($\dot{D}$)

Drift consists of unevaporated liquid water droplets mechanically swept along with the exhaust airstream. Modern cellular PVC drift eliminators restrict drift loss to $0.001%$ to $0.005%$ of circulating water flow:

$\dot{D} = 0.00005 \times \text{GPM}_{\text{circ}}$

Because drift loss is negligible compared to evaporation and blowdown in modern towers, $\dot{D}$ is frequently neglected in manual exam hand calculations unless explicitly provided.

3. Cycles of Concentration ($C$ or $\text{COC}$)

As pure water ($H_2O$) evaporates, all dissolved mineral salts (calcium, magnesium, silica, chlorides) remain behind in the circulating basin water. The Cycles of Concentration ($C$) measures the degree of mineral concentration in the basin relative to raw incoming makeup water:

$C = \frac{\text{TDS}_{\text{basin}}}{\text{TDS}_{\text{makeup}}} = \frac{\text{Conductivity}_{\text{basin}}}{\text{Conductivity}_{\text{makeup}}} = \frac{\text{Chlorides}_{\text{basin}}}{\text{Chlorides}_{\text{makeup}}}$

From a steady-state dissolved solids mass balance ($M \times X_{\text{makeup}} = (B + D) \times X_{\text{basin}}$):

$C = \frac{\dot{M}}{\dot{B} + \dot{D}} \approx \frac{\dot{M}}{\dot{B}} = \frac{\dot{E} + \dot{B}}{\dot{B}} = \frac{\dot{E}}{\dot{B}} + 1$

4. Blowdown (Bleed) Rate ($\dot{B}$)

To prevent dissolved minerals from precipitating as hard scale on condenser tubes, water must be intentionally drained from the basin:

$\dot{B} = \frac{\dot{E}}{C - 1} - \dot{D} \approx \frac{\dot{E}}{C - 1}$

5. Total Makeup Water Rate ($\dot{M}$)

$\dot{M} = \dot{E} + \dot{B} = \dot{E} + \frac{\dot{E}}{C - 1} = \dot{E}\left(1 + \frac{1}{C - 1}\right) = \dot{E}\left(\frac{C}{C - 1}\right)$

Water Savings vs Cycles of Concentration (for E = 100 GPM):

Cycles of Conc (C)   Blowdown (B)   Total Makeup (M)   Water Savings Relative to C=2
-----------------------------------------------------------------------------------
 C = 2.0               100.0 GPM       200.0 GPM       Baseline (High water waste!)
 C = 3.0                50.0 GPM       150.0 GPM       25.0% Makeup Water Saved
 C = 4.0                33.3 GPM       133.3 GPM       33.3% Makeup Water Saved
 C = 5.0                25.0 GPM       125.0 GPM       37.5% Makeup Water Saved
 C = 7.0                16.7 GPM       116.7 GPM       41.7% Makeup Water Saved
 C = 10.0               11.1 GPM       111.1 GPM       44.4% (Diminishing returns / scale risk)

Most commercial cooling towers operate between $3.0$ and $6.0$ Cycles of Concentration.

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4. Waterside Economizers ("Free Cooling")

A Waterside Economizer utilizes cold cooling tower water to produce chilled water without running the chiller compressor when ambient wet-bulb temperatures are sufficiently low (typically $T_{\text{wb}} \le 45^\circ\text{F}$ to $50^\circ\text{F}$).

+-----------------------------------------------------------------------------------------+
| PLATE-AND-FRAME WATERSIDE ECONOMIZER SCHEMATIC                                          |
+-----------------------------------------------------------------------------------------+
| Cooling Tower Water (45°F) ===> [ Plate Heat Exchanger ] ===> Return to Tower (55°F)    |
|                                          ||                                             |
|                                    (Thermal Transfer)                                   |
|                                          ||                                             |
| Chilled Water Supply (47°F) <=== [ Plate Heat Exchanger ] <=== Return CHW (57°F)        |
|       |                                                                                 |
|       +===> Bypasses Chiller Evaporator (Chiller Compressor is OFF: ~90% Power Saved!) |
+-----------------------------------------------------------------------------------------+

• Plate-and-Frame Isolation: Uses an ASME-rated gasketed plate heat exchanger with close approach ($1.5^\circ\text{F}$ to $3.0^\circ\text{F}$) to completely isolate dirty open tower water from the clean closed chilled water loop.
• Direct Injection / Strainer Cycle: Direct filtering of tower water into the chilled water loop (rarely used due to severe coil clogging, oxygen corrosion, and biological fouling risks).

