Medium model of Ideal gas with constant cp and cv. All other quantities, e.g. transport properties, are constant.
Information
Extends from Interfaces.PartialPureSubstance (base class for pure substances of one chemical substance).
Package Content
| Name | Description |
|---|
| cp_const | Constant specific heat capacity at constant pressure |
| cv_const=cp_const - R_gas | Constant specific heat capacity at constant volume |
| R_gas | medium specific gas constant |
| MM_const | Molar mass |
| eta_const | Constant dynamic viscosity |
| lambda_const | Constant thermal conductivity |
| T_min | Minimum temperature valid for medium model |
| T_max | Maximum temperature valid for medium model |
| T0=reference_T | Zero enthalpy temperature |
 ThermodynamicState
| Thermodynamic state of ideal gas |
| FluidConstants
| fluid constants |
 BaseProperties
| Base properties of ideal gas |
 setState_pTX
| Return thermodynamic state from p, T, and X or Xi |
| setState_phX
| Return thermodynamic state from p, h, and X or Xi |
| setState_psX
| Return thermodynamic state from p, s, and X or Xi |
| setState_dTX
| Return thermodynamic state from d, T, and X or Xi |
| setSmoothState
| Return thermodynamic state so that it smoothly approximates: if x > 0 then state_a else state_b |
| pressure
| Return pressure of ideal gas |
| temperature
| Return temperature of ideal gas |
| density
| Return density of ideal gas |
| specificEnthalpy
| Return specific enthalpy |
| specificInternalEnergy
| Return specific internal energy |
| specificEntropy
| Return specific entropy |
| specificGibbsEnergy
| Return specific Gibbs energy |
| specificHelmholtzEnergy
| Return specific Helmholtz energy |
| dynamicViscosity
| Return dynamic viscosity |
| thermalConductivity
| Return thermal conductivity |
| specificHeatCapacityCp
| Return specific heat capacity at constant pressure |
| specificHeatCapacityCv
| Return specific heat capacity at constant volume |
| isentropicExponent
| Return isentropic exponent |
| velocityOfSound
| Return velocity of sound |
| specificEnthalpy_pTX
| Return specific enthalpy from p, T, and X or Xi |
| temperature_phX
| Return temperature from p, h, and X or Xi |
| density_phX
| Return density from p, h, and X or Xi |
| isentropicEnthalpy
| Return isentropic enthalpy |
| isobaricExpansionCoefficient
| Returns overall the isobaric expansion coefficient beta |
| isothermalCompressibility
| Returns overall the isothermal compressibility factor |
| density_derp_T
| Returns the partial derivative of density with respect to pressure at constant temperature |
| density_derT_p
| Returns the partial derivative of density with respect to temperature at constant pressure |
| density_derX
| Returns the partial derivative of density with respect to mass fractions at constant pressure and temperature |
| molarMass
| Returns the molar mass of the medium |
| Inherited |
|---|
 setState_pT
| Return thermodynamic state from p and T |
 setState_ph
| Return thermodynamic state from p and h |
| setState_ps
| Return thermodynamic state from p and s |
| setState_dT
| Return thermodynamic state from d and T |
| density_ph
| Return density from p and h |
| temperature_ph
| Return temperature from p and h |
| pressure_dT
| Return pressure from d and T |
| specificEnthalpy_dT
| Return specific enthalpy from d and T |
| specificEnthalpy_ps
| Return specific enthalpy from p and s |
| temperature_ps
| Return temperature from p and s |
| density_ps
| Return density from p and s |
| specificEnthalpy_pT
| Return specific enthalpy from p and T |
| density_pT
| Return density from p and T |
| ThermoStates | Enumeration type for independent variables |
| mediumName="unusablePartialMedium" | Name of the medium |
| substanceNames={mediumName} | Names of the mixture substances. Set substanceNames={mediumName} if only one substance. |
| extraPropertiesNames=fill("", 0) | Names of the additional (extra) transported properties. Set extraPropertiesNames=fill("",0) if unused |
| singleState | = true, if u and d are not a function of pressure |
| reducedX=true | = true if medium contains the equation sum(X) = 1.0; set reducedX=true if only one substance (see docu for details) |
| fixedX=false | = true if medium contains the equation X = reference_X |
| reference_p=101325 | Reference pressure of Medium: default 1 atmosphere |
| reference_T=298.15 | Reference temperature of Medium: default 25 deg Celsius |
| reference_X=fill(1/nX, nX) | Default mass fractions of medium |
| p_default=101325 | Default value for pressure of medium (for initialization) |
| T_default=Modelica.SIunits.Conversions.from_degC(20) | Default value for temperature of medium (for initialization) |
