An evaporative cooling tower is a device that is used to remove waste heat from the water used in an industrial process equipment or a machinery by rejecting that waste heat into the environment. When water is mixed with air in a cooling tower configuration, a heat transfer process takes places that involves a latent heat transfer due to the vaporization of a small amount of water and a sensible heat transfer reflecting the difference in temperatures of water and air.
Based on the theory developed by Merkel, the heat transfer process that occurs in a cooling tower by considering the enthalpy potential difference as the driving force is described by the Merkel equation:
$\frac{{KaV}}{L} $ | $=$ | Tower characteristic | |
$T{}_1 $ | $=$ | Hot water temperature (inlet) | |
$T{}_2 $ | $=$ | Cold water temperature (outlet) | |
$h' $ | $=$ | Enthalpy of saturated air at water temperature | |
$h $ | $=$ | Enthalpy of main airstream | |
${c_{pw}}$ | $=$ | Specific heat capacity of water | |
$d{T_w}$ | $=$ | Temperature differential of water |
The Merkel Number application solves the equation (1) numerically using the four-point Chebyshev numerical method employing the following models for the calculation of water and air properties:
Properties of Water and Steam
Properties of Humid Air
Property | Range in SI Units | SI Units |
---|---|---|
HOT WATER TEMPERATURE | 1.0 ≤ T ≤ 90.0 | °C |
COLD WATER TEMPERATURE | 1.0 ≤ T ≤ 90.0 | °C |
WET-BULB TEMPERATURE | 1.0 ≤ T ≤ 90.0 | °C |
PRESSURE | 60000 ≤ P ≤ 110000 | Pa |
RATIO L/G | 0.01 ≤ L/G ≤ 5.0 | 1 |
Property | Range in I-P Units | I-P Units |
---|---|---|
HOT WATER TEMPERATURE | 33.8 ≤ T ≤ 194.0 | °F |
COLD WATER TEMPERATURE | 33.8 ≤ T ≤ 194.0 | °F |
WET-BULB TEMPERATURE | 33.8 ≤ T ≤ 194.0 | °F |
PRESSURE | 8.70226426 ≤ P ≤ 15.95415115 | psia |
RATIO L/G | 0.01 ≤ L/G ≤ 5.0 | 1 |
Demand Curves allows to calculate and plot in a log-log graph isolines resulting from the integration of equation (1) using as a parameter an approach value. It also calculates the approach given a pair of values determined by KaV/L and L/G, both in the SI and I-P system of units. The definition of the input variables for calculation of the demand curves is given in Table X.
For a specific tower, there is a characteristic curve in the form of a plot of tower characteristic, $KaV/L$, versus water to air flow ratio, $L/G$. This plot is described with an equation of the following form:
Input Variable | Definition |
---|---|
WET-BULB TEMPERATURE | Temperature of air wet-bulb entering the cooling tower |
COOLING RANGE | Difference between hot water temperature and cold water temperature |
PRESSURE | Total pressure referred to atmospheric |
COEFFICIENT C | Constant defined for a particular packing design |
EXPONENT N | Exponent defined for a particular packing design |
Property | Range in SI Units | SI Units |
---|---|---|
WET-BULB TEMPERATURE | 1.0 ≤ T ≤ 90.0 | °C |
COOLING RANGE | 0.1 ≤ T ≤ 90.0 | °C |
PRESSURE | 60000 ≤ P ≤ 110000 | Pa |
COEFFICIENT C | 1.0 ≤ C ≤ 3.0 | 1 |
EXPONENT N | -2.0 ≤ N ≤ -0.1 | 1 |
KaV/L | 0.1 ≤ KaV/L ≤ 5.0 | 1 |
L/G | 0.1 ≤ L/G ≤ 5.0 | 1 |
Approach | 1.0 ≤ T ≤ 60.0 | °C |
Property | Range in SI Units | SI Units |
---|---|---|
WET-BULB TEMPERATURE | 33.8 ≤ T ≤ 194.0 | °F |
COOLING RANGE | 0.1 ≤ T ≤ 162.0 | °F |
PRESSURE | 8.70226426 ≤ P ≤ 15.95415115 | psia |
COEFFICIENT C | 1.0 ≤ C ≤ 3.0 | 1 |
EXPONENT N | -2.0 ≤ N ≤ -0.1 | 1 |
KaV/L | 0.1 ≤ KaV/L ≤ 5.0 | 1 |
L/G | 0.1 ≤ L/G ≤ 5.0 | 1 |
Approach | 1.0 ≤ T ≤ 140.0 | °F |
Mechanical Draft allows the evaluation of the performance capability of mechanical draft cooling towers based on the Acceptance Test Code CTI ATC-105 from test data points using the characteristic curve method.
