Modelica.Media.Common

Data structures and fundamental functions for fluid properties

Information

Package description

Package Modelica.Media.Common provides records and functions shared by many of the property sub-packages. High accuracy fluid property models share a lot of common structure, even if the actual models are different. Common data structures and computations shared by these property models are collected in this library.

Extends from Modelica.Icons.Package (Icon for standard packages).

Package Content

Name Description
Modelica.Media.Common.Rate Rate  
Modelica.Media.Common.MolarFlowRate MolarFlowRate  
Modelica.Media.Common.MolarReactionRate MolarReactionRate  
Modelica.Media.Common.MolarEnthalpy MolarEnthalpy  
Modelica.Media.Common.DerDensityByEntropy DerDensityByEntropy  
Modelica.Media.Common.DerEnergyByPressure DerEnergyByPressure  
Modelica.Media.Common.DerEnergyByMoles DerEnergyByMoles  
Modelica.Media.Common.DerEntropyByTemperature DerEntropyByTemperature  
Modelica.Media.Common.DerEntropyByPressure DerEntropyByPressure  
Modelica.Media.Common.DerEntropyByMoles DerEntropyByMoles  
Modelica.Media.Common.DerPressureByDensity DerPressureByDensity  
Modelica.Media.Common.DerPressureBySpecificVolume DerPressureBySpecificVolume  
Modelica.Media.Common.DerPressureByTemperature DerPressureByTemperature  
Modelica.Media.Common.DerVolumeByTemperature DerVolumeByTemperature  
Modelica.Media.Common.DerVolumeByPressure DerVolumeByPressure  
Modelica.Media.Common.DerVolumeByMoles DerVolumeByMoles  
Modelica.Media.Common.IsenthalpicExponent IsenthalpicExponent  
Modelica.Media.Common.IsentropicExponent IsentropicExponent  
Modelica.Media.Common.IsobaricVolumeExpansionCoefficient IsobaricVolumeExpansionCoefficient  
Modelica.Media.Common.IsochoricPressureCoefficient IsochoricPressureCoefficient  
Modelica.Media.Common.IsothermalCompressibility IsothermalCompressibility  
Modelica.Media.Common.JouleThomsonCoefficient JouleThomsonCoefficient  
MINPOS=1.0e-9 Minimal value for physical variables which are always > 0.0
AMIN=MINPOS Minimal init area
AMAX=1.0e5 Maximal init area
ANOM=1.0 Nominal init area
MOLMIN=-1.0*MINPOS Minimal Mole Number
MOLMAX=1.0e8 Maximal Mole Number
MOLNOM=1.0 Nominal Mole Number
DMIN=1e-6 Minimal init density
DMAX=30.0e3 Maximal init density
DNOM=1.0 Nominal init density
LAMMIN=MINPOS Minimal thermal conductivity
LAMNOM=1.0 Nominal thermal conductivity
LAMMAX=1000.0 Maximal thermal conductivity
ETAMIN=MINPOS Minimal init dynamic viscosity
ETAMAX=1.0e8 Maximal init dynamic viscosity
ETANOM=100.0 Nominal init dynamic viscosity
EMIN=-1.0e10 Minimal init energy
EMAX=1.0e10 Maximal init energy
ENOM=1.0e3 Nominal init energy
SMIN=-1.0e6 Minimal init entropy
SMAX=1.0e6 Maximal init entropy
SNOM=1.0e3 Nominal init entropy
MDOTMIN=-1.0e5 Minimal init mass flow rate
MDOTMAX=1.0e5 Maximal init mass flow rate
MDOTNOM=1.0 Nominal init mass flow rate
MASSXMIN=-1.0*MINPOS Minimal init mass fraction
MASSXMAX=1.0 Maximal init mass fraction
MASSXNOM=0.1 Nominal init mass fraction
MMIN=-1.0*MINPOS Minimal init mass
MMAX=1.0e8 Maximal init mass
MNOM=1.0 Nominal init mass
MMMIN=0.001 Minimal initial molar mass
MMMAX=250.0 Maximal initial molar mass
MMNOM=0.2 Nominal initial molar mass
MOLEYMIN=-1.0*MINPOS Minimal init mole fraction
MOLEYMAX=1.0 Maximal init mole fraction
MOLEYNOM=0.1 Nominal init mole fraction
GMIN=-1.0e8 Minimal init momentum flux
GMAX=1.0e8 Maximal init momentum flux
GNOM=1.0 Nominal init momentum flux
POWMIN=-1.0e8 Minimal init power or heat
POWMAX=1.0e8 Maximal init power or heat
POWNOM=1.0e3 Nominal init power or heat
PMIN=1.0e4 Minimal init pressure
PMAX=1.0e8 Maximal init pressure
PNOM=1.0e5 Nominal init pressure
COMPPMIN=-1.0*MINPOS Minimal init pressure
COMPPMAX=1.0e8 Maximal init pressure
COMPPNOM=1.0e5 Nominal init pressure
KAPPAMIN=1.0 Minimal init isentropic exponent
KAPPAMAX=1.7 Maximal init isentropic exponent
KAPPANOM=1.2 Nominal init isentropic exponent
SEMIN=-1.0e8 Minimal init specific energy
SEMAX=1.0e8 Maximal init specific energy
SENOM=1.0e6 Nominal init specific energy
SHMIN=-1.0e8 Minimal init specific enthalpy
SHMAX=1.0e8 Maximal init specific enthalpy
SHNOM=1.0e6 Nominal init specific enthalpy
SSMIN=-1.0e6 Minimal init specific entropy
SSMAX=1.0e6 Maximal init specific entropy
SSNOM=1.0e3 Nominal init specific entropy
CPMIN=MINPOS Minimal init specific heat capacity
CPMAX=1.0e6 Maximal init specific heat capacity
CPNOM=1.0e3 Nominal init specific heat capacity
TMIN=1.0 Minimal init temperature
TMAX=6000.0 Maximal init temperature
