Introduction

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

• Formulations from the IAPWS (International Association for the Properties of Water and Steam) IAPWS-IF97 Industrial formulation (Revision 2007) and related models.

Properties of Humid Air

• Thermodynamic and psychrometric property algorithms from the ASHRAE Research Project 1485.
• Scientific Formulation IAPWS-95, IAPWS Formulation 2008 and IAPWS Formulation 2006. Properties of dry air are from the NIST Reference equation of Lemmon et al.

Graphical User Interface

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.

Range of Input Variables

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

Calculation Results

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.

Merkel Number

Introduction

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

• Formulations from the IAPWS (International Association for the Properties of Water and Steam) IAPWS-IF97 Industrial formulation (Revision 2007) and related models.

Properties of Humid Air

• Thermodynamic and psychrometric property algorithms from the ASHRAE Research Project 1485.
• Scientific Formulation IAPWS-95, IAPWS Formulation 2008 and IAPWS Formulation 2006. Properties of dry air are from the NIST Reference equation of Lemmon et al.

Graphical User Interface

Range of Input Variables

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

Introduction

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:

Graphical User Interface

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

Range of Input Variables

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

Calculation Results

Introduction

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 42 properties of humid air, water, steam, ice and psychrometrics.
• Allows for 17 combinations of two thermodynamic properties to be entered as input variables:
• • Dry-bulb Temperature / Wet-bulb Temperature
  • Dry-bulb Temperature / Dew Point Temperature
  • Dry-bulb Temperature / Relative Humidity
  • Dry-bulb Temperature / Humidity Ratio
  • Dry-bulb Temperature / Specific Enthalpy
  • Dry-bulb Temperature / Specific Volume
  • Wet-bulb Temperature / Dew Point Temperature
  • Wet-bulb Temperature / Relative Humidity
  • Wet-bulb Temperature / Humidity Ratio
  • Dew Point Temperature / Relative Humidity
  • Dew Point Temperature / Specific Enthalpy
  • Dew Point Temperature / Specific Volume
  • Relative Humidity / Humidity Ratio
  • Relative Humidity / Specific Enthalpy
  • Relative Humidity / Specific Volume
  • Humidity Ratio / Specific Enthalpy
  • Humidity Ratio / Specific Volume
• Supports input parameters and calculation results in both SI (metric) and I-P (english) system of units.
• For each combination of input thermodynamic variables, it calculates and provides the user with information about the appropriate values in the valid range of computations.
• Calculation results can be saved to a to a database for later retrieval.
• Calculation results can be exported to excel/pdf file formats.

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

• Formulations from the IAPWS (International Association for the Properties of Water and Steam) IAPWS-IF97 Industrial formulation (Revision 2007) and related models.

Properties of Humid Air

• Thermodynamic and psychrometric property algorithms from the ASHRAE Research Project 1485.
• Scientific Formulation IAPWS-95, IAPWS Formulation 2008 and IAPWS Formulation 2006. Properties of dry air are from the NIST Reference equation of Lemmon et al.

Graphical User Interface

Range of Input Variables

Property	Range in SI Units	SI Units
DRY-BULB TEMPERATURE	-143.15 ≤ Tdb ≤ 350.0	°C
WET-BULB TEMPERATURE	-143.15 ≤ Twb ≤ 350.0	°C
DEW POINT TEMPERATURE	-143.15 ≤ Tdp ≤ 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	m3/kg
PRESSURE	10.0 ≤ P ≤ 10.0E6	Pa

Property	Range in I-P Units	I-P Units
DRY-BULB TEMPERATURE	-225.67 ≤ Tdb ≤ 662.0	°F
WET-BULB TEMPERATURE	-225.67 ≤ Twb ≤ 662.0	°F
DEW POINT TEMPERATURE	-225.67 ≤ Tdp ≤ 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	ft3/lb
PRESSURE	0.00145 ≤ P ≤ 1450.4	psia

Calculation Results

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)/m3	lb(w)/ft3
Parts per million by weight	ppmw	ppmw
Parts per million by volume	ppmv	ppmv
Enhancement Factor	[-]	[-]
Specific Volume of Dry Air	m3/kg, cm3/g	ft3/lb, in3/lb
Specific Volume of Humid Air	m3/kg, cm3/g	ft3/lb, in3/lb
Specific Volume of Saturated Water	m3/kg, cm3/g	ft3/lb, in3/lb
Specific Volume of Saturated Ice	m3/kg, cm3/g	ft3/lb, in3/lb
Specific Volume of Water Vapor	m3/kg, cm3/g	ft3/lb, in3/lb
Density of Dry Air	kg/m3, g/cm3	lb/ft3, lb/in3
Density of Humid Air	kg/m3, g/cm3	lb/ft3, lb/in3
Density of Saturated Water	kg/m3, g/cm3	lb/ft3, lb/in3
Density of Saturated Ice	kg/m3, g/cm3	lb/ft3, lb/in3
Density of Water Vapor	kg/m3, g/cm3	lb/ft3, lb/in3
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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