Medium model of an ideal gas based on NASA source
Information
This model calculates medium properties
for an ideal gas of a single substance, or for an ideal
gas consisting of several substances where the
mass fractions are fixed. Independent variables
are temperature T and pressure p.
Only density is a function of T and p. All other quantities
are solely a function of T. The properties
are valid in the range:
200 K ≤ T ≤ 6000 K
The following quantities are always computed:
| Variable |
Unit |
Description |
| h |
J/kg |
specific enthalpy h = h(T) |
| u |
J/kg |
specific internal energy u = u(T) |
| d |
kg/m^3 |
density d = d(p,T) |
For the other variables, see the functions in
Modelica.Media.IdealGases.Common.SingleGasNasa.
Note, dynamic viscosity and thermal conductivity are only provided
for gases that use a data record from Modelica.Media.IdealGases.FluidData.
Currently these are the following gases:
Ar
C2H2_vinylidene
C2H4
C2H5OH
C2H6
C3H6_propylene
C3H7OH
C3H8
C4H8_1_butene
C4H9OH
C4H10_n_butane
C5H10_1_pentene
C5H12_n_pentane
C6H6
C6H12_1_hexene
C6H14_n_heptane
C7H14_1_heptene
C8H10_ethylbenz
CH3OH
CH4
CL2
CO
CO2
F2
H2
H2O
He
N2
N2O
NH3
NO
O2
SO2
SO3
Sources for model and literature:
Original Data: Computer program for calculation of complex chemical
equilibrium compositions and applications. Part 1: Analysis
Document ID: 19950013764 N (95N20180) File Series: NASA Technical Reports
Report Number: NASA-RP-1311 E-8017 NAS 1.61:1311
Authors: Gordon, Sanford (NASA Lewis Research Center)
Mcbride, Bonnie J. (NASA Lewis Research Center)
Published: Oct 01, 1994.
Known limits of validity:
The data is valid for
temperatures between 200 K and 6000 K. A few of the data sets for
monatomic gases have a discontinuous 1st derivative at 1000 K, but
this never caused problems so far.
This model has been copied from the ThermoFluid library
and adapted to the Modelica.Media package.
Extends from Interfaces.PartialPureSubstance (base class for pure substances of one chemical substance).
Package Content
| Name | Description |
|---|
 ThermodynamicState
| thermodynamic state variables for ideal gases |
| FluidConstants
| Extended fluid constants |
| excludeEnthalpyOfFormation=true | If true, enthalpy of formation Hf is not included in specific enthalpy h |
| referenceChoice=Choices.ReferenceEnthalpy.ZeroAt0K | Choice of reference enthalpy |
| h_offset=0.0 | User defined offset for reference enthalpy, if referenceChoice = UserDefined |
| data | Data record of ideal gas substance |
| fluidConstants | constant data for the fluid |
 BaseProperties
| Base properties of ideal gas medium |
 setState_pTX
| Return thermodynamic state as function of p, T and composition X |
| setState_phX
| Return thermodynamic state as function of p, h and composition X |
| setState_psX
| Return thermodynamic state as function of p, s and composition X |
| setState_dTX
| Return thermodynamic state as function of d, T and composition X |
| 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 |
| specificHeatCapacityCp
| Return specific heat capacity at constant pressure |
| specificHeatCapacityCv
| Compute specific heat capacity at constant volume from temperature and gas data |
| isentropicExponent
| Return isentropic exponent |
| velocityOfSound
| Return velocity of sound |
| isentropicEnthalpyApproximation
| approximate method of calculating h_is from upstream properties and downstream pressure |
| 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 |
| cp_T
| Compute specific heat capacity at constant pressure from temperature and gas data |
| cp_Tlow
| Compute specific heat capacity at constant pressure, low T region |
| cp_Tlow_der
| Compute specific heat capacity at constant pressure, low T region |
| h_T
| Compute specific enthalpy from temperature and gas data; reference is decided by the
refChoice input, or by the referenceChoice package constant by default |
| h_T_der
| derivative function for h_T |
| h_Tlow
| Compute specific enthalpy, low T region; reference is decided by the
refChoice input, or by the referenceChoice package constant by default |
| h_Tlow_der
| Compute specific enthalpy, low T region; reference is decided by the
refChoice input, or by the referenceChoice package constant by default |
| s0_T
| Compute specific entropy from temperature and gas data |
| s0_Tlow
| Compute specific entropy, low T region |
| dynamicViscosityLowPressure
| Dynamic viscosity of low pressure gases |
| dynamicViscosity
| dynamic viscosity |
| thermalConductivityEstimate
| Thermal conductivity of polyatomic gases(Eucken and Modified Eucken correlation) |
| thermalConductivity
| thermal conductivity of gas |
| molarMass
| return the molar mass of the medium |
 T_h
| Compute temperature from specific enthalpy |
| T_ps
| Compute temperature from pressure and specific entropy |
| 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 |
| C_nominal=1.0e-6*ones(nC) | Default for the nominal values for the extra 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 w.r.t. pressure at const specific enthalpy |
| density_derh_p
| Return density derivative w.r.t. specific enthalpy at constant pressure |
| specificEnthalpy_pTX
| Return specific enthalpy from p, T, and X or Xi |
| specificEntropy_pTX
| Return specific enthalpy from p, T, and X or Xi |
| density_pTX
| Return density 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 |
| 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 Boolean excludeEnthalpyOfFormation=true
"If true, enthalpy of formation Hf is not included in specific enthalpy h";
constant ReferenceEnthalpy referenceChoice=Choices.