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5. Legionella Control & ASHRAE Standard 188 / Guideline 12

Legionella pneumophila is a waterborne bacterium responsible for Legionnaires' disease, a severe and potentially fatal form of bacterial pneumonia. Cooling towers provide an ideal amplification environment if unmanaged.

Favorable Growth Conditions for Legionella

• Water Temperatures: Proliferates between $68^\circ\text{F}$ and $122^\circ\text{F}$ ($20^\circ\text{C}$ to $50^\circ\text{C}$), with optimum rapid growth occurring at $95^\circ\text{F}$ to $115^\circ\text{F}$ ($35^\circ\text{C}$ to $46^\circ\text{C}$)—precisely matching typical cooling tower basin operating temperatures.
• Biofilm, Slime & Algae: Provide nutrients and protective amoebae hosts that shield bacteria from chemical biocides.
• Stagnant Water: Dead legs in condenser water piping or idle tower basins.

ASHRAE Standard 188 Compliance & Risk Management

1. Water Management Program (WMP): Mandatory written protocol detailing system schematics, hazard identification, control points, biocide dosing, testing frequencies, and corrective action thresholds.
2. Biocide Regimen: Dual chemical dosing combining a continuous oxidizing biocide (chlorine, stabilized bromine, or chlorine dioxide) with scheduled shock dosing of an alternating non-oxidizing biocide (isothiazolone, glutaraldehyde, or DBNPA) to eliminate biocide resistance.
3. Physical Design Safeguards:
   • High-efficiency drift eliminators limiting drift to $< 0.005%$.
   • ASHRAE 62.1 Separation Distance: Cooling tower exhaust must be located a minimum of $25\text{ feet}$ away from any building outdoor air intake, operable window, or door.
   • Automated continuous blowdown controlled by electrical conductivity sensors.
   • Sump basin heaters with thermostat controls to prevent winter freezing when idle.

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6. Worked Example: Central Plant Cooling Tower Mass Balance

Problem: A central chilled water plant operates a $1,200\text{ ton}$ water-cooled chiller producing $44.0^\circ\text{F}$ chilled water with a specific power of $0.60\text{ kW/ton}$. The cooling tower circulates condenser water at $3.0\text{ GPM/ton}$ ($3,600\text{ GPM}$) with entering water temperature $T_{\text{EWT}} = 95.0^\circ\text{F}$ and leaving water temperature $T_{\text{LWT}} = 85.0^\circ\text{F}$. Ambient design wet-bulb temperature is $T_{\text{wb}} = 78.0^\circ\text{F}$. The raw makeup water contains $120\text{ ppm}$ Total Dissolved Solids (TDS), and water treatment maintains basin water at $600\text{ ppm}$ TDS. Drift loss is $0.003%$ of circulating flow. Latent heat of vaporization is $h_{fg} = 1,050\text{ Btu/lbm}$.

Find:

1. The cooling tower Range, Approach, and Thermal Effectiveness ($\varepsilon$).
2. The Total Heat of Rejection ($\text{THR}$) in $\text{Btu/hr}$.
3. The Evaporation rate ($\dot{E}$) in $\text{GPM}$.
4. The Cycles of Concentration ($C$), Blowdown rate ($\dot{B}$) in $\text{GPM}$, and Total Makeup water rate ($\dot{M}$) in $\text{GPM}$.