TNOM=320.0 Nominal init temperature
LMIN=MINPOS Minimal init thermal conductivity
LMAX=500.0 Maximal init thermal conductivity
LNOM=1.0 Nominal init thermal conductivity
VELMIN=-1.0e5 Minimal init speed
VELMAX=1.0e5 Maximal init speed
VELNOM=1.0 Nominal init speed
VMIN=0.0 Minimal init volume
VMAX=1.0e5 Maximal init volume
VNOM=1.0e-3 Nominal init volume
Modelica.Media.Common.ThermoFluidSpecial ThermoFluidSpecial Property records used by the ThermoFluid library
Modelica.Media.Common.SaturationProperties SaturationProperties Properties in the two phase region
Modelica.Media.Common.SaturationBoundaryProperties SaturationBoundaryProperties Properties on both phase boundaries, including some derivatives
Modelica.Media.Common.IF97BaseTwoPhase IF97BaseTwoPhase Intermediate property data record for IF 97
Modelica.Media.Common.IF97PhaseBoundaryProperties IF97PhaseBoundaryProperties Thermodynamic base properties on the phase boundary for IF97 steam tables
Modelica.Media.Common.GibbsDerivs GibbsDerivs Derivatives of dimensionless Gibbs-function w.r.t. dimensionless pressure and temperature
Modelica.Media.Common.HelmholtzDerivs HelmholtzDerivs Derivatives of dimensionless Helmholtz-function w.r.t. dimensionless pressure, density and temperature
Modelica.Media.Common.TwoPhaseTransportProps TwoPhaseTransportProps Defines properties on both phase boundaries, needed in the two phase region
Modelica.Media.Common.PhaseBoundaryProperties PhaseBoundaryProperties Thermodynamic base properties on the phase boundary
Modelica.Media.Common.NewtonDerivatives_ph NewtonDerivatives_ph Derivatives for fast inverse calculations of Helmholtz functions: p & h
Modelica.Media.Common.NewtonDerivatives_ps NewtonDerivatives_ps Derivatives for fast inverse calculation of Helmholtz functions: p & s
Modelica.Media.Common.NewtonDerivatives_pT NewtonDerivatives_pT Derivatives for fast inverse calculations of Helmholtz functions:p & T
Modelica.Media.Common.ExtraDerivatives ExtraDerivatives Additional thermodynamic derivatives
Modelica.Media.Common.BridgmansTables BridgmansTables Calculates all entries in Bridgmans tables if first seven variables given
Modelica.Media.Common.FundamentalConstants FundamentalConstants Constants of the medium
Modelica.Media.Common.AuxiliaryProperties AuxiliaryProperties Intermediate property data record
Modelica.Media.Common.GibbsDerivs2 GibbsDerivs2 Derivatives of Gibbs function w.r.t. pressure and temperature
Modelica.Media.Common.NewtonDerivatives_dT NewtonDerivatives_dT Derivatives for fast inverse calculations of Gibbs function
Modelica.Media.Common.gibbsToBridgmansTables gibbsToBridgmansTables Calculates base coefficients for Bridgman's tables from gibbs enthalpy
Modelica.Media.Common.helmholtzToBridgmansTables helmholtzToBridgmansTables Calculates base coefficients for Bridgmans tables from Helmholtz energy
Modelica.Media.Common.gibbsToBoundaryProps gibbsToBoundaryProps Calculate phase boundary property record from dimensionless Gibbs function
Modelica.Media.Common.helmholtzToBoundaryProps helmholtzToBoundaryProps Calculate phase boundary property record from dimensionless Helmholtz function
Modelica.Media.Common.cv2Phase cv2Phase Compute isochoric specific heat capacity inside the two-phase region
Modelica.Media.Common.cvdpT2Phase cvdpT2Phase Compute isochoric specific heat capacity inside the two-phase region and derivative of pressure w.r.t. temperature
Modelica.Media.Common.gibbsToExtraDerivs gibbsToExtraDerivs Compute additional thermodynamic derivatives from dimensionless Gibbs function
Modelica.Media.Common.helmholtzToExtraDerivs helmholtzToExtraDerivs Compute additional thermodynamic derivatives from dimensionless Helmholtz function
Modelica.Media.Common.Helmholtz_ph Helmholtz_ph Function to calculate analytic derivatives for computing d and t given p and h
Modelica.Media.Common.Helmholtz_pT Helmholtz_pT Function to calculate analytic derivatives for computing d and t given p and t
Modelica.Media.Common.Helmholtz_ps Helmholtz_ps Function to calculate analytic derivatives for computing d and t given p and s
Modelica.Media.Common.smoothStep smoothStep Approximation of a general step, such that the characteristic is continuous and differentiable
Modelica.Media.Common.Gibbs2_ph Gibbs2_ph Function to calculate analytic derivatives for computing T given p and h
Modelica.Media.Common.Gibbs2_dT Gibbs2_dT Function to calculate analytic derivatives for computing p given d and T
Modelica.Media.Common.Gibbs2_ps Gibbs2_ps Function to calculate analytic derivatives for computing d and t given p and s