ReferenceEnthalpy.ZeroAt0K "Choice of reference enthalpy";
constant SpecificEnthalpy h_offset=0.0
"User defined offset for reference enthalpy, if referenceChoice = UserDefined";
constant IdealGases.Common.DataRecord data
"Data record of ideal gas substance";
constant FluidConstants[nS] fluidConstants "constant data for the fluid";
thermodynamic state variables for ideal gases
Information
Extends from (Minimal variable set that is available as input argument to every medium function).
Modelica definition
redeclare record extends ThermodynamicState
"thermodynamic state variables for ideal gases"
AbsolutePressure p "Absolute pressure of medium";
Temperature T "Temperature of medium";
end ThermodynamicState;
Extended fluid constants
Information
Extends from (critical, triple, molecular and other standard data of fluid).
Modelica definition
redeclare record extends FluidConstants "Extended fluid constants"
Temperature criticalTemperature "critical temperature";
AbsolutePressure criticalPressure "critical pressure";
MolarVolume criticalMolarVolume "critical molar Volume";
Real acentricFactor "Pitzer acentric factor";
Temperature triplePointTemperature "triple point temperature";
AbsolutePressure triplePointPressure "triple point pressure";
Temperature meltingPoint "melting point at 101325 Pa";
Temperature normalBoilingPoint "normal boiling point (at 101325 Pa)";
DipoleMoment dipoleMoment
"dipole moment of molecule in Debye (1 debye = 3.33564e10-30 C.m)";
Boolean hasIdealGasHeatCapacity=false
"true if ideal gas heat capacity is available";
Boolean hasCriticalData=false "true if critical data are known";
Boolean hasDipoleMoment=false "true if a dipole moment known";
Boolean hasFundamentalEquation=false "true if a fundamental equation";
Boolean hasLiquidHeatCapacity=false
"true if liquid heat capacity is available";
Boolean hasSolidHeatCapacity=false "true if solid heat capacity is available";
Boolean hasAccurateViscosityData=false
"true if accurate data for a viscosity function is available";
Boolean hasAccurateConductivityData=false
"true if accurate data for thermal conductivity is available";
Boolean hasVapourPressureCurve=false
"true if vapour pressure data, e.g., Antoine coefficents are known";
Boolean hasAcentricFactor=false "true if Pitzer accentric factor is known";
SpecificEnthalpy HCRIT0=0.0
"Critical specific enthalpy of the fundamental equation";
SpecificEntropy SCRIT0=0.0
"Critical specific entropy of the fundamental equation";
SpecificEnthalpy deltah=0.0
"Difference between specific enthalpy model (h_m) and f.eq. (h_f) (h_m - h_f)";
SpecificEntropy deltas=0.0
"Difference between specific enthalpy model (s_m) and f.eq. (s_f) (s_m - s_f)";
end FluidConstants;
Base properties of ideal gas medium
Information
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 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 medium"
equation
assert(T >= 200 and T <= 6000, "
Temperature T (= "
+ String(T) + " K) is not in the allowed range
200 K <= T <= 6000 K required from medium model \""
+ mediumName + "\".
");
MM = data.MM;
R = data.R;
h = h_T(data, T, excludeEnthalpyOfFormation, referenceChoice, h_offset);
u = h - R*T;
// Has to be written in the form d=f(p,T) in order that static
// state selection for p and T is possible
d = p/(R*T);
// connect state with BaseProperties
state.T = T;
state.p = p;
end BaseProperties;
Return thermodynamic state as function of p, T and composition X
Information
Extends from Modelica.Icons.Function (Icon for functions).
Inputs
Outputs
Modelica definition
redeclare function setState_pTX
"Return thermodynamic state as function of p, T and composition X"
extends Modelica.Icons.Function;
input AbsolutePressure p "Pressure";
input Temperature T "Temperature";
input MassFraction X[:]=reference_X "Mass fractions";
output ThermodynamicState state;
algorithm
state := ThermodynamicState(p=p,T=T);
end setState_pTX;
Return thermodynamic state as function of p, h and composition X
Information
Extends from Modelica.Icons.Function (Icon for functions).
Inputs
Outputs
Modelica definition
redeclare function setState_phX
"Return 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[:]=reference_X "Mass fractions";
output ThermodynamicState state;
algorithm
state := ThermodynamicState(p=p,T=T_h(h));
end setState_phX;
Return thermodynamic state as function of p, s and composition X
Information
Extends from Modelica.Icons.Function (Icon for functions).
