modelCarnot_TCon
Extends from Annex60.Fluid.Chillers.BaseClasses.PartialCarnot_T (Partial model for chiller with performance curve adjusted based on Carnot efficiency).
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 ηCarnot,0, or a COP0 at the nominal conditions, together with the evaporator temperature Teva,0 and the condenser temperature Tcon,0, in which case the model computes the Carnot effectivness as
ηCarnot,0 = COP0 ⁄ (Tcon,0 ⁄ (Tcon,0-Teva,0)).
The heat pump COP is computed as the product
COP = ηCarnot,0 COPCarnot ηPL,
where COPCarnot is the Carnot efficiency and ηPL is a polynomial in heating part load ratio yPL that can be used to take into account a change in COP at part load conditions. This polynomial has the form
ηPL = a1 + a2 yPL + a3 yPL2 + ...
where the coefficients ai
are declared by the parameter a.
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
For a similar model that can be used as a chiller, see Annex60.Fluid.Chillers.Examples.Carnot_TEva.
Parameters
| Type | Name | Default | Description |
|---|---|---|---|
| Modelica.SIunits.HeatFlowRate | QCon_flow_max | Modelica.Constants.inf | Maximum heat flow rate for heating (positive) |
| Assumptions | |||
| Boolean | allowFlowReversal1 (from PartialFourPort) | true | = false to simplify equations, assuming, but not enforcing, no flow reversal for medium 1 |
| Boolean | allowFlowReversal2 (from PartialFourPort) | true | = false to simplify equations, assuming, but not enforcing, no flow reversal for medium 2 |
| Nominal condition | |||
| Modelica.SIunits.MassFlowRate | m1_flow_nominal (from PartialFourPortInterface) | Nominal mass flow rate | |
| Modelica.SIunits.MassFlowRate | m2_flow_nominal (from PartialFourPortInterface) | Nominal mass flow rate | |
| Modelica.SIunits.HeatFlowRate | QEva_flow_nominal (from Carnot) | Nominal cooling heat flow rate (QEva_flow_nominal < 0) | |
| Modelica.SIunits.HeatFlowRate | QCon_flow_nominal (from Carnot) | Nominal heating flow rate | |
| Modelica.SIunits.TemperatureDifference | dTEva_nominal (from Carnot) | -10 | Temperature difference evaporator outlet-inlet |
| Modelica.SIunits.TemperatureDifference | dTCon_nominal (from Carnot) | 10 | Temperature difference condenser outlet-inlet |
| Modelica.SIunits.Pressure | dp1_nominal (from Carnot) | Pressure difference over condenser | |
| Modelica.SIunits.Pressure | dp2_nominal (from Carnot) | Pressure difference over evaporator | |
| Advanced | |||
| Medium1.MassFlowRate | m1_flow_small (from PartialFourPortInterface) | 1E-4*abs(m1_flow_nominal) | Small mass flow rate for regularization of zero flow |
| Medium2.MassFlowRate | m2_flow_small (from PartialFourPortInterface) | 1E-4*abs(m2_flow_nominal) | Small mass flow rate for regularization of zero flow |
| Boolean | homotopyInitialization (from Carnot) | true | = true, use homotopy method |
| Advanced › Diagnostics | |||
| Boolean | show_T (from PartialFourPortInterface) | false | = true, if actual temperature at port is computed |
| Efficiency | |||
| Boolean | use_eta_Carnot_nominal (from Carnot) | true | Set to true to use Carnot effectiveness etaCarnot_nominal rather than COP_nominal |
| Real | etaCarnot_nominal (from Carnot) | COP_nominal/(TUse_nominal/(TCon_nominal - TEva_nominal)) | Carnot effectiveness (=COP/COP_Carnot) used if use_eta_Carnot_nominal = true |
| Real | COP_nominal (from Carnot) | etaCarnot_nominal*TUse_nominal/(TCon_nominal - TEva_nominal) | Coefficient of performance at TEva_nominal and TCon_nominal, used if use_eta_Carnot_nominal = false |
| Modelica.SIunits.Temperature | TCon_nominal (from Carnot) | 303.15 | Condenser temperature used to compute COP_nominal if use_eta_Carnot_nominal=false |
| Modelica.SIunits.Temperature | TEva_nominal (from Carnot) | 278.15 | Evaporator temperature used to compute COP_nominal if use_eta_Carnot_nominal=false |
| Real[:] | a (from Carnot) | {1} | Coefficients for efficiency curve (need p(a=a, yPL=1)=1) |
| Flow resistance › Condenser | |||
| Boolean | from_dp1 (from Carnot) | false | = true, use m_flow = f(dp) else dp = f(m_flow) |
| Boolean | linearizeFlowResistance1 (from Carnot) | false | = true, use linear relation between m_flow and dp for any flow rate |
| Real | deltaM1 (from Carnot) | 0.1 | Fraction of nominal flow rate where flow transitions to laminar |
| Flow resistance › Evaporator | |||
| Boolean | from_dp2 (from Carnot) | false | = true, use m_flow = f(dp) else dp = f(m_flow) |
| Boolean | linearizeFlowResistance2 (from Carnot) | false | = true, use linear relation between m_flow and dp for any flow rate |
| Real | deltaM2 (from Carnot) | 0.1 | Fraction of nominal flow rate where flow transitions to laminar |
| Dynamics › Condenser | |||