By determining design and test conditions for a particular mechanical draft cooling tower, the manufacturer´s characteristic curve parameters and a design liquid to gas ratio (L/G), Mechanical Draft calculates the cooling capability at design conditions, plotting in a log-log graph each of the input data conditions as well as the resulting intercept results (denoted as a result data) given as a pair of values determined by KaV/L and L/G in the SI and I-P system of units.
Mechanical Draft solves the energy equation by integrating the Merkel equation numerically using the four-point Chebyshev numerical method employing the following models for the calculation of water and air properties:
Properties of Water and Steam
Properties of Humid Air
Input Variable | Definition |
---|---|
WATER FLOW RATE | Quantity of hot water flowing into the tower. |
HOT WATER TEMPERATURE | Temperature of inlet water. |
COLD WATER TEMPERATURE | Average temperature of the cold water basin discharge (outlet). |
WET-BULB TEMPERATURE | Temperature of air wet-bulb entering the cooling tower. |
DRY-BULB TEMPERATURE | Temperature of air dry-bulb entering the cooling tower. |
FAN POWER | Power input to the fan drive assembly, excluding power losses in the driver. |
PRESSURE | Total pressure referred to atmospheric. |
COEFFICIENT C | Constant defined for a particular packing design. |
EXPONENT N | Exponent defined for a particular packing design. |
DESIGN L/G RATIO C | Ratio of water flow rate to airflow rate at design. |
TOWER TYPE | $Forced$ draft: fan located near the bottom, forcing the air from bottom to top. $Induced$ draft: fan located at the top inducing suction from the tower and discharging it into the atmosphere. |
Property | Range in SI Units | SI Units |
---|---|---|
WATER FLOW RATE | 0.5 ≤ Flow ≤ 100000.0 | kg/s |
HOT WATER TEMPERATURE | 1.0 ≤ T ≤ 90.0 | °C |
COLD WATER TEMPERATURE | 1.0 ≤ T ≤ 90.0 | °C |
WET-BULB TEMPERATURE | 1.0 ≤ T ≤ 90.0 | °C |
DRY-BULB TEMPERATURE | 1.0 ≤ T ≤ 90.0 | °C |
FAN POWER | 1.0 ≤ Fan ≤ 1.0E6 | W |
PRESSURE | 60000 ≤ P ≤ 110000 | Pa |
COEFFICIENT C | 1.0 ≤ C ≤ 3.0 | 1 |
EXPONENT N | -2.0 ≤ N ≤ -0.1 | 1 |
DESIGN L/G RATIO | 0.1 ≤ L/G ≤ 5.0 | 1 |
KaV/L | 0.1 ≤ KaV/L ≤ 5.0 | 1 |
L/G | 0.1 ≤ L/G ≤ 5.0 | 1 |
APPROACH | 1.0 ≤ T ≤ 60.0 | °C |
Property | Range in I-P Units | I-P Units |
---|---|---|
WATER FLOW RATE | 7.92 ≤ Flow ≤ 1585032.22 | gpm |
HOT WATER TEMPERATURE | 33.8 ≤ T ≤ 194.0 | °F |
COLD WATER TEMPERATURE | 33.8 ≤ T ≤ 194.0 | °F |
WET-BULB TEMPERATURE | 33.8 ≤ T ≤ 194.0 | °F |