Inputs
Outputs
Modelica definition
redeclare function setState_psX
"Return thermodynamic state as function of p, s and composition X"
extends Modelica.Icons.Function;
input AbsolutePressure p "Pressure";
input SpecificEntropy s "Specific entropy";
input MassFraction X[:]=reference_X "Mass fractions";
output ThermodynamicState state;
algorithm
state := ThermodynamicState(p=p,T=T_ps(p,s));
end setState_psX;
Return thermodynamic state as function of d, T and composition X
Information
Extends from Modelica.Icons.Function (Icon for functions).
Inputs
Outputs
Modelica definition
redeclare function setState_dTX
"Return thermodynamic state as function of d, T and composition X"
extends Modelica.Icons.Function;
input Density d "density";
input Temperature T "Temperature";
input MassFraction X[:]=reference_X "Mass fractions";
output ThermodynamicState state;
algorithm
state := ThermodynamicState(p=d*data.R*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/(data.R*state.T);
end density;
Return specific enthalpy
Information
Extends from Modelica.Icons.Function (Icon for functions), (Return specific enthalpy).
Inputs
Outputs
Modelica definition
redeclare function extends specificEnthalpy
"Return specific enthalpy"
extends Modelica.Icons.Function;
algorithm
h := h_T(data,state.T);
end specificEnthalpy;
Return specific internal energy
Information
Extends from Modelica.Icons.Function (Icon for functions), (Return specific internal energy).
Inputs
Outputs
Modelica definition
redeclare function extends specificInternalEnergy
"Return specific internal energy"
extends Modelica.Icons.Function;
algorithm
u := h_T(data,state.T) - data.R*state.T;
end specificInternalEnergy;
Return specific entropy
Information
Extends from Modelica.Icons.Function (Icon for functions), (Return specific entropy).
Inputs
Outputs
Modelica definition
redeclare function extends specificEntropy "Return specific entropy"
extends Modelica.Icons.Function;
algorithm
s := s0_T(data, state.T) - data.R*Modelica.Math.log(state.p/reference_p);
end specificEntropy;
Return specific Gibbs energy
Information
Extends from Modelica.Icons.Function (Icon for functions), (Return specific Gibbs energy).
Inputs
Outputs
Modelica definition
redeclare function extends specificGibbsEnergy
"Return specific Gibbs energy"
extends Modelica.Icons.Function;
algorithm
g := h_T(data,state.T) - state.T*specificEntropy(state);
end specificGibbsEnergy;
Return specific Helmholtz energy
Information
Extends from Modelica.Icons.Function (Icon for functions), (Return specific Helmholtz energy).
Inputs
Outputs
Modelica definition
redeclare function extends specificHelmholtzEnergy
"Return specific Helmholtz energy"
extends Modelica.Icons.Function;
algorithm
f := h_T(data,state.T) - data.R*state.T - state.T*specificEntropy(state);
end specificHelmholtzEnergy;
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_T(data, state.T);
end specificHeatCapacityCp;
Compute specific heat capacity at constant volume from temperature and gas data
Information
Extends from (Return specific heat capacity at constant volume).
Inputs
Outputs
Modelica definition
redeclare function extends specificHeatCapacityCv
"Compute specific heat capacity at constant volume from temperature and gas data"
algorithm
cv := cp_T(data, state.T) - data.R;
end specificHeatCapacityCv;
Return isentropic exponent
Information
Extends from (Return isentropic exponent).
Inputs
Outputs
Modelica definition
redeclare function extends isentropicExponent
"Return isentropic exponent"
algorithm
gamma := specificHeatCapacityCp(state)/specificHeatCapacityCv(state);
end isentropicExponent;
Return velocity of sound
Information
Extends from Modelica.Icons.Function (Icon for functions), (Return velocity of sound).
Inputs
Outputs
Modelica definition
redeclare function extends velocityOfSound "Return velocity of sound"
extends Modelica.Icons.Function;
algorithm
a := sqrt(max(0,data.R*state.T*cp_T(data, state.T)/specificHeatCapacityCv(state)));
end velocityOfSound;
approximate method of calculating h_is from upstream properties and downstream pressure
Information
Extends from Modelica.Icons.Function (Icon for functions).
Inputs
| Type | Name | Default | Description |
|---|
| Pressure | p2 | | downstream pressure [Pa] |
| ThermodynamicState | state | | properties at upstream location |
| Boolean | exclEnthForm | excludeEnthalpyOfFormation | If true, enthalpy of formation Hf is not included in specific enthalpy h |
| ReferenceEnthalpy | refChoice | referenceChoice | Choice of reference enthalpy |
| SpecificEnthalpy | h_off | h_offset | User defined offset for reference enthalpy, if referenceChoice = UserDefined [J/kg] |
Outputs
Modelica definition
function isentropicEnthalpyApproximation
"approximate method of calculating h_is from upstream properties and downstream pressure"
extends Modelica.Icons.Function;
input SI.Pressure p2 "downstream pressure";
input ThermodynamicState state "properties at upstream location";
input Boolean exclEnthForm=excludeEnthalpyOfFormation
"If true, enthalpy of formation Hf is not included in specific enthalpy h";
input ReferenceEnthalpy refChoice=referenceChoice
"Choice of reference enthalpy";
input SpecificEnthalpy h_off=h_offset
"User defined offset for reference enthalpy, if referenceChoice = UserDefined";
output SI.SpecificEnthalpy h_is "isentropic enthalpy";
protected
IsentropicExponent gamma = isentropicExponent(state) "Isentropic exponent";
algorithm
h_is := h_T(data,state.T,exclEnthForm,refChoice,h_off) +
gamma/(gamma - 1.0)*state.p/density(state)*((p2/state.p)^((gamma - 1)/gamma) - 1.0);
end isentropicEnthalpyApproximation;
Return isentropic enthalpy
Information
Extends from (Return isentropic enthalpy).