| h_default=specificEnthalpy_pTX(p_default, T_default, X_default) | Default value for specific enthalpy of medium (for initialization) |
| X_default=reference_X | Default value for mass fractions of medium (for initialization) |
| nS=size(substanceNames, 1) | Number of substances |
| nX=nS | Number of mass fractions |
| nXi=if fixedX then 0 else if reducedX then nS - 1 else nS | Number of structurally independent mass fractions (see docu for details) |
| nC=size(extraPropertiesNames, 1) | Number of extra (outside of standard mass-balance) transported properties |
 prandtlNumber
| Return the Prandtl number |
 heatCapacity_cp
| alias for deprecated name |
| heatCapacity_cv
| alias for deprecated name |
| beta
| alias for isobaricExpansionCoefficient for user convenience |
| kappa
| alias of isothermalCompressibility for user convenience |
 density_derp_h
| Return density derivative wrt pressure at const specific enthalpy |
| density_derh_p
| Return density derivative wrt specific enthalpy at constant pressure |
| density_pTX
| Return density from p, T, and X or Xi |
| temperature_psX
| Return temperature from p,s, and X or Xi |
| density_psX
| Return density from p, s, and X or Xi |
| specificEnthalpy_psX
| Return specific enthalpy from p, s, and X or Xi |
| AbsolutePressure
| Type for absolute pressure with medium specific attributes |
| Density
| Type for density with medium specific attributes |
| DynamicViscosity
| Type for dynamic viscosity with medium specific attributes |
| EnthalpyFlowRate
| Type for enthalpy flow rate with medium specific attributes |
| MassFlowRate
| Type for mass flow rate with medium specific attributes |
| MassFraction
| Type for mass fraction with medium specific attributes |
| MoleFraction
| Type for mole fraction with medium specific attributes |
| MolarMass
| Type for molar mass with medium specific attributes |
| MolarVolume
| Type for molar volume with medium specific attributes |
| IsentropicExponent
| Type for isentropic exponent with medium specific attributes |
| SpecificEnergy
| Type for specific energy with medium specific attributes |
| SpecificInternalEnergy
| Type for specific internal energy with medium specific attributes |
| SpecificEnthalpy
| Type for specific enthalpy with medium specific attributes |
| SpecificEntropy
| Type for specific entropy with medium specific attributes |
| SpecificHeatCapacity
| Type for specific heat capacity with medium specific attributes |
| SurfaceTension
| Type for surface tension with medium specific attributes |
| Temperature
| Type for temperature with medium specific attributes |
| ThermalConductivity
| Type for thermal conductivity with medium specific attributes |
| PrandtlNumber
| Type for Prandtl number with medium specific attributes |
| VelocityOfSound
| Type for velocity of sound with medium specific attributes |
| ExtraProperty
| Type for unspecified, mass-specific property transported by flow |
| CumulativeExtraProperty
| Type for conserved integral of unspecified, mass specific property |
| ExtraPropertyFlowRate
| Type for flow rate of unspecified, mass-specific property |
| IsobaricExpansionCoefficient
| Type for isobaric expansion coefficient with medium specific attributes |
| DipoleMoment
| Type for dipole moment with medium specific attributes |
| DerDensityByPressure
| Type for partial derivative of density with resect to pressure with medium specific attributes |
| DerDensityByEnthalpy
| Type for partial derivative of density with resect to enthalpy with medium specific attributes |
| DerEnthalpyByPressure
| Type for partial derivative of enthalpy with resect to pressure with medium specific attributes |
| DerDensityByTemperature
| Type for partial derivative of density with resect to temperature with medium specific attributes |
 Choices
| Types, constants to define menu choices |
Types and constants
constant SpecificHeatCapacity cp_const
"Constant specific heat capacity at constant pressure";
constant SpecificHeatCapacity cv_const= cp_const - R_gas
"Constant specific heat capacity at constant volume";
constant SpecificHeatCapacity R_gas "medium specific gas constant";
constant MolarMass MM_const "Molar mass";
constant DynamicViscosity eta_const "Constant dynamic viscosity";
constant ThermalConductivity lambda_const "Constant thermal conductivity";
constant Temperature T_min "Minimum temperature valid for medium model";
constant Temperature T_max "Maximum temperature valid for medium model";
constant Temperature T0= reference_T "Zero enthalpy temperature";
Thermodynamic state of ideal gas
Information
Extends from (Minimal variable set that is available as input argument to every medium function).
