Cooling Tower Theory
What is a Cooling Tower?
A cooling tower is a heat rejection device that removes waste heat to the atmosphere through the cooling of water by evaporation. Cooling towers are widely used in HVAC systems, power plants, refineries, and industrial processes to cool process water or condenser water.
The cooling process involves both sensible heat transfer (temperature difference) and latent heat transfer (evaporation), with evaporation typically providing 70-90% of the total cooling effect.
Key Performance Parameters
1. Range
The range is the temperature difference between hot water entering and cold water leaving the tower:
Range = Thot - Tcold
Range is determined by the process heat load and water flow rate. A larger range means more heat is being removed per unit of water flow.
2. Approach
The approach is the temperature difference between cold water leaving the tower and the ambient wet bulb temperature:
Approach = Tcold - Twet bulb
- Smaller approach = closer to theoretical limit = larger/more expensive tower
- Typical approach: 2-5°C for large installations, 5-10°C for smaller systems
- Approach below 2°C is generally not economical
3. Effectiveness
The effectiveness indicates how well the tower performs relative to the theoretical maximum:
Effectiveness (ε) = Range / (Thot - Twet bulb) × 100%
Higher effectiveness means better performance. Typical values are 60-85%.
Merkel Theory
The Merkel equation is the fundamental relationship for cooling tower performance analysis. It relates the tower characteristic (KaV/L) to the thermal performance:
KaV/L = ∫ (dT) / (hs - ha)
where K = mass transfer coefficient, a = contact area per unit volume,
V = tower volume, L = water mass flow rate
The integral is evaluated from cold water to hot water conditions. The Merkel number (KaV/L) or NTU (Number of Transfer Units) represents the tower's ability to transfer heat and mass.
Key assumptions in Merkel theory:
- Lewis number equals 1.0 (ratio of thermal to mass diffusivity)
- Water loss by evaporation is negligible
- Enthalpy of saturated air is a function of temperature only
L/G Ratio (Liquid-to-Gas Ratio)
The L/G ratio is the mass flow rate of water divided by the mass flow rate of air:
L/G = (Water flow rate, kg/h) / (Air flow rate, kg/h)
- Typical range: 0.75 to 1.5
- Higher L/G requires larger tower volume but lower air flow (fan power)
- Lower L/G requires higher air flow but smaller tower
- Optimal L/G balances capital cost vs. operating cost
Water Losses and Makeup
1. Evaporation Loss
Evaporation is the primary cooling mechanism and accounts for most water loss:
Evaporation (%) ≈ 0.1% × Range (°C)
For example, a 10°C range results in approximately 1% evaporation loss.
2. Blowdown
Blowdown removes concentrated minerals to prevent scaling and corrosion:
Blowdown = Evaporation / (Cycles of Concentration - 1)
Typical cycles of concentration: 3-5 for most systems, up to 6-8 with good water treatment.
3. Drift Loss
Drift is water droplets carried out by air flow. Modern drift eliminators reduce this to 0.001-0.02% of circulation rate.
4. Makeup Water
Makeup = Evaporation + Blowdown + Drift
Typical makeup is 1.5-3% of circulation rate, depending on range and cycles of concentration.
Types of Cooling Towers
Counterflow Towers
Air flows vertically upward through the fill, opposite to the downward flow of water. This provides the most efficient heat transfer but requires more pumping head.
- ✓ Best thermal performance
- ✓ Smallest footprint for given capacity
- ✗ Higher pumping costs
- ✗ More susceptible to freezing
Crossflow Towers
Air flows horizontally through the fill while water falls downward. Water distribution is by gravity through hot water basins.
- ✓ Lower pumping head
- ✓ Easier maintenance access
- ✓ Better freeze protection
- ✗ Larger footprint
- ✗ Slightly lower thermal efficiency
Draft Types
| Type | Description | Applications |
|---|---|---|
| Induced Draft | Fan at top pulls air through tower | Most common, better performance |
| Forced Draft | Fan at bottom pushes air through tower | Better air distribution, lower height |
| Natural Draft | Buoyancy-driven flow, no fans | Large power plants, hyperbolic shape |
Design Considerations
Fill Selection
- Film fill: Creates thin water film, high efficiency, clean water
- Splash fill: Water breaks into droplets, less efficient, handles dirty water
- Hybrid fill: Combines both types for moderate fouling
Water Quality
- Monitor total dissolved solids (TDS)
- Control pH (typically 6.5-8.5)
- Add biocides to prevent algae and bacteria growth
- Use corrosion inhibitors
- Install filtration for suspended solids
Environmental Factors
- Design wet bulb temperature (use 2.5% or 5% exceedance values)
- Fog and plume formation in cold weather
- Freezing protection (basin heaters, variable speed fans)
- Noise control for residential areas
- Drift elimination to reduce water waste and legionella risk
Common Applications
HVAC Systems
- • Chiller condenser cooling
- • District cooling plants
- • Data center cooling
Power Generation
- • Steam turbine condensers
- • Combined cycle plants
- • Geothermal power
Industrial Processes
- • Refinery cooling systems
- • Chemical plant heat rejection
- • Steel mill cooling
Other Applications
- • Food processing
- • Plastics manufacturing
- • Injection molding cooling
Typical Design Values
| Parameter | Typical Range |
|---|---|
| Approach | 2-10°C (smaller is better but more expensive) |
| Range | 5-15°C (HVAC), 10-20°C (industrial) |
| L/G Ratio | 0.75-1.5 |
| Evaporation Loss | 0.5-2% of circulation |
| Cycles of Concentration | 3-5 (typical), up to 8 (with good treatment) |
Design Limitations
Important: The calculator uses simplified correlations. Real cooling tower design requires:
- Detailed Merkel integration using psychrometric properties
- Fill manufacturer performance curves (KaV/L vs. L/A)
- Consideration of altitude, air density, and humidity effects
- Fan performance curves and motor sizing
- Structural design for wind and seismic loads
- Water treatment chemistry and blowdown controls
- Certified testing per CTI (Cooling Technology Institute) standards
References
- ASHRAE Handbook - HVAC Systems and Equipment, Chapter 40: Cooling Towers (2020)
- Cooling Technology Institute (CTI), "CTI Code Tower," Test Code (2017)
- Merkel, F., "Verdunstungskühlung," VDI-Zeitschrift, 70, 123-128 (1925)
- Walker, W.H., Lewis, W.K., McAdams, W.H., Gilliland, E.R., "Principles of Chemical Engineering," 3rd Edition, McGraw-Hill (1937)
- Cheremisinoff, N.P., Cheremisinoff, P.N., "Cooling Towers: Selection, Design and Practice," Ann Arbor Science (1981)
- Kröger, D.G., "Air-Cooled Heat Exchangers and Cooling Towers," PennWell (2004)