DRY-BULB TEMPERATURE | 33.8 ≤ T ≤ 194.0 | °F |
FAN POWER | 0.001342 ≤ Fan ≤ 1341.022 | bhp |
PRESSURE | 8.702264 ≤ P ≤ 15.954151 | psia |
COEFFICIENT C | 1.0 ≤ C ≤ 3.0 | 1 |
EXPONENT N | -2.0 ≤ N ≤ -0.1 | 1 |
DESIGN L/G RATIO | 0.1 ≤ L/G ≤ 5.0 | 1 |
KaV/L | 0.1 ≤ KaV/L ≤ 5.0 | 1 |
L/G | 0.1 ≤ L/G ≤ 5.0 | 1 |
APPROACH | 1.0 ≤ T ≤ 140.0 | °F |
Result Variable | Definition |
---|---|
APPROACH | Approach calculated at design data. |
INTERCEPT L/G AT APPROACH | Value of L/G ratio calculated at result point (L/G value of the intersection of the demand curve calculated on the approach at design and the curve parallel to the characteristic curve defined on the test point). |
INTERCEPT KaV/L | Value of KaV/L ratio calculated at result point (KaV/L value of the intersection of the demand curve calculated on the approach at design and the curve parallel to the characteristic curve defined on the test point). |
TOWER CAPABILITY | Cooling capability result calculated for a data test. |
Psychrometrics Calculator allows the calculation of physical properties of humid air, water, steam, ice and psychrometrics commonly used in the design and operation of cooling towers.
Calculation of the properties of humid air, water, steam, ice and psychrometrics are based on the precision provided by the mathematical formulations of the following thermodynamic and transport properties models:
Properties of Water and Steam
Properties of Humid Air
Property | Range in SI Units | SI Units |
---|---|---|
DRY-BULB TEMPERATURE | -143.15 ≤ T_{db} ≤ 350.0 | °C |
WET-BULB TEMPERATURE | -143.15 ≤ T_{wb} ≤ 350.0 | °C |
DEW POINT TEMPERATURE | -143.15 ≤ T_{dp} ≤ 350.0 | °C |
RELATIVE HUMIDITY | 0 .0 ≤ RH ≤ 100.0 | [%] |
HUMIDITY RATIO | 0.0 ≤ W ≤ 10.0 | kg/kg |
SPECIFIC ENTHALPY | -311.357 ≤ h ≤ 32135.848 | kJ/kg |
SPECIFIC VOLUME | 1.469E-3 ≤ v ≤ 3.055E5 | m^{3}/kg |
PRESSURE | 10.0 ≤ P ≤ 10.0E6 | Pa |
Property | Range in I-P Units | I-P Units |
---|---|---|
DRY-BULB TEMPERATURE | -225.67 ≤ T_{db} ≤ 662.0 | °F |
WET-BULB TEMPERATURE | -225.67 ≤ T_{wb} ≤ 662.0 | °F |
DEW POINT TEMPERATURE | -225.67 ≤ T_{dp} ≤ 662.0 | °F |
RELATIVE HUMIDITY | 0 .0 ≤ RH ≤ 100.0 | [%] |
HUMIDITY RATIO | 0.0 ≤ W ≤ 10.0 | lb/lb |
SPECIFIC ENTHALPY | -126.174 ≤ h ≤ 13823.61 | Btu/lb |
SPECIFIC VOLUME | 2.353E-2 ≤ v ≤ 4.893E6 | ft^{3}/lb |
PRESSURE | 0.00145 ≤ P ≤ 1450.4 | psia |
Property | SI Units | I-P Units |
---|---|---|
Dry-Bub Temperature | °C | °F |
Wet-Bulb Temperature | °C | °F |
Dew Point Temperature | °C | °F |
Humid Air Pressure | Pa, kPa, bar, mmHg | psia, inHg, inH2O, atm |