Inputs
| Type | Name | Default | Description |
|---|
| Boolean | exclEnthForm | excludeEnthalpyOfFormation | If true, enthalpy of formation Hf is not included in specific enthalpy h |
| ReferenceEnthalpy | refChoice | referenceChoice | Choice of reference enthalpy |
| SpecificEnthalpy | h_off | h_offset | User defined offset for reference enthalpy, if referenceChoice = UserDefined [J/kg] |
| AbsolutePressure | p_downstream | | downstream pressure [Pa] |
| ThermodynamicState | refState | | reference state for entropy |
Outputs
Modelica definition
redeclare function extends isentropicEnthalpy
"Return isentropic enthalpy"
input Boolean exclEnthForm=excludeEnthalpyOfFormation
"If true, enthalpy of formation Hf is not included in specific enthalpy h";
input ReferenceEnthalpy refChoice=referenceChoice
"Choice of reference enthalpy";
input SpecificEnthalpy h_off=h_offset
"User defined offset for reference enthalpy, if referenceChoice = UserDefined";
algorithm
h_is := isentropicEnthalpyApproximation(p_downstream,refState,exclEnthForm,refChoice,h_off);
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/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 := 1.0/state.p;
end isothermalCompressibility;
Returns the partial derivative of density with respect to pressure at constant temperature
Information
Extends from (Return density derivative w.r.t. 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
ddpT := 1/(state.T*data.R);
end density_derp_T;
Returns the partial derivative of density with respect to temperature at constant pressure
Information
Extends from (Return density derivative w.r.t. 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
ddTp := -state.p/(state.T*state.T*data.R);
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 w.r.t. mass fraction).
Inputs
Outputs
| Type | Name | Description |
|---|
| Density | dddX[nX] | Derivative of density w.r.t. 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;
Compute specific heat capacity at constant pressure from temperature and gas data
Information
Extends from Modelica.Icons.Function (Icon for functions).
Inputs
Outputs
Modelica definition
function cp_T
"Compute specific heat capacity at constant pressure from temperature and gas data"
extends Modelica.Icons.Function;
input IdealGases.Common.DataRecord data "Ideal gas data";
input SI.Temperature T "Temperature";
output SI.SpecificHeatCapacity cp "Specific heat capacity at temperature T";
algorithm
cp := smooth(0,if T < data.Tlimit then data.R*(1/(T*T)*(data.alow[1] + T*(
data.alow[2] + T*(1.*data.alow[3] + T*(data.alow[4] + T*(data.alow[5] + T
*(data.alow[6] + data.alow[7]*T))))))) else data.R*(1/(T*T)*(data.ahigh[1]
+ T*(data.ahigh[2] + T*(1.*data.ahigh[3] + T*(data.ahigh[4] + T*(data.
ahigh[5] + T*(data.ahigh[6] + data.ahigh[7]*T))))))));
end cp_T;
Compute specific heat capacity at constant pressure, low T region
Information
Extends from Modelica.Icons.Function (Icon for functions).
Inputs
Outputs
Modelica definition
function cp_Tlow
"Compute specific heat capacity at constant pressure, low T region"
annotation(derivative=cp_Tlow_der);
extends Modelica.Icons.Function;
input IdealGases.Common.DataRecord data "Ideal gas data";
input SI.Temperature T "Temperature";
output SI.SpecificHeatCapacity cp "Specific heat capacity at temperature T";
algorithm
cp := data.R*(1/(T*T)*(data.alow[1] + T*(
data.alow[2] + T*(1.*data.alow[3] + T*(data.alow[4] + T*(data.alow[5] + T
*(data.alow[6] + data.alow[7]*T)))))));
end cp_Tlow;
Compute specific heat capacity at constant pressure, low T region
Information
Extends from Modelica.Icons.Function (Icon for functions).
