Package with moist air model that decouples pressure and temperature and that has no liquid water
Information
This is a medium model that is identical to
Buildings.Media.GasesPTDecoupled.MoistAir, except that
the water vapor is not condensing to the liquid phase if
Xi[Water] > X_sat. Instead, all water is assumed in vapor phase.
This new formulation often leads to smaller systems of nonlinear equations
because it allows to invert the function T_phX analytically.
Package Content
Types and constants
constant Integer Water=1
"Index of water (in substanceNames, massFractions X, etc.)";
constant Integer Air=2
"Index of air (in substanceNames, massFractions X, etc.)";
constant Real k_mair = steam.MM/dryair.MM "ratio of molar weights";
constant Buildings.Media.PerfectGases.Common.DataRecord dryair=
Buildings.Media.PerfectGases.Common.SingleGasData.Air;
constant Buildings.Media.PerfectGases.Common.DataRecord steam=
Buildings.Media.PerfectGases.Common.SingleGasData.H2O;
Parameters
| Type | Name | Default | Description |
|---|
| Advanced |
| Boolean | preferredMediumStates | false | = true if StateSelect.prefer shall be used for the independent property variables of the medium |
Modelica definition
redeclare replaceable model extends BaseProperties(
T(stateSelect=if preferredMediumStates then StateSelect.prefer else StateSelect.default),
p(stateSelect=if preferredMediumStates then StateSelect.prefer else StateSelect.default),
Xi(stateSelect=if preferredMediumStates then StateSelect.prefer else StateSelect.default))
/* p, T, X = X[Water] are used as preferred states, since only then all
other quantities can be computed in a recursive sequence.
If other variables are selected as states, static state selection
is no longer possible and non-linear algebraic equations occur.
*/
MassFraction x_water "Mass of total water/mass of dry air";
Real phi "Relative humidity";
protected
constant SI.MolarMass[2] MMX = {steam.MM,dryair.MM}
"Molar masses of components";
// MassFraction X_liquid "Mass fraction of liquid water";
// MassFraction X_steam "Mass fraction of steam water";
MassFraction X_air "Mass fraction of air";
MassFraction X_sat
"Steam water mass fraction of saturation boundary in kg_water/kg_moistair";
MassFraction x_sat
"Steam water mass content of saturation boundary in kg_water/kg_dryair";
AbsolutePressure p_steam_sat "Partial saturation pressure of steam";
constant AbsolutePressure pStp = 101325 "Pressure for which dStp is defined";
constant Density dStp = 1.2 "Fluid density at pressure pStp";
equation
assert(T >= 200.0 and T <= 423.15, "
Temperature T is not in the allowed range
200.0 K <= (T ="
+ String(T) + " K) <= 423.15 K
required from medium model \"" + mediumName + "\".");
MM = 1/(Xi[Water]/MMX[Water]+(1.0-Xi[Water])/MMX[Air]);
p_steam_sat = min(saturationPressure(T),0.999*p);
X_sat = min(p_steam_sat * k_mair/max(100*Modelica.Constants.eps, p - p_steam_sat)*(1 - Xi[Water]), 1.0)
"Water content at saturation with respect to actual water content";
// X_liquid = max(Xi[Water] - X_sat, 0.0);
// X_steam = Xi[Water]-X_liquid;
X_air = 1-Xi[Water];
h = specificEnthalpy_pTX(p,T,Xi);
R = dryair.R*(1 - Xi[Water]) + steam.R*Xi[Water];
//
u = h - R*T;
// d = p/(R*T);
d/dStp = p/pStp;
/* Note, u and d are computed under the assumption that the volume of the liquid
water is neglible with respect to the volume of air and of steam
*/
state.p = p;
state.T = T;
state.X = X;
// this x_steam is water load / dry air!!!!!!!!!!!
x_sat = k_mair*p_steam_sat/max(100*Modelica.Constants.eps,p - p_steam_sat);
x_water = Xi[Water]/max(X_air,100*Modelica.Constants.eps);
phi = p/p_steam_sat*Xi[Water]/(Xi[Water] + k_mair*X_air);
end BaseProperties;
Steam water mass fraction of saturation boundary in kg_water/kg_moistair
Inputs
| Type | Name | Default | Description |
|---|
| ThermodynamicState | state | | shermodynamic state |
Outputs
| Type | Name | Description |
|---|
| MassFraction | X_sat | steam mass fraction of sat. boundary [kg/kg] |
Modelica definition
function Xsaturation = Buildings.Media.PerfectGases.MoistAir.Xsaturation
"Steam water mass fraction of saturation boundary in kg_water/kg_moistair";
Thermodynamic state as function of p, T and composition X
Inputs
Outputs
| Type | Name | Description |
|---|
| ThermodynamicState | state | |
Modelica definition
redeclare function setState_pTX
"Thermodynamic state as function of p, T and composition X"
extends Buildings.Media.PerfectGases.MoistAir.setState_pTX;
end setState_pTX;
Thermodynamic state as function of p, h and composition X
Information
Function to set the state for given pressure, enthalpy and species concentration.
