This is the base package for medium models of incompressible fluids based on tables. The minimal data to provide for a useful medium description is tables of density and heat capacity as functions of temperature.
It should be noted that incompressible media only have 1 state per control volume (usually T), but have both T and p as inputs for fully correct properties. The error of using only T-dependent properties is small, therefore a Boolean flag enthalpyOfT exists. If it is true, the enumeration Choices.independentVariables is set to Choices.independentVariables.T otherwise it is set to Choices.independentVariables.pT.
To implement a new medium model, create a package that extends TableBased and provides one or more of the constant tables:
tableDensity = [T, d]; tableHeatCapacity = [T, Cp]; tableConductivity = [T, lam]; tableViscosity = [T, eta]; tableVaporPressure = [T, pVap];
The table data is used to fit constant polynomials of order npol, the temperature data points do not need to be same for different properties. Properties like enthalpy, inner energy and entropy are calculated consistently from integrals and derivatives of d(T) and Cp(T). The minimal data for a useful medium model is thus density and heat capacity. Transport properties and vapor pressure are optional, if the data tables are empty the corresponding function calls can not be used.
Extends from Modelica.Media.Interfaces.PartialMedium (Partial medium properties (base package of all media packages)).
Name | Description |
---|---|
enthalpyOfT=true | true if enthalpy is approximated as a function of T only, (p-dependence neglected) |
densityOfT=size(tableDensity, 1) > 1 | true if density is a function of temperature |
T_min | Minimum temperature valid for medium model |
T_max | Maximum temperature valid for medium model |
T0=273.15 | reference Temperature |
h0=0 | reference enthalpy at T0, reference_p |
s0=0 | reference entropy at T0, reference_p |
MM_const=0.1 | Molar mass |
npol=2 | degree of polynomial used for fitting |
neta=size(tableViscosity, 1) | number of data points for viscosity |
tableDensity | Table for rho(T) |
tableHeatCapacity | Table for Cp(T) |
tableViscosity | Table for eta(T) |
tableVaporPressure | Table for pVap(T) |
tableConductivity | Table for lambda(T) |
TinK | true if T[K],Kelvin used for table temperatures |
hasDensity=not (size(tableDensity, 1) == 0) | true if table tableDensity is present |
hasHeatCapacity=not (size(tableHeatCapacity, 1) == 0) | true if table tableHeatCapacity is present |
hasViscosity=not (size(tableViscosity, 1) == 0) | true if table tableViscosity is present |
hasVaporPressure=not (size(tableVaporPressure, 1) == 0) | true if table tableVaporPressure is present |
invTK=if size(tableViscosity, 1) > 0 then invertTemp(tableViscosity[:, 1], TinK) else fill(0, 0) | |
poly_rho=if hasDensity then Poly.fitting(tableDensity[:, 1], tableDensity[:, 2], npol) else zeros(npol + 1) | |
poly_Cp=if hasHeatCapacity then Poly.fitting(tableHeatCapacity[:, 1], tableHeatCapacity[:, 2], npol) else zeros(npol + 1) | |
poly_eta=if hasViscosity then Poly.fitting(invTK, Math.log(tableViscosity[:, 2]), npol) else zeros(npol + 1) | |
poly_pVap=if hasVaporPressure then Poly.fitting(tableVaporPressure[:, 1], tableVaporPressure[:, 2], npol) else zeros(npol + 1) | |
poly_lam=if size(tableConductivity, 1) > 0 then Poly.fitting(tableConductivity[:, 1], tableConductivity[:, 2], npol) else zeros(npol + 1) | |
invertTemp | function to invert temperatures |
BaseProperties | Base properties of T dependent medium |
setState_pTX | Returns state record, given pressure and temperature |
setState_dTX | Returns state record, given pressure and temperature |
setState_pT | returns state record as function of p and T |
setState_phX | Returns state record, given pressure and specific enthalpy |
setState_ph | returns state record as function of p and h |
setState_psX | Returns state record, given pressure and specific entropy |
setState_ps | returns state record as function of p and s |
setSmoothState | Return thermodynamic state so that it smoothly approximates: if x > 0 then state_a else state_b |
specificHeatCapacityCv | Specific heat capacity at constant volume (or pressure) of medium |
specificHeatCapacityCp | Specific heat capacity at constant volume (or pressure) of medium |
dynamicViscosity | Return dynamic viscosity as a function of the thermodynamic state record |
thermalConductivity | Return thermal conductivity as a function of the thermodynamic state record |
s_T | compute specific entropy |
specificEntropy | Return specific entropy as a function of the thermodynamic state record |
h_T | Compute specific enthalpy from temperature |
h_T_der | Compute specific enthalpy from temperature |
h_pT | Compute specific enthalpy from pressure and temperature |
density_T | Return density as function of temperature |
temperature | Return temperature as a function of the thermodynamic state record |
pressure | Return pressure as a function of the thermodynamic state record |
density | Return density as a function of the thermodynamic state record |
