Component 111: Cooling Tower (Natural Draft)

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Component 111: Natural Draft Cooling Tower (Merkel)

Specifications

Line connections
1	Air Inlet
2	Air Outlet
3	Cooling Water Inlet
4	Cooling Water Outlet
5	Makeup Inlet
6	Blow Down
7	Flue gas Inlet (optional)
8	Control inlet for performance factor (PACKPERF - as h) or T4

General Transient modeling User Input Values Physics Used Displays Example

General

Component 111 simulates a natural draft cooling tower with a counter current wet cooling zone. The wet cooling zone model is based on the Merkel equation (e.g. VDI Wärmeatlas, section Mj).

There is as of Release 11 an identification mode for these cooling towers.
The flag FIDENT allows to control whether
• the cooling water outlet temperature T4 is to be calculated (FIDENT=0)
• the cooling water outlet temperature T4 is to be specified, and the air flow is to be calculated (FIDENT=1)
• the cooling water outlet temperature T4 is to be specified, and the Merkel number is to be calculated (FIDENT=2)
It is also possible to specify a wind correction.

Also, a kernel expression can be specified for the packing characteristic factor C, the performance factor K, and the wind correction.

Now the Merkel cooling towers can also be used in the INTMAT mode (integration of the material data into the equation system). Thus for models containing these components a material data reconciliation is possible too.

Annotation

There is a performance factor PACKPERF by means of which a change of the cooling tower performance can be simulated. This parameter has been made accessible via a logic line, so that an adjustment is possible.

Note on the T4 specification:

T4 specification by the control inlet (port 8) in identification mode 1 and 2
T4 specification as specification value in the component (User Input Values): Using switch FWETZONE = 0 and thus as a value in PWETZONE

Transient modeling

Component 111 enables the modeling of transient regimes (time-dependent computations). This type of calculation is activated with the switch FINST.

A cooling tower features transient behavior mostly in the water basin which acts as a big water storage. The wet zone with fill or packing material also features some significant mass and acts as indirect storage delaying the cooled water temperature changes e.g. at load changes. Finally, the cooling tower shell wall also acts as an indirect storage influencing however only the air outlet state.

Cooling tower transient computations are possible for drain mode (FCIRC=1) and without hybrid mode (FHYBRID=0) only. In cooling tower transient computations the air outlet humidity is always computed (FHUM=1).

The user input values for the transient modeling are classified in the following groups.

Water basin definition - here the water basin geometric details are specified. The water basin transient mass and energy balance is computed assuming homogeneous mixing of water inside the basin. Depending on the flag value FSPIN one can either specify the water basin level (FSPIN=0) or compute the level specifying both the inlet and the outlet water mass flow (FSPIN=1).

Fill or packing material definition - here the geometric and material details of the fill or packing material (wet zone) are specified. The fill or packing material part is defined by the volume of the wet zone WZVOL, the void volume fraction PHI (i,e, the volume portion of the wet zone not occupied by the fill or packing material) as well as the fill or packing material specific surface area FV.

Heat transfer coefficients - in this group the heat and mass transfer coefficients, in particular for the simulation of the evaporation and the heat transfer in the wet zone, are specified. The heat transfer between water and air is controlled by the coefficient ALPHIWAN at Design conditions (defined by the air to water ratio) and is scaled by the corresponding parameters PACKFACT, PACKEXP, PACKPERF at off-design conditions. The mass transfer (water evaporation) is controlled by the coefficient BETAWAN at Design conditions and is scaled by the corresponding parameters PACKFACT, PACKEXP, PACKPERF at off-design conditions. There are two alternatives to specify the mass transfer coefficient. One can either specify the value of BETAWAN directly or by specifying the value of ALPHIWAN and the Lewis factor LEF defined as

\[ Le_f = \frac{\alpha}{\rho \beta c_p} \]

Here \(\alpha\) and \(\beta\) are the heat and mass transfer coefficients respectively. \(\rho\) and \(c_p\) are the air density and heat capacity.

Shell wall material definition - here the geometric and material details of the cooling tower shell wall are specified.

After spefifying all geometric details of the cooling tower one can match the results of the steady state Merkel equation model implemented in the component 111 for the wet zone by adjusting the values of ALPHIWAN, BETAWAN (or LEF) at steady state conditions.

In case of identification calculation - FIDENT > 0 - the values of the heat and the mass transfer coefficient water to air (\(\alpha\) and \(\beta\)) are adjusted to match the specified temperature T4.