Inputs
| Type | Name | Default | Description |
|---|
| DataRecord | data | | Ideal gas data |
| Temperature | T | | Temperature [K] |
| Real | dT | | Temperature derivative |
Outputs
| Type | Name | Description |
|---|
| Real | cp_der | Derivative of specific heat capacity |
Modelica definition
function cp_Tlow_der
"Compute specific heat capacity at constant pressure, low T region"
extends Modelica.Icons.Function;
input IdealGases.Common.DataRecord data "Ideal gas data";
input SI.Temperature T "Temperature";
input Real dT "Temperature derivative";
output Real cp_der "Derivative of specific heat capacity";
algorithm
cp_der := dT*data.R/(T*T*T)*(-2*data.alow[1] + T*(
-data.alow[2] + T*T*(data.alow[4] + T*(2.*data.alow[5] + T
*(3.*data.alow[6] + 4.*data.alow[7]*T)))));
end cp_Tlow_der;
Compute specific enthalpy from temperature and gas data; reference is decided by the
refChoice input, or by the referenceChoice package constant by default
Information
Extends from Modelica.Icons.Function (Icon for functions).
Inputs
| Type | Name | Default | Description |
|---|
| DataRecord | data | | Ideal gas data |
| Temperature | T | | Temperature [K] |
| Boolean | exclEnthForm | excludeEnthalpyOfFormation | If true, enthalpy of formation Hf is not included in specific enthalpy h |
| ReferenceEnthalpy | refChoice | referenceChoice | Choice of reference enthalpy |
| SpecificEnthalpy | h_off | h_offset | User defined offset for reference enthalpy, if referenceChoice = UserDefined [J/kg] |
Outputs
Modelica definition
function h_T "Compute specific enthalpy from temperature and gas data; reference is decided by the
refChoice input, or by the referenceChoice package constant by default"
import Modelica.Media.Interfaces.PartialMedium.Choices;
extends Modelica.Icons.Function;
input IdealGases.Common.DataRecord data "Ideal gas data";
input SI.Temperature T "Temperature";
input Boolean exclEnthForm=excludeEnthalpyOfFormation
"If true, enthalpy of formation Hf is not included in specific enthalpy h";
input Choices.ReferenceEnthalpy refChoice=referenceChoice
"Choice of reference enthalpy";
input SI.SpecificEnthalpy h_off=h_offset
"User defined offset for reference enthalpy, if referenceChoice = UserDefined";
output SI.SpecificEnthalpy h "Specific enthalpy at temperature T";
// annotation (InlineNoEvent=false, Inline=false,
// derivative(zeroDerivative=data,
// zeroDerivative=exclEnthForm,
// zeroDerivative=refChoice,
// zeroDerivative=h_off) = h_T_der);
algorithm
h := smooth(0,(if T < data.Tlimit then data.R*((-data.alow[1] + T*(data.
blow[1] + data.alow[2]*Math.log(T) + T*(1.*data.alow[3] + T*(0.5*data.
alow[4] + T*(1/3*data.alow[5] + T*(0.25*data.alow[6] + 0.2*data.alow[7]*T))))))
/T) else data.R*((-data.ahigh[1] + T*(data.bhigh[1] + data.ahigh[2]*
Math.log(T) + T*(1.*data.ahigh[3] + T*(0.5*data.ahigh[4] + T*(1/3*data.
ahigh[5] + T*(0.25*data.ahigh[6] + 0.2*data.ahigh[7]*T))))))/T)) + (if
exclEnthForm then -data.Hf else 0.0) + (if (refChoice
== Choices.ReferenceEnthalpy.ZeroAt0K) then data.H0 else 0.0) + (if
refChoice == Choices.ReferenceEnthalpy.UserDefined then h_off else
0.0));
end h_T;
derivative function for h_T
Information
Extends from Modelica.Icons.Function (Icon for functions).
Inputs
| Type | Name | Default | Description |
|---|
| DataRecord | data | | Ideal gas data |
| Temperature | T | | Temperature [K] |
| Boolean | exclEnthForm | excludeEnthalpyOfFormation | If true, enthalpy of formation Hf is not included in specific enthalpy h |
| ReferenceEnthalpy | refChoice | referenceChoice | Choice of reference enthalpy |
| SpecificEnthalpy | h_off | h_offset | User defined offset for reference enthalpy, if referenceChoice = UserDefined [J/kg] |
| Real | dT | | Temperature derivative |
Outputs
| Type | Name | Description |
|---|
| Real | h_der | Specific enthalpy at temperature T |
Modelica definition
function h_T_der "derivative function for h_T"
import Modelica.Media.Interfaces.PartialMedium.Choices;
extends Modelica.Icons.Function;
input IdealGases.Common.DataRecord data "Ideal gas data";
input SI.Temperature T "Temperature";
input Boolean exclEnthForm=excludeEnthalpyOfFormation
"If true, enthalpy of formation Hf is not included in specific enthalpy h";
input Choices.ReferenceEnthalpy refChoice=referenceChoice
"Choice of reference enthalpy";
input SI.SpecificEnthalpy h_off=h_offset
"User defined offset for reference enthalpy, if referenceChoice = UserDefined";
input Real dT "Temperature derivative";
output Real h_der "Specific enthalpy at temperature T";
algorithm
h_der := dT*cp_T(data,T);
end h_T_der;
Compute specific enthalpy, low T region; reference is decided by the
refChoice input, or by the referenceChoice package constant by default
Information
Extends from Modelica.Icons.Function (Icon for functions).
