CT-Natural

$9989

One (1) Installation License
For Commercial Use
One-Year Email Support
Free Minor Upgrades

BUY 64-bit Version

Requirements

•
Windows Versions (64-bit): Windows 11, Windows 10
•
Application is available only in 64-bit version.

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CT-Natural (User Guide)

CT-Natural

Version 2.0

Computational software to analyze and determine cooling performance curves and thermophysical operational variables in natural draft counterflow wet cooling towers.

All calculations are performed employing accurate numerical techniques implementing some of the most precise mathematical models for the properties of humid air, water and steam developed for industrial purposes.

Natural Draft Counterflow Cooling Towers.

Demand Curves.

Merkel Number.

Psychrometrics Calculator.

Natural Draft

Numerical calculation and graphical display of operational variables in natural draft counterflow cooling towers based on a mathematical model of heat and mass transfer between water film and humid air in the cooling fill.

Graphical and numerical calculation of operational variables in natural draft counterflow cooling towers based on a mathematical model of heat and mass transfer between water film in the cooling fill and humid air.

Complete validation of input variables, informing the user of the correct range of variables for a valid data calculation.

Creation of projects in a database that describe a particular set of atmospheric and operational conditions together with tower characteristics, and data calculation results for later retrieval or recalculation.

Generation of high-quality pdf files of temperature curve plots and data calculation points for a particular project.

Generation of excel and pdf files of numerical results of data calculations.

Supports input variables and calculation results in SI (metric) and I-P (English) system of units.

Demand Curves

Calculation and graphical display of demand curves and approach data points.

Calculation and graphical display of demand curves following the integration of Merkel´s equation.

Calculation and graphical display of approach data points.

Complete validation of input variables.

Creation of projects in a database that describe a particular set of input variables together with the calculated demand curves and approach data points for later retrieval or recalculation.

Generation of high-quality pdf files of demand curve plots.

Generation of excel and pdf files of approach data point calculations results.

Supports input variables and calculation results in SI (metric) and I-P (English) system of units.

Merkel Number

Calculation of Merkel number using the Chebyshev numerical method.

Calculation of Merkel number using the Chebyshev numerical method.

Complete validation of input variables, informing of the correct range of variables for a valid calculation.

Supports input variables and calculation results in SI (metric) and I-P (English) system of units.

Psychrometrics Calculator

A psychrometrics calculator based on the latest mathematical models to numerically evaluate the properties of humid air, water, steam and ice.

Calculation of 42 properties of humid air, water, steam, ice and psychrometrics.

It allows for 17 combinations of two thermodynamic properties to be entered as input parameters.

Complete validation of input thermodynamic properties, it calculates and provides the user with information about the appropriate input values in the valid range of computations.

Supports input variables and calculation results in SI (metric) and I-P (English) system of units.

Introduction

A natural draft counterflow wet cooling tower (NDCWCT) is a device that utilizes the effects of mass and energy transfer to cool water by providing cold air flows “through”a hot water flow. The heat rejected to the atmosphere is in the form of latent and sensible heat and is carried away by the air flow through the tower. The water is cooled first by breaking it up into droplets (or spray), and then by making it flow in the form of thin films inside the cooling fill, allowing it to come into contact with the air which eventually carries the heat away into the atmosphere.

Considering that most of the heat and mass transfer ocurrs in the cooling fill for this type of cooling tower, the numerical calculations performed in Natural Draft (version 2.0) are focused only in the cooling fill zone. Figure 1 shows an schematic of a NDCWCT and some of the input variables required for the computations of the thermophysical variables and cooling performance.

Figure 1.

Schematic of a NDCWCT and some of the input variables in Natural Draft.

An energy formulation that incorporates the heat and mass transfer process between water and humid air in the cooling fill is numerically solved to calculate isotherms of the outlet water temperature given a set of atmospheric and operating conditions in a NDCWCT.

Some of the assumptions and simplifications considered in the energy model used in Natural Draft are summarized as follows:

Calculations of heat and mass transfer are conducted in the cooling fill zone.

Operation of the cooling tower is under steady-state conditions, without considering wind effects.

Water and air flow rates are uniform over the cross sections of the cooling tower.

Humid air is saturated when leaving the cooling fill, i.e., Relative Humidity (Outlet) = 100%.

For the calculation of the thermophysical properties of water, steam and humid air used in the numerical solution of the energy model used in Natural Draft, the following formulations of properties are implemented:

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

Figure 2.

Graphical User Interface in Natural Draft.

Input Variable	Definition
TEMPERATURE (INLET)	Temperature of dry-bulb air entering the cooling tower.
RELATIVE HUMIDITY (INLET)	Relative humidity of air entering the cooling tower.
PRESSURE (INLET)	Total pressure referred to atmospheric, at the entrance of the cooling tower.
RELATIVE HUMIDITY (OUTLET)	Relative humidity of air leaving the cooling fill.
EFFECTIVE SHELL HEIGHT	Normally taken as height from middle of packing to top of tower shell.
COOLING FILL AREA	Total packing area normal to air flow.
WATER FLOW RATE	Mass water flow entering into the cooling tower.
WATER LOADING	Mass water flow per unit plain area of packing (calculated).
COOLING RANGE	Difference between hot water temperature and cold water temperature.
WATER TEMPERATURE (OUTLET)	Estimated average temperature of the cold water basin discharge (outlet).
HEAT TRANSFER ADJUSTMENT	Adjustment factor for the heat transfer process in the cooling fill.
COEFFICIENT C	Constant defined for a particular packing design.
EXPONENT N	Exponent defined for a particular packing design.
COEFFICIENT R	Constant for resistance curve characteristic for a particular cooling tower.
EXPONENT M	Exponent for resistance curve characteristic of a particular cooling tower.