User Input Values

FFU	Switch (on/off) Like in Parent Profile (Sub Profile option only) Expression =0: Off (No Air calculations, input cooling range DT34N = T3 -T4) =1: On
DT34N	Cooling range (Only for FFU = 0)
FMODE	Calculation mode (design / off-design) Like in Parent Profile (Sub Profile option only) Expression =0: Global = 1: local Off-Design =-1: local Design
FIDENT	Identification mode: Like in Parent Profile (Sub Profile option only) Expression = 0: No identification, T4 is calculated = 1: T4 is specified by control inlet, the air flow is calculated, so that this temperature is reached. = 2: T4 is specified by control inlet, the Merkel Number is calculated, so that this temperature is reached.
FWETZONE	Switch for wet zone mode: The wet zone is designed using a characteristic parameter WETZONE. The FWETZONE switch determines, how this parameter should be interpreted: Like in Parent Profile (Sub Profile option only) Expression =0: PWETZONE is interpreted as the water outlet temperature (T4). The Merkel number is then calculated from this. This is the integral of Merkel's main equation over the water temperature. The integration limits are the water inlet and outlet temperatures of the wet zone. =1: PWETZONE is interpreted as a temperature approximation (approach temperature) between the water outlet (T4) and the wet bulb temperature (TWB1) of the inlet air. The wet bulb temperature is therefore the cooling limit temperature (which would be achievable with an infinitely large area), since the evaporation of the water can result in an additional cooling below the air inlet temperature. The temperature approximation is also called the cooling limit distance. It is usually set at 5 K, in practice cooling limit distances between 4 K and 7 K can be found. T4 is determined from the cooling limit distance and then the Merkel number, as with FWETZONE = 0. =2: PWETZONE is interpreted as a Merkel number (Me). In this case, the water outlet temperature is to be found as the integration limit so that the integral of Merkel's main equation gives the desired Merkel number. =3: PWETZONE is interpreted as NTU ("number of transfer units"). This results in the Merkel number for Me = NTU * AWR, with the air / water ratio AWR = M4 / M1_dry. The water outlet temperature is then calculated from the Merkel number as with FWETZONE = 2.
PWETZONE	Parameter for wet-zone Cooling water outlet temperature T4 (for FWETZONE=0) wet-zone temperature approach (for FWETZONE=1) Merkel number (for FWETZONE=2) NTU (for FWETZONE=3) Physical key figure (dimensionless), definition: NTU = (k * A) / (m * cp)
AWR	Dry Air/ Water Ratio, Design
FPACKFACT	Flag for Packing characteristic factor C (off design) Like in Parent Profile (Sub Profile option only) Expression =0: Internally by the specification value =1: PACKFACT= Port_8.P/(1 bar) =2: Expression EPACKFACT
PACKFACT	Packing-Characteristic Factor (C), off-design
EPACKFACT	Expression for Packing-Characteristic Factor (C) evalexpr:REAL; begin // TODO: calculate return value and set val to it evalexpr:=1.0; end;
PACKEXP	Packing-Characteristic Exponent (M), off-design
FPACKPERF	Specification of performance factor , off-design Like in Parent Profile (Sub Profile option only) Expression =0: Internally by the specification value =1: PACKPERF= Port_8.H/(1 kJ/kg) =2: Expression EPACKPERF
PACKPERF	Packing-Characteristic Performance Factor (K), off-design
EPACKPERF	Expression for PACKPERF evalexpr:REAL; begin // TODO: calculate return value and set val to it evalexpr:=1.0; end;
FMERKEL	Switch for Merkel equation Like in Parent Profile (Sub Profile option only) Expression =0: Standard Merkel Equation =1: Enhanced Merkel Equation
FHUM	Handling of wet-zone outlet humidity Like in Parent Profile (Sub Profile option only) Expression =0: wet-zone outlet relative humidity is user input =1: wet-zone outlet relative humidity will be calculated
PHI2	wet-zone outlet relative humidity (FHUM=0)
DRIFT	Drift loss fraction
FCIRC	Switch for water circulation type Like in Parent Profile (Sub Profile option only) Expression =0: Closed circulation. Determine makeup and purge flow rate via the parameter COC =1: Open circulation. No makeup and purge flow
COC	Cycles of concentration in a closed circulation loop Warning: According to VGB R 455 P is COC = makeup water / purge water = Z/A This is a simplification that is not valid for components 111/112, because here the calculation is based on the real increase in concentration of salts under consideration of drift losses (DRIFT).
FSTACK	Switch for stack mode Like in Parent Profile (Sub Profile option only) Expression =0: pressure drop is input =1: stack height is input
PSTACK	Stack Parameter Pressure drop (FSTACK=0) Effective stack height (FSTACK=1)