| Modelica.SIunits.Time | tau1 (from Carnot) | 60 | Time constant at nominal flow rate (used if energyDynamics1 <> Modelica.Fluid.Types.Dynamics.SteadyState) |
| Modelica.SIunits.Temperature | T1_start (from Carnot) | Medium1.T_default | Initial or guess value of set point |
| Dynamics › Evaporator | |||
| Modelica.SIunits.Time | tau2 (from Carnot) | 60 | Time constant at nominal flow rate (used if energyDynamics2 <> Modelica.Fluid.Types.Dynamics.SteadyState) |
| Modelica.SIunits.Temperature | T2_start (from Carnot) | Medium2.T_default | Initial or guess value of set point |
| Dynamics › Evaporator and condenser | |||
| Modelica.Fluid.Types.Dynamics | energyDynamics (from Carnot) | Modelica.Fluid.Types.Dynamics.SteadyState | Type of energy balance: dynamic (3 initialization options) or steady state |
Connectors
| Type | Name | Default | Description |
|---|---|---|---|
| Modelica.Fluid.Interfaces.FluidPort_a | port_a1 (from PartialFourPort) | Fluid connector a1 (positive design flow direction is from port_a1 to port_b1) | |
| Modelica.Fluid.Interfaces.FluidPort_b | port_b1 (from PartialFourPort) | Fluid connector b1 (positive design flow direction is from port_a1 to port_b1) | |
| Modelica.Fluid.Interfaces.FluidPort_a | port_a2 (from PartialFourPort) | Fluid connector a2 (positive design flow direction is from port_a2 to port_b2) | |
| Modelica.Fluid.Interfaces.FluidPort_b | port_b2 (from PartialFourPort) | Fluid connector b2 (positive design flow direction is from port_a2 to port_b2) | |
| Modelica.Blocks.Interfaces.RealOutput | QCon_flow (from Carnot) | Actual heating heat flow rate added to fluid 1 | |
| Modelica.Blocks.Interfaces.RealOutput | P (from Carnot) | Electric power consumed by compressor | |
| Modelica.Blocks.Interfaces.RealOutput | QEva_flow (from Carnot) | Actual cooling heat flow rate removed from fluid 2 | |
| Modelica.Blocks.Interfaces.RealInput | TSet | Condenser leaving water temperature |
Components
| Type | Name | Default | Description |
|---|---|---|---|
| Medium1.MassFlowRate | m1_flow (from PartialFourPortInterface) | port_a1.m_flow | Mass flow rate from port_a1 to port_b1 (m1_flow > 0 is design flow direction) |
| Modelica.SIunits.PressureDifference | dp1 (from PartialFourPortInterface) | port_a1.p - port_b1.p | Pressure difference between port_a1 and port_b1 |
| Medium2.MassFlowRate | m2_flow (from PartialFourPortInterface) | port_a2.m_flow | Mass flow rate from port_a2 to port_b2 (m2_flow > 0 is design flow direction) |
| Modelica.SIunits.PressureDifference | dp2 (from PartialFourPortInterface) | port_a2.p - port_b2.p | Pressure difference between port_a2 and port_b2 |
| Medium1.ThermodynamicState | sta_a1 (from PartialFourPortInterface) | Medium1.setState_phX(port_a1.p, noEvent(actualStream(port_a1.h_outflow)), noEvent(actualStream(port_a1.Xi_outflow))) | Medium properties in port_a1 |
| Medium1.ThermodynamicState | sta_b1 (from PartialFourPortInterface) | Medium1.setState_phX(port_b1.p, noEvent(actualStream(port_b1.h_outflow)), noEvent(actualStream(port_b1.Xi_outflow))) | Medium properties in port_b1 |
| Medium2.ThermodynamicState | sta_a2 (from PartialFourPortInterface) | Medium2.setState_phX(port_a2.p, noEvent(actualStream(port_a2.h_outflow)), noEvent(actualStream(port_a2.Xi_outflow))) | Medium properties in port_a2 |
| Medium2.ThermodynamicState | sta_b2 (from PartialFourPortInterface) | Medium2.setState_phX(port_b2.p, noEvent(actualStream(port_b2.h_outflow)), noEvent(actualStream(port_b2.Xi_outflow))) | Medium properties in port_b2 |
| Real | yPL (from Carnot) | if COP_is_for_cooling then QEva_flow/QEva_flow_nominal else QCon_flow/QCon_flow_nominal | Part load ratio |
| Real | etaPL (from Carnot) | if evaluate_etaPL then 1 else Annex60.Utilities.Math.Functions.polynomial(a = a, x = yPL) | Efficiency due to part load (etaPL(yPL=1)=1) |
| Real | COP (from Carnot) | etaCarnot_nominal_internal*COPCar*etaPL | Coefficient of performance |
| Real | COPCar (from Carnot) | TUse/Annex60.Utilities.Math.Functions.smoothMax(x1 = 1, x2 = TCon - TEva, deltaX = 0.25) | Carnot efficiency |
| Modelica.SIunits.Temperature | TCon (from Carnot) | Medium1.temperature(staB1) | Condenser temperature used to compute efficiency |
| Modelica.SIunits.Temperature | TEva (from Carnot) | Medium2.temperature(staB2) | Evaporator temperature used to compute efficiency |
Revisions
-
January 3, 2017, by Michael Wetter:
Removed parameterseffInpEvaandeffInpConand updated documentation. This is for issue 497. -
August 8, 2016, by Michael Wetter:
Changed default temperature to compute COP to be the leaving temperature as use of the entering temperature can violate the 2nd law if the temperature lift is small.
This is for Annex 60, issue 497. -
November 25, 2015 by Michael Wetter:
First implementation.