Annex60.Fluid.HeatPumps

Name	Description
Carnot_TCon	Heat pump with prescribed condenser leaving temperature and performance curve adjusted based on Carnot efficiency
Carnot_y	Reversible heat pump with performance curve adjusted based on Carnot efficiency
Examples	Collection of models that illustrate model use and test models
Validation	Collection of models that validate the heat pump models

Heat pump with prescribed condenser leaving temperature and performance curve adjusted based on Carnot efficiency

Annex60.Fluid.HeatPumps.Carnot_TCon

Information

This is a model of a heat pump whose coefficient of performance COP changes with temperatures in the same way as the Carnot efficiency changes. The control input is the setpoint of the condenser leaving temperature, which is met exactly at steady state if the heat pump has sufficient capacity.

The model allows to either specify the Carnot effectivness η_Carnot,0, or a COP₀ at the nominal conditions, together with the evaporator temperature T_eva,0 and the condenser temperature T_con,0, in which case the model computes the Carnot effectivness as

where COP_Carnot is the Carnot efficiency and η_PL is a polynomial in heating part load ratio y_PL that can be used to take into account a change in COP at part load conditions. This polynomial has the form

On the Dynamics tag, the model can be parametrized to compute a transient or steady-state response. The transient response of the model is computed using a first order differential equation for the evaporator and condenser fluid volumes. The heat pump outlet temperatures are equal to the temperatures of these lumped volumes.

Typical use and important parameters

When using this component, make sure that the condenser has sufficient mass flow rate. Based on the evaporator mass flow rate, temperature difference and the efficiencies, the model computes how much heat will be removed by to the evaporator. If the mass flow rate is too small, very low outlet temperatures can result, possibly below freezing.

The condenser heat flow rate QCon_flow_nominal is used to assign the default value for the mass flow rates, which are used for the pressure drop calculations. It is also used to compute the part load efficiency. Hence, make sure that QCon_flow_nominal is set to a reasonable value.

The maximum heating capacity is set by the parameter QCon_flow_max, which is by default set to infinity.

The coefficient of performance depends on the evaporator and condenser leaving temperature since otherwise the second law of thermodynamics may be violated.

Notes

Parameters

Connectors

Modelica definition

Type	Name	Default	Description
replaceable package Medium1	PartialMedium	Medium 1 in the component
replaceable package Medium2	PartialMedium	Medium 2 in the component
HeatFlowRate	QCon_flow_max	Modelica.Constants.inf	Maximum heat flow rate for heating (positive) [W]
Nominal condition
MassFlowRate	m1_flow_nominal	QCon_flow_nominal/cp1_defaul...	Nominal mass flow rate [kg/s]
MassFlowRate	m2_flow_nominal	QEva_flow_nominal/cp2_defaul...	Nominal mass flow rate [kg/s]
HeatFlowRate	QEva_flow_nominal	-QCon_flow_nominal*(COP_nomi...	Nominal cooling heat flow rate (QEva_flow_nominal < 0) [W]
HeatFlowRate	QCon_flow_nominal		Nominal heating flow rate [W]
TemperatureDifference	dTEva_nominal	-10	Temperature difference evaporator outlet-inlet [K]
TemperatureDifference	dTCon_nominal	10	Temperature difference condenser outlet-inlet [K]
Pressure	dp1_nominal		Pressure difference over condenser [Pa]
Pressure	dp2_nominal		Pressure difference over evaporator [Pa]
Efficiency
Boolean	use_eta_Carnot_nominal	true	Set to true to use Carnot effectiveness etaCarnot_nominal rather than COP_nominal
Real	etaCarnot_nominal	COP_nominal/(TUse_nominal/(T...	Carnot effectiveness (=COP/COP_Carnot) used if use_eta_Carnot_nominal = true [1]
Real	COP_nominal	etaCarnot_nominal*TUse_nomin...	Coefficient of performance at TEva_nominal and TCon_nominal, used if use_eta_Carnot_nominal = false [1]
Temperature	TCon_nominal	303.15	Condenser temperature used to compute COP_nominal if use_eta_Carnot_nominal=false [K]
Temperature	TEva_nominal	278.15	Evaporator temperature used to compute COP_nominal if use_eta_Carnot_nominal=false [K]
Real	a[:]	{1}	Coefficients for efficiency curve (need p(a=a, yPL=1)=1)
Assumptions
Boolean	allowFlowReversal1	true	= false to simplify equations, assuming, but not enforcing, no flow reversal for medium 1
Boolean	allowFlowReversal2	true	= false to simplify equations, assuming, but not enforcing, no flow reversal for medium 2
Advanced
MassFlowRate	m1_flow_small	1E-4*abs(m1_flow_nominal)	Small mass flow rate for regularization of zero flow [kg/s]
MassFlowRate	m2_flow_small	1E-4*abs(m2_flow_nominal)	Small mass flow rate for regularization of zero flow [kg/s]
Boolean	homotopyInitialization	true	= true, use homotopy method
Diagnostics
Boolean	show_T	false	= true, if actual temperature at port is computed
Flow resistance
Condenser
Boolean	from_dp1	false	= true, use m_flow = f(dp) else dp = f(m_flow)
Boolean	linearizeFlowResistance1	false	= true, use linear relation between m_flow and dp for any flow rate
Real	deltaM1	0.1	Fraction of nominal flow rate where flow transitions to laminar [1]
Evaporator
Boolean	from_dp2	false	= true, use m_flow = f(dp) else dp = f(m_flow)
Boolean	linearizeFlowResistance2	false	= true, use linear relation between m_flow and dp for any flow rate
Real	deltaM2	0.1	Fraction of nominal flow rate where flow transitions to laminar [1]
Dynamics
Condenser
Time	tau1	60	Time constant at nominal flow rate (used if energyDynamics1 <> Modelica.Fluid.Types.Dynamics.SteadyState) [s]
Temperature	T1_start	Medium1.T_default	Initial or guess value of set point [K]
Evaporator
Time	tau2	60	Time constant at nominal flow rate (used if energyDynamics2 <> Modelica.Fluid.Types.Dynamics.SteadyState) [s]
Temperature	T2_start	Medium2.T_default	Initial or guess value of set point [K]
Evaporator and condenser
Dynamics	energyDynamics	Modelica.Fluid.Types.Dynamic...	Type of energy balance: dynamic (3 initialization options) or steady state