Inputs
| Type | Name | Default | Description |
|---|
| DataRecord | data | | Ideal gas data |
| Temperature | T | | Temperature [K] |
| Boolean | exclEnthForm | excludeEnthalpyOfFormation | If true, enthalpy of formation Hf is not included in specific enthalpy h |
| ReferenceEnthalpy | refChoice | referenceChoice | Choice of reference enthalpy |
| SpecificEnthalpy | h_off | h_offset | User defined offset for reference enthalpy, if referenceChoice = UserDefined [J/kg] |
Outputs
Modelica definition
function h_Tlow "Compute specific enthalpy, low T region; reference is decided by the
refChoice input, or by the referenceChoice package constant by default"
import Modelica.Media.Interfaces.PartialMedium.Choices;
extends Modelica.Icons.Function;
input IdealGases.Common.DataRecord data "Ideal gas data";
input SI.Temperature T "Temperature";
input Boolean exclEnthForm=excludeEnthalpyOfFormation
"If true, enthalpy of formation Hf is not included in specific enthalpy h";
input Choices.ReferenceEnthalpy refChoice=referenceChoice
"Choice of reference enthalpy";
input SI.SpecificEnthalpy h_off=h_offset
"User defined offset for reference enthalpy, if referenceChoice = UserDefined";
output SI.SpecificEnthalpy h "Specific enthalpy at temperature T";
// annotation (Inline=false,InlineNoEvent=false, derivative(zeroDerivative=data,
// zeroDerivative=exclEnthForm,
// zeroDerivative=refChoice,
// zeroDerivative=h_off) = h_Tlow_der);
algorithm
h := data.R*((-data.alow[1] + T*(data.
blow[1] + data.alow[2]*Math.log(T) + T*(1.*data.alow[3] + T*(0.5*data.
alow[4] + T*(1/3*data.alow[5] + T*(0.25*data.alow[6] + 0.2*data.alow[7]*T))))))
/T) + (if
exclEnthForm then -data.Hf else 0.0) + (if (refChoice
== Choices.ReferenceEnthalpy.ZeroAt0K) then data.H0 else 0.0) + (if
refChoice == Choices.ReferenceEnthalpy.UserDefined then h_off else
0.0);
end h_Tlow;
Compute specific enthalpy, low T region; reference is decided by the
refChoice input, or by the referenceChoice package constant by default
Information
Extends from Modelica.Icons.Function (Icon for functions).
Inputs
| Type | Name | Default | Description |
|---|
| DataRecord | data | | Ideal gas data |
| Temperature | T | | Temperature [K] |
| Boolean | exclEnthForm | excludeEnthalpyOfFormation | If true, enthalpy of formation Hf is not included in specific enthalpy h |
| ReferenceEnthalpy | refChoice | referenceChoice | Choice of reference enthalpy |
| SpecificEnthalpy | h_off | h_offset | User defined offset for reference enthalpy, if referenceChoice = UserDefined [J/kg] |
| Real | dT | | Temperature derivative [K/s] |
Outputs
| Type | Name | Description |
|---|
| Real | h_der | Derivative of specific enthalpy at temperature T [J/(kg.s)] |
Modelica definition
function h_Tlow_der "Compute specific enthalpy, low T region; reference is decided by the
refChoice input, or by the referenceChoice package constant by default"
import Modelica.Media.Interfaces.PartialMedium.Choices;
extends Modelica.Icons.Function;
input IdealGases.Common.DataRecord data "Ideal gas data";
input SI.Temperature T "Temperature";
input Boolean exclEnthForm=excludeEnthalpyOfFormation
"If true, enthalpy of formation Hf is not included in specific enthalpy h";
input Choices.ReferenceEnthalpy refChoice=referenceChoice
"Choice of reference enthalpy";
input SI.SpecificEnthalpy h_off=h_offset
"User defined offset for reference enthalpy, if referenceChoice = UserDefined";
input Real dT(unit="K/s") "Temperature derivative";
output Real h_der(unit="J/(kg.s)")
"Derivative of specific enthalpy at temperature T";
algorithm
h_der := dT*cp_Tlow(data,T);
end h_Tlow_der;
Compute specific entropy from temperature and gas data
Information
Extends from Modelica.Icons.Function (Icon for functions).
Inputs
Outputs
| Type | Name | Description |
|---|
| SpecificEntropy | s | Specific entropy at temperature T [J/(kg.K)] |
Modelica definition
function s0_T
"Compute specific entropy from temperature and gas data"
extends Modelica.Icons.Function;
input IdealGases.Common.DataRecord data "Ideal gas data";
input SI.Temperature T "Temperature";
output SI.SpecificEntropy s "Specific entropy at temperature T";
algorithm
s := noEvent(if T < data.Tlimit then data.R*(data.blow[2] - 0.5*data.alow[
1]/(T*T) - data.alow[2]/T + data.alow[3]*Math.log(T) + T*(
data.alow[4] + T*(0.5*data.alow[5] + T*(1/3*data.alow[6] + 0.25*data.alow[
7]*T)))) else data.R*(data.bhigh[2] - 0.5*data.ahigh[1]/(T*T) - data.
ahigh[2]/T + data.ahigh[3]*Math.log(T) + T*(data.ahigh[4]
+ T*(0.5*data.ahigh[5] + T*(1/3*data.ahigh[6] + 0.25*data.ahigh[7]*T)))));
end s0_T;
Compute specific entropy, low T region
Information
Extends from Modelica.Icons.Function (Icon for functions).