specificEnthalpy | Return specific enthalpy as a function of the thermodynamic state record |
specificInternalEnergy | Return specific internal energy as a function of the thermodynamic state record |
T_ph | Compute temperature from pressure and specific enthalpy |
T_ps | Compute temperature from pressure and specific enthalpy |
Polynomials_Temp | Temporary Functions operating on polynomials (including polynomial fitting); only to be used in Modelica.Media.Incompressible.TableBased |
Inherited | |
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 |
FluidConstants | critical, triple, molecular and other standard data of fluid |
ThermodynamicState | Minimal variable set that is available as input argument to every medium function |
prandtlNumber | Return the Prandtl number |
specificGibbsEnergy | Return specific Gibbs energy |
specificHelmholtzEnergy | Return specific Helmholtz energy |
heatCapacity_cp | alias for deprecated name |
heatCapacity_cv | alias for deprecated name |
isentropicExponent | Return isentropic exponent |
isentropicEnthalpy | Return isentropic enthalpy |
velocityOfSound | Return velocity of sound |
isobaricExpansionCoefficient | Return overall the isobaric expansion coefficient beta |
beta | alias for isobaricExpansionCoefficient for user convenience |
isothermalCompressibility | Return overall the isothermal compressibility factor |
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 |
density_derp_T | Return density derivative w.r.t. pressure at const temperature |
density_derT_p | Return density derivative w.r.t. temperature at constant pressure |
density_derX | Return density derivative w.r.t. mass fraction |
molarMass | Return the molar mass of the medium |
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 |
constant Boolean enthalpyOfT=true "true if enthalpy is approximated as a function of T only, (p-dependence neglected)";
constant Boolean densityOfT = size(tableDensity,1) > 1 "true if density is a function of temperature";
constant Temperature T_min "Minimum temperature valid for medium model";
constant Temperature T_max "Maximum temperature valid for medium model";
constant Temperature T0=273.15 "reference Temperature";
constant SpecificEnthalpy h0=0 "reference enthalpy at T0, reference_p";
constant SpecificEntropy s0=0 "reference entropy at T0, reference_p";
constant MolarMass MM_const=0.1 "Molar mass";
constant Integer npol=2 "degree of polynomial used for fitting";
constant Integer neta=size(tableViscosity,1) "number of data points for viscosity";
constant Real[:,2] tableDensity "Table for rho(T)";
constant Real[:,2] tableHeatCapacity "Table for Cp(T)";
constant Real[:,2] tableViscosity "Table for eta(T)";
constant Real[:,2] tableVaporPressure "Table for pVap(T)";
constant Real[:,2] tableConductivity "Table for lambda(T)";
constant Boolean TinK "true if T[K],Kelvin used for table temperatures";
constant Boolean hasDensity = not (size(tableDensity,1)==0) "true if table tableDensity is present";
constant Boolean hasHeatCapacity = not (size(tableHeatCapacity,1)==0) "true if table tableHeatCapacity is present";
constant Boolean hasViscosity = not (size(tableViscosity,1)==0) "true if table tableViscosity is present";
constant Boolean hasVaporPressure = not (size(tableVaporPressure,1)==0) "true if table tableVaporPressure is present";
final constant Real invTK[neta] = if size(tableViscosity,1) > 0 then invertTemp(tableViscosity[:,1],TinK) else fill(0,0);
final constant Real poly_rho[:] = if hasDensity then Poly.fitting(tableDensity[:,1],tableDensity[:,2],npol) else zeros(npol+1);
final constant Real poly_Cp[:] = if hasHeatCapacity then Poly.fitting(tableHeatCapacity[:,1],tableHeatCapacity[:,2],npol) else zeros(npol+1);
final constant Real poly_eta[:] = if hasViscosity then Poly.fitting(invTK, Math.log(tableViscosity[:,2]),npol) else zeros(npol+1);
final constant Real poly_pVap[:] = if hasVaporPressure then Poly.fitting(tableVaporPressure[:,1],tableVaporPressure[:,2],npol) else zeros(npol+1);
final constant Real poly_lam[:] = if size(tableConductivity,1)>0 then Poly.fitting(tableConductivity[:,1],tableConductivity[:,2],npol) else zeros(npol+1);
Type | Name | Default | Description |
---|---|---|---|
Real | table[:] | table temperature data | |
Boolean | Tink | flag for Celsius or Kelvin |
Type | Name | Description |
---|---|---|
Real | invTable[size(table, 1)] | inverted temperatures |
function invertTemp "function to invert temperatures" input Real[:] table "table temperature data"; input Boolean Tink "flag for Celsius or Kelvin"; output Real invTable[size(table,1)] "inverted temperatures"; algorithm for i in 1:size(table,1) loop invTable[i] := if TinK then 1/table[i] else 1/Cv.from_degC(table[i]); end for; end invertTemp;
Note that the inner energy neglects the pressure dependence, which is only true for an incompressible medium with d = constant. The neglected term is p-reference_p)/rho*(T/rho)*(partial rho /partial T). This is very small for liquids due to proportionality to 1/d^2, but can be problematic for gases that are modeled incompressible.