Type	Name	Description
FluidPort_a	port_a1	Fluid connector a1 (positive design flow direction is from port_a1 to port_b1)
FluidPort_b	port_b1	Fluid connector b1 (positive design flow direction is from port_a1 to port_b1)
FluidPort_a	port_a2	Fluid connector a2 (positive design flow direction is from port_a2 to port_b2)
FluidPort_b	port_b2	Fluid connector b2 (positive design flow direction is from port_a2 to port_b2)
output RealOutput	QCon_flow	Actual heating heat flow rate added to fluid 1 [W]
output RealOutput	P	Electric power consumed by compressor [W]
output RealOutput	QEva_flow	Actual cooling heat flow rate removed from fluid 2 [W]
input RealInput	TSet	Condenser leaving water temperature [K]

model Carnot_TCon "Heat pump with prescribed condenser leaving temperature and performance curve adjusted based on Carnot efficiency" extends Annex60.Fluid.Chillers.BaseClasses.PartialCarnot_T( final COP_is_for_cooling = false, final QEva_flow_nominal = -QCon_flow_nominal*(COP_nominal-1)/COP_nominal, PEle(y=QCon_flow/COP), redeclare HeatExchangers.HeaterCooler_T con( final from_dp=from_dp1, final dp_nominal=dp1_nominal, final linearizeFlowResistance=linearizeFlowResistance1, final deltaM=deltaM1, final Q_flow_maxHeat=QCon_flow_max, final Q_flow_maxCool=0, final tau=tau1, final T_start=T1_start, final energyDynamics=energyDynamics, final homotopyInitialization=homotopyInitialization), redeclare HeatExchangers.HeaterCooler_u eva( final from_dp=from_dp2, final dp_nominal=dp2_nominal, final linearizeFlowResistance=linearizeFlowResistance2, final deltaM=deltaM2, final tau=tau2, final T_start=T2_start, final energyDynamics=energyDynamics, final homotopyInitialization=homotopyInitialization, final Q_flow_nominal=QEva_flow_nominal)); parameter Modelica.SIunits.HeatFlowRate QCon_flow_max( min=0) = Modelica.Constants.inf "Maximum heat flow rate for heating (positive)"; Modelica.Blocks.Interfaces.RealInput TSet(unit="K") "Condenser leaving water temperature"; protected Modelica.Blocks.Math.Gain yEva(final k=1/QEva_flow_nominal) "Normalized evaporator heat flow rate"; Modelica.Blocks.Math.Add QEva_flow_internal(final k1=-1) "Heat removed by evaporator"; initial equation assert(QCon_flow_nominal > 0, "Parameter QCon_flow_nominal must be positive."); assert(COP_nominal > 1, "The nominal COP of a heat pump must be bigger than one."); equation connect(TSet, con.TSet); connect(con.Q_flow, QCon_flow); connect(QEva_flow_internal.u1, con.Q_flow); connect(QEva_flow_internal.u2, PEle.y); connect(QEva_flow_internal.y, yEva.u); connect(QEva_flow, QEva_flow_internal.y); connect(yEva.y, eva.u); end Carnot_TCon;

Annex60.Fluid.HeatPumps.Carnot_y

Information

This is model of a heat pump whose coefficient of performance COP changes with temperatures in the same way as the Carnot efficiency changes. The input signal y is the control signal for the compressor.

where COP_Carnot is the Carnot efficiency and η_PL is a polynomial in the heating part load ratio y_PL that can be used to take into account a change in COP at part load conditions. This polynomial has the form

Typical use and important parameters

When using this component, make sure that the evaporator and the condenser have sufficient mass flow rate. Based on the mass flow rates, the compressor power, temperature difference and the efficiencies, the model computes how much heat will be added to the condenser and removed at the evaporator. If the mass flow rates are too small, very high temperature differences can result.

The maximum heating capacity is set by the parameter QCon_flow_max, which is by default set to infinity.

The coefficient of performance depends on the evaporator and condenser leaving temperature since otherwise the second law of thermodynamics may be violated.