This function needed to be reimplemented in order for the medium model to use
the implementation of T_phX provided by this package as opposed to the
implementation provided by its parent package.
Inputs
Outputs
| Type | Name | Description |
|---|
| ThermodynamicState | state | |
Modelica definition
redeclare function setState_phX
"Thermodynamic state as function of p, h and composition X"
extends Modelica.Icons.Function;
input AbsolutePressure p "Pressure";
input SpecificEnthalpy h "Specific enthalpy";
input MassFraction X[:] "Mass fractions";
output ThermodynamicState state;
algorithm
state := if size(X,1) == nX then ThermodynamicState(p=p,T=T_phX(p,h,X),X=X) else
ThermodynamicState(p=p,T=T_phX(p,h,X), X=cat(1,X,{1-sum(X)}));
end setState_phX;
Thermodynamic state as function of d, T and composition X
Inputs
Outputs
| Type | Name | Description |
|---|
| ThermodynamicState | state | |
Modelica definition
redeclare function setState_dTX
"Thermodynamic state as function of d, T and composition X"
extends Buildings.Media.PerfectGases.MoistAir.setState_dTX;
end setState_dTX;
Gas constant (computation neglects liquid fraction)
Inputs
| Type | Name | Default | Description |
|---|
| ThermodynamicState | state | | thermodynamic state |
Outputs
Modelica definition
redeclare function gasConstant
"Gas constant (computation neglects liquid fraction)"
extends Buildings.Media.PerfectGases.MoistAir.gasConstant;
end gasConstant;
Saturation curve valid for 273.16 <= T <= 373.16. Outside of these limits a (less accurate) result is returned
Inputs
| Type | Name | Default | Description |
|---|
| Temperature | Tsat | | saturation temperature [K] |
Outputs
Modelica definition
function saturationPressureLiquid =
Buildings.Media.PerfectGases.MoistAir.saturationPressureLiquid
"Saturation curve valid for 273.16 <= T <= 373.16. Outside of these limits a (less accurate) result is returned";
Saturation curve valid for 223.16 <= T <= 273.16. Outside of these limits a (less accurate) result is returned
Inputs
| Type | Name | Default | Description |
|---|
| Temperature | Tsat | | sublimation temperature [K] |
Outputs
Modelica definition
function sublimationPressureIce =
Buildings.Media.PerfectGases.MoistAir.sublimationPressureIce
"Saturation curve valid for 223.16 <= T <= 273.16. Outside of these limits a (less accurate) result is returned";
Saturation curve valid for 223.16 <= T <= 373.16 (and slightly outside with less accuracy)
Inputs
| Type | Name | Default | Description |
|---|
| Temperature | Tsat | | saturation temperature [K] |
Outputs
Modelica definition
redeclare function extends saturationPressure
"Saturation curve valid for 223.16 <= T <= 373.16 (and slightly outside with less accuracy)"
algorithm
psat := Buildings.Utilities.Math.spliceFunction(saturationPressureLiquid(Tsat),sublimationPressureIce(Tsat),Tsat-273.16,1.0);
end saturationPressure;
Gas pressure
Inputs
Outputs
Modelica definition
redeclare function pressure "Gas pressure"
extends Buildings.Media.PerfectGases.MoistAir.pressure;
end pressure;
Gas temperature
Inputs
Outputs
Modelica definition
redeclare function temperature "Gas temperature"
extends Buildings.Media.PerfectGases.MoistAir.temperature;
end temperature;
Gas density
Inputs
| Type | Name | Default | Description |
|---|
| ThermodynamicState | state | | |
Outputs
| Type | Name | Description |
|---|
| Density | d | Density [kg/m3] |
Modelica definition
redeclare function density "Gas density"
extends Modelica.Icons.Function;
input ThermodynamicState state;
output Density d "Density";
algorithm
d :=state.p*1.2/101325;
end density;
Specific entropy (liquid part neglected, mixing entropy included)
Inputs
Outputs
Modelica definition
redeclare function specificEntropy
"Specific entropy (liquid part neglected, mixing entropy included)"