Modelica.Media.Common.Rate

Parameters

NameValue
Custom Parameters
quantity"Rate"
unit"s-1"

Modelica.Media.Common.MolarFlowRate

Parameters

NameValue
Custom Parameters
quantity"MolarFlowRate"
unit"mol/s"

Modelica.Media.Common.MolarReactionRate

Parameters

NameValue
Custom Parameters
quantity"MolarReactionRate"
unit"mol/(m3.s)"

Modelica.Media.Common.MolarEnthalpy

Parameters

NameValue
Custom Parameters
quantity"MolarEnthalpy"
unit"J/mol"

Modelica.Media.Common.DerDensityByEntropy

Parameters

NameValue
Custom Parameters
quantity"DerDensityByEntropy"
unit"kg2.K/(m3.J)"

Modelica.Media.Common.DerEnergyByPressure

Parameters

NameValue
Custom Parameters
quantity"DerEnergyByPressure"
unit"J/Pa"

Modelica.Media.Common.DerEnergyByMoles

Parameters

NameValue
Custom Parameters
quantity"DerEnergyByMoles"
unit"J/mol"

Modelica.Media.Common.DerEntropyByTemperature

Parameters

NameValue
Custom Parameters
quantity"DerEntropyByTemperature"
unit"J/K2"

Modelica.Media.Common.DerEntropyByPressure

Parameters

NameValue
Custom Parameters
quantity"DerEntropyByPressure"
unit"J/(K.Pa)"

