modelWetCoilWetRegime
Information
This model implements the calculation for a 100% wet coil.
The equations from Braun (1988) and Mitchell and Braun (2012a and b), which are essentially the extension of the ε-NTU approach to simultaneous sensible and latent heat transfer, are utilized.
The mathematical equations are analogous to that of the sensible heat exchanger. However, the key distinction is that the heat transfer is driven by an enthalpy difference not by an temperature difference. This change in the driving potential results in re-defining capacitances and heat transfer coefficients accordingly.
The total heat transfer rate is expressed as
Qtot=ε* C*min (hair,in-hsat(Twat,in)),
where ε*=f(Cr*,NTU*) and f is the same ε-NTU relationships (depending on the heat exchanger configuration) for the sensible heat exchanger.
hair,in and hsat(Twat,in) are the specific enthalpies of the incoming moist air and saturated moist air at the water inlet temperature.
The capacitances of water and air streams are defined as
C*air=mair and C*wat=mwatcp,wat/csat,
where csat is an specific heat capacity, which indicates the sensitivity of the enthalpy of the staturated moist air w.r.t. the temperature, and is defined here as csat=(hsat(Twat,out)-hsat(Twat,in)) /(Twat,out-Twat,in).
The capacitance ratio and minimum capacitance are naturally defined as
Cr*=min(C*air,C*wat)/max(C*air,C*wat) and C*min=min(C*air,C*wat).
The number of transfer unit for the wet-coil is defined as NTU*=UA*/C*min, where
UA*=1/(1/(UAair/cp,air)+1/(UAwat/csat).
References
Braun, James E. 1988. "Methodologies for the Design and Control of Central Cooling Plants". PhD Thesis. University of Wisconsin - Madison. Available online.
Mitchell, John W., and James E. Braun. 2012a. Principles of heating, ventilation, and air conditioning in buildings. Hoboken, N.J.: Wiley.
Mitchell, John W., and James E. Braun. 2012b. "Supplementary Material Chapter 2: Heat Exchangers for Cooling Applications". Excerpt from Principles of heating, ventilation, and air conditioning in buildings. Hoboken, N.J.: Wiley. Available online.
Parameters
| Type | Name | Default | Description |
|---|---|---|---|
| Real | cpEff0 | 2050 | Used for scaling |
| Real | cpWat0 | 4200 | Used for scaling |
| Real | delta | 1E-3 | Small value used for smoothing |
| Modelica.Units.SI.SpecificHeatCapacity | cpDum | 1 | Dummy cp to eliminate the warning message of the unit mismatch when using the eps-NTU model for the wet coil |
| Modelica.Units.SI.TemperatureDifference | dTWat | 0.1 | Temperature differential used to compute the finite difference of the saturated specific enthalpy |
| Real | tau | 6*60 | Time constant for state estimation: introduced to avoid the algebraic loop of the wet coil equations |
Components
| Type | Name | Default | Description |
|---|---|---|---|
| Modelica.Units.SI.ThermalConductance | UAWat | UA for water side | |
| Modelica.Units.SI.MassFlowRate | mWat_flow | Mass flow rate of water | |
| Modelica.Units.SI.MassFlowRate | mWatNonZer_flow | Non-zero mass flow rate of water | |
| Modelica.Units.SI.SpecificHeatCapacity | cpWat | Specific heat capacity of water | |
| Modelica.Units.SI.Temperature | TWatIn | Water temperature at inlet | |
| Modelica.Units.SI.MassFlowRate | mWat_flow_nominal | Mass flow rate of water at nominal conditions | |
| Modelica.Units.SI.Pressure | pAir | Pressure on air-side of coil | |
| Modelica.Units.SI.ThermalConductance | UAAir | UA for air side | |
| Modelica.Units.SI.MassFlowRate | mAir_flow | Mass flow rate of air | |
| Modelica.Units.SI.MassFlowRate | mAirNonZer_flow | Non-zero mass flow rate of water | |
| Modelica.Units.SI.SpecificHeatCapacity | cpAir | Specific heat capacity of moist air at constant pressure | |
| Modelica.Units.SI.Temperature | TAirIn | Temperature of air at inlet | |