It should be noted that incompressible media only have 1 state per control volume (usually T), but have both T and p as inputs for fully correct properties. The error of using only T-dependent properties is small, therefore a Boolean flag enthalpyOfT exists. If it is true, the enumeration Choices.independentVariables is set to Choices.independentVariables.T otherwise it is set to Choices.independentVariables.pT.
Enthalpy is never a function of T only (h = h(T) + (p-reference_p)/d), but the error is also small and non-linear systems can be avoided. In particular, non-linear systems are small and local as opposed to large and over all volumes.
Entropy is calculated as
s = s0 + integral(Cp(T)/T,dt)
which is only exactly true for a fluid with constant density d=d0.
Extends from (Base properties (p, d, T, h, u, R, MM and, if applicable, X and Xi) of a medium).
Type | Name | Default | Description |
---|---|---|---|
Temperature | T_start | 298.15 | initial temperature [K] |
Boolean | standardOrderComponents | true | if true, and reducedX = true, the last element of X will be computed from the other ones |
Pressure_bar | p_bar | Cv.to_bar(p) | Absolute pressure of medium in [bar] [bar] |
Advanced | |||
Boolean | preferredMediumStates | false | = true if StateSelect.prefer shall be used for the independent property variables of the medium |
redeclare model extends BaseProperties( final standardOrderComponents=true, p_bar=Cv.to_bar(p), T_degC(start = T_start-273.15)=Cv.to_degC(T), T(start = T_start, stateSelect=if preferredMediumStates then StateSelect.prefer else StateSelect.default)) "Base properties of T dependent medium" // redeclare parameter SpecificHeatCapacity R=Modelica.Constants.R, SI.SpecificHeatCapacity cp "specific heat capacity"; parameter SI.Temperature T_start = 298.15 "initial temperature"; equation assert(hasDensity,"Medium " + mediumName + " can not be used without assigning tableDensity."); assert(T >= T_min and T <= T_max, "Temperature T (= " + String(T) + " K) is not in the allowed range (" + String(T_min) + " K <= T <= " + String(T_max) + " K) required from medium model \"" + mediumName + "\"."); R = Modelica.Constants.R; cp = Poly.evaluate(poly_Cp,if TinK then T else T_degC); h = if enthalpyOfT then h_T(T) else h_pT(p,T,densityOfT); if singleState then u = h_T(T) - reference_p/d; else u = h - p/d; end if; d = Poly.evaluate(poly_rho,if TinK then T else T_degC); state.T = T; state.p = p; MM = MM_const;end BaseProperties;
Type | Name | Default | Description |
---|---|---|---|
AbsolutePressure | p | Pressure [Pa] | |
Temperature | T | Temperature [K] | |
MassFraction | X[:] | reference_X | Mass fractions [kg/kg] |
Type | Name | Description |
---|---|---|
ThermodynamicState | state | thermodynamic state record |
redeclare function extends setState_pTX "Returns state record, given pressure and temperature" algorithm state := ThermodynamicState(p=p,T=T); end setState_pTX;
Type | Name | Default | Description |
---|---|---|---|
Density | d | density [kg/m3] | |
Temperature | T | Temperature [K] | |
MassFraction | X[:] | reference_X | Mass fractions [kg/kg] |
Type | Name | Description |
---|---|---|
ThermodynamicState | state | thermodynamic state record |
redeclare function extends setState_dTX "Returns state record, given pressure and temperature" algorithm assert(false, "for incompressible media with d(T) only, state can not be set from density and temperature"); end setState_dTX;
Type | Name | Default | Description |
---|---|---|---|
AbsolutePressure | p | pressure [Pa] | |
Temperature | T | temperature [K] |
Type | Name | Description |
---|---|---|
ThermodynamicState | state | thermodynamic state |
function setState_pT "returns state record as function of p and T" input AbsolutePressure p "pressure"; input Temperature T "temperature"; output ThermodynamicState state "thermodynamic state"; algorithm state.T := T; state.p := p; end setState_pT;
Type | Name | Default | Description |
---|---|---|---|
AbsolutePressure | p | Pressure [Pa] | |