Modelica definition
redeclare record extends ThermodynamicState
"Thermodynamic state of ideal gas"
AbsolutePressure p "Absolute pressure of medium";
Temperature T "Temperature of medium";
end ThermodynamicState;
fluid constants
Information
Extends from (critical, triple, molecular and other standard data of fluid).
Modelica definition
redeclare record extends FluidConstants "fluid constants"
end FluidConstants;
Base properties of ideal gas
Information
This is the most simple incompressible medium model, where
specific enthalpy h and specific internal energy u are only
a function of temperature T and all other provided medium
quantities are assumed to be constant.
Extends from .
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))
"Base properties of ideal gas"
equation
assert(T >= T_min and T <= T_max, "
Temperature T (= " + String(T) + " K) is not
in the allowed range (" + String(T_min) + " K <= T <= " + String(T_max)
+ " K)
required from medium model \"" + mediumName + "\".
");
h = specificEnthalpy_pTX(p,T,X);
u = h-R*T;
R = R_gas;
d = p/(R*T);
MM = MM_const;
state.T = T;
state.p = p;
end BaseProperties;
Return thermodynamic state from p, T, and X or Xi
Information
Extends from Modelica.Icons.Function (Icon for a function).
Inputs
Outputs
Modelica definition
redeclare function setState_pTX
"Return thermodynamic state from p, T, and X or Xi"
extends Modelica.Icons.Function;
input AbsolutePressure p "Pressure";
input Temperature T "Temperature";
input MassFraction X[:]=reference_X "Mass fractions";
output ThermodynamicState state "thermodynamic state record";
algorithm
state := ThermodynamicState(p=p,T=T);
end setState_pTX;
Return thermodynamic state from p, h, and X or Xi
Information
Extends from Modelica.Icons.Function (Icon for a function).
Inputs
Outputs
Modelica definition
redeclare function setState_phX
"Return thermodynamic state from p, h, and X or Xi"
extends Modelica.Icons.Function;
input AbsolutePressure p "Pressure";
input SpecificEnthalpy h "Specific enthalpy";
input MassFraction X[:]=reference_X "Mass fractions";
output ThermodynamicState state "thermodynamic state record";
algorithm
state := ThermodynamicState(p=p,T=T0+h/cp_const);
end setState_phX;
Return thermodynamic state from p, s, and X or Xi
Information
Extends from Modelica.Icons.Function (Icon for a function).
Inputs
Outputs
Modelica definition
redeclare replaceable function setState_psX
"Return thermodynamic state from p, s, and X or Xi"
extends Modelica.Icons.Function;
input AbsolutePressure p "Pressure";
input SpecificEntropy s "Specific entropy";
input MassFraction X[:]=reference_X "Mass fractions";
output ThermodynamicState state "thermodynamic state record";
algorithm
state := ThermodynamicState(p=p,T=Modelica.Math.exp(s/cp_const + Modelica.Math.log(reference_T))
+ R_gas*Modelica.Math.log(p/reference_p));
end setState_psX;
Return thermodynamic state from d, T, and X or Xi
Information
Extends from Modelica.Icons.Function (Icon for a function).