Step-by-Step Solution:

Step 1: Calculate Range, Approach, and Thermal Effectiveness. $\text{Range} = T_{\text{EWT}} - T_{\text{LWT}} = 95.0^\circ\text{F} - 85.0^\circ\text{F} = 10.0^\circ\text{F}$ $\text{Approach} = T_{\text{LWT}} - T_{\text{wb}} = 85.0^\circ\text{F} - 78.0^\circ\text{F} = 7.0^\circ\text{F}$

$\varepsilon_{\text{tower}} = \frac{\text{Range}}{\text{Range} + \text{Approach}} = \frac{10.0}{10.0 + 7.0} = \frac{10.0}{17.0} = 0.5882 \implies 58.8\%$

Step 2: Calculate Total Heat of Rejection (THR). $\dot{Q}_{\text{evap}} = 1,200\text{ tons} \times 12,000\text{ Btu/(hr}\cdot\text{ton)} = 14,400,000\text{ Btu/hr}$ $\dot{W}_{\text{comp}} = 1,200\text{ tons} \times 0.60\text{ kW/ton} \times 3,412.14\text{ Btu/(hr}\cdot\text{kW)} = 2,456,741\text{ Btu/hr}$ $\text{THR} = 14,400,000 + 2,456,741 = 16,856,741\text{ Btu/hr}$

Check with hydronic balance: $\text{THR} = 500 \times 3,600\text{ GPM} \times 10.0^\circ\text{F} = 18,000,000\text{ Btu/hr}$ (reflecting nominal full capacity rating). Using actual thermal load $\text{THR} = 16,856,741\text{ Btu/hr}$:

Step 3: Calculate Evaporation Rate ($\dot{E}$). $\dot{E}\text{ (lbm/hr)} = \frac{16,856,741\text{ Btu/hr}}{1,050\text{ Btu/lbm}} = 16,054.04\text{ lbm/hr}$ $\dot{E}\text{ (GPM)} = \frac{16,054.04\text{ lbm/hr}}{8.337\text{ lbm/gal} \times 60\text{ min/hr}} = \frac{16,054.04}{500.22} = 32.09\text{ GPM}$

(Using empirical shortcut: $\dot{E} \approx 0.0008 \times 3,600 \times 10.0 \times \frac{16.857}{18.0} = 28.8 \times 0.936 = 26.96$ to $32.1\text{ GPM}$).

Step 4: Calculate Cycles of Concentration, Blowdown, and Makeup. $C = \frac{\text{TDS}_{\text{basin}}}{\text{TDS}_{\text{makeup}}} = \frac{600\text{ ppm}}{120\text{ ppm}} = 5.00$

$\text{Drift Loss: } \dot{D} = 0.00003 \times 3,600\text{ GPM} = 0.108\text{ GPM}$

$\dot{B} = \frac{\dot{E}}{C - 1} - \dot{D} = \frac{32.09\text{ GPM}}{5.0 - 1.0} - 0.108 = \frac{32.09}{4.0} - 0.108 = 8.023 - 0.108 = 7.915\text{ GPM}$

$\dot{M} = \dot{E} + \dot{B} + \dot{D} = 32.09 + 7.915 + 0.108 = 40.11\text{ GPM}$

$\text{Daily Makeup Water Consumption} = 40.11\frac{\text{gal}}{\text{min}} \times 1,440\frac{\text{min}}{\text{day}} = 57,758\text{ Gallons/day}$

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7. NCEES Reference Handbook Navigation & Exam Tips

• Cooling Tower Equations: Key formulas: $\text{Range} = T_{\text{EWT}} - T_{\text{LWT}}$, $\text{Approach} = T_{\text{LWT}} - T_{\text{wb}}$, $\dot{E} \approx 0.0008 \times \text{GPM} \times \text{Range}$, $\dot{B} = \frac{\dot{E}}{C - 1}$, and $\dot{M} = \dot{E} \left(\frac{C}{C - 1}\right)$.
• Range Invariance Rule: Remember that cooling tower Range depends only on heat load and water flow rate ($q = 500 \times \text{GPM} \times \text{Range}$). It does NOT depend on tower fan speed or ambient wet-bulb.
• Approach Minimum Limit: The approach can approach zero only with an infinite surface area. Any exam option suggesting leaving water colder than ambient wet-bulb violates the Second Law of Thermodynamics.