extends Buildings.Media.PerfectGases.MoistAir.specificEntropy;
end specificEntropy;
Enthalpy of vaporization of water
Inputs
| Type | Name | Default | Description |
|---|
| Temperature | T | | temperature [K] |
Outputs
Modelica definition
redeclare function extends enthalpyOfVaporization
"Enthalpy of vaporization of water"
algorithm
r0 := 2501014.5;
end enthalpyOfVaporization;
Specific heat capacity of water (liquid only) which is constant
Inputs
Outputs
Modelica definition
function HeatCapacityOfWater
"Specific heat capacity of water (liquid only) which is constant"
extends Modelica.Icons.Function;
input Temperature T;
output SpecificHeatCapacity cp_fl;
algorithm
cp_fl := 4186;
end HeatCapacityOfWater;
Enthalpy of liquid (per unit mass of liquid) which is linear in the temperature
Inputs
| Type | Name | Default | Description |
|---|
| Temperature | T | | temperature [K] |
Outputs
Modelica definition
redeclare replaceable function extends enthalpyOfLiquid
"Enthalpy of liquid (per unit mass of liquid) which is linear in the temperature"
annotation(derivative=der_enthalpyOfLiquid);
algorithm
h := (T - 273.15)*4186;
end enthalpyOfLiquid;
Temperature derivative of enthalpy of liquid per unit mass of liquid
Inputs
Outputs
Modelica definition
replaceable function der_enthalpyOfLiquid
"Temperature derivative of enthalpy of liquid per unit mass of liquid"
extends Modelica.Icons.Function;
input Temperature T "temperature";
input Temperature der_T "temperature derivative";
output SpecificHeatCapacity der_h "derivative of liquid enthalpy";
algorithm
der_h := 4186;
end der_enthalpyOfLiquid;
Enthalpy of steam per unit mass of steam
Inputs
| Type | Name | Default | Description |
|---|
| Temperature | T | | temperature [K] |
Outputs
Modelica definition
redeclare function enthalpyOfCondensingGas
"Enthalpy of steam per unit mass of steam"
annotation(derivative=der_enthalpyOfCondensingGas);
extends Modelica.Icons.Function;
input Temperature T "temperature";
output SpecificEnthalpy h "steam enthalpy";
algorithm
h := (T-273.15) * steam.cp + Buildings.Media.GasesPTDecoupled.MoistAirNoLiquid.enthalpyOfVaporization(T);
end enthalpyOfCondensingGas;
Derivative of enthalpy of steam per unit mass of steam
Inputs
Outputs
Modelica definition
replaceable function der_enthalpyOfCondensingGas
"Derivative of enthalpy of steam per unit mass of steam"
extends Modelica.Icons.Function;
input Temperature T "temperature";
input Temperature der_T "temperature derivative";
output SpecificHeatCapacity der_h "derivative of steam enthalpy";
algorithm
der_h := steam.cp;
end der_enthalpyOfCondensingGas;
Enthalpy of gas mixture per unit mass of gas mixture
Inputs
Outputs
Modelica definition
redeclare replaceable function extends enthalpyOfGas
"Enthalpy of gas mixture per unit mass of gas mixture"
algorithm
h := Buildings.Media.GasesPTDecoupled.MoistAirNoLiquid.enthalpyOfCondensingGas(T)*X[Water]
+ Buildings.Media.GasesPTDecoupled.MoistAirNoLiquid.enthalpyOfDryAir(T)*(1.0-X[Water]);
end enthalpyOfGas;
Enthalpy of dry air per unit mass of dry air
Inputs
| Type | Name | Default | Description |
|---|
| Temperature | T | | temperature [K] |
Outputs
Modelica definition
replaceable function enthalpyOfDryAir
"Enthalpy of dry air per unit mass of dry air"
annotation(derivative=der_enthalpyOfDryAir);
extends Modelica.Icons.Function;
input Temperature T "temperature";
output SpecificEnthalpy h "dry air enthalpy";
algorithm
h := (T - 273.15)*dryair.cp;
end enthalpyOfDryAir;
Derivative of enthalpy of dry air per unit mass of dry air
Inputs
Outputs
Modelica definition
replaceable function der_enthalpyOfDryAir
"Derivative of enthalpy of dry air per unit mass of dry air"
extends Modelica.Icons.Function;
input Temperature T "temperature";
input Temperature der_T "temperature derivative";
output SpecificHeatCapacity der_h "derivative of dry air enthalpy";