FCFWIND	Specification of wind correction factor Like in Parent Profile (Sub Profile option only) Expression =0: None =1: value CFWIND =2: value CWTDT =3: Airflow factor = Port_8.M/(1kg/s) =4:Cooling water outlet offset = Port_8.M/(1 kg/s)(1K) =5: Charlie lookup CWINDAIRFLOW, wind speed x = Port_8.M/(1 kg/s)(1 m/s) =6: Charlie lookup CWINDCWTDT, wind speed x = Port_8.M/(1 kg/s)*(1 m/s) =7: Expression ECFWIND corrects airflow (factor) =8: Expression ECFWIND corrects cooling water temperature (offset)
CFWIND	Wind correction factor for air flow
CWTDT	Wind correction temperature offset for cooling water outlet (dt)
ECFWIND	Expression wind correction factor function evalexpr:REAL; var val:real; internals:array of InternalValue; n:integer; i:integer; WindSpeed:real; comp111: ebscomp111; begin internals := keGetInternals(); n := length( internals ); { for i := 0 to n-1 do begin println( internals[i].name, ": ", internals[i].value ); end; } if (n > 0) then WindSpeed:=internals[0].value; comp111 := ebscomp111(keGetComp); if comp111.FCFWIND = 7 then begin val:= 1; // Factor end else begin val := 0; // offset end; // println( "Return Value: ", val ); evalexpr := val; end;
FHYBRID	Switch for hybrid mode Like in Parent Profile (Sub Profile option only) Expression =0: Off =1: manual Input =2: Set margin to plume formation (temperature approach)
MGNPLUME	margin to plume formation (FHYBRID=2)
FHX	Switch for heat exchanger mode Like in Parent Profile (Sub Profile option only) Expression =0: Off =1: Effectiveness =2: Temperature change, active for Hybrid = 1 =3: Area
PHX	heat exchanger parameter Like in Parent Profile (Sub Profile option only) Expression Effectiveness (if FHX=1) Temperature change (if FHX=2) Area (if FHX=3)
WATRAT	Dry zone/total water - flow ratio
AIRRAT	Dry zone/total air - flow ratio
KAIR	Air side heat transfer coefficient
KWAT	Water side heat transfer coefficient
FOUL	Fouling factor
PLGASEXP	Off-design exponent gas side
PLWATEXP	Off-design exponent water side
HXFRAC	Active fraction of heat exchanger (Off-Design)
FINIT	Flag: Initializing state =0: Global, which is controlled via global variable "Transient mode" under Model Options "Extras" ->"Model Options" -> "Simulation" -> "Transient" -> Combo Box "Transient mode" (See -> Used Physics / equations -> Global Initialization of Transient Components ) =1: First run -> Initializing while calculating steady state values =2: Continuation run -> Values from previous time step are input for the present ones
SHEIG	Shell height
SVOL	Shell volume
THWALL	Shell wall thickness
RHOS	Density of the shell wall material
LAMS	Heat conductivity of the shell wall material
CS	Heat capacity of the shell wall material
NFLS	Number of points in flow direction: dry zone
WZVOL	Wet zone volume
PHI	Free cross section fraction
FV	Outer surface to volume ratio
RHOFM	Density of fill or packing material
LAMFM	Heat conductivity of fill or packing material
CFM	Heat capacity of fill or packing material
NFLWZ	Number of points in flow direction: wet zone
FSPIN	Transient balance calculation mode 0: Liquid level given, mass flows computed 1: Mass flows given, liquid level computed
VF	Liquid volume fraction (liquid level) at the end of the time step
VMIN	Volume at liquid volume fraction value 0
VMAX	Volume at liquid volume fraction value 1
FLVCALC	Liquid volume calculation mode 0: linear between VMIN and VMAX 1: Using ELV
ELV	Function for the liquid volume computation
TWBEG	Temperature in water basin at time step begin (relevant for transient time steps only)
ALPHIS	Inner heat transfer coefficient between air and shell wall
ALPHIFP	Inner heat transfer coefficient between water and fill or packing material
ALPHIWAN	Heat transfer coefficient water to air (nominal value)
FCALCMT	Mass transfer coefficient water to air calculation 0: compute mass transfer coefficient value using Lewis factor input value (LEF) 1: use directly BETAWAN value and Off-design factors and exponents
LEF	Lewis factor input value
BETAWAN	Mass transfer coefficient water to air (nominal value)
ALPHO	Outer heat transfer coefficient (to ambient)
AWRN	Air to water ratio (nominal)
MERKELN	Merkel number (nominal)
DP12N	Air side pressure drop (nominal)
HSTACKN	Required stack height (nominal)
RHO1N	Ambient air density (nominal)
PHI1RAT	Ambient air humidity ratio
PHI2RAT	Air outlet humidity ratio
RHO2	Air outlet density
M2N	Outlet air flow (nominal)
MDRYWZ	Wet zone dry air mass flow
MAIRHXN	Heat Exchanger air mass flow (nominal)
MWATHXN	Heat Exchanger water mass flow (nominal)
KNAIR	Air side heat transfer coefficient (nominal)
KNWAT	Water side heat transfer coefficient (nominal)
AHX	Heat exchanger area
VMSTACK	Stack volume flow

The identification value marked in blue is a reference value for off-design calculations. The actual off-design values refer to the values used in the equations.