Modelica.Media.Common.DerEntropyByMoles

Parameters

NameValue
Custom Parameters
quantity"DerEntropyByMoles"
unit"J/(mol.K)"

Modelica.Media.Common.DerPressureByDensity

Parameters

NameValue
Custom Parameters
quantity"DerPressureByDensity"
unit"Pa.m3/kg"

Modelica.Media.Common.DerPressureBySpecificVolume

Parameters

NameValue
Custom Parameters
quantity"DerPressureBySpecificVolume"
unit"Pa.kg/m3"

Modelica.Media.Common.DerPressureByTemperature

Parameters

NameValue
Custom Parameters
quantity"DerPressureByTemperature"
unit"Pa/K"

Modelica.Media.Common.DerVolumeByTemperature

Parameters

NameValue
Custom Parameters
quantity"DerVolumeByTemperature"
unit"m3/K"

Modelica.Media.Common.DerVolumeByPressure

Parameters

NameValue
Custom Parameters
quantity"DerVolumeByPressure"
unit"m3/Pa"

Modelica.Media.Common.DerVolumeByMoles

Parameters

NameValue
Custom Parameters
quantity"DerVolumeByMoles"
unit"m3/mol"

Modelica.Media.Common.IsenthalpicExponent

Parameters

NameValue
Custom Parameters
quantity"IsenthalpicExponent"
unit"1"

Modelica.Media.Common.IsentropicExponent

Parameters

NameValue
Custom Parameters
quantity"IsentropicExponent"
unit"1"

Modelica.Media.Common.IsobaricVolumeExpansionCoefficient

Parameters

NameValue
Custom Parameters
quantity"IsobaricVolumeExpansionCoef...
unit"1/K"

Modelica.Media.Common.IsochoricPressureCoefficient

Parameters

NameValue
Custom Parameters
quantity"IsochoricPressureCoefficient"
unit"1/K"

Modelica.Media.Common.IsothermalCompressibility

Parameters

NameValue
Custom Parameters
quantity"IsothermalCompressibility"
unit"1/Pa"

Modelica.Media.Common.JouleThomsonCoefficient

Parameters

NameValue
Custom Parameters
quantity"JouleThomsonCoefficient"
unit"K/Pa"

Modelica.Media.Common.SaturationProperties Modelica.Media.Common.SaturationProperties

Properties in the two phase region

Information

Extends from Modelica.Icons.Record (Icon for records).

Modelica.Media.Common.SaturationBoundaryProperties Modelica.Media.Common.SaturationBoundaryProperties

Properties on both phase boundaries, including some derivatives

Information

Extends from Modelica.Icons.Record (Icon for records).

Modelica.Media.Common.IF97BaseTwoPhase Modelica.Media.Common.IF97BaseTwoPhase

Intermediate property data record for IF 97

Information

Extends from Modelica.Icons.Record (Icon for records).

Modelica.Media.Common.IF97PhaseBoundaryProperties Modelica.Media.Common.IF97PhaseBoundaryProperties

Thermodynamic base properties on the phase boundary for IF97 steam tables

Information

Extends from Modelica.Icons.Record (Icon for records).

Modelica.Media.Common.GibbsDerivs Modelica.Media.Common.GibbsDerivs

Derivatives of dimensionless Gibbs-function w.r.t. dimensionless pressure and temperature

Information

Extends from Modelica.Icons.Record (Icon for records).

Modelica.Media.Common.HelmholtzDerivs Modelica.Media.Common.HelmholtzDerivs

Derivatives of dimensionless Helmholtz-function w.r.t. dimensionless pressure, density and temperature

Information

Extends from Modelica.Icons.Record (Icon for records).

Modelica.Media.Common.TwoPhaseTransportProps Modelica.Media.Common.TwoPhaseTransportProps

Defines properties on both phase boundaries, needed in the two phase region

Information

Extends from Modelica.Icons.Record (Icon for records).

Modelica.Media.Common.PhaseBoundaryProperties Modelica.Media.Common.PhaseBoundaryProperties

Thermodynamic base properties on the phase boundary

Information

Extends from Modelica.Icons.Record (Icon for records).

Modelica.Media.Common.NewtonDerivatives_ph Modelica.Media.Common.NewtonDerivatives_ph

Derivatives for fast inverse calculations of Helmholtz functions: p & h

Information

Extends from Modelica.Icons.Record (Icon for records).

