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
Rate
MolarFlowRate
MolarReactionRate
MolarEnthalpy
DerDensityByEntropy
DerEnergyByPressure
DerEnergyByMoles
DerEntropyByTemperature
DerEntropyByPressure
DerEntropyByMoles
DerPressureByDensity
DerPressureBySpecificVolume
DerPressureByTemperature
DerVolumeByTemperature
DerVolumeByPressure
DerVolumeByMoles
IsenthalpicExponent
IsentropicExponent
IsobaricVolumeExpansionCoefficient
IsochoricPressureCoefficient
IsothermalCompressibility
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
ThermoFluidSpecial	Property records used by the ThermoFluid library
SaturationProperties	Properties in the two phase region
SaturationBoundaryProperties	Properties on both phase boundaries, including some derivatives
IF97BaseTwoPhase	Intermediate property data record for IF 97
IF97PhaseBoundaryProperties	Thermodynamic base properties on the phase boundary for IF97 steam tables
GibbsDerivs	Derivatives of dimensionless Gibbs-function w.r.t. dimensionless pressure and temperature
HelmholtzDerivs	Derivatives of dimensionless Helmholtz-function w.r.t. dimensionless pressure, density and temperature
TwoPhaseTransportProps	Defines properties on both phase boundaries, needed in the two phase region
PhaseBoundaryProperties	Thermodynamic base properties on the phase boundary
NewtonDerivatives_ph	Derivatives for fast inverse calculations of Helmholtz functions: p & h
NewtonDerivatives_ps	Derivatives for fast inverse calculation of Helmholtz functions: p & s
NewtonDerivatives_pT	Derivatives for fast inverse calculations of Helmholtz functions:p & T
ExtraDerivatives	Additional thermodynamic derivatives
BridgmansTables	Calculates all entries in Bridgmans tables if first seven variables given
FundamentalConstants	Constants of the medium
AuxiliaryProperties	Intermediate property data record
GibbsDerivs2	Derivatives of Gibbs function w.r.t. pressure and temperature
NewtonDerivatives_dT	Derivatives for fast inverse calculations of Gibbs function
gibbsToBridgmansTables	Calculates base coefficients for Bridgman's tables from gibbs enthalpy
helmholtzToBridgmansTables	Calculates base coefficients for Bridgmans tables from Helmholtz energy
gibbsToBoundaryProps	Calculate phase boundary property record from dimensionless Gibbs function
helmholtzToBoundaryProps	Calculate phase boundary property record from dimensionless Helmholtz function
cv2Phase	Compute isochoric specific heat capacity inside the two-phase region
cvdpT2Phase	Compute isochoric specific heat capacity inside the two-phase region and derivative of pressure w.r.t. temperature
gibbsToExtraDerivs	Compute additional thermodynamic derivatives from dimensionless Gibbs function
helmholtzToExtraDerivs	Compute additional thermodynamic derivatives from dimensionless Helmholtz function
Helmholtz_ph	Function to calculate analytic derivatives for computing d and t given p and h
Helmholtz_pT	Function to calculate analytic derivatives for computing d and t given p and t
Helmholtz_ps	Function to calculate analytic derivatives for computing d and t given p and s
smoothStep	Approximation of a general step, such that the characteristic is continuous and differentiable
Gibbs2_ph	Function to calculate analytic derivatives for computing T given p and h
Gibbs2_dT	Function to calculate analytic derivatives for computing p given d and T
Gibbs2_ps	Function to calculate analytic derivatives for computing d and t given p and s
OneNonLinearEquation	Determine solution of a non-linear algebraic equation in one unknown without derivatives in a reliable and efficient way

Modelica.Media.Common.Rate

Parameters

Name	Value
Custom Parameters
quantity	"Rate"
unit	"s-1"

Modelica.Media.Common.MolarFlowRate

Parameters

Name	Value
Custom Parameters
quantity	"MolarFlowRate"
unit	"mol/s"