Inputs
Outputs
Modelica definition
redeclare function setState_dTX
"Return thermodynamic state from d, T, and X or Xi"
extends Modelica.Icons.Function;
input Density d "density";
input Temperature T "Temperature";
input MassFraction X[:]=reference_X "Mass fractions";
output ThermodynamicState state "thermodynamic state record";
algorithm
state := ThermodynamicState(p=d*R_gas*T,T=T);
end setState_dTX;
Return thermodynamic state so that it smoothly approximates: if x > 0 then state_a else state_b
Information
Extends from (Return thermodynamic state so that it smoothly approximates: if x > 0 then state_a else state_b).
Inputs
| Type | Name | Default | Description |
|---|
| Real | x | | m_flow or dp |
| ThermodynamicState | state_a | | Thermodynamic state if x > 0 |
| ThermodynamicState | state_b | | Thermodynamic state if x < 0 |
| Real | x_small | | Smooth transition in the region -x_small < x < x_small |
Outputs
| Type | Name | Description |
|---|
| ThermodynamicState | state | Smooth thermodynamic state for all x (continuous and differentiable) |
Modelica definition
redeclare function extends setSmoothState
"Return thermodynamic state so that it smoothly approximates: if x > 0 then state_a else state_b"
algorithm
state := ThermodynamicState(p=Media.Common.smoothStep(x, state_a.p, state_b.p, x_small),
T=Media.Common.smoothStep(x, state_a.T, state_b.T, x_small));
end setSmoothState;
Return pressure of ideal gas
Information
Extends from (Return pressure).
Inputs
Outputs
Modelica definition
redeclare function extends pressure "Return pressure of ideal gas"
algorithm
p := state.p;
end pressure;
Return temperature of ideal gas
Information
Extends from (Return temperature).
Inputs
Outputs
Modelica definition
redeclare function extends temperature
"Return temperature of ideal gas"
algorithm
T := state.T;
end temperature;
Return density of ideal gas
Information
Extends from (Return density).
Inputs
Outputs
| Type | Name | Description |
|---|
| Density | d | Density [kg/m3] |
Modelica definition
redeclare function extends density "Return density of ideal gas"
algorithm
d := state.p/(R_gas*state.T);
end density;
Return specific enthalpy
Information
Extends from Modelica.Icons.Function (Icon for a function), (Return specific enthalpy).
Inputs
Outputs
Modelica definition
redeclare function extends specificEnthalpy
"Return specific enthalpy"
extends Modelica.Icons.Function;
algorithm
h := cp_const*(state.T-T0);
end specificEnthalpy;
Return specific internal energy
Information
Extends from Modelica.Icons.Function (Icon for a function), (Return specific internal energy).
Inputs
Outputs
Modelica definition
redeclare function extends specificInternalEnergy
"Return specific internal energy"
extends Modelica.Icons.Function;
algorithm
// u := (cp_const-R_gas)*(state.T-T0);
u := cp_const*(state.T-T0) - R_gas*state.T;
end specificInternalEnergy;
Return specific entropy
Information
Extends from Modelica.Icons.Function (Icon for a function), (Return specific entropy).
Inputs
Outputs
Modelica definition
redeclare function extends specificEntropy "Return specific entropy"
extends Modelica.Icons.Function;
algorithm
s := cp_const*Modelica.Math.log(state.T/T0) - R_gas*Modelica.Math.log(state.p/reference_p);
end specificEntropy;
Return specific Gibbs energy
Information
Extends from Modelica.Icons.Function (Icon for a function), (Return specific Gibbs energy).
Inputs
Outputs
Modelica definition
redeclare function extends specificGibbsEnergy
"Return specific Gibbs energy"
extends Modelica.Icons.Function;
algorithm
g := cp_const*(state.T-T0) - state.T*specificEntropy(state);
end specificGibbsEnergy;
Return specific Helmholtz energy
Information
Extends from Modelica.Icons.Function (Icon for a function), (Return specific Helmholtz energy).