Water Vapor Partial Pressure | Pa, kPa, bar, mmHg | psia, inHg, inH2O, atm |
Dry Air Partial Pressure | Pa, kPa, bar, mmHg | psia, inHg, inH2O, atm |
Saturation Water Vapor Pressure | Pa, kPa, bar, mmHg | psia, inHg, inH2O, atm |
Dry Air Mole Fraction | [-] | [-] |
Water Mole Fraction | [-] | [-] |
Dry Air Mass Fraction | [-] | [-] |
Water Mass Fraction | [-] | [-] |
Humidity Ratio | kg(w)/kg(da), g(w)/kg(da) | lb(w)/lb(da), gr(w)/lb(da) |
Saturation Humidity Ratio | kg(w)/kg(da), g(w)/kg(da) | lb(w)/lb(da), gr(w)/lb(da) |
Relative Humidity | [%] | [%] |
Absolute Humidity | kg(w)/m^{3} | lb(w)/ft^{3} |
Parts per million by weight | ppmw | ppmw |
Parts per million by volume | ppmv | ppmv |
Enhancement Factor | [-] | [-] |
Specific Volume of Dry Air | m^{3}/kg, cm^{3}/g | ft^{3}/lb, in^{3}/lb |
Specific Volume of Humid Air | m^{3}/kg, cm^{3}/g | ft^{3}/lb, in^{3}/lb |
Specific Volume of Saturated Water | m^{3}/kg, cm^{3}/g | ft^{3}/lb, in^{3}/lb |
Specific Volume of Saturated Ice | m^{3}/kg, cm^{3}/g | ft^{3}/lb, in^{3}/lb |
Specific Volume of Water Vapor | m^{3}/kg, cm^{3}/g | ft^{3}/lb, in^{3}/lb |
Density of Dry Air | kg/m^{3}, g/cm^{3} | lb/ft^{3}, lb/in^{3} |
Density of Humid Air | kg/m^{3}, g/cm^{3} | lb/ft^{3}, lb/in^{3} |
Density of Saturated Water | kg/m^{3}, g/cm^{3} | lb/ft^{3}, lb/in^{3} |
Density of Saturated Ice | kg/m^{3}, g/cm^{3} | lb/ft^{3}, lb/in^{3} |
Density of Water Vapor | kg/m^{3}, g/cm^{3} | lb/ft^{3}, lb/in^{3} |
Specific Enthalpy of Dry Air | J/kg, kJ/kg | Btu/lb, ft lbf/lb |
Specific Enthalpy of Humid Air | J/kg, kJ/kg | Btu/lb, ft lbf/lb |
Specific Enthalpy of Saturated Water | J/kg, kJ/kg | Btu/lb, ft lbf/lb |
Specific Enthalpy of Saturated Ice | J/kg, kJ/kg | Btu/lb, ft lbf/lb |
Specific Enthalpy of Water Vapor | J/kg, kJ/kg | Btu/lb, ft lbf/lb |
Specific Entropy of Dry Air | J/(kg·K), kJ/(kg·K) | Btu/(lb·°R), ft lbf/ (lb·°R) |
Specific Entropy of Humid Air | J/(kg·K), kJ/(kg·K) | Btu/(lb·°R), ft lbf/ (lb·°R) |
Specific Entropy of Saturated Water | J/(kg·K), kJ/(kg·K) | Btu/(lb·°R), ft lbf/ (lb·°R) |
Specific Entropy of Saturated Ice | J/(kg·K), kJ/(kg·K) | Btu/(lb·°R), ft lbf/ (lb·°R) |
Specific Entropy of Water Vapor | J/(kg·K), kJ/(kg·K) | Btu/(lb·°R), ft lbf/ (lb·°R) |
Specific Internal Energy of Dry Air | J/kg, kJ/kg | Btu/lb, ft lbf/lb |
Specific Internal Energy of Humid Air | J/kg, kJ/kg | Btu/lb, ft lbf/lb |
Specific Isobaric Heat Capacity of Humid Air | kJ/(kg·K) | Btu/(lb·°R) |
Compressibility of Humid Air | [-] | [-] |
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