Modelica.Media.Common.NewtonDerivatives_ps Modelica.Media.Common.NewtonDerivatives_ps

Derivatives for fast inverse calculation of Helmholtz functions: p & s

Information

Extends from Modelica.Icons.Record (Icon for records).

Modelica.Media.Common.NewtonDerivatives_pT Modelica.Media.Common.NewtonDerivatives_pT

Derivatives for fast inverse calculations of Helmholtz functions:p & T

Information

Extends from Modelica.Icons.Record (Icon for records).

Modelica.Media.Common.ExtraDerivatives Modelica.Media.Common.ExtraDerivatives

Additional thermodynamic derivatives

Information

Extends from Modelica.Icons.Record (Icon for records).

Modelica.Media.Common.BridgmansTables Modelica.Media.Common.BridgmansTables

Calculates all entries in Bridgmans tables if first seven variables given

Information

Important: the phase equilibrium conditions are not yet considered. this means that Bridgman's tables do not yet work in the two phase region. Some derivatives are 0 or infinity anyways. Idea: Do not use the values in Bridgmans table directly, all derivatives are calculated as the quotient of two entries in the table. The last letter indicates which variable is held constant in taking the derivative. The second letters are the two variables involved in the derivative and the first letter is always a d to remind of differentiation.

Example 1: Get the derivative of specific entropy s w.r.t. Temperature at
constant specific volume (between identical to constant density)
constant volume  --> last letter v
Temperature      --> second letter T
Specific entropy --> second letter s
--> the needed value is dsv/dTv
Known variables:
Temperature T
pressure p
specific volume v
specific inner energy u
specific enthalpy h
specific entropy s
specific Helmholtz energy f
specific gibbs enthalpy g
Not included but useful:
density d
In order to convert derivatives involving density use the following
rules:
at constant density == at constant specific volume
ddx/dyx = -d*d*dvx/dyx with y,x any of T,p,u,h,s,f,g
dyx/ddx = -1/(d*d)dyx/dvx with y,x any of T,p,u,h,s,f,g
Usage example assuming water as the medium:
model BridgmansTablesForWater
extends ThermoFluid.BaseClasses.MediumModels.Water.WaterSteamMedium_ph;
Real derOfsByTAtConstantv "derivative of sp. entropy by temperature at constant sp. volume"
ThermoFluid.BaseClasses.MediumModels.Common.ExtraDerivatives dpro;
ThermoFluid.BaseClasses.MediumModels.Common.BridgmansTables bt;
equation
dpro = ThermoFluid.BaseClasses.MediumModels.SteamIF97.extraDerivs_pT(p[1],T[1]);
bt.p = p[1];
bt.T = T[1];
bt.v = 1/pro[1].d;
bt.s = pro[1].s;
bt.cp = pro[1].cp;
bt.alpha = dpro.alpha;
bt.gamma = dpro.gamma;
derOfsByTAtConstantv =  bt.dsv/bt.dTv;
                ...
end BridgmansTablesForWater;
                

Extends from Modelica.Icons.Record (Icon for records).

Modelica.Media.Common.FundamentalConstants Modelica.Media.Common.FundamentalConstants

Constants of the medium

Information

Extends from Modelica.Icons.Record (Icon for records).

Modelica.Media.Common.AuxiliaryProperties Modelica.Media.Common.AuxiliaryProperties

Intermediate property data record

Information

Extends from Modelica.Icons.Record (Icon for records).

Modelica.Media.Common.GibbsDerivs2 Modelica.Media.Common.GibbsDerivs2

Derivatives of Gibbs function w.r.t. pressure and temperature

Information

Extends from Modelica.Icons.Record (Icon for records).

Modelica.Media.Common.NewtonDerivatives_dT Modelica.Media.Common.NewtonDerivatives_dT

Derivatives for fast inverse calculations of Gibbs function

Information

Extends from Modelica.Icons.Record (Icon for records).

Modelica.Media.Common.gibbsToBridgmansTables Modelica.Media.Common.gibbsToBridgmansTables

Calculates base coefficients for Bridgman's tables from gibbs enthalpy

Information

Extends from Modelica.Icons.Function (Icon for functions).