SpecificEnthalpy | h | Specific enthalpy [J/kg] | |
MassFraction | X[:] | reference_X | Mass fractions [kg/kg] |
Type | Name | Description |
---|---|---|
ThermodynamicState | state | thermodynamic state record |
redeclare function extends setState_phX "Returns state record, given pressure and specific enthalpy" algorithm state :=ThermodynamicState(p=p,T=T_ph(p,h)); end setState_phX;
Type | Name | Default | Description |
---|---|---|---|
AbsolutePressure | p | pressure [Pa] | |
SpecificEnthalpy | h | specific enthalpy [J/kg] |
Type | Name | Description |
---|---|---|
ThermodynamicState | state | thermodynamic state |
function setState_ph "returns state record as function of p and h" input AbsolutePressure p "pressure"; input SpecificEnthalpy h "specific enthalpy"; output ThermodynamicState state "thermodynamic state"; algorithm state :=ThermodynamicState(p=p,T=T_ph(p,h)); end setState_ph;
Type | Name | Default | Description |
---|---|---|---|
AbsolutePressure | p | Pressure [Pa] | |
SpecificEntropy | s | Specific entropy [J/(kg.K)] | |
MassFraction | X[:] | reference_X | Mass fractions [kg/kg] |
Type | Name | Description |
---|---|---|
ThermodynamicState | state | thermodynamic state record |
redeclare function extends setState_psX "Returns state record, given pressure and specific entropy" algorithm state :=ThermodynamicState(p=p,T=T_ps(p,s)); end setState_psX;
Type | Name | Default | Description |
---|---|---|---|
AbsolutePressure | p | pressure [Pa] | |
SpecificEntropy | s | specific entropy [J/(kg.K)] |
Type | Name | Description |
---|---|---|
ThermodynamicState | state | thermodynamic state |
function setState_ps "returns state record as function of p and s" input AbsolutePressure p "pressure"; input SpecificEntropy s "specific entropy"; output ThermodynamicState state "thermodynamic state"; algorithm state :=ThermodynamicState(p=p,T=T_ps(p,s)); end setState_ps;
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 |
Type | Name | Description |
---|---|---|
ThermodynamicState | state | Smooth thermodynamic state for all x (continuous and differentiable) |
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;
Type | Name | Default | Description |
---|---|---|---|
ThermodynamicState | state | thermodynamic state record |
Type | Name | Description |
---|---|---|
SpecificHeatCapacity | cv | Specific heat capacity at constant volume [J/(kg.K)] |
redeclare function extends specificHeatCapacityCv "Specific heat capacity at constant volume (or pressure) of medium" algorithm assert(hasHeatCapacity,"Specific Heat Capacity, Cv, is not defined for medium " + mediumName + "."); cv := Poly.evaluate(poly_Cp,if TinK then state.T else state.T - 273.15);end specificHeatCapacityCv;
Type | Name | Default | Description |
---|---|---|---|
ThermodynamicState | state | thermodynamic state record |
Type | Name | Description |
---|---|---|
SpecificHeatCapacity | cp | Specific heat capacity at constant pressure [J/(kg.K)] |
redeclare function extends specificHeatCapacityCp "Specific heat capacity at constant volume (or pressure) of medium" algorithm assert(hasHeatCapacity,"Specific Heat Capacity, Cv, is not defined for medium " + mediumName + "."); cp := Poly.evaluate(poly_Cp,if TinK then state.T else state.T - 273.15);end specificHeatCapacityCp;
Type | Name | Default | Description |
---|---|---|---|
ThermodynamicState | state | thermodynamic state record |
Type | Name | Description |
---|---|---|
DynamicViscosity | eta | Dynamic viscosity [Pa.s] |
redeclare function extends dynamicViscosity "Return dynamic viscosity as a function of the thermodynamic state record" algorithm assert(size(tableViscosity,1)>0,"DynamicViscosity, eta, is not defined for medium " + mediumName + "."); eta := Math.exp(Poly.evaluate(poly_eta, 1/state.T));end dynamicViscosity;
Type | Name | Default | Description |
---|---|---|---|
ThermodynamicState | state | thermodynamic state record |
Type | Name | Description |
---|---|---|
ThermalConductivity | lambda | Thermal conductivity [W/(m.K)] |