Generally, all inputs that are visible are required. But, often default values are provided.

For more information on colour of the input fields and their descriptions see Edit Component\Specification values

For more information on design vs. off-design and nominal values see General\Accept Nominal values

Characteristic Lines

Characteristic Line 1, CWINDAIRFLOW: CF(air mass flow) = f (wind speed)

CF = Correction factor

   X-Axis         1         wind speed                         1^st point
                        2          wind speed                    2^nd point
                        .
                      N         wind speed                       last point
   Y-Axis         1          CF (air mass flow)              1^st point
                       2          CF (air mass flow)             2^nd point
                         .                                                                .
                         N         CF (air mass flow)              last point

Characteristic Line 2, CWINDCWTDT: dT( cooling water temperature) = f (wind speed)

   X-Axis          1          wind speed                                        1^st point
                        2          wind speed                                          2^nd point
                         .
                      N          wind speed                                          last point

    Y-Axis          1          dT (cooling water temperature)           1^st point
                         2          dT (cooling water temperature)          2^nd point
                                                                   .
                        N          dT (cooling water temperature)           last point

Physics Used

The natural draft cooling tower consists of four zones, which are shown schematically in the following picture. These zones are the wet cooling zone, the dry cooling zone, the cooling tower basin and the stack.

The dry cooling zone can be activated by the user (FHYBRID). In design mode, the distribution of dry to wet cooling duty will be set by the air and water flow ratios between dry and wet zone, the wet zone size and the heat exchanger size.

The physics of the dry zone is described according to the rules for a normal air-water cross-flow heat exchanger, the physics of the wet cooling zone according to the rules of Merkel's equation.

The part-load performance of the wet zone is a characteristic of the Merkel number as a function of the dry air to water ratio.

A draft model describes the relationship between stack height, stack inlet condition (i.e. the air outlet temperature of the cooling zones) and air . As a special feature it is possible to add flue gas to increase the draft.

Wet zone

Design:

Water outlet temperature given:

The Merkel Number will be calculated, by integration of the Merkel equation.

Merkel number given:

Find the corresponding water outlet temperature to get the desired Merkel number.

Off-Design:

Via the relationship: Me = MeDesign * K*C*(AWR/AWRDesign) ^m the actual Merkel number will be calculated. Then a solver finds the corresponding water outlet for this Merkel number. K, C and m are defined as PACKPERF, PACKFACT and PACKEXP.

Integration of the Merkel equation:

If the wet zone outlet humidity is set by the user (FHUM=0) the Merkel number can be determined by numerical quadrature. An Implementation of algorithm 699 from TOMS; TRANSACTIONS ON MATHEMATICAL SOFTWARE, VOL. 17, NO. 4, DECEMBER, 1991, PP. 457-461 is used.

If the wet zone outlet humidity is calculated (FHUM=1) a System of ordinary differential equations needs to be solved. Here a Runge-Kutta Method of order 5 is used (Dormand-Prince).

Heat exchanger

The heat exchanger is modelled as single pass with the NTU-Effectiveness Method. (VDI Wärmeatlas, Section Ca; Compact Heat Exchangers; by W.M. Kays and A.L. London)

The Off-Design correlation for the heat transfer coefficients is for the air-side:

k Gas Off-Design = k Gas Design *(v Gas Off-Design / v Gas Design)m1 (Default m1=0.8, m1 corresponds to PLGASEXP))

for the water side:

k Water Off-Design = k Water Design *(v Water Off-Design / v Water Design)m2 (Default m2=0.8, m2 corresponds to PLWATEXP)

Water density is considered constant

Stack and air flow

Design:

In design mode, the air flow will be determined by the parameter AWR. The relationship between pressure drop and required stack height H is given by:

with rho = density, and g = gravitational constant

Off-Design:

In Off-Design mode, the pressure drop can be calculated by the following equation:

The dry and wet zone air flow can be determined from the following equations:

with A = cross sectional area:

and elimination of we get the final off-design equation for the air flow:

Component Displays

Display Option 1

Example

Click here >> Component 111 Demo << to load an example.

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