Inputs
Outputs
| Type | Name | Description |
|---|
| SpecificEntropy | s | Specific entropy at temperature T [J/(kg.K)] |
Modelica definition
function s0_Tlow "Compute specific entropy, low T region"
extends Modelica.Icons.Function;
input IdealGases.Common.DataRecord data "Ideal gas data";
input SI.Temperature T "Temperature";
output SI.SpecificEntropy s "Specific entropy at temperature T";
algorithm
s := data.R*(data.blow[2] - 0.5*data.alow[
1]/(T*T) - data.alow[2]/T + data.alow[3]*Math.log(T) + T*(
data.alow[4] + T*(0.5*data.alow[5] + T*(1/3*data.alow[6] + 0.25*data.alow[
7]*T))));
end s0_Tlow;
Dynamic viscosity of low pressure gases
Information
The used formula are based on the method of Chung et al (1984, 1988) referred to in ref [1] chapter 9.
The formula 9-4.10 is the one being used. The Formula is given in non-SI units, the follwong onversion constants were used to
transform the formula to SI units:
- Const1_SI: The factor 10^(-9.5) =10^(-2.5)*1e-7 where the
factor 10^(-2.5) originates from the conversion of g/mol->kg/mol + cm^3/mol->m^3/mol
and the factor 1e-7 is due to conversionfrom microPoise->Pa.s.
- Const2_SI: The factor 1/3.335641e-27 = 1e-3/3.335641e-30
where the factor 3.335641e-30 comes from debye->C.m and
1e-3 is due to conversion from cm^3/mol->m^3/mol
References:
[1] Bruce E. Poling, John E. Prausnitz, John P. O'Connell, "The Properties of Gases and Liquids" 5th Ed. Mc Graw Hill.
Author
T. Skoglund, Lund, Sweden, 2004-08-31
Extends from Modelica.Icons.Function (Icon for functions).
Inputs
| Type | Name | Default | Description |
|---|
| Temp_K | T | | Gas temperature [K] |
| Temp_K | Tc | | Critical temperature of gas [K] |
| MolarMass | M | | Molar mass of gas [kg/mol] |
| MolarVolume | Vc | | Critical molar volume of gas [m3/mol] |
| Real | w | | Acentric factor of gas |
| DipoleMoment | mu | | Dipole moment of gas molecule [debye] |
| Real | k | 0.0 | Special correction for highly polar substances |
Outputs
Modelica definition
function dynamicViscosityLowPressure
"Dynamic viscosity of low pressure gases"
extends Modelica.Icons.Function;
input SI.Temp_K T "Gas temperature";
input SI.Temp_K Tc "Critical temperature of gas";
input SI.MolarMass M "Molar mass of gas";
input SI.MolarVolume Vc "Critical molar volume of gas";
input Real w "Acentric factor of gas";
input DipoleMoment mu "Dipole moment of gas molecule";
input Real k = 0.0 "Special correction for highly polar substances";
output SI.DynamicViscosity eta "Dynamic viscosity of gas";
protected
parameter Real Const1_SI=40.785*10^(-9.5)
"Constant in formula for eta converted to SI units";
parameter Real Const2_SI=131.3/1000.0
"Constant in formula for mur converted to SI units";
Real mur=Const2_SI*mu/sqrt(Vc*Tc)
"Dimensionless dipole moment of gas molecule";
Real Fc=1 - 0.2756*w + 0.059035*mur^4 + k
"Factor to account for molecular shape and polarities of gas";
Real Tstar "Dimensionless temperature defined by equation below";
Real Ov "Viscosity collision integral for the gas";
algorithm
Tstar := 1.2593*T/Tc;
Ov := 1.16145*Tstar^(-0.14874) + 0.52487*exp(-0.7732*Tstar) + 2.16178*exp(-2.43787
*Tstar);
eta := Const1_SI*Fc*sqrt(M*T)/(Vc^(2/3)*Ov);
end dynamicViscosityLowPressure;
dynamic viscosity
Information
Extends from (Return dynamic viscosity).