redeclare function extends thermalConductivity "Return thermal conductivity as a function of the thermodynamic state record" algorithm assert(size(tableConductivity,1)>0,"ThermalConductivity, lambda, is not defined for medium " + mediumName + "."); lambda := Poly.evaluate(poly_lam,if TinK then state.T else Cv.to_degC(state.T));end thermalConductivity;
Type | Name | Default | Description |
---|---|---|---|
Temperature | T | temperature [K] |
Type | Name | Description |
---|---|---|
SpecificEntropy | s | specific entropy [J/(kg.K)] |
function s_T "compute specific entropy" input Temperature T "temperature"; output SpecificEntropy s "specific entropy"; algorithm s := s0 + (if TinK then Poly.integralValue(poly_Cp[1:npol],T, T0) else Poly.integralValue(poly_Cp[1:npol],Cv.to_degC(T),Cv.to_degC(T0))) + Modelica.Math.log(T/T0)* Poly.evaluate(poly_Cp,if TinK then 0 else Modelica.Constants.T_zero);end s_T;
Type | Name | Default | Description |
---|---|---|---|
ThermodynamicState | state | thermodynamic state record |
Type | Name | Description |
---|---|---|
SpecificEntropy | s | Specific entropy [J/(kg.K)] |
redeclare function extends specificEntropy "Return specific entropy as a function of the thermodynamic state record" protected Integer npol=size(poly_Cp,1)-1; algorithm assert(hasHeatCapacity,"Specific Entropy, s(T), is not defined for medium " + mediumName + "."); s := s_T(state.T);end specificEntropy;
Type | Name | Default | Description |
---|---|---|---|
Temperature | T | Temperature [K] |
Type | Name | Description |
---|---|---|
SpecificEnthalpy | h | Specific enthalpy at p, T [J/kg] |
function h_T "Compute specific enthalpy from temperature" annotation(derivative=h_T_der); import Modelica.SIunits.Conversions.to_degC; extends Modelica.Icons.Function; input SI.Temperature T "Temperature"; output SI.SpecificEnthalpy h "Specific enthalpy at p, T"; algorithm h :=h0 + Poly.integralValue(poly_Cp, if TinK then T else Cv.to_degC(T), if TinK then T0 else Cv.to_degC(T0));end h_T;
Type | Name | Default | Description |
---|---|---|---|
Temperature | T | Temperature [K] | |
Real | dT | temperature derivative |
Type | Name | Description |
---|---|---|
Real | dh | derivative of Specific enthalpy at T |
function h_T_der "Compute specific enthalpy from temperature" import Modelica.SIunits.Conversions.to_degC; extends Modelica.Icons.Function; input SI.Temperature T "Temperature"; input Real dT "temperature derivative"; output Real dh "derivative of Specific enthalpy at T"; algorithm dh :=Poly.evaluate(poly_Cp, if TinK then T else Cv.to_degC(T))*dT;end h_T_der;
Type | Name | Default | Description |
---|---|---|---|
Pressure | p | Pressure [Pa] | |
Temperature | T | Temperature [K] | |
Boolean | densityOfT | false | include or neglect density derivative dependence of enthalpy |
Type | Name | Description |
---|---|---|
SpecificEnthalpy | h | Specific enthalpy at p, T [J/kg] |
function h_pT "Compute specific enthalpy from pressure and temperature" import Modelica.SIunits.Conversions.to_degC; extends Modelica.Icons.Function; input SI.Pressure p "Pressure"; input SI.Temperature T "Temperature"; input Boolean densityOfT = false "include or neglect density derivative dependence of enthalpy"; output SI.SpecificEnthalpy h "Specific enthalpy at p, T"; algorithm h :=h0 + Poly.integralValue(poly_Cp, if TinK then T else Cv.to_degC(T), if TinK then T0 else Cv.to_degC(T0)) + (p - reference_p)/Poly.evaluate(poly_rho, if TinK then T else Cv.to_degC(T)) *(if densityOfT then (1 + T/Poly.evaluate(poly_rho, if TinK then T else Cv.to_degC(T)) *Poly.derivativeValue(poly_rho,if TinK then T else Cv.to_degC(T))) else 1.0);end h_pT;
Type | Name | Default | Description |
---|---|---|---|
Temperature | T | temperature [K] |
Type | Name | Description |
---|---|---|
Density | d | density [kg/m3] |
function density_T "Return density as function of temperature" input Temperature T "temperature"; output Density d "density"; algorithm d := Poly.evaluate(poly_rho,if TinK then T else Cv.to_degC(T));end density_T;
Type | Name | Default | Description |