Modelica.Media.Common.MolarReactionRate

Parameters

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

Modelica.Media.Common.MolarEnthalpy

Parameters

Name	Value
Custom Parameters
quantity	"MolarEnthalpy"
unit	"J/mol"

Modelica.Media.Common.DerDensityByEntropy

Parameters

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

Modelica.Media.Common.DerEnergyByPressure

Parameters

Name	Value
Custom Parameters
quantity	"DerEnergyByPressure"
unit	"J/Pa"

Modelica.Media.Common.DerEnergyByMoles

Parameters

Name	Value
Custom Parameters
quantity	"DerEnergyByMoles"
unit	"J/mol"

Modelica.Media.Common.DerEntropyByTemperature

Parameters

Name	Value
Custom Parameters
quantity	"DerEntropyByTemperature"
unit	"J/K2"

Modelica.Media.Common.DerEntropyByPressure

Parameters

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

Modelica.Media.Common.DerEntropyByMoles

Parameters

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

Modelica.Media.Common.DerPressureByDensity

Parameters

Name	Value
Custom Parameters
quantity	"DerPressureByDensity"
unit	"Pa.m3/kg"

Modelica.Media.Common.DerPressureBySpecificVolume

Parameters

Name	Value
Custom Parameters
quantity	"DerPressureBySpecificVolume"
unit	"Pa.kg/m3"

Modelica.Media.Common.DerPressureByTemperature

Parameters

Name	Value
Custom Parameters
quantity	"DerPressureByTemperature"
unit	"Pa/K"

Modelica.Media.Common.DerVolumeByTemperature

Parameters

Name	Value
Custom Parameters
quantity	"DerVolumeByTemperature"
unit	"m3/K"

Modelica.Media.Common.DerVolumeByPressure

Parameters

Name	Value
Custom Parameters
quantity	"DerVolumeByPressure"
unit	"m3/Pa"

Modelica.Media.Common.DerVolumeByMoles

Parameters

Name	Value
Custom Parameters
quantity	"DerVolumeByMoles"
unit	"m3/mol"

Modelica.Media.Common.IsenthalpicExponent

Parameters

Name	Value
Custom Parameters
quantity	"IsenthalpicExponent"
unit	"1"

Modelica.Media.Common.IsentropicExponent

Parameters

Name	Value
Custom Parameters
quantity	"IsentropicExponent"
unit	"1"

Modelica.Media.Common.IsobaricVolumeExpansionCoefficient

Parameters

Name	Value
Custom Parameters
quantity	"IsobaricVolumeExpansionCoef...
unit	"1/K"

Modelica.Media.Common.IsochoricPressureCoefficient

Parameters

Name	Value
Custom Parameters
quantity	"IsochoricPressureCoefficient"
unit	"1/K"

Modelica.Media.Common.IsothermalCompressibility

Parameters

Name	Value
Custom Parameters
quantity	"IsothermalCompressibility"
unit	"1/Pa"

Modelica.Media.Common.JouleThomsonCoefficient

Parameters

Name	Value
Custom Parameters
quantity	"JouleThomsonCoefficient"
unit	"K/Pa"

Modelica.Media.Common.SaturationProperties

Properties in the two phase region

Information

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

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

Intermediate property data record for IF 97

Information

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

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

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

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

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

Thermodynamic base properties on the phase boundary

Information

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

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

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

Information

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

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

Additional thermodynamic derivatives

Information

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

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

Constants of the medium

Information

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

Modelica.Media.Common.AuxiliaryProperties

Intermediate property data record

Information

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

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

Derivatives for fast inverse calculations of Gibbs function

Information

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

Modelica.Media.Common.gibbsToBridgmansTables

Calculates base coefficients for Bridgman's tables from gibbs enthalpy

Information

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

Inputs

Name	Description
g	Dimensionless derivatives of Gibbs function

Outputs

Name	Description
v	Specific volume [m3/kg]
p	Pressure [Pa]
T	Temperature [K]
s	Specific entropy [J/(kg.K)]
cp	Heat capacity at constant pressure [J/(kg.K)]
alpha	Isobaric volume expansion coefficient [1/K]
gamma	Isothermal compressibility [1/Pa]