Inputs
Outputs
Modelica definition
redeclare replaceable function extends dynamicViscosity
"dynamic viscosity"
algorithm
assert(fluidConstants[1].hasCriticalData,
"Failed to compute dynamicViscosity: For the species \"" + mediumName + "\" no critical data is available.");
assert(fluidConstants[1].hasDipoleMoment,
"Failed to compute dynamicViscosity: For the species \"" + mediumName + "\" no critical data is available.");
eta := dynamicViscosityLowPressure(state.T,
fluidConstants[1].criticalTemperature,
fluidConstants[1].molarMass,
fluidConstants[1].criticalMolarVolume,
fluidConstants[1].acentricFactor,
fluidConstants[1].dipoleMoment);
end dynamicViscosity;
Thermal conductivity of polyatomic gases(Eucken and Modified Eucken correlation)
Information
This function provides two similar methods for estimating the
thermal conductivity of polyatomic gases.
The Eucken method (input method == 1) gives good results for low temperatures,
but it tends to give an underestimated value of the thermal conductivity
(lambda) at higher temperatures.
The Modified Eucken method (input method == 2) gives good results for
high-temperatures, but it tends to give an overestimated value of the
thermal conductivity (lambda) at low temperatures.
Extends from Modelica.Icons.Function (Icon for functions).
Inputs
| Type | Name | Default | Description |
|---|
| SpecificHeatCapacity | Cp | | Constant pressure heat capacity [J/(kg.K)] |
| DynamicViscosity | eta | | Dynamic viscosity [Pa.s] |
| Integer | method | 1 | 1: Eucken Method, 2: Modified Eucken Method |
Outputs
Modelica definition
function thermalConductivityEstimate
"Thermal conductivity of polyatomic gases(Eucken and Modified Eucken correlation)"
extends Modelica.Icons.Function;
input SpecificHeatCapacity Cp "Constant pressure heat capacity";
input DynamicViscosity eta "Dynamic viscosity";
input Integer method(min=1,max=2)=1
"1: Eucken Method, 2: Modified Eucken Method";
output ThermalConductivity lambda "Thermal conductivity [W/(m.k)]";
algorithm
lambda := if method == 1 then eta*(Cp - data.R + (9/4)*data.R) else eta*(Cp
- data.R)*(1.32 + 1.77/((Cp/Modelica.Constants.R) - 1.0));
end thermalConductivityEstimate;
thermal conductivity of gas
Information
Extends from (Return thermal conductivity).
Inputs
| Type | Name | Default | Description |
|---|
| Integer | method | 1 | 1: Eucken Method, 2: Modified Eucken Method |
| ThermodynamicState | state | | thermodynamic state record |
Outputs
Modelica definition
redeclare replaceable function extends thermalConductivity
"thermal conductivity of gas"
input Integer method=1 "1: Eucken Method, 2: Modified Eucken Method";
algorithm
assert(fluidConstants[1].hasCriticalData,
"Failed to compute thermalConductivity: For the species \"" + mediumName + "\" no critical data is available.");
lambda := thermalConductivityEstimate(specificHeatCapacityCp(state),
dynamicViscosity(state), method=method);
end thermalConductivity;
return 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
"return the molar mass of the medium"
algorithm
MM := data.MM;
end molarMass;
Compute temperature from specific enthalpy
Inputs
Outputs
Modelica definition
function T_h "Compute temperature from specific enthalpy"
input SpecificEnthalpy h "Specific enthalpy";
output Temperature T "Temperature";
protected
package Internal
"Solve h(data,T) for T with given h (use only indirectly via temperature_phX)"
extends Modelica.Media.Common.OneNonLinearEquation;
redeclare record extends f_nonlinear_Data
"Data to be passed to non-linear function"
extends Modelica.Media.IdealGases.Common.DataRecord;
end f_nonlinear_Data;
redeclare function extends f_nonlinear
algorithm
y := h_T(f_nonlinear_data,x);
end f_nonlinear;
// Dummy definition has to be added for current Dymola
redeclare function extends solve
end solve;
end Internal;
algorithm
T := Internal.solve(h, 200, 6000, 1.0e5, {1}, data);
end T_h;
Compute temperature from pressure and specific entropy
Inputs
Outputs
Modelica definition
function T_ps
"Compute temperature from pressure and specific entropy"
input AbsolutePressure p "Pressure";
input SpecificEntropy s "Specific entropy";
output Temperature T "Temperature";
protected
package Internal
"Solve h(data,T) for T with given h (use only indirectly via temperature_phX)"
extends Modelica.Media.Common.OneNonLinearEquation;
redeclare record extends f_nonlinear_Data
"Data to be passed to non-linear function"
extends Modelica.Media.IdealGases.Common.DataRecord;
end f_nonlinear_Data;
redeclare function extends f_nonlinear
algorithm
y := s0_T(f_nonlinear_data,x)- data.R*Modelica.Math.log(p/reference_p);
end f_nonlinear;
// Dummy definition has to be added for current Dymola
redeclare function extends solve
end solve;
end Internal;
algorithm
T := Internal.solve(s, 200, 6000, p, {1}, data);
end T_ps;
Automatically generated Fri Nov 12 16:31:32 2010.
Modelica.Media.IdealGases.Common.SingleGasNasa.ThermodynamicState
Modelica.Media.IdealGases.Common.SingleGasNasa.BaseProperties
Modelica.Media.IdealGases.Common.SingleGasNasa.setState_pTX