| Modelica.Units.SI.MassFraction | X_wAirIn | Mass fraction of water in moist air at inlet | |
| Buildings.Fluid.Types.HeatExchangerFlowRegime | cfg | Configuration of the heat exchanger | |
| Modelica.Units.SI.MassFlowRate | mAir_flow_nominal | Mass flow rate of air at nominal conditions | |
| Modelica.Units.SI.SpecificEnthalpy | hAirIn | Specific enthalpy of air at inlet conditions | |
| Buildings.Utilities.Psychrometrics.hSat_pTSat | hSatWatInM | Model to calculate saturated specific enthalpy of air at water inlet temperature | |
| Modelica.Units.SI.SpecificEnthalpy | hSatWatIn | Saturated specific enthalpy of air at water inlet temperature | |
| Buildings.Utilities.Psychrometrics.hSat_pTSat | hSatWatIn_dT_M | Model to calculate derivative of saturated specific enthalpy of air at water inlet temperature | |
| Modelica.Units.SI.SpecificHeatCapacity | dhSatdTWatIn | Finite difference of saturated moist air enthalpy at water inlet temperature | |
| Real | NonZerDelWatTem | Regularization water temperature difference between inlet and outlet | |
| Modelica.Units.SI.SpecificEnthalpy | hAirOut | Specific enthalpy of moist air at the air outlet | |
| Buildings.Utilities.Psychrometrics.hSat_pTSat | hSatWatOutM | Model to calculate saturated specific enthalpy of air at water outlet temperature | |
| Modelica.Units.SI.SpecificEnthalpy | hSatWatOut | Saturated specific enthalpy of air at water outlet temperature | |
| Modelica.Units.SI.Temperature | TSurEff | Effective surface temperature of the coil to split sensible and latent heat from total heat transfer rate | |
| Modelica.Units.SI.SpecificEnthalpy | hSatSurEff | Enthalpy of saturated moist air at the effective surface temperature | |
| Buildings.Utilities.Psychrometrics.hSat_pTSat | hSatSurEffM | An object to calculate the saturated enthalpy of moist air at the coil surface temperature | |
| Buildings.Utilities.Psychrometrics.hSat_pTSat | hSatSurEffMinM | An object to calculate a lower bound of the saturated enthalpy of moist air at the coil surface temperature | |
| Modelica.Units.SI.SpecificHeatCapacity | cpEff | Effective specific heat: change in enthalpy with respect to temperature along the saturation line at the local water temperature | |
| Modelica.Units.SI.MassFlowRate | UASta | Overall mass transfer coefficient for dry coil | |
| Real | NTUAirSta | Number of transfer units for air-side only (NTU_a*) | |
| Real | epsSta | Effectiveness for heat exchanger (e*) | |
| Modelica.Units.SI.MassFlowRate | CStaMin | Min of product of mass flow rates and specific heats; analogous to Cmin | |
| Modelica.Units.SI.MassFlowRate | CStaMin_flow_nominal | min(mAir_flow_nominal, mWat_flow_nominal*cpEff0/cpWat0) | Analogus to CMin_flow_nominal, only for a regularization |
| Modelica.Units.SI.MassFlowRate | CStaMax_flow_nominal | max(mAir_flow_nominal, mWat_flow_nominal*cpEff0/cpWat0) | Analogus to CMax_flow_nominal, only for a regularization |
| Modelica.Units.SI.MassFlowRate | deltaCStaMin | delta*min(mAir_flow_nominal, mWat_flow_nominal*cpEff0/cpWat0) | Min of product of mass flow rates and specific heats, analogous to Cmin |
| Modelica.Units.SI.Temperature | TWatOutEst | State estimation of temperature of water at outlet | |
| Modelica.Units.SI.HeatFlowRate | QTot_flow | Total heat flow from water to air stream | |
| Modelica.Units.SI.HeatFlowRate | QSen_flow | Sensible heat flow from water to air stream | |
| Modelica.Units.SI.Temperature | TWatOut | Temperature at the water outlet | |
| Modelica.Units.SI.Temperature | TSurAirIn | Coil surface temperature at the air inlet | |
| Modelica.Units.SI.Temperature | TAirOut | Temperature at the air outlet |
Revisions
-
April 18, 2023, by Michael Wetter:
Set start value forNTUAirSta.
This is for IBPSA, #1728. -
Jan 21, 2021, by Donghun Kim:
First implementation.