Inputs

NameDescription
gDimensionless derivatives of Gibbs function

Outputs

NameDescription
vSpecific volume [m3/kg]
pPressure [Pa]
TTemperature [K]
sSpecific entropy [J/(kg.K)]
cpHeat capacity at constant pressure [J/(kg.K)]
alphaIsobaric volume expansion coefficient [1/K]
gammaIsothermal compressibility [1/Pa]

Modelica.Media.Common.helmholtzToBridgmansTables Modelica.Media.Common.helmholtzToBridgmansTables

Calculates base coefficients for Bridgmans tables from Helmholtz energy

Information

Extends from Modelica.Icons.Function (Icon for functions).

Inputs

NameDescription
fDimensionless derivatives of Helmholtz function

Outputs

NameDescription
vSpecific volume [m3/kg]
pPressure [Pa]
TTemperature [K]
sSpecific entropy [J/(kg.K)]
cpHeat capacity at constant pressure [J/(kg.K)]
alphaIsobaric volume expansion coefficient [1/K]
gammaIsothermal compressibility [1/Pa]

Modelica.Media.Common.gibbsToBoundaryProps Modelica.Media.Common.gibbsToBoundaryProps

Calculate phase boundary property record from dimensionless Gibbs function

Information

Extends from Modelica.Icons.Function (Icon for functions).

Inputs

NameDescription
gDimensionless derivatives of Gibbs function

Outputs

NameDescription
satPhase boundary properties

Modelica.Media.Common.helmholtzToBoundaryProps Modelica.Media.Common.helmholtzToBoundaryProps

Calculate phase boundary property record from dimensionless Helmholtz function

Information

Extends from Modelica.Icons.Function (Icon for functions).

Inputs

NameDescription
fDimensionless derivatives of Helmholtz function

Outputs

NameDescription
satPhase boundary property record

Modelica.Media.Common.cv2Phase Modelica.Media.Common.cv2Phase

Compute isochoric specific heat capacity inside the two-phase region

Information

Extends from Modelica.Icons.Function (Icon for functions).

Inputs

NameDescription
liqProperties on the boiling curve
vapProperties on the condensation curve
xVapour mass fraction [1]
TTemperature [K]
pProperties [Pa]

Outputs

NameDescription
cvIsochoric specific heat capacity [J/(kg.K)]

Modelica.Media.Common.cvdpT2Phase Modelica.Media.Common.cvdpT2Phase

Compute isochoric specific heat capacity inside the two-phase region and derivative of pressure w.r.t. temperature

Information

Extends from Modelica.Icons.Function (Icon for functions).

Inputs

NameDescription
liqProperties on the boiling curve
vapProperties on the condensation curve
xVapour mass fraction [1]
TTemperature [K]
pProperties [Pa]

Outputs

NameDescription
cvIsochoric specific heat capacity [J/(kg.K)]
dpTDerivative of pressure w.r.t. temperature

Modelica.Media.Common.gibbsToExtraDerivs Modelica.Media.Common.gibbsToExtraDerivs

Compute additional thermodynamic derivatives from dimensionless Gibbs function

Information

Extends from Modelica.Icons.Function (Icon for functions).

Inputs

NameDescription
gDimensionless derivatives of Gibbs function

Outputs

NameDescription
dproAdditional property derivatives

Modelica.Media.Common.helmholtzToExtraDerivs Modelica.Media.Common.helmholtzToExtraDerivs

Compute additional thermodynamic derivatives from dimensionless Helmholtz function

Information

Extends from Modelica.Icons.Function (Icon for functions).

Inputs

NameDescription
fDimensionless derivatives of Helmholtz function

Outputs

NameDescription
dproAdditional property derivatives

Modelica.Media.Common.Helmholtz_ph Modelica.Media.Common.Helmholtz_ph

Function to calculate analytic derivatives for computing d and t given p and h

Information

Extends from Modelica.Icons.Function (Icon for functions).

Inputs

NameDescription
fDimensionless derivatives of Helmholtz function

Outputs

NameDescription
nderivsDerivatives for Newton iteration to calculate d and t from p and h

Modelica.Media.Common.Helmholtz_pT Modelica.Media.Common.Helmholtz_pT

Function to calculate analytic derivatives for computing d and t given p and t

Information

Extends from Modelica.Icons.Function (Icon for functions).