Modelica.Media.Common.helmholtzToBridgmansTables

Calculates base coefficients for Bridgmans tables from Helmholtz energy

Information

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

Inputs

Name	Description
f	Dimensionless derivatives of Helmholtz function

Outputs

Name	Description
v	Specific volume [m3/kg]
p	Pressure [Pa]
T	Temperature [K]
s	Specific entropy [J/(kg.K)]
cp	Heat capacity at constant pressure [J/(kg.K)]
alpha	Isobaric volume expansion coefficient [1/K]
gamma	Isothermal compressibility [1/Pa]

Modelica.Media.Common.gibbsToBoundaryProps

Calculate phase boundary property record from dimensionless Gibbs function

Information

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

Inputs

Name	Description
g	Dimensionless derivatives of Gibbs function

Outputs

Name	Description
sat	Phase boundary properties

Modelica.Media.Common.helmholtzToBoundaryProps

Calculate phase boundary property record from dimensionless Helmholtz function

Information

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

Inputs

Name	Description
f	Dimensionless derivatives of Helmholtz function

Outputs

Name	Description
sat	Phase boundary property record

Modelica.Media.Common.cv2Phase

Compute isochoric specific heat capacity inside the two-phase region

Information

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

Inputs

Name	Description
liq	Properties on the boiling curve
vap	Properties on the condensation curve
x	Vapour mass fraction [1]
T	Temperature [K]
p	Properties [Pa]

Outputs

Name	Description
cv	Isochoric specific heat capacity [J/(kg.K)]

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

Name	Description
liq	Properties on the boiling curve
vap	Properties on the condensation curve
x	Vapour mass fraction [1]
T	Temperature [K]
p	Properties [Pa]

Outputs

Name	Description
cv	Isochoric specific heat capacity [J/(kg.K)]
dpT	Derivative of pressure w.r.t. temperature

Modelica.Media.Common.gibbsToExtraDerivs

Compute additional thermodynamic derivatives from dimensionless Gibbs function

Information

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

Inputs

Name	Description
g	Dimensionless derivatives of Gibbs function

Outputs

Name	Description
dpro	Additional property derivatives

Modelica.Media.Common.helmholtzToExtraDerivs

Compute additional thermodynamic derivatives from dimensionless Helmholtz function

Information

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

Inputs

Name	Description
f	Dimensionless derivatives of Helmholtz function

Outputs

Name	Description
dpro	Additional property derivatives

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

Name	Description
f	Dimensionless derivatives of Helmholtz function

Outputs

Name	Description
nderivs	Derivatives for Newton iteration to calculate d and t from p and h

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

Name	Description
f	Dimensionless derivatives of Helmholtz function

Outputs

Name	Description
nderivs	Derivatives for Newton iteration to compute d and t from p and t

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

Name	Description
f	Dimensionless derivatives of Helmholtz function

Outputs

Name	Description
nderivs	Derivatives for Newton iteration to compute d and t from p and s

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);

    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

Name	Description
x	Abscissa value
y1	Ordinate value for x > 0
y2	Ordinate value for x < 0
x_small	Approximation of step for -x_small <= x <= x_small; x_small > 0 required

Outputs

Name	Description
y	Ordinate value to approximate y = if x > 0 then y1 else y2

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

Name	Description
g	Dimensionless derivatives of Gibbs function

Outputs

Name	Description
nderivs	Derivatives for Newton iteration to calculate d and t from p and h

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

Name	Description
g	Dimensionless derivatives of Gibbs function

Outputs

Name	Description
nderivs	Derivatives for Newton iteration to compute p from d and T

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

Name	Description
g	Dimensionless derivatives of Gibbs function

Outputs

Name	Description
nderivs	Derivatives for Newton iteration to compute T from p and s

Automatically generated Thu Dec 19 17:20:15 2019.