Thermal Analysis and Design of Cooling Towers

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Thermal Analysis and Design of Cooling Towers

• P M V Subbarao
• Professor
• Mechanical Engineering Department
• I I T Delhi

Pay material for Electric Power.
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Natural Draught Cooling Tower
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Artistic to Scientific Design of Cooling Towers

• The art of evaporative cooling is quite ancient,
  although it is only relatively recently that it
  has been studied scientifically.
• Merkel developed the theory for the thermal
  evaluation of cooling towers in 1925.
• This work was largely neglected until 1941 when
  the paper was translated into English.
• Since then, the model has been widely applied.
• The Merkel theory relies on several critical
  assumptions to reduce the solution to a simple
  hand calculation.
• Because of these assumptions, the Merkel method
  does not accurately represent the physics of heat
  and mass transfer process in the cooling tower
  fill.

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Parameters of Cooling Towers

• A number of parameters describe the performance
  of a cooling tower.
• Range is the temperature difference between the
  hot water entering the cooling tower and the cold
  water leaving.
• The range is virtually identical with the
  condenser rise.
• Note that the range is not determined by
  performance of the tower, but is determined by
  the heat loading.

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• Approach is the difference between the
  temperature of the water leaving the tower and
  the wet bulb temperature of the entering air.
• The approach is affected by the cooling tower
  capability.
• For a given heat loading, water flow rate, and
  entering air conditions, a larger tower will
  produce a smaller approach i.e., the water
  leaving the tower will be colder.
• Water/Air Ratio (mw/ma) is the mass ratio of
  water (Liquid) flowing through the tower to the
  air (Gas) flow.
• Each tower will have a design water/air ratio.
• An increase in this ratio will result in an
  increase of the approach, that is, warmer water
  will be leaving the tower.
• A test ratio is calculated when the cooling tower
  performance is evaluated.

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Thermodynamics of Air Water Systems
Humidity Ratio
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Local Cooling Tower Theory
Heat is transferred from water drops to the
surrounding air by the transfer of sensible and
latent heat
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Global Conservation Laws for Evaporative Cooling
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SSSF Model for Cooling Tower

• First Law Analysis

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Enthalpy of Wet air
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Local Heat and Mass Transfer in water air system
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Local Air-side control volume of fill
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Mechanism of Heat Transfer in Cooling Towers

• Heat transfer in cooling towers occurs by two
  major mechanisms
• Sensible heat from water to air (convection) and
• transfer of latent heat by the evaporation of
  water (diffusion).
• Both of these mechanisms operate at air-water
  boundary layer.
• The total heat transfer is the sum of these two
  boundary layer mechanisms.
• The total heat transfer can also be expressed in
  terms of the change in enthalpy of each bulk
  phase.
• A fundamental equation o f heat transfer in
  cooling towers (the Merkel equation) is obtained.

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The Merkel Method

• The Merkel method, developed in the 1920s, relies
  on several critical assumptions to reduce the
  solution to a simple manual iteration.
• These assumptions are
• The resistance for heat transfer in the water
  film is negligible,
• The effect of water loss by evaporation on energy
  balance or air process state is neglected,
• The specific heat of air-stream mixture at
  constant pressure is same as that of the dry air,
  and
• The ratio of hconv/hdiff (Lewis factor) for humid
  air is unity.
• Merkel combined equations for heat and water
  vapor transfer into a single equation similar as

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where                kAV/mw tower
characteristic                    k mass
transfer coefficient                    A
contact area/tower volume                    V
active cooling volume/plan area                  
  mw water flow rate                 T1 hot
water temperature                 T2 cold
water temperature                 T bulk water
temperature                hsa enthalpy of
saturated air-water vapor mixture at bulk water
temperature                        (J/kg dry
air)                ha enthalpy of air-water
vapor mixture (J/kg dry air )
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Temperature Enthalpy Diagram of Air Water System
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Tower Characteristics

• Tower Characteristic (MeM or NTU) is a
  characteristic of the tower that relates tower
  design and operating characteristics to the
  amount of heat that can be transferred.
• For a given set of operating conditions, the
  design constants that depend on the tower fill.
• For a tower that is to be evaluated using the
  characteristic curve method, the manufacturer
  will provide a tower characteristic curve.

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Charts for Merkel Number
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Height of Natural Draught Cooling Toer
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Forced Draught Cooling Towers
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SUPPLY TOWER CHARACTERISTIC

• The supply tower characteristic of the cooling
  tower can be evaluated with the help of cooling
  tower fill characteristics curves provided by
  manufacturer which takes into account the effect
  of rain and spray zones as well as fill fouling.
• These curves are certified by the cooling tower
  institute.

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MUNTERS 120/60 FILL 4 height
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MUNTERS 120/60 FILL 3 Height
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Generalized Equation for Cooling Tower Supply

• A generalized equation for cooling tower supply
  can be developed from the manufacturer curves
  (known as the supply equation) and is of the
  form

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Air Side Pressure Drop

• Manufacturer pressure drop curves are available
  for pressure drops at the inlet louvers, drift
  eliminators and the fill packing.
• These curves are shown in the following slides.
• Using curve fitting software, generalized
  pressure drop equations are found developed so as
  to calculate the pressure drops.

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PRESSURE DROP ACROSS FILL
BRENTWOOD 1900 FILL OF 4FT FILL HEIGHT
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BHP OF THE FAN

• The total pressure drop (PD) across the cooling
  tower which is the summation of the pressure
  drops across the drift eliminators, inlet louvers
  and the fill packing (constituting the static
  pressure drop) and also the velocity pressure
  drop is calculated.
• Now, the total fan power required is calculated
  as
• BHP (CFM PD)/ (n 6356)
• where n is the efficiency of the fan.

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ANOTHER METHOD

• We can also map the demand curve foe varying
  KAV/L values with varying L/G on the
  manufacturers curves for tower characteristics in
  order to find the L/G ratio of the cooling tower.
• After obtaining the L/G ratio all the steps to be
  followed are same as the previous method.

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Loss of Water

• Evaporation Rate is the fraction of the
  circulating water that is evaporated in the
  cooling process.
• A typical design evaporation rate is about 1 for
  every 12.5?C range at typical design conditions.
• It will vary with the season, since in colder
  weather there is more sensible heat transfer from
  the water to the air, and therefore less
  evaporation.
• The evaporation rate has a direct impact on the
  cooling tower makeup water requirements.

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• Drift is water that is carried away from the
  tower in the form of droplets with the air
  discharged from the tower.
• Most towers are equipped with drift eliminators
  to minimize the amount of drift to a small
  fraction of a percent of the water circulation
  rate.
• Drift has a direct impact on the cooling tower
  makeup water requirements.
• Recirculation is warm, moist air discharged from
  the tower that mixes with the incoming air and
  re-enters the tower.
• This increases the wet bulb temperature of the
  entering air and reduces the cooling capability
  of the tower.
• During cold weather operation, recirculation may
  also lead to icing of the air intake areas.