Inputs
Outputs
Modelica definition
redeclare function extends specificHelmholtzEnergy
"Return specific Helmholtz energy"
extends Modelica.Icons.Function;
algorithm
f := (cp_const-R_gas)*(state.T-T0) - state.T*specificEntropy(state);
end specificHelmholtzEnergy;
Return dynamic viscosity
Information
Extends from (Return dynamic viscosity).
Inputs
Outputs
Modelica definition
redeclare function extends dynamicViscosity
"Return dynamic viscosity"
algorithm
eta := eta_const;
end dynamicViscosity;
Return thermal conductivity
Information
Extends from (Return thermal conductivity).
Inputs
Outputs
Modelica definition
redeclare function extends thermalConductivity
"Return thermal conductivity"
algorithm
lambda := lambda_const;
end thermalConductivity;
Return specific heat capacity at constant pressure
Information
Extends from (Return specific heat capacity at constant pressure).
Inputs
Outputs
Modelica definition
redeclare function extends specificHeatCapacityCp
"Return specific heat capacity at constant pressure"
algorithm
cp := cp_const;
end specificHeatCapacityCp;
Return specific heat capacity at constant volume
Information
Extends from (Return specific heat capacity at constant volume).
Inputs
Outputs
Modelica definition
redeclare function extends specificHeatCapacityCv
"Return specific heat capacity at constant volume"
algorithm
cv := cv_const;
end specificHeatCapacityCv;
Return isentropic exponent
Information
Extends from (Return isentropic exponent).
Inputs
Outputs
Modelica definition
redeclare function extends isentropicExponent
"Return isentropic exponent"
algorithm
gamma := cp_const/cv_const;
end isentropicExponent;
Return velocity of sound
Information
Extends from (Return velocity of sound).
Inputs
Outputs
Modelica definition
redeclare function extends velocityOfSound
"Return velocity of sound "
algorithm
a := sqrt(cp_const/cv_const*R_gas*state.T);
end velocityOfSound;
Return specific enthalpy from p, T, and X or Xi
Information
Extends from Modelica.Icons.Function (Icon for a function).
Inputs
Outputs
Modelica definition
redeclare function specificEnthalpy_pTX
"Return specific enthalpy from p, T, and X or Xi"
extends Modelica.Icons.Function;
input AbsolutePressure p "Pressure";
input Temperature T "Temperature";
input MassFraction X[nX] "Mass fractions";
output SpecificEnthalpy h "Specific enthalpy at p, T, X";
algorithm
h := cp_const*(T-T0);
end specificEnthalpy_pTX;
Return temperature from p, h, and X or Xi
Information
Extends from Modelica.Icons.Function (Icon for a function).
Inputs
Outputs
Modelica definition
redeclare function temperature_phX
"Return temperature from p, h, and X or Xi"
extends Modelica.Icons.Function;
input AbsolutePressure p "Pressure";
input SpecificEnthalpy h "Specific enthalpy";
input MassFraction X[nX] "Mass fractions";
output Temperature T "Temperature";
algorithm
T := h/cp_const + T0;
end temperature_phX;
Return density from p, h, and X or Xi
Information
Extends from Modelica.Icons.Function (Icon for a function).
Inputs
Outputs
| Type | Name | Description |
|---|
| Density | d | density [kg/m3] |
Modelica definition
redeclare function density_phX
"Return density from p, h, and X or Xi"
extends Modelica.Icons.Function;
input AbsolutePressure p "Pressure";
input SpecificEnthalpy h "Specific enthalpy";
input MassFraction X[nX] "Mass fractions";
output Density d "density";
algorithm
d := density(setState_phX(p,h,X));
end density_phX;
Return isentropic enthalpy
Information
Extends from (Return isentropic enthalpy).
