Buildings.Fluid.HeatExchangers.CoolingTowers.BaseClasses
Package with base classes for Buildings.Fluid.HeatExchangers.CoolingTowers
Information
This package contains base classes that are used to construct the models in Buildings.Fluid.HeatExchangers.CoolingTowers.
Extends from Modelica.Icons.BasesPackage (Icon for packages containing base classes).
Package Content
| Name | Description |
|---|---|
 CoolingTower
|
Base class for cooling towers |
 CoolingTowerVariableSpeed
|
Base class for cooling towers with variable speed fan |
 Merkel
|
Model for thermal performance of Merkel cooling tower |
 Characteristics
|
Functions for fan characteristics |
| Functions
|
Buildings.Fluid.HeatExchangers.CoolingTowers.BaseClasses.CoolingTower
Base class for cooling towers
Information
Base class for a steady-state cooling tower.
The variable TAirHT is used to compute the heat transfer with the water side of the cooling tower.
For a dry cooling tower, this is equal to the dry-bulb temperature.
For a wet cooling tower, this is equal to the wet-bulb temperature.
Extends from Buildings.Fluid.Interfaces.TwoPortHeatMassExchanger (Partial model transporting one fluid stream with storing mass or energy).
Parameters
| Type | Name | Default | Description |
|---|---|---|---|
| replaceable package Medium | PartialMedium | Medium in the component | |
| Nominal condition | |||
| MassFlowRate | m_flow_nominal | Nominal mass flow rate [kg/s] | |
| PressureDifference | dp_nominal | Pressure difference [Pa] | |
| Assumptions | |||
| Boolean | allowFlowReversal | true | = false to simplify equations, assuming, but not enforcing, no flow reversal |
| Advanced | |||
| MassFlowRate | m_flow_small | 1E-4*abs(m_flow_nominal) | Small mass flow rate for regularization of zero flow [kg/s] |
| Diagnostics | |||
| Boolean | show_T | false | = true, if actual temperature at port is computed |
| Flow resistance | |||
| Boolean | from_dp | false | = true, use m_flow = f(dp) else dp = f(m_flow) |
| Boolean | linearizeFlowResistance | false | = true, use linear relation between m_flow and dp for any flow rate |
| Real | deltaM | 0.1 | Fraction of nominal flow rate where flow transitions to laminar |
| Dynamics | |||
| Nominal condition | |||
| Time | tau | 30 | Time constant at nominal flow (if energyDynamics <> SteadyState) [s] |
| Equations | |||
| Dynamics | energyDynamics | Modelica.Fluid.Types.Dynamic... | Type of energy balance: dynamic (3 initialization options) or steady state |
| Dynamics | massDynamics | energyDynamics | Type of mass balance: dynamic (3 initialization options) or steady state |
| Initialization | |||
| AbsolutePressure | p_start | Medium.p_default | Start value of pressure [Pa] |
| Temperature | T_start | Medium.T_default | Start value of temperature [K] |
| MassFraction | X_start[Medium.nX] | Medium.X_default | Start value of mass fractions m_i/m [kg/kg] |
| ExtraProperty | C_start[Medium.nC] | fill(0, Medium.nC) | Start value of trace substances |
Connectors
| Type | Name | Description |
|---|---|---|
| FluidPort_a | port_a | Fluid connector a (positive design flow direction is from port_a to port_b) |
| FluidPort_b | port_b | Fluid connector b (positive design flow direction is from port_a to port_b) |
| output RealOutput | TLvg | Leaving water temperature [K] |
Modelica definition
partial model CoolingTower "Base class for cooling towers"
extends Buildings.Fluid.Interfaces.TwoPortHeatMassExchanger(
redeclare final Buildings.Fluid.MixingVolumes.MixingVolume vol);
Modelica.Blocks.Interfaces.RealOutput TLvg(
final unit="K",
displayUnit="degC") "Leaving water temperature";
Modelica.SIunits.HeatFlowRate Q_flow = preHea.Q_flow
"Heat input into water circuit";
protected
Modelica.Thermal.HeatTransfer.Sources.PrescribedHeatFlow preHea
"Prescribed heat flow";
Modelica.Thermal.HeatTransfer.Sensors.TemperatureSensor TVol
"Water temperature in volume, leaving at port_b";
equation
connect(preHea.port, vol.heatPort);
connect(TVol.port, vol.heatPort);
connect(TVol.T, TLvg);
end CoolingTower;
Buildings.Fluid.HeatExchangers.CoolingTowers.BaseClasses.CoolingTowerVariableSpeed
Base class for cooling towers with variable speed fan
Information
Base model for a steady-state or dynamic cooling tower with a variable speed fan. This base model is used for both the Merkel and York calculation.
Extends from Buildings.Fluid.HeatExchangers.CoolingTowers.BaseClasses.CoolingTower (Base class for cooling towers).
Parameters
| Type | Name | Default | Description |
|---|---|---|---|
| replaceable package Medium | PartialMedium | Medium in the component | |
| Nominal condition | |||
| MassFlowRate | m_flow_nominal | Nominal mass flow rate [kg/s] | |
| PressureDifference | dp_nominal | Pressure difference [Pa] | |
| Heat transfer | |||
| Temperature | TAirInWB_nominal | 273.15 + 25.55 | Nominal outdoor (air inlet) wetbulb temperature [K] |
| Temperature | TWatIn_nominal | Nominal water inlet temperature [K] | |
| Temperature | TWatOut_nominal | Nominal water outlet temperature [K] | |
| Real | fraFreCon | 0.125 | Fraction of tower capacity in free convection regime [1] |
| Fan | |||
| Real | fraPFan_nominal | 275/0.15 | Fan power divided by water mass flow rate at design condition [W/(kg/s)] |
| Power | PFan_nominal | fraPFan_nominal*m_flow_nominal | Fan power [W] |
| Real | yMin | 0.3 | Minimum control signal until fan is switched off (used for smoothing between forced and free convection regime) [1] |
| fan | fanRelPow | fanRelPow(r_V={0,0.1,0.3,0.6... | Fan relative power consumption as a function of control signal, fanRelPow=P(y)/P(y=1) |
| Assumptions | |||
| Boolean | allowFlowReversal | true | = false to simplify equations, assuming, but not enforcing, no flow reversal |
| Advanced | |||
| MassFlowRate | m_flow_small | 1E-4*abs(m_flow_nominal) | Small mass flow rate for regularization of zero flow [kg/s] |
| Diagnostics | |||
| Boolean | show_T | false | = true, if actual temperature at port is computed |
| Flow resistance | |||
| Boolean | from_dp | false | = true, use m_flow = f(dp) else dp = f(m_flow) |
| Boolean | linearizeFlowResistance | false | = true, use linear relation between m_flow and dp for any flow rate |
| Real | deltaM | 0.1 | Fraction of nominal flow rate where flow transitions to laminar |
| Dynamics | |||
| Nominal condition | |||
| Time | tau | 30 | Time constant at nominal flow (if energyDynamics <> SteadyState) [s] |
| Equations | |||
| Dynamics | energyDynamics | Modelica.Fluid.Types.Dynamic... | Type of energy balance: dynamic (3 initialization options) or steady state |
| Dynamics | massDynamics | energyDynamics | Type of mass balance: dynamic (3 initialization options) or steady state |
| Initialization | |||
| AbsolutePressure | p_start | Medium.p_default | Start value of pressure [Pa] |
| Temperature | T_start | Medium.T_default | Start value of temperature [K] |
| MassFraction | X_start[Medium.nX] | Medium.X_default | Start value of mass fractions m_i/m [kg/kg] |
| ExtraProperty | C_start[Medium.nC] | fill(0, Medium.nC) | Start value of trace substances |
Connectors
| Type | Name | Description |
|---|---|---|
| FluidPort_a | port_a | Fluid connector a (positive design flow direction is from port_a to port_b) |
| FluidPort_b | port_b | Fluid connector b (positive design flow direction is from port_a to port_b) |
| output RealOutput | TLvg | Leaving water temperature [K] |
| input RealInput | TAir | Entering air wet bulb temperature [K] |
| input RealInput | y | Fan control signal [1] |
| output RealOutput | PFan | Electric power consumed by fan [W] |
Modelica definition
model CoolingTowerVariableSpeed "Base class for cooling towers with variable speed fan"
extends Buildings.Fluid.HeatExchangers.CoolingTowers.BaseClasses.CoolingTower;
import cha = Buildings.Fluid.HeatExchangers.CoolingTowers.BaseClasses.Characteristics;
parameter Modelica.SIunits.Temperature TAirInWB_nominal = 273.15 + 25.55
"Nominal outdoor (air inlet) wetbulb temperature";
parameter Modelica.SIunits.Temperature TWatIn_nominal
"Nominal water inlet temperature";
parameter Modelica.SIunits.Temperature TWatOut_nominal
"Nominal water outlet temperature";
parameter Real fraFreCon(min=0, max=1, final unit="1") = 0.125
"Fraction of tower capacity in free convection regime";
parameter Real fraPFan_nominal(unit="W/(kg/s)") = 275/0.15
"Fan power divided by water mass flow rate at design condition";
parameter Modelica.SIunits.Power PFan_nominal = fraPFan_nominal*m_flow_nominal
"Fan power";
parameter Real yMin(min=0.01, max=1, final unit="1") = 0.3
"Minimum control signal until fan is switched off (used for smoothing
between forced and free convection regime)";
replaceable parameter cha.fan fanRelPow(
r_V = {0, 0.1, 0.3, 0.6, 1},
r_P = {0, 0.1^3, 0.3^3, 0.6^3, 1})
constrainedby cha.fan
"Fan relative power consumption as a function of control signal, fanRelPow=P(y)/P(y=1)";
Modelica.Blocks.Interfaces.RealInput TAir(
final min=0,
final unit="K",
displayUnit="degC")
"Entering air wet bulb temperature";
Modelica.Blocks.Interfaces.RealInput y(unit="1") "Fan control signal";
Modelica.Blocks.Interfaces.RealOutput PFan(
final quantity="Power",
final unit="W")=
Buildings.Utilities.Math.Functions.spliceFunction(
pos=cha.normalizedPower(per=fanRelPow, r_V=y, d=fanRelPowDer) * PFan_nominal,
neg=0,
x=y-yMin+yMin/20,
deltax=yMin/20)
"Electric power consumed by fan";
protected
parameter Real fanRelPowDer[size(fanRelPow.r_V,1)]
"Coefficients for fan relative power consumption as a function
of control signal";
initial equation
// Check validity of relative fan power consumption at y=yMin and y=1
assert(cha.normalizedPower(per=fanRelPow, r_V=yMin, d=fanRelPowDer) > -1E-4,
"The fan relative power consumption must be non-negative for y=0."
+ "\n Obtained fanRelPow(0) = "
+ String(cha.normalizedPower(per=fanRelPow, r_V=yMin, d=fanRelPowDer))
+ "\n You need to choose different values for the parameter fanRelPow.");
assert(abs(1-cha.normalizedPower(per=fanRelPow, r_V=1, d=fanRelPowDer))<1E-4,
"The fan relative power consumption must be one for y=1."
+ "\n Obtained fanRelPow(1) = "
+ String(cha.normalizedPower(per=fanRelPow, r_V=1, d=fanRelPowDer))
+ "\n You need to choose different values for the parameter fanRelPow."
+ "\n To increase the fan power, change fraPFan_nominal or PFan_nominal.");
end CoolingTowerVariableSpeed;
Buildings.Fluid.HeatExchangers.CoolingTowers.BaseClasses.Merkel
Model for thermal performance of Merkel cooling tower
Information
Model for the thermal peformance of the Merkel cooling tower.
For the documentation, see Buildings.Fluid.HeatExchangers.CoolingTowers.Merkel.
Extends from Modelica.Blocks.Icons.Block (Basic graphical layout of input/output block).
Parameters
| Type | Name | Default | Description |
|---|---|---|---|
| replaceable package Medium | Modelica.Media.Interfaces.Pa... | Medium in the component | |
| Nominal condition | |||
| MassFlowRate | m_flow_nominal | Nominal mass flow rate of water [kg/s] | |
| Real | ratWatAir_nominal | Water-to-air mass flow rate ratio at design condition [1] | |
| Heat transfer | |||
| Temperature | TAirInWB_nominal | Nominal outdoor (air inlet) wetbulb temperature [K] | |
| Temperature | TWatIn_nominal | Nominal water inlet temperature [K] | |
| Temperature | TWatOut_nominal | Nominal water outlet temperature [K] | |
| Real | fraFreCon | Fraction of tower capacity in free convection regime [1] | |
| UAMerkel | UACor | redeclare parameter Building... | Coefficients for UA correction |
| Fan | |||
| Real | yMin | Minimum control signal until fan is switched off (used for smoothing between forced and free convection regime) [1] | |
Connectors
| Type | Name | Description |
|---|---|---|
| replaceable package Medium | Medium in the component | |
| input RealInput | y | Fan control signal [1] |
| input RealInput | m_flow | Water mass flow rate [kg/s] |
| input RealInput | TWatIn | Inlet water temperature [K] |
| input RealInput | TAir | Entering air wet bulb temperature [K] |
| output RealOutput | Q_flow | Heat removed from water |
Modelica definition
block Merkel "Model for thermal performance of Merkel cooling tower"
extends Modelica.Blocks.Icons.Block;
replaceable package Medium =
Modelica.Media.Interfaces.PartialMedium "Medium in the component";
parameter Modelica.SIunits.MassFlowRate m_flow_nominal
"Nominal mass flow rate of water";
final parameter Modelica.SIunits.MassFlowRate mAir_flow_nominal=
m_flow_nominal/ratWatAir_nominal
"Nominal mass flow rate of air";
parameter Real ratWatAir_nominal(min=0, unit="1")
"Water-to-air mass flow rate ratio at design condition";
parameter Modelica.SIunits.Temperature TAirInWB_nominal
"Nominal outdoor (air inlet) wetbulb temperature";
parameter Modelica.SIunits.Temperature TWatIn_nominal
"Nominal water inlet temperature";
parameter Modelica.SIunits.Temperature TWatOut_nominal
"Nominal water outlet temperature";
parameter Real fraFreCon(min=0, max=1, final unit="1")
"Fraction of tower capacity in free convection regime";
replaceable parameter Buildings.Fluid.HeatExchangers.CoolingTowers.Data.UAMerkel
UACor
constrainedby Buildings.Fluid.HeatExchangers.CoolingTowers.Data.UAMerkel
"Coefficients for UA correction";
parameter Real yMin(min=0.01, max=1, final unit="1")
"Minimum control signal until fan is switched off (used for smoothing
between forced and free convection regime)";
final parameter Modelica.SIunits.HeatFlowRate Q_flow_nominal(max=0)=
-m_flow_nominal*cpWat_nominal*(TWatIn_nominal-TWatOut_nominal)
"Nominal heat transfer, (negative)";
final parameter Modelica.SIunits.ThermalConductance UA_nominal=
NTU_nominal*CMin_flow_nominal
"Thermal conductance at nominal flow, used to compute heat capacity";
final parameter Real eps_nominal=
Q_flow_nominal/((TAirInWB_nominal - TWatIn_nominal) * CMin_flow_nominal)
"Nominal heat transfer effectiveness";
final parameter Real NTU_nominal(min=0)=
Buildings.Fluid.HeatExchangers.BaseClasses.ntu_epsilonZ(
eps=min(1, max(0, eps_nominal)),
Z=Z_nominal,
flowRegime=Integer(Buildings.Fluid.Types.HeatExchangerConfiguration.CounterFlow))
"Nominal number of transfer units";
Modelica.Blocks.Interfaces.RealInput y(unit="1") "Fan control signal";
Modelica.Blocks.Interfaces.RealInput m_flow(final unit="kg/s")
"Water mass flow rate";
Modelica.Blocks.Interfaces.RealInput TWatIn(
final min=0,
final unit="K",
displayUnit="degC")
"Inlet water temperature";
Modelica.Blocks.Interfaces.RealInput TAir(
final min=0,
final unit="K",
displayUnit="degC")
"Entering air wet bulb temperature";
Modelica.SIunits.Temperature TAirOut(
displayUnit="degC")
"Outlet air temperature";
Modelica.SIunits.MassFlowRate mAir_flow
"Air mass flow rate";
Modelica.SIunits.MassFraction FRWat
"Ratio actual over design water mass flow ratio";
Modelica.SIunits.MassFraction FRAir
"Ratio actual over design air mass flow ratio";
Real eps(min=0, max=1, unit="1") "Heat exchanger effectiveness";
Modelica.SIunits.SpecificHeatCapacity cpWat "Heat capacity of water";
Modelica.SIunits.ThermalConductance CAir_flow
"Heat capacity flow rate of air";
Modelica.SIunits.ThermalConductance CWat_flow
"Heat capacity flow rate of water";
Modelica.SIunits.ThermalConductance CMin_flow(min=0)
"Minimum heat capacity flow rate";
Modelica.SIunits.HeatFlowRate QMax_flow
"Maximum heat flow rate into air";
Modelica.SIunits.ThermalConductance UAe(min=0)
"Thermal conductance for equivalent fluid";
Modelica.SIunits.ThermalConductance UA "Thermal conductance";
Modelica.Blocks.Interfaces.RealOutput Q_flow "Heat removed from water";
protected
final package Air = Buildings.Media.Air "Package of medium air";
final parameter Air.ThermodynamicState staAir_default=Air.setState_pTX(
T=TAirInWB_nominal,
p=Air.p_default,
X=Air.X_default[1:Air.nXi]) "Default state for air";
final parameter Medium.ThermodynamicState
staWat_default=Medium.setState_pTX(
T=TWatIn_nominal,
p=Medium.p_default,
X=Medium.X_default[1:Medium.nXi]) "Default state for water";
parameter Real delta=1E-3 "Parameter used for smoothing";
parameter Modelica.SIunits.SpecificHeatCapacity cpe_nominal=
Buildings.Fluid.HeatExchangers.CoolingTowers.BaseClasses.Functions.equivalentHeatCapacity(
TIn = TAirInWB_nominal,
TOut = TAirOutWB_nominal)
"Specific heat capacity of the equivalent medium on medium 1 side";
parameter Modelica.SIunits.SpecificHeatCapacity cpAir_nominal=
Air.specificHeatCapacityCp(staAir_default)
"Specific heat capacity of air at nominal condition";
parameter Modelica.SIunits.SpecificHeatCapacity cpWat_nominal=
Medium.specificHeatCapacityCp(staWat_default)
"Specific heat capacity of water at nominal condition";
parameter Modelica.SIunits.ThermalConductance CAir_flow_nominal=
mAir_flow_nominal*cpe_nominal
"Nominal capacity flow rate of air";
parameter Modelica.SIunits.ThermalConductance CWat_flow_nominal=
m_flow_nominal*cpWat_nominal
"Nominal capacity flow rate of water";
parameter Modelica.SIunits.ThermalConductance CMin_flow_nominal=
min(CAir_flow_nominal, CWat_flow_nominal)
"Minimal capacity flow rate at nominal condition";
parameter Modelica.SIunits.ThermalConductance CMax_flow_nominal=
max(CAir_flow_nominal, CWat_flow_nominal)
"Maximum capacity flow rate at nominal condition";
parameter Real Z_nominal(
min=0,
max=1) = CMin_flow_nominal/CMax_flow_nominal
"Ratio of capacity flow rate at nominal condition";
parameter Modelica.SIunits.Temperature TAirOutWB_nominal(fixed=false)
"Nominal leaving air wetbulb temperature";
Real UA_FAir "UA correction factor as function of air flow ratio";
Real UA_FWat "UA correction factor as function of water flow ratio";
Real UA_DifWB
"UA correction factor as function of differential wetbulb temperature";
Real corFac_FAir "Smooth factor as function of air flow ratio";
Real corFac_FWat "Smooth factor as function of water flow ratio";
Modelica.SIunits.SpecificHeatCapacity cpEqu
"Specific heat capacity of the equivalent fluid";
initial equation
// Heat transferred from air to water at nominal condition
Q_flow_nominal = mAir_flow_nominal*cpe_nominal*(TAirInWB_nominal - TAirOutWB_nominal);
assert(eps_nominal > 0 and eps_nominal < 1,
"eps_nominal out of bounds, eps_nominal = " + String(eps_nominal) +
"\n To achieve the required heat transfer rate at epsilon=0.8, set |TAirInWB_nominal-TWatIn_nominal| = "
+ String(abs(Q_flow_nominal/0.8*CMin_flow_nominal)) +
"\n or increase flow rates. The current parameters result in " +
"\n CMin_flow_nominal = " + String(CMin_flow_nominal) +
"\n CMax_flow_nominal = " + String(CMax_flow_nominal));
equation
// For cp water, we use the inlet temperatures because the effect is small
// for actual water temperature differences, and in case of Buildings.Media.Water,
// cp is constant.
cpWat = Medium.specificHeatCapacityCp(Medium.setState_pTX(
p=Medium.p_default,
T=TWatIn,
X=Medium.X_default));
// Determine the airflow based on fan speed signal
mAir_flow = Buildings.Utilities.Math.Functions.spliceFunction(
pos=y*mAir_flow_nominal,
neg=fraFreCon*mAir_flow_nominal,
x=y - yMin + yMin/20,
deltax=yMin/20);
FRAir = mAir_flow/mAir_flow_nominal;
FRWat = m_flow/m_flow_nominal;
// UA for equivalent fluid
// Adjust UA
UA_FAir =Buildings.Fluid.Utilities.extendedPolynomial(
x=FRAir,
c=UACor.cAirFra,
xMin=UACor.FRAirMin,
xMax=UACor.FRAirMax)
"UA correction factor as function of air flow fraction";
UA_FWat =Buildings.Fluid.Utilities.extendedPolynomial(
x=FRWat,
c=UACor.cWatFra,
xMin=UACor.FRWatMin,
xMax=UACor.FRWatMax)
"UA correction factor as function of water flow fraction";
UA_DifWB =Buildings.Fluid.Utilities.extendedPolynomial(
x=TAirInWB_nominal - TAir,
c=UACor.cDifWB,
xMin=UACor.TDiffWBMin,
xMax=UACor.TDiffWBMax)
"UA correction factor as function of differential wet bulb temperature";
corFac_FAir =Buildings.Utilities.Math.Functions.smoothHeaviside(
x=FRAir - UACor.FRAirMin/4,
delta=UACor.FRAirMin/4);
corFac_FWat =Buildings.Utilities.Math.Functions.smoothHeaviside(
x=FRWat - UACor.FRWatMin/4,
delta=UACor.FRWatMin/4);
UA = UA_nominal*UA_FAir*UA_FWat*UA_DifWB*corFac_FAir*corFac_FWat;
UAe = UA*cpEqu/Buildings.Utilities.Psychrometrics.Constants.cpAir;
// Capacity for air and water
CAir_flow =abs(mAir_flow)*cpEqu;
CWat_flow =abs(m_flow)*cpWat;
CMin_flow =Buildings.Utilities.Math.Functions.smoothMin(
CAir_flow,
CWat_flow,
delta*CMin_flow_nominal);
// Calculate epsilon
eps = Buildings.Fluid.HeatExchangers.BaseClasses.epsilon_C(
UA=UAe,
C1_flow=CAir_flow,
C2_flow=CWat_flow,
flowRegime=Integer(Buildings.Fluid.Types.HeatExchangerConfiguration.CounterFlow),
CMin_flow_nominal=CMin_flow_nominal,
CMax_flow_nominal=CMax_flow_nominal,
delta=delta);
// QMax_flow is maximum heat transfer into medium air: positive means heating
QMax_flow = CMin_flow*(TWatIn - TAir);
eps*QMax_flow =CAir_flow*(TAirOut - TAir);
cpEqu =
Buildings.Fluid.HeatExchangers.CoolingTowers.BaseClasses.Functions.equivalentHeatCapacity(
TIn=TAir,
TOut=TAirOut);
Q_flow = -eps * QMax_flow;
end Merkel;