Inputs

NameDescription
fDimensionless derivatives of Helmholtz function

Outputs

NameDescription
nderivsDerivatives for Newton iteration to compute d and t from p and t

Modelica.Media.Common.Helmholtz_ps Modelica.Media.Common.Helmholtz_ps

Function to calculate analytic derivatives for computing d and t given p and s

Information

Extends from Modelica.Icons.Function (Icon for functions).

Inputs

NameDescription
fDimensionless derivatives of Helmholtz function

Outputs

NameDescription
nderivsDerivatives for Newton iteration to compute d and t from p and s

Modelica.Media.Common.smoothStep Modelica.Media.Common.smoothStep

Approximation of a general step, such that the characteristic is continuous and differentiable

Information

This function is used to approximate the equation

y = if x > 0 then y1 else y2;

by a smooth characteristic, so that the expression is continuous and differentiable:

y = smooth(1, if x >  x_small then y1 else
              if x < -x_small then y2 else f(y1, y2));

In the region -x_small < x < x_small a 2nd order polynomial is used for a smooth transition from y1 to y2.

If mass fractions X[:] are approximated with this function then this can be performed for all nX mass fractions, instead of applying it for nX-1 mass fractions and computing the last one by the mass fraction constraint sum(X)=1. The reason is that the approximating function has the property that sum(X) = 1, provided sum(X_a) = sum(X_b) = 1 (and y1=X_a[i], y2=X_b[i]). This can be shown by evaluating the approximating function in the abs(x) < x_small region (otherwise X is either X_a or X_b):

X[1]  = smoothStep(x, X_a[1] , X_b[1] , x_small);
X[2]  = smoothStep(x, X_a[2] , X_b[2] , x_small);
   ...
X[nX] = smoothStep(x, X_a[nX], X_b[nX], x_small);

or

X[1]  = c*(X_a[1]  - X_b[1])  + (X_a[1]  + X_b[1])/2
X[2]  = c*(X_a[2]  - X_b[2])  + (X_a[2]  + X_b[2])/2;
   ...
X[nX] = c*(X_a[nX] - X_b[nX]) + (X_a[nX] + X_b[nX])/2;
c     = (x/x_small)*((x/x_small)^2 - 3)/4

Summing all mass fractions together results in

sum(X) = c*(sum(X_a) - sum(X_b)) + (sum(X_a) + sum(X_b))/2
       = c*(1 - 1) + (1 + 1)/2
       = 1

Extends from Modelica.Icons.Function (Icon for functions).

Inputs

NameDescription
xAbscissa value
y1Ordinate value for x > 0
y2Ordinate value for x < 0
x_smallApproximation of step for -x_small <= x <= x_small; x_small > 0 required

Outputs

NameDescription
yOrdinate value to approximate y = if x > 0 then y1 else y2

Modelica.Media.Common.Gibbs2_ph Modelica.Media.Common.Gibbs2_ph

Function to calculate analytic derivatives for computing T given p and h

Information

Extends from Modelica.Icons.Function (Icon for functions).

Inputs

NameDescription
gDimensionless derivatives of Gibbs function

Outputs

NameDescription
nderivsDerivatives for Newton iteration to calculate d and t from p and h

Modelica.Media.Common.Gibbs2_dT Modelica.Media.Common.Gibbs2_dT

Function to calculate analytic derivatives for computing p given d and T

Information

Extends from Modelica.Icons.Function (Icon for functions).

Inputs

NameDescription
gDimensionless derivatives of Gibbs function

Outputs

NameDescription
nderivsDerivatives for Newton iteration to compute p from d and T

Modelica.Media.Common.Gibbs2_ps Modelica.Media.Common.Gibbs2_ps

Function to calculate analytic derivatives for computing d and t given p and s

Information

Extends from Modelica.Icons.Function (Icon for functions).

Inputs

NameDescription
gDimensionless derivatives of Gibbs function

Outputs

NameDescription
nderivsDerivatives for Newton iteration to compute T from p and s
Automatically generated Thu Oct 1 16:08:02 2020.