Table 1.

Definition of input variables in Natural Draft.

Range of Input Variables

Property	Range in SI Units	SI Units
TEMPERATURE (INLET)	-20.0 ≤ T ≤ 60.0	°C
RELATIVE HUMIDITY (INLET)	0.0 ≤ R.H. ≤ 100.0	%
PRESSURE (INLET)	60000.0 ≤ P ≤ 110000.0	Pa
RELATIVE HUMIDITY (OUTLET)	R.H. = 100.0	%
EFFECTIVE SHELL HEIGHT	10.0 ≤ Height ≤ 300.0	m
COOLING FILL AREA	19.64 ≤ Area ≤ 31415.92	m²
HEAT TRANSFER ADJUSTMENT	-1.0 ≤ Factor ≤ 1.0	1
WATER FLOW RATE	0.5 ≤ Flow ≤ 100000.0	kg/s
COOLING RANGE	1.0 ≤ T ≤ 50.0	°C
WATER TEMPERATURE (OUTLET)	1.0 ≤ T ≤ 70.0	°C
COEFFICIENT C	1.0 ≤ C ≤ 3.0	1
EXPONENT N	-2.0 ≤ N ≤ -0.1	1
COEFFICIENT R	20.0 ≤ R ≤ 500.0	1
EXPONENT M	-4.0 ≤ M ≤ 4.0	1
KaV/L	0.1 ≤ KaV/L ≤ 5.0	1
L/G	0.1 ≤ L/G ≤ 5.0	1
PERFORMANCE CURVE	1.0 ≤ T ≤ 60.0	°C

Table 2.

Full range of input variables for Natural Draft in SI Units.

Calculation Results

Figure 3.

Numerical Results in a calculation project in Natural Draft.

Result Variable	Definition
Inlet Wet-bulb Temperature	Wet-bulb temperature of air entering the cooling tower.
Inlet Enthalpy	Specific enthalpy of air entering the cooling tower.
Inlet Water Mass Faction	Water mass fraction at the entrance of the cooling tower.
Inlet Water Vapor Pressure	Water vapor pressure at the entrance of the cooling tower.
Inlet Density	Specific density of air entering the cooling tower.
Outlet Dry-bulb Temperature	Dry-bulb temperature of air leaving the cooling fill inside the cooling tower.
Outlet Wet-bulb Temperature	Wet-bulb temperature of air leaving the cooling fill inside the cooling tower.
Outlet Enthalpy	Specific enthalpy of air leaving the cooling fill inside the cooling tower.
Outlet Water Mass Faction	Water mass fraction leaving the cooling fill inside the cooling tower.
Outlet Water Vapor Pressure	Water vapor pressure leaving the cooling fill inside the cooling tower.
Outlet Density	Specific density of air leaving the cooling fill inside the cooling tower.
Density Difference	Density difference of air at the entrance of the cooling tower and air leaving the cooling fill.
Pressure Difference	Pressure difference at the entrance of the cooling tower and leaving the cooling fill.
Airflow Rate	Airflow rate leaving the cooling fill.
Heat Energy Flow	Total amount of heat energy transferred from the cooling tower.
Average Air Velocity	Average air velocity of humid air in the cooling fill.
Loss Coefficient	Non-dimensional coefficient referred to the pressure loss in the cooling fill.
L/G	Calculated ratio of water flow rate to airflow rate
KaV/L	Calculated tower characteristic (Merkel number).
Inlet Water Temperature	Calculated inlet water temperature.
Outlet Water Temperature	Calculated outlet water temperature.

Table 3.

Definition of calculation result variables in Natural Draft.

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:

$\frac{{KaV}}{L} = \int_{{T_2}}^{{T_1}} {\frac{{{c_{pw}}d{T_w}}}{{h' - h}}}$

where

$\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

Figure 1.

Merkel Number calculation in CT-Natural.

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

Table 1. Full ranges of input variables for calculation of Merkel Number in SI Units.

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

Table 2. Full ranges of input variables for calculation of Merkel Number in I-P Units.

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:

$\frac{{KaV}}{L} = c{\left( {\frac{L}{G}} \right)^{ - n}}$

Where $L$ = water flow rate; $G$ = airflow rate; $c$ = constant defined for a particular packing design, or the intercept of the characteristic curve at $L/G$ = 1; $n$ = exponent related to packing design determined from test data.

Graphical User Interface

Figure 2. Graphical User Interface for Demand Curves.

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

Table 3. Definition of input variables in Demand Curves.

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

Table 4. Full ranges of input variables in Demand Curves (SI Units).

Property	Range in I-P 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

Table 5. Full ranges of input variables in Demand Curves (I-P Units).

Calculation Results

Figure 3.

Numerical Results in a Demand Curves calculation project.

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

Figure 1. Graphical User Interface in Psychrometrics Calculator.

Range of Input Variables

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	m³/kg
PRESSURE	10.0 ≤ P ≤ 10.0E6	Pa

Table 1. Full range of input variables in Psychrometrics Calculator (SI Units).

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	ft³/lb
PRESSURE	0.00145 ≤ P ≤ 1450.4	psia

Table 2. Full range of input variables in Psychrometrics Calculator (I-P Units).

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	[-]	[-]