Inputs
Outputs
Modelica definition
redeclare function extends isentropicEnthalpy
"Return isentropic enthalpy"
algorithm
/* s = cp_const*log(refState.T/T0) - R_gas*log(refState.p/reference_p)
= cp_const*log(state.T/T0) - R_gas*log(p_downstream/reference_p)
log(state.T) = log(refState.T) +
(R_gas/cp_const)*(log(p_downstream/reference_p) - log(refState.p/reference_p))
= log(refState.T) + (R_gas/cp_const)*log(p_downstream/refState.p)
= log(refState.T) + log( (p_downstream/refState.p)^(R_gas/cp_const) )
= log( refState.T*(p_downstream/refState.p)^(R_gas/cp_const) )
state.T = refstate.T*(p_downstream/refstate.p)^(R_gas/cp_const)
*/
h_is := cp_const*(refState.T*(p_downstream/refState.p)^(R_gas/cp_const) - T0);
end isentropicEnthalpy;
Returns overall the isobaric expansion coefficient beta
Information
Extends from (Return overall the isobaric expansion coefficient beta).
Inputs
Outputs
Modelica definition
redeclare function extends isobaricExpansionCoefficient
"Returns overall the isobaric expansion coefficient beta"
algorithm
/* beta = 1/v * der(v,T), with v = 1/d, at constant pressure p:
v = R*T/p
der(v,T) = R/p
beta = p/(R*T)*R/p
= 1/T
*/
beta := 1/state.T;
end isobaricExpansionCoefficient;
Returns overall the isothermal compressibility factor
Information
Extends from (Return overall the isothermal compressibility factor).
Inputs
Outputs
Modelica definition
redeclare function extends isothermalCompressibility
"Returns overall the isothermal compressibility factor"
algorithm
/* kappa = - 1/v * der(v,p), with v = 1/d at constant temperature T.
v = R*T/p
der(v,T) = -R*T/p^2
kappa = p/(R*T)*R*T/p^2
= 1/p
*/
kappa := 1/state.p;
end isothermalCompressibility;
Returns the partial derivative of density with respect to pressure at constant temperature
Information
Extends from (Return density derivative wrt pressure at const temperature).
Inputs
Outputs
Modelica definition
redeclare function extends density_derp_T
"Returns the partial derivative of density with respect to pressure at constant temperature"
algorithm
/* d = p/(R*T)
ddpT = 1/(R*T)
*/
ddpT := 1/(R_gas*state.T);
end density_derp_T;
Returns the partial derivative of density with respect to temperature at constant pressure
Information
Extends from (Return density derivative wrt temperature at constant pressure).
Inputs
Outputs
Modelica definition
redeclare function extends density_derT_p
"Returns the partial derivative of density with respect to temperature at constant pressure"
algorithm
/* d = p/(R*T)
ddpT = -p/(R*T^2)
*/
ddTp := -state.p/(R_gas*state.T*state.T);
end density_derT_p;
Returns the partial derivative of density with respect to mass fractions at constant pressure and temperature
Information
Extends from (Return density derivative wrt mass fraction).
Inputs
Outputs
| Type | Name | Description |
|---|
| Density | dddX[nX] | Derivative of density wrt mass fraction [kg/m3] |
Modelica definition
redeclare function extends density_derX
"Returns the partial derivative of density with respect to mass fractions at constant pressure and temperature"
algorithm
dddX := fill(0,nX);
end density_derX;
Returns the molar mass of the medium
Information
Extends from (Return the molar mass of the medium).
Inputs
Outputs
| Type | Name | Description |
|---|
| MolarMass | MM | Mixture molar mass [kg/mol] |
Modelica definition
redeclare function extends molarMass
"Returns the molar mass of the medium"
algorithm
MM := MM_const;
end molarMass;
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Modelica.Media.Interfaces.PartialSimpleIdealGasMedium.ThermodynamicState
Modelica.Media.Interfaces.PartialSimpleIdealGasMedium.BaseProperties
Modelica.Media.Interfaces.PartialSimpleIdealGasMedium.setState_pTX