---|---|---|---|
ThermodynamicState | state | thermodynamic state record |
Type | Name | Description |
---|---|---|
Temperature | T | Temperature [K] |
redeclare function extends temperature "Return temperature as a function of the thermodynamic state record" algorithm T := state.T;end temperature;
Type | Name | Default | Description |
---|---|---|---|
ThermodynamicState | state | thermodynamic state record |
Type | Name | Description |
---|---|---|
AbsolutePressure | p | Pressure [Pa] |
redeclare function extends pressure "Return pressure as a function of the thermodynamic state record" algorithm p := state.p;end pressure;
Type | Name | Default | Description |
---|---|---|---|
ThermodynamicState | state | thermodynamic state record |
Type | Name | Description |
---|---|---|
Density | d | Density [kg/m3] |
redeclare function extends density "Return density as a function of the thermodynamic state record" algorithm d := Poly.evaluate(poly_rho,if TinK then state.T else Cv.to_degC(state.T));end density;
Type | Name | Default | Description |
---|---|---|---|
ThermodynamicState | state | thermodynamic state record |
Type | Name | Description |
---|---|---|
SpecificEnthalpy | h | Specific enthalpy [J/kg] |
redeclare function extends specificEnthalpy "Return specific enthalpy as a function of the thermodynamic state record" algorithm h := if enthalpyOfT then h_T(state.T) else h_pT(state.p,state.T);end specificEnthalpy;
Type | Name | Default | Description |
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ThermodynamicState | state | thermodynamic state record |
Type | Name | Description |
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SpecificEnergy | u | Specific internal energy [J/kg] |
redeclare function extends specificInternalEnergy "Return specific internal energy as a function of the thermodynamic state record" algorithm u := if enthalpyOfT then h_T(state.T) else h_pT(state.p,state.T) - (if singleState then reference_p/density(state) else state.p/density(state));end specificInternalEnergy;
Type | Name | Default | Description |
---|---|---|---|
AbsolutePressure | p | pressure [Pa] | |
SpecificEnthalpy | h | specific enthalpy [J/kg] |
Type | Name | Description |
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Temperature | T | temperature [K] |
function T_ph "Compute temperature from pressure and specific enthalpy" input AbsolutePressure p "pressure"; input SpecificEnthalpy h "specific enthalpy"; output Temperature T "temperature"; protectedpackage Internal "Solve h(T) for T with given h (use only indirectly via temperature_phX)" extends Modelica.Media.Common.OneNonLinearEquation; redeclare record extends f_nonlinear_Data "superfluous record, fix later when better structure of inverse functions exists" constant Real[5] dummy = {1,2,3,4,5}; end f_nonlinear_Data; redeclare function extends f_nonlinear "p is smuggled in via vector" algorithm y := if singleState then h_T(x) else h_pT(p,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, T_min, T_max, p, {1}, Internal.f_nonlinear_Data());end T_ph;
Type | Name | Default | Description |
---|---|---|---|
AbsolutePressure | p | pressure [Pa] | |
SpecificEntropy | s | specific entropy [J/(kg.K)] |
Type | Name | Description |
---|---|---|
Temperature | T | temperature [K] |
function T_ps "Compute temperature from pressure and specific enthalpy" input AbsolutePressure p "pressure"; input SpecificEntropy s "specific entropy"; output Temperature T "temperature"; protectedpackage Internal "Solve h(T) for T with given h (use only indirectly via temperature_phX)" extends Modelica.Media.Common.OneNonLinearEquation; redeclare record extends f_nonlinear_Data "superfluous record, fix later when better structure of inverse functions exists" constant Real[5] dummy = {1,2,3,4,5}; end f_nonlinear_Data; redeclare function extends f_nonlinear "p is smuggled in via vector" algorithm y := s_T(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(s, T_min, T_max, p, {1}, Internal.f_nonlinear_Data()); end T_ps;