algorithm
der_h := dryair.cp;
end der_enthalpyOfDryAir;
Specific heat capacity of gas mixture at constant pressure
Inputs
Outputs
Modelica definition
redeclare replaceable function extends specificHeatCapacityCp
"Specific heat capacity of gas mixture at constant pressure"
algorithm
cp := dryair.cp*(1-state.X[Water]) +steam.cp*state.X[Water];
end specificHeatCapacityCp;
Specific heat capacity of gas mixture at constant volume
Inputs
Outputs
Modelica definition
redeclare replaceable function extends specificHeatCapacityCv
"Specific heat capacity of gas mixture at constant volume"
algorithm
cv:= dryair.cv*(1-state.X[Water]) +steam.cv*state.X[Water];
end specificHeatCapacityCv;
dynamic viscosity of dry air
Inputs
Outputs
Modelica definition
redeclare function extends dynamicViscosity
"dynamic viscosity of dry air"
algorithm
eta := 1.85E-5;
end dynamicViscosity;
Thermal conductivity of dry air as a polynomial in the temperature
Inputs
Outputs
Modelica definition
redeclare function extends thermalConductivity
"Thermal conductivity of dry air as a polynomial in the temperature"
algorithm
lambda := Polynomials_Temp.evaluate({(-4.8737307422969E-008), 7.67803133753502E-005, 0.0241814385504202},
Cv.to_degC(state.T));
end thermalConductivity;
Specific enthalpy
Inputs
Outputs
Modelica definition
redeclare function extends specificEnthalpy "Specific enthalpy"
algorithm
h := Buildings.Media.GasesPTDecoupled.MoistAirNoLiquid.h_pTX(state.p, state.T, state.X);
end specificEnthalpy;
Specific internal energy
Inputs
Outputs
Modelica definition
redeclare function extends specificInternalEnergy
"Specific internal energy"
extends Modelica.Icons.Function;
algorithm
u := Buildings.Media.GasesPTDecoupled.MoistAirNoLiquid.h_pTX(state.p,state.T,state.X) - gasConstant(state)*state.T;
end specificInternalEnergy;
Specific Gibbs energy
Inputs
Outputs
Modelica definition
redeclare function extends specificGibbsEnergy
"Specific Gibbs energy"
extends Modelica.Icons.Function;
algorithm
g := Buildings.Media.GasesPTDecoupled.MoistAirNoLiquid.h_pTX(state.p,state.T,state.X) - state.T*specificEntropy(state);
end specificGibbsEnergy;
Specific Helmholtz energy
Inputs
Outputs
Modelica definition
redeclare function extends specificHelmholtzEnergy
"Specific Helmholtz energy"
extends Modelica.Icons.Function;
algorithm
f := Buildings.Media.GasesPTDecoupled.MoistAirNoLiquid.h_pTX(state.p,state.T,state.X)
- gasConstant(state)*state.T
- state.T*Buildings.Media.GasesPTDecoupled.MoistAirNoLiquid.specificEntropy(state);
end specificHelmholtzEnergy;
Compute specific enthalpy from pressure, temperature and mass fraction
Inputs
Outputs
Modelica definition
function h_pTX
"Compute specific enthalpy from pressure, temperature and mass fraction"
extends Modelica.Icons.Function;
input SI.Pressure p "Pressure";
input SI.Temperature T "Temperature";
input SI.MassFraction X[nX] "Mass fractions of moist air";
output SI.SpecificEnthalpy h "Specific enthalpy at p, T, X";
algorithm
h := (T - 273.15)*dryair.cp * (1 - X[Water]) + ((T-273.15) * steam.cp + 2501014.5) * X[Water];
end h_pTX;
Compute temperature from specific enthalpy and mass fraction
Inputs
Outputs
Modelica definition
function T_phX
"Compute temperature from specific enthalpy and mass fraction"
extends Modelica.Icons.Function;
input AbsolutePressure p "Pressure";
input SpecificEnthalpy h "specific enthalpy";
input MassFraction[:] X "mass fractions of composition";
output Temperature T "temperature";
algorithm
T := 273.15 + (h-2501014.5 * X[Water])/(dryair.cp * (1 - X[Water])+steam.cp*X[Water]);
end T_phX;
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BaseProperties
Xsaturation
setState_pTX
Buildings.Media.GasesPTDecoupled.MoistAirNoLiquid.BaseProperties
Buildings.Media.GasesPTDecoupled.MoistAirNoLiquid.setState_pTX