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.Units.SI.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;

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.Units.SI.Temperature TAirInWB_nominal=273.15 + 25.55 "Nominal outdoor (air inlet) wetbulb temperature"; parameter Modelica.Units.SI.Temperature TWatIn_nominal "Nominal water inlet temperature"; parameter Modelica.Units.SI.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.Units.SI.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;

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.Units.SI.MassFlowRate m_flow_nominal "Nominal mass flow rate of water"; final parameter Modelica.Units.SI.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.Units.SI.Temperature TAirInWB_nominal "Nominal outdoor (air inlet) wetbulb temperature"; parameter Modelica.Units.SI.Temperature TWatIn_nominal "Nominal water inlet temperature"; parameter Modelica.Units.SI.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.Units.SI.HeatFlowRate Q_flow_nominal(max=0) = - m_flow_nominal*cpWat_nominal*(TWatIn_nominal - TWatOut_nominal) "Nominal heat transfer, (negative)"; final parameter Modelica.Units.SI.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.Units.SI.Temperature TAirOut(displayUnit="degC") "Outlet air temperature"; Modelica.Units.SI.MassFlowRate mAir_flow "Air mass flow rate"; Modelica.Units.SI.MassFraction FRWat "Ratio actual over design water mass flow ratio"; Modelica.Units.SI.MassFraction FRAir "Ratio actual over design air mass flow ratio"; Real eps(min=0, max=1, unit="1") "Heat exchanger effectiveness"; Modelica.Units.SI.SpecificHeatCapacity cpWat "Heat capacity of water"; Modelica.Units.SI.ThermalConductance CAir_flow "Heat capacity flow rate of air"; Modelica.Units.SI.ThermalConductance CWat_flow "Heat capacity flow rate of water"; Modelica.Units.SI.ThermalConductance CMin_flow(min=0) "Minimum heat capacity flow rate"; Modelica.Units.SI.HeatFlowRate QMax_flow "Maximum heat flow rate into air"; Modelica.Units.SI.ThermalConductance UAe(min=0) "Thermal conductance for equivalent fluid"; Modelica.Units.SI.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.Units.SI.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.Units.SI.SpecificHeatCapacity cpAir_nominal= Air.specificHeatCapacityCp(staAir_default) "Specific heat capacity of air at nominal condition"; parameter Modelica.Units.SI.SpecificHeatCapacity cpWat_nominal= Medium.specificHeatCapacityCp(staWat_default) "Specific heat capacity of water at nominal condition"; parameter Modelica.Units.SI.ThermalConductance CAir_flow_nominal= mAir_flow_nominal*cpe_nominal "Nominal capacity flow rate of air"; parameter Modelica.Units.SI.ThermalConductance CWat_flow_nominal= m_flow_nominal*cpWat_nominal "Nominal capacity flow rate of water"; parameter Modelica.Units.SI.ThermalConductance CMin_flow_nominal=min( CAir_flow_nominal, CWat_flow_nominal) "Minimal capacity flow rate at nominal condition"; parameter Modelica.Units.SI.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.Units.